Contents
Part 1 Introduction to Kinetics and Many-Body Theory
1. Boltzmann Equation
1.1 Heuristic Derivation
of the Semiclassical Boltzmann Equation
1.2 Approach to Equilibrium, H-Theorem
1.3 Linearization, Eigenfunction Expansion
2. Numerical Solutions of the Boltzmann Equation
2.1 Linearized Coulomb Boltzmann Kinetics
of a 2D Electron Gas
2.2 Ensemble Monte Carlo Simulation
2.2.1 General Theory
2.2.2 Simulation of the Relaxation Kinetics
of a 2D Electron Gas
2.3 N+N-N+-Structure: Boltzmann Equation Analysis
3. Equilibrium Green Function Theory
3.1 Second Quantization
3.2 Green Functions
3.2.1 Examples of Measurable Quantities
3.3 Fluctuation-Dissipation Theorem
3.4 Perturbation Expansion of the Green Function
3.5 Examples of Simple Solvable Models
3.5.1 Free-Particle Green Function
3.5.2 Resonant-Level Model
3.6 Self-Energy
3.6.1 Electron-Phonon Interaction
3.6.2 Elastic Impurity System; Impurity Averaging
3.7 Finite Temperatures
Part 11 Nonequilibrium Many-Body Theory
4. Contour Ordered Green Functions
4.1 General Remarks
4.2 Two Transformations
4.3 Analytic Continuation
5 Basic Quantum Kinetic Equations
5.1 The Kadanoff-Baym Formulation
5.2 The Keldysh Formulation
6. Boltzmann Limit
6.1 Gradient Expansion
6.2 Quasiparticle Approximation
6.3 Recovery of the Boltzmann Equation
7 Gauge Invariance
7.1 Choice of Variables
7.2 Gauge Invariant Quantum Kinetic Equation
7.2.1 Driving Term
7.2.2 Collision Term
7.3 Retarded Green Function
8. Quantum Distribution Functions
8.1 Relation to Observables, and the Wigner Function
8.2 Generalized Kadanoff-Baym Ansatz
8.3 Summary of the Main Formal Results
Part III Quantum Transport in Semiconductors
9. Linear Transport
9.1 Quantum Boltzmann Equation
9.2 Linear Conductivity of Electron-Elastic Impurity Systems
9.2.1 Kubo Formula
9.2.2 Quantum Kinetic Formulation
9.3 Weak Localization Corrections to Electric Conductivity
10. A Model for Dynamical Disorder:
The Gaussian White Noise Model
10.1 Introduction
10.2 Determination of the Retarded Green Function
10.3 Kinetic Equation for the GWN
10.4 Other Transport Properties
11. Quantum High-Field Transport in Semiconductors
11.1 Introduction
11.2 Free Green Functions and Spectral Functions
in an Electric Field
11.3 Resonant-Level Model in High Electric Fields
11.3.1 Introduction
11.3.2 Retarded Green Function: Single Impurity Problem
11.3.3 Retarded Green Function: Dilute Concentration
of Impurities
11.3.4 Analytic Continuation
11.3.5 Quantum Kinetic Equation
11.4 Quantum Kinetic Equation for Electron-Phonon Systems
11.5 An Application:
Collision Broadening for a Model Semiconductor
11.5.1 Analytical Considerations
11.5.2 A Simple Model:
Optical Phonon Emission at T = 0
11.6 Spatially Inhomogeneous Systems
12. Transport in Mesoscopic Semiconductor Structures
12.1 Introduction
12.2 Nonequilibrium Techniques
in Mesoscopic Tunneling Structures
12.3 Model Hamiltonian
12.4 General Expression for the Current
12.5 Non-Interacting Resonant-Level Model
12.6 Resonant Tunneling with Electron-Phonon Interactions
12.7 Transport Through a Coulomb Island
13. Time-Dependent Phenomena
13.1 Introduction
13.2 Applicability to Experiments
13.3 Mathematical Formulation
13.4 Average Current
13.5 Time-Dependent Resonant-Level Model
13.5.1 Response to Harmonic Modulation
13.5.2 Response to Step-Like Modulation
13.6 Linear-Response
13.7 Fluctuating Energy Levels
Part IV Theory of Ultrafast Kinetics
in Laser-Excited Semiconductors
14. Optical Free-Carrier Interband Kinetics
in Semiconductors
14.1 Interband Transitions in Direct-Gap Semiconductors
14.2 Free-Carrier Kinetics Under Laser-Pulse Excitation
14.3 The Optical Free-Carrier Bloch Equations
15. Interband Quantum Kinetics
with LO-Phonon Scattering
15.1 Derivation of the Interband Quantum Kinetic Equations
15.2 Approximations for the Green Functions G and G
15.3 Intraband Quantum Kinetics
15.4 Linear Polarization Kinetics, Phonon Sidebands
15.5 Coupled Interband Kinetic Equations
in Diagonal Approximation
15.6 Numerical Studies
16. Exciton Quantum Kinetics in Polar Semiconductors
16.1 Interband Quantum Kinetic Equations
with Excitonic Effects
16.2 Quantum Beats and Urbach Tail
16.2.1 LO-Phonon Quantum Beats
16.2.2 Urbach Tail Absorption
16.3 Excitonic Optical Stark Effect
16.4 Coupled Quantum Kinetics of Electrons and Phonons
16.5 Quantum Coherence of the Green Functions
17. Two-Pulse Excitation
17.1 Calculation of the Photon Echo
17.2 Calculation of the Four-Wave Mixing Signal
17.3 Comparison with Four-Wave Mixing Experiments
18. Coulomb Quantum Kinetics in a Dense Electron Gas
18.1 Introduction
18.2 Derivation of a Closed Quantum Kinetic Description
18.3 Simplifying Approximations
18.3.1 Initial Time Regime Without Screening
and Energy Conservation
18.3.2 Time-Dependent Plasmon Pole Approximation
18.3.3 Instantaneous Static Potential Approximation
19. Interband Coulomb Quantum Kinetics,
Optical Dephasing
19.1 Interband Quantum Kinetic Equations
with Coulomb Interaction
19.2 Early Stage of the Coulomb Quantum Kinetics
19.3 Quasi-Classical Theory of the Polarization Decay
20. The Build-Up of Screening
After Ultra-Short Pulse Excitation
20.1 The Model
20.2 Numerical Results
References
Subject Index
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