Surface electron transport and quantum size effect in electron conductivity of thin films with statistically rough boundaries

Abstract

We derived the classical and quantum static electron conductivity of films with randomly rough boundaries beyond the perturbation theory via the approximation of mildly sloping asperities, when the r.m.s. height ζ of boundary defects is less than their lengthL. The classical is a function of three parameters:dII, ζIL, andk F L (d is the film thickness,I a bulk mean free path of electrons) and admits full numerical analysis. The quantum depends ond andI separately. We revealed fundamental quantum dips of vs.d due to spatial quantization of electron-surface scattering frequency and calculated the residual conductivity as bulk collisions vanish (I→∞). The residual conductivity may have both quantum and exclusively classical origins at definite conditions. The theoretical results were tested against recent experimental data.