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

Abstract

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 (Cad) 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 Cad on Cu (Δdec S° = 260 ± 20 J mol–1 K–1). The latter value is used to estimate the vanishingly small Cad 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.

Extending the Predictive Growth Kinetics for the CVD Synthesis of Graphene on Copper to the Low-Pressure Regime

“…An entropy decrease during adsorption is qualitatively expected and the order of 6 R seems reasonable. In contrast to the case of the decomposition to C-ad, we cannot relate the entropy change exclusively to the configurational entropy change because rotations and vibrations contribute to the entropy.…”

“…The attachment term in eq treats the diffusive impingement of adsorbates from a pre-equilibrated CH x -ad phase with mean adsorbate velocity v̅ . One can describe v̅ as the mean velocity of a two-dimensional ideal gas or as the one of a two-dimensional lattice gas . The latter treatment describes the kinetics at higher precision but requires knowledge of the pre-equilibrated adsorbate phase.…”

“…The induced optical contrast allowed us to determine the amount and size of the synthesized graphene flakes by using an optical microscope (Olympus BH-2 microscope, 20×/100× magnification) connected to a Canon D500 Camera body. For CVD growth above 10 mbar, a procedure was identified that leads to graphene flake growth at a constant flake density . However, applying lower CVD pressures leads to continuous nucleation of new graphene flakes during the entire CVD growth process.…”

“…For this purpose, fundamental understanding of the relevant CVD growth processes is required. It was already shown that the applied gas-phase composition and temperature defines the graphene growth rate − and also strongly influences the resulting flake shape, , the island nucleation density, , and the resulting crystallinity. , Systematic studies on the graphene growth on Cu tried to identify different regimes in the CVD ( p (CH 4 ), p (H 2 ), T ) parameter space allowing to connect the acquired results to molecular processes dominating the growth at the respective conditions. ,,− However, different contradicting growth models were derived, and a debate arose which methane decomposition product feeds the growing graphene flakes during CVD synthesis. , Also theoretical studies combining kinetic Monte Carlo and density functional theory (DFT) calculations tried to identify CVD conditions where the population of CH x -ad species with x ≠ 0 can be predicted. − …”

Analytical Model of CVD Growth of Graphene on Cu(111) Surface

“…To our best knowledge, there has only been a very restricted number of attempts [ 30 , 31 ] to describe the nucleation and time evolution of the macro-ensemble of graphene flakes within kinetic nucleation theories, where the compact phase is formed from the 2D lattice gas of feeding particles. Therefore, in this work, we develop an analytical kinetic model of the nucleation and growth of graphene on the Cu(111) surface which, in analogy with kMC, utilises DFT barriers to express the rate constants of elementary steps.…”