GROUND-STATE ENERGY OF AN EXTERIOR SURFACE POLARON

The binding energy and the root-mean-square distance to the surface of an exterior polaron, whose wave function does not penetrate the cryst al, are calculated for an ideal polar crystal surface. Only the image states are considered. We consider dynamically the electronic coupling to both excitons and phonons. Three variational approaches are used a nd compared: a weak-coupling theory including zero- and one-phonon ter ms, a strong-coupling approach involving displaced oscillators and a G reen's function Fock approximation. For the three cases, a Gaussian el ectronic ansatz is used which, for most cases, gives lower energy than a Coulomb one. The effect of the electronic recoil in the three cases is investigated and we conclude that recoil effects are important eve n in the direction perpendicular to the surface. We find that the stro ng-coupling approach can never be used for any real crystal, the coupl ing to surface modes decaying rapidly away from the surface. On the ot her hand, the weak-coupling limit is quite good for many polar crystal s and we show that, in this case, the binding energy depends only on t he static dielectric constant (epsilon(s)). For all possible values of the parameters, the Green's function calculation gives the best bindi ng energies (lowest ground-state energy). Numerical results are given for a few representative semiconductors and dielectrics.