Matching formalism for surface states and surface resonances

Abstract

A method for finding localized states and resonances at surfaces and at interfaces of periodic media, like solids or superlattices, has been formulated. The logarithmic derivatives of matched solutions in the case of localized states, and the local density of states in the case of resonances, are calculated using the concept of a transfer matrix.$-— The method is applied to studying the electronic surface states in GaAs/${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As superlattices and the image-induced resonances of the (111) surface of silver.