Unraveling the Influence of Metal Substrates on Graphene Nucleation from First-Principles Study

Using ab initio calculations, we systematically investigate graphene nucleation on 10 representative metal substrates that have been used in graphene growth by chemical vapor deposition. We find that the metal substrates can be divided into three categories with respect to the competition between carbon-carbon (C-C) and carbon-metal (C-M) interactions, which leads to the distinct critical size (N_c) dependence of the smallest graphene precursor on the substrates. The C-M interactions are weak on Ag, Au, Cu, and Co substrates, and the chemical potential of carbon decreases monotonically to approach that of graphene as the size of the carbon clusters increases. We observed an N_c around C₁₃-C₁₄ corresponding to the structural transition from a linear chain to sp² configuration on these substrates. In contrast, the C-M interactions are strong on Ru, Pt, Rh, and Ir substrates, and the extremely stable carbon monomer thermodynamically determines the larger N_c about C₁₉. The third category is Ni and Pd substrates, for which carbon atoms tend to penetrate into the first layer of the metal substrates, implying a more complicated graphene nucleation mechanism. We also discuss the growth kinetics of the small carbon clusters as well as the effect of the practical environment, like surface defects, on graphene nucleation.