Numerical Methods for Semiconductor Heterostructures with Band Nonparabolicity
Resource
Journal of Computational Physics,190,141-158.
Journal
Journal of Computational Physics
Journal Issue
190
Pages
141-158
Date Issued
2003-09
Date
2003-09
Author(s)
Abstract
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. © 2003 Elsevier B.V. All rights reserved.
SDGs
Type
journal article