Localization in thin copper films

Resistance measurements in zero magnetic field have been made on thin Cu films (30 to 500 {}) between 1 to 100 K with the goal of determining the relevant scattering times. The elastic scattering time τ₀ is limited by the thickness d of the samples and is well described by τ₀=vFd. With the assumption that the inelastic scattering time τᵢ has a temperature dependence given by τᵢ∝T^-P, then the high-temperature resistance data yielded P=1.9±0.3. These measurements also demonstrate that the localization phenomena extend to temperatures much greater than the temperature Tₘᵢₙ 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 (τₛₒ<~τᵢ).