By G P Zhigal'skii; Brian K Jones
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P. K. 18]. 6 Illustration of the decrease in the critical thickness hcr with a decrease of the density of nuclei at different condensation temperatures: Tc1 > Tc2 . 6 illustrates the increase of hcr with a decrease of the density of nuclei for different condensation temperatures, Tc1 and Tc2 (Tc1 > Tc2 ). For films precipitated on various substrates the critical thickness is very varied. If the precipitated material has a higher affinity with the material of the substrate a continuous film is formed at a smaller thickness.
In the first stages of metal deposition the film is formed from separate nuclei. The first atoms staying on to a substrate gather in small islands by surface diffusion. Then these increase in size and eventually become so large that they begin to join one another. Then they join together to form a continuous film. The thickness at which the layer shows metal conductivity is called the critical thickness, hcr . Thus if the film thickness is smaller than the critical thickness the electrical resistance will be much larger up to a value which exceeds the resistivity of the bulk metal by some orders of magnitude.
6]: jT ¼ AR T 2 expðÀ 0 =kT Þ ð2:7Þ where AR is the Richardson constant and 0 is the work function of the metal. The dependence of the current on temperature is determined mainly by the exponential factor, as the pre-exponential factor AR T 2 depends only weakly on temperature. For a system of two metal islands with a vacuum space between them, the magnitude of the thermal electron emission current depends exponentially on the height of the potential barrier between the islands. 7b. P. K. Jones À Be2 =d kT ð2:8Þ Conduction in discontinuous films 43 where A1 is a factor depending weakly on temperature and the distance between islands.