Influence of surface and grain-boundary scattering on the resistivity of copper in reduced dimensions

We examine the influence of surface and grain-boundary scattering on the total electrical resistivity of copper as dimensions are reduced close to the bulk electron mean free path (39 nm). Through resistivity and grain size characterization on copper wires with sizes down to $\text{95×130\hspace{0.17em}}{\mathrm{nm}}^2$ in a temperature range of 4.2 to 293 K, it was found that the influence of surface scattering is less than previously speculated, while grain-boundary scattering is dominant. A reduction of the background scattering length due to small grains accounts for the observed behavior. The reflection coefficient varies as expected from impurity enrichment in the grain boundaries.