Using a variational procedure within the effective mass approximation, we have calculated the hydrogenic impurity binding energy as well as the impurity-related nonlinear optical absorption in a single quantum ring with axial n-type delta-doping. The delta-like potential along the z-direction is analytically modeled with a Hartree-like confining profile fitted to a one-dimensional Thomas-Fermi-based potential in the local density approximation. Both on-center and on-edge impurity positions are considered and the energies of the impurity states are examined as functions of the vertical size of the ring. It is found that the effect of changes in the geometry of the quantum ring leads to a shifting of the resonant peaks of the intra-band optical spectrum.
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