Transport theory in metallic films: Crossover from the classical to the quantum regime

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Abstract
Using the quantum-statistical approach, we have developed a unified transport theory of metallic films. A general description for the conductivity in metallic films has been rigorously formulated in the presence of both impurity scattering and surface roughness. An explicit connection between the quasiclassical and present quantum approaches is also presented. We show that the quasiclassical theory by Fuchs [Proc. Cambridge Philos. Soc. 34, 100 (1938)] and Sondheimer [Adv. PHys. 1, 1 (1952)] can be reformed to be applicable to ultrathin metallic films by introducing a treatment of the surface via angle-dependent specularity parameters and including the quantum size effect. Moreover, to the lowest-order approximation in the theory, the previous quantum-approach results and discussions have naturally been recovered.