a ×100 objective lens (with a numerical aperture of 0.9). The signal
was collected using the same objective lens, analysed with a 0.75-m
monochromator and detected with a liquid-nitrogen-cooled charge-
coupled-device (CCD) camera. The E2g band of hBN is located at
1,371 cm−1 and its FWHM value is 14.5 cm−1, confirming that the trans-
ferred hBN film is monolayer thick with high crystalline quality.X-ray diffraction measurements
X-ray diffraction (XRD; Bruker D8-Discover) θ–2θ and 360° azimuthal
(φ) scans were conducted using a Cu Kα radiation source (λ = 1.54 Å). An
XRD azimuthal φ scan of twinned Cu (111) films was operated at χ = 70.5°,
ω = 16.2° and 2θ = 43.3°; an XRD azimuthal φ scan of untwinned Cu (111)
films was operated at χ = 70.5°, ω = 21.5° and 2θ = 43.3°.First-principles calculations
First-principles calculations were carried out using DFT as implemented
in the Vienna ab initio simulation package (VASP)^19 within MedeA soft-
ware^20. We used the projector augmented wave method, the exchange–
correlation potential described by the Perdew–Burke–Ernzerhof (PBE)
generalized gradient approximation (GGA)^21 , and van der Waals cor-
rection vdW-DF (optB86b) functionals^22 in order to calculate the dis-
tance and binding energy between BN molecules and copper substrates.
For the plane-to-plane and edge-to-step epitaxy model, a rigid B 6 N 7
molecule is physically absorbed onto a 6 × 6 and a 6 ×7 3 Cu (111) sur-
face with a thickness of four copper layers, using a 2 × 2 × 1 and a 2 × 1 × 1
k-grid, respectively. To eliminate spurious interactions resulting from
the slab model of the supercell, the vacuum thickness is larger than
17 Å, the in-plane distance of a B 6 N 7 molecule away from another side
of the step edge is at least 10 Å, and the energy cutoff of the plane waves
is 400 eV. The lattice constant of Cu (111) used in simulation is a = 2.6 Å
at a reaction temperature of 1,000 °C, with hBN assuming the same
lattice constant for simplification. The interlayer distance of Cu (111)
is 2.05 Å. The height of the BN molecule from the Cu surface is optimized
until the change in the energy and the force reach 10−4 eV and 10−2 eV Å−1,
respectively. For plane-to-plane epitaxy, the optimized vertical dis-
tances from the top layer of the Cu surface, d, for six configurations
are d = 1.98 Å for NIBII, d = 1.77 Å for NIIBIII, d = 2.03 Å for NIIIBI, d = 1.98 Å
for NIBIII, d = 1.77 Å for NIIIBII, and d = 2.03 Å for NIIBI. Binding energies
are defined by −Eb = EB6N7–Cu − EB6N7 − ECu, where EB6N7–Cu is the total energy
of the hBN flake/Cu (111) system, and EB6N7 and ECu are the energies of
the B 6 N 7 flake and Cu substrate (with or without a step edge); the cal-
culated binding energies of six total stacking structures in the presence
of a step are plotted by varying the in-plane distance, Di, to the step
edge. The six lowest energetic configurations in the presence of a step
are located at Di=2a/3 for NIBII (d = 1.99 Å), 4 a/3 for NIIBIII (d = 1.77 Å),
1.5a/3 for NIIIBI (d = 2.08 Å), 2.5a/3 for NIBIII (d = 1.98 Å), 1.5a/3 for
NIIIBII (d = 1.84 Å), and 2 a/3 for NIIBI (d = 2.06 Å) (Extended Data Fig. 8).
Note that when Di is less than 3/a 3 (too close to the step-edge), the
energy dramatically increases.
We study here the energy difference between NIBIII (0°) and NIBII (60°),
the two lowest-energy structures docking to A-step and B-step edges,
with different lengths of docking contact. We construct a model of a
BN stripe composed of aromatic rings docking to the step edge. We
find that the energy difference between the two configurations NIBIII
(0°) and NIBII (60°)—an indicator of selectivity for mono-orientation—
increases rapidly with the docking contact, and approaches a δE of
roughly 0.78 eV, amplifying the Boltzmann selectivity factor eδ/EkBT
(with a kBT of around 0.11 eV at 1,300 K) for a contact length of just five
to six hexagons to more than 10^3 (Extended Data Fig. 9a, b). The large
energy difference means that the step edge plays the role of ‘orientation
filter’, allowing a predominant phase of BN (a mono-orientation) dur-
ing growth. Factually, the competing subcritical nuclei must be larger
and, especially, are probably elongated along the step-edge to allow a
more energetically favourable contact. Obviously such an energy value
roughly scales with the contact length, C, and the selectivity factor
increases very rapidly with size, as exp(C).
The effect of misfit and misalignment of BN to the step edge can
be studied by calculating the binding energy of a B 7 N 7 molecule at a
three-hexagon contact length with a small tilt angle along the step
edge (the aligned structure with a tilt angle of zero corresponds to
NIBIII and NIBII). The lattice constants of Cu (111) and hBN are allowed
to be different as aCu111 = 2.6 Å and ahBN = 2.5 Å, with a 3.8% lattice misfit.
We find that, although the total binding energy is weakened because
of lattice misfit (that is, there is a weaker interaction of plane-to-plane
epitaxy), the energy difference between the 0° and 60° orientations
remains nearly the same (from 0.3 eV to 0.27 eV). The calculated binding
weakens as the tilted angle becomes larger, indicating that the most
stable configuration during the initial nucleation growth occurs when
docking is tight and well aligned to the step edge (Extended Data Fig. 9c,
d). The result suggests that mono-orientated hBN was epitaxially grown
on Cu (111) in a manner that was guided mostly by step edges, and that
the moiré was formed to release the strain between Cu (111) and hBN
(lattice mismatch or surface topography) after a large area of film had
grown. We note that the cooling step after large-area hBN growth will
result in strains that might be released by local straining of hBN and
formation of a moiré pattern. Therefore, we believe that moiré does
not actually affect the growth process, but occurs afterwards.Data availability
All data needed to evaluate our conclusions are found in the main text
and the Extended Data. Further data related to the paper are available
from the corresponding authors on reasonable request.- Hsu, W.-F. et al. Monolayer MoS 2 enabled single-crystalline growth of AlN on Si(100)
using low-temperature helicon sputtering. ACS Appl. Nano Mater. 2 , 1964–1969
(2019). - Jin, L., Fu, Q., Mu, R., Tan, D. & Bao, X. Pb intercalation underneath a graphene layer on
Ru(0001) and its effect on graphene oxidation. Phys. Chem. Chem. Phys. 13 , 16655–16660
(2011). - Kresse, G. & Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and
semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6 , 15–50 (1996). - MedeA (Materials Design Inc, 2016).
- Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple.
Phys. Rev. Lett. 77 , 3865–3868 (1996). - Klimeš, J., Bowler, D. R. & Michaelides, A. Van der Waals density functionals applied to
solids. Phys. Rev. B 83 , 195131 (2011). - Yankowitz, M. et al. Emergence of superlattice Dirac points in graphene on hexagonal
boron nitride. Nat. Phys. 8 , 382–386 (2012). - Joshi, S. et al. Boron nitride on Cu (111): an electronically corrugated monolayer. Nano
Lett. 12 , 5821–5828 (2012).
Acknowledgements Tse-An Chen, C.-P.C., H.-S.P.W. and L.-J.L. acknowledge support from the
Taiwan Semiconductor Manufacturing Company (TSMC). W.-H.C. acknowledges support from
the Ministry of Science and Technology of Taiwan (grants MOST-108-2119-M-009-011-MY3 and
MOST-107-2112-M-009-024-MY3) and from the CEFMS of the National Chiao Tung University,
supported by the Ministry of Education of Taiwan. Y.Z. acknowledges financial support from
the National Natural Science Foundation of China (grant 51861135201). Q.F. thanks the National
Natural Science Foundation of China (grants 21688102 and 21825203) and the Strategic
Priority Research Program of the Chinese Academy of Sciences (grant XDB17020000) for
financial support. B.I.Y. acknowledges support from the US Department of Energy (grant DE-
SC0012547) and a stimulating discussion with T. Ivanov (US Army Research Laboratory). Tse-
An Chen and L.-J.L. acknowledge useful discussions with S. Brems at Imec.Author contributions L.-J.L. and Tse-An Chen conceived the project. Tse-An Chen, C.-C.T. and
C.-K.W. grew the hBN by CVD, performed the transfer of hBN, and carried out EBSD, Raman and
AFM measurements. C.-P.C. performed first-principles calculations, and C.-P.C. and B.I.Y.
carried out theoretical analysis. R.L. and Q.F. performed μ-LEED measurements. Y.Z. and S.P.
performed STM experiments. C.-K.W., Tzu-Ang Chao and W.-C.C. fabricated the metal–
insulator–metal device and the MoS 2 FET. Tse-An Chen, C.-K.W. and Tzu-Ang Chao performed
electrical measurements. L.-J.L., W.-H.C. and H.-S.P.W. supervised the project. All of the authors
discussed the results and wrote the paper.Competing interests The authors declare no competing interests.Additional information
Correspondence and requests for materials should be addressed to B.I.Y., W.-H.C. or L.-J.L.
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