Finite element solution of the fundamental equations of semiconductor devices. I

Author:
Miloš Zlámal

Journal:
Math. Comp. **46** (1986), 27-43

MSC:
Primary 65N30

MathSciNet review:
815829

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Abstract: We investigate the nonstationary equations of the semiconductor device theory consisting of a Poisson equation for the electric potential and of two highly nonlinear continuity equations for carrier densities *n* and *p*. We use simplicial elements with linear polynomials and four-node two-dimensional and eight-node three-dimensional isoparametric elements. There are constructed finite element solutions such that the current densities , and the electric field strength are constant on each element. Two schemes are proposed: one is nonlinear, the other is partly linear. The schemes preserve the property of the exact solution (corresponding to the physical meaning) that the carrier densities *n* and *p* are positive. Existence of the solution is proved in both cases, unicity in the second case. A subsequent paper II will be devoted to problems of stability and convergence.

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DOI:
https://doi.org/10.1090/S0025-5718-1986-0815829-6

Article copyright:
© Copyright 1986
American Mathematical Society