A calculation of the electrical conductivity of thin films of potassium and sodium

Calculations have been carried out on the electrical conductivity of both perfect and imperfect films of potassium at temperatures between 200K and 20K and of perfect films of sodium at temperatures between 200K and 50K, for two values of the specularity parameter p=0 and p=0.5. In all cases, the Boltzmann equation was solved numerically with a realistic electron-phonon interaction being used in the scattering term. It was found that, for all the above films, for a given value of p, the ratio of the mean resistivity of the film to that of the bulk crystal depends almost exclusively on a single parameter, kappa , the ratio of the film thickness to the effective electron mean free path. While the results of the Fuchs-Sondheimer theory agree with theirs for large values of kappa , the authors find that for smaller values of kappa the conductivity of the films is appreciably less than predicted by this theory. An explanation of this breakdown of the Fuchs-Sondheimer theory is proposed.