Alignment of 3-fold symmetric 2D materials on high-symmetric substrates

Chapter 4 A general theory of 2D materials alignment on crystalline substrates with different

4.3 Alignment of 2D materials on low-index high symmetric substrates

4.3.2 Alignment of 3-fold symmetric 2D materials on high-symmetric substrates

hBN has the same honeycomb lattice structure as graphene, but it shows a lower symmetry (C3V) due to its binary composition. Both experimental observations and theoretical calculations have shown that CVD grown hBN islands show triangular shapes enclosed by nitrogen terminated ZZ (ZZN) edges under most experimental conditions.^336-338 Therefore, the interaction between ZZN edge of hBN and a substrate plays a critical role in determining the alignment orientation on this substrate.

By DFT calculations, we explored the binding strength of the hBN ZZN edge on low-index high symmetric Cu surfaces with different alignment orientations. Figure 4.5(a-c) shows the atomic configurations and corresponding binding energies. Due to the smaller lattice mismatch (~1.8%) between ZZN direction of hBN and Cu<110> direction (2.510 Å for hBN ZZN lattice and 2.556 Å for

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Cu<110> lattice) and the closely packed Cu<110> atomic arrays, the most stable alignment orientation of hBN growing on these substrates satisfies that a ZZN direction of hBN is parallel to a Cu<110>

direction, which is as same as graphene growing on the three high symmetric Cu surfaces. As already discussed in Chapter 2, previous DFT study already shows that the weak vdW interaction between the hBN bulk and the Cu(111) surface is strongest when a ZZ direction of hBN is aligned along a Cu<110>

direction.¹¹³ Therefore, it can be seen that both the strong interaction between hBN ZZN edge and the substrate and the weak interaction between hBN bulk and the substrate favor the alignment of hBN ZZ direction along Cu<110> direction.

Figure 4.5 Binding energies of hBN ZZN edge attaching to three low-index high symmetric Cu surfaces, which are Cu(111) (a), Cu(100) (b) and Cu(110) (c) surfaces. Similar to the configurations in Figure.

4.3, hBN ZZ nanoribbons were used and the boron terminated ZZ (ZZB) edges are passivated by hydrogen to avoid their interaction with the Cu substrates.

Different from graphene and hBN, the edges of TMDCs are usually self-passivated by chalcogen, as already revealed by both experimental and theoretical studies.^318,339 In addition, due to the three-atomic-thick structure of TMDCs, their binding stiffness is much higher than that of graphene and hBN and, consequently the edges of TMDC islands do not bend towards the substrate surface. Therefore, the alignment orientation of TMDCs on a substrate should be determined by the weak interaction between the TMDC bulk and the substrate surface.

Here, to explore the orientation a TMDC island on FCC TM(111) substrates, we use a triangular WS2 cluster with three tungsten terminated ZZ (ZZW) edges that are passivated by S on the Au(111) surface as an example, the interactions between the WS2 cluster and the Au(111) surface under different rotation angles are calculated by DFT, as shown in Figure 4.6(a), where the rotation angle is defined to be 0° when a ZZW direction is parallel to a <110> direction of the Au(111) substrate.

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The binding energy of the WS2 cluster on the Au(111) surface is defined as:

𝐸_𝐵 = (𝐸_{𝐶𝑙𝑢𝑠𝑡𝑒𝑟} + 𝐸_𝑆𝑢𝑏− 𝐸_𝑇) 𝑁⁄ _𝑊, (4.3)

where ECluster and Esub are the energies of the WS2 cluster and the substrate, respectively. ET is the total energy of the system with the WS2 cluster adsorbed on the Au(111) surface. NW is the number of W atoms in the WS2 cluster.

Figure 4.6 (a) The configuration of a WS2 cluster on the high symmetric Au(111) surface, h is the distance between WS2 and the Au(111) surface. (b) Comparison of the WS2 cluster with different orientations on the Au(111) surface, the binding energies of the top-hcp and top-fcc structures are 0.653 and 0.645 eV/W atoms, respectively. (c) Binding energy of WS2 on the Au(111) surfaces in the unit of eV/W atom, and the distance as a function of relative angles between Au<110> and ZZW directions.

Firstly, we testify that the Au(111) substrate can be regarded to be C6V symmetric for the system of WS2/Au(111). The WS2 cluster with 0° and 60° orientation angles on the Au(111) surface is compared, as shown in Figure 4.6(b). The binding energy difference of the two orientations is only 0.008 eV/W atom, which means that the effect of the second- and third- layer Au atoms on the WS2- Au(111) interaction is negligible and the Au(111) substrate can be viewed to be C6V symmetric for the WS2/Au(111) system. Therefore the periodic range for the rotation angle of the WS2 cluster on the Au(111) substrate can be limited in 0-60°. Figure 4.6(c) shows the binding energies and the distance between the triangular WS2 cluster on the Au(111) substrate, and obviously, the WS2-Au(111) interaction is strongest when a ZZ direction of WS2 is along a Au<110> direction.

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Figure 4.7 Illustrations showing the alignment of C3V-2D material islands on FCC{111} (a), FCC{100}

(b) and FCC{110} (c) surfaces. ZZN edges aligning along <110> directions are marked by blue lines.

The mirror planes of the 2D material and the substrates along different directions are denoted by dashed lines.

Based on the most stable alignment principle of 3-fold symmetric 2D materials on the three low-index high symmetric Cu surfaces, i.e., ZZ // Cu<110>, we revealed the alignment of 3-fold symmetric 2D material islands on FCC(111), FCC(100) and FCC(110) surfaces, as shown in Figure 4.7(a-c). C3V (D3H) 2D materials, such as hBN (MoS2), are mirror symmetric with respect to only AC directions. On the FCC(111) surface (Figure 4.7(a)), the mirror symmetry planes along AC directions of the 2D material only correspond to the mirror planes along the FCC<211> directions, while no mirror symmetry planes of the 2D material correspond to the FCC<110> ones. Consequently, a new orientation labeled as “1” appears and thus there are totally two most stable orientations that have an 60°

misorientation angle for the 2D material on the FCC(111) surface. The FCC(100) surface has two mirror planes along the two FCC<110> directions and another two mirror planes along the two FCC<100>

directions. Among these four mirror planes, only one of them is coincident with a mirror plane of the 2D material, and thus the other three mirror planes result in three new alignment orientations of the 2D material, labelled as “1, 2, 3” respectively, as shown in Figure 4.7(b). The FCC(110) surface has two mirror symmetry planes along the FCC<110> and FCC<100> directions, respectively. Only the FCC<100> mirror plane coincides with one AC mirror plane of the 2D material, and therefore there will be two alignment orientations for a 3-fold symmetric 2D material on the FCC(110) surface, as shown in Figure 4.7(c).

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