  Growing large-area single-crystal monolayers is the holy grail of graphene
synthesis. In this work, the efficiency of graphene growth and the quality of
their continuous films are explored through the time evolution of individual
domains and their surface coverage on the substrate. Our phase-field modeling
results and experimental characterization clearly demonstrate the critical
roles of the deposition flux, edge-reaction kinetics and the surface diffusion
of active carbon sources in modulating the pattern evolution and rate of
growth. The contrast in edge-kinetics-limited and surface-diffusion-limited
regimes is remarkable, which can be characterized by the evolution of domain
patterns and considered as an indicator of the growth regime. Common features
exist in these two regimes, showing that the growth rate scales with time as t2
in the early stage of growth and is regime-independent, which is explained by
the coarsen profiles of carbon concentration for both the compact and dendritic
domains. The rate decays rapidly in the final stage of growth due to the
competition between neighboring domains on the limited carbon sources diffusing
on the substrate, which is highly regime-sensitive and extremely low in the
surface-diffusion-limited regime with narrow gaps between the domains to be
filled. Based on these findings, synthesis strategies to improve the growth
efficiency and film quality are discussed.
