Some remarks on the Green's function calculation of electronic states at solid surfaces

The LCAO tight-binding method for computing electronic states in insulators and semiconductors has been recently recovered, in the Green's function formalism, for treating localized perturbations in ideal lattices. After a brief review of this method applied to surfaces, we face out the problem of a symmetry transformation turning an infinitely thick slab into a semi-infinite crystal. In this way conceptual and computational simplifications are achieved. We derive a formal expression for the charge density excess produced by a localized perturbation on the surface layer. This quantity is useful for the problem of inelastic scattering of atoms by surface phonons. © 1982 Società Italiana di Fisica.