Optical absorption at its onset in sputter deposited hafnia–titania nanolaminatesMassiel Cristina Cisneros-Morales and Carolyn Rubin Aita Citation: Journal of Applied Physics 108, 123506 (2010); doi: 10.1063/1.3520678 View online: http://dx.doi.org/10.1063/1.3520678 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/108/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Atomic layer deposited high-κ nanolaminates for silicon surface passivation J. Vac. Sci. Technol. B 32, 03D110 (2014); 10.1116/1.4863499 Addendum to “Phase selection and transition in Hf-rich hafnia-titania nanolaminates” (on SiO2) [J. Appl.Phys.109, 123523 (2011)]: Hafnon formation J. Appl. Phys. 111, 109904 (2012); 10.1063/1.4719968 Phase selection and transition in Hf-rich hafnia-titania nanolaminates J. Appl. Phys. 109, 123523 (2011); 10.1063/1.3597321 Erratum: “Suppression of near-edge optical absorption band in sputter deposited HfO 2 – Al 2 O 3 nanolaminatescontaining nonmonoclinic HfO 2 ” [Appl. Phys. Lett.92, 141912 (2008)] Appl. Phys. Lett. 97, 269904 (2010); 10.1063/1.3533378 Crystallization, metastable phases, and demixing in a hafnia-titania nanolaminate annealed at high temperature J. Vac. Sci. Technol. A 28, 1161 (2010); 10.1116/1.3474973

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Optical absorption at its onset in sputter deposited hafnia–titaniananolaminates

Massiel Cristina Cisneros-Morales and Carolyn Rubin Aitaa�

Department of Chemistry and Biochemistry, University of Wisconsin–Milwaukee, P.O. Box 413, Milwaukee,Wisconsin 53201, USA

�Received 23 September 2010; accepted 26 October 2010; published online 20 December 2010�

The onset of the fundamental optical absorption edge in sputter deposited HfO2–TiO2 nanolaminatefilms grown on unheated substrates was investigated. Three bilayer architectures were examined,representing overall film chemistry from 0.51 to 0.72 atom fraction Hf. The goal was to determinethe absorption coefficient, ��E�, versus incident photon energy, E, and to model this dependence interms of the absorption behavior of specific functional units within the nanolaminate. Persistenceand amalgamation models were applied, representing the extremes of segregated cation and mixedcation structures, respectively, and both were found to be unsatisfactory. Consideration ofphysiochemical data for the nanolaminates led to the development of a modified persistence modelfor absorption. ��E� was decomposed into contributions from �I� broad �9 nm-thick� interfacialregions that were chiefly o-HfTiO4, and �II� regions remote from interfaces that contained materialbased on a highly defective m-HfO2 lattice. The absorption edge at its onset in all nanolaminateswas determined by short-range atomic order characteristic of o-HfTiO4. An indirect band gap ofEG=3.25�0.02 eV was determined for this compound. © 2010 American Institute of Physics.�doi:10.1063/1.3520678�

I. INTRODUCTION

Hafnia–titania thin films have recently been consideredas ultrathin high permittivity dielectrics for SiO2 replacementin microelectronic devices.1–7 The success of this applicationdepends upon the character of electronic transitions at theonset of ultraviolet absorption. In the research reported here,we investigated the fundamental optical absorption edge�FOAE� of sputter deposited HfO2–TiO2 nanolaminatefilms. Three bilayer architectures were examined, represent-ing overall film chemistry from 0.51 to 0.72 Hf atom fractionHf. Our goal was to determine the dependence of the opticalabsorption coefficient, ��E�, on incident photon energy, E,and to model this dependence in terms of the absorptionbehavior of specific functional units within the nanolaminate.

A convenient way to fabricate a nanocomposite thin filmis to sputter deposit a multilayer stack in which the thicknessof each type of layer is on the order of a few nanometers.8

Sputter deposition is a plasma process, and species that ar-rive at the growth interface carry additional energy beyondthermal energy, as compared to atomic layer deposition orthermal evaporation. One consequence is that sputter depos-ited oxides that are not network formers are frequently nano-crystalline, even when grown on unheated substrates. Theresulting structures can be different than those predictedfrom a bulk equilibrium phase diagram, i.e., they are meta-stable. Another consequence is that mixed cation structurescan be formed, especially in cases where the partners havesome degree of miscibility in bulk. These mixed cation struc-tures can significantly affect film properties because of thelarge interfacial contribution to the total volume of the nano-laminate.

The bulk HfO2–TiO2 pseudobinary temperature versuscomposition phase diagram shows limited miscibility with-out a common end-member lattice.9–11 The standard tempera-ture and pressure �STP� end-member phases are monoclinic�m� HfO2 with a baddelyite lattice structure and tetragonalTiO2 with a rutile �r� lattice structure. One compound isstable at STP, nominally HfTiO4, which in fact is a solidsolution Hf1−xTixO2 with x ranging from �0.4 to 0.53.HfTiO4 has an orthorhombic �o� lattice structure.

Previous results for sputter deposited HfO2–TiO2 nano-laminates show that an extensive �up to 9 nm-wide� mixedcation interfacial structure forms during growth12,13 and re-mains stable upon annealing to moderate temperature �973K�.13 A consideration herein is the nature of the functionalabsorption units in the interfacial structure. From an elec-tronic transition perspective, does the interface consist of amixture of individual oxides, i.e, �HfO2�x�TiO2�1−x, anatomic scale amalgamation, HfxTi1−xO2, or a combinationthereof as the dominant cation species is changed from Ti�Hf� to Hf �Ti�? To answer this question, we examine ��E�versus E data in terms of two extreme models, persistenceand amalgamation.14 Rejecting both extremes, we present amodified persistence model that best describes our experi-mental results.

II. EXPERIMENTAL PROCEDURE

A. Growth

HfO2–TiO2 films with the bilayer architectures recordedin Table I were grown by radio frequency-excited reactivesputter deposition in the previously described13 cryogenicallypumped multiple cathode programmable reactor. Three typesof substrates were used: Suprasil II fused SiO2 rounds, Au-a�Electronic mail: aita@uwm.edu.

JOURNAL OF APPLIED PHYSICS 108, 123506 �2010�

0021-8979/2010/108�12�/123506/8/$30.00 © 2010 American Institute of Physics108, 123506-1

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coated glass squares, and �111�-cut Si wafers from which thenascent SiO2 layer had not been removed. Each type of sub-strate was used for a specific analytical technique, discussedbelow. The SiO2 and Si substrates were ultrasonically rinsedfor 5 min each in trichloroethylene, acetone, isopropyl alco-hol, and deionized water, and dried with compressed99.998% dry N2 gas before placement on the rotating anodeof the reactor.

The chamber pressure before backfilling with the reac-tive sputtering gas was �1�10−7 torr. The sputtering gascontained 80% Ar–20% O2 at a total pressure of 20 mtorr.With shutters covering the substrates, the 99.998% Hf and99.995% Ti targets were “presputtered,” conditioned by sput-tering with the reactive gas to establish dynamic equilibriumbetween the rate of surface oxide formation and the rate ofdissociation of this oxide at the target surface due to thesputtering process.8 The shutters were opened and the sub-strates were sequentially positioned under the targets to buildup the nanolaminate structure after the presputter. The depo-sition rate was 2.0 nm/min for HfO2 �Refs. 15 and 16� and0.65 nm/min for TiO2.17 Further details of deposition param-eters, including thickness control of individual layers, havebeen previously given.12,13 The first and last layers depositedon the substrate in all nanolaminates were HfO2. Single layerHfO2 and TiO2 films were also grown using the same param-eters used to grow these constituents in the nanolaminates.

The films’ architectural parameters are recorded in TableI. The cation atom fraction in a bilayer was calculated fromthe volume fraction using the densities of the rutile phase ofTiO2 �4.26 g /cm3� �Ref. 18� and the monoclinic phase ofHfO2 �9.68 g /cm3�.19 A total HfO2 thickness of 167 nm waskept constant in all architectures.

B. Characterization

Spectrophotometry. The optical transmission, T, and re-flectance, R, of normal incidence radiation by films on fusedSiO2 was determined as a function of incident photon wave-length, �, using spectrophotometry. Measurements weremade from 190 nm���1100 nm at room temperature inlaboratory air. For transmission measurements, the spectrom-eter was operated in single beam mode. The spectrometerwas background-corrected to the transmission through air. AT versus � scan of laboratory air showed T�99.97% for ��191.13 nm �E�6.498 eV�. T dropped from 99.97% to

94.00% between 101.13 and 190 nm �E=6.537 eV�. Ab-sorption by laboratory air was therefore discounted as con-tributing to a significant decrease in T over the spectral rangeinvestigated here. For reflection measurements, the spec-trometer was calibrated with an Al mirror standard becauseAl has a reflectivity of �90% over the entire wavelengthregion of interest here.20

The expression

T = �1 − R�exp�− ��E�x� �1�

was used to calculate ��E� for film thickness x in the regionof high optical density where the effect of multiple reflec-tions from the film-substrate interface on the magnitude ofthe transmitted signal is negligible. For all architectures, thethickness of individual layers is much smaller than one-quarter wavelength of the incident radiation in that oxide.Each constituent in a bilayer is therefore exposed to the sameelectric field, and a film appears as a single dielectric slab tothe incident radiation rather than as a multilayer stack inwhich T and R at each interface need to be considered in acalculation of ��E�.

Physiochemical analysis. X-ray diffraction �XRD� datafor the nanolaminates are reported elsewhere.12,13 Data per-tinent to the present study will be reviewed in Sec. III A. Tosummarize the technique used to obtain these data, XRD wascarried out using unresolved Cu K� radiation �wavelength�x-ray=0.1542 nm�. The diffractometer was calibrated usingan unstressed Si powder standard with �111�Si at 2�=28.42° �Ref. 21� and a full width at one-half maximumintensity of 0.24°. Data were acquired over the 2�=15° –70° range at a 0.44°/min scan rate. In addition, highresolution patterns of selected diffraction peaks were ob-tained from the average of ten scans of each peak taken at therate of 0.28°/min. Precise peak position �2��hkl��, maximumintensity, and the full width at one-half the maximum inten-sity were measured from these data. The interplanar spacing,d�hkl�, of a set of planes was determined using Braggs’ law

n�x-ray = 2d�hkl� sin ��hkl�, �2�

where n is the order of the diffraction peak.A confocal Raman microscope with a He–Ne laser

�632.8 nm� excitation source and a 1 to 2 m beam diameterwas used to investigate the films’ short-range order. Weakspectra were obtained from films on fused SiO2, and so films

TABLE I. Architecture of HfO2–TiO2 nanolaminates.

FilmFilm thickness

�nm�

Nominala

HfO2 /TiO2

layerthickness

�nm�

No.HfO2 /TiO2

layers

HfO2

vol.fraction

Hfatom

fraction

5H4T 293 5/4 33/32 0.54 0.518H4T 236 8/4 20/19 0.67 0.6412H4T 220 12/4 14/13 0.74 0.72H �HfO2� 167 167/0 1/0 1.0 1.0T �TiO2� 87 0/87 0/1 0 0

aThe term “nominal” is used to designate the layer thickness of an individual constituent in the absence ofextended interfacial mixing to form an alloy or compound.

123506-2 M. C. Cisneros-Morales and C. R. Aita J. Appl. Phys. 108, 123506 �2010�

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on Au-coated laboratory glass substrates were used to obtainstronger signals. The spectral resolution of the microscopewas 0.5 cm−1 and the peak half-width was better than3 cm−1. Twenty scans from each film were collected to en-sure a good signal-to-noise ratio.

X-ray photoelectron spectroscopy �XPS� of films grownon Si �111� from which the native oxide had not been re-moved was used for speciation using a 1486.6 eV Al K�radiation source. Data was obtained at the sample surfacebefore and after sputter cleaning using a 1 keV Ar+ ion beamfor 5 min. Peak binding energy was referenced to the 1sphotoelectron peak of adventitious C at 284.6 eV.

III. RESULTS AND DISCUSSION

A. Physiochemistry

Table II records the standard 2� position and interplanarspacing of all relevant peaks22–30 discussed next. Note theinclusion of phases that are not bulk equilibrium structures atSTP. Tetragonal �t� HfO2 is a high temperaturepolymorph.9–11 o-HfO2 is a high pressure polymorph stablebetween 4 and 14.5 GPa in bulk material.11,31 It was identi-fied along with t-HfO2 as an initially nucleated phase in thinHfO2 layers grown by reactive sputter deposition at roomtemperature.15 m-HfTiO4 is a high pressure polymorph stablebetween 1 and 9 GPa in bulk material22 and recently, formedat ambient pressure and elevated temperature in thin filmsfabricated by the sol-gel method.32 Nanocrystalline rutile isan intergrowth structure formed in thin TiO2 layers sputterdeposited at room temperature.27–29 It is based on a rutilelattice containing �-PbO2-type TiO2 growth defects.

Broad XRD patterns of all films yield major peaks solelyin the 27° 2�34° range. The high resolution patterns inthis 2� range are shown in Fig. 1. The numbers at the top ofFig. 1 correspond to the standard peak assignments given inTable II. The pattern for single layer HfO2 consists of a large

primary peak assigned to �1̄11� m-HfO2 �no. 1� and a smallshoulder assigned to �111� HfO2 �no. 2�. There are possiblecontributions from �111� t-HfO2 �no. 8� and �211� o-HfO2

�no. 7�. These two HfO2 phases are the initially nucleatedphases in ultrathin layers, and transform to m-HfO2 as thefilm thickens.15 The pattern of single layer TiO2 consists ofan extremely weak, very broad peak centered at 2�27.5°,which is the XRD signature of nanomosaic TiO2.27–29

As discussed in Refs. 12 and 13, the XRD pattern of film5H4T has possible contributions from �111� o-HfTiO4 �no. 4�due to interfacial mixing by particle bombardment8 orsurfaction,33 as well as �111� t-HfO2 �no. 8� and �211�o-HfO2 �no. 7�. The XRD patterns of films 8H4T and 12H4T

TABLE II. Crystallographic parameters of relevant standards for comparison with observed XRD peaks.

Phase Lattice type Space group �no.� Assignment hkl2�

�deg�d�hkl��nm� Occurrence

HfO2 Monoclinic23 P21 /c �14� 1 1̄11 28.35 0.3148 STPa

2 111 31.65 0.2827TiO2 Tetragonal24 P42 /mnm �136� 3 110 27.46 0.3248 STP

Orthorhombic Pbcn �60��mosaic�b �intergrowth�

HfTiO4 Orthorhombic25 Pnab �60� 4 111 30.43 0.2937 STPHfTiO4 Monoclinic22 P21 /c �14� 5 1̄11 29.15c 0.3063 HPe

1̄11 29.49d 0.30296 111 32.53c 0.2752

111 32.93d 0.2719HfO2 Orthorhombicf Pbca �61� 7 211 30.94 0.2890 HPHfO2 Tetragonal26 P42 /nmc �137� 8 111 30.06 0.2988 HTg

aSTP: Standard temperature and pressure.bTetragonal rutile structure with planar defects of orthorhombic �-PbO2-type TiO2.27–29

cAt 1 GPa.dAt 9 GPa.eHP: High pressure.fCalculated from a=0.983 nm, b=0.517, c=0.496 nm.30

gHT: High temperature.

26 28 30 32 34

5H4T

678 253 1

H

8H4T

12H4T

Intensity

2 (deg)

100 CPS T

4

FIG. 1. XRD patterns of HfO2–TiO2 nanolaminates and single layer HfO2

and TiO2 films on fused SiO2 substrates. The numbers and dashed linesindicate the positions of standard peaks recorded in Table II.

123506-3 M. C. Cisneros-Morales and C. R. Aita J. Appl. Phys. 108, 123506 �2010�

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consist of a primary peak, attributed to �1̄11� m-HfO2 planes�no. 1�, and a secondary peak at higher angle. Possible con-tributions to the secondary peak come from �111� m-HfO2

�no. 2�, and also from �111� t-HfO2 �no. 8� and �211� o-HfO2

�no. 7� associated with small HfO2 crystallite size, and �111�o-HfTiO4 �no. 4� associated with interfacial mixing.

Comparison of the patterns for films 8H4T, 12H4T, andH shows the primary and secondary peaks shift in differentdirections with increasing HfO2 layer thickness. Consideringthe primary peak, application of Braggs’ law �Eq. �2�� showsthat m-HfO2 d�1̄11� expands as the HfO2 layer thickness in-creases. Previous results show that d�1̄11� deviation from thebulk standard is due to two factors. �1� The incorporation ofTi into the m-HfO2 lattice �denoted m-HfO2:Ti� causes d�1̄11�to contract.12,13 �2� Dipole-dipole repulsion at the surface ofindividual nanocrystallites causes d�1̄11� to expand.34

The shift in the secondary peak position to higher 2�,i.e., toward �111� m-HfO2 with increasing HfO2 thickness inthe 8H4T→12H4T→H film sequence occurs because of thereduction or elimination of contributions from other thanm-HfO2. Recall that t-HfO2 and o-HfO2 phases occur insmall HfO2 crystallites chiefly found in thinner HfO2

layers,15 and o-HfTiO4 is associated with interfacialmixing.13

From the data presented above, we propose thato-HfTiO4 forms closest to a metallurgical interface. �An ar-gument in Ref. 12 based on a nondisruptive phase transitionallows us to surmise that o-HfTiO4 formation occurs at anHfO2-on-TiO2 interface.� Nonmonoclinic HfO2 phases �pos-sibly doped with Ti� and m-HfO2:Ti are formed when Ti/Hfratio available for reaction at that growth interface falls be-low that required to form o-HfTiO4.

Raman shift spectra for films 5H4T, 12H4T, a 300 nm-thick HfO2 film �denoted “H”� on glass-coated Au substratesare shown in Fig. 2. The spectrum of film 8H4T, not shownhere, is similar to that of 12H4T. The broad peaks indicate

local bond disorder due in part to solid solution effects,35 i.e.,the random distribution of Ti and Hf in o-HfTiO4 andm-HfO2:Ti. All of the shifts in film H can be attributed tom-HfO2,36 as recorded in Table III�a�. All of the shifts in film5H4T can be attributed to o-HfTiO4,35 as recorded in TableIII�b�.

Comparing the spectra of film 5H4T with that of film12H4T we find: �1� peak 9 flattens to include peaks 2 and 3;�2� peak 10 shifts toward the position of peak 4; �3� peaks 5and 6 appear and grow; �4� peak 11 is diminished; �5� peak 6appears, �6� peak 12 is diminished. These observations indi-cate a change in overall short-range order from that ofo-HfTiO4 to m-HfO2 with increasing HfO2 layer thicknessand are consistent with the overall changes in nanocrystallin-ity observed by XRD �Fig. 1�.

Table IV records the binding energy for Hf 4f andTi 2p photoelectrons determined by XPS under conditionsof exposure to laboratory air and after sputter etching. In thecase of film 5H4T, similar values for o-HfTiO4 have beenreported.6,37 Note the presence of Ti in the outermost “nomi-nal” HfO2 layer in film 5H4T and its absence in the outer-most HfO2 layers of films 8H4T and 12H4T. This result isconsistent with XRD and Raman shift data that show film5H4T to be a mixed cation structure. The insensitivity of theHf 4f electron binding energy to the presence of Ti seenhere has previously been reported.37

B. Optical behavior

All films are transparent and colorless to the unaided eyein transmitted light. The experimental absorption coefficient,��E�EXP, was calculated using Eq. �1� and is graphed versusE in the far ultraviolet spectral region in Fig. 3. Figure 3�a�shows that ��E�EXP for the nanolaminates as a group liesbetween the curves for single layer TiO2 and HfO2 films.Band-tailing, that is, additional electronic states that extendthe FOAEs of the nanolaminates to lower energy than theFOAE of TiO2, is not observed. Data for the nanolaminatesare shown on an expanded scale in Fig. 3�b�.

150 300 450 600 750

76

121110

9

8

5

4

32

12H4T

Intensity(arb.u.)

Raman shift (cm-1)

H

5H4T

1

FIG. 2. Raman shift spectra for films 5H4T, 12H4T, a 300 nm-thick HfO2

film �denoted “H”� on glass-coated Au substrates. The numbers above peaksrefer to their assignments in Table III.

TABLE III. Correlation between peaks observed in films H and 5H4T �Fig.2� and the position of Raman shifts from o-HfTiO4 and m-HfO2 standards.

Observed peakShift in standard

�cm−1�

�a� Film H m-HfO2 �Ref. 36�1 113, 133, 1482 242, 2573 324, 3374 383, 3995 496, 5206 551, 5777 640, 671�b� Film 5H4T o-HfTiO4 �Ref. 35�8 112, 1259 245, 285, 31010 388, 42011 575, 585, 630, 64512 787

123506-4 M. C. Cisneros-Morales and C. R. Aita J. Appl. Phys. 108, 123506 �2010�

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We next examine the ��E�EXP versus E curves in Fig. 3in light of the role of specific functional metal-oxygen units.As mentioned in the Introduction, two extreme models thatcan be used to analyze ��E�EXP are persistence andamalgamation.14 In a persistence model, the absorption coef-ficient for the mixture, ��E�, can be decomposed into thesum of discrete components according to Vegard’s rule.38

The FOAE retains the character of each partner. For ex-ample, sputter deposited nanolaminates whose FOAEs obeya persistence model in general consist of partners that haveno bulk miscibility and very limited electronic interactionbetween constituents, such as ZrO2–Al2O3 �Ref. 39� andHfO2–Al2O3.40

The application of a persistence model to HfO2–TiO2

yields

��E� = fHfO2��E�HfO2

+ �1 − fHfO2���E�TiO2

, �3�

where ��E� for each constituent oxide is weighted by itsvolume fraction, f, in a bilayer. At the other extreme, an

amalgamated FOAE does not retain the characteristics of theindividual constituents.

Applying Eq. �3� to film 5H4T using values for fHfO2from Table I, and equating ��E�HfO2

and ��E�TiO2with ��E�H

and ��E�T, respectively, we obtain

��E�5H4T = 0.54��E�H + 0.46��E�T. �4�

Figure 4 graphs four quantities: ��E�EXP, ��E�5H4T calcu-lated from Eq. �4�, ��E�T, and ��E�H. Note that ��E�H doesnot contribute to Eqs. �3� and �4� below E5.4 eV. Weconclude from this figure that the FOAE of film 5H4T cannotbe decomposed into a weighted mixture of contributionsfrom HfO2 and TiO2 according to the persistence model.This conclusion is consistent with physiochemical data thatshow that film 5H4T consists chiefly of a titanate and is nota mixture of the two constituent oxides in which each oneretains its identity. Furthermore, it is in agreement with theanalysis of Jahn–Teller distortion in HfTiO4 by Lucovsky etal.41 These investigators reported that the transmission metal� states which form the valence and conduction band edgesare predominantly Ti-like �note the similar shape of ��E�EXP

and ��E�T curves in Fig. 4� and shifted by less than 0.5 eVfrom their values in TiO2.

If the structure of film 5H4T is formed at the interfacesof the other nanolaminates, then Eq. �3� is not appropriate formodeling ��E�EXP for films 8H4T and 12H4T. We carried outthis exercise and found that it was indeed the case. We nextdeveloped a modified persistence equation that decomposes��E� into an o-HfTiO4-rich interfacial region �denoted “IF”�

TABLE IV. Cation core electron binding energy in HfO2–TiO2 nanolaminates.

Film

Binding energy�eV�

Hf 4f7/2 Hf 4f5/2 Hf 4d5/2 Hf 4d3/2 Ti 2p3/2 Ti 2p1/2

Surface5H4T 16.4 18.1 212.9 223.6 458.3 464.28H4T 16.3 17.9 212.8 223.5 ¯ ¯

12H4T 16.3 17.9 212.7 223.5 ¯ ¯

Sputter cleaned5H4T 17.0 18.6 213.2 223.9 458.8 464.58H4T 16.5 18.2 212.9 223.6 ¯ ¯

12H4T 17.0 18.6 213.3 223.9 ¯ ¯

3.00 4.00 5.00 6.000

1

2

3

4(b)

E (eV)

(E) EXP(105cm

-1)

8H4T

12H4T

5H4T

3.00 4.00 5.00 6.000

2

4

6

8(a)

(E) EXP(105cm

-1)

H

12H4T

5H4T

8H4T

T

FIG. 3. ��E�EXP vs E for �a� all films and �b� the nanolaminates shown on anexpanded scale.

3.00 4.00 5.00 6.000

2

4

6

85H4T

(E)(10

5cm

-1)

E (eV)

EXP

Eq. 4

H

T

FIG. 4. Optical absorption in film 5H4T analyzed using a persistence modelgiven by Eq. �4�: ��E�EXP, ��E�Eq.4, ��E�H, and ��E�T vs E.

123506-5 M. C. Cisneros-Morales and C. R. Aita J. Appl. Phys. 108, 123506 �2010�

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that contains the material in each bilayer identical to film5H4T, and a region remote from an interface �denoted “XS”�that contains the excess Hf-rich material

��E� = fIF��E�IF + �1 − fIF���E�XS. �5�

fIF is calculated by dividing the thickness of a bilayer in5H4T �9 nm� by the thickness of a bilayer in 8H4T �12 nm�or 12H4T �16 nm�, yielding fIF,8H4T=0.75 and fIF,12H4T

=0.56.Three quantities are graphed versus E in Fig. 5 for

�a� film 8H4T and �b� film 12H4T: ��E�EXP, ��E�IF=fIF

��E�EXP,5H4T, and ��E�XS=��E�EXP−��E�IF. In the case ofboth films, ��E�EXP and ��E�IF overlap for E�4.45 eV forboth films. These results show that electron states associatedwith o-HfTiO4 determine the onset of the FOAE in the Hf-rich nanolaminates, and furthermore excludes an amalgam-ation model, whose earmark is a shift in the FOAE onsettoward higher E with increasing Hf atomic fraction.

Figure 6�a� shows that a linear dependence of ��E�EXP1/2

versus E is observed for the nanolaminates. This functionaldependence of ��E�EXP

1/2 on E is characteristic of an allowedindirect band gap.42 Data for TiO2 is shown for comparison.Figure 6�b� shows data for the nanolaminates normalized by�fIF

1/2�. Extrapolation of the data to ��E�=0 in either figureyields the optical band gaps of the films, EG, as recorded inFig. 6�b�. The average value of these data yields EG

=3.25�0.02 eV, a slightly higher energy than EG

=3.20 eV for TiO2. As a point of comparison, EG was foundto vary between 3.21 eV and 3.33 eV by Studenyak et al.43

and 3.42 eV by Domaradzki et al.37 for nanocomposites �notnanolaminates� of comparable Hf atomic fraction to films inthis study. Ye et al.7 obtain a band gap for nanocomposites

that is higher than that reported by the other investigators37,43

because Ye et al. neglected the contribution from states at theonset of optical absorption.

Fulton et al.44 demonstrated the localized nature of in-terband transitions at the FOAE onset in HfTiO4. A generalrule by Tauc states that interband optical transitions localizedover distances on the order of the lattice constant are rela-tively unchanged by disorder.45 We therefore propose that EG

given above is representative of the optical band gap ofo-HfTiO4 at STP.

��E�XS graphed in Fig. 5 is due to states not associatedwith o-HfTiO4. Figure 7 graphs ��E�XS for films 8H4T and12H4T and ��E�EXP for film H. The two vertical lines indi-cate optical absorption benchmarks we previously reportedfor single layer m-HfO2:16,34 the onset of intrinsic absorptionproposed to be polaronic in origin at E=5.65 eV, and theonset of O 2p→Hf 5d interband electronic transitions atE=6.24 eV.

3.00 4.00 5.00 6.000

1

2

3

4

XS

(a) 8H4T

(E)(10

5cm

-1)

IF

EXP

3.00 4.00 5.00 6.000

1

2

3

4

XS

(E)(10

5cm

-1)

E (eV)

IF

EXP

(b) 12H4T

FIG. 5. Optical absorption in �a� film 8H4T and �b� film 12H4T analyzedusing a modified persistence model given by Eq. �5�. ��E�EXP, and decom-position of ��E� into ��E�IF �interface� and ��E�XS �excess� contributions vsE.

3.20 3.60 4.00 4.400

150

300

450

600

T5H4T8H4T12H4T

(E) EXP1/2(cm-1/2)

(a)

3.20 3.60 4.00 4.400

150

300

450 (b)

EG(eV)

5H4T 3.248H4T 3.2712H4T 3.24

((E) EXP/f IF)1/2

E (eV)

FIG. 6. �a� ��E�EXP1/2 and �b� ���E�EXP / fIF�1/2 vs E for the nanolaminates.

��E�EXP1/2 for single layer TiO2 is included in �a� for comparison. The values

of EG are included in �b�.

4.00 4.50 5.00 5.50 6.00 6.500.0

0.4

0.8

1.2

1.68H4T12H4TH

(E) XS(105cm

-1)

E (eV)

FIG. 7. ��E�XS for films 8H4T and 12H4T and ��E�EXP for film H vs E. Thevertical lines indicate two absorption benchmarks in m-HfO2 �Refs. 16 and34�: the onset of intrinsic polaronic absorption at E=5.65 eV, and the onsetof O 2p→Hf 5d interband electronic transitions at E=6.24 eV. Absorp-tion between 4.45 and 5.65 eV is attributed to defect states in the nanolami-nates that are not intrinsic to o-HfTiO4 or m-HfO2.

123506-6 M. C. Cisneros-Morales and C. R. Aita J. Appl. Phys. 108, 123506 �2010�

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��E�XS between 4.45 eV�E�5.65 eV cannot be at-tributed to either absorption by o-HfTiO4 or by polaronic orinterband transitions in m-HfO2. However, absorption by de-fect states in this energy region in m-HfO2 have been thesubject of much recent study and is generally associated withO interstitials, O vacancies, or O vacancy-induced Hf bond-ing irregularity at nanocrystalline boundaries �see, for ex-ample, Refs. 41 and 46–60�. In addition, XRD data �Sec.III A� show that m-HfO2 is doped with Ti. Although the ef-fect of Ti as a dopant in m-HfO2 has not been explicitlyexplored in the literature, we deduce that it is similar to thatof a small amount of Ti in m-ZrO2. In that case, both discretefeatures and “smearing” of the edge were observed at E di-rectly below the onset of interband absorption in m-ZrO2.61

IV. SUMMARY

The optical absorption edge at its onset in sputter depos-ited HfO2–TiO2 nanolaminate films grown on unheated sub-strates was investigated. Three bilayer architectures were ex-amined, representing overall film chemistry from 0.51 to0.72 atomic fraction Hf �nominal HfO2 volume fraction from0.54 to 0.74�. The goal was to determine the dependence of��E� on �E� and to model this dependence in terms of theabsorption behavior of specific functional units within thenanolaminate. In summary:

�1� Persistence and amalgamation models were applied, rep-resenting the extremes of segregated cation and mixedcation structures, respectively, and both models werefound to be unsatisfactory.

�2� Consideration of physiochemical data led to the devel-opment of a modified persistence model for absorption.��E� was decomposed into contributions from �I� broad�9 nm-thick� interfacial regions that were chieflyo-HfTiO4, and �II� regions remote from interfaces thatcontained material based on a highly defective m-HfO2

lattice.�3� The absorption edge at its onset in all nanolaminates was

determined by short-range atomic order characteristic ofo-HfTiO4. An indirect band gap of EG=3.25�0.02 eVwas determined for this compound.

ACKNOWLEDGMENTS

This work was supported by a Catalyst Grant throughthe UWM Research Foundation from a gift from RockwellAutomation Charitable Corporation and by Advanced Ex-perimental Coatings Laboratory discretionary funds.

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