Two-Dimensional Resistivity of Ultrathin Metal Films

Extremely thin (monolayer to 100 Å) continuous metallic films of Pt can be formed on Si substrates. In the thinnest films the conductance is found to be $S=S_0+{\alpha }^1\left(\frac{e^2}{{\pi }^2\hslash }\right)$ $\ln T+\delta T^2$, with ${\alpha }^1=0.75\mathrm{}\pm 0.15$ 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.