Novel growth mechanism of epitaxial graphene on metals

Graphene, a hexagonal sheet of $sp^2$-bonded carbon atoms, has extraordinary properties which hold immense promise for future nanoelectronic applications. Unfortunately, the popular preparation methods of micromechanical cleavage and chemical exfoliation of graphite do not easily scale up for application purposes. Epitaxial graphene provides an attractive alternative, though there are many challenges, not least of which is the absence of an understanding of the complex atomistic assembly kinetics of graphene. Here, we present a simple rate theory of epitaxial graphene growth on close-packed metal surfaces. Based on recent low-energy electron-diffraction microscopy experiments (LEEM) \cite{loginova09}, our theory supposes that graphene islands grow predominantly by the addition of five-atom clusters, rather than solely by the capture of diffusing carbon atoms. With suitably chosen kinetic parameters, our theory produces a time-dependent carbon adatom density that is in quantitative agreement with measured data. The temperature-dependence of this adatom density at the onset of nucleation leads us to predict that the smallest stable precursor to graphene growth is an immobile island composed of six five-atom clusters. Our findings provide a starting point for more detailed simulations which will yield important input to developing strategies for the large-scale production of epitaxial graphene.