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

Abstract

We study the variations of the electrical conductivity \ensuremath{\sigma} with thickness d of ultrathin metallic films. In the limit \ensuremath{\xi}${\mathrm{k}}_{\mathrm{F}}$\ensuremath{\ll}1, where \ensuremath{\xi} is the correlation length describing the film surface roughness and ${\mathrm{k}}_{\mathrm{F}}$ is the electron Fermi wave vector, we show that \ensuremath{\sigma} follows a universal law, \ensuremath{\sigma}\ensuremath{\sim}${\mathrm{d}}^{2.3}$, independent of any adjustable parameter. This law accounts for recent experimental data on ${\mathrm{CoSi}}_{2}$ down to d=10 A\r{}. Moreover, the measurements of \ensuremath{\sigma} are well fitted when we introduce in its theoretical expression the values of the surface roughness parameters recently estimated from electron microscopy.