Two-Dimensional Resistivity of Ultrathin Metal Films

Abstract

Extremely thin (monolayer to 100 \AA{}) continuous metallic films of Pt can be formed on Si substrates. In the thinnest films the conductance is found to be $S={S}_{0}+{\ensuremath{\alpha}}^{1}(\frac{{e}^{2}}{{\ensuremath{\pi}}^{2}\ensuremath{\hbar}})$ $\mathrm{ln}T+\ensuremath{\delta}{T}^{2}$, with ${\ensuremath{\alpha}}^{1}=0.75\ifmmode\pm\else\textpm\fi{}0.15$ from liquid-He temperatures up to $T>~390$ K. Thicker films show a transition as a function of temperature from two- to three-dimensional behavior, with a corresponding resistivity minimum. The negative magnetoresistance is in good agreement with predictions of localization theory.