Electronic states at the surface of a polar crystal

Abstract

The problem of an electron at the ideal surface of a polar crystal is investigated. The electronic and lattice polarizabilities are treated dynamically at the same time: the coupling of the electron to surface and bulk polar (LO) phonons and to surface and bulk excitons is considered simultaneously. The ground-state energy of this system is then calculated variationally, using the Fock approximation, for which the electronic recoil effects are taken into account even in the direction perpendicular to the surface. The result that is obtained is valid for any values of the coupling strengths. In the static limit, we obtain directly the classical image potential results. For the case of an exterior polaron (equilibrium position of the electron outside the crystal), a bound state is always found close to the surface, as expected because of the attractive image potential. For an interior polaron (equilibrium position of the electron inside the crystal), a surface bound-state is found only for large values of the coupling constants, when the electron wavefunction is well localized around the electron. Furthermore, this binding, when it exists, is so close to the surface that the continuum model may not be valid. As a consequence of these calculations, no interior bound-state is expected for III–V or II–VI semiconductors with an ideal surface. On the other hand, exterior polarons are expected in most alkali halides.