Mathematical and Numerical Modelling of Heterostructure Semiconductor Devices: From Theory to Programming
The commercial development of novel semiconductor devices requires that their properties 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. In particular, the existence of interfaces between different material layers in heterostructures means that quantum solutions must be found in the quantum wells which are formed at these interfaces.
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++; these chapters are self-contained, and do not rely on the reader having met these topics before. 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.
Written for anyone who is interested in learning about, or refreshing their knowledge of, some of the basic mathematical and numerical methods involved in device modelling, this book is suitable for advanced undergraduate and graduate students, lecturers and researchers working in the fields of electrical engineering and semiconductor device physics, and for students of other mathematical and physical disciplines starting out in device modelling.
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 subjectsCase studies show how the numerical techniques can be tailored to the specific problems of device modellingIncludes 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