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A. Bruno-Alfonso, et al, Phys. Rev. B 61, 15887 (2000)
https://doi.org/10.1103/PhysRevB.61.15887

(1) The overall result for standard structures (quantum wells, quantum well wires and quantum dots) is that reduction of characteristic sizes increases the effective strength of the carrier-impurity interaction, thus enhancing the corresponding binding energy.
(2) Separate dependences on  and z is exact for infinite-barrier quantum well wires only. However, it still works quite well for finite-barriers if carrier penetration is weak.
(3) The singularities exhibited in the DOS of impurity states are associated with different positions of the donor inside the quantum ring.
(4) For 1s-like shallow-donor states, the quantum ring behaves as a quantum well wire for almost all values of the internal radius which are greater than the effective Bohr radius.
(5) A detailed study of the electronic states including shallow-donor excited levels, valence states, interface roughness, disorder, spin, excitonic, electron-phonon, and electron-electron interactions is fundamental for an optical characterization of quantum rings.