半导体多层膜中的电子和声子 : 第2版

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

纳米技术的发展催生了只有几个分子厚度的半导体结构，这给该结构中电子和声子的物理带来了重要影响。《半导体多层膜中的电子和声子(第二版)（英文影印版）》阐述了量子阱和量子线中的电子和声子囚禁对半导体特性的影响。第二版中加入了电子自旋弛豫、六角纤锌晶格、氮化物结构和太赫兹源等方面的内容。本书独特之处在于对光学声子的微观理论的阐述，其由囚禁引起的径向性质改变以及与电子的相互作用等。
　　本书适合半导体物理领域的研究者和研究生阅读。

《半导体多层膜中的电子和声子(第二版)（英文影印版）》是影印版英文专著，原书由剑桥大学出版社于2009年出版。半导体科学与技术是当代最重要的研究领域。因之催生的各种应用数不胜数。半导体多层膜则是纳米技术发展的产物，具有重要的科研价值和巨大的应用潜力。本书作为研究其中电子和声子的学术专著，一定会给这一领域的研究者以很大的收获。