The effect of surface roughness and grain-boundary scattering on the electrical conductivity of thin metallic wires

Abstract

We report a new formula for the electrical conductivity of a thin wire of rectangular cross-section, obtained from an exact solution of the Boltzmann equation by assuming perfectly diffuse surface scattering and absence of grain boundaries. Also, we calculate the electrical conductivity of polycrystalline metallic wires, both for the case of rectangular and circular cross-sections and for arbitrary values of Fuchs' specularity parameter, by means of a seminumerical procedure that solves the Boltzmann equation by summing over classical trajectories in accordance with Chambers' method. Following Szczyrbowski and Schmalzbauer, the scattering by grain boundaries is represented by a peculiar specularity parameter and a boundary transmittance. The difference between one and the sum of these two probabilities measures the probability of diffuse scattering. We examine the dependence of the conductivity on the values of these parameters and the effects of disorder on the diameters of the grains.