Analysis of a finite element method forthe drift-diffusion semiconductor device equations: the multidimensional case

Zhangxin Chen, Bernardo Cockburn

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

An explicit finite element method for numerically solvingthe drift-diffusion semiconductor device equations in two space dimensionsis analyzed.The method is based on the use of a mixed finite element method for the approximationof the electric field and a discontinuousupwinding finite element method for the approximationof the electron and hole concentrations. The mixed method gives an approximate electricfield in the precise form needed by the discontinuous method, which is triviallyconservative and fully parallelizable. It is proven that the method producesuniformly bounded concentrations and electric fields and that it convergesto the exact solution provided there is a convergent subsequence of the electronconcentrations. Numerical simulations are presented that display theperformance of the method and indicate the behavior of the solution.

Original languageEnglish (US)
Pages (from-to)1-28
Number of pages28
JournalNumerische Mathematik
Volume71
Issue number1
DOIs
StatePublished - Aug 1995

Keywords

  • Mathematics Subject Classification (1991): 65N30, 35L60, 35L65

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