Grain boundary scattering in Ru and Cu interconnects

We study grain boundary scattering as a source of resistance increase in narrow interconnects. We consider both copper and a potential next-generation metal, ruthenium. The increase in resistance due to grain boundary scattering is often calculated using the Mayadas and Schatzkes model, which in addition to the average grain size depends on the bulk resistivity, the electron mean free path, and the average reflection coefficient at grain boundaries. We demonstrate a workflow to calculate all the latter three material properties using first-principles calculations. Calculated values for copper are used to verify our method, while experimental results for the cubic phase of ruthenium are unavailable and thus must rely on first-principles calculations. Using an automated workflow, we consider significantly more grain boundary structures than in other works, and find an almost twice as large average reflection coefficient for copper than previously reported. In spite of the larger copper reflection coefficient, the corresponding reflection coefficients for ruthenium grain boundaries are consistently larger, but with a smaller variation than observed for copper. Our results demonstrate the importance of studying a large set of grain boundary structures.