Quantum Kinetics in Transport and Optics of Semiconductors (eBook)

Hartmut Haug obtained his Ph. D. (Dr. rer. nat. 1966) in Physics at the University of Stuttgart. From 1967 to 1969 he was a faculty member at the Department of Electrical Engeneering, University of Wisconsin in Madiason. After working as a scientific staff member at the Philips Research Laboratories in Eindhoven from 1969 to 1973, he joined the Institute of Theoretical Physics of the J.W.Goethe-University Frankfurt, where he was a full professor from 1975 to 2001 and currently is an emeritus. He has been a visiting scientist at many international research centers and universities. Antti-Pekka Jauho obtained his Ph.D in Theoretical Condensed Matter Physics at Cornell University, USA, in 1982. He has been a faculty member at University of Copenhagen, Nordita (Copenhagen), and, since 1993, at Technical University of Denmark, where he has been Professor of Theoretical Nanotechnology at MIC, Department of Micro and Nanotechnology, since 2003. He is also a Distinguished Professor of the Finnish Academy since 2007, and spends half of his time at the Technical University of Helskinki, Finland.

Preface 7
Preface to the First Edition 9
Contents 14
Introduction to Kinetics and Many- Body Theory 19
1 Boltzmann Equation 20
1.1 Heuristic Derivation of the Semiclassical Boltzmann Equation 20
1.2 Approach to Equilibrium: H-Theorem 22
1.3 Linearization: Eigenfunction Expansion 25
2 Numerical Solutions of the Boltzmann Equation 28
2.1 Introduction 28
2.2 Linearized Coulomb Boltzmann Kinetics of a 2D Electron Gas 29
2.3 Ensemble Monte Carlo Simulation 37
2.4 N+ N- N+ Structure: Boltzmann Equation Analysis 46
3 Equilibrium Green Function Theory 51
3.1 Second Quantization 51
3.2 Density Matrix Equations: An Elementary Derivation of a Non- Markovian Quantum Kinetic Equation 54
3.3 Green Functions 57
3.4 Fluctuation–Dissipation Theorem 61
3.5 Perturbation Expansion of the Green Function 63
3.6 Examples of Simple Solvable Models 66
3.7 Self-Energy 68
3.8 Finite Temperatures 74
Nonequilibrium Many-Body Theory 76
4 Contour-Ordered Green Functions 77
4.1 General Remarks 77
4.2 Two Transformations 78
4.3 Analytic Continuation 83
5 Basic Quantum Kinetic Equations 88
5.1 Introductory Remarks 88
5.2 The Kadanoff–Baym Formulation 88
5.3 Keldysh Formulation 90
6 Boltzmann Limit 92
6.1 Gradient Expansion 92
6.2 Quasiparticle Approximation 94
6.3 Recovery of the Boltzmann Equation 95
7 Gauge Invariance 97
7.1 Choice of Variables 97
7.2 Gauge Invariant Quantum Kinetic Equation 99
7.3 Retarded Green Function 103
8 Quantum Distribution Functions 105
8.1 Relation to Observables, and the Wigner Function 105
8.2 Generalized Kadanoff–Baym Ansatz 106
8.3 Summary of the Main Formal Results 109
Quantum Transport in Semiconductors 111
9 Linear Transport 112
9.1 Quantum Boltzmann Equation 112
9.2 Linear Conductivity of Electron- Elastic Impurity Systems 115
9.3 Weak Localization Corrections to Electrical Conductivity 122
10 Field-Dependent Green Functions 126
10.1 Free Green Functions and Spectral Functions in an Electric Field 126
10.2 A Model for Dynamical Disorder: The Gaussian White Noise Model 132
10.3 Introduction to High-Field Transport in Semiconductors 140
10.4 Resonant-Level Model in High Electric Fields 142
10.5 Quantum Kinetic Equation for Electron– Phonon Systems 155
10.6 An Application: Collision Broadening for a Model Semiconductor 159
10.7 Spatially Inhomogeneous Systems 162
11 Optical Absorption in Intense THz Fields 168
11.1 Introductory Remarks 168
11.2 Optical Absorption as a Response Function 169
11.3 Absorption Coefficient in Terms of the Time- Dependent Dielectric Susceptibility 173
11.4 Static Electric Field 174
11.5 Harmonically Varying External Electric Fields 175
11.6 Dynamical Franz–Keldysh Effect: Excitonic Effects 182
12 Transport in Mesoscopic Semiconductor Structures 191
12.1 Introduction 191
12.2 Nonequilibrium Techniques in Mesoscopic Tunneling Structures 194
12.3 Model Hamiltonian 195
12.4 General Expression for the Current 196
12.5 Current Conservation 201
12.6 Noninteracting Resonant-Level Model 202
12.7 Density Functional Theory and Modeling of Molecular Electronics 205
12.8 Resonant Tunneling with Electron– Phonon Interactions 206
12.9 Transport in a Semiconductor Superlattice 208
12.10 Transport in Atomic Gold Wires: Signature of Coupling to Vibrational Modes 212
12.11 Transport Through a Coulomb Island 215
13 Time-Dependent Phenomena 223
13.1 Introduction 223
13.2 Applicability to Experiments 224
13.3 Mathematical Formulation 225
13.4 Average Current 227
13.5 Time-Dependent Resonant-Level Model 228
13.6 Linear-Response 237
13.7 Fluctuating Energy Levels 239
13.8 Noise 240
Theory of Ultrafast Kinetics in Laser- Excited Semiconductors 250
14 Optical Free-Carrier Interband Kinetics in Semiconductors 251
14.1 Interband Transitions in Direct- Gap Semiconductors 251
14.2 Free-Carrier Kinetics Under Laser-Pulse Excitation 259
14.3 The Optical Free-Carrier Bloch Equations 263
15 Interband Quantum Kinetics with LO- Phonon Scattering 266
15.1 Derivation of the Interband Quantum Kinetic Equations 266
15.2 The Spectral Green Functions Grµ. and Gaµ. 273
15.3 Intraband Relaxation 286
15.4 Interband-Polarization Dephasing 288
15.5 Numerical Strategies 290
16 Two-Pulse Spectroscopy 293
16.1 Introductory Remarks 293
16.2 Thin Samples 295
16.3 Low-Intensity Two-Beam Experiments 296
17 Coulomb Quantum Kinetics in a Dense Electron– Hole Plasma 307
17.1 Introduction 307
17.2 Screening in the Nonequilibrium GF Theory 308
17.3 Coulomb Quantum Kinetics 312
17.4 Plasmon-Pole Approximation for the Two- Time- Dependent Potential 315
18 The Buildup of Screening 323
18.1 Screening of the Coulomb Interaction 323
18.2 Time-Dependent Screening of Phonon-Mediated and Coulomb Interactions 326
19 Femtosecond Four-Wave Mixing with Dense Plasmas 336
19.1 Time-Resolved Four-Wave Mixing 336
19.2 Time-Integrated Four-Wave Mixing 339
19.3 Four-Wave Mixing with Coherent Control 340
References 345
Index 356