The over-step coalescence of carbon atoms on copper surface in the CVD growth of graphene: density functional calculations

The ways in which carbon atoms coalesce over the steps on copper (111) surface are ascertained by density functional theory (DFT) calculations in the context of chemical vapor deposition (CVD) growth of graphene. Two strategies, (1) by putting carbon atoms on and under the steps separately and (2) by importing additional carbon atoms between the ones separated by the steps, have been attempted to investigate if an over-step coalescence of carbon atoms could take place. Based on analyses about the optimized configurations and adsorption energies of carbon atoms nearby the steps, as well as the energy evolution curve of the system throughout the geometry optimizations process, we determined the main way in which graphene grows over the steps continuously: the carbon atoms, adsorbed additionally on the locations between the already existing ones which are separated by the steps, link them (these carbon atoms separated by the steps) together. The direct over-step coalescence of the carbon atoms separated by the steps is very difficult, although the energy barrier preventing their coalescence can be weakened by importing carbon atoms on and under the steps gradually. Our results imply potential applications in directing the fabrication of graphene with particular structure by controlling the surface topography of copper substrate.