Interaction of Slow Electrons with the Surface of a Model Dielectric: Theory of Surface Polarons

We discuss the interaction of a slow electron with the surface of a semi-infinite dielectric with dielectric constant that differs from unity by virtue of the presence of an infrared-active TO phonon. We obtain an expression for the effective interaction energy between the electron and the surface which reduces to the expression obtained from image-potential theory when the electron is far from the surface, either inside or outside the crystal. When the electron is near the surface, the effective potential differs from the image potential and becomes nonlocal. The form of the image potential is obtained by adapting to the present problem a method used by Lee, Low, and Pines in bulk polaron theory. We have applied the theory to the study of the binding of electrons to the crystal surface produced by the coupling of the electron to surface optical phonons and bulk LO phonons. We consider both the case where the electron is outside the crystal and trapped on the surface (the exterior-surface polaron) and the case where it is on the inside (the interior-surface polaron).