Chapter 2 Theoretical foundation on the growth of 2D materials
2.1 CVD growth of single-crystal graphene
2.1.1 Nucleation of graphene on a substrate
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Figure 2.1 Nucleation of graphene. (a) The most stable structures of C11 and C12 on the Ni(111) surface.244 (b) Formation energies of various carbon structures on the Ni(111) surface (c) The most stable structures of C7 and C10 near a step edge of the Ni(111) surface.245 (d) Energies of carbon structures on a Ni(111) terrace or near a step versus the cluster size (N). (e) Nucleation barrier (G*) and corresponding nucleation size (N*) of graphene on a Ni(111) terrace or near a step. (f) Nucleation rate of graphene on a Ni(111) terrace or near a step.
The effect of step edges on the nucleation of graphene has also been studied, as displayed in Figure 2.1(c-d), both carbon chains and carbon networks near a Ni step edge are more stable than those on a Ni(111) terrace,245 implying that graphene nucleation near a step edge of the substrate is more preferred. Besides, it was found that the critical number of carbon atoms for the most stable carbon cluster changing from a sp chain to a sp2 network is reduced to 10 near a step edge. Due to its mono- element-composition, the nucleation barrier (G*) of graphene is only a function of the chemical potential difference (Δμ) of carbon precursors on a TM surface in relative to the graphene film, and from Figure 2.1(e) we see that the nucleation barrier of graphene on a Ni(111) terrace is always larger than that near a Ni step edge, and the critical nucleation size of graphene near a Ni step edge is smaller than that on a terrace area of the substrate. In general, a high nucleation barrier leads a low nucleation rate and thus a
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low nucleation density. Figure 2.1(f) shows the nucleation rates of graphene on a terrace and near a step edge, the smaller Δμ value, the lower nucleation rate. For example, at Δμ =0.2 eV, the nucleation rate of graphene on the Ni(111) terrace is smaller than 10-12 cm-2s-1, while that near a step edge is several orders of magnitude higher (~10-3 cm-2s-1). Therefore, under a near equilibrium condition and on TM surfaces with a low density of step edges, it is possible to obtain only one graphene nucleus over the whole substrate and make it grow in to a WSSC graphene film, which has been realized by Wu et al. in 2016.66
The stabilities of carbon clusters with the number of carbon atoms in a range of 16 ~ 26, which are possible precursors during graphene nucleation, were also explored by DFT calculations.246,247 The formation energy profile and the corresponding second order derivatives of C16~26 clusters on 4 different TM surfaces are shown in Figure 2.2 (a1). Obviously, C21 and C24 are the two most stable carbon clusters regardless the types of the substrate.246 Figures 2.2 (a2) and (a3) present the atomic configuration of the most stable C21 and C24 clusters, where the C24 cluster is composed of 7 hexagons while the C21 consists of 4 hexagons and 3 pentagons. The curved planar structure of the C21 cluster induced by carbon pentagons results in a better passivation of the cluster edge by the TM substrates, because a graphene edge tends to stand upright on the TM substrate.264 To testify the configuration of the C21 cluster, its scanning tunneling microscopy (STM) images on the Rh(111) surface at voltages of -1.0 V and 1.0 V were simulated, which are well consistent with experimental observations of carbon clusters on Rh(111) surface at the initial stage of graphene growth, as demonstrated in Figures 2.2 (a4-7).
Figure 2.2 (a1) Formation energy profile (upper panel) of carbon clusters on different TM surfaces and its second order derivative (lower panel). The structures of magic C21 and C24 clusters are shown in (a2) and (a3). The simulated STM images of C21 on Rh(111) surface at the voltages of -1.0 V and 1.0 V are shown in (a4) and (a5), respectively. Experimentally obtained STM images of a carbon cluster on Rh(111) surfaces during CVD process are shown in (a6) an (a7).246 (b-c) Energies of C clusters with and without dangling C atoms on the Ru(0001) surface. 247
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It should be noted that, a branched C24 carbon cluster with three dangling carbon atoms respectively attaching to the three pentagons of the C21 structure was found to be more stable than the C24 cluster purely consisting of carbon hexagonal rings on both the Ru(0001) and Rh(111) surfaces.247 As exhibited in Figure 2.2(b-c), changing three of the six hexagons at the edge of a C24 cluster consisting of only hexagonal rings to three pentagons with three dangling carbon atoms decreased the formation energy of the carbon cluster by 1.99 eV. Similarly, attaching one carbon atom to each of the three pentagons of the C21 cluster can decrease the total energy of the systems by 2.6 eV. Therefore, the branched C24 carbon cluster with three dangling carbon atoms is also a possible precursor for graphene nucleation. It can be seen that carbon pentagons might be essential to construct stable carbon clusters on various TM surfaces because of the curved planar structure induced by them, and in fact, such carbon pentagons were frequently observed in MD simulations of graphene growth based on different force fields.245,248,250
Above discussions show that the stabilities of various carbon structures, including carbon chains, carbon rings and sp2 carbon networks, on various TM metal surfaces have been extensively studied, and the transition from carbon chains to sp2 carbon networks in the nucleation process of graphene growth has been revealed by theoretical studies. It was found the nucleation barrier is dependent of the chemical potential of carbon and a low nucleation density can be reached by adjusting the ambient environment, which proves that it is possible to synthesize WSSC graphene from formation and growth of only one graphene nucleus in the whole substrate surface.