Wavelet-based galerkin method for semiconductor device simulation.

by Chan Chung-Kei, Thomas.Thesis (M.Phil.)--Chinese University of Hong Kong, 1998.Includes bibliographical references (leaves 125-[129]).Abstract also in Chinese.Chapter 1 --- Introduction --- p.1Chapter 2 --- Semiconductor Device Physics --- p.5Chapter 2.1 --- IC Design Methodology --- p.6Chapter 2.1.1 --- System Level --- p.7Chapter 2.1.2 --- Circuit Level --- p.7Chapter 2.1.3 --- Device Level --- p.8Chapter 2.1.4 --- Process Level --- p.8Chapter 2.2 --- Classification of Device Models --- p.8Chapter 2.2.1 --- Circuit Models --- p.9Chapter 2.2.2 --- Physical Models --- p.10Chapter 2.3 --- Classical Drift-Diffusion model --- p.13Chapter 2.3.1 --- Basic Governing Equations in Semiconductors --- p.13Chapter 2.3.2 --- Shockley-Read-Hall Recombination Statics --- p.15Chapter 2.3.3 --- Boundary Conditions --- p.18Chapter 2.4 --- pn Junction at equilibrium --- p.20Chapter 2.4.1 --- The depletion approximation --- p.23Chapter 2.4.2 --- Current-voltage Characteristics --- p.26Chapter 3 --- Iteration Scheme --- p.30Chapter 3.1 --- Gummel's iteration scheme --- p.31Chapter 3.2 --- Modified Gummel's iteration scheme --- p.35Chapter 3.3 --- Solution of Differential Equation --- p.38Chapter 3.3.1 --- Finite Difference Method --- p.38Chapter 3.3.2 --- Moment Method --- p.39Chapter 4 --- Theory of Wavelets --- p.43Chapter 4.1 --- Multi-resolution Analysis --- p.43Chapter 4.1.1 --- Example of MRA with Haar Wavelet --- p.46Chapter 4.2 --- Orthonormal basis of Wavelets --- p.52Chapter 4.3 --- Fast Wavelet Transform --- p.56Chapter 4.4 --- Wavelets on the interval --- p.62Chapter 5 --- Galerkin-Wavelet Method --- p.66Chapter 5.1 --- Wavelet-based Moment Methods --- p.67Chapter 5.1.1 --- Wavelet transform on the stiffness matrix --- p.67Chapter 5.1.2 --- Wavelets as basis functions --- p.68Chapter 5.2 --- Galerkin-Wavelet method --- p.69Chapter 5.2.1 --- Boundary Conditions --- p.73Chapter 5.2.2 --- Adaptive Scheme --- p.74Chapter 5.2.3 --- The Choice of Classes of Wavelet Bases --- p.76Chapter 6 --- Numerical Results --- p.80Chapter 6.1 --- Steady State Solution --- p.81Chapter 6.1.1 --- Daubechies Wavelet N = 2 --- p.82Chapter 6.1.2 --- Daubechies Wavelet N=5 --- p.84Chapter 6.1.3 --- Discussion on Daubechies wavelets N = 2 and N=5 --- p.86Chapter 6.2 --- Transient Solution --- p.91Chapter 6.3 --- Convergence --- p.99Chapter 7 --- Conclusion --- p.103Chapter A --- Derivation for steady state --- p.107Chapter A.1 --- Generalized Moll-Ross Relation --- p.107Chapter A.2 --- Linearization of PDEs --- p.110Chapter B --- Derivation for transient state --- p.113Chapter C --- Notation --- p.119Chapter D --- Elements in the Stiffness Matrix --- p.122Bibliography --- p.12