  The development of wafer-scale continuous single-crystal graphene layers is
key in view of its prospective applications. To this end, here we pave the way
for a graphene growth model in the framework of the Langmuir adsorption theory
and two dimensional crystallization. In specific, we model the nucleation and
growth of graphene on copper using methane as carbon precursor. The model leads
to identification of the range of growth parameters (temperature and gas
pressures) that uniquely entails the final surface coverage of graphene. This
becomes an invaluable tool to address the fundamental problems of continuity of
polycrystalline graphene layers, and crystalline grain dimensions. The model
shows agreement with the existing experimental data in the literature. On the
basis of the "contour map" for graphene growth developed here and existing
evidence of optimized growth of large graphene grains, novel insights for
engineering wafer-scale continuous graphene films are provided.
