Finite element solution of the fundamental equations of semiconductor devices. I
Author:
Miloš Zlámal
Journal:
Math. Comp. 46 (1986), 2743
MSC:
Primary 65N30
DOI:
https://doi.org/10.1090/S00255718198608158296
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 $\psi$ and of two highly nonlinear continuity equations for carrier densities n and p. We use simplicial elements with linear polynomials and fournode twodimensional and eightnode threedimensional isoparametric elements. There are constructed finite element solutions such that the current densities ${{\mathbf {J}}_n}$, ${{\mathbf {J}}_p}$ and the electric field strength $\left \ {\nabla \psi } \right \$ 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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Article copyright:
© Copyright 1986
American Mathematical Society