Two-Dimensional Localization in Thin Copper Films

Resistance measurements have been made on low-resistivity thin Cu films (50-500 Å) between 1 and 20 K. A logarithmic temperature dependence of the resistance is observed. For a resistance per square of $R<\mathrm{}20\mathrm{}$ Ω/□, good agreement is obtained with the localization theory. The amplitude of the resistance variation and its large magnetic-field dependence exclude possible Coulomb-interaction effects predicted by Altshuler et al. as the main source of the observed behavior.