CLASSICAL AND QUANTUM-SIZE EFFECTS IN ELECTRON CONDUCTIVITY OF FILMS WITH ROUGH BOUNDARIES

We derive the classical static conductivity [sigma] for a film with mi ldly sloping boundary asperities, when their root-mean-square height z eta is less than their mean length L. The formulas admit a numerical a nalysis of [sigma] versus d/l and parameters zeta/L and k(F)L (d is th e sample thickness, l is a bulk mean free path of electrons, and k(F) is the Fermi wave number). The decrease of the conductivity with incre asing k(F)L is demonstrated. At small-scale boundary defects (k(F)L < 1), we also build the quantum theory of the electron transport. Depend encies of [sigma] on l and d are studied. We reveal quantum dips of th e conductivity versus kFd/pi when a new conducting electron channel op ens. The dips are caused by the size quantization of an electron-surfa ce scattering frequency. The quasiclassical theory of [sigma] at large -scale asperities (k(F)L >> 1) is presented. In this case the residual conductivity due to the electron-surface interaction may have both qu antum and classical origins. The relation between quantum and classica l effects in the film conductivity is clarified. The theoretical resul ts are tested against recent experimental data.