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

We study the variations of the electrical conductivity with thickness d of ultrathin metallic films. In the limit k₅1, where is the correlation length describing the film surface roughness and k₅ is the electron Fermi wave vector, we show that follows a universal law, d^2. 3, independent of any adjustable parameter. This law accounts for recent experimental data on CoSi₂ down to d=10 A. Moreover, the measurements of are well fitted when we introduce in its theoretical expression the values of the surface roughness parameters recently estimated from electron microscopy.