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

Abstract

Although the CVD synthesis of graphene on Cu(111) is an industrial process of outstanding importance, its theoretical description and modeling are hampered by its multiscale nature and the large number of elementary reactions involved. In this work, we propose an analytical model of graphene nucleation and growth on Cu(111) surfaces based on the combination of kinetic nucleation theory and the DFT simulations of elementary steps. In the framework of the proposed model, the mechanism of graphene nucleation is analyzed with particular emphasis on the roles played by the two main feeding species, C and C2. Our analysis reveals unexpected patterns of graphene growth, not typical for classical nucleation theories. In addition, we show that the proposed theory allows for the reproduction of the experimentally observed characteristics of polycrystalline graphene samples in the most computationally efficient way.

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

“…By analyzing the occurrence map (Figure 4) and the frequency of events, we can conclude that C and C 2 species played the primary role in graphene growth under the considered conditions. This observation is in line with the findings of a recent study that used analytical kinetic modeling to investigate graphene nucleation and growth [58]. The inclusion of ring closure reactions in the reaction set is essential for the accurate simulation of graphene growth pathways, which we will discuss in more detail in the following section.…”

“…Since Li et al reported activation energy barriers of the set of reactions happening during the CVD of graphene on Cu(111) using CH 4 and H 2 as precursors [64], we firstly analyzed the impact of the DFT method choices on the energy values. As pointed out in our previous study, we found strong co-adsorption effects on the activation energy barrier, especially for reactions on the slab edge [58]. In particular, the activation energy barrier of C 2 attachment to the edge (one of the three most crucial reactions in the growing process) was doubled with an increase of the supercell, i.e., 1.22 eV instead of 0.58 eV, which was reported by Li et al [53].…”

“…All barriers of attachment were calculated with respect to individualized species, as explained in Ref. [58].…”

“…Numerous theoretical studies, employing ab initio calculations [51], molecular dynamics (MD) [52], and kinetic Monte Carlo (KMC) simulations [53][54][55][56][57], have been reported to model the CVD growth mechanisms of graphene and the impact of different CVD parameters. Recently, Popov et al [58] proposed an analytical kinetic model of the graphene nucleation and growth in CVD on Cu(111) based on a combination of kinetic nucleation theory and density functional theory (DFT) calculations.…”