Electronic states at the surfaces of crystals

The wave functions and energies of both the normal and surface electronic states of a finite linear chain are determined in terms of the overlap integrals by the approximation of tight binding, it being assumed that the interaction of atomic s -states with p -states can be neglected. It is shown that the existence of surface states depends on the ratio of two overlap integrals being greater than unity, and reasons are given for expecting this to be so.