  We study step flow growth of epitaxial graphene on 6H-SiC using a one
dimensional kinetic Monte Carlo model. The model parameters are effective
energy barriers for the nucleation and propagation of graphene at the SiC
steps. When the model is applied to graphene growth on vicinal surfaces, a
strip width distribution is used to characterize the surface morphology.
Additional kinetic processes are included to study graphene growth on SiC
nano-facets. Our main result is that the original nano-facet is fractured into
several nano-facets during graphene growth. This phenomenon is characterized by
the angle at which the fractured nano-facet is oriented with respect to the
basal plane. The distribution of this angle across the surface is found to be
related to the strip width distribution for vicinal surfaces. As the terrace
propagation barrier decreases, the fracture angle distribution changes
continously from two-sided Gaussian to one-sided power-law. Using this
distribution, it will be possible to extract energy barriers from experiments
and interpret the growth morphology quantitatively.
