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Mathematical and Numerical Modelling of Heterostructure Semiconductor Devices: From Theory to Programming

  • Textbook
  • © 2009

Overview

Authors:
  1. E.A.B. Cole

    1. Dept. Mathematics, University of Leeds, Leeds, United Kingdom

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  • Entirely self-contained: the basic ideas of quantum mechanics and statistical mechanices are introduced and developed and numerical techniques, such as multigrids and genetic computing, are explained in a manner that is comprehensible to readers who have had no previous contact with these subjects

  • Case studies show how the numerical techniques can be tailored to the specific problems of device modelling

  • Includes sections of computer code, written in C++, and written in a simple and transparent way so that the reader can re-write it in his or her own favourite programming language

  • Includes supplementary material: sn.pub/extras

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Table of contents (15 chapters)

  1. Front Matter

    Pages I-XV
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  2. Overview and physical equations

    1. Front Matter

      Pages 1-1
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    2. Overview of device modelling

      • E. A. B. Cole
      Pages 3-20

    3. Quantum mechanics

      • E. A. B. Cole
      Pages 21-87

    4. Equilibrium thermodynamics and statistical mechanics

      • E. A. B. Cole
      Pages 89-113

    5. Density of states and applications—1

      • E. A. B. Cole
      Pages 115-142

    6. Density of states and applications—2

      • E. A. B. Cole
      Pages 143-159

    7. The transport equations and the device equations

      • E. A. B. Cole
      Pages 161-185

  3. Mathematical and numerical methods

    1. Front Matter

      Pages 187-187
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    2. Basic approximation and numerical methods

      • E. A. B. Cole
      Pages 189-219

    3. Fermi and associated integrals

      • E. A. B. Cole
      Pages 221-228

    4. The upwinding method

      • E. A. B. Cole
      Pages 229-245

    5. Solution of equations: the Newton and reduced method

      • E. A. B. Cole
      Pages 247-258

    6. Solution of equations: the phaseplane method

      • E. A. B. Cole
      Pages 259-282

    7. Solution of equations: the multigrid method

      • E. A. B. Cole
      Pages 283-301

    8. Approximate and numerical solutions of the Schrödinger equation

      • E. A. B. Cole
      Pages 303-337

    9. Genetic algorithms and simulated annealing

      • E. A. B. Cole
      Pages 339-376

    10. Grid generation

      • E. A. B. Cole
      Pages 377-387

  4. Back Matter

    Pages 389-406
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Keywords

About this book

Part of my lecturing work in the School of Mathematics at the University of Leeds involved teaching quantum mechanics and statistical mechanics to mathematics undergraduates, and also mathematical methods to undergraduate students in the School of Electronic and Electrical Engineering at the University. The subject of this book has arisen as a result of research collaboration on device modelling with members of the School of Electronic and Electrical Engineering. I wanted to write a book which would be of practical help to those wishing to learn more about the mathematical and numerical methods involved in heteroju- tion device modelling. I have introduced only a comparatively small number of t- ics, and the reader may think that other important topics should have been included. But of the topics which I have introduced, I hope that I have given the reader some practical advice concerning the implementation of the methods which are discussed. This practical advice includes demonstrating how the implementation of the me- ods may be tailored to the speci?c device being modelled, and also includes some sections of computer code to illustrate this implementation. I have also included some background theory regarding the origins of the routines.

Reviews

From the reviews:

“The book covers a wide spectrum of topics that are fundamental for modelling and simulation of semiconductor electron devices … . It is addressed to undergraduate and graduate students in mathematics and electrical engineering as well as researchers who would like to get different perspectives on the subject. … The monograph is self-contained since a standard background in calculus is enough to read it. This is surely a good textbook for Ph.D. students in applied mathematics.” (Vittorio Romano, Mathematical Reviews, Issue 2011 e)

“This well-written book involves the basic physical theory of semiconductor device modelling and the numerical methods to solve the corresponding equations. … Problems are formulated to improve the skill of the reader … . In order to support the reader, in the implementation of the methods, some simple codes written in C++ are included. … A great advantage of this monograph consists in the presentation of the whole cycle of semiconductor device modelling … .” (Georg Hebermehl, Zentralblatt MATH, Vol. 1252, 2012)

Authors and Affiliations

  • Dept. Mathematics, University of Leeds, Leeds, United Kingdom

    E.A.B. Cole

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