Synthesis of Extended Atomically Perfect Zigzag Graphene - Boron Nitride Interfaces

The combination of several materials into heterostructures is a powerful method for controlling material properties. The integration of graphene (G) with hexagonal boron nitride (BN) in particular has been heralded as a way to engineer the graphene band structure and implement spin- and valleytronics in 2D materials. Despite recent efforts, fabrication methods for well-defined G-BN structures on a large scale are still lacking. We report on a new method for producing atomically well-defined G-BN structures on an unprecedented length scale by exploiting the interaction of G and BN edges with a Ni(111) surface as well as each other.

to hydrocarbons which slowly converts to graphene (G) on a timescale of hours. S1 The solubility of carbon in the nickel crystal increases substantially above 870 K, leading to the eventual absorption of carbon species on the surface into the bulk. S2 In between these limits, a narrow temperature window exists where graphene may be grown directly on the surface in a self-limiting fashion. Embedded graphene domains are obtained on clean samples while some residual carbon contamination results in graphene growth on top of the first nickel layer. S3 Tight growth temperature constraints do not exists for the growth of BN, but high quality samples are only obtained at temperatures above 1070 K where graphene is not stable on the surface. This leads us to adopting a reverse growth protocol when compared with most other works in the field, beginning with the deposition of BN at high temperatures and finishing the samples by attaching graphene to the BN crystallites at lower temperature. BN was grown by low pressure chemical vapor deposition (CVD) from a borazine (B 3 N 3 H 6 , Chemos GmbH) precursor at 1070 K as described in the manuscript. Figure S1 shows sketched p-T-diagrams for the preparation of pristine BN seeds as well as the attachment of straight or jagged graphene to the seeds.

Additional Structural Information
The local work function of a surface can be measured in STM by performing dI/dV spectroscopy in the field emission regime. The work function of G and BN may be measured on samples containing only one of the two materials and an assignment of materials on the heterolayer may be made or confirmed by comparing the work function measured on different parts of the sample against the references containing only one as shown below. The first peak in either series (∼1.8 V for BN and ∼2.3 V for graphene) arise from a quantum well state between the buried Ni(111) surface and the graphene or BN adlayer. S4,S5 Figure S1: Sketched p-T-diagrams: Preparation conditions for (a) pristine BN seeds, (b) BN seeds with jagged graphene domains, and (c) straight graphene domains Figure S2: a) Atomically resolved STM image of a G-BN interface. A series of dI/dV spectra in the constant-current mode between 1 V and 10 V are taken along the dotted line. b) Individual sample spectra showcasing the differences between the FERs of G and BN. c) Contour plot of all spectra taken along the dotted line in panel a with an abrupt change of the work function close to the interface region. S3

S2
Both G and BN grown directly on Ni(111) naturally expose ZZ edges as revealed by atomically resolved STM images close to the G/Ni(111) and BN/Ni(111) interface as shown below. Figure S3: a) STM image near the BN/Ni(111) interface. The BN lattice is resolved in some parts of the image and extrapolation towards the interface reveals it to be ZZ oriented (10 mV, 1 nA). b) Atomically resolved STM image of G triangles attached to a BN edge showing their edges to be ZZ oriented as well (10 mV, 5 nA).

Computational methods and results
We study computationally the edge of hexagonal boron nitride (BN) embedded in Ni (111), and the interface between graphene (G) and h-BN on Ni(111). The experiments show that the interfaces are in the zigzag (ZZ) directions, and therefore we omit the cases with armchair edges in the computations. Moreover, the armchair G/BN interfaces are expected to be unfavourable if either C-B or C-N bonds are energetically more favourable than the other than the other. The main objective is to determine whether the G/BN zigzag interfaces are with C-B or C-N bonds. We also discuss whether the interfaces can reconstruct.

BN embedded in Ni(111)
In order to solve the zigzag edge energies of BN embedded in Ni(111), we devise model systems containing a triangular island of BN, see Figure S4. The supercells are relaxed in a Monkhorst-Pack grid of 8 × 8 × 1 k-points. Such islands with zigzag edges have more B or N-terminated edge sites, associated with the sublattice imbalance. In fact, one requires model systems with more zigzag edge of one type, since the zigzag edge energies cannot be solved in the ribbon geometry alone. S6 The interface energy is defined intuitively as the energy of "a system with the interface" minus the energy of "a system without the interface", namely the same number of atoms forming only bulk material. We can write for the edge or interface energy Figure S4: The relaxed computational supercells, viewed from the top and side, containing a triangular zigzag nanoisland of BN embedded in Ni(111) with B-terminated (a-b) and Nterminated (c-d) edges. The red and blue spheres represent boron and nitrogen atoms, and the grey and yellow spheres represent nickel atoms below and at the top layer of the Ni (111) substrate.

S5
where E is the energy of the computational supercell, E s is the energy of the substrate only, n i is the number of atoms of type i excluding the substrate, and µ i is the energy of an atom of type i, forming BN or the top layer of Ni (111), both adsorbed on the substrate. Even if it is not explicitly visible in the notation, the energies µ i contain the adsorption energy and the formation energy of the bulk material.
A triangular BN nanoisland has a total of 3L edge sites at the triangle sides and three additional sites at the corners. Therefore, we can decompose the total edge energies of the two model systems, see Figure S4 and Figure 4 in the main manuscript, as where γ B,N are the B and N-terminated zigzag edge energies per edge atom. Evaluating the model system total edge energies Γ △ and Γ ▽ by using Eq. 1, readily allows us to solve for γ B and γ N .
By considering the total edge energy Γ of a system containing both the B and Nterminated triangular nanoislands, and requiring Γ = Γ △ + Γ ▽ , it follows that where µ BN is the energy of a two-atom unit cell of BN on the substrate. The energies or chemical potentials of individual B and N atoms, µ B and µ N , are therefore directly related.
Furthermore, to allow any chemical environment preferring either more B or more N atoms in the system, we write where µ 0 B,N are the reference energies that we take as the energies of isolated B and N atoms, ε is a constant of 1 2 (µ BN+s − E s − µ 0 B − µ 0 N ) to meet the requirement of Equation (4), and µ S6 is a free parameter and chemical potential for B atoms, also directly related to the chemical potential of N atoms. If µ = 0, both B and N atoms are at the same potential with respect to their reference energies, and neither is energetically preferred in the system. Otherwise µ controls whether the system is B or N rich with more zigzag edge of the that kind.
The zigzag edge energies of BN embedded in Ni (111) can now be solved The B-terminated zigzag edges are preferred if µ > −0.53 eV. However, it is difficult to estimate the value of µ in the experiments.
It is well-known that the bare zigzag edge of BN reconstructs to an alternating pentagonheptagon (57)

Graphene/BN interfaces on Ni(111)
To evaluate the G/BN interface energies, we have devised a computational supercell containing a 22-atom triangular nanoisland of BN embedded in graphene on the Ni(111) substrate.
The supercell is relaxed in a Monkhorst-Pack grid of 8 × 8 × 1 k-points, and the relaxed atomic structures are shown in Figure S5. Such systems are already qualitatively similar to what has been measured in the experiments.
As in the case of BN islands embedded in Ni (111), there are more B or N atoms in the model systems, which also translates into having more C atoms occupying the other S7 sublattice associated with the top or fcc sites. This has to be taken into account when evaluating the interface energies Again, the energies of individual atoms are assumed to sum up to the energies of bulk BN and graphene on the substrate. We can estimate the carbon atom energies µ Ctop and µ C fcc by assuming the following set of equations where in each case the adsorption distances are fixed to the top-fcc value. This ensures that Figure S5: The relaxed computational supercells, viewed from the top and side, containing a triangular zigzag nanoisland of BN embedded in graphene on Ni(111) with C-B (a-b) and C-N (c-d) interfaces at the triangle sides. The red, blue, black and grey spheres represent boron, nitrogen, graphene and nickel atoms, respectively.
S8 the energies of carbon atoms on each site are comparable. The three equations can be solved, and we get that µ Ctop is 0.40 eV lower than µ C fcc , which clearly implies that the sublattice imbalance of C atoms has to be taken into account.
The zigzag C-B and C-N interface energies per bond can be evaluated in the same manner as in the case of BN embedded in Ni (111). The interface energies are where µ is the chemical potential as defined in Eq. (5). We have also evaluated the interface energies without the substrate, obtaining It is expected that the honeycomb lattice at the interface is not broken even if the interface reconstructs in some way. Namely, since the B, N and C atoms prefer the top and fcc sites on the substrate, there would be an associated energy cost to moving the atoms elsewhere, for instance by bond rotation or by formation of 57-type reconstructions. Additionally, there are no dangling bonds at the G/BN interface that would need relaxing. We have therefore restricted our study of the possible interface reconstructions to Klein-type interfaces.
We have relaxed periodic systems with BN ribbons embedded in graphene on Ni(111), see Figure S6a-c. The ribbons have two interfaces that correspond to the edge directions of the two distinct triangular nanoislands. First, we simulated a system with both C-B and C-N zigzag interfaces, see Figure S6a, containing 6 B, 6 N, and 12 C atoms in the computational unit cell that was relaxed using a grid of 4 × 40 × 1 k-points. Moreover, the carbon atom closest to the N-terminated zigzag edge of BN had to fixed to its adsorption distance, since otherwise nearby carbon atoms would not stay adsorbed on the substrate. This could be physical, or it can also be an artifact from the PBE exchange-correlation functional. We did not have the same problem with the model systems containing the triangular nanoislands, most likely due to the more complicated geometry where the interface cannot fold as easily.
In any case, the sum of the zigzag interface energies is which agrees very well with the energies in Eq. 11 that were obtained using the geometries with triangular nanoislands.
The energies of the Klein interfaces can be readily evaluated by slightly modifying the zigzag interfaces. The relaxed ribbon systems containing Klein interfaces are shown in Figure   S6b and S6c. Here again, the carbon atoms next to the nitrogen atoms are fixed to the S10 graphene adsorption distance. The resulting Klein interface energies are We have plotted the zigzag and Klein interface energies in Figure S6d. It is clear that the Klein interfaces have much higher energies at reasonable values of µ. Furthermore, in a N-(B-)rich system the BN edges are most likely in the N-(B-)terminated zigzag edge directions, but after graphene growth this direction supports only the C-B (C-N) Klein edge that has more B (N) atoms. Therefore we conclude that the zigzag interfaces are not likely to reconstruct.