Dependence of energy gap on magnetic field in semiconductor nano-scale quantum rings

Abstract

We study the electron and hole energy states for a complete three-dimensional (3D) model of semiconductor nanoscale quantum rings in an external magnetic field. In this study, the model formulation includes: (i) the position dependent effective mass Hamiltonian in non-parabolic approximation for electrons, (ii) the position dependent effective mass Hamiltonian in parabolic approximation for holes, (iii) the finite hard wall confinement potential, and (iv) the Ben Daniel-Duke boundary conditions. To solve this 3D non-linear problem, we apply the non-linear iterative method to obtain self-consistent solutions. We find a non-periodical oscillation of the energy band gap between the lowest electron and hole states as a function of external magnetic fields. The result is useful in describing magneto-optical properties of the nano-scale quantum rings. (C) 2003 Elsevier Science B.V. All rights reserved.