Conductivity and Mobility of Thin Lead Films

From measurements of electric conductivity made on thin films of Pb obtained by condensing the metal on cooled glass surfaces at rates from 5×${10}^{12}$ to 100×${10}^{12}$ atoms ${\sec .\mathrm{}}^{-1\mathrm{}}$ ${\mathrm{cm}}^{-2\mathrm{}}$ under high vacuum conditions designed to eliminate contamination, the following results are obtained: The critical film thickness ($d_c$) at which the (specific) conductivity ($\sigma$) begins changing rapidly from its low value ($\approx {10}^{-6\mathrm{}}$ mho·${\mathrm{cm}}^{-1\mathrm{}}$) in the thinnest films to that of the bulk metal (${\sigma }_0$, $\approx {10}^6$ mho·${\mathrm{cm}}^{-1\mathrm{}}$) is in the neighborhood of 60A for room temperature films, and of 30A for films cooled with liquid air. The mutual configuration of the condensed Pb atoms is unstable and changes with time, shown by a decrease observed in the conductivity when the film is isolated from external influences, and in the eventual appearance of a granular structure visible under the ultramicroscope. In some cases a reproducible dependence of the conductivity on the applied potential difference was observed. These effects are in harmony with the mechanism expected from considerations of the thermodynamic stability of such films, i.e., with a tendency toward aggregation resulting in the removal of mobile atoms into crystallization centers, and thus in formation of gaps which obstruct the conduction electrons. Certain deficiencies in quantitative reproducibility are ascribed to variations in the physical surface conditions on the plate where the film is condensed, presumably affecting the mobility of the layers condensed first.