Quantum Transport in Semiconductors

By: David Ferry (Editor), Carlo Jacoboni (Editor)

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Hardcover | 29 February 1992

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316 Pages

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The majority of the chapters in this volume represent a series of lectures. that were given at a workshop on quantum transport in ultrasmall electron devices, held at San Miniato, Italy, in March 1987. These have, of course, been extended and updated during the period that has elapsed since the workshop was held, and have been supplemented with additional chapters devoted to the tunneling process in semiconductor quantum-well structures. The aim of this work is to review and present the current understanding in nonequilibrium quantum transport appropriate to semiconductors. Gen erally, the field of interest can be categorized as that appropriate to inhomogeneous transport in strong applied fields. These fields are most likely to be strongly varying in both space and time. Most of the literature on quantum transport in semiconductors (or in metallic systems, for that matter) is restricted to the equilibrium approach, in which spectral densities are maintained as semiclassical energy conserving delta functions, or perhaps incorporating some form of collision broadening through a Lorentzian shape, and the distribution functions are kept in the equilibrium Fermi-Dirac form. The most familiar field of nonequilibrium transport, at least for the semiconductor world, is that of hot carriers in semiconductors.

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Non-Fiction Science Physics Electricity Engineering & Technology Other Technologies & Applied Sciences Applied Optics Mechanical Engineering & Materials Materials Science Materials & States of Matter Condensed Matter Physics including Liquid State & Solid State Physics Chemistry

Analytical Chemistry Spectrum Analysis Crystallography Energy Technology & Engineering Electrical Engineering

Principles of Quantum Transport
Introduction	p. 1
The General Problem	p. 3
Quantum Dynamics and Representations	p. 4
The Density Matrix	p. 6
Second Quantization	p. 8
Green's Functions	p. 10
Wigner Functions	p. 11
Kinetic Equations and Irreversibility	p. 14
The Kubo Formula and Linear Response
Linear Response Theory	p. 18
The Zero-Frequency Form	p. 21
Relaxation and Green's Functions	p. 22
Some Examples for the Conductivity	p. 23
The Metallic Conductivity	p. 23
Localized Conductivity in the Site Approximation	p. 25
Extension to Two-Time Functions	p. 28
The Quasiequilibrium Statistical Operator	p. 29
The Balance Equations	p. 32
References	p. 35
Path Integral Method: Use of Feynman Path Integrals in Quantum Transport Theory
Introduction	p. 37
Formulation of the Problem	p. 38
Conservation Laws and Constants of the Motion	p. 41
Approximations for Computations	p. 45
Self-Consistency for the Approximate Influence Functional	p. 48
Carrier-Energy Distributions	p. 50
Concluding Remarks	p. 52
References	p. 52
Quantum Transport in Solids: The Density Matrix
Introduction	p. 53
Accelerated Bloch Representation: Quantum Transport	p. 56
Dynamical Wannier Representation: Quantum Transport	p. 58
Discussion and Summary	p. 61
References	p. 65
The Quantum Hall and Fractional Quantum Hall Effects
Introduction	p. 67
The Quantum Hall Effect	p. 68
The Measurement	p. 68
Interpretation of the Measurement	p. 69
Laughlin's Gedankenexperiment	p. 69
Aspects of a Microscopic Theory of the Quantum Hall Effect	p. 71
Edge States	p. 75
The Fractional Quantum Hall Effect	p. 77
Interpretation of the Measurement: Many-Body Gap and Fractional Charge	p. 79
Zeros and Flux Quanta	p. 80
Laughlin's Wave Function	p. 81
Haldane's Argument	p. 83
Other Filling Fractions--the Hierarchy	p. 85
Microscopic Trial Wave Functions for the Hierarchy	p. 87
Higher Landau Levels	p. 87
Ring Exchange	p. 89
Dictionary of Standard Results (more or less)	p. 90
Hamiltonian and Energy Spectrum	p. 90
Gauge Choice	p. 91
Conserved Momenta, Magnetic Translations, and Rotations	p. 93
The Single-Particle Green's Function	p. 95
Exactness of Laughlin's Wave Function	p. 97
The Hierarchy	p. 98
References	p. 99
Green's Function Methods: Quantum Boltzmann Equation for Linear Transport
Introduction	p. 101
Time-Dependent Green's Functions	p. 102
Six Green's Functions	p. 102
Time Loops and the S-Matrix Expansion	p. 105
Dyson's Equation	p. 109
Electron Self-Energies	p. 113
Quantum Boltzmann Equation	p. 120
Wigner Distribution Function	p. 120
Quantum Boltzmann Equation with Electric Field	p. 122
Solutions to the QBE	p. 131
References	p. 140
Green's Function Methods: Nonequilibrium, High-Field Transport Antti-Pekka Jauho
Contour-Ordered Green's Functions	p. 141
Analytic Continuation	p. 145
The Kadanoff-Baym Formulation	p. 148
Keldysh formulation	p. 149
Remarks on Transient Response	p. 149
Relation to Boltzmann Equation	p. 151
Gauge-Invariant Formulation	p. 154
Spectral Densities	p. 155
Impurity Scattering	p. 155
Free Particles in a Uniform Electric Field	p. 156
The Barker-Ferry Equation for High-Field Electron-Phonon Transport	p. 157
Steady-State Transport Equation Transformed into a Numerically Tractable Form	p. 160
Application to a Simple Model Semiconductor	p. 162
Numerical Results	p. 165
References	p. 168
Numerical Techniques for Quantum Transport and Their Inclusion in Device Modeling
Introduction	p. 169
Resonant Tunneling	p. 169
Quantum Well	p. 172
Many Body	p. 174
Conclusions	p. 177
References	p. 178
Wave Packet Studies of Tunneling through Time-Modulated Semiconductor Heterostructures
Introduction	p. 179
Wave Packets and Tunneling Times	p. 180
Resonant Tunneling in the Presence of Inelastic Processes	p. 187
References	p. 191
Tunneling Times in Quantum Mechanical Tunneling
Introduction	p. 193
Lifetime of a Metastable State, Phase Times, and Dwell Time	p. 195
The Decay of a Prepared State	p. 195
The Phase Times	p. 196
The Dwell Time	p. 199
Lifetime of a Metastable State	p. 201
Clocks for Measuring Traversal Times	p. 202
Time-Modulated Barrier	p. 203
The Larmor Clock	p. 208
The Dynamical Image Potential for Tunneling Electrons	p. 212
The Shunted Josephson Junction	p. 221
Conclusions	p. 226
Appendixes	p. 229
References	p. 237
Wigner Function Modeling of the Resonant Tunneling Diode
Introduction	p. 239
The Wigner Distribution Function	p. 244
Description of a Statistical System Using the Wigner Function	p. 244
Evaluation of Observables	p. 247
Initial Conditions	p. 248
Relationship to the Equation of Motion	p. 248
Computation of the Initial State	p. 250
Numerical Techniques	p. 254
Discretization	p. 255
Stability and Convergence	p. 255
Boundaries and Contacts	p. 257
Tests of the Numerical Algorithms	p. 260
Self-Consistent Potentials	p. 265
Scattering	p. 265
Application to the Resonant Tunneling Diode	p. 266
Structure To Be Simulated	p. 266
I-V Characteristics	p. 267
Bistability	p. 271
Zero-Bias Anomaly	p. 272
Transient Behavior	p. 276
Spacer Layers	p. 279
Summary	p. 282
References	p. 285
Index	p. 289
Table of Contents provided by Blackwell. All Rights Reserved.

Quantum Transport in Semiconductors

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