Resistivity size effect in epitaxial Ru(0001) layers

Epitaxial Ru(0001) layers are sputter deposited onto Al2O3(0001) substrates and their resistivity ρ measured both in situ and ex situ as a function of thickness d = 5–80 nm in order to quantify the resistivity scaling associated with electron-surface scattering. All layers have smooth surfaces with a root-mean-square roughness 0.4 nm, exhibit an epitaxial relationship with the substrate: Ru0001||Al2O30001 and Ru101¯0||Al2O3112¯0, and show no resistance change upon air exposure, suggesting negligible resistivity contributions from geometric surface roughness and grain boundary scattering and negligible changes in the surface scattering specularity p upon oxygen exposure. The room temperature ρ vs d data are well described by the semiclassical Fuchs-Sondheimer (FS) model, indicating a bulk electron mean free path λ = 6.7 ± 0.3 nm. However, the measured ρo × λ product at 77 K is 43% lower than at 295 K, suggesting a breakdown of the FS model and/or a thickness-dependent electron-phonon coupling and/or a temperature- or environment-dependent p. Transport simulations employing the ruthenium electronic structure determined from first-principles and a constant relaxation time approximation indicate that ρ is strongly (by a factor of two) affected by both the transport direction and the terminating surfaces. This is quantified with a room temperature effective mean free path λ*, which is relatively small for transport along the hexagonal axis independent of layer orientation (λ* = 4.3 nm) and for (0001) terminating surfaces independent of transport direction (λ* = 4.5 nm), but increases, for example, to λ* = 8.8 nm for (112¯0) surfaces and transport along 11¯00. Direct experiment-simulation comparisons show a 12% and 49% higher λ from experiment at 77 and 295 K, respectively, confirming the limitations of the semi-classical transport simulations despite correct accounting of Fermi surface and Fermi velocity anisotropies. The overall results demonstrate a low resistivity scaling for Ru, suggesting that 10 nm half-pitch Ru interconnect lines are approximately 2 times more conductive than comparable Cu lines.