On the energy levels of three dimensional quantum dot with irregular shape

Tsung-Min Hwang, Wen Wei Lin, Wei Cheng Wang, Weichung Wang

Research output: Contribution to conferencePaper

Abstract

Nanoscale semiconductor quantum dots (QDs) have been intensively studied in their physics and applications. In addition to theoretical and experimental methods, numerical simulations can also provide useful insights into a QD's electronic and optical properties. However, effective and feasible numerical methods for three dimensional (3D) quantum structures are rarely available. We present novel methods for calculating bound state energies and their corresponding wave functions of a 3D QD model. The model assumes that a irregular shape single low-band-gap semiconductor QD island is embedded in a wideband-gap semiconductor matrix. The heterojunction of the QD can be approximated by an arbitrary smooth function to fit real world QDs nicely. The Schrödinger equation approximating the model in cylindrical coordinate is discretized by using a body fitting finitedifference method. The scheme comes from directly discretization of the Schrödinger equations in curvilinear coordinate system with a clever choice of coordinate axis in the computational domain that gives a sharp local truncation error estimate near the interface and at the same time guarantees the symmetry and positivity of the resulting matrix. As long as the grids are non-crossing, this procedure gives a symmetric and positive definite matrix, regardless of the regularity of the grids. The induced eigenvalue problems are then solved by the Jacobi-Davidson methods. Our numerical experiment results show that the proposed methods can be very efficient and achieve the second order convergence rate.

Original languageEnglish
Publication statusPublished - 2004 Dec 1
EventEuropean Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004 - Jyvaskyla, Finland
Duration: 2004 Jul 242004 Jul 28

Other

OtherEuropean Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004
CountryFinland
CityJyvaskyla
Period04/7/2404/7/28

Fingerprint

Jacobi-Davidson Method
Heterojunction
Jacobian matrices
Eigenvalues and Eigenfunctions
Jacobian matrix
Quantum Dots
Computational methods
Energy Levels
Eigenvalues and eigenfunctions
Computational Methods
Electron energy levels
Semiconductor quantum dots
Schrödinger Equation
Heterojunctions
Irregular
Three-dimensional
Semiconductors
Grid
Co-ordinate axis
Curvilinear Coordinates

Keywords

  • Energy levels
  • Irregular shapes
  • Jacobi-Davidson method
  • Large scale eigenproblem
  • Schrödinger equation
  • Semiconductor quantum dot

ASJC Scopus subject areas

  • Artificial Intelligence
  • Applied Mathematics

Cite this

Hwang, T-M., Lin, W. W., Wang, W. C., & Wang, W. (2004). On the energy levels of three dimensional quantum dot with irregular shape. Paper presented at European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004, Jyvaskyla, Finland.

On the energy levels of three dimensional quantum dot with irregular shape. / Hwang, Tsung-Min; Lin, Wen Wei; Wang, Wei Cheng; Wang, Weichung.

2004. Paper presented at European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004, Jyvaskyla, Finland.

Research output: Contribution to conferencePaper

Hwang, T-M, Lin, WW, Wang, WC & Wang, W 2004, 'On the energy levels of three dimensional quantum dot with irregular shape' Paper presented at European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004, Jyvaskyla, Finland, 04/7/24 - 04/7/28, .
Hwang T-M, Lin WW, Wang WC, Wang W. On the energy levels of three dimensional quantum dot with irregular shape. 2004. Paper presented at European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004, Jyvaskyla, Finland.
Hwang, Tsung-Min ; Lin, Wen Wei ; Wang, Wei Cheng ; Wang, Weichung. / On the energy levels of three dimensional quantum dot with irregular shape. Paper presented at European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004, Jyvaskyla, Finland.
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