Numerical Analysis For Systems With Memory Arising From Semiconductor Simulations

Simulation of Amorphous Silicon microelectronic devices gives rise to a system of coupled nonlinear partial differential equations with memory terms. In this paper we discuss semidiscrete finite element approximation schemes employed for the numerical discretization of such systems. Existence, uniqueness and error analysis are presented. 1. Introduction In the past decade, integrated circuits employing amorphous silicon as the semiconductor layer have shown considerable promise for applications as liquid crystal displays, image sensors and solar cells. The mathematical model used to simulate such devices involves five differential equations [21], two of which can be directly integrated and viewed as a memory term in the remaining three. The specific equations are presented below in Section 2, where all mathematically irrelevant positive constants have been set to unity and only one trapped charge state is considered for simplicity of presentation. We observe that we allow a saturation ..