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An Approximation of Three-Dimensional Semiconductor Devices by Mixed Finite Element Method and Characteristics-Mixed Finite Element Method

Part of:Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  05 August 2015

Qing Yang and
Yirang Yuan
Qing Yang*
Affiliation:
School of Mathematical Science, Shandong Normal University, Jinan, 250014, China
Yirang Yuan
Affiliation:
Institute of Mathematics, Shandong University, Jinan, 250100, China
*
*Email address: sd_yangq@163.com (Q. Yang); yryuan@sdu.edu.cn (Y. Yuan)

Abstract

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The mathematical model for semiconductor devices in three space dimensions are numerically discretized. The system consists of three quasi-linear partial differential equations about three physical variables: the electrostatic potential, the electron concentration and the hole concentration. We use standard mixed finite element method to approximate the elliptic electrostatic potential equation. For the two convection-dominated concentration equations, a characteristics-mixed finite element method is presented. The scheme is locally conservative. The optimal L2-norm error estimates are derived by the aid of a post-processing step. Finally, numerical experiments are presented to validate the theoretical analysis.

Keywords

Three-dimensional semiconductor devicescharacteristics-mixed finite element methodmixed finite element methodpost-processing steperror bound

MSC classification

Secondary:65M15: Error bounds65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

Information

Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 8 , Issue 3 , August 2015, pp. 356 - 382
Copyright
Copyright © Global-Science Press 2015 

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