The unique electronic properties of graphene offer the possibility that it
could replace silicon when microelectronics evolves to nanoelectronics.
Graphene grown epitaxially on silicon carbide is particularly attractive in
this regard because SiC is itself a useful semiconductor and, by suitable
manipulation of the growth conditions, epitaxial films can be produced that
exhibit all the transport properties of ideal, two-dimensional graphene desired
for device applications. Nevertheless, there is little or no understanding of
the actual kinetics of growth, which is likely to be required for future
process control. As a step in this direction, we propose a local heat release
mechanism to explain finger-like structures observed when graphene is grown by
step flow decomposition of SiC(0001). Using a continuum equation of motion for
the shape evolution of a moving step, a linear stability analysis predicts
whether a shape perturbation of a straight moving step grows or decays as a
function of growth temperature, the background pressure of Si maintained during
growth, and the effectiveness of an inert buffer gas to retard the escape of Si
atoms from the crystal surface. The theory gives semi-quantitative agreement
with experiment for the characteristic separation between fingers observed when
graphene is grown in a low-pressure induction furnace or under ultrahigh vacuum
conditions.Comment: 4 pages, 5 figure