An iterative method for single and vertically stacked semiconductor quantum dots simulation

Yiming Li*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

We present in this paper a computational effective nonlinear iterative method for calculating the electron energy spectra in single and vertically stacked InAs/GaAs semiconductor quantum dots. The physical model problem is formulated with the effective one electronic band Hamiltonian, the energy- and position-dependent electron effective mass approximation, and the Ben Daniel-Duke boundary conditions. The multishift QR algorithm is implemented in the nonlinear iterative method for solving the corresponding nonlinear eigenvalue problem. This method converges monotonically when solving the nonlinear Schrödinger equation for all quantum dot simulations. Numerical results show that the electron energy spectra are significantly dependent on the number of coupled layers. For the excited states, the layer dependence effect has been found to be weaker than that for the ground state.

Original languageEnglish
Pages (from-to)711-718
Number of pages8
JournalMathematical and Computer Modelling
Volume42
Issue number7-8
DOIs
StatePublished - Oct 2005

Keywords

  • Coupling effect
  • Electronic structure
  • Energy spectra
  • Modelling and simulation
  • Multishift QR method
  • Nonlinear eigenvalue problem
  • Semiconductor nanostructure
  • Single quantum dot
  • Vertically stacked quantum dot
  • Wave function

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