Effect of Shape and Size on Electron Transition Energies for Nanoscale InAs/GaAs Quantum Rings

In this paper, we study the impact of the sizes and the shapes of nanoscale semiconductor quantum rings on the electron and hole energy states. A three-dimensional effective one band Schrödinger equation is solved numerically for semiconductor quantum rings with disk, cut-bottom-elliptical, and conical shapes. For small InAs/GaAs quantum rings we have found a sufficient difference in the ground state and excited state (l = −1) electron energies for rings with the same volume but different shapes. Volume dependence of the electron and hole energies can vary over a wide range and depends significantly on the ring shapes. It is found that a non-periodical oscillation of the energy band gap between the lowest electron and hole states as a function of external magnetic fields.