Effects of interface defects on polaron states in GaAs-${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As quantum wells

Effects of interface defects on polaron states in GaAs-${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As quantum wells (QW’s) are investigated theoretically by introducing a coordinate transformation that transforms QW’s with defect interfaces to those with planar interfaces with an effective potential associated with the interface defects. The interface defects are idealized as an infinite track or a cylindrical hollow protruding into the barrier material on one of the interfaces. Polaron ground-state energies are calculated variationally as functions of the defect lateral sizes. For GaAs-${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As QW’s with well width d less than 150 Å, the changes in polaron ground-state energies due to interface defects are expected to lead to sizable effects on optical experiments, such as broadening of the luminescence, absorption, and excitation spectra of GaAs-${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As QW’s, but our calculation predicts smaller spectrum broadenings than those predicated by a previous theory for the same interface disorder. Changes in polaron self-energies and polaron effective masses caused by interface defects are negligible for materials with weak electron–LO-phonon interactions, such as GaAs for which the Fröhlich coupling constant ${\mathrm{\alpha }}_{\mathrm{LO}}$ is less than 0.1. Effects of interface defects on exciton states in QW’s are discussed qualitatively.