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Quantum Transport in Semiconductors : Physics of Solids and Liquids - David K. Ferry

Quantum Transport in Semiconductors

Physics of Solids and Liquids

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

Paperback Published: 29th February 1992
ISBN: 9780306438530
Number Of Pages: 292

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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.

Principles of Quantum Transport
Introductionp. 1
The General Problemp. 3
Quantum Dynamics and Representationsp. 4
The Density Matrixp. 6
Second Quantizationp. 8
Green's Functionsp. 10
Wigner Functionsp. 11
Kinetic Equations and Irreversibilityp. 14
The Kubo Formula and Linear Response
Linear Response Theoryp. 18
The Zero-Frequency Formp. 21
Relaxation and Green's Functionsp. 22
Some Examples for the Conductivityp. 23
The Metallic Conductivityp. 23
Localized Conductivity in the Site Approximationp. 25
Extension to Two-Time Functionsp. 28
The Quasiequilibrium Statistical Operatorp. 29
The Balance Equationsp. 32
Referencesp. 35
Path Integral Method: Use of Feynman Path Integrals in Quantum Transport Theory
Introductionp. 37
Formulation of the Problemp. 38
Conservation Laws and Constants of the Motionp. 41
Approximations for Computationsp. 45
Self-Consistency for the Approximate Influence Functionalp. 48
Carrier-Energy Distributionsp. 50
Concluding Remarksp. 52
Referencesp. 52
Quantum Transport in Solids: The Density Matrix
Introductionp. 53
Accelerated Bloch Representation: Quantum Transportp. 56
Dynamical Wannier Representation: Quantum Transportp. 58
Discussion and Summaryp. 61
Referencesp. 65
The Quantum Hall and Fractional Quantum Hall Effects
Introductionp. 67
The Quantum Hall Effectp. 68
The Measurementp. 68
Interpretation of the Measurementp. 69
Laughlin's Gedankenexperimentp. 69
Aspects of a Microscopic Theory of the Quantum Hall Effectp. 71
Edge Statesp. 75
The Fractional Quantum Hall Effectp. 77
Interpretation of the Measurement: Many-Body Gap and Fractional Chargep. 79
Zeros and Flux Quantap. 80
Laughlin's Wave Functionp. 81
Haldane's Argumentp. 83
Other Filling Fractions--the Hierarchyp. 85
Microscopic Trial Wave Functions for the Hierarchyp. 87
Higher Landau Levelsp. 87
Ring Exchangep. 89
Dictionary of Standard Results (more or less)p. 90
Hamiltonian and Energy Spectrump. 90
Gauge Choicep. 91
Conserved Momenta, Magnetic Translations, and Rotationsp. 93
The Single-Particle Green's Functionp. 95
Exactness of Laughlin's Wave Functionp. 97
The Hierarchyp. 98
Referencesp. 99
Green's Function Methods: Quantum Boltzmann Equation for Linear Transport
Introductionp. 101
Time-Dependent Green's Functionsp. 102
Six Green's Functionsp. 102
Time Loops and the S-Matrix Expansionp. 105
Dyson's Equationp. 109
Electron Self-Energiesp. 113
Quantum Boltzmann Equationp. 120
Wigner Distribution Functionp. 120
Quantum Boltzmann Equation with Electric Fieldp. 122
Solutions to the QBEp. 131
Referencesp. 140
Green's Function Methods: Nonequilibrium, High-Field Transport Antti-Pekka Jauho
Contour-Ordered Green's Functionsp. 141
Analytic Continuationp. 145
The Kadanoff-Baym Formulationp. 148
Keldysh formulationp. 149
Remarks on Transient Responsep. 149
Relation to Boltzmann Equationp. 151
Gauge-Invariant Formulationp. 154
Spectral Densitiesp. 155
Impurity Scatteringp. 155
Free Particles in a Uniform Electric Fieldp. 156
The Barker-Ferry Equation for High-Field Electron-Phonon Transportp. 157
Steady-State Transport Equation Transformed into a Numerically Tractable Formp. 160
Application to a Simple Model Semiconductorp. 162
Numerical Resultsp. 165
Referencesp. 168
Numerical Techniques for Quantum Transport and Their Inclusion in Device Modeling
Introductionp. 169
Resonant Tunnelingp. 169
Quantum Wellp. 172
Many Bodyp. 174
Conclusionsp. 177
Referencesp. 178
Wave Packet Studies of Tunneling through Time-Modulated Semiconductor Heterostructures
Introductionp. 179
Wave Packets and Tunneling Timesp. 180
Resonant Tunneling in the Presence of Inelastic Processesp. 187
Referencesp. 191
Tunneling Times in Quantum Mechanical Tunneling
Introductionp. 193
Lifetime of a Metastable State, Phase Times, and Dwell Timep. 195
The Decay of a Prepared Statep. 195
The Phase Timesp. 196
The Dwell Timep. 199
Lifetime of a Metastable Statep. 201
Clocks for Measuring Traversal Timesp. 202
Time-Modulated Barrierp. 203
The Larmor Clockp. 208
The Dynamical Image Potential for Tunneling Electronsp. 212
The Shunted Josephson Junctionp. 221
Conclusionsp. 226
Appendixesp. 229
Referencesp. 237
Wigner Function Modeling of the Resonant Tunneling Diode
Introductionp. 239
The Wigner Distribution Functionp. 244
Description of a Statistical System Using the Wigner Functionp. 244
Evaluation of Observablesp. 247
Initial Conditionsp. 248
Relationship to the Equation of Motionp. 248
Computation of the Initial Statep. 250
Numerical Techniquesp. 254
Discretizationp. 255
Stability and Convergencep. 255
Boundaries and Contactsp. 257
Tests of the Numerical Algorithmsp. 260
Self-Consistent Potentialsp. 265
Scatteringp. 265
Application to the Resonant Tunneling Diodep. 266
Structure To Be Simulatedp. 266
I-V Characteristicsp. 267
Bistabilityp. 271
Zero-Bias Anomalyp. 272
Transient Behaviorp. 276
Spacer Layersp. 279
Summaryp. 282
Referencesp. 285
Indexp. 289
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780306438530
ISBN-10: 0306438534
Series: Physics of Solids and Liquids
Audience: General
Format: Paperback
Language: English
Number Of Pages: 292
Published: 29th February 1992
Country of Publication: US
Dimensions (cm): 23.39 x 15.6  x 1.91
Weight (kg): 0.62

Earn 678 Qantas Points
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