Size effect of resistivity due to surface roughness scattering in alternative interconnect metals: Cu, Co, Ru, and Mo

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The resistivity size effect of thin films due to atomically rough surfaces is investigated using first-principles quantum transport simulations with the disorder scattering treated by the nonequilibrium mean-field approach. Within the exact muffin-tin orbital--based first-principles method, the Madelung potential of film in device structure is constructed by implementing the boundary-condition correction. Cu(001), Co(0001), Ru(0001), and Mo(001) thin films are modeled with the thickness $d=1--10$ nm. The random surface roughness is represented by an alloy model, consisting of one monolayer of ${\text{M}}_{x}{\text{Va}}_{1\ensuremath{-}x}$ and ${\text{M}}_{1\ensuremath{-}x}{\text{Va}}_{x}$ on the respective top and bottom surfaces. The results of all metal films indicate that the first-principles resistivity ${\ensuremath{\rho}}_{s}$ induced by surface roughness scattering is proportional to $1/d$. Our simulated resistivity results are consistent with the experimental measurements of epitaxial metal layers. We find that, for the same thickness, Mo films present the highest ${\ensuremath{\rho}}_{s}$, significantly larger than the other metals. The thin-film resisitivity ${\ensuremath{\rho}}_{s}$ of Co is about 1.6 times that of Cu, while Ru results is slightly higher than Cu results. For all metal films, we obtain the parameter ${\ensuremath{\gamma}}_{s}$ characterizing the intensity of surface roughness scattering as a function of $x$. Furthermore, we find the proportionality constant ${\ensuremath{\alpha}}_{s}$ versus $x$ for the mean-free path ${\ensuremath{\lambda}}_{s}={\ensuremath{\alpha}}_{s}\ifmmode\times\else\texttimes\fi{}d$ for surface roughness scattering. Our results show that at the high $x>0.2, {\ensuremath{\alpha}}_{s}$ is rather close to a constant, with values of 4.5, 2.8, 2.1, and 1.0 for the respective Cu, Ru, Co, and Mo. We conclude that, compared to Co, Ru is competitive in resistivity size effect of surface roughness for an alternative to Cu interconnect for future technology nodes.