Efficient solution of the schrödinger-poisson equations in semiconductor device simulations

Alex Trellakis, Till Andlauer, Peter Vogl

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations

Abstract

This paper reviews the numerical issues arising in the simulation of electronic states in highly confined semiconductor structures like quantum dots. For these systems, the main challenge lies in the efficient and accurate solution of the self-consistent one-band and multi-band Schrödinger-Poisson equations. After a brief introduction of the physical background, we first demonstrate that unphysical solutions of the Schrödinger equation due to the presence of material boundaries can be avoided by combining a suitable ordering of the differential operators with a robust discretization method like box discretization. Next, we discuss algorithms for the efficient solution of the resulting sparse matrix problems even on small computers. Finally, we introduce a predictor-corrector-type approach for the stabilizing the outer iteration loop that is needed to obtain a self-consistent solution of both Schrödinger's and Poisson's equation.

Original languageEnglish
Title of host publicationLarge-Scale Scientific Computing - 5th International Conference, LSSC 2005, Revised Papers
Pages602-609
Number of pages8
DOIs
StatePublished - 2006
Event5th International Conference on Large-Scale Scientific Computing, LSSC 2005 - Sozopol, Bulgaria
Duration: 6 Jun 200510 Jun 2005

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3743 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference5th International Conference on Large-Scale Scientific Computing, LSSC 2005
Country/TerritoryBulgaria
CitySozopol
Period6/06/0510/06/05

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