An iterative method for single and vertically stacked semiconductor quantum dots simulation

We present in this paper a computational effective nonlinear iterative method for calculating the electron energy spectra in single and vertically stacked InAs/GaAs semiconductor quantum dots. The physical model problem is formulated with the effective one electronic band Hamiltonian, the energy- and position-dependent electron effective mass approximation, and the Ben Daniel-Duke boundary conditions. The multishift QR algorithm is implemented in the nonlinear iterative method for solving the corresponding nonlinear eigenvalue problem. This method converges monotonically when solving the nonlinear Schrödinger equation for all quantum dot simulations. Numerical results show that the electron energy spectra are significantly dependent on the number of coupled layers. For the excited states, the layer dependence effect has been found to be weaker than that for the ground state.