Substrate Screening for the Epitaxial Growth of a Single-Crystal Graphene Wafer

Epitaxial growth of a two-dimensional (2D) single crystal necessitates the symmetry group of the substrate being a subgroup of that of the 2D material. As a consequence of the theory of 2D material epitaxy, high-index surfaces, which own very low symmetry, have been successfully used to grow various 2D single crystals, while the rule of selecting the best substrates for 2D single crystal growth is still absent. Here, extensive density functional theory calculations were conducted to investigate the growth of graphene on abundant high-index Cu substrates. Although step edges are commonly regarded as the most active sites for graphene nucleation, our study reveals that, in some cases, graphene nucleation on terraces is superior than that near a step edge. To achieve parallel alignments of graphene islands, it is essential to either suppress terrace nucleation or ensure consistent orientations templated by both the terrace and step edge. In agreement with most experimental observations, we show that Cu substrates for the growth of single-crystalline graphene include vicinal Cu(111) surfaces, vicinal Cu(110) surfaces with Miller indices of (nn1) (n > 3), and vicinal Cu(100) surfaces with Miller indices of (n11) (n > 3).