Thin film resistivity scaling of metals with conduction band anisotropy

The resistivity of metal thin films is generally understood to increase with decreasing film thickness due to increased boundary surface and grain boundary scattering, the latter being a direct consequence of the average grain size typically reducing for thinner films. Recently, several experiments and ab initio simulations have demonstrated a dependency of resistivity scaling on the crystal orientation of the film, particularly in the case of an anisotropic Fermi surface. This anisotropy cannot be captured by the commonly used Mayadas-Shatzkes resistivity scaling model, which adopts an isotropic effective mass approximation for the electrons. As a qualitative understanding of the impact of conduction band anisotropy is currently lacking, we have extended the Mayadas-Shatzes approach to account for grain boundary and boundary surface scattering as well as the anisotropy of the electronic structure. Recently, we calibrated the extended model with Fermi surfaces obtained from ab initio simulations and successfully applied the model to Cu and Ru thin films, with a nearly isotropic and anisotropic Fermi surface respectively (arXiv:1711.00796).