Application of Iterative Methods for Solving Nonsymmetric Linear Systems in the Simulation of Semiconductor Processing

This paper presents a systematic comparison of recently developed iterative methods for solving nonsymmetric linear equations arising from the numerical simulation of semiconductor processing. A non comprehensive survey of the literature concerning iterative solvers is given including theoretical studies as well as current articles on practical applications. In particular, we consider the conjugate gradient-type algorithms CGS, Bi-CGSTAB and GMRES as well as the Broyden type secant method GB specially adapted to the linear case. At the moment these methods are among the most frequently applied techniques for the solution of nonsymmetric linear systems. The algorithms, including ILU-D (incomplete LU-diagonal decomposition) as a preconditioner, are given and their performance is compared on an industrial application within the process simulator MIMAS II. The simulation of semiconductor processing is an important and challenging area of industrial application and therefore an ideal eld for testing the performance of iterative methods in real life problems. To highlight the physical background of this application, the physics of process simulation is brie y sketched.