  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.
