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|Title:||Eigensolutions of the Wigner-Eisenbud problem for a cylindrical nanowire within finite volume method|
|Authors:||Racec, Paul N.; Schade, Stanley; Kaiser, Hans-Christoph|
|Published in:||Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik, Volume 1709, ISSN 0946-8633|
|Publisher:||Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik|
|Abstract:||We present a finite volume method for computing a representative range of eigenvalues and eigenvectors of the Schrödinger operator on a three dimensional cylindrically symmetric bounded domain with mixed boundary conditions. More specifically, we deal with a semiconductor nanowire which consists of a dominant host material and contains heterostructure features such as double-barriers or quantum dots. The three dimensional Schrödinger operator is reduced to a family of two dimensional Schrödinger operators distinguished by a centrifugal potential. Ultimately, we numerically treat them by means of a finite volume method. We consider a uniform, boundary conforming Delaunay mesh, which additionally conforms to the material interfaces. The 1/r singularity is eliminated by approximating r at the vertexes of the Voronoi boxes. We study how the anisotropy of the effective mass tensor acts on the uniform approximation of the first K eigenvalues and eigenvectors and their sequential arrangement. There exists an optimal uniform Delaunay discretization with matching anisotropy. This anisotropic discretization yields best accuracy also in the presence of a mildly varying scattering potential, shown exemplarily for a nanowire resonant tunneling diode. For potentials with 1/r singularity one retrieves the theoretically established first order convergence, while the second order convergence is recovered only on uniform grids with an anisotropy correction.|
|Keywords:||Finite element method; Schrödinger operator; cylindrical coordinates; R-matrix formalism; Wigne-Eisenbud problem; nanowire|
|License:||This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.|
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
|Appears in Collections:||Mathematik|
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