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 conferencePaperpeer-review

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
EventEuropean Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004 - Jyvaskyla, Finland
Duration: 2004 Jul 242004 Jul 28

Conference

ConferenceEuropean Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004
Country/TerritoryFinland
CityJyvaskyla
Period2004/07/242004/07/28

Keywords

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

ASJC Scopus subject areas

  • Artificial Intelligence
  • Applied Mathematics

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