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

Abstract

In this paper we present a novel exponentially tted nite element method with triangular elements for the decoupled continuity equations in the drift-diusion model of semiconductor devices. The continuous problem is rst formulated as a variational problem using a weighted inner product. A Bubnov-Galerkin nite 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 rst-order seminorms of the exact solution, the exact flux and the coecient 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. R esum e. Dans cet article nous pr esentons une m ethode d' el ements nis avec el ements triangulaires et adaptation exponentielle pour les equations de continuit ed ecoupl ees dans le mod ele de convection- diusion des semi-conducteurs. AMS Subject Classication. Primary 65N30, 65P05.