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

Achieving atomically flat surface of metals has been shown can significantly enhance their oxidation resistance and advance their electronic-optical applications. However, surface energy minimization of polycrystalline metals during traditional heat treatments generally develops a large number of surface steps and facets that have low surface energy. Moreover, surface diffusion is further limited by three-dimensional Ehrlich-Schwoebel barriers due to the formation of steps and facets. Therefore, formation of atomically flat surface is both energetically unfavorable and kinetically unstable. Here, we covered graphene (Gr) on Copper (Cu) surface and performed systematic and statistical analysis of microstructures in 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 minimizing strain energy of Gr 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, accelerating formation of atomically flat surface. When h ≥ 5, strain energy minimization of Gr will trigger step-bunching instability, decomposing large steps and thus facilitating surface diffusion to develop atomically flat surface. The present results not only enrich understanding of formation mechanism of Gr/Cu interface, but also suggest a potential strategy to achieve atomically flat surfaces by high-temperature annealing graphene-covered metals.