Theory of the Growth of Epitaxial Graphene on Close-Packed Metals

We present a simple rate theory of epitaxial graphene growth on close-packed metals. Motivated by recent low-energy electron microscopy experiments [E. Loginova, N.C.Bartelt, P.J. Feibelman, and K.F. McCarty, New Journal of Physics, {\bf 10}, 093026 (2008)], 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, we find quantitative agreement with (i) the measured time-evolution of the adatom density and (ii) the measured temperature-dependence of the adatom density at the onset of nucleation by assuming that the smallest stable precursor to graphene growth is an immobile island composed of six five-atom clusters.