Electronic states of on- and off-center donors in quantum rings of finite width

The electronic states of a hydrogenic donor in two-dimensional quantum rings are calculated by taking into account the finite width of the potential well in the ring. In addition, a strong magnetic field is applied perpendicular to the quantum ring. Using the effective-mass approximation at the Γ valley, the radial Hamiltonian for the envelope-function is exactly diagonalized in the case of on-center donors. The corresponding energy levels for different angular momenta are studied as a function of the applied magnetic field. In the case of off-center donors, a perturbation approach is considered and its limitations are discussed. Finally, we calculate the absorption spectra and oscillator strength for different intraband transitions, specifically for on-center donors.