Confined electron and hydrogenic donor states in a spherical quantum dot of GaAs-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Ga</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mi mathvariant="normal">−</mml:mi><mml:mi mathvariant="italic">x</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Al</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="italic">x</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>As

According to hydrogenic-effective-mass theory, exact solutions and quantum-level structures are presented for confined electron and hydrogenic donor states in a spherical quantum dot (SQD) of GaAs-${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As. Calculated results reveal that the values of the quantum levels of a confined electron in a SQD can be quite different for cases with finite and infinite barrier heights. The quantum-level sequence and degeneracy for an electron in a SQD are similar to those of a super- atom of GaAs-${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As but different from those in a Coulomb field. There is stronger confinement and larger binding energy for a hydrogenic donor in a SQD of GaAs-${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As than in the corresponding quantum-well wires and two-dimensional quantum-well structures. The binding energy and its maximum of the ground state of a donor at the center of a quantum well are found to be strongly dependent on the well dimensionality and barrier height.