A Computational Technique for Electron Energy States Calculation in Nano-Scopic Three-Dimensional InAs/GaAs Semiconductor Quantum Rings Simulation

We study theoretically the electron energy states for three-dimensional (3D) nano-scopic semiconductor quantum rings. In this study, the model formulation includes: (i) the effective one-band Hamiltonian approximation, (ii) the position and energy dependent quasi-particle effective mass approximation, (iii) the finite hard wall confinement potential, and (iv) the Ben Daniel-Duke boundary conditions. To calculate the energy levels, the 3D model is solved by nonlinear iterative algorithm to obtain self-consistent solutions. The model and solution method provide a novel way to calculate the energy levels of nano-scopic semiconductor quantum ring and are useful to clarify the principal dependencies of quantum ring energy states on material band parameter, ring size and shape. We find the energy levels strongly depend on the radial cross section shapes of quantum rings. The dependence of energy states on shapes of 3D quantum ring reveals a significant difference from results derived on basis of 2D approaches.