Chapter 7 Alignment of hBN islands on low symmetric Cu substrates
7.3 Results and discussions
7.3.1 Alignment of hBN islands on Cu{111}-based high-index low symmetric substrates
Figure 7.3(a) shows the six atomic configurations of straight hBN edges attached to straight Cu step edges on Cu{111}-based low symmetric surfaces, i.e., hBN ZZN, ZZB and AC edges attached to Cu<110> and Cu<211> steps, respectively. From atomic configurations, it can be seen that both hBN ZZN and hBN ZZB edges show a perfect structural match with the Cu<110> step, while hBN AC edge only matches to the Cu<211> step. The formation energies of these interfaces are calculated and shown in in Figure 7.3(b). It should be noted that, the formation energies are functions of the chemical potential of nitrogen (or boron) due to the unbalanced stoichiometry of hBN edges, and here the chemical potenial of nitrogen is chosen as the reference. During CVD growth of hBN, the range of ππ is usually between the reference of N2 (ππ =-8.31eV) and the reference of Ξ±-boron bulk (ππ=-10.84 eV). From Figure 7.3(b), it can be seen that in a N-rich environment the interfaces with hBN ZZN edge attached to stragith Cu step edges are energically perfered, while a under B-rich condition the interfaces with hBN ZZB edge are more stable. It is noted that, on Cu substrates with straight <211> step edges (lower panel of Figure 7.3(b)), alought the Cu<211> step edge has a good structural mach with hBN AC edge, the interface with hBN AC edge is most stable only when ππ is smaller than -9.61 eV, and the interface with hBN ZZN edge is still ebergetically favored under a N-rich condition.
Figure 7.3 The orientation of hBN islands along straight step edges of Cu{111}-based surfaces. (a) Configurations of three straight hBN edges attached to two straigth step edges. (b) Formation energies of straight hBN edges attached to straigth step edges as a function of chemical potential of nitrogen, ππ. (c) Illustrations of hBN islands along straight step edges at different ππ ranges corresponding to (b). Triangles denote the orientations of hBN islands with three ZZN edges and different orientations are distinguished by colors.
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In practice, the step edges on Cu{111}-base high-index low symmetric are not always straight ones, and instead most of them are tilted ones. We have assumed that a tilted step edge can be view to be constructed by stragith step segments, as shown in Figure 7.3(c). The alignment of hBN islands on Cu substrates with tilted step edges are dependent on the orientations of the straight step segments and also on the amibient condition. For a high ππ, i.e., a N-rich condition (regime I in Figure 7.3(b) and structure I in Figure 7.3(c)), both Cu<110> and Cu<211> step edges passivated by hBN ZZN edge are energetically favorable, and concequently the orientation of hBN will change if the Cu step edge changes from <110> direction to <211> direction and vice versa. If ππ is in regime II (Figure 7.3(b), and structure II on Figure 7.3(c)), where hBN ZZN edges perfer to attach to Cu<110> step edges and hBN AC edges prefers to attach to Cu<211> step edges, two orientations of hBN islands appears along Cu<211> step edges if a mirror refelection is operated on the structure with hBN AC edge attaching to a Cu<211> step edge, despite one of them are equvialent with the orientaiton of hBN along Cu<110>
step edges (structure II in Figure 7.3(c)). Further decreasing ππ to regime III (Figure 7.3(b)), i.e., under a B-rich condition, Cu<110> step edges prefer to be attached by hBN ZZB edges and Cu<211> step edges prefer hBN AC edges, and consequently hBN islands regime III show opposite orientations along Cu<211> step edges, which is similar to that in regime II.
Based on the above predicted orientations of hBN islands on Cu{111}-base high-index low symmetric substrates with the two straight step edges, the orientations of hBN islands on an arbitary tilted step edge of Cu{111}-based surfaces are futher explored. As discussed in Figure 7.2(c-d), a tilted step edge on a substrate perfers to passivated by a structural matched tilted hBN edge. Here a few rules are assumed to construct the structural matching interface between a hBN edge and a titl Cu step edge:
(i) each kink of the tilted Cu step edge should be docked by one kink of the hBN edge; (ii) there should also be a one-to-one docking relation for the segments of the hBN edge and those of the Cu step edge;
(iii) if there are more than one orientations of hBN islands that satisfy the above two geometry rules, such as that a tilted Cu step edge with <211> segments can be passivated by two tilted hBN edges with the same AC segments but different kinks, the most preferential orientation of the hBN island should be determined by the interface between kinks with the lowest formation energy.
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Figure 7.4 The evolution of hBN orientation along step edges of Cu{111}-based surfaces. (a) The orientation of hBN islands versus step edge direction at ππ=-8.21~ -9.61 eV. (b) Illustration of hBN islands along SE<211>iΓ<110> and SE<110>iΓ<211> corresponding to (a). (c) The orientation of hBN islands versus step edge direction at ππ=-9.61~ -9.92 eV. (d) Illustration of hBN islands along SE<110>iΓ<211>
corresponding to (b). (e) The orientation of hBN islands versus step edge direction at ππ=-9.92~ -10.84 eV. (f-h) The alignment of hBN islands along a curved step edge with direction varying from -180 to 180Β° at different ππ ranges, corresponding to (a), (c) and (e), respectively. Pure colors at margin means small orientation variations while gradient colors represent large orientation variations.
By using above proposed rules, we predicted the orientations of hBN islands on Cu{111}-based high-index low symmetric substrates with step edges along different orientations within the chemical
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potential range of β9.61 ππ < ππ < β8.31 ππ (Figure 7.4(a-b) and (f)). The same as that in Chapter 5, the exact Cu[110] direction on the Cu substrate is chosen as the reference orientation for both the hBN island and the Cu step edge. On Cu{111}-based high-index low symmetric substrates with step edges dominated by [110] segments, including SE[211iΓ[110]Μ ] and SE[121]iΓ[110] ones (SE represent step edge, superscripts and subscripts denote the segment and kink structures, which introduced in the section 5.2), which show orientations ranging from -19.1o to 19.1ΒΊ, hBN islands show an misorientation angle ranging from -0.36ΒΊ to 0.36ΒΊ for β9.61 ππ < ππ < β8.31 ππ and the small misorientation angle is ascribed to the perfect match in kink heights between tilted hBN edges with ZZ segments (0.217 nm) and SE<211>iΓ<110>step edges (0.221 nm) (see Figure 7.4(b)). On Cu{111}-based high-index low symmetric substrates with step edges dominated by [211Μ ] segments, including SE[110]iΓ[211Μ ] and SE[101iΓ[211Μ ]Μ ] ones, of which the orientation angle is from 19.1o to 41.9ΒΊ, hBN islands show misorientation angles ranging from 30ΒΊβ7.86ΒΊ to 30ΒΊ+7.86ΒΊ at β9.61 ππ < ππ< β8.31 ππ because of the large difference in kink heights between tilted hBN edges with ZZ segments (0.217 nm) and SE<110>iΓ<211> step edges (0.128 nm) (see Figure 7.4(b)). Figure 7.4(f) demonstrates the orientations of hBN islands on the Cu{111}-based high- index low symmetric substrates with step edge directions varying from -180ΒΊ to 180ΒΊ, where pure colors at the margin indicate small orientation variations of hBN islands and gradient colors represent large orientation variations. Obviously, unidirectionally aligned hBN islands can only be synthesized on Cu{111}-based high-index low symmetric substrates with SE<211>iΓ<110>step edges when β9.61 ππ <
ππ < β8.31 ππ.
Similar to above analysis, we also investigated the orientations of hBN islands on Cu{111}- based high-index low symmetric substrates for regime II (β9.92 ππ < ππ < β9.61 ππ), where tilted SE<211>iΓ<110> step edges are preferred to be passivated by tilted hBN edges dominated by ZZN segments and tilted SE<110>iΓ<211> step edges prefer to be passivated by tilted hBN edges dominated by AC segments.
Due to the small kink height differences for both of these two cases, the orientation change of hBN islands is negligible (< 0.5o). As shown in Figure 7.4(c), on Cu substrates with step edge orientations ranging from -29.99o to 29.99ΒΊ respect to a Cu<110> direction, the orientations of hBN islands are almost the same. Despite antiparallel hBN islands will be formed on Cu substrates with straight SE0<211>at 30ΒΊ+60ΒΊΓ π, where n is an integer, there is only one orientation along SE<110>iΓ<211> step edges because the mirror symmetry is broken by the existence of kinks (Figure 7.4(d)). Figure 7.4(g) demonstrates the overall evolution of hBN islands with the change of Cu step edge orientation. Our theoretical predictions are well consistent with the experimental observation on hBN growth on vicinal Ir(111) surfaces, where hBN show only one orientation on a vicinal Ir(111) surface with <110>
dominated step edges but two orientations on a vicinal Ir(111) surface with <211> dominated step edges.362
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In regime III (β10.84 ππ < ππ < β9.92 ππ), where SE<211>iΓ<110> step edges prefer to be passivated by tilted hBN edges with ZZB segments and SE<110>iΓ<211> step edges prefer to be attached by hBN edges with AC segments, hBN islands on Cu substrates show opposite orientations as compared to regime II, as shown in Figure 5(e) and (h).
From above discussions, we can see that unidirectionaly aligned hBN agrains can be synthesized on Cu{111}-based high-index low symmetric substrates with SE<211>iΓ<110> step edges, while antiparrallel hBN islands might be obtained on Cu{111}-based high-index low symmetric substrates with SE<110>iΓ<211>step edges. From Chapter 4, we have shown that hBN islands show antiparallel orientations on ideal Cu(111) substrates, and therefore lowering the symmetry of the substrate is promising in realizing the epitaxial growth of hBN.