Numerical calculation of the electronic structure for three-dimensional quantum dots

Publikationstyp
Preprint
Date Issued
2005-08
Sprache
English
Author(s)
Voß, Heinrich 
Institut
Mathematik E-10  
TORE-DOI
10.15480/882.58
TORE-URI
http://tubdok.tub.tuhh.de/handle/11420/60
First published in
Preprints des Institutes für Mathematik;Bericht 91
Preprints des Institutes für Mathematik  
Number in series
91
Citation
Preprint. Published in: Computer Physics CommunicationsVolume 174, Issue 6, 15 March 2006, Pages 441-446
Publisher DOI
10.1016/j.cpc.2005.12.003
Scopus ID
2-s2.0-33344457300
In some recent papers Li, Voskoboynikov, Lee, Sze and Tretyak suggested an iterative scheme for computing the electronic states of quantum dots and quantum rings taking into account an electron effective mass which depends on the position and electron energy level. In this paper we prove that this method converges globally and linearly in an alternating way, i.e. yielding lower and upper bounds of a predetermined energy level in turn. Moreover, taking advantage of the Rayleigh functional of the governing nonlinear eigenproblem, we propose a variant which converges even quadratically thereby reducing the computational cost substantially. Two examples of finite element models of quantum dots of different shapes demonstrate the efficiency of the method.
Subjects
quantum dot
nonlinear eigenproblem
Schrödinger equation
Rayleigh functional
computer simulation
DDC Class
510: Mathematik
Lizenz
http://rightsstatements.org/vocab/InC/1.0/
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