The resistivity of thin Cu films depends on film thickness as the dimensions approach the electron mean-free-path for Cu of 39 nm. The key size-dependent contributions are from electron-surface scattering, grain boundary scattering, and surface roughness-induced scattering. Measurements with pseudoepitaxial Cu films deposited on Si have been undertaken to reduce effects of grain boundaries and surface roughness and suggest an electron-scattering parameter of p = 0.12. Overlayers of metal films on the Cu generally increase the resistivity for Ta and Pt overlayers, and may reduce the resistivity for Au and Al. The resistivity increase may also be reversed if the overlayer oxidizes. (C) 2004 American Vacuum Society.