Three-dimensional numerical semiconductor device simulation: algorithms, architectures, results

The authors present SECOND, a program for large-scale semiconductor device simulation with truly three-dimensional grids. Since 3-D simulations necessitate large computing resources, the choice of algorithms and their implementation become of utmost importance. The authors investigated the most commonly used numerical algorithms for the solution of the classical drift-diffusion equations. The study included coupled and noncoupled point and block schemes, direct and preconditioned iterative linear solvers, and several distinct ordering and coloring techniques. Structures with regular and irregular grids were analyzed. These algorithms were compared on a variety of machines including workstations, minisupers, and supercomputers. Results of transient simulations are presented to illustrate the approach