A new exponentially fitted triangular finite element method for the continuity equations in the drift-diffusion model of semiconductor devices

School of Mathematics and Statistics Curtin University of Technology, Perth 6845, Australia.

Received: 29 November 1995
Revised: 2 April 1997
Revised: 25 November 1997

Abstract

In this paper we present a novel exponentially fitted finite element method with triangular elements for the decoupled continuity equations in the drift-diffusion model of semiconductor devices. The continuous problem is first formulated as a variational problem using a weighted inner product. A Bubnov-Galerkin finite element method with a set of piecewise exponential basis functions is then proposed. The method is shown to be stable and can be regarded as an extension to two dimensions of the well-known Scharfetter-Gummel method. Error estimates for the approximate solution and its associated flux are given. These h-order error bounds depend on some first-order seminorms of the exact solution, the exact flux and the coefficient function of the convection terms. A method is also proposed for the evaluation of terminal currents and it is shown that the computed terminal currents are convergent and conservative.

Résumé

Dans cet article nous présentons une méthode d'éléments finis avec éléments triangulaires et adaptation exponentielle pour les équations de continuité découplées dans le modèle de convection-diffusion des semi-conducteurs.