Mathematical and Numerical Modelling of Heterostructure Semiconductor Devices: From Theory to Programming [electronic resource] / by E.A.B. Cole.

Overview and physical equations -- Overview of device modelling -- Quantum mechanics -- Equilibrium thermodynamics and statistical mechanics -- Density of states and applications—1 -- Density of states and applications—2 -- The transport equations and the device equations -- Mathematical and numerical methods -- Basic approximation and numerical methods -- Fermi and associated integrals -- The upwinding method -- Solution of equations: the Newton and reduced method -- Solution of equations: the phaseplane method -- Solution of equations: the multigrid method -- Approximate and numerical solutions of the Schrödinger equation -- Genetic algorithms and simulated annealing -- Grid generation.

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.