Surface roughness mediated specularity parameter of thin Cu films

Abstract

Roughness-induced resistivity variation of thin metal films is conveniently described by the Fuchs-Sondheimer model, where the phenomenological parameter p is used to quantify the extent of specular scattering at surfaces. However, p is a lumped parameter and does not include microscopic information that characterizes roughness, viz., auto-correlation function, root-mean-square height, and correlation length. In this work, we extract these roughness parameters for Cu films of thickness ranging from 31nm to 95nm. We find that the roughness-roughness correlation function is an exponential with a characteristic correlation length that increases monotonically with the film thickness. Using this, we predict the roughness parameter-dependent specularity coefficient, which has an implicit thickness dependency. This alters the resistivity scaling compared to the prevailing model of resistivity scaling, where p is assumed to be a constant.