Amorphous Chalcogenide Semiconductorsand Related Materials

Keiji Tanaka · Koichi Shimakawa

Amorphous ChalcogenideSemiconductors and RelatedMaterials

123

Keiji TanakaGraduate School of EngineeringDepartment of Applied PhysicsHokkaido UniversityKita-kuSapporo 060-8628, Japankeiji@eng.hokudai.ac.jp

Koichi ShimakawaFaculty of EngineeringGifu UniversityYanaidoGifu 501-1193, Japanand

Nagoya Industrial Science InstituteNagoya 460-0008, Japankoichi@gifu-u.ac.jp

ISBN 978-1-4419-9509-4 e-ISBN 978-1-4419-9510-0DOI 10.1007/978-1-4419-9510-0Springer New York Dordrecht Heidelberg London

Library of Congress Control Number: 2011926594

© Springer Science+Business Media, LLC 2011All rights reserved. This work may not be translated or copied in whole or in part without the writtenpermission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York,NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use inconnection with any form of information storage and retrieval, electronic adaptation, computer software,or by similar or dissimilar methodology now known or hereafter developed is forbidden.The use in this publication of trade names, trademarks, service marks, and similar terms, even if they arenot identified as such, is not to be taken as an expression of opinion as to whether or not they are subjectto proprietary rights.

Printed on acid-free paper

Springer is part of Springer Science+Business Media (www.springer.com)

Preface

Photonic, electronic, and photo-electric applications of non-crystalline1 solids arerapidly growing in recent years. Such growth seems to synchronize with the devel-opment of oxide glass1 fibers and related devices for optical communications, whichstarted near the end of the last century. Otherwise, we can trace its growth back to theuse of amorphous1 Se films at around 1950 as xerographic photoreceptors in copy-ing machines. In addition, recent applications of thin films, including Ge–Sb–Te todigital versatile disks (DVDs) and amorphous hydrogenated Si (a-Si:H) to solar cellsand thin-film transistors (TFTs), are remarkable. On the other hand, we also knowthat fundamental studies on amorphous chalcogenide semiconductor have yieldedseveral universal and revolutionary concepts such as “mobility edge” and “magiccoordination number,” and some of these concepts have been applied to other mate-rials. The authors therefore believe that, to study fundamentals and applications ofnon-crystalline insulators and semiconductors, amorphous chalcogenides2 such asSe, As2S3, and Ge–Sb–Te continue to be instructive and valuable substances.

The aim of this monograph is to be an introductory textbook in amorphouschalcogenide and related materials. This text will be suitable for graduate students.Actually, KT has used this text (unpublished versions) in seminars for graduatestudents, who start to study amorphous materials in the departments of appliedphysics, inorganic chemistry, and electronics. The present text will also be valuableto researchers working on related materials such as oxides, a-Si:H films, and organicsemiconductors. This book also serves in comparative understandings of amor-phous and crystalline semiconductors. The readers will see that, for such purposes,chalcogenide could be a good bridging material, since some simple compounds canbe obtained in both crystalline and non-crystalline forms. Of course, for materialsand topics dealt with in this book, several excellent books, listed at the end of thePreface, are already available. However, those are more or less difficult or detailedfor students and research beginners. Zallen’s book (1983) gives a good introduction

1These terminologies are defined in Section 1.1.2Oxford English Dictionary defines “chalco” as a stem, which is a combining form of Greekχαλκóς (copper and brass), and “gen” as an adjective suffix giving the sense “born in a certainplace or condition.” We know that minerals such as Cu2S may be an origin of “chalcogen.”

v

vi Preface

for students and researchers, while the content is focused on some fundamental sub-jects. The authors, therefore, have tried to write a book on glassy semiconductor onthe level of the book Introduction to Solid State Physics by Kittel.

The present book treats disordered solids, exemplified in Fig. 1, and its relatedapplications in Table 1. To keep the total page into an appropriate length, wewill proceed as follows: Experimental methods may be briefly sketched. We thenlook at fundamental observations, trying to grasp their interpretations from unifiedstandpoints and to draw simple pictures as possible. We will try to bridge atomicstructures and physical properties (Fig. 2). In such ways, relationships among dif-ferent macroscopic properties can be understood. The authors have also tried topoint out the remaining and controversial problems.

We will consider the amorphous chalcogenide material from two standpoints:One is as a kind of glass. At present, we utilize at least three kinds of photonic(highly pure) glasses, which are the oxide, chalcogenide, and halide, all thesebeing treated as (semi-)transparent insulators. In these three kinds of glasses, both

Si(Ge)Si(Ge)O2 – As2O3GeS(Se)2 – As2S(Se,Te)3 – S(Se,Te)Ge-Sb-Te, Ag(Cu)-As-S(Se)

Fig. 1 Relationships between materials of interest. Si(Ge) is tetrahedrally coordinated, producingthree-dimensional networks. Inserting O to ≡Si−Si≡ bonds produces ≡Si−O−Si≡ connections,giving three-dimensional continuous random SiO2 networks. GeO2 has structures similar to that inSiO2. O can be changed to S, Se, and Te, producing GeS(Se,Te)2. With a change in the cation fromGe to As, the atomic coordination number decreases from 4 to 3, giving As2O(S,Se,Te)3. And, inpure S(Se,Te), the structure is molecular as rings and polymeric chains

Table 1 Typical materials and related applications described in this text. For abbreviations, seethe text

Film Bulk

Insulator SiO2 (fiber)

Semiconductor Se (vidicon, x-ray imager)Ge2Sb2Te5 (DVD)a-Si:H (solar cell, TFT)

ATOMICSTRUCTURE

DensityElasticconstant

Electricalconductivity

Opticaltransparency

Fig. 2 A goal of solid-state science, which intends to give universal understandings of macro-scopic properties through simple theories on the basis of known atomic structures

Preface vii

oxygen (O) and chalcogens (S, Se, and Te) belong to the group VIb (16) atoms inthe periodic table. Accordingly, the oxide and chalcogenide glasses possess manycommon features, which will be understood from a unified point of view. In addi-tion, in these glasses, simple compositions such as SiO2 and As2Se3, which alsosolidify into crystals, are available. And, for the crystal we have had firmer sci-entific knowledge. Therefore, the group VIb glass can be an interesting target forunderstanding the glass property through comparisons with that of the correspond-ing crystal. We also mention here that the chalcogenide glass containing group I(1 and 11) atoms such as Li and Ag also exhibits (super)ionic conduction.

The other aspect of chalcogenide is as a kind of amorphous semiconductor.As an amorphous semiconductor (or photoconductor), we had utilized a-Se pho-toreceptors in copying machines, although it has now been taken over by organicphotoconductors. We have also developed phase-change memories using Ge–Sb–Tefilms. In fundamentals, a lot of concepts such as the mobility edge, charged defects,and Phillip’s magic number have been proposed. Applications of these conceptsto other materials will extend our total understanding of the solid-state science.Nevertheless, amorphous semiconductor physics has remained far behind that ofcrystalline. Actually, famous texts on solid-state physics, by Kittel for example, dealmostly with single crystals.

The reader may notice that the first (glass) and the second (amorphous semi-conductor) standpoints mentioned above have been taken mainly by chemists andphysicists, respectively. They also tend to employ different words for pointing nearlythe same concepts, e.g., LUMO (lowest unoccupied molecular orbital)–HOMO(highest occupied molecular orbital) in molecular chemistry and conduction–valence bands in physics. However, an important fact here is the interplay betweenbond and band, developed by Phillips in the famous book, Bonds and Bands inSemiconductors. We will try to take such an approach in the present text.

We list several books published in the present and related fields.

Written by Physicists

J. Tauc, Amorphous and Liquid Semiconductors (Plenum, London, 1974).N.F. Mott and E.A. Davis, Electronic Processes in Non-Crystalline Materials,

2nd Ed. (Clarendon, Oxford, 1979).J.M. Ziman, Models of Disorder (Cambridge University Press, Oxford, 1979).R. Zallen, The Physics of Amorphous Solids (Wiley, New York, NY, 1983).S.R. Elliott, Physics of Amorphous Materials, 2nd Ed. (Longman Scientific &

Technical, Essex, 1990).K. Morigaki, Physics of Amorphous Semiconductors (World Scientific,

Singapore, 1999).M.A. Popescu, Non-Crystalline Chalcogenides (Kluwer, Dordrecht, 2000).J. Singh and K. Shimakawa, Advances in Amorphous Semiconductors (Taylor

& Francis, London, 2003).

viii Preface

Written by Chemists

Z.U. Borisova, Glassy Semiconductors (Plenum, New York, NY, 1981).A. Feltz, Amorphe und Glasartige Anorganische Festkrper (Akademie-Verlag,

Berlin, 1983).R.H. Doremus, Glass Science, 2nd Ed. (Wiley, New York, NY, 1994).V.F. Kokorina, Glasses for Infrared Optics (CRC, Boca Raton, FL, 1996).M. Yamane and Y. Asahara, Glasses for Photonics (Cambridge University

Press, Cambridge, 2000).

Edited Volumes

J. Zarzycki (Ed.), Materials Science and Technology Vol. 9, Glasses andAmorphous Materials (VCH, Weinheim, 1991).

G. Pacchioni, L. Skuja, and D.L. Griscom (Eds.), Defects in SiO2 and RelatedDielectrics: Science and Technology (Kluwer, Dordrecht, 2000).

H.S. Nalwa (Ed.), Handbook of Advanced Electronic and Photonic Materialsand Devices Vol. 5 (Academic, San Diego, CA, 2001).

A.V. Kolobov (Ed.), Photo-Induced Metastability in AmorphousSemiconductors (Wiley-VCH, Weinheim, 2003).

G. Lucovsky and M. Popescu (Eds.), Non-Crystalline Materials forOptoelectronics Vol. 1 (INOE, Bucharest, 2004).

R. Fairman and B. Ushkov (Eds.), Semiconducting Chalcogenide Glass(Elsevier, Amsterdam, 2004). I (Glass Formation, Structure, and StimulatedTransformations in C.G.), II (Properties of Chalcogenide Glasses), and III(Applications of Chalcogenide Glasses).

Acknowledgements

Finally, we are particularly grateful to M. Mikami and N. Terakado for prepar-ing many illustrations. Discussions with S. Nonomura, A. Saitoh, Y. Shinozuka,M. Tatsumisago, and T. Uchino were extremely valuable to write this book. Lastbut not least, we are thankful to Kazunobu Tanaka, who had led us to the researchon chalcogenide glasses, and to Safa Kasap, without whom this text could not havebeen published.

Sapporo, Japan Keiji TanakaGifu, Japan Koichi Shimakawa

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Non-crystalline, Amorphous, and Glassy . . . . . . . . . . . . . . 11.2 Crystalline Versus Non-crystalline . . . . . . . . . . . . . . . . . 31.3 Characteristic Feature . . . . . . . . . . . . . . . . . . . . . . . . 6

1.3.1 Amorphous Material . . . . . . . . . . . . . . . . . . . . 61.3.2 Amorphous Chalcogenide . . . . . . . . . . . . . . . . . . 7

1.4 Historical Background: Chalcogenide and Oxide . . . . . . . . . . 81.5 Atomic and Electron Configurations . . . . . . . . . . . . . . . . 101.6 Ionicity, Covalency, and Metallicity of Atomic Bonds . . . . . . . 121.7 Variety in Chalcogenides . . . . . . . . . . . . . . . . . . . . . . 14

1.7.1 Elemental . . . . . . . . . . . . . . . . . . . . . . . . . . 151.7.2 Binary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161.7.3 Ternary and More Complicated . . . . . . . . . . . . . . . 17

1.8 Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181.8.1 Glass (Bulk, Fiber) . . . . . . . . . . . . . . . . . . . . . 181.8.2 Film and Others . . . . . . . . . . . . . . . . . . . . . . . 20

1.9 Dependence upon Experimental Variables . . . . . . . . . . . . . 23References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292.1 Ideal Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292.2 Practical Structure . . . . . . . . . . . . . . . . . . . . . . . . . . 312.3 Short-Range Structure . . . . . . . . . . . . . . . . . . . . . . . . 34

2.3.1 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . 342.3.2 Observations . . . . . . . . . . . . . . . . . . . . . . . . 39

2.4 Medium-Range Structure . . . . . . . . . . . . . . . . . . . . . . 412.4.1 Small Medium-Range Structure . . . . . . . . . . . . . . 422.4.2 First Sharp Diffraction Peak . . . . . . . . . . . . . . . . 442.4.3 Boson Peak . . . . . . . . . . . . . . . . . . . . . . . . . 48

2.5 Defect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502.6 Computer Simulations . . . . . . . . . . . . . . . . . . . . . . . 532.7 Homogeneity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 542.8 Surface and Nano-structures . . . . . . . . . . . . . . . . . . . . 56References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

ix

x Contents

3 Structural Properties . . . . . . . . . . . . . . . . . . . . . . . . . . 633.1 Structure and Properties . . . . . . . . . . . . . . . . . . . . . . . 633.2 Glass Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . 643.3 Crystallization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693.4 Thermal and Other Properties . . . . . . . . . . . . . . . . . . . . 713.5 Magic Numbers: 2.4 and 2.67 . . . . . . . . . . . . . . . . . . . . 743.6 Ionic Conduction . . . . . . . . . . . . . . . . . . . . . . . . . . 77References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

4 Electronic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . 854.1 Electronic Structure . . . . . . . . . . . . . . . . . . . . . . . . . 854.2 Band Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 894.3 Bandgap and Mobility Edge . . . . . . . . . . . . . . . . . . . . 914.4 Gap States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 924.5 Optical Property . . . . . . . . . . . . . . . . . . . . . . . . . . . 954.6 Optical Absorption . . . . . . . . . . . . . . . . . . . . . . . . . 96

4.6.1 Tauc Gap . . . . . . . . . . . . . . . . . . . . . . . . . . 974.6.2 Urbach Edge . . . . . . . . . . . . . . . . . . . . . . . . . 994.6.3 Weak Absorption Tail . . . . . . . . . . . . . . . . . . . . 100

4.7 Refractive Index . . . . . . . . . . . . . . . . . . . . . . . . . . . 1024.8 Optical Nonlinearity . . . . . . . . . . . . . . . . . . . . . . . . . 1034.9 Electrical Conduction . . . . . . . . . . . . . . . . . . . . . . . . 106

4.9.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . 1064.9.2 Carrier Transport . . . . . . . . . . . . . . . . . . . . . . 1074.9.3 Meyer–Neldel Rule . . . . . . . . . . . . . . . . . . . . . 1104.9.4 AC Conductivity . . . . . . . . . . . . . . . . . . . . . . 112

4.10 Compositional Variation . . . . . . . . . . . . . . . . . . . . . . 113References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

5 Photo-Electronic Properties . . . . . . . . . . . . . . . . . . . . . . . 1215.1 Photo-Excitation and Relaxation . . . . . . . . . . . . . . . . . . 1215.2 Photoluminescence . . . . . . . . . . . . . . . . . . . . . . . . . 123

5.2.1 CW Photoluminescence . . . . . . . . . . . . . . . . . . . 1245.2.2 Time-Resolved Photoluminescence . . . . . . . . . . . . . 127

5.3 Photo-Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1285.4 Photoconduction . . . . . . . . . . . . . . . . . . . . . . . . . . 128

5.4.1 CW Photoconduction . . . . . . . . . . . . . . . . . . . . 1285.4.2 Time-Resolved Photoconduction . . . . . . . . . . . . . . 132

5.5 Avalanche Breakdown . . . . . . . . . . . . . . . . . . . . . . . 135References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

6 Light-Induced Phenomena . . . . . . . . . . . . . . . . . . . . . . . 1416.1 Overall Features . . . . . . . . . . . . . . . . . . . . . . . . . . . 1416.2 Thermal Effects in Chalcogenide . . . . . . . . . . . . . . . . . . 1436.3 Photon Effects in Chalcogenide . . . . . . . . . . . . . . . . . . . 145

6.3.1 Classification and Overall Features . . . . . . . . . . . . . 1456.3.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . 147

Contents xi

6.3.3 Computer Simulation . . . . . . . . . . . . . . . . . . . . 1486.3.4 Photo-Enhanced Crystallization . . . . . . . . . . . . . . . 1486.3.5 Photo-Polymerization . . . . . . . . . . . . . . . . . . . . 1506.3.6 Giant Photo-Contraction . . . . . . . . . . . . . . . . . . 1516.3.7 Other Irreversible Changes . . . . . . . . . . . . . . . . . 1526.3.8 Reversible Photodarkening and Refractive Index Increase . 1526.3.9 Other Reversible Changes . . . . . . . . . . . . . . . . . . 1606.3.10 Photoinduced Phenomena at Low Temperatures . . . . . . 1656.3.11 Transitory Changes . . . . . . . . . . . . . . . . . . . . . 1686.3.12 Vector Effects . . . . . . . . . . . . . . . . . . . . . . . . 1716.3.13 Photo-Chemical Effects . . . . . . . . . . . . . . . . . . . 174

6.4 Photon Effects in Oxide Glasses . . . . . . . . . . . . . . . . . . 1796.5 Light-Induced Phenomena in Amorphous Si:H Films . . . . . . . 181

6.5.1 Thermal Effects in Amorphous Si:H Films . . . . . . . . . 1816.5.2 Photon Effects in Amorphous Si:H Films . . . . . . . . . 182

6.6 Photon Effects in Organic Polymers . . . . . . . . . . . . . . . . 184References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

7 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1957.1 Overall Features . . . . . . . . . . . . . . . . . . . . . . . . . . . 1957.2 Optical Device . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

7.2.1 Optical Fiber . . . . . . . . . . . . . . . . . . . . . . . . 1987.2.2 Metal-Doped Fiber . . . . . . . . . . . . . . . . . . . . . 2007.2.3 Waveguide . . . . . . . . . . . . . . . . . . . . . . . . . . 203

7.3 Photo-Structural Device . . . . . . . . . . . . . . . . . . . . . . . 2057.4 Phase Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208

7.4.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . 2087.4.2 Optical Phase Change (DVD) . . . . . . . . . . . . . . . . 2107.4.3 Electrical Phase Change (PRAM) . . . . . . . . . . . . . . 211

7.5 Electrical Device . . . . . . . . . . . . . . . . . . . . . . . . . . 2147.6 Photo-Electric Device . . . . . . . . . . . . . . . . . . . . . . . . 214

7.6.1 Copying Photoreceptor . . . . . . . . . . . . . . . . . . . 2157.6.2 Vidicon and X-Ray Imager . . . . . . . . . . . . . . . . . 2157.6.3 Solar Cell . . . . . . . . . . . . . . . . . . . . . . . . . . 217

7.7 Ionic Device and Others . . . . . . . . . . . . . . . . . . . . . . . 2187.7.1 Ionic Memories . . . . . . . . . . . . . . . . . . . . . . . 2187.7.2 Ion Sensor . . . . . . . . . . . . . . . . . . . . . . . . . . 2197.7.3 Battery . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

8 Future Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2298.1 Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2298.2 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230

Appendix: Publications on Related Crystals . . . . . . . . . . . . . . . . 232

Material Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237

Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239

This is Blank Page Integra xii

List of Abbreviations

DOS density of stateD(E) density of stateDVD digital versatile diskESR electron spin resonanceEXAFS extended x-ray absorption fine spectroscopyFSDP first sharp diffraction peakHOMO highest occupied molecular orbitalLUMO lowest unoccupied molecular orbitalMD molecular dynamicsRDF radial distribution functionTFT thin-film transistorTOF time of flight

xiii

This is Blank Page Integra xiv

List of Acronyms

a amorphousc crystallineg glassyt timeτ characteristic timeT temperatureTc crystallization temperatureTg glass transition temperatureTm melting temperatureZ coordination number

xv

Chapter 1Introduction

Abstract We begin with the terminology and definition of several words, whichmay be somewhat confusing. Comparison of crystal and amorphous materials ismade from physical standpoints. Among many non-crystalline solids, we shed lighton oxide and chalcogenide glasses with brief histories. The readers will see howglass has made an impact on the present society. We also see the importance of uni-fied understanding of glasses containing VIb elements in the periodic table. Thereare many kinds of chalcogenide glasses, which will be discussed in terms of atomicelements.

Keywords Crystal · Amorphous material · Disorder · Quasi-equilibrium ·VIb glass · Obsidian · Preparation dependence · Pressure dependence

1.1 Non-crystalline, Amorphous, and Glassy

At the outset, it may be valuable to define the terminology. We divide the con-densed matter, which includes liquids and solids, into two: crystal and non-crystal.As imagined from external shapes with flat and conchoidal faces in Fig. 1.1, thecrystal has periodically positioned atomic structures, and in non-crystals the atomicstructure is disordered. As examples, most of the stones and rocks on the earth arecrystalline,1 and liquids are non-crystalline, with a known exception being liquidcrystals. However, there exist non-crystalline solids, which are synonymous withamorphous materials in the book by Mott and Davis (1979).

Mott and Davis (1979) have defined glass, among amorphous materials, as theone which can be solidified into a non-crystal from the melt. Glassy and vitreous, thewords being derived from an Indo-European root and Latin (Doremus 1994), maybe synonymously used. Their definitions can be expressed using a mathematical setnotation as

non-crystalline (disordered) ⊃ amorphous ⊃ glassy ≈ vitreous.

1It is mentioned that glassy substances on the earth are limited to obsidian, etc., while those seemrather common on the moon (Saal et al. 2008).

1K. Tanaka, K. Shimakawa, Amorphous Chalcogenide Semiconductors and RelatedMaterials, DOI 10.1007/978-1-4419-9510-0_1, C© Springer Science+Business Media, LLC 2011

2 1 Introduction

Fig. 1.1 Quartz (left), crystalline SiO2 with a melting temperature of 1730◦C and fused silica(right) SiO2 glass with a glass transition temperature of ∼1500◦C (http://geology.com/minerals/quartz.shtml, © Geology.com, reprinted with permission). Quartz cleaves, while the glass cracksconchoidally

Fig. 1.2 GENESIS (Global Energy Network Equipped with Solar cells and InternationalSuperconductor grids) project using a-Si:H solar cells and superconductor cables, announced fromSanyo Electric Co., Ltd., in 2001 (© Tokyu Construction Co., Ltd., reprinted with permission)

An amorphous hydrogenated Si (a-Si:H) film (Fig. 1.2) is “amorphous,” but notglassy, because the film is produced from vapor or plasma phases. The film cannotbe prepared through the conventional melt quenching of liquid Si (Bhat et al. 2007).On the other hand, the window glass is a typical oxide glass, since it is preparedthrough the quenching of melts.

Phillips (1980) and Elliott (1990) may prefer a different definition. The non-crystalline solid is divided into amorphous and glassy, which does not and doesexhibit the glass transition, respectively, i.e., a gradual transition between a glassy

1.2 Crystalline Versus Non-crystalline 3

and the supercooled liquidus state (see Section 3.2). In their definition, the amor-phous and the glassy seem to be incompatible:

amorphous ∩ glassy (vitreous) = ø (empty set).

In this definition, films such as a-Si:H are amorphous, since the film, whenheated, crystallizes without showing glass transition. Very thin (∼10 nm) SiO2films in MOS (metal–oxide–semiconductor) structures may be amorphous in bothdefinitions, while melt-quenched SiO2 is clearly a typical glass.

In short, the definition by Mott–Davis depends upon the preparation method andthat by Phillips and Elliott depends upon the property. We then see that vacuum-evaporated As2S3 films are amorphous in Mott’s definition because it is not meltquenched, but it is glassy in Phillips’ sense because it exhibits a glassy nature.We will follow in principle the definition by Mott and Davis.

1.2 Crystalline Versus Non-crystalline

Crystalline and non-crystalline materials can be defined as the condensed mat-ters which have periodic and non-periodic atomic structures. To make the contrastclearer, let the crystal be a single crystal in the following. In many cases, a poly-crystal may possess intermediate properties between the single crystal and theamorphous material.

The crystal and the amorphous material may be distinguished from externalshapes (Fig. 1.1). Non-metallic crystals tend to exhibit regular anisotropic shapessuch as the cubic form of NaCl and the hexagonal form of quartz crystals, thelatter giving rise to useful non-centrosymmetric properties such as optical bire-fringence, piezo-electricity, and optical second-harmonic generation. The cleavedsurfaces (cleavage) may be atomically flat. We can prepare such ultimately flat sur-faces also by using sophisticated vacuum techniques like molecular beam epitaxy.In addition, we can now pick up and put a single atom from and on the surface(Fishlock et al. 2000). In contrast, the glass breaks conchoidally, which reflectsdisordered atomic structures. For such fractured surfaces, atomic manipulation ispractically impossible.

Very roughly, a single crystal is more difficult to prepare than a glass. For prepar-ing a single crystal, e.g., c-Si wafers, the purity must be very high (∼ten 9’s), sinceimpurities tend to destroy the atomic periodicity, as illustrated in Fig. 1.3 (left).

Fig. 1.3 An impurity atom,which is substitutional andinterstitial, in crystal (left)and non-crystal (right)

4 1 Introduction

In addition, since most of the crystals are in thermal equilibrium state,2 cooling ofthe melt from high temperatures needs a long duration (>days). As exemplified inFig. 1.3 (right), the glass can contain foreign atoms, due to flexible disordered struc-tures. Actually, the purity of silica glass fibers, the purest glass available at present,may be on ppm (∼six 9’s) levels. The disordered atomic structure is more flexi-ble and has lower density, and accordingly, an included ion may move smoothly,which is promising for applications to solid-state batteries. In addition, glass havinga quasi-equilibrium state must be prepared through rapid quenching within a short(millisecond to hours, depending upon the material) duration. Owing to this feature,we can prepare wide glass plates, utilized for windows, etc., and long optical fiberswithin commercially feasible times. Naturally, the price per unit scale (volume, area,length) can become cheaper than that of the crystal.

Shapes of wavefunctions in a crystal and a non-crystal are contrastive. As illus-trated in Fig. 1.4, in a single crystal all the electron wavefunctions are extended,but in a non-crystal the wavefunction of electrons and holes at band edges andmid-gaps is localized. In consequence, the electron (hole) mobility in a non-crystalbecomes smaller than that in the corresponding crystal, since the localized electron(hole) in band edges governs the mobility. On the other hand, in optical absorp-tion, the difference between these two materials appears to be smaller than that inthe electron transport, since the localized state gives just a small contribution to theoptical absorption. Note that similar situations apply to lattice vibrations. The lattice

Fig. 1.4 Electron wavefunctions and band structures in (a) an ideal crystal, (b) a disorderednetwork with a dangling bond, and (c) a fully connected strained network

2A known exception is the diamond, which is a non-equilibrium phase of carbon on the earth’ssurface. The equilibrium phase is semi-metallic graphite.

1.2 Crystalline Versus Non-crystalline 5

Table 1.1 Comparison of crystal and amorphous material

Crystal Amorphous material

Atom position Periodic Short (medium) range orderHomogeneity Yes Macroscopically yesIsotropy No YesStructure controllability Atomic Nano-scaleSample dimension Small LargeStability (equilibrium) Yes Meta- (quasi-)Wavefunctions Extend LocalizeIon mobility (cm2/Vs) (in AgAsS2) 10−12 10−10

Electron (hole) mobility (cm2/Vs) ∼103 �100

Electron–lattice interaction Small Large

vibrations are also extended and localized in crystals and non-crystals, which pro-vide higher and lower thermal conductivities. But, no big difference exists betweenheat capacities in a crystal and its corresponding non-crystal. Table 1.1 lists othercontrastive features in crystals and amorphous materials.

It should be noted that the understanding of properties in non-crystals, specif-ically the amorphous material, in terms of solid-state science remains far behindthat in the crystal. Why has the amorphous material science been immature? Thereason is simple. Fundamental physics on single crystals treats one (a few)-particleproblems, but the non-crystalline physics must deal with many-particle problems.In crystalline physics, we first determine the atomic structure using diffractionexperiments, defining the unit cell, and then try to connect observed macroscopicproperties with the structure using the periodicity principle. In many cases, theone-electron approximation or the harmonic vibration approximation can providebasic and firm insights (Kittel 2005). But, for a non-crystalline material we cannotdefine the unit cell. We must consider the whole lattice structure including 1022−23

atoms/cm3, which is in principle impossible. In addition, we cannot yet identify thedisordered structure. Necessarily, we must follow some approximations, but for theapproximation, no principal methods (such as the one-electron approximation andBloch function formalism) have been available. Instead, we may employ computersimulations, which are not straightforward.

Despite the immature science mentioned above, as exemplified in Table 1.2,applications of amorphous materials to photonic and electronic devices are grow-ing, the details being described in Chapter 7. The best known may be the opticalfiber of silica glasses and peripheral devices such as optical amplifiers and wave-length filters. Such optical components are more or less difficult to prepare usingcrystals. In addition, photoconducting devices, specifically large area (∼m2 size)films, have been developed. An invaluable material may be a-Si:H films, which areindispensable to large area solar cells (Fig. 1.2). Also, tellurides are employed asDVD (digital versatile disk) films, which undergo the so-called optical phase changebetween crystalline and amorphous states. We should note, however, that in manyof these applications the inorganic non-crystalline material is in competition withorganic polymers.

6 1 Introduction

Table 1.2 Comparison of applications in crystalline and amorphous non-metals

Applications Crystalline Amorphous

Photonic SHG Fiber, optical amplifier, DVDElectronic IC Flexible film devices, TFTPhoto-electronic Laser, photodiode, CCD Solar cell, vidicon, x-ray detector

SHG stands for second-harmonic generation, DVD digital versatile disk, IC integrated circuits,TFT thin-film transistor, and CCD charge-coupled device

1.3 Characteristic Feature

1.3.1 Amorphous Material

The non-crystalline solid, i.e., amorphous material, possesses two characteristicfeatures. One is structural disorder and the other is quasi-equilibriumness (seeTable 1.3). These features yield a wide variety of materials and also pose difficultproblems.

The disorder affords infinite (∼1050) numbers of materials with arbitrary combi-nations of atoms, or atomic units, with continuously varied compositions (Zanottoand Coutinho 2004). The disordered structure may be continuous, without contain-ing grain boundaries and distinct heterogeneities. For instance, the composition ofwindow glass is 74SiO2·16Na2O·10CaO, which may be selected after balancingproperties and production cost. In addition, the disordered structure can be a matrixwhich incorporates exotic elements such as transition metals and rare earth atoms.Nevertheless, insensitivity or tolerance to included atoms causes lower efficienciesin atomic doping effects. We know as an example that for the p–n type control ofsemiconductors, ppm-level dopants may be sufficient in c-Si, while percent-orderdopants are needed for a-Si:H films.

On the other hand, the amorphous material, including glasses, lies in quasi-equilibrium states. In other words, its property cannot be uniquely determined bytemperature and pressure. The property gradually changes with time. Because of

Table 1.3 A general viewon structures andthermodynamic equilibriumof crystal, liquid, gas, andglass

Atomic structureThermodynamicalstate

Crystal Periodic EquilibriumLiquid Disordered EquilibriumGas Random EquilibriumGlass Disordered Quasi-equilibrium

(meta-stable)

1.3 Characteristic Feature 7

this quasi-equilibriumness, we can and must prepare a sample within short dura-tion, which affords to produce wide and long samples. As a consequence, however,sample properties depend upon its preparation methods, conditions, and prehistory.The sample properties can also be modified by electronic excitation, e.g., light illu-mination, as will be described in Chapter 6. We therefore face not only a variety ofcompositions but also a variety of modified properties for a fixed composition. Thisfeature can be a merit or demerit in applications. Note that biological substancessuch as proteins also exhibit quasi-equilibrium properties (Stec 2004).

1.3.2 Amorphous Chalcogenide

Glassy chalcogenides can be characterized by the structure and the energy gap. Thematerial can also be compared with other materials such as an amorphous materialand a semiconductor.

Figure 1.5 locates several amorphous materials as functions of optical gap Egand atomic structure. Organic polymers and inorganic glasses including oxidesand halides are, in general, insulators and are transparent having energy gaps of5–10 eV. On the other hand, amorphous chalcogenide and tetrahedral materialssuch as a-Si:H are semiconductors with energy gaps of 1–3 eV. Structurally, a-Seand polymers such as polyethylene (–CH2–) are characterized by one-dimensionalchains, i.e., the network dimension is one (Zallen 1983). Chalcogenide glasses suchas As2S(Se)3 and GeS(Se)2 are assumed to have two-dimensional (distorted layersas crumpled paper) structures, though there may be some controversy, as describedin Chapter 2. And, oxide glasses and tetrahedral materials have three-dimensionalnetwork structures.

Figure 1.6 characterizes chalcogenide as a glass (horizontal) and a semiconduc-tor (vertical). As a glass, the structure becomes more rigid in the order of polymer,chalcogenide, and oxide. On the other hand, semiconductor properties, e.g., car-rier mobility, and also material price per unit area become better and higher in theorder of organic, chalcogenide, tetrahedral (a-Si:H), and crystalline. This price order

chalcogenide

polymer

Eg(eV)

oxide/halide

tetrahedral

10

5

0 1 2 3Network dimension

Fig. 1.5 Characterization oftypical disordered solids inscales of the optical gap Egand the network dimension(see Section 2.4). The blackhorizontal band denotes thephoton energy of visible light

8 1 Introduction

Fig. 1.6 Characterization oftypical disordered solids inscales of glass andsemiconductor

may be governed by preparation procedures of these materials: coating, vacuumevaporation, glow discharge deposition, and epitaxial growth, respectively.

1.4 Historical Background: Chalcogenide and Oxide

The chalcogenide glass has a markedly different history from that of the oxide.As shown in Fig. 1.7, the oxide glass has a history longer than 5000 years, while thechalcogenide has so to say just a half-century history.

Fig. 1.7 History of glasses, including oxide, chalcogenide, and fluoride. The pictures on the right-hand side show, from the top to the bottom, obsidian arrows, a floating method for producingwindow glasses, and an Er-doped fiber amplifier (EDFA)

1.4 Historical Background: Chalcogenide and Oxide 9

A brief historical view of the oxide glass may be the following (Doremus 1994):The first use of the oxide glass by mankind seemed to start with natural glassessuch as obsidian, a kind of alumino-silicate (SiO2–Al2O3) glasses containing crys-talline particles such as Fe2O3. The black and hard glass was utilized as knivesand arrowheads at stone ages (Fig. 1.7, top). About 5000 years ago, people atMesopotamia might have accidentally discovered a production method of artificialglasses using sand (SiO2) and salt (NaCl), which could yield soda-silicate glasses(SiO2–Na2O) in charcoal fires (Breinder 2005). Because of unavoidable metallicimpurities such as Fe, glasses at that era were necessarily colored, which might makethe glass as ornaments. In the Roman age (1st century B.C.–A.D. 5th century), how-ever, transparent wine glasses became available. Later, in the 17th century, Galileiand Newton employed transparent glasses as optical components, e.g., lenses andprisms. Optical instruments such as eyeglasses, telescopes, microscopes, and prismmonochromators were devised. Gradually, wider and flatter glass plates becameavailable, which were employed as stained glasses in churches. Glass plates couldalso be coated with silver, producing mirrors, which replaced polished metal mir-rors. However, the glass might have been very expensive till the 19th century.Around 1955, Pilkington and coworkers developed the so-called floating method(Fig. 1.7, middle) for commercial production of large glass plates, which became tobe widely utilized as windows. And, at the end of the 20th century, researchers inCorning devised a preparation method, called outside vapor deposition, which canproduce ultimately-transparent and long (∼100 km) glass fibers, a kind of photonicsglasses, in which the purity (better than ppm) is a determinative factor as that inmany crystalline semiconductors. In addition, functional devices as fiber amplifiers(Fig. 1.7, bottom) have been produced.

On the other hand, notable studies on the chalcogenide glass started at ∼1950in Russia and the USA as materials featuring four different properties. Thoseare semiconductor, ion conductor, infrared transmitting glass, and xerographicphotoreceptor. In St. Petersburg in Russia (Leningrad in USSR), Kolomiet’s groupin Ioffe Institute (Fig. 1.8) discovered the glassy (vitreous) semiconductor whensurveying photoconducting materials (Kolomiets 1964b). They evinced that thereexists a material which has disordered atomic structures and bandgap energy of∼2 eV. At the same time, researchers in Leningrad State University studied thechalcogenide glass from chemical points of view, i.e., as ion-conducting (Borisova1981) and infrared transmitting materials (Kokorina 1996). It is a surprising coin-cidence that all the studies started independently from physical and chemicalstandpoints in the same city. On the other hand, in the USA, As–S glasses weredemonstrated to be stable infrared transmitting materials (Frerichs 1953), whichmight be developed for military purposes as lenses in night goggles. In addition, theglass was revealed to work as a good sealing material (Flaschen et al. 1960). On theother hand, a-Se films were utilized as photoreceptors in xerography, the principlehaving been patented by Carlson in 1937 (see Chapter 7).

Because of these different histories and other factors, the oxide and thechalcogenide glass have been studied in different societies. The oxide has beendeveloped in ceramic industries for a long time and investigated by inorganic

10 1 Introduction

Fig. 1.8 Professor Kolomietsin his office (1987, summer)

chemists more or less empirically. The chalcogenide is studied also by chemistsas new glasses and, in addition, as amorphous semiconductors by physicists and asphotonics glasses by application-oriented researchers. Such situations tend to limita unified understanding of these glasses. For instance, similar kinds of neutral dan-gling bonds are called as an E′ center and a D0 in the oxide and the chalcogenidesociety, respectively. Under the circumstances, unified descriptions of physical andchemical ideas will be very important.

1.5 Atomic and Electron Configurations

From the top of the group VIb (16) atoms in the periodic table (Fig. 1.9), we seeO, S, Se, and Te with a period increase from 2 to 5. The number of valence electronsin these atoms is 6 with a common outer electron configuration of s2p4.

In the s2p4 configuration, the p state is responsible for chemical bonding in manycases because, as shown in Fig. 1.10, the energy of the p state lies higher than thatof the s state. (As known, the only one exception is the one-electron system H.) The

Group

Period

I(a/b)

1,11

IIa

2

IIIb

13

IVb

14

Vb

15

VIb

16

VIIb

17

VIII ZERO

18

1 H He

2 Li Be B C N O F Ne

3 Na Mg Al Si P S Cl Ar

4 K/Cu Ge As Se Br Fe

5 /Ag Sn Sb Te I

6 /Au Pb

Fig. 1.9 Chalcogen (S, Se, and Te) and related atoms in the periodic table and sizes of atoms andions (Pauling 1960). The size, which is assumed to be spherical, is estimated from atomic distancesin crystals

1.5 Atomic and Electron Configurations 11

Fig. 1.10 Electron energiesof the p and the s state, Epand Es, in several atoms ofinterest. The values areobtained from table 2.2 inHarrison (1980). Solid linesconnect the values of thegroup VIb (16) atoms, anddashed lines connect those ofthe same periods. For Si andGe, the energies of sp3 states,−8.3 and −8.4 eV, are alsoplotted by diamonds

p state has three electron lobes, px, py, and pz, each being able to take two electronswith up and down spins. Then, following the so-called Hund rule (Kittel 2005), thefour electrons of the p state produce one filled lobe, e.g., pz, and two half-filledlobes, px and py, as illustrated in the upper middle panel in Fig. 1.11.

These two kinds of p states take different roles in the solids. The paired pz elec-trons form a non-bonding state, with the wavefunction being similar to that in anisolated atom. Correspondingly, the energy level is located at the same positionas that in an isolated atom, with some broadening arising from interatomic vander Waals-type interaction (the upper right in Fig. 1.11). This state forms the top

Fig. 1.11 Comparison of Se and Si in amorphous structures (left), electron distributions of theatoms in solids (center), and energy levels in the isolated atoms and solids (right). Se and Si haveentangled chain structures and cross-linked networks with p4 and sp3 electron distributions. Notethat gross features of the electron distributions and energy levels are the same with those in thecorresponding crystals. The energy gap appears between LP (lone-pair electron) and σ ∗ in Se andbetween σ and σ ∗ in Si

12 1 Introduction

of the valence band in solids. Kastner (1972), who emphasized this peculiar non-bonding p electron feature, designated the chalcogenide, e.g., Se and As2S3, as alone-pair electron semiconductor. Needless to say, the idea can be applied to theoxide, e.g., SiO2, as well. Note that this origin of the valence band is markedly dif-ferent from that in the conventional semiconductors such as Si and GaAs, in whichsp3 hybridization occurs, as illustrated in the lower middle in Fig. 1.11. On the otherhand, the electrons in px and py orbitals in the p4 configuration produce covalentbonds with neighboring atoms, giving rise to bonding states σ , which have lower(stabilized) energies than that of the original p state. As a result, the VIb atom cantake twofold coordination with neighboring atoms. That is, the coordination numberfollows the so-called 8−N rule (Mott and Davis 1979), where N = 6 in the presentcase. The covalent bond accompanies also the anti-bonding state σ ∗, which formsthe conduction band. Note that this p4 bonding scheme is inherent to the covalentgroup VIb material, irrespective of crystalline or non-crystalline structures.

There are, however, at least three notable exceptions from the twofold coordina-tion. The first is tetrahedral coordination in some chalcogenides. It is known that,in crystalline semiconductors such as CdS, S atoms (or S2– ions) are fourfold coor-dinated, which is ascribed to the sp3 hybridized wavefunction. Such a tetrahedralconfiguration may be energetically favored in the crystal because of the fairly ionicCd–S bonds and long-range structural periodicity. A similar situation seems to occurin amorphous In–S, as proposed by Narushima et al. (2004). On the other hand, thetetrahedral configuration of O atoms may be less common (CdO, ZnO), which isprobably due to much higher sp3 hybridization energy, arising from a greater energydifference of Ep − Es ≈ 15 eV in O than that (∼10 eV) in S and Se (Fig. 1.10).The second exception can be pointed out for ionic (or ion-conducting) glasses suchas Cu(Ag)–As(Sb)–S(Se), in which S and Se are demonstrated to have coordinationnumbers of 3 – 4 (Simdyankin et al. 2005). Such coordination changes can be under-stood using a formal valence shell model, proposed by Liu and Taylor (1989), whichassumes formal transfer of lone-pair electrons from S(Se) to Cu(Ag). The last excep-tion may be telluride materials such as Ge–Sb–Te, a famous DVD material, in whichTe appears to form sixfold coordination with Ge and Sb. This high coordination canbe regarded as a manifestation of metallic character of Te (Ep − Es ≈ 8.5 eV), inwhich the six valence electrons are likely to be mixed up in energy.

1.6 Ionicity, Covalency, and Metallicity of Atomic Bonds

Solid has a variety of atomic bonds including ionic, covalent, metallic, and alsoweaker van der Waals types. In elemental solids such as Si and Se, all thechemical bonds are purely covalent. In multi-component solids, heteropolar bondsare included, which are ionic to some degree. However, as shown in Fig. 1.12a,an ionic degree in As(Si,Ge)–O(S,Se,Te) bonds varies, and it decreases from O toTe. Recalling that the bond ionicity, the difference in electro-negativity of bondingatoms, of Na–Cl is 2.1 (Pauling 1960), we see in Fig. 1.12a that a Si(Ge)–O bond

1.6 Ionicity, Covalency, and Metallicity of Atomic Bonds 13

Fig. 1.12 Comparison of (a) bond ionicity, (b) macroscopic density d, and (c) optical gap Egin typical binary systems consisting of Si(Ge, As) and group VIb atoms. For instance, the datadenoted as Si(Ge) in (a) show, from O to Te, the ionicities of Si(Ge)–O, Si(Ge)–S, Si(Ge)–Se, andSi(Ge)–Te bonds. The data in (b) and (c) show d and Eg in pure chalcogen solids (� with dot-dashlines) and stoichiometric glasses SiO(S, Se, Te)2 (� with dashed lines), GeO(S, Se, Te)2 (× withsolid lines), and As2O(S, Se, Te)3 (◦ with solid lines)

with ∼1.7 is relatively ionic and As–Se with ∼0.4 is mostly covalent. The oxide ismuch more ionic than the chalcogenide.

The ionicity and covalency in the oxide and chalcogenide provide different fea-tures in compositional variations. We know that it is difficult to prepare a glass witha composition of, e.g., Si35O65, but preparation of As35S65 glass is straightforward.In the chalcogenide, composition tuning is attained in atomic ratios. On the otherhand, in the oxide glass, the compositional variation can be obtained in chemicalunits, as 74SiO2·16NaO2·10CaO. Here, the unit may be characterized either as anetwork former (SiO2) or as a network modifier (Na2O and CaO). We have utilized,for a long time, this kind of compositional tuning in oxide glasses for obtaining

Fig. 1.13 A schematicrepresentation of SiO2–Na2Oglass. Note that Si is four foldcoordinated in athree-dimensional view

14 1 Introduction

selected properties. For instance, thermal shaping of SiO2 glass needs high tem-peratures (∼1500◦C), which is inconvenient in mass production. Then, additionof modifier Na2O to silica networks disrupts firm ≡Si–O– connections to ionic≡Si–O– –Na+ bonds, as illustrated in Fig. 1.13, which can decrease the shapingtemperature. We have discovered also that further addition of CaO is effective forenhancing chemical stability (Doremus 1994).

1.7 Variety in Chalcogenides

There exist many kinds of amorphous chalcogenides (Borisova 1981, Popescu2000), and classification may be valuable. We can classify the amorphouschalcogenide into the elemental, binary, ternary, etc., and the alloys can be dividedinto stoichiometric (As2S3, GeSe2) and non-stoichiometric compositions (S–Se,As–Se).

Otherwise, we can classify the material with respect to the chalcogen included:sulfide, selenide, and telluride. As illustrated in Fig. 1.14, with an order of O, S, Se,and Te, the bond character changes from ionic, covalent, to metallic. We know thatthe covalent bond is directional and the ionic and metallic bonds are fairy isotropic.Important defects, such as dangling and wrong bonds, also seem to change withthis order.

Among many chalcogenide materials, how can we select one composition fora study? To obtain fundamental insights, we may need the simplest, elemen-tal material such as a-Se. However, the non-crystalline solid appears to pose adilemma to physicists, who prefer simplicity, that is, topological disorder producedonly by the twofold coordinated chalcogen is difficult to suppress crystalliza-tion. Actually, evaporated a-Se films are likely to crystallize within a few months,depending upon humidity, at room temperature. Compositional disorder is required

covalent metallic

O

S Se Tedirectional

ionic

wrongbond

isotropicdanglingbond

Fig. 1.14 Bond charactersand major defects in groupVIb glasses such asAs2O(S,Se,Te)3

1.7 Variety in Chalcogenides 15

for glass stability, and accordingly, multi-component alloys are of major concern.The non-crystalline solid appears to be inherently a kind of atomically complexsystem.

1.7.1 Elemental

For the elements, the sequence of S, Se, and Te shows that bonding changes frommolecular, covalent, to metallic. Among these three elements, only Se is availableas amorphous films and glassy ingots at room temperature. In contrast, amorphousS and Te are unstable at room temperature, immediately crystallizing, so that studieson these materials are relatively limited.

Several molecular allotropes are known for S. Among those, the most stableappears to be S8 ring molecules. However, as illustrated in Fig. 1.15, the small disk-shaped molecules can be regularly packed, which are easily crystallized. Glassy S,which is composed of S chains, is obtained when the melt stored above ∼160◦C,the so-called polymerization temperature, is quenched to temperatures below theglass transition temperature of –30◦C (Stolz et al. 1994). a-S films can be preparedthrough vacuum evaporation onto cooled substrates (Tanaka 1986).

Se is the only elemental glass available at room temperature (Zingaro andCooper 1974). The glassy structure is the simplest, consisting mainly of entangled−Se−Se− chains (Fig. 1.11). In addition, depending upon preparation procedures,small amounts of ring molecules such as Se8 may be included. Note that the stablestructure of c-Se is composed of aligned helical chains, as shown in Fig. 1.15.An important property of a-Se is that the material exhibits peculiar photoconductingproperties, which have been and are widely applied to photoconductor devices (seeSection 7.6).

Telluride is much more metallic, having less directional chemical bonds. As aresult, the material is likely to crystallize, and the bulk glass cannot be prepared(Bureau et al. 2009). Studies on pure a-Te films are few (Takahashi and Harada1982). It is mentioned here that pure pnictides (P, As, and Sb) can be prepared as

Fig. 1.15 Atomic structuresof c-S consisting of S8 rings(left) and c-Se(Te) of helicalchains (right)

16 1 Introduction

amorphous films, and bulk samples in some cases, while studies are very limited(Greaves et al. 1979).

1.7.2 Binary

The binary alloys, which have been extensively studied, are As2S(Se)3 (Fig. 1.16).These stoichiometric glasses are fairly covalent and stable, having optical gaps of∼2.4 (∼1.8) eV and the glass transition temperatures of ∼200◦C (Borisova 1981),both properties being convenient for experiments. As will be described in Section3.5, the average atomic coordination number is 2.4, which is assumed to be asignature of stable glasses. Electrically, As2S3 is a good insulator, and As2Se3 issemi-conducting. On the other hand, As2Te3 is substantially conductive and likelyto crystallize, probably due to less-directional metallic bonds of Te, so that studieson the amorphous forms are few.

To understand the property of a glass, we may need the corresponding crystal.However, it is difficult to prepare single-crystalline As2S3 (Yang et al. 1986), andinstead, we employ the corresponding mineral orpiment (Fig. 1.16) for experiments.On the other hand, single-crystalline As2Se3 can be prepared through vapor growth(Kitao et al. 1969, Smith et al. 1979). As shown in Fig. 1.16, As2S(Se)3 crystalshave layer-type structures, exhibiting cleavage in the a–c plane.

Experimental studies on GeS(Se)2 seem to be fewer than those on As2S(Se)3.The reason may be, at least, the following: One is that the preparation of GeS(Se)2

Fig. 1.16 An As2S3 glass rod (Eg ≈ 2.4 eV and Tg ≈ 200◦C) (upper left), an orpiment specimen(Eg ≈ 2.6 eV and Tm ≈ 300◦C) (lower left), and its atomic structure orthogonal to the b axis (upperright) and to the c axis (lower right)

1.7 Variety in Chalcogenides 17

glasses is more difficult than that of As2S(Se) and, in addition, glass propertiescritically depend upon preparation conditions (see Fig. 1.18 for GeS2). This featuremay be connected with a greater average coordination number of 2.67 and/or to theexistence of two crystalline polymorphs having layer and three-dimensional forms(with the optical gaps of ∼3.2 and ∼3.5 eV in c-GeS2 (Weinstein et al. 1982)).The other is that thermal vacuum evaporation of GeS(Se)2 is more difficult (seeSection 1.8). Some researchers employ radio-frequency sputtering in Ar atmosphere(Utsugi and Mizushima 1978). Ge–Te is fairly metallic so that the glass is difficultto prepare except around the eutectic composition Ge15Te85, and most studies havebeen done for amorphous films (Takahashi and Harada 1982, Piarristeguy et al.2009).

Studies on other binary alloys, including non-stoichiometric compositions, arestill fewer. For As(Ge)–S(Se,Te) glasses, it is interesting to note that, as shownin Fig. 1.17, selenide has the widest glass-forming regions. This feature may beascribed to the covalent heteropolar bonds and the similar cation–anion sizes inthe selenide systems. Other glasses have been less studied. Binary sulfides andselenides alloyed with B, P, and Si are relatively unstable, some being hygroscopic,and accordingly, experimental studies are few (Greaves and Sen 2007). SiS(Se,Te)2are difficult to prepare and unstable (Jackson and Grossman 2001), which may bedue to much smaller Si atoms (ion) than S(Se,Te) (see Fig. 1.9).

1.7.3 Ternary and More Complicated

For ternary alloys, we can envisage several kinds of systems: the chalcogen mixtureS–Se–Te, the anion-mixed system such as As–S–Se, and the cation-mixed systemsuch as Ge–Sb–Te. Studies on ternary chalcogenide are relatively limited, except

0 50 100

As-S

As-Se

As-Te

Ge-S

Ge-Se

Ge-Te

Chalcogen concentration [at.%]

Fig. 1.17 Glass-formingregions of typical binarychalcogenide glasses (datafrom Borrisova 1981)

18 1 Introduction

Fig. 1.18 An oxy-chalcogenide system, xGeO2–(100–x)GeS2 (Terakado and Tanaka 2008,© Elsevier, reprinted with permission). Three kinds of colors for the same compositions seemto arise from small compositional deviations and different preparation conditions

some selected compositions as follows: First, sputtered Ge–Sb–Te films, specif-ically Ge2Sb2Te5, have been extensively studied in recent applications to DVDs(see Section 7.4). Second, ionic chalcogenides such as Ga–La–S have been stud-ied as host glasses for doping rare-earth atoms such as Er and Pr. The glass isutilized for light amplifiers (Section 7.2). Third, Ag and Li chalcogenides suchas Ag–As–S and LiS–SiS2 attract considerable interest as (super-)ion-conductingglasses (Sections 3.6 and 7.7). Ionic bonds such as –S–Ag+ seem to provide semi-free sites for Ag+. We also note here that all the ionic and ion-conducting glassescannot be binary. For instance, an ion-conducting Ag2S becomes necessarily crys-talline, but Ag–As(Ge)–S is a glassy ionic conductor. The reason may be speculatedstraightforwardly.

In addition to multi-component chalcogenide glasses, we can prepare oxy-chalcogenide (Terakado and Tanaka 2008) and chalco-halide glasses (Lucas 1999,Balda et al. 2009). An example, GeO2–GeS2 glass, is shown in Fig. 1.18. Suchglasses may be useful for understanding an intrinsic property of the chalcogenide,since the property changes with the replacement of S by O atoms.

1.8 Preparation

Non-crystalline solids with different macroscopic forms can be prepared through avariety of methods (Elliott 1990). Specifically, three forms are utilized, which arebulk, fiber, and film. In addition, we can prepare powdered and nano-scale samples.

1.8.1 Glass (Bulk, Fiber)

What kinds of materials can vitrify? The thermodynamics predicts that if a meltis cooled down very slowly, all the melts will crystallize just below the meltingtemperature. On the other hand, molecular dynamics simulations demonstrate thatif a melt is quenched very rapidly (∼1012 K/s) to 0 K, all the melts, even liquid Ar,will solidify into non-crystalline solids (Sano et al. 2004). Practical situations lie inbetween these extrema.

1.8 Preparation 19

Hence, a more valuable question is the following: What kinds of materials canvitrify under practically available quenching rates slower than ∼107 K/s, which isobtainable in splat cooling (Elliott 1990)? Such a problem was considered as early as1932 by Zachariasen from a microscopic point of view (Mackenzie 1987). Knowncriteria for the glass formation arise from kinetic, structural, and chemical factors(Liu and Taylor 1989, Chechetkina 1991, Doremus 1994). Though such analyses areimportant, persevering work is required for obtaining practical results. And, com-prehensive data of the glass-forming region have been collected, e.g., by researchersin eastern Europe (Borisova 1981, Popescu 2000). In practical experiments, evenfor a fixed system, the glass-forming region depends upon many factors such asthe reacting temperature Tq, from which a melt is quenched, quenching rate dT/dt(10−2–102 K/s), and thermal capacity of quenched samples including an ampoule,which is employed for vacuum sealing of the melt. Figure 1.19 shows an exampleof reported glass-forming regions for the Ag–As–S system (Yoshida and Tanaka1995).

In addition, it should be underlined that also the property of melt-quenchedglasses depends upon preparation procedures, as being exemplified for As2S(Se)3(Cimpl et al. 1981, Yang et al. 1986, Tanaka 1987) and GeS(Se)2 (Zhilinskaya et al.1992, Holomb et al. 2005). Figure 1.20 shows that, in melt-quenched As2S3 glass,the optical bandgap considerably depends upon the reacting temperature Tq and thequenching rate (Tanaka 1987).

After preparation, the ingot may be shaped by polishing and/or annealed for sta-bilization. In some cases, annealing effects on electronic and thermal properties aresubstantial (Wang et al. 2007, Allen et al. 2008). For optical experiments, we mayneed thin samples, which can be prepared by polishing, the thinnest being ∼10 μm(Hamanaka et al. 1977). In addition, squeezing of viscous glasses under heating is aconvenient way for obtaining thin bulk samples (Frerichs 1953, Brandes et al. 1970).On the other hand, we may also need thick (long) samples for investigation of lowoptical attenuations, for which fiber samples can be employed. Such optical fibers

Fig. 1.19 Glass-formingregions of Ag–As–S glassunder three (solid, dashed,and dotted lines) differentmelt-quenching conditions(modified from Yoshida andTanaka 1995)

20 1 Introduction

Fig. 1.20 Optical gapenergies of g-As2S3 as afunction of the temperatureTq, from which the melt isslowly cooled ∼10 K/s (◦),rapidly quenched 10−2 K/s(•), and rapidly quenched andannealed at the glasstransition temperature Tg (�)(Tanaka 1987, © AmericanPhysical Society, reprintedwith permission). Tm and Tbdepict the melting and theboiling temperature

are produced from glass rods, which are prepared in several ways, and by drawingthe rod in inert atmosphere at around the glass transition temperature (Nishii andYamashita 1998).

1.8.2 Film and Others

Thin-film samples are produced in several ways such as evaporation and sputtering(Elliott 1990). The thickness can be varied from ∼10 nm to ∼50 μm. Needlessto say, substrate cleaning by chemical and physical methods is very important,specifically for thin (≤500 nm) films. Here, the most serious problem may be thecomposition deviation along the deposition process. In addition, it is plausible thatthe composition varies along the film thickness. We should also note that, in gen-eral, atomic structures of as-deposited films are substantially different from those inbulk glasses. Deposited films are fairly unstable, which undergo structural relaxationupon storage. Otherwise, a film is annealed at some temperature for stabilization andhomogenization, the annealing condition being intensively studied (Choi et al. 2010,Rowlands et al. 2010). For thick films, rapid thermal annealing (Ramachandran andBishop 2005) seems to be effective for suppressing cracking arising from relativelylarge thermal expansions (Table 3.1).

In addition, the substrate sometimes plays an important role, not only in the ther-mal expansion but in other properties. The most common substrates may be someoxide glass such as silica and borosilicate. However, a photoinduced phenomenonof As2S3 on viscous grease (Section 6.3.12) manifests that the substrate exertsgreat mechanical constraints upon the film. The electrical conductivity may alsobe important, as seen in a photo-enhanced vaporization (Section 6.3.15). We alsoemploy sapphire and Si wafer substrates, having high thermal conductivity, forsuppressing temperature rises under light illumination.

1.8 Preparation 21

Thermal evaporation is the most common preparation method of chalcogenidefilms having simple compositions such as pure Se. The film property, however,is known to markedly depend upon the temperature of substrates, and when it is∼50◦C, a-Se films having high photoconductivity are obtained. It is plausible thatthe substrate temperature governs the atomic structure, including the ratio of ringand chain molecules and also their size and length. In addition, surprisingly, Suzukiet al. (1987) have demonstrated that mean Se chain lengths and xerographic proper-ties of evaporated Se films depend upon chemical reaction temperature of employedbulk pellets. However, the details remain unknown.

Evaporation of compounds is more difficult. For instance, contrary to commonfeatures, flash evaporation (through pouring a powdered sample onto a high-temperature boat) of As2S3 causes substantial compositional deviation (Tanaka1974). Slow evaporation with a deposition rate of ∼1 nm/s is preferred. Similarresults are reported for As2Se3 (Bando et al. 1991). Another feature, which is worthmentioning, is that GeS2 sublimates, not evaporates. Accordingly, Knudsen-typeboats (covered crucibles) give smaller compositional deviations, while the devia-tion is still substantial as shown in Fig. 1.21 (Tanaka et al. 1984). In addition, asillustrated in Fig. 1.22, the film and bulk with nearly the same composition of GeS2manifest largely different optical gaps of ∼2.5 and ∼3.2 eV (Tanaka et al. 1984).It should be also mentioned that Chopra’s group (Kumar et al. 1989) has discoveredthat obliquely deposited As and Ge chalcogenide films have substantially differentfilm structures.

Sputtering in Ar gas is also a common technique. Ge2Sb2Te5 films for DVDapplications can be prepared through dc sputtering (Kato and Tanaka 2005).Ge–As–S(Se) films, which are electrically insulating, can be prepared using radio-frequency sputtering (Utsugi and Mizushima 1980, Tan et al. 2010). Oxide filmssuch as SiO2 can also be radio-frequency sputtered, while the oxygen content tends

Fig. 1.21 Compositiondeviations in As100–xSx andGe100–xSx films in vacuumevaporation. Thecompositions of evaporatedfilms tend to approach thestoichiometric compositionsAs2S3 and GeS2

22 1 Introduction

Fig. 1.22 Optical absorptionedges of GeS2 and As2S3 inbulk samples (solid lines),as-evaporated films (dottedlines), and annealed films(dashed lines)

to decrease. Accordingly, reactive sputtering using mixed Ar and oxygen gas ispreferred. In general, the sputtering seems to produce more dense films that thoseprepared by the evaporation.

Other thin-film preparation methods have also been employed. Spin coatingsusing appropriate solutions, originally developed for organic resists, provide a non-expensive procedure for preparing thin chalcogenide films (Chern and Lauks 1982,Kohouteka et al. 2007, Song et al. 2010); the methods do not need vacuum. Glowdischarge deposition, a technique widely employed for preparing a-Si:H films,has also been applied to deposition of hydrogenated chalcogenide films such asAs(Ge,Si)–S(Se):H (Šmíd and Fritzshe 1980, Nagels et al. 2003). Chemical vapordeposition is also employed for obtaining hydrogenated samples (Katsuyama et al.1986, Curry et al. 2005). Laser ablations, shown in Fig. 1.23, using pulsed (Hansenand Robitaille 1987, Wang et al. 2007) and continuous-wave (González-Leal et al.2009) sources have been applied to As2S3 and other materials. A pulsed method canproduce not only films, but fibrous and spherical samples (Juodkazis et al. 2006).

Fig. 1.23 Two arrangementsof laser ablation:(a) conventional type and(b) irradiation throughtransparent substrates

1.9 Dependence upon Experimental Variables 23

In addition, less common methods have been employed. Examples are sol–gelproduction of Ge–S films (Martins et al. 1999) and other chemical reactions, whichhave produced As2S3 powders (Onodera et al. 1969), GeSx aerogels (Kalebailaet al. 2006), Se films (Peled 1986), Sb2S3 films (Grozdanov et al. 1994), andnano-samples of As–S (Lee et al. 2007) and Se–Te (Kaur and Bakshi 2010).Amorphization by mechanical milling, which was developed for producing amor-phous metals, has also been applied to Ge-chalcogenides (Tani et al. 2001), Se(Tani et al. 2001, Zhao et al. 2004), and Li-chalcogenide glasses (Minami et al.2010).

1.9 Dependence upon Experimental Variables

Measurements of some physical property as a function of thermodynamic variablesare common tactics for understanding the property in solid-state science. Here, thethermodynamic variables are, in general, temperature and pressure. Temperaturevariations modify atomic vibrations, which may provide similar effects, irrespec-tive of atomic periodicity, upon thermal expansions, heat capacities, etc. (seeSection 3.4). On the other hand, the compression may cause different behaviors incrystals and non-crystals, as exemplified by Si and Se in the following.

Envisage an ideal Si single crystal, a cubic crystal with the diamond structureconsisting of only one type of bond. If it is subjected to hydrostatic compression,the atomic distance and cell dimension will be elastically reduced, which may berecovered to the initial state by depressurizing. However, if the material is a-Si(:H),which contains some atomic voids, the compression may preferentially collapsethe voids. Actually, as shown in Fig. 1.24 (left), linear compression behaviors inc-Si and a-Si:H are substantially different. In a-Si:H, plastic shrinkage appears,and depressurizing to 1 atm produces densified samples (Minomura 1984), whichwill relax gradually. Similar compression behaviors can be pointed out for g-SiO2(Pathasarathy and Gopal 1985).

The situations are different in Se and chalcogenide glasses (Durandurdu 2009,Vaccari et al. 2009), which contain covalent and van der Waals bonds. Irrespectiveof c- and a-Se, hydrostatic pressure compresses preferentially the van der Waalsbond first, and after that, the bond angle may be modified, the bond length beingintact until ultimate compression or structural transitions occur. These features arenot very different in c- and a-Se, as is suggested from the compression behaviors inFig. 1.24 (left). In the Se solids, pressure effects are prominent due to the soft vander Waals bond, but the effect of disorder is comparatively small.

For non-crystalline solids, the pressure study has provided fruitful insights. Thecompression can produce novel non-crystalline materials (Sen et al. 2006, Brazhkinet al. 2010) including pure Ge (Bhat et al. 2007). Valuable insights have alsobeen obtained from uniaxial compression, which is assumed to change an isotropicamorphous structure to anisotropic (Tallant et al. 1988) or can produce anisotropicglasses (Tanaka 1989b). It should also be mentioned that the advent of diamond

24 1 Introduction

Fig. 1.24 A diamond anvilcell for pressure opticalexperiments

anvil cells (Fig. 1.25) and related techniques since ∼1970 (Jayaraman 1986) hasstimulated pressure experiments, specifically those using laser and x-ray beams.

In addition to the thermodynamic studies, two experiments, which are more orless unique to amorphous materials, are on composition variations and preparationprocedures. Importance of compositional studies, though the experiments are moreor less monotonous, in amorphous materials should be emphasized. Specifically,since the covalent chalcogenide glass can be compositionally varied in atomic ratios,studies on continuous composition variations provide important insight, an example

Fig. 1.25 Linear compressions −�L(P)/L (left) and optical bandgaps Eg(P) in several crystalline(c-) and amorphous materials as a function of hydrostatic pressure (Tanaka 1989a). Polyethyleneand polyacetylene are abbreviated as PE and PA. In amorphous Ge and As, phase transitions tometallic crystalline phases occur at 60 and 40 kbar. For GeS2, the film (f) and the melt-quenchedglass (g) show different behaviors, while for As2S3 no big differences appear

References 25

being the concept of magic numbers, as will be described in Section 3.5. In addi-tion, studies on preparation procedures are also invaluable due to quasi-stability(Section 1.3). It should be noted that such studies on composition and preparationare, in principle, needless or non-existing for (ideal) single crystals such as Si andGaAs.

References

Allen, C., Belev, G., Johanson, R., Kasap, S.O.: Relaxation of electrical properties of stabilizedamorphous selenium based photoconductors. J. Non-Cryst. Solids 354, 2711–2714 (2008)

Balda, R., García-Revilla, S., Fernández, J., Seznec, V., Nazabal, V., Zhang, X.H., Adam, J.L.,Allix, M., Matzen, G.: Upconversion luminescence of transparent Er3+-doped chalcohalideglass–ceramics. Opt. Mater. 31, 760–764 (2009)

Bando, T., Gosain, D.P., Okano, S., Suzuki, M.: Effects of preparation conditions of the bulk andsource temperature on the composition of As2Se3 films. Thin Solid Films 195, 237–244 (1991)

Bhat, M.H., Molinero, V., Soignard, E., Solomon, V.C., Sastry, S., Yarger, J.L., Angell, C.A.:Vitrification of a monatomic metallic liquid. Nature 448, 787–790 (2007)

Borisova, Z.U.: Glassy Semiconductors. Plenum, New York, NY (1981)Brandes, R.G., Laming, F.P., Peason, A.D.: Optically formed dielectric gratings in thick films of

arsenic-sulfur glass. Appl. Opt. 9, 1712–1714 (1970)Brazhkin, V.V., Katayama, Y., Kondrin, M.V., Lyapin, A.G., Saitoh, H.: Structural transformation

yielding an unusual metallic state in liquid As2S3 under high pressure. Phys. Rev. B 82, 140202(2010)

Breinder, S.J.: The discoverers of glass. Science 307, 1563 (2005)Bureau, B., Boussard-Pledel, C., Lucas, P., Zhang, X., Lucas, J.: Forming glasses from Se and

Te. Molecules 14, 4337–4350 (2009)Chechetkina, E.A.: Rawson’s criterion and intermolecular interactions in glass-forming melts.

J. Non-Cryst. Solids 128, 30–47 (1991)Chern, G.C., Lauks, I.: Spin-coated amorphous chalcogenide films. J. Appl. Phys. 53, 6979–6982

(1982)Cimpl, Z., Kosek, F., Husa, V., Svoboda, J.: Refractive index of arsenic trisulphide. Czech. J. Phys.

B 31, 1191–1194 (1981)Choi Dhoi, D.-Y., Madden S., Bulla, D., Wang, R., Rode, A., Luther-Davies, B.: Thermal annealing

of arsenic tri-sulphide thin film and its influence on device performance. J. Appl. Phys. 107,053106 (2010)

Curry, R.J., Mairaj, A.K., Huang, C.C., Eason, R.W., Grivas, C., Hewak, D.W., Badding, J.V.:Chalcogenide glass thin films and planar waveguides. J. Am. Ceram. Soc. 88, 2451–2455(2005)

Doremus, R.H.: Glass Science 3rd ed. Wiley, New York, NY (1994)Durandurdu, M.: High-density amorphous phase of GeS2 glass under pressure. Phys. Rev. B 79,

205202 (2009)Elliott, S.R.: Physics of Amorphous Materials 2nd ed. Longman Scientific & Technical, Essex

(1990)Fishlock, T.W., Oral, A., Egdell, R.G., Pethica, J.B.: Manipulation of atoms across a surface at

room temperature. Nature 404, 743–745 (2000)Flaschen, S.S., Pearson, A.D., Northover, W.R.: Formation and properties of low-melting glasses in

the ternary systems As-TI-S, As-TI-Se, and As-Se-S. J. Am. Ceram. Soc. 43, 274–275 (1960)Frerichs, R.: New optical glasses with good transparency in the infrared. J. Opt. Soc. Am. 43,

1153–1157 (1953)González-Leal, J.M., Gámez, A.J., Angel, J.A., Jimenez-Garay, R.: Light structured deposition (1):

Material properties. J. Non-Cryst. Solids 355, 1989–1992 (2009)

26 1 Introduction

Greaves, G.N., Elliott, S.R., Davis, E.A.: Amorphous arsenic. Adv. Phys. 28, 49–141 (1979)Greaves, G.N., Sen, S.: Inorganic glasses, glass-forming liquids and amorphizing solids. Adv. Phys.

56, 1–166 (2007)Grozdanov, I., Ristov, M., Sinadinovski, Gj., Mitreski, M.: Fabrication of amorphous Sb2S3 films

by chemical deposition. J. Non-Cryst. Solids 175, 77–83 (1994)Hamanaka, H., Tanaka, K., Iizima, S.: Reversible photostructural change in melt-quenched As2S3

glass. Solid State Commun. 23, 63–65 (1977)Hansen, S.G., Robitaille, T.E.: Characterization of the pulsed laser evaporation process: Selenium

thin-film formation. Appl. Phys. Lett. 50, 359–361 (1987)Harrison, W.A.: Electronic Structure and the Properties of Solids. Freeman, San Francisco, CA

(1980)Holomb, R., Johansson, P., Mitsa, V., Rosola, I.: Local structure of technologically modi-

fied g-GeS2: Resonant Raman and absorption edge spectroscopy combined with ab initiocalculations. Philos. Mag. B 85, 2947–2960 (2005)

Jackson, K., Grossman, S.: Chain formation and the origin of structure in the Raman spectrum ofa-SiSe2. Phys. Rev. B 65, 012206 (2001)

Jayaraman, A.: Ultrahigh pressures. Rev. Sci. Instrum. 57, 1013–1031 (1986)Juodkazis, S., Misawa, H., Louchev, O.A., Kitamura, K.: Femtosecond laser ablation of

chalcogenide glass: Explosive formation of nano-fibres against thermo-capillary growth ofmicro-spheres. Nanotechnology 17, 4802–4805 (2006)

Kalebaila, K.K., Georgiev, D.G., Brock, S.L.: Synthesis and characterization of germanium sulfideaerogels. J. Non-Cryst. Solids 352, 232–240 (2006)

Kastner, M.A.: Bonding bands, lone-pair bands, and impurity states in chalcogenide semiconduc-tors. Phys. Rev. Lett. 28, 355–357 (1972)

Kato, T., Tanaka, K.: Electronic properties of amorphous and crystalline Ge2Sb2Te5 films. Jpn.J. Appl. Phys. 44, 7340–7344 (2005)

Katsuyama, T., Satoh, S., Matsumura, H.: Fabrication of high-purity chalcogenide glasses bychemical vapor deposition. J. Appl. Phys. 59, 1446 (1986)

Kaur, G., Bakshi, M.S.: Nonideal mixing of Se-Te in aqueous micellar phase for nanoalloys overthe whole mole mixing range with morphology control from nanoparticles to nanoribbons.J. Phys. Chem. C 114, 143–154 (2010)

Kitao, M., Asakura, N., Yamada, S.: Preparation of As2Se3 single crystals. Jpn. J. Appl. Phys. 8,499–500 (1969)

Kittel, C.: Introduction to Solid State Physics, 8th ed. Wiley, New York, NY (2005)Kohouteka, T., Wagnera, T., Orava, J., Krbal, M., Fejfar, A., Mates, T., Kasap, S.O., Frumar, M.:

Surface morphology of spin-coated As–S–Se chalcogenide thin films. J. Non-Cryst. Solids 353,1437–1440 (2007)

Kokorina, V.F.: Glasses for Infrared Optics. CRC Press, Boca Raton, FL (1996)Kolomiets, B.T.: The role of adsorption layers in exo-electron emission from oxide surfaces. Phys.

Status Solidi 7, 359–363 (1964a)Kolomiets, B.T.: Vitreous semiconductors (II). Phys. Status Solidi 7, 713–731 (1964b)Kumar, A., Malhotra, L.K., Chopra, K.L.: Infrared and x-ray photoelectron spectroscopic study of

photostructural changes in amorphous P-Ge-Se thin films. J. Appl. Phys. 65, 1671–1675 (1989)Lee, J.H., Kim, M.G., Yoo, B., Myung, N.V., Maeng, J., Lee, T., Dohnalkova, A.C., Fredrickson,

J.K., Sadowsky, M.J., Hur, H.G.: Iogenic formation of photoactive arsenic-sulfide nanotubesby Shewanella sp. strain HN-41. Proc. Natl. Acad. Sci. USA 104, 20410–20415 (2007)

Liu, J.Z., Taylor, P.C.: A general structural model for semiconducting glasses. Solid State Commun.70, 81–85 (1989)

Lucas, J.: Infrared glasses. Curr. Opin. Solid State Mater. Sci. 4, 181–187 (1999)Mackenzie, J.D.: Applications of Zachariasen’s rules to different types of noncrystalline solids.

J. Non-Cryst. Solids 95–96, 441–448 (1987)Martins, O., Xu, J., Almeida, R.M.: Sol–gel processing of germanium sulfide based films. J. Non-

Cryst. Solids 256–257, 25–30 (1999)

References 27

Minami, K., Hayashi, A., Tatsumisago, M.: Mechanochemical synthesis of Li2S-P2S5 glasselectrolytes with lithium salts. Solid State Ionics 181, 1505–1509 (2010)

Minomura, S.: Pressure effects on the local atomic structure. In: Pankove, J.I. (ed.) Semiconductorsand Semimetals, Vol. 21A, Chap. 13, pp. 273–290. Academic Press, San Diego (1984)

Mott, N.F., Davis, E.A.: Electronic Processes in Non-Crystalline Materials 2nd ed. Clarendon,Oxford (1979)

Nagels, P., Mertens, R., Tichy, L.: Reversible photodarkening in amorphous AsxS100-x films pre-pared by thermal evaporation and plasma-enhanced chemical vapour deposition. Mater. Lett.57, 2494–2500 (2003)

Narushima, S., Hiroki, M., Ueda, K., Shimizu, K., Kamiya, T., Hirano, M., Hosono, H.: Electricalproperties and local structure of n-type conducting amorphous indium sulphide. Philos. Mag.Lett. 84, 665–671 (2004)

Nishii, J., Yamashita, T.: Chalcogenide glass-based fibers. In: Sanghera, J.S., Aggarwal, I.D. (eds.)Infrared Fiber Optics, Chap. 4, pp.143–184. CRC Press, Boca Raton, FL (1998)

Onodera, N., Suga, H., Seki, S.: Glass transition in amorphous precipitates. J. Non-Cryst. Solids 1,331–334 (1969)

Pathasarathy, G., Gopal, E.S.R.: Effect of high pressure on chalcogenide glasses. Bull. Mater. Sci.7, 271–302 (1985)

Pauling, L.: The Nature of the Chemical Bond 3rd ed. Cornell University Press, Ithaca, NY(1960)

Peled, A.: Optical parameters of photodeposited a-Se thin films. Philos. Mag. B 53, 171–177(1986)

Phillips, J.C.: Structural principles of amorphous and glassy semiconductors. J. Non-Cryst. Solids35–36, 1157–1165 (1980)

Piarristeguy, A.A., Barthelemy, E., Krbal, M., Frayret, J., Vigreux, C., Pradel, A.: Glass forma-tion in the GexTe100-x binary system: Synthesis by twin roller quenching and co-thermalevaporation techniques. J. Non-Cryst. Solids 355, 2088–2091 (2009)

Popescu, M.A.: Non-Crystalline Chalcogenides. Kluwer, Dordrecht (2000)Ramachandran, S., Bishop, S.G.: Photoinduced integrated-optic devices in rapid thermally

annealed chalcogenide glasses. IEEE J. Select. Topics Quant. Electron. 11, 260–270 (2005)Rowlands, C., Lei, S., Elliott, S.R.: Rapid prototyping of low-loss IR chalcogenide-glass waveg-

uides by controlling remelting. ChemPhysChem 11, 2393–2398 (2010)Saal, A.E., Hauri, E.H., Cascio, M.L., Van Orman, J.A., Rutherford, M.C., Cooper, R.F.: Volatile

content of lunar volcanic glasses and the presence of water in the Moon’s interior. Nature 454,192–195 (2008)

Sano, Y., Nishio, K., Koga, J., Yamaguchi, T., Yonezawa, F.: Simulational study of glass transitionin argon. J. Non-Cryst. Solids 345, 546–550 (2004)

Sen, S., Gaudio, S., Aitken, B.G., Lesher, C.E.: Observation of a pressure-induced first-orderpolyamorphic transition in a chalcogenide glass at ambient temperature. Phys. Rev. Lett. 97,025504 (2006)

Simdyankin, S.I., Elstner, M., Niehaus, T.A., Frauenheim, T., Elliott, S.R.: Influence of copper onthe electronic properties of amorphous chalcogenides. Phys. Rev. B 72, 020202 (2005)

Šmíd, V., Fritzsche, H.: Hydrogenated chalcogenide glasses As2-xSe3+x and As2-xS3+x prepared byplasma decomposition. Solid State Commun. 33, 735–738 (1980)

Smith, B.A., Cowlam, N., Shamah, A.M.: The crystal growth and atomic structure of As2(Se,S)3

compounds. Philos. Mag. B 39, 111–132 (1979)Song, S., Dua, J., Arnold, C.B.: Influence of annealing conditions on the optical and structural

properties of spin-coated As2S3 chalcogenide glass thin films. Opt. Express 18, 5472–5480(2010)

Stec, B.: Living and nonliving matter. Science 305, 41–44 (2004)Stolz, M., Winter, R., Howells, W.S., McGreevy, R.L., Egelstaff, P.A.: The structural properties of

liquid and quenched sulphur II. J. Phys. Condens. Matter 6, 3619–3628 (1994)

28 1 Introduction

Suzuki, K., Matsumoto, K., Hayata, H., Nakamura, N., Minari, N.: Mass spectroscopic study ofevaporated Se films and melt-quenched Se glasses. J. Non-Cryst. Solids 95–96, 555–562 (1987)

Takahashi, T., Harada, Y.: Photoemission study of the crystallization of amorphous Te film. J. Non-Cryst. Solids 47, 417–420 (1982)

Tallant, D.R., Michalske, T.A., Smith, W.L.: The effects of tensile stress on the Raman spectrumof silica glass. J. Non-Cryst. Solids 106, 380–383 (1988)

Tan, W.C., Solmaz, M.E., Gardner, J., Atkins, R., Madsen, C.: Optical characterization of a-As2S3thin films prepared by magnetron sputtering. J. Appl. Phys. 107, 033524 (2010)

Tanaka, K.: Evidence for reversible photostructural change in local order of amorphous As2S3film. Solid State Commun. 15, 1521–1524 (1974)

Tanaka, K.: Configurational and structural models for photodarkening in glassy chalcogenides.Jpn. J. Appl. Phys. 25, 779–786 (1986)

Tanaka, K.: Chemical and medium-range orders in As2S3 glass. Phys. Rev. B 36, 9746–9752(1987)

Tanaka, K.: Pressure studies of amorphous semiconductors. In: Borossov, M., Kirov, N., Vavrek,A. (eds.) Disordered Systems and New Materials, pp. 290–309. World Scientific, Singapore(1989a)

Tanaka, K.: Pressure-induced squeezing phenomenon in uniaxially compressed glass. Jpn. J. Appl.Phys. 28, L679–L681 (1989b)

Tanaka, K., Kasanuki, Y., Odajima, A.: Physical properties and photoinduced changes of amor-phous Ge-S films. Thin Solid Films 117, 251–260 (1984)

Tani Y, Shirakawa Y., Shimosaka A., Hidaka J.: Crystalline-amorphous transitions of Ge-Se alloysby mechanical grinding. J. Non-Cryst. Solids 293, 779–784 (2001)

Terakado, N., Tanaka, K.: The structure and optical properties of GeO2–GeS2 glasses. J. Non-Cryst. Solids 354, 1992–1999 (2008)

Utsugi, Y., Mizushima, Y.: Photostructural change of lattice-vibrational spectra in Se-chalcogenideglass. J. Appl. Phys. 49, 13470–3475 (1978)

Utsugi, Y., Mizushima, Y.: Photostructural change in the Urbach tail in chalcogenide glasses.J. Appl. Phys. 51, 1773–1779 (1980)

Vaccari, M., Garbarino, G., Yannopoulos, S.N., Andrikopoulos, K.S., Pascarelli, S.: High pressuretransition in amorphous As2S3 studied by EXAFS. J. Chem. Phys. 131, 224502 (2009)

Wang, R.P., Rode, A., Madden, S., Luther-Davies, B.: Physical aging of arsenic trisulfide thickfilms and bulk materials. J. Am. Ceram. Soc. 90, 1269–1271 (2007)

Weinstein, B.A., Zallen, R., Slade, M.L.: Pressure-optical studies of GeS2 glasses and crystals:Implications for network topology. Phys. Rev. B 25, 781–792 (1982)

Yang, C.Y., Paesler, M.A., Sayers, D.E.: First crystallization of arsenic trisulfide from bulk glass:The synthesis of orpiment. Mater. Lett. 4, 233–235 (1986)

Yoshida, N., Tanaka, K.: Photoinduced Ag migration in Ag-As-S glasses. J. Appl. Phys. 78,1745–1750 (1995)

Zallen, R.: The Physics of Amorphous Solids. Wiley, New York, NY (1983)Zanotto, E.D., Coutinho, F.A.B.: How many non-crystalline solids can be made from all the

elements of the periodic table? J. Non-Cryst. Solids 347, 285–288 (2004)Zhao, Y.H., Lu, K., Liu, T.: EXAFS study of mechanical-milling-induced solid-state amorphization

of Se. J. Non-Cryst. Solids 333, 246–251 (2004)Zhilinskaya, E.A., Valeev, N.Kh., Oblasov, A.K.: GexS1−x glasses. II. Synthesis conditions and

defect formation. J. Non-Cryst. Solids 146, 285–293 (1992)Zingaro, R.A., Cooper, W.C. (eds.): Selenium. Van Nostrand Reinhold Company, New York, NY

(1974)

Chapter 2Structure

Abstract Atomic and microscopic structures of chalcogenide glasses are discussedfrom theoretical and experimental points of view. Starting with discussion on anideal glass structure, we will see continuous studies performed for grasping atomicstructures in disordered materials. Experimental methods and deduced results forthe short-range and medium-range structures (orders) in glasses are introduced.Structural defects, which are likely to produce localized states in the bandgap, arediscussed. In addition to these atomic structures, we shed light upon inhomogeneityand nano-structures in chalcogenide glasses.

Keywords Density · FSDP · Boson peak · Distorted layer · Wrong bond · Danglingbond · Homogeneity · Multi-layer

2.1 Ideal Structure

What is an ideal glass structure? For a crystal, we can envisage its ideal structure asone in which the structure is perfectly periodic with no defects at all (Fig. 2.1). Theatomic position can be uniquely determined. Such a structure could conceptually beobtained through infinitely slow cooling of the corresponding melt to 0 K. In a sim-plified theory, crystal surfaces are tentatively neglected under the so-called periodicboundary condition, and the structure becomes a starting framework for analyses ofmacroscopic properties (Kittel 2005). Or, in the exact opposite, we can envisage acompletely random atomic structure in an ideal gas. In this case, the atomic positioncan neither be predicted nor fixed. But, its property such as pressure at a given tem-perature can theoretically be evaluated through statistical mechanics for an assembly

Fig. 2.1 Two-dimensionalviews of (a) crystal (closepacked), (b) liquid and glass(dense random packing), and(c) gas

29K. Tanaka, K. Shimakawa, Amorphous Chalcogenide Semiconductors and RelatedMaterials, DOI 10.1007/978-1-4419-9510-0_2, C© Springer Science+Business Media, LLC 2011

30 2 Structure

of point-like substances (atom or molecule) having no interactions. The physicalproperties are uniquely fixed under a fixed temperature and volume. Having seenthese ultimate examples, we are tempted to assume that the ideal should imply auniquely defined structure, at least, in a statistical sense. Ideal must be unique. Canwe imagine such an ideal structure for a glass?

It seems impossible to envisage the unique structure for a disordered lattice. Forinstance, in the two local structures illustrated in Fig. 2.2, both including fourfoldcoordinated one-kind atoms in (a) a 6-atom ring with a dangling bond and (b) astrained but completely bonded 5-atom ring, which has a smaller total (electronplus lattice) energy? The structure in (b) can be regarded as a part of the famousPolk model proposed for a-Si (Turnbull and Polk 1972), which contains no dan-gling bonds. Several authors may assume that such continuous random networksare ideal. But, the structure must be highly strained. And, even for such fullyconnected structures, a variety of atomic ring structures with different formationenergies possibly exist. It seems that we cannot envisage an ideal glass structure.

Disorder implies a lot of varieties between the two ideal (ultimate) structures ofcrystal and gas. The amorphous structure is neither periodic, as that in a crystal,nor completely random, as that in an ideal gas. The non-crystalline structure spansa wide range between the completely perfect and the completely random structure:single crystal (periodic) ← non-crystal → ideal gas (completely random). We mustconsider a variety of intermediates. It should be noted, however, that liquid has alsoa disordered structure.

Then, what is the difference between a liquid and an amorphous material? In con-trast to the liquid, which is thermodynamically equilibrated, the non-crystalline solidis in quasi-equilibrium, or is meta-stable. Strictly speaking, an amorphous materialdoes not take a thermodynamically defined phase, but it takes just a spontaneousstate, which necessarily changes with time. After infinitely long storage, the glassis believed to relax to a crystal. Actually, we know that a-Se films crystallize fromsurfaces within a few weeks when stored in humid atmospheres. We also knowthat the surface of glassy flakes, which are dug at prehistoric ruins, often appearsmicaceous or crystalline. In addition, a glass property depends upon preparationmethods. Actually, as shown in Fig. 2.3, as-evaporated and annealed As2S3 filmsgive markedly different x-ray diffraction patterns.

Fig. 2.2 Two bondingstructures for fourfoldcoordinated atoms such as Si.(a) A 6-membered ring with adangling bond, and (b) astrained 5-membered ring

2.2 Practical Structure 31

Fig. 2.3 X-ray diffraction patterns of As2S3 films in an as-evaporated state (◦) and after annealing(•) at 180◦C (DeNeufville et al. 1973, © Elsevier, reprinted with permission)

Nevertheless, meta-stability has provided an unresolved problem on the unique-ness of glassy states. We here recall the so-called Kauzmann’s paradox, detailed inSection 3.2. The most stable glass may be obtained at the Kauzmann temperatureTK, since the free energy can be uniquely defined. Kauzmann’s glass may be ideal.However, the idea is macroscopic, and we have never obtained the glass nor seenthe atomic structure at the conceptual temperature TK.

2.2 Practical Structure

Determination of atomic bonding structures is a prerequisite in solid-state sci-ence. For crystals, the structure can be determined in principle through analysesof Bragg peaks in x-ray diffraction patterns. However, as exemplified in Figs. 2.3and 2.4, the non-crystalline solid does not provide sharp Bragg peaks but gives

Fig. 2.4 X-ray diffractionpatterns of glassy andcrystalline (hexagonal) GeO2,obtained using the Cu Kα

line, showing halos and sharppeaks

32 2 Structure

Fig. 2.5 Comparison of thedensities for glassy andcrystalline As2(Se-Te)3 alloys(Thornburg 1973, © Springer,reprinted with permission)

only broad halos. Considering such observations, Zachariasen (1932) proposed theso-called continuous random network model for oxide glasses such as Si(Ge)O2,while the real structure could not be determined. We here see fatal limitations ofthe traditional structural analysis. The limitation still remains, posing the biggestproblem in science on non-crystalline materials. Then, how can we get insight intothe atomic structure? We can see just the tip of an iceberg as described below.

A rough idea can be grasped from the macroscopic density (Fig. 2.5). It is knownfor simple glasses that the glass is less dense than the corresponding crystal by10–20% (Thornburg 1973, Hobbs and Yuan 2000), which varies with preparationprocedures and storage after preparation. This observation suggests that atomicpacking in the glass and the crystal is not very different. More generally, the densi-ties of a glass, the corresponding crystal, and the melt can be regarded roughly as thesame in comparison with that in the gas, which has nearly completely random andtime-varying atomic (molecular) structures with an average separation of ∼5 nm at1 atm (Fig. 2.1). Specifically, since the glass is produced from the melt, it is rea-sonable to envisage that the structures have some resemblances. We then assumethat the atomic potential, which fixes the bond distance and atomic coordination,governs the density in all condensed matters.

To analyze the amorphous structure in atomic scales, we can classify it intotwo elements, as shown in Fig. 2.6: normal bonding structures and defective struc-tures (Ovshinsky and Adler 1978). A normal bond can be defined as topologically

Normal bonding structure

Atomic structure short-range ~ coordination number, bond length, bond anglemedium-range ~ dihedral angle, ring, intermolecular and dimensional structure

Defects ~ ill-coordination such as dangling bond and wrong bond

Fig. 2.6 A classification of amorphous atomic structures

2.2 Practical Structure 33

Fig. 2.7 Structure models of (a) g-SiO2 (three-dimensional continuous random network),(b) g-As2S3 (two-dimensional distorted layers), (c) g-Se (one-dimensional entangled chains), and(d) c-SiO2. In (a) and (d), Si and O are shown by circles with four and twofold coordination.In (b), As and S are shown by solid and open circles with three and twofold coordination. Notethat (a) includes a small ring and an E′ center, (b) contains wrong bonds (As−As and S−S), and(c) contains a few ring molecules. The bond lengths are 0.16 nm in SiO2, 0.23 nm in As2S3, and0.24 nm in Se so that side lengths of these illustrations are 2–3 nm

the same atom connection with that existing in the corresponding crystal. In SiO2glass, it is SiO4/2 (≡Si–O–) tetrahedral connections, as illustrated in Fig. 2.7a. Thenormal bonding structure can further be divided into the short (�0.5 nm) and themedium-range (0.5−3 nm) structure, as will be described later. On the other hand,the defective structure resembles a defect in practical crystals. The examples arean E′ center in g-SiO2, which is a Si dangling bond (≡Si•), and a wrong bond(Halpern 1976), i.e., a Si homopolar bond (≡Si−Si≡), both non-existing in theideal SiO2 crystal. We here underline that these defective structures are point-likedefect (<0.5 nm). Defects such as dislocations and stacking faults, which sometimesplay important roles in crystals, do not exist in amorphous materials. We also notethat the point-like defect is spatially isolated from each other in normal bondingmatrices. The isolation may be a consequence arising from the non-existence oflong-range atomic periodicity in the glass. If the Si wrong bonds would gather, theassembly might become a Si nano-crystal.

A note on small rings should be added. As known, c-SiO2 takes a variety ofatomic structures, in which the most common is the quartz, or β-quartz (the high-temperature form, Fig. 1.1). The crystal structure is hexagonal (Fig. 2.7d) consistingof SiO4/2 tetrahedra, which contain 3 (6 atom)- and 6-membered (12 atom) rings.On the other hand, in g-SiO2, it is plausible that a variety of rings exist. And,some researchers assume small rings such as 3- and 4-membered rings as defects.However, since the structure has spatial extension of ∼1 nm and the concentrationmay be greater than ∼1 at.% in some cases (Kohara and Suzuya 2005), it seems tobe better to regard such small rings as strained normal bonds. As will be describedlater, the present classification is more useful to consideration of electronic struc-tures, since the relaxed and strained normal bonds govern, respectively, the band andband-edge electronic states. On the other hand, the defects tend to produce mid-gapstates.

In the following, we will see how the non-crystalline structure has been explored.In principle, the normal bonding structure has been investigated through structural

34 2 Structure

measurements using, e.g., x-ray diffraction and EXAFS (extended x-ray absorptionfine structures) (Elliott 1990). We note here that, in these x-ray experiments, recentprogress of synchrotron radiation sources can dramatically shorten the exposuretime (∼40 ps) and increase the spatial resolution (∼100 nm) of the inspected area(Tanaka et al. 2009). In addition to these and other direct structural studies, versa-tile and circumstantial observations are also valuable for sketching the structure.For instance, pressure dependence of optical gaps (Fig. 1.25) gives insight intothe amorphous structure, through comparing the result with those obtained for thecorresponding crystal. Also, computer simulations have become valuable tools asdescribed in Section 2.6.

2.3 Short-Range Structure

2.3.1 Experiments

Provided that a glass is homogeneous and has a simple composition, we can exper-imentally determine its short-range structure (Greaves and Sen 2007). Here, theshort-range structure is determined by three parameters: the coordination number Zof atoms, the bond length r, and the bond angle θ .

The short-range structure can be inferred from radial distribution function ρ(r),which can be calculated from x-ray (e-beam and neutron) diffraction patterns, anexample being shown in Fig. 2.8. Let us assume an elementary system such as a-Se;the diffracted intensity I at an x-ray wavenumber Q can be written as (Elliott 1990)

I(Q) ∝ f (Q)2∫

4πr2 [ρ(r)−ρ0] (sin Qr)/(Qr) dr with Q = 4π sin θs/λ, (2.1)

where f is the atomic scattering factor, ρ0 an average atomic density, 2θs the scat-tering angle, and λ the x-ray wavelength. Accordingly, from measured I(Q), we cancalculate ρ(r), which provides Z, r, and θ , respectively, from the first-peak intensity,

Fig. 2.8 Diffracted x-ray intensity I(Q) and calculated radial distribution function ρ(r) of a-Se(modified from Andonov (1982))

2.3 Short-Range Structure 35

Fig. 2.9 An illustration of a c-Se chain. The bond length is ∼0.24 nm, bond angle ∼103◦, anddihedral angle (the angle between the triangular planes defined by ABC and BCD atoms) ±102◦

the first-peak position r1, and the second-peak position r2 with r1 value. Note thatthis equation is useful also for crystals.

Debye equation gives a deduced form of the above equation for a pair of atomswhich are randomly oriented, as those in gas, liquid, and glass (Elliott 1990):

I(Q) ∝∑

ij

fifj sin(Qrij)/(Qrij), (2.2)

where rij is the distance between an atomic pair. We see that I(Q) of disorderedmaterials appears as a summation of sinc functions (sin x/x), which provide broadhalo patterns. Here, a straightforward analysis shows the following: Reflecting thefunctional shape, the halo at the smallest wavenumber gives the strongest peak atQ1, which satisfies Q1rij ≈ 7.7. This relation is useful for estimating the responsiblepair distance rij (Tanaka 1990).

However, for multi-component glasses, direct applications of the above proce-dures are difficult. We cannot determine the structure from only one diffractionpattern, since f changes with atom species. We may then utilize anomalous x-raydiffraction methods (Elliott 1990), in which f becomes also a function of x-ray wave-lengths. If a glass contains n kinds of atoms, diffraction patterns using n +1 x-raywavelengths can give n +1 simultaneous (coupled) equations:

I(Q, λ) ∝∑

ij

fi(Q, λ)fj(Q, λ)∫

4πr2[ρij(r) − ρ0] (sin Qr)/(Qr) dr, (2.3)

which can uniquely determine ρij(r) for ij pairs (i and j ≤ n). The isotope-substitutedneutron diffraction follows a similar principle (Petri et al. 2000), in which f changeswith isotopes. Provided that the atomic discrimination is successful, these methodsmay give longer-range atomic correlation (Hosokawa et al. 2009) than that given byEXAFS, the principle being described below.

EXAFS may give more direct information for the structure in multi-componentsystems (Elliott 1990, Armand et al. 1992, Vaccari et al. 2009). In EXAFS experi-ments, x-ray transmittance (or absorbance) of a sample of interest is measured as afunction of x-ray energy E (= 2πc�/λ). As illustrated in Fig. 2.10, the absorbanceabruptly changes at a core-electron excitation energy, e.g., at the K edge EK, and

36 2 Structure

Fig. 2.10 A schematic of EXAFS (left) and its emerging mechanism (right)

small intensity modulation “EXAFS” χi(E) appears just above this threshold energyat around E − EK ≤ 500 eV.

Why does such an oscillation appear? The oscillating EXAFS χi(k) can beregarded as an x-ray transmission spectrum which is modulated by the interfer-ence of x-ray excited electron waves with a wavenumber of k = 2π/λe =[2m(E − EK)]1/2/�, where λe is the electron wavelength (∼0.2 nm) and m is theelectron mass. In Fig. 2.10 (right), the electron wave spreading from the central atomand those being reflected back by surrounding (lower right) atoms interfere, whichmodulates x-ray transmittance through electron excitation efficiency.1 By scanningthe x-ray energy E, the interference varies, and accordingly, the x-ray transmis-sion spectrum has information of the surrounding atoms (atomic species, distance,number). Mathematically, at a slightly higher x-ray energy E than a core-electronexcitation energy EK of specified single atoms i, χi(k) contains a term as (Elliott1990)

χi(k) ∝∑

j

Zij exp(−2rij/L) sin{2 krij + ϕj(k)}, (2.4)

where Zij is the number of atoms (coordination number) at a distance of rij arounda specified i atom, L is the electron mean free path, and ϕj(k) is the phase changeoccurring when an excited electron is reflected at a neighboring atom j. If the phasechange can be known using a reference material as related crystals, we can deter-mine rij from oscillating EXAFS spectra. (In other words, when analyzing EXAFSoscillations, we implicitly assume the species of neighboring atoms.) The amplitudeof χi(k) is proportional to the coordination number Z of the specified atom, i.e., thenumber of atoms reflecting the electron waves, which can also be determined withlower accuracy depending upon the value of L and so on.

1Note that, in the optical Fabry–Perot-type interference, the sinusoidal fringe in transmission spec-tra is produced by modulation of multiply-reflected light. For the EXAFS, we may use a metaphor:imagine that we (x-ray photons) are walking in a swimming pool, producing water waves (elec-tron waves) and feeling reflected waves (electron waves) from pool sides (surrounding atoms). Ourwalk may be smooth or difficult, depending upon the interference by the waves.

2.3 Short-Range Structure 37

We underline three characteristics for the EXAFS. First, the EXAFS is usefulspecifically for multi-component systems. Since EK is fixed by an atom, we candetermine peripheral structures around the specified atom i. Second, as imaginedfrom the principle, Fig. 2.10 (right), it is more or less difficult to obtain a sec-ond nearest-neighbor peak in close-packed atomic structures from EXAFS spectra.Finally, as known from the principle, EXAFS experiments prefer x-ray beams hav-ing not characteristic peaks, but smooth and continuous spectra. Accordingly, theconventional x-ray tubes are less appropriate. Intense beams obtained as synchrotronorbital radiation are much effective to reduce exposure time and improve spatialresolution.

As an example, an EXAFS result around Ge in crystalline and glassy GeS2 isshown in Fig. 2.11 (Armand et al. 1992). We see in the right figure the strong firstpeak at ∼0.2 nm (Ge−S distance) and two weaker peaks at ∼0.26 and ∼0.31 nm, thelatter being identified to the two kinds of second-nearest Ge−S−Ge pairs (in edge-and corner-sharing tetrahedra) illustrated in the inset. The peak positions are verysimilar to those of the crystal, which evinces existence of the short-range structuralorder in this glass.

Direct images of amorphous structures can be obtained using two methods.Transmission electron microscopy is able to provide direct images and also diffrac-tion patterns. For instance, Young and Thege (1971) take electron diffractionpatterns of a-As2S3. However, the image for insulating materials such as sulfidesand oxides tends to become blurred due to charge-up. To the authors’ knowl-edge, no atomic images have been obtained for such insulating glasses. On theother hand, scanning tunneling and atomic force microscopy have been appliedfor obtaining surface images (Tominaga et al. 1992, Ichikawa 1995). However,we may have some doubts about reliability and/or reproducibility of the surface-sensitive images. Nevertheless, atomic images obtained for Se films (Peled et al.1995) and cleaved surfaces of oxide glasses (Poggemann et al. 2003) seem gen-uine. Specifically, Poggemann et al. (2003) take a histogram of obtained atomicimages for a few glasses, as exemplified for g-SiO2 in Fig. 2.12, which appears

Fig. 2.11 An EXAFS spectrum for Ge in c-GeS2 (left) and RDFs for Ge in c- and g-GeS2 (right).The inset in the right-hand side shows the distances corresponding to the three peaks (Armandet al. 1992, © Elsevier, reprinted with permission)

38 2 Structure

Fig. 2.12 An atomic force microscopy image of a vacuum-fractured surface of g-SiO2 (left) andthe distribution of atomic (white regions) distances (right) (Poggemann et al. 2003, © Elsevier,reprinted with permission), which is compared with an x-ray radial distribution function (RDF)reported by Kohara and Suzuki (2005)

to be consistent with the radial distribution function ρ(r) deduced from x-ray pat-terns (Kohara and Suzuya 2005). Further studies including comparisons of surfacestructures of a glass and the corresponding crystal will be very interesting.

In addition to these direct structural experiments, there are less direct ones. Thoseare vibrational spectroscopy (infrared transmission, Raman scattering, and inelasticneutron scattering), several spin-related methods, and photoelectron spectroscopy.

Infrared and Raman spectroscopy measure the intensity and frequency(wavenumber) of vibrational modes (Elliott 1990). As known, the frequency is writ-ten as ω ∼ (κ/M)1/2, where κ is the force constant of a spring connecting a pair ofatoms (or atomic units) and M is the atomic mass. Accordingly, the peak frequencygives insight into the vibrational mode, which is an optical phonon in crystals (Kittel2005) or a molecular vibration in disordered materials, e.g., vibrations of AsS3/2 ing-As2S3, as shown in Fig. 2.13. On the other hand, the spectral intensity I(ω, T) iswritten for disordered materials as (Shuker and Gammon 1970, Martin and Brenig1974)

I(ω, T) = g(ω) C(ω)[n(ω, T) + 1]/ω, (2.5)

where g(ω) is the density of vibrational modes, C(ω) the opto-vibrational couplingconstant, and n(ω, T) the Bose–Einstein (Planck) distribution. Here, it is known thatinfrared transmission and Raman scattering spectroscopy follow different selectionrules in the coupling constant. However, disordered structures tend to make theselection rules loose. In addition, Raman scattering spectroscopy becomes exper-imentally more useful, due to the recent progress of lasers and imaging detectorsat visible to near-infrared wavelengths. We can obtain not only the conventionalRaman scattering spectra (Yannopoulos and Andrikopoulos 2004) in short exposuretimes for small probe areas (�1 μm), but also resonant (Tanaka and Yamaguchi1998) and nonlinear (Klein et al. 1977) Raman scattering spectra. Therefore, Ramanscattering spectroscopy becomes more commonly employed.

2.3 Short-Range Structure 39

Fig. 2.13 Raman scatteringspectra of (a) glassy, (b)as-evaporated, and (c)crystalline As2S3.Responsible vibrationalmodes are shown for (a)

As an example, Fig. 2.13 shows Raman scattering spectra of glassy, as-evaporated, and crystalline As2S3. The broad and relatively sharp spectra of theglass and the as-evaporated film suggest that these are cross-linked and molecular,respectively (Lucovsky et al. 1975, Malyj and Griffiths 1987). On the other hand,the sharp peaks in the crystal correspond to optical phonons near the G point in theBrillouin zone (Kittel 2005).

Spin-related methods can probe peripheral structures around a spin throughits resonance frequency, peak width, etc. (Elliott 1990). Related studies forchalcogenide glasses include electron spin resonance (ESR) of Mn2+ in Mn-dopedAs–Se(Te) (Watanabe et al. 1976), nuclear magnetic resonance (NMR) of 31P inP–Se (Lathrop and Eckert 1993) and 77Se in selenide compounds (Bureau et al.2004, Gjersing et al. 2010, Kibalchenko et al. 2010), nuclear quadrupole resonance(NQR) of 75As in As–S(Se,Te) (Taylor et al. 2003), and Mössbauer spectroscopy of125Te in As–Te (Tenhover et al. 1983). These studies owe more or less the spe-cific samples and/or measuring instruments, and accordingly, fixed groups havepublished their results.

Finally, x-ray photoelectron spectroscopy (XPS) of core-electron states can probethe valence of constituent atoms through comparing with some references. It candiscriminate Ge4+ and Ge2+ in Ge–S glasses (Takebe et al. 2001) and peripheral cir-cumstances around Ge in a-Ge1Sb2Te4 films (Klein et al. 2008) and Ge–Se glasses(Golovchak et al 2009).

2.3.2 Observations

Direct and indirect experimental studies suggest that the short-range (≤0.5 nm)structure of a glass is similar to that in the corresponding crystal. An example forSe is summarized in Table 2.1. The coordination number Z seems to satisfy the

40 2 Structure

Table 2.1 Comparison of atomic parameters in c-Se (hexagonal) and g-Se (Andonov 1982)

Z r (nm) θ Φ ρ (g/cm3)

Hex Se 2.0 0.23 105◦ 102◦ 4.80g-Se 2.0 ± 0.04 0.23 ± 0.002 105±0.5◦ 70–110◦ 4.25

Z is the atomic coordination number, r the bond length, θ the bond angle, Φ the dihedral angle (seeFig. 2.9), ρ the density

Table 2.2 Bond lengths (in nm) and bond angles around the VIb atoms (in parentheses) in the VIbelemental materials (O, S, Se, and Te) and amorphous As2O(S,Se,Te)3 and GeO(S,Se,Te)2. Thebond angle in a-GeTe2 is unclear

O S Se Te

Elemental 0.12 in O2 0.21 (106◦) 0.23 (105◦) 0.29 (103◦)As- 0.18 (∼130◦) 0.23 (∼100◦) 0.24 (∼105◦) 0.27 (∼90◦)Ge- 0.18 (∼105◦) 0.22 (80–110◦) 0.24 (80–100◦) 0.26 (?)

so-called 8−N rule (Mott and Davis 1979), where N is the atomic group number inthe previous IUPAC form, with an accuracy of ∼10%, which may reflect experimen-tal uncertainty and effects of dangling bonds. The bond distance r is fixed with anaccuracy of �r/r ≈ 1%. The bond angle also shows a similar result in Se. However,for alloys (Table 2.2), it seems difficult to accurately determine the bond angle,which distributes roughly at �θ/θ ≈ 5 − 10%, where θ is the angle for a groupVIb atom such as the Si–O–Si angle. (Note that the angle is not uniquely fixedeven in the crystal, which contains different kinds of atomic units.) On the otherhand, experiments show that the cation angle, such as O–Si–O and S–As–S, is moretightly fixed due to steric restrictions. In short, we regard that there exists the short-range structural order in glasses. Note that the fluctuation ratios of r (∼1%) andθ (5–10%) imply comparable strain energies in bond distance and angle, kr(�r)2 ≈kθ (r�θ )2, since kθ /kr ≈ 1/10 in the force constants (Lucovsky et al. 1975).This result suggests that an energetic equilibrium is satisfied in the short-rangescale.

In more detail, there exist some variations in the short-range structures. First, thecoordination number, which is a direct consequence of the electron configurations2p4 of the group VIb atoms, is modified when ionic and metallic characters areadded. As described in Section 1.5, the metallic effect is appreciable in tellurides.Second, the bond length r increases in proportion to the period (2–5) in the periodictable, e.g., from 0.12 to 0.29 nm in the elements (Table 2.2), in accordance with theatomic size (Fig. 1.9). Third, and which should be underlined, we see that the bondangles are appreciably different between the oxide and the chalcogenide. As listed inTable 2.2, it is ∼130◦ in As2O3 and ∼100◦ in As2S(Se,Te)3, which may be approx-imated very roughly to 180◦ (ionic) and 90◦ (covalent). These characteristic angles

2.4 Medium-Range Structure 41

are favorable to produce the so-called corner-shared and edge-shared configurations(see Fig. 2.15), which will be connected to the medium-range structure.

Having seen the chemical bonding in elemental and stoichiometric binaryglasses, we turn to more complicated glasses, including non-stoichiometric binaryand ternary glasses. It was mentioned in Section 1.6 that the oxide can producethe mixtures, such as SiO2–Na2O, which consist of stoichiometric units, SiO2 andNa2O. Naturally, as shown in Fig. 1.13, the glass contains only Si–O bonds, whichare relatively covalent, and Na–O ionic bonds. The homopolar bond such as O−Omay be included in a defective level. In contrast, it is straightforward to preparenon-stoichiometric chalcogenide glasses, e.g., As(Ge)–S(Se,Te) in the limited glass-forming regions (see Fig. 1.17). As(Ge)-rich and As(Ge)-deficient glasses, whichdeviate from the stoichiometric compositions As2S(Se,Te)3 and GeS(Se)2, necessar-ily contain homopolar bonds, As(Ge)–As(Ge) and S(Se,Te)–S(Se,Te), respectively,in addition to the heteropolar bond As(Ge)–S(Se,Te). And, As15S85 glass is demon-strated to be a mixture of As–S networks and S molecules (Tsuchihashi andKawamoto 1971). Here, a principle on the atomic bonding seems to be the pref-erence of heteropolar bonds (As–S, As–Te, Ge–S, etc.), since these have strongerbond energies than those of the homopolar bonds (As–As, S–S, etc.) (see Table 2.4).

In non-stoichiometric ternary alloys such as As–S–Se, Ge–Sb–Te, and Ag(Cu)–As–S, we will face more critical problems. For instance, in Ge–As–S, which bondis preferred between Ge–S and As–S? Difference of the bond energies is sub-tle as listed in Table 2.4. We may also wonder if a Ge–As–S glass possesses anintermediate property between those in Ge–S and As–S glasses. Universal under-standings, which should take also the quasi-equilibriumness into account, have notbeen obtained.

As we have seen in this section, the short-range structure is determined by thechemical bonding, and accordingly, the existence of structural orders is plausible.Nevertheless, no further structural order could be envisaged, e.g., in the continuousrandom network model originally proposed by Zachariasen (1932). But, this viewhas been completely reformed as described below.

2.4 Medium-Range Structure

Historically, the first implication of a medium-range order in glasses is believedto have been presented by Vaipolin and Porai-Koshits (1963) for g-As2S(Se,Te)3.Successive studies have demonstrated the existence of some medium-range struc-tural orders with scales of 0.5–3 nm, at least, in simple glasses. However, the“some” order remains controversial, because there are no experimental tools explic-itly determining the atomic structure having such scales in disordered materials.This has become one of the biggest subjects covering structures and properties inglasses. In the following, we will see the present status of our understanding on themedium-range order from short to longer scales (Elliott 1991), not along a historicalsequence.

42 2 Structure

2.4.1 Small Medium-Range Structure

The short side length of ∼0.5 nm of the medium-range structure must be connectedto the short-range structure covering atomic structures up to the second nearestneighbors. We then envisage a position of the third nearest-neighbor atom, which isdetermined by the dihedral angle (see Fig. 2.9) in twofold coordinated structures, thesimplest example being Se. In the hexagonal-type c-Se, the atomic connection is alltrans, being explicitly determined. On the other hand, the radial distribution functionof a-Se gives no clear peaks corresponding to the third nearest neighbor (Fig. 2.8).This fact suggests that the dihedral angle is randomly distributed between trans andcis configurations (Andonov 1982), resulting in the so-called entangled chain struc-ture (Fig. 2.7c). However, it is more or less difficult to experimentally distinguishbetween a long curled chain and a ring molecule. In the tetrahedral connection as inSi, we can envisage staggered and eclipsed conformations, illustrated in Fig. 2.14.As known, c-Si consists of only the staggered connection, while radial distributionfunctions of a-Si(:H) do not show a clear third-nearest peak, which suggests mixedstructures with staggered, eclipsed, and intermediate configurations (Bodapati et al.2006). In short, in a-Se and a-Si(:H), no third nearest-neighbor correlations seem toexist. However, such results are not universal as we see below.

We next see the fourth nearest neighbor, which is involved in the corner- andedge-shared connections of atomic units, as illustrated in Fig. 2.15. Here, it is inter-esting to compare the chalcogenide glasses, As2S(Se)3 and GeS(Se)2, with the cor-responding oxide glasses, As2O3 and Si(Ge)O2. It has been demonstrated that, in thechalcogenide glass, the corner- and edge-shared units of AsS(Se)3/2 and GeS(Se)4/2exist, while the oxide glass contains only corner-shared connections (Kohara and

Fig. 2.14 Staggered andeclipsed conformations fortetrahedrally connectedSi atoms

Fig. 2.15 Edge- (left) and corner-shared (right) tetrahedra (GeS4/2) in GeS2. For As2S(Se,Te)3,envisage triangular pyramid structures without one S atom outside

2.4 Medium-Range Structure 43

Suzuya 2005). Pauling (1960) suggests that the corner- and edge-sharing can berelated with the ionic and covalent bonds with the ideal bonding angles of 180◦and 90◦. Note that these connections of the atomic units automatically fix thethird-neighbor distances.

Next to these scales, we may consider the ring statistics (Greaves and Sen2007). Here, the edge-shared connection contains a 2-membered (4-atom) ring,which tends to define rigid and flat segmental planes. On the other hand, disor-dered corner-shared structures are likely to produce three-dimensional continuousrandom networks, which cannot fix the ring size. In a-S(Se), entangled long chainsand ring molecules consisting of several atoms (Fig. 2.7) may co-exist. However, wedo not have any convincing experimental methods which can explicitly determinethe ring statics and the chain length. We can just envisage the structure with a com-bination of experimental results and computer simulations such as reverse MonteCarlo method, which is introduced in Section 2.6.

An exception, which has been partially resolved, is the ring statics in g-SiO2.Through comparisons between theoretical calculations and Raman scattering spec-tra in g-SiO2, Galeener’s group has identified the so-called D1 (495 cm−1) andD2 (606 cm−1) peaks, indicated in Fig. 2.16, to vibrational modes of 4- and3-membered rings, respectively (Barrio et al. 1993). These small rings are assumedto be fairly stable, and its density is estimated at ∼1 at.%. (To the authors’ knowl-edge, the small rings do not produce any peaks in optical absorption spectra.) Similarstudies have been done for B2O3 (Nicholas et al. 2004). Small rings are also pointedout for a-Si:H (Du and Zhang 2005).

We then wish to apply similar spectral analyses to other materials such asGeO(S,Se)2 and As2S(Se,Te)3. Actually, Kotsalas and Raptis (2001) have offereda plausible interpretation for the so-called A1 companion line, a small peak at∼374 cm−1 above the main peak of 342 cm–1, in g-GeS2. However, Raman scat-tering spectra in heavier atomic systems shift to lower wavenumbers, consequentlyresulting in substantial overlaps of characteristic peaks, and the spectra make thepeak identification difficult. More detailed analyses seem to be needed for obtainingconvincing insights.

Fig. 2.16 Raman scatteringspectra (HH and HV) ofg-SiO2 (Barrio et al. 1993,© American Physical Society,reprinted with permission)

44 2 Structure

2.4.2 First Sharp Diffraction Peak

We then come to the big problem concerning the first (lowest wavenumber) sharpdiffraction peak (FSDP). Vaipolin and Porai-Koshits (1963) discovered, as shown inFig. 2.17, using the Cu Kα x-ray line that g-As2S(Se)3 present relatively sharp halopeaks, referred to as the FSDPs, at θ ≈ 14◦ (QFSDP = 4π sin θ/λ ≈ 10 nm−1 =1 A−1) with a peak width �θ of ∼5◦. In As2Te3, the peak merges into a shoul-der. Provided that the Bragg equation is applicable to the peak position, we obtaina structural period of ∼0.6 nm. They also noticed that the FSDP position is similarto that of a Bragg peak appearing in As2S(Se)3 layer crystals (Fig. 1.16). In addi-tion, the Scherrer equation D � λ/(�θ cos θ ), being derived for polycrystallinematerials, suggests a correlated domain size D of 2−3 nm. Taking these results intoaccount, they have proposed the so-called distorted layer model for the glasses, i.e.,deformed covalent layers with somewhat correlated interlayer distances of ∼0.6 nm(see Fig. 2.7b). The layer may be a “raft,” in which the edge is terminated bychalcogen dimers, in a structural model proposed by Phillips (1979). Note thatthese models are different from polycrystalline structures, in which the domainsare crystallites.

At first glance, the existence of such large correlated regions of 2−3 nm in theglass appeared anomalous. We may assume that the application of the Scherrer equa-tion is problematic. On the other hand, a variety of experiments have been done forthe FSDP. The experiments cover many kinds of chalcogenide glasses with differentpreparations and under varied temperatures and pressures (Busse 1984, Cervinka1988, Elliott 1991). Through these studies, we tried to grasp atomic structures

Fig. 2.17 Comparisons ofhalo patterns and crystallinepeaks in (a) As2S3,(b) As2Se3, and (c) As2Te3,shown from the top to thebottom (modified fromVaipolin and Porai-Koshits(1963))

2.4 Medium-Range Structure 45

giving rise to the FSDP. However, in short, the results have given an impetus ofcontinuing controversy. We also underline that, before ∼1985, the FSDP had beenassumed to be located at QFSDP ≈ 10 nm−1, and that the peak was inherent to thechalcogenide glasses such as As2S3 and GeSe2. No one might assume that the oxideglass possesses a FSDP, since its first peak is located at Q ≈ 16 nm−1.

However, Wright et al. (1985) have presented a different definition. They noticed,as shown in Fig. 2.18, that the FSDP in the chalcogenide glasses satisfies a condi-tion of QFSDPr ≈ 2 − 3, where r is the nearest-neighbor distance, and this criterionmeets also the first, but not so sharp, diffraction peak in g-SiO2. The FSDP was re-defined as “QFSDPr ≈ 2 − 3,” and this definition has been applied to many oxide,halide, chalcogenide, and elemental glasses (Moss and Price 1985). Then, severalresearchers have tried to obtain unified understandings of this seemingly more uni-versal criterion, QFSDPr ≈ 2−3. We should, however, note that the half-width of thepeak in Si(Ge)O2 suggests a correlation distance of 1−2 nm (Greaves and Sen 2007,Lucovsky and Phillips 2009), substantially shorter than that in the chalcogenides.

Since then, considerable studies have been performed for the FSDP in oxideglasses, specifically Si(Ge)O2 (Kohara and Suzuya 2005, Greaves and Sen 2007).It has been amply demonstrated that g-Si(Ge)O2 has continuous random networkstructures, and some researchers make efforts in answering the question “Whydoes the continuous random network exhibit such a peak?” Studies on complicatedoxide glasses have also been performed. Gaskell et al. (1991) demonstrate a cationdistribution order persisting over ∼1 nm in CaO–SiO2 glass. Other materials such as

Fig. 2.18 Comparison ofx-ray structure curves S of(a) SiO2 and (b) GeSe2 inhorizontal scales of Q (lower)and Qr (upper) (modifiedfrom Wright et al. 1985)

46 2 Structure

glassy ZnCl2 (Salmon et al. 2005), a-As (Tanaka 1988), and a-P (Zaug et al. 2008)also present the FSDPs.

In short, there seems to be a consensus that some kinds of medium-range orderswith scales of 1–3 nm exist in simple glasses, while the real atomic structureis controversial. For the group VIb stoichiometric glasses such as Si(Ge)O2 andAs2S(Se)3, there are roughly two ideas. One insists, taking QFSDPr ≈ 2 − 3seriously, that the oxide and the chalcogenide possess qualitatively the samemedium-range order, in which three-dimensional network structures have been pre-sumed as a starting concept (Zaug et al. 2008, Massobrio and Pasquarello 2008,Lucovsky and Phillips 2009), the model hereafter referred to as a three-dimensionalview. The others, including Zallen (1983), Cervinka (1988), and Bradaczek andPopescu (2000), assume that the oxide has three-dimensional and the chalcogenidehas two-dimensional structures, the idea being consistent with the original view byVaipolin and Porai-Koshit (1963). The present authors believe that this dimensionalview is more intuitive and instructive, at least with the following three reasons.

First, the dimensional view is consistent with interpretations made for zero-dimensional (point-like) and one-dimensional molecular materials. Examples of thezero-dimensional materials are molecular CCl4 liquids (Salmon et al. 2005) andas-evaporated As2S3 films (consisting of molecules such as As4S4) (DeNeufvilleet al. 1973, Wright et al. 1985), and those of one-dimensional molecules are organicpolymers such as polyethylene (Fischer and Dettenmaier 1978) and polysilane(Tanaka and Nitta 1989). These zero- and one-dimensional molecules exhibit clearFSDPs, as exemplified in Fig. 2.19, which are ascribed without any ambiguity tointermolecular correlation of van der Waals-type bonding. The fact that a-Se con-sisting of Se chains does not show a clear FSDP, but a shoulder, is ascribed to theshort inter-chain distance (∼0.4 nm), which is similar to the second-nearest intra-chain distance of ∼0.37 nm (Andonov 1982). Extrapolating these insights, we canassume that the two-dimensional (layer) structure gives the FSDP, which reflectsthe van der Waals-type correlation, in the chalcogenide glass. The peak in three-dimensional glasses should be ascribed to different origins. Also consistent with

Fig. 2.19 Scattering curvesof two one-dimensionalorganic materials, C12H26 at25◦C (dashed line) andpolyethylene at 160◦C (solidline) consisting of chainmolecules (Fischer andDettenmaier 1978, ©Elsevier, reprinted withpermission)

2.4 Medium-Range Structure 47

the different origins of the first peaks are the appreciably different correlation dis-tances, ∼2 and ∼1 nm, estimated from the FSDP widths in chalcogenide and oxide(Greaves and Sen 2007, Lucovsky and Phillips 2009).

Second, the dimensional view is consistent with the material variation in the VIbglasses. We saw in Fig. 1.12b that the density in As2O(S,Se,Te)3 and GeO(S,Se)2does not monotonically change, showing clear minima at the sulfides. The densityminimum at the sulfides can be understood by taking the dimensional view intoaccount, including longer van der Waals distances (∼0.5 nm) than the covalent bond(0.2–0.3 nm), as described in Section 4.10.

The third reason is posed from pressure dependence. Upon hydrostatic com-pression, the position of FSDPs in polyethylene (Yamamoto et al. 1977) andchalcogenide glasses (Tanaka 1998) dramatically shifts to lower diffraction angles,while that in Si(Ge)O2 is more or less intact (Guthrie et al. 2004). In addition, asillustrated in Fig. 2.20, it should be noted that pressure behaviors of the FSDP ing-GeS2 and the interlayer distance in layer-type c-GeS2 are similar (Tanaka 1986).We may imagine compression of crumpled (glass) and stacked (crystal) papers(covalent layers) here, in which the paper separations give the diffraction peaks.It should also be mentioned that pressure dependence of optical absorption edges(Fig. 1.25) is consistent with the dimensional view (Zallen 1983).

In short, the authors’ standpoint can be summarized as follows: What is impor-tant in disordered materials science is an intuitive description of seemingly vagueobservations in terms of “simple pictures.” The picture should be useful also forunderstanding macroscopic properties of many kinds as possible. In this con-text, the dimensional view seems to be more instructive. Controversy betweenthe dimensional and the three-dimensional view may arise from the terminologyor the definition of FSDP: Q ≈ 10 nm−1 and QFSDPr ≈ 2 − 3. The univer-sality QFSDPr ≈ 2 − 3 may be coincidental, which arises from the fact thatthe van der Waals distance is approximately equal to twice the covalent bond

Fig. 2.20 Comparison ofatomic distances d in g-GeS2glass (•) and the layer-typec-GeS2 (◦) under hydrostaticcompression. The distance dis calculated for the glassfrom the FSDP position andfor the crystal from theinterlayer x-ray peak.Fractional change �l/l inmacroscopic linearcompressibility for the glassis also shown by a dotted linewith an error bar (Tanaka1986, © Elsevier, reprintedwith permission)

48 2 Structure

distance. Note that the two models are in agreement for g-SiO2 and also a-Si:H,the structure being grasped unambiguously as three-dimensional continuous randomnetworks.

2.4.3 Boson Peak

Probably related with the FSDP is the so-called Boson peak in Raman scatteringspectra, a broad peak appearing at 20–50 cm−1 (0.6–1.5 THz, ∼5 meV), which islower than the conventional vibrational modes by an order. Krishnan (1953) mayhave been the first who noticed this anomalous low-frequency peak in a glass, SiO2.(Note that such a low-frequency broad peak has never appeared in c-SiO2 and sim-ilar crystals, since the optical phonon is located at higher frequencies.) For the peakin chalcogenide glasses, Nemanich (1977) performed a comprehensive study, whogave the name of “Boson peak,” the reason being that the spectral shape at low-frequency limits appears to be governed by the Bose factor, {n(ω, T)+1}/ω � ω−2.Since then, many studies have been published for the peak in oxide and chalcogenideglasses (Greaves and Sen 2007) and even in proteins (Ciliberti et al. 2006). Becauseof this universal feature being inherent to disordered materials, a variety of charac-teristics have been investigated. For instance, in g-As2S3, the peak becomes smallerunder hydrostatic compression (Fig. 2.21; Andrikopoulos et al. 2006) and is inten-sified by temperature rise (Yasuoka et al. 1986). The peak position depends uponpreparation conditions of the glass ingot, such as quenching rate of the melt (Tanaka1987). We also add that far-infrared absorption spectroscopy detects a similar peak(Ohsaka and Ihara 1994).

Several models have been proposed for the origin of the Boson peak. The vibra-tional wavenumber k is given as k = (1/s)(κ/M)1/2, where s is the sound velocity,

Fig. 2.21 Raman scatteringspectra of As2S3 as a functionof hydrostatic compression(Andrikopoulos et al. 2006,© Elsevier, reprinted withpermission)

2.4 Medium-Range Structure 49

κ a force constant, and M a reduced mass. Accordingly, we can ascribe the lowwavenumber of Boson peaks to some vibrations of nearly-free atomic units hav-ing small κ , which may be related with van der Waals forces. Phillips (1981)followed this view, proposing that the Boson peak is a kind of rigid-layer modes,which are vibrations of crystalline layers held together by van der Waals forces.Or, the low wavenumber may be due to atomic clusters having large masses, whichmay be related with medium-range structures. Martin and Brenig (1974), assuminginhomogeneous cluster structures with the Gaussian-type correlation function char-acterized by a spatial scale σ , derived a peak shape for an acoustic Raman scatteringmode in disordered materials as

I(k) ∼ (σ 3k3/s5){n(k) + 1} exp (−k2σ 2/s2), (2.6)

where n(k) is the Bose factor. This equation gives the position of Boson peaksat max ∼ s/σ . Nemanich (1977) followed this idea, obtaining σ ≈ 0.7 nm inAs2S(Se)3, which is substantially smaller than the correlated scale of 2−3 nminferred from the FSDP.

Researches on the Boson peak appear to follow labyrinths as those of the FSDP.Malinovsky and Sokolov (1986) demonstrated, as shown in Fig. 2.22, that theshapes of Boson peaks of many glasses are the same if the spectrum is normal-ized with the peak frequency max, or the corresponding energy Emax. Novikov andSokolov (1991) found a proportionality between the normalized FSDP position andthe Boson peak wavenumber, QFSDPr ∝ maxc/s, where c is the velocity of light.Afterward, the problem was extended to universal understandings of the FSDP andthe Boson peak. Later, such studies have been further extended to understanding

Fig. 2.22 Boson peaks inseveral glasses, normalizedby the peak energy Emax.(1) As2S3 withEmax = 26 cm−1,(2) Bi4Si3O12 with 34 cm–1,(3) SiO2 with 52 cm–1,(4) B2O3 with 28 cm–1,(5) B2O3–Li2O with 88 cm–1,and (6) GeS2 with 22 cm–1

(Malinovsky and Sokolov1986, © Elsevier, reprintedwith permission)

50 2 Structure

correlations between the Boson peak, the FSDP, and thermal properties includingthe known low-temperature anomalies (Section 3.4) and glass transition parameters(Sokolov et al. 1993). The final elucidation remains (Grigera et al. 2003, Taraskinet al. 2006, Ruocco 2008, Baldi et al. 2010).

2.5 Defect

Defect structures are also controversial. At the outset, we may recall what the defectis in disordered structures (see Section 2.2). In crystals, it is traditional to assumean ideal structure, and some deviations from that can be regarded as the defects,which are classified into point defects (color center in NaCl, etc.), line defects (dis-location, etc.), stacking faults, grain boundaries, etc. (Kittel 2005). However, sincewe cannot envisage the ideal amorphous structure, the definition of defects becomesnecessarily vague. On the other hand, it is reasonable to assume that only point-likedefects can exist in glasses, since the other defects require some long-range atomiccorrelations, which must be lacking in non-crystals.

We define the defect in a non-crystalline solid as a connected or disconnectedatomic bond, or a point defect-like structure, which cannot exist in the correspond-ing ideal crystal. This definition implicitly assumes that the defect arises in theshort-range scale. Naturally, if the corresponding crystal does not exist, e.g., non-stoichiometric glasses such as Ge-doped g-SiO2, this definition is meaningless.Otherwise, since the defect is a deviated structure from the normal bonding net-work, the defective site should be rare, e.g., being smaller than ∼1% of the totalbonds. A dangling bond and an ill-coordinated bond are typical defects. Note thatthe density of ∼1% can be neglected in structural properties such as the elasticconstant and heat capacity at room temperature, while the defect may provide sub-stantial effects upon electronic properties if it produces a mid-gap state, which ismore or less common.

Is it possible to detect such a few point-like defects in disordered structures?X-ray measurements, including diffraction and EXAFS, seem to be insufficient insensitivity (�5 at.%), so that we usually employ two methods. One is the Ramanscattering spectroscopy, while its sensitivity seems to be, at the best, ∼1 at.%. Theother is the electron spin resonance (ESR), which seems to have a sensitivity of ppm(Griscom 2000). However, the method can detect only unpaired electrons, such asE′ centers in silica glasses and D0 defects in chalcogenide glasses. In addition tothese methods, there are some non-direct methods. An example is the comparisonof experimental optical spectra with some calculations, which may predict that adefect produces mid-gap absorption and/or photoluminescence peaks. Such opticalinvestigations are more useful in the oxide than in the chalcogenide, since the for-mer has a wider optical gap and the defect peak is likely to appear in the visiblewavelength region, which can easily be detected. In the following, we will examineSi(Ge)O2 and As2S3 (and Se) as examples of the oxide and the chalcogenide glass(Table 2.3). Ge-chalcogenides such as g-GeS(Se)2 are likely to possess intermediateproperties between these materials.

2.5 Defect 51

Table 2.3 Defects in SiO2 and As2S3 glasses

Relatedatoms

Normalbonding D0 Wrong bond Coordinational Molecular

Si ≡Si– ≡Si• (E′) ≡Si–Si≡(ODC)

−Si− (ODC)

O –O– –O• (NBOHC),–O–O• (POR)

–O–O– (POL) O2, O3

As =As– =As• under exc.∗ =As–As= =As (P2)S –S– (C2) -S• under exc.∗ –S–S– =S– (C3)

A covalent and a dangling bond are represented by – and •, respectively. NBOHC stands for non-bridging oxygen hole center, ODC for oxygen-deficient center, POR for per-oxy radical, and POLfor per-oxy linkage. P and C stand for pnictogen and chalcogen, respectively. In As2S3, ESR signalin the dark is below a detection limit (∼1015 cm–3), appearing only under light excitation (∗) atlow temperatures

Defects in g-Si(Ge)O2 can be divided into Si(Ge) related and O related(Pacchioni et al. 2000). The most famous Si(Ge)-related defect is a kind of dan-gling bond, E′ center (≡Si•), which is ESR active, and accordingly, it can be easilydetected. On the other hand, ESR-inactive defects are twofold coordinated Si (–Si–)and Si homopolar bond (≡Si–Si≡); the latter can be regarded as a kind of oxygen-deficient center (ODC). Existence of these defects is suggested from optical studies.The O-related defect includes non-bridging oxygen hole center (NBOHC; oxygendangling bond, –O•) and per-oxy radical (POR; –O–O•), which are ESR active,and per-oxy linkage (POL; oxygen wrong bond, –O–O–), which is ESR inactive.In addition, oxygen molecules, O2 and O3, seem to be produced by radiation. It isplausible that the density of these defects, typically ∼ 1018 cm−3, depends uponsamples.

For the chalcogenide glass, many kinds of defects have been proposed(Ovshinsky and Adler 1978), while experimentally confirmed ones are a few. Sincethe chalcogenide glass is covalent, it is straightforward to envisage the wrong bonds(Halpern 1976) or like-atom (homopolar) bonds in stoichiometric compositions. Thewrong bond is neutral in charge in covalent materials, and because of this charac-ter the defect becomes appreciable in density. Actually, the wrong bonds, As−Asand S−S (Fig. 2.23), in g-As2S3 with concentrations of ∼1% are inferred fromchemical analyses (Kosek et al. 1983) and Raman scattering studies (Tanaka 1987).In addition, Vanderbilt and Joannopoulos (1981) suggest the wrong-bond densityof ∼0.5% in g-As2Se3 using a canonical factor, exp(−�E/kTg), where �E is theenergy difference between hetero and homopolar bonds. In such calculations, how-ever, we should be careful about the selection of bond energies, which depend uponthe sources, as listed in Table 2.4. For g-GeSe2, Zhou et al. (1991) did not detectany wrong bonds using EXAFS, while Petri et al. (2000) have found substantialnumbers (∼4%) of wrong bonds using isotope-substituted neutron diffraction. The

52 2 Structure

S

SS

S

S

As

As

As

As

As

Fig. 2.23 Wrong bonds,As−As and S−S, in g-As2S3.The gray lobes attached to Sdepict lone-pair electrons

Table 2.4 Bond energies of interest in units of kcal/mol, selected for As–S (Pauling 1960,Tsuchihashi and Kawamoto 1971, Popescu 2001) and Ge–S (Kawamoto and Tsuchihashi 1971,Popescu 2001) glasses

As–S As–As S–S Ge–Ge Ge–S

PaulingTsuchihashi–KawamotoPopescu

476162

323248

513367

3844

566863

The values selected by Pauling may be obtained from related gases with different atomic coordi-nation from that in the glasses, and accordingly, the value seems to provide unreasonable estimatesin the present purpose

difference may be attributed to different sample preparations and/or experimentalmethods.

The dangling bond is a known defect. However, in the chalcogenide glass,the common dangling bond having an unpaired electron, D0 in Mott’s notation,appears only in Ge–S(Se) (Arai and Namikawa 1973, Elliott 1990). Pure Se andAs-chalcogenides present no ESR signals (<1016 cm−3) in the dark, which meansthat there are no neutral dangling bonds having unpaired electrons. In these mate-rials, the ESR signal appears only under illumination at low temperatures (seeSection 6.3.10). Mott and many researchers have related the appearance of D0 underillumination to the presence of charged dangling bonds (D+ and D−) in the dark, theidea being discussed in Section 4.4.

Note that here we neglect impurities, such as O in a-Se and Fe in g-As2S3(Churbanov and Plotrichenko 2004), and intentionally doped atoms such as H, F,and Cl in g-SiO2 (Pacchioni et al. 2000). Due to the disordered structure, however,it is common that a glass contains comparatively larger amounts of impurities thanthose in the corresponding crystal. Actually, a difficulty of studying g-SiO2 is that,in addition to small deviations from the 1:2 stoichiometric ratio, the glass is likely

2.6 Computer Simulations 53

to contain impurities such as Al and OH (Doremus 1994). Accordingly, the charac-terization of impurities is a prerequisite for studies of defect-related properties, e.g.,mid-gap optical absorption and photoluminescence. For such impurity evaluations,we may utilize spectroscopic methods such as x-ray fluorescence, plasma emission,and infrared absorption, which possess detection sensitivities of ppm–ppb.

2.6 Computer Simulations

Since the non-crystalline structure cannot be determined explicitly, structural mod-eling has played an important role. In early studies, the modeling employed physical“balls-and-sticks,” a known example being the so-called Polk model for a-Si(Turnbull and Polk 1972). Such approaches may still be valuable for obtainingintuitive ideas, since the model can be deformed by hand (Tanaka 1998).

Gradually, computer simulations have become indispensable. A lot of studieshave employed classical molecular dynamics (MD) calculations and other methods,which rely upon Newton’s equation and empirical potentials. For instance, Brabec(1991) and Antonio et al. (1992) have simulated, respectively, bonding structures ofAs2S3 and SiSe2 glasses having 1790 and 5184 atoms.

At present, most studies perform the so-called ab initio MD calculation. It isbased upon Schrödinger’s equation taking all relevant wavefunctions into account.However, the calculation is limited to a system having 200−300 atoms contained innanometer-sized cubes, which may be imposed on the periodic boundary condition(Greaves and Sen 2007, Drabold and Estreichen 2007). The simulation follows the“cook-and-quench” type, in which a liquid having a fixed atomic composition is firstequilibrated, e.g., at 1000 K, followed by a thermal quench to 300 K. We expect thatthese ab initio calculations can reproduce not only the atomic structure but also avariety of macroscopic properties (Fig. 2.24).

However, at present, the ab initio calculation seems to be valuable but withlimited scope. It can reproduce experimental radial distribution functions and vibra-tional spectra, which characterize the short-range structure. However, the numberof atoms 200–300, which corresponds to a cubic side number of ∼5 atoms, is stillinsufficient for obtaining insights into the medium-range structure. In addition, the

Atomic

structures

Macroscopic

properties

SIMULATION

Fig. 2.24 A goal of computersimulations, from which wemay extract unified concepts

54 2 Structure

biggest problem may be liquid quenching. In all MD simulations for glasses, thequenching rate from a melt is enormously fast, e.g., 1011−1014 K/s, which is gov-erned by needed computational times, and as a result, a simulated glass is likely tocontain too many defects. Therefore, MD calculations may predict what kinds ofdefects can exist in the amorphous material, but it is nearly impossible to estimatethe defect density in real samples.

There are other computational methods. Specifically, the reverse Monte Carlomethod is frequently utilized in analyses of experimentally obtained structural data(Kohara and Suzuya 2005, Greaves and Sen 2007, Itoh and Fukunaga 2009, Cliffeet al. 2010). In this method, we first distribute finite numbers (≤5000) of atoms in acube having a volume, which gives an appropriate atomic density, and then move theatoms randomly until the resultant structure agrees satisfactorily with experimentaldata in wavenumber and/or real spaces. Otherwise, novel calculation methods as astatistical computation method, which is not limited by the time scale, may be morepromising, while the system is limited to, e.g., 64 Se atoms (Mauro and Loucks2007).

2.7 Homogeneity

Up to now, we have implicitly assumed that the amorphous structure is continuousand homogeneous. Is this assumption justified? It should be kept in mind that almostall of the structural measurements described above, except real space measurementssuch as transmission electron microscopy and atomic force microscopy, presumestructural homogeneity. Unfortunately, the present x-ray methods, Raman scatter-ing spectroscopy, etc., cannot have spatial resolution better than ∼100 nm. Thesemethods present structural information averaged over the probed area. However,the structural inhomogeneity is likely to arise, at least, from two origins: densityfluctuations and chemical factors.

Glass necessarily contains density fluctuations. This is because the glass isquenched from the corresponding melt, which undergoes time-varying density fluc-tuations. The fluctuating amplitude �ρ/ρ of a few percent is theoretically derived(see Section 7.2). Experimentally, the amplitude and spatial scale (∼2 nm in silica)can be probed using small-angle x-ray and light scatterings (Greaves and Sen 2007).The density fluctuation is a critical problem in preparations of optical fibers and soforth. In addition, recent studies suggest that, during aging processes at temperaturesbelow the glass transition temperature, so-called dynamic heterogeneity appears,which may lead to crystalline nucleation (Yunker et al. 2009).

Apart from the density fluctuation, the reported microscopic views are notconclusive. Structural homogeneity in atomic bonding can be conjectured in theelemental a-Se (Andonov 1982), having entangled chain and ring structures. Simplestoichiometric glasses such as As2S3 provide no small-angle x-ray scattering sig-nals (Bishop and Shevchik 1974), suggesting certain homogeneity. Hosokawaet al. (2008) draw a similar conclusion for As2S3 from inelastic x-ray scattering.

2.7 Homogeneity 55

However, a more sensitive method, positron lifetime spectroscopy, detects micro-voids of ∼0.5 nm in diameter with a volume fraction of 10−5–10−2% in g-As2Se3(Jensen et al. 1994). As references, we note that a-Si:H and similar films presentmarked signals indicating the existence of small voids (Muramatsu et al. 1989).

However, the glass structure critically depends upon preparation procedures andstorage conditions, which are likely to govern homo and heterogeneity. Actually,Ležal et al. (1993) demonstrate that light scattering characteristics in g-As2S3depend upon the quenching rate of melts. Boolchand et al. (2001) assert thatGeS(Se)2 is phase-separated in nano-scales through self-organization (Chen et al.2008). Non-stoichiometric glasses such as As(Ge)-S(Se) tend to phase-separate(Tichý et al. 1984, Bychkov et al. 2006). More complicated glasses may be inhomo-geneous, the examples being Ag-chalcogenide glasses (Mitkova et al. 1999) andmodifier-mixed oxide glasses such as Na2O(PbO)–SiO2 illustrated in Fig. 2.25,which is in contrast to a homogeneous structure, Fig. 1.13. Spinodal decompositionin multi-component oxide glasses has been well known (Doremus 1994). An oxy-chalcogenide glass GeO2–GeS2 appears to be heterogeneous in electron microscopyimages (Terakado and Tanaka 2008). Finally, it should be mentioned that partially

Fig. 2.25 A schematicillustration of an oxide glassconsisting of phase-separatednetwork former (gray) andmodifier (white) regions(Greaves 1985, © Elsevier,reprinted with permission)

Fig. 2.26 Ascanning-electronmicroscopy image of anobliquely deposited1 μm-thick As2S3 film(Starbov et al. 1992,© Elsevier, reprinted withpermission)

56 2 Structure

controlled inhomogeneity, a kind of nano-structures, can be produced by obliqueevaporation, the examples being given for Se (Krišciunas et al. 1983) and As2S3 inFig. 2.26 (Starbov et al. 1992).

2.8 Surface and Nano-structures

The surface gives a special problem in solid-state science. Particularly, in crys-tals, atomic periodicity is broken at the surface, and accordingly, surface atomsnecessarily produce unique surface structures. In c-Si, the ideal surface must havemany dangling bonds, while practical surfaces have undergone surface reconstruc-tion or oxidation. In contrast, it is likely that, in amorphous materials, the surfacehas smaller roles than those in single crystals, since the interior atomic structure isalready disordered.

Despite such speculations, some surface effects have been reported for amor-phous materials. Isobe et al. (1986) and Mamontova et al. (1988) demonstrate thatsurface structures affect photoconductive and electrical properties in (As-)Se. Inamand Drabold (2008) theoretically predict that oxidation changes surface conductanceof Ge2Sb2Te5 films. In silica glass, it is well known that the surface is terminatedby Si–OH groups (Doremus 1994).

Recently, nano-structured materials have attracted substantial interest, asreviewed for chalcogenide by Tanaka (2004). Among the many topics, focus hasbeen placed on surface manipulation. Here, we should note a characteristic differ-ence of the surface manipulation in crystalline and non-crystalline solids. As known,using scanning tunneling microscopes, Eigler and Schweizer (1990) have manip-ulated single atoms on atomically flat surfaces of single crystals. However, suchatomic manipulation seems to be difficult in amorphous materials, due to the exis-tence of medium-range (2−3 nm) orders. In non-crystalline solids, the smalleststructural unit which can be artificially manipulated may be attained not at theatomic scale, but at the nano-scale.

The multi-layer system has been the most extensively studied nano-structurefrom a fundamental and technological point of view. And, notable studies have beenreported for amorphous chalcogenide semiconductors. Nesheva et al. (2005) havecomprehensively studied variations of the glass transition temperature, the opticalgap, etc., as functions of layer thicknesses for GeS2/CdSe multi-layers. However, assummarized in Fig. 2.27 (Tanaka 2004), thickness dependences of reported studiesare not reproducible.

In addition, we should be careful in interpretations. With a decrease in layerthickness, a blue shift of optical absorption edges (or optical gap Eg) tends to appear,which is often interpreted as a quantum-well effect. However, the effect can appearonly when the mean free path of electrons and/or holes is longer than the layerthickness (Kittel 2005). Nevertheless, the mean free path of electrons, e.g., in a-Si:H films is reported to be ∼1 nm (Okamoto et al. 1991), and accordingly, thequantum-well interpretation may be misleading. The blue shift possibly appears as a

References 57

Fig. 2.27 Dependence ofthermal and optical propertieson the thicknesses of films(solid symbols) andmulti-layer periods (opensymbols) (modified fromTanaka 2004). (a) Thecrystallization temperature Tc(dashed lines) of Se and GeTeand the glass transitiontemperature Tg (solid lines)of Se and As2S3 are shown.(b) The optical gap Eg of Se,As2S3, and As2Se3 is shown

result of vague layer boundaries, which are likely to govern macroscopic propertiesin thinner layer structures, since material diffusion becomes more evident in suchsystems (Adarsh et al. 2005).

Finally, it may be valuable to refer to some related studies. Regarding techno-logical developments, we note a pioneering study by Maruyama (1982) on multi-layered chalcogenide films for vidicon targets. Chong et al. (2008) have studiedcrystalline–amorphous multi-layers using GeTe/Sb2Te3 stacks. We also mentionthat substantial studies have been done for ultrathin films (Tanaka 2004, Raoux et al.2008) and chalcogen-impregnated zeolites (Poborchii et al. 2002, Tanaka and Saitoh2009), which provide nano-dot and/or single-chain structures.

References

Adarsh, K.V., Sangunni, K.S., Kokenyesi, S., Ivan, I., Shipljak, M.: Enhancement ofphotoluminescence intensity by photoinduced interdiffusion in nanolayered a-Se/As2S3 films.J. Appl. Phys. 97, 044314 (2005)

Andonov, P.: Studies of non-crystalline forms of selenium. J. Non-Cryst. Solids 47, 297–339(1982)

Andrikopoulos, K.S., Christofilos, D., Kourouklis, G.A., Yannopoulos, S.N.: Pressure dependenceof the Boson peak in glassy As2S3 studied by Raman scattering. J. Non-Cryst. Solids 352,4594–4600 (2006)

58 2 Structure

Antonio, G.A., Kalia, R.K., Nakano, A., Vashishta, P.: Crystalline fragments in glasses. Phys. Rev.B 45, 7455–7458 (1992)

Arai, K., Namikawa, H.: ESR in Ge-S glasses. Solid State Commun. 13, 1167–1170 (1973)Armand, P., Ibanez, A., Dexpert, H., Philippot, E.: Short and medium range order in germanium

sulfide glasses: A low temperature X-ray absorption spectroscopy study. J. Non-Cryst. Solids139, 137–145 (1992)

Baldi, G. V., Giordano, M., Monaco, G., Ruta, B.: Sound attenuation at terahertz frequencies andthe boson peak of vitreous silica. Phys. Rev. Lett. 104, 195501 (2010)

Barrio, R.A., Galeener, F.L., Martínez, E., Elliott, R.J.: Regular ring dynamics in AX2 tetrahedralglasses. Phys. Rev. B 48, 15672 (1993)

Bishop, S.G., Shevchik, N.J.: Small angle x-ray scattering evidence for the absence of voids inchalcogenide glasses. Solid State Commun. 15, 629–633 (1974)

Bodapati, A., Treacy, M.M.J., Falk, M., Kieffer, J., Keblinski, P.: Medium range order and theradial distribution function. J. Non-Cryst. Solids 352, 116–122 (2006)

Boolchand, P., Georgiev, D.G., Goodman, B.: Discovery of the intermediate phase in chalcogenideglasses. J. Optoelectron. Adv. Mater. 3, 703–720 (2001)

Brabec, C.J.: Structural model of amorphous arsenic sulfide. Phys. Rev. B 44, 13332–13342 (1991)Bradaczek, H., Popescu, M.: Microparacrystalline model for medium range order in covalent

glasses. J. Optoelectron. Adv. Mater. 2, 153–158 (2000)Bureau, B., Zhang, X.H., Smektala, F., Adam, J.-L., Troles, J., Ma, H., Boussard-Pledel, C., Lucas,

J., Lucas, P., Coq, D.L., Riley, M.R., Simmons, J.H.: Recent advances in chalcogenide glasses.J. Non-Cryst. Solids 345–346, 276–283 (2004)

Busse, L.E.: Temperature dependence of the structures of As2Se3 and AsxS1-x glasses near theglass transition. Phys. Rev. B 29, 3639–3651 (1984)

Bychkov, E., Miloshova, M., Price, D.L., Benmore, C.J., Lorriaux, A.: Short, intermediate andmesoscopic range order in sulphur-rich binary glasses. J. Non-Cryst. Solids 352, 63–70 (2006)

Cervinka, L.: Medium-range order in amorphous materials. J. Non-Cryst. Solids 106, 291–300(1988)

Chen, P., Holbrook, C., Boolchand, P., Georgiev, D.G., Jackson, K.A., Micoulaut, M.: Intermediatephase, network demixing, boson and floppy modes, and compositional trends in glass transitiontemperatures of binary AsxS1−x system. Phys. Rev. B 78, 224208 (2008)

Chong, T.C., Shi, L.P., Wei, X.Q., Zhao, R., Lee, H.K., Yang, P., Du, A.Y.: Crystalline amorphoussemiconductor superlattice. Phys. Rev. Lett. 100, 136101 (2008)

Churbanov, M., Plotrichenko, M.F.: Optical fibers from high-purity arsenic chalcogenide glasses.In: Fairman, R., Ushkov, B. (eds.) Semiconducting Chalcogenide Glass III, Chap. 5. pp. 209–230 Elsevier, Amsterdam (2004)

Ciliberti, S., De Los Rios, P., Piazza, F.: Glasslike structure of globular proteins and the bosonpeak. Phys. Rev. Lett. 96, 198103 (2006)

Cliffe, M.J., Dove, M.T., Drabold, D.A., Goodwin, A.L.: Structure determination of disorderedmaterials from diffraction data. Phys. Rev. Lett. 104, 125501 (2010)

DeNeufville, J.P., Moss, S.C., Ovshinsky, S.R.: Photostructural transformations in amorphousAs2Se3 and As2S3 films. J. Non-Cryst. Solids 13, 191–223 (1973)

Doremus, R.H.: Glass Science 2nd ed. Wiley, New York, NY (1994)Drabold, D.A., Estreichen, S.K. (eds.): Theory of Defects in Semiconductors. Springer, Berlin

(2007)Du, M.H., Zhang, S.B.: Topological defects and the Staebler-Wronski effect in hydrogenated

amorphous silicon. Appl. Phys. Lett. 87, 191903 (2005)Eigler, D.M., Schweizer, E.K.: Positioning single atoms with a scanning tunnelling microscope.

Nature 344, 524–526 (1990)Elliott, S.R.: Physics of Amorphous Materials 2nd ed. Longman Scientific & Technical, Essex

(1990)Elliott, S.R.: Medium-range structural order in covalent amorphous solids. Nature 354, 445–452

(1991)

References 59

Fischer, E.W., Dettenmaier, M.: Structure of polymeric glasses and melts. J. Non-Cryst. Solids 31,181–205 (1978)

Gaskell, P.H., Eckersley, M.C., Barnes, A.C., Chieux, P.: Medium-range order in the cationdistribution of a calcium silicate glass. Nature 350, 675–677 (1991)

Gjersing, E.L., Sen, S., Aitken, B.G.: Structure, connectivity, and configurational entropy ofGexSe100-x glasses: Results from 77Se MAS NMR spectroscopy. J. Phys. Chem. 114,8601–8608 (2010)

Golovchak, R., Shpotyuk, O., Kozyukhin, S., Kovalskiy, A., Miller, A.C., Jain, H.: Structuralparadigm of Se-rich Ge-Se glasses by high-resolution x-ray photoelectron spectroscopy.J. Appl. Phys. 105, 103704 (2009)

Greaves, G.N.: EXAFS and the structure of glass. J. Non-Cryst. Solids 71, 203–217 (1985)Greaves, G.N., Sen, S.: Inorganic glasses, glass-forming liquids and amorphizing solids. Adv. Phys.

56, 1–166 (2007)Grigera, T.S., Martín-Mayor, V., Parisi, G., Verrocchio, P.: Phonon interpretation of the ‘boson

peak’ in supercooled liquids. Nature 422, 289–292 (2003)Griscom, D.L.: The nature of point defects in amorphous silicon dioxide. In: Pacchioni, G., Skuja,

L., Griscom, D.L. (eds.) Defects in SiO2 and Related Dielectrics: Science and Technology,pp. 117–160. Kluwer, Dordrecht (2000)

Guthrie, M., Tulk, C.A., Benmore, C.J., Xu, J., Yager, J.L., Klug, D.D., Tse, J.S., Mao, H.K.,Hemley, R.J.: Formation and structure of a dense octahedral glass. Phys. Rev. Lett. 93, 115502(2004)

Halpern, V.: Localized electron states in the arsenic chalcogenides. Philos. Mag. 34, 331–335(1976)

Hobbs, L.W., Yuan, X.: Topology and topological disorder in silica. In: Pacchioni, G., Skuja,L., Griscom, D.L. (eds.) Defects in SiO2 and Related Dielectrics: Science and Technology,pp. 37–72. Kluwer, Dordrecht (2000)

Hosokawa, S., Matsuishi, K., Inui, M., Kajihara, Y., Tsutsui, S., Baron, A.Q.R.: Collectivedynamics of As2S3 glass investigated by inelastic X-ray scattering. J. Non-Cryst. Solids 354,2715–2718 (2008)

Hosokawa, S., Oh, I., Sakurai, M., Pilgrim, W.-C., Boudet, N., Berar, J.-F.: Anomalous X-rayscattering study of the local structure in Ge-Se glasses. Phys. Status Solidi (a) 206, 1736–1739(2009)

Ichikawa, K.: The nanoscopic structure of annealed Ge20Te80 glass: Quasi-atomic-scale imagingusing atomic-force microscopy. J. Phys.: Condens. Matter 7, L135–L139 (1995)

Inam, F., Drabold, D.A.: Theoretical study of an amorphous chalcogenide surface. J. Non-Cryst.Solids 354, 2495–2499 (2008)

Isobe, T., Kobayashi, S., Kiwaki, H.: Photoconduction mechanism of amorphous selenium: Effectof surface recombination. Jpn. J. Appl. Phys. 25, 580–582 (1986)

Itoh, K., Fukunaga, T.: Structure of Na2S-GeS2 glasses studied by using neutron and x-raydiffraction and reverse Monte Carlo modeling. Solid State Ionics 180, 351–355 (2009)

Jensen, K.O., Salmon, P.S., Penfold, I.T., Coleman, P.G.: Microvoids in chalcogenide glassesstudied by positron annihilation. J. Non-Cryst. Solids 170, 57–64 (1994)

Kawamoto, Y., Tsuchihashi, S.: Properties and structure of glasses in the system Ge-S. J. Am.Ceram. 54, 131–135 (1971)

Kibalchenko, M., Yates, J.R., Massobrio, C., Pasquarello, A.: Structural assignments of NMRchemical shifts in GexSe1-x glasses via first-principles calculations for GeSe2, GeSe9, and GeSecrystals, Phys. Rev. B 82, 020202 (2010)

Kittel, C.: Introduction to Solids State Physics 8th ed. Wiley, New York, NY (2005)Klein, P.B., Taylor, P.C., Treacy, D.J.: Two-phonon vibrational spectra of As2S3. II. Comparison

of the crystalline and amorphous forms. Phys. Rev. B 16, 4511–4518 (1977)Klein, A., Dieker, H., Späth, B., Fons, P., Kolobov, A., Steimer, C., Wuttig, M.: Changes in

electronic structure and chemical bonding upon crystallization of the phase change materialGeSb2Te4. Phys. Rev. Lett. 100, 016402 (2008)

60 2 Structure

Kohara, S., Suzuya, K.: Intermediate-range order in vitreous SiO2 and GeO2. J. Phys: Condens.Matter 17, S77–S86 (2005)

Kosek, F., Chlebny, J., Cimpl, Z., Mašek, J.: Structural and physical properties of the AsSx system.Philos. Mag. B 47, 627–639 (1983)

Kotsalas, I.P., Raptis, C.: Structural Raman studies of GexS1-x chalcogenide glasses.J. Optoelectron. Adv. Mater. 3, 675–684 (2001)

Krišciunas, V., Petretis, Br., Rinkunas, R.: Anisotropic properties and structure of amorphous filmsof selenium. Thin Solid Films 102, 111–116 (1983)

Krishnan, R.S.: The scattering of light in fused quartz and its Raman spectrum. Proc. Indian Acad.Sci. A 37, 377–385 (1953)

Lathrop, D., Eckert, H.: Structural equilibria in chalcogenide glass formation. A re-examinationof 31P magic-angle spinning NMR studies of the system phosphorus-arsenic-selenium. J. Non-Cryst. Solids 160, 111–115 (1993)

Ležal, D., Konák, K., Poláková, S., Petrovská, B.: Extrinsic scattering losses in As2S3 glasses.J. Non-Cryst. Solids 161, 301–303 (1993)

Lucovsky, G., Nemanich, R.J., Solin, S.A., Keezer, R.C.: Coordination dependent vibrationalproperties of amorphous semiconductors alloys. Solid State Commun. 17, 1567–1572 (1975)

Lucovsky, G., Phillips, J.C.: Symmetry determined medium range order (MRO) contributions tothe first sharp diffraction peak (FSDP) in non-crystalline oxide and chalcogenide glasses. Phys.Status Solidi (b) 246, 1806–1812 (2009)

Malinovsky, V.K., Sokolov, A.P.: The nature of boson peak in Raman scattering in glasses. SolidState Commun. 57, 757–761 (1986)

Malyj, M., Griffiths, J.E.: Extended defect structures in bulk As2S3 glass I. The effects of thermaltreatment on Raman spectra. Solid State Commun. 62, 667–670 (1987)

Mamontova, T.N., Kochemirovskii, A.S., Pivovarova, L.V.: Electronic processes on the surface ofAs-Se chalcogenide glassy semiconductors. Phys. Status Solidi (a) 107, 11–43 (1988)

Martin, A.J., Brenig, W.: Model for Brillouin scattering in amorphous solids. Phys. Status Solidi(b) 64, 163–172 (1974)

Maruyama, E.: Amorphous built-in-field effect photoreceptors. Jpn. J. Appl. Phys. 21, 213–223(1982)

Massobrio, C., Pasquarello, A.: Short and intermediate range order in amorphous GeSe2. Phys.Rev. B 77, 144207 (2008)

Mauro, J.C., Loucks, R.J.: Selenium glass transition: A model based on the enthalpy landscapeapproach and nonequilibrium statistical mechanics. Phys. Rev. B 76, 174202 (2007)

Mitkova, M., Wang, Yu., Boolchand, P.: Dual chemical role of Ag as an additive in chalcogenideglasses. Phys. Rev. Lett. 83, 3848–3851 (1999)

Moss, S.C., Price, D.L.: Random packing of structural units and the first sharp diffraction peak inglasses. In: Adler, D., Fritzsche, H., Ovshinsky, S.R. (eds.) Physics of Disordered Materials,pp. 77–95. Plenum, New York, NY (1985)

Mott, N.F., Davis, E.A.: Electronic Processes in Non-Crystalline Materials 2nd ed. Clarendon,Oxford (1979)

Muramatsu, S., Shimada, T., Kajiyama, H., Azuma, K., Watanabe, T., Kamiyama, T., Suzuki,K.: Medium-range order of amorphous silicon germanium alloys: Small-angle x-ray scatteringstudy. Jpn. J. Appl. Phys. 28, L1092–L1095 (1989)

Nemanich, R.J.: Low-frequency inelastic light scattering from chalcogenide glasses and alloys.Phys. Rev. B 16, 1655–1674 (1977)

Nesheva, D., Levi, Z., Aneva, Z.: Size effects and lattice disorder in GeS2/CdSe nanostructures.J. Optoelectron. Adv. Mater. 7, 1837–1846 (2005)

Nicholas, J., Sinogeikin, S., Kieffer, J., Bass, J.: Spectroscopic evidence of polymorphism invitreous B2O3. Phys. Rev. Lett. 92, 215701 (2004)

Novikov, V.N., Sokolov, A.P.: A correlation between low-energy vibrational spectra and first sharpdiffraction peak in chalcogenide glasses. Solid State Commun. 77, 243–247 (1991)

References 61

Ohsaka, T., Ihara, T.: Far-infrared study of low-frequency vibrational states in As2S3 glass. Phys.Rev. B 50, 9569–9572 (1994)

Okamoto, H., Hattori, K., Hamakawa, Y.: A theoretical consideration on the electroabsorptionspectra of amorphous semiconductors. J. Non-Cryst. Solids 137, 627–630 (1991)

Ovshinsky, S.R., Adler, D.: Local structure, bonding, and electric properties of covalent amorphoussemiconductors. Contemp. Phys. 19, 109–126 (1978)

Pacchioni, G., Skuja, L., Griscom, D.L. (eds.): Defects in SiO2 and Related Dielectrics: Scienceand Technology. Kluwer, Dordrecht (2000)

Pauling, L.: The Nature of Chemical Bond. Cornell University Press, Ithaca, NY (1960)Peled, A., Baranauskas, V., Rodrigues, C., Art-Weisman, D., Grantman, L., Frisem, A.A.:

Characterization of photodeposited selenium planar structures by scanning force microscopy.J. Appl. Phys. 77, 6208 (1995)

Petri, I., Salmon, P.S., Fischer, H.E.: Defects in a disordered world: The structure of glassy GeSe2.

Phys. Rev. Lett. 84, 2413–2416 (2000)Phillips, J.C.: Topology of covalent non-crystalline solids I: Short-range order in chalcogenide

alloys. J. Non-Cryst. Solids 34, 153–181 (1979)Phillips, J.C.: Topology of covalent non-crystalline solids II: Medium-range order in chalcogenide

alloys and a-Si(Ge). J. Non-Cryst. Solids 43, 37–77 (1981)Poborchii, V.V., Linder, G.G., Sato, M.: Selenium dimers and linear chains in one-dimensional

cancrinite nanochannels: Structure, dynamics, and optical properties. J. Chem. Phys. 116,2609–2617 (2002)

Popescu, M.A.: Non-crystalline chalcogenide. Kluwer, Dordrecht (2001)Poggemann, J.F., Heide, G., Frischat, G.H.: Direct view of the structure of different glass fracture

surfaces by atomic force microscopy. J. Non-Cryst. Solids 326, 15–20 (2003)Raoux, S., Jordan-Sweet, J.L., Kellock, A.J.: Crystallization properties of ultrathin phase change

films. J. Appl. Phys. 103, 114310 (2008)Ruocco, G.: Glasses: When disorder helps. Nat. Mater. 7, 842–843 (2008)Salmon, P.S., Martin, R.A., Mason, P.E., Cuello, G.J.: Topological versus chemical ordering in

network glasses at intermediate and extended length scales. Nature 435, 75–78 (2005)Shuker, R., Gammon, R.W.: Raman-scattering selection-rule breaking and the density of states in

amorphous materials. Phys. Rev. Lett. 25, 222–225 (1970)Sokolov, A.P., Rössler, E., Kisliuk., A., Quitmann, D.: Dynamics of strong and fragile glass

formers: Differences and correlation with low-temperature properties. Phys. Rev. Lett. 71,2062 –2065 (1993)

Starbov, N., Starbova, K., Dikova, J.: Surface microstructure and growth morphology of vacuumdeposited a-As2S3 thin films. J. Non-Cryst. Solids 139, 222–230 (1992)

Takebe, H., Maeda, H., Morinaga, K.: Compositional variation in the structure of Ge–S glasses.J. Non-Cryst. Solids 291, 14–24 (2001)

Tanaka, K.: High-pressure structural changes in chalcogenide glasses. Solid State Commun. 58,469–471 (1986)

Tanaka, K.: Chemical and medium-range orders in As2S3 glass. Phys. Rev. B 36, 9746–9752(1987)

Tanaka, K.: Studies of amorphous arsenic under pressure. Philos. Mag. B 57, 473–481 (1988)Tanaka, K.: Structural studies of amorphous Se under pressure. Phys. Rev. B 42, 11245–11251

(1990)Tanaka, K.: Medium-range structure in chalcogenide glasses. Jpn. J. Appl. Phys. 37, 1747–1753

(1998)Tanaka, K.: Nanostructured chalcogenide glasses. In: Nalwa, H.S. (ed.) Encyclopedia of

Nanoscience and Nanotechnology Vol. 7, pp. 629–640. American Scientific Publishers,Valencia (2004)

Tanaka, Y., Fukuyama, Y., Yasuda, N., Kim, J., Murayama, H., Kohara, S., Osawa, H., Nakagawa,T., Kimura, S., Kato, K., Yoshida, F., Kamioka, H., Moritomo, Y., Matsunaga, T., Kojima,

62 2 Structure

R., Yamada, N., Toriumi, K., Ohshima, T., Tanaka, H., Takata, M.: Development of picosec-ond time-resolved microbeam X-ray diffraction technique for investigation of optical recordingprocess. Jpn. J. Appl. Phys. 48, 03A001 (2009)

Tanaka, K., Nitta, S.: Pressure dependence of structural and electronics properties of polysilanealloys. Phys. Rev. B 39, 3258–3264 (1989)

Tanaka, K., Saitoh, A.: Optical nonlinearities of Se-loaded zeolite (ZSM-5): A molded nanowiresystem. Appl. Phys. Lett. 94, 241905 (2009)

Tanaka K., Yamaguchi, M.: Resonant Raman scattering in GeS2. J. Non-Cryst. Solids 227–230,757–760 (1998)

Taraskin, S.N., Simdyankin, S.I., Elliott, S.R., Neilson, J.R., Lo, T.: Universal features of terahertzabsorption in disordered materials. Phys. Rev. Lett. 97, 055504 (2006)

Taylor, P.C., Su, T., Hari, P., Ahn, E., Kleinhammes, A., Kuhns, P.L., Moulton, W.G., Sullivan,N.S.: Structural and photostructural properties of chalcogenide glasses: Recent results frommagnetic resonance measurements. J. Non-Cryst. Solids 326, 193–198 (2003)

Tenhover, M., Boolchand, P., Bresser, W.J.: Atomic-structure and crystallization of AsxTe1-xglasses. Phys. Rev. B 27, 7533–7538 (1983)

Terakado, N., Tanaka, K.: Nanoscale heterogeneous structures in GeO2–GeS2 glasses. Jpn. J. Appl.Phys. 47, 7972 (2008)

Thornburg, D.D., Physical properties of the As2 (Se,Te)3 glasses. J. Electron. Mater. 2, 495–532(1973)

Tichý, L., Ryšavá, N., Tríska, A., Tichá, H., Klikorka, J.: Qualitative calorimetry of some sulphurrich glasses. Solid State Commun. 49, 903–906 (1984)

Tominaga, J., Haratani, S., Handa, T., Yanagiuchi, K.: Scanning tunneling microscopy image ofGeSb2Te4 thin films. Jpn. J. Appl. Phys. 31, L799–L802 (1992)

Tsuchihashi, S., Kawamoto, Y.: Properties and structure of glasses in the system As-S. J. Non-Cryst. Solids 5, 286–305 (1971)

Turnbull, D., Polk, E.: Structure of amorphous semiconductors. J. Non-Cryst. Solids 8–10, 19–35(1972)

Vaccari, M., Garbarino, G., Yannopoulos, S.N., Andrikopoulos, K.S., Pascarelli, S.: High pressuretransition in amorphous As2S3 studied by EXAFS. J. Chem. Phys. 131, 224502 (2009)

Vaipolin, A.A., Porai-Koshits, E.A.: Structural models of glasses and the structures of crystallinechalcogenides. Sov. Phys.- Solid State 5, 497–500 (1963)

Vanderbilt, D., Joannopoulos, J.D.: Theory of defect states in glassy As2Se3. Phys. Rev. B 23,2596–2606 (1981)

Watanabe, I., Inagaki, Y., Shimizu, T.: Electron spin resonance of Mn2+ in As-Se and As-Te glasses.J. Non-Cryst. Solids 22, 109–123 (1976)

Wright, A.C., Sinclair, R.N., Leadbetter, A.J.: Effect of preparation method on the structure ofamorphous solids in the system As-S. J. Non-Cryst. Solids 71, 295–302 (1985)

Yamamoto, T., Miyaji, H., Asai, K.: Structure and properties of high pressure phase ofpolyethylene. Jpn. J. Appl. Phys. 16, 1891–1898 (1977)

Yannopoulos, S.N., Andrikopoulos, K.S.: Raman scattering study on structural and dynamicalfeatures of noncrystalline selenium. J. Chem. Phys. 121, 4747–4758 (2004)

Yasuoka, H., Onari, S., Arai, T.: Low frequency light scattering in amorphous As2S3. J. Non-Cryst.Solids 88, 35–42 (1986)

Young, P.A., Thege, W.G.: Structure of evaporated films of arsenic trisulphide. Thin Solid Films 7,41–49 (1971)

Yunker, P., Zhang, Z., Aptowicz, K.B., Yodh, A.G.: Irreversible rearrangements, correlateddomains, and local structure in aging glasses. Phys. Rev. Lett. 103, 115701 (2009)

Zachariasen, W.H.: The atomic arrangement in glass. J. Am. Chem. Soc. 54, 3841–3851 (1932)Zallen, R.: The Physics of Amorphous Solids. Wiley, New York, NY (1983)Zaug, J.M., Soper, A.K., Clark, S.M.: Pressure-dependent structures of amorphous red phosphorus

and the origin of the first sharp diffraction peaks. Nat. Mater. 7, 890–899 (2008)Zhou, W., Paesler, M., Sayers, D.E.: Structure of germanium-selenium glasses: An X-ray-

absorption fine-structure study. Phys. Rev. B. 43, 2315–2321 (1991)

Chapter 3Structural Properties

Abstract This chapter describes physical properties governed by normal atomicbonds. One of the biggest and long-standing problems is glass transition, at whichspecific heat, thermal expansion, and viscosity exhibit marked changes. Thermalcrystallization is also studied extensively, specifically in relation to phase-changememories. We also take brief views of structural properties at low and roomtemperatures. Importance of the atomic coordination number, which affects struc-tural properties, is also discussed. There exist magic coordination numbers at 2.4(Phillips) and 2.67 (Tanaka); the origin of these numbers is discussed. We also referto ion transport.

Keywords Glass transition · Kauzmann temperature · Free volume · Fragility ·Crystallization · Magic number · Ionic conduction

3.1 Structure and Properties

What is the relationship between the three kinds (short range, medium range, anddefect) of structural elements and structure-related (non-electronic) properties? Wehere can neglect the defect, since its density is smaller than ∼1 at.% and most of thestructural properties, except those at low temperatures, are determined by normalbonding structures. (The defect may play important roles in electronic properties.)Accordingly, it is natural to assume that the short-range structure governs structuralproperties, which are possibly modified by medium-range structures.

Examples of the structure-related properties are shown in Table 3.1. Amongthose, the most important may be the thermal and mechanical property, includingglass transition and crystallization. In glass transition, specific heat and viscositygradually change from liquidus to solidus values. On the other hand, thermal crys-tallization becomes an important problem, in relation to the phase change, the topicbeing described in Section 7.4. A related property is the thermal conductivity, whichis smaller in a glass than that in the corresponding crystal, due to phonon localiza-tion. Another important property is elastic, including concepts of magic numbers.It is also known that chalcogenide glass has marked acoustic nonlinearity, while theorigin has not been considered deeply. The last subject described in this chapter isionic conduction, which is in general more prominent than that in the crystal. Thefeature will be utilized in solid-state batteries (Section 7.7.3).

63K. Tanaka, K. Shimakawa, Amorphous Chalcogenide Semiconductors and RelatedMaterials, DOI 10.1007/978-1-4419-9510-0_3, C© Springer Science+Business Media, LLC 2011

64 3 Structural Properties

Table 3.1 Comparison of density ρ, bulk modulus B, specific heat c, thermal conductivity κ , linearthermal expansion coefficient β, glass transition temperature Tg, and Debye temperature TD of thethree materials (room temperature) polyethylene, g-As2S3, and g-SiO2. Note that the Dulong–Petitspecific value is 25 J/mol K for an elemental system. The thermal conductivity of As2S3 scattersamong reports

Material ρ (g/cm3) B(×1010N/m2) c(J/mol·K) κ(W/m·K) β (×10−5K−1) Tg (K) TD (K)

Polyethylene 0.95 ∼0.2 ∼30 0.4 15 150 ∼50As2S3 3.2 1.25 120 0.2–0.5 2.5 460 450SiO2 2.2 3.65 45 1.4 0.06 1450 500

We first note a remarkable difference between a glass and an amorphous mate-rial in the thermal transitions. Glass naturally shows glass transition because it isprepared from the corresponding melt. When heated, silica glass undergoes a glasstransition and gradually becomes a liquid, without showing crystallization or melt-ing transitions. An a-Se film, g-Se as well, undergoes a glass transition at ∼50◦C,crystallizes to a hexagonal crystal at ∼120◦C, and melts at 217◦C (Fig. 3.2). But,an amorphous film does not necessarily show glass transition. a-Si:H films, whenheated, exhaust H at ∼300◦C and directly crystallize to c-Si above ∼500◦C. Glasstransition has never been experimentally detected (Hedler et al. 2004). We shouldalso note that these thermal behaviors depend upon heating rates. If a-Se films areheated very slowly at the rate of 1◦C/day, only crystallization may take place at alower temperature. How can we understand these features?

3.2 Glass Transition

Glass transition appears more or less commonly. It appears not only in inorganicglasses but also in organic materials including bio-polymers as proteins (Lee andWand 2001). Because of such commonality, the phenomenon has been one of thebiggest problems in solid-state science (Elliott 1990, Angell et al. 2000, Debenedettiand Stillinger 2001) since the pioneering work by Kauzmann (1948), but it remainsvague. We here outline the fundamentals.

It is known that when a glass rod is heated it gradually becomes viscous. Thanksto this gradual softening, we can deform the glass to an arbitrary shape throughblowing, moulding, stretching, and so forth. The glass transition temperature Tgis defined as the transforming temperature between a glass and the viscous super-cooled liquidus state.

The left illustration in Fig. 3.1 shows enthalpy H curves as a function of a config-uration coordinate1 at three temperatures. At a higher temperature (liquid) than the

1The configuration coordinate is often used in these kinds of representations, while the meaningmay not be correctly understood. Suppose we have a solid (molecule) consisting of N atoms. Foruniquely identifying the atomic structure (position) in the three-dimensional space, we need 3 N−6coordinates for an N ≥ 3 system. In other words, if we fix a single point in a (3 N −6)-dimensionalHilbert space, the structure is uniquely determined. (The simplest example for a system of N = 2

3.2 Glass Transition 65

Fig. 3.1 Enthalpy H (or volume V) of a material as functions of atomic configuration (left) andtemperature (right). TR is room temperature, and the suffixes of temperature T in the right-handside illustration denote hypothetical (0), glass transition (g), crystallization (c), melting (m), andboiling (b)

endo- thermic

(a)

(b)

Fig. 3.2 Relative specific heats of (a) a-Se and (b) hexagonal Se (modified from Andonov 1982)

melting temperature Tm, the liquid has a configuration with the smallest enthalpy.At room temperature TR, in general, the crystal has the smallest enthalpy. In contrast,a glass has a minimal energy, which corresponds to the quasi-equilibriumness.

Next, let us trace the enthalpy H(T) of a material as a function of temperature,illustrated in the right-hand side in Fig. 3.1. Such curves can be obtained fromthe specific heat C(T) (Fig. 3.2), which can be taken using scanning thermalcalorimeters (Kasap and Tonchev 2006) and successive integration, since H(T) =∫

C(T)d T .2

is the atomic distance in H2 molecules, in which case the configuration coordinate becomes one-dimensional.) We here symbolize the 3 N − 6 axes with a single (or may be double) axis, whichis the configuration coordinate. In some special problems concerning a point defect, we may beinterested only in an atomic distance around the defect. In such cases, the 3 N − 6 axes may bereduced to a single distance axis, which can be regarded also as the configuration coordinate.2Recall that the enthalpy is given as H = U + PV , Helmholtz free energy F = U − TS, Gibbsfree energy G = H − TS (U is the internal mechanical energy, P the pressure, V the volume, T the

66 3 Structural Properties

Fig. 3.3 Free energyF(= U − TS) as a function oftemperature T

We here envisage an ideal crystal at 0 K (see Fig. 3.3). The entropy must bezero, and U governs the free energy, since F = U − TS. Heating increases TS,but when U � TS, F ≈ U, and the crystal has the lowest free-energy structure.At the melting temperature Tm, however, we have a condition of Uc = TmSl andFc = Fl, and accordingly, the first-order phase transition from a crystal (c) to aliquid (l) takes place. After the transition, F is governed by −TS term, and a higherentropy structure is preferred, which corresponds to the disordered liquid phase.Now, if the liquid is cooled down slowly, it undergoes crystallization at Tm. Thesecrystal–liquid transformations occur under thermal equilibrium, the condition beingsatisfied under infinitesimally small temperature variations.

Nevertheless, if the melt is rapidly cooled, it may deviate from the thermal equi-librium, being super-cooled without showing any signatures at Tm. Here, “rapid”means a time interval between 10−5 s−1 and 1 day, depending upon the material,in which the disordered atomic structure in a liquid cannot afford enough time tobe relaxed into an ordered structure, due to viscosity. With decreasing temperature,as illustrated in Fig. 3.1, the viscosity η rapidly increases reflecting clustering ofmolecular units (Berthier et al. 2005). This viscosity increase is approximated formany materials by the Vogel–Tamman–Fulcher equation (Elliott 1990, Doremus1994):

η(T) ∝ exp[B/(T − T0)], (3.1)

where B and T0 (<T) are constants. And at some temperature, which is calledas the glass transition temperature Tg (>T0), the super-cooled liquid becomes asolid. Here, the solid is empirically defined as a condensed matter in which the

temperature, and S the entropy), the specific heat at a constant volume cV = (∂U/∂T)V, and thespecific heat at a constant pressure cP = (∂H/∂T)P. If the PV term can be neglected, H = U, andaccordingly, F = G. The free energy is freely usable as work and TS is a thermodynamic energywhich cannot be utilized as work.

3.2 Glass Transition 67

viscosity is greater than ∼1013 poise (= 1012Pa · s), because above this value amatter retains its external shape in experimental timescales. At the glass transitiontemperature, the specific heat (cV or cP) also changes from a liquidus to a solidusvalue, which is nearly the same in glass and crystal (as is seen from the parallelenthalpy curves in Fig. 3.1). Configurational freedom is frozen at this temperature,and only vibrational energy gives the specific heat. In short, glass transition can begrasped both in mechanical viscosity and in thermodynamic quantities. In addition,other properties may also change at the glass transition temperature, an examplebeing photoconductivity in As2Se3 (Thio et al. 1984).

A big problem is at what temperature glass transition occurs. For the problem,the best known empirical relation may be

Tg (2/3)Tm (3.2)

(Kauzmann 1948, Wang et al. 2010). Or, as shown in Fig. 3.4, many simple glassesconsisting of covalent (ionic) and van der Waals bonds follow a relationship

ln Tg = 1.6Z + 2.3, (3.3)

where Z(= 1 − 2.7) is the average coordination number of atoms (Tanaka 1985).Many other ideas have been proposed for the value of Tg (Elliott 1990, Tichy andTicha 1995, Kerner and Micoulaut 1997, Naumis 2006). However, interpretationsof these relations remain to be studied.

More precisely, glass transition does not occur at a fixed temperature. We knowthat the melting temperature is uniquely determined at 1 atm. However, the glasstransition temperature increases if the heating rate d T/d t in thermal analyses is

Fig. 3.4 Dependence of theglass transition temperatureTg of various materials on theaverage coordination numberZ of constituent atoms(Tanaka 1985) (© Elsevier,reprinted with permission).The results for the molecules,which are held by hydrogenbonding, are denoted by opensymbols

68 3 Structural Properties

increased. It may vary over ∼50 K (Jund et al. 1997, Saiter et al. 2005). Accordingly,reported glass transition temperatures should be regarded as representative values.Otherwise, the temperature may be defined as a limiting value at d T/d t → 0.

At this point, we may ask if glass transition is a kind of phase transition.On the basis of this problem, it can be answered unambiguously that practicallyobserved glass transitions arise from relaxational phenomena, since the temperatureis determined as a function of heating or cooling rates.

However, Kauzmann (1948) pointed out a paradox, more than a half-centuryago, with the concept of the so-called entropy crisis (Greaves and Sen 2007). If thetemperature is lowered very slowly, and if crystallization can be suppressed, does Tgdecrease infinitely? If it decreased, the enthalpy of a super-cooled liquid could makea cross-point X in Fig. 3.1, and it would become smaller than that of the correspond-ing crystal. But, this seems very unrealistic, or paradoxical. And, we may envisagea critical temperature TK(< Tg), the so-called Kauzmann temperature, at which theenthalpy lines of super-cooled liquid and crystal make a cross-point. Empirically,this temperature TK, corresponding to X in Fig. 3.1, seems to appear at ∼T0 in theVogel–Tamman–Fulcher equation (3.1). Following such a notion, we could envisagethat a super-cooled state is retained down to TK, where the most stable (and prob-ably uniquely determined) glass appears. In this view, the ideal glass transition canbe regarded as a second-order phase transition. Nevertheless, such an ultimatelystable glass has never been obtained experimentally or theoretically by computersimulations. Saiter et al. (2005) have examined using thermal analyses a relaxationprocess in Ge-Se glasses aged over 13 years, while the relaxation seems to be stillincomplete. The idea of an ideal glass remains conceptual.

Microscopic mechanisms of glass transition are extensively studied, and manyideas have been proposed (Elliott 1990, Das 2004, Greaves and Sen 2007). The sim-plest and the most intuitive may be the free volume concept proposed by Cohen andTurnbull (1959). Here, the “free volume” means a void in which an atom can movefree from constraints (Zallen 1983). In this model, T0 in the Vogel–Tamman–Fulcherequation is regarded as the temperature at which the free volume VF disappears, i.e.,VF ∝ T−T0. However, the free volume may be too conceptual and the model cannotexplain relaxational phenomena. At present, it is believed that microscopic dynam-ics of glass transition can be grasped by the mode-coupling theory (Das 2004),which takes a self-consistent nonlinear feedback interaction between density fluctu-ations. Otherwise, further developments of an energy landscape scenario (Stillinger1995) will be valuable. The reader may refer to newer works including computersimulations (Langer 2006, Wilson and Salmon 2009).

Relaxation behaviors in super-cooled liquids have also been studied extensively.We first note that, as shown in Fig. 3.1, the super-cooled liquid (a known examplebeing honey) is also in quasi-equilibrium, while its thermodynamical state isuniquely determined as it is located on a straight line which is extrapolated fromthe melt.

Angell (1988) has emphasized for the super-cooled liquid that there are two ulti-mate types of temperature dependence in the viscosity η(T). As shown in Fig. 3.5,strong glasses such as SiO2 follow an Arrhenius type η ∝ exp[E/(kBT)], where E is

3.3 Crystallization 69

Fig. 3.5 Viscosities η(T) ofoxide, chalcogenide, andZnCl2 glasses as a function ofTg/T (modified from Elliott(1990) and Tverjanovich(2002))

a temperature-independent activation energy, and fragile glasses such as Se followthe Vogel–Tamman–Fulcher behavior, η ∝ exp[B/(T − T0)]. We may assume that,in the strong glass, T0 = 0 in this equation. Angell has also proposed a measure ofglass fragility as (Angell 1995)

m = d(log η)/d(Tg/T)∣∣T=Tg , (3.4)

which can encompass all the widespread behaviors between the two ultimates.In this definition, m ≈ 17 in SiO2, ∼35 in As2S3, and ∼50 in Se. The fragilityseems to be a useful macroscopic measure. However, the viscosity is a collectivephenomenon encompassing atomic and macroscopic motions, and structural inter-pretations of m remain to be studied (Wilson and Salmon 2009, Angell and Ueno2009).

Finally, we note that glass transition occurs also as functions of pressure(Eisenberg 1963), chemical bonding (Corezzi et al. 2002), and electronic excitation(Hisakuni and Tanaka 1995). For instance, Yu et al. (2009) demonstrate that glasstransitions appear in liquid S and Se upon rapid compression. It has also beendemonstrated that ∂Tg/∂P > 0 in oxide and chalcogenide glasses including Se andAs2S3 (Tanaka 1984).

3.3 Crystallization

Thermal crystallization occurs in many disordered solids when heated. Elementalamorphous solids such as S and Se are likely to crystallize, since the materialhas only topological structural disorders. a-Si films also crystallize above ∼500◦C.

70 3 Structural Properties

In contrast, crystallization can be appreciably suppressed in multi-componentglasses, because of the compositional disorder. Actually, stable glasses such as SiO2and As2S3 do not crystallize, they just continuously transform to a liquid throughthe super-cooled states. Otherwise, As2S3 can be partially crystallized by annealingat 300◦C for 12 days (Yang et al. 1986). Selenides such as As2Se3 are more likely tocrystallize. Te-alloys easily crystallize or decompose, reflecting metallic and fairlyisotropic atomic bonds.

Crystallization brings some changes in macroscopic properties. When a transpar-ent oxide glass is crystallized, it tends to become frosty, which may be problematic.On the other hand, crystallization (and amorphization) in Te-alloy films, accompa-nying optical and electrical changes, is a central subject in the recent phase-changememory (Section 7.4). Crystallization occurs also when an amorphous material issubjected to pressure (see Fig. 1.25).

Similar to glass transition, crystallization is not a phase transition, but arelaxational phase change. The crystallization temperature Tc also becomes higherwith the heating rate ∂ T/∂ t, which is set at 1–20 K/min in conventional calorimetrymeasurements. Then, what is the difference between glass transition and crystalliza-tion? A clear difference is, as suggested from Figs. 3.1 and 3.2, that glass transitionappears endothermic but crystallization is exothermic. In addition, the changebetween a glass and the super-cooled liquid may be reversible, while a crystal can-not directly transform to the glass. Crystallization is a kind of disorder-to-orderstructural relaxation.

Figure 3.6 implies that crystallization occurs with a rate of � exp(−EB/kBT),where � is a typical vibrational frequency (∼1013 Hz) and EB is the barrier heightbetween a disordered state and the corresponding crystalline phase. In Ge2Sb2Te3films, Tc ≈ 150◦C and EB ≈ 2 − 4 eV, the latter being dependent upon sam-ple preparations and measuring methods (Section 7.4). It seems that roughly atkTc ≈ EB/100 crystallization occurs, which proceeds through nucleation andgrowth (Doremus 1994).

What determines the value of EB? When a glass is transformed into a crystal, dis-ordered bonds must be cut and re-connected to the ordered structure. Accordingly,

configuration

enth

alpy

Fig. 3.6 Enthalpy of a glassand the crystal in aconfigurational space

3.4 Thermal and Other Properties 71

Fig. 3.7 Crystallization pressure Pc and temperature Tc as a function of (a) the bond energy (fromPauling) and (b) atomic coordination number for some elemental materials. Lines connect theatoms at the same periodicity in the periodic table

it may be plausible that EB, and accordingly Tc, correlates with the bond strength.However, as shown in Fig. 3.7a, Tc in elemental amorphous materials does not cor-relate with the bond energy (of Pauling). Nevertheless, we can see in Fig. 3.7b thatTc increases with the coordination number Z. Actually, Tc (K) 190Z seems to bea good approximation for the materials listed. This observation suggests that ther-mal bond rearrangement becomes more difficult in higher Z materials, having higherdimensional structures. Probably, the bond energy ranging between 1.4 and 2.2 eVplays a secondary role. In contrast, as shown in Fig. 3.7a, crystallization pressurePc (evaluated at room temperature (Fig. 1.25)) for As, Ge, and Se seems to increasewith the bond energy. (No data are available for Pc in Si, P, and S.) These contrastingobservations imply that compression directly cuts the covalent bond, while heatinginduces thermal segmental motions, both leading to crystallization. Similar studiesfor alloys will be interesting.

3.4 Thermal and Other Properties

Comparison of thermal properties in crystalline and non-crystalline materialsat room temperature shows interesting features. We here discuss heat capacityand thermal conductivity, the behaviors resembling electronic heat capacity andelectrical conductivity, described in Chapter 4.

The lattice specific heat c at room temperature is mostly irrespective of (dis-)orderness of atomic structures. It may follow the Dulong–Petit law (Kittel 2005),c = 3 NkB, where N is the Avogadro’s number and kB the Boltzmann constant.In non-metals, the specific heat is given as c = ∂U/∂T , where U is the vibrationalenergy, which is given as

U =∫

� ω D(ω) n(ω) dω, (3.5)

72 3 Structural Properties

where D(ω) is the vibrational density of state and n(ω) is the Planck distribu-tion function. Therefore, the similarity of crystalline and non-crystalline values isascribed to similar vibrational spectra, which can be measured, e.g., using inelasticneutron scattering or estimated from Raman scattering spectroscopy (see Equation(2.5)).

On the other hand, the thermal conductivity of a glass is substantially smallerthan that of the corresponding crystal. For instance, it is smaller by an order ing-SiO2 than that in c-SiO2. The thermal conductivity κ is given as κ = cvsL, wherec is the specific heat, vs the sound velocity, and L the mean free path of phonons(Kittel 2005). Since c and vs are comparable in the two forms, the smaller thermalconductivity in g-SiO2 is attributable to a shorter mean free path of phonons in dis-ordered networks. Actually, the values (at 80 K) in c- and g-SiO2 are reported to be40 (Kittel 2005) and ∼1 nm (Graebner et al. 1986), the latter being a manifestationof phonon localization.

The low-temperature anomaly of thermal and elastic properties in glasses hasbeen a big topic, which still remains controversial (Pohl et al. 2002). After the dis-covery of universal temperature variations by Zeller and Pohl (1971), a lot of studieshave been reported for g-SiO2, while those for chalcogenides such as g-As2S3 arefewer (Berret and Meissner 1988, Honolka et al. 2002). Table 3.2 summarizes thelow-temperature thermal characteristics. As known (Kittel 2005), the specific heatand thermal conductivity in insulating single crystals are understandable using theDebye T3 law at low temperatures. On the other hand, insulating glasses manifest theheat capacity having linear temperature dependence below ∼1 K, the absolute valuebeing greater than that in the corresponding crystal. We thus envisage additionalvibrational modes in the glass, which give rise to this linear dependence. In addi-tion, there exists some evidence which suggests that the responsible atomic structurehas not a multi- (as the conventional harmonic oscillator), but two-level excitationstates, the density being estimated at ∼1020 cm−3. Studies have then been focusedon the atomic structure, which is still vague. Or, the responsible structure may varyamong materials and samples. As mentioned in Section 2.4, this topic seems to berelated with FSDPs and Boson peaks, giving rise to challenging subjects. It shouldalso be mentioned that, exceptionally, a-Si films, which consist of rigid tetrahedralnetworks, do not exhibit the anomaly (Pohl et al. 2002).

Elasticity is an important macroscopic property of solids, including amorphousmaterials (Rouxel 2007). Experimental methods employed are common to allthe solids. Elastic constants E under static states can be determined from stress–strain curves. The bulk modulus can directly be measured through compressionexperiments. Or, a dynamical elastic constant is calculated as E = ρvs

2 from

Table 3.2 Comparison oftemperature dependences ofspecific heat c and thermalconductivity κ in crystal andglass such as SiO2 below∼1 K

c κ

Crystal T3 T3

Glass T1 T1

3.4 Thermal and Other Properties 73

the material density ρ and the sound velocity vs. The latter can be measuredusing acoustic methods (Kittel 2005) and Brillouin scattering spectroscopy asν = 2(vS/λ) sin(θ/2), where ν is the Brillouin shift, λ the laser wavelength inthe material, and θ the scattering angle of the light. We here mention that, in manyamorphous materials including a-Si:H films (Grimsditch et al. 1978), the lightscattering experiment detects only longitudinal waves, transversal waves beingundetectable (Nemanich 1977, Evich et al. 2004). The amorphous material behavesas a liquid at optical frequencies.

Comparing static elastic properties of a chalcogenide glass and crystal, an exam-ple for Se being listed in Table 3.3, contrastive features are manifested. In general,the glass appears to be softer, which is attributable to less dense and disorderedstructures (Novikov and Sokolov 2004). In addition, it should be noted that thedeformations in insulating glass and crystal are also contrastive. The crystal exhibitselastic and plastic deformations, the latter accompanying motions of defects such asdislocations and stacking faults (Kittel 2005). On the other hand, the glass, whichdoes not contain those defects, is likely to deform viscously after elastic shapechanges (Doremus 1994).

It is known that solubility of the oxide and the chalcogenide glass is contrastive.As-S(Se) glasses are known to have durability in acid solutions, while these are eas-ily soluble in alkaline solutions, as shown in Fig. 3.8 (Glase et al. 1957). Mamedov(1993) suggests that the solubility of As2S3 in alkaline solutions initiates with As

Table 3.3 Comparison ofsome elastic constants ofglassy (Rouxel 2007) andcrystalline (hexagonal) Se(Zingaro and Cooper 1974)

Bulk modulus(GPa)

Young’s modulus(GPa) Poisson’s ratio

Glass 9.6 10.3 0.32Crystal 17.4 23.4 0.27

Fig. 3.8 Surfacedeformations (swelling andattack) of As2S3 and Pyrex insolutions as a function of pH(modified from Glase et al.1957)

74 3 Structural Properties

oxidation: As2S3 + 6OH−(alkali) → 2AsO33− + 3H2S. On the other hand, it is

known that common soda-silicate glasses, SiO2–Na2O, dissolve into acids such asSiO−Na+ + H+ (acid) → SiOH + Na+ (Doremus 1994), while the glass is rela-tively stable in alkaline. Exceptionally, however, some oxide glasses such as Pyrex(81SiO2·13B2O3·4Na2O·2Al2O3) are stable in acids (Fig. 3.8).

3.5 Magic Numbers: 2.4 and 2.67

Continuous composition changes are inherent to the glass, for which many stud-ies have been reported. Here, it should be recalled, as mentioned in Section 1.6,that there is the notable difference between the oxide and the chalcogenide. In theoxide glass the change occurs in molecular units as xNa2O–(100−x)SiO2, wherex = 0 − 60 mol%, but the atomic ratio in Si–O can hardly be modified, being pos-sible only at defective levels (less than percent). In the chalcogenide, by contrast,a wide change can occur in the atomic ratio as AsxSe100−x, where x can be variedat 0−60 at.% (Borisova 1981). Such a difference is ascribable to the ionicity andcovalency in atomic bonds.

In short, chalcogenide glass is intrinsically covalent, and the atomic compositioncan be continuously varied. In such systems, the average coordination number Z peratom becomes an important parameter, which can be defined as

Z = {4x + 3y + 2(100 − x − y)}/100, (3.6)

for Ge(Si)xAs(P, Sb)yS(Se)100−x−y, where 4, 3, and 2 represent the coordinationnumbers of covalent bonds. Note that the coordination number of Te is likely tovary between 2 and 6, due to metallic character, and the atom may be excluded fromthe following argument.

How does a property change with Z? Several types of composition dependencein Ge–As–S(Se) are summarized in Fig. 3.9 (Tanaka 1989, Wang et al. 2009, Yanget al. 2010): (a) glass transition temperature (Fig. 3.4) and FSDP position, (b) atomicvolume and optical bandgap energy (Fig. 4.26), (c) elastic constant and Bosonpeak position, and (d) FSDP intensity and photodarkening. We see here markedsignatures at Z = 2.4 (b) and 2.67 (b, c, and d).

Phillips (1979) and other researchers (Döhler et al. 1980, Thorpe 1983) haveemphasized the importance of Zc = 2.4 with the following idea: Suppose that thecovalent bond (the bond length and the bond angle) is sufficiently rigid, and thatthis rigidity topologically fixes steric freedom of atom positions. Then, the numberof spatial constraints NCO (Z) for a Z-coordinated atom can be written as

Nco(Z) = Z/2 + (2Z − 3), (3.7)

where Z/2 and 2Z − 3 arise from the distance and the angular constraints (seeFig. 3.10a). They further assume that when Nco(Z) = 3 (three-dimensional space)the network is the most stable, or just rigid. This equality with Equation (3.7) gives

3.5 Magic Numbers: 2.4 and 2.67 75

Fig. 3.9 Dependence ofseveral physical properties onthe average atomiccoordination number Z

Fig. 3.10 Geometricalconstraints of a covalent bondOA in (a) three- and (b)two-dimensional spaces

Zc = 2.4. If Z > 2.4 and Z < 2.4, the atomic bond is necessarily strained (rigid)and too flexible (floppy), and such glasses are assumed to become unstable dueto strain and entropy. As2S(Se)3 satisfies the critical condition Zc = 2.4, whichcan explain the stability of these glasses. Note that neither the chemical nature ofbonds nor the medium-range order is taken into account in this idea. It is admirablethat this very simple and revolutionary idea, just topological without using quantummechanics and complicated calculations, has given a firm base for understandingthe compositional variation in covalent glasses. The topological idea has then beendeveloped, at least, to three directions.

First, Tanaka (1989) has extended this idea to layered structures. In this case, wecan write the constraint-dimension balance as Z/2 + (Z − 1) = 3 (see Fig. 3.10b),which gives Zc = 2.67. It seems that a two-dimensional amorphous structure is themost stable at the critical average coordination number of Zc = 2.67.

These two magic numbers, 2.4 and 2.67, can explain the composition depen-dence of physical properties shown in Fig. 3.9 (Tanaka 1989). For instance, the

76 3 Structural Properties

minimum atomic volume at 2.4 can be related to the most stable and compact amor-phous structure. On the other hand, the maximal volume at 2.67 may be relatedto a two-dimensional structure, in which the van der Waals bond with wide inter-layer separations provides the coarsest volume (Vateva et al. 1993). The physicalproperties ((b), (c), and (d)) exhibiting signatures at 2.67 are assumed to reflect thetwo-dimensional structure. For the details in optical gap and atomic volume, seeSection 4.10.

Second, Boolchand et al. (2001) have emphasized that the transition from floppyto rigid structures does not occur at the critical composition 2.4. Instead, they arguethat there exists an intermediate region, called “Boolchand phase,” between thetwo. The phase is assumed to be self-organized. Since the self-organized structurecan absorb some constraint, the threshold becomes a compositional region, not afixed point. The glass has no more homogeneous continuous random network struc-tures (Micoulaut and Phillips 2007). However, experimental evidence suggesting theintermediate phase is subtle, and the phase possibly depends upon sample prepara-tion and storage conditions. In addition, how we can compromise the self-organizedstructure and the medium-range structure has not been known.

Finally, Phillips’ idea has been extended to oxide glasses (Phillips and Kerner2008). In their treatment, SiO2 forms a stable glass, because the number of con-straint is 2.4, not 2.67 as in GeS(Se)2, provided that the angular constraint of Oatoms can be neglected due to ionicity. In a recent paper, they demonstrate the stabil-ity of window glass in a similar way with a composition of 74SiO2·16Na2O·10CaO.It is surprising that just a combination of topological argument with short-rangestructures can explain the stability of such complicated glasses.

However, we should note that the topological idea is not universal. For instance,as shown in Fig. 3.11, composition dependences of the glass transition temperaturesin the P–S(Se) systems are markedly different, though the coordination numbersare common. We should consider some difference in constituent molecular units,i.e., a kind of medium-range structures. In addition, it is known that the Urbach

Fig. 3.11 Glass transitiontemperatures Tg in thePxS(Se)100−x systems(modified from Greaves andSen 2007)

3.6 Ionic Conduction 77

energy EU shows minima at stoichiometric compositions (Fig. 4.15), not necessarilyat Z = 2.4, which manifests the importance of chemical orders.

3.6 Ionic Conduction

We know a marked ionic conduction in liquids such as NaCl-solved water, whichis in contrast to a negligible conduction in NaCl crystals. However, in some solids,Group I cation such as Li and Ag is mobile, giving rise to prominent ionic con-ductions. Specifically, in some crystals such as AgI, at temperatures above 150◦C,the ionic electrical conductivity σ ion is higher than ∼1 S/cm, being comparable tothat of the ionic liquid, which deserves the name of a “super-ionic conductor” or“fast ion conductor.” For such materials, extensive researches have been performed,stemming from battery applications (see Section 7.7) and from understanding theconduction mechanism. Note that the anion conduction is not common, the reasonbeing speculated straightforwardly.

Figure 3.12 presents several marked features of the electrical conduction in crys-tals and glasses. First, we see three kinds of materials: the ion conductor beingplotted on the left vertical line, the electronic conductor on the lower horizon-tal line, and the others being ion–electron (hole) mixed conductors. Second, anotable difference between crystal and glass is that there are binary ion-conductingcrystals such as Ag2S, but no binary ion-conducting glasses. The ion-conductingglass is ternary such as Ag–As–S or more complicated alloys. Third, for the samecomposition of AgAsS2, the glass possesses a higher ionic conduction than that

Fig. 3.12 Electronic (σe) and ionic (σi) conductivities of some solids and NaCl solution (×). Allthe solids without g- and a- are crystalline. Filled and open circles at σi = 10−15 S/cm denote theelectron and the hole conduction, respectively. Since conductivities less than 10−15 S/cm cannotbe reliably measured, these are plotted at 10−15 S/cm

78 3 Structural Properties

of the crystal. This tendency is in marked contrast to that of the electronic con-duction, as exemplified for c- and a-Se in the figure. The reason for a higherionic conductivity in the glass may be related with less dense and more flexibleglass structures containing free volumes, through which an ion can move freely(Tuller 2006).

In more detail, we are interested in a universal microscopic model for under-standing σ ion in a variety of glasses. Putting it concretely, we want to interpretdependence of the ionic conductivity σ ion on T, P, f, N, etc., where T is temper-ature, P pressure, f frequency of applied electric fields, and N cation concentration.Here, following the conventional way, we write for a group I cation as

σion = e Nion μion (3.8)

and

μion = e Dσ /(kB T), (3.9)

where Nion is the mobile ion density, μion the mobility, and Dσ the correspondingdiffusion coefficient. Accordingly, the problem is reduced to know the behaviors ofNion and μion, the typical values evaluated from an electrical time-of-flight measure-ment being 1019 cm−3 and 10−4 cm2/V·s in g-Ag50As17S33 at room temperature(Tanaka et al. 1999). Note that the ion density is much smaller than the Ag con-centration of ∼1023 cm−3. Microscopically, we can write for a cation jumpingprocess as

μion = (e/kBT) γ a2ν exp(Ea/EMN) exp (−Ea/kBT), (3.10)

where γ is a geometric factor which comes from a random-walk theory (= 1/6 forjumps in three dimensions), a the jump distance, ν an effective attempt frequency(∼1013 Hz), Ea the activation energy of jumps, and EMN the so-called Meyer–Neldelenergy (Ngai 1998, Section 4.9.3), which is introduced for quantitative explana-tion of the prefactor. For instance, Belin et al. (2000) report Ea ≈ 0.3 eV inan Ag2S–GeS2 glass. This equation gives ∂μion/∂T > 0, which is consistent withobserved temperature dependence of ∂σion/∂ T > 0, the feature being similar tothat in the electronic conduction in semiconductors. On the other hand, as exem-plified for g-Ag1As40Se60 in Fig. 3.13, pressure dependence σion(P) tends to show∂σion/∂ P < 0, which is opposite to that in the electronic conductivity in similarmaterials (g-As40Se60). The negative dependence is ascribable to the importance offree volumes in the ionic conduction.

The conventional interpretation of the activation energy Ea is to follow theAnderson–Stuart model (Elliott 1990, Doremus 1994). Following Fig. 3.14, weestimate Ea for a jump of a cation X from the left-hand side, where it is bondedto a non-bonding anion A, to the right-hand side, where it will be bonded to anon-bonding anion B as

Ea = +ECoulomb(AX) − ECoulomb(XB) + Eelastic, (3.11)

3.6 Ionic Conduction 79

Fig. 3.13 Pressuredependence of the electricalconductivity, normalized atthe 1 atm value, ing-As40Se60 (hole conduction)and g-Ag1As40Se60 (Ag+

conduction) (Arai et al. 1973,© Elsevier, reprinted withpermission)

rr

A BX

Fig. 3.14 A schematicillustration of a cation in abinary glass, following theAnderson–Stuart model

where the first and the second terms depict the Coulombic energies and the last termis the elastic energy needed for passing through the central channel produced bybonded atoms. Following the Anderson–Stuart model, we may assume that, with adecrease in r(AX), ECoulomb(AX) increases, giving rise to an increase in Ea.

However, this picture seems to be too simplified. Plotting Ea in many ion-conducting glasses as a function of the nearest-neighbor distance r around theion, Fig. 3.15, we notice interesting features in the oxide and the chalcogenide(Tanaka et al. 1999), with an exceptional result of AgI–AgPO3. One is that Eaof the chalcogenide is smaller than that of the oxide, which implies that σ ion islikely to become higher. The other is the opposite trend: With an increase in r,Ea tends to increase and decrease in the oxide and the chalcogenide, respectively.That is, the oxide glass appears not to follow the Anderson–Stuart model. For totalunderstanding, we may need quantum-mechanical considerations.

The oxide and the chalcogenide show another contrastive feature for the mobileatom. It seems that Cu is more mobile in the oxide while Ag is more mobile in thechalcogenide (Minami 1987, Bychkov 2009). Or, in the chalcogenide, Ag appearsto be more mobile than Cu (Vlasov and Bychkov 1984, Abe and Nakamura 1988).

80 3 Structural Properties

Fig. 3.15 The activationenergy Ea of ionicconductions in oxide andchalcogenide glasses as afunction of the nearestcation–anion distance r andthe corresponding Coulombicenergy Ec (Tanaka et al. 1999,© Wiley-VCH Verlag GmbH& Co. KGaA., reprinted withpermission)

In the atomic series of Cu, Ag, and Au, why does the larger Ag than Cu show ahigher ionic conduction?

An explanation is to ascribe the feature to the energy levels of Cu and Ag.Comparative structural (Salmon and Liu 1996) and photoemission (Itoh 1997) stud-ies for selenide glasses suggest that Cu and Ag are more covalently and ionicallybonded to Se, the characteristics being governed by the energies of valence electronsin Cu and Ag. Accordingly, Ag+ ions are mobile, and Cu atoms tend to strengthenthe network connectivity (Liu and Taylor 1989), giving rise to an increase in theglass transition temperature (Borisova 1981). On the other hand, Au seems to existas an isolated neutral atom (Kawaguchi et al. 1996). We also mention here thatAg and Cu in chalcogenide glasses possess a kind of mixed-cation effect (Rauet al. 2001): the existence of conductivity extrema at an intermediate compositionbetween Ag and Cu, which is commonly observed in oxide glasses (Doremus 1994).

For the dependence of Ea on the cation concentration N, as shown in Fig. 3.16,Bychkov (2009) has discovered for Ag+ in Ag2S–As2S3 glasses three regions sep-arated by the boundaries at N ≈ 30 ppm and ∼5 at.%. He assumes that below30 ppm, Ag+ ions are isolated (dilute limit); above 30 ppm percolative conductionchannels appear; and above a few atomic percent, preferential conduction path-ways are formed by highly connected ion units. However, the 30 ppm appears tobe much lower than the percolative threshold, which commonly occurs at 10–20%(Zallen 1983). To compromise this quantitative discrepancy, he further proposed the“allowed volume” with a spherical radius of ∼2 nm for ion conduction, to which

References 81

Fig. 3.16 Ag-diffusionactivation energy inAg2S–As2S3 glasses as afunction of Ag concentration(Bychkov 2009, © Elsevier,reprinted with permission)

the percolative idea may be applied. However, physical meaning of the allowed vol-ume seems to be vague. Phase-separated structures may be responsible (Mitkovaet al. 1999). In addition, there are many unresolved characteristics, an examplebeing σion(f ) ∝ f 1 (Dyre et al. 2009), which resembles that of electronic responses(Section 4.9.4).

Finally, we refer to the ion–electron (hole) mixed conduction (Fig. 3.12). Sincethe oxide glass has bandgap energies wider than ∼5 eV, electronic conductioncan be neglected in many cases. On the other hand, the chalcogenide has a gapof 1−3 eV, and accordingly, both the ionic and the electronic conduction arelikely to co-exist (Shimakawa and Nitta 1978). Specifically, the selenide glass withEg ≈ 2 eV behaves as an ion–hole mixed conductor (Vlasov et al. 1987). The mixedconduction plays important roles in the photodoping process (see Section 6.3.13).

References

Abe, H., Nakamura, Y.: The effect of Cu doping on the DC conductivity and thermoelectric powerof As2Se3-based glasses. Phys. Status Solidi (a) 107, 315–319 (1988)

Andonov, P.: Studies of non-crystalline forms of selenium. J. Non-Cryst. Solids 47, 297–339(1982)

Angell, C.A.: Structural instability and relaxation in liquid and glassy phases near the fragile liquidlimit. J. Non-Cryst. Solids 102, 205–221 (1988)

Angell, C.A.: Formation of glasses from liquids and biopolymers. Science 267, 1924–1935 (1995)Angell, C.A., Ngai, K.L., McKenna, G.B., McMillan, P.F., Martin, S.W.: Relaxation in glassform-

ing liquids and amorphous solids. J. Appl. Phys. 88, 3113–3157 (2000)Angell, C.A., Ueno, K.: Soft is strong. Nature 462, 45–46 (2009)Arai, K., Kumata, K., Kadota, K., Yamamoto, K., Namikawa, H., Saito, S.: Pressure effects on

electrical conduction in glasses. J. Non-Cryst. Solids 13, 131–139 (1973)

82 3 Structural Properties

Belin, R., Taillades, G., Pradel, A., Ribes, M.: Ion dynamics in superionic chalcogenide glasses:Complete conductivity spectra. Solid State Ionics 136–137, 1025–1029 (2000)

Berret, J.F., Meissner, M.: How universal are the low temperature acoustic properties of glasses?Z. Phys. B 70, 65–72 (1988)

Berthier, L., Biroli, C., Bouchaud, J.P., Cipelletti, L., Masri, D.El., L′Hôte, D., Ladieu, F., Pierno,M.: Direct experimental evidence of a growing length scale accompanying the glass transition.Science 310, 1797–1800 (2005)

Boolchand, P., Georgiev, D.G., Goodman, B.: Discovery of the intermediate phase in chalcogenideglasses. J. Optoelectron. Adv. Mater. 3, 703–720 (2001)

Borisova, Z.U.: Glassy Semiconductors. Plenum, New York, NY (1981)Bychkov, E.: Superionic and ion-conducting chalcogenide glasses: Transport regimes and struc-

tural features. Solid State Ionics 180, 510–516 (2009)Cohen, M.H., Turnbull, D.: Molecular transport in liquids and glasses. J. Chem. Phys. 31, 1164

(1959)Corezzi, S., Fioretto, D., Rolla, P.: Bond-controlled configurational entropy reduction in chemical

vitrification. Nature 420, 653–656 (2002)Das, S.P.: Mode-coupling theory and the glass transition in supercooled liquids. Rev. Mod. Phys.

76, 785–851 (2004)Debenedetti, P.G., Stillnger, F.H.: Supercooled liquids and the glass transition. Nature 410,

259–267 (2001)Döhler, G.H., Dandoloff, R., Bilz, H.: A topological-dynamical model of amorphycity. J. Non-

Cryst. Solids 42, 87–95 (1980)Doremus, R.H.: Glass Science 2nd ed. Wiley, New York, NY (1994)Dyre, J.C., Maass, P., Roling, B., Sidebottom, D.L.: Fundamental questions relating to ion

conduction in disordered solids. Rep. Prog. Phys. 72, 046501 (2009)Eisenberg, A.: The multi-dimensional glass transition. J. Phys. Chem. 67, 1333–1336 (1963)Elliott, S.R.: Physics of Amorphous Materials 2nd ed. Longman Scientific & Technical, Essex

(1990)Evich, R.M., Perechinskii, S.I., Gad’mashi, Z.P., Shpak, I.I., Vysochanskii, Yu.M., Slivka, V.Yu.:

Mandelshtam-Brillouin scattering in As2S3 and GeS2 chalcogenide glasses. Glass Phys. Chem.30, 14–16 (2004)

Glase, F.W., Blackburn, D.H., Osmalov, J.S., Hubbard, D., Black, M.H.: Properties of arsenicsulfide glass. J. Res. Natl. Bur. Stand. 59, 83–92 (1957)

Graebner, J.E., Golding, B., Allen, L.C.: Phonon localization in glasses. Phys. Rev. B 34,5696–5701 (1986)

Greaves, G.N., Sen, S.: Inorganic glasses, glass-forming liquids and amorphizing solids. Adv. Phys.56, 1–166 (2007)

Grimsditch, M., Senn, W., Winterling, G., Brodsky, M.H.: Brillouin scattering from hydrogenatedamorphous silicon. Solid State Commun. 26, 229–233 (1978)

Hedler, A., Klaumünzer, S.L., Wesch, W.: Amorphous silicon exhibits a glass transition. Nat.Mater. 3, 804–809 (2004)

Hisakuni, H., Tanaka, K.: Optical microfabrication of chalcogenide glasses. Science 270, 974–975(1995)

Honolka, J., Kasper, G., Hunklinger, S.: Correlation of low-energy excitations with photodarkeningin a-As2S3. Europhys. Lett. 57, 382–388 (2002)

Itoh, M.: Electronic structures of Ag(Cu)-As-Se glasses. J. Non-Cryst. Solids 210, 178–186 (1997)Jund, P., Caprion, D., Jullien, R.: Is there an ideal quenching rate for an ideal glass? Phys. Rev.

Lett. 79, 91–94 (1997)Kasap, S., Tonchev, D.: Thermal properties and thermal analysis: Fundamentals, experimental

technique and applications. In: Kasap, S., Capper, P. (eds.) Springer Handbook of Electronicand Photonic Materials, pp. 385–408. Springer, New York, NY (2006)

Kauzmann, W.: The nature of the glassy state and the behavior of liquids at low temperatures.Chem. Rev. 43, 219–256 (1948)

References 83

Kawaguchi, T., Maruno, S., Elliott, S.R.: Effect of addition of Au on the physical, electrical andoptical properties of bulk glassy As2S3. J. Appl. Phys. 80, 5625 (1996)

Kerner, R., Micoulaut, M.: On the glass transition temperature in covalent glasses. J. Non-Cryst.Solids 210, 298–305 (1997)

Kittel, C.: Introduction to Solids State Physics 8th ed. Wiley, New York, NY (2005)Langer, J.S.: Excitation chains at the glass transition. Phys. Rev. Lett. 97, 115704 (2006)Lee, A.L., Wand, A.J.: Microscopic origins of entropy, heat capacity and the glass transition in

proteins. Nature 411, 501–504 (2001)Liu, J.Z., Taylor, P.C.: A general structural model for semiconducting glasses. Solid State Commun.

70, 81–85 (1989)Mamedov, S.: On the macromolecular mechanism of dissolution of As2S3 films in organic

solutions. Thin Solid Films 226, 215–218 (1993)Micoulaut, M., Phillips, J.C.: Onset of rigidity in glasses: From random to self-organized networks.

J. Non-Cryst. Solids 353, 1732–1740 (2007)Minami, T.: Recent progress in superionic conducting glasses. J. Non-Cryst. Solids 95–96,

107–118 (1987)Mitkova, M., Wang, Yu., Boolchand, P.: Dual chemical role of Ag as an additive in chalcogenide

glasses. Phys. Rev. Lett. 83, 3848–3851 (1999)Naumis, G.G.: Variation of the glass transition temperature with rigidity and chemical composition.

Phys. Rev. B 73, 172202 (2006)Nemanich, R.J.: Low-frequency inelastic light scattering from chalcogenide glasses and alloys.

Phys. Rev. B 16, 1655–1674 (1977)Ngai, K.L.: Meyer-Neldel rule and anti Meyer-Neldel rule of ionic conductivity – Conclusions

from the coupling model. Solid State Ionics 105, 231–235 (1998)Novikov, V.N., Sokolov, A.P.: Poisson′s ratio and the fragility of glass-forming liquids. Nature 431,

961–963 (2004)Phillips, J.C.: Topology of covalent non-crystalline solids I: Short-range order in chalcogenide

alloys. J. Non-Cryst. Solids 34, 153–181 (1979)Phillips, J.C., Kerner, R.: Structure and function of window glass and pyrex. J. Chem. Phys. 128,

174506 (2008)Pohl, R.O., Liu, X., Thompson, E.: Low-temperature thermal conductivity and acoustic attenuation

in amorphous solids. Rev. Mod. Phys. 74, 991–1013 (2002)Rau, C., Armand, P., Pradel, A., Varsamis, C.P.E., Kamitsos, E.I., Granier, D., Ibanez, A., Philippot,

E.: Mixed cation effect in chalcogenide glasses Rb2S-Ag2S-GeS2. Phys. Rev. B 63, 184204(2001)

Rouxel, T.: Elastic properties and short- to medium-range order in glasses. J. Am. Ceram. Soc. 90,3019–3039 (2007)

Saiter, J.M., Arnoult, M., Grenet, J.: Very long physical ageing in inorganic polymers exemplifiedby the GexSe1-x vitreous system. Physica B 355, 370–376 (2005)

Salmon, P.S., Liu, J.: The coordination environment of Ag and Cu in ternary chalcogenide glasses.J. Non-Cryst. Solids 205–207, 172–175 (1996)

Shimakawa, K., Nitta, S.: Influence of silver additive on electronic and ionic natures in amorphousAs2Se3. Phys. Rev. B 18, 4348–4354 (1978).

Stillinger, F.H.: A topographic view of supercooled liquids and glass formation. Science 267,1935–1939 (1995)

Tanaka, K.: Photodarkening in amorphous As2S3 and Se under hydrostatic pressure. Phys. Rev.B 30, 4549–4554 (1984)

Tanaka, K.: Glass transition of covalent glasses. Solid State Commun. 54, 867–869 (1985)Tanaka, K.: Structural phase transitions in chalcogenide glasses. Phys. Rev. B 39, 1270–1279

(1989)Tanaka, K., Miyamoto, Y., Itoh, M., Bychkov, E.: Ionic conduction in glasses. Phys. Status Solidi

(a) 173, 317–322 (1999)

84 3 Structural Properties

Thio, T., Monroe, D., Kastner, M.A.: Evidence for thermally generated defects in liquid and glassyAs2Se3. Phys. Rev. Lett. 52, 667–670 (1984)

Thorpe, M.F.: Continuous deformations in random networks. J. Non-Cryst. Solids 57, 355–370(1983)

Tichy, L., Ticha, H.: Covalent bond approach to the glass-transition temperature of chalcogenideglasses. J. Non-Cryst. Solids 189, 141–146 (1995)

Tuller, H.L.: Ionic conduction and applications. In: Kasap, S.O., Capper, P. (eds.) SpringerHandbook of Electronic and Photonic Materials, Chap. 11, pp. 213–228. Springer, New York,NY (2006)

Tverjanovich, A.: Calculation of viscosity of chalcogenide glasses near glass transition temperaturefrom heat capacity or thermal expansion data. J. Non-Cryst. Solids 298, 226–231 (2002)

Vateva, E., Skordeva, E., Arsova, D.: Average coordination number dependence of photostructuralchanges in amorphous Ge-As-S films. Philos. Mag. B 67, 225–235 (1993)

Vlasov, Yu.G., Bychkov, E.A.: Ionic and electronic conductivity in the copper-silver-arsenic-selenium glasses. Solid State Ionics 14, 329–335 (1984)

Vlasov, Yu.G., Bychkov, E.A., Seleznev, B.L.: Compositional dependence of ionic conductivityand diffusion in mixed chalcogen Ag-containing glasses. Solid State Ionics 24, 179–187 (1987)

Wang, L.M., Li, Z., Chen, Z., Zhao, Y., Liu, R., Tian, Y.: Glass transition in binary eutectic systems:Best glass-forming composition. J. Phys. Chem. B 114, 12080–12084 (2010)

Wang, R.P., Smith, A., Luther-Davies, B., Kokkonen, H., Jackson I.: Observation of two elasticthresholds in GexAsySe1-x-y glasses. J. Appl. Phys. 105, 056109 (2009)

Wilson, M., Salmon, P.S.: Network topology and the fragility of tetrahedral glass-forming liquids.Phys. Rev. Lett. 103, 157801 (2009)

Yang, G., Bureau, B., Rouxel, T., Gueguen, Y., Gulbiten, O., Roiland, C., Soignard, E., Yarger, J.L.,Troles, J., Sangleboeuf, J.-C., Lucas, P.: Correlation between structure and physical propertiesof chalcogenide glasses in the AsxSe1−x system. Phys. Rev. B 82, 195206 (2010)

Yang, C.Y., Paesler, M.A., Sayers, D.E.: First crystallization of arsenic trisulfide from bulk glass:The synthesis of orpiment. Mater. Lett. 4, 233–235 (1986)

Yu, P., Wang, W.H., Wang, R.J., Lin, S.X., Liu, X.R., Hong, S.M., Bai, H.Y.: Understanding excep-tional thermodynamic and kinetic stability of amorphous sulfur obtained by rapid compression.Appl. Phys. Lett. 94, 11910 (2009)

Zallen, R.: The Physics of Amorphous Solids. Wiley, New York, NY (1983)Zeller, R.C., Pohl, R.O.: Thermal conductivity and specific heat of noncrystalline solids. Phys. Rev.

B 4, 2029–2041 (1971)Zingaro, R.A., Cooper, W.C.: Selenium. Van Nostrand Reinhold Company, New York, NY (1974)

Chapter 4Electronic Properties

Abstract Electronic density of states in the extended and localized states governoptical and electrical properties. We see, in this chapter, that studies on elec-tronic properties have yielded a lot of valuable ideas, such as Tauc gap, mobilityedge, and charged defects. In addition, concepts originally proposed for crystalssuch as polaron and Urbach edge bear special importance in chalcogenide glasses.We also consider optical nonlinearity, which is prominent in the chalcogenideglass. Electrical conduction mechanisms, under dc and ac electric fields, are alsodiscussed. It is suggested that the Meyer–Neldel law is important to obtain fullunderstanding of the transport mechanisms. The final section refers to compositiondependence of the bandgap energy.

Keywords Ioffe-Regel rule · Lone-pair electron · Polaron · Charged defect · Urbachedge · Nonlinear optics · Meyer-Neldel rule · Hopping

4.1 Electronic Structure

As illustrated in Fig. 4.1, the electronic structures in crystals and non-crystalsshow characteristic features. For the crystal, we can calculate under a one-electronapproximation, using Bloch functions in known periodic structures, the electrondispersion curve (electron energy E – wavenumber k), from which the elec-tron density of state (DOS) D(E) is straightforwardly calculated (Kittel 2005).In contrast, Bloch functions cannot be assumed for disordered materials. Thewavenumber k is no more a good quantum number, due to the localization ofelectron wavefunctions to spatial extent of �r, which must satisfy the uncertainty

atomic energy leveland bonding

D(E)

D(E)

Atomicstructure

E~kBloch functionCrystal

Non-crystal

Fig. 4.1 Relationships between atomic and electronic structures in crystals and non-crystals

85K. Tanaka, K. Shimakawa, Amorphous Chalcogenide Semiconductors and RelatedMaterials, DOI 10.1007/978-1-4419-9510-0_4, C© Springer Science+Business Media, LLC 2011

86 4 Electronic Properties

principle �k·�r ∼ 1. Or, the electron mean free path is assumed to be of theorder of ∼1/k, which is the so-called Ioffe–Regel rule (Mott and Davis 1979,Elliott 1990). Accordingly, the dispersion curve cannot be delineated. However, theDOS is still a useful quantity, which may be estimated as follows: First, molec-ular energy levels are assumed from a bonding structure and the energy level(Fig. 1.10) of constituent atoms. The molecular level broadens into a band, reflectingpartial extensions and overlaps of related wavefunctions, and the resulting energy-level density determines the DOS. Computer simulations will provide its detailedshape.

It may be instructive to sketch out a rough view of relationships between atomicand band structures using the tetrahedrally coordinated two-dimensional latticesshown in Fig. 4.2. Note that the short-range structures of these three clusters aresimilar. (The bond angle may be strained in these two-dimensional lattices, but itcan be reduced in the three-dimensional space.) We here consider the roles offeredby the short-range, medium-range, and defective structures (Table 4.1).

First, the DOS in a glass is similar to that in the corresponding crystal, since bothare governed by the short-range atomic structure. Accordingly, the bandgap energiesand also optical absorptions at �ω > Eg are roughly the same.

Fig. 4.2 Three tetrahedrallycoordinated clusters and thecorresponding bandstructures: (a) crystal,(b) strained lattice with adangling bond, and(c) strained fully connectednetwork

Table 4.1 Effects of structural elements (left) upon some electronic properties

Structure

Optical absorption

Transport Photoluminescence(�ω > Eg) (�ω ∼ Eg) (�ω < Eg)

Short range ©◦ © © ©Medium range ©◦ ? ? ?Defect © ©◦ © ©◦Impurity ©◦ ©◦ ?Inhomogeneity ? ? ©◦Polaronic effects are neglected. Double and single circles denote strong and medium effects,respectively.“?” remains to be studied.

4.1 Electronic Structure 87

Second, however, the band edge seems to critically depend upon the structuralperiodicity. In a hypothetical ideal single crystal (a), the edges of the conductionand the valence band are flat in space, and all the electron wavefunctions extendover the crystal. However, in disordered structures, the band edge may be mod-ified by medium-range structures, e.g., (b) a 5-membered ring and (c) a strained3-membered ring. And, the modifications may be different in the conduction and thevalence band. Provided that the bond is of sp3 type as in Si, an angular strain givesgreater effects upon the valence band edge, because it is governed by the directionalp orbital, in contrast to the conduction band edge being governed by the spherical sorbital (Phillips 1973). Or, in the chalcogenide, the conduction and the valence bandare composed of anti-bonding and lone-pair electron states (Fig. 1.11), which willreflect structural disorders differently.

Third, a defect provides some effects. A dangling bond, if it is in solid Si, pro-duces a mid-gap state. For this reason, pure a-Si has a lot of mid-gap states. Thestate will govern mid-gap optical absorption and photoluminescence. Instead, ina-Si:H, the dangling bond can be terminated by a H atom, and the mid-gap state isreduced. It is plausible that the preparation and prehistory affect more strongly theband edges and gap states than the gross electronic structure.

It may be valuable to add a remark about atomic (impurity) doping and the Fermienergy. In single-crystalline semiconductors such as Si and GaAs, minute atomicdoping (less than ∼0.01 at.%) can shift the energy position of the Fermi levelfrom the mid-gap to a band edge, exhibiting a change in the electrical activationenergy from Eg/2 (intrinsic) to ∼0 (extrinsic). However, such a doping effect hardlyappears in oxide and chalcogenide glasses, with some exceptions (Ovshinsky andAdler 1978, Tohge et al. 1980, Narushima et al. 2004). In most of the chalcogenides,the activation energy is ∼Eg/2, which suggests that the Fermi level is pinnednear the middle of the bandgap. Even in a-Si:H, percent-order (∼5%) dopants areneeded for producing n- and p-type a-Si:H, which means that the doping efficiencyis much lower in amorphous semiconductors. The fluctuating band structure maymodify the states produced by dopants and/or the flexible amorphous structuremay compensate the inherent (spatially constraint in the crystal) coordination ofdopants.

As illustrated in Fig. 4.3, in the band structure, an electron undergoes three kindsof movements: (i) energetic transition, (ii) transport including (de-)trapping, and

Fig. 4.3 Three kinds ofelectron movements,transition (solid arrows),transport (dashed arrow), andhopping (dotted doublearrow), in a semiconductorhaving gap states

88 4 Electronic Properties

(iii) local motions between gap states. The energetic transition occurs as a resultof optical processes (absorption/emission) or thermal relaxation (vibrational). Thetransport can occur as drift and diffusion under dc electric fields and gradients ofcarrier densities. Finally, a carrier may move between gap states through tunneling.Here, it should be mentioned that “hopping” has been used in two ways: quantal andclassical, which should be distinguished. Zallen (1983) states that “The term hop-ping is an abbreviation for the phonon-assisted quantum-mechanical tunneling of anelectron from one localized to another.” We will follow this terminology. It shouldalso be noted that, in the conventional band model, the atomic structure is assumedto be rigid.

However, the polaron, originally proposed for ionic crystals (Kittel 2005), addsvariety and complexity to electronic (electrical and optical) properties in flexible dis-ordered lattices (Emin 1975, Abe and Toyozawa 1981, Emin 2008). The band modelcannot enclose the polaron, and instead, we may employ the energy configurationdiagram as in Fig. 4.4 for representing the dynamics. Here, the energy in the verticalscale is the total energy of an electron (or hole) and N deforming atoms (strainedbonds). The horizontal configuration axis symbolizes a 3N Euclidean space of con-stituent atoms (see Fig. 3.1). In the simplest case, such as a point defect, the axis mayrepresent the interatomic spacing near the electron. And, the energy curves of theground and the excited states of this electron-atom system become parabolic undera harmonic approximation for strain energies. In this representation, the polaron canbe expressed as the laterally shifted energy minimum of an excited state. (In a rigidlattice, the energy minimum is located above the point O.) As a consequence, inphotoluminescence, the emission energy (EPL) becomes smaller than the absorp-tion energy (Eexc), the energy difference Eexc − EPL appearing as a Stokes shift(Street 1976). We can also envisage more complicated systems such as bi-polaron,excitonic polaron, and self-trapped polaron.

Fig. 4.4 A polaron in anenergy configuration diagramwith schematic square-latticestructures, in which open andsolid circles represent atomsand electrons, respectively

4.2 Band Structure 89

4.2 Band Structure

How can we experimentally determine the DOS structure? Naturally, we probe theDOS with photons. The valence band DOS can be straightforwardly determinedby photoelectron spectroscopy using ultraviolet and x-ray photons (Elliott 1990).On the other hand, the conduction band DOS can be investigated using inversephotoelectron spectroscopy, a kind of electron-excited luminescence spectroscopy(Matsuda et al. 1996, Ono et al. 1996). An example of structures obtained for Seis shown in Fig. 4.5. The energy resolution of these measurements is typically∼0.5 eV, which is not sufficient for probing the band-edge and bandgap states.Another drawback of photoelectron spectroscopy is the limited escape depth of elec-trons (∼10 nm), i.e., it is surface sensitive. In addition, the charge-up of investigatedinsulating materials resulting from electron emission is likely to deform obtainedspectra, which may be suppressed by carbon coating or compensated by intentionalelectron flooding. On the other hand, wide-range optical spectra contain informationof the DOS (see Equation (4.1)). For instance, it is conventional to obtain spectraldielectric functions, which correspond to the joint DOSs of valence and conductionbands, from ultraviolet reflection spectra (Sobolev and Sobolev 2004). Otherwise,since the inverse photoemission is less sensitive, a combination of the photoelectronand the optical spectroscopy may be more useful for determination of the conductionand valence band structures (Lippens et al. 2000).

The DOS has been theoretically analyzed. Originally, the analyses followed tight-binding calculations and, recently, ab initio computer simulations (Drabold andEstreichen 2007), in which gloss features are consistent. However, for band-edge

Fig. 4.5 DOSs of an amorphous (upper) and a crystalline (lower) Se determined by photoelectronand inverse photoelectron spectroscopy (Ono et al. 1996, © IOP Publishing Ltd., reprinted withpermission)

90 4 Electronic Properties

and gap states, the results depend upon calculations. In addition, it seems moredifficult to take polaronic effects into account.

The most important and unique feature in the electronic structures of simpleoxides and chalcogenides, irrespective of glass and crystal, is the character ofthe valence band. As shown in Fig. 1.11, the upper edge (HOMO) of the valenceband is produced by lone-pair electron states of chalcogen atoms (electron-filledpz states in Fig. 1.11) (Kastner 1972). The bandwidth is governed by the inter-action among lone-pair electrons, as suggested by pressure studies (Zallen 1983,Tanaka 1989a). Below the lone-pair electron band, there exists another occupiedband, which originates from bonding states, e.g., σ (As–S) in As2S3. On the otherhand, the conduction band (LUMO) is produced from the anti-bonding state σ ∗. Or,in oxides such as SiO2, which is partially ionic, it is governed by vacant d states ofcation Si4+.

Figure 4.6 compares (a) a chemical bond diagram for SiO2 and calculated dis-persion curves for (b) c-SiO2 (Chelikowsky and Schluter 1977) and (c) c-As2Se3(Tarnow et al. 1986). The common feature for the lone-pair electron bands can bepointed out in the dispersion diagrams at 0 to −4 eV in c-SiO2 and 0 to −5 eV inc-As2Se3. Below the lone-pair electron bands, there exists another band at around−10 eV, which arises from the bonding states. Note that the width of the lone-pairelectron band in SiO2 is smaller than the σ -band width, while the opposite holds inAs2Se3. This feature may reflect different strengths of interaction between lone-pairelectrons. We also see in c-SiO2 that the electron effective mass (1/m∗ ∝∂E2/∂ k2)is substantially smaller than the hole mass. A chemical interpretation of this resultmay be obtained by recalling the relatively spherical, and extended, d-state of Si.In contrast, such a clear mass difference is not seen in c-As2Se3.

It is difficult to identify effects of medium-range structures on the electronicstructure. For crystals, we can point out substantially different bandgap energies (3.5and ∼3.6 eV) in three-dimensional GeS2 and two-dimensional GeS2, both having

Fig. 4.6 (a) A chemical bond diagram for SiO2 and electronic dispersion curves in (b) c-SiO2 and(c) c-As2Se3 (modified from Griscom 1977 and Tanaka 2004). Note that, for the vertical axes inthe three figures, the tops of the valence band (HOMO level) and the scales are common

4.3 Bandgap and Mobility Edge 91

Fig. 4.7 Occupied (gray)and unoccupied (white)energy levels of Cu, Pb, andNa in SiO2 glass

similar short-range structures consisting of ≡Ge−S− connections (Weinstein et al.1982). For non-crystals, known examples are limited. As2S3 glass and its as-evaporated film have nearly the same short-range structures including =As–S–linkages and similar optical gaps of ∼2.4 eV. In detail, however, the film exhibits aslightly wider optical gap by ∼50 meV, which may be ascribed to smaller widths ofthe valence band reflecting molecular structures in as-evaporated films (Fig. 2.3).

Electronic structures in multi-component systems have been studied less deeply.Figure 4.7 summarizes energy levels of Na, Cu, and Pb in silica glass. Na and Cuatoms produce one band, while heavier Pb gives both HOMO and LUMO states. Forthe chalcogenide, limited materials such as Ag(Cu)–As–S(Se) (Simdyankin et al.2005a) and Ge–Sb–Te (Xu et al. 2009) have been studied with specific reference toionic conduction and phase change. However, if the concentrations of every compo-nent are comparable, for which we cannot apply a dilute limit approximation, it isdifficult to obtain certain universal insights into the electronic structure.

The electronic structure governs electronic properties: optical, electrical, andphoto-electrical. The optical property is understandable in principle through theconventional transition-probability formulation, provided that the structure is rigidso that polaron effects can be neglected. The electrical property is more difficultto interpret, because the carrier transport is markedly influenced by band-edge andmid-gap states. Photo-electrical property is the most difficult to understand, becauseit appears through optical excitation and carrier transport.

4.3 Bandgap and Mobility Edge

In a rigorous sense, the concept of the bandgap energy Eg in amorphous semi-conductors still remains vague. In a crystalline semiconductor, if it is intrinsic,Eg

o = Ege, where Eg

o and Ege are optically and electrically determined (from

the optical absorption edge and from temperature dependence of the electricalconductivity) bandgap energies. However, pioneering studies on amorphous semi-conductors have demonstrated that Eg

o < Ege. This observation has delivered the

so-called Mott-CFO model (Cohen et al. 1969, Mott and Davis 1979). In this model,as shown in Fig. 4.8, the DOS smoothly reduces around the band edges. In contrast,reflecting spatially fluctuating potentials, the mobility is assumed to abruptly (or

92 4 Electronic Properties

Fig. 4.8 Spatial fluctuations of the band edges (center), the DOS (left), and the mobility (right) asa function of electron energy (Fritzsche 1971, © Elsevier, reprinted with permission)

discontinuously at 0 K) drop to zero at the band edges. This mobility edge distin-guishes extended and localized wavefunctions (Baranovskii and Rubel 2006). Underthis model, we assume that the optical gap Eg

o is governed by the DOS, and theelectrical Eg

e is equal to the gap between the mobility edges.However, the Mott-CFO model should be regarded as a guiding idea. The model

is a kind of modified band model, following a “frozen-lattice” approximation, andaccordingly, it cannot account for polaron effects. The model may be applied toamorphous tetrahedral semiconductors, in which the conduction and the valencebands arise from anti-bonding and bonding states of fourfold coordinated (rigid)sp3 electrons. However, it seems difficult to apply the model to the chalcogenide,which contains the valence and the conduction band having different origins. Themodel also faces an experimental problem. To determine a value of the mobility gap,we may examine spectral dependence of photoconductivity, expecting an abruptphotocurrent increase at �ω≥Eg

e(>Ego). However, in some materials such as a-Se,

there exists a so-called non-photoconducting gap, i.e., the photoconducting edgeis blue-shifted from the optical gap, which is ascribed to geminate (exciton-likeelectron–hole pairs) recombination processes (see Section 5.4). In short, it is notstraightforward to determine the mobility gap.

4.4 Gap States

The defect is likely to produce a gap state. However, for obtaining experimentallyreproducible results on the gap state, we need to adopt several precautions. First,when investigating the gap state, which may have a density less than ∼1018cm−3,we should have a sample with purity higher than ∼five 9’s. Raw materials for pro-ducing a sample may have a purity of six 9’s, while the value is just nominal,materials being often oxidized (Churbanov and Plotnichenko 2004). It is also knownthat electronic properties in a-Se are likely to be affected by minute impurities(Kasap et al. 2009, Benkhedir et al. 2009). Second, the gap state must be sensitiveto preparation conditions and prehistory of the samples. Third, the measurement

4.4 Gap States 93

itself may have some problems. Gap states can be probed optically, electrically, andphoto-electrically. Among these, the optical method seems to be the most reliable,since it does not need the electrode, which is likely to add interfacial effects onobtained results (Tsiulyanu 2004). On the other hand, theoretical results largelydepend upon their formulations (Drabold and Estreichen 2007), because local-ized defect states are likely to have strong interaction with disordered lattices, thesituation which is more or less difficult to analyze.

The wrong bond, the existence in g-As2S(Se,Te)3 being structurally confirmed(with densities of 1–10% as described in Section 2.5), possibly causes major gapstates. However, its energy location is speculative. It seems that cation and anionwrong bonds, respectively, do and do not produce gap states. Halpern (1976) pro-poses that As–As σ bonds in As2S3 produce states above the valence band. On theother hand, Vanderbilt and Joannopoulos (1981) and Tanaka (2002) propose thatAs–As σ ∗ states are located below the conduction band, which seem to providegap states with a characteristic energy EW, giving rise to a weak absorption tail(Section 4.6). For GeS2, it is known that the bulk and the evaporated film have sub-stantially different optical bandgaps: 3.2 eV in bulk and ∼2.5 eV in film, for whichthe smaller film gap is ascribed to a lot of Ge–Ge wrong bonds (Tanaka et al. 1984).Actually, Hachiya (2003) demonstrated through first-principles calculations that theGe–Ge wrong bond in GeS2 produces a σ ∗ state near the bottom of the conduc-tion band. For SiO2, Mukhopadhyay et al. (2005) theoretically predict that σ (Si–Si)bonds give rise to occupied states at ∼2 eV above the valence band edge. Otherdefects, which may produce gap states, have been proposed (Ovshinsky and Adler1978, Tarnow et al. 1989, Simdyankin et al. 2005), while almost all have not beenexperimentally confirmed.

A repeated subject on defects in chalcogenides is the charged dangling bond,D+ and D− in the notation by Street and Mott (1975). Here, D stands for an atomhaving a dangling bond. The atom is in general neutral, which is expressed as D0.However, it was known that the chalcogenide glass, except Ge-chalcogenides, doesnot provide ESR signals. Or, more precisely, the spin density of unpaired electrons ina-Se and As-chalcogenide glasses is smaller than an instrumental detection limit of∼1015 spin/cm3 (Agarwal 1973), which manifests the non-existence of D0. Despitesuch observations, experiments demonstrate, e.g., pinned (doping-insensitive) Fermilevel and trap-limited hole transport, which may suggest the existence of substan-tial numbers of gap states. To settle down these puzzling features, Street and Mott(1975) have proposed, taking the concept of negative electron correlation energy(attracting two electrons) proposed by Anderson (1975) into account, that positivelyand negatively charged dangling bonds, D+ and D−, exist in more stable ways thanthe neutral D0. Note that these charged defects are ESR-inactive, consistent with theobservation, since there are no unpaired electrons in D+ and D−. They also haveestimated the density of the charged defect at 1017 − 1018cm−3.

Later, Kastner et al. (1976) developed the concept, proposing a valence-alternation pair model, which relates the charged defects to the ill-coordinated atoms(Fig. 4.9). They use notations such as C1

−, which denotes a onefold coordinatednegatively charged chalcogen. In this model, formation energies of 2C1

0 (2D0) and

94 4 Electronic Properties

−2Eσ

−2Eσ+Δ

−3Eσ

− Eσ

−Eσ+ULP

Fig. 4.9 Structure of a chalcogen in normal (C20) and defective (other) states (Kastner et al. 1976,

© American Physical Society, reprinted with permission) and the electronic energies. The energylevel consists of the three: from the top σ ∗, lone-pair electron, and σ states. Adjusting an energyscale for the lone-pair electron state as a reference, we define −Eσ to be the bonding energy,Eσ + � the anti-bonding (∼bandgap) energy, and ULP the correlation energy between pairs oflone-pair electrons

C3+ + C1

− are estimated to be −2Eσ and −4Eσ + ULP, which suggests higherchemical stability of the charged pair and, accordingly, supports their existence.Rigorously speaking, the concepts by Street and Mott (charged dangling bond)and Kastner et al. (valence-alternation pairs) are somewhat different, while we willhereafter regard these models to be conceptually the same.

The charged pair model has been widely employed and extended (Mott and Davis1979). It is theoretically predicted that D− and D+ produce gap states, respectively,above the valence band and below the conduction band. Many observations such asthe Urbach energy, ESR, and photoluminescence have been interpreted on the basisof this model (Kolobov et al. 1998, Taylor 2006). Some researchers extend this ideaalso to the oxide, SiO2 (Martin-Samos et al. 2007). On the other hand, Baranovskiiand Karpov (1987) propose a model, which applies Anderson’s concept (1975) topolarons.

In contrast to such wide applications, the charged pair model remains a sub-ject of controversy. Structural experiments are unable to give convincing results.Indeed, we have no tools which can detect point-like defects with a density of∼1018 cm−3 in disordered lattices. Raman scattering spectroscopy may be the mostsuitable for detecting ESR-insensitive defects, while its sensitivity seems to be∼1%, ∼1020cm−3, at the best. In addition, some experiments provide negativeresults for the existence, an example being the viscosity in Se. Liquid Se is assumedto be a mixture of chain molecules, and as shown in Fig. 4.10 the lengths at themelting point Tm are estimated to be 105−106 from viscosity and magnetic measure-ments (Warren and Dupree 1980). When quenched into a glassy state, chain endswill be connected, so that the chain will become longer. Thus, the dangling bondbecomes fewer than 1016 cm−3, which is substantially smaller than the predictedcharged defect density of 1018 cm−3.

4.5 Optical Property 95

Fig. 4.10 Average chainlength of Se as a function oftemperature (modified fromWarren and Dupree 1980).Full curves are obtained from77Se NMR, MWP frommagnetic susceptibility, andKB from viscosity. Tm is themelting temperature and Tc isthe super-critical temperature

The model is questionable also from a theoretical point of view. In non-crystalline solids, any kind of (point) defects might exist, and accordingly, whatis important is the number density N, which can be estimated from the formationenergy G as N = N0 exp(−G/kB Tg) under an assumption of local thermal equi-librium at the glass transition temperature Tg. If N < 1015 cm−3, the defect will beneglected in practice. However, theoretical estimation of G is very difficult, since weshould consider related charge distributions and lattice distortions. Actually, calcu-lations for the simplest materials, a-Se (Vanderbilt and Joannopoulos 1983) and a-S(Itoh and Nakao 1986), cannot provide conclusive evidence of the (non-)existence.In short, although the charged pair model remains a good working hypothesis, itsexistence has not been confirmed.

4.5 Optical Property

Having seen the relationship between the atomic and the electronic structure, thenext subject is to relate the electronic structure with optical properties. Here, thefundamental optical properties are absorption and refraction with the coefficients α

and n (or, equivalently, ε1 and ε2), which are connected through Kramers–Krönigrelations (Kittel 2005).

Which is a more intuitive quantity, α or n? Comparing absorption and refraction,we know that absorption is related more directly to the DOS with a simpler expres-sion such as Equation (4.1). Accordingly, it is instructive to consider the absorption(or ε2) first, the examples being given in Fig. 4.11, which will be transformed to

96 4 Electronic Properties

10–6

10–4

10–2

100

106

104

102

0 1 2 3 4 5 6 7 8 9 10 11 12 13

Abs

orpt

ion

coef

ficie

nt (

cm–1

)

Photon energy (eV)

10 K

As2S3

180 KSiO2

10 K

Fig. 4.11 Optical absorption (solid lines) and photoconductive (dashed lines) spectra in As2S3and SiO2 glasses. Without the results indicated as 10 and 180 K, the spectra are obtained at roomtemperature (Tanaka 2002, © INOE, reprinted with permission)

the refractive index (or ε1) through the Kramers–Krönig relation. Note that the opti-cal absorption at infrared regions arises from atomic vibrations, while this sectionfocuses on the electronic transition.

4.6 Optical Absorption

The optical absorption coefficient, α(�ω), for electronic transitions in disorderedsemiconductors can be written as (Mott and Davis 1979)

α(�ω) ∝ |< ϕf| H|ϕi >|2∫

Df(E + �ω) Di(E) dE, (4.1)

where ϕ is an electron wavefunction (not Bloch functions, but atomic), H theelectron–light interaction Hamiltonian, D the density of state, E the electron energy,and the subscripts i and f initial and final states, respectively. In this equation, thewave-vector conservation rule is neglected due to localized wavefunctions in dis-ordered materials (Section 4.1). Absorption occurs through the so-called non-directtransition. In addition, the transition probability |< ϕf| H|ϕi >|2 is assumed to beindependent of E, which seems to be a critical assumption. Polaron effects arealso neglected implicitly. Under these frameworks, as given by Equation (4.1), theabsorption coefficient can be expressed simply by a product of the transition prob-ability |< ϕf| H|ϕi >|2 and the convolution integral

∫Df(E + �ω)Di(E)d E of the

DOSs.On the other hand, experimentally obtained absorption spectra α(�ω) in amor-

phous semiconductors such as As2S(Se)3 have been approximated by the three func-tions. From high to low absorption regions, α(�ω) ∝ (�ω − Eg

T)n, exp(�ω/EU),and exp(�ω/EW), as described below.

4.6 Optical Absorption 97

4.6.1 Tauc Gap

At α � 103cm−1, we approximate the absorption spectrum as (Mott and Davis1979)

α(�ω) ∝ (�ω − EgT)n. (4.2)

Here, EgT is the so-called Tauc optical gap and n = 2 in simple materials such

as As2S(Se)3 and n = 1 in a-Se.1 At �ω = EgT, α ≈ 103 − 104cm−1 in many

materials. It should be noted that, for evaluating absorption spectra at these highabsorption regions from optical transmittances, we need thin samples with thick-nesses of ∼α−1, which is 1–10 μm. Such thin samples may be prepared throughvacuum deposition, while the property is likely to be different from that of the corre-sponding bulk glass. Taking such features into account, reproducibility of absorptionspectra among many reports is acceptable, as exemplified for As2S3 in Fig. 4.12.In oxide glasses, the absorption edge is located at ultraviolet regions, reflectingbandgap energies greater than ∼5 eV, so that the absorption spectra have been eval-uated in a few materials such as Si(Ge)O2 (Saito and Ikushima 2000, Terakado andTanaka 2008).

Temperature dependence of EgT (or Eg) has been studied for several materials.

As exemplified in Fig. 4.13 for As2Se3, ∂ Eg/∂ T < 0 in amorphous semiconductors

Fig. 4.12 Optical absorptionedges of a-As2S3 at roomtemperature, reported fromseveral groups. Note thatlower and higher absorptionsthan ∼103cm−1 are measuredusing bulk samples anddeposited films. Tauc gaps arelocated at 2.35–2.40 eV

1Theoretically, we may multiply the right-hand side by 1/ω, while the factor gives least effects.Absorption with n = 2 appears also in indirect transitions in crystals, which suggests that static andvibrational disorders play similar (neglecting and suppressing wavenumber conservation) roles inthe electronic excitation.

98 4 Electronic Properties

Fig. 4.13 Temperaturedependences of the opticalgap Eg and the Urbach energyEU of As2Se3 (modified fromAndreev et al. 1976)

(Andreev et al. 1976, Tichý et al. 1996, Inagawa et al. 1997). The negative depen-dence can be interpreted following the conventional electron–phonon couplingmodel for semiconductors.

On the other hand, pressure dependence is interesting. To the authors’ knowl-edge, all the amorphous semiconductors exhibit negative pressure dependence∂ Eg/∂ P � 0, as in Fig. 4.14 for g-As2S3 (Weinstein et al. 1980). In detail,however, ∂ Eg/∂ P ≈ 0 in a-Si(Ge):H, while negative pressure dependence isprominent (∼10 meV/kbar) in the chalcogenide (Fig. 1.25), which is interpreted asa manifestation of widening of the lone-pair electron band resulting from enhancedintermolecular interaction by compression (Zallen 1983, Tanaka 1989). Notethat ∂ Eg/∂ P > 0 in many (direct-gap) crystalline semiconductors such as ZnTe

Fig. 4.14 Optical transmittance of a-As2S3, in comparison with that in c-ZnTe, as a function ofhydrostatic compression (Weinstein et al. 1980, © Elsevier, reprinted with permission). The upperand lower scales apply to ZnTe and As2S3

4.6 Optical Absorption 99

(Figs. 1.25 and 4.14), which can be ascribed to reductions in covalent bond lengths(Ghahramani and Sipe 1989).

As shown in Fig. 4.12, the high absorption spectra experimentally obtained arefairly reproducible, while the interpretation remains vague. It has not been eluci-dated whether the Tauc curve arises from band-to-band (extended-extended states)or band-to-edge (extended-localized states) transitions. If the Tauc gap is governedby the transitions between the extended states, it should be equal to the mobilitygap, which is not consistent with observations. (For a-C:H films, Cherkashinin et al.(2006) report a big difference: the mobility gap of ∼5.3 eV and the Tauc gap of∼1 eV.) Such results probably evince that the Tauc gap arises from optical transi-tions between localized and extended states. Then, does the localized state belongto the valence band or the conduction band? In addition, why can the curve be fittedto such high photon energy regions up to (1.5 − 2) × Eg in a-As2S3? We have notyet obtained clear answers.

4.6.2 Urbach Edge

At 103cm−1 � α � 100cm−1, α follows the so-called weakly temperature-dependent Urbach edge (Mott and Davis 1979). The curve has an exponentialform as

α(�ω) ∝ exp (�ω/EU), (4.3)

where EU is referred to as the Urbach energy. It possesses positive temperaturedependence, ∂ EU/∂ T > 0 (Fig. 4.13), in many chalcogenide glasses (Andreevet al. 1976, Tichý et al. 1996), which is common to that in crystals such as AgBrand GaAs (Johnson and Tiedje 1995). On the other hand, as exemplified in Fig. 4.14,∂ EU/∂ P > 0 for all the chalcogenide glasses examined (Tanaka 1989). We shouldmention, however, that not all the glasses exhibit the Urbach edge, as demonstratedfor a ternary system As–S–Te (Farag and Edmond 1986).

Origins of the Urbach edge are also unclear. The temperature-dependent Urbachedge, α ∝ exp(�ω/kBT), appearing in polar crystals has been interpreted by assum-ing optical absorption by excitons in electric fields. In contrast, in many amorphoussemiconductors, the Urbach edge is nearly temperature independent around roomtemperature (Fig. 4.13), which is interpreted in two ways. The first one ascribesit to a polaron effect (Fig. 4.4). If the lattice is flexible as in Se, electron–latticeinteraction possibly governs the absorption spectrum (Abe and Toyozawa 1981).On the other hand, several studies using structural and optical experiments for a-Si:H, As2S3, and SiO2 (Kranjcec et al. 2009) suggest close connections betweenEU and static structural disorder, which support an idea based on disorder-inducedband tailings (Ihm 1985, Pan et al. 2008, Sadigh et al. 2011). It is also mentionedthat Okamoto et al. (1996) have theoretically considered a correlation between Eg

T

and EU, the result requiring a total understanding of the Tauc and the Urbach curve.

100 4 Electronic Properties

Coordination number Z

Fig. 4.15 The Urbach energyEU as a function of theaverage coordination numberZ (Oheda 1979, Andreevet al. 1976) for the glassysystems listed

In addition to these ambiguous origins, the Urbach curve manifests, at least, twopuzzling features as the following.

One is the existence of a minimal Urbach energy of EU ≥ 50 − 60 meV inamorphous materials (Tanaka 2002). The value is surprisingly universal (Dunstan1982) including SiO2 (Saito and Ikushima 2000), As2S3, Se, Ge2Sb2Te5 (Kato andTanaka 2005), other chalcogenide alloys (Inagawa et al. 1997), and even a-Si:H andpolyacetylene (Weinberger et al. 1984), despite big differences of Eg ≈ 1 − 10 eV.However, no ideas have been put forward on this universality. If the Urbach energy isdetermined by structural order, the minimal energy may imply a “minimal structuraldisorder.” In contrast, we should also note that some materials such as GeO(S)2show less steep Urbach edges (Terakado and Tanaka 2008), which may be governedby defects. In addition, as shown in Fig. 4.15, in non-stoichiometric binary alloys,the Urbach energy tends to become greater than the minimal values at stoichiometriccompositions.

The other is the existence of an Urbach-edge focus. The feature has been dis-covered for a-Si:H films by Cody et al. (1981), which was pointed out later alsofor temperature variations in As2S3 and SiO2 (Kranjcec et al. 2009). In α =α0 exp (�ω/EU), α0 and EU have a relation as α0 = α00 exp(EU/E0), where α00and E0 are constants characterizing the focusing point. This relationship appearsfunctionally similar to that of the Meyer–Neldel rule (Section 4.9.3), while itsimplication remains to be considered.

4.6.3 Weak Absorption Tail

Below ∼100cm−1, α shows another more gradual exponential spectrum:

α(�ω) ∝ exp(�ω/EW), (4.4)

4.6 Optical Absorption 101

which is referred to as a “weak absorption tail” or “residual absorption” (Mott andDavis 1979). For instance, EW ≈ 200 meV in g-As2S3 (Tanaka et al. 2002). Precisemeasurements of this absorption tail, however, are relatively difficult due to thesmall absorption (≤ 100 cm−1), which should be distinguished from light scattering.Accordingly, reported results are few. In some measurements, photo-thermal spec-troscopy, which is less influenced by light scattering, has been employed (Tanakaet al. 2002). Note that it is not clear if a-Se exhibits the absorption tail (Tanaka et al.2002). The situation in g-SiO2 is also unclear, which gives several absorption peaks(not the exponential tail) below the Urbach edge, which are attributed to defects andimpurities (Kajihara et al. 2008).

For the absorption tail in g-As2S(Se)3, impurities are undoubtedly an origin.An example is shown by the solid lines in Fig. 4.16a, in which the Fe content inAs2S3 is systematically changed (Tauc 1975). We see that Tauc’s purest As2S3 sam-ple, denoted as “pure,” has maximal absorption of 10−1 cm−1 at ∼1.5 eV, whilethe level is further decreased by one order in a more recent sample (Tanaka et al.2002). In addition, Kitao et al. (1977) have demonstrated systematic increases inthe tail absorption, without a notable change in the Urbach edge, by addition of Ag(<2.5 at.%) to As2Se3. Therefore, it is tempting to assume that the absorption tailwill disappear in ultimately pure samples.

Nevertheless, the composition dependence shown in Fig. 4.16b reveals anotherfeature. In the As–S system, the weak absorption tail appears to be most prominentaround the stoichiometric composition As2S3 (Tanaka et al. 2002). We then envisage

0.5 1 1.5 2 2.5 3

Photon energy (eV)

x = 35

4 14 0

2 5

4 3

1 7

10–2

10–1

100

101

0 2 0 4 0 6 0As at .%

α (c

m–1

)

10–3

10–1

10–2

100

101

102 102

103

10–3

10–1

10–2

100

101

103

104

1 1.5 2 2.5

(a) (b)

3

Abs

orpt

ion

coef

ficie

nt (

cm–1

)

Abs

orpt

ion

coef

ficie

nt (

cm–1

)

Photon energy (eV)

200 ppm

120

26

pure

Fig. 4.16 Dependences of the weak absorption tail on (a) purity in As2S3 and (b) composition inAsxS100–x (modified from Tanaka et al. 2002). In (a), the solid lines are given by Tauc and circledspectra are by Tanaka for two kinds of samples. Note that the vertical scales of the two graphsare common. The inset in (b) shows the composition dependence of the absorption coefficient at�ω = 1.5 eV

102 4 Electronic Properties

that the wrong bond such as As–As is responsible for the tail. Actually, as mentionedin Section 4.4, Vanderbilt and Joannopoulos (1981) theoretically suggest that anAs–As σ ∗ bond produces a gap state below the conduction band in As2Se3. On theother hand, Andreev et al. (1976) assume that the tail in As2Se3 reflects free-carrierabsorption, since the absorption becomes higher at higher temperatures in propor-tion to the dc electrical conductivity. It seems that the weak absorption tail arisesfrom several origins including impurities. However, why the tail is exponential hasnot been considered so far.

4.7 Refractive Index

Once the absorption spectrum has being determined, now turn to the refrac-tive index. Figure 4.17 presents n0(ω) for g-As2S(Se)3 (Young 1971, Butterfield1974). We can calculate the refractive index spectrum n0(ω) using Kramers–Krönigrelation:

n0(ω) = 1 + (c/π ) P∫

{α()/(2 − ω2)}d, (4.5)

which is derived from a causality principle (Kittel 2005). Here, c is the light velocityand P denotes the principal value. This equation shows that, for calculating n0, weneed the data of α() at = 0 − ∞, which is practically impossible. Accordingly,

Fig. 4.17 Refractive indexspectra of g-As2S3 (solidline) and g-As2Se3 (dashedline). The wavelengthscorresponding to the Taucoptical gaps are indicated

4.8 Optical Nonlinearity 103

W-D

Fig. 4.18 Relationship between an atomic bonding structure and optical properties (α, Eg, β,n0, n2) with some equations connecting the properties (modified from Tanaka (2006)). The dou-ble arrows represent linear and nonlinear Kramers–Krönig relations and W-D stands for theWemple–DiDomenico relation

some approximations are taken into account. For instance, assuming that absorptionin semiconductors arises from a classical single oscillator, Moss (1985) has deriveda simple equation, the so-called Moss rule:

n04Eg [eV] = 77 [eV]. (4.6)

Alternatively, Wemple and DiDomenico (1969) approximate the dispersion ofrefractive index as

n0(ω) = [1 + E0Ed/{E02 − (�ω)2}], (4.7)

where E0 is the oscillator energy, which is nearly equal to an average separationbetween the conduction (σ ∗) and the valence (lone-pair electron) band, and Ed isthe oscillator strength. In As2S3, E0 ≈ 4.8 eV and Ed ≈ 22 eV.

On the other hand, the refractive index in wide-gap materials may be expressedby the polarizability. An example often employed for the oxide glass is the Lorentz–Lorenz formula (Equation (6.2)).

4.8 Optical Nonlinearity

The recent progress of nonlinear optics is remarkable, which corresponds to theadvancement of laser technology. At present, a commercially available laser canemit light pulses with a peak power of 1 MW, and if the power is focused to aspot with a diameter of 1 μm, the irradiance reaches 1014 W/cm2. (Note that theionization energy of electrons in H atoms of 13.6 eV corresponds to the field irradi-ance of 5 × 1016 W/cm2 (Boyd 2003)). If such intense light is absorbed in a solid,its temperature rises, and ultimately the solid will vaporize. Or, if the irradiance is

104 4 Electronic Properties

short enough (∼fs), being shorter than thermal relaxation time (∼ps), the field mayinduce athermal nonlinear (multi-photon) phenomena, including nonlinear absorp-tion, ionization, and sputtering. These phenomena are utilized for laser machining,harmonic generation, etc.

Extensive studies have been performed on optical nonlinearity of the secondand the third order (Boyd 2003). For simplicity, we take the polarization P andthe electric field E to be scalar quantities. P can then be written down in CGSunits as

P = χ (1)E + χ (2)EE + χ (3)EEE + · · · , (4.8)

where the first term χ (1)E depicts the conventional linear response, which is relatedto the linear refractive index n0 via n0 = {1 + 4πχ (1)}1/2. The second-order non-linear susceptibility χ (2) can be utilized for generation of second-overtone (2ω)signals, but it is zero in materials having centro-symmetric structures such as con-ventional glass. It exists only in some crystals and poled glasses (Tanaka 2006).Hence, in common isotropic glasses, the last term becomes the lowest-order nonlin-earity. This can be rewritten as χ (3)IE, where I is the light intensity. Accordingly,we may approximate the refractive index n in the glass as

n = n0 + n2I. (4.9)

We here note that n2 in glasses may be smaller than that in crystals (Boyd 2003),because specific atomic structures cannot be produced. However, the glass can belengthened as optical fibers, and thus, apparent nonlinearity can become greater.In addition, the nonlinearity can be added only to selected regions in a glass by light-induced crystallization (Takahashi et al. 2009). For chalcogenide glasses, studiednonlinearities cover self-wave modulations such as self-(de)focusing (Hughes et al.2009), optical bistability (Ogusu et al. 2008), white continuum generation (Psailaet al. 2007), stimulated scattering (Xiong et al. 2009), and third-harmonic generation(Douady et al. 2005) (see also Section 7.2).

Under similar assumptions to those employed in the one-photon absorption(Equation (4.1)), the two-photon absorption (Fig. 4.19b) coefficient β(�ω) can bewritten as (Tanaka 2006)

Fig. 4.19 Schematicillustrations of (a)one-photon, (b) two-photon,and (c) two-step absorption

4.8 Optical Nonlinearity 105

β(�ω) ∝ ∣∣ ∑s

< ϕf|H |ϕs >< ϕs| H|ϕi > /(Esi − �ω)∣∣2

∫Df(E + 2�ω)Di(E) d E,

(4.10)where s is a (virtual) intermediate state and Esi = Es − Ei. In this equation, theconvolution integral is essentially the same as that in Equation (4.1), except forreplacement of �ω by 2�ω. However, the transition probability is markedly differentwith the addition of a denominator Esi −�ω. Similar to the linear optical properties,the intensity-dependent refractive index n2 can practically be related with β as

n2(ω) ≈ (c/π ) P∫

{β(�)/(�2 − ω2)} d�. (4.11)

Reflecting these relations, as shown in Fig. 4.20, β and n2 spectra shift to�ω ≈ Eg/2.

In amorphous semiconductors having mid-gap states, the two-photon processtends to show different behaviors from those in the crystal in two respects. Oneis the occurrence of a two-step absorption, Fig. 4.19c, which referes to successiveone-photon absorptions through a mid-gap state. The other is a resonant two-photonabsorption, in which Esi − �ω becomes zero for a mid-gap state. Which process ismore dominant depends upon the cross sections of each process, which may varywith �ω. Enck (1973) reports a pioneering experiment of two-photon absorptionsfor a-Se.

The two-photon process is interesting from the point of view of application, anda lot of studies have been published for materials having high n2. Boling et al.(1978) have demonstrated that, in transparent materials, n2 increases with n0. On theother hand, Tanaka (2006) has adopted a universal relationship to glasses. The rela-tionship, which was developed for crystalline semiconductors and insulators bySheik-Bahae et al. (1990), takes the form of

(b)(a)

Fig. 4.20 Spectral dependence of (a) linear absorption α, linear refractive index n0, two-photonabsorption β, and intensity-dependent refractive index n2 in direct-gap semiconductors and(b) α (dashed lines) and β (solid lines) in some glasses (Tanaka 2006, © Springer, reprinted withpermission)

106 4 Electronic Properties

Fig. 4.21 Dependences of n0and n2 on Eg withexperimental results ofglasses, crystals, andzeolite-Se (Saitoh andTanaka, 2011). Sheik-Bahae’srelation n2∼1/Eg

4 and Mossrule n0∼Eg

1/4 are shown byupper and lower lines

n2 (esu) = K G(�ω/Eg)/(n0Eg4),2 (4.12)

where Eg is the bandgap energy (1–10 eV), K a fixed constant (= 3.4 × 10−8 forEg in eV unit), and G(�ω/Eg) a spectral function. For a glass, we may take the Taucgap as Eg, if it is known, or otherwise the photon energy �ω at α ≈ 104cm−1.Note that this equation contains no fitting parameters. We see in Fig. 4.21 thatthe universal line gives reasonable, but not satisfactory, agreements with publisheddata for glasses. The worse agreement in the glass compared to that in crystals(Sheik-Bahae et al. (1990)) may be partly due to experimental difficulties includ-ing quasi-stabilities in glasses. In addition, the band-tail states, which are not takeninto account in the equation, possibly cause larger deviations in smaller bandgapglasses such as Ag20As32Se48. From the fitting, we can predict that a maximal n2obtainable in homogeneous materials at the optical communication wavelength of∼1.5 μm is 10−3 cm2/GW.

4.9 Electrical Conduction

4.9.1 Background

Before describing the electronic transport in glasses, it may be valuable to recall thefundamentals in crystalline semiconductors (Kittel 2005). The electrical conductiv-ity σ can be written in the Drude model for a unipolar (electron or hole) system asσ = eμN, where N is the carrier density and μ is the mobility, which is written asμ = eτ/m∗ using a collision time τ and an effective mass m∗. If the carrier is anelectron, N is given as N = ∫

DC(E) F(E) d E, where DC(E) is the density of state ofthe conduction band and F(E) the Fermi distribution function. Under the condition

2A slightly different expression was given later. See Saitoh and Tanaka (2011).

4.9 Electrical Conduction 107

of EC − EF � kBT , where Ec is the energy of the conduction band bottom and EFthe Fermi energy, σ can be approximated as

σ ≈ eμNC exp[−(Ec − EF)/kBT] = σ0 exp(−�E/kBT), (4.13)

where NC is the effective density of state of the conduction band and �E (= Ec−EF)is the activation energy. In crystalline semiconductors, the conduction type as n andp is defined with respect to the species of majority carriers, which is connectedwith the position of the Fermi level EF. Experimentally, the carrier density N isdetermined from Hall effect measurements (∼1/eN). And, the (band) mobility μ iscalculated from σ and N.

However, in amorphous semiconductors, the Hall effect is useless for determi-nation of the carrier type. The Hall voltage exhibits an opposite sign (holes andelectrons give negative and positive voltages) to that determined by thermopower(Kittel 2005). This phenomenon is called the pn anomaly (Mott and Davis 1979,Elliott 1990), which is assumed to occur when the carrier mean free path approachesthe interatomic distance. As a consequence, we cannot apply a standard transporttheory based on Boltzmann equation to the amorphous semiconductor. A quantuminterference effect of electron transport near the mobility edge may be needed forunderstanding the pn anomaly (Mott 1993).

We then determine the conduction type using other methods. In relativelyconducting materials such as As2Te3, thermopower is useful. Alternatively, theconduction type in insulating glasses such as As2S(Se)3 has been probed usingphoto-electrical methods such as xerographic discharge, optical time of flight, orDember effect, which are assumed to contain information of μτ (see Section 5.4).For instance, g-As2S3 gives a time-of-flight signal only of holes. Accordingly, wecan state that “the hole is mobile in g-As2S3,” but it may cause misunderstandingif we write that “g-As2S3 is of p-type.” We also note that the mobility determinedfrom the time-of-flight method is not the so-called band mobility, but an effectiveone including (de-)trapping processes.

4.9.2 Carrier Transport

It is known that carrier transports in the oxide and the chalcogenide glass are con-trastive. A general tendency is, as listed in Tables 4.2 and 4.3, that electrons aremobile in the oxide but holes are mobile in the chalcogenide. Interestingly, in almostall of the corresponding crystals, electrons appear to be more mobile.

Table 4.2 List of mobilecarriers in the crystalline andglassy materials

Crystal Glass

SiO2 e eAs2S(Se)3 e hSe h (e) h

108 4 Electronic Properties

Tabl

e4.

3Ta

ucop

tical

gap

Eg

T,U

rbac

hen

ergy

EU

,ste

epne

sspa

ram

eter

sof

the

vale

nce

band

edge

E0

Van

dth

eco

nduc

tion

band

edge

E0

C,e

lect

ron

and

hole

mob

ilitie

sμ

ean

dμ

hat

room

tem

pera

ture

,and

theo

retic

alef

fect

ive

mas

ses

me∗ /

m0

and

mh∗ /

m0

(m0

isth

efr

eeel

ectr

onm

ass)

(mod

ified

from

Tana

ka20

02)

Mat

eria

lE

gT

[eV

]E

U[m

eV]

E0

V[m

eV]

E0

C[m

eV]

μe

[cm

2/V

s]μ

h[c

m2/V

s]m

e∗ /m

0m

h∗ /

m0

c-S

g-Se

∼4 2.0

5826

5×10

–4

5×10

–3,7

×10–3

1−10

0.10

−0.2

0.5,

4.5

c-Se

(hex

)1.

9X

6−28

c-Se

(rin

g)2.

22

0.2

g-A

s 2S 3

2.4

5455

X10

–5,1

0–10

1.1,

7.5

c-A

s 2S 3

∼2.8

10.

1−1

c-A

s 4S 4

2.4

0.02

12g-

As 2

Se3

1.8

5046

X10

–59.

3c-

As 2

Se3

∼2.1

1−10

,20−

80X

0.3

0.3

g-A

s 2Te

30.

853

3310

–310

–3

g-G

eS2

3.2

130

100

g-G

eSe 2

2.2

7363

0.2

0.04

g-Si

O2

∼9∼6

020

−40

<10

–5

c-Si

O2

∼10

0.3

5−10

g-G

eO2

5.8

∼60

a-Si

:H∼1

.848

4227

0.2

0.01

Opt

ical

gaps

ofcr

ysta

lsar

eev

alua

ted

asph

oton

ener

gies

atth

eab

sorp

tion

coef

ficie

ntof

∼104

cm–1

.Xm

eans

that

nosi

gnal

sar

eob

tain

ed

4.9 Electrical Conduction 109

Why is a hole more mobile in the chalcogenide glass? Some proposals havebeen offered, but the origin is not elucidated. Kolobov (1996) ascribes the feature torelaxation of the valence-alternation defects, C3

+ and C1−, in which the former is

assumed to be more effective in trapping electrons. Tanaka (2002) proposes that theimmobility of electrons is governed by the tail state below the conduction band.The tail state in As2S(Se)3 seems to arise from σ ∗(As–As) states as mentionedpreviously, which reduce electron transport through trapping.

We here note, however, that at least three kinds of electron-mobile non-crystalline chalcogenides are known to exist. First, Ovshinsky (1977) demonstratedthe so-called chemical modification, which denotes an extrinsic conduction in sput-tered chalcogenide films doped by transition metals (Ni, etc.). Such modificationmight be plausible, since a sputtered film could be far from equilibrium. Second,Tohge et al. (1980) discovered electron conductions in Bi- and Pb-containingchalcogenide glasses. Matsuda et al. (1996) have demonstrated using (inverse) x-rayphotoelectron spectroscopy that, in Bi–Ge–Se films, the Fermi level approaches theconduction band with an increase in Bi. However, it has not been known if the samesituation occurs in the bulk glass. Third, Narushima et al. (2004) demonstrated thata-In49S51 films show prominent electron conduction with mobility of 26 cm2/V s,which may be related to fourfold coordinated S atoms, in a similar way to that inc-CdS, etc.

Figure 4.22, which compares reported mobilities μ in amorphous and crys-talline semiconductors as a function of the bandgap Eg, presents interesting features.First, in the crystal, a general tendency is a decrease in the band mobility with anincrease in Eg, which is understood through the kp perturbation theory predictingμ ∝ Eg

−1 (Kittel 2005). We see similar tendencies in chalcogen (Te, Se, and S) andchalcogenide crystals (As2Se3, As4Se4, and As2S3). Second, among the glasses,SiO2 shows an exceptionally high electron mobility of ∼30 cm2/V s, which maybe a macroscopic value, being limited by (de-)trapping processes. This electronmobility in g-SiO2 appears to be related with that in the corresponding crystal.We see in the dispersion curve (Fig. 4.6b) of c-SiO2 that the effective electron

Fig. 4.22 Relations betweenthe energy gap Eg and theband and macroscopicmobilities μ for crystalline(square) and amorphous(circles) materials. Solid andopen symbols depict electronand hole, respectively

110 4 Electronic Properties

Fig. 4.23 Tauc gap (solidline) and electron (•) and hole(◦) mobilities in As-Sesystem (data from Fisheret al. 1976 and Péturssonet al. 1991)

mass is appreciably (by an order) smaller than the hole mass. The result can beinterpreted chemically, i.e., Si4+ d-electron wavefunctions extend more widely thanO2− lone-pair electron wavefunctions. And, as known, the smaller mass gives ahigher band mobility. In addition, the d-electron wavefunction is more sphericalthan the p-electron wavefunction, and accordingly, the former is possibly less sen-sitive to structural disordering, giving rise to ∼30 cm2/V s. This high mobility isconsistent with a long mean free path of electrons in g-SiO2 of ∼3 nm (Chua andOsterberg 2004). Third, except for SiO2, (semi-)elemental materials including a-Se(hole) and a-Si:H (electron) have macroscopic mobilities of ∼1 cm2/V s, which aresubstantially higher than those (10−2−10−8cm2/V s) in binary chalcogenide alloys.Adriaenssens and Eliat (1996) have pointed out a similar tendency for a-Si(C,S):Hfilms, which they ascribe to the difference in potential fluctuations in elemental andmulti-component non-crystalline materials. Finally, we see that the hole mobility inamorphous As2S(Se,Te)3 decreases with an increase in Eg. This trend may implythat trapping states with a depth of Et, which may scale with Eg, govern the holetransport.

However, there remain many results which wait for further consideration. Forinstance, how can we interpret the composition dependence of electron and holemobilities in As-Se glasses, shown in Fig. 4.23?

Effects of impurities, such as oxygen, on the electrical conduction in a-Se havebeen repeatedly studied for two reasons (Belev et al. 2007). One is that the mate-rial is the simplest amorphous semiconductor, and the other is that a-Se films havebeen employed in photoconductive devices. However, impurity effects have not beenelucidated. We also mention here that the mean Se chain length appears to be animportant factor affecting photo-electric properties (Suzuki et al. 1987).

4.9.3 Meyer–Neldel Rule

Amorphous semiconductors present a puzzling feature in the prefactor of electricalconduction (Elliott 1990, Mott 1993). As known, in a standard transport theory

4.9 Electrical Conduction 111

for disordered semiconductors, σ 0 in Equation (4.13) takes a constant value ofeμN (∼150 S/cm). In contrast, Meyer and Neldel discovered in a variety of TiO2samples that the prefactor σ 0 can be written as (Mehta 2010)

σ0 = σ00 exp (�E/EMN), (4.14)

where σ 00 is a constant (10−17−1 S/cm−1), �E the activation energy (Ec − EFfor electron), and EMN (25−60 meV) a characteristic energy. This relation, whichis now called as the “Meyer–Neldel rule,” universally holds for many groupsof materials such as a-Si:H films (Stuke 1987) and As–S–Se glasses (Fig. 4.24)(Shimakawa and Abdel-Wahab 1997, Mehta 2010). The Meyer–Neldel rule is alsofound in organic semiconductors (Kemeny and Rosenberg 1970), liquid semicon-ductors (Fortner et al. 1995), and ionic conductors (Ngai 1998). The prefactor σ 0can no more be regarded as a microscopic conductivity, since the largely varyingvalue of σ 0 is not easy to be understood by the standard theory. Instead, σ 00 mayhave a physical meaning of a microscopic conductivity, i.e., σ00 = eμN.

Although the universal interpretation of the Meyer–Neldel rule is still a matterof debate, the most accepted one for a-Si:H is to assume a statistical shift of Fermilevels, or a temperature-dependent Fermi level, EF(T) = EF(0) − γ T , where EF(0)is a constant and γ takes a positive value (Elliott 1990, Overhof and Thomas 1989).Then, the activation energy �E for electrons becomes Ec−EF(T) = Ec−EF(0)+γ T .By inserting this �E into Equation (4.13), we have σ = σ0 exp(−�E/kBT) =σ0 exp(−γ /kB) exp(−�E(0)/kBT), where �E(0) = Ec − EF(0). In such cases,the actual pre-exponential term appears to be not σ 0 in Equation (4.13), butσ0 exp(−γ /kB), with �E(0) corresponding to the observed activation energy �E.We can also show that γ /kB becomes a function of �E(0), in agreement withEquation (4.14).

However, the model cannot quantitatively explain small σ 00 in other materials.For this problem, Emin (1975, 2008) interprets the value of 10−15−10−5 S/cm in

Fig. 4.24 Thepre-exponential factor σ 0plotted as a function of theelectrical activation energy�E, the slopes correspondingto 1/EMN, for the threechalcogenide systemsindicated (modified fromShimakawa andAbdel-Wahab 1997)

112 4 Electronic Properties

chalcogenide glasses using a polaron concept. Shimakawa and Abdel-Wahab (1997)interpret 10−17−10−3 S/cm in organic semiconductors using an electron tunnelingmodel. The latter model is applicable also to the transport in chalcogenide glasses,since the chalcogenide is assumed to have low-dimensional (chain, layer) structuresand hence the carrier must tunnel through intermolecular potential barriers. Yelonet al. (2006) propose a model by introducing the concept of multi-excitation entropy.

We here add two interesting features. One is a correlation, which is similar inform to Equation (4.14), which exists between σ 00 and EMN:

σ00 = σ ′00 exp (EMN/ES), (4.15)

for many chalcogenide glasses such as P(As)–S(Se,Te) (Shimakawa and Abdel-Wahab 1997), where ES is a constant (∼1.7 meV). No interpretation has been givenfor this correlation. The other is that the functional formula of the Meyer–Neldelrule and the Urbach-edge focus (see Section 4.6.2) are the same, which may be justa coincidence or, otherwise, may arise from a common origin.

4.9.4 AC Conductivity

In ac electrical conductivity, disordered semiconductors exhibit a peculiar depen-dence on frequency. The complex electrical conductivity is defined as σ (ω) =iωε0ε(ω), where ω is the angular frequency of applied electric fields and ε(ω) thecomplex dielectric constant, which is written as ε = ε1 − iε2. Here, ωε0ε2(ω) iscalled the ac conductivity or ac loss, which is written also as σ (ω) for simplicity.The ac conductivity may arise from hopping of electrons, which can be treated asalternating atomic (or molecular) dipoles, and hence the response in general is givenby a Debye-type equation, 1/(1 + iωτ ), where τ is a relaxation time (Kittel 2005).

In contrast, it is known that many disordered semiconductors and insulators,including chalcogenides (Fig. 4.25) and a-Si:H films, exhibit σ (ω) with a power-lawdependence at ω = 102−1010 Hz:

σ (ω) = Aωs, (4.16)

where A and s(< 1.0) are temperature-dependent parameters (Mott and Davis 1979,Elliott 1990). This dependence is often called “dispersive ac loss.”

Interpretations of the dispersive loss may be performed in two ways (Elliott1987). One is to postulate a distribution P(τ ) of τ in the Debye-type equation.Hopping conduction between impurities in compensated c-Si is analyzed using thisidea, in which the electronic hopping distance is assumed to be equivalent to thedipole length. In this model, the parameter A corresponds to the number of dipoles,and hence, the number of hopping sites can be estimated from Equation (4.16).This model may be applied also to evaluations of defects in disordered semiconduc-tors (Elliott 1987, Ganjoo and Shimakawa 1994). The other model assumes kinds

4.10 Compositional Variation 113

electronic

vibrational

interbandtransition

Fig. 4.25 AC conductivity ing-As2Se3 at 300 K

of Maxwell–Wagner effects: the dispersive ac loss arising from macro- or meso-scopic scale inhomogeneities in disordered insulators. A classical effective mediumapproximation is useful for analyses of such inhomogeneous media (Kirkpatrik1973, Shimakawa and Ganjoo 2002).

4.10 Compositional Variation

We can analyze dependence of physical properties on constituent atoms in two ways.One is to characterize the atoms along horizontal directions in the periodic table, anexample being the Z dependence described in the elastic property (Section 3.5). Theother is along vertical directions in the table, or the periodicity.

For the Z dependence in covalent chalcogenide glasses, we can point out simi-lar dependences for the atomic volume Va and the optical gap Eg (Tanaka 1989).Figure 4.26 shows that both tend to decrease with increases in Z, accompanying(traces of) minima at 2.4 and maxima at 2.67. How can we grasp such resemblingZ dependences? A plausible interpretation is as follows.

The atomic volume (per mole) Va for a D-dimensional solid can be estimated as

Va(D) � Na rDR3−D, (4.17)

where Na is the Avogadro number and r and R denote the lengths of covalent(∼0.2 nm) and van der Waals (∼0.5 nm) bonds, respectively. We here assume thatfor a change in Z from 2 to 2.4, D changes from 1 to 2, which causes the decrease inVa. From 2.4 to 2.67, structural analyses (Section 2.4) imply that R increases from∼0.5 to ∼0.6 nm and, accordingly, Va increases. From 2.67 to 4, it is reasonable toassume a gradual change in D from 2 to 3, giving rise to the Va decrease.

114 4 Electronic Properties

(a) (b)

Fig. 4.26 Dependences of (a) atomic volume and (b) optical gap on the average coordination num-ber Z in some sulfide and selenide glasses (Tanaka 1989, © American Physical Society, reprintedwith permission)

On the other hand, the optical gap Eg can be written as

Eg � E0 − Ev/2 − Ec/2, (4.18)

where E0 (5−10 eV) is the energy separation between the centers of the conductionand valence bands, and Ev and Ec are their band widths (∼4 eV). Here, provided thatthe atom periodicity is held constant, E0 remains constant, which reflects the bondstrength in simple tight-binding models, or it is at least modified monotonically.Next, in lone-pair electron semiconductors such as the chalcogenide glasses, Ev ∝exp(−R/ξ ), where ξ is assumed to be a constant representing a spatial extensionof lone-pair electrons, and Ec ∝ <T> Z, where <T> represents a transfer integral,which increases with an increase in spatial extension of bonding electrons. We thencan relate the decrease in Eg from 2 to 2.4 with the increase in Z. The increase in Egfrom 2.4 to 2.67 is ascribed to the increase in R. Lastly, the Eg decrease from 2.67to 4 again reflects the Z increase. Note that this kind of Z dependence cannot existin the oxide glass and is less clear in the telluride material, due to their ionic andmetallic characters.

The Eg decrease with the periodicity can also be understood. For instance,Fig. 1.12c shows that Eg in As2O(S,Se,Te)3 is ∼4, 2.4, 1.8, and 0.8 eV, which isunderstood to be a manifestation of a decrease in E0, arising from reduction of thecovalent bond strength, in Equation (4.18) (see Fig. 1.10).

In addition, we can point out an interesting feature of Eg in the periodicity.As shown in Fig. 1.12c, Eg of the oxides, Si(Ge)O2 and As2O3, appreciably changeswith the cation atoms (Si, Ge, As), while Eg in Si(Ge,As)–Te appears to be uniquely

References 115

determined by Te, mostly irrespective of the cation species. It seems that all theamorphous telluride materials have Eg of ∼1.0 eV. Why? A notion is to take themetallicity of Te into account. Jovari et al. (2008) demonstrate that, in As–Te, themetallicity causes a lot (∼50%) of Te–Te homopolar bonds, i.e., the atomic bondis chemically disordered. This observation may suggest that Te clusters govern theoptical gaps in tellurides, which become nearly equal to that in pure a-Te.

References

Abe, S., Toyozawa, Y.: Interband absorption spectra of disordered semiconductors in the coherentpotential approximation. J. Phys. Soc. Jpn. 50, 2185−2194 (1981)

Adriaenssens, G.J., Eliat, A.: In: Andriesh, A., Bertolotti, M. (eds.) Physics and Applications ofNon-Crystalline Semiconductors in Optoelectronics, pp. 77–91. Kluwer, Dordrecht (1996)

Agarwal, S.C.: Nature of localized states in amorphous semiconductors − A study by electron spinresonance. Phys. Rev. B 7, 685−691 (1973)

Anderson, P.W.: Model for the electronic structure of amorphous semiconductors. Phys. Rev. Lett.34, 953−955 (1975)

Andreev, A.A., Kolomiets, B.T., Mazets, T.F., Manukyan, A.L., Pavlov, S.K.: Temperature depen-dence of the absorption edge of As2Se3 and AsSe in the solid and liquid states. Sov. Phys. SolidState 18, 29−31 (1976)

Baranovskii, S.D., Karpov, V.G.: Localized electron states in glassy semiconductors (review). Sov.Phys. Semicond. 21, 1−10 (1987)

Baranovskii, S., Rubel, O.: Charge transport in disordered materials. In: Kasap, S., Capper, P. (eds.)Springer Handbook of Electronic and Photonic Materials, Chap. 9. pp. 161–181 Springer,New York, NY (2006)

Belev, G., Tonchev, D., Fogal, B., Allen, C., Kasap, S.O.: Effects of oxygen and chlorine on chargetransport in vacuum deposited pure a-Se films. J. Phys. Chem. Solids 68, 972−977 (2007)

Benkhedir, M.L., Mansour, M., Djefaflia, F., Brinza, M., Adriaenssens, G.J.: Photocurrent mea-surements in chlorine-doped amorphous selenium. Phys. Status Solidi (b) 246, 1841−1844(2009)

Boling, N.L., Glass, A.J., Owyoung, A.: Empirical relationships for predicting nonlinear refractiveindex changes in optical solids. IEEE J. Quant. Electron. 14, 601−608 (1978)

Boyd, R.W.: Nonlinear Optics 2nd ed. Academic, Amsterdam (2003)Butterfield, A.W.: The optical properties of vitreous AsxSe1-x thin films. Thin Solid Films 21,

287−296 (1974)Chelikowsky, J.R., Schluter, M.: Electron states in α-quartz: A self-consistent pseudopotential

calculation. Phys. Rev. B 15, 4020−4029 (1977)Cherkashinin, G., Ambacher, O., Schiffer, T., Schmidt, G.: Mobility edge in hydrogenated

amorphous carbon. Appl. Phys. Lett. 88, 172114 (2006)Chua, K.-B., Österberg, U.: Electron mean free path in fused silica and optical fiber perform.

J. Appl. Phys. 95, 6204−6208 (2004)Churbanov, M.F., Plotnichenko, V.G.: Optical fibers from high-purity arsenic chalcogenide glasses.

In: Fairman, R., Ushkov, B. (eds.) Semiconducting Chalcogenide Glass III, Chap. 5. pp. 209–230 Elsevier, Amsterdam (2004)

Cody, G.D., Tiedje, T., Abeles, B., Brooks, B., Goldstein, Y.: Disorder and the optical-absorptionedge of hydrogenated amorphous-silicon. Phys. Rev. Lett. 47, 1480−1483 (1981)

Cohen, M.H., Fritzsche, H., Ovshinsky, S.R.: Simple band model for amorphous semiconductingalloys. Phys. Rev. Lett. 22, 1065−1068 (1969)

Douady, J., Boulanger, B., Fuchs, E., Smektala, F., Troles, J.: Symmetry and phase-matching prop-erties of third-harmonic generation under the photoelastic effect in Ge-As-Se chalcogenideglasses. J. Opt. Soc. Am. B 22, 1486−1492 (2005)

116 4 Electronic Properties

Drabold, D.A., Estreichen, S.K. (eds.): Theory of Defects in Semiconductors. Springer, Berlin(2007)

Dunstan, D.J.: Evidence for a common origin of the Urbach tails in amorphous and crystallinesemiconductors. J. Phys. C: Solid State Phys. 15, L419−L424 (1982)

Elliott, S.R.: Ac conduction in amorphous-chalcogenide and pnictide semiconductors. Adv. Phys.36, 135−218 (1987)

Elliott, S.R.: Physics of Amorphous Materials 2nd ed. Longman Scientific & Technical, Essex(1990)

Emin, D.: Phonon-assisted transition rates I. Optical-phonon-assisted hopping in solids. Adv. Phys.24, 305−348 (1975)

Emin, D.: Generalized adiabatic polaron hopping: Meyer-Neldel compensation and Poole-Frenkelbehavior. Phys. Rev. Lett. 100, 166602 (2008)

Enck, R.C.: Two-photon photogeneration in amorphous selenium. Phys. Rev. Lett. 31, 220−223(1973)

Farag, A., Edmond, J.T.: Optical absorption and electrical conductivity of glasses in the systemsAs2S3-xTex (for small x) and As2-ySbyS3. Philos. Mag. B 53, 413−430 (1986)

Fisher, F.D., Marshall, J.M., Owen, A.E.: Transport properties and electronic structure of glassesin the arsenic-selenium system. Philos. Mag. B 33, 261−275 (1976)

Fortner, J., Karpov, V.G., Saboungi, M.-L.: Meyer–Neldel rule for liquid semiconductors. Appl.Phys. Lett. 66, 997−999 (1995)

Fritzsche, H.: Optical and electrical energy gaps in amorphous semiconductors. J. Non-Cryst.Solids 6, 49−71 (1971)

Ganjoo, A., Shimakawa, K.: Estimation of density of charged defects in amorphous chalcogenidesfrom a.c. conductivity: Random-walk approach for bipolarons based on correlated barrierhopping. Philos. Mag. Lett. 70, 287−291 (1994)

Ghahramani, E., Sipe, J.E.: Pressure dependence of the band gaps of semiconductors. Phys. Rev.B 40, 12516−12519 (1989)

Griscom, D.L.: The electronic structure of SiO2: A review of recent spectroscopic and theoreticaladvances. J. Non-Cryst. Solids 24, 155−234 (1977)

Hachiya, K.: Electronic structure of the wrong-bond states in amorphous germanium sulphides.J. Non-Cryst. Solids 321, 217−224 (2003)

Halpern, V.: Localized electron states in the arsenic chalcogenides. Philos. Mag. 34, 331−335(1976)

Hughes, M.A., Yang, W.J., Hewak, D.W.: Spectral broadening in femtosecond laser writtenwaveguides in chalcogenide glass. J. Opt. Soc. Am. B 26, 1370−1378 (2009)

Ihm, J.: Optical absorption tails and the structure of chalcogenide glasses. J. Phys. C: Solid StatePhys. 18, 4741−4751 (1985)

Inagawa, I., Morimoto, S., Yamashita, T., Shirotani, I.: Temperature dependence of transmissionloss of chalcogenide glass fibers. Jpn. J. Appl. Phys. 36, 2229−2235 (1997)

Itoh, S., Nakao, K.: Electronic structure of VAP in sulfur. J. Phys. Soc. Jpn. 55, 268−273 (1986)Johnson, S.R., Tiedje, T.: Temperature dependence of the Urbach edge in GaAs. J. Appl. Phys. 78,

5609−5613 (1995)Jovari, P., Yannopoulos, S.N., Kaban, I., Kalampounias, A., Lishchynskyy, I., Beuneu, B.,

Kostadinova, O., Welter, E., Schops, A.: Structure of AsxTe100−x (20 ≤ x ≤ 60) glasses inves-tigated with X-ray absorption fine structure, X-ray and neutron diffraction, and reverse MonteCarlo simulation. J. Chem. Phys. 129, 214502 (2008)

Kajihara, K., Hirano, M., Skuja, L., Hosono, H.: Intrinsic defect formation in amorphous SiO2 byelectronic excitation: Bond dissociation versus Frenkel mechanisms. Phys. Rev. B 78, 094201(2008)

Kasap, S., Frey, J.B., Belev, G., Tousignant, O., Mani, H., Laperriere, L., Reznik, A., Rowlands,J.A.: Amorphous selenium and its alloys from early xeroradiography to high resolution X-rayimage detectors and ultrasensitive imaging tubes. Phys. Status Solidi (b) 246, 1794−1805(2009)

References 117

Kastner, M.: Bonding bands, lone-pair bands, and impurity states in chalcogenide semiconductors.Phys. Rev. Lett. 28, 355−357 (1972)

Kastner, M., Adler, D., Fritzsche, H.: Valence-alternation model for localized gap states in lone-pairsemiconductors. Phys. Rev. Lett. 37, 1504−1507 (1976)

Kato, T., Tanaka, K.: Electronic properties of amorphous and crystalline Ge2Sb2Te5 films. Jpn.J. Appl. Phys. 44, 7340−7344 (2005)

Kemeny, G., Rosenberg, B.: Theory of the pre-exponential factor in organic semiconductors.J. Chem. Phys. 52, 4151 (1970)

Kirkpatrik, S.: Percolation and conduction. Rev. Mod. Phys. 45, 574−588 (1973)Kitao, M., Mochizuki, T., Ikeda, H., Hasegawa, H., Yamada, S.: Optical absorption and

photoconductivity of amorphous As2Se3. Rep. Electron. Lab. Shizuoka Univ. 12, 45−54 (1977)Kittel, C.: Introduction to Solid State Physics 8th ed. Wiley, New York, NY (2005)Kolobov, A.V.: On the origin of p-type conductivity in amorphous chalcogenides. J. Non-Cryst.

Solids 198−200, 728−731 (1996)Kolobov, A.V., Kondo, M., Oyanagi, H., Matsuda, A., Tanaka, K.: Negative correlation energy and

valence alternation in amorphous selenium: An in situ optically induced ESR study. Phys. Rev.B 58, 12004−12010 (1998)

Kranjcec, M, Studenyak, I.P., Kurik, M.V.: On the Urbach rule in non-crystalline solids. J. Non-Cryst. Solids 355, 54−57 (2009)

Lippens, P.E., Jumas, J.C., Olivier-Fourcade, J., Aldon, L., Gheorghiu-du la Rocque, A., Snmaud,C.: Electronic structure of Ge-As-Te glasses. J. Phys. Chem. Solids 61, 1761−1767 (2000)

Martin-Samos, L., Limoge, Y., Roma, G.: Defects in amorphous SiO2: Valence alternation pairmodel. Phys. Rev. B 76, 104203 (2007)

Matsuda, O., Ohba, T., Murase, K., Ono, I., Grekos, P., Kouchi, T., Nakatake, M., Tamura, M.,Namatame, H., Hosokawa, S., Taniguchi, M.: Photoemission and inverse-photoemission studyof the electronic structure of p- and n-type amorphous Ge-Se-Bi films. J. Non-Cryst. Solids198, 688−691 (1996)

Mehta, N.: Meyer-Neldel rule in chalcogenide glasses: Recent observations and their conse-quences. Curr. Opin. Solid State Mater. Sci. 14, 95−106 (2010)

Moss, T.S.: Relations between the refractive index and energy gap of semiconductors. Phys. StatusSolidi (b) 131, 415−427 (1985)

Mott, N.F.: Conduction in Non-Crystalline Materials 2nd ed. Clarendon Press, Oxford (1993)Mott, N.F., Davis, E.A.: Electronic Processes in Non-Crystalline Materials. Clarendon Press,

Oxford (1979)Mukhopadhyay, S., Sushko, P.V., Stoneham, A.M., Shluger, A.L.: Correlation between the atomic

structure, formation energies, and optical absorption of neutral oxygen vacancies in amorphoussilica. Phys. Rev. B 71, 235204 (2005)

Narushima, S., Hiroki, M., Ueda, K., Shimizu, K., Kamiya, T., Hirano, M., Hosono, H.: Electricalproperties and local structure of n-type conducting amorphous indium sulphide. Philos. Mag.Lett. 84, 665−671 (2004)

Ngai, K.L.: Meyer–Neldel rule and anti Meyer–Neldel rule of ionic conductivity: Conclusionsfrom the coupling model. Solid State Ionics 105, 231−235 (1998)

Ogusu, K., Takayama, K.: Optical bistability in photonic crystal microrings with nonlineardielectric materials. Opt. Express 16, 7525−7539 (2008)

Oheda, H.: The exponential absorption edge in amorphous Ge–Se compounds. Jpn. J. Appl. Phys.18, 1973−1978 (1979)

Okamoto, H., Hattori, K., Hamakawa, Y.: Phenomenological scaling of optical absorption inamorphous semiconductors. J. Non-Cryst. Solids 198−200, 124−127 (1996)

Ono, I., Grekos, P.C., Kouchi, T., Nakatake, M., Tamura, M., Hosokawa, S., Namatame, H.,Taniguchi, M.: A study of electronic states of trigonal and amorphous Se using ultravio-let photoemission and inverse-photoemission spectroscopies. J. Phys.: Condens. Matter 8,7249−7261 (1996)

118 4 Electronic Properties

Overhof, H., Thomas, P.: Electronic Transport in Hydrogenated Amorphous Semiconductors.Springer, Berlin (1989)

Ovshinsky, S.R.: Chemical modification of amorphous chalcogenides. In: Spear, W.E. (ed.) 7thICALS Amorphous and Liquid Semiconductors, pp. 519−523. University of Edinburgh,Edinburgh (1977)

Ovshinsky, S.R., Adler, D.: Local structure, bonding, and electronic properties of covalentamorphous semiconductors. Contemp. Phys. 19, 109−126 (1978)

Pan, Y., Inam, F., Zhang, M., Drabold, D.A.: Atomistic origin of Urbach tails in amorphous silicon.Phys. Rev. Lett. 100, 206403 (2008)

Pétursson, J., Marshall, J.M., Owen, A.E.: Optical absorption in As-Se glasses. Philos. Mag. B 63,15−31 (1991)

Phillips, J.C.: Bonds and Bands in Semiconductors. Academic, New York, NY (1973)Psaila, N.D., Thomson, R.R., Bookey, H.T., Shen, S., Chiodo, N., Osellame, R., Cerullo, G., Jha,

A., Kar, A.K., Ajoy, K.: Supercontinuum generation in an ultrafast laser inscribed chalcogenideglass waveguide. Opt. Express 15, 15776−15781 (2007)

Sadigh, B., Erhart, P., Aberg, D., Trave, A., Schwegler, E., Bude, J.: First-principle calculations ofthe Urbach tail in optical absorption spectra of silica glass. Phys. Rev. Lett. 106, 027401 (2011)

Saito, K., Ikushima, A.J.: Absorption edge in silica glass. Phys. Rev. B 62, 8584−8587 (2000)Saitoh, A. Tanaka, K.: Optical nonlinearity in chalcogenide glasses for near-infrared all-optical

devices. J. Optoelectron. Adv. Mater. 13, 71–74 (2011)Sheik-Bahae, M., Hagan, D.J., Van Stryland, E.W.: Dispersion and band-gap scaling of the elec-

tronic Kerr effect in solids associated with two-photon absorption. Phys. Rev. Lett. 65, 96−99(1990)

Shimakawa, K., Abdel-Wahab, F.: The Meyer–Neldel rule in chalcogenide glasses. Appl. Phys.Lett. 70, 652−654 (1997)

Shimakawa, K., Ganjoo, A.: Ac photoconductivity of hydrogenated amorphous silicon: Influenceof long-range potential fluctuations. Phys. Rev. B 65, 165213 (2002)

Simdyankin, S.I., Elstner, M., Niehaus, T.A., Frauenheim, T., Elliott, S.R.: Influence of copper onthe electronic properties of amorphous chalcogenides. Phys. Rev. B 72, 020202(R) (2005a)

Simdyankin, S.I., Niehaus, T.A., Natarajan, G., Frauenheim, Th., Elliott, S.R.: New type of chargeddefect in amorphous chalcogenides. Phys. Rev. Lett. 94, 086401 (2005b)

Sobolev, V. Val., Sobolev, V.V.: Optical spectra of arsenic chalcogenide in a wide energy rangeof fundamental absorption. In: Fairman, R., Ushkov, B. (eds.) Semiconducting ChalcogenideGlass II, Chap. 5, pp. 201–228. Elsevier, Amsterdam (2004)

Street, R.A.: Luminescence in amorphous semiconductors. Adv. Phys. 25, 397−453 (1976)Street, R.A., Mott, N.F.: States in the gap in glassy semiconductors. Phys. Rev. Lett. 35,

1293−1296 (1975)Stuke, J.: Problems in the understanding of electronic properties of amorphous silicon. J. Non-

Cryst. Solids 97−98, 1−14 (1987)Suzuki, K., Matsumoto, K., Hayata, H., Nakamura, N., Minari, N.: Mass spectrometric study of

evaporated Se films and melt-quenched Se glasses. J. Non-Cryst. Solids 95−96, 555−562(1987)

Takahashi, Y., Masai, H., Fujiwara, T.: Nucleation tendency and crystallizing phase in silicateglasses: A structural aspect. Appl. Phys. Lett. 95, 071904 (2009)

Tanaka, K.: Pressure studies of amorphous semiconductors. In: Borossov, M., Kirov, N., Vavrek,A. (eds.) Disordered Systems and New Materials, pp. 290−309. World Scientific, Singapore(1989a)

Tanaka, K.: Structural phase transitions in chalcogenide glasses. Phys. Rev. B 39, 1270−1279(1989b)

Tanaka, K.: Wrong bond in glasses: A comparative study on oxides and chalcogenides. J. Opt.Adv. Matter 4, 505−512 (2002)

Tanaka, K.: In: Lucovsky G., Popescu M. (eds.) Non-Crystalline Materials for Optoelectronics,Chap. 4. INOE, Bucharest (2004)

References 119

Tanaka, K.: Optical nonlinearity in photonic glasses. In: Kasap, S., Capper, P. (eds.) SpringerHandbook of Electronic and Photonic Materials, Chap. 44. Springer, New York, NY (2006)

Tanaka, K., Gotoh, T., Yoshida, N., Nonomura, S.: Photothermal deflection spectroscopy ofchalcogenide glasses. J. Appl. Phys. 91, 125 (2002)

Tanaka, K., Kasanuki, Y., Odajima, A.: Physical properties and photoinduced changes of amor-phous Ge-S films. Thin Solid Films 117, 251−260 (1984)

Tarnow, E., Antonelli, A., Joannopoulos, J.D.: Crystalline As2Se3: Electronic and geometricalstructure. Phys. Rev. B 34, 4059–4073 (1986)

Tarnow, E., Joannopoulos, J.D., Payne, M.C.: Antisites, antistructures, and bond-switchingreactions in layered chalcogenides. Phys. Rev. B 39, 6017−6024 (1989)

Tauc, J.: Highly transparent glasses. In: Mitra, S.S., Bendow, B. (eds.) Optical Properties of HighlyTransparent Solids, pp. 245−260. Plenum, New York, NY (1975)

Taylor, P.C.: The localization of electrons in amorphous semiconductors: A twenty-first centuryperspective. J. Non-Cryst. Solids 352, 839−850 (2006)

Terakado, N., Tanaka, K.: The structure and optical properties of GeO2–GeS2 glasses. J. Non-Cryst. Solids 354, 1992−1999 (2008)

Tichý, L., Tichá, H., Nagels, P., Sleeckx, E., Callaerts, R.: Optical gap and Urbach edge slope ina-Se. Mater. Lett. 26, 279−283 (1996)

Tohge, N., Minami T., Yamamoto, Y., Tanaka, M.: Electrical and optical properties of n-typesemiconducting chalcogenide glasses in the system Ge-Bi-Se. J. Appl. Phys. 51, 1048−1053(1980)

Tsiulyanu, D.: Heterostructures on chalcogenide glass and their applications. In: Fairman, R.,Ushkov, B. (eds.) Semiconducting Chalcogenide Glass III, Chap. 2. Elsevier, Amsterdam(2004)

Vanderbilt, D., Joannopoulos, J.D.: Theory of defect states in glassy As2Se3. Phys. Rev. B 23,2596−2606 (1981)

Vanderbilt, D., Joannopoulos, J.D.: Total energies in Se. III. Defects in the glass. Phys. Rev. B 27,6311−6321 (1983)

Warren, Jr, W.W., Dupree, R.: Structural and electronic transformations of liquid selenium at hightemperature and pressure: A77Se NMR study. Phys. Rev. B 22, 2257−2275 (1980)

Weinberger, B.R., Roxlo, C.B., Etemad, S., Baker, G.L., Orenstein, J.: Optical absorption in poly-acetylene: A direct measurement using photothermal deflection spectroscopy. Phys. Rev. Lett.53, 86−89 (1984)

Weinstein, B.A., Zallen, R., Slade, M.L.: The effect of pressure on optical properties of As2S3glass. J. Non-Cryst. Solids 35−36, 1255−1259 (1980)

Weinstein, B.A., Zallen, R., Slade, M.L., Mikkelsen, J.C.: Pressure-optical studies of GeS2 glassesand crystals – Implications for network topology. Phys. Rev. B 25, 781−792 (1982)

Wemple, S.H., DiDomenico, Jr, M.: Optical dispersion and the structure of solids. Phys. Rev. Lett.23, 1156−1160 (1969)

Xiong, C., Magi, E., Luan, F., Tuniz, A., Dekker, S., Sanghera, J.S., Shaw, L.B., Aggarwal, I.D.,Eggleton, B.J.: Characterization of picosecond pulse nonlinear propagation in chalcogenideAs2S3 fiber. Appl. Opt. 48, 5467−5474 (2009)

Xu, M., Cheng, Y.Q., Sheng, H.W., Ma, E.: Nature of atomic bonding and atomic structure in thephase-change Ge2Sb2Te5 glass. Phys. Rev. Lett. 103, 195502 (2009)

Yelon, A., Movaghar, B., Crandal, R.S.: Multi-excitation entropy: Its role in thermodynamics andkinetics. Rep. Prog. Phys. 69, 1145−1194 (2006)

Young, P.A.: Optical properties of vitreous arsenic trisulphide. J. Phys. C: Solid State 4, 93−106(1971)

Zallen, R.: The Physics of Amorphous Solids. Wiley, New York, NY (1983)

Chapter 5Photo-Electronic Properties

Abstract Photo-excited electrons relax to ground states through several ways. Oneof the processes can be probed through photoluminescence, in which the most puz-zling feature in amorphous chalcogenides may be the so-called half-gap rule ofthe peak energy. The origin will be discussed. Another photo-electronic propertyis the photoconduction. Most amorphous chalcogenides are good photoconductors,for which steady-state and transient characteristics are briefly discussed. Finally, werefer to a carrier avalanche effect in a-Se films, which has been applied to highlysensitive vidicons.

Keywords Photoluminescense · Half-gap rule · Photoconduction · Non-photoconducting gap · Avalanche breakdown · Time-of-flight · Dispersive transport ·Dember effect

5.1 Photo-Excitation and Relaxation

The photon provides two kinds of excitations in condensed matters: photo-electronicand photo-vibrational. These excitations relax through successive processes, and inmany cases, the energy �ω of photons is converted ultimately to a temperature riseof the matter.

What happens in a semiconductor (or insulator) crystal when it is excited by aphoton? In general, the photo-electronic excitation occurs with a photon having anarbitrary energy. An x-ray photon (�ω � Eg) can excite a core electron, whichmay successively produce many electrons and holes in conduction and valencebands. If �ω > Eg (super-gap excitation), an excited electron will relax to the bot-tom of the conduction band, emitting the excess energy of �ω − Eg as severalphonons (Evib ≈ 10 meV) within picosecond relaxation times. A bandgap pho-ton with �ω ≈ Eg of visible light or so is likely to generate a pair of electronand hole. A sub-gap photon with �ω ≤ Eg may produce an exciton, a coupledelectron-hole pair. Lastly, if the light is intense and pulsed, nonlinear excitationby photons with energy of n�ω ≥ Eg, where n is the number of photons simul-taneously absorbed, may take place. And these electronic excitations will providethree kinds of responses: (i) temperature rise �T; (ii) luminescence, which tends tobecome stronger when illuminated at lower temperatures; and (iii) photo-electriceffects such as photoconduction (in a sample subjected to an electric field) and

121K. Tanaka, K. Shimakawa, Amorphous Chalcogenide Semiconductors and RelatedMaterials, DOI 10.1007/978-1-4419-9510-0_5, C© Springer Science+Business Media, LLC 2011

122 5 Photo-Electronic Properties

Fig. 5.1 Relaxational processes of photo-excited electrons (•) and holes (◦) in an amorphous semi-conductor: a geminate recombination, b sub-gap excitation and thermal hole-release, c bandgapexcitation and (de-)trapping of a hole, d non-geminate recombination, and e polaron (electron)formation

photo-voltaic effects, an example being the Dember voltage (Section 5.3). On theother hand, an infrared photon with �ω ≈ Evib � Eg excites atomic vibra-tions called optical phonons, which thermalize through nonlinear phonon–phononinteraction, resulting in a temperature rise.

The photo-excitation in amorphous semiconductors is somewhat different(Fig. 5.1), since the concepts of bandgap energies and phonons are vague. With anincrease in the photon energy, several unique processes occur. Infrared photons with�ω � Eg excite spatially localized (molecular) vibrations, instead of the opticalphonon, in disordered materials. If �ω < Eg, the photon may be absorbed by mid-gap states and (b) an excited electron (hole) in the state may be thermally re-excitedto a band. If �ω ≤ Eg, the energy corresponding to the exciton excitation in crys-tals, (a) an excited electron–hole pair1 may geminately recombine2 non-radiatively,giving rise to a thermal spike, which will be localized in nanometer scales. Or, atlow temperatures, it may radiatively recombine, giving rise to luminescence. On theother hand, a photon with �ω ≥ Eg gives several relaxation paths, which are classi-fied into vertical or horizontal transfers in a band picture, as illustrated in Fig. 5.1.Among these, the most common process may be (d) a non-geminate and non-radiative recombination, giving rise to a temperature rise. If the photon is absorbed

1The authors are reluctant to use the word “exciton” in disordered systems (Kasap et al. 2006),since the exciton radius may be larger than the structural disorder in amorphous materials. Theword “electron–hole pair” may cause less misunderstanding.2“Geminate recombination” means a recombination of a photoexcited electron–hole pair. It occurswhen the thermalization process (with a distance of ∼ [D(�ω − Eg)/Evib]1/2, where D is the dif-fusion coefficient of a mobile carrier), which dissipates the excess energy of �ω − Eg, cannotovercome a Coulombic electron–hole attractive force.

5.2 Photoluminescence 123

0

5

10

10–2

10–1

100

0 100 200 300

Pho

toex

pans

ion

PE

(μm

)

Pho

toco

nduc

tion

PC

and

P

hoto

lum

ines

cenc

e P

L (a

rb. u

nit)

Temperature (K)

PL

PE

PC

Fig. 5.2 Temperaturedependence ofphotoluminescence intensity(PL), photo-expansion (PE)(see Section 6.3.9), andphotoconduction (PC) ing-As2S3 (Tanaka 2000,© Elsevier, reprinted withpermission)

in an insulator, Dember voltages may appear. If the insulator is subjected to an elec-tric field, excited carriers may transit the sample, giving rise to (c) photocurrents.Otherwise, in flexible atomic networks, (e) the electron may be self-trapped, form-ing a kind of polaron states, a coupled and relaxed electron–lattice system (Fig. 4.4).The polaron state may be quenched into quasi-stable structural changes, which canbe regarded as a kind of photo-structural changes (see Chapter 6).

We here note that, in many cases, the photoluminescence and the photo-conduction are complementary, as exemplified in temperature dependence inFig. 5.2. Photoluminescence intensity is proportional to gηβ, where g is the car-rier generation rate, η the creation efficiency of geminate pairs, and β the fractionof geminate pairs which recombine radiatively. On the other hand, a photocurrentincreases as g(1 − η)μτ , where μ is the carrier mobility and τ is the lifetime.

5.2 Photoluminescence

The photoluminescence in chalcogenide and oxide glasses has been extensivelystudied. Historically, photoluminescence experiments had started using cw lasers,the results for the chalcogenide being comprehensively reviewed by Street (1976).The glass has a bandgap of ∼2 eV so that we can employ several kinds of lasersfor excitation. However, photoluminescence detection at (near) infrared regionsis more or less limited in sensitivity. Actually, photoluminescence studies fortellurides with Eg 1 eV are few. With developments of lasers, photoluminescenceexperiments shifted to those employing pulsed and/or polarized light excitations.In addition, more sophisticated measurements such as optically detected magneticresonance (ODMR), which detects spin resonance of excited electrons by monitor-ing photoluminescence intensity (Elliott 1990), have been employed. On the otherhand, the energy gap of the oxide is greater (5–10 eV), which limits available lasersfor excitation. Upon ultraviolet excitations, however, the luminescence is likely toappear in visible regions, which can be detected with high sensitivity using theconventional photomultipliers and semiconductor devices.

124 5 Photo-Electronic Properties

Since the photoluminescence is governed by mid-gap states, we may envisagestrong impurity effects upon photoluminescence. However, the effect is not univer-sal in chalcogenide glasses. Street (1976) asserts that special care about samplepurity is not required for the experiments. Actually, Pfister et al. (1978) havedemonstrated that Tl in As2Se3, which reduces hole mobility, has no effect uponphotoluminescence (and photoinduced ESR). Bishop et al. (1979) also have demon-strated that a photoluminescence efficiency in As2Se3 is insensitive to intentionallydoped atoms such as Cu and I up to ∼1 at.%. Koós et al. (1981) arrive at a similarconclusion for GeSe2. However, it has been repeatedly demonstrated that electricalproperties of Se are very sensitive to (ppm orders of) O and Cl impurities (LaCourseet al. 1970, Benkhedir et al. 2009), which is consistent with a photoluminescenceresult (Bishop et al. 1979). In addition, variations of photoluminescence spectrain different-grade SiO2 samples are well known (Sakurai and Nagasawa 2000).These seemingly controversial behaviors may be ascribed to respective impurity–host combinations, in which the impurity does or does not produce an active mid-gapstate. We should also take dependence upon preparation methods into account(Street 1976).

5.2.1 CW Photoluminescence

Among several marked features in steady-state photoluminescence, the most puz-zling may be the so-called half-gap photoluminescence (Figs. 5.3 and 5.4). In simplechalcogenide glasses such as As2S(Se)3 and GeS(Se)2, when excited by lightwith a photon energy of �ω ≈ 0.9Eg (Urbach-edge regions), broad (∼0.3 eV)photoluminescence peaks appear, with strong Stokes shifts, at “EPL ≈ Eg/2.” Wealso see in Fig. 5.3 similar features for simple oxide glasses, SiO2 (Gee and Kastner1980) and GeO2 (Terakado and Tanaka 2006).

For understanding the origin of an empirical rule, EPL ≈ Eg/2, varieties ofphotoluminescence characteristics have been studied. Temperature dependence hasmanifested that the position and width of photoluminescence peaks change little(Street 1976). Nevertheless, as shown in Fig. 5.5, the photoluminescence inten-sity tends to exponentially decrease with an increase in temperature, ∼exp (−T/T0),where T0 ≈ 0.1Tg (Gee and Kastner 1980). The dependence can be accounted forby assuming phonon-assisted tunneling of carriers to non-radiative recombinationpaths. On the other hand, pressure studies are limited due to experimental difficultiesof compressions at low temperatures. Weinstein (1984) has examined the feature inc-As2S3 and a-As2SeS2 at 13 K and demonstrated that both samples show the samepressure dependence: ∂EPL/∂P � 0 with ∂Eg/∂P < 0, the latter being well demon-strated (see Fig. 4.14). As the consequence, the Stokes shift becomes smaller withcompression, so that the half-gap rule tends to violate. Pulsed excitation gives morecomplicated results, such as a shift of the peak energy with delay time (Murayama1983).

5.2 Photoluminescence 125

Fig. 5.3 Photoluminescence (PL), photoluminescence excitation (PLE), and absorption spectra(solid lines) of the three glasses as a function of a photon energy reduced by the optical gap(modified from Gee and Kastner 1980 and Terakado and Tanaka 2006)

Fig. 5.4 Photoluminescence(PL) peak energy as a func-tion of photoluminescenceexcitation (PLE) peakenergies for oxide andchalcogenide glasses andchalcogen crystals (c-). Theline shows EPL = EPLE/2

126 5 Photo-Electronic Properties

Fig. 5.5 Temperaturevariations ofphotoluminescence intensitiesin Suprasil (circles), As2S3(�), and Se (�). Thetemperature T is normalizedby the glass transitiontemperature Tg (Gee andKastner 1980, © Elsevier,reprinted with permission)

Material variations have also been studied. Roughly, photoluminescence behav-iors in glass and the corresponding crystal appear to be similar, as demonstrated forAs2S(Se)3 (Street 1976). Crystalline samples such as c-As2S(Se)3 also appear tofollow the half-gap rule, though impurity effects may exist (Street 1976, Weinstein1984). In contrast, we see in Fig. 5.4 that elemental chalcogens, S and Se, manifestconsiderable deviations from the half-gap rule. Photoluminescence in orthorhombicc-S, consisting of S8 molecules, gives a peak at 2.6 eV under excitation at 3.4 eV(Street 1976), i.e., EPL > Eg/2. A similar result is demonstrated also for polymericg-S (Oda et al. 1984). On the other hand, both a- and c-Se show the opposite devi-ation, EPL < Eg/2 (Bishop et al. 1979, Lundt and Weiser 1983). It is reported thatthe half-gap rule is violated also in Ge-rich Ge-S(Se) glasses (Seki et al. 2003). It isalso mentioned here that, for the intensity, luminescence in a-Se is known to bemuch weaker (10–1–10–2) than that in As-S(Se) (Bishop et al. 1979).

The origin of the half-gap photoluminescence remains to be studied. A straight-forward interpretation is to postulate recombination centers at positions of ∼Eg/2in the bandgap. However, the center is likely to produce ESR signals and alsooptical absorptions at �ω � Eg/2, which have been assumed not to exist. (Theweak absorption tail described in Section 4.6 was neglected.) Then, Street andMott (1975) proposed the charged defects concept (Section 4.4), in which the half-gap photoluminescence is assumed to arise from D0 states. Light excitation convertsD+ and D– to D0, which is assumed to become a radiative recombination center.Here, strong electron–phonon coupling with large Stokes shift is implicitly assumed.

5.2 Photoluminescence 127

However, why the D0 state is located at ∼Eg/2 in lone pair electron systemsremains unclear. (In contrast, in a-Si, it is reasonable to assume that D0 states arelocated at the mid-gap.) Instead, Baranovskii and Karpov (1987) have interpretedthe rule using a polaron model. Later, Ristein and others have ascribed the half-gap photoluminescence to self-trapped triplet excitons (Ristein et al. 1990, Maoet al. 1993). However, similar to the defect model, these models cannot explainwhy the Stokes shift is ∼Eg/2. On the other hand, for the oxide glass such asSiO2, photoluminescence has been ascribed to a kind of oxygen-deficient cen-ters, e.g., twofold-coordinated Si atoms, Si20 (Trukhin 2000). In this model, thephotoluminescence peak at around the half-gap is assumed to be accidental.

5.2.2 Time-Resolved Photoluminescence

Although the photoluminescence in chalcogenide glasses under cw excitationappears to present a single peak (Fig. 5.3), time- or frequency-resolved experi-ments have manifested several peaks having different time constants. For g-As2S3,in Fig. 5.6, Murayama (1983) demonstrate, through a time-resolved measurement ata cryogenic temperature using bandgap excitation with a pulse of 10 ns, three decaycomponents with time constants of 20 ns, 2 μs, and 200 μs. On the other hand, afrequency-resolved experiment by Aoki et al. (2005) detects two components hav-ing lifetimes peaking at ∼10 ns and ∼100 μs. This work does not detect the 2 μscomponent, which may be due to different excitation levels, the pulse being muchmore intense. These authors ascribe the fast components at 10−20 ns to lattice-deforming electron–hole pairs (Murayama 1983) and singlet excitons (Aoki et al.2005). The slowest components, 100–200 μs, are ascribed to localized electrons

Fig. 5.6 Transient (left) (Murayama 1983, © Elsevier, reprinted with permission) and frequency-resolved (right) (Aoki et al. 2005, © INOE, reprinted with permission) photoluminescence ing-As2S3

128 5 Photo-Electronic Properties

and holes (Murayama 1983) and triplet excitons (Aoki et al. 2005). Despite the dif-ferent terminologies being employed, the real entities may be similar. It is plausiblethat the slowest component corresponds to the cw photoluminescence.

Spectral investigations of transient photoluminescence have provided valuable,but controversial, insights into the mobility gap. Higashi and Kastner (1981) con-clude, on the basis of measurements of luminescence characteristics as a functionof excitation energy, that the mobility gap in As2S3 is located at 2.3 eV, the positionbeing similar to that of the Tauc optical gap. However, through similar experiments,Murayama concludes the mobility gap to be 2.6 eV (Murayama 1983), suggestingthat the energy is similar to the bandgap in the corresponding crystal. Reasons forthis quantitative discrepancy have not been examined.

5.3 Photo-Voltage

The Dember voltage, i.e., photo-voltages arising from concentration gradients ofphoto-generated carriers, can determine the species (electron or hole) of mobile car-riers (Goldman et al. 1978). Suppose an insulating material, which has a groundedback electrode, is illuminated by highly absorbed light and the surface voltage VDis measured through a floating electrode. The voltage is given as

VD = (kBT/e) ln(ni/nb), (5.1)

where ni and nb are carrier densities at the illuminated and the back surface. And thepolarity reflects the species of mobile carriers. Despite this simple principle, studieson Dember photo-voltages in amorphous semiconductors are a few (Fotland 1960,Kolomiets 1964, Wey and Fritzsche 1972, Tanaka et al. 1995).

5.4 Photoconduction

5.4.1 CW Photoconduction

The photoconductivity, a current flow in an insulator or wide-gap semiconduc-tor3 under electric fields and light excitation, was discovered for c-Se more thana century ago. For amorphous semiconductors, extensive studies were initiated byWeimer and Cope (1951) and by Kolomiets’ group (Kolomiets and Lyubin 1973).Many studies have been reported for Se and As2Se3, which demonstrate unique pho-toconductive characteristics in amorphous semiconductors, while a few for As2S3and other materials due to small photocurrents. These photoconductivity results

3Experimentally, it is more or less difficult to distinguish photo-currents and photo-thermal cur-rents in small-gap semiconductors such as a-As2Te3 (Tanaka 2007). The ideal photocurrent flowsunder fixed temperatures, while light illumination necessarily rises sample temperature, whichincreases the electrical conductivity in proportion to exp(−Eg/2kBT).

5.4 Photoconduction 129

pose fundamental problems in electronic excitation and transport in disorderedsystems. Understanding the photoconductivity is required also for applicationsto devices such as Se-target vidicons (Section 7.6). For x-ray photoconductivity,see Section 7.6.

The photocurrent ipc appears when photo-generated carriers in a sample driftbetween a pair of electrodes which are subjected to a bias voltage (Bube 1960).Under the simplest situation, where (de-)trapping processes could be neglected, thecarrier density n is given as

dn/dt = ηαI − n/τ , (5.2)

where η is a carrier generation efficiency, α an absorption coefficient, I incidentlight intensity taking light reflection into account, and τ a carrier lifetime gov-erned by recombination. The equation gives the steady-state carrier density asn = ηαIτ , and accordingly, the steady photocurrent (current density) becomesipc = enμE = eηαIτμE, where τμE = τVd is called “Schubweg” (flying dis-tance). Important steady-state photocurrent characteristics are the variations withlight intensity, spectrum, and temperature.

The light intensity dependence follows the one formulated for crystalline mate-rials (Bube 1960, Adriaenssens 2006). Here, we slightly modify the generation ratein Equation (5.2) as

dn/dt = ηαI − n(n/τ1 + N/τ2), (5.3)

where N is the density of recombination centers and τ 1,2 are recombination timesfor two processes. We then see that, with an increase in the light intensity and thecorresponding n from n/τ1 � N/τ2 to n/τ1 � N/τ2, the recombination changesfrom a monomolecular to a bimolecular type, giving rise to the variations of ipc ∝I1 and I1/2. This characteristic change in the intensity dependence can be employedfor estimating the effective density n/τ 1 and N/τ 2.

More informative is the spectral dependence. In crystalline photoconductors, e.g.,in c-Se shown in Fig. 5.7b, it is common that a photoconduction spectrum gives a

Fig. 5.7 Photocurrent and optical density spectra of (a) a-Se and (b) c-Se (modified from Gilleo1951)

130 5 Photo-Electronic Properties

peak near the optical absorption edge. At the sub-gap region (longer wavelengths),the efficiency decreases reflecting a lack of excitation energy. At the super-gapregion, where photo-electronic excitation occurs very near to the surface due to highabsorption, surface recombination of photo-generated carriers is likely to suppressthe photocurrent. In amorphous materials, as shown in Fig. 5.7a, the high-energyreduction tends to become less noticeable, which suggests a smaller role of the sur-face recombination (Gilleo 1951, Shimakawa et al. 1974). We here mention that,for spectral measurements, the constant photocurrent method (CPM), which takesphotoconductive spectra under fixed photocurrents (by varying light intensities), hasoften been employed for disordered semiconductors (Tanaka and Nakayama 1999,Adriaenssens 2006).

In many amorphous materials, as exemplified in Fig. 5.7a for a-Se, thephotoconduction spectrum appears to be blue shifted from the optical absorptionedge. At least, three interpretations, including exciton, geminate recombination, andmobility gap, have been proposed for the blue-shifted spectra, while the distinctionbetween these ideas seems to be indefinite. Evrard and Trukhin (1982) point outthat, in g-SiO2 with Eg ≈ 10 eV, the shift is ∼2 eV (Fig. 4.11) and interpret itas an exciton effect, the concept in disordered materials still remaining an impor-tant topic (Messina et al. 2010). On the other hand, in a-Se with Eg ≈ 2 eV, thedeviation of photoconduction spectrum is 0.4 eV (Fig. 5.7a), which is termed a “non-photoconducting gap,” which has been understood as a manifestation of geminaterecombination (Mott and Davis 1979, Elliott 1990). It should be mentioned that c-Swith Eg ≈ 4 eV also exhibits a non-photoconducting gap of ∼0.5 eV (Spear andAdams 1966). We may then assume that the non-photoconducting gap is character-istic of low-dimensional solids, irrespective of structural order. Next, as shown inFig. 4.11, g-As2S3 presents a photoconductive edge at ∼2.6 eV at low temperatures(Tanaka and Nakayama 1999), where the Tauc gap is ∼2.4 eV. Recalling that thebandgap in c-As2S3 is ∼2.6 eV, we can assume that the photoconductive edge cor-responds to the mobility edge. The same conclusion is drawn by Murayama (1983)from photoluminescence spectra. Incidentally, in a-Si:H films, the optical and pho-toconductive edges are located at nearly the same positions (Tanaka and Nakayama1999).

Comparison of photoconductive, photoluminescence excitation, and absorptionspectra provides two valuable insights (Tanaka 2001). As shown in Fig. 5.8, inter-estingly, the photoconductive spectrum (CPM) in g-As2S3 does not show the weakabsorption tail, which appears also in the photoluminescence excitation (PLE) spec-trum. As listed in Table 4.2, g-As2S3 is hole conductive (electrons are immobile),and accordingly, this result implies that, as illustrated in Fig. 5.8, the weak absorp-tion tail arises from localized states below the conduction band. On the other hand,for the Urbach edge, optical absorption, photoconductive, and photoluminescenceexcitation spectra in Fig. 5.8 show similar slopes, which suggests that the Urbachedge is governed by the DOS above the valence band. Since the valence band ismade up from lone pair electron states, we can assume that the Urbach edge ing-As2S3 reflects interatomic interaction between lone pair electrons. The same pic-ture can be drawn for other chalcogenides which have similar values of Urbachenergy EU and the valence band edge steepness Eo

v in Table 4.3.

5.4 Photoconduction 131

105

103

101

10–1

10–3

10–51 1.5 2 2.5 3

Abs

orpt

ion

coef

ficie

nt (

cm–1

)

Photon energy (eV)

CPM

α

PLE

Energy

Den

sity

-of-

stat

e

Fig. 5.8 Comparison of three spectra for g-As2S3 at room temperature (left) and deduced DOS(right) (Tanaka 2001, © INOE, reprinted with permission). α is the optical absorption, PLE thephotoluminescence excitation, and CPM the constant photocurrent method. The dotted line in theDOS indicates the mobility edge and the circles show an electron–hole pair

In addition, as shown in Fig. 5.9, g-As2S3 manifests anomalous dependence ofthe photoconduction spectrum upon excitation levels (Tanaka 1998). It shows aredshift from ∼2.4 to ∼2.0 eV under higher excitations, which is interpreted asa filling effect of trap levels. a-Si:H films and g-As2Se3 do not show such intensitydependence. The peculiar feature is attributable to slow carrier transits in g-As2S3.

Studies on impurity effects are not comprehensive. Hammam et al. (1990) havedemonstrated that photoconduction characteristics in As2Se3 are influenced byintentionally added As2O3 of ∼1 at.%, which is no more a doping level. On theother hand, the same group reports that, in evaporated a-Se, only ∼10 ppm Cl mod-ifies photoconduction characteristics (Benkhedir et al. 2009). Why is only a-Se verysensitive to impurities?

Fig. 5.9 Photocurrentspectra in a-As2S3 as afunction of the light intensityindicated (Tanaka 1998,© American Institute ofPhysics, reprinted withpermission). The crosses (+)are obtained using cw lightand others are by 5 ns pulses

132 5 Photo-Electronic Properties

5.4.2 Time-Resolved Photoconduction

Photocurrent transients, which appear after pulsed light excitations, are governedby carrier generation and recombination, and in addition, by transport. Hence,the mobility becomes an important parameter for interpretations. As known, inthe Drude model for a crystalline semiconductor, the mobility μ is written asμ = eτ /m∗, where τ represents the scattering time (normally governed by phononsand impurities). In amorphous semiconductors, it is plausible that there existmany gap states with distributed energy depths, which tend to suppress the carriertransport through hopping, (de-)trapping, and recombination. Here, the (quantummechanical) hopping is usually neglected at room temperature. The (de-)trappingand recombination are, respectively, governed by shallow and deep gap states.Nevertheless, in some experiments, in which photo-excited electrons and holesare spatially separated by electric fields, the recombination can also be neglected.In such cases, only the (de-)trapping governs the transient characteristic, and ameasured drift mobility μd is reduced as

μd = μ(Nc/Nt) exp(−Et/kT), (5.4)

where Nc is the effective DOS at the band edge (Equation 4.13) and Nt and Et are thetrap density and the depth, respectively (Mott and Davis 1979). Or, it is more naturalto assume that the trap density is distributed in energy in disordered semiconductors.Accordingly, the main interest of transient photocurrent measurements is to knowthe trap distribution Nt(E) or to obtain DOSs of localized states.

There are several time-resolved photoconductive methods (Adriaenssens 2006).Among those, optical time of flight (TOF), transient photoconductivity, and xero-graphic discharge have been frequently employed. Experimentally, these methodsneed, respectively, sandwich, planar, and back electrode samples. The former twomethods measure photocurrents under constant applied voltages, and the last mon-itors a decay of surface voltages after initial charging processes. In addition tothese transient methods, a frequency-resolved method, the so-called modulatedphotoconductivity, can also be employed for obtaining DOSs of gap states.

The optical TOF works as illustrated in Fig. 5.10. A pulsed super-bandgap lightimpinges upon an insulating sample having sandwich electrodes, which exert anelectric field to the sample. The polarity of the voltage applied to the front elec-trode determines the species (electron or hole) of moving carriers. The pulsedlight is strongly absorbed near the (semi-)transparent front electrode, and a photo-generated thin carrier packet drifts accompanying diffusion broadening through thesample, giving rise to a corresponding external current, which traces the carriertransport.

The optical TOF experiment gives two kinds of responses: Gaussian (non-dispersive) and dispersive transport (Mott and Davis 1979, Elliott 1990). In theGaussian transport, which is observed commonly in insulating crystals and also insome amorphous materials, as a-Se at room temperature, a step-like current (a inFig. 5.10) with a decay edge at tT = L/vd, where L and vd are a sample thicknessand a carrier velocity, appears. On the other hand, a long featureless signal appears

5.4 Photoconduction 133

(a) (b)initial

display

a

b

time

curr

ent

Fig. 5.10 A schematic illustration of optical time-of-flight experiments and the responses:(a) Gaussian (non-dispersive) transport and (b) dispersive transport on a display (center) and ina sample (right)

in many amorphous semiconductors such as As2Se(Te)3 and also in a-Se at lowtemperatures, which is ascribed to the so-called dispersive transport. The feature-less diffusion-controlled signal, when plotted in double logarithmic scales, givestwo straight lines as

I(t) ∼ t−(1−α) when t < tT and t−(1+α) when t > tT, (5.5)

where α is called as a dispersion parameter and tT gives a nominal carrier-transittime.

The dispersive transport has been analyzed by Scher and Montroll (1975). Theyapply a continuous-time random walk theory to charge carriers in a disorderedinsulator which is subjected to an electric field. The motion of charge carriers at theband edge is interrupted by trapping by localized states; the carrier waiting there fora time interval of τ , and then, being thermally activated to a mobility edge. For thewaiting time, the two models, (classical) multiple trapping and (quantal) multiplehopping, have been proposed (Elliott 1990).

The above idea suggests that the dispersive current reflects the distribution D(τ )of the waiting time, which is governed by the DOS of gap states D(E). In view ofthe multiple-trapping model, the detrapping time τ of carriers is estimated as

τ ≈ −1 exp(Et/kBT), (5.6)

where is the attempt to escape frequency (usually approximated by a vibrationalfrequency ∼1013 Hz), Et the trap depth, and T the temperature. Putting kBT =25 meV and τ ≈ 10−8 s (TOF experiments can cover time spans of nanosecondsto milliseconds), we obtain Et ≈ 0.3 eV. That is, we can estimate the DOS at adepth of ∼0.3 eV. Practically, more elegant analyses using inverse Laplace trans-formation are employed for estimating the gap-state DOSs. Many studies have beenconducted, mainly for Se and As–Se (Adriaenssens 2006).

The transient photoconductivity gives similar insights (Naito et al. 1994,Adriaenssens 2006). The decay after pulsed excitation follows I(t) ∼ t−(1−α), which

134 5 Photo-Electronic Properties

is the same with that in the TOF at t < tT in Equation (5.5), as expected. Preparationof planar electrode samples is usually easier than that of the sandwich electrode, andaccordingly, the transient photoconductivity becomes a convenient way for gettinginformation of the trap distribution. Nevertheless, since the sample has the symmet-ric electrode structure, the method cannot distinguish the species of transit carriers:electrons or holes.

The xerographic discharge method can be employed for probing deeper trapsthan ∼0.5 eV (Abkowitz 1992, Weiss and Abkowitz 2006). The method was devel-oped for analyses of a xerographic copying process (Section 7.6), and it has beenapplied to examinations of trap-limited transport processes and DOSs of deepstates. Many experiments have been performed for a-Se films, having a typicalthickness of ∼50 μm, which are deposited onto, e.g., an Al plate. As shownin Fig. 5.11, the sample is corona charged, dark decayed, and photo dischargedthrough photoconduction, during which the surface potential is monitored using acapacitively coupled electrometer. And, the time variations give several materialparameters. For instance, a residual surface potential VR at a delay time τ d ≈ 1–104

s gives the density N(Et) for trapped carriers with a depth of Et as N(Et) ≈ τ d dVR/dt.Quantitatively, it is not difficult to measure a surface voltage of 5 V, which maycorrespond to the charge density as small as 1012 cm−3.4

Insights into DOSs can be obtained also by using frequency domain experimentssuch as the modulated photocurrent method (Oheda 1979, Adriaenssens 2006).In this method, we measure the phase delay () between modulated excitationlight (∼I sin(t)) with photon energy of �ω > Eg and its generating ac photocurrent∼ipcsin(t +) as a function of the modulation frequency . The current, which is

Fig. 5.11 A response ofxerographic discharges.A typical charging durationis ∼1 min

4Note that in the simplest case, VR = eNL2/(2εRε0), where L is the sample thickness, εR therelative dielectric constant, and ε0 the vacuum dielectric constant.

5.5 Avalanche Breakdown 135

Fig. 5.12 Reported DOSs fora-Se above the valence band.The solid line is reported byKoughia and Kasap (2006),the dashed line by Abkowitz(1992), and the dotted line bySong et al. (1999)

characterized with ipc and (), gives information of the localized state DOS; thehigher is, the shallower trap levels are probed.

Extensive studies using these photoconductive methods have given the DOSsin a-Se and a-As2Se3, while the results are controversial. For a-Se, as comparedin Fig. 5.12 for the states (governing hole transport) above the valence band,two kinds of results have been repeatedly reported (Abkowitz 1992, Song et al.1999, Koughia and Kasap 2006). One is an exponentially decaying distributionD(E) ∝ exp(−E/E0), where E0 = kBT/α and α is the dispersive parameter inEquation (5.5), and the other provides a broad peak at 0.3–0.4 eV above the valenceband. The absolute values also scatter among the reports, which may be due todifferences in a-Se films with respect to purities (Belev et al. 2007), evaporatingconditions, post-storage durations, etc. For instance, Pfister and Morgan (1980)have demonstrated that as-evaporated As2Se3 films are much more defective thanannealed films.

It seems that the exponential DOS is more plausible. The photoconductive DOSshould be consistent with the results obtained from optical absorption, which givesa joint DOS of the valence and the conduction bands (Equation (4.1)). And we seein Section 4.6 that any peaks have never been uncovered for the optical absorptionedge in chalcogenide glasses; just the exponential Urbach edge (EU ≈ 50 meV)and weak absorption tail. Therefore, the exponential DOS edge appears to be moreuniversal. Otherwise, we may assume that the small and broad peaks at 0.3–0.4 eVin Fig. 5.12 are masked by the Urbach edge.

5.5 Avalanche Breakdown

The avalanche breakdown under high electric fields is a common phenomenon incrystalline semiconductors, while it is unlikely to occur in amorphous semicon-ductors due to small carrier mobilities. Surprisingly, however, Juška and Arlauskas

136 5 Photo-Electronic Properties

Fig. 5.13 A multiplicationefficiency β ofphoto-generated holes βp andelectrons βn as a function ofthe electric field E in a 70 μmthick a-Se film. βp→p is amultiplication efficiencysolely by holes. The insetshows a typical time-of-flightsignal of holes under chargemultiplications (Juška andArlauskas 1980, ©Wiley-VCH Verlag GmbH& Co. KGaA., reprinted withpermission)

(1980) have discovered the avalanche breakdown in a-Se at a threshold field of∼106 V/cm (Fig. 5.13), which is twice that in c-GaP having a comparable bandgapof ∼2.3 eV (Cesnys et al. 2004). On the other hand, Tanioka et al. (1987) havediscovered that the charge multiplication occurs also in vidicon targets (Section7.6). Charge multiplications have been found also for junction structures in a-Si:Hfilms (Toyama et al. 1995, Akiyama et al. 2002) and organic polymers (Katsumeet al. 1996, Conwell 1998) at ∼107 V/cm. However, it remains to be studied if themechanisms of these carrier multiplications are common.

The avalanche breakdown in amorphous semiconductors has attracted substan-tial interest. As known, the avalanche breakdown in crystalline semiconductors isdescribed by a Baraff’s model (Kasap et al. 2004). A carrier, accelerated undera high field, gains enough kinetic energy, giving rise to impact carrier ionization,and generated carriers repeat the carrier multiplication process. However, since thecarrier in amorphous semiconductors is assumed to have a short mean free path,sufficient acceleration for the impact ionization seems to be difficult. On this prob-lem, Kasap et al. (2004) have applied a lucky drift model, in which the carrieris assumed to undergo elastic collisions with disordered structures (and inelasticwith lattice vibrations). Lucky elastic collisions can increase the carrier energy, ulti-mately giving rise to a sufficient energy (>Eg) for the impact ionization. The reasonwhy the avalanche breakdown is remarkable only in a-Se is ascribed to its relativelyhigh hole mobility and small vibrational energy of ∼30 meV, which suppresses acontribution of inelastic collisions. Jandieri et al. (2009) apply this idea also to theelectrical switching in a-Ge2Sb2Te5 films (Section 7.4.3).

However, further studies seem to be necessary. A puzzling result is that the meanfree path between elastic collisions in a-Se, obtained after parameter fitting, is just∼0.5 nm (Kasap et al. 2004), which is comparable to the atomic distance. For sucha short scale, can we apply a picture assuming particle (hole) acceleration?

References 137

References

Abkowitz, M.A.: Light-induced changes in the DOS of chalcogenide glasses studied by xero-graphic techniques. J. Non-Cryst. Solids 141, 188–199 (1992)

Adriaenssens, G.J.: Photoconductivity in materials research. In: Kasap, S., Capper, P. (eds.)Springer Handbook of Electronic and Photonic Materials, Chap. 7, pp. 137–146. Springer, NewYork, NY (2006)

Akiyama, M., Hanada, M., Takao, H., Sawada, K., Ishida, M.: Excess noise characteristics ofhydrogenated amorphous silicon p-i-n photodiode films. Jpn. J. Appl. Phys. 41, 2552–2555(2002)

Aoki, T., Saito, D., Ikeda, K., Kobayashi, S., Shimakawa, K.: Radiative recombination processes inchalcogenide glasses deduced by lifetime measurements over 11 decades. J. Opt. Adv. Matter7, 1749–1757 (2005)

Baranovskii, S.D., Karpov, V.G.: Localized electron states in glassy semiconductors (review). Sov.Phys. Semicond. 21, 1–10 (1987)

Belev, G., Tonchev, D., Fogal, B., Allen, C., Kasap, S.O.: Effects of oxygen and chlorine on chargetransport in vacuum deposited pure a-Se films. J. Phys. Chem. Solids 68, 972–977 (2007)

Benkhedir, M.L., Mansour, M., Djefaflia, F., Brinza, M., Adriaenssens, G.J.: Photocurrent mea-surements in chlorine-doped amorphous selenium. Phys. Status Solidi (b) 246, 1841–1844(2009)

Bishop, S.G., Strom, U., Friebele, E.J., Taylor, P.C.: The effects of impurities uponphotoluminescence and optically induced paramagnetic states in chalcogenide glasses. J. Non-Cryst. Solids 32, 359–372 (1979)

Bube, R.H. Photoconductivity of Solids. Wiley, New York, NY (1960)Cesnys, A., Juška, G., Montrimas, E.: Charge carrier transfer at high electric fields in noncrys-

talline semiconductors. In: Fairman R., Ushkov, B. (eds.) Semiconducting Chalcogenide GlassII, Chap. 2, pp. 15–55. Elsevier, Amsterdam (2004)

Conwell, E.M.: Hot electrons and impact ionization in poly (p-phenylene vinylene). Phys. Rev.B 57, R12670–R12672 (1998)

Elliott, S.R.: Physics of Amorphous Materials 2nd ed. Longman, London (1990)Evrard, R., Trukhin, A.N.: Photoelectric properties and the energy gap of SiO2. Phys. Rev. B 25,

4102–4105 (1982)Fotland, R.A.: Some electrical properties of amorphous selenium films. J. Appl. Phys. 31,

1558–1565 (1960)Gee, C.M., Kastner, M.: Photoluminescence from E band centers in amorphous and crystalline

SiO2. J. Non-Cryst. Solids 40, 577–586 (1980)Gilleo, M.A.: Optical absorption and photoconductivity of amorphous and hexagonal selenium.

J. Chem. Phys. 19, 1291–1297 (1951)Goldman, S.R., Kalikstein, K., Kramer, B.: Dember-effect theory. J. Appl. Phys. 49, 2849–2854

(1978)Hammam, M., Adriaenssens, G.J., Dauwen, J., Seynhaeve, G., Grevendonk, W.: Influence of

oxygen on the electronic gap-state density of a-As2Se3. J. Non-Cryst. Solids 119, 89–94 (1990)Higashi, G.S., Kastner, M.: Excitation-energy dependence of photoluminescence bandwidth in

a-As2Se3: Observation of the mobility gap? Phys. Rev. Lett. 47, 124–127 (1981)Jandieri, K., Rubel, O., Baranovskii, S.D., Reznik, A., Rowlands, J.A., Kasap, S.O.: Lucky-drift

model for impact ionization in amorphous semiconductors. J. Mater. Sci.: Mater. Electron. 20,S221–S225 (2009)

Juška, G., Arlauskas, K.: Impact ionization and mobilities of charge carriers at high electric fieldsin amorphous selenium. Phys. Status Solidi (a) 59, 389–393 (1980)

Kasap, S., Koughia, C., Singh, J., Ruda, H., O’Leary, S.K.: Optical properties of electronic materi-als: Fundamentals and characterization. In: Kasap, S., Capper, P. (eds.) Handbook of Electronicand Photonic Materials, Chap. 3, pp. 47–77. Springer, New York, NY (2006)

138 5 Photo-Electronic Properties

Kasap, S., Rowlands, J.A., Baranovskii, S.D., Tanioka, K.: Lucky drift impact ionization inamorphous semiconductors. J. Appl. Phys. 96, 2037–2048 (2004)

Katsume, T., Hiramoto, M., Yokoyama, M.: Photocurrent multiplication in naphthalene tetracar-boxylic anhydride film at room temperature. Appl. Phys. Lett. 69, 3722–3724 (1996)

Kolomiets, B.T.: Vitreous semiconductors (II). Phys. Status Solidi 7, 713–731 (1964)Kolomiets, B.T., Lyubin, V.M.: Photoelectric phenomena in amorphous chalcogenide semiconduc-

tors. Phys. Status Solidi (a) 17, 11–46 (1973)Koós, M., Kósa Somogyi, I., Vassilyev, V.A.: Photoluminescence in doped and annealed GeSe2

glass. J. Non-Cryst. Solids 43, 245–253 (1981)Koughia, K., Kasap, S.O.: Density of states of a-Se near the valence band. J. Non-Cryst. Solids

352, 1539–1542 (2006)LaCourse, W.C., Twaddell, V.A., Mackenzie, J.D.: Effects of impurities on the electrical conduc-

tivity of glassy selenium. J. Non-Cryst. Solids 3, 234–236 (1970)Lundt, H., Weiser, G.: Mid-gap luminescence and its excitation spectrum in trigonal selenium

single crystals. Solid State Commun. 48, 827–830 (1983)Mao, J., Rapelje, K.A., Blodgett-Ford, S.J., Delos, J.B., König, A., Rinneberg, H.: Photoabsorption

spectra of atoms in parallel electric and magnetic fields. Phys. Rev. A 48, 2117–2126 (1993)Messina, F., Vella, E., Cannas, M., Boscaino, R.: Evidence of delocalized excitons in amorphous

solid. Phys. Rev. Lett. 105, 116401 (2010)Mott, N.F., Davis, E.A.: Electronic Processes in Non-crystalline Materials. Clarendon Press,

Oxford (1979)Murayama, K.: Time-resolved photoluminescence in chalcogenide glasses. J. Non-Cryst. Solids

59–60, 983–990 (1983)Naito, H., Ding, J., Okuda, M.: Determination of localized-state distributions in amorphous

semiconductors from transient photoconductivity. Appl. Phys. Lett. 64, 1830–1832 (1994)Oda, S., Kastner, M.A., Wasserman, E.: Transient photoluminescence and photo-induced optical

absorption in polymeric and crystalline sulphur. Philos. Mag. B 50, 373–377 (1984)Oheda, H.: The exponential absorption edge in amorphous Ge-Se compounds. Jpn. J. Appl. Phys.

18, 1973–1978 (1979)Pfister, G., Liang, K.S., Morgan, M.: Hole transport, photoluminescence, and photoinduced spin

resonance in thallium-doped amorphous As2Se3. Phys. Rev. Lett. 41, 1318–1321 (1978)Pfister, G., Morgan, M.: Defects in chalcogenide glasses l. The influence of thermally induced

defects on transport in a-As2Se3. Philos. Mag. B 41, 191–207 (1980)Ristein, J., Taylor, P.C., Ohlsen, W.D., Weiser, G.: Radiative recombination center in As2Se3 as

studied by optically detected magnetic resonance. Phys. Rev. B 42, 11845–11856 (1990)Sakurai, Y., Nagasawa, K.: Radial distribution of some defect-related optical absorption and PL

bands in silica glasses. J. Non-Cryst. Solids 277, 82–90 (2000)Scher, H., Montroll, E.W.: Anomalous transit-time dispersion in amorphous solids. Phys. Rev.

B 12, 2455–2477 (1975)Seki, M., Hachiya, K., Yoshida, K.: Photoluminescence excitation process and optical absorption

in Ge-S chalcogenide glasses. J. Non-Cryst. Solids 324, 127–132 (2003)Shimakawa, K., Yoshida, A., Arizumi, T.: Photoconduction of glasses in the Te-Se-Sb system.

J. Non-Cryst. Solids 16, 258–266 (1974)Song, H.-Z., Adriaenssens, G.J., Emelianova, E.V., Arkhipov, V.I.: Distribution of gap states in

amorphous selenium thin films. Phys. Rev. B 59, 10607–10613 (1999)Spear, W.E., Adams, A.R.: Photogeneration of charge carriers and related optical properties in

orthorhombic sulphur. J. Phys. Chem. Solids 27, 281–290 (1966)Street, R.A.: Luminescence in amorphous semiconductors. Adv. Phys. 25, 397–453 (1976)Street, R.A., Mott, N.F.: Status in the gap in glassy semiconductors. Phys. Rev. Lett. 35, 1293–1296

(1975)Tanaka, K.: Free-carrier generation in amorphous semiconductors by intense subgap excitation.

Appl. Phys. Lett. 73, 3435–3437 (1998)

References 139

Tanaka, K.: Sub-gap excitation effects in As2S3 glass. J. Non-Cryst. Solids 266–269, 889–893(2000)

Tanaka, K.: The charged defect exists? J. Optoelectron. Adv. Mater. 3, 189–198 (2001)Tanaka, K.: Comment on “Investigation of the optical and electronic properties of Ge2Sb2Te5

phase change material in its amorphous, cubic, and hexagonal phases”. J. Appl. Phys. 101,026111 (2007)

Tanaka, K., Itoh, M., Yoshida, M., Ohto, M.: Photoelectric properties of Ag-As-S glasses. J. Appl.Phys. 78, 3895–3901 (1995)

Tanaka, K., Nakayama, S.: Band-tail characteristics in amorphous semiconductors studied by theconstant-photocurrent method. Jpn. J. Appl. Phys. 38, 3986–3992 (1999)

Tanioka, K., Yamazaki, J., Shidara, K., Taketoshi, K., Kawamura, T., Ishioka, S., Takasaki, Y.: Anavalanche-mode amorphous selenium photoconductive layer for use as a camera tube target.IEEE Electron Device Lett. 8, 392–394 (1987)

Terakado, N., Tanaka, K.: Photo-induced phenomena in GeO2 glass. J. Non-Cryst. Solids 352,3815–3822 (2006)

Toyama, T., Hiratsuka, K., Okamoto, H., Hamakawa, Y.: Hot-electron-induced electrolumines-cence and avalanche multiplication in hydrogenated amorphous silicon. J. Appl. Phys. 77,6354–6357 (1995)

Trukhin, A.N.: Excitons, localized states in silicon dioxide and related crystals and glasses. In:Pacchioni, G., Skuja, L., Griscom, D.L. (eds.) Defects in SiO2 and Related Dielectrics: Scienceand Technology, pp. 235–283. Kluwer, Dordrecht (2000)

Weimer, P.K., Cope, A.D.: Photoconductivity in amorphous selenium. RCA Rev. 12, 314–334(1951)

Weinstein, B.A.: Anomalous pressure response of luminescence in c-As2S3 and a-As2SeS2:Consequences for defect structure in chalcogenides. Philos. Mag. B 50, 709–729 (1984)

Weiss, D.S. Abkowitz, M.: Organic photoconductors. In: Kasap, S., Capper, P. (eds.) SpringerHandbook of Electronic and Photonic Materials, Chap. 39, pp. 953–982. Springer, New York,NY (2006)

Wey, H.-Y., Fritzsche, H.: Photovoltalic effect and space charge capacitance of amorphoussemiconductor-metal contacts. J. Non-Cryst. Solids 8–10, 336–340 (1972)

Chapter 6Light-Induced Phenomena

Abstract Light-induced structural changes are the most exciting phenomena inamorphous chalcogenides. We will overview thermal and photon effects andtheir mechanisms. These include bulk effects such as irreversible, reversible, andtransitory changes. There exist also photo-chemical reactions, the most knownbeing photodoping. In addition, these changes are either scalar (isotropic) or vec-tor (anisotropic) upon excitation of linearly polarized light. It is also shown thatcomputer simulations aid to understand the mechanisms. Light-induced phenomenain oxide, a-Si:H, and polymers are briefly discussed for comparison.

Keywords Photodarkening · Photo-crystallization · Photo-polymerization ·Photodoping · Photo-deformation · Vector effects · E′ center · Staebler-Wronskieffect

6.1 Overall Features

Radiation effects are widespread in this world. Most common may be the photosyn-thesis in plants and the vision in animals. Moreover, Toyozawa suggests that the lighttriggers syntheses of biological lives (Toyozawa 2003). In solid-state science, weknow the photographic reaction in Ag-halide crystals such as AgBrxCl1–x (Itoh andStoneham 2001), color center formation in alkali halides (Itoh and Stoneham 2001),and photo-polymerization in organic photoresist films (Kozawa and Tagawa 2010).In all these phenomena, the photo-electronic excitation induces successive structuralchanges. We also note that, for the photo-structural change to occur, two conditionsare required, which are electron–lattice coupling and electron localization.

The electron–lattice coupling is important also in crystals. Surveying the photo-structural change in crystals, we see that two kinds of materials are liable to bemodified (Itoh and Stoneham 2001, Toyozawa 2003). One is the ionic crystal asalkali halides, which is more likely to undergo the change than the covalent asc-Si. The other is low-dimensional crystals. Specifically, in low-dimensional organiccrystals, a photoinduced atomic change can induce cooperative phase transitions.These observations suggest that the strong electron–lattice coupling is a prerequisiteto the photo-structural change.

On the other hand, comparing crystal and non-crystal, we see that the radiationeffect is more prominent in the non-crystal (Itoh and Stoneham 2001, Toyozawa

141K. Tanaka, K. Shimakawa, Amorphous Chalcogenide Semiconductors and RelatedMaterials, DOI 10.1007/978-1-4419-9510-0_6, C© Springer Science+Business Media, LLC 2011

142 6 Light-Induced Phenomena

2003). In the ideal crystal, the wavefunction of an excited electron extends over thewhole sample volume, and accordingly, a quantum efficiency of photo-structuralchanges becomes very small. Otherwise, at finite temperatures, thermal latticevibrations may spontaneously localize the electron wavefunction to some atomicsite, which may undergo a bonding change. On the other hand, in the non-crystal,an excited electron and hole are promptly localized, due to disordered atomicstructures, and as a result, some atomic change is likely to occur.

Actually, the radiation effect in non-crystalline solids has attracted considerableinterest for a long time. The first discovery may be traced to a note on photoinducedfluidity in a-Se by Vonwiller (1919). For the oxide glass, a lot of studies hadbeen done before the 1970s in nuclear sciences (Lell et al. 1966). Weeks (1956)and Primak and Kampwirth (1968) found in g-SiO2, respectively, the so-calledradiation-induced E′-center formation and a radiation compaction. However, theseworks appeared not to arouse extensive studies. World-wide researches seem tostart after ∼1970 with two discoveries: optical and electrical phase changes inchalcogenides by Ovshinsky and coworkers (Ovshinsky and Fritzsche 1973) anda photoinduced refractive index change in silica glass fibers by Hill et al. (1978).

These two discoveries manifest marked differences between the chalcogenideand the oxide. The chalcogenide, having smaller bandgap energy (1−3 eV) andmore flexible atomic structures, is sensitive to illumination of visible light, as exem-plified in Table 6.1. We also know that a-Si:H films with bandgap energy of ∼1.7 eVundergo the so-called Staebler–Wronski effect upon illumination of visible light,a kind of photoinduced defect creation phenomena. Some photo-sensitive organicpolymers possess similar features. On the other hand, since the oxide glass hascomparatively rigid structures with bandgap energies greater than ∼5 eV, radiationeffects are less prominent, which appear under exposures of energetic beams such asγ-rays and intense light pulses. Or, the effects are likely to appear in optical fibers,since the fiber can provide sufficient light–matter interaction lengths.

It should be mentioned that many kinds of structural changes are triggered inthe chalcogenide also by other stimuli (Popescu 2001). Among the stimuli, elec-tron beam effects have been extensively studied, since we can inspect the change

Table 6.1 Typical photoinduced phenomena appearing in amorphous (glassy) oxide, sulfide,selenide, and telluride

VIb atom Photon Photo-thermal Thermal

O Refractive index increaseS Darkening, fluidity AnisotropySe CrystallizationTe Phase change

In the first line, photon means a pure photo-electro-structural change, photo-thermal a photo-structural change which is thermally activated in some temperature ranges, and thermal representsan optically induced thermal effect. With a decrease in the optical gap, the thermal contributionincreases

6.2 Thermal Effects in Chalcogenide 143

in situ in electron microscopes and also can produce fine patterns just by scan-ning a focused beam. Studies on other stimuli are fewer, which include x-rays(Hayashi and Shimakawa 1996), γ-rays (Shpotyuk 2004), neutrons (Lukášik andMacko 1981), ions (Guorong et al. 2001, Suzuki and Hosono 2002), and mechanicalimpacts (Suzuki et al. 1980). Induced changes by these stimuli may appear to besimilar to those induced by light, or there may be some differences due to thecharge, energy, and mass of the excitations. X- and γ-ray photons have longerpenetration depths than ∼50 μm, and accordingly, thick samples can be irradi-ated. Ion implantations can provide unique effects which depend upon the ionspecies.

For the chalcogenide, a variety of light-induced phenomena have been discov-ered. These can be divided into the two, whether the light-induced temperaturerise is determinative or not, i.e., thermal or photon (athermal) effects, which aredescribed in Sections 6.2 and 6.3.

6.2 Thermal Effects in Chalcogenide

The energy of photons absorbed in a solid is converted ultimately to a tempera-ture rise in many cases. Accordingly, opto-thermal changes commonly occur uponintense light illumination. Pulsed-laser ablation is a known example. However, it isnot clear if there are any characteristic differences between photo-electro-thermalchanges, which are induced by bandgap light, and pure opto-thermal changes,which are induced through direct vibrational excitations by infrared light. In otherwords, it is unclear if the electronic excitation plays some roles in the photo-electro-thermal change, partly because comparative opto-(non-electronic)-thermal studieshave been few.

At present, the most well-known thermal process in chalcogenides is the opti-cal phase change in telluride films, Ge–Sb–Te. The principle was opened fromOvshinsky’s group around 1970, which is described in Section 7.4.

The transmittance oscillation, Fig. 6.1, discovered by Hajtó et al. (1977) is afantastic phenomenon. Suppose that a free-standing GeSe2 film with a thickness of5 μm is exposed to focused light (∼200 μm in diameter) emitted from a conven-tional He–Ne laser (633 nm) with a light intensity of 10 mW. Then, surprisingly, theintensity of transmitted light oscillates with a typical frequency of ∼10 Hz, whichcan be noticed even by naked eyes. The phenomenon may be regarded as a kind ofoptical bistability.

Substantial work has been done, while the mechanism remains controversial.Hajtó and Jánossy (2003) propose that the oscillation process is partially thermal.First, light exposure gives rise to a photodarkening phenomenon (see Section 6.3.8),which in turn decreases transmitted light intensity. At the same time, the increasinglight energy absorbed in the film gives a temperature rise, which anneals the sample,recovering the initial higher transmittance. And, this process is repeated, resulting

144 6 Light-Induced Phenomena

time

transmittanceFig. 6.1 Transmittanceoscillation in free GeSe2films exposed to He–Ne laserlight of 1.7 kW/cm2 (upper)and 2.6 kW/cm2 (lower)

in the oscillation. In contrast, Phillips (1982) assumes that the oscillation occurs asa result of athermal photo-crystallization and amorphization. Recently, Tao et al.(2009) have proposed an interference model, in which constructive and destructiveinterference in the film is assumed to cause the oscillation. Though the mechanismbeing controversial, if the oscillating frequency could be higher, the phenomenonwould attract more interest in applications. Oscillation phenomena appear also inAsSe, As2Se3, As2S3 (Hajtó and Jánossy 2003), and even in a-Si:H (Abdulhalimet al. 1989). Nevertheless, if the mechanisms of these phenomena are commonremains to be studied.

Matsuda and Yoshimoto (1975) have demonstrated light-induced transitorymotion using bimetallic structures consisting of mica and Sb(As)-S films (Fig. 6.2).From temperature dependence and time constant of the effect, they conclude thatthe motion is caused by light-induced thermal expansion.

Fig. 6.2 A sketch of light-induced bending experiments and a typical response (Matsuda andYoshimoto 1975, © American Institute of Physics, reprinted with permission)

6.3 Photon Effects in Chalcogenide 145

6.3 Photon Effects in Chalcogenide

6.3.1 Classification and Overall Features

A variety of photo-electro-structural changes have been reported (Tanaka 1990,Shimakawa et al. 1995, Fritzsche 2000, Popescu 2001, Kolobov 2003), and someclassification may be valuable for grasping a perspective. Here, it should be notedthat the classification is likely to cause confusions due to the terminology, a phe-nomenon being named by its appearance or by its (estimated) mechanism. Forinstance, photo-bleaching (appearance) may appear as results of photo-oxidationand/or photoinduced bond conversion (mechanisms). Readers should take care ofthis point.

First, a photon effect is classified whether it occurs in bulk samples or as chemicalreactions with other elements as Ag (photodoping) or O (photo-oxidation). We herenote that these two processes manifest contrastive temperature dependences. Manybulk effects, except photo-enhanced crystallization, are more prominent at lowertemperatures, which implies the importance of localized atomic motions inducedby excited electronic carriers. Thermal relaxation tends to reduce or erase the bulkphoto-effects. In contrast, the photo-chemical reaction becomes less efficient atlower temperatures, probably because thermally activated atomic migration is arate-limiting process.

The bulk effect can be classified into memorized and transitory changes. Thememorized means that the effect exists in (quasi-)stable after cessation of illumina-tion, and the transitory means that the effect appears only during illumination, asthe photoconductivity. In addition, these two kinds of changes may be either scalaror vector, whether the change does not or does reflect the polarization direction ofexcitation light. The scalar change is isotropic, being governed by the energy ofphotons, while the vector is anisotropic, being influenced by the light polarization.

The memorized change can further be divided into irreversible and reversible,depending on if the change can be erased by an annealing treatment at some tem-peratures. In other words, the irreversible is a change toward a stabler equilibriumstate, as exemplified by photo-crystallization in a-Se and photo-polymerization inas-evaporated As2S3 films. On the other hand, the reversible change occurs towardan unstabler state, as in photodarkening and photoinduced electron spin resonance,which can be erased by annealing at temperatures of ∼Tg and ∼Tg/2. Roughly, thestabilization (irreversible) phenomena are more prominent, which may be a reasonwhy the mechanisms have relatively been understood.

It is valuable to grasp the irreversible and the reversible change in the scales ofquasi-stability and structural disorder. Figure 6.3 shows the relationship betweenas-prepared (disordered), illuminated, and annealed (ordered) states. The annealedstate must have the lowest free energy and smallest disorder, and photo-excitationalways produces unstabler and more disordered states. Such a photoinduced changemay resemble a defect creation in alkali halide crystals (Itoh and Stoneham2001), and it is reversible. On the other hand, as-prepared states are likely to beenergetically higher or lower than the illuminated state, depending upon preparation

146 6 Light-Induced Phenomena

ordered

disordered illuminated

excited

(a) (b)

kBT

configuration

Adi

abat

ic p

oten

tial

Fig. 6.3 Relationships among disordered (as-prepared), illuminated, and ordered (annealed) statesin (a) stability disorder scales and (b) an energy configuration diagram. Solid and dashed arrowsshow photo- and thermally induced changes

methods. Probably, the vacuum evaporation produces substantially unstable and dis-ordered structures, because the evaporation causes very rapid quenching of gaseousmolecules to solids on substrates. Then, illumination effects become irreversible.

The photoinduced change provides modifications in macroscopic properties, asexemplified in Table 6.2. The most common change, or the one being detectablewith high sensitivities, appears in optical properties: absorption and refractiveindex. Changes in sample volume (density) and shape may also appear. Mechanicalproperties such as elastic constant, hardness, and viscosity are also likely to bemodified. In addition, light illumination tends to change chemical etching charac-teristics. From a quantitative point of view, it had been believed (till ∼2000) thatphoto-chemical reaction such as photodoping gives the most prominent changes,irreversible the next, reversible following it, and vector the smallest. Recently,however, prominent vector deformations have been discovered, as described inSection 6.3.12.

It is believed that the photoinduced phenomena are inherent to, or substantiallyprominent in, amorphous chalcogenides. For instance, it has been amply demon-strated that the photodarkening does not appear in c-As2S3 (orpiment) (Hamanakaet al. 1977). The photodoping in c-As2S3 is demonstrated to be very inefficient(∼1/100) (Imura et al. 1983). However, it should be mentioned that some relatively

Table 6.2 Changes in some macroscopic properties with typical photoinduced phenomena

Phenomena Optical Deformation Elastic Etching

Irreversible © © ©◦ ©◦Reversible © © © ©Vector � ©◦ ? ?Transitory � � © �Photodoping ©◦ © ? ©◦Question marks indicate no related studies to the authors’ knowledge

6.3 Photon Effects in Chalcogenide 147

unstable chalcogenide crystals as c-As2S2 undergo photo-structural changesincluding photo-amorphization (Matsuda and Kikuchi 1973, Frumar et al. 1995,Shimakawa et al. 1995, Naumov et al. 2007).

6.3.2 Experimental

Some remarks on experiments of photoinduced phenomena may be valuable.We here emphasize that, in analyses of observations, it is important to considergeometrical factors such as sample thickness, size of light spot, and substrate.

The thickness should be compared with the penetration depth of excitationlight. The light, which may be monochromatic and propagating along the x-axis,is absorbed as exp(–αx), where α is the absorption coefficient. Accordingly, weassume that the light is absorbed within a penetration depth of ∼α−1, which is typ-ically 0.1−1 μm for super-gap light, 1−10 μm for bandgap light, and ∼1 mm forsub-gap light. We hence can envisage that photo-excitation occurs in a layer froma sample surface to the penetration depth. If the sample is sufficiently thinner thanthe depth, a photoinduced effect occurs uniformly throughout the film thickness.In such cases, analyses of time variations are straightforward, e.g., the transmittinglight intensity I(t) may exponentially decrease in a photodarkening process.

However, if the sample is thicker than the depth, we should be careful of a self-feedback effect in optical changes. Actually, in the photodarkening, a photoinducedincrease in absorption, which reduces α−1, tends to limit a darkened layer to thepenetration depth, despite prolonged exposures. The situation can be analyzed ina phenomenological way (Tanaka and Ohtsuka 1977). Provided that the reactionfollows a first-order process, following Lambert’s law, we write down the spatio-temporal changes in α and I induced by monochromatic light as

∂α(x, t)/∂t = K I(x, t) {αs − α(x, t)} and ∂ I(x, t)/∂x = −α(x, t)I(x, t), (6.1)

where K and αs are a reaction constant and a saturated absorption coefficient.The analysis demonstrates that for a photodarkening process, in which αs > αi(initial absorption coefficient), the reacted region is practically restricted to asurface layer of ∼αi

−1. Here, the transmitted light intensity may appear asa Kohlrausch–Williams–Watts-type stretched exponential, exp[−(t/τ )β ], whereβ < 1.0 (Shimakawa et al. 2009). It should be noted, however, that if carrier dif-fusion is prominent, as in photodoping (Tanaka 1991), the thickness restriction isrelaxed.

Excitation light is sometimes focused to a spot with a diameter of ∼10 μmin order to increase the irradiance. When the size of light spots is much smallerthan the penetration depth and the sample thickness, volume effects can appear,as will be described for a giant photo-expansion (Section 6.3.9). In addition,Nakamura et al. (1996) demonstrate the importance of boundary effects on photo-crystallization of a-GeSe2 films, the material having two crystalline forms of two-and three-dimensional.

148 6 Light-Induced Phenomena

Finally, we note that a variety of sample forms have been employed for studyingthe photoinduced phenomenon. Commonly employed are polished bulk samples,fibers, films on rigid substrates as oxide glasses, and Si wafers. Less studied arebimetallic structures (Figs. 6.2 and 6.26). In addition, Tanaka and coworkers haverecently demonstrated that As2S3 films deposited upon viscous substrates manifestanomalous shape changes under illumination (Fig. 6.27). The substrate appears toexert big constraints on macroscopic deformations of deposited films.

6.3.3 Computer Simulation

Notable computer-aided studies have been performed on bulk photon effects, asreviewed by Drabold et al. (2003) and Simdyankin and Elliott (2007). Historically,in the beginning, calculations followed the conventional tight binding analyses forsome modeled structures. Then, the calculation shifted to structures produced byclassical molecular dynamics. Recently, most studies follow the so-called ab initiosimulations (see Section 2.6), which may be divided into two: quantal moleculardynamics calculations using density functional theories for disordered structuresand quantum chemical calculations for clusters (Shimojo et al. 1998). In addi-tion, Kugler’s group has developed tight binding molecular dynamics simulations(Hegedus et al. 2005, Lukács et al. 2008).

These recent studies treat photoinduced effects as follows: First, plausibleatomic structures have been constructed through, e.g., relaxing presumed clustersor the ab initio molecular dynamics following “melt and quench” procedures (seeSection 2.6). Then, an electron is taken from HOMO (valence band) and added toLUMO (conduction band), and resulting structural changes are traced as a functionof time, which may be bond distortions, defect creation, and/or structural relaxation.Analyzed materials are mostly simple ones such as pure S(Se) and As2S(Se)3.

Reported time variations are instructive, while some cautions are needed forinterpreting the results. First, there exist some crucial problems for the initial atomicstructures, as described in Section 2.6. Second, in most studies, the excited carrierstill exists in HOMO and LUMO in the final state. The simulated structure is duringillumination (transitory change), not after illumination as the photodarkening. Third,the calculations have not been able to treat rigorously the photo-electronic excitationprocess. We cannot predict the position where a photo-electronic excitation isinduced by a photon having a fixed energy. In addition, illumination effects ofpolarized light have not been analyzed.

6.3.4 Photo-Enhanced Crystallization

Photo-enhanced crystallization in a-Se is a well-known irreversible change, whichwas comprehensively studied by Dresner and Stringfellow (1968). When evapo-rated a-Se films were exposed to light (∼1 W/cm2) emitted from a mercury lamp

6.3 Photon Effects in Chalcogenide 149

Fig. 6.4 Spherulites (with adiameter of ∼0.1 mm)produced by photo-irradiationon the surface of an a-Se film.The color is artificial

at ∼50◦C, crystal growths became dramatically faster, i.e., giving a rate increase bytwo orders than that in the dark. Opto-thermal temperature rise could be neglectedunder their experimental conditions. They also demonstrated that illumination atlower temperatures cannot crystallize a-Se, which suggests that the illumination justenhances the thermal crystallization. Accordingly, the word “photo-enhanced” maybe preferred to “photoinduced.” It was also demonstrated that the crystal growthcan be controlled by a flux of holes, not electrons, toward crystalline–amorphousboundaries. We thus speculate that the hole cuts entangled chain molecules, whichassist thermal alignment of Se molecules and successive crystal growth. Thephoto-enhanced crystallization of a-Se films is a big problem in photoconductiveapplications (see Section 7.6), which attract renewed interest. In many cases, smallamounts of As are added to a-Se for suppressing the crystallization, but the additionconcomitantly reduces the mobility of holes (see Fig. 4.23).

a-Se films show related phenomena to the photo-crystallization. Larmagnac et al.(1982) demonstrate that photo-relaxation occurs as a prelude to the crystallization.It is also known that, upon illumination of linearly polarized light, oriented crys-tallization, or vector crystallization appears (Innami and Adachi 1999). In addition,Roy et al. (1998) have demonstrated, by tuning the photon energy of excitationlight, a light-selective suppression of photo-crystallization. Since a-Se is the sim-plest amorphous semiconductor, we expect that studies on the material will revealfundamental insights into the photoinduced phenomenon.

Other materials show similar or related phenomena. Raman scattering spec-troscopy, which is more sensitive than direct microscope observations, has beenapplied to investigate photo-crystallization behaviors in GeSe2 (Sakai et al. 2003)and As-Se (Mikla and Mikhalko 1995). Brazhkin et al. (2007) have recently reportedphoto-crystallization of pressure-synthesized AsS bulk glass, which is composedwith As4S4 molecules. Pattern formation discovered in liquid S by Sakaguchi andTamura (2007) may be a kind of photo-crystallization. It should also be mentionedthat a photo-crystallization occurs also in protein (Murai et al. 2010), the fact sug-gesting that the phenomenon is common to one-dimensional molecular systems.In c-As2S3 (Frumar et al. 1995) and c-As1Se1 (Shimakawa et al. 1995), an appar-ently opposite phenomenon to the photo-crystallization, i.e., photo-amorphizationoccurs. Finally, it should be mentioned that if the photo-crystallization bears

150 6 Light-Induced Phenomena

some relation to the photo-thermal phase change in telluride films, described inSection 7.4, awaits further studies.

6.3.5 Photo-Polymerization

DeNeufville et al. (1974) have reported a comprehensive study of irreversiblephotoinduced changes in as-evaporated As2S(Se)3 films. When an as-evaporatedAs2S3 film with Eg ≈ 2.4 eV and n ≈ 2.5 is exposed to bandgap illumination atroom temperature, the film shows a redshift of the optical absorption edge “irre-versible photodarkening” by ∼0.1 eV (Fig. 6.5a), a refractive index increase of∼0.1, a thickness compaction of ∼1% (Kasai et al. 1974), and elastic hardeningof ∼20% (Tanaka et al. 1981). In addition, there appear dramatic changes in etchingrates of the film by alkali solutions and plasmas (Lyubin 2009). Thermal annealingat glass transition temperatures of ∼200◦C, which yields stabler As2S3 networks,gives similar, but not the same, macroscopic changes.

The principal mechanism has been understood to be photo-polymerization(DeNeufville et al. 1974). Vacuum-evaporated As2S3 films seem to consist ofmolecular species such as As4S4, As4S6, and S clusters, as illustrated in Fig. 6.5b,and these species undergo mutual polymerization upon bandgap illumination, result-ing in As2S3 networks. This microscopic structural change has been confirmedusing several methods such as x-ray diffraction (Fig. 2.3). A markedly sharp x-ray

Fig. 6.5 Irreversible changes in (a) the optical absorption edge (DeNeufville et al. 1974,© Elsevier, reprinted with permission) and (b) an atomic model for as-evaporated As2S3 films(modified from Nemanich et al. 1978)

6.3 Photon Effects in Chalcogenide 151

FSDP, which probably reflects the size of the molecules in as-evaporated films,becomes weaker and broader with the polymerization. Since the As2S3 networkis constructed with As–S bonds, this polymerization accompanies conversions fromhomo- (As–As and S–S in As4S4 and S clusters) to heteropolar As–S bonds, whichare stabler (see Table 2.4). The appreciable redshift (∼0.1 eV) of the optical absorp-tion edge in Fig. 6.5a, i.e., a reduction of the bandgap, may be ascribed to a changein electron wavefunctions from molecular to more extended ones. Reduction of anetching rate may be ascribed to the formation of stronger heteropolar bonds. In a pio-neering work, Keneman (1971) applied this phenomenon to holographic storages ofrefractive index and relief types.

It is plausible that some irreversible photo-polymerization appears in anyas-deposited films, since the irreversible change is a kind of stabilization processes.Koseki et al. (1978) demonstrate that Se films evaporated onto cooled substratesform the so-called red Se structure, being composed of Se ring molecules, whichare polymerized to chain molecules upon light illumination. Yellow As also seemsto show photo-polymerization (Rodionov et al. 1995). On the other hand, As2Se3films undergo less prominent changes than those in As2S3 (DeNeufville et al. 1974,Trunov et al. 2009), probably because as-evaporated species are not molecular asthose in As2S3. Ge–S(Se) films, which are obtained by vacuum sublimation, donot show clear photo-polymerization. Irreversible changes have also been reported,e.g., for Cu–As–Se (Asahara et al. 1975), Ga–La–S (Youden et al. 1993), and S-richAs–S bulk glasses (Kyriazis and Yannopoulos 2009).

6.3.6 Giant Photo-Contraction

Singh et al. (1979) have discovered giant photo-contraction in obliquely evapo-rated Ge–Se films. As shown in Fig. 6.6, obliquely evaporated GeSe3 films (incidentangle of 80◦) with a thickness of ∼1 μm undergo a volume contraction of 10–20%upon bandgap illumination. Irradiation of He+ ions gives a contraction of, surpris-ingly, ∼40% (Chopra et al. 1982). Naturally, it is plausible that properties such asoptical absorption and etching rates substantially change. Structural studies have

Fig. 6.6 Giantphoto-contraction inobliquely deposited GeSe3films (∼1 μm thick) as afunction of the oblique angle(modified from Singh et al.1979)

152 6 Light-Induced Phenomena

demonstrated that micro-voids existing in between columnar structures (Fig. 2.24)in obliquely evaporated films collapse with illumination (Kumar et al. 1989). Thus,for this phenomenon, we know the initial and final structures.

However, further problems remain. Why does the void collapse upon irradia-tion? And, why is the phenomenon remarkable in Ge–Se films, especially GeSe3?Viscosity reduction and surface tension may be responsible. On this problem,Lukács et al. (2008) recently report tight-binding molecular dynamics simulationsfor pure Se.

6.3.7 Other Irreversible Changes

Photo-bleaching, an increase in optical transmittance reflecting a blueshift of opticalabsorption edge, sometimes appears. Berkes et al. (1971) have reported a pioneer-ing study on the photo-bleaching in As–S(Se) films. Tanaka and Kikuchi (1973)demonstrate a photo-bleaching phenomenon in flash-evaporated films of As2S3.

It is reasonable to assume that photo-decomposition (phase-separation) causesthe photo-bleaching. In the flash-evaporated films, the intense heating tends toreduce the S content, producing As-rich AsxS3 (x > 2) films, which seem to exhibithigher optical absorption than that in illuminated As2S3 films (Tanaka and Ohtsuka1978). Then, a photoinduced decomposition, AsxS3 (x > 2) → As + As2S3, mayoccur in the As-rich As–S films or in locally As-rich regions in As2S3 films.Decomposed As atoms seem to migrate through unknown mechanisms over macro-scopic distances, segregating and producing As clusters, which may be oxidizedto c-As2O3, as actually detected (Section 6.3.15). Evaporated Ge–S(Se) films alsoundergo photo-decomposition.

In addition, anomalous irreversible changes have been reported for As–S(Se)systems. Photo-hardening is reported for g-As3Se2 (Asahara and Izumitani 1974)and annealed films (Kolomiets and Lyubin 1978). In ternary alloys such as Ge–As–Sfilms, irreversible volume expansions appear upon illumination (Knotek et al. 2009).In multi-layer structures consisting of As2S3/Se, photo-diffusion of Se atoms overthe layer structures appears (Tanaka et al. 1990, Adarsh et al. 2005).

6.3.8 Reversible Photodarkening and Refractive Index Increase

6.3.8.1 Overall Features

Reversible photodarkening, often referred to as “photodarkening,” and correspond-ing refractive index increase are phenomena universally observed in covalentchalcogenide glasses. The phenomena are simple, bulky, and quantitatively repro-ducible in stoichiometric compositions, and accordingly, it has attracted greatinterest, as reviewed several times, e.g., by Tanaka (1990), Pfeiffer et al. (1991),Shimakawa et al. (1995), Fritzsche (2000), and Kolobov (2003).

6.3 Photon Effects in Chalcogenide 153

Fig. 6.7 Photodarkening inan As2S3 film at 80 K

Many experiments have been performed for As2S3, due to its proper Eg(∼2.4 eV) and Tg (∼200◦C∼470 K). Samples can be As2S3 films or polished bulkflakes (being preferred for fundamental studies), which have been annealed at∼180◦C, just below the glass transition temperature. The thickness should be thin-ner than ∼10 μm, which corresponds to the penetration depth of bandgap light with�ω ≈ Eg. When such a sample is exposed to bandgap illumination at room tem-perature, it undergoes a (nearly) parallel redshift �E by ∼50 meV of the opticalabsorption edge (Fig. 6.7), or more precisely, a redshift of the Urbach edge and areduction of the Tauc gap, which cause a color change of the sample from yellowishto orange, the naming origin of photodarkening.1 The shift can be recovered witha successive annealing treatment at ∼180◦C, and the illumination–annealing cyclecan be repeated many times. The redshift of ∼50 meV accompanies a refractiveindex increase of ∼0.03 at transparent wavelengths, which are quantitatively con-nected through the Kramars–Krönig relation or simply by the so-called Moss rule(Utsugi 1999).

A variety of photodarkening characteristics have been investigated, which willbe discussed in the following sections. For the time dependence of photodarkeningprocesses, see Section 6.3.2.

6.3.8.2 Dependence upon Temperature and Pressure

The photodarkening has been investigated as functions of temperature Ti and pres-sure Pi, respectively, at which a sample is illuminated (Tanaka 1990, Pfeiffer et al.

1The word “photodarkening” may refer to, in general, a decrease in optical transmittances, andactually, it is employed in that sense by some researchers. However, it should be noted that, in thepresent context, the photodarkening represents a redshift of optical absorption edges.

154 6 Light-Induced Phenomena

(b)

(a)

Fig. 6.8 Magnitudes of the redshift �E as functions of (a) temperature Ti normalized to Tg forseveral stoichiometric chalcogenides listed and (b) hydrostatic pressure P in Se

1991, Shimakawa et al. 1995, Fritzsche 2000). For the temperature dependence, ithas been demonstrated, as shown in Fig. 6.8a (Tanaka 1983), that �E in elementaland stoichiometric chalcogenides decreases with an increase in Ti/Tg and becomeszero at Ti/Tg ≈ 1. This dependence manifests that thermal relaxation suppresses thephotodarkening. On the other hand, it is fairly difficult to examine pressure effects,since the glass transition temperature tends to become higher under compressionas shown in Fig. 6.8b (Tanaka 1990, Ikemoto et al. 2002), and the illumination–annealing should be performed under fixed pressures. Following such procedures,Tanaka (1990) has demonstrated, as shown in Fig. 6.8b, that �E in Se first increaseswith compression, which can be related to an increase in Tg, while �E turns todecrease above ∼1.5 GPa (=15 kbar). As described in Section 2.4, x-ray stud-ies have demonstrated that compression reduces the intermolecular van der Waals(interlayer) distance, ultimately producing isotropic bonds. Therefore, �E decreaseimplies that photodarkening relies upon the dual bonding structure, consisting ofcovalent and van der Waals bonds.

6.3.8.3 Dependence upon Excitation Light

It is natural to assume that the photodarkening is induced by absorbed light (Tanaka1990, Pfeiffer et al. 1991, Shimakawa et al. 1995, Fritzsche 2000). Alternatively,non-absorbed light cannot put any energy to a material for inducing some photo-electro changes. Actually, as shown in Fig. 6.9a, efficiency of the photodarkeningin As2S3 normalized by an absorbed photon shows a dramatic decrease at �ω ≤Eg(∼2.4 eV). This observation suggests that excitation of lone pair electrons is a

6.3 Photon Effects in Chalcogenide 155

(a) (b)

quan

tum

effi

cien

cyqu

antu

m e

ffici

ency

Fig. 6.9 Dependence of (a) a quantum efficiency and (b) saturated redshift and refractive indexincrease on the photon energy of excitation in As2S3 (Eg ≈ 2.4 eV) (modified from Shimakawaet al. 1995)

prerequisite to the photodarkening. However, we see in Fig. 6.9b that the sat-urated �E and the corresponding refractive index increase �n, after prolongedillumination, provide much milder dependence upon the photon energy. Urbach-edge light with photon energy of 2.0–2.4 eV can also give marked (∼1/2) opticalchanges. It seems that the quantum efficiency is governed by photo-excitation pro-cess, while the saturated value reflects an equilibrated state determined by excitationand thermal relaxation (Tanaka 1990).

Illumination with other photon energies appears to give a different excitationprocess from that of the photodarkening. Mid-gap light with �ω ≈ Eg/2 may excitelocalized states, and if it is intense, nonlinear optical excitation occurs, inducinga refractive index increase without photodarkening (Tanaka 2004). On the otherhand, effects of (ultra-)super-gap light, i.e., soft x-ray, which can excite core elec-trons and/or bonding electrons, remain to be studied (Hayashi and Shimakawa1996).

Dependence upon light intensity was investigated for bandgap illumination. It hasbeen demonstrated that the reciprocity law between the intensity and the exposuretime holds only in a rough sense. In detail, as shown in Fig. 6.10 (Tanaka 1990),�E increases in proportion to ln I, where I is the light intensity (∼50 mW/cm2).However, the figure also shows that the intensity dependence becomes negligible at80 K. These results can be quantitatively understood as �E being determined from abalance between photo-excitations and thermal relaxations. It should be mentionedthat dependence of �E on I of sub-gap light shows a slightly different behavior(Fig. 6.16).

156 6 Light-Induced Phenomena

Fig. 6.10 Dependence of photodarkening �E upon the intensity I of bandgap light (∼2.54 eV)in As2S3 at exposure temperatures of 80 and 290 K (Tanaka 1990, © Elsevier, reprinted withpermission). The solid point at 290 K is obtained using a pulsed dye laser, for which the horizontalscale depicts the time-averaged power. The solid lines show theoretical results with the right-handside scale

Effects of cw and pulsed bandgap illuminations seem to be controversial. Tanaka(1990) demonstrates for As2S3 that if the total doses are fixed, cw and pulse excita-tions (3 ns, 488 nm, 0.5 MW/cm2) give the same �E (Fig. 6.10). On the other hand,Rosenblum et al. (1999) have reported a “strong” photosensitivity increase in AsSefilms upon pulse excitations of 5 ns, 532 nm, and 10 MW/cm2. The difference maybe due to different materials and/or peak intensities.

6.3.8.4 Dependence upon Materials

Dependence upon materials and glass compositions may be more interesting(Tanaka 1990, Shimakawa et al. 1995, Reznik et al. 2006). The photodarkeningappears universally in covalent chalcogenide glasses, including elemental S andSe, stoichiometric (as As2S3), and non-stoichiometric multi-component alloys(as Ge–As–S). Naturally, the magnitude varies with materials.

As shown in Fig. 6.8, for elemental and stoichiometric glasses, when scaled withTi/Tg, �E decreases in the order of sulfide, selenide, and telluride. Tellurides hardlyshow the photodarkening (Tanaka 1990, Hayashi et al. 1997). It is known that, in thisorder, the dual bonding structure, consisting of covalent and van der Waals bonds,changes to a metallic character. Therefore, the dependence on the chalcogen speciesreinforces the idea that the dual bonding structure is essential for photodarkening.

Regarding compositional variations in binary As(Ge)–S(Se) systems, as shownin Fig. 3.9d, the material with Z = 2.67 tends to exhibit maximal photodarkening(Tanaka 1990). This result is probably governed by, at least, two factors. One is that,as shown in Fig. 3.9a, with increasing Z, the glass transition temperature Tg becomeshigher, so that Ti/Tg at Ti ≈ 300 K decreases, which increases �E, as suggested inthe temperature dependence. On the other hand, in glass with Z ≥ 2.67, the amor-phous structure becomes to be three-dimensionally cross-linked, i.e., the role of

6.3 Photon Effects in Chalcogenide 157

the van der Waals interaction is reduced, which seems to suppress photodarkening.It should be mentioned, however, that photodarkening characteristics in As–S(Se)and Se films are not modified by hydrogenation (Fritzsche et al. 1981, Nagels et al.1995), which may decrease Z.

In contrast, it is interesting to point out that some materials do (or may) not showthe photodarkening. First, photodarkening does not appear in ultrathin (∼10 nm)As2S3 films (Hayashi and Mitsuishi 2002). We may speculate that photo-excitedcarriers diffuse over ∼10 nm and recombine at the surface of films, thereby giv-ing rise to no photo-structural changes. Second, photodarkening does not appearin the crystal as c-As2S3 (orpiment) (Hamanaka et al. 1977). The disorder seemsto be a prerequisite. Third, behaviors in ionic chalcogenide glasses are controver-sial. Liu and Taylor (1987) have demonstrated that Cu-alloyed As2S(Se)3 do notexhibit photodarkening, which can be interpreted in two ways: fourfold coordinationof S in the alloy makes the glass network too rigid or the Cu–S(Se) level exist-ing at the valence band top masks the modification of lone pair states (Aniya andShimojo 2006). The photodarkening neither appears in Na–Ge–S glasses (Tanakaet al. 2003), which is understandable following similar ideas. We also note that, in anion-conducting glass as Ag–As–S, photo-ionic effects (described in Sections 6.3.13and 6.3.14) tend to mask the photodarkening. In contrast, Loeffler et al. (1998)report reversible photoinduced structural changes in Ga–Ge–S glasses upon pulseexposures. Fourth, results for the oxide glass are also controversial. Taylor’s groupdemonstrated a parallel redshift (∼0.8 eV) of the optical absorption edge (at ∼3 eV)in g-As2O3 under x-ray irradiation (Hari et al. 2003). But, Terakado and Tanaka(2007) have detected no redshifts in g-GeO2 upon exposures to bandgap light. In theglassy GeS2–GeO2 system, photodarkening becomes smaller with an increase in theGeO2 content, disappearing at around 50GeS2–50GeO2. Finally, it is inconclusiveif the photodarkening appears in the pnictide such as a-As (Mytilineou et al. 1980)and a-P (Hosono et al. 1985). We also mention here that, in As-rich As–Se and Ge–S(Se) films, quantitative reproducibility of the photodarkening is worse, probablydue to strong dependence of amorphous structures upon preparation conditions.

6.3.8.5 Mechanisms

Why does the photodarkening, i.e., the photoinduced redshift of absorption edges,occur in the chalcogenide? It is known that the redshifts are induced also by temper-ature rising and hydrostatic compression (Figs. 4.13 and 4.14), so that a comparisonof these three changes may be interesting (Tanaka 1990). However, as described,photodarkening is erased by annealing and suppressed by compression. We thusassume that photodarkening appears through a unique structural change.

Several circumstantial evidences support that the valence band broadeningcauses photodarkening (Tanaka 1990, Shimakawa et al. 1995, Fritzsche 2000).For instance, Eguchi and Hirai (1990) have demonstrated for thin a-As2S3 (Eg ≈2.4 eV) films that the photodarkening is a manifestation of broadening of the mainoptical absorption band centered at �ω ≈ 5 eV, which reflects optical transitionsfrom lone pair electron (valence band) to covalent anti-bonding states (conduction

158 6 Light-Induced Phenomena

band). Here, the conduction band is possibly intact due to a rigid anti-bonding char-acter. Accordingly, it is reasonable to ascribe the photodarkening to a broadening ofthe valence band. (Unfortunately, the photoelectron spectroscopy has not sufficientspectral resolution for detecting this change.) The problem is, therefore, reduced toa broadening mechanism of the lone pair electron band with light illumination. Forthis problem, Malinovsky and Novikov (1986) have suggested that thermal spikes,which are produced by recombination of localized electronic carriers, cause localstructural disordering, which may broaden the valence band. However, such con-ceptual models face a difficulty in explaining detailed features as the light intensityand the composition dependence.

As reviewed by several researchers (Tanaka 1990, Pfeiffer et al. 1991,Shimakawa et al. 1995), the configuration coordinate model delineates moredetailed features for atomic structural changes. For instance, Tanaka (1990) hasproposed a model, illustrated in Fig. 6.11, which can quantitatively explain thephotodarkening variations with temperature, light intensity, and exposure time. Heassumes that an adiabatic potential of photodarkening sites is expressed with asingle- and double-well model, an excited state having a single minimum of Z andground states having a stable X and a quasi-stable Y configuration. The density ofsuch sites is estimated to be ∼1% of total atoms. (Note that this density correspondsto an atomic site in a cube with a side length of five atoms, i.e., 1–2 nm, or, one sitein a volume pertaining to the medium-range order.) The excitation energy of Y issmaller than that of X, and accordingly, we can assume that �E ∝ NY , where NY

is the number of atomic sites having Y configuration. Then, in the annealed state, itis reasonable to envisage that all the sites have X configuration. Bandgap excitationinduces an energy configuration change as X → Z′ → Z → Y , which gives rise tophotodarkening. On the other hand, annealing assists a thermal relaxation processY→X, surmounting the barrier in between. Here, the barrier height EB seems to varyfrom site to site, and in g-As2S3, it is estimated at 0.5–1.5 eV.

An important problem is the atomic structure, which can possess an energy con-figuration relation as that in Fig. 6.11. Despite many experiments and theoreticalmodels, however, we cannot attain the final elucidation of structural mechanisms.

Fig. 6.11 An energyconfiguration model forphotodarkening

6.3 Photon Effects in Chalcogenide 159

The main reason is subtle structural changes, which cannot be experimentally identi-fied. Structural studies demonstrate that the nearest-neighbor configuration remainsintact, at least, in a-Se and stoichiometric alloys (Pfeiffer et al. 1991, Kolobov et al.1997). It is plausible that the structural disordering, which appears as broadeningof FSDPs (Tanaka 1975), is an origin of the redshift (Kolobov et al. 1997, Honolkaet al. 2002, Lucas et al. 2005). Nevertheless, the origin of FSDP remains controver-sial, as described in Section 2.4. Since the initial and the final structures cannot beidentified, the transformation dynamics remain necessarily more speculative.

The atomic structural modification may arise from medium-range structures, asintermolecular disordering, or from defective structures (Tanaka 1990, Pfeiffer et al.1991, Shimakawa et al. 1995). A bond-twisting motion illustrated in Fig. 6.12a,which quantitatively satisfies the bistable configuration model (Fig. 6.11), causessuch intermolecular disordering (Tanaka 1990). Shimakawas’ model, Fig. 6.12c,assuming Coulombic repulsion between segmental structures induced by photo-generated immobile electrons, also ascribes the photodarkening to the interlayerdisordering (Shimakawa et al. 1998). On the other hand, defective models have beenrepeatedly presented (Fritzsche 2000, Simdyankin and Elliott 2007). For instance,it is assumed that the conversion of normal bonds to D+ and D− is the origin ofphotodarkening. Otherwise, the bond conversion from heteropolar to homopolar

(a)

(b)

(c)

Fig. 6.12 Structural models for the photodarkening assuming (a) bond-twisting (Tanaka 1990),(b) structural changes through defects (Kolobov et al. 1997), and (c) Coulombic layer movements(Shimakawa et al. 1998)

160 6 Light-Induced Phenomena

may be responsible, while the model cannot be applied to pure S and Se. Kolobovet al. (1997) propose, on the basis of EXAFS studies for a-Se, that both the inter-molecular disordering and charged defects are produced by bandgap illumination,as illustrated in Fig. 6.12b.

6.3.9 Other Reversible Changes

It has been demonstrated that bandgap illumination induces reversible changes ina variety of properties (Pfeiffer et al. 1991, Shimakawa et al. 1995). Experimentsusing x-ray diffraction (Tanaka 1975) and vibrational spectroscopy (Iijima and Mita1977) have detected structural changes, which suggest enhancement of structuraldisorders. As for macroscopic properties, reversible changes in sample volumes(Hamanaka et al. 1976), thermal properties (Kolomiets et al. 1979), mechani-cal properties (Kolomiets and Lyubin 1978), chemical properties (Kolomiets andLyubin 1978), and electrical properties (Hamada et al. 1972) have been discovered,as described later.

However, at the present stage, it is not necessarily clear if these changes aredirectly connected with the photodarkening. There is a possibility that bandgapillumination causes several kinds of atomic changes, including structural disorder-ing and creation of defects, which cause these changes individually (Lucas et al.2005, Holomb et al. 2006, Yang et al. 2009). It is also plausible that super- andsub-bandgap illuminations induce different structural changes.

In addition, we should be careful about temporal behaviors. Tanaka (1998)has demonstrated different growth rates of the photodarkening (redshift) and aphotoinduced volume expansion. However, since the redshift is probed with trans-mitted light and the expansion is evaluated at the surface, which needs transfersof some atomic changes to the surface, the different temporal changes may neces-sarily appear, even if the both originate from a common atomic change. Nakagawaet al. (2010) have also demonstrated different time variations of the photodarkening,volume expansion, and photoconductive degradation, giving rise to a conclusion ofno direct relationship between the three. However, their measurements are carriedout in situ, and accordingly, the results may be influenced by transitory changes(Section 6.3.11).

6.3.9.1 Photoinduced Electrical Changes

Since the photodarkening is a change in optical absorption, we straightforwardlyenvisage resulting photoconductive changes. Actually, Hamada et al. (1972) discov-ered in Ge1As4Se5 films a photoconductivity decrease by light illumination, whichwas removed by annealing near the glass transition temperature. The phenomenonappears to be similar to the so-called Staebler–Wronski effect, a photoinducedphotoconductivity degradation in a-Si:H films (Section 6.5.2), and such similar-ity has motivated further studies for the chalcogenide (Shimakawa et al. 1995,

6.3 Photon Effects in Chalcogenide 161

Fig. 6.13 Temperaturedependence of dark current(dashed line) andphotocurrent under lightillumination of 2.8 eV and1 mW/cm2 in annealed (solidline) and light-soaked (dottedline) in g-As2S3. Solid arrowsindicate the changes inducedby light soaking (Hg lamp for30 min) (Toyosawa andTanaka 1997, © AmericanPhysical Society, reprintedwith permission)

Toyosawa and Tanaka 1997, Kounavis and Mytilineou 1999). As illustrated inFig. 6.13 for As2S3, the photo-degradation depends on temperature at which theillumination was performed. It shows a maximal decrease at ∼300 K, while atlower temperatures than ∼150 K the photocurrent increases upon light illumination.The decrease and increase may be caused by defect creation and enhanced absorp-tion. Due to these degradation effects, it remains vague if the photoconductionspectrum redshifts with the photodarkening. It has also been demonstrated thatthe photoinduced photoconductivity degradation becomes less prominent with adecrease in the bandgap of materials: No and a little changes appear in As2Te3(Eg ≈ 0.84 eV) (Hayashi et al. 1997, Toyosawa and Tanaka 1997) and Sb2Se3(Eg ≈ 1.24 eV) (Aoki et al. 1999), which are consistent with small photodarkeningin narrow-gap chalcogenide glasses.

Light illumination also affects ac conductivities (Shimakawa et al. 1995).Bandgap illumination increases capacitance (imaginary part of the ac conductiv-ity) by ∼15% in As-Se films, which is recovered by subsequent annealing at170◦C. It has also been demonstrated that the ac conductivity (real part) in a-As2S3increases after prolonged illumination However, the annealing characteristic is notsimple. Although the conductivity increase induced by illumination at 90 K isannealed out at around 200 K, the increase induced at room temperature is removedby annealing near the glass transition temperature. This result suggests that twokinds of defective centers are photoinduced: One is quasi-stable at low temperaturesand the other at high temperatures.

The photoconductive degradation and ac conductivity increase can be ascribed tophoto-creation of defective centers. To interpret the details, Shimakawa et al. (1995)have adopted the modified charged defect model, proposed by Kastner et al. (seeSection 4.4). They assume that there are two kinds of spatial arrangements of thecharged defect; randomly-isolated and paired (intimate) defects. The former mayact as recombination centers for photo-excited carriers, reducing photocurrents, andthe latter may be responsible for the ac conductivity change.

162 6 Light-Induced Phenomena

Fig. 6.14 A setup for measuring thickness changes in g-As2S3 and an obtained trace onthe recorder (Hamanaka et al. 1976, © Elsevier, reprinted with permission), which shows aphotoinduced expansion of ∼10 nm

6.3.9.2 Photoinduced Volume Changes

Hamanaka et al. (1976) have discovered that bandgap illumination gives a vol-ume change. They detect, after illumination at room temperature, a volume (filmthickness) expansion of ∼0.4% in As2S3 and contraction of ∼0.2% in Ge1As4Se5,both of which can be recovered by annealing at the glass-transition temperatures.Similar volume changes have been uncovered in annealed films or bulk samples ofchalcogenides (Mikhailov et al. 1990, Calvez et al. 2009), and even in a-Se films atroom temperature (Asao and Tanaka 2007).

Why do the expansion and contraction appear? On this problem, Tanaka (1998)has found an interesting tendency. The amorphous material having a compact struc-ture exhibits an expansion and vise versa. Here, the degree of compactness can beevaluated using a density ratio R = ρg/ρc, where ρg and ρc are the densities of aglass and the corresponding crystal, respectively. In an ultimate case, in alkali-halidesingle crystals (R = 1), irradiation produces Schottky defects, which may appear asa volume expansion (Kittel 2005). This fact implies that, in relatively dense mate-rials, the photoinduced disordering causes a volume expansion. In similar ways,as listed in Table 6.3, the amorphous material with R � 0.85 appears to photo-expand. On the other hand, in a glass having relatively open structures as g-SiO2,irradiation tends to compress the structure through some photo-electro-structuralmechanisms.

What is the motive force of the volume expansion? There are roughly twoideas. One is an atomic mechanism. Tanaka (1998) assumes that the disordering inintermolecular distances, which may be caused by the photoinduced bond twisting(Fig. 6.12a), is responsible for the expansion. If a glass structure is not dense, inter-changes in atomic bonds may cause a volume contraction, as observed in SiO2 andGe1As4Se5. On the other hand, Shimakawa et al. (1998) propose an electrical model(Fig. 6.12c). Coulombic repulsion forces produced by photo-generated electrons,which are immobile in the chalcogenide glass of interest, trigger the expansion.However, this idea has difficulty in explaining the contraction. We also note that all

6.3 Photon Effects in Chalcogenide 163

Table 6.3 Radiation-induced volume changes and related data in some glassy (g-) and crystalline(c-) materials (Tanaka 1998, Asao and Tanaka 2007, Terakado and Tanaka 2007)

Material Excitation �V/V (%) ρg ρc R

g-Se Light +0.3 4.25 4.80 0.89g-As2S3 Light +0.4, +0.7 3.2 3.43 0.93g-As2Se3 Light +0.7 4.58 4.75 0.96g-GeS2 Light +0.5 2.7 2.94 0.92g-GeO2 Light +0.2 3.7 4.2 0.88g-Ge1As4Se5 Light −0.2g-SiO2 e-Beam, neutron −3 2.2 2.65 0.83g-SiO2Na2O Light +c-SiO2 e-Beam, neutron +10, +15c-KBr X-ray +0.0001

the models cannot offer quantitative interpretations (Emelianova et al. 2004). Forinstance, why does g-As2S3 expand by ∼0.4% at room temperature?

Hisakuni and Tanaka (1994) have discovered that the volume expansion in As2S3becomes ∼5%, greater by an order, when exposed to intense sub-gap light of∼2.0 eV. Upon exposures at 10 K, an actual expansion amounts to ∼20 μm (Tanakaet al. 2006). This giant expansion by sub-gap illumination was a big surprise,because as shown in the spectral dependence (Fig. 6.9), it had been believed thatthe photo-structural change became prominent under bandgap illumination (�ω ≈2.4 eV in As2S3). Why can the less energetic photons, i.e., Urbach-edge light, givesuch a giant volume expansion?

The giant photo-expansion appears, as illustrated in Fig. 6.15, through a volu-metric enhancement of the conventional expansion (Hisakuni and Tanaka 1994).Suppose that an illuminated cylinder, with a light spot of size 2r and a penetrationdepth L (≈ α−1), is expanding with a ratio of �V0/V. The expansions toward side-and rear-ward directions, however, cannot occur, due to the existence of periph-eral un-illuminated regions. Here, we assume a kind of fluidity in the illuminatedvolume (see Fig. 6.22), which is able to transform the expansions toward the freesurface. Then, an observed expansion �L/L appearing at the surface can be written

Fig. 6.15 Giant photo-expansion in g-As2S3 (left) (Hisakuni and Tanaka 1994, © AmericanInstitute of Physics, reprinted with permission) and its mechanism (right)

164 6 Light-Induced Phenomena

as �L/L = (�V0/V)(1+L/r). This r dependence with �V0/V ≈ 0.4%, which is anintrinsic volume expansion in g-As2S3 at room temperature (Hamanaka et al. 1976),has given quantitative agreements with experimental results. We here underline thatL > r is a necessary condition for the giant expansion, which can be satisfied forsub-bandgap light. In other words, the giant photo-expansion appears as a result ofa geometrical amplification of the conventional photo-expansion. This quantitativeagreement also suggests that the intrinsic fractional expansion is independent of thephoton energy of illumination at 2.0–2.4 eV.

Here, we should be careful about light intensity. Figure 6.16 shows thephotodarkening �E, the fractional expansion �L/L, and the photoinduced fluidityη−1 (Section 6.3.11) as a function of the absorbed light intensity αI in g-As2S3.We see that, under bandgap illumination of 2.4 eV, �E ∝ ln I (Fig. 6.10)and �L/L ≈ 0.4%, as described. On the other hand, under sub-gap illuminationof 2.0 eV (α ≈ 1 cm−1), �E becomes comparable to that induced by bandgapillumination at αI ≥ 102 W/cm3, where the giant photo-expansion becomes greaterwith the light intensity. We also note that the photoinduced fluidity (η−1) becomesprominent at the same region.

This intensity dependence gives an interesting insight (Tanaka 2003). Theabsorbed light intensity of ∼102 W/cm3 corresponds to a photon number of∼1020 s–1 cm–3. Then, suppose a photo-electronic excitation with a quantumefficiency of unity, the same number of carriers is excited, which is trapped instan-taneously (with timescales of picosecond). A typical trap depth can be assumed tobe ∼0.5 eV, for which the thermal releasing time becomes ∼1 ms, and accord-ingly, the trapped carrier density is 1017–1018 cm−3 in steady state. This is thedensity giving rise to a transitory photoconduction redshift, which has been inter-preted to arise from the filling up of trapping states (Section 5.4.1). It seems that

Fig. 6.16 Dependence of the photodarkening �E (solid line (–) and circles ( )), the fractionalexpansion �L/L (squares (�)), and the photoinduced fluidity η–1 (triangles (�)) upon absorbedlight intensity in g-As2S3 (Tanaka et al. 2006, © INOE, reprinted with permission). The solid lineand solid squares are obtained using bandgap light (2.4 eV) and others are by Urbach-edge light(2.0 eV)

6.3 Photon Effects in Chalcogenide 165

the intense Urbach-edge light, which has longer penetration lengths, behaves as if itwere bandgap light.

6.3.9.3 Photoinduced Thermal, Mechanical, and Chemical Changes

Bandgap illumination induces reversible changes also in structural properties. First,the glass-transition temperature becomes higher with illumination (Kolomiets et al.1979, Lucas et al. 2005). Second, reversible changes in mechanical propertiesappear (Kolomiets and Lyubin 1978). Tanaka et al. (1981) have evaluated, usingsurface acoustic waves propagating in a-As2S3 films, reductions of elastic constantsto be ∼10%. Honolka et al. (2002) have discovered for As2S3 at low temperaturesa strong effect of the photodarkening upon tunneling states. Third, etching prop-erties also change (Lyubin 2009), i.e., irradiated regions in annealed films tend tobe etched more easily. All these changes imply some structural disordering withillumination, which is consistent with other observations.

6.3.10 Photoinduced Phenomena at Low Temperatures

6.3.10.1 Observations

At low temperatures of Ti/Tg � 0.5, bandgap illumination induces specific phenom-ena, in addition to the photodarkening (Shimakawa et al. 1995). The phenomenainclude the so-called photoluminescence fatigue (intensity decrease), mid-gapabsorption formation, and ESR signal emergence. A common feature to thesechanges is, as shown in Fig. 6.17, the disappearance upon heating to ∼Tg/2, whichis 200−300 K in g-As2S(Se)3 (Hautala et al. 1988). Note that the photodarkening,which does not accompany induced ESR signals, disappears at ∼Tg. It shouldbe mentioned that the corresponding crystal such as c-As2S3 shows no similarphotoinduced phenomena. It should also be mentioned that Ge-alloy glasses presentdifferent and complicated changes. In Ge–S glasses, not only the photoluminescencefatigue, but also a photoluminescence enhancement appears (Seki and Hachiya

Fig. 6.17 Annealingbehaviors of photoinducedESR (total, type I, and typeII), mid-gap absorption, andphotodarkening in g-As2S3(modified from Hautala et al.1988)

166 6 Light-Induced Phenomena

2003). In g-GeO2, photoinduced ESR appears, while photoluminescence andmid-gap absorption scarcely change (Terakado and Tanaka 2006).

The low-temperature photoinduced phenomenon was first noticed by Cernogoraet al. (1973) as the fatigue of photoluminescence in g-As2Se3. Afterward, decreasesin the photoluminescence intensity to 1/2–10−2 have been observed in manychalcogenide glasses (Street 1976). The fatigue remains stable at low tempera-tures, while it can be recovered by heating or infrared irradiation. Detailed studieshave demonstrated complicated features in inducing and annealing kinetics andalso in photoluminescence spectra (Tada and Ninomiya 1991). Putting such obser-vations aside, we can assume that the photoluminescence fatigue represents adensity increase in non-radiative recombination centers. However, since the ori-gin of photoluminescence appearing at the half-gap in chalcogenide glasses isspeculative (see Section 5.2), the fatigue remains unanswered.

A few years later, Bishop et al. (1977) discovered a photoinduced mid-gapabsorption, the spectrum distributing at Eg/2−Eg (Fig. 6.18). As shown in Fig. 6.17,a thermal annealing behavior of the mid-gap absorption is similar to that of thephotoluminescence fatigue.

Bishop et al. (1977) also discovered an emergence of ESR signals at aroundg ≈ 2.00, the so-called photoinduced ESR. The density of induced spins varies at1017–1020 cm−3, depending upon the intensity of excitation light. For low intensity(∼1 mW/cm2) at 4.2 K, the density saturates at ∼1017 cm−3 in As2S(Se)3 and∼1016 cm−3 in Se. These centers, denoted type I in Fig. 6.17, are annealed outat around 200 K. The center is also bleached by infrared irradiation with the pho-ton energy in the optically induced mid-gap absorption band. At high excitation

Fig. 6.18 Optical absorptionspectra of g-As2S3 reportedfrom three groups (Biegelsenand Street 1980, © AmericanPhysical Society, reprintedwith permission). Theright-hand side “INITIAL” isthe spectrum of annealedsamples, which is redshiftedby light excitation of 2.41 and2.54 eV. Sub-gap light of1.92 eV recovers partially theredshift (to thephoto-darkened state).Quantitative differences mayarise from differentexperimental conditions assample thicknesses

6.3 Photon Effects in Chalcogenide 167

intensities (≥100 mW/cm2), the spin density exceeds 1020 cm−3 (Biegelsen andStreet 1980, Hautala et al. 1988). This stabler center, denoted type II in Fig. 6.17, isannealed out at ∼300 K.

6.3.10.2 Mechanisms

It is still vague if the three changes (photoinduced changes in photoluminescence,mid-gap absorption, and ESR) arise from a common structural change. Specifically,to the authors’ knowledge, no studies have been reported for dependence of themid-gap absorption upon excitation light intensity. In addition, since we are dealingwith the spin density as small as ∼1016 cm−3, impurity effects should be carefullyexamined. Nevertheless, it seems highly plausible that newly created “some kindsof defects” dominate these photoinduced changes.

The conventional interpretation is to use the charged defect model (Shimakawaet al. 1995). We can envisage a conversion of D+ and D− to D0 upon photo-excitation. The neutral dangling bond D0, which inherently produces a spin signal,possibly acts as a non-radiative recombination center for excited carriers. However,if D0 can accompany the mid-gap, absorption is not clear (see Section 4.4).

Using the concept, Shimakawa et al. (1995) have proposed a detailed conver-sion mechanism. As shown in Fig. 6.19 for a-As2S3, they ascribe the low-level(∼1017 cm−3) ESR centers to the conventional D0 defects, (a) −S−As•−S−and •S−As=, where – and • denote a covalent bond and an unpaired electron,respectively, and the high-level (∼1020 cm−3) centers to combinations of wrong anddangling bonds, (b) =As−As•−S− and =As−S−S•. This idea is consistent withthe experimental results reported by Bishop et al. (1977) and Hautala et al. (1988).

However, as repeatedly argued, there is no direct experimental evidence of thecharged defects (Tanaka 2001a). Otherwise, we may speculate that the D0 defect isproduced, not from the charged defects D+ and D−, but from normal bonds andother defects. The example is given by Hautala et al. (1988), who assume thatphotoinduced breaking of =As−As= wrong bonds in As2S(Se)3, which results inan unpaired electron of =As•, is a primary origin of the mid-gap absorption and

(a) (b)

As0

S−

Fig. 6.19 Schematic illustrations of photo-generation processes of (a) an intimate pair (left) and arandom pair (right) of neutral defects, As0 and S0, and (b) combined defects of wrong and danglingbonds =As−As0 and −S−S0, respectively (modified from Shimakawa et al. 1995)

168 6 Light-Induced Phenomena

ESR signal. We should admit that there still remain unclear and unsolved problemsin the defect structure in chalcogenide glasses (Zhugayevych and Lubchenko 2010).

6.3.11 Transitory Changes

6.3.11.1 Optical Changes

Several kinds of transitory changes, which appear only during illumination or justafter pulsed excitation, have been demonstrated. Matsuda et al. (1974) may be thefirst, who noticed such an optical change, the optical stopping effect. As shown inFig. 6.20, they utilized an optical-guided wave structure consisting of a prism cou-pler and an AsS4 film, in which He–Ne laser light (633 nm) was propagated asguided light streak. When a blue light beam emitted from a He–Cd laser (442 nm)hitted the red-guided streak, the streak appeared to stop at the point. If the blue lightwas turned off, the streak propagated again. Later, Vasilyev et al. (1977) performed aspectral study, which demonstrate that As2S3 films present transitory optical absorp-tion at Eg/2 – Eg, if the spectrum is probed during bandgap illumination. Figure 6.21shows a similar result reported by Iijima and Kurita (1980). These transient absorp-tions induced by cw illumination seem to correspond to a transitory (dynamical)refractive index increase (Tanaka 1980) and also to transient optical changes inducedby pulsed light (Tanaka 1989, Sakaguchi and Tamura 2008).

Here, a repeated question is if the transitory change is related to, or a part of,a memory effect. The spectral shape in Fig. 6.21 distributing at sub-gap regionssuggests that the absorption is attributable to creation of transient mid-gap states,which may also give rise to the mid-gap absorption appearing at low temperatures(Fig. 6.18). However, the responsible atomic structure is speculative, as describedpreviously. On the other hand, Kolobov et al. (1997) have demonstrated through insitu EXAFS experiments that the coordination number (Z ≈ 2) in a-Se increasesby ∼5% during illumination, which implies an increase in the number of threefold-coordinated Se atoms. It awaits further studies to connect these optical and structuralchanges.

Fig. 6.20 An experimental setup demonstrating the optical stopping effect and a response(Matsuda et al. 1974, © American Institute of Physics, reprinted with permission)

6.3 Photon Effects in Chalcogenide 169

Fig. 6.21 A measuring setup of transitory absorptions and the spectra obtained for g-As2S3 films(Iijima and Kurita 1980, © American Institute of Physics, reprinted with permission)

6.3.11.2 Mechanical Changes

Transitory mechanical changes appear under illumination. As reviewed byYannopoulos and Trunov (2009), hardness reduction and photo-viscous effects con-tinue to attract considerable interest. Specifically, since the first note by Vonwiller(1919), extensive studies have been done for Se under bandgap illumination(Koseki and Odajima 1982, Poborchii et al. 1999, Palyok et al. 2002). However,the glass transition temperature of a-Se is just above room temperature, andaccordingly, distinction between photo-electronic and opto-thermal effects is notstraightforward.

Under these circumstances, Hisakuni and Tanaka (1995) have discovered thatAs2S3 (Eg ≈ 2.4 eV) exposed to intense sub-gap illumination presents dramaticathermal photoinduced fluidity or photoinduced glass transition. The time varia-tion in Fig. 6.22 manifests that the sample undergoes a dramatic elongation only

Fig. 6.22 Photoinducedfluidity in a g-As2S3 flakeunder illumination of He–Nelaser light (Tanaka 2003,© Wiley-VCH, reprinted withpermission)

170 6 Light-Induced Phenomena

under illumination. The upper left inset is a photograph of an As2S3 flake withmillimeter size and micrometer thickness, which has been exposed three times toa focused He–Ne laser (633 nm, 2.0 eV) beam under a stretching force. The threedeformed regions are produced by the elongations of three times. Quantitatively, amaximal photoinduced viscosity (the inverse of fluidity) is estimated at ∼1012 P(≈ 1011 Pa s), which is a typical value obtained at the glass transition temperature,∼200◦C.

Since the opto-mechanical experiment is more or less difficult, known featuresof the photoinduced fluidity are mostly qualitative (Tanaka 2003). First, two nec-essary exposure conditions for this phenomenon in As2S3 are the high intensity(>102 W/cm2) and the photon energy (∼2.0 eV) lying in the Urbach-edge region.Second, it has been demonstrated that the phenomenon becomes greater when theexposure is provided at lower temperatures in an investigated range of 284–312 K.This temperature dependence manifests that the phenomenon cannot be understoodas a thermal fluidity but a photo-electronic fluidity. Third, material variation has notbeen investigated in detail. However, since the giant photo-expansion (Fig. 6.15)is understandable to appear through some motive forces and the fluidity, we canassume that the photoinduced fluidity is believed to be universal in, and limitedto, the covalent chalcogenide glass (Gump et al. 2004, Calvez et al. 2008, Gueguenet al. 2010). Polyethylene sheets and Pyrex-glass fibers showed only thermal fluidityupon violet or ultraviolet illumination.

Mechanisms of the photoinduced fluidity remain speculative. It is plausible thatthe electronic excitation gives rise to bond breaking and successive bond inter-change, as previously suggested for a-Se by Koseki and Odajima (1982). It is alsonoted that the related trapped carrier density is 1017–1018 cm−3 (see Fig. 6.16).We therefore assume that the trap behaves as a knot in As2S3 networks, whichis electronically released by photo-carriers. This phenomenon may be regardedas an amorphous version of the so-called electronic melting (the melting inducednot by thermal but by electronic excitation), the concept being proposed for crys-talline semiconductors by Van Vechten et al. (1979). Since the lifetime of trappedcarriers in amorphous semiconductors is much longer than that of free carri-ers in crystalline semiconductors, the softening may occur under moderate lightintensities.

Ikeda and Shimakawa (2004) have demonstrated transient volume expansions.Under illumination of 100 mW/cm2 of 532 nm light, an As2Se3 film with a thick-ness of ∼500 nm undergoes a thickness (volume) expansion of ∼10 nm, whichcorresponds to a fractional expansion of ∼2%. However, a problem for this obser-vation may be the thermal expansion which inevitably appears. Probably consistentwith their experimental observation is the one given by Hegedus et al. (2005), whodemonstrate using computer simulation that electron addition to the conductionband in a-Se yields a volume expansion, which gives rise to a greater contribu-tion than a contraction produced by holes. Further studies are valuable for thecorrespondence between the experiment and the simulation.

6.3 Photon Effects in Chalcogenide 171

6.3.12 Vector Effects

6.3.12.1 Optical Changes

Zhdanov and Malinovsky (1977) have discovered a photoinduced anisotropicchange in optical properties in g-As2S(Se)3, a phenomenon similar to the Weigerteffect long been known for photographic plates. When an As2S3 film is exposedto linearly polarized bandgap light, in addition to the conventional photodarkening(�E ≈ 50 meV) and related refractive index increase (�n ≈ 0.03), a dichroicabsorption edge shift (dichroism) of ∼5 meV (Fig. 6.23) and a birefringence of∼0.002 at transparent wavelengths appear (Kimura et al. 1985, Tanaka 2001b,Lyubin and Klebanov 2003). Interestingly, the induced anisotropy in covalentchalcogenide glasses is negative,2 i.e., �E(//) < �E(⊥) and n(//) < n(⊥), where// and ⊥ symbolize the states of linearly polarized excitation and probe light.In addition to these optical anisotropies, Lyubin and Klebanov (2003) have foundan anisotropic photoconductivity for a-As50Se50 films. Photocurrents are greater inthe direction orthogonal to the electric field of light, which may be consistent withthe negative optical anisotropy. It is mentioned that the glass exhibits photoinducedgyrotropy (circular birefringence) (Lyubin and Klebanov 2003), which remains tobe studied. It is also mentioned that in AgAsS2 films the photoinduced anisotropyis positive (Tanaka 2001).

Is the optical anisotropic change (vector effect) related to photodarkening andthe corresponding photoinduced refractive index change (scalar effect)? Since the

Fig. 6.23 Photoinduced dichroism in an annealed As2S3 film at 25◦C (modified from Kimura et al.1985). E(//) and E(⊥) show the positions of absorption edges probed by linearly polarized lightwith parallel and perpendicular polarizations to the exciting linearly polarized bandgap light. Thedifference between “annealed” and “illuminated” corresponds to the conventional photodarkening

2We follow this terminology, though the usage of “negative” and “positive” is confusing.

172 6 Light-Induced Phenomena

z

y

x

Fig. 6.24 Anisotropicelements in a macroscopicallyisotropic glass represented bythe three thick bars directingto x-, y-, and z-axes

anisotropic change is ∼1/10 of the isotropic in magnitude, some researchers haveassumed that the anisotropic change is a part of the isotropic. However, varia-tions of the anisotropy with light intensity, spectrum, and illuminating temperaturehave manifested some qualitative differences between the two (Tanaka 2001b).Therefore, at present, it is common to assume that different structural changes areresponsible for the anisotropic optical changes (Fritzsche 2009).

Fritzsche has presented a clear-cut phenomenological explanation for the neg-ative optical anisotropy (Fritzsche 2000). We naturally assume for a glass thatthe initial state is isotropic, which is modeled in Fig. 6.24 with three orthogonalanisotropic elements parallel to the x-, y-, and z-axes. Suppose linearly polarizedlight with the electric field along the x-direction is incident upon the x–y plane ofthe sample. Under the condition, if a dipole orientation along the electric field wereresponsible, the situation commonly appearing in dielectrics under dc electric fields,the orientation would provide a positive change. Alternatively, he has assumed thatelectrons and holes in x-elements are selectively excited, and when these carrierswill relax, the x-element may turn to the y- or z-direction through thermal vibra-tions. As a result, the number of x-elements becomes fewer than that of y, resultingin negative anisotropy. This model can explain several features including opticalanisotropy induced by unpolarized light which is incident upon a sample sidewall,the y–z plane in Fig. 6.24 (Tanaka 2001).

However, a problem is the entity of the anisotropic element (Tanaka 2001,Fritzsche 2009). Notable structural studies have been reported, while the resultsseem to be controversial. It seems that structural determinations of the element willbe very challenging, since the vector change is just ∼1/10 of the scalar. On the otherhand, several ideas have been proposed for the microscopic changes, as illustratedin Fig. 6.25, including orientations of defects and layer (chain) structures. The chainorientation model (e) is consistent with photoinduced oriented crystallization in a-Se(Innami and Adachi 1999).

6.3.12.2 Anisotropic Shape Changes

Krecmer et al. (1997) have discovered a photoinduced transitory anisotropic (vector)deformation, called “opto-mechanical effect” (Stuchlik and Elliott 2007). As illus-trated in Fig. 6.26, a bilayer cantilever consisting of an As–S(Se) film and aminiature Si3N4 probe for atomic force microscopes bends upwardly and down-wardly, in response to the polarization direction of incident linearly polarized

6.3 Photon Effects in Chalcogenide 173

Fig. 6.25 Proposed atomic structures of anisotropic elements (Tanaka 2001, © Academic Press,reprinted with permission). The illustrations show, from atomic (∼0.2 nm) to medium-rangescales (∼2 nm), orientations of (a) lone pair electrons, (b) covalent bonds, (c) charged defects,(d) AsS(Se)3/2 triangular units, (e) chains, and (f) segmental layers

Fig. 6.26 Schematicillustration of theopto-mechanical effect, inwhich a thermal bimetalliceffect is neglected for clarity

bandgap light. When the illumination is switched off, the cantilever becomes flat.Light illumination also gives a bias bending which reflects thermal expansions(Fig. 6.2), while the polarization-dependent deflection cannot be ascribed to thermaleffects (Asao and Tanaka 2007).

On the other hand, memorized vector deformations offer a surprising variety.Tanaka et al. (1999) have discovered that a cat-whisker pattern (Fig. 6.27a) appearsin a-AgAsS2 films when exposed to linearly polarized bandgap light. The patternseems to reflect Ag concentration modifications produced by streaks of scatteredlight. Saliminia et al. (2000) have demonstrated for a-As2S3 films that, underexposure to focused linearly polarized bandgap light, the giant scalar expansion(Fig. 6.15) gradually changes to an anisotropic M-shaped deformation along theelectric field (Fig. 6.27b). The M-shaped deformation ultimately changes to chaoticpatterns upon prolonged exposures, as shown in the right-hand side photograph ofFig. 6.27b (Tanaka and Asao 2006).

In addition, as reviewed by Tanaka and Mikami (2009) and Yannopoulos andTrunov (2009), partially or semi-free As–S(Se) shows dramatic deformations.Among those, the vector deformation, Fig. 6.27c, appearing in semi-free As2S3flakes (Tanaka 2008) may be the most dramatic deformation in abiotic solids. Here,

174 6 Light-Induced Phenomena

(c)

50 µm (a) (b)

Fig. 6.27 Vector deformations in (a) an AgAsS2 film (2.0 eV, 500 W/cm2, 3 h) (Tanaka et al.1999, © American Institute of Physics, reprinted with permission), (b) an As2S3 film depositedonto slide glass (2.3 eV and 200 W/cm2 for 0.5, 30 min, and 25 h) (Tanaka and Asao 2006, ©INOE, reprinted with permission), (c) and an As2S3 flake (∼0.1 mm in diameter) laid on grease(Tanaka 2008, © Japan Society of Applied Physics, reprinted with permission). The electric fieldof linearly polarized light is vertical in all these photographs

semi-free means that the As2S3 flake is laid (or deposited) on viscous grease, notdeposited upon rigid substrates as commonly employed. Or, the flake, which is fixedto a rigid base as a cantilever, shows the same deformations. Illumination of linearlypolarized light to such semi-free As2S3 flakes gives two kinds of deformations:an anisotropic U-shaped deformation with the direction being parallel to the elec-tric field and successive screwing elongation, which is orthogonal to the electricfield. On the other hand, semi-free As2S3 films, when exposed to linearly polarizedlight, undergo sinusoidal wrinkling, the direction being orthogonal to the electricfield (Tanaka and Mikami 2009). It is also mentioned that under two-beam interfer-ence of polarized light, grating formations in chalcogenide films depend upon thepolarization state (Trunov et al. 2010).

Several ideas have been put forth for these transitory and memorized vectordeformations (Tanaka and Mikami 2009, Yannopoulos and Trunov 2009). The mostcommon is to assume some kinds of atomic motions, such as photoinduced align-ment of microscopic structures (Fig. 6.25). Similar ideas have been assumed forphoto-deformations in dye-doped organic polymers. On the other hand, Tanaka andMikami (2009) propose an optical force model for deformations in semi-free sam-ples, in which photon momentum (wavenumber) and spin (polarization) provide themotive forces. Further studies will be valuable.

6.3.13 Photo-Chemical Effects

6.3.13.1 Photodoping

The photodoping is a surprising phenomenon, which was first reported by Kostyshinet al. (1966). Comprehensive reviews are given by Kolobov and Elliott (1991) and

6.3 Photon Effects in Chalcogenide 175

Frumar and Wagner (2003). Suppose we have a bilayer structure consisting of asemi-transparent Ag film (∼10 nm thick) and an a-AsS2 film (∼1 μm), which seemsto be the best material combination for the phenomenon. This bilayer sample isfairly stable if it is stored in the dark. Nevertheless, when it is exposed to light, e.g.,using a high-pressure mercury lamp, the Ag film is readily dissolved, or “doped,”into the chalcogenide film. The photodoping gives a remarkable optical change frommetallic reflectivity of the Ag/As–S structure to semi-transparent orange color of anAg–As–S/As–S film. In addition, the reaction causes marked changes in chemicalproperties as etching rates.

A variety of photodoping characteristics have been investigated (Kolobov andElliott 1991, Frumar and Wagner 2003). As shown in Fig. 6.28, the Ag profile isstep like with a nearly fixed Ag concentration of ∼25 at.%, i.e., the doped layerbeing roughly a-AgAsS2, which is very different from the conventional diffusionprofile. We can assume, accordingly, that the bilayer structure consisting of Ag/AsS2changes to Ag/AgAsS2/AsS2, and ultimately, to an AgAsS2/AsS2. Or, if the initialthicknesses of Ag and AsS2 films are optimal, the photodoping produces a singlelayer of a-AgAsS2.

For the material combination, it has been demonstrated that photodopingoccurs widely in Ag/As(Ge)–S(Se) structures. For the metal, Cu is less effi-ciently photodoped, despite it being more efficiently thermally diffused. For thechalcogenide, all the binary compositions seem to exhibit the photodoping insome degrees. The photodoping appears to be inherent to the hole-mobile covalentchalcogenide glass. On the other hand, Ag/S(Se) thermally reacts to c-As2S(Se).Behaviors in electron mobile chalcogenide glasses, containing Bi, are not conclu-sive (Tanaka 1991). The photodoping does not occur, or at least very inefficient, inGa2S3-based glasses (Kitagawa et al. 2006) and in chalcogenide crystals, c-GeS2and c-As2S3. The photodoping neither occurs in a-P (Kawashima et al. 1990) norg-GeO2 (Terakado and Tanaka 2009).

A repeated problem is the motive force of Ag dissolution into the chalcogenide.Experiments suggest that Ag migrates as a cation. Actually, Saji and Ohoka (1985)demonstrate for Ag/GeS2 films that an application of electric fields (∼104 V/cm)changes a photodoping rate by a factor of a half. In addition, Tanaka and Sanjoh(1993) assert through several experiments that the diffusion of photo-generated

Fig. 6.28 An intermediate state (Ag/AgAsS2/AsS2) of the photodoping in Ag/AsS2 system. (a)Ag concentration profile, (b) band diagram, and (c) schematic atomic structure, in which the blackcircle is an Ag atom, the big open circle an As, and the small open circle an S

176 6 Light-Induced Phenomena

Fig. 6.29 Glass-forming regions in the Ag–As–S system (left) and estimated free energy curvealong As–S and Ag–S lines (right)

holes governs the motion of Ag+ ions. In short, we can conclude that the motiveforce of the Ag dissolution is the counterflow of holes: j(Ag+) = j(hole).

Another important problem is why the composition of the doped region is fixedat, i.e., AgAsS2 in the Ag/As–S system. On this problem, Owen et al. (1985) havepointed out an interesting fact: the composition of the doped region corresponds toa glass formation region in the Ag–As–S system (Fig. 6.29). This finding impliesthat the photodoping occurs between the compositions of minimal free energies,from As–S to AgAsS2. This idea is consistent with several observations on compo-sitions. For instance, the photodoping rate in the Ag/AsxS100–x system is maximalat x ≈ 33 at.%, which is AsS2 (Kolobov and Elliott 1991). The photodoping isefficient also for Ag2S/As2S3, since the tie-line of the two compositions passesthrough AgAsS2 (Fig. 6.29). By contrast, the Ag/As2S3 system produces inhomo-geneous photodoped regions. The photodoping is less efficient in the Ag/As–Sesystem (Ogusu et al. 2004), which has no isolated glass-forming regions such asAgAsS2.

Despite the understandings of fundamental features of the photodoping, furtherstudies remain. It will be fruitful to analyze the photo-electro-ionic process in moredetails. Specifically, the interaction between holes and Ag+ ions in a-AgAsS2, whichis an ion-hole mixed conductor (see Sections 3.6 and 7.7), is a valuable subject to bestudied. In addition, it is interesting to consider why the photodoping is prominentfor Ag. Are the group Ia atoms such as Li also photodoped?

6.3.13.2 Photo-Surface Deposition and Photo-Chemical Modification

Maruno and Kawaguchi have discovered a “photoinduced surface deposition,” aseemingly opposite phenomenon to the photodoping (Kawaguchi et al. 2001). When

6.3 Photon Effects in Chalcogenide 177

(a) (b)Fig. 6.30 Scanning electronmicroscopy images ofphoto-surface deposited Agon bulk Ag45As15S40 glassesafter illumination of anultrahigh-pressure Hg lampwith intensities of (a) 200 and(b) 530 mW/cm2 (Kawaguchiet al. 2001, © AcademicPress, reprinted withpermission)

Ag-chalcogenide glasses such as Ag45As15S40 and Ag35Ge20Se45 are exposed tolight, dendritic (or flower)-like Ag particles with diameters of micrometers segregateto the illuminated surface, the examples being shown in Fig. 6.30. Here, a markedpoint is that the sample glass contains a lot of Ag. The photo-surface depositiondoes not appear in Cu-chalcogenide systems.

Later, Yoshida and Tanaka (1995) have found a phenomenon called “photo-chemical modification.” In a-AgAsS2 films, Ag always accumulates to illuminatedregions, where the Ag content can increase by ∼5 at.%. Note that, in this phe-nomenon, Ag always gathers to an illuminated region upon repeated exposures,which is in contrast to the (nearly) irreversible Ag motions in the photodopingand photo-surface deposition (Kawaguchi et al. 2001). Ag–As–S films also showanisotropic deformations when exposed to linearly polarized light (Fig. 6.27a).

Mechanisms of the photo-surface deposition and photo-chemical modificationcan be understood using the two ideas proposed for the photodoping (Kawaguchiet al. 2001). The motive force of Ag+ motion is the photo-electro-ionic, j(Ag+)= j(hole), both flowing in opposite directions, for satisfying the charge neutrality.On the other hand, Owens’ model assumes the minimal free energy at AgAsS2,so that AgxAsS2 glasses with x > 1 (25 at.%), employed for the photo-surfacedeposition, tend to separate to Ag and AgAsS2, in which the reaction is assumedto be assisted by the photo-electronic force. In the photo-chemical modificationin AgAsS2, the Ag content is forced to be modulated (∼5 at.%) by the flowof photo-generated holes. The fringes and streaks in Fig. 6.27a are understoodas deformations reflecting the photo-chemical modification, which is induced byinterference and scattered light.

6.3.13.3 Photo-Oxidation

Photo-oxidation is a phenomenon commonly observed when a chalcogenide film isexposed to (super-)bandgap light in oxygen ambient, as in air (Berkes et al. 1971,DeNeufville et al. 1974, Apling et al. 1975). When as-evaporated As2S(Se)3 (orAs-rich As–S) films are exposed to (super-)bandgap light, the film surface is

178 6 Light-Induced Phenomena

Fig. 6.31 An As2O3 crystal(∼3 μm) on an as-evaporatedAs2S3 film produced by x-rayirradiation (Apling et al.1975, © Elsevier, reprintedwith permission)

covered by fine As2O3 crystals (Fig. 6.31), which make the film smoggy. Thepowdered c-As2O3 can easily be detected using x-ray diffraction. Interestingly, thephoto-oxidation becomes less marked if Ag or Cu is added to As2Se3 films (Ogusuet al. 2005).

The photo-oxidation can be understood as a kind of photo-chemical reactions.It must be triggered by bond breaking with a photon, followed by clustering of Asatoms, i.e., the photo-decomposition (Section 6.3.7), which will be oxidized. Thereaction process can qualitatively be written as (DeNeufville et al. 1974)

As-rich As−S → As2S3 + As and As + O2 → As2O3.

Here, As-rich regions may exist even in As2S3 films due to structural heterogene-ity, or As–As bonds may work as embryos of the reaction. It probably depends uponfilm structures and ambient atmosphere if the photo-bleaching is due simply to thephoto-decomposition (Section 6.3.7) or the photo-oxidation.

Related features in Ge-chalcogenides are somewhat different. As-evaporatedGe–S(Se) films seem to contain a lot of Ge dangling bonds, which are easily photo-oxidized, as detected by, e.g., infrared spectroscopy (Márquez et al. 1997). Hortonet al. (1996) demonstrate that the photo-oxidation of GeS2 films markedly changessticking behaviors of Ag and Zn films. However, in these materials, c-GeO2 does notappear. There may exist some difference in atomic migrations between As and Ge.

6.3.13.4 Photo-Enhanced Vaporization

Janai et al. (1978) have discovered a phenomenon named “photo-enhanced vapor-ization.” When an as-evaporated As2S3 film is illuminated in air at ∼200◦C using,e.g., an Hg lamp (∼10 mW/cm2), the film becomes thinner through vaporizationwith a rate of ∼1 nm/s. High humidity enhances the vaporization rate, which sug-gests the vaporization of photo-produced As2O3. Spectral studies demonstrate thatthe vaporization becomes efficient upon exposure of ∼2.5 eV photons, the energysubstantially higher than the optical gap of ∼2.0 eV in As2S3 at ∼200◦C. Thisspectral result implies that the excitation of σ electrons, not lone pair electrons, of

6.4 Photon Effects in Oxide Glasses 179

As–S (and/or As–As) is responsible for the oxidation. Interestingly, the vaporizationrate depends upon substrates, glass or metal, which implies the existence of someelectronic effects.

6.4 Photon Effects in Oxide Glasses

The oxide glass has a substantially wider bandgap (>5 eV) than that in thechalcogenide, and accordingly, studies on photoinduced phenomena have been com-paratively limited. Before ∼1970, we had known only two kinds of radiation effectsinduced by high-energy beams such as γ-rays; formation of defects, including colorand E′ centers (Lell et al. 1966), and the so-called radiation compaction (Primak andKampwirth 1968). In addition, the radiation-induced amorphization of c-SiO2 wasknown for a longer time (Lell et al. 1966). A revolutionary change appeared with theadvent of optical fibers. The optical fiber, giving rise to long light–matter interac-tion lengths, afforded to discover a photoinduced refractive index grating (Hill et al.1978), which is now commercialized. Many studies stemming from fundamentaland applied viewpoints have followed, as described below (Pacchioni et al. 2000).

Hill et al. (1978) discovered a photoinduced refractive index increase (∼10−3)in Ge-SiO2 fibers (∼1 m long) using cw Ar lasers. This discovery attracts muchinterest, since it can produce in a simple way a fiber Bragg grating, which is utilizedas wavelength selectors (Section 7.3). The induction mechanism has been studiedextensively. It is demonstrated from spectral and compositional studies that defect(Ge E′ center) creation is responsible for the optical change. In addition, Poumellecet al. (1995) noticed a volume compaction upon illumination of ultraviolet light,which may be regarded as a kind of radiation compactions. In Ge–SiO2 fibers, it is

Fig. 6.32 Density(∼1/volume) changes inc- and g-SiO2 upon neutronirradiation (modified fromLell et al. 1966)

180 6 Light-Induced Phenomena

highly plausible that photo-electronic excitation occurs around Ge atoms, which actas “atomic dyes,” and in response, the Ge E′ centers will be produced (Pacchioniet al. 2000). However, why does the volume compaction occur? And, why does therefractive index increase?

Radiation effects have been studied also for nominally pure g-SiO2 using excimerand fs lasers (Pacchioni et al. 2000). Roughly, the photoinduced phenomena appearto be similar to those in Ge–SiO2, with smaller efficiencies. However, for g-SiO2,which is likely to contain various defects (E′ centers, etc.) and impurities such asAl, Cl, and OH, it is difficult to identify the location of photo-electronic excitation.It should also be mentioned that the radiation effect changes in different samples.For instance, Smith et al. (2001) demonstrate that H2-loaded g-SiO2 expands uponultraviolet (248 nm) pulse excitations. In addition, other photoinduced phenomenahave been discovered for g-SiO2. Super-bandgap illumination (10−100 eV) inducesphoto-decomposition, producing Si crystals (Boero et al. 2005). Photoinducedanisotropy is also discovered (Borrelli et al. 2002).

What is the relationship among the refractive index increase, the defect creation,and the volume compaction in silica glasses? It seems that the defect formation can-not quantitatively account for the refractive index increase (Pacchioni et al. 2000).Instead, the volume compaction possibly governs the optical change as follows: TheLorentz–Lorenz formula for the refractive index n in an insulator having dipoleswith a concentration Ni and a polarizability αi is written in cgs unit as (Kittel 2005).

(n2 − 1)/(n2 + 2) = (4π/3) �αiNi (6.2)

Here, suppose �αi = 0, we obtain

�n/n = −{

(n2 − 1)(n2 + 2)/(6n2)}

�V/V , (6.3)

i.e., a volume compaction, �V < 0, gives rise to a refractive index increase, �n > 0.We can actually obtain a quantitative agreement. A problem is, therefore, why theradiation causes the volume compaction. A plausible scenario is as follows (Uchinoet al. 2002): A photon creates a defect, probably an E′ center, which triggers thevolume compaction through some mechanism presently unspecified. The defectmay behave as a catalyst. Note that, in terms of the Lorentz–Lorenz formula, thephotodarkening in the chalcogenide (Section 6.3.8), which accompanies a refrac-tive index increase, should be related with an increase in �αiNi, since it occurs ingeneral with the volume expansion, not the compaction as that in the oxide.

It is interesting to compare the photoinduced changes in a typical oxide, SiO2,and a chalcogenide, As2S3. Here, since the bandgap energy Eg (∼10 and 2.4 eV) andthe glass transition temperature Tg (∼1500 and ∼450 K) in SiO2 and As2S3 are sub-stantially different, some normalization is needed for grasping material dependence.Figure 6.33 shows notable photoinduced phenomena in normalized representationson �ω/Eg and Ti/Tg axes, where �ω is the photon energy of excitation light and Tiis the temperature at which the sample is illuminated. For SiO2, when illuminated

6.5 Light-Induced Phenomena in Amorphous Si:H Films 181

As2S3SiO2

Δ n

Fig. 6.33 Comparison ofphotoinduced phenomena inSiO2 and As2S3 glasses asfunctions of the normalizedphoton energy �ω/Eg andillumination temperatureTi/Tg. The arrows show thepositions at Ti = 300 K. SiO2shows a refractive indexincrease �n anddecomposition, while As2S3shows all the changesindicated

at room temperature, Ti/Tg ≈ 0.2, bandgap and pulsed mid-gap exposures provide,respectively, photo-decomposition and a refractive index increase, the latter beingrelated to the densification (radiation compaction), as described above. On the otherhand, As2S3 shows all the phenomena: the photo-decomposition upon super-gapillumination at room temperature (Ti/Tg ≈ 0.5), the photodarkening upon bandgapand intense sub-gap illuminations at room temperature, the mid-gap absorption atlow temperatures of Ti/Tg ≈ 0.2, and the refractive index increase upon mid-gapexcitation.

In short, important remarks are as follows: A common feature to these glassesis that photoinduced phenomena do not appear when Ti/Tg ≈ 1. Or, manyphotoinduced phenomena can be recovered with annealing at Tg. In addition, inboth glasses, super-bandgap light gives rise to the photo-decomposition, produc-ing wrong bonds or micro-crystals. Existence of the defect creation processes atTi/Tg ≈ 0.2 may also be common, which appear as the refractive index increasein SiO2 and mid-gap absorption in As2S3. However, a marked difference is that thephotodarkening appears only in As2S3. The phenomenon appears to be inherent tothe chalcogenide glass consisting of covalent and van der Waals bonds.

6.5 Light-Induced Phenomena in Amorphous Si:H Films

6.5.1 Thermal Effects in Amorphous Si:H Films

Laser-induced crystallization of a-Si(:H) films has attracted great interest due toapplications to thin-film transistors (Suzuki 2006). In technology, XeCl excimerlasers (λ = 308 nm with pulse duration of ∼30 ns) are employed for crystalliza-tion of a-Si(:H) films (∼50 nm in thickness) deposited upon a-SiO2 layers. Themost important characteristic in this application is a high mobility as possible, for

182 6 Light-Induced Phenomena

which the grain size of crystallized films should be large. At present, obtained lat-eral sizes (∼50 μm) of crystalline grains are much greater than the film thickness.The crystallization mechanism is believed to be purely thermal, i.e., through a rapidmelt-mediated phase transformation with a super-lateral growth mode (Im et al.1993). Despite the thermal growth, however, Horita et al. (2007) demonstrate thatthe crystallization can be controlled by the electric field of linearly polarized laserpulses. Accordingly, it may be interesting to compare this thermal crystallizationwith the photo-enhanced crystallization of a-Se (Section 6.3.4). It is also mentionedthat amorphization of c-Si films can be induced using fs laser pulses (Jia et al. 2004).

6.5.2 Photon Effects in Amorphous Si:H Films

6.5.2.1 Observations

The so-called Staebler–Wronski effect is the most known and problematicphotoinduced phenomenon in a-Si:H films (Morigaki 1999, Shimizu 2004).As shown in Fig. 6.34, upon bandgap illumination, which is sometimes referredto as “light soaking” in this research area, with intensity of 200 mW/cm2 for 2 hat room temperature, the photo- and dark conductivities decrease by one and fourorders of magnitude. The degraded state is meta-stable, which can be recoveredby annealing at ∼450 K. It is mentioned that a smaller bandgap material such asa-Ge:H films (Eg ≈ 1.1 eV) exhibits smaller degradation. Since the effect is seriousin device applications, specifically in solar cells, a huge number of studies have been

Fig. 6.34 Staebler–Wronski effect and Morigaki’s model (1988)

6.5 Light-Induced Phenomena in Amorphous Si:H Films 183

published, as reviewed by Morigaki (1999), Shimizu (2004), and others. However,the final elucidation and countermeasure remain.

In addition to the photoconductive degradation, the light soaking changes a vari-ety (at least, nine) of electronic and structural properties, as listed below (Morigaki1999, Shimizu 2004). We see that some photoinduced changes, specifically elec-tronic, strongly resemble those in the chalcogenide glass (Section 6.3.10).

Electronic changes are as follows: First, under excitation of bandgap light of�ω ≈1.8 eV at low temperatures, a broad photoluminescence at ∼1.3 eV fatigues,and at the same time a low-energy peak at ∼0.8 eV appears. There seem to be twophotoluminescence centers having different kinetics in thermal recovery. Second, itis discovered that prolonged illumination at cryogenic temperatures increases ESRsignals roughly by an order. The induced spins are thermally annealed partially at∼100 K and completely at 430 K. Third, optical spectra are also modified in twospectral regions. One is an increase in mid-gap absorption after prolonged irradia-tion, which has been detected using photo-deflection spectroscopy and a constantphotocurrent method. Annealing kinetics of the induced absorptions is not sim-ple. The other is a slope decrease in the Urbach edge, which has been attributedto an increase in structural disorder. Fourth, the ac conductivity also changes. Lightsoaking of a-Si:H films at room temperature increases and decreases the ac conduc-tivity (measured at ∼1 kHz) at 1–80 and 80–300 K (Shimakawa et al. 1995). Theseconductivity changes are removed by thermal annealing at 430 K. Fifth, polarizedelectro-absorption is modified by illumination, which is recovered by annealing at470 K. The change may imply some gross structural changes, not creation of defectsas dangling bonds.

In addition, we also see intrinsic structural changes. First, it has beendiscovered that an intensity of small-angle neutron scattering, which is sensitiveto H distributions, increases after prolonged illumination. The result suggests clus-tering of H atoms. Second, a photoinduced change in the infrared absorption spectraappears. The intensity of the Si–H stretching mode at ∼2000 cm−1 is increased by∼1% by light soaking and recovered by annealing. Third, a reversible change in x-ray photoelectron spectroscopy appears. The Si 2p peak at around −100 eV shifts by∼0.1 eV to a lower binding energy with light soaking. Such a change does not occurin (non-hydrogenated) a-Si films. Fourth, light soaking provides a volume expansionwith a fraction of 4 × 10−6 in a-Si:H films, the value being much smaller than that(∼4 × 10−3) in g-As2S3. Time evolutions of the photoinduced expansion and ESRsignals, probed at room temperature, are similar, which may suggest an intimate cor-relation between the structural and electronic changes. However, later studies havedemonstrated that the volume change critically depends upon the method of filmdepositions.

6.5.2.2 Mechanisms

As seen above, many photoinduced phenomena appear in a-Si:H films, whilethe interrelation remains unclear. Among those, the most problematic is thephotoconduction degradation, Staebler–Wronski effect, and accordingly, its mecha-nism has been extensively studied.

184 6 Light-Induced Phenomena

It is believed that the Staebler–Wronski effect is caused by the formation ofdefects (Morigaki 1999, Shimizu 2004). The defect is probably dangling bondsof Si atoms (∼1017 cm−3). Nevertheless, how the dangling bond is photo-createdis speculative. Specifically, it is still ambiguous whether the defect creation isrelated with H atoms or not. A process proposed by Morigaki (1988) is shownin Fig. 6.34, in which a defect is created through photoinduced cessation of weakSi–Si bonds and successive H diffusion. The produced dangling bond may also trig-ger structural changes such as the increase in Si–H stretching mode and the volumeexpansions. Otherwise, the defect may have some correlation with micro-voids,the inner surface being covered by H atoms. In addition to understand the mech-anism, the most important technological subject is a method which can suppress theStaebler–Wronski effect, but it remains midway to the achievement.

Here, it is tempting to envisage some similarities between the three photoinducedprocesses: the Staebler–Wronski effect in a-Si:H films, the defect creation inchalcogenide glasses at low temperatures (Section 6.3.10), and Hills’ gratingsin Ge-doped SiO2 (Section 6.4). However, since a-Si:H films do not show theglass transition, it is challenging to apply unified treatments to these photoinducedphenomena (Shimakawa et al. 1995).

6.6 Photon Effects in Organic Polymers

We sometimes experience sunburn, a kind of photoinduced phenomena. Organicmolecules seem to be susceptible to radiation effects. It may start withphoto-electronic bond cessation and successive polymerization and/or oxidation.Otherwise, in small molecules as dyes, it may appear as photoinduced twistingmotions of atomic bonds.

The most known photoinduced phenomenon in organic polymers is probablythe photo-polymerization process (Kozawa and Tagawa 2010). In the conventionalphotoresist process in semiconductor industries, it is combined with etching forproducing fine patterns. At present, irradiation of laser light with a wavelength of∼200 nm and successive dry etching make it possible to reproduce patterns with aresolution finer than ∼50 nm. The polymerization process accompanies an increasein refractive indices, which can be utilized for holographic storages. As describedin Section 6.3.5, as-evaporated As2S3 films also undergo the photo-polymerizationand etching endurance, which is employed as an inorganic photoresistprocess.

Photoinduced phenomena in azobenzene-doped polymers have attracted wideinterest recently (Barrett et al. 2007). As illustrated in Fig. 6.35, the dye showsreversible isomerization between cis- and trans-conformation upon illumination ofultraviolet (∼365 nm) and visible (∼570 nm) light. When the dye is illuminatedby polarized light, the transformation can produce anisotropic structures, whichaccompany not only optical changes as birefringence but also prominent changes inmacroscopic shapes if the transformation occurs cooperatively. In some cases, the

References 185

Fig. 6.35 Photoinducedchange from trans- tocis-configurations of anazobenzene molecule and thethermal (or photo-) recovery

shape change resembles the vector change in chalcogenide glasses (Section 6.3.12).Due to versatile molecular engineering techniques, the dye-doped organic polymeris promising for advanced photoinduced materials.

A notable difference between the photoinduced changes in the chalcogenide glassand the polymer is the following: In the dye–polymer system, it is conceivablethat light excites the dye, and its isomerization process causes successive struc-tural changes in surrounding molecules. Accordingly, a problem in a photoinducedprocess is focused upon the successive structural change. On the other hand, in thechalcogenide, the excited species cannot be identified, which may be some defectivesites or disordered structures. It is plausible that the excited species change with thephoton energy of excitation, light intensity, temperature, and so forth. As a result,following structural changes become largely speculative.

References

Abdulhalim, I., Beserman, R., Weil, R.: Structural changes and crystallization of amorphoushydrogenated silicon generated by laser irradiation. Phys. Rev. B 39, 1081–1091 (1989)

Adarsh, K.V., Sangunni, K.S., Kokenyesi, S., Ivan, I., Shipljak, M.: Enhancement ofphotoluminescence intensity by photoinduced interdiffusion in nanolayered a-Se/As2S3 filmsJ. Appl. Phys. 97, 044314 (2005)

Aniya, M., Shimojo, F.: Atomic structure and bonding properties in amorphous Cux(As2S3)1−x byab initio molecular-dynamics simulations. J. Non-Cryst. Solids 352, 1510–1513 (2006)

Aoki, T., Shimada, H., Hirao, N., Yoshida, N., Shimakawa, K., Elliott, S.R.: Reversiblephotoinduced changes of electronic transport in narrow-gap amorphous Sb2Se3. Phys. Rev.B 59, 1579–1581 (1999)

Apling, A.J., Daniel, M.F., Leadbetter, A.J.: The oxidation of amorphous films of arsenicchalcogenides. Thin Solid Films 27, L11–L13 (1975)

Asahara, Y., Izumitani, T.: An effect of irradiation on As6Se4 glass. J. Non-Cryst. Solids 15,343–346 (1974)

Asahara, Y., Ishibashi, Y., Izumitani, T.: Effect of the third elements on the optical memory effectof As-Se glasses. Jpn. J. Appl. Phys. 14, 289–290 (1975)

Asao, H., Tanaka, K.: Polarization-dependent photoinduced mechanical deformations in covalentchalcogenide glasses. J. Appl. Phys. 102, 043508 (2007)

Barrett, C.J., Mamiya, J., Yager, K.G., Ikeda, T.: Photo-mechanical effects in azobenzene-containing soft materials. Soft Matter 3, 1249–1261 (2007)

186 6 Light-Induced Phenomena

Berkes, J.S., Ing, S.W., Hillegas, W.J.: Photodecomposition of amorphous As2Se3 and As2S3.J. Appl. Phys. 42, 4908–4916 (1971)

Biegelsen, D.K., Street, R.A.: Photoinduced defects in chalcogenide glasses. Phys. Rev. Lett. 44,803–806 (1980)

Bishop, S.G., Strom, U., Taylor, P.C.: Optically induced metastable paramagnetic states inamorphous semiconductors. Phys. Rev. B 15, 2278–2294 (1977)

Boero, M., Oshiyama, A., Silvestrelli, P.L., Murakami, K.: Free energy molecular dynamics simu-lations of pulsed-laser-irradiated SiO2: Si–Si bond formation in a matrix of SiO2. Appl. Phys.Lett. 86, 201910 (2005)

Borrelli, N.F., Smith, C.M., Price, J.J., Allan, D.C.: Polarized excimer laser-induced birefringencein silica. Appl. Phys. Lett. 80, 219–221 (2002)

Brazhkin, V.V., Gavrilyuk, A.G., Lyapin, A.G., Timofeev, Yu.A., Katayama, Y., Kohara, S.: AsS:Bulk inorganic molecular-based chalcogenide glass. Appl. Phys. Lett. 91, 031912 (2007)

Calvez, L., Yang, Z., Lucas, O.: Light-induced matrix softening of Ge-As-Se network glasses.Phys. Rev. Lett. 101, 177402 (2008)

Calvez, L., Yang, Z., Lucas, O.: Reversible giant photocontraction in chalcogenide glass. Opt.Express 17, 18581–18589 (2009)

Cernogora, J., Mollot, F., Guillaume, B.: Radiative recombination in amorphous As2Se3. Phys.Status Solidi (a) 15, 401–407 (1973)

Chopra, K.L., Harshavardhan, K.S., Rajagopalan, S., Malhotra, L.K.: Ion-induced physical andoptical densification in obliquely deposited Se0.75Ge0.25 films. Appl. Phys. Lett. 40, 428–430(1982)

DeNeufville, J.P., Moss, S.C., Ovshinsky, S.R.: Photostructural transformations in amorphousAs2Se3 and As2S3 films. J. Non-Cryst. Solids 13, 191–223 (1974)

Drabold, D.A., Zhang, X., Li, J.: First-principles molecular dynamics and photo structuralresponse in amorphous silicon and chalcogenide glasses. In: Kolobov, A.V. (ed.) Photo-InducedMetastability in Amorphous Semiconductors, Chap. 15, pp. 260–278. Wiley-VCH, Weinheim(2003)

Dresner, J., Stringfellow, G.B.: Electronic processes in the photo-crystallization of vitreousselenium. J. Phys. Chem. Solids 29, 303–311 (1968)

Eguchi, H., Hirai, M.: Spectral variation of amorphous As2S3 after the initial annealing andphotodarkening. J. Phys. Soc. Jpn. 59, 4542–4546 (1990)

Emelianova, E.V., Adriaenssens, G.J., Arkhipov, V.I.: The role of photogenerated charges inphotoinduced expansion of chalcogenide glasses. Philos. Mag. Lett. 84, 47–51 (2004)

Fritzsche, H.: Light-induced effects in glasses. In: Boolchand, P. (ed.) Insulating andSemiconducting Glasses, Chap. 10, pp. 653–690. World Scientific, Singapore (2000)

Fritzsche, H.: Critical discussion of models proposed to explain photo-induced anisotropies inchalcogenide glasses. Phys. Status Solidi (b) 246, 1768–1772 (2009)

Fritzsche, H., Smid, V., Ugur, H., Gaczi, P.J.: Plasma-deposited hydrogenated chalcogenideglasses. J. Phys. 42, C4, 669–702 (1981)

Frumar, M., Wagner, T.: Ag doped chalcogenide glasses and their applications. Curr. Opin. SolidState Mater. Sci. 7, 117–126 (2003)

Frumar, M., Firth, A.P., Owen, A.E.: Optically induced crystal-to-amorphous-state transition inAs2S3. J. Non-Cryst. Solids 192–193, 447–450 (1995)

Gueguen, Y., Sangleboeuf, J.C., Keryvin, V., Lépine, E., Yang, Z., Rouxel, T., Point, C., Bureau,B., Zhang, X.-H., Lucas, P.: Photoinduced fluidity in chalcogenide glasses at low and highintensities: A model accounting for photon efficiency. Phys. Rev. B 82, 134114 (2010)

Gump, J., Finker, I., Xia, H., Sooryakumar, R., Bresser, W.J., Boolchand, P.: Light-induced giantsoftening of network glasses observed near the mean-field rigidity transition. Phys. Rev. Lett.92, 245501 (2004)

Guorong, C., Zheng, H., Jijian, C.: Surface modification of chalcogenide glasses by N2 plasmatreatment. J. Non-Cryst. Solids 288, 226–229 (2001)

References 187

Hajtó, J., Jánossy, I.: Photo-induced non-linearity and transmittance oscillation in GeSe2 andAs2S3. In: Kolovov, A.V. (ed.) Photo-Induced Metastability in Amorphous Semiconductors,Chap. 9, pp. 138–159. Wiley-VCH, Weinheim (2003)

Hajtó, J., Zentai, G., Kósa Somogyi, I.: Light-induced transmittance oscillation in GeSe2 thin films.Solid State Commun. 23, 401–403 (1977)

Hamada, A., Saito, M., Kikuchi, M.: Photo-darkening effect in amorphous As-Se-Ge films. SolidState Commun. 11, 1409–1412 (1972)

Hamanaka, H., Tanaka, K., Iizima, S.: Reversible photostructural change in melt-quenched As2S3glass. Solid State Commun. 23, 63–65 (1977)

Hamanaka, H., Tanaka, K., Matsuda, A., Iizima, S.: Reversible photo-induced volume changes inevaporated As2S3 and As4Se5Ge1 films. Solid State Commun. 19, 499–501 (1976)

Hari, P., Guzel, S., Su, T., Taylor, P.C., Kuhns, P.L., Moulton, W.G., Sullivan, N.S.: Photodarkeningeffect in glassy As2S3 and As2O3. J. Non-Cryst. Solids 326–327, 199–204 (2003)

Hautala, J., Ohlsen, W.D., Taylor, P.C.: Optically induced electron-spin resonance in AsxS1-x. Phys.Rev. B 38, 11048–11060 (1988)

Hayashi, K., Mitsuishi, N.: Thickness effect of the photodarkening in amorphous chalcogenidefilms. J. Non-Cryst. Solids 299, 949–952 (2002)

Hayashi, K., Hikida, Y., Shimakawa, K., Elliott, S.R.: Absence of photodegradation in amorphouschalcogenide films with a narrow optical bandgap. Philos. Mag. Lett. 76, 233–236 (1997)

Hayashi, K., Shimakawa, K.: Photoinduced effects in amorphous chalcogenide films by vacuumultra-violet light. J. Non-Cryst. Solids 198, 696–699 (1996)

Hegedus, J., Kohary, K., Pettifor, D.G., Shimakawa, K., Kugler, S.: Photoinduced volume changesin amorphous selenium. Phys. Rev. Lett. 95, 206803 (2005)

Hill, K.O., Fujii, Y., Johnson, D.C., Kawasaki, B.S.: Photosensitivity in optical fiber waveguides:Application to reflection filter fabrication. Appl. Phys. Lett. 32, 647–649 (1978)

Hisakuni, H., Tanaka, K.: Giant photoexpansion in As2S3 glass. Appl. Phys. Lett. 65, 2925–2927(1994)

Hisakuni, H., Tanaka, K.: Optical microfabrication of chalcogenide glasses. Science 270, 217–218(1995)

Holomb, R., Mateleshko, N., Mitsa, V., Jophansson, P., Matic, A., Veres, M.: New evidence oflight-induced structural changes detected in As–S glasses by photon energy dependent Ramanspectroscopy. J. Non-Cryst. Solids 352, 1607–1611 (2006)

Honolka, J., Kasper, G., Hunklinger, S.: Correlation of low-energy excitations with photodarkeningin a-As2S3. Europhys. Lett. 57, 382–388 (2002)

Horita, S., Kaki, H., Nishioka, K.: Surface modification of an amorphous Si thin film crystallizedby a linearly polarized Nd:YAG pulse laser beam. J. Appl. Phys. 102, 13501 (2007)

Horton, J.H., Hardacre, C., Baddeley, C.J., Moggridge, G.D., Ormerod, R.M., Lambert, R.M.: Theeffect of photo-oxidation on the sticking and reactivity of Ag on amorphous GeS2. J. Phys.:Condens. Matter 8, 707–718 (1996)

Hosono, H., Satake, T., Hosoe, M., Abe, Y.: Reversible optical change of amorphous redphosphorus in reduced phosphate glasses. J. Am. Ceram. Soc. 68, 7–9 (1985)

Iijima, M., Kurita, S.: Transient photoinduced phenomena in amorphous chalcogenide thin films.J. Appl. Phys. 51, 2103–2105 (1980)

Iijima, M., Mita, Y.: Reversible photostructural change in chalcogenide glass films observed ininfrared absorption spectra. Solid State Commun. 24, 665–667 (1977)

Ikeda, Y., Shimakawa, K.: Real-time in situ measurements of photoinduced volume changes inchalcogenide glasses. J. Non-Cryst. Solids 338–340, 539–542 (2004)

Ikemoto, H., Tsuzuki, T., Inui, M., Yao, M., Endo, H.: Photodarkening of amorphous seleniumunder high pressure. Z. Phys. Chem. 216, 1107–1121 (2002)

Im, J.S., Kim, H.J., Thompson, M.O.: Phase transformation mechanisms involved in excimer lasercrystallization of amorphous silicon films. Appl. Phys. Lett. 63, 1969–1971 (1993)

Imura, T., Kubota, K., Hiraki, A., Tanaka, K.: Photodoping of Ag into single crystal As2S3. Jpn.J. Appl. Phys. 52, 2459–2461 (1983)

188 6 Light-Induced Phenomena

Innami, T., Adachi, S.: Structural and optical properties of photocrystallized Se films. Phys. Rev.B 60, 8284–8289 (1999)

Itoh, N., Stoneham, A.M.: Materials Modification by Electronic Excitation. Cambridge UniversityPress, Cambridge (2001)

Janai, M., Rudman, P.S., Mandelbaum, A.: Mass spectrometric analysis of arsenic trisulfide.J. Non-Cryst. Solids 27, 67–73 (1978)

Jia, J., Li, M., Thompson, C.V.: Amorphization of silicon by femtosecond laser pulses. Appl. Phys.Lett. 84, 3205–3207 (2004)

Kasai, M., Nakatsui, H., Hajimoto, Y.: Photodepression in As-S thin films. J. Appl. Phys. 45,3209–3210 (1974)

Kawaguchi, T., Tanaka, K., Elliott, S.R.: Photoinduced and electron-beam phenomena in Ag-rich amorphous chalcogenide semiconductors. In: Nalwa, H.S. (ed.) Handbook of AdvancedElectronic and Photonic Materials and Devices, Vol. 5, Chap. 3, pp. 92–117. Academic, SanDiego, CA (2001)

Kawashima, K., Hosono, H., Abe, Y.: Effect of composition on the rates of photodarkening andsilver photodoping in amorphous P-Se films. Appl. Phys. Lett. 57, 1595–1596 (1990)

Keneman, S.A.: Hologram storage in arsenic trisulfide thin films. Appl. Phys. Lett. 19, 205–207(1971)

Kimura, K., Murayama, K., Ninomiya, T.: Change in optical anisotropy of localized states asso-ciated with reversible photostructural change in a-As2S3 films. J. Non-Cryst. Solids 77–78,1203–1206 (1985)

Kitagawa, R., Takebe, H., Kuwabara, M.: Behavior of Ag photodoping in sulfide bulk glasses.J. Non-Cryst. Solids 352, 2643–2646 (2006)

Kittel, C.: Introduction of Solid State Physics, 8th ed. Wiley, New York, NY (2005)Knotek, P., Arsova, D., Vateva, E., Tichý, L.: Photo-expansion in Ge-As-S amorphous film moni-

tored by digital holographic microscopy and atomic force microscopy. J. Opt. Adv. Matter 11391–394 (2009)

Kolobov, A.V. (ed.): Photo-Induced Metastability in Amorphous Semiconductors. Wiley-VCH,Weinheim (2003)

Kolobov, A.V., Elliott, S.R.: Photodoping of amorphous chalcogenides by metals. Adv. Phys. 40,625–684 (1991)

Kolobov, A.V., Oyanagi, H., Tanaka, K., Tanaka, K.: Structural study of amorphous selenium by insitu EXAFS: Observation of photoinduced bond alternation. Phys. Rev. B 55, 726–734 (1997)

Kolomiets, B.T., Lantratova, S.S., Lyubin, V.M., Shilo, V.P.: Relation between glass-transition tem-perature and optical memory-erasure temperature of glassy chalcogenide semiconductors. Sov.Phys. Solid State 21, 594–596 (1979)

Kolomiets, B.T., Lyubin, V.M.: Reversible photoinduced changes in the properties of chalcogenidevitreous semiconductors. Mater. Res. Bull. 13, 1343–1350 (1978)

Koseki, H., Odajima, A.: Photo-induced stress relaxation in amorphous selenium films. Jpn.J. Appl. Phys. 21, 424–428 (1982)

Koseki, H., Ueno, T., Odajima, A.: Thermal and photo effects on the textural change of redamorphous selenium. Jpn. J. Appl. Phys. 17, 1143–1144 (1978)

Kostyshin, M.T., Mikhailovskaya, E.V., Romanenko, P.F.: Photographic sensitivity effect in thinsemiconducting films on metal substrates. Sov. Phys. Solid State 8, 451–452 (1966)

Kounavis, P., Mytilineou, E.: Photostructural changes in amorphous semiconductors studied by themodulated photocurrent method. J. Phys.: Condens. Matter 11, 9105–9114 (1999)

Kozawa, T., Tagawa, S.: Radiation chemistry in chemically amplified resists. Jpn. J. Appl. Phys.49, 030001 (2010)

Krecmer, P., Moulin, A.M., Stephenson, R.J., Rayment, T., Welland, M.E., Elliott, S.R.: Reversiblenanocontraction and dilatation in a solid induced by polarized light. Science 277, 1799–1802(1997)

Kumar, A., Malhotra, L.K., Chopra, K.L.: Infrared and x-ray photoelectron spectroscopic study ofphotostructural changes in amorphous P-Ge-Se thin films. J. Appl. Phys. 65, 1671–1675 (1989)

References 189

Kyriazis, F., Yannopoulos, S.N.: Colossal photostructural changes in chalcogenide glasses:Athermal photoinduced polymerization in AsxS100−x bulk glasses revealed by near-bandgapRaman scattering. Appl. Phys. Lett. 94, 101901 (2009)

Larmagnac, J.P., Grenet, J., Michon, P.: Photo-dependence of sub-Tg relaxation in a-Se thin films.Philos. Mag. B 45, 627–638 (1982)

Lell, E., Kreidl, N.J., Hensler, J.R.: Radiation effects in quartz, silica and glasses. In: Burke,J.E.(ed.) Progress in Ceramic Sciences, Vol. 4, pp. 1–94. Pergamon, Oxford (1966)

Liu, J.Z., Taylor, P.C.: Absence of photodarkening in bulk, glassy As2S3 and As2Se3 alloyed withcopper. Phys. Rev. Lett. 59, 1938–1941 (1987)

Loeffler, P., Schwarz, T., Sautter, H., Lezal, D.: Structural changes of GeGaS bulk glasses inducedby UV exposure. J. Non-Cryst. Solids 232–234, 526–531 (1998)

Lucas, P., King, E.A., Doraiswamy, A., Jivaganont, P.: Competitive photostructural effects in Ge-Seglass. Phys. Rev. B 71, 104207 (2005)

Lukács, R., Hegedüs, J., Kugler, S.: Structure and photoinduced volume changes of obliquelydeposited amorphous selenium. J. Appl. Phys. 104, 103512 (2008)

Lukášik, D., Macko, P.: Vickers hardness number of neutron irradiated chalcogenide Ge-S glasses.J. Non-Cryst. Solids 44, 397–399 (1981)

Lyubin, V.: Chalcogenide glassy photoresists: History of development, properties, and applications.Phys. Status Solidi (b) 246, 1758–1767 (2009)

Lyubin, V.M., Klebanov, M.L.: Photo-induced anisotropy in chalcogenide glassy semiconductors.In: Kolovov, A.V. (ed.) Photo-Induced Metastability in Amorphous Semiconductors, Chap. 6,pp. 91–108. Wiley-VCH, Weinheim (2003)

Malinovsky, V.K., Novikov, V.N.: Nonequilibrium phonons and photostructure transformations inchalcogenide glasses. J. Non-Cryst. Solids 85, 93–99 (1986)

Márquez, E., Bernal-Oliva, A.M., González-Leal, J.M., Prieto-Alcón, R., Jiménez-Garay, R.: Onthe irreversible photo-bleaching phenomenon in obliquely-evaporated GeS2 glass films. J. Non-Cryst. Solids 222, 250–257 (1997)

Matsuda, A., Kikuchi, M.: Photo-synthesis of As3S2 crystal from As-As2S2 mixture. Solid StateCommun. 12, 359–361 (1973)

Matsuda, A., Yoshimoto, N.: Laser-light-induced relaxation in amorphous Sb2S3 films. J. Appl.Phys. 46, 2334–2336 (1975)

Matsuda, A., Mizuno, H., Takayama, T., Saito, M., Kikuchi, M.: “Stopping effect” on guided lightin As-S films by a laser beam. Appl. Phys. Lett. 24, 314–315 (1974)

Mikhailov, M.D., Karpova, E.A., Cimpl, Z., Kosek, F.: Photo- and thermally induced change in thevolume of thin chalcogenide films. Phys. Status Solidi (a) 117, 467–475 (1990)

Mikla, V.I., Mikhalko, I.P.: Laser-induced structural transformation of AsxSe1-x thin amorphousfilms. J. Non-Cryst. Solids 180, 236–243 (1995)

Morigaki, K.: Microscopic mechanism for the photo-creation of dangling bonds in a-Si:H. Jpn.J. Appl. Phys. 27, 163–168 (1988)

Morigaki, K.: Physics of Amorphous Semiconductors. Imperial College Press, London (1999)Murai, R., Yoshikawa, H.Y., Takahashi, Y., Maruyama, M., Sugiyama, S., Sazaki, G., Adachi, H.,

Takano, K., Matsumura, H., Murakami, S., Inoue, T., Mori, Y.: Enhancement of femtosecondlaser-induced nucleation of protein in a gel solution. Appl. Phys. Lett. 96, 043702 (2010)

Mytilineou, E., Taylor, P.C., Davis, E.A.: On the absence of photodarkening in pnictide amorphoussemiconductors. Solid State Commun. 35, 497–499 (1980)

Nagels, P., Sleeckx, E., Callaerts, R., Tichy, L.: Structural and optical properties of amorphousselenium prepared by plasma-enhanced CVD. Solid State Commun. 94, 49–52 (1995)

Nakagawa, N., Shimakawa, K., Itoh, T., Ikeda, Y.: Dynamics of principal photoinduced effectsin amorphous chalcogenides: In-situ simultaneous measurements of photodarkening, volumechanges, and defect creation. Phys. Status Solidi (c) 7, 857–860 (2010)

Nakamura, M., Wang, Y., Matsuda, O., Inoue, K., Murase, K.: Laser spot size dependence ofphoto-induced crystallization process in amorphous GeSe2 film. J. Non-Cryst. Solids 198–200,740–743 (1996)

190 6 Light-Induced Phenomena

Naumov, P., Makreski, P., Jovanovski, G.: Direct atomic scale observation of linkage isomerizationof As4S4 clusters during the photoinduced transition of realgar to pararealgar. Inorg. Chem. 46,10624–10631 (2007)

Nemanich, R.J., Connell, G.A.N., Hayes, T.M., Street, R.A.: Thermally induced effects inevaporated chalcogenide films. I. Structure. Phys. Rev. B 18, 6900–6914 (1978)

Ogusu, K., Hosokawa, Y., Maeda, S., Minakata, M., Li, H.: Photo-oxidation of As2Se3,Ag-As2Se3, and Cu-As2Se3 chalcogenide films. J. Non-Cryst. Solids 351, 3132–3138 (2005)

Ogusu, K., Maeda, S., Kitao, M., Li, H., Minakata, M.: Optical and structural properties ofAg(Cu)–As2Se3 chalcogenide films prepared by a photodoping. J. Non-Cryst. Solids 347,159–165 (2004)

Ovshinsky, S.R., Fritzsche, H.: Amorphous semiconductors for switching, memory, and imagingapplications. IEEE Trans. Electron Devices 20, 91–105 (1973)

Owen, A.E., Firth, A.P., Ewen, P.J.S.: Photo-induced structural and physico-chemical changes inamorphous chalcogenide semiconductors. Philos. Mag. B 52, 347–362 (1985)

Pacchioni, G., Skuja, L., Griscom, D.L. (eds.): Defects in SiO2 and Related Dielectrics: Scienceand Technology. Kluwer, Dordrecht (2000)

Palyok, V., Szabo, I.A., Beke, D.L., Kikineshi, A.: Surface grating formation and erasing on a-Sefilms. Appl. Phys. A-Mater. Sci. Process. 74, 683–687 (2002)

Pfeiffer, G., Paesler, M.A., Agarwal, S.C.: Reversible photodarkening of amorphous arsenicchalcogens. J. Non-Cryst. Solids 130, 111–143 (1991)

Phillips, J.C.: Thermal and athermal laser annealing. Comments Solid State Phys. 10, 165–171(1982)

Poborchii, V.V., Kolobov, A.V., Tanaka, K.: Photomelting of selenium at low temperature. Appl.Phys. Lett. 74, 215–217 (1999)

Popescu, M.A.: Non-crystalline chalcogenides, Chap. 3, pp. 209–292. Kluwer, Dordrecht (2001)Poumellec, B., Riant, I., Niay, P., Bernage, P., Bayon, J.F.: UV induced densification during Bragg

grating inscription in Ge:SiO2 preforms: Interferometric microscopy investigations. Opt. Mater.4, 404–409 (1995)

Primak, W., Kampwirth, R.: The radiation compaction of vitreous silica. J. Appl. Phys. 39,5651–5658 (1968)

Reznik, A., Lui, B.J.M., Rowlands, J.A.S., Baranovskii, D., Rubel, O., Lyubin, V., Klebanov, M.,Kasap, S.O., Ohkawa, Y., Matsubara, T., Miyakawa, K., Kubota, M., Tanioka, K., Kawai, T.:Kinetics of the photostructural changes in a-Se films. J. Appl. Phys. 100, 113506 (2006)

Rodionov, A., Kalendarev, R., Eiduss, J.: Photostimulated structural changes in yellow arsenic.J. Phys.: Condens. Matter 7, 5805–5814 (1995)

Rosenblum, G., Sfez, B.G., Kotler, Z., Lyubin, V., Klebanov, M.: Nonlinear optical effects inchalcogenide photoresists. Appl. Phys. Lett. 75, 3249–3251 (1999)

Roy, A., Kolobov, A.V., Tanaka, K.: Laser-induced suppression of photocrystallization rate inamorphous selenium films. J. Appl. Phys. 83, 4951–4956 (1998)

Saji, M., Ohoka, T.: Electric field dependence of photodoping process in the amorphous GeS2.Denki-Gakkai Ronbunshi (in Japanese) 8, 47–47 (1985)

Sakaguchi, Y., Tamura, K.: Laser-induced pattern formation in liquid sulfur: An indication of laser-induced phase transition to ordered polymer. Eur. Phys. J. E 22, 315–324 (2007)

Sakaguchi, Y., Tamura, K.: Nanosecond dynamics of photodarkening in amorphous chalcogenide.J. Non-Cryst. Solids 354, 2679–2682 (2008)

Sakai, K., Maeda, K., Yokoyama, H., Ikari, T.: Photo-enhanced crystallization by laser irradiationand thermal annealing in amorphous GeSe2. J. Non-Cryst. Solids 320, 223–230 (2003)

Saliminia, A., Galstian, T.V., Villeneuve, A.: Optical field-induced mass transport in As2S3chalcogenide glasses. Phys. Rev. Lett. 85, 4112–4115 (2000)

Seki, M., Hachiya, K.: Partial recovery of the fatigued photoluminescence in germanium sulfideglass. J. Phys.: Condens. Matter 15, 4555–4565 (2003)

Shimakawa, K., Kolobov, A., Elliott, S.R.: Photoinduced effects and metastability in amorphoussemiconductors and insulators. Adv. Phys. 44, 475–588 (1995)

References 191

Shimakawa, K., Nakagawa, N., Itoh, T.: The origin of stretched exponential function in dynamicresponse of photodarkening in amorphous chalcogenides. Appl. Phys. Lett. 95, 051908 (2009)

Shimakawa, K., Yoshida, N., Ganjoo, A., Kuzukawa, Y.: A model for the photostructural changesin amorphous chalcogenides. Philos. Mag. Lett. 77, 153–158 (1998)

Shimizu, T.: Staebler-Wronski effect in hydrogenated amorphous silicon and related alloy films.Jpn. J. Appl. Phys. 43, 3257–3268 (2004)

Shimojo, F., Hoshino, K., Zempo, Y.: Photo-induced bond breaking in the S-8 ring: An ab initiomolecular-dynamics simulation. J. Phys.: Condens. Matter 10, L177–L182 (1998)

Shpotyuk, O.I.: Radiation-induced effects in chalcogenide vitreous semiconductors. In: Fairman,R., Ushkov, B. (eds.) Semiconducting Chalcogenide Glass I, Chap. 6, pp. 215–260. Elsevier,Amsterdam (2004)

Simdyankin, S.I., Elliott, S.R.: Light induced effects in amorphous and glassy solids. In: Drabold,D.A., Estreichen, S.K. (eds.) Theory of Defects in Semiconductors, pp. 269–284. Springer,Berlin (2007)

Singh, B., Rajagopalan, S., Bhat, P.K., Pandya, D.K., Chopra, K.L.: Photocontraction effect inamorphous Se1−xGex films. Solid State Commun. 29, 167–169 (1979)

Smith, C.M., Borrelli, N.F., Price, J.J., Allan, D.C.: Excimer laser-induced expansion in hydrogen-loaded silica. Appl. Phys. Lett. 78, 2452–2454 (2001)

Street, R.A.: Luminescence in amorphous semiconductors. Adv. Phys. 25, 397–453 (1976)Stuchlik, M., Elliott, S.R.: All-optical actuation of amorphous chalcogenide-coated cantilevers.

J. Non-Cryst. Solids 353, 250–262 (2007)Suzuki, T.: Flat panel displays for ubiquitous product applications and related impurity doping

technologies. J. Appl. Phys. 99, 111101 (2006)Suzuki, T., Hosono, H.: Ion-beam doping of silver in amorphous As2S3 thin films. J. Appl. Phys.

92, 1821–1824 (2002)Suzuki, M., Okano, S., Nagaoka, H., Hata, T.: Structural changes in As-S glasses induced by

acoustic flux injection. J. Non-Cryst. Solids 35–36, 1067–1072 (1980)Tada, T., Ninomiya, T.: Optically induced metastable defects in a-As2S3. J. Non-Cryst. Solids

137–138, 997–1000 (1991)Tanaka, K.: Reversible photoinduced change in intermolecular distance in amorphous As2S3

network. Appl. Phys. Lett. 26, 243–245 (1975)Tanaka, K.: Photo-induced dynamical changes in amorphous As2S3 films. Solid State Commun.

34, 201–204 (1980)Tanaka, K.: Mechanisms of photodarkening in amorphous chalcogenides. J. Non-Cryst. Solids

59–60, 925–928 (1983)Tanaka, K.: Transient-grating study of amorphous As2S3 films. J. Appl. Phys. 65, 2042–2046

(1989)Tanaka, K.: Photoinduced structural changes in chalcogenide glasses. Rev. Solid State Sci. 4,

641–659 (1990)Tanaka, K.: Physics and applications of photodoping in chalcogenide glasses. J. Non-Cryst. Solids

137–138, 1021–1026 (1991)Tanaka, K.: Photoexpansion in As2S3 glass. Phys. Rev. B 57, 5163–5167 (1998)Tanaka, K.: The charged defect exists? J. Opt. Adv. Mater. 3, 189–198 (2001a)Tanaka, K.: Photoinduced anisotropy in chalcogenide glass. In: Nalwa, H.S. (ed.) Handbook of

Advanced Electronic and Photonic Materials and Devices, Vol. 5, Chap. 4, pp. 120–139.Academic, San Diego, CA (2001b)

Tanaka, K.: Sub-gap photo-induced phenomena in chalcogenide glasses. In: Kolobov, A.V. (ed.)Photo-Induced Metastability in Amorphous Semiconductors, Chap. 5, pp. 69–90. Wiley-VCH,Weinheim (2003)

Tanaka, K.: Midgap photon effects in As2S3 glass. Philos. Mag. Lett. 84, 601–606 (2004)Tanaka, K.: Visible anisotropic deformation of chalcogenide glass by illumination of linearly

polarized light. Appl. Phys. Express 1, 012006 (2008)

192 6 Light-Induced Phenomena

Tanaka, K., Asao, H.: Photoinduced anisotropic deformation in As2S3 glass. Jpn. J. Appl. Phys.45, 1668–1674 (2006)

Tanaka, K., Kikuchi, M.: On the interpretation of photographic effects in amorphous As-S films.Solid State Commun. 13, 669–671 (1973)

Tanaka, K., Mikami, M.: Photo-induced deformations in chalcogenide glass: Atomic or opticalforce? J. Opt. Adv. Mater. 11, 1885–1890 (2009)

Tanaka, K., Ohtsuka, Y.: Transient characteristics of photochromic processes. J. Opt. (Paris) 8,121–126 (1977)

Tanaka, K., Ohtsuka, Y.: Photo-induced optical changes in amorphous As-S films. Thin Solid Films48, 17–26 (1978)

Tanaka, K., Sanjoh, H.: Photodoping dynamics in the Ag/As-S system. J. Appl. Phys. 74,1106–1110 (1993)

Tanaka, K., Gotoh, T., Hayakawa, H.: Anisotropic patterns formed in Ag-As-S ion-conductingamorphous semiconductor films by polarized light. Appl. Phys. Lett. 75, 2256–2258 (1999)

Tanaka, K., Ichimura, Y., Komasaki, M.: Photoinduced effect in glassy chalcogenide heterojunc-tions. Thin Solid Films 189, 51–58 (1990)

Tanaka, K., Kawakami, N., Odajima, A.: Photoinduced elastic changes in amorphous As2S3 films.Jpn. J. Appl. Phys. 20, L874–L876 (1981)

Tanaka, K., Nemoto, N., Nasu, H.: Photoinduced phenomena in Na2S-GeS2 glasses. Jpn. J. Appl.Phys. 42, 6748–6752 (2003)

Tanaka, K., Saitoh, A., Terakado, N.: Giant photo-expansion in chalcogenide glass. J. Opt. Adv.Mater. 8, 2058–2065 (2006)

Tao, H., Yang, Z., Lucas, P.: Origin of photo-induced transmitting oscillations in chalcogenideglasses. Opt. Express 17, 18165–18170 (2009)

Terakado, N., Tanaka, K.: Photo-induced phenomena in GeO2 glass. J. Non-Cryst. Solids 352,3815–3822 (2006)

Terakado, N., Tanaka, K.: Photoinduced phenomena in GeO2-GeS2 glasses. Jpn. J. Appl. Phys. 46,L265–L267 (2007)

Terakado, N., Tanaka, K.: Ag-photodoping in nano-structured GeO2-GeS2 glasses. Phys. StatusSolidi (c) 6, S75–S78 (2009)

Toyosawa, N., Tanaka, K.: Photocurrent enhancement in light-soaked chalcogenide glasses. Phys.Rev. B 56, 7416–7421 (1997)

Toyozawa, Y.: Optical Processes in Solids. Cambridge University Press, Cambridge (2003)Trunov, M.L., Lytvyn, P.M., Dyachyns’ka, O.M.: Alternating matter motion in photoinduced mass

transport driven and enhanced by light polarization in amorphous chalcogenide films. Appl.Phys. Lett. 97, 031905 (2010)

Trunov, M.L., Nagy, P.M., Takats, V., Lytvyn, P.M., Kokenyesi, S., Kalman, E.: Surface morphol-ogy of as-deposited and illuminated As-Se chalcogenide thin films. J. Non-Cryst. Solids 355,1993–1997 (2009)

Uchino, T., Takahashi, T., Ichii, M., Yoko, T.: Microscopic model of photoinduced and pressure-induced UV spectral changes in germanosilicate glass. Phys. Rev. B 65, 172202 (2002)

Utsugi, Y.: Linear relationship between photo-induced changes in gap energy and refractive indexof chalcogenide glasses. Phys. Status Solidi (b) 212, R9–R10 (1999)

Van Vechten, J.A., Tsu, R., Saris, F.W.: Nonthermal pulsed laser annealing of Si; plasma annealing.Phys. Lett. A 74, 422–426 (1979)

Vasilyev, V.A., Pavlov, S.K., Kolomiets, B.T.: The photostimulated light absorption in vitreousAs2Se3 and As2S3. In: Kosa Somogyi, I. (ed.) Amorphous Semiconductors ’76, pp. 189–193.Akad, Kiado, Budapest (1977)

Vonwiller, O.U.: Notes on the elastic properties of selenium. Nature 104, 347 (1919)Weeks, R.A.: Paramagnetic resonance of lattice defects in irradiated quartz. J. Appl. Phys. 27,

1376–1381 (1956)

References 193

Yang, Z., Anheier, N.C., Qiao, H.A., Lucas, P.: Simultaneous microscopic measurements ofphotodarkening and photoexpansion in chalcogenide films. J. Phys. D: Appl. Phys. 42, 135412(2009)

Yannopoulos, S.N., Trunov, M.L.: Photoplastic effects in chalcogenide glasses: A review. Phys.Status Solidi (b) 246, 1773–1785 (2009)

Yoshida, N., Tanaka, K.: Photoinduced Ag migration in Ag–As–S glasses. J. Appl. Phys. 78,1745–1750 (1995)

Youden, K.E., Grevatt, T., Eason, R.W., Rutt, H.N., Deol, R.S., Wylangowski, G.: Pulsed laserdeposition of Ga-La-S chalcogenide glass thin film optical waveguides. Appl. Phys. Lett. 63,1601–1603 (1993)

Zhdanov, V.G., Malinovsky, V.K.: Photoinduced birefringence and dichroism in As2S3 films. Sov.Tech. Phys. Lett. 3, 387–388 (1977)

Zhugayevych, A., Lubchenko, V.: An intrinsic formation mechanism for midgap electronic statesin semiconducting glasses. J. Chem. Phys. 132, 044508 (2010)

Chapter 7Applications

Abstract A variety of applications, present and potential, of non-crystalline insu-lators and semiconductors including amorphous chalcogenides are described in a“tree growth manner.” History and trend of optical devices, fibers, and waveguidesare described. Great success has been attained in phase change memories (DVDs),x-ray medical image sensors, highly sensitive vidicons, and xerography. We referalso to other applications such as holographic memories, nonlinear devices, solarcells, and ionic devices.

Keywords Optical fiber · Phase change · DVD · Image sensor · Vidicon ·Xerography · Solar cell · Ionic device

7.1 Overall Features

The tree in Fig. 7.1 shows relationships between fundamentals and applications ofnon-crystalline insulators and semiconductors. We see the two roots. One is a disor-dered structure, which also raises the liquid, except for liquid crystals. Nevertheless,photo-electronic applications of non-crystalline liquids are very limited, an exam-ple being Kerr cells using polar liquids as nitrobenzene (C6H5NO2). Accordingly,we may focus upon the disordered solid, i.e., amorphous material, which growsalso from the other root of quasi-equilibriumness. On the other hand, macroscopicshapes of the opto-electric devices have three branches: fiber, film, and others.

195K. Tanaka, K. Shimakawa, Amorphous Chalcogenide Semiconductors and RelatedMaterials, DOI 10.1007/978-1-4419-9510-0_7, C© Springer Science+Business Media, LLC 2011

196 7 Applications

Fig. 7.1 A tree of non-crystalline devices

In more detail, the fundamentals (bold), characteristic properties, and applica-tions (italics) of amorphous chalcogenides and related materials can be connectedas follows:

Disordered structure

→ multi-component and varied compositions → EDFA

→ small impurity effect, inefficient dopant effect→ higher ion mobility → solid-state battery, ionic memory

→ localized electron wavefunction→ small electron mobility, electrically insulating, (avalanche multiplication?)

→ vidicon, X-ray imager

→ localized lattice vibration → small thermal conductivity

Quasi-equilibriumness

→ fast sample preparation →low cost and big sample → fiber, thin-film solar cell, TFT

→ dependence upon preparation methods and prehistory

→ photo(electro)-induced phenomena → Bragg reflector fiber, DVD, PRAM

Table 7.1 lists some photo-electronic applications of non-crystalline oxide andchalcogenide (group VIb) solids. Here, we see an interesting trend. The applicationchanges, in correspondence to a decrease in the optical gap energy from the oxide(5–10 eV) to the telluride (∼1 eV), from optical, photo-structural, photo-conductive,

7.2 Optical Device 197

Table 7.1 Representative optical and electrical properties and applications of group VIb amor-phous materials (glasses)

Material

Transparentwavelength(µm) (photonenergy [eV])

Refractiveindex

Resistivity(� cm) Optical

Photo-Structural

Photo-Conductive

Opto-thermal

Oxide 0.2–2 (0.6–5) 1.6 1015 Fiber Braggreflector

Sulfide 0.6–10(0.1–2.5)

2.5 >1015 IR optics Holometer

Selenide 0.8–15(0.08–2.0)

2.8 1012 IR optics CopyVidiconX-rayImager

Telluride 1–20(0.06–1.0)

3.0 104 DVD

and opto-thermal (Table 6.1). Such a trend is understandable through a comparisonof the optical gap Eg with the visible light energy (�ω ≈ 2 eV) That is, for opticalapplications, the glass must be transparent, which requires Eg > 3 eV, being satis-fied with the oxide (Section 7.2). Photo-structural changes are prominent in sulfides,which are covalent and molecular (Section 7.3). For photoconductive applications,the condition of Eg > 2 eV must be satisfied, so that the chalcogenide, specificallypure a-Se, is the most suitable (Section 7.6). As known, a-Se has the highest carrier(hole) mobility in the chalcogenide glass, which is also important in applicationssuch as x-ray detectors. Finally, the telluride has some metallic character with lessdirectional atomic bonds and small Eg, which are required for optical (DVD) andelectrical, thermally induced phase-change recordings (Section 7.4).

7.2 Optical Device

Oxide and chalcogenide glasses are employed as light-transmitting media. As shownin Fig. 7.2, SiO2 is transparent from a deep ultraviolet to near-infrared region(λ ≈ 200 nm to 3 µm), in which the ultraviolet and infrared transmission edges aregoverned by electronic and lattice-vibrational absorptions, respectively. An impor-tant photonics application is the optical fiber for communications at λ � 1.55 µm(Section 7.2.1).

On the other hand, infrared transmission is a unique characteristic of thechalcogenide glass. As2Te3 can transmit infrared light at a wavelength region ofλ ≈ 2 − 20 µm. However, as shown in Fig. 7.2, the transmittance in chalcogenideglasses at transparent regions is lower (≤70%) due to higher light reflectionarising from greater refractive indices (n ≥ 2.5). Accordingly, anti-reflection coat-ing is preferred. Another characteristic of the chalcogenide glass is relatively low

198 7 Applications

Fig. 7.2 Comparison ofultraviolet–infraredtransmission spectra ofseveral glass plates with athickness of ∼2 mm(modified from Kumta andRisbud 1990)

glass transition temperatures. Owing to that, glass can be shaped through squeez-ing or molding into, e.g., infrared-transmitting lenses for night viewers. In addition,the high refractive index affords new devices as multi-layered mirrors at infraredregions (Clement et al. 2006, Kondakci et al. 2009) and photonic crystals (Popescuet al. 2009, Kohoutek et al. 2011).

In addition to the optical transparency, the glass has notable characteristics whencompared with other materials (see Figs. 1.5 and 1.6). In comparison with crystals,the glass can be produced in large sizes, and it can be shaped into arbitrary forms bypolishing, molding, and drawing. Note that the molding and drawing are entirely dueto the existence of glass transitions. Also, wide-area non-crystalline films can be pre-pared through vacuum evaporation, sputtering, sol–gel technique, etc., as describedin Section 1.8. In comparison with organic polymers, the glass is more thermallystable and radiation resistant. The polymer cannot be infrared transmitting, due tohigh-frequency atomic vibrations. However, the glass is heavier, more breakable,and generally, more expensive than the polymer.

7.2.1 Optical Fiber

The optical communication has progressed concomitantly with attenuation reduc-tion and functionalization of silica fibers. The concept of optical fiber communica-tion was proposed by Kao and Hockham (1966), and Kao was awarded the 2009Nobel Prize in physics. Indeed, we are surprised at dramatic developing historyof the fiber communication. Around 1970, a minimal transmission loss of a glassfiber was 20 dB/km (1 cm−1 = 434 dB/m, 1 dB/m = 0.0023 cm−1), the valuebeing governed by impurities. Although short (∼m) fibers had been utilized formedical inspections, few researchers expected that the fiber would afford distantsignal transmission. Gradually, the loss was reduced with inventions of new prepa-ration methods such as vapor axial deposition using purified gases. And, the productenabled us to communicate through the optical fiber, in which one digitalized opticalsignal with a modulation frequency of ∼50 Mb/s was transferred. The optical signal

7.2 Optical Device 199

naturally weakened when transmitting over long (∼10 km) distances. Accordingly,the optical signal was detected by a photo-detector, electrically amplified, and thenconverted again to an optical signal using a modulated laser diode.

At present, such an elementary system has completely been revolved. The trans-mission loss has been reduced to 0.2 dB/km (Thomas et al. 2000), as shown inFig. 7.3, and it becomes practical to transmit a signal through a fiber with a lengthof ∼80 km. In 2005, as schematically illustrated in Fig. 7.4, a single fiber trans-mits digital signals of 32 different wavelengths in parallel, each being modulatedat 10 Gbit/s, the system being referred to as “wavelength division multiplexing”(WDM). In this system, signals with different wavelengths are combined into andresolved from a fiber using dispersive elements as prisms or fiber Bragg gratings(FBGs) (see Section 7.3). And the 32 signals are optically amplified through stimu-lated emission by an Er3+-doped fiber amplifier (EDFA) (Section 7.2.2). The WDM

Fig. 7.3 Optical absorptionin g-SiO2 (solid lines) andc-SiO2 (dashed line)(modified from Griscom1991). The inset shows amagnified view at around theoptical communication region(modified from Thomas et al.2000)

Fig. 7.4 A schematic illustration of a WDM system, equipped with an Er-doped optical amplifier,which transmits four signals with different wavelengths of ∼1.55 µm (modified from http://www.moritex.co.jp/products/opt/optical-fiber-filter.php)

200 7 Applications

is now changing to dense WDM (DWDM) having transmission capacities of Tbit/sper fiber.

For the optical fiber made from silica glass, we still seek superior performances.A fundamental one may be more reduced light attenuation (= loss). Here, theattenuation is determined by absorption and scattering, i.e., attenuation =absorption + scattering. The absorption can be electronic, vibrational, defective, andimpurity originated (Thomas et al. 2000) as described in Section 4.6. The electronicand vibrational are inherent to a material, but the defective and impurity originatedshould be suppressed as possible by sophisticated purification and preparation pro-cedures. On the other hand, the light scattering is caused by spatial fluctuationsof fiber shapes and glass density, the latter being inevitable to the glass, since itis quenched from a density-fluctuating liquid. The scattering loss αs arising fromsuch intrinsic density fluctuation, which has been formulated by Smoluchowski andEinstein, can be written as (Ikushima et al. 2000)

αs � (8π3/3λ4)n8p2βTkBTg, (7.1)

where λ is the wavelength, n the refractive index, p the photoelastic constant, βT theisothermal compressibility, and Tg the glass transition temperature. This equationsuggests that a glass having a lower glass transition temperature is preferred forreducing the scattering loss. In this context, SiO2 having the highest Tg(∼1500◦C)among the glass appears to be inappropriate. Nevertheless, simple (stoichiometric)glass is preferred for obtaining atomically homogeneous structures. If we mightemploy SiO2–Na2O glass having a lower Tg, the compositional disorder wouldincrease the light scattering. It seems that further reduction of the fiber attenuationis challenging.

Another development is in progress. As known, the present communication sys-tem utilizes the 1.5 µm wavelength (�ω � 0.8 eV) band. This band has beenselected taking the two factors into account (Fig. 7.3): one being the λ−4 scatter-ing loss (see Equation (7.1)), originating from the so-called Rayleigh scattering,and the other being vibrational absorption rising at λ ≈ 2 µm in silica. However,for wider wavelength communications, an absorption peak at 1.4 µm due to –OHvibrations was an obstacle, which has been recently suppressed through chemicalreductions. The communication wavelength will be extended from 1.5–1.6 µm to awider 1.3–1.6 µm band (DWDM).

The chalcogenide glass can also be drawn as fibers, which transmit infrared light.The fiber is employed for spectroscopy and power transmission for, e.g., biologicaland medical (surgery) purposes (Nishii and Yamashita 1998, Snopatin et al. 2009,Bureau et al. 2009). For instance, the fiber can transmit 10–100 W infrared light(λ = 5 and 10.6 µm) emitted from CO and CO2 gas lasers. Here, a fundamentalproblem is again the transmission loss, which is substantially higher than that (∼0.2dB/km) in silica, due to lower glass purity, higher refractive index (αs ∝ n8), andother problems (Snopatin et al. 2009). The loss has been decreased to 12 dB/km inan As2S3 multi-mode fiber at a wavelength of 3 µm (Snopatin et al. 2009), which iscomparable to 10 dB/km in halide (AlF3) glass fibers. It should be mentioned that

7.2 Optical Device 201

relatively low glass transition temperature of the chalcogenide glass will be suitablefor preparing micro-structured fibers including photonic structures (Coulombieret al. 2010). These fibers are also useful for nonlinear applications at near- (Liaoet al. 2009, Xiong et al. 2009, Shinkawa et al. 2009, Florea et al. 2009) and mid-infrared regions (Hu et al. 2010, Ung and Skorobogatiy 2010, Cherif et al. 2010).

7.2.2 Metal-Doped Fiber

The atomic doping plays an important role in functional fibers. The disorderedand flexible atomic structure of glasses is appropriate for incorporating metallicelements, such as transition metal atoms and rare earth ions (Tver’yanovichi andTverjanovich 2004). Using this characteristic, we can prepare not only passive fiberdevices as Co-doped attenuators (Morishita and Tanaka 2003) but also active devicesas rare earth ion-doped amplifiers (Desurvire 1994).

In the fiber amplifier, rare earth ions work as stimulated emission centers(Desurvire 1994). Rare earth atoms are likely to be charged in the valenceof 3+, and accordingly, the ion has an unfilled 4f electron state which is shieldedby outermost electrons in 5s and 5p orbital. In Er, for instance, the structure of outerelectrons is 4f12 5s2 5p6 6s2, so that Er3+ has 4f12 5s2 5p5 electrons. (Note that thef state is able to have 14 electrons.) Accordingly, in some conditions, radiative f–ftransitions can occur with relatively high efficiencies. Actually, as shown in Fig. 7.5,Er3+, when excited by 0.8 µm light (4I15/2 → 4I9/2), can amplify 1.5 µm light(4I13/2 → 4I15/2). Here, a quantum efficiency η of the amplification is approximatelywritten as

Fig. 7.5 Energy levels of Er3+ (left) and Pr3+ (right) ions with transition energies presented inlight wavelength (modified from Tver’yanovichi and Tverjanovich 2004)

202 7 Applications

η ≈ WR/(WR + WNR) , (7.2)

where WR and WNR are radiative and non-radiative transition rates. WR is estimatedusing the so-called Judd–Ofelt theory. On the other hand, WNR is governed by multi-phonon emission to a host glass as follows:

WNR ≈ {1 − exp (−Ev/kT)}−E/Ev , (7.3)

where E is the energy difference between an excited state and the next lowerenergy state (∼6500 cm−1 for 4I13/2 in Er3+) and Ev (∼1200 cm−1) is a typ-ical vibration wavenumber of the host (silica) glass. In consequence, the silicaEDFA (Fig. 1.7) has given a satisfactory performance for the 1.5 µm amplifica-tion, while it is not satisfactory for the DWDM system operating at a wider band of1.3−1.6 µm.

The chalcogenide glass is promising for the DWDM amplifier. We first note thatEr3+ has no appropriate energy levels for amplification of 1.3 µm light. Instead,we may employ Pr3+(1G4 → 3H5), which has smaller E (∼3000 cm−1), so thatthe oxide glass having the high Ev is not suitable for a host due to increased WNR.The chalcogenide glass, reflecting heavier atomic mass, has lower Ev(∼300 cm−1),and accordingly, WNR becomes smaller, giving rise to higher η. Using this fea-ture, Ohishi et al. (1994) have fabricated Pr3+-doped As–S fiber amplifiers, PDFA.In such applications, however, the chalcogenide is competitive with the halide glass(Lucas 1999). Or, chalco-halide glasses may be more preferred.

Here, we should select special chalcogenide glasses in the optical amplifier. Forefficient PDFAs, Pr3+ ions must be doped with a concentration of ∼1000 ppm(Tver’yanovichi and Tverjanovich 2004). But, covalent chalcogenide glasses suchas As2S3 cannot afford such a high doping, resulting in precipitation of metallic par-ticles. Instead, we may employ ionic chalcogenide glasses, which are compoundswith Na, Al, Ga, La, etc. Such cation is likely to polarize S atoms, which becomean anion, providing a stable location for Pr3+. In Ga2S3–GeS2 glasses, for instance,a suggested local structure around a rare earth ion R3+ is ≡Ga∼S∼R3+∼S∼Ga≡,where ≡ of Ga represents threefold coordination, and ∼ stands for an ionic bond.The chalcogen can afford such structural flexibility. However, a problem is that theseionic chalcogenide glasses tend to react with water vapor (as NaCl does).

One of the interesting features of the rare earth ion-doped chalcogenide glassesis the photoluminescence through host excitation (Bishop et al. 2000). In the oxideglass, optically excited rare earth ions emit photons after some non-radiative relax-ation. The host glass acts just as a perturbing matrix. Such a process, �ω0→�ω2 inFig. 7.6, also exists in the chalcogenide. On the other hand, Bishop et al. (2000) havediscovered, e.g., in Er-doped GaGeAsS glasses, that photons having an energy com-parable to the Urbach edge of the host chalcogenide glass can provide luminescenceof the rare earth ion (�ω1→�ω2). This result suggests a process, which consistsof host photo-excitation, energy transfer from the host to rare earth ions, and lightemission from the ion. The energy transfer process, which may be a resonant trans-fer, has not been elucidated. Since the Urbach edge is spectrally more extended than

7.2 Optical Device 203

Fig. 7.6 Direct (�ω0) andhost (�ω1) excitations of rareearth ions (REI) in achalcogenide glass emitting�ω2 photons

the sharp absorption peaks of rare earth ions, the broadband excitation of rare earthions can be attained. Excitation using sunlight may be possible. However, the hostexcitation is likely to induce the photodarkening as well, which gives a fatigue inluminescence efficiency (Harada and Tanaka 1999). It is mentioned that the hostexcitation is demonstrated also for Er-doped a-Si:H films (Fuhs et al. 1997).

We here note that other types of optical fiber amplifiers have been proposedand demonstrated. The most promising may be the one which employs nonlineareffects such as stimulated Raman and Brillouin scattering (Abedin 2005, Jacksonand Anzueto-Sánchez 2006, Stegeman et al. 2006). Due to higher optical nonlinear-ities (see Section 4.8), the chalcogenide glass is superior to the oxide also in theseapplications.

7.2.3 Waveguide

Optical communication now needs waveguide devices, which can be more com-pact than the fiber. It will be very convenient if we can fabricate the rare earth ionamplifier in optical integrated circuits with a size of ∼1 cm. Or, such waveguidesmay be integrated with semiconductor and ferroelectric devices. Actually, pioneer-ing studies on chalcogenide glass waveguide have been reported since the 1970s(Matsuda et al. 1974, Watts et al. 1974, Klein 1974). The waveguide with a highrefractive index of ∼2.5 is suitable for confining propagating light. Recently, suchstudies are advanced with combinations of a variety of thin-film preparation tech-niques as pulsed laser deposition (Seddon et al. 2006). In addition, sophisticatedstructures such as three-dimensional Ge22As20Se58 waveguides buried in g-As2S3,having a propagation loss of 0.04 dB/cm at a wavelength of 9.3 µm (Coulombieret al. 2008), are fabricated.

Extensive studies have also been directed toward the ultra-fast (picosecondrange) all-optical waveguide switch using optical nonlinearity (Suzuki et al. 2009,Vo et al. 2010, Eggleton et al. 2011). As described in Section 4.8, the refractiveindex n of a glass can be written as n = n0 + n2I, and by using the intensity-dependent second term n2I, we can modify the optical path length of an armin a waveguide interferometer. For instance, in Fig. 7.7, the control beam with

204 7 Applications

Fig. 7.7 An all-opticalwaveguide switch using aMach–Zehnderinterferometer

intensity of I switches on and off the output signal. The device will replace electro-optical switches presently utilized, which employ the Pockels effect and direct lasermodulation.

In such nonlinear applications, the chalcogenide glass seems to be very promis-ing. In the optical integrated circuits with a waveguide length of ∼1 cm, sufficientlyhigh nonlinearity is needed at the communication wavelength of ∼1.5 µm, or thephoton energy of EOC ≈ 0.8 eV. As described in Section 4.8, the optical nonlinearityincreases with a ratio of EOC/Eg(< 1), and accordingly, the chalcogenideglass having smaller Eg(≈ 1∼3 eV) than the oxide appears to have feasiblepotentials.

Nevertheless, at least, two problems must be settled. One is the connectionbetween a chalcogenide device and a silica fiber. A smaller Eg of the chalcogenideprovides a higher refractive index (∼2.5), which is likely to cause high reflectionloss at the connection. Anti-reflection devices (or coating) are required. The otheris that, for compact all-optical switches, the nonlinearity appears to be still insuf-ficient. The waveguide switch may require higher nonlinearities by two to threeorders of magnitude than that available with a chalcogenide glass having an appro-priate optical gap of ∼2.0 eV. For this purpose, nano-structured (Tanaka and Saitoh2009) or photonic-structured (Suzuki et al. 2009) chalcogenide waveguides may bepromising, provided that we can compromise a high nonlinearity and a fast response.In addition, optical absorption of the chalcogenide glass may also be problematic.With respect to the so-called figures of merit (Table 7.2), which take optical absorp-tions into account, the chalcogenide glass is not superior to the oxide. Needlessto say, in nonlinear applications, the chalcogenide glass is competitive also withother materials such as crystalline semiconductors (Kamiya and Tsuchiya 2005)and organic materials (Haque and Nelson 2010).

We here point out other nonlinearities. As listed in Table 7.3, it has been demon-strated that, not only the optical, but elastic nonlinearity (Rouvaen et al. 1975) andphoto-elastic constants (Lainé and Seddon 1995) in the chalcogenide glass are sub-stantially greater than that in the oxide glass such as silica. However, to the authors’knowledge, no developments have been reported in practical applications.

7.3 Photo-Structural Device 205

Table 7.2 Linear (Eg, n0, α0) and nonlinear (n2, βmax) optical properties and figures of merit ofnonlinearity (2βλ0/n2, n2/a0) in some glasses

Glass Eg (eV) n0 α0 (cm–1)n2 (×10–20

m2/W)βmax(cm/GW) 2βλ0/n2

n2/α0(cm3/GW)

SiO2 10 1.5 10–6 2 1 <10 0.2BK-7 4 1.5 3SF-59 3.8 2.0 30 10As2S3 2.4 2.5 10–3 200 50 0.1 0.02BeF2 10 1.3 0.8

Eg is an optical gap energy, n0 the refractive index, α0 the attenuation coefficient, n2 the intensity-dependent refractive index, and βmax the maximal two-photon absorption coefficient. Except Egand βmax, the values are evaluated at wavelengths of 1−1.5 µm. BK-7 is a borosilicate glass andSF-59 represents data for lead-silicate glasses with ∼57 mol.% PbO

Table 7.3 Comparison of nonlinear coefficients in As2S3 and SiO2 glasses

Material M2 (×1015/s3 kg) Ma (×10−12 s2/kg) χ (3) (×10−14 esu)

As2S3 433 240 500SiO2 1.5 0.4 3

M2 is the photo-elastic figure of merit, Ma the nonlinear acoustic figure of merit, and χ (3)

the third-order nonlinear optical susceptibility

7.3 Photo-Structural Device

Photo-structural devices may be unique to the amorphous group VIb materi-als. At present, Bragg-reflector fibers (permanent) and optical phase-change disks(erasable) have been commercialized. In addition, a lot of applications have beenproposed and demonstrated. In the following, we will see these applications inoxides and chalcogenides, except the phase change device, which is described inSection 7.4.

Bragg-reflector fibers, the production principle being discovered by Hill et al.(Section 6.4), have been commercialized and widely utilized as wavelength filtersin WDM systems (Askins 2000). As illustrated in Fig. 7.8, the refractive index inthe core, consisting of Ge–SiO2, of optical fibers can be spatially modulated byexposures to excimer laser light through photoinduced refractive index change ofn ≈ 10−3. The sinusoidally modulated structure, or the so-called Hills’ grating,reflects light with a wavelength of λ which satisfies the Bragg condition λ = 2d,where d is the modulated periodicity.

For photoinduced phenomena in sulfides and selenides such as As2S3 andGeSe2, there are many proposals, but few have been commercialized. Those includeholographic memories, photoresists, and other active and passive optical devices.For the fundamental of these phenomena, see Chapter 6.

The optical memory can be non-erasable or erasable. Zembutsu et al. (1975)demonstrated using sputtered Ge–As–S–Se films and gas lasers that one page of

206 7 Applications

Fig. 7.8 A fiber Bragg grating (FBG). The input consists of four signals with different wave-lengths, in which only one selected signal is reflected and the remaining three are transmittedthrough the grating (modified from http://www.moritex.co.jp/products/opt/optical-fiber-filter.php)

newspapers can be holographically stored in a memory spot of 1.5 mm in diameter,which can be thermally erased using an infrared lamp (Fig. 7.9). The holographicmemory has been developed, e.g., as “Holometer” (González-Leal et al. 2003) andother systems (Teteris 2003, Ozols et al. 2006), which employ semiconductor lasers,optical fibers, and computers. However, at the present stage in an optical memorymarket, DVD flourishes (see Section 7.4), and accordingly, it is questionable if thereis an open space for analogue holographic memories. We also note that ultimatestorage capacities in the holographic and binary memories, 1 Tbit/cm3, are princi-pally the same (Van Heerden 1963). To dramatically enhance the capacity in optical

Fig. 7.9 An erasable holographic memory system using Ge–As–Se films (left), a hologram (cen-ter), and a reconstructed image (right) (modified from Zembutsu et al. 1975). In the systemillustration, O is a memorized object and sample is the chalcogenide film

7.3 Photo-Structural Device 207

memories, we must utilize spectrum and polarization multiplexing (Zijlstra et al.2009).

Many researchers have demonstrated applications of the photo-polymerization(Section 6.3.5) to photoresist processes (Jain and Vlcek 2008). Keneman(1974) reported a pioneering work on relief holograms, which are producedin as-evaporated As2S3 films through light illumination and chemical etching.A Bulgarian group produced, using chalcogenide films as inorganic photore-sists, linear scales and gratings up to 1.6 m long, circular encoder gratings,and diffraction and kinoform optical elements (www.clf.bas.bg). Lyubin et al.(2008) and other researchers applied three-dimensional photoresist processes insulfides and selenides to production of photonic crystal structures. As describedin Section 7.7, relief structures have been produced also through the photodopingprocess. In such photoresist applications, however, the chalcogenide is competitivewith organic resists in versatility and cost.

Photoinduced phenomena have been applied to formation of optical waveg-uides and the devices. There are many proposals of such studies from the 1970s(Zakery and Elliott 2003, Petit et al. 2008). High-quality channeled waveguidesare produced through wet and dry etchings of irradiated films (Choi et al. 2008).Chalcogenide waveguides, employing the optical stopping effect (Zou et al. 2006)and the photoinduced refractive index change (Tanaka et al. 1985), have beenapplied also to all-optical switches, though the response speed is not fast.

In addition, photoinduced phenomena have been utilized for fabrication of pas-sive optical devices. Tanaka et al. (1995) produced self-induced Bragg gratingsin As2S3 optical fibers and also microlenses (∼10 µm diameter), the examplesbeing shown in Fig. 7.10. The production principle has been applied also to self-developing microlenses for optical fibers and laser diodes (Saitoh and Tanaka 2003).

Fig. 7.10 Photoinducedlenses (spherical andcylindrical) (left) and thefocusing images (right)(Hisakuni and Tanaka 1995).The minimal scale on theright-hand side photographsis 10 µm

208 7 Applications

Shokooh-Saremi et al. (2006) produce, using an interferometer, Bragg gratingsin As2S3 rib waveguides. Sudoh et al. (1997) and Song et al. (2006) apply thephotoinduced refractive index change to wavelength tuning of semiconductor lasers.The refractive index change can also be employed for preparing photonic structures(Lee et al. 2009). In addition, Gelbaor et al. (2011) utilize the vector effect (Section6.3.12) in As2S3 for alignment of liquid crystals. Here, it should be mentioned thatnot light beams but electron beams are also useful for preparing micro-scale patterns(Handa et al. 1980, Ruan et al. 2007, Liu et al. 2008). These applications wait forfurther advances (Calvez et al. 2010).

7.4 Phase Change

7.4.1 Background

The most widely commercialized product using chalcogenide films at present isundoubtedly the optical phase-change disk, named DVD (digital versatile disk). Thephase change is now being applied also to a rewritable electrical memory, the so-called PRAM (phase-change random access memory).

As shown in Figs. 7.11 and 7.12, the phase changes have simple dynamics. Or,the operating principles of the electrical and the optical are believed to be essen-tially the same, i.e., electrical Joule heating (Ovshinsky 1968) and optical heating(Feinleib et al. 1971), which can change the structure of telluride films betweenamorphous and crystalline states (Fig. 7.12). For amorphization, the crystalline filmis heated above the melting temperature (∼600◦C), which is followed by rapidquenching. For crystallization, the amorphous film is heated to the crystallizationtemperature (∼150◦C), stored there a little bit for crystal growth, and cooled downto room temperature. These amorphous–crystalline structural transformations inthe telluride film modify its electrical resistance by four orders of magnitude (seeFig. 7.16) and optical reflectivity by ∼5%, which are read using low-voltage andweak-light pulses.

Fig. 7.11 Dynamics oftemperature rising inducedoptically or electrically inamorphous telluride films

7.4 Phase Change 209

Fig. 7.12 Free energy as a function of atomic configuration (left) and temperature (right) for aphase-change material, Ge2Sb2Te5. Note that there exist two crystalline phases of cubic (fcc) andhexagonal. See also Fig. 7.16

However, applications of the phase change required long developments. Thephase changes, both electrical and optical, in amorphous telluride films such asTe81Ge15Sb2S2 were discovered in Ovshinsky’s group in the 1960s (Ovshinsky1968, Feinleib et al. 1971). And, in the 1970s, many researchers tried to produce ran-dom access memories using the electrical phase change. However, the crystallizationprocess was too slow, requiring electrical pulses with durations of sub-milliseconds.This operation speed could not be competitive with that (sub-microseconds) in c-Sidevices at that time. On the other hand, at the beginning of 1970s, we did nothave compact lasers of ∼30 mW class, and accordingly, the optical phase changewas studied using big gas (Ar and Kr) lasers. Of course, such lasers could notbe employed for commercial products. With these reasons, despite the initial sen-sational announcement by Ovshinsky, the phase change seemed to be graduallyforgotten. However, later, Yamada et al. (1991) discovered that the ternary alloysconsisting of GeTe–Sb2Te3 (see Fig. 7.13) often abbreviated as GST (Ge–Sb–Te)exhibit rapid crystallizations. Specifically, a stoichiometric composition Ge2Sb2Te5(GST225) exhibits a crystallization time less than ∼50 ns upon excitation by laserpulses. Then, the optical phase change using GST films, with combination ofsemiconductor lasers, was developed to DVD systems. The best DVD system avail-able in 2010 has a memory capacity of 50 GB/disk, which utilizes a blue semicon-ductor laser emitting light with a wavelength of 405 nm. The film shows fast phasechanges also upon electrical pulses, and accordingly, electrical RAMs are beingdeveloped.

210 7 Applications

Fig. 7.13 A ternary composition diagram depicting phase-change alloys, with their years of dis-covery as a phase-change material and their uses (in squares) in optical storage products. Thecrystallization time becomes faster from the left-hand side (∼10 µs) to the right-hand side (∼30 ns)(modified from Wuttig and Yamada 2007)

7.4.2 Optical Phase Change (DVD)

The optical phase change has been believed to be induced by direct optical heat-ing. Here, the two important performances are the operation speed and the memorycapacity.

The operation speed is governed by writing and erasing times of a memoryspot, with the reading much faster. The writing (amorphization) is attained using ashort (∼10 ns) and intense light pulse, which heats crystalline GST films above themelting temperature, followed with a rapid quenching, which is governed by heatconduction to peripheral layers (see Fig. 7.14). On the other hand, erasing includesthe crystallization (crystallite nucleation and growth) of amorphous marks, whichnaturally needs longer duration. We are then interested in the reason why the GSTfilm exhibits a fast crystallization time of ∼50 ns. It is also an important subject tobe answered if the crystallization time can further be shortened.

To understand the fast crystallization mechanism, atomic changes accompa-nying the phase change should be revealed. However, at present, the changeremains controversial (Lucovsky and Phillips 2008, Sun et al. 2010), because ofexperimental difficulties in determination of atomic structures in thin (∼20 nm)GST films, which are sandwiched in between protective layers as ZnS–SiO2(Fig. 7.14). There seems to be, at least, two ideas. One is the conventional, assumingphase changes between crystalline (ordered) and amorphous (disordered) struc-tures (Wuttig and Yamada 2007). An ab initio molecular dynamics simulation ofthe crystallization process by Hegedüs and Elliott (2008) seems to support this

7.4 Phase Change 211

Fig. 7.14 A cross-sectionalview of tri-layer DVDsdeveloped in Panasonic. Thinfilms are deposited ontopolycarbonate substrates of1.1 mm thickness (modifiedfrom Yamada et al. 2009)

model. The other, which has been proposed by Kolobov et al. (2004), emphasizes,not the amorphous–crystalline change, but an octahedral–tetrahedral configurationalchange of Ge atoms, which are bonded to Te. In the latter model, the short-rangestructure clearly changes. The understanding will be necessary for further develop-ment of phase change memories (Kolobov et al. 2004). On the other hand, newmaterials exhibiting much shorter crystallization times are intensively explored(Lencer et al. 2008). Interestingly, the optical phase-change behavior seems to berelatively insensitive to impurities in the materials (Jiang and Okuda 1991, Seo et al.2000).

We here mention that a possibility of athermal electronic phase changes hasbeen repeatedly suggested or demonstrated (Feinleib et al. 1971, Solis et al. 1996,Zhang et al. 2007). The atomic bonding may change within picosecond scales justafter photo-electronic excitation, before the rising of lattice temperature. If sucha process, a kind of electronic melting (see Section 6.3.11), could be practicallyavailable, the operation speed would become faster by three to four orders than thepresent one.

The other important issue is the memory capacity, which is determined in prin-ciple by the size of memory bits. In the optical system, the bit size is governed bythe size d of a laser light spot, which is limited by diffraction as d ≈ λ/N, where λ isthe wavelength of a laser and N is the numerical aperture of focusing lenses. Here,λ (∼405 nm) and N (∼0.85) with a Gaussian light intensity distribution give rise toa minimal memory diameter of ∼150 nm, which is nearly an optical limit. Then, forobtaining smaller spots, some groups have proposed ideas of new optical systems,which employ near-filed effects (Matsumoto et al. 2004) or nonlinear phenomena

212 7 Applications

(Simpson et al. 2010). Another idea for increasing the memory capacity per diskis to increase the number of GST layers. In 2010, we can purchase DVDs havingdoubly stacked layers, which have a memory capacity of 50 GB. Further, Yamadaet al. (2009) have developed a tri-layer disk, shown in Fig. 7.14, having 100 GBcapacity.

7.4.3 Electrical Phase Change (PRAM)

Recently, studies on the electrical phase change are dramatically increasing withdevelopments of PRAMs (Fig. 7.15). The reader may refer to, e.g., a recent note byAtwood (2008) and a review by Terao et al. (2009). Though the basic mechanismof the thermal phase changes being common to that of the optical, the electricalprocess has some intrinsic features and also inherent problems.

Figure 7.16 shows the resistivity of sputter-deposited amorphous Ge2Sb2Te5films as a function of temperature (Kato and Tanaka 2005). We see the four states:amorphous, crystalline including cubic and hexagonal phases, and liquidus. And,at room temperature, between the amorphous state and the cubic phase there existsa difference in resistivity by four orders of magnitude. Accordingly, we can uti-lize electrically conducting marks, written in amorphous films, as bits in PRAMs.Since the resistivity difference is very big, PRAMs can operate, not only binary, butmulti-valued memories (Wu et al. 2009). However, several problems remain.

One concerns the atomic structure. As described in Section 7.4.2, the struc-tural change between the two states has not been identified. Accordingly, why theelectrical resistivity exhibits such a big change has not been understood (Jang et al.2010, Cai et al. 2010). In addition, a role of the metallic hexagonal phase remainsvague (Youm et al. 2007). When a bit mark is written in an amorphous state (setprocess), we just heat the film up to ∼200◦C, obtaining the cubic phase. The glasstransition at ∼100◦C (Kalb et al. 2007) does not appear in the resistivity curve.On the other hand, when a crystalline bit with the cubic phase is erased (reset pro-cess), it is melted above 600◦C, and the liquid is quenched into the amorphous state.But, we see in Fig. 7.16 that there exists the hexagonal phase at 300−600◦C. Is thehexagonal phase by-passed in the amorphization process? Or, is it possible to induce

Fig. 7.15 A PRAM chip produced in Samsung Electronics (© Samsung Electronics Co., Ltd.,reprinted from http://www.samsung.com/global/business/semiconductor/newsView.do?news_id=322, with permission)

7.4 Phase Change 213

phase changes between an amorphous state, the cubic phase, and the hexagonalphase?

The other problem is the mechanism of electrical switching, which must occurbefore the thermal crystallization (Madam and Shaw 1988, Krebs et al. 2009,Pandian et al. 2009, Lee et al. 2010, Yeo et al. 2010, Choi and Lee 2010). As shownin Fig. 7.16, the amorphous state in GST films has a high resistivity, e.g., ∼104

� cm, which must be switched to a conducting state, a prerequisite of generatingsufficient Joule heats for thermal crystallization. Experiments have demonstratedthat the conducting state appears as electric filaments. Nevertheless, it remainsto be an unresolved problem for a long time why such conducting filaments areproduced. Many models have been proposed on the formation mechanism, whichare trap filling by injected carriers, avalanche multiplication, etc. Alternatively,Nardone et al. (2009) have proposed a non-thermal field-induced nucleationmodel.

Compositional stability upon the electrical phase change is also a crucial issue.When a conducting crystalline state in c-GSTs is converted to the amorphous statethrough a liquidus state, electrical decomposition or phase separation seems to occur(Saitoh et al. 2008, Nam et al. 2008), which possibly limits the repeatability of thephase change process.

We may need new materials suitable for the electrical phase change. As we seein Fig. 7.16, the cubic c-GST is fairly conductive, so that the structural changefrom that to the amorphous state needs a high current (Fujisaki 2010). For this

amorphous

cubic

liquidhexagonalTc2 Tm

Tg

Tc1

Fig. 7.16 Temperature dependence of resistivity in two Ge2Sb2Te5 films with thicknesses of110 nm (open symbols) and 510 nm (solid symbols). The symbols are changed for amorphous(◦, •), cubic (�, �), hexagonal (�), and liquid (∇) forms (modified from Kato and Tanaka 2005).See also Fig. 7.12

214 7 Applications

problem, Kim et al. (2007) have proposed to add nitrogen to GSTs, which canincrease the electrical resistance. Alternatively, Devasia et al. (2010) have suggestedreplacement of Te to Se. Otherwise, new compositions may be preferred (Zhu et al.2010).

Finally, it should be mentioned that the electrical process can reveal an ultimatecharacteristic of the phase change phenomenon. As easily understood, in the elec-trical phase change, the mark size is governed by the size of electrodes. Using thisfeature, several groups have demonstrated that the minimal size of phase changemarks obtainable at room temperature is 10–50 nm (Satoh et al. 2006, Hamann et al.2006), which seems to be governed by amorphous–crystalline interfacial energy.This size is also favorable to reductions in the switching current (Xiong et al. 2011).This ultimate size could be the biggest advantage of this kind of atomic memoriesover electronic and/or dipolar memories (Scott 2004, Fujisaki 2010).

7.5 Electrical Device

Are there any purely electrical applications of amorphous chalcogenides? Exceptfor the PRAM, such products have been very limited (Glebov 2004). We knowwide uses of thin-film field effect transistors (TFTs) using amorphous and laser-crystallized Si:H films in liquid-crystal panels. We also know that amorphous oxidesemiconductors appear to be promising for TFTs (Chong et al. 2010). But, why isthe chalcogenide limited? A plausible reason is the smaller carrier mobility andlower electrical conductivity (see Section 4.9). In addition, the gap state, whichseems to exist in amorphous chalcogenide films, suppresses the conductance con-trol by gate voltages in TFTs. Nevertheless, some studies of interest are referred tobelow.

Hosono’s group has performed notable studies. Narushima et al. (2004) havedemonstrated surprisingly high electrical conductivity and electron mobility of 0.1S/cm and 26 cm2/V s, respectively, in a-In49S51 films. These values suggest thatthe Fermi level is located near the conduction band bottom, which provides the n+

conduction, a kind of metallic conductivity. This amorphous film is more or lessflexible, which may be employed as transparent electrodes, instead of crystallineSnO2 or In–Sn–O (ITO) films. The group also demonstrates TFTs using amorphousoxide semiconductors, which are deposited upon plastic substrates (Nomura et al.2004). However, a trial of preparing TFTs using a-CuGaS(Se)2 films has not beensucceeded (Hiramatsu et al. 2008), probably due to mid-gap states.

Use of electrical switching (or phase-change) films for three-terminal devicesappears to be attracting. Such studies have been reported since the 1980s (Coldrenet al. 1980). Recently, Song et al. (2008) employed GSTs for fabricating TFTs. Thedevice may operate as a transistor memory. Rectifying properties have been investi-gated for hetero-, glass–metal, and glass–crystal junctions which include amorphouschalcogenide films (Tsiulyanu 2004).

7.6 Photo-Electric Device 215

7.6 Photo-Electric Device

Unique photoconductive properties of a-Se have been utilized for a long time. Themost known is the xerography, patented by Carlson in 1937, which was commer-cialized by Xerox Corp in 1950. Otherwise, we may trace the use of Se to c-Sephotocells, the function being discovered in the 19th century. Developments are stillin progress (Wang et al. 2009, Goldan et al. 2010). Other chalcogenide films suchas As2Se3 have not been utilized, probably due to lower hole mobility.

In comparison with photo-electric devices using crystalline semiconductors suchas Si and GaAs, the amorphous device has, at least, three notable features. First,light emitting devices using amorphous semiconductors have not been reported.Second, as described below, the photoconducting films are available, but no photo-voltaic devices have been produced using the chalcogenide. Third, the amorphousphotoconductors, which may have large areas, exhibit slower response times thanthose of the crystalline. Reasons of these features are worth to be considered.

7.6.1 Copying Photoreceptor

The xerographic photoreceptor for copying machines was the first practical appli-cation of a-Se films (Pai and Springett 1993). This usage owes a unique featureof a-Se films: electrically insulating in the dark and highly photoconductive (seeFig. 5.11). In addition, the film with a thickness of ∼50 µm and lateral sizes of∼30 cm, the width corresponding to that of copied papers, can easily be depositedonto cylindrical metal drums (for continuous operation) using vacuum evaporation.

The copying process runs through the eight steps (Fig. 7.17): (a) electricalcharging (positive for a-Se) of the a-Se film by corona discharge of air and

(f) (e)(d)

(c) (b) (a)

Fig. 7.17 Schematic illustrations (cross-sectional) of the xerographic copying process (modifiedfrom Mott and Davis 1979): (a) corona charge, (b) image exposure, (c) hole drift, (d) latent image,(e) toner development, and (f) toner transfer

216 7 Applications

water molecules, which deposits such ions as (H2O)nH+ and H+; (b) image expo-sure, which generates electrons and holes; (c) hole drift; (d) recombination ofphoto-generated electrons with the surface ions, which produces a latent image;(e) development by (negatively charged) toner particles; (f) toner transfer from a-Sefilm to a paper (using positive corona discharge), which is followed by (g) toner fix-ing by heating and (h) photoreceptor cleaning (not shown). This imaging process hasbeen applied also to laser printers, in which the image exposure is provided throughscanning laser light which is modulated by digital signals. In these applications,however, a-Se photoreceptors have been replaced by organic polymer films (Weissand Abkowitz 2006), probably due to cost and environmental problems. As known,the organic film can be prepared just by coating without using the vacuum process.

7.6.2 Vidicon and X-Ray Imager

Photoconduction of chalcogenide films has been utilized in vidicons, vacuum tubetelevision cameras. In the vidicon, illustrated in Fig. 7.18, an optical image isfocused upon a chalcogenide film, converted to a photoconductive pattern, andfinally transformed to a current signal through scanning an electron beam. Sincethe device is a kind of vacuum tubes with a typical glass tube size of 4 cm indiameter and 15 cm in length, being liable to be broken, it has been replacedby CCDs (charge-coupled devices). However, HARP (high-gain avalanche rush-ing amorphous photoconductor) vidicons, which utilize avalanche multiplication ofphoto-excited carriers in a-Se films (Fig. 7.18), are demonstrated to have highersensitivity by ∼100 times than that of CCDs (Tanioka 2007). Using such advan-tage, the vidicon is employed as night scopes. However, the glass tube is stillbulky and fragile. To overcome these drawbacks, researchers in NHK (JapanBroadcasting Corporation) have combined the a-Se avalanche multiplication filmwith an active matrix electron emitter array. The device is now becoming more com-pact and rigid with a diameter of ∼5 cm and a thickness of ∼1 cm (Negishi et al.2007).

Fig. 7.18 A photograph (left) of a 2/3 in. HARP vidicon (© Nippon Hoso Kyokai, reprinted fromhttp://www.nhk.or.jp/strl/publica/dayori-new/jp/qa-9904.html with permission) and schematiccross-sectional views (right) of a conventional (upper) and a HARP (lower) vidicon

7.6 Photo-Electric Device 217

Fig. 7.19 An x-ray imager using an a-Se film with a thickness of 1 mm and a lateral size of23×23 cm2. The segment is square shaped with a side length of 150 µm

Thick a-Se films are employed also for x-ray detection, illustrated in Fig. 7.19(Adachi et al. 2000, Kasap et al. 2009). The operation principle is essentially thesame as that of the photoconductor, with a difference detecting not visible but x-rayphotons. a-Se is suitable for photo-electronic x-ray detection, because it can effi-ciently absorb x-ray photons, due to the heavy atomic weight.1 In addition, we canprepare smooth and homogeneous (no grain boundaries) thick (∼1 mm) a-Se films.The films deposited upon TFTs have been demonstrated to be suitable for takingmedical images with high resolution. Further, the x-ray sensitivity and the avalanchemultiplication, developed for the vidicon, are now combined into x-ray HARP-FEA(field emitter array) detectors (Miyoshi et al. 2008).

7.6.3 Solar Cell

The solar cell (Fig. 1.2) is believed to be vitally important for settling environmentalproblems. The operation principle of a solar cell, a photo-voltaic effect in a semicon-ductor p–n junction, was demonstrated using c-Si by Chapin et al. in 1954, whichhas been applied also to amorphous semiconductors, a-Si:H films, by Carlson andWronski (1976).

1Note μ(cm−1) ∝ ρλ3N3, where μ is the x-ray absorption coefficient, ρ the density, λ the x-raywavelength, and N (= 34 in Se) the atomic number. Te appears to be preferred in this context, butit is semi-metallic, and not photoconductive.

218 7 Applications

Among several characteristics of the solar cell, the most important is undoubtedlythe conversion efficiency from light to electrical power. A theoretical calculationpredicts that, under solar radiation, the maximal efficiency of ∼30% is obtainablefor a single p–n junction cell of a semiconductor having the energy gap of ∼1.5 eV.Actually, practical (single or poly-) crystalline cells provide an efficiency of ∼20%,but the a-Si:H cell is limited to ∼10%. What causes this difference of 20 and 10%?

In comparison with c-Si cells, the a-Si:H cell has, at least, two disadvantages.One is a wider optical gap (∼1.7 eV) than 1.1 eV in c-Si. As the result, the amor-phous film cannot absorb sun light of �ω ≤ 1.7 eV (λ ≥ 0.7 µm), where the solarspectrum has considerable energy. (Nevertheless, the open-circuit voltage tends toincrease with the energy gap. Actually, it is ∼0.9 and ∼0.5 V in a- and c-Si devices.)The other factor affecting the efficiency arises from a transport process of photo-excited carriers. For instance, the mobility-lifetime (μτ ) product (or, equivalentlythe carrier diffusion length) is, typically, ∼10−6 cm2/V in a-Si:H films (Hoheiseland Fuhs 1988) and ∼10−2 cm2/V in c-Si. The small value of μτ product in a-Si:Hmeans that photo-excited carriers are likely to be trapped and/or recombined beforereaching output electrodes. To overcome this inferior transport property in a-Si:Hfilms, we now employ the drift of carriers using p–i–n cell structures, not diffusionin a p–n structure, the latter being employed in the conventional c-Si solar cells.However, a thickness of the i-layers, 300−400 nm, selected for obtaining substan-tial internal fields, makes light absorption smaller. Therefore, we face a trade-offbetween the light absorption and the carrier transport. Otherwise, we will prefertandem junction cells consisting of varied bandgap layers.

Despite these disadvantages, why is the amorphous solar cell widely utilized?The biggest advantage is a lower cell price, which may be governed by two fac-tors. One is the amount of Si sources. The thicknesses of a-Si:H and c-Si cellsare typically ∼1 and ∼100 µm, which are selected taking higher and lower opti-cal absorption coefficients by two orders, resulting from non-direct (wavenumbernegligible) and indirect (phonon-assisted) transitions (see Section 4.6). The otheris that the amorphous film can be prepared through low-temperature processes invacuum, such as glow discharge and photo-enhanced chemical vapor depositions,which are specifically suitable to fabricate wide area cells on flexible substrates aspolymer films. These deposition processes are appropriate also for preparing high-performance cells having tandem (e.g., three) junctions with controlled bandgaps of1.5–2.0 eV.

Are there any ideas of solar cells using oxide and chalcogenide glasses?There are a few: the one being to use a p–n hetero-junction such as Au/As2Se3/Ge20Bi11Se69/Au (Tohge et al. 1988). Nevertheless, if such chalcogenide devicescan be competitive in many respects, including cost, with a-Si:H devices it seemsto be pessimistic. Another idea is a photo-chemical cell, the principle being demon-strated using Ag–As–S ion-hole mixed conducting films (Yoshida et al. 1997). In thecell, photo-excited carriers force to move Ag+ ions (charge), which give an electricpower in the dark as discharge currents. The idea, a device combining a solar celland a battery, appears to be promising, while its efficiency must be improved.

7.7 Ionic Device and Others 219

7.7 Ionic Device and Others

Chalcogenide glasses, containing cation such as Ag+ and Li+ have been applied toionic devices including memory, photoresist, sensor, and battery. To the authors’knowledge, however, commercialization still remains.

It should be also noted that insulating, relatively soft, and stable sulfide glassescan be employed as sealing materials. In a pioneering work, Flaschen et al. (1960)demonstrate that annealed As2S3 films work as good sealing materials. It can alsobe utilized as an insulating layer for GaAs and InP semiconductor devices (Madaand Wada 1998).

7.7.1 Ionic Memories

The ion moves under electric fields, and the position of ions can be employed forstoring information. Using the principle, Utsugi (1990) demonstrated nano-scalewrite-once ionic memories (Fig. 7.20), in which Ag+ ions in Ag/Ge–Se bilayerstructures are forced to move by electric fields in a scanning tunneling microscope.Detailed studies have been reported also by Ohto and Tanaka (1997).

What is the potential of an erasable ionic memory? We may assume that a slowermotion of ions than that of electrons is problematic. However, if the bit size can bereduced to nanometer scales, an ion is able to move with a response time of approx-imately nanoseconds. Based on such concepts, several ideas have been proposed forerasable ionic memories using amorphous chalcogenides (Kozicki et al. 2005, Chenet al. 2009).

Photodoping, described in Section 6.3.13, has provided a lot of photoresist appli-cations (Frumar and Wagner 2003). The process, in combination with chemicaletching, also produces infrared optical devices as gratings. Not only wet etching but

Fig. 7.20 A nano-Einstein,with a scale of 100 nm(courtesy of Utsugi 1990)

220 7 Applications

dry (plasma) etching has been employed for converting irradiated regions to reliefs(Jain and Vlcek 2008). A Japanese group has demonstrated ultrahigh resolution(∼1 nm) of the photodoping process, and applications to photoresist process usingsynchrotron orbital radiation (Saito et al. 1988) and to x-ray holograms (Somemuraet al. 1992). Optical recording characteristics in GeS2/Ag(Cu) films have also beenstudied (Kato et al. 2006).

7.7.2 Ion Sensor

The first demonstration of chalcogenide ion sensors may be the one reported byBaker and Trachtenberg (1971) in Texas Inst. The principle is simple, but practi-cal operations still remain vague, as reviewed by Vassilev and Boycheva (2005),Schoning et al. (2007), and Conde Garrido et al. (2009). In Fig. 7.21, the centralmembrane is made from a chalcogenide glass containing A+ ions, the left-hand sidesolution 1 is a reference, and the right is a liquid to be inspected for the concentra-tion of A+ ions. Then, the voltage V appearing between the electrodes 1 and 2 isgiven as

V = (RT/nF) ln(a1/a2), (7.4)

where R is the gas constant (=kBNa), T the temperature, n the charge number ofmeasured ions, F the Faraday constant (=eNa), and a the activity, which is equal tothe mole concentration x for an ideal mixture. Accordingly, by measuring V, we canestimate x2. Following this principle, Vassilev and Boycheva (2005) demonstrateCu2+-ion sensing using Cu–As–Se glasses. However, the sensor must satisfy severalconditions, such as the sensitivity only to an inspected ion, i.e., total insensitivity toother ions, and chemical durability to ion-containing liquids, which are more or lessdifficult. The sensor is being developed as miniature field effect transistor types,toward “electronic nose” or “electronic tongue.”

Fig. 7.21 A principalconfiguration of ion sensors(modified from Baker andTrachtenberg 1971)

References 221

7.7.3 Battery

Efficient and light-weight batteries have been required in many areas, includingelectronics and vehicles. The battery has a structure of anode/electrolyte/cathode, inwhich the glass is a promising candidate for the electrolyte in all solid-state batteries.(Note that common electrolytes at present are liquidus or paste like.) Hence, con-siderable studies have been performed for glassy electrolytes. Note that not films,but powder forms are preferred for the electrolyte, since the powder can increase thearea of reacting interfaces.

Here, a comparison of oxide and sulfide, e.g., Li2O(S)–SiO(S)2, shows an inter-esting trend. The sulfide provides a higher conductivity (∼10−4 S/cm) of Li+ ions,which is understood to be a manifestation of higher polarizability of S than O atoms,which gives greater freedom to the ion. Indeed, Kitaura et al. (2010) have produceda high-performance rechargeable batteries having a three-layer structure consistingof In (cathode), 80Li2S20P2S5 glass-ceramic powder (electrolyte), and a compositepowder containing LiCoO2 (anode). Provided that reliability and safety are over-come, the compact and light-weight battery will be utilized for electric vehicles in anear future.

References

Abedin, K.S.: Observation of strong stimulated Brillouin scattering in single-mode As2Se3chalcogenide fiber. Opt. Express 13, 10266–10271 (2005)

Adachi, S., Hori, N., Sato, K., Tokuda, S., Sato, T., Uehara, K., Izumi, Y., Nagata, H., Yoshimura,Y., Yamada, S.: Experimental evaluation of a-Se and CdTe flat-panel x-ray detectors for digitalradiography and fluoroscopy. Proc. SPIE 38, 3977–3986 (2000)

Askins, C.G.: Periodic UV-induced index modulations in doped-silica optical fibers: formation andproperties of the fiber Bragg grating. In: Pacchioni, G., Skuja, L., Griscom, D.L. (eds.) Defectsin SiO2 and Related Dielectrics: Science and Technology pp. 391–426. Kluwer, Dordrecht(2000)

Atwood, G.: Phase-change materials for electronic memories. Science 321, 210–211 (2008)Baker, C.T., Trachtenberg, I.: Ion selective electrochemical sensors—Fe+3, Cu+2. J. Electrochem.

Soc. 118, 571–576 (1971)Bishop, S.G., Turnbull, D.A., Aitken, B.G.: Excitation of rare earth emission in chalcogenide

glasses by broadband Urbach edge absorption. J. Non-Cryst. Solids 266–269, 876–883 (2000)Bureau, B., Maurugeon, S., Charpentier, F., Adam, J.-L., Boussard-Pledel, C., Zhang, X.:

Chalcogenide glass fibers for infrared sensing and space optics. Fiber Integrated Opt. 28, 65–80(2009)

Cai, B., Drabold, D.A., Elliott, S.R.: Structural fingerprints of electronic change in the phase-change-material: Ge2Sb2Te5. Appl. Phys. Lett. 97, 191908 (2010)

Calvez, L., Yang, Z., Lucas, P.: Composition dependence and reversibility of photoinducedrefractive index changes in chalcogenide glass. J. Phys. D: Appl. Phys. 43, 445401–445408(2010)

Carlson, D.E., Wronski, C.R.: Amorphous silicon solar cell. Appl. Phys. Lett. 28, 671–673 (1976)Chen, L., Li, Q.C., Guo, H.X., Gao, L.G., Xia, Y.D., Yin, J., Liu, Z.G.: Monte Carlo simulation

of the percolation in Ag30Ge17Se53 amorphous electrolyte films. Appl. Phys. Lett. 95, 242106(2009)

222 7 Applications

Cherif, R., Ben Salem, A., Zghal, M., Beshard, P., Chartier, T., Brilland, L., Troles, J.: Highlynonlinear As2Se3-based chalcogenide photonic crystal fiber for midinfrared supercontinuumgeneration. Opt. Eng. 49, 095002 (2010)

Choi, Y., Lee, Y.K.: Double electrical percolation phenomenon during the crystallization of anamorphous Ge2Sb2Te5 thin film under continuous heating. Appl. Phys. Lett. 96, 041910 (2010)

Choi, D.-Y., Madden, S., Rode, A., Wang, R., Luther-Davies, B.: Dry etching characteristics ofamorphous As2S3 film in CHF3 plasma. J. Appl. Phys. 104, 113305 (2008)

Chong, E., Chun, Y.S., Lee, S.Y.: Amorphous silicon-indium-zinc oxide semiconductor thin filmtransistors processed below 150◦C. Appl. Phys. Lett. 97, 102102 (2010)

Clement, T.J., Ponnampalam, N., Nguyen, H.T., DeCorby, R.G.: Improved omnidirectional reflec-tors in chalcogenide glass and polymer by using the silver doping technique. Opt. Express 14,1789–1796 (2006)

Coldren, L.A., Bösch, M.A., Rentschler, J.A.: Multistate amorphous-semiconductor switch. Appl.Phys. Lett. 36, 688–690 (1980)

Conde Garrido, J.M., Macoretta, F., Ureña, M.A., Arcondo, B.: Application of Ag–Ge–Se basedchalcogenide glasses on ion-selective electrodes. J. Non-Cryst. Solids 355, 2079–2082 (2009)

Coulombier, Q., Brilland, L., Houizot, R., Chartier, T., N’Guyen, T.N., Smektala, F., Renversez,G., Monteville, A., Mechin, D., Pain, T., Orain, H., Sangleboeuf, J.-C., Troles, J.: Castingmethod for producing low-loss chalcogenide microstructured optical fibers. Opt. Express 18,9107–9112 (2010)

Coulombier, Q., Zhang, S.Q., Zhang, X.H., Bureau, B., Lucas, J., Boussard-Pledel, C., Troles,J., Calvez, L., Ma, H., Maurugeon, S., Guillevic, E.: Planar waveguide obtained by burying aGe22As20Se58 fiber in As2S3 glass. Appl. Opt. 47, 5750–5752 (2008)

Desurvire, E.: Erbium-Doped Fiber Amplifiers: Principles and Applications. Wiley, New York, NY(1994)

Devasia, A., Kurinec, S., Campbell, K.A., Raoux, S.: Influence of Sn Migration on phase transitionin GeTe and Ge2Se3 thin films. Appl. Phys. Lett. 96, 141908 (2010)

Eggleton, B.J., Luther-Davies, B., Richardson, K.: Chalcogenide photonics. Nature Photonics 5,141–148 (2011)

Feinleib, J., deNeufville, J., Moss, S.C., Ovshinsky, S.R.: Rapid reversible light-induced crystal-lization of amorphous semiconductors. Appl. Phys. Lett. 18, 254–257 (1971)

Flaschen, S.S., Pearson, A.D., Northover, W.R.: Formation and properties of low-melting glasses inthe ternary systems As-TI-S, As-TI-Se, and As-Se-S. J. Am. Ceram. Soc. 43, 274–275 (1960)

Florea, C., Bashkansky, M., Sanguhera, J., Aggrawal, I., Dutton, Z.: Slow-light generation throughBrillouin scattering in As2S3 fibers. Opt. Mater. 32, 358–361 (2009)

Frumar, M., Wagner, T.: Ag doped chalcogenide glasses and their applications. Curr. Opin. SolidState Mater. Sci. 7, 117–126 (2003)

Fuhs, W., Ulber, I., Weiser, G., Bresler, M.S., Gusev, O.B., Kuznetsov, A.N., Kudoyarova,V.K., Terukov, E.I., Yassievich, I.N.: Excitation and temperature quenching of Er-inducedluminescence in a-Si:H(Er). Phys. Rev. B 56, 9545–9551 (1997)

Fujisaki, Y.: Current status of nonvolatile semiconductor memory technology. Jpn. J. Appl. Phys.49, 100001 (2010).

Gelbaor, M., Klebanov, M., Lyubin, V., Abdulhalim, I.: Permanent photoalighment of liquidcrystals on nanostructured chalcogenide glassy thin films. Appl. Phys. Lett. 98, 071909 (2011)

Glebov, A.S.: The nature of the current instability in chalcogenide vitreous semiconductors. In:Fairman, R., Ushkov, B. (eds.) Semiconducting Chalcogenide Glass II, Chap. 3, pp. 57–144.Elsevier, Amsterdam (2004)

Goldan, A.H., Tousignant, O., Laperrière, L., Karim, K.S.: Reduced photocurrent lag using unipo-lar solid-state photoconductive detector structures: Application to stabilized n-i-p amorphousselenium. Appl. Phys. Lett. 96, 053507 (2010)

González-Leal, J.M., Krecmer, P., Prokop, J., Elliott, S.R.: Evaluation of multiplexing inhigh-density holographic memories. In: Kolobov, A.V. (ed.) Photo-Induced Metastability inAmorphous Semiconductors, Chap. 20. pp. 338–357. Wiley-VCH, Weinheim (2003)

References 223

Griscom, D.L.: Optical-properties and structure of defects in silica glass. J. Ceram. Soc. Jpn. 99,923–942 (1991)

Hamann, H.F., O’Boyle, M., Martin, Y.C., Rooks, M., Wickramasinghe, H.K.: Ultra-high-densityphase-change storage and memory. Nat. Mater. 5, 383–387 (2006)

Handa, Y., Suhara, T., Nishihara, H., Koyama, J.: Microgratings for high-efficiency guided-beamdeflection fabricated by electron-beam direct-writing techniques. Appl. Opt. 19, 2842–2847(1980)

Haque, S.A., Nelson, J.: Toward organic all-optical switching. Science 327, 1466–1467 (2010)Harada, H., Tanaka, K.: Photoluminescence from Pr3+-doped chalcogenide glasses excited by

bandgap light. J. Non-Cryst. Solids 246, 189–196 (1999)Hegedüs, J., Elliott, S.R.: Microscopic origin of the fast crystallization ability of Ge-Sb-Te phase-

change memory materials. Nat. Mater. 7, 399–405 (2008)Hiramatsu, H., Yanagi, H., Kamiya, T., Hirano, M., Matsunami, N., Shimizu, K., Hosono, H.:

Electrical and optical properties of copper-based chalcogenide thin films deposited by pulsedlaser deposition at room temperature: Toward p-channel thin film transistor fabricable at roomtemperature. Phys. Status Solidi (a) 205, 2007–2012 (2008)

Hisakuni, H., Tanaka, K.: Optical fabrication of microlenses in chalcogenide glasses. Opt. Lett. 20,958–960 (1995).

Hoheisel, M., Fuhs, W.: Drift mobility in n- and p-conducting a-Si:H. Philos. Mag. B 57, 411–419(1988)

Hu, J., Menyuk, C.R., Shaw, L.B., Sanghera, J.S., Aggarwal, D.: Maximizing the bandwidth ofsupercontinuum generation in As2Se3 chalcogenide fibers. Opt. Express 18, 6722–6739 (2010)

Ikushima, A.J., Fujiwara, T., Saito, K.: Silica glass: A material for photonics. J. Appl. Phys. 88,1201–1213 (2000)

Jackson, S.D., Anzueto-Sánchez, G.: Chalcogenide glass Raman fiber laser. Appl. Phys. Lett. 88,221106 (2006)

Jain, H., Vlcek, M.: Glasses for lithography. J. Non-Cryst. Solids 354, 1401–1406 (2008)Jang, M.H., Park, S.J., Park, S.J., Cho, M.-H., Kurmaev, E.Z., Finkelstein, L.D., Chang, G.S.: The

origin of the resistance change in GeSbTe films. Appl. Phys. Lett. 97, 152113 (2010)Jiang, F., Okuda, M.: The effect of doping on the erasure speed and stability of reversible phase-

change optical recording films. Jpn. J. Appl. Phys. 30, 97–100 (1991)Kalb, J.A., Wuttig, M., Spaepen, F.: Calorimetric measurements of structural relaxation and glass

transition temperatures in sputtered films of amorphous Te alloys used for phase changerecording. J. Mater. Res. 22, 748–754 (2007)

Kamiya, T., Tsuchiya, M.: Progress in ultrafast photonics. Jpn. J. Appl. Phys. 44, 5875–5888(2005)

Kao, K.C., Hockham, C.A.: Dielectric-fiber surface waveguides for optical frequencies. Proc. Inst.Electr. Eng. 133, 1151–1158 (1966)

Kasap, S., Frey, J.B., Belev, G., Tousignant, O., Mani, H., Laperriere, L., Reznik, A., Rowland,J.A.: Amorphous selenium and its alloys from early xeroradiography to high resolution x-rayimage detectors and ultrasensitive imaging tubes. Phys. Status Solidi (b) 246, 1794–1805(2009)

Kato, N., Fukano, T., Takeda, Y., Takeichi, A., Motohiro, T., Kawai, S.: GeS2/metal thin filmbilayered structures as write-once-type optical recording materials. J. Appl. Phys. 100, 113115(2006)

Kato, T., Tanaka, K.: Electronic properties of amorphous and crystalline Ge2Sb2Te5 films. Jpn.J. Appl. Phys. 44, 7340–7344 (2005)

Keneman, S.A.: Surface relief holograms in evaporated arsenic trisulfide films. Thin Solid Films21, 281–285 (1974)

Kim, Y., Hwang, U., Cho, Y.J., Park, H.M., Cho, M.H., Cho, P.S., Lee, J.H.: Change in electricalresistance and thermal stability of nitrogen incorporated Ge2Sb2Te5 films. Appl. Phys. Lett. 90,021908 (2007)

224 7 Applications

Kitaura, H., Hayashi, A., Tadanaga, K., Tatsumisago, M.: All-solid-state lithium secondary bat-teries using LiMn2O4 electrode and Li2S–P2S5 solid electrolyte. J. Electrochem. Soc. 157,A407–A411 (2010)

Klein, R.M.: Chalcogenide glasses as passive thin film structures for integrated optics. J. Electron.Mater. 3, 79–99 (1974)

Kohoutek, T., Orava, J., Sawada, T., Fudouzi, H.: Inverse opal photonic crystal of chalcogenideglass by solution processing. J. Colloid Interface Sci. 353, 454–458 (2011)

Kolobov, A.V., Fons, P., Frenkel, A.I., Ankudinov, A.L., Tominaga, J., Uruga, T.: Understandingthe phase-change mechanism of rewritable optical media. Nat. Mater. 3, 703–708 (2004)

Kondakci, H.E., Yaman, M., Koylu, O., Dana, A., Bayindir, M.: All-chalcogenide glass omnidi-rectional photonic band gap variable infrared filters. Appl. Phys. Lett. 94, 111110 (2009)

Kozicki, M.N., Park, M., Mitkova, M.: Nanoscale memory elements based on solid-state elec-trolytes. IEEE Trans. Nanotech. 4, 331–338 (2005)

Krebs, D., Raoux, S., Rettner, C.T., Burr, G.W., Salinga, M., Wuttig, M.: Threshold field of phasechange memory materials measured using phase change bridge devices. Appl. Phys. Lett. 95,082101 (2009)

Kumta, P.N., Risbud, S.H.: Novel glasses in rare-earth sulfide systems. Am. Ceram. Soc. Bull. 69,1977–1984 (1990)

Lainé, M., Seddon, A.B.: Chalcogenide glasses for acousto-optic devices. J. Non-Cryst. Solids184, 30–35 (1995)

Lee, M.W., Grillet, C., Tomljenovic-Hanic, S., Magi, E.C., Moss, D.J., Eggleton, B.J., Gai, X.,Madden, S., Choi, D.Y., Bulla, D.A.P., Luther-Davies, B.: Photowritten high-Q cavities in two-dimensional chalcogenide glass photonic crystals. Opt. Lett. 34, 3671–3673 (2009)

Lee, S., Jeong, D.S., Jeong, J., Zhe, W., Park, Y.-W., Ahn, H.W., Cheong, B.: A study on thetemperature dependence of the threshold switching characteristics of Ge2Sb2Te5. Appl. Phys.Lett. 96, 023501 (2010)

Lencer, D., Salinga, M., Grabowski, B., Hickel, T., Neugebauer, J., Wuttig, M.: A map for phase-change materials. Nat. Mater. 7, 972–977 (2008)

Liao, M., Chaudhari, C., Qin, G., Yan, X., Kito, C., Suzuki, T., Ohishi, Y., Matsumoto, M., Misumi,T.: Fabrication and characterization of a chalcogenide-tellurite composite microstructure fiberwith high nonlinearity. Opt. Express 17, 21608–21614 (2009)

Liu, W.C., Hoffman, G., Zhou, W., Reano, R.M., Boolchand, P., Sooryakumar, R.: Slab waveguidesand nanoscale patterning of pulsed laser- deposited Ge0.2Se0.8 chalcogenide films. Appl. Phys.Lett. 93, 041107 (2008)

Lucas, J.: Infrared glasses. Curr. Opin. Solid State Mater. Sci. 4, 181–187 (1999)Lucovsky, G., Phillips, J.C.: Reversible chemical phase separation in on-state of art rewritable

Ge2Sb2Te5 optical phase change memories J. Non-Cryst. Solids 354, 2753–2756 (2008)Lyubin, V., Arsh, A., Klebanov, M., Dror, R., Sfez, B.: Nonlinear photoresists for maskless pho-

tolithography on the basis of Ag-doped As2S3 glassy films. Appl. Phys. Lett. 92, 011118(2008)

Mada, Y., Wada, K.: Passivation of an n-type InP surface with an As2S3 film. J. Appl. Phys. 83,2025–2029 (1998)

Madam, A., Shaw, M.P.: The Physics and Applications of Amorphous Semiconductors,Chap. 5. Academic, Boston, MA (1988)

Matsuda, A., Mizuno, H., Takayama, T., Saito, M., Kikuchi, M.: “Stopping effect” on guided lightin As-S films by a laser beam. Appl. Phys. Lett. 24, 314–315 (1974)

Matsumoto, T., Shimano, T., Saga, H., Sukeda, H., Kiguchi, M.: Highly efficient probe with awedge-shaped metallic plate for high density near-field optical recording. J. Appl. Phys. 95,3901–3905 (2004)

Miyoshi, T., Igarashi, N., Matsugaki, N., Yamada, Y., Hirano, K., Hyodo, K., Tanioka, K., Egami,N., Namba, M., Kubota, M., Kawai, T., Wakatsuki, S.: Development of an X-ray HARP-FEAdetector system for high-throughput protein crystallography. J. Synchrotron Rad. 15, 281–284(2008)

References 225

Morishita, Y., Tanaka, K.: Microscopic structures in Co-doped SiO2–GeO2 glasses and fibers. Jpn.J. Appl. Phys. 42, 7456–7460 (2003)

Mott, N.F., Davis, E.A.: Electronic Processes in Non-Crystalline materials. p. 541. ClarendonPress, Oxford (1979)

Nam, S.W., Kim, C., Kwon, M.H., Lee, H.S., Wi, J.S., Lee, D., Lee, T.Y., Khang, Y., Kim, K.B.:Phase separation behavior of Ge2Sb2Te5 line structure during electrical stress biasing. Appl.Phys. Lett. 92, 111913 (2008)

Nardone, M., Karpov, V.G., Jackson, D.C.S., Karpov, I.V.: A unified model of nucleation ofswitching. Appl. Phys. Lett. 94, 103509 (2009)

Narushima, S., Hiroki, M., Ueda, K., Shimizu, K., Kamiya, T., Hirano, M., Hosono, H.: Electricalproperties and local structure of n-type conducting amorphous indium sulphide. Philos. Mag.Lett. 84, 665–671 (2004)

Negishi, N., Matsuba, Y., Tanaka, R., Nakada, T., Sakemura, K., Okuda, Y., Watanabe, A.,Yoshikawa, T., Ogasawara, K.: Development of a high-resolution active-matrix electron emit-ter array for application to high-sensitivity image sensing. J. Vac. Sci. Technol. 25, 661–665(2007)

Nishii, J., Yamashita, T.: Chalcogenide glass-based fibers. In: Sanghera, J.S., Aggarwal, I.D. (eds.)Infrared Fiber Optics, Chap. 4, pp. 143–184. CRC Press, Boca Raton, FL (1998)

Nomura, K., Ohta, H., Takagi, A., Kamiya, T., Hirano, M., Hosono, H.: Room-temperature fabrica-tion of transparent flexible thin-film transistors using amorphous oxide semiconductors. Nature432, 488–492 (2004)

Ohishi, Y., Mori, A., Kanamori, T., Fujiura, K., Sudo, S.: Fabrication of praseodymium-dopedarsenic sulfide chalcogenide fiber for 1.3-µm fiber amplifier. Appl. Phys. Lett. 65, 13–15 (1994)

Ohto, M., Tanaka, K.: Scanning tunneling spectroscopy of Ag–As–Se ion-conducting glasses.Appl. Phys. Lett. 71, 3409–3411 (1997)

Ovshinsky, S.R.: Reversible electrical switching phenomena in disordered structures. Phys. Rev.Lett. 21, 1450–1453 (1968)

Ozols, A., Saharovs, D., Reinfelde, M.: Holographic recording in amorphous As2S3 films at633 nm. J. Non-Cryst. Solids 352, 2652–2656 (2006)

Pai, D.M., Springett, B.E.: Physics of electrophotography. Rev. Mod. Phys. 65, 163–211 (1993)Pandian, R., Kooi, B.J., Oosthoek, J.L.M., Dool, P., Palasantzas G., Pauza, A.: Polarity-dependent

resistance switching in GeSbTe phase-change thin films: The importance of excess Sb infilament formation. Appl. Phys. Lett. 95, 252109 (2009)

Petit, L., Carlie, N., Anderson, T., Jiyeon, C., Richardson M., Richardson, K.C.: Progress on thephotoresponse of chalcogenide glasses and films to near-infrared femtosecond laser irradiation:A review. IEEE J. Select Topics Quant. Electron. 14, 1323–1334 (2008)

Popescu, M., Savastru, D., Popescu, A., Miclos, S., Lorinczi, A., Sava, F., Velea, A., Baschir,L., Ciobanu, M., Matel, E., Socol, G., Mihailescu, I.N., Niciu, H.: Chalcogenide photonicstructures. J. Optoelectron. Adv. Mater. Rapid Commun. 3, 851–859 (2009)

Rouvaen, J.M., Torguet, R., Bridoux, E., Haine, F.: Nonlinear steering and mixing of acousticwaves in arsenic trisulfide. Appl. Phys. Lett. 27, 519–521 (1975)

Ruan, Y., Kim, M.K., Lee, Y.H., Luther-Davies, B., Rode, A.: Fabrication of high-Q chalcogenidephotonic crystal resonators by e-beam lithography. Appl. Phys. Lett. 90, 071102 (2007)

Saito, K., Utsugi, Y., Yoshikawa, A.: X-ray lithography with a Ag-Se/Ge-Se inorganic resist usingsynchrotron radiation. J. Appl. Phys. 63, 565–567 (1988)

Saitoh, A., Donuma, T., Tanaka, K.: Un-stability of sputtered Ge2Sb2Te5 films in electrical phasechanges. Appl. Phys. Express 1, 021501 (2008)

Saitoh, A., Tanaka, K.: Self-developing aspherical chalcogenide-glass microlenses for semicon-ductor lasers. Appl. Phys. Lett. 83, 1725–1727 (2003)

Samsung: Samsung to Mass Produce 65 nm PRAM in June. www.hitechreview.com/.../9302/(2009). Accessed 10 November 2010.

Satoh, H., Sugawara, K., Tanaka, K.: Nanoscale phase changes in crystalline Ge2Sb2Te5 filmsusing scanning probe microscopes. J. Appl. Phys. 99, 024306 (2006)

226 7 Applications

Schoning, M.J., Kloock, J.P.: About 20 years of silicon-based thin-film sensors with chalcogenideglass materials for heavy metal analysis: Technological aspects of fabrication and miniaturiza-tion. Electroanalysis 19, 2029–2038 (2007)

Scott, J.C.: Is there an immortal memory? Science 304, 62–63 (2004)Seddon, A.B., Pan, W.J., Furniss, D., Miller, C.A., Rowe, H., Zhang, D., Brearty, E.M., Zhang,

Y., Loni, A., Sewell P., Bensonsuch, T.M.: Fine embossing of chalcogenide glasses – A newfabrication route for photonic integrated circuits. J. Non-Cryst. Solids 352, 2515–2520 (2006)

Seo, H., Jeong, T.H., Park, J.W., Yeon, C., Kim, S.J., Kim, S.Y.: Investigation of crystallizationbehavior of sputter-deposited nitrogen-doped amorphous Ge2Sb2Te5 thin films. Jpn. J. Appl.Phys. 39, 745–751 (2000)

Shinkawa, K., Oda, Y., Ma, Z., Ogusu, K.: Transient stimulated Brillouin scattering in multimodeAs2S3 glass fiber. Jpn. J. Appl. Phys. 48, 070215 (2009)

Shokooh-Saremi, M., Ta′eed, V.G., Baker, N.J., Littler, I.C.M., Moss, D.J., Eggleton, B.J., Ruan,Y.L., Luther-Davies, B.: High-performance Bragg gratings in chalcogenide rib waveguideswritten with a modified Sagnac interferometer. J. Opt. Soc. Am. B 23, 1323–1331 (2006)

Simpson, R.E., Fons, P., Wang, X., Kolobov, A.V., Fukaya, T., Tominaga, J.: Non-melting super-resolution near-field aperture in Sb-Te alloys. Appl. Phys. Lett. 97, 161906 (2010)

Snopatin, G.E., Churbanov, M.F., Pushkin, A.A., Gerasimenko, V.V., Dianov, E.M., Plotnichenko,V.G.: High purity arsenic-sulfide glasses and fibers with minimum attenuation of 12 dB/km.J. Optoelectron. Adv. Mater. Rapid Commun. 3, 669–671 (2009)

Solis, J., Afonso, C.N., Hyde, S.C.W., Barry, N.P., French, P.M.W.: Existence of electronicexcitation enhanced crystallization in GeSb amorphous thin films upon ultrashort laser pulseirradiation. Phys. Rev. Lett. 76, 2519–2522 (1996)

Somemura, Y., Yoshikawa, A., Utsugi, Y.: Characteristics of Ag-Se/Ge-Se as a recording mediumfor x-Ray holograms. Jpn. J. Appl. Phys. 31, 3712–3715 (1992)

Song, S., Howard, S.S., Liu, Z., Dirisu, A.O., Gmachl, C.F., Arnold, C.B.: Mode tuning of quantumcascade lasers through optical processing of chalcogenide glass claddings. Appl. Phys. Lett. 89,041115 (2006)

Song, K.B., Sohn, S.W., Kim, J.H., Kim, K.A., Cho, K.: Chalcogenide thin-film transistors usingoxygenated n-type and p-type phase change materials. Appl. Phys. Lett. 93, 043514 (2008)

Stegeman, R., Stegeman, G., Delfyett, Jr. P., Petit, L., Carlie, N., Richardson, K., Couzi, M.: Ramangain measurements and photo-induced transmission effects of germanium- and arsenic-basedchalcogenide glasses. Opt. Express 14, 11702–11708 (2006)

Sudoh, T.K., Nakano, Y., Tada, K.: Wavelength trimming technology for multiple-wavelengthdistributed-feedback laser arrays by photo-induced refractive index change. Electron. Lett. 33,216–217 (1997)

Sun, Z., Zhou, J., Blomqvist, A., Johansson, B., Ahuja, R.: Comment on “Formation of large voidsin the amorphous phase-change memory Ge2Sb2Te5 alloy” reply. Phys. Rev. Lett. 104, 019602(2010)

Suzuki, K., Hamachi, Y., Baba, T.: Fabrication and characterization of chalcogenide glass photoniccrystal waveguides. Opt. Express 17, 22393–22400 (2009)

Tanaka, K., Saitoh, A.: Optical nonlinearities of Se-loaded zeolite (ZSM-5): A molded nanowiresystem. Appl. Phys. Lett. 94, 241905 (2009)

Tanaka, K., Imai, Y., Odajima, A.: Photo-optical devices by amorphous As–S waveguides. J. Appl.Phys. 57, 4897–4900 (1985)

Tanaka, K., Toyosawa, N., Hisakuni, H.: Photoinduced Bragg gratings in As2S3 optical fibers. Opt.Lett. 20, 1976–1978 (1995)

Tanioka, K.: The ultra sensitive TV pickup tube from conception to recent development. J. Mater.Sci. Mater. 18, S321–S325 (2007)

Terao, M., Morikawa, T., Ohta, T.: Electrical phase-change memory: Fundamentals and state of theart. Jpn. J. Appl. Phys. 48, 080001 (2009)

Teteris, J.: Holographic recording in amorphous chalcogenide thin films. Curr. Opin. Solid StateMater. Sci. 7, 127–134 (2003)

References 227

Thomas, G.A., Shraiman, B.I., Glodis, P.F., Stephen, M.J.: Towards the clarity limit in optical fibre.Nature 404, 262–264 (2000).

Tohge, N., Kanda, K., Minami, T.: Electrical and photovoltaic properties of amorphouschalcogenide thin-film p-n junctions. Appl. Phys. Lett. 53, 580–582 (1988)

Tsiulyanu, D.: Heterostructures on chalcogenide glass and their applications. In: Fairman, R.,Ushkov, B. (eds.) Semiconducting Chalcogenide Glass III, Chap.2, pp. 57–101. Elsevier,Amsterdam (2004)

Tver’yanovichi, Yu.S., Tverjanovich, A.: Rare-earth doped chalcogenide glass. In: Fairman, R.,Ushkov, B. (eds.) Semiconducting Chalcogenide Glass III, Chap.4, pp. 169–207. Elsevier,Amsterdam (2004)

Ung, B., Skorobogatiy, M.: Chalcogenide microporous fibers for linear and nonlinear applicationsin the mid-infra red. Opt. Express 18, 8647–8659 (2010)

Utsugi, Y.: Nanometre-scale chemical modification using a scanning tunnelling microscope.Nature 90, 747–749 (1990)

Van Heerden, P.J.: Theory of optical information storage in solids. Appl. Opt. 2, 393–400 (1963)Vassilev, V.S., Boycheva, S.V.: Chemical sensors with chalcogenide glassy membranes. Talanta 67,

20–27 (2005)Vo, T.D., Hu, H., Galili, M., Palushani, E., Xu, J., Oxenlowe, L.K., Madden, S.J., Choi, D.Y.,

Bulla, D.A.P., Pelusi, M.D., Schroeder, J., Luther-Davies, B., Eggleton, B.J.: Photonic chipbased transmitter optimization and receiver demultiplexing of a 1.28 Tbit/s OTDM signal. Opt.Express 18, 17252–17261 (2010)

Wang, K., Chen, F., Belev, G., Kasap, S., Karim, K.S.: Lateral metal-semiconductor-metalphotodetectors based on amorphous selenium. Appl. Phys. Lett. 95, 013505 (2009)

Watts, R.K., de Wit, M., Holton, W.C.: Nonoxide chalcogenide glass films for integrated optics.Appl. Opt. 13, 2329–2332 (1974)

Weiss, D.S., Abkowitz, M.: Organic photoconductor. In: Kasap, S., Capper, P. (eds.) SpringerHandbook of Electronic and Photonic Materials, Chap. 39, pp. 953–982. Springer, New York,NY (2006)

Wu, L., Song, Z., Rao, F., Gong, Y., Feng, S.: Multistate storage through successive phase changeand resistive change. Appl. Phys. Lett. 94, 243115 (2009)

Wuttig, M., Yamada, N.: Phase-change materials for rewriteable data storage. Nat. Mater. 6,824–832 (2007)

Xiong, C., Magi, E., Luan, F., Tuniz, A., Dekker, S., Sanghera, J.S., Shaw, L.B., Aggrawal, I.D.,Eggleton, B.J.: Characterization of picoseconds pulse nonlinear propagation in chalcogenideAs2S3 fiber. Appl. Opt. 48, 5467–5474 (2009)

Xiong, F., Liao, A.D., Estrada, D., Pop, E.: Low-power switching of phase-change materials withcarbon nanotube electrodes. Science 332, 568–570 (2011).

Yamada, N., Kojima, R., Nishihara, T., Tsuchino, A., Tomekawa, Y., Kusada, H.: 100 GBrewritable triple-layer optical disk having Ge-Sb-Te films. Proc. E∗PCOS 2009 23–28 (2009)

Yamada, N., Ohno, E., Nishiuchi, K., Akahira, N., Takao, M.: Rapid-phase transitions of GeTe-Sb2Te3 pseudobinary amorphous thin films for an optical disk memory. J. Appl. Phys. 69,2849–2856 (1991)

Yeo, E.G., Shi, L.P., Zhao, R., Lim, K.G., Chong, T.C., Adesida, I.: Parasitic capacitance effect onprogramming performance of phase change random access memory devices. Appl. Phys. Lett.96, 043506 (2010)

Yoshida, N., Harada, H., Tanaka, K.: Solid-state photochemical cell: persistent photo-generatedvoltage in ion-conducting amorphous semiconductor Ag-As-S. Solid State Ionics 95, 323–326(1997)

Youm, M.S., Kim, Y.T., Sung, M.Y.: Observation of hexagonal nuclei in the once melt-quenchedGe2Sb2Te5 phase change contact dimensions. Appl. Phys. Lett. 91, 083508 (2007)

Zakery, A., Elliott, S.R.: Optical properties and applications of chalcogenide glasses: A review.J. Non-Cryst. Solids 330, 1–12 (2003)

228 7 Applications

Zembutsu, S., Toyoshima, Y., Igo, T., Nagai, H.: Properties of (Se,S)-based chalcogenide glassfilms, and an application to a holographic supermicrofiche. Appl. Opt. 14, 3073–3077 (1975)

Zhang, G., Gan, F., Lysenko, S., Liu, H.: Observation of ultrafast carrier dynamics in amorphousGe2Sb2Te5 films induced by femtosecond laser pulses. J. Appl. Phys. 101, 033127 (2007)

Zhu, H., Yin, J., Xia, Y., Liu, Z.: Ga2Te3 phase change material for low-power phase changememory application. Appl. Phys. Lett. 97, 083504 (2010)

Zijlstra, P., Chon, J.W.M., Gu, M.: Five-dimensional optical recording mediated by surfaceplasmons in gold nanorods. Nature 459, 410–413 (2009)

Zou, L.E., Chen, B.X., Chen, L., Yuan, Y.F., Hamanaka, M., Iso, M.: Fabrication of an As2S8stripe waveguide with an optical stopping effect by exposure to ultraviolet irradiation. Appl.Phys. Lett. 88, 153510 (2006)

Chapter 8Future Prospects

Abstract In this chapter, we summarize notable problems that are unresolved andalso try to predict future prospects of amorphous chalcogenides.

Keywords Unresolved problems · Future applications · Photonics · Electronics ·Ionics · Se · GST

8.1 Fundamentals

The goal of solid-state science is to connect atomic structures and macroscopic prop-erties using simple theories (Fig. 2 in Preface). However, we cannot yet identify theamorphous structure. In addition, macroscopic properties are likely to vary depend-ing upon the quasi-stability of non-crystalline solids. Needless to say, in theoreticalanalyses, such an assumption as the periodic boundary condition cannot be appliedto the disordered structure, and hence, the amorphous materials science remains farbehind the crystalline materials science. We here summarize marked progresses andthe remaining problems. For details, see the related chapters.

With regard to atomic structures (Chapter 2), we have grasped the short-range(≤0.5 nm) structure in simple glasses. However, we are still at speculative lev-els on the medium-range (2–3 nm) structure and ESR-insensitive defects, the mainreasons being insufficient experimental tools. In addition, heterogeneous structureswith correlation lengths of ∼10 nm scales may exist, which are more difficult todetermine.

In structural properties (Chapter 3), the importance of the magic numbers, 2.4and 2.67, for understanding compositional variations has been amply demonstrated.However, the glass transition and the crystallization remain to be big problems inamorphous materials. The glass transition appears to be influenced by the medium-range structure, for which we are groping in the dark. In addition, to obtainan elucidation of the universal low-temperature properties, we wish to identifyresponsible atomic structures.

Electronic properties (Chapters 4, 5, and 6) should be studied further. It canbe said that we have been able to connect the short-range structure to gross elec-tronic structures. However, many problems remain to be considered. For opticalproperties, why do most of amorphous materials exhibit the exponential Urbachedge? And, why does the Urbach-edge energy in simple glasses such as As2S3

229K. Tanaka, K. Shimakawa, Amorphous Chalcogenide Semiconductors and RelatedMaterials, DOI 10.1007/978-1-4419-9510-0_8, C© Springer Science+Business Media, LLC 2011

230 8 Future Prospects

and SiO2, and even in a-Si:H, show a common value of ∼50 meV? Note that,despite this fixed Urbach energy, the optical gaps widely vary at 1–10 eV. Themeaning of the Tauc gap also remains to be vague. For the photoluminescence,the unique half-gap spectrum has been interpreted by using D0, but why is the D0

level located at the mid-gap in lone pair electron semiconductors? Alternatively,the photoluminescence spectrum has been interpreted using the idea of self-trappedexcitons, but why should the exciton emit universally the half-gap photons? Forthe electronic transport, why are holes more mobile in almost all the chalcogenideglasses? What is the reason for the Meyer–Neldel rule in electrical conductiv-ity? How can we compromise the concepts of the mobility edge and the polaronin chalcogenide glasses? Why is the avalanche multiplication unique to a-Se?Photo-structural changes also present many challenging problems, but we needdefinite insights into the initial structure (before illumination) for obtaining firmunderstandings.

In short, there remain several unanswered scientific problems in qualitative, andmore in quantitative, senses. To advance the science, we need tempting motivations,which may arise from applicable potentials.

8.2 Applications

What are the future applications of the group VIb glass (Chapter 7), specificallythe chalcogenide glass? History shows that future prediction entails a lot of hardwork. Actually, in the 1970s, few people could have imagined an earth surroundedby optical fiber networks. Yet in the 1990s, we could not have imagined the presentprosperity of optical phase-change memories, which have been revived by the dis-covery of fast phase-change GeTe–Sb2Te3 films. Despite the difficulty, it may bechallenging to predict the future in some area.

First, it is beyond doubt that the optical fiber communication system will developstill further, and related optical devices with ultimate performances are required.Fiber devices as optical amplifiers and Bragg reflectors will be improved for densewavelength division multiplexing systems. Functional optical integrated circuitsusing optical nonlinearities are needed, in which the glass will compete with semi-conductor and ferroelectric materials. Related micro-optical components will bedeveloped.

Second, what is the future of memories? Simple extrapolation of the present tech-nology predicts that the capacity of DVD memories will reach ∼1 TB/disk withdevelopments of, e.g., multi-layer and multi-level recording techniques. On the otherhand, a dramatic increase in the operating speed in a near future will be difficult.We should recognize, however, that the optical memory must compete with mag-netic memories as hard disks in many applications. The hard disk is approachinga capacity of ∼1 TB/pack with a faster operation speed, which may be supe-rior to the phase-change memory. For the optical memory, holographic recordingusing sulfide films may be an alternative, while its capacity is still limited by light

8.2 Applications 231

wavelength. Then, one promising direction of optical memories is to use spec-tral multiplexing. We can expect that the persistent spectral hole burning systemcombined with wavelength-tunable compact lasers will be able to memorize 1000bits in a diffraction-limited light spot in a three-dimensional space, which will becapable of producing peta-byte memories. For that purpose, stable (organic or inor-ganic) sensitizer-doped amorphous films must be developed. Finally, at present, afuture prediction of PRAM seems to be very critical. The potential is still beingexplored, while there are several competing devices as magnetic and ferroelectricmemories.

What is the future for the photoconductive devices? X-ray detection andavalanche-multiplied photoconduction are surely the greatest advantages of a-Seapplications in recent years. The performance will be developed further, not onlylimited to medical and television purposes. We here recognize that Se remains tobe a tempting material both from science and application over nearly a century.Despite that, we cannot yet understand attracting fundamental properties even inthis simplest system, a-Se, as described in the present text!

Ionic applications are more difficult to be predicted. Ionic memories, sensors,and batteries are surely important, while there exist competing materials such asorganic polymers and ceramic crystals. We may recall here that the xerographicphotoreceptor has been completely replaced from a-Se to organic photoconductors,due to the price and ecological issue. Therefore, some unique advantages, utiliz-ing ionic and/or ion-hole conductions, should be emphasized in the forthcomingapplications.

232 8 Future Prospects

Appendix: Publications on Related Crystals

Comparisons of the glass and crystal provide valuable insight, as described in thistext, since elemental and stoichiometric glasses have the corresponding crystalswith the same composition and the crystalline physics is much more advancedthan that of the non-crystalline. We here list related publications in a historicalorder on simple chalcogenide crystals of interest. In addition to these publicationsbelow, we may consult Landolt–Bornstein (Group III Condensed Matter, NumericalData and Functional Relationships in Science and Technology, Volume 41C:Non-Tetrahedrally Bonded Elements and Binary Compounds I), which containscomprehensive data on some chalcogenide crystals.

S and Se

Cook, B.E., Spear, W.E.: The optical properties of orthorhombic sulphur crystals in the vacuumultraviolet. J. Phys. Chem. Solids 30, 1125–1134 (1969)

Zingaro, R.A., Cooper, W.C.: Selenium, Van Nostrand Reinhold, New York, NY (1974)Nielsen, P.: Photoemission studies of sulfur. Phys. Rev. B 10, 1673–1682 (1974)Salaneck, W.R., Lipari, N.O., Paton, A., Zallen, R., Liang, K.S.: Electronic structure of S8. Phys.

Rev. B 12, 1493–1500 (1975)Robins, L.H., Kastner, M.A.: Recombination and excited-state absorption at photoluminescence

centres in crystalline and amorphous arsenic triselenide. Philos. Mag. B 50, 29–51 (1984)Abass, A.K., Ahmad, N.H.: Absorption edge of pure and selenium-doped α-sulfur single crystals.

Phys. Status Solidi (a) 91, 627–630 (1985)Oda, S., Kastner, M.A.: Transient photoluminescence and photo-induced optical absorption in

polymeric and crystalline sulphur. Philos. Mag. B 50, 373–377 (1984)Nagata, K., Miyamoto, Y., Nishimura, H., Suzuki, H., Yamasaki, S.: Photoconductivity and pho-

toacoustic spectra of trigonal, rhombohedral, orthorhombic, and α-, β-, and γ -monoclinicselenium. Jpn. J. Appl. Phys. 24, L858–L860 (1985)

Lundt, H., Weiser, G.: Defect luminescence and its excitation spectra in As-doped Se singlecrystals. Philos. Mag. B 51, 367–380 (1985)

Chen, C.Y., Kastner, M.A., Robins, L.H.: Transient photoluminescence and excited-state opticalabsorption in trigonal selenium. Phys. Rev. B 32, 914–917 (1985)

Chen, C.Y., Kastner, M.A.: Transient photoinduced optical absorption spectroscopy in trigonalselenium. Phys. Rev. B 33, 1073–1075 (1986)

Povoa, J.M., Leal Ferreira, G.F.: Anomalies in the electronic time-of-flight current trace in sulfur.Phys. Rev. B 47, 1610–1612 (1993)

As2S(Se)3

Evans, B.L., Young, P.A.: Optical properties of arsenic trisulphide. Proc. R. Soc. A297, 230–243(1967)

Kolomiets, B.T., Mamontova, T.N., Babaev, A.A.: Radiative recombination in vitreous and singlecrystal As2S3 and As2Se3. J. Non-Cryst. Solids 4, 289–294 (1970)

Drews, R.E., Emerald, R.L., Slade, M.L., Zallen, R.: Interband spectra of As2S3 and As2Se3crystals and glasses. Solid State Commun. 10, 293–296 (1972)

Zallen, R., Slade, M.: Rigid-layer modes in chalcogenide crystals. Phys. Rev. B 9, 1627–1637(1974)

Appendix: Publications on Related Crystals 233

Zallen, R., Blossey, D.F.: The optical properties, electronic structure, and photoconductivityof arsenic chalcogenide layer crystals. Physics and Chemistry of Materials with LayeredStructures, edited by E. Mooser (D. Reidel Publishing Company, Dordrecht, 1976)pp. 231–272.

Smith, B.A., Cowlam, N., Shamah, A.M.: The crystal growth and atomic structure of As2(Se,S)3

compounds. Philos. Mag. B 39, 111–132 (1979)

As2S3

Morimoto, N.: The crystal structure of orpiment (As2S3) refined. Mineralogical J. 1, 160–169(1954)

Mullen, D.J.E., Nowacki, W.: Refinement of the crystal structure of realgar, AsS and orpiment,As2S3. Z. Kristallogr. 136, 48–65 (1972)

Lisitra, M.P., Berezhinsky, L.I., Valakh, M.Ya., Yaremko, A.M.: Exciton peculiarities in the As2S3

layer crystal. Phys. Lett. 42A, 51–52 (1972)Perrin, J., Cazaux, J., Soukiassians, P.: Optical constants and electronic structure of crystalline and

amorphous As2S3 in the 3 to 35 eV range. Phys. Status Solidi (b) 62, 343–350 (1974)Blossey, D.F., Zallen, R.: Surface and bulk photoresponse of crystalline As2S3. Phys. Rev. B 9,

4306–4313 (1974)Schein, L.B.: Temperature independent drift mobility along the molecular direction of As2S3. Phys.

Rev. B 15, 1024–1034 (1977)Murayama K., Bösch, M.A.: Radiative recombination in crystalline As2S3. Phys. Rev. B 23,

6810–6812 (1981)Rebenstorff, D., Weiser, G.: Electric-field-modulated spectra of orpiment (As2S3) near the energy

gap. Philos. Mag. B 46, 207220 (1982)Weistein, B.A.: Anomalous pressure studies of luminescence in c-As2S3 and a-As2SeS2:

Consequences for defect structure in chalcogenides. Philos. Mag. B 50, 709–729 (1984)Shimoi, Y., Fukutome, H.: Degeneracy in the crystal structure of As2S3. J. Phys. Soc. Jpn. 59,

1264–1276 (1990)McNeil, L.E., Grimsditch, M.: Elastic constants of As2S3. Phys. Rev. B 44, 4174–4177(1991)Zallen, R.: Effect of pressure on optical properties of crystalline As2S3. High Pressure Res. 24,

117–118 (2004)Espeau, P., Tamarit, J.Li., Barrio, M., Lopez, D.O., Perrin, M.A., Allouchi, H., Ceolin, R.: Solid

state studies on synthetic and natural crystalline arsenic(III) sulfide, As2S3 (orpiment): Newdata for an old compound. Chem. Mater. 18, 3821–3826 (2006)

Bonazzi, P., Bindi, L.: A crystallographic review of arsenic sulfides: Effects of chemical variationsand changes induce by exposure to light. Z. Kristallogr. 223, 132–147 (2008)

Gibbs, G. V., Wallace, A. F., Zallen, R., Downs, R. T., Ross, N. L., Cox, D. F., Rosso, K. M.: Bondpaths and van der Waals interactions in orpiment, As2S3. J. Phys. Chem. A 114, 6550–6557(2010)

As4S4

Street, G.B., Gill, W.D.: Photoconductivity and drift mobilities in single crystal realgar (As4S4).Phys. Status Solidi 18, 601–607 (1966)

Mullen, D.J.E., Nowacki, W.: Refinement of the crystal structures of realgar, AsS and orpimentAs2S3. Z. Kristallogr. 136, 48–65 (1972)

234 8 Future Prospects

Street, R.A., Austin, I.G., Searle, T.M.: Photoluminescence in chalcogenide crystals showingsmall polaron conduction; Orthorhombic sulphur and As4S4. J. Phys. C: Solid State Phys. 8,1293–1300 (1975)

As2Se3

Kitao, M., Asakura, N., Yamada, S.: Preparation of As2Se3 single crystals. Jpn. J. Appl. Phys. 8,499–500 (1969)

Shaw, R.F., Liang, W.Y., Yoffe, A.D.: Optical properties, photoconductivity, and energy levels incrystalline and amorphous arsenic triselenide. J. Non-Cryst. Solids 4, 29–42 (1970)

Sussmann, R.S., Searle, T.M., Austin, I.G.: Absorption and electro-absorption in single-crystalAs2Se3 near the fundamental edge. J. Phys. C: Solid State Phys. 8, L564–L568 (1975)

Marshall, J.M.: Electron transport in arsenic triselenide single crystals. J. Phys. C: Solid State Phys.10, 1283–1290 (1977)

Althaus, H.L., Weiser, G., Nagel, S.: Optical spectra and band structure of As2Se3. Phys. StatusSolidi (b) 87, 117–128 (1978)

Sussmann, B.S., Searle, T.M., Austin, I.G.: The excitonic gaps and Urbach tail in crystallineAs2Se3: Absorption and electroabsorption studies. Philos. Mag. B 44, 665–683 (1981)

Kanishcheva, A.S., Mikhailov, Yu.N., Zhukov, E.G., Grevtseva, T.G.: Redetermination of the crys-tal structure of As2Se3 and a comparison of the coordination of As(III) in chalcogenides andtheir analogs. Inorg. Mater. 19, 1744–1748 (1984)

Marshall, J.M., Barclay, R.P., Main, C., Dunn, C.: The transient photodecay process and its inter-pretation in the case of disordered single crystals of arsenic triselenide. Philos. Mag. B 52,997–1004 (1985)

Brunst, G., Weiser, G.: Defect-controlled conductivity in As2Se3 single crystals. Philos. Mag. B 51,67–77 (1985)

Antonelli, A., Tarnow, E., Joannopoulos, J.D.: New insight into the electronic structure of As2Se3.Phys. Rev. B 33, 2968–2971 (1986)

Tarnow, E., Antonelli, A., Joannopoulos, J.D.: Crystalline As2Se3: Electronic and geometricstructure. Phys. Rev. B 34, 4059–4073 (1986)

Tarnow, E., Antonelli, A., Joannopoulos, J.D.: Crystalline As2Se3: Optical properties. Phys. Rev.B 34, 8718–8727 (1986)

Kitao, M., Nishimoto, T., Yamada, S.: Emission and excitation spectra of photoluminescence ofAs2Se3 single crystals. Phys. Status Solidi(a) 103, K149–K152 (1987)

Ristein, J., Weiser, G.: Thermalization of excited carriers through band states studied byphotoluminescence in As2Se3 and Se single crystals. Philos. Mag. B 56, 51–62 (1987)

Ristein, J., Weiser, G.: Recombination of germinate pairs in As2Se3 single crystals. Philos. Mag.B 54, 533–542 (1987)

Robins, L.H., Kastner, M.A.: Anomalous magnetic properties of triplet excited states in crystallineand amorphous arsenic triselenide. Phys. Rev. B 35, 2867–2885 (1987)

Ristein, J., Weiser, G.: Microscopic structure of the radiative centre in As2Se3 crystals. Solid StateCommun. 66, 361–365 (1988)

Ristein, J., Taylor, P.C., Ohlsen, W.D., Weiser, G.: Radiative recombination center in As2Se3 asstudied by optically detected magnetic resonance. Phys. Rev. B 42, 11845–11856 (1990)

GeS(Se)2

Inoue, K., Matsuda, O., Murase, K.: Raman spectra of tetrahedral vibrations in crystallinegermanium dichalcogenides, GeS2 and GeSe2, in high and low temperature forms. Solid StateCommun. 79, 905–910 (1991)

Appendix: Publications on Related Crystals 235

Ho, C.H., Lin, S.L., Wu, C.C.: Thermoreflectance study of the electronic structure ofGe(Se1−xSx)2. Phys. Rev. B 72, 125313 (2005)

GeS2

Zachariasen, W.H.: The crystal structure of germanium disulphide. J. Chem. Phys. 4, 618–619(1936)

Prewitt, C.T., Young, H.S.: Germanium and silicon disulfides: Structure and synthesis. Science149, 535–537 (1965)

Rubenstein, M., Roland, G.: A monoclinic modification of germanium disulfide, GeS2. ActaCrystallogr. B27, 505–506 (1971)

Dittmar, Von G., Schäfer, H.: Die Kristallstructur von H.T.-GeS2. Acta Cryst. B31, 2060–2064(1975)

Saji, M., Kubo, H.: Electrical properties of GeS2 single crystals. Rept. Nagoya Inst. Technol. 32,213–221 (1980) (in Japanese)

Weinstein, B.A., Zallen, R., Slade, M.L.: Pressure-optical studies of GeS2 glasses and crystals:Implications for network topology. Phys. Rev. B 25, 781–792 (1982)

GeSe2

Aspens, D.E., Phillips, J.C., Tai, K.L.: Optical spectra and electronic structure of crystalline andglassy Ge(S,Se)2. Phys. Rev. B 23, 816–822 (1981)

Popovic, Z.V.: Optical absorption band edge of single crystal β-GeSe2. Phys. Lett. A 110, 426–428(1985)

Popovic, Z.V., Gajic, R.: New vibrational modes in the far-infrared spectra of germaniumdiselenide. Phys. Rev. B 33, 5878–5879 (1986)

Nikolic, P.M., Todorovic, D.M., Vujatovic, S.S., Djuric, S., Mihailovic, P., Blagojevic, V.,Radulovic, K.T., Bojicic, A.I., Vasiljevic-Radovic, D., Elazar, J., Urosevic, D.: Anisotropy inthermal and electronic properties of single crystal GeSe2 obtained by the photoacoustic method.Jpn. J. Appl. Phys. 37, 4925–4930 (1998)

Popovic, Z.V., Jakšic, Z., Raptis, Y.S., Anastassakis, E.: High-pressure Raman-scattering study ofgermanium diselenide. Phys. Rev. B 57, 3418–3422 (1998)

Material Index

AAg1As40Se60, 78–79Ag20As32Se48, 106Ag2S, 18, 77Ag2S-As2S3, 80–81Ag2S-GeS2, 78Ag45As15S40, 177Ag-As-S, 18–19, 77, 157, 175–177, 218AgAsS2, 5, 77, 171–177AgBrxCl1-x, 141a-Ge:H, 182AlF3, 200As, 15, 21, 24, 33, 51, 71, 73–74, 114,

175, 178As(Ge, Si)-S(Se):H, 22As100-xSx, 21As2O(S, Se, Te)3, 13–14, 47, 114As2S3, 3, 12, 14, 16, 19–24, 30–31, 33,

37–39, 44–46, 48–57, 64, 69–70,72–74, 90–91, 93, 96–103, 107, 126–128,144–145, 148, 150–157, 161–163, 165,168–171, 174–176, 178, 180–181, 184,200, 202, 204–207, 219, 229

As2Se3, 16, 21, 44, 57, 67, 70, 90, 97–98,101–102, 109, 124, 128, 131, 135, 144,151, 170, 178, 215

As2Te3, 16, 44, 107, 161, 197As3Se2, 152a-Si:H, 2–3, 5–7, 22–23, 43, 48, 55–56,

64, 73, 87, 99–100, 110–112, 130–131,136, 142, 144, 160, 182–183, 203,217–218, 230

As-S, 9, 23, 41, 52, 101, 151–152,178–179, 202

As-Se(Te), 39AsxS3, 152Azobenzene, 184–185

BB2O3, 43, 49B2O3-Li2O, 49Bi-Ge-Se, 109Bi4Si3O12, 49BK-7 (borosilicate glass), 204

CC12H26, 46c-As2S2, 147c-As2S3, 108, 124, 130, 146, 149, 157,

165, 175c-As2Se3, 90, 108CCl4, 46CdO, 12CdS, 12c-S, 15, 125, 130c-GeS2, 17, 37, 47, 175c-SiO2, 33, 48, 72, 90, 108, 163, 179, 199c-Se, 15, 35, 40, 42, 108, 126, 128–129, 215c-SnO2, 214Cu(Ag)-As(Sb)-S(Se), 12Cu-As-Se, 151, 220CuGaS(Se)2, 214

EEr-doped a-Si:H, 203Er-doped chalcogenides, 202

FFe2O3, 9

GGaAs, 12, 25, 87, 99, 215, 219Ga-Ge-S, 157Ga-La-S, 18, 151Ge100-xSx, 21Ge15Te85, 17

237K. Tanaka, K. Shimakawa, Amorphous Chalcogenide Semiconductors and RelatedMaterials, DOI 10.1007/978-1-4419-9510-0, C© Springer Science+Business Media, LLC 2011

238 Material Index

Ge1As4Se5, 160, 162Ge2Sb2Te5 (GST), 18, 21, 56, 100, 136,

209–214Ge-As-S, 41, 152, 156, 206GeO(S, Se)2, 43, 47GeO(S, Se, Te)2, 13, 40GeO2-GeS2, 18, 55GeS2, 17, 21, 24, 37, 42, 49, 90, 93, 178GeS2-GeO2, 15750GeS2-50GeO2, 157Ge-Sb-Te, 12, 17–18, 41, 91, 143, 209Ge-Se, 17, 39, 68, 151–152GeSe2, 14, 45, 124, 143–144, 149, 205GeSe3, 151–152Ge-SiO2, 179–180, 205GeTe-Sb2Te3, 209, 230GST, 209–214

HHydrogenated amorphous silicon, 2, 182–185

IIn49S51, 109, 214In-Sn-O (ITO), 214

NNa2O, 13–14, 41Na2O(PbO)-SiO2, 55NaCl, 3, 9, 50, 77, 202Na-Ge-S, 157

PP, 15, 17, 71Polyethylene, 7, 24, 46–47, 64, 170Pr-doped chalcogenides, 202

P-Se, 39Pyrex, 73–74, 170

SS, 10, 12–15, 17–18, 40–42, 51–52, 69, 71,

109, 125, 142, 149–152, 156–157, 160,175, 202

Sb, 12, 15Se, 10–13, 15, 21, 23, 33, 37, 39–40, 42, 46,

50, 52, 54, 56, 65, 69, 71, 73, 80, 89,94–95, 99, 106–107, 124–126, 128, 133,142, 148–149, 151–152, 154, 156–157,160, 166, 169, 214–217, 231

SF-59 (lead-silicate glass), 204Si, 2, 11–12, 17, 23, 30, 33, 42, 51, 87, 90,

114, 127, 148, 180, 184, 214, 217Si(C, S):H, 110SiO(S, Se, Te)2, 13SiO2, 2–3, 14, 33, 45, 90–91, 96, 109, 124,

204–205SiO2-Al2O3, 9SiO2-Na2O, 9, 13, 41, 74, 20074SiO2-16Na2O-10CaO, 13, 76SiS(Se, Te)2, 17

TTe, 10, 12–16, 40, 70, 74, 109, 114, 142, 211,

214, 217Te81Ge15Sb2S2, 209

XxGeO2-(100-x)GeS2, 18xNa2O-(100-x)SiO2, 74

ZZnCl2, 46, 69ZnO, 12

Subject Index

AAb-initio, 53, 89, 148, 210Ac conductivity, 112–113, 161, 183Anisotropic shape change, 172–174Anomalous x-ray diffraction, 35Atomic coordination number, 16, 40, 63,

71, 75Atomic force microscopy (AFM), 37–38, 54Atomic periodicity, 3, 23, 56Atomic volume, 74, 76, 3Avalanche breakdown, 135–136Average atomic density, 34

BBirefringence, 3, 171, 184Blue-shift, 92, 130Bond

ionicity, 12–13twisting, 159

Boolchand phase, 76Boson peak, 48–50, 72, 74Brillouin scattering, 203Bulk modulus, 64, 72–73

CCarrier lifetime, 129Carrier multiplication, 136Carrier-transit time, 133Chain, 7, 11, 15, 21, 33, 35, 42–43, 54, 57,

94–95, 110, 149, 151, 172–173Charge coupled device (CCD), 6, 216Charged defect, 93–94, 126, 160–161,

167, 173Chemical doping, 6, 18, 87, 131Chemical vapor deposition (CVD), 22, 218Cis-conformation, 184Configuration coordinate, 64–65, 158

Conservation rule, 96Constant photocurrent method (CPM),

130–131, 183Continuous random network, 30, 32, 33, 41,

43, 45, 48, 76Cook-and-quench method, 53Corner-share, 41–43Coulombic layer movement, 159Covalency, 12–17, 23–24, 40–41, 43–44, 47,

51, 67, 71, 75, 80, 99, 113–114,141, 152, 154, 156–157, 167,170–171, 173, 175, 181, 197, 202

Crystallization, 14, 57, 63–66, 68–71, 104,144–145, 147–150, 172, 181–182,208–213, 229

DDangling bond, 4, 10, 29–30, 32–33, 40,

50–52, 56, 86–87, 93–94, 167, 178,183–184

D0 center, 10, 50–52, 93, 126–127, 167, 230Debye

relaxation, 112temperature, 64

Defect creation, 142, 145, 148, 161, 180–181,184

Dember, 107, 121–123, 128Dense random packing, 29Density-functional theory, 148(De-)trapping, 87, 107, 109, 122, 129, 132Diamond-anvil cell, 24Dichroism, 171Digital versatile disk (DVD), 5–6, 208Dihedral angle, 32, 35, 40, 42Dispersive transport, 132–133Distorted layer, 7, 33, 44Drift mobility, 132Drude model, 106, 132

239

240 Subject Index

EE′ center, 10, 33, 50, 142, 179–180Eclipsed conformation, 42Edge-share, 41–43Effective density-of-states, 107Elastic constant, 50, 72–74, 146, 165, 200, 204Electrical phase-change, 142, 208, 212–214Electrical switching, 136, 213–214Electrolyte, 221Electron density-of-state (DOS), 85–86, 89,

91–92, 95–96, 130–135Electro-negativity, 12Electronic melting, 170, 211Electron-lattice interaction, 5, 99Electron spin resonance (ESR), 39, 50–52,

93–94, 124–125, 145, 165–168,183, 229

Erbium doped fiber amplifier (EDFA), 8, 199,202

Evaporation, 8, 15, 17, 20–22, 56, 146,198, 215

EXAFS, 34, 35–37, 50–51, 160, 168Exciton, 88, 92, 99, 121–122, 127–128,

130, 230

FFabry–Perot type interference, 36Fast ion-conductor, 77Fiber amplifier, 8–9, 199, 201–203Fiber Bragg grating (FBG), 179, 199, 206Figure-of-merit, 205First sharp diffraction peak (FSDP), 44–50, 72,

74, 151, 159Flash evaporation, 21, 152Floating method, 8–9Formal valence-shell model, 12Free-carrier absorption, 102Free volume, 68, 78Frequency-resolved photoluminescence,

127–128

GGeminate recombination, 122, 130Giant photo

contraction, 151–152expansion, 147, 163–164, 170

Glass transition temperature, 2, 15–16, 20, 54,56–57, 64, 66–68, 74, 76, 80, 95,126, 150, 153–154, 156, 160–162,165, 169–170, 180, 198, 200

Glow discharge, 8, 22, 218

HHalf-gap photoluminescence, 124–125Holographic storage, 151, 184HOMO, 90–91, 148Hopping, 87–88, 112, 116, 132–133Hund rule, 11

IIdeal glass, 29–30, 68Impact ionization, 136Impurity, 3, 53, 86–87, 124–125, 131, 167, 198Infrared spectroscopy, 178Intimate pair of defect, 161, 167Ioffe–Regel rule, 86Ionicity, 12–14, 74, 76Ionic transport, 77–81Ion mobility, 5Irreversible photoinduced change, 145–146,

150

KKauzmann’s paradox, 31Kramers–Krönig relation, 95–96, 102–103,

153

LLaser ablation, 22, 143Lattice vibration, 4, 136, 142, 196–197Light

induced bending, 144soaking, 161, 182–183

Liquid crystals, 1, 195, 208Lone-pair electron, 11–12, 52, 87, 90, 94,

98, 103, 110, 114, 127, 130, 154,157–158, 173, 178, 230

Long-range structure, 12, 33, 50Low-temperature anomaly, 50, 72Lucky drift, 136LUMO, 90–91, 148

MMagic number, 25, 63, 74–77, 229Maxwell–Wagner effect, 113Mean-free path, 36, 56, 72, 86, 107, 110, 136Medium-range structure, 41–50, 53, 63, 76, 87,

90, 159Melting temperature, 2, 18, 65–67, 95,

208, 210Melt-quench, 2–3, 19, 245-Membered ring, 30, 876-Membered ring, 30Metallicity, 12–14, 115Meyer–Neldel rule, 78, 100, 110–112, 230

Subject Index 241

Micro-lense, 207Mid-gap optical absorption, 53, 87Mobility edge, 91–92, 107, 130–131, 133, 230Mobility gap, 92, 99, 128, 130Molecular dynamics (MD), 18, 53–54, 148,

152, 210Monte Carlo method, 43, 54Mossbauer spectroscopy, 39Moss rule, 103, 106, 153Mott-CFO model, 91–92Multi-layer structure, 152

NNano-structure, 55–57, 204Network

former, 13, 55modifier, 13

Neutron diffraction, 34–35, 51Nonlinear vibrational spectra, 38Non-photoconducting gap, 92, 130Non-radiative recombination, 122, 124,

166–167Normal bond, 32–33, 50, 63, 159, 1678–N rule, 12, 40Nuclear magnetic resonance (NMR), 39, 95Nuclear quadrupole resonance (NQR), 39

OObsidian, 1, 8–9Optical

absorption, 4, 22, 43, 47, 53, 56, 86–87,91, 96–102, 125, 130–131, 135,150–153, 157, 160, 166, 168, 199,204, 218

bandgap, 19, 24, 74, 93fiber, 4–5, 19, 54, 104, 142, 179, 197–200,

203, 205–207, 230induced thermal change, 142nonlinearlity, 103–106, 203–204phase-change, 5, 143, 205, 208–211, 230phonon, 38–39, 48, 122stopping effect, 168, 207waveguide, 203–204, 207

Opto-mechanical, 172–173

PPenetration depth, 143, 147, 153, 163Phase-change random-access memory

(PRAM), 208, 212–214, 231Photo

amorphization, 147, 148bleaching, 145, 152, 178chemical modification, 176–177

conduction, 121, 123, 128–135, 161, 164,183, 216, 231

crystallization, 144–145, 147, 149darkening, 74, 143, 145–147diffusion, 152doping, 81, 145–147, 174–177, 207,

219–220electric devices, 215–219electron spectroscopy, 38–39, 89, 109,

158, 183enhanced

crystallization, 145, 148–150, 182vaporization, 20, 178–179

inducedanisotropy, 171, 180bond conversion, 145defect creation, 142degradation, 160–161, 183ESR, 124, 165–166fluidity, 142, 164, 169–170mid-gap absorption, 166

luminescence, 50, 53, 86–88, 94, 123–128,130–131, 165–167, 183, 202, 230

fatigue, 165–166oxidation, 145, 177–178polymerization, 141, 145, 150–151,

184, 207surface deposition, 176–177thermal change, 101, 142, 150, 165voltage, 128voltaic effect, 217

Photo-deflection spectroscopy (PDS), 183Photonics glass, 9–10Piezo-electricity, 3Plasma emission spectroscopy, 53Pn anomaly, 107Poisson’s ratio, 73Polaron, 85–86, 88, 90–92, 94, 96, 99, 112,

122–123, 127, 230Polk model, 30, 53Polymerization temperature, 15Positron lifetime spectroscopy, 55μτ-Product, 218

QQuantum efficiency, 142, 155, 164, 201Quasi-equilibrium, 4, 6–7, 30, 41, 65, 68,

195–196

RRadial distribution function (RDF), 34, 37–38,

42, 53Radiation compaction, 142, 179, 181

242 Subject Index

Radiative recombination, 126Raman scattering, 38–39, 43, 48–51, 54, 72,

94, 149γ-Ray, 142–143, 179Red-shift, 131, 150–151, 153–155, 157,

159–161, 164, 166Refractive index, 96, 102–105, 142, 146,

150–160, 168, 171, 179–181,197–198, 200, 203–205, 207

Reverse Monte Carlo method, 43, 54Reversible photoinduced change, 145–146,

157, 160, 183Ring, 15, 21, 30, 32, 42–43, 54, 87, 151

SScalar effect, 171Scanning tunneling microscopy (STM), 37, 56Schubweg, 129Se8 ring, 15Second-harmonic generation, 3, 6Self-focusing, 104Short-range structure, 34–42, 53, 63, 76, 86, 91Silica glass, 4–5, 50, 56, 64, 91, 142, 180, 198,

200, 202Single crystal, 3–5, 16, 23, 25, 30, 56, 72, 87,

162Small-angle x-ray scattering, 54Solar cell, 2, 5–6, 182, 196, 217–218Sol-gel, 23, 198Solid-state battery, 195Specific heat, 63–66, 71–72Spin coating, 22Spinodal decomposition, 55Sputtering, 17, 20–22, 104, 198S8 ring, 15Staebler–Wronski effect, 142, 160, 182–184Staggered conformation, 42Stoichiometry, 13–14, 16–17, 21, 41, 46,

51–52, 54, 77, 100–101, 152, 154,156, 159, 200, 209, 232

Stokes shift, 88, 124, 126–127Stretched exponential function, 147Sub-gap light, 147, 155, 163, 166Supercooling liquid, 3Super-gap light, 132, 147, 155, 177

TTauc gap, 85, 97–99, 106, 110, 130, 153, 230Thermal

conductivity, 5, 20, 63–64, 71–72

equilibrium state, 4expansion, 20, 23, 63–64, 144, 170, 173relaxation, 88, 104, 145, 154–155, 158spike, 122, 158

Thermopower, 107Thin-film transistor (TFT), 181, 214Tight-binding, 114, 152Time of flight, 78, 107, 132–133Trans-conformation, 184Transient photoconductivity, 132–134Transitory change, 145, 148, 160, 168Transmittance oscillation, 143–144Two-photon absorption, 104–105, 205Two-step absorption, 104–105

UUrbach

edge, 99–101, 124, 130, 135, 153, 155,163–164, 170, 183, 202, 229

energy, 94, 98–100, 108, 130, 230

VValence alternation pair, 94van der Waals force, 49Vector effect, 171–174VIb glass, 14, 47, 230Vidicon, 6, 57, 129, 136, 195, 197, 216–217Viscosity, 63, 66–69, 94–95, 146, 152, 170Vogel–Tamman–Fulcher equation, 66, 68

WWavelength division multiplexing (WDM),

198–199, 205, 230Weak absorption tail, 93, 100–102, 125, 130,

135Wrong bond, 14, 32–33, 51–52, 93, 102,

167, 181

XXerographic, 9, 21, 107, 132, 134, 215, 231X-ray

diffraction method, 35fluorescence spectroscopy, 53imager, 195, 197, 216–217photoconduction, 216, 231

X-ray photoelectron spectroscopy (XPS), 39

YYoung’s modulus, 73