Surface-induced resistivity of ultrathin metallic films: A limit law

We study the variations of the electrical conductivity σ with thickness d of ultrathin metallic films. In the limit ξ${\mathrm{k}}_{\mathrm{F}}$≪1, where ξ is the correlation length describing the film surface roughness and ${\mathrm{k}}_{\mathrm{F}}$ is the electron Fermi wave vector, we show that σ follows a universal law, σ∼${\mathrm{d}}^{2.3}$, independent of any adjustable parameter. This law accounts for recent experimental data on ${\mathrm{CoSi}}_2$ down to d=10 Å. Moreover, the measurements of σ are well fitted when we introduce in its theoretical expression the values of the surface roughness parameters recently estimated from electron microscopy.