The Stationary Semiconductor Device EquationsSpringer Science & Business Media, 09/03/2013 - 195 من الصفحات In the last two decades semiconductor device simulation has become a research area, which thrives on a cooperation of physicists, electrical engineers and mathe maticians. In this book the static semiconductor device problem is presented and analysed from an applied mathematician's point of view. I shall derive the device equations - as obtained for the first time by Van Roosbroeck in 1950 - from physical principles, present a mathematical analysis, discuss their numerical solu tion by discretisation techniques and report on selected device simulation runs. To me personally the most fascinating aspect of mathematical device analysis is that an interplay of abstract mathematics, perturbation theory, numerical analysis and device physics is prompting the design and development of new technology. I very much hope to convey to the reader the importance of applied mathematics for technological progress. Each chapter of this book is designed to be as selfcontained as possible, however, the mathematical analysis of the device problem requires tools which cannot be presented completely here. Those readers who are not interested in the mathemati cal methodology and rigor can extract the desired information by simply ignoring details and proofs of theorems. Also, at the beginning of each chapter I refer to textbooks which introduce the interested reader to the required mathematical concepts. |
المحتوى
1 | |
Mathematical Modeling of Semiconductor Devices | 7 |
Analysis of the Basic Stationary Semiconductor Device | 31 |
Singular Perturbation Analysis of the Stationary Semiconductor | 68 |
Discretisation of the Stationary Device Problem | 131 |
Numerical Simulation A Case Study | 178 |
Appendix | 184 |
190 | |
طبعات أخرى - عرض جميع المقتطفات
The Stationary Semiconductor Device Equations <span dir=ltr>P.A. Markowich</span> لا تتوفر معاينة - 2014 |
The Stationary Semiconductor Device Equations <span dir=ltr>P.A. Markowich</span> لا تتوفر معاينة - 2010 |
عبارات ومصطلحات مألوفة
applied bias applied potentials approximation approximation error assume asymptotic expansions boundary conditions boundary value problem carrier concentrations computation continuity equations current density current relations Debye length defined denote depend derive device models discrete solutions domain doping concentration doping profile electric field error estimate finite difference grad grid hi+1 holds implies iteration junction layer layer terms Lemma Lipschitz continuous Markowich Math mathematical maximum principle mesh methods mobilities MOS-transistor Neumann Nonlinear numerical obtain Ohmic contacts one-dimensional order of magnitude p-region parameter physical piecewise linear pn-diode pn-junction Poisson's equation proof recombination-generation rate recombination-generation term reduced solution resp right hand side satisfies scaled Schottky contacts segments Selberherr semiconductor device equations semiconductor device problem semiconductor-oxide interface singular perturbation sufficiently small Theorem thermal equilibrium U₁ unique v₁ variable vector voltage y₁ zeroth order ΘΩΝ ΧΕΩ