Binding energy of the 2$p_0$-like level of a hydrogenic donor in GaAs-${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$${\mathrm{Al}}_{\mathrm{x}}$As quantum-well structures

Recently we reported a calculation of the binding energy of the 2$p_0$-like level of a hydrogenic donor associated with the first conduction subband in a GaAs-${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Al}}_{\mathrm{x}}$As quantum-well structure. It was found that the value of the binding energy of this level decreased as the well width was reduced, and became zero for a well width of about 650 Å. In this Brief Report we present results which demonstrate that this peculiar behavior of the 2$p_0$ state is due to the fact that it is closely associated with the second electron subband, and remains bound with respect to it (with increasing binding energy) as the well width is reduced.