Finite Element Resolution of the 3D Stationary Semiconductor Device Equations on Multiprocessors

Abstract

This paper describes a three-dimensional simulator for semiconductor devices in stationary state developed on a message passing multiprocessor. A Gummel style nonlinear iteration was used, and the Poisson and the continuity equations were discretized using the finite element method. A new iterative scheme was introduced in order to solve the nonlinear Poisson equation. The nonsymmetric continuity equations were solved using a Conjugate Gradient type method, the Bi-CGSTAB. We carried out the parallelization of these approaches and their mapping onto a multiprocessor system. We introduce a new method for the distribution of the finite element sparse matrices over the multiprocessor. This method leads to highly efficient algorithms, because it obtains a good load balance and limits all the communications to length 1.