Size effects in the electrical resistivity of polycrystalline nanowires

Grain-boundary and surface scattering are known to increase the electrical resistivity of thin metallic films and wires. The length scale at which these produce appreciable effects is of the order of the electronic mean free path. For the well-studied case of thin films, both mechanisms can, in principle, be used to explain the observed thickness dependence on resistivity. In order to evaluate which of these mechanisms is more relevant, we have carried out an experimental study of the width dependence of the resistivity of narrow thin-film polycrystalline gold wires (nanowires), and computed the expected behavior on the basis of both surface and grain-boundary scattering mechanisms independently. We find that the resistivity increases as wire width decreases in a manner which is dependent on the mean grain size and cannot be explained adequately by either model alone. We propose a modification to the well-known model of Mayadas and Shatzkes, incorporating the variation of mean grain size on wire dimensions.