標題: Numerical methods for semiconductor heterostructures with band nonparabolicity
作者: Wang, WC
Hwang, TM
Lin, WW
Liu, JL
應用數學系
Department of Applied Mathematics
關鍵字: semiconductor quantum dot;the Schrodinger equation;energy levels;wave functions;cubic eigenvalue problems;matrix reduction;cubic Jacobi-Davidson method;explicit nonequivalence deflation
公開日期: 1-Sep-2003
摘要: This article presents numerical methods for computing bound state energies and associated wave functions of three-dimensional semiconductor heterostructures with special interest in the numerical treatment of the effect of band nonparabolicity. A nonuniform finite difference method is presented to approximate a model of a cylindrical-shaped semiconductor quantum dot embedded in another semiconductor matrix. A matrix reduction method is then proposed to dramatically reduce huge eigenvalue systems to relatively very small subsystems. Moreover, the nonparabolic band structure results in a cubic type of nonlinear eigenvalue problems for which a cubic Jacobi-Davidson method with an explicit nonequivalence deflation method are proposed to compute all the desired eigenpairs. Numerical results are given to illustrate the spectrum of energy levels and the corresponding wave functions in rather detail. (C) 2003 Elsevier B.V. All rights reserved.
URI: http://dx.doi.org/10.1016/S0021-9991(03)00268-7
http://hdl.handle.net/11536/27573
ISSN: 0021-9991
DOI: 10.1016/S0021-9991(03)00268-7
期刊: JOURNAL OF COMPUTATIONAL PHYSICS
Volume: 190
Issue: 1
起始頁: 141
結束頁: 158
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