Length dependence of localization and electron-electron interaction effects in thin metal films

The electrical properties of thin films of ${\mathrm{Au}}_{40}$ ${\mathrm{Pd}}_{60}$ and of Pt with lengths as small as 0.25 μm have been studied. At temperatures below about 10 K, the resistance increases with decreasing temperature due to localization and electron-electron interaction effects, as found in previous studies of much longer films. For films with lengths shorter than about 5 μm, the resistance rise decreases as the length of the film is decreased. This behavior is in agreement with general expectations concerning finite-size effects in these systems. However, it does not appear that the theory, at least in its present form, can account quantitatively for our results.