Efficient multigrid poisson solver for device simulations

Marco Saraniti, Achim Rein, Gunther Zandler, Peter Vogl, Paolo Lugli

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


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 magnitudes 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.

Original languageEnglish (US)
Pages (from-to)141-149
Number of pages9
JournalIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Issue number2
StatePublished - Feb 1996
Externally publishedYes

ASJC Scopus subject areas

  • Software
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering


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