Numerical methods for semiconductor heterostructures with band nonparabolicity

Weichung Wang, Tsung-Min Hwang, Wen Wei Lin, Jinn Liang Liu

    研究成果: 雜誌貢獻文章同行評審

    29 引文 斯高帕斯(Scopus)

    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.

    原文英語
    頁(從 - 到)141-158
    頁數18
    期刊Journal of Computational Physics
    190
    發行號1
    DOIs
    出版狀態已發佈 - 2003 九月 1

    ASJC Scopus subject areas

    • Numerical Analysis
    • Modelling and Simulation
    • Physics and Astronomy (miscellaneous)
    • Physics and Astronomy(all)
    • Computer Science Applications
    • Computational Mathematics
    • Applied Mathematics

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