Theoretical model for fast calculations of the electrical resistivity of thin metallic films with rough surfaces

A model of electron gas scattering at surface inhomogeneities was developed and applied to describe a surface roughness influence on the electrical resistivity of thin metallic films. The model is developed to be simple enough for fast calculations without detailed investigation of surface topology. The film’s shape is assumed to be described by the average thickness, the surface rms, and the correlation length. The scattering mechanism corresponds to electrical potential changes caused by inhomogeneities. It was found that the electrical resistivity of thin films increases with the increase of the roughness of surface for films of any thickness, whereas the law of this effect depends on film’s thickness. Basing on the developed model, formulas for the electrical resistivity as a function of the roughness rms and the correlation length in cases of thick enough, thin, and extremely thin films have been obtained and discussed with comparison to other models already in literature and experimental data.