Effects of dielectric mismatch on the impurity binding energies in GaAs-${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As quantum wells

The effects of the image potential due to dielectric mismatch on the impurity states in GaAs-${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As quantum wells are investigated using the variational method. The results show that the effects of the image potential on the impurity binding energies in GaAs-${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As quantum wells are important, especially when the width of quantum well becomes small. The comparison with the results in the GaAs quantum well with an infinitely high confining potential and the dependence of the effects of the image potential on the composition x are discussed.