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

Abstract

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