Surface and grain boundary contributions in the electrical resistivity of metallic nanofilms

The surface and grain boundary contributions in the electrical resistivity ρ of Au, Al and Cu films deposited by thermal evaporation with thickness from 3 to 100 nm on glass substrates were determined. The ρ values were measured and theoretically evaluated following the Fuchs-Sondheimer, the Mayadas-Shatzkes, and the combined models. A method to measure the grain size and its distribution from atomic force microscopy images was implemented, finding a lognormal behavior in all cases. We obtained that surface (p) and grain boundary reflection (R) coefficients decrease as the film thickness increases, showing R coefficient, higher values and most important changes than p coefficient. We concluded that high ρ values are mainly due to grain boundaries' contributions