Self-assembly of ordered graphene nanodot arrays

The ability to fabricate nanoscale domains of uniform size in two-dimensional materials could potentially enable new applications in nanoelectronics and the development of innovative metamaterials. However, achieving even minimal control over the growth of two-dimensional lateral heterostructures at such extreme dimensions has proven exceptionally challenging. Here we show the spontaneous formation of ordered arrays of graphene nano-domains (dots), epitaxially embedded in a two-dimensional boron–carbon–nitrogen alloy. These dots exhibit a strikingly uniform size of 1.6 ± 0.2 nm and strong ordering, and the array periodicity can be tuned by adjusting the growth conditions. We explain this behaviour with a model incorporating dot-boundary energy, a moiré-modulated substrate interaction and a long-range repulsion between dots. This new two-dimensional material, which theory predicts to be an ordered composite of uniform-size semiconducting graphene quantum dots laterally integrated within a larger-bandgap matrix, holds promise for novel electronic and optoelectronic properties, with a variety of potential device applications.


Supplementary Note 2. Growth and STM characterization of graphene-hexagonal boron nitride (hBN) in-plane heterostructures synthesized by alternating the streams of the relative precursors
We have investigated the possibility of creating BCN alloy structures by alternating the streams of the gas precursors (i.e., ethylene and borazine), as a comparison to the study by Lu et al. performed using Ru(0001) as the growth substrate 1 .
Exposing a complete monolayer (ML) of graphene on Ir(111) to 5 langmuir (L) of borazine vapour at 1000 K led to formation of neither BCN alloy nor in-plane graphene-hBN heterostructures. Indeed, no visible change to the graphene layer was observed after STM investigation. This is most probably due to the fact that the complete monolayer of graphene protected the Ir substrate which hindered the decomposition of borazine.
Next, we exposed 0.8ML of graphene to 5 L of borazine vapor at 1000 K. STM analysis showed areas of bare Ir and some with small hBN islands in addition to the graphene regions. No BCN alloy was observed. Then, we increased the borazine dose by 12L at a growth temperature of 1200K. The formation of in-plane heterostructures of pure graphene and hBN was achieved (Supplementary Figure  2). Furthermore we noticed a small decrease in graphene coverage probably due to etching from atomic hydrogen formed during the decomposition of borazine molecules. In conclusion, we could not see any alloying between C, B and N on Ir by using a growth method consisting of alternating the stream of the gas precursors.

Supplementary Note 3. Additional structural characterization of graphene nanodots and BCN alloy
Atomically resolved STM pictures have been used to provide insight into the structure of graphene nanodots and the surrounding BCN alloy. The lattice spacing, orientation, size and shape of the graphene nanodots can be characterized in great detail. Below, STM images of the nanodot phase allow, for instance, determination of lattice constants in agreement with those expected for graphene. Structural characterization of the BCN-alloyed regions, however, is more difficult because of the intrinsic elemental inhomogeneity. In topographic images, the disordered bright and dark spots within the BCN-alloyed regions dominate the contrast. Only after filtering the STM images, it is possible to resolve locally the honeycomb structure of the BCN alloy. Filtering techniques applied to selected images have also been used to demonstrate the structural properties of the two different types of region; the ordered graphene nanodots and the heterogeneous BCN alloy. The STM data have been processed using WSxM 2 (for first derivative and laplacian filters) and Gwyddion 3 (further analysis). In order to provide quantitative information about the shape of the graphene dots, we have quantified how far they deviate from a compact shape. We have calculated the area and perimeter of several dots in different high resolution STM images (due to the small size of the dots, only high resolution images allow for a fine measurement of these features), then for each area, we have calculated what is the perimeter of a (ideal) hexagon with that area. The ratio between the actual perimeter and the ideal perimeter gives a measure of how irregular the dot is, with 1 being a hexagon, and >>1 being extremely irregular. As not all the dots show clearly a hexagonal shape, we have then also used a similar approach to compare the perimeter of the best-fit ellipse and an ideal circle. This again informs about how far the dot shape deviates from a compact shape. These data are collected in the histograms in Supplementary  Figure 9, along with a histogram for the ratio of major to minor axis for the best-fit ellipse. From the data above we can conclude that the elongation (elliptical vs compact shape) captures much of the deviation from ideal circles or hexagons, but the islands are still significantly more irregular than the best-fit ellipse, as evidenced by the actual to ideal perimeter ratio (Supplementary Figure 9a, average being 1.08±0.06) being higher than the perimeter ratio for the best-fit ellipse to same-area circle (Supplementary Figure 9b, average being 1.04±0.03).

Supplementary Note 4. X-ray photoemission spectroscopy
In order to estimate the amount of B, C and N on the surface for each sample, we have collected the B(1s), C(1s), Ir(4d) and N1s photoelectrons emitted when samples were irradiated with the same incident photon energy (610 eV). By growing full ML coverage of graphene (hBN) on Ir and setting the resulting C/Ir ratio equal to 1 (B/Ir = 0.5 and N/Ir = 0.5) we can work out the corresponding abundance of these elements in alloyed samples. The relative amount of the individual elements is reported in the Supplementary Table 1. As referred to in the main text LEEM experiments show that upon exposure to ethylene, graphene flakes nucleate and grow first on the Ir surface while the borazine partial pressure is still being adjusted. Hence we expect the XPS data for alloyed samples to represent a mixture of graphene flakes and alloyed regions. The abundance of C can then be partially allocated to regions with fast growing graphene flakes in all samples. In all alloyed samples there is an excess of B over N. This finding can be explained by (i) the energetic preference for B-C bonds at interfaces between BCN and graphene regions (in analogy to what is observed at the interface between hBN and graphene islands grown on Ir(111) 5,6 ), and (ii) the presence of small quantities of B dissolved in the Ir crystal 7,8 .
Ultimately, we have characterized the interaction between the BCN layer and the Ir substrate, by looking at the Ir(4f 7/2 ) core level (Supplementary Figure 10).   The interaction between graphene and the Ir substrate is weak, and the Ir 4f 7/2 can be fit using two, namely bulk and surface, components. In the case of hBN, the interaction with the substrate is stronger, so that the surface component splits into the clean surface component as used to fit the graphene data and a new surface component, Interface 1. The Interface 1 peak represents Ir surface atoms bound strongly to B and N atoms in the overlying hBN layer 7,9 . The 30/70 sample can be fit using the three components (that is, the bulk peak, the clean surface component and the interface 1 component). The 50/50 and 70/30 samples require introduction of a second interface component, Interface 2, to fit accurately the data. The second Interface component again represents surface Ir atoms bound to the overlying layer.