Energy states of vertically aligned quantum dot array with nonparabolic effective mass

Tsung Min Hwang, Weichung Wang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


The electronic properties of a three-dimensional quantum dot array model formed by vertically aligned quantum dots are investigated numerically. The governing equation of the model is the Schrödinger equation which is incorporated with a nonparabolic effective mass approximation that depends on the energy and position. Several interior eigenvalues must be identified from a large-scale high-order matrix polynomial. In this paper, we propose numerical schemes that are capable of simulating the quantum dot array model with up to 12 quantum dots on a personal computer. The numerical experiments also lead to novel findings in the electronic properties of the quantum dot array model.

Original languageEnglish
Pages (from-to)39-51
Number of pages13
JournalComputers and Mathematics with Applications
Issue number1
Publication statusPublished - 2005 Jan


  • Cubic Jacobi-Davidson method
  • Cubic large-scale eigenvalue problems
  • Energy levels
  • Matrix reduction
  • Semiconductor quantum dot array
  • The Schrödinger equation

ASJC Scopus subject areas

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics


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