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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 $ \psi $ 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 $ {{\mathbf{J}}_n}$, $ {{\mathbf{J}}_p}$ and the electric field strength $ \left\Vert {\nabla \psi } \right\Vert$ 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