Classical and quantum size effects in electron conductivity of films with rough boundaries

We derive the classical static conductivity 〈{σ}〉 for a film with mildly sloping boundary asperities, when their root-mean-square height {ζ} is less than their mean length L. The formulas admit a numerical analysis of 〈{σ}〉 versus d/l and parameters {ζ}/L and kFL (d is the sample thickness, l is a bulk mean free path of electrons, and kF is the Fermi wave number). The decrease of the conductivity with increasing kFL is demonstrated. At small-scale boundary defects (kFL1), we also build the quantum theory of the electron transport. Dependencies of 〈{σ}〉 on l and d are studied. We reveal quantum dips of the conductivity versus kFd/{π} when a new conducting electron channel opens. The dips are caused by the size quantization of an electron-surface scattering frequency. The quasiclassical theory of 〈{σ}〉 at large-scale asperities (kFL{}1) is presented. In this case the residual conductivity due to the electron-surface interaction may have both quantum and classical origins. The relation between quantum and classical effects in the film conductivity is clarified. The theoretical results are tested against recent experimental data.