Numerical methods for semiconductor heterostructures with band nonparabolicity

Authors:
Weichung Wang;Tsung-Min Hwang;Wen-Wei Lin;Jinn-Liang Liu
Affiliations:
Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung 811, Taiwan;Department of Mathematics, National Taiwan Normal University, Taipei 116, Taiwan;Department of Mathematics, National Tsing Hua University, Hsinchu 300, Taiwan;Department of Applied Mathematics, National Chiao Tung University, Hsinchu 300, Taiwan
Venue:
Journal of Computational Physics
Year:
2003

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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.