Calculation of induced electron states in three-dimensional semiconductor artificial molecules

Yi-Ming Li*, O. Voskoboynikov, C. P. Lee, S. M. Sze

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


The energy levels calculation of electrons confined in small three-dimensional (3D) coupled quantum InxGa1-xAs dots embedded in GaAs semiconductor matrix is presented. The quantum dots have disk shapes and are separated (in the disk symmetry axis direction) by a certain distance. Based on the effective one electronic band Hamiltonian, the energy and position dependent electron effective mass approximation, a finite height hard-wall 3D confinement potential, and the Ben Daniel-Duke boundary conditions, the problem is formulated and solved for the disk-shaped coupled quantum dots. To calculate the ground and induced state energy levels, the nonlinear 3D Schrödinger equation (SE) is solved with a developed nonlinear iterative method to obtain the final self-consistent solutions. In the iteration loops, the Schrödinger equation is discretized with a nonuniform mesh finite difference method, and the matrix eigenvalue problem is solved with the balanced and shifted QR method. Our complete 3D approach demonstrates a principal possibility that the number of bound electronic states in the system can be changed when the interdot (vertical) distance is modified. However, it is impossible to produce an additional possibility to manipulate the system electronic properties within only a two-dimensional (2D) simulation.

Original languageEnglish
Article number44
Pages (from-to)209-213
Number of pages5
JournalComputer Physics Communications
Issue number1-2
StatePublished - Aug 2002


  • Computer simulation
  • Electron energy levels
  • Nonlinear iteration algorithm
  • Semiconductor artificial molecules

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