Vertical coupling effects and transition energies in multilayer InAs/GaAs quantum dots

We investigate the transition energy of vertically stacked semiconductor quantum dots with a complete three-dimensional (3D) model in an external magnetic field. In this study, the model formulation includes: (1) the position-dependent effective mass Hamiltonian in non-parabolic approximation for electrons, (2) the position-dependent effective mass Hamiltonian in parabolic approximation for holes, (3) the finite hard-wall confinement potential, and (4) the Ben Daniel-Duke boundary conditions. To solve the nonlinear problem, a nonlinear iterative method is implemented in our 3D nanostructure simulator. For multilayer small InAs/GaAs quantum dots, we find that the electron-hole transition energy is dominated by the number of stacked layers. The inter-distance d plays a crucial role in the tunable states of the quantum dots. Under zero magnetic field for a 10-layer QDs structure with d=1.0 nm, there is about 30% variation in the electron ground state energy. Dependence of the magnetic field on the electron-hole transition energy is weakened when the number of stacked layers is increased. Our investigation is constructive in studying the magneto-optical phenomena and quantum optical structures.