Localization in thin copper films

Resistance measurements in zero magnetic field have been made on thin Cu films (30 to 500 Å) between 1 to 100 K with the goal of determining the relevant scattering times. The elastic scattering time ${\tau }_0$ is limited by the thickness $d$ of the samples and is well described by ${\tau }_0=\frac{v_F}{d}$. With the assumption that the inelastic scattering time ${\tau }_i$ has a temperature dependence given by ${\tau }_i\propto T^{-P}$, then the high-temperature resistance data yielded $P=1.9\mathrm{}\pm 0.3$. 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 (${\tau }_{\mathrm{so}}<~{\tau }_i$).