Nonlinear wave methods for charge transport:
Gespeichert in:
| Hauptverfasser: | , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Weinheim
Wiley-VCH
2010
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| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XI, 276 S. Ill., graph. Darst. |
| ISBN: | 9783527406951 |
Internformat
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Datensatz im Suchindex
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| adam_text |
Titel: Nonlinear wave methods for charge transport
Autor: Bonilla, Luis L.
Jahr: 2010
Contents
Preface IX
Acknowledgments XI
1 Introduction 1
1.1 Overview of Nonlinear Wave Phenomena 1
1.2 Nonlinear Waves and Electronic Transport in Materials 3
1.3 Structural Outline of the Book 7
2 Dynamical Systems, Bifurcations,
and the Chapman-Enskog Method 9
2.1 Introduction 9
2.2 Review of Dynamical Systems Concepts 9
2.2.1 Attractors 10
2.2.1.1 Steady States - Fixed Points 10
2.2.1.2 Limit Cycles 12
2.2.1.3 Chaotic Attractors 14
2.2.2 Bifurcations - Basic Definitions and Types 18
2.2.2.1 Saddle-Node Bifurcation (Local) 19
2.2.2.2 Transcritical and Pitchfork Bifurcations (Local) 20
2.2.2.3 Hopf Bifurcation (Local) 21
2.2.2.4 Degenerate Hopf and Takens-Bogdanov Bifurcations
(Local, Co-dimension 2) 23
2.2.2.5 Heteroclinic and Homodinic Connections as Examples
of Nonlocal Bifurcations 26
2.3 Analysis of the Hopf Bifurcation:
An Introduction to the Chapman-Enskog Method 28
2.3.1 Multiple Scales and Chapman-Enskog Methods 28
2.3.2 General Formulation of the Hopf Problem Using CEM 28
2.3.2.1 An Example from Physiology 32
2.3.3 Utility of the CEM for Higher Order Bifurcations 34
2.3.3.1 Degenerate Simple Eigenvalue 34
2.3.3.2 Degenerate Hopf Bifurcation 37
Nonlinear Wave Methods for Charge Transport. Luis L. Bonilla and Stephen W. Teitsworth
Copyright © 2010 WILEY-VCH Verkg GmbH Co. KGaA, Weinheim
ISBN: 978-3-527-40695-1
VI Contents
3 Excitable Media I: Continuum Systems 43
3.1 Introduction 43
3.2 Basic Excitability-the FitzHugh-Nagumo System 43
3.3 Matched Asymptotics: Excitability and Oscillations 47
3.4 The Scalar Bistable Equation;
Wave Pulses as Heteroclinic Connections 51
3.4.1 Wave Fronts Near w = u 0 and a Formula for dcjdw 54
3.4.2 Wave Fronts for a Cubic Source 56
3.4.3 Linear Stability of the Wave Fronts 57
3.5 Traveling Waves of the FitzHugh-Nagumo System 58
3.5.1 Wave Fronts 58
3.5.2 Pulses of the FHN System 59
3.5.3 Wave Trains 62
4 Excitable Media II: Discrete Systems 65
4.1 Introduction 65
4.2 The Spatially Discrete Nagumo Equation 66
4.2.1 Depinning Transition of Wave Fronts 69
4.2.2 Construction of the Wave Front Profile Near the Depinning Transition 70
4.2.3 Wave Front Velocity Far from the Depinning Transition 75
4.3 Asymptotic Construction of Pulses 76
4.4 Numerically Calculated Pulses 79
4.5 Propagation Failure 83
4.6 Pulse Generation at a Boundary 85
4.7 Concluding Remarks 87
5 Electronic Transport in Condensed Matter:
From Quantum Kinetics to Drift-diffusion Models 89
5.1 Introduction 89
5.1.1 Wigner Function for Non-interacting Particles in an External Potential 90
5.1.2 Classical Limit 91
5.1.3 Boltzmann Transport Equation and BGK Collision Model 92
5.1.4 Parabolic Scaling 94
5.1.5 Derivation of a Drift-Diffusion Equation 97
5.1.5.1 Method of Multiple Scales 97
5.1.5.2 Chapman-Enskog Method 99
5.1.5.3 Einstein Relation 100
5.2 Superlattices 100
5.2.1 Kinetic Theory Description of a Superlattice
with a Single Populated Miniband 102
5.2.1.1 Wigner Equation 103
5.2.1.2 Equivalent form of the Quantum Kinetic Equation 109
5.2.2 Derivation of Reduced Equations for n and F 110
5.2.2.1 Nondimensional Wigner Equation 111
5.2.2.2 Derivation of a Reduced System 113
5.3 Concluding Remarks 119
Contents I VII
6 Electric Field Domains in Bulk Semiconductors I: the Gunn Effect 125
6.1 Introduction 125
6.2 ./V-shaped Current-Field Characteristics and Kroemer's Model 126
6.2.1 Intervalley Transfer Mechanism 127
6.2.2 Kroemer's Drift-Diffusion Model 130
6.2.3 Boundary Conditions 131
6.2.4 Nondimensionalization 132
6.3 Stationary Solutions and Their Linear Stability in the Limit L » 1 136
6.3.1 Stationary States and Their Linear Stability under Current Bias 136
6.3.2 Construction of the Stationary Solution
and of P (J) under Voltage Bias 137
6.3.3 Linear Stability of the Stationary Solution under Voltage Bias 140
6.4 Onset of the Gunn Effect 147
6.4.1 The Linear Inhomogeneous Problem and Secular Terms 147
6.4.2 Hopf Bifurcation 148
6.4.3 Amplitude Equation for In L 3 1 152
6.5 Asymptotics of the Gunn Effect for Long Samples
and N-shaped Electron Velocity 154
6.5.1 General Formulation of Asymptotics for 6 = O(l) 155
6.5.1.1 A Single Dipole Wave 157
6.5.1.2 Several Dipole Waves 159
Shedding Waves at the Cathode 159
Overall Gunn Oscillation 160
Explicit Formulation of Asymptotics for d -*¦ 0+ 161
Asymptotics of the Gunn Effect for Long Samples
and Saturating Electron Velocity 163
A Single Dipole Wave 163
The Dipole Wave Arrives at the Anode 166
Coexistence of Two Dipole Waves 167
Explicit Formulation of Asymptotics for d ?? 0+ 168
One Pulse Far from the Contacts 168
The Pulse Reaches the Anode 169
Coexistence of Two Pulses 169
References on the ID Gunn Effect and Closing Remarks 170
Electric Field Domains in Bulk Semiconductors II:
Trap-mediated Instabilities 175
Introduction 175
Drift-Diffusion Transport Model for Trap-Mediated System 177
Nondimensional Form and the Reduced Model 180
Steady States, J-E Curves, and Steady Wave Solutions
on the Infinite Line under Current Bias 182
7.5 Nonlinear Wave Solutions in Finite Samples under Voltage Bias 188
6.5.1.3
6.5.1.4
6.5.2
6.6
6.6.1
6.6.2
6.6.3
6.6.4
6.6.4.1
6.6.4.2
6.6.4.3
6.7
7
7.1
7.2
7.3
7.4
VIII Contents
7.6 Multiple Shedding of Wavefronts in Extrinsic Material 191
7.6.1 Numerical Results of Wavefront Shedding 192
7.6.2 Asymptotic Model for Wavefront Shedding 196
8 Nonlinear Dynamics in Semiconductor Superlattices 203
8.1 Introduction 203
8.2 Spatially Discrete Model for the Doped Weakly Coupled SL 208
8.2.1 Tunneling Current Density 210
8.2.2 Boundary Conditions 212
8.2.3 Photoexcitation in an Undoped SL 213
8.2.4 Continuous Drift-Diffusion Model for a Strongly Coupled SL 213
8.3 Nondimensionalization of the Discrete Drift-Diffusion Model 214
8.4 Wave Fronts and Stationary States under Current Bias 215
8.4.1 Pinning 217
8.4.1.1 Pinning of Wave Fronts with a Single Active Well 219
8.4.1.2 Continuum Limit 223
8.4.1.3 RoleofDifrusivity 225
8.5 Static Field Domains in Voltage-Biased SLs 226
8.6 Relocation of EFDs 229
8.7 Self-Sustained Oscillations of the Current 237
8.7.1 Asymptotic Theory 238
8.7.2 Dependence of the Oscillations on Control Parameters 242
8.7.2.1 Doping Density 242
8.7.2.2 Temperature 244
8.7.2.3 Effect of Other Parameters on Self-Oscillations 246
8.8 Spin Transport in Dilute Magnetic Semiconductor Superlattices 246
9 Nonlinear Wave Methods for Related Systems in the Physical World 255
9.1 Introduction 255
9.1.1 NNDC, SNDC, and ZNDC 255
9.2 Superlattice Transport Model with Both Vertical
and Lateral Dynamics 257
9.3 Semi-Insulating GaAs 260
9.4 Multidimensional Gunn Effect 263
9.5 Fluctuations in Gunn Diodes 264
9.6 Dynamics of Dislocations in Mechanical Systems; Nanoarrays 265
Index 273 |
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| spellingShingle | Bonilla, Luis L. 1956- Teitsworth, Stephen Winthrop Nonlinear wave methods for charge transport Elektronischer Transport (DE-588)4210733-7 gnd Nichtlineare Wellenausbreitung (DE-588)4140376-9 gnd |
| subject_GND | (DE-588)4210733-7 (DE-588)4140376-9 |
| title | Nonlinear wave methods for charge transport |
| title_auth | Nonlinear wave methods for charge transport |
| title_exact_search | Nonlinear wave methods for charge transport |
| title_full | Nonlinear wave methods for charge transport Luis L. Bonilla and Stephen W. Teitsworth |
| title_fullStr | Nonlinear wave methods for charge transport Luis L. Bonilla and Stephen W. Teitsworth |
| title_full_unstemmed | Nonlinear wave methods for charge transport Luis L. Bonilla and Stephen W. Teitsworth |
| title_short | Nonlinear wave methods for charge transport |
| title_sort | nonlinear wave methods for charge transport |
| topic | Elektronischer Transport (DE-588)4210733-7 gnd Nichtlineare Wellenausbreitung (DE-588)4140376-9 gnd |
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