Preface page xi
Introduction 1
1 Simple Models of the Electron-Phonon Interaction 9
1.1 General Remarks 9
1.2 Early Models of Optical-Phonon Confinement 10
1.2.1 The Dielectric-Continuum (DC) Model 11
1.2.2 The Hydrodynamic (HD) Model 16
1.2.3 The Reformulated-Mode (RM) Model 18
1.2.4 Hybrid Modes 21
1.3 The Interaction of Electrons with Bulk Phonons 22
1.3.1 The Scattering Rate 22
1.3.2 The Coupling Coefficients 24
1.3.3 The Overlap Integral in 2D 27
1.3.4 The 2D Rates 29
1.3.5 The 1D Rates 34 Preface page xi
Introduction 1
1 Simple Models of the Electron-Phonon Interaction 9
1.1 General Remarks 9
1.2 Early Models of Optical-Phonon Confinement 10
1.2.1 The Dielectric-Continuum (DC) Model 11
1.2.2 The Hydrodynamic (HD) Model 16
1.2.3 The Reformulated-Mode (RM) Model 18
1.2.4 Hybrid Modes 21
1.3 The Interaction of Electrons with Bulk Phonons 22
1.3.1 The Scattering Rate 22
1.3.2 The Coupling Coefficients 24
1.3.3 The Overlap Integral in 2D 27
1.3.4 The 2D Rates 29
1.3.5 The 1D Rates 34
1.4 The Interaction with Model Confined Phonons 35
2 Quantum Confinement of Carriers 42
2.1 The Effective-Mass Equation 42
2.1.1 Introduction 42
2.1.2 The Envelope-Function Equation 44
2.1.3 The Local Approximation 46
2.1.4 The Effective-Mass Approximation 48
2.2 The Confinement of Electrons 49
2.3 The Confinement of Holes 53
2.4 Angular Dependence of Matrix Elements 62
2.5 Non-Parabolicity 64
2.6 Band-Mixing 66
3 Quasi-Continuum Theory of Lattice Vibrations 67
3.1 Introduction 67
3.2 Linear-Chain Models 69
3.2.1 Bulk Solutions 69
3.2.2 Interface between Nearly Matched Media 71
3.2.3 Interface between Mismatched Media 75
3.2.4 Free Surface 75
3.2.5 Summary 76
3.3 The Envelope Function 76
3.4 Non-Local Operators 78
3.5 Acoustic and Optical Modes 80
3.6 Boundary Conditions 83
3.7 Interface Model 85
3.8 Summary 91
Appendix: The Local Approximation 94
4 Bulk Vibrational Modes in an Isotropic Continuum 97
4.1 Elasticity Theory 97
4.2 Polar Material 104
4.3 Polar Optical Waves 105
4.4 Energy Density 107
4.5 Two-Mode Alloys 114
5 Optical Modes in a Quantum Well 119
5.1 Non-Polar Material 119
5.2 Polar Material 122
5.3 Barrier Modes: Optical-Phonon Tunnelling 127
5.4 The Effect of Dispersion 137
5.5 Quantization of Hybrid Modes 137
6 Superlattice Modes 141
6.1 Superlattice Hybrids 141
6.2 Superlattice Dispersion 144
6.3 General Features 148
6.4 Interface Polaritons in a Superlattice 154
6.5 The Role of LO and TO Dispersion 155
6.6 Acoustic Phonons 157
7 Optical Modes in Various Structures 160
7.1 Introduction 160
7.2 Monolayers 160
7.2.1 Single Monolayer 162
7.2.2 Double Monolayer 166
7.3 Metal-Semiconductor Structures 170
7.4 Slab Modes 173
7.5 Quantum Wires 176
7.6 Quantum Dots 181
8 Electron-Optical Phonon Interaction in a Quantum Well 182
8.1 Introduction 182
8.2 Scattering Rate 183
8.3 Scattering Potentials for Hybrids 184
8.4 Matrix Elements for an Indefinitely Deep Well 185
8.5 Scattering Rates for Hybrids 187
8.6 Threshold Rates 189
8.7 Scattering by Barrier LO Modes 192
8.8 Scattering by Interface Polaritons 194
8.9 Summary of Threshold Rates in an Indefinitely Deep Well 197
8.9.1 Intrasubband Rates 197
8.9.2 Intersubband Rates 198
8.10 Comparison with Simple Models 199
8.11 The Interaction in a Superlattice 202
8.12 The Interaction in an Alloy 205
8.13 Phonon Resonances 206
8.14 Quantum Wire 208
8.15 The Sum-Rule 209
Appendix: Scalar and Vector Potentials 212
9 Other Scattering Mechanisms 217
9.1 Charged-Impurity Scattering 217
9.1.1 Introduction 217
9.1.2 The Coulomb Scattering Rate 220
9.1.3 Scattering by Single Charges 221
9.1.4 Scattering by Fluctuations in a Donor Array 223
9.1.5 An Example 225
9.2 Interface-Roughness Scattering 227
9.3 Alloy Scattering 230
9.4 Electron-Electron Scattering 231
9.4.1 Basic Formulae for the 2D Case 231
9.4.2 Discussion 234
9.4.3 Electron-Hole Scattering 236
9.5 Phonon Scattering 236
9.5.1 Phonon-Phonon Processes 236
9.5.2 Charged-Impurity Scattering 239
9.5.3 Alloy Fluctuations and Neutral Impurities 240
9.5.4 Interface-Roughness Scattering 241
10 Quantum Screening 244
10.1 Introduction 244
10.2 The Density Matrix 245
10.3 The Dielectric Function 248
10.4 The 3D Dielectric Function 250
10.5 The Quasi-2D Dielectric Function 252
10.6 The Quasi-1D Dielectric Function 259
10.7 Lattice Screening 265
10.8 Image Charges 266
10.9 The Electron-Plasma/Coupled-Mode Interaction 268
10.10 Discussion 272
11 The Electron Distribution Function 275
11.1 The Boltzmann Equation 275
11.2 Net Scattering Rate by Bulk Polar-Optical Phonons 276
11.3 Optical Excitation 278
11.4 Transport 281
11.4.1 The 3D Case 284
11.4.2 The 2D Case 286
11.4.3 The 1D Case 288
11.4.4 Discussion 289
11.5 Acoustic-Phonon Scattering 290
11.5.1 The 3D Case 291
11.5.2 The 2D Case 293
11.5.3 The 1D Case 294
11.5.4 Piezoelectric Scattering 296
11.6 Discussion 296
11.7 Acoustic-Phonon Scattering in a Degenerate Gas 300
11.7.1 Introduction 300
11.7.2 Energy- and Momentum-Relaxation Rates 300
11.7.3 Low-Temperature Approximation 304
11.7.4 The Electron Temperature 306
11.7.5 The High-Temperature Approximation 306
12 Spin Relaxation 311
12.1 Introduction 311
12.2 The Elliot-Yafet process 313
12.3 The D'yakonov-Perel Process 317
12.3.1 The DP Mechanism in a Quantum Well 322
12.3.2 Quantum Wires 324
12.4 The Rashba Mechanism 326
12.5 The Bir-Aranov-Pikus Mechanism 326
12.6 Hyperfine Coupling 329
Appendix 1 332
Appendix 2 333
Appendix 3 335
13 Electrons and Phonons in the Wurtzite Lattice 336
13.1 The Wurtzite Lattice 336
13.2 Energy Band Structure 338
13.3 Eigenfunctions 340
13.4 Optical Phonons 343
13.5 Spontaneous Polarization 346
Appendix 1 Symmetry 347
14 Nitride Heterostructures 349
14.1 Single Heterostructures 349
14.2 Piezoelectric Polarization 351
14.3 Polarization Model of Passivated HFET with Field Plate 354
14.4 The Polarization Superlattice 358
14.4.1 Strain 358
14.4.2 Deformation Potentials 359
14.4.3 Fields 359
14.5 The AlN/GaN Superlattice 360
14.6 The Quantum-Cascade Laser 366
Appendix Airy Functions 368
15 Terahertz Sources 369
15.1 Introduction 369
15.2 Bloch Oscillations 370
15.3 Negative-Mass NDR 373
15.3.1 The Esaki-Tsu Approach 375
15.3.2 Lucky Drift 376
15.3.3 The Hydrodynamic Model 377
15.4 Ballistic Transport 378
15.4.1 Optical-Phonon-Determined Transit-Time Oscillations 379
15.4.2 Transit-Time Oscillations in a Short Diode 379
15.4.3 Negative-Mass NDR 380
15.4.4 Bloch Oscillations 383
15.5 Femtosecond Generators 387
15.5.1 Optical Non-Linear Rectification. 387
15.5.2 Surge Current 388
15.5.3 Dember Diffusion 388
15.5.4 Coherent Phonons 389
15.5.5 Photoconductive Switch 389
15.6 CW Generators 389
15.6.1 Photomixing 389
15.6.2 Quantum-Cascade Lasers 390
Appendix 392
Appendix 1 The Polar-Optical Momentum-Relaxation Time in a
2D Degenerate Gas 393
Appendix 2 Electron/Polar Optical Phonon Scattering Rates in
a Spherical Cosine Band 395
References 397
Index 406