A model for the epitaxial growth of graphene on 6H-SiC

We introduce a kinetic model for the growth of epitaxial graphene on 6H-SiC. The model applies to vicinal surfaces composed of half-unit-cell height steps where experiment shows that step flow sublimation of SiC promotes the formation and growth of graphene strips parallel to the step edges. The model parameters are effective energy barriers for the nucleation and subsequent propagation of graphene at the step edges. Using both rate equations and kinetic Monte Carlo simulations, two distinct growth regimes emerge from a study of the layer coverage and distribution of top-layer graphene strip widths as a function of total coverage, vicinal angle, and the model parameters. One regime is dominated by the coalescence of strips. The other regime is dominated by a novel "climb-over" process which facilitates the propagation of graphene from one terrace to the next. Comparing our results to scanning microscopy studies will provide the first quantitative insights into the kinetics of growth for this unique epitaxial system.