Electrical Resistivity Of Atomically Smooth Single-Crystal Cu Films

We investigate using the Boltzmann transport equation the electrical resistivity of atomically smooth single-crystal Cu(111) and Cu(001) films with thickness 1-45 nm. Our transport calculations show that, in the absence of grain-boundary scattering and surface perturbations, the resistivity of Cu films of thickness comparable to the electron mean free path (40 nm for bulk copper) is close to the bulk resistivity. The resistivity increases trivially for sub-40-nm-thick films. These single-crystal Cu films show an intrinsic limit of resistivity. A steep increase in resistivity observed for ultrathin films is due to enhanced finite-size effects. We explain the cause of increase in resistivity by investigating the electronic structure at the Fermi level.