Chapter 2 Theoretical foundation on the growth of 2D materials
2.1 CVD growth of single-crystal graphene
2.1.3 Mechanisms of alignment and coalescence of graphene islands on a TM surface
The route of synthesizing WSSC graphene films via seamless stitching of large number of graphene islands requires all graphene islands have the same orientation on a wafer-scale substrate.68,69,77,78,274 In general, a single crystalline TM substrate is required for this method. Here, we discuss the effect of the interaction between graphene and a substrate on the orientation of graphene islands on the substrate.
Experimentally, unidirectionally aligned graphene islands were broadly observed on single crystalline TM surfaces, especially on the Cu(111) surface, graphene islands generally present a hexagonal shape with their ZZ edges aligning along Cu<110> directions.42,275 By DFT calculations, Zhang et al. explored the aligned mechanism of graphene islands on Cu(111) surface and the interactions between the Cu(111) substrate and graphene bulk/edge were studied.265 Figure 2.4(a) reveals that the graphene bulk - Cu(111) interaction is strongest at the 0º rotation angle with graphene ZZ direction paralleling to the Cu<110> direction, meanwhile the distance between graphene film and the Cu(111) surface reaches the minimum value. It is noted that the interaction between the graphene bulk and Cu(111) surface is not sensitive to the rotation angle, showing a binding energy variation within 5 meV per carbon atom. When a graphene island is grown on the Cu(111) surface, the graphene edge also interacts with the Cu(111) surface. Figure 2.4(b) shows the binding energy profiles of C24 and C54 clusters to the Cu(111) surface as functions of the rotational angle, where the edges of the carbon clusters are passivated by the Cu substrate rather than hydrogen. It is obvious that the interaction is very sensitive to the rotation angle, and the rotation barrier increases significantly with the size of the cluster, indicating the orientation of a graphene island is determined in the early stage of its growth if its edges are passivated by the substrate. In addition, from this study, we can also know that the vdW interaction between the graphene bulk and the substrate will determine the orientation of a graphene island when its edges are well-passivated by hydrogen rather than the substrate.
36
Figure 2.4 Interaction between graphene and the Cu(111) substrate.265 (a) Optimized distance and binding energies of graphene layer on the Cu(111) surface versus the rotation angle (θ). (b) Energy profiles of C24 and C54 clusters versus the rotation angle.
In practice, it is difficult to obtain atomic flat substrate surfaces at macroscale, instead step edges on Cu substrates were broadly observed during the graphene CVD growth.276-281 Therefore, the effect of the step edges of substrates on the graphene orientation cannot be ignored. Due to the compact atomic arrangement and high stability, step edges along <110> directions are mostly formed on low- index surfaces of an FCC TM foil.124,282 Gao et al. theoretically compared graphene nucleation on a flat Ni(111) terrace and near a Ni<110> step edge.245 As shown in Figure 2.5(a), the formation energies of both graphene ZZ and AC edges attaching to the Ni<110> step edge are much lower than those attaching to a flat terrace, suggesting that the nucleation of graphene near a step edge is more energetically preferred. Yuan et al. further explored the formation energies of various graphene edges attaching to a Cu<110> step edge.283 As shown in Figure 2.5(b), the lowest formation energy appears at the 0º rotation angle, where the graphene ZZ edge aligns along a Cu<110> step edge, which is attributed to the straightness of both the graphene ZZ edge and Cu<110> step edge and the small lattice mismatch between them.
37
Figure 2.5 Interaction of a graphene layer near a step edge of TM substrates. (a) Structures and formation energies of graphene ZZ and AC edges attaching to a Ni(111) terrace and a Ni(111) step edge.245 (b) Formation energies of various graphene edges and a Cu<110> step edge versus the orientation angle.283
Except for the alignment of graphene islands on a TM surface, the coalescence behaviors of well-aligned and mis-aligned graphene islands have also been revealed, as shown in Figure 2.6.79 The attachment of C atoms to a concave corner formed from the coalescence of two well-aligned graphene islands leads to a decrease of the formation energy (Figure 2.6(a)). Figure 2.6(b) shows the transformation of a sharp concave corner to a dull concave corner by sequentially attaching C atoms to low-energy sites of the concave corner formed from the coalescence of two well-aligned graphene islands, which can be used as an indicator of the grain boundary-free coalescence between two aligned graphene islands, as introduced in Figure 1.7. On the contrary, the concave corner formed from the coalescence of two mis-aligned graphene islands will remain sharp during the growth process. As shown in Figures 2.6(d-e), the coalescence of two mis-aligned graphene islands leads to the formation of a grain boundary between them and the concave corner corresponds to one end of the grain boundary.
Adding C atoms to the concave corner between two mis-aligned graphene islands always results in an increase of the formation energy, while the structures with attaching C atoms to the two ZZ edges of the concave conner show lower formation energies, indicating that the growth of concave corner between mis-aligned graphene islands is governed by growth of the two ZZ edges of the concave corner (Figure 2.6(f)) and as a result, the sharp concave structure remains unchanged. It should be noted that the coalescence behavior of graphene also applies to other 2D materials, as also demonstrated in this study.
38
Figure 2.6 Theoretical analyses of the coalescence of two well-aligned or mis-aligned graphene islands.79 (a-b) The process of adding C atoms to a concave corner between two well-aligned graphene islands. (c) Schematic of the growth behavior at a concave corner between two well-aligned graphene islands. Red arrows mark the kink sites and black arrows indicate growth direction. (d-e) The process and the corresponding formation energy (ΔEF) profile of adding C atoms to a concave corner between two mis-aligned graphene islands. (f) Schematic of kink formation at graphene edges near a concave corner between two mis-aligned graphene islands.
In summary, the orientation of a graphene island on a substrate is determined by both the interaction between the graphene bulk and the substrate and the interaction between graphene edges and the substrate. In addition, the coalescence behaviors of well-aligned and mis-aligned graphene islands are distinguishable from the growth behavior of the concave corners formed from the coalescence of neighboring graphene islands. Above theoretical studies proved that on an ideal (111) surface of an FCC TM, a graphene island prefers to align its ZZ direction aligning along the <110>
direction of the substrate if the graphene edges have been passivated by hydrogen. In addition, if the graphene growth is far from equilibrium and the graphene edges are passivated by the substrate, multi- orientations of graphene islands will appear, because of the high rotation barriers of small graphene clusters on the substrate. In practice, step edges appear on the substrates and it was found that the
39
graphene ZZ edge prefers to align along the substrate <110> step edges. Currently, we can see that, to ensure graphene islands that have a C6V symmetry to show a unidirectional orientation, Cu substrates that have only one <110> direction or several <110> directions with an 60o misorientation angle with respect to each other are required. Comparing with Cu foils with high-index surfaces, low-index Cu foils with high symmetries, such as Cu(111), Cu(110) and Cu(100), are more easier to be obtained by annealing polycrystalline Cu foils because of their lower surface energies. Among them, the Cu(111) surface has three equivalent <110> directions with an 60o misorientation angle and the Cu(110) has only one <110> direction, implying that both surfaces can be used to template the growth of unidirectional graphene islands. In fact, The synthesis of WSSC graphene films by the seamless stitching method have already been realized on single crystalline Cu(111) surfaces.67,69,78 In contrast, the grown graphene islands on the Cu(100) surface that has two orthogonal <110> directions generally shows two orientation.284-287 In Chapter 4, we will present a general theory on the epitaxial growth of 2D materials on an arbitrary substrate.
Last but not least, we would like to note that the strength of graphene-substrate interaction also plays an important role in the coalescence of aligned graphene islands. For example, on the chemically active Ni(111) substrate, the coalescence may induce a line defect despite the graphene islands are unidirectional, because the relatively strong interaction between graphene and the Ni(111) surface prevents the translational sliding of the graphene islands on the substrate.288,289 In contrast, on the Cu(111) or Ge(110) surfaces that have a weak interaction with graphene, the unidirectionally aligned graphene islands can seamlessly merge into a perfect single crystal, which were discussed in Chapter 1.