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

Tsung-Min Hwang, Weichung Wang

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

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
Volume49
Issue number1
DOIs
Publication statusPublished - 2005 Jan 1

Fingerprint

Effective Mass
Quantum Dots
Electron energy levels
Semiconductor quantum dots
Energy
Electronic Properties
Electronic properties
Matrix Polynomial
Personal Computer
Personal computers
Model
Numerical Scheme
Governing equation
Interior
Numerical Experiment
Polynomials
Higher Order
Eigenvalue
Three-dimensional
Approximation

Keywords

  • 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

Cite this

Energy states of vertically aligned quantum dot array with nonparabolic effective mass. / Hwang, Tsung-Min; Wang, Weichung.

In: Computers and Mathematics with Applications, Vol. 49, No. 1, 01.01.2005, p. 39-51.

Research output: Contribution to journalArticle

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