Lecture Notes in Physics

By: Ansgar JÃ¼ngel

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Hardcover | 17 March 2009

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336 Pages

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23.5 x 15.88 x 1.27

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Semiconductor devices are ubiquitous in the modern computer and telecommunications industry. A precise knowledge of the transport equations for electron flow in semiconductors when a voltage is applied is therefore of paramount importance for further technological breakthroughs.

In the present work, the author tackles their derivation in a systematic and rigorous way, depending on certain key parameters such as the number of free electrons in the device, the mean free path of the carriers, the device dimensions and the ambient temperature. Accordingly a hierarchy of models is examined which is reflected in the structure of the book: first the microscopic and macroscopic semi-classical approaches followed by their quantum-mechanical counterparts.

Industry Reviews

From the reviews: "The book is a comprehensive review of the main transport equations in semiconductors, presenting the state of the art from the point of view of mathematical modeling. ! The book is addressed to applied mathematicians, solid state physicists and electrical and electronic engineers, but it is as well a good introduction for graduate and Ph.D. students specializing in the transport of charge carriers in semiconductors." (Vittorio Romano, Mathematical Reviews, Issue 2011 k)

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Introduction
Basic Semiconductor Physics	p. 3
Semiconductor Crystals	p. 3
The Schröet;dinger Equation	p. 6
Electrons in a Periodic Potential	p. 9
The Semi-Classical Picture	p. 21
The k.p Method	p. 27
Semiconductor Statistics	p. 32
References	p. 43
Derivation of Macroscopic Equations	p. 45
The Boltzmann Equation and its Scalings	p. 45
Maxwellians	p. 48
Hydrodynamic Models	p. 50
Diffusion Models	p. 52
Reference	p. 54
Microscopic Semi-Classical Models
Collisionless Models	p. 57
The Liouville Equation	p. 57
The Vlasov Equation	p. 61
References	p. 69
Scattering Models	p. 71
The Boltzmann Equation	p. 71
Properties of Collision Operators	p. 78
Additional Topics	p. 89
References	p. 94
Macroscopic Semi-Classical Models
Drift-Diffusion Equations	p. 99
Derivation from the Boltzmann Equation	p. 99
The Bipolar Model	p. 108
Thermal Equilibrium State and Boundary Conditions	p. 112
High-Field Models	p. 114
Drift-Diffusion Models Using Fermi-Dirac Statistics	p. 120
References	p. 125
Energy-Transport Equations	p. 129
Derivation from the Boltzmann Equation	p. 129
Some Explicit Models	p. 139
Symmetrization and Entropy	p. 146
Drift-Diffusion Formulation	p. 149
References	p. 153
Spherical Harmonics Expansion Equations	p. 157
Derivation from the Boltzmann Equation	p. 157
Some Explicit Models	p. 163
Diffusion Approximation	p. 164
References	p. 169
Diffusive Higher-Order Moment Equations	p. 171
Derivation from the Boltzmann Equation	p. 172
Some Explicit Examples	p. 181
Drift-Diffusion Formulation	p. 184
Symmetrization and Entropy	p. 188
References	p. 193
Hydrodynamic Equations	p. 195
Derivation from the Boltzmann Equation	p. 195
Extended Hydrodynamic Equations	p. 203
Relaxation-Time Limits	p. 208
References	p. 211
Microscopic Quantum Models
The Schröet;dinger Equation	p. 217
Density-Matrix Formulation	p. 217
Transparent Boundary Conditions	p. 221
References	p. 229
The Wigner Equation	p. 231
The Quantum Liouville Equation	p. 231
The Quantum Vlasov Equation	p. 238
Wigner-Boltzmann Equations	p. 242
References	p. 246
Macroscopic Quantum Models
Quantum Drift-Diffusion Equations	p. 251
Quantum Maxwellians	p. 252
Derivation from the Wigner-Boltzmann Equation	p. 257
Quantum Fluid Entropy	p. 264
The Entropic Quantum Drift-Diffusion Model	p. 266
References	p. 272
Quantum Diffusive Higher-Order Moment Equations	p. 275
Derivation from the Wigner-Boltzmann Equation	p. 275
The Quantum Energy-Transport Model	p. 277
References	p. 282
Quantum Hydrodynamic Equations	p. 283
Zero-Temperature Quantum Hydrodynamic Equations	p. 283
Mixed-State Schröet;dinger Models and Quantum Hydrodynamics	p. 286
Wigner-Boltzmann Equations and Quantum Hydrodynamics	p. 291
Extended Quantum Hydrodynamic Equations	p. 303
References	p. 306
Index	p. 309
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Lecture Notes in Physics

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

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Paperback

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