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222 | Nature | Vol 579 | 12 March 2020

Article

the B 6 N 7 seed to the 0° (or 60°) orientation when docking to the A (or
B) steps (Fig. 3a). In Fig. 3a, b the distance between the Cu step edge
and the B 6 N 7 zigzag edge for each configuration has been determined
by energy minimization (Extended Data Fig. 8). The resulting binding
energy for each configuration changes in a subtle yet very important

way with the presence of Cu step edges (Fig. 3b): the two configurations

NIBII (60°) and NIBIII (0°), which were nearly degenerate when consider-

ing only plane-to-plane epitaxy, are now separated by δE values of

approximately 0.23  eV, this value raising in proportion with the

docking length, rapidly amplifying the Boltzmann selectivity factor

–9.5

–9.0

–8.5

–8.0

–7.5

–7.0

–6.5

Binding energy (eV)

Astep

Bstep

NIIBI NIIIBII NIBIII

NIIIBI NIIBIII NIBII

ab

0°

60°

Top-layer Cu

First-layer Cu

Second-layer Cu

Third-layer Cu

NIIIBI NIIBIII NIBII NIBIII NIIIBII NIIBI

60° 0°

Plane only

Edge-to-step

N

B

Bottom Cu

Fig. 3 | DFT calculations of epitaxy at nucleation, with and without
considering step-edge docking. a, Lowest-energy atomic arrangements for
six B 6 N 7 –Cu (111) configurations, considering the edge docking to two typical
step-edge terminations (A and B) of top-layer Cu (111). b, Calculated binding

energies for the six B 6 N 7 –Cu (111) configurations, with and without including

the edge-to-step epitaxy effect. The bottom image is a three-dimensional view

of the NIBII–Cu (111) configuration.

hBN

Two-inch hBN/Cu/sapphire

Two-inch hBN lm

Four-inch SiO 2 /Si

ab c

hBN

2cm

TRT/PMMA/hBN

Fig. 4 | Schematic and photographs illustrating the wafer-scale hBN transfer
processes. a, As-grown two-inch hBN film on a Cu (111)/sapphire wafer. Top,
schematic; bottom, photograph. b, Electrochemical delamination, using an
aqueous solution of NaOH (1 M) as the electrolyte, the Cu layer in the TRT/
PMMA/ hBN/Cu (111)/sapphire stack as the cathode, and a platinum (Pt) foil as

the anode, with an applied DC voltage of 4 V. During this process, the TRT/

PMMA/hBN stacked film is detached from the Cu (111)/sapphire through the

generation of hydrogen bubbles at the hBN/Cu interface. PMMA, poly(methyl

methacrylate); TRT, thermal release tape. c, Two-inch monolayer hBN film

transferred onto a four-inch SiO 2 / S i w a fe r.