Mathematical and numerical modelling of heterostructure semiconductor devices: from theory to programming

The commercial development of novel semiconductor devices requires that theirproperties be examined as thoroughly and rapidly as possible. These properties are investigated by obtaining numerical solutions of the highly nonlinear coupled set of equations which govern their behaviour. This book presents some of the mathematical and numerical techniques associated with the investigation.It begins with introductions to quantum and statistical mechanics. Later chapters then cover finite differences; multigrids; upwinding techniques; simulated annealing; mesh generation; and the reading of computer code in C++. The author explains how the methods can be adapted to the specific needs of device modelling, the advantages and disadvantages of each method, the pitfalls to avoid, and practical hints and tips for successful implementation. Sections of computer code are included to illustrate the methods used." 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 INDICE: Part I Overview and physical equations.- 1 Overview of device modeling.- 2 Quantum mechanics.- 3 Equilibrium thermodynamics and statistical mechanics.- 4 Density of states and applications – 1.- 5 Density of states and applications – 2.- 6 The transport equations and the device equations.- Part II Mathematical and numerical methods.- 7 Basic approximation and numerical methods.- 8 Fermi and associated integrals.- 9 The upwinding method.- 10 Solution ofequations: the Newton and reduced method.- 11 Solution of equations: the phaseplane method.- 12 Solution of equations: the multigrid method.- 13 Approximate and numerical solutions of the Schr¨odinger equation.- 14 Genetic algorithmsand simulated annealing.- 15 Grid generation.- A The theory of contractive mapping.

• ISBN: 978-1-84882-936-7
• Editorial: Springer
• Encuadernacion: Rústica
• Páginas: 418
• Fecha Publicación: 01/12/2009
• Nº Volúmenes: 1
• Idioma: Inglés