半导体光学和输运现象 影印版

1．Some Basic Facts on Semiconductors 1

1.1 Semiconductor Heterostructures 2

1.2 Doped and Modulation-Doped Semiconductors 4

2．Interaction of Matter and Electromagnetic Fields 7

2.1 Microscopic Maxwell Equations 8

2.2 The Many-Particle Hamiltonian 10

2.3 Second Quantization for Particles 12

2.4 Quantization of Electromagnetic Fields 19

2.4.1 Coherent States 22

2 5 The Interaction Hamiltonian of Fields and Particles 24

2.6 Macroscopic Maxwell Equations and Response Functions 29

2.6.1 Direct Calculation of Induced Charges and Currents 30

2.6.2 Phenomenological Theory of Linear Response 32

2.6.3 Time-Dependent Perturbation Theory 34

2.6.4 Longitudinal Response Functions 35

2.6.5 Transverse Response Functions 40

2.7 Measurable Quantities in Optics 43

2.7.1 Linear Optical Susceptibility and Macroscopic Polarization 46

2.7.2 Absorption Coefficient 47

2.8 Problems 48

3．One-Particle Properties 51

3.1 Hartree-Fock Theory for Zero Temperature 52

3.2 Hartree-Fock Theory for Finite Temperature 55

3.3 Band Structure and Ground-State Properties 60

3.3.1 The Local-Density Approximation 60

3.3.2 Lattice Periodicity 65

3.4 The Effective-Mass Approximation 69

3.5 kp Perturbation Theory for Degenerate Bands 73

3.6 Transition Matrix Elements 77

3.7 Density of States 80

3.8 Position of the Chemical Potential 81

3.9 Problems 83

4．Uncorrelated Optical Transitions 85

4.1 The Optical Bloch Equations 86

4.2 Linear Optical Properties 91

4.3 Nonlinear Optical Properties 94

4.3.1 Perturbation Analysis in the Frequency Domain 95

4.3.2 Introducing the Bloch Vector 97

4.3.3 Perturbation Analysis in the Time Domain 103

4.3.4 Alternative Approaches 107

4.4 Semiconductor Photodetectors 109

4.4.1 The Field-Field Correlation Function and its Relation to Coherence 110

4.5 Problems 113

5．Correlated Transitions of Bloch Electrons 115

5.1 Equations of Motion in the Hartree-Fock Approximation 115

5.2 Linear Optical Properties:The Continuum of Interband Transitions 119

5.2.1 The Bethe-Salpeter Equation 122

5.2.2 The Dielectric Function 124

5.3 Solution by Continued Fractions 127

5.4 Problems 131

6．Correlated Transitions near the Band Edge 135

6.1 The Semiconductor Bloch Equations 135

6.2 Linear Optical Properties:Bound Electron-Hole Pairs 138

6.2.1 The Coulomb Green's Function 140

6.2.2 Optical Properties due to Bound Electron-Hole Pairs 144

6.2.3 Numerical Methods 149

6.2.4 Excitons in Quantum Wells 150

6.2.5 Propagation of Light:Polaritons and Cavity Polaritons 154

6.3 Nonlinear Optical Properties 159

6.3.1 The Local-Field Approximation 159

6.3.2 Numerical Solutions 166

6.4 Problems 172

7．Influence of Static Magnetic Fields 175

7.1 One-Particle Properties 176

7.1.1 Effective Mass Theory for Isolated Bands 178

7.1.2 Degenerate Bloch Electrons in a Magnetic Field 181

7.1.3 One-Particle States in Quantum Wells 186

7.2 Optical Properties of Magneto-Excitons 188

7.2.1 Evaluation of the Coulomb Matrix Element 189

7.2.2 Linear Optical Properties 191

7.2.3 Semiconductor Bloch Equations in Two and Three Dimensions 196

7.2.4 Bose Condensation of Magnetoexcitons in Two Dimensions 198

7.2.5 Nonlinear Absorption of Magnetoexcitons in Quantum Wells 201

7.3 Problems 204

8．Influence of Static Electric Fields 207

8.1 Introduction 207

8.2 Uncorrelated Optical Transitions in Uniform Electric Fields 209

8.2.1 Optical Absorption 211

8.3 Correlated Optical Transitions in Uniform Electric Fields 213

8.3.1 An Analytical Model 214

8.3.2 Representation in Parabolic Coordinates 217

8.4 Quantum Wells in Electric Fields 218

8.5 Superlattices in Electric Fields 222

8.5.1 One-Particle States in Superlattices 222

8.5.2 Semiconductor Bloch Equations 231

8.6 Problems 235

9．Biexcitons 237

9.1 Truncation of the Many-Particle Problem in Coherently Driven Systems 240

9.1.1 Decomposition of Expectation Values 241

9.2 Equations of Motion in the Coherent Limit 244

9.2.1 Variational Methods 245

9.2.2 Eigenfunction Expansion 247

9.3 Bound-State and Scattering Contributions 252

9.3.1 Separation of Bound States 252

9.3.2 Biexcitonic Scattering Contributions 254

9.4 Signatures of Biexcitonic Bound States 256

9.4.1 Nonlinear Absorption 257

9.4.2 Four-Wave Mixing 259

9.5 Problems 264

10．Nonequilibrium Green's Functions 265

10.1 Time Evolution under the Action of External Fields 266

10.2 Definitions of One-Particle Green's Functions 269

10.3 Equations of Motion of One-Particle Green's Functions 273

10.4 Screened Interaction,Polarization,and Vertex Function 278

10.5 Quantum Kinetic Equations 281

10.5.1 The Two-Time Formalism 284

10.5.2 Reduction of Propagators to Single Time Functions 288

10.6 The Self-Energy in Different Approximations 291

10.6.1 Ground-State Energy 293

10.6.2 The Screened Hartree-Fock Approximation 294

10.7 The Screened Interaction 296

10.7.1 Separation of the Intraband and the Interband Susceptibility 297

10.7.2 The Screened Interaction in Random Phase Appproximation 298

10.8 The Second-Order Born Approximation 304

10.9 Problems 310

11．The Electron-Phonon Interaction 313

11.1 The Phonon-Induced Interaction 314

11.2 The Phonon Green's Function 317

11.2.1 Eigenmodes of Lattice Vibrations 317

11.2.2 Green's Function Representation of the Density-Density Correlation Function 321

11.3 Electron-Phonon Coupling in the Long-Wavelength Limit 323

11.3.1 Coupling to Longitudinal Optical Phonons 325

11.3.2 Coupling to Acoustic Phonons 328

11.4 The Phonon Self-Energy 330

11.4.1 The Polaron 331

11.4.2 Dephasing Induced by Phonons 336

11.5 Nonequilibrium Phonons 347

11.5.1 Renormalization of Phonons 347

11.5.2 Kinetic Equation for the Phonon Green's Function 349

11.6 Problems 356

12．Scattering and Screening Processes 359

12.1 Carrier-Phonon Scattering 360

12.1.1 Luminescence Spectra 361

12.1.2 Four-Wave-Mixing Experiments 365

12.1.3 Nonequilibrium Phonons 368

12.2 Carrier-Carrier Scattering 369

12.2.1 The Limit of Quasi-Equilibrium 378

12.3 Scattering in the Presence of Bound States 382

12.3.1 Exciton-Phonon Scattering 382

12.3.2 Exciton-Exciton versus Exciton-Electron Scattering 383

12.4 Problems 385

13．The Semiconductor Laser 387

13.1 Introduction 387

13.2 Semiclassical Approach 389

13.2.1 The Semiconductor Bloch Equations in a Cavity 389

13.2.2 The Standard Rate Equations 393

13.2.3 Extended Rate Equations 396

13.2.4 Spectral Hole-Burning 402

13.3 Quantum Theory 404

13.3.1 The Photon Kinetics 404

13.3.2 The Carrier Kinetics 407

13.3.3 The Semiconductor Laser Linewidth 409

13.4 Problems 413

14．Classical Transport 415

14.1 Transport Coefficients(Without Magnetic Field) 417

14.1.1 Electrical Conductivity 419

14.1.2 Peltier Coefficient 419

14.1.3 Thermal Conductivity 420

14.2 Transport Coefficients(with Magnetic Field) 420

14.2.1 Hall Effect and Hall Resistance 422

14.3 Towards Ballistic Electrons:The Hot-Electron Transistor 424

14.4 Problems 426

15．Electric Fields in Mesoscopic Systems 429

15.1 Elementary Approach 429

15.1.1 Resonant TunnelingⅠ 431

15.1.2 Quantized Conductance 435

15.1.3 Coulomb Blockade and the SET Transistor 439

15.2 Resonant TunnelingⅡ 443

15.2.1 Boundary Conditions and Discretization 445

15.2.2 Scattering Contributions 447

15.2.3 Numerical Results 448

15.2.4 Time-Dependent Phenomena 449

15.3 Problems 450

16．Electric and Magnetic Fields in Mesoscopic Systems 453

16.1 The Integer Quantum Hall Effect 453

16.2 Edge Channels and the Landauer-Büttiker Multiprobe Formula 455

16.2.1 Edge Channels 456

16.3 Microscopic Derivation of the Landauer-Büttiker Formula 462

16.3.1 Linear Response Theory 462

16.3.2 The Multiprobe Landauer-Büttiker Formula 466

16.4 The Fractional Quantum Hall Effect 468

16.5 Magnetotransport Through Dot or Antidot-Lattices 470

16.6 Problems 475

References 477

Index 491