Chapter 2 Theoretical foundation on the growth of 2D materials
2.2 CVD growth of single-crystal hBN film
2.2.2 Mechanisms of hBN alignment on a TM surface
Compared to the C6V graphene, the C3v hBN islands usually present a triangle shape and generally show multi-orientation on low-index TM surfaces.303-305 As shown in Figure 2.9(a), hBN islands on the Cu(111), Cu(110) and Cu(100) surfaces have two, two and four equivalent orientations, respectively, consistent with the binding energy profiles as functions of the rotation angle of a triangular hBN cluster on these surfaces (Figure 2.9(b)), which show that there are two maxima in binding energy profile in one periodicity of the hBN/Cu(111) system and four maxima in the binding energy profile in one periodicity of the hBN/Cu(100) system.113 Previous DFT studies also demonstrated that the vdW interaction between the hBN bulk and the FCC(111) surface also has two local maxima, corresponding to the lattice relationship with N atoms located on the top of metal atoms and B atoms on the fcc and hcp sites, respectively, which are the same as those illustrated in Figure 2.9(a).304,306-308 Therefore, it can be inferred that a ZZ direction of a hBN island prefers to align along the <110> direction of low-index FCC TM surfaces.
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Figure 2.9 The alignment of h-BN islands on low-index TM substrates.113 (a) Atomic structures of hBN on the Cu(111), Cu(110) and Cu(100), respectively. (b) The binding energies between hBN and Cu substrate as a function of their relative angle.
Different from low-index surfaces, a high-index surface normally possesses a lower symmetry because the existence of atomic step edges and/or kinks at the step edges. Interestingly, hBN islands with unidirectional orientation are observed broadly on such low symmetric surfaces.123 In 2016, unidirectionally aligned hBN islands were first reported on Cu(102) and Cu(103) surfaces (see Figure 2.10(a-b)), and DFT calculations in Figure 2.10(c-d) confirmed that there is only one minimum in the binding energy profiles of a triangular hBN island on these two surfaces as a function of the island rotation angle, corresponding to the configurations with one ZZ edge of hBN paralleling to the step edge direction (see Figure 2.10(e-f)).80 It is worth noting that on the high-index Cu(102) and Cu(103) surfaces, the step edges are along Cu<010> direction, which is different with the case of hBN on low- index Cu surfaces, where one of ZZ directions of hBN prefers to align along the Cu<110> direction.
Obviously, step edges on a substrate play a critical role in determining the alignment of grown hBN islands.
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Figure 2.10 (a-b) SEM images of grown hBN triangles on Cu(102) and Cu(103) surfaces with a scale bar of 20 μm.80 Black dashed arrows represent the Cu[010] direction. (c-d) Energy profile of hBN on Cu(102) and Cu(103) surfaces as a function of their relative angle. (e-f) Atomic configurations with the lowest energy corresponding to (c-d).
In Chapter 1, Figure 1.12 and Figure 1.13 present the experimental success in WSSC hBN synthesis by seamless stitching of unidirectionally aligned hBN islands on a WSSC vicinal Cu(110) surface and a WSSC Cu(111) surface with a high concentration of step edges, respectively, and we introduce the alignment mechanisms of hBN islands in these two works.
For hBN grown on a vicinal Cu(110) surface, an atomic-resolution STM image (Figure 2.11(a)) proved that the hBN island shows a ZZ edge at the interface between the grown hBN and the obtained surface, and low-energy electron diffraction (LEED) pattern confirmed that the step edges on the obtained surface is along Cu<211> direction.84 We performed theoretical calculations to explore the formation energies of interfaces between various hBN edges with the Cu<211> step edge. As shown in Figure 2.11(b-c), where γ denotes the relative angle between a hBN ZZ direction and the Cu<211> step edge, there is only one local minimum located at γ = 0º, where the nitrogen-terminated ZZ edge of hBN is parallel with the Cu<211> step edge, confirming the unique orientation of hBN islands on the obtained vicinal Cu(110) substrate.
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Figure 2.11 Alignment mechanism of hBN on vicinal Cu(110) surfaces. (a) Atomic-resolution STM image showing the interface between hBN edge and Cu substrate.84 (b) Atomic configuration of the interface of a nitrogen-terminated hBN ZZ edge aligning along a Cu<211> step edge of a vicinal Cu(110), γ is the relative angle between them. (c) Formation energy of hBN edges attaching to the Cu<211> step edge as a function of γ. (d) Schematic of meandering step edges on a high-index substrate.309 (e) Schematic of interface between a hBN island and a tilted step edge with kinks. (f) Atomic configuration of the interface between a tilted hBN edge and a tilted step edge.
Practically, step edges on a substrate cannot be always straight, instead curved step edges with varying directions are frequently observed, especially under a high temperature for CVD growth of 2D materials.310-312 The effect of such curved step edges on the alignment of hBN islands has also been investigated.309 Figure 2.11(d) illustrates the meandering step edges on a substrate, due to the variation of step edge direction, hBN islands along such step edges may show different orientations. At the atomic scale, a meandering step edge consists of straight atomic segments and kinks. As shown in Figure 2.11(e), only if there is a tilted hBN edge which has kinks complementary to the meandering step edge, the orientation of hBN islands and therefore their unidirectional alignment can be maintained during the growth. From the atomic configuration in Figure 2.11(f), it can be seen that the kink height difference between hBN ZZ edge and Cu<211> step edge is only 0.08 Å, which is the reason for the tight docking of hBN ZZ edge to the Cu<211> step edge. For Cu step edges along other directions on vicinal Cu(110) surfaces, their kink heights show much larger difference with that of ZZ edge of hBN, and therefore step edges along Cu<211> direction is the key to ensure unidirectionally aligned hBN islands. Besides, due to the existence of step edge, the seamless coalescence of unidirectionally aligned hBN islands on vicinal Cu surfaces requires that the step height is close to the sp2 B-N bond length (1.44 Å), and the step height of Cu<211> step on vicinal Cu(110) surfaces is 1.27 Å. Therefore,
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seamless coalescence of hBN islands on such kind of Cu surfaces can be realized, which has been verified by the MD simulations.
The alignment mechanism of hBN islands on a highly stepped Cu(111) surface was also studied.124 As discussed above, triangular hBN islands should have two alignment orientations on an ideal Cu(111) surface. As shown in Figure 2.12, the STM image shows that the step edges on the obtained Cu(111) surface are composed of two typical step-edge terminations (A and B). By DFT calculations, the binding energies of a B6N7 cluster attaching to these two types of step edges and to a flat Cu(111) terrace are compared, it turns out that the binding energy of the two most stable configurations, NIBII (60°) and NIBIII (0°), attaching to the Cu(111) terrace are almost degenerate, whereas a difference of ~ 0.23 eV appears when attaching to the two types of step edges. Besides, the binding energy difference can further increase in proportional to the size of the hBN cluster, making the NIBII configuration to be the dominant orientation on the highly stepped Cu(111) surface.
Figure 2.12 Alignment mechanism of hBN on highly stepped Cu(111) surfaces.124 (a) STM image of a highly stepped Cu(111) surface and schematic showing the step edges is composed by two types of segments (A and B). (b-c) Binding energy and atomic configurations of a B6N7 cluster attaching to the two typical step edges of the Cu(111) surface.
From above discussions, it can be seen that although hBN islands have at least two most stable alignment orientations on all low-index surfaces of a FCC TM foil, unidirectionally aligned hBN islands can be realized on low symmetric high-index TM surfaces due to the strong binding between one of the edges of the hBN island and the step edge of the substrate. Therefore, instead of low-index surfaces, high-index surfaces might be more promising in synthesizing WSSC 2D materials, as will be revealed in Chapter 4.
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2.3 CVD growth of single-crystal monolayer TMDC films