Quasi-hydrodynamic Semiconductor EquationsSpringer Science & Business Media, 01.02.2001 - 293 Seiten In this book a hierarchy of macroscopic models for semiconductor devices is presented. Three classes of models are studied in detail: isentropic drift-diffusion equations, energy-transport models, and quantum hydrodynamic equations. The derivation of each of the models is shown, including physical discussions. Furthermore, the corresponding mathematical problems are analyzed, using modern techniques for nonlinear partial differential equations. The equations are discretized employing mixed finite-element methods. Also, numerical simulations for modern semiconductor devices are performed, showing the particular features of the models. |
Inhalt
Introduction | 1 |
12 Quasihydrodynamic semiconductor models | 15 |
Basic Semiconductor Physics | 21 |
22 Inhomogeneous semiconductors | 23 |
The Isentropic Driftdiffusion Model | 27 |
312 The isentropic modelscaling | 30 |
313 The convergence result | 34 |
32 Existence of transient solutions | 36 |
433 Proof of the existence result | 138 |
44 Longtime behavior of the transient solution | 151 |
45 Regularity and uniqueness of transient solutions | 154 |
452 Uniqueness of transient solutions | 164 |
46 Existence of steadystate solutions | 168 |
47 Uniqueness of steadystate solutions | 175 |
48 Numerical approximation | 178 |
482 Numerical results | 183 |
322 Proof of the existence result | 38 |
33 Uniqueness of transient solutions | 48 |
34 Localization of vacuum solutions | 62 |
342 Proofs of the main results | 65 |
343 Numerical examples | 83 |
35 Numerical approximation | 90 |
352 Numerical examples in one space dimension | 94 |
353 The mixed finite element discretization in two space dimensions | 99 |
354 Numerical examples in two space dimensions | 105 |
36 Currentvoltage characteristics of diodes | 110 |
362 Highinjection currentvoltage characteristics | 111 |
The Energytransport Model | 117 |
412 A driftdiffusion formulation for the current densities | 125 |
413 A nonparabolic band approximation | 128 |
414 Parabolic band approximation | 129 |
42 Symmetrization and entropy function | 131 |
43 Existence of transient solutions | 135 |
432 Semidiscretization | 137 |
The Quantum Hydrodynamic Model | 189 |
52 Existence and positivity of steadystate solutions | 195 |
522 Positivity and nonpositivity properties | 204 |
53 Uniqueness of steadystate solutions | 207 |
54 A nonexistence result for the steadystate problem | 210 |
55 The classical limit | 215 |
552 The classical limit in the subsonic steady state | 220 |
553 Numerical examples | 233 |
56 Currentvoltage characteristics for tunneling diodes | 236 |
562 Analytical and numerical currentvoltage characteristics | 240 |
57 A positivitypreserving numerical scheme for the quantum driftdiffusion model | 242 |
existence of the discrete system | 245 |
572 Stability bounds and convergence results | 251 |
573 Numerical examples | 260 |
References | 265 |
289 | |
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