Numerical methods for semiconductor heterostructures with band nonparabolicity

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)141-158
Number of pages18
JournalJournal of Computational Physics
Issue number1
Publication statusPublished - 2003 Sept 1


  • Cubic Jabobi-Davidson method
  • Cubic eigenvalue problems
  • Energy levels
  • Explicit nonequivalence deflation
  • Matrix reduction
  • Semiconductor quantum dot
  • The Schrödinger equation
  • Wave functions

ASJC Scopus subject areas

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


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