PREFACE ...................................................... xiii
INTRODUCTION .................................................. xiv
1.1 Survey of advances in semiconductor physics .............. xiv
1.2 Physics behind semiconductors ............................ xvi
1.3 Role of this book ...................................... xviii
1.4 Properties of key materials ............................. xxii
1.5 Frequently used quantities ............................. xxiii
1 STRUCTURAL PROPERTIES OF SEMICONDUCTORS .................... 1
1.1 Introduction ............................................... 1
1.2 Crystal growth ............................................. 2
1.2.1 Bulk Crystal Growth ................................. 2
1.2.2 Epitaxial Crystal Growth ............................ 3
1.2.3 Epitaxial Regrowth .................................. 9
1.3 Crystal structure ......................................... 10
1.3.1 Basic Lattice Types ................................ 12
1.3.2 Basic Crystal Structures ........................... 15
1.3.3 Notation to Denote Planes and Points in a Lattice:
Miller Indices ..................................... 16
1.3.4 Artificial Structures: Superlattices and Quantum
Wells .............................................. 21
1.3.5 Surfaces: Ideal Versus Real ........................ 22
1.3.6 Interfaces ......................................... 23
1.3.7 Defects in Semiconductors .......................... 24
1.4 Strained heterostructures ................................. 26
1.5 Strained tensor in lattice mismatched epitaxy ............. 32
1.6 Polar materials and polarization charge ................... 35
1.7 Technology challenges ..................................... 41
1.8 Problems .................................................. 41
1.9 References ................................................ 44
2 SEMICONDUCTOR BANDSTRUCTURE ............................... 46
2.1 Introduction .............................................. 46
2.2 Bloch theorem and crystal momentum ........................ 47
2.2.1 Significance of the k-vector ........................ 49
2.3 Metals, insulators, and semiconductors .................... 51
2.4 Tight binding method ...................................... 54
2.4.1 Bandstructure Arising From a Single Atomic
s-Level ............................................ 57
2.4.2 Bandstructure of Semiconductors .................... 60
2.5 Spin-orbit coupling ....................................... 62
2.5.1 Symmetry of Bandedge States ......................... 68
2.6 Orthogonalized plane wave method .......................... 70
2.7 pseudopotential method .................................... 71
2.8 к • p method .............................................. 74
2.9 Selected bandstructures ................................... 80
2.10 Mobile carriers: intrinsic carriers ....................... 84
2.11 Doping: donors and acceptors .............................. 92
2.11.1 Carriers in Doped Semiconductors ................... 95
2.11.2 Mobile Carrier Density and Carrier Freezeout ....... 96
2.11.3 Equilibrium Density of Carriers in Doped
Semiconductors ..................................... 97
2.11.4 Heavily Doped Semiconductors ....................... 99
2.12 Technology challenges .................................... 102
2.13 Problems ................................................. 104
2.14 References ............................................... 107
3 BANDSTRUCTURE MODIFICATIONS .............................. 109
3.1 Bandstructure of semiconductor alloys .................... 109
3.1.1 GaAs/AlAs Alloy ................................... 113
3.1.2 InAs/GaAs Alloy ................................... 113
3.1.3 HgTe/CdTe Alloy ................................... 116
3.1.4 Si/Ge Alloy ....................................... 117
3.1.5 InN, GaN, AlN System .............................. 117
3.2 Bandstructure modifications by heterostructures .......... 118
3.2.1 Bandstructure in Quantum Wells .................... 119
3.2.2 Valence Bandstructure in Quantum Wells ............ 123
3.3 Sub-2-dimensional systems ................................ 124
3.4 Strain and deformation potential theory .................. 129
3.4.1 Strained Quantum Wells ............................ 137
3.4.2 Self-Assembled Quantum Dots ....................... 140
3.5 Polar heterostructures ................................... 142
3.6 Technology issues ........................................ 145
3.7 Problems ................................................. 145
3.8 References ............................................... 149
4 TRANSPORT: GENERAL FORMALISM ............................. 152
4.1 Introduction ............................................. 152
4.2 Boltzmann transport equation ............................. 153
4.2.1 Diffusion-Induced Evolution of ƒk(r) .............. 155
4.2.2 External Field-Induced Evolution of ƒk(r) ......... 156
4.2.3 Scattering-Induced Evolution of ƒk(r) ............. 156
4.3 Averaging procedures ..................................... 163
4.4 Transport in a weak magnetic field: Hall mobility ........ 165
4.5 Solution of the boltzmann transport equation ............. 168
4.5.1 Iterative Approach ................................ 168
4.6 Balance equation: transport parameters ................... 169
4.7 Technology issues ........................................ 175
4.8 Problems ................................................. 176
4.9 References ............................................... 177
5 DEFECT AND CARRIER-CARRIER SCATTERING .................... 179
5.1 Ionized impurity scattering .............................. 181
5.2 Alloy scattering ......................................... 191
5.3 Neutral impurity scattering .............................. 194
5.4 Interface roughness scattering ........................... 196
5.5 Carrier-carrier scattering ............................... 198
5.5.1 Electron-Hole Scattering .......................... 198
5.5.2 Electron-Electron Scattering: Scattering of
Identical Particles ............................... 201
5.6 Auger processes and impact ionization .................... 205
5.7 Problems ................................................. 213
5.8 References ............................................... 214
6 LATTICE VIBRATIONS: PHONON SCATTERING .................... 217
6.1 Lattice vibrations ....................................... 217
6.2 Phonon statistics ........................................ 223
6.2.1 Conservation Laws in Scattering of Particles
Involving Phonons .................................. 224
6.3 Polar optical phonons .................................... 225
6.4 Phonons in heterostructures .............................. 230
6.5 Phonon scattering: general formalism ..................... 231
6.6 Limits on phonon wavevectors ............................. 237
6.6.1 Intravalley Acoustic Phonon Scattering ............ 238
6.6.2 Intravalley Optical Phonon Scattering ............. 239
6.6.3 Intervalley Phonon Scattering ..................... 240
6.7 Acoustic phonon scattering ............................... 241
6.8 Optical phonons: deformation potential scattering ........ 243
6.9 Optical phonons: polar scattering ........................ 246
6.10 Intervalley scattering ................................... 251
6.11 Electron-plasmon scattering .............................. 252
6.12 Technology issues ........................................ 253
6.13 Problems ................................................. 254
6.14 References ............................................... 257
7 VELOCITY-FIELD RELATIONS IN SEMICONDUCTORS ............... 260
7.1 Low field transport ...................................... 261
7.2 High field transport: Monte Carlo simulation ............. 264
7.2.1 Simulation of Probability Functions by Random
Numbers ........................................... 265
7.2.2 Injection of Carriers ............................. 266
7.2.3 Free Flight ....................................... 269
7.2.4 Scattering Times .................................. 269
7.2.5 Nature of the Scattering Event .................... 271
7.2.6 Energy and Momentum After Scattering .............. 272
7.3 Steady state and transient transport ..................... 288
7.3.1 GaAs, Steady State ................................ 288
7.3.2 GaAs, Transient Behavior .......................... 290
7.3.3 High Field Electron Transport in Si ............... 291
7.4 Balance equation approach to high field transport ........ 292
7.5 Impact ionization in semiconductors ...................... 295
7.6 Transport in quantum wells ............................... 296
7.7 Transport in quantum wires and dots ...................... 303
7.8 Technology issues ........................................ 305
7.9 Problems ................................................. 306
7.10 References ............................................... 308
8 COHERENCE, DISORDER, AND MESOSCOPIC SYSTEMS .............. 312
8.1 Introduction ............................................. 312
8.2 Zener-Bloch oscillations ................................. 313
8.3 Resonant tunneling ....................................... 316
8.4 Quantum interference effects ............................. 323
8.5 Disordered semiconductors ................................ 324
8.5.1 Extended and Localized States ..................... 326
8.5.2 Transport in Disordered Semiconductors ............ 328
8.6 Mesoscopic systems ....................................... 334
8.6.1 Conductance Fluctuations and Coherent Transport ... 335
8.6.2 Columb Blockade Effects ........................... 337
8.7 Tecnology issues ......................................... 340
8.8 Problems ................................................. 342
8.9 References ............................................... 343
9 OPTICAL PROPERTIES OF SEMICONDUCTORS ..................... 345
9.1 Introduction ............................................. 345
9.2 Maxwell equations and vector potential ................... 346
9.3 Electrons in an electromagnetic field .................... 351
9.4 Interband transitions .................................... 358
9.4.1 Interband Transitions in Bulk Semiconductors ...... 358
9.4.2 Interband Transitions in Quantum Wells ............ 361
9.5 Indirect interband transitions ........................... 364
9.6 Intraband transitions .................................... 370
9.6.1 Intraband Transitions in Bulk Semiconductors ...... 371
9.6.2 Intraband Transitions in Quantum Wells ............ 371
9.6.3 Interband Transitions in Quantum Dots ............. 374
9.7 Charge injection and radiative recombination ............. 376
9.7.1 Spontaneous Emission Rate ......................... 376
9.7.2 Gain in a Semiconductor ........................... 378
9.8 nonradiative recombination ............................... 381
9.8.1 Charge Injection: Nonradiative Effects ............ 381
9.8.2 Nonradiative Recombination: Auger Processes ....... 382
9.9 Semiconductor light emitters ............................. 385
9.9.1 Light Emitting Diode .............................. 386
9.9.2 Laser Diode ....................................... 387
9.10 Charge injection and вandgap renormalization ............. 395
9.11 Technology issues ........................................ 396
9.12 Problems ................................................. 396
9.13 References ............................................... 400
10 EXCITONIC EFFECTS AND MODULATION OF OPTICAL PROPERTIES ... 402
10.1 Introduction ............................................. 402
10.2 Excitonic states in semiconductors ....................... 403
10.3 Optical properties with inclusion of excitonic effects ... 408
10.4 Excitonic states in quantum wells ........................ 413
10.5 Excitonic absorption in quantum wells .................... 414
10.6 exciton broadening effects ............................... 416
10.7 Modulation of optical properties ......................... 420
10.7.1 Electro-Optic Effect .............................. 421
10.7.2 Modulation of Excitonic Transitions: Quantum
Confined Stark Effect ............................. 426
10.7.3 Optical Effects in Polar Heterostructures ......... 431
10.8 Exciton quenching ........................................ 432
10.9 Technology issues ........................................ 434
10.10 Problems ................................................ 436
10.11 References .............................................. 437
11 SEMICONDUCTORS IN MAGNETIC FIELDS ........................ 440
11.1 Semiclassical dynamics of electrons in a magnetic field .. 441
11.1.1 Semiclassical Theory of Magnetotransport .......... 447
11.2 Quantum mechanical approach to electrons in a magnetic
field .................................................... 451
11.3 Aharnov-Bohm effect ...................................... 457
11.3.1 Quantum Hall Effect ............................... 460
11.4 Magneto-optics in Landau levels .......................... 465
11.5 Excitons in magnetic field ............................... 467
11.6 Magnetic semiconductors and Spintronics .................. 469
11.6.1 Spin Selection: Optical Injection ................. 470
11.6.2 Spin Selection: Electrical Injection and Spin
Transistor ........................................ 471
11.7 Technology issues ........................................ 474
11.8 Problems ................................................. 474
11.9 References ............................................... 476
STRAIN IN SEMICONDUCTORS ...................................... 478
A.1 Elastic strain ........................................... 478
A.2 Elastic constants ........................................ 480
EXPERIMENTAL TECHNIQUES ....................................... 484
B.1 High resolution X-ray diffraction ........................ 484
B.1.1 Double Crystal Diffraction ......................... 487
B.2 Drift mobility and Hall mobility ......................... 487
B.2.1 Haynes-Schockley Experiment ........................ 488
B.2.2 Hall Effect for Carrier Density and Hall Mobility .. 490
B.3 Photoluminescence (PL) and excitation photoluminescence
(PLE) .................................................... 490
B.4 Optical pump probe experiments ........................... 494
QUANTUM MECHANICS: USEFUL CONCEPTS ............................ 499
C.1 Density of states ........................................ 499
C.2 Stationary perturbation theory ........................... 504
C.2.1 Nondegenerate Case ................................. 504
C.2.2 Degenerate Case .................................... 507
C.3 Time dependent perturbation theory and Fermi golden
rule ..................................................... 509
C.4 Bound state problem: matrix techniques ................... 511
IMPORTANT PROPERTIES OF SEMICONDUCTORS ........................ 514
INDEX ......................................................... 527
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