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 threedimensional (3D) model in an external magnetic field. In this study, the model formulation includes: (1) the positiondependent 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 1⁄4 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. 2004 Elsevier B.V. All rights reserved.