Electrical resistivity of metallic thin films with rough surfaces

The electrical resistivity of metallic thin films due to the scattering of conduction electrons with rough surfaces and with a random distribution of static impurities within the film is calculated here quantum mechanically using Mori's formalism. The detailed profiles of the surfaces enter into our theory through the single-particle wave functions and energies, which are calculated with the help of a nonconformal coordinate transformation. A detailed analysis of the roughness contribution to the resistivity is made in the small-roughness regime and with the assumption of a Gaussian form for the surface profile autocorrelation functions. The structures of the Fermi levels are studied, and effects due to the discreteness of the levels are also investigated. Our surface-roughness resistivity does not saturate with decreasing film thickness, in agreement with experimental findings.