Localization in thin copper films

Abstract

Resistance measurements in zero magnetic field have been made on thin Cu films (30 to 500 \AA{}) between 1 to 100 K with the goal of determining the relevant scattering times. The elastic scattering time ${\ensuremath{\tau}}_{0}$ is limited by the thickness $d$ of the samples and is well described by ${\ensuremath{\tau}}_{0}=\frac{{v}_{F}}{d}$. With the assumption that the inelastic scattering time ${\ensuremath{\tau}}_{i}$ has a temperature dependence given by ${\ensuremath{\tau}}_{i}\ensuremath{\propto}{T}^{\ensuremath{-}P}$, then the high-temperature resistance data yielded $P=1.9\ifmmode\pm\else\textpm\fi{}0.3$. These measurements also demonstrate that the localization phenomena extend to temperatures much greater than the temperature ${T}_{min}$ at which the resistance minimum occurs. At low temperatures in the thinnest films, deviations in the resistance from the logarithmic temperature dependence are observed; this effect is attributed to strong spin-orbit scattering which dominates the inelastic scattering at low temperatures (${\ensuremath{\tau}}_{\mathrm{so}}<~{\ensuremath{\tau}}_{i}$).