Relationship between graphene nucleation density and epitaxial growth orientation on Cu(111) surfaces

Crystal domain alignment is required to produce large, single-crystal, two-dimensional materials which are synthesized by epitaxial growth, but it has been unclear what is needed to achieve the alignment. It is presumed to be possible when the symmetries of the two-dimensional material and substrate are consistent. However, experiments show that although graphene and the Cu(111) surface have the same symmetry, graphene domains grown on Cu(111) are not always well aligned. We developed a physical model and used first principles calculations to explain these observations. It is found that small hexagonal graphene domains are always misorientated on the Cu(111) substrate because the vertexes of the graphene domains have preferred binding sites. These misorientation angles vary with the domain size, with near-perfect alignment of the domains on the substrate only being achieved when they become hundreds of nanometers in size. Our results indicate that low nucleation density of graphene on Cu(111) surfaces is necessary to achieve epitaxial alignment of graphene domains.