Localization of electrons in thin films with rough surfaces

A system of noninteracting electrons in a thin metal film which experience arbitrarily weak scattering from a randomly rough surface is shown to be always in localized states. The frequency-and wave-vector-dependent density response function, the frequency-dependent conductivity, and the localization length are calculated at $T=0$ in the ω→0, →q→→0 limits. We find that the localization length r₀ depends on the film thickness d as r₀∝exp(d³l³), where l³ is a constant depending on the Fermi energy and surface roughness.