Numerical simulation of three dimensional pyramid quantum dot

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

80 Citations (Scopus)


We present a simple and efficient numerical method for the simulation of the three-dimensional pyramid quantum dot heterostructure. The pyramid-shaped quantum dot is placed in a computational box with uniform mesh in Cartesian coordinates. The corresponding Schrödinger equation is discretized using the finite volume method and the interface conditions are incorporated into the discretization scheme without explicitly enforcing them. The resulting matrix eigenvalue problem is then solved using a Jacobi-Davidson based method. Both linear and non-linear eigenvalue problems are simulated. The scheme is 2nd order accurate and converges extremely fast. The superior performance is a combined effect of the uniform spacing of the grids and the nice structure of the resulting matrices. We have successfully simulated a variety of test problems, including a quintic polynomial eigenvalue problem with more than 32 million variables.

Original languageEnglish
Pages (from-to)208-232
Number of pages25
JournalJournal of Computational Physics
Issue number1
Publication statusPublished - 2004 May 1


  • Finite volume method
  • Heterostucture
  • Large scale polynomial eigenvalue problem
  • Schrödinger equation
  • Semiconductor pyramid quantum dot

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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