Systems of Nonlinear Algebraic Equations Arising in Simulation of Semiconductor Devices
Sheikh, Qasim Mohammad
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https://hdl.handle.net/2142/69528
Description
Title
Systems of Nonlinear Algebraic Equations Arising in Simulation of Semiconductor Devices
Author(s)
Sheikh, Qasim Mohammad
Issue Date
1983
Department of Study
Computer Science
Discipline
Computer Science
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Computer Science
Abstract
In this thesis we present several formulations of the system of elliptic partial differential equations that model a semiconductor device. We use standard finite difference methods to discretize these equations and derive systems of nonlinear equations. Due to the extremely large number of unknowns it is prohibitively expensive to use Newton's method. However, the Jacobians of these systems are relatively simple to compute. Hence, it is practical to exploit the properties of these systems and develop a class of Newton-like methods based on splittings of the Jacobians. We state and prove sufficient conditions on device parameters for convergence of these methods.
We also describe a multigrid method for solving these systems. Several multigrid methods for solving such systems are available in the literature. The most common approach for solving the nonlinear system is to first linearize the system and then use a multigrid method to solve this linear system. We apply the multigrid method directly to the nonlinear system. This approach gives us a nonlinear system to be solved at each grid. Our approach enables us to blend the multigrid method and the point Gauss-Seidel-Newton method. We give numerical examples to compare this method and the Newton-like methods.
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