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}{}kF^-1, where kF 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}{∝}dˢ; similar effects are obtained for semiconducting quantum wells.