Influence of surface roughness on the conductivity of metallic and semiconducting quasi-two-dimensional structures

At low temperature, the conductivity σ of metallic films or of semiconducting quantum wells is limited by surface-roughness scattering. The expression for σ includes an autocorrelation function (ACF) associated with the roughness. We report a theoretical study of the dependence of σ on the shape, and the correlation length ξ of the ACF. It is concluded that σ depends strongly on the choice of the ACF for ξ≫${\mathit{k}}_{\mathit{F}}^{\mathrm{-}1}$, where ${\mathit{k}}_{\mathit{F}}$ is the Fermi wave vector. For metallic films, the mean variation of σ with thickness d cannot be approximated by the usual power law, σ∝${\mathit{d}}^{\mathit{s}}$; similar effects are obtained for semiconducting quantum wells.