Efficient Poisson Solver for Semiconductor Device Modeling Using the Multi-Grid Preconditioned BiCGSTAB Method

This paper presents the performance results of an efficient algorithm for solving the three dimensional Poisson equation. The multi-grid method exploits the efficient oscillatory error reduction of basic iterative methods by smoothing on a set of progressively coarsened grids. When used as a preconditioner for BiCGSTAB method, a computationally demanding solver can be shown to be effective for large scale simulations. Varying the number of grids used and the level of overrelaxation as well as exploring the benefits of semicoarsening in the multi-grid preconditioner reveals the underlying strengths of this combined scheme. The convergence properties of the developed solver are tested on a 3D split-gate silicon on insulator (SOI) device. © 2002, Kluwer Academic Publishers.