An Approximation of Three-Dimensional Semiconductor Devices by Mixed Finite Element Method and Characteristics-Mixed Finite Element Method
Year: 2015
Numerical Mathematics: Theory, Methods and Applications, Vol. 8 (2015), Iss. 3 : pp. 356–382
Abstract
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 $L^2$-norm error estimates are derived by the aid of a post-processing step. Finally, numerical experiments are presented to validate the theoretical analysis.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2015.my12031
Numerical Mathematics: Theory, Methods and Applications, Vol. 8 (2015), Iss. 3 : pp. 356–382
Published online: 2015-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
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