Mixed finite volume methods for semiconductor device simulation

Abstract

We deal with the two-dimensional numerical solution of the Van Roosbroeck system, widely employed in modern semiconductor device simulation. Using the well-known Gummel's decoupled algorithm leads to the iterative solution of a nonlinear Poisson equation for the electric potential and two linearized continuity equations for the electron and hole current densities. The numerical approximation is based on the dual mixed formulation for a self-adjoint second-order elliptic operator by using the Raviart-Thomas (RT) finite elements of lowest degree on a triangular partition of the device domain. In this article, we propose a suitable variant of the RT method, based on the diagonalization of the element mass matrix. This is achieved by use of an appropriate numerical integration that eliminates the fluxes and gives rise to a cell-centered finite volume scheme for the scalar unknown with the same approximation properties of the mixed approach, but at a reduced computational cost. The above procedure suggests also a natural way to introduce in the frame of the classical Box Method (BM) suitable vector basis functions (edge elements) to represent the current field over each mesh triangle. This issue may be profitably employed both as a postprocessing tool, as well as a technique for solving the current continuity equations when source terms depending on the current itself are included in the mathematical model. Simulations of realistic semiconductor devices are then included to demonstrate the accuracy and stability of the new method. © 1997 John Wiley & Sons, Inc.