Transition energies of vertically coupled multilayer nanoscale InAs/GaAs semiconductor quantum dots of different shapes

The energy spectra of vertically coupled multilayer nanoscale semiconductor quantum dots (QDs) are theoretically studied using a unified three-dimensional (3D) model. The model formulation includes (1) the position-dependent effective mass Hamiltonian in a nonparabolic approximation for electrons, (2) the position-dependent effective mass Hamiltonian in a parabolic approximation for holes, (3) the finite hard wall confinement potential, and (4) Ben Daniel-Duke boundary conditions. To solve a nonlinear problem, a nonlinear iterative method is further improved in our developed 3D QD simulator. At an applied magnetic field (B), we explore the transition energy and the energy band gap of disk (DI)-, ellipsoid (EL)- and cone (CO)-shaped vertically coupled multilayer nanoscale semiconductor quantum dots. We find that the electron transition energy of vertically coupled multilayer InAs/GaAs QDs depends on their shape and is strongly dominated by the number of stacked layers (N), The interdistance (d) among InAs QDs plays a crucial role in the tunable states of these QDs. In DI-shaped vertically coupled 10-layer QDs at B = OT and d = 1.0 nm, we find approximately 40% variation in electron ground state energy, which is larger than that (∼20% variation) in CO-shaped QDs. In QDs at a nonzero magnetic field, the electron transition energy decreases with increasing N. In QDs with d = 1 nm, the rate of decrease is low when N > 6. This results in QDs with energy band gaps having similar dependences on N. This study implies different applications in magnetooptical phenomena and quantum optical structures.