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

In this paper we present a novel exponentially fitted finite element method with triangular éléments for the decoupled continuity équations 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 estimâtes for the approximate solution and its associated flux are given. These /i-order error bounds depend on some first-order seminorms of the exact solution, the exact flux and the coefficient function of the convection ternis. A method is also proposed for the évaluation 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 convectiondiffusion des semi-conducteurs. AMS Subject Classification. Primary 65N30, 65P05. Received: November 29, 1995. Revised: April 2, 1997 and November 25, 1997.