AN EFFICIENT MULTIGRID POISSON SOLVER FOR DEVICE SIMULATIONS

The aim of this paper is to show that the multigrid approach can provi de an efficient two-dimensional Poisson solver used in the analysis of realistic semiconductor devices based on particle simulators. Our rob ust implementation of the multigrid method is faster by one or two ord ers of magnitudes than standard successive over-relaxation solvers and is capable, at the same time, of efficiently handling highly inhomoge neous grids and irregular boundary conditions relevant for realistic d evices. All essential parts of the algorithm, such as coarsening, prol ongation, restriction, and relaxation, have been adapted and optimized to deal with these complex geometries and large variations in the cha rge density. In particular, a new variant of the Gauss-Seidel-type rel axation scheme is introduced that is particularly suited for grids tha t lack globally dominant directions. As an example, the multigrid Pois son solver has been applied to two different electronic devices, a GaA s High Electron Mobility Transistor and a Si Metal Oxide Semiconductor Field Effect Transistor.