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The Stationary Semiconductor Device Equations

  • Book
  • © 1986

Overview

Authors:
  1. Peter A. Markowich

    1. Institut für Angewandte und Numerische Mathematik, Technische Universität Wien, Vienna, Austria

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Part of the book series: Computational Microelectronics (COMPUTATIONAL)

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Table of contents (6 chapters)

  1. Front Matter

    Pages I-IX
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  2. Introduction

    • Peter A. Markowich
    Pages 1-6

  3. Mathematical Modeling of Semiconductor Devices

    • Peter A. Markowich
    Pages 7-30

  4. Analysis of the Basic Stationary Semiconductor Device Equations

    • Peter A. Markowich
    Pages 31-67

  5. Singular Perturbation Analysis of the Stationary Semiconductor Device Problem

    • Peter A. Markowich
    Pages 68-130

  6. Discretisation of the Stationary Device Problem

    • Peter A. Markowich
    Pages 131-177

  7. Numerical Simulation — A Case Study

    • Peter A. Markowich
    Pages 178-183

  8. Back Matter

    Pages 184-195
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About this book

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.

Authors and Affiliations

  • Institut für Angewandte und Numerische Mathematik, Technische Universität Wien, Vienna, Austria

    Peter A. Markowich

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