Fast Iterative Solution of Carrier Continuity Equations for Three-Dimensional Device Simulation

In this paper the use of iterative methods for the solution of the carrier continuity equations in three-dimensional semiconductor device simulators is summarized. An overview of the derivation of the linear systems from the basic stationary semiconductor device equations is given and the algebraic properties of the nonsymmetric coefficient matrices are discussed. Results from the following classes of iterative methods are presented: The classical conjugate gradient (CG), the symmetrized conjugate gradient (SCG), the generalized minimum residual (GMRES), and the conjugate gradient squared (CGS) method. Preconditioners of incomplete factorization type with partial fill-in are considered. High performance implementations for these algorithms on vector, concurrent, and vector-concurrent computers are presented.