Nature | Vol 579 | 12 March 2020 | 221presents perfect lattice coherence at the patching boundary (Extended
Data Fig. 5g–j), indicating that the formation of moiré patterns does not
affect the overall hBN orientation. We believe that the hBN completes
the single-crystal growth at high temperatures, and that the strain asso-
ciated with sample cooling after growth results in the formation of local
moiré pattern. Other characterizations, including X-ray photoelectron
spectroscopy (XPS) and Raman spectroscopy, prove the B–N chemi-
cal bonding structures (Fig. 2e, f). Transmission electron microscope
(TEM) and atomic force microscope (AFM) images consistently show
that the as-grown hBN is indeed a monolayer (Fig. 2g, h).
We recognize that, once the Cu (111) thin films are prepared and
formed untwinned at 1,050 °C as described above, the mono-orientated
growth of hBN flakes can be realized at various growth temperatures
ranging from 995 °C to 1,070 °C (Extended Data Fig. 6). However, a
lower growth temperature (995 °C to 1,010 °C) usually leads to lower-
quality hBN flakes, which are easily oxidized in a subsequent oxidation
test at 150 °C in air. Therefore, we used a higher growth temperature
(typically 1,050 °C) to ensure high-quality single-crystal hBN growth.
To explain the preferred orientation of hBN on Cu (111), we consider
a small and rigid B 6 N 7 molecule (that is, an energetically favourable
N-terminated three-ring structure^12 ) as the probe seed. We first examine
the effect of plane-to-plane epitaxy, using density functional theory
(DFT) to calculate the binding energies of six typical atomic stacking
configurations (Fig. 3a), where NIBIII, NIIIBII and NIIBI are defined as the 0°
orientation, and NIBII, NIIBIII and NIIIBI are the 60° (inverted) orientation.
The notation NiBj represents the stacking of N atoms in registry with
(above) the Cu atoms in the ith layer, while B atoms register with the
Cu atoms in the jth layer. The calculations show that the stacking with
N atoms on top of the first-layer Cu atoms (NIBIII (0°) and NIBII (60°))
exhibits the lowest energy, while B atoms on top of the first-layer Cu
atoms (NIIBI (0°) and NIIIBI (60°)) are energetically unfavourable. The
preferential registrations reflect the electron affinity of the B and N
atoms, which leads to attractive (or repulsive) Coulomb interactions
between N (or B) atoms and the first-layer Cu atoms, and hence affects
the structural stability. We find that the lowest-energy structures for
0° (NIBIII) and 60° (NIBII) orientations exhibit an energy difference of
only 0.05 eV or so, much smaller than the thermal energy kBT at the
growth temperature (roughly 0.1 eV), indicating that the plane-to-plane
registry is insufficient to achieve mono-oriented growth, in agreement
with simulations^13.
In fact the Cu (111) surface is not perfectly flat and many terraced
meandering steps exist, as revealed in STM images (Fig. 2d and Extended
Data Fig. 7a–d). Recent theory showed that one must consider the role
of these step edges in guiding hBN growth^14. Other work^5 suggests that
docking at the vicinal step edges on the Cu (110) surface governs the
single-crystal hBN growth, based on the assumption that the Cu terrace
steps trend only up or down all the way across the whole vicinal surface
of the Cu foil. However, our STM results clearly reveal that the terrace
steps of the Cu (111) surface trend both up and down across the wafer,
and that the edge-docking can seemingly yield hBN in both directions,
unless the binding energies differ enough to favour one direction over
another. To capture this in our model, we add an extra layer of Cu atoms
(red in Fig. 3 ) on top of the first layer, forming two opposite step edges
(A- and B-step edges in Fig. 3a and Extended Data Fig. 7f ). This restricts7008009001,0001,1001,2001,3001,400186188190192194196 4006008001,0001,2001,4001,6001,8002,0002,2002,400394396398400402404B1s N1shBN/Cu hBN/Cu hBN/Cu10 nmefdgha b0.7nm0.5μmc0.5nm20 μm0.25 nm40 nm 2nm 1nm1618202224261,200 1,300 1,400 1,5001,371 cm–1FWHM: 14.5cm-120 μmBindingenergy(eV) Ramanshift(cm–1)Intensity(kcounts)
IntensityFig. 2 | Growth and atomic structures of single-crystal hBN on Cu (111) f ilms.
a, Optical microscope image of hBN grown on different Cu (111) grains. Black
dashed lines indicate twin grain boundaries. Oppositely oriented f lakes are
marked by red and blue dashed triangles. b, Mono-oriented hBN f lakes on
single-crystal Cu (111) films. c, μ-LEED patterns of hBN monolayers at nine
different areas randomly selected from the 1.5 × 1.5 cm^2 sample surface. All
μ-LEED patterns show that the hBN monolayers have the same orientation as
the Cu (111) surfaces. d, Left to right, large-scale STM image (Vtip = −1 .008 V;
Itip = 3.90 n A; T = 300 K) and atomic-scale STM images (Vtip = −0.003 V;
Itip = 5 4. 508 n A; Vtip = −0.003 V, Itip = 46.50 nA; T = 300 K) of hBN/Cu (111) with
measured lattice constant 2.50 ± 0.1 Å. We measured the height of each step
from the left-hand image to be roughly 2 Å. e, XPS spectra measured from an
as-grown monolayer hBN film on Cu (111)/sapphire. The binding energies of the
B 1s and N 1s orbitals at 190.4 eV and 398.0 eV confirm the formation of hBN.
f, Raman spectrum of a transferred hBN film, where the E2g mode at 1,371 cm−1
with a full-width at half-maximum (FWHM) of 14.5 cm−1 confirms that the hBN is
a monolayer. g, Cross-sectional TEM image of a monolayer hBN transferred
onto SiO 2 /Si, where the thickness of hBN is around 0.5 nm. h, AFM image of a
single-crystal hBN film transferred onto a SiO 2 /Si substrate.