Systems of Nonlinear Algebraic Equations Arising in Simulation of Semiconductor Devices
type: CreativeWork
description: 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.
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.
author: Sheikh, Qasim Mohammad
keywords: Computer Science
date published: 2014-12-15T19:25:31Z
date modified: 2026-07-22T22:26:01Z
provider: University of Illinois - Urbana-Champaign
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: University of Illinois at Urbana-Champaign

PropertyValue
property ID: Handle
value: http://hdl.handle.net/2142/69528