A 3D Rectangular Mixed Finite Element Method to Solve the Stationary Semiconductor Equations

Abstract

A mixed finite element method using rectangular elements is presented to solve the drift-diffusion model of semiconductors. The method, which is, on the one hand, a classical primal mixed finite element method, generalizes the one-dimensional Scharfetter-Gummel scheme to three dimensions in a natural way. The major contribution to a successful implementation of the method is the development of a fast and exact numerical evaluation of exponential fitted integrals, to which considerable attention has been devoted. The essentials of the efficient computation of these integrals are described, with full details to be presented elsewhere. In order to use computer resources parsimoniously, with the help of Lagrange multipliers, admissible bases on irregular rectangular meshes are constructed which allow a local element refinement. To validate the method, the modeling of a three-dimensional magneto transistor is presented.

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