46230645 Electronic and Op to Electronic Properties of Semiconductor Structures

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Electronic and Optoelectronic Properties of Semiconductor Structures presents the underlying physics behind devices that drive todays technologies. The book covers important details of structural properties, bandstructure, transport, optical and magnetic properties of semiconductor structures. Effects of low-dimensional physics and strain two important driving forces in modern device technology are also discussed. In addition to conventional semiconductor physics the book discusses self-assembled structures, mesoscopic structures and the developing field of spintronics. The book utilizes carefully chosen solved examples to convey important concepts and has over 250 figures and 200 homework exercises. Real-world applications are highlighted throughout the book, stressing the links between physical principles and actual devices. Electronic and Optoelectronic Properties of Semiconductor Structures provides engineering and physics students and practitioners with complete and coherent coverage of key modern semiconductor concepts. A solutions manual and set of viewgraphs for use in lectures is available for instructors.

received his Ph.D. from the University of Chicago and is Professor of Electrical Engineering and Computer Science at the University of Michigan, Ann Arbor. He has held visiting positions at the University of California, Santa Barbara and the University of Tokyo. He is the author of over 250 technical papers and of seven previous textbooks on semiconductor technology and applied physics.

Electronic and Optoelectronic Properties of Semiconductor StructuresJasprit SinghUniversity of Michigan, Ann Arbor

Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, So Paulo Cambridge University Press The Edinburgh Building, Cambridge , United Kingdom Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521823791 Cambridge University Press 2003 This book is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2003 - - - - ---- eBook (NetLibrary) --- eBook (NetLibrary) ---- hardback --- hardback

Cambridge University Press has no responsibility for the persistence or accuracy of s for external or third-party internet websites referred to in this book, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.

CONTENTSPREFACE INTRODUCTIONI.1 I.2 I.3 SURVEY OF ADVANCES IN SEMICONDUCTORPHYSICS

xiii xiv xiv xvi xviii

PHYSICS BEHIND SEMICONDUCTORS ROLE OF THIS BOOK

1

STRUCTURAL PROPERTIES OF SEMICONDUCTORS1.1 1.2 INTRODUCTION CRYSTAL GROWTH 1.2.1 Bulk Crystal Growth 1.2.2 Epitaxial Crystal Growth 1.2.3 Epitaxial Regrowth CRYSTAL STRUCTURE 1.3.1 Basic Lattice Types 1.3.2 Basic Crystal Structures 1.3.3 Notation to Denote Planes and Points in a Lattice: Miller Indices 1.3.4 Artificial Structures: Superlattices and Quantum Wells 1.3.5 Surfaces: Ideal Versus Real 1.3.6 Interfaces 1.3.7 Defects in Semiconductors

1 1 2 2 3 9 10 12 15 16 21 22 23 24

1.3

vi

Contents

1.4 1.5 1.6 1.7 1.8 1.9

STRAINED HETEROSTRUCTURES STRAINED TENSOR IN LATTICE MISMATCHED EPITAXY POLAR MATERIALS AND POLARIZATION CHARGE TECHNOLOGY CHALLENGES PROBLEMS REFERENCES

26 32 35 41 41 44 46 46 47 49 51 54 57 60 62 68 70 71 74 80 84 92 95 96 97 99 102 104 107

2

SEMICONDUCTOR BANDSTRUCTURE2.1 2.2 2.3 2.4 INTRODUCTION BLOCH THEOREM AND CRYSTAL MOMENTUM 2.2.1 Significance of the k-vector METALS, INSULATORS, AND SEMICONDUCTORS TIGHT BINDING METHOD 2.4.1 Bandstructure Arising From a Single Atomic s-Level 2.4.2 Bandstructure of Semiconductors SPIN-ORBIT COUPLING 2.5.1 Symmetry of Bandedge States ORTHOGONALIZED PLANE WAVE METHOD PSEUDOPOTENTIAL METHOD k p METHOD SELECTED BANDSTRUCTURES MOBILE CARRIERS: INTRINSIC CARRIERS DOPING: DONORS AND ACCEPTORS 2.11.1 Carriers in Doped Semiconductors 2.11.2 Mobile Carrier Density and Carrier Freezeout 2.11.3 Equilibrium Density of Carriers in Doped Semiconductors 2.11.4 Heavily Doped Semiconductors TECHNOLOGY CHALLENGES PROBLEMS REFERENCES

2.5 2.6 2.7 2.8 2.9 2.10 2.11

2.12 2.13 2.14

Contents

vii

3

BANDSTRUCTURE MODIFICATIONS3.1 BANDSTRUCTURE OF SEMICONDUCTOR ALLOYS 3.1.1 GaAs/AlAs Alloy 3.1.2 InAs/GaAs Alloy 3.1.3 HgTe/CdTe Alloy 3.1.4 Si/Ge Alloy 3.1.5 InN, GaN, AlN System BANDSTRUCTURE MODIFICATIONS BY HETEROSTRUCTURES 3.2.1 Bandstructure in Quantum Wells 3.2.2 Valence Bandstructure in Quantum Wells SUB-2-DIMENSIONAL SYSTEMS STRAIN AND DEFORMATION POTENTIAL THEORY 3.4.1 Strained Quantum Wells 3.4.2 Self-Assembled Quantum Dots POLAR HETEROSTRUCTURES TECHNOLOGY ISSUES PROBLEMS REFERENCES

109 109 113 113 116 117 117 118 119 123 124 129 137 140 142 145 145 149 152 152 153 155 156 156 163 165 168 168 169 175 176 177

3.2

3.3 3.4

3.5 3.6 3.7 3.8

4

TRANSPORT: GENERAL FORMALISM4.1 4.2 INTRODUCTION BOLTZMANN TRANSPORT EQUATION 4.2.1 Diffusion-Induced Evolution of fk(r) 4.2.2 External Field-Induced Evolution of fk(r) 4.2.3 Scattering-Induced Evolution of fk(r) AVERAGING PROCEDURES TRANSPORT IN A WEAK MAGNETIC FIELD: HALL MOBILITY SOLUTION OF THE BOLTZMANN TRANSPORT EQUATION 4.5.1 Iterative Approach BALANCE EQUATION: TRANSPORT PARAMETERS TECHNOLOGY ISSUES PROBLEMS REFERENCES

4.3 4.4 4.5 4.6 4.7 4.8 4.9

viii

Contents

5

DEFECT AND CARRIERCARRIER SCATTERING5.1 5.2 5.3 5.4 5.5 IONIZED IMPURITY SCATTERING ALLOY SCATTERING NEUTRAL IMPURITY SCATTERING INTERFACE ROUGHNESS SCATTERING CARRIERCARRIER SCATTERING 5.5.1 ElectronHole Scattering 5.5.2 ElectronElectron Scattering: Scattering of Identical Particles AUGER PROCESSES AND IMPACT IONIZATION PROBLEMS REFERENCES

179 181 191 194 196 198 198 201

5.6 5.7 5.8

205 213 214

6

LATTICE VIBRATIONS: PHONON SCATTERING6.1 6.2 LATTICE VIBRATIONS PHONON STATISTICS 6.2.1 Conservation Laws in Scattering of Particles Involving Phonons POLAR OPTICAL PHONONS PHONONS IN HETEROSTRUCTURES PHONON SCATTERING: GENERAL FORMALISM LIMITS ON PHONON WAVEVECTORS 6.6.1 Intravalley Acoustic Phonon Scattering 6.6.2 Intravalley Optical Phonon Scattering 6.6.3 Intervalley Phonon Scattering ACOUSTIC PHONON SCATTERING OPTICAL PHONONS: DEFORMATION POTENTIAL SCATTERING OPTICAL PHONONS: POLAR SCATTERING INTERVALLEY SCATTERING

217 217 223 224 225 230 231 237 238 239 240 241 243 246 251

6.3 6.4 6.5 6.6

6.7 6.8 6.9 6.10

Contents

ix

6.11 6.12 6.13 6.14

ELECTRONPLASMON SCATTERING TECHNOLOGY ISSUES PROBLEMS REFERENCES

252 253 254 257

7

VELOCITY-FIELD RELATIONS IN SEMICONDUCTORS7.1 7.2 LOW FIELD TRANSPORT HIGH FIELD TRANSPORT: MONTE CARLO SIMULATION 7.2.1 Simulation of Probability Functions by Random Numbers 7.2.2 Injection of Carriers 7.2.3 Free Flight 7.2.4 Scattering Times 7.2.5 Nature of the Scattering Event 7.2.6 Energy and Momentum After Scattering STEADY STATE AND TRANSIENT TRANSPORT 7.3.1 GaAs, Steady State 7.3.2 GaAs, Transient Behavior 7.3.3 High Field Electron Transport in Si BALANCE EQUATION APPROACH TO HIGH FIELD TRANSPORT IMPACT IONIZATION IN SEMICONDUCTORS TRANSPORT IN QUANTUM WELLS TRANSPORT IN QUANTUM WIRES AND DOTS TECHNOLOGY ISSUES PROBLEMS REFERENCES

260 261 264 265 266 269 269 271 272 288 288 290 291 292 295 296 303 305 306 308

7.3

7.4 7.5 7.6 7.7 7.8 7.9 7.10

8

COHERENCE, DISORDER, AND MESOSCOPIC SYSTEMS8.1 8.2 8.3 INTRODUCTION ZENER-BLOCH OSCILLATIONS RESONANT TUNNELING

312 312 313 316

x

Contents

8.4 8.5

QUANTUM INTERFERENCE EFFECTS DISORDERED SEMICONDUCTORS 8.5.1 Extended and Localized States 8.5.2 Transport in Disordered Semiconductors MESOSCOPIC SYSTEMS 8.6.1 Conductance Fluctuations and Coherent Transport 8.6.2 Columb Blockade Effects TECNOLOGY ISSUES PROBLEMS REFERENCES

323 324 326 328 334 335 337 340 342 343

8.6

8.7 8.8 8.9

9

OPTICAL PROPERTIES OF SEMICONDUCTORS9.1 9.2 9.3 9.4 INTRODUCTION MAXWELL EQUATIONS AND VECTOR POTENTIAL ELECTRONS IN AN ELECTROMAGNETIC FIELD INTERBAND TRANSITIONS 9.4.1 Interband Transitions in Bulk Semiconductors 9.4.2 Interband Transitions in Quantum Wells INDIRECT INTERBAND TRANSITIONS INTRABAND TRANSITIONS 9.6.1 Intraband Transitions in Bulk Semiconductors 9.6.2 Intraband Transitions in Quantum Wells 9.6.3 Interband Transitions in Quantum Dots CHARGE INJECTION AND RADIATIVE RECOMBINATION 9.7.1 Spontaneous Emission Rate 9.7.2 Gain in a Semiconductor NONRADIATIVE RECOMBINATION 9.8.1 Charge Injection: Nonradiative Effects 9.8.2 Nonradiative Recombination: Auger Processes SEMICONDUCTOR LIGHT EMITTERS 9.9.1 Light Emitting Diode 9.9.2 Laser Diode CHARGE INJECTION AND BANDGAP RENORMALIZATION TECHNOLOGY ISSUES

345 345 346 351 358 358 361 364 370 371 371 374 376 376 378 381 381 382 385 386 387 395 396

9.5 9.6

9.7

9.8

9.9

9.10 9.11

Contents

xi

9.12 9.13

PROBLEMS REFERENCES

396 400

10

EXCITONIC EFFECTS AND MODULATION OF OPTICAL PROPERTIES10.1 10.2 10.3 10.4 10.5 10.6 10.7 INTRODUCTION EXCITONIC STATES IN SEMICONDUCTORS OPTICAL PROPERTIES WITH INCLUSION OF EXCITONIC EFFECTS EXCITONIC STATES IN QUANTUM WELLS EXCITONIC ABSORPTION IN QUANTUM WELLS EXCITON BROADENING EFFECTS MODULATION OF OPTICAL PROPERTIES 10.7.1 ElectroOptic Effect 10.7.2 Modulation of Excitonic Transitions: Quantum Confined Stark Effect 10.7.3 Optical Effects in Polar Heterostructures EXCITON QUENCHING TECHNOLOGY ISSUES

40