A Mixed Method for the Mixed Initial Boundary Value Problems of Equations of Semiconductor Devices

In this article, the approximation of nonstationary equations of the semiconductor device with mixed boundary conditions is considered. The approximate procedure of this system using a Galerkin method that makes use of a mixed finite element method for the potential equation combined with a finite e...

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Bibliographic Details
Published in:SIAM journal on numerical analysis Vol. 31; no. 3; pp. 731 - 744
Main Authors: Zhu, Jiang, Wu, Hongwei, Wang, Yuanming
Format: Journal Article
Language:English
Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.06.1994
Subjects:
426000 - Engineering- Components, Electron Devices & Circuits- (1990-)
990200 - Mathematics & Computers
Approximation
Boundary conditions
BOUNDARY-VALUE PROBLEMS
CALCULATION METHODS
CARRIER MOBILITY
ENGINEERING
Exact sciences and technology
Finite element analysis
Finite element method
GALERKIN-PETROV METHOD
GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
ITERATIVE METHODS
Mathematical methods in physics
MATHEMATICAL MODELS
Mathematical procedures
MOBILITY
Numerical approximation and analysis
Ordinary and partial differential equations, boundary value problems
Physics
SEMICONDUCTOR DEVICES
Semiconductors
Sobolev spaces
Uniqueness
Finite element method
Semiconductor devices
Sobolev space
Initial value problem
Boundary-value problems
Galerkin method
Mixed method
ISSN:0036-1429, 1095-7170
Online Access:Get full text
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Summary:In this article, the approximation of nonstationary equations of the semiconductor device with mixed boundary conditions is considered. The approximate procedure of this system using a Galerkin method that makes use of a mixed finite element method for the potential equation combined with a finite element method for the concentration equations is presented. Due to the poor regularity properties of the solutions to the semiconductor equations caused by mixed boundary conditions, a nonstandard analysis for the semidiscrete Galerkin procedure is used. Existence and uniqueness of the approximate solution is proved. A convergence analysis is also given for the method.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:0036-1429
1095-7170
DOI:10.1137/0731039