Effect of image forces on the binding energies of impurity atoms in ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As/GaAs/${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As quantum wells

The present work investigates the effect of image forces due to the dielectric mismatch in ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Al}}_{\mathit{x}}$As/GaAs/${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Al}}_{\mathit{x}}$As superlattices on the binding energies of hydrogenic impurity atoms placed at the center of a ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Al}}_{\mathit{x}}$As/ GaAs/${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Al}}_{\mathit{x}}$As quantum well. The theory of images of classical electrodynamics is used to derive the potential energy of an impurity carrier (electron or hole) in a GaAs quantum well. Since the image-potential energy diverges as the charge approaches the interfaces, one can use the Lang-Kohn theory to study this system. It is pointed out that the image forces are important factors in studies of the binding energies of impurity atoms in GaAs quantum wells of narrow widths. Furthermore an accurate determination of image-plane locations in superlattice structures requires further investigations.