Verlagslink DOI: 10.1016/j.cpc.2005.12.003
Titel: Numerical calculation of the electronic structure for three-dimensional quantum dots
Sprache: Englisch
Autor/Autorin: Voß, Heinrich
Schlagwörter: quantum dot;nonlinear eigenproblem;Schrödinger equation;Rayleigh functional;computer simulation
Erscheinungsdatum: 2005
Quellenangabe: Preprint. Published in: Computer Physics Communications Volume 174, Issue 6, 15 March 2006, Pages 441-446
Serie/Report Nr.: Preprints des Institutes für Mathematik;Bericht 91
Zusammenfassung (englisch): 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.
URI: http://tubdok.tub.tuhh.de/handle/11420/60
URN: urn:nbn:de:gbv:830-opus-1139
DOI: 10.15480/882.58
Institut: Mathematik E-10
Mathematics E-10
Dokumenttyp: Preprint (Vorabdruck)
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