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

The energy levels calculation of electrons confined in small three-dimensional (3D) coupled quantum In_xGa_1-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.