Electron transition energy for vertically coupled InAs/GaAs semiconductor quantum dots and rings

Yi-Ming Li*, Hsiao Mei Lu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We investigate the transition energy of vertically coupled quantum dots and rings (VCQDs and VCQRs) with a three-dimensional (3D) model under an applied magnetic field. The model formulation includes (1) the position-dependent effective mass Hamiltonian in the nonparabolic approximation for electrons, (2) the position-dependent effective mass Hamiltonian in the parabolic approximation for holes, (3) the finite hard-wall confinement potential, and (4) the Ben Daniel-Duke boundary conditions. We explore small VCQDs and VCQRs with disk (DI) and conical (CO) shapes. For small VCQDs and VCQRs, the electron-hole transition energy is dominated by the interdistance d which plays a crucial role in the tunable states of structures. Under zero magnetic field, there is about 25% variation in the electron ground state energy for both InAs/GaAs DI-shaped VCQDs and VCQRs with d varying from 0.4 nm to 4.8nm. The energy spectra of the CO-shaped VCQDs are the most stable against the structure interdistance deviations (among dots and rings of the same volume). For a fixed d, VCQDs show diamagnetic shift; contrarily, VCQRs imply a nonperiodical transition among the lowest electron energy states. The energy band gap of VCQRs oscillates nonperiodically between the lowest electron and holes states as a function of external magnetic fields. Our investigation is constructive for studying the magneto-optical phenomena of the nanoscale semiconductor artificial molecules.

Original languageEnglish
Pages (from-to)2104-2109
Number of pages6
JournalJapanese Journal of Applied Physics, Part 1: Regular Papers and Short Notes and Review Papers
Issue number4 B
StatePublished - Apr 2004


  • Electron transition energy
  • Magnetic field effects
  • Modeling and simulation
  • Semiconductor artificial molecules
  • Vertically coupled quantum dots
  • Vertically coupled quantum rings

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