Iterative Methods in Semiconductor Device Simulation

A number of Krylov-subspace methods and their applicability to the drift-diffusion equations for semiconductor devices are surveyed. Triangular (non-tensor-product) grids are appropriate for these highly nonsymmetric problems. The role of the underlying discretization is considered, including both the traditional box-method variant of the Scharfetter-Gummel scheme and a new upwinding (streamline- diffusion-like) procedure. Several preconditioners are discussed, including a novel alternate-block-factorization method. Graph coloring is used to enhance performance on vector computers.