Systems of Nonlinear Algebraic Equations Arising in Simulation of Semiconductor Devices

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Computer Science

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Sheikh, Qasim Mohammad

• Computer Science

Identifier

(UMI)AAI8410047

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/69528