In this paper, we present various distributed algorithms for solving semiconductor device equations in three-dimensions and its implementation on a network of workstations using PVM. Previous studies in the parallel algorithms for three dimensional semiconductor device simulations mostly focused on the fine grained parallelism. Yet, the higher performance-to-cost ratio of the distributed computing has recently attracted much attention. In this work, we will study the coarse grain parallelism using a cluster of DECstations resided in the MAGNUMS Lab. at the University of Massachusetts.
Two iterative procedures are tested and their performance in the sequential and parallel implementation are compared. In the first method, the solution of the local problem obtained by either direct or other iterative methods is used as a preconditioner for the global Krylov subspace iterative method, e.g., the BICGSTAB method. In the second method, a nonlinear Gauss-Seidel method is used to solve the local problem and a Jacobi method for the global iteration. We refer to this method as the Jacobi nonlinear Gauss-Seidel(JNGS). The efficiency of these two methods is compared along with the CPU time required to achieve convergence to a pre-determined level of accuracy.
The performance of the JNGS algorithm applied to the solution of a three-dimensional submicron Metal-Oxide-Semiconductor Field Effect Transistor (MOSFET) simulation on a cluster of DECstation5000 will be be reported. The cluster of workstations is simultaneously shared by other users and some fluctuation in the performance has been observed. Yet, a near ideal speedup is clearly indicated from the simulation result. However, as the drain voltage is increased, the number of iterations required to solve the problem also increases. The deterioration of the convergence rate is due to a larger coupling between Poisson's and continuity equations at high drain bias.