Electron states of semiconductor quantum ring with geometry and size variations

Heterostructured semiconductor quantum rings (QR) are studied by a three-dimensional model in a single sub-band approach with energy dependent electron effective mass. Nonlinear confinement energy problem is numerically solved by the finite element method. Effects of boundary conditions corresponding to various QR/substrate configurations are analyzed. General relation for the size dependence of the QR confined energy is derived. The contribution to confinement energy due to the presence of external magnetic field is compared with the effect of variation of QR geometrical parameters. Applicability of the model is tested by comparison with experimental data.