Spectrum and binding of an off-center donor in a spherical quantum dot

The energy levels and binding energies of an off-center donor in a GaAs-${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As spherical quantum dot are calculated by a linear variational method. The results clearly show the quantum size effect. The location effects of a donor ion on splitting, level ordering, and binding of the donor states are studied. It is found that the alteration of the position of a single Coulomb center can largely change the single-electron spectrum in a quantum dot with a larger radius.