Electron-phonon interactions and electron inversion layers on polar semiconductors

We have examined the phonon contributions to the proper self-energy of electrons in an inversion layer formed on the surface of a polar semiconductor. The electron then interacts with both bulk LO phonons and surface polaritons via the Fr\"ohlich mechanism. For a simple model of the inversion layer, we have calculated contributions to the proper self-energy from both interband and intraband electron-phonon scatterings. We consider the case where the phonon energies nearly match the gap between the lowest (occupied) and first excited (empty) subband, and comment on the applicability of our results to electrons confined near the interface of GaAsGaₓAl_1-xAs heterostructures.