An efficient multigrid Poisson solver for device simulations

The aim of this paper is to show that the multigrid approach can provide an efficient two-dimensional Poisson solver used in the analysis of realistic semiconductor devices based on particle simulators. Our robust implementation of the multigrid method is faster by one or two orders of magnitude than standard successive over-relaxation solvers and is capable, at the same time, of efficiently handling highly inhomogeneous grids and irregular boundary conditions relevant for realistic devices. All essential parts of the algorithm, such as coarsening, prolongation, restriction, and relaxation, have been adapted and optimized to deal with these complex geometries and large variations in the charge density. In particular, a new variant of the Gauss-Seidel-type relaxation scheme is introduced that is particularly suited for grids that lack globally dominant directions. As an example, the multigrid Poisson solver has been applied to two different electronic devices, a GaAs High Electron Mobility Transistor and a Si Metal Oxide Semiconductor Field Effect Transistor.