The electrical resistivity of rough thin films: A model based on electron reflection at discrete step edges

The effect of the surface roughness on the electrical resistivity of metallic thin films is described by electron reflection at discrete step edges. A Landauer formalism for incoherent scattering leads to a parameter-free expression for the resistivity contribution from surface mound-valley undulations that is additive to the resistivity associated with bulk and surface scattering. In the classical limit where the electron reflection probability matches the ratio of the step height h divided by the film thickness d, the additional resistivity Δρ =  3/2/(g0d) × ω/ξ, where g0 is the specific ballistic conductance and ω/ξ is the ratio of the root-mean-square surface roughness divided by the lateral correlation length of the surface morphology. First-principles non-equilibrium Green's function density functional theory transport simulations on 1-nm-thick Cu(001) layers validate the model, confirming that the electron reflection probability is equal to h/d and that the incoherent formalism matches the coherent...