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Analysis of Charge Transport

A Mathematical Study of Semiconductor Devices

  • Book
  • © 1996

Overview

Authors:
  1. Joseph W. Jerome

    1. Department of Mathematics, Northwestern University, Evanston, USA

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-XI
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  2. Introduction

    1. Introduction

      • Joseph W. Jerome
      Pages 1-6

  3. Modeling of Semiconductor Devices

    1. Front Matter

      Pages 7-7
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    2. Development of Drift-Diffusion Models

      • Joseph W. Jerome
      Pages 9-26

    3. Moment Models: Microscopic to Macroscopic

      • Joseph W. Jerome
      Pages 27-50

  4. Computational Foundations

    1. Front Matter

      Pages 51-51
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    2. A Family of Solution Fixed Point Maps: Partial Decoupling

      • Joseph W. Jerome
      Pages 53-88

    3. Nonlinear Convergence Theory for Finite Elements

      • Joseph W. Jerome
      Pages 89-122

  5. Mathematical Theory

    1. Front Matter

      Pages 123-123
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    2. Numerical Fixed Point Approximation in Banach Space

      • Joseph W. Jerome
      Pages 125-142

    3. Construction of the Discrete Approximation Sequence

      • Joseph W. Jerome
      Pages 143-154

  6. Back Matter

    Pages 155-167
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Keywords

About this book

This book addresses the mathematical aspects of semiconductor modeling, with particular attention focused on the drift-diffusion model. The aim is to provide a rigorous basis for those models which are actually employed in practice, and to analyze the approximation properties of discretization procedures. The book is intended for applied and computational mathematicians, and for mathematically literate engineers, who wish to gain an understanding of the mathematical framework that is pertinent to device modeling. The latter audience will welcome the introduction of hydrodynamic and energy transport models in Chap. 3. Solutions of the nonlinear steady-state systems are analyzed as the fixed points of a mapping T, or better, a family of such mappings, distinguished by system decoupling. Significant attention is paid to questions related to the mathematical properties of this mapping, termed the Gummel map. Compu­ tational aspects of this fixed point mapping for analysis of discretizations are discussed as well. We present a novel nonlinear approximation theory, termed the Kras­ nosel'skii operator calculus, which we develop in Chap. 6 as an appropriate extension of the Babuska-Aziz inf-sup linear saddle point theory. It is shown in Chap. 5 how this applies to the semiconductor model. We also present in Chap. 4 a thorough study of various realizations of the Gummel map, which includes non-uniformly elliptic systems and variational inequalities. In Chap.

Authors and Affiliations

  • Department of Mathematics, Northwestern University, Evanston, USA

    Joseph W. Jerome

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