Surface roughness dependence of the electrical resistivity of W(001) layers

Abstract

The resistivity ρ of epitaxial W(001) layers grown on MgO(001) at 900 °C increases from 5.63 ± 0.05 to 27.6 ± 0.6 μΩ-cm with decreasing thickness d = 390 to 4.5 nm. This increase is due to electron-surface scattering but is less pronounced after in situ annealing at 1050 °C, leading to a 7%–13% lower ρ for d < 20 nm. The ρ(d) data from in situ and ex situ transport measurements at 295 and 77 K cannot be satisfactorily described using the existing Fuchs-Sondheimer (FS) model for surface scattering, as ρ for d < 9 nm is larger than the FS prediction and the annealing effects are inconsistent with a change in either the bulk mean free path or the surface scattering specularity. In contrast, introducing an additive resistivity term ρmound which accounts for surface roughness resolves both shortcomings. The new term is due to electron reflection at surface mounds and is, therefore, proportional to the ballistic resistance times the average surface roughness slope, divided by the layer thickness. This is confirmed by a measured linear relationship between ρmound and σ/(Ld), where the root-mean-square roughness σ and the lateral correlation length L of the surfaces are directly measured using atomic force microscopy and X-ray reflectivity.