Insight into the Thermodynamics of Graphene Growth on Copper

Abstract

High-precision thermodynamic data were derived for single-layer graphene growth on Cu by measuring an increase or decrease in graphene flake size during chemical vapor deposition (CVD) in a reactive CH4/H2 atmosphere. An immediate flake shape change was observed when crossing the thermodynamic equilibrium of graphene formation, which was used as a sensitive criterion when systematically varying the CVD parameters during growth at 975–1080 °C. Extraction of the reaction enthalpy (ΔR H° = 91.8 ± 2.4 kJ·mol–1) and entropy (ΔR S° = 108.0 ± 1.8 J·mol–1·K–1) provides the anchoring point highly needed for calibration of experimental reactor studies or theoretical work. Comparing the Gibbs free energy with the thermodynamic data of graphite formation verifies that self-limiting single-layer graphene growth on copper occurs purely kinetically. Thermodynamics always favors the formation of multilayer graphene. Identifying the CVD parameter space where multilayer graphene is formed while single-layer graphene decays will foster the development of future synthesis strategies. The gained knowledge is transferable to other CVD-based graphene growth systems.

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

“…When entering the graphene instability regime of the CVD parameter space (red), already formed flakes are etched in the hydrogen rich atmosphere and shrink while developing a circular, compact island shape as shown in a recent study. 30 Note that etching of hexagonally shaped holes in graphene reported in the literature 31−33 was not seen in this study when crossing the thermodynamic equistability line. This observation indicates the high purity of the conducted experiments, because hole etching was attributed to the presence of oxygen containing impurities in the gas feed when finding that holes are not formed in purified hydrogen.…”

“…30 Already formed graphene flakes are stable on the Cu support at thermal equilibrium, whereas they decay at Q exp > K eq or grow in size when applying conditions relating to Q exp < K eq . 30 The chosen parameters during graphene synthesis at given temperature can be visualized in a p(H 2 )−w-plot with logarithmic scales where diagonals from the top-left to the bottom-right of the graph relate to CVD conditions of equal mass action constant Q exp . 31 Figure 1a displays such a graph where the position of the thermodynamic equilibrium is indicated and the deviation from equilibrium is visualized when applying CVD conditions that lead to graphene growth (blue) or graphene decay (red).…”

“…Here, the pre-exponential term of the detachment rate can be expressed by thermodynamic values, making use of the fact that graphene flakes stop growing when reaching thermodynamic equilibrium. Having determined the thermodynamic potentials of graphene growth on Cu in a separate study 30 allows one to derive the rate equation as outlined in detail in the Supporting Information leading to the flake growth velocity v as…”

“…Due to the improvement of the kinetic model, CVD experiments could be included for the data set where the island growth velocities approach v = 0 μm h −1 , i.e., where CVD parameters close to thermal equilibrium (Q exp ∼ K eq ) were used. The precise experimental measurement of the thermodynamic equilibrium at Q exp ∼ K eq was the topic of a recent publication 30 and including such data points enhanced the usable data of the parameter space. As already mentioned, the knowledge of the equilibrium parameter space allowed one to reduce the amount of unknown CVD parameters during the derivation of eq 5 (see the Supporting Information).…”

“…where graphene flakes should stop to grow or even decay. The thermodynamic stability of graphene on Cu was mapped out in a recent study 30 and, as already mentioned, this knowledge entered the kinetic model in eq 5. Consequently, the blue labeled data violate thermodynamics and of course contradict the predictions of the kinetic growth model.…”