Controlling GaN Nucleation Via O₂-Plasma-Perforated Graphene Masks on c-Plane Sapphire

Atomically thin, perforated graphene on c-plane sapphire functions as a nanoscale mask that enables GaN growth through thru-holes. We tune the perforated-area fraction f_p by controlled O₂-plasma exposure and quantify its impact on early stage nucleation: the nucleation-site density scales with f_p, while the nucleation-delay time decreases approximately as 1/f_p. Time-resolved areal coverage and domain counts exhibit systematic f_p-dependent trends. A kinetic Monte Carlo (kMC) model that coarse-grains atomistic events─adatom arrival, surface diffusion, attachment at exposed sapphire within perforations, and coalescence (the first front–front contact between laterally growing domains)─reproduces these trends using a constant per-site nucleation rate. Fitting the kMC simulation data yields onset times t₀ for the nucleation delay that closely match independently observed no-growth thresholds (Set 1:28.5 s vs ∼ 30 s; Set 2:38 s vs ∼ 35 s), validating the kMC–experiment mapping and highlighting plasma dose as an activation threshold for plasma-induced thru-hole formation in 2D materials. Together, experiment and kMC identify f_p as a single, surface-engineerable parameter governing GaN nucleation statistics on perforated graphene masks, providing a quantitative basis and process window for epitaxial lateral overgrowth/thru-hole epitaxy workflows that employ two-dimensional masks.