Pre-coalescence scaling of graphene island sizes

Graphene grown using cold-wall chemical vapor deposition on Cu surfaces follows a classical nucleation and growth mechanism. Following nucleation at the earliest growth stages, isolated crystallites grow, impinge, and coalesce to form a continuous layer. During the pre-coalescence growth regime, the size distributions of graphene crystallites exhibit scaling of the form N(s) = θ/⟨s⟩² g(s/⟨s⟩), where s is the island area, θ is the graphene coverage, ⟨s⟩ is the average island area, N is the areal density, and g(x) is a scaling function. For graphene grown on Cu surfaces that have been annealed in a reducing Ar + H₂ ambient, excellent data collapse onto a universal Avrami scaling function is observed irrespective of graphene coverage, surface roughness, or Cu grain size. This result is interpreted to indicate attachment-limited growth and desorption of diffusing C-containing species. Graphene grown on Cu surfaces that were annealed in a non-reducing environment exhibits a qualitatively different scaling function, indicating diffusion-limited growth with a lower attachment barrier combined with C detachment from the graphene edges.