Surface and grain-boundary scattering in nanometric Cu films

We report a quantitative analysis of both surface and grain-boundary scattering in Cu thin films with independent variation in film thickness (27 to 158 nm) and grain size (35 to 425 nm) in samples prepared by subambient temperature film deposition followed by annealing. Film resistivities of carefully characterized samples were measured at both room temperature and at 4.2 K and were compared with physical models that include the effects of surface and grain-boundary scattering. Grain-boundary scattering is found to provide the strongest contribution to the resistivity increase. However, a weaker, but significant, role is observed for surface scattering. We find that the data are best fit when the Mayadas and Shatzkes' model of grain-boundary scattering and the Fuchs and Sondheimer's model of surface scattering resistivity contributions are combined using Matthiessen's rule (simple addition of resistivities). This finding implies that grain-boundary scattering preserves the component of electron momentum parallel to the grain-boundary plane. Using Matthiessen's rule, we find our data are well described by a grain-boundary reflection coefficient of 0.43 and a surface specularity coefficient of 0.52. This analysis finds a significantly lower contribution from surface scattering than has been reported in previous works and we attribute this difference to the careful quantitative microstructural characterization performed on our samples. The effects of surface roughness, impurities, voids, and interactions between surface and grain-boundary scattering are also examined and their importance is evaluated.