Predicting Graphene Growth on Cu: Universal Kinetic Growth Model and Its Experimental Verification

The kinetics of the chemical vapor deposition (CVD) of graphene on Cu in CH₄ + H₂ were investigated by monitoring the graphene flake size as a function of CVD growth time. A growth model was set up which relates the CVD parameters to the mass action constant Q_exp of the methane decomposition reaction toward graphene at a given temperature T. Graphene growth was shown to proceed from pre-equilibrated adsorbed carbon (C_ad) within a wide CVD parameter range. The model not only leads to the correct scaling relation of the growth kinetics but quantitatively determines how far the CVD parameters deviate from thermal equilibrium and correctly predicts the absolute flake size increase per time. Fitting experimental data delivers the energy barrier for carbon detachment from the graphene island edge (E_det = 4.7 ± 0.3 eV) and the methane decomposition entropy toward C_ad on Cu (Δ_decS° = 260 ± 20 J mol^-1 K^-1). The latter value is used to estimate the vanishingly small C_ad equilibrium concentration of 3 × 10^-10 monolayers at 1045 °C. The universal validity of the model is proven by comparison with literature data providing the correct order of magnitude growth velocities up to 1000 μm/h. The performed reactor experiments deliver data that match the predicted flake growth velocity with a precision of about 50%. The obtained results can be used to calibrate any hot wall CVD reactor setup for the methane decomposition reaction toward graphene on Cu. The description can be directly applied for any hydrocarbon in the gas feed, and the technique can be easily applied for other catalytic support surfaces.