Tailoring commensurability of hBN/graphene heterostructures using substrate morphology and epitaxial growth conditions

Hexagonal boron nitride (hBN) has played an important role in the progression of two-dimensional (2D) material systems as a superior dielectric substrate and an encapsulation layer for electronic applications.^1,2 As a 2D wide-bandgap material, hBN can act as a tunnel barrier or gate dielectric for vertically stacked heterostructures with potential uses in flexible and transparent electronics.^3,4 Additional interest in recent years has focused on leveraging “twistronics,” or phenomena that occur in 2D heterostructures with layers rotationally misaligned, or twisted, relative to one another.⁵ This twist creates different structural and electronic periodicities than the fully commensurate relation and can even break translational symmetry.⁵ For example, hBN/graphene heterostructures can have drastically different properties depending on the interlayer twist angle, as the interplanar atomic potential field of the hBN lattice can break the sublattice symmetry of graphene.^6,7 This modulates graphene's band structure both on an atomic scale (when a B or N atom is directly on top of a C atom) and in periodicities up to ∼14 nm due to Moiré lattices occurring from varying commensurate relations as a function of twist angle and lattice mismatch.⁸ Experiments have shown that rotationally aligned hBN/graphene heterostructures can allow for the realization of Hofstadter's butterfly^9–12 or Mott insulating states in trilayer graphene,¹³ while incommensurate relations enable resonant tunneling through hBN barriers¹⁴ and allow for the probing of innate features of encapsulated 2D material, such as superconductivity in bilayer graphene.¹⁵ Rotational misalignment between hBN and graphene has also recently been found to allow for higher carrier mobility in graphene due to a reduction in Umklapp electron-electron scattering.¹⁶ 

These alignment-dependent properties can be compelling from a scientific perspective but may complicate device fabrication when not controlled. The requirement for specific rotational alignment or misalignment between layers necessitates use of single-crystal films in devices, assembled by either film transfer or direct growth. Currently, epitaxial growth is the only method capable of producing fully commensurate heterostructures with well-defined interlayer stacking sequences. Epitaxial thin film growth is also an inherently scalable technique capable of forming wafer-scale single-crystal films. In order for epitaxial hBN growth to be widely adopted, growth parameters should be able to direct the epitaxial rotational alignment and form heterostructures where both twist and stacking order is fully defined.

Most current epitaxial hBN growth efforts focus on monolayer (ML) deposition on transition metal substrates, which provide an excellent epitaxial lattice match, a catalytic substrate for single-monolayer specificity, and an easier integration with graphene growth technology. Unfortunately, the lack of single-crystal metal substrates and reliance on film transfer to insulating/semiconducting substrates reduce the utility of these growths for highly demanding electronic applications. The need for multilayer hBN for gate dielectrics and substrates without significant leakage currents also drives research into multilayer growth capability. Recently, high-temperature chemical vapor deposition (CVD) has produced epitaxial hBN multilayer thin films on technologically relevant substrates like Al₂O₃(0001) and SiC(0001),^17–22 but in order to create epitaxial 2D heterostructures, hBN growth must be optimized on other 2D material as well.

Graphene's similar sp² bonding and small ∼1.7% lattice mismatch make it an excellent substrate for hBN, suggesting direct growth of hBN films on highly oriented pyrolytic graphite (HOPG)^23–25 or epitaxial graphene (EG) on SiC(0001) substrates^26–28 as promising approaches. The hBN/EG/SiC(0001) system, in particular, is a useful testbed for investigating epitaxial growth of hBN due to its well-characterized properties, single crystalline orientation, and inherent scalability. In this system, few-ML EG can be controllably formed by subliming silicon at high temperatures from Si-face SiC(0001).²⁹ This EG provides a robust, temperature-stable substrate for epitaxial growth of hBN on an area limited by the size of available SiC wafers, which can be ≥150 mm in diameter. In addition, while van der Waals (vdW) epitaxy has been known to accommodate large lattice mismatches and still maintain an epitaxial in-plane rotational alignment,^30,31 it has been found that a 30° twist between hBN and graphene is a metastable configuration accessible through substitutional growth²⁶ or thermal annealing of hBN flakes exfoliated on graphite substrates.³² This 30° orientation has also been observed in graphene growth on hBN exfoliated flakes.^33,34 If growth conditions exist where either the 0° or 30° twisted epitaxial orientation can be selectively stabilized, wafer-scale epitaxial hBN/graphene heterostructures with tunable levels of commensurate lattices can be formed without exfoliation and manual stacking of layers.

Despite the similarity in the crystal structure, there are complex subtleties which make growth of hBN on graphene challenging. The growth of 3-fold symmetric hBN on 6-fold symmetric graphene typically results in twin domains, or domains with different polarities, that produce antiphase boundary defects when they coalesce.^26,35,36 Unfortunately, molecular beam epitaxy (MBE) of hBN on monolayer EG substrates has been dominated by preferential nucleation from common defects such as graphene wrinkles or step edges, complicating the already difficult hBN/graphene growth.^24,28 Both defect mechanisms need to be addressed through further growth optimization and understanding of nucleation in this system.

This paper investigates the nucleation and epitaxial orientation of multilayer hBN films grown by a novel high-temperature plasma-assisted chemical beam epitaxy (PE-CBE) technique. This technique was found to be able to produce multilayer hBN films with appreciable (up to ∼8 nm/h) growth rates. Structural and chemical analysis of the grown films provides insight into the nucleation mechanisms of hBN on EG in two growth regimes accessible with the PE-CBE method. Both the 0° and the 30° rotational alignments between hBN and graphene are stabilized and can be selected by changing the growth rate. The hBN nuclei edges were found to be arm-chair terminated, as elucidated from transmission electron microscopy (TEM) and atomic force microscopy (AFM) data. These results may be broadly applicable to other van der Waals material growth on EG substrates as well as other growth methods such as MBE (Ref. 28) and CVD (Ref. 37).

The hBN films were grown using PE-CBE in a VG V80 MBE system equipped with plasma and gas precursor sources. The chamber's solid SiC heater module (UHV Design) enabled growth with substrate temperatures up to 1500 °C as measured by a thermocouple placed at a similar distance from the heater as the substrate. The substrate temperature was calibrated using reflection high energy electron diffraction (RHEED) measurements of the Si(111) native oxide desorption temperature (T ∼ 760–900 °C),³⁸ SiC native oxide desorption (T ∼ 1000 °C),³⁹ and graphitization of SiC (T ∼ 1200 °C),⁴⁰ resulting in the substrate temperature being ∼100 °C lower than the thermocouple reading. The base pressure of this turbomolecular-pumped system was ∼10⁻¹⁰ Torr. Borazine [(BH)₃(NH)₃, Gelest, 97% purity] was selected as a precursor due to its success in previous CBE studies^41–48 and its relative simplicity compared to the complex decomposition pathway of ammonia borane.⁴⁹ The borazine was kept below 0 °C to prevent decomposition and to lower the vapor pressure for flux control. Before each growth, the nitrogen plasma and precursor fluxes were set using the chamber pressure gauges, a Pfeiffer PKR 251 combination Pirani/cold cathode gauge and a nude ion gauge. A Veeco UNI-bulb RF nitrogen plasma cell, which was fed by 6N purity nitrogen gas that was passed through a chemical getter purifier (SAES Getters S.p.A.), was used to supply active nitrogen during deposition.

The 4–5 ML thick EG substrates were prepared by subliming Si from n-type, 4°-offcut 4H-SiC(0001) in an inert Ar atmosphere at ∼1600 °C. Details of the EG growth process can be found in Nyakiti et al.⁵⁰ The EG substrates were solvent cleaned using 10-min agitations in acetone and isopropanol, rinsed with de-ionized water, and blown dry with nitrogen supplied from liquid nitrogen boil-off before being loaded into the UHV system within 30 min of cleaning. The substrates were then outgassed at 400 °C for 90 min in a preparation chamber with a base pressure of ∼10⁻¹⁰ Torr prior to analysis and growth.

The samples were analyzed by x-ray photoelectron spectroscopy (XPS) before and after hBN growth by transferring the samples in vacuo to a Surface Science Laboratory SSX-100 XPS system equipped with a monochromatic Al-Kα source at a 55° photoelectron emission angle. A pass energy of 150 meV was used for survey scans and composition analysis, while a pass energy of 24.5 meV was used for peak position measurements. For all samples, a low-energy electron flood gun was utilized during XPS acquisition to minimize charging effects. The XPS system was calibrated using an elemental gold standard, and charging was compensated by shifting the spectra binding energy by ≤0.25 eV to set the EG C 1s peak to 284.5 eV.⁵¹ casaxps software was used for all fitting and analysis of XPS spectra.⁵² Core levels were fit using Shirley backgrounds and mixed 30% Gaussian, 70% Lorenzian lineshapes, except for the graphitic C 1s peak which used a Tougaard background with an asymmetric peak shape fit to the graphite C 1s peak.⁵² XPS overlayer thickness measurements of the hBN films were obtained using the attenuation of the C 1s substrate peak after hBN growth.^53,54 It should be noted that all XPS estimated film thicknesses are “average thicknesses” over the ∼1 mm-wide x-ray spot. This estimate assumes the overlayers are of uniform thickness despite AFM and TEM showing thickness variations in the hBN.⁵⁵ 

After initial XPS analyses, the samples were transferred back to the growth chamber. The substrate heater power was brought to an output power corresponding to a thermocouple temperature of ∼1450 °C and allowed to stabilize for approximately 5–10 min. During this temperature ramp and stabilization, the plasma conditions were established and stabilized. Growth was initiated by opening a shutter to expose the substrate to the precursor and plasma fluxes. Film growth was monitored by an in situ RHEED system with a differentially pumped electron source. Upon growth completion, the borazine precursor line was shut and the sample was cooled under the nitrogen plasma flux until the substrate temperature was below 500 °C.

This paper focuses on the analysis of samples corresponding to two different growth rates. In these regimes, the substrate heater power (corresponding to 1450 °C thermocouple), nitrogen plasma conditions (500 W, 10⁻³ Torr), and growth time (15 min) were all kept constant. Nominal borazine fluxes corresponding to chamber pressures of ∼7 × 10⁻⁴ Torr were used. For all growths, the borazine precursor bottle was fully opened and the active precursor flux was set by the borazine vapor pressure. Variations in active precursor flux resulted in a high growth rate (7.8 ± 1.6 nm/h) sample and a low growth rate (3.1 ± 0.6 nm/h) sample, as recorded by the XPS effective thickness measurements through substrate peak attenuation.⁵⁶ These thickness measurements have systematic uncertainties of ∼20% due to the limited accuracy of the calculated electron attenuation length (EAL).⁵⁷ 

The resulting film morphology and epitaxial orientation are further explored through ex situ AFM and TEM. AFM measurements were performed in tapping mode in an Asylum Research MFP-3D AFM system using set points between 400 and 700 mV. For TEM and scanning TEM (STEM), cross-sectional samples were prepared in an FEI Helios Dualbeam Nanolab 650 focused Ga ion beam system, using polishing steps down to 2 kV to reduce damage to the lamella. An FEI Titan FEG TEM/STEM system was used for imaging cross sections at 300 kV. For annular dark field (ADF) and bright field (BF) STEM and energy dispersive x-ray spectroscopy (EDS), a ThermoFisher Talos G2 200X STEM with ChemiSTEM EDS detectors was utilized at 200 kV. ADF-STEM images were taken at an angular range of 24–47 mrad and BF-STEM at 17 mrad. High-resolution TEM (HRTEM) images were calibrated to the 4H-SiC(0004) interplanar spacing of 2.5205 Å.⁵⁸ All TEM cross sections were imaged along the SiC[1$1¯$00] zone axis, parallel to the macrostep edges.

RHEED patterns of the high growth rate hBN surface before and after deposition are seen in Fig. 1, showing streaky diffraction indicative of a smooth surface. The patterns also provide evidence that the hBN is not rotated relative to the EG in this growth mode, as the (1 × 1) surface reconstruction does not change except for a potential slight contraction in streak spacing corresponding to a 2 ± 0.2% lattice expansion, indicating growth of commensurate, unstrained hBN.

Figure 2 shows XPS spectra taken before and after hBN growth. The EG samples exhibited minimal oxygen near the detection limit with no forms of carbon apart from that corresponding to carbon in SiC and graphene in the XPS survey spectrum shown in Fig. 2(a) after outgassing in vacuo. A prominent C 1s peak at 284.5 eV binding energy in Fig. 2(b) corresponds to the surface EG layers while a smaller C 1s peak around ∼283.5 eV corresponds to the C–Si bonds in the SiC(0001) substrate. The EG carbon peak dominates over the C–Si peak, indicating the presence of multiple EG layers.

After hBN growth, B 1s and N 1s peaks shown in Figs. 2(c) and 2(d), respectively, were found at 190.66 ± 0.05 and 398.21 ± 0.05 eV, respectively, matching earlier reports.^23,59 No features corresponding to sp³-hybridized B bonding (∼191.4 eV), indicative of nitrogen-deficient films, are present, and no shoulders are present in the C 1s or Si 2p peaks indicating a lack of interfacial reactions with the grown hBN.⁶⁰ Oxygen was not detected in the BN films by XPS. Stoichiometry was measured using the B 1s to N 1s core level integrated peak area ratio, corrected by the associated relative sensitivity factors. The B/N ratio was found to be 1.03 ± 0.04 for the high growth rate hBN film compared to 0.81 ± 0.04 for the low growth rate film. Stoichiometry of a sample grown at the same growth temperature and borazine flux conditions without additional plasma exposure was found to be slightly nitrogen poor (B/N = 1.27 ± 0.04), showing the additional active nitrogen may contribute to improved film stoichiometry.

In the hBN grown on EG substrates, no shoulders can be resolved in the B 1s peaks, but the N 1s core level spectra can be deconvoluted into two peaks. The lower binding energy N 1s peak (∼398.3 eV) corresponds to N–B bonding, while the higher binding energy (∼399.1 eV) likely corresponds to N–N bonding found in 5–7 ring defects.⁶¹ This peak accounted for 6.3% of the total N 1s core level peak area in the nitrogen-rich low growth rate film and 5.4% of the high growth rate film's N 1s peak, indicating these features did not have a strong dependence on the growth rate or film stoichiometry. Despite the differences in B/N ratios, XPS spectra confirm both films are solely comprised of BN.

Room temperature ex situ AFM of PE-CBE and CBE hBN growths without plasma exposure on EG/SiC(0001) substrates are shown in Fig. 3. Figures 3(c) and 3(d) show the fast and slow PE-CBE growths at 1450 °C, respectively. In both cases, the hBN nuclei show well-defined edges, which is indicative of good crystallinity. When hBN was grown at the same temperature (1450 °C) but without the presence of the nitrogen plasma [Fig. 3(a)] or with plasma exposure but at a lower substrate temperature [1300 °C, Fig. 3(b)], the deposited films appear to have less well-defined edges. These features, coupled with the higher surface roughness as indicated by the larger vertical scales, show that hBN growth degrades when conducted at lower temperatures or without plasma flux when using this technique.

Two predominant hBN film morphologies can be discerned from the detailed AFM micrographs of single terrace surfaces after growth: (1) nuclei of various shapes forming in the middle of macrostep terraces, as seen in Fig. 3(c) and (2) triangular nuclei preferentially nucleating at the edges of SiC(0001) macrosteps produced during EG growth, as seen in Fig. 3(d). Higher magnification images with different color maps [Figs. 3(e) and 3(g)] show more detail of the hBN nuclei. The nuclei of the high growth rate film show some triangular shapes, but multilayers and different shapes are also present. A line scan (averaged over the width of the line) shows that these surface features correspond to single monolayers of hBN, as indicated by the dashed black lines corresponding to the hBN(0002) interplanar spacing of 3.33 Å. The nuclei present in the low growth rate film consist of multiple layers of hBN equilateral triangular domains with parallel edges as seen in Fig. 3(g), with individual monolayer steps resolved in another averaged line scan perpendicular to one of the nuclei edges [Fig. 3(h)].

Figure 4 shows cross-sectional STEM images and corresponding elemental maps of the high growth rate PE-CBE hBN on an EG terrace. BF-STEM provides a contrast between the hBN and EG layers. This chemical specificity is confirmed by EDS performed during STEM imaging. The separation of C and N signals in the EDS-based elemental maps of Fig. 4, complemented by the contrast in BF-STEM, implies that the EG layers survive the PE-CBE growth of hBN with no detectable intermixing. These results confirm the heterostructures have abrupt interfaces between the EG and hBN, consistent with the XPS results.

The epitaxial alignment of the hBN to the EG/SiC(0001) substrate can be found through cross-sectional HRTEM. Figure 5 shows HRTEM images also taken in the [1$1¯$00] zone axis of the SiC(0001) substrate, providing a view along the terraces and the associated macrosteps. In Fig. 5(a), an atomic-resolution image of the high growth rate hBN in the middle of a terrace shows lattice fringing in the top 2D layers with a spacing of 2.14 ± 0.25 Å corresponding to {10$1¯$0} planes in hBN and a (0002) interplanar spacing of 3.37 ± 0.22 Å. These spacings are in agreement with previously reported values of 2.17 and 3.33 Å, respectively.⁶² In the slower growth, lattice fringing seen in Fig. 5(b) with a periodicity of 1.25 ± 0.16 Å corresponding to the {11$2¯$0}_hBN spacing of 1.25 Å can be found in the multilayer hBN nuclei that formed on the macrosteps. No evidence of the {11$2¯$0}_hBN interplanar spacing has been found in TEM of the faster growth despite imaging in the same [1$1¯$00]_SiC zone axis. This difference in hBN fringe spacing corresponds to a different rotational alignment between the hBN and the EG substrate. The rotational alignments for the fast [Fig. 5(c)] and slow [Fig. 5(f)] growth rate films are schematically shown, with green, orange, blue, and red spheres corresponding to nitrogen, boron, carbon, and silicon, respectively.

Additional HRTEM and ADF-STEM in Figs. 6(a) and 6(b), respectively, provide an interesting example of wrinkling (indicated by dark blue arrows) and delamination (indicated by light green arrows) of the 2D layers in this vdW heterostructure. These features are unique to vdW materials systems, stemming from the weak out-of-plane bonding and tight in-plane bonding that prevents crystallographic defects from propagating through multiple basal planes. Wrinkles similar to those seen in past multilayer EG growth on Si-face SiC(0001) were found in AFM scans of the EG substrates before hBN deposition.^63–66 These wrinkles can be seen by AFM after deposition in Figs. 3(a)–3(d) as well. The curvature associated with these wrinkles, and the curvature associated with the corners of the EG/SiC macrostep features, may have implications for hBN nucleation and epitaxial alignment. This possibility is explored further in Sec. IV.

Cross-sectional TEM only provides small sample sizes of localized thickness rather than the global average. Therefore, growth rates are reported using the “average thickness” from XPS substrate attenuation measurements. The thickness d of an overlayer A on a substrate B can be determined from the attenuation of core level peaks from elements in the substrate. This thickness is given by the following equation:⁵⁶ 

where λ is the EAL of electrons travelling through the overlayer material, θ is the emission angle from surface normal, I_B is the intensity of the attenuated core level substrate peak intensity, and $IB∞$ is the unattenuated substrate core level peak intensity. In this case, the appropriate EAL was determined using the NIST EAL database.⁵⁷ The thickness estimates using the average XPS substrate attenuation of the C 1s peaks show the high growth rate film has 5.9 ± 1.2 ML (2.0 ± 0.4 nm) hBN, while the low growth rate has 2.3 ± 0.4 ML (0.78 ± 0.16 nm) hBN. In addition to XPS, TEM and AFM of exfoliated layers were used for accurate local thickness measurements. AFM of the high growth rate hBN film transferred via tape exfoliation indicates a thickness of 5.0 ± 0.5 nm. However, TEM analysis shows roughly 3–15 ML (1–5 nm) thick hBN films above 4–5 ML EG (Fig. 7), with the thicker films more often present on the macrostep edges than the terrace faces.

While a previous study of hBN on EG using borazine as a precursor has reported intercalative monolayer growth of the hBN layer underneath graphene,²⁶ in the present study no such intercalation was detected. The cross-sectional EDS profiles in Fig. 4 clearly show hBN growing on top of the EG layer with the reported PE-CBE growth method. This difference is likely due to suppression of precursor intercalation by a thicker EG layer than the monolayer system reported by Mende et al.²⁶ Regardless, our results now confirm that a similar metastable rotational alignment to that found in Mende et al.²⁶ appears possible in direct growth of hBN on EG, enabling vertically grown hBN/graphene heterostructures of arbitrary hBN thickness with no concern over suppression of intercalation for substitution to occur.

It is important to note that this study produced hBN instead of rhombohedral BN (rBN) despite previous work finding the rBN polytype to be more stable, both experimentally and theoretically, in metal-organic CVD (MOCVD) growths on 6H-SiC(0001) substrates.^17,18,67,68 One likely reason why hBN was formed instead of rBN is the different starting surface. In our study, smooth multilayer epitaxial graphene, without any substantial Moiré lattice observed in AFM before deposition, was utilized. This differs from rBN growths by Chubarov et al. which used bare 6H-SiC(0001) substrates without epitaxial graphene.¹⁸ In addition to higher rBN stability on SiC, Sutter et al. found hBN grew on Ru(0001), while rBN grew on monolayer graphene-coated Ru(0001).⁶⁹ They suggested that the graphene changed the stability of the hBN stacking configuration.⁶⁹ The corrugated monolayer graphene Moiré lattice on Ru(0001) may be responsible for stabilizing rBN in their work, while the flat multilayer epitaxial graphene may stabilize hBN in this reported work. Differences in growth conditions between CBE, MOCVD, and sputtering may also influence the relative stabilities of hBN and rBN.

It is apparent from the AFM images in Figs. 3(c) and 3(d) that a decrease in the growth rate decreases the overall density of nucleation and increases the probability of nucleation at macrostep edges. The distinct change in nucleation density is consistent with the decreasing growth rate/lower precursor flux creating a lower density of surface adatoms and therefore longer effective mean free path of adatoms on the surface. This longer mean free path means that the adatoms are more likely to reach favorable nucleation sites before interacting with other adatoms to form critical nuclei. Growth at the substrate macrostep edges/facets is likely more energetically favorable than on the terraces, as evidenced by the preferential macrostep nucleation in the AFM of Fig. 3(c). While step edges in traditional epitaxial growth are favorable nucleation sites due to the higher number of dangling bonds, the macrostep edges in this system are blanketed by continuous EG, nominally free of dangling bonds. This is confirmed in several locations by cross-sectional TEM in Figs. 4–6, where the curvature of the vdW-bonded material can be seen, typically without interruption or evidence of pinholes where the SiC(0001) lattice can affect nucleation. Therefore, an explanation other than out-of-plane bonding is required.

We believe that the curvature and associated strain of the EG layer induced by coverage of the macrostep can cause these macrostep locations to be preferable nucleation sites. Curvature in sp²-bound carbon structures is commonly suggested to result in higher out-of-plane electron densities and higher chemical reactivity as the flat sp²-bound carbon is distorted to a more tetragonal, sp³-like configuration. This “pyramidization” is found to increase reactivity of fullerenes^70,71 and of single-walled carbon nanotubes, with higher curvature nanowires exhibiting higher reactivities.^72,73 Greater adsorption of aromatic molecules on both convex⁷⁴ and concave^72,73,75 surfaces is also found due to curvature considerations. While the radii of curvature of the macrosteps in the EG system are typically much larger (∼2 nm) than those of carbon nanotubes (∼0.2–0.6 nm), this effect may still contribute enough to cause these macrostep sites, especially the top corner of the macrostep, to be more favorable. In addition, the associated strain from the bend may allow for improved local lattice matching, promoting adhesion/interaction of the borazine molecule with the macrostep corners.⁷⁴ The direction of curvature can also influence rotational alignment, as it has been found that a planar organic molecule tends to favor a 30° rotational alignment to the top of a graphene ripple, while it prefers a 0° rotational alignment in the ripple valley.⁷⁵ No direct evidence of a preference for either the top or bottom macrostep corners has been detected in this study, likely due to the relative difficulty in finding exact nucleation sites in TEM and AFM, but the combination of these factors suggests the top macrostep corner is the most favorable nucleation site.

It may be possible that the epitaxial orientation of the hBN is dictated by the underlying SiC lattice by a process called “remote epitaxy.”^76,77 In papers by Kim et al.⁷⁶ and Kong et al.⁷⁷ they report that the effects that allow for remote epitaxy do not persist through multiple graphene layers for compounds without largely ionic bonding. The ionicity of SiC and BN are close to GaAs and GaN, which did not show remote epitaxy for >2 ML graphene. Although the in-plane [10$1¯$0] rBN//[10$1¯$0] SiC relation (equivalent to the 30° metastable hBN/EG alignment here) is found in MOCVD growth by Chubarov et al.,^17,18 the fact that we use 4–5 ML EG substrates makes it very unlikely that remote epitaxy is playing a significant role in this case.

While nucleation appears to favor curved graphene surfaces, there is little evidence of hBN nucleating off of EG wrinkles in the middle of surface terraces. These wrinkles are believed to form to relieve strain, both from the lattice mismatch between the EG and SiC, and the strain built up upon cooling from the EG growth temperature (∼1600 °C), as there is a large mismatch in the coefficient of thermal expansion (CTE) between SiC and EG.^65,78,79 The difference between the in-plane CTE of EG (Refs. 80 and 81) and hBN (Ref. 80) is not large (−8.0 ± 0.7 × 10⁻⁶ and ∼−2.8 × 10⁻⁶ K⁻¹ at room temperature, respectively) relative to SiC (Ref. 82) (3.3 × 10⁻⁶ K⁻¹), so we hypothesize that the strain-induced wrinkles (and likely the associated delamination as well) form upon cooling at the EG/SiC interface rather than the hBN/EG interface. In the cross-sectional TEM images in Fig. 6, a wrinkle can be seen at the top of the macrostep, as indicated by a dark blue arrow. These images clearly show the wrinkle occurring at the EG/SiC interface, providing evidence that supports our hypothesis, but it is unknown if other wrinkles exhibit the same behavior. At the growth temperatures utilized in this work (approaching the 1600 °C of EG growth), the strain between the EG and SiC is reduced, and, therefore, there should be fewer wrinkles/buckles to act as preferential nucleation sites. No nucleation of hBN off EG wrinkles is seen in the AFM images in this study, lending credence to this hypothesis. Other reports of hBN growth on EG have seen some nucleation off of EG wrinkles at growth temperatures around 850 °C, which is likely cold enough where the features are still present.²⁸ 

The presented results offer evidence of two PE-CBE growth modes of hBN on EG. For the faster growth rate, a higher density of hBN nuclei occur with more hBN nuclei appearing in the middle of EG terraces. With a slower growth rate, hBN nuclei are preferentially located on the ∼20 nm high substrate macrostep edges, produced by step-bunching of SiC during EG growth.^83–87 The nuclei formed at the step edges have more symmetrical triangular features seen in AFM in Fig. 3(g), with sharply defined, parallel edges such that they form triangular multilayer pyramids. In contrast, the nuclei formed on the terraces during faster growth predominantly show irregular nuclei edges and the multilayers are less uniform in appearance, as seen in Fig. 3(e).

This increase in nuclei edge and shape uniformity with the lower growth rate can be qualitatively determined by recording the distribution of orientations of the linear nuclei edges in AFM images. Histograms of the nuclei step edge angles from a 25 μm² area for the fast growth and from a 100 μm² area for the slow growth are shown in Figs. 7(a) and 7(b), respectively. Angles of edges exhibiting contrast consistent with ∼1–3 hBN layers were measured manually. The lower growth rate sample has a sharper distribution of nuclei edge angles, indicating a greater degree of nuclei edge uniformity than the higher growth rate sample. The peaks around 60° and 120° indicate a preference for equilateral triangular domains with one edge aligned to the SiC(0001) macrostep edge (along 0°). No peak is recorded at 0° since hBN edges in that orientation are obscured by the macrostep. hBN nuclei have been found with a variety of shapes, orientations, and curvatures in CVD growths depending on the local chemical potential or growth kinetics.^60,87,88 This variance lends credence to the possibility that the thermodynamically stable edge in the high growth rate chemical environment may be different relative to the low growth rate environment, producing more jagged, disordered edges.⁸⁹ Nonuniform hBN edges can also be explained by changes in local stoichiometry due to differing rate of supply and diffusivity of available adatoms on the surface.^87,89

The crystallographic termination of the different hBN nuclei edges cannot be identified by AFM alone, and therefore additional measurements are required to determine epitaxial alignment. For that reason, cross-sectional HRTEM was correlated with topographic information from AFM to determine the hBN/substrate rotational alignment in both growth conditions. The TEM in Figs. 5(d) and 5(e) confirms the triangular hBN domains that nucleate from substrate macrostep edges are comprized of hBN with a 30° metastable rotational alignment to the EG lattice, while Figs. 5(a) and 5(b) show the mid-terrace films are directly aligned to the underlying EG. It follows that the macrostep-edge nucleation site has some attribute that makes the 30° metastable rotational alignment preferable over the direct alignment, but the precise nature of the feature is yet to be determined.

While the AFM and TEM utilized cannot resolve the edge termination of the hBN nuclei, the nuclei shapes in AFM can be correlated to the hBN/substrate alignment to indirectly examine the likely edge termination. This correlation finds the arm-chair edge shape is present for the macrostep-nucleated multilayer triangular hBN nuclei grown by the low growth rate PE-CBE. Figure 8 shows how triangles in the orientation present in Fig. 3(e) must have the arm-chair termination to show lattice fringes corresponding to the ${112¯0}hBN$ interplanar spacing when viewed in the zone axis utilized in the HRTEM in Fig. 5(d).

The triangular nuclei shape found in the slow growth mode is different from the hexagonal domains found in MBE-grown hBN on both EG (Ref. 28) and HOPG substrates^23,24,90 but similar to the shape of hBN domains grown on graphene/Co substrates^90,91 and domains grown substitutionally on EG.²⁶ The formation of the arm-chair edges present in this study is not typical for hBN depositions on transition metal substrates where zig-zag edges are found to be generally preferable.^88,92 N-terminated zig-zag edges were found to be most stable on metal surfaces^87,89 but the arm-chair edge is predicted to be stable in vacuum and in vdW-bonded systems.^93,94 The arm-chair edge termination may be stabilized by the higher nitrogen plasma to borazine ratio of the low growth rate deposition, which can affect the local chemical potential during growth. The relatively high nitrogen content (up to B/N = 0.81 ± 0.04) and secondary N–N feature in the N 1s core level peaks determined by XPS provide evidence that these films were subjected to different local chemical environments than other reported growths.

A high-temperature, plasma-assisted CBE technique was shown to produce hBN multilayers at temperatures of 1450 °C in a UHV-based system on CVD-grown epitaxial multilayer graphene on SiC(0001) substrates. The inclusion of a RF nitrogen flux resulted in improved film microstructure and hBN nuclei with more well-defined edges. No additional phase formation, intercalation, or intermixing with the EG layer was observed by XPS and TEM. By lowering the borazine precursor flux to an equivalent growth rate of 3.1 ± 0.6 nm/h, a 30° metastable hBN/graphene epitaxial relation could be selected over a fully commensurate relation that was present when a higher growth rate corresponding to 7.8 ± 1.6 nm/h was utilized. In addition, hBN nucleation was shown to predominantly occur at macrostep edges of offcut EG substrates during growths with lower growth rates, while higher growth rates resulted in more nucleation in the middle of the EG terraces. The hBN that nucleated off of the macrostep edges appeared to be twisted 30° relative to the EG lattice, while the mid-terrace nuclei exhibited a direct epitaxial relation (0° twist) to the EG lattice. These mid-terrace nuclei formed by higher growth rates showed relatively disordered edges, but the nuclei grown with lower growth rates formed uniform triangular pyramids with sharp, parallel edges. These edges were confirmed to be arm-chair terminated, a termination not typically seen in depositions on transition metal substrates, by correlating the domain shape in AFM with atomic-resolution cross-sectional HRTEM. This novel plasma-enhanced growth technique was capable of growing multilayer hBN over single-crystal EG substrates at appreciable growth rates, while still allowing for in situ and UHV-based in vacuo characterization. The twist-controlled epitaxy of hBN on EG highlighted in this work shows how different levels of commensurability can be achieved solely by tuning growth parameters during vdW epitaxy, thereby reducing the reliance on manual rotation during film transfer and increasing the viability of scalable, single-crystal heterostructure growth.

This work was supported in part by Office of Naval Research (ONR) (No. N00014-16-1-2865). The authors would like to acknowledge the use of the VESTA software package for creating the schematic diagrams used in Figs. 5 and 8.⁹⁵ This work made use of MRL Central Facilities supported by the MRSEC Program of the National Science Foundation (NSF) under Award No. DMR-1121053. Research at the U.S. Naval Research Laboratory is supported by the ONR. D.J.P. was supported by the Department of Defense (DoD) through the National Defense Science and Engineering Graduate Fellowship (NDSEG) Program. S.G.R. would like to acknowledge the support of the American Society for Engineering Education and U.S. Naval Research Laboratory postdoctoral fellowship. S.G.R. was funded by the Laboratory University Collaboration Initiative (LUCI) Program sponsored by the Basic Research Office, Office of Undersecretary of Defense for Research & Engineering. Supplemental epitaxial graphene samples for this publication were provided by the Pennsylvania State University Two-Dimensional Crystal Consortium—Materials Innovation Platform (2DCC-MIP) which is supported by NSF Cooperative Agreement No. DMR-1539916.