Achieving atomically flat copper surface: Formation of mono-atomic steps and associated strain energy mechanisms

Recent studies have demonstrated that achieving an atomically flat surface for metals can significantly enhance their oxidation resistance and further advance their electronic-optical applications. However, traditional heat treatments for polycrystalline metals tend to create numerous low-surface-energy steps and facets due to surface energy minimization. Moreover, surface diffusion is further limited by three-dimensional Ehrlich-Schwoebel barriers due to the formation of steps and facets. Therefore, achieving atomically flat surfaces is energetically unfavorable and kinetically unstable. Here, we covered graphene (Gr) on Copper (Cu) surface and performed systematic and statistical analysis of microstructures on three types of graphene-Cu (Gr/Cu) interfaces: annealed Cu, transferred and high-temperature deposited Gr/Cu interfaces. We found that mono-atomic steps formed at high-temperature deposited Gr/Cu interface, in comparison with multi-atomic steps at annealed Cu and transferred Gr/Cu interfaces. Molecular statics/dynamics simulations and thermodynamic analysis suggest that formation of mono-atomic steps can be ascribed to the minimization of Gr strain energy and high-temperature assisted surface diffusion. When a step height (h) is smaller than five atomic planes (h < 5), strain energy minimization of Gr will prevent step bunching (a non-uniform surface morphology), accelerate the formation of atomically flat surface. When h >= 5, Gr strain energy minimization will trigger step-bunching instability, decompose large steps and thus facilitate the surface diffusion to develop atomically flat surface. The present results may suggest a potential strategy to achieve atomically flat surface of bulk metals by high-temperature treatment.