Step-directed Epitaxy of Uni-directional Hexagonal Boron Nitride on Vicinal Ge(110)

Chan-cuk Hwang; Chao Zhao; Cheol-Joo Kim; Feng Ding; Jonghwan Kim; Ju-Hyun Jung; Jun-Ho Park; Seong-Jun Yang; Seung-Hwa Baek; Su-Beom Song

REVIEW 3 major objections 6 minor 4 references

Step-directed Epitaxy of Uni-directional Hexagonal Boron Nitride on Vicinal Ge(110)

T0 review · 3 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read This paper reports that tuning hydrogen partial pressure during CVD growth on a stepped Ge(110) surface yields wafer-scale, monolayer, single-crystalline hexagonal boron nitride films that can be mechanically exfoliated and stacked in…

desk verdict The unidirectional hBN-on-Ge growth and its hydrogen-pressure control are solid, but the wafer-scale single-crystal claim outruns the evidence: only 1 mm² LEED and a 1 µm SHG map support it. read the letter →

arxiv 2507.18985 v1 pith:45I57HIH submitted 2025-07-25 cond-mat.mtrl-sci

Ju-Hyun Jung , Chao Zhao , Seong-Jun Yang , Jun-Ho Park , Woo-Ju Lee , Su-Beom Song , Jonghwan Kim , Chan-Cuk Hwang

show 3 more authors

Seung-Hwa Baek Feng Ding Cheol-Joo Kim

This is my paper · ORCID

classification cond-mat.mtrl-sci

keywords hexagonalboronnitrideepitaxyhydrogenpassivationchemicalvapordepositionvanderWaalsassemblysinglecrystalvicinalGe(110)stackingorder

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper reports a way to grow hexagonal boron nitride (hBN) as a continuous monolayer film that is single-crystalline across a 2-inch wafer, on a germanium substrate cut at a small angle so that atomic steps guide every crystal domain to point the same way. The key lever is hydrogen partial pressure during growth: too little or too much hydrogen leaves domains pointing in two opposite directions, but at an intermediate pressure almost all domains align. Because the film sits on hydrogen-passivated germanium rather than on a metal, it can be mechanically exfoliated and stacked layer by layer with pristine interfaces. The authors demonstrate controlled rhombohedral and hexagonal bilayer stacking, and use the films as dielectrics that reduce trap states in graphene and MoS2 devices. The claim matters because wafer-scale single-crystal hBN with clean assembly would give electronics a scalable insulating buffer layer.

What carries the argument

The central mechanism is hydrogen-passivation-controlled Ge-N edge bonding at atomic steps. On the vicinal Ge(110) surface, the step edge provides Ge atoms with dangling bonds that can bond to N-terminated zigzag edges of hBN. The paper's DFT calculations show that when hydrogen pressure is high, van der Waals interaction gives nearly equal stability to two orientations (θ=0° and 60°); when hydrogen is scarce, the terrace and edges behave differently. At an intermediate chemical potential, the equilibrium favors direct Ge-N bonds at the step and H-passivated terraces, creating a deep energy minimum at θ=0° and a maximum at 60°, so every domain stitches into one orientation. This equilibrium binding-energy difference, rather than growth kinetics, is what the paper proposes as the orientation-selection mechanism.

What would settle it

Grow hBN on the [001]-miscut Ge(110) substrate while sweeping PH2 around the claimed optimum and use high-resolution electron microscopy or X-ray photoelectron spectroscopy to look for direct Ge-N bonds specifically at step edges; if no Ge-N bonding appears at the pressure where alignment reaches nearly 100%, the mechanism collapses. Alternatively, recompute the θ=0° versus θ=60° formation-energy difference with a converged k-point mesh and thicker Ge slabs: if θ=0° is not the global minimum at the stated hydrogen chemical potential, the thermodynamic-selection claim is not supported.

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Extended reading notes

Core claim

The central discovery is that step-directed epitaxy of hBN on vicinal Ge(110) can be made uni-directional by tuning the hydrogen chemical potential, and that the resulting monolayer film is single-crystalline, wafer-scale, and mechanically exfoliable. On a Ge(110) surface miscut toward [001], the substrate symmetry is reduced so that atomic steps run along one direction; triangular hBN grains nucleate with an N-terminated zigzag edge along the step. At the optimum H2 partial pressure, DFT-based free-energy calculations indicate that hydrogen passivates the Ge terraces but leaves the step-edge Ge atoms able to form direct Ge-N bonds with the hBN edge, making one crystallographic orientation the global energy minimum. Experimental LEED and SHG show 3-fold, uni-directional symmetry at this pressure, and the merged film has no measurable grain boundaries. The same films can be exfoliated and assembled into bilayers with chosen stacking order, verified by TEM diffraction and ARPES band splitting.

Load-bearing premise

The load-bearing premise is that, at the right hydrogen pressure, the edges of the germanium steps shed their hydrogen and bond directly to nitrogen atoms along the hBN edges while the flat terraces stay hydrogen-covered, and that this energy difference—rather than growth speed—is what makes every crystal point the same way.

Editorial extensions

If this is right

If correct, wafer-scale single-crystal monolayer hBN becomes available on a semiconductor substrate rather than only on metals.
Because the film sits on hydrogen-passivated germanium, it can be mechanically exfoliated and stacked layer by layer with pristine interfaces, enabling controlled stacking orders such as rhombohedral and hexagonal.
Controlled rhombohedral stacking would make large-area ferroelectric and nonlinear-optical hBN stacks practical.
The hBN dielectric suppresses interfacial trap density by roughly an order of magnitude in graphene FETs and improves MoS2 subthreshold swing, supporting use as a scalable insulator.
The non-monotonic dependence of alignment on PH2 gives a growth knob for switching between bi-directional and uni-directional crystal populations.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The DFT energy differences that select θ=0° over θ=60° are below 0.01 eV with a 1x1x1 k-point mesh; a converged calculation could shift the preferred orientation, so the quantitative predictive range is untested.
The same chemistry—hydrogen-passivated terraces plus chemically active step edges—might extend to other nitride monolayers on hydrogen-passivating semiconductor surfaces.
Controlling step bunching during growth, which the paper associates with wrinkle formation, could yield even flatter films.
The wafer-scale single-crystal claim is supported by SHG uniformity and LEED over about 1 mm2; full-wafer diffraction mapping would be a natural confirmation.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Worth a read. The paper's real result is new: unidirectionally aligned monolayer hBN grown on vicinal Ge(110), with orientation selectable by hydrogen partial pressure. The non-monotonic χalign(PH2) curve and the LEED switching between 6-fold and 3-fold are convincing, and the mechanical exfoliation plus controlled stacking of the assembled bilayers is a useful demonstration. For the 2D growth community, this is a meaningful step beyond prior Ge work, which only achieved aligned (not unidirectional) growth. The DFT story—H passivation on the terrace, de-passivation at the step edge allowing Ge–N bonds—is a plausible mechanism and consistent with the experiment, even if the numbers are rough.

The weak point is exactly where the stress-test note lands. The abstract and Table S1 claim wafer-scale single-crystalline hBN over a 2-inch wafer, but the orientation-sensitive data are local: LEED over ~1 mm² (stated in Methods) and one SHG map at 1 µm scale. The SEM and transmission spectra show morphology and thickness, not lattice orientation. The 97% alignment reported in Figure S4 for partial coverage means ~3% anti-parallel grains, and nothing in the current data rules out that such domains persist outside the probed regions of the full film. That is a load-bearing gap, because the paper's headline advantage over layer-by-layer assembly of polycrystalline film is precisely single crystallinity at scale.

Also worth flagging, but minor: the DFT uses a 1×1×1 k-point mesh and three-layer Ge slab, and the key energy differences on the flat terrace are below 0.01 eV—those specific numbers should not be leaned on. The formation-energy comparison for the step edge is more robust qualitatively, though Eq. 2 imports an edge energy from the authors' earlier work. Neither of these is fatal; they are secondary to the experimental demonstration.

My verdict: the core claim—unidirectional hBN on Ge with H2-controlled alignment—holds up as a new result. The wafer-scale single-crystal statement needs more evidence before it becomes part of the permanent record. A serious referee should see it; I would send it to peer review, but with a request for wafer-scale orientation mapping (SHG or other orientation-sensitive probe over cm scale), a clear statement of alignment statistics on full films, and a soft-pedaling of the DFT quantitative precision. I'd cite it for the growth mechanism, not yet for wafer-scale single crystallinity.

Referee Report

3 major / 6 minor

Summary. The paper reports CVD growth of monolayer hexagonal boron nitride (hBN) on vicinal Ge(110) substrates with a miscut toward [001], where Ge atomic steps guide unidirectional alignment of hBN domains. The authors show that the fraction of aligned triangular grains varies non-monotonically with hydrogen partial pressure, reaching near-unity at an optimized PH2, as characterized by SEM, AFM, and LEED. DFT calculations are used to propose that the optimum alignment arises from a balance between hydrogen passivation of the Ge terrace and direct Ge–N bonding at step edges. The grown films are mechanically exfoliated and assembled into bilayers with controlled rhombohedral or hexagonal stacking, and are demonstrated as dielectric interlayers in graphene and MoS2 field-effect transistors with reduced interfacial trap densities.

Significance. If the central claim holds, the work would provide a practical route to wafer-scale single-crystalline hBN that can be cleanly exfoliated, combining the advantages of metal-grown single-crystal hBN (large area, uniform thickness) with the clean-transfer capability of Ge-based growth. The demonstration of controlled stacking order through layer-by-layer assembly of such films is also valuable for applications in ferroelectric and nonlinear-optical devices. Important strengths of the manuscript include the systematic dependence of alignment on hydrogen partial pressure, the detailed local structural characterization (LEED, AFM, SEM, TEM), and the explicit DFT-based mechanistic model. However, as detailed in the major comments, the headline 'wafer-scale single-crystalline' claim is not directly evidenced, and the DFT energy differences underlying the proposed mechanism require convergence verification.

major comments (3)

[Section 2.3, Figure 3, and Methods] The claim that the film is 'single-crystalline' over a 2-inch wafer (Abstract; Table S1) is extrapolated from measurements that are local in extent. LEED patterns are obtained over an area of ~1 mm2 (Methods, 'All LEED patterns were obtained over an area of ~1 mm2'), the SHG polarization plot and map in Fig. 3d,e are from a single ~1 µm region, and the SEM images in Fig. 3b and Fig. S9 are local fields. No orientation-sensitive measurement spans the wafer: there is no SHG mapping or LEED at multiple positions across the 2-inch wafer, no XRD pole figure, and no dark-field TEM. The 97% alignment statistic in Fig. S4 also applies only to partial-coverage samples on one substrate, so the data do not exclude anti-parallel or misoriented domains elsewhere in the full film. The transition from 'unidirectionally aligned grains in the probed regions' to 'wafer-scale single-crystalline film' is therefore an extrapolation and should be either directly demonstrated or explicitly qualified.
[Section 2.4, Computational Details (Eqs. 1–4, Fig. 4, Fig. S10)] The DFT conclusion that θ = 0° is a deep global minimum at intermediate PH2 rests on energy differences of order 0.01 eV (Fig. 4c,f) and on free-energy differences between H-H and Ge-N edge models (Fig. S10) of similar magnitude. All calculations use a 1×1×1 k-point mesh on a three-layer Ge slab (Computational Details), and no convergence tests with respect to k-point sampling, slab thickness, or the DFT-D3 dispersion correction are reported. Because the energy differences are comparable to the numerical uncertainty of such calculations, the predicted orientation preference and the relative stability of Ge-N versus H-passivated edges need to be verified with denser k-point meshes (e.g., 2×2×1 or 3×3×1) and, ideally, a second dispersion-correction scheme. Without these tests, the proposed hydrogen-mediated selection mechanism is not quantitatively supported.
[Section 2.3, Figure 3b, and Methods] The seamless stitching of aligned domains into a grain-boundary-free film is inferred from SEM morphology (uniform contrast and aligned triangular voids) rather than directly demonstrated. The Methods state that dark-field TEM imaging was performed, but no dark-field images are presented. Dark-field TEM over a statistically meaningful area, or an equivalent orientation-resolved technique, is needed to exclude the presence of small-angle grain boundaries or minority anti-parallel domains within the continuous film. This is load-bearing for the 'single-crystalline' claim and for the comparison in Table S1.

minor comments (6)

[Throughout] The notation '[11!0]', '[11!1]', and '[11!2!]' appears garbled; the overline notation for negative Miller indices should be typeset correctly to avoid confusion with exclamation marks.
[Section 2.1] The group symmetry symbols 'C2V' and 'Cs or CV' should be written in standard form as C2v and Cs (or C1), with proper subscripts and italics.
[Computational Details] Equations (1) and (2) are typeset illegibly due to symbol encoding issues; please ensure all variables (E_B, E_f, E_total, E_Ge, E_hBN, A, L, ε_edge) render correctly and unambiguously.
[Abstract and Conclusion] The abstract states 'wafer-scale single crystalline hBN films' while the conclusion says 'large-scale hBN monolayer films with uni-directional crystallography'; the wording should be aligned with the actual evidence presented and with the revised claims made in response to Major Comment 1.
[Section 5 (Device results)] The MoS2 FET mobility and subthreshold swing values (12 to 15.8 cm2/V·s and 2.3 to 1.2 V/dec) and the graphene mobility values would benefit from reporting the number of devices measured and an uncertainty estimate, since single numbers are presented without error bars.
[Figure S11 caption] The XRD data in Fig. S11b are obtained on an assembled 10-layer hBN stack, while the main text and Figs. 5d,e describe bilayer assemblies; the relationship between these two sample types should be clarified so the reader understands the scope of the stacking-order demonstration.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular reduction found: the DFT orientation-selection argument is computed from explicit hBN/Ge models, and the cited edge-energy and symmetry results are independent inputs rather than fitted outputs.

full rationale

I walked the claimed derivation chain: (i) the experimental uni-directional alignment is established by SEM grain statistics, LEED spot asymmetry, and SHG six-fold response; (ii) the theoretical explanation in Section 2.4 computes hBN/Ge binding and interface formation energies from explicit supercell models as a function of misorientation angle θ and hydrogen chemical potential, rather than fitting to the measured χalign(PH2) values; (iii) the only imported numerical quantity is the hBN free-edge formation energy ε_edge in Eq. (2), referred to the authors' previous study (ref 10), which is a parameter-free DFT quantity and is used in a standard thermodynamic cycle. It is not extracted from the present experimental alignment data, so the predicted θ = 0 minimum is not equivalent to the input by construction. The symmetry theorem from ref 13 (Ding et al.) is invoked as background to motivate step-induced symmetry breaking, but the paper's single-crystallinity claim rests on measured LEED asymmetry, SHG, and growth-time SEM observations, not on that theorem alone. The exfoliation/layer-by-layer assembly procedure cites the authors' prior method paper (ref 18), but this is procedural rather than load-bearing for the central crystallographic prediction. The main weakness is an evidence-extrapolation gap, not circularity: orientation-sensitive LEED covers ~1 mm2, the SHG map covers ~1 μm, and no orientation measurement spans the full 2-inch wafer, so the 'wafer-scale single-crystalline' conclusion is stronger than the local probes strictly support. That is a correctness/validation concern, not a self-referential reduction of the derivation to its inputs. I therefore find no significant circularity.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

No fitted parameters or invented entities are introduced. The main burden is the transferability of DFT energies, including an edge-energy input from prior work, and the assumption that thermodynamic energy minima control grain orientation.

assumptions (4)

domain assumption PBE-GGA with DFT-D3 and a 1x1x1 k-point mesh adequately captures relative binding and formation energies of hBN/Ge interfaces.
Computational details in Section 4; energy differences as small as 0.01 eV and barriers near 0.046 eV are used to distinguish orientations.
domain assumption The hBN edge formation energy epsilon_hBN from ref 10 is transferable to this interface and is used in Eq. 2.
Eq. 2 defines the interface formation energy using epsilon_hBN from the authors' prior study; an error in this quantity would shift the theta-dependent formation energy curves in Figure 4f.
domain assumption Only N-terminated zigzag hBN edges participate in step bonding, as inferred from AFM interior angles.
Figure S5 assigns 60-degree vertices to N-terminated zigzag edges; if B-terminated or mixed edges form at steps, the Ge-N bonding selection mechanism would change.
domain assumption Thermodynamic equilibrium energy minima control grain orientation, with kinetic attachment barriers neglected.
The paper attributes orientation selection to energy minima at theta equals 0 and 60 degrees but does not model kinetics or growth dynamics.

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Pith. "Pith review of Step-directed Epitaxy of Uni-directional Hexagonal Boron Nitride on Vicinal Ge(110)." pith.science (2026). https://pith.science/paper/45I57HIH

@misc{pith2026250718985,
  author       = {Pith},
  title        = {Pith review of: Step-directed Epitaxy of Uni-directional Hexagonal Boron Nitride on Vicinal Ge(110)},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/45I57HIH}},
  note         = {Machine review of arXiv:2507.18985}
}

read the original abstract

Insulating hexagonal boron nitride (hBN) films with precisely controlled thickness are ideal dielectric components to modulate various interfaces in electronic devices. To achieve this, high-quality hBN with controlled atomic configurations must be able to form pristine interfaces with various materials in devices. However, previously reported large-scale hBN films with uniform thickness either are polycrystalline or are not suitable for atomically clean assembly via mechanical exfoliation, limiting their applications in device technology. Here, we report the large-scale growth of monolayer single crystalline hBN films on Ge(110) substrates by using chemical vapor deposition (CVD). Vicinal Ge(110) substrates are used for the step-directed epitaxial growth of hBN, where Ge atomic steps act as the hBN nucleation sites, guiding the uni-directional alignments of multiple hBN domains. Density functional theory (DFT) calculations reveal that the optimum hydrogen passivations on both hBN edges and Ge surfaces enable the epitaxial coupling between hBN and the Ge step edges and the single crystallinity of the final hBN films. Using epitaxially grown monolayer hBN films, we fabricate a few hBN films with controlled stacking orders and pristine interfaces through a layer-by-layer assembly process. These films function as high-quality dielectrics to enhance carrier transport in graphene and MoS<sub>2</sub> channels.

Figures

Figures reproduced from arXiv: 2507.18985 by the authors.

**Figure 2.** Effect of hydrogen partial pressure on the crystallographic alignment of hBN. [PITH_FULL_IMAGE:figures/full_fig_p015_2.png] view at source ↗

**Figure 3.** Wafer-scale formations of single-crystalline hBN. (a) Schematic of the sequential process of hBN film formation through the merging of unidirectional grains on Ge(110) substrates with a miscut. (b) SEM images of as-grown hBN samples at different growth times (4, 8, and 12 hours from left to right). (c) Optical transmission contrast spectra measured at the positions indicated in inset (inset : the hBN film transferr… view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: DFT calculations of binding energy between hBN and Ge. (a) Schematics of an hBN grain with N-terminated zigzag edges on Ge(110). The angle (θ) indicates the misorientation between the hBN edge and the Ge [11!0] direction. (b) Schematics of the side view of hBN on (top)…

**Figure 5.** Figure 5: Applications of single-crystalline hBN films. (a) Schematic illustration of the layer-by-layer assembly process. (b, c) ARPES data for (b) asgrown monolayer and (c) assembled bilayer hBN films. In the assembled bilayer hBN, band splitting (indicated by a red arrow) oc…

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Works this paper leans on

4 extracted references · 4 canonical work pages

[4]

) are calculated using the following two equations: 𝐸!=(𝐸#$#%&−𝐸’(−𝐸)*+)𝐴⁄, (1) 𝐸

Experimental Section Growth of hBN: Ge (110) substrates miscut by 4° toward [001] or [11!0] (PAM-XIAMEN) were cleaned in 20% HF solution for 3 min to remove native oxides. The Ge substrates were then loaded in a quartz tube, which was evacuated to 40 mTorr and subsequently refilled to atmospheric pressure with combinations of 99.99% H2 and 99.99% Ar. The ...

work page
[6]

and excitonic insulators for exciton circuitry.[7] While single-crystalline bulk hBN flakes are mostly used for these purposes, the limited scale of bulk crystals, typically below a few tens of micrometers wide, hampers their widespread application for large-scale arrays of devices. hBN films grown by chemical vapor deposition are ideal for large-scale ap...

work page
[14]

S.; Choi, S

Lee, J. S.; Choi, S. H.; Yun, S. J.; Kim, Y. I.; Boandoh, S.; Park, J.-H.; Shin, B. G.; Ko, H.; Lee, S. H.; Kim, Y.-M.; et al. Wafer-scale single-crystal hexagonal boron nitride film via self-collimated grain formation. Science 2018, 362 (6416), 817-821. [15] Bets, K. V.; Gupta, N.; Yakobson, B. I. How the complementarity at vicinal steps enables growth o...

work page 2018
[28]

Y.; Al Ezzi, M

Lee, H. Y.; Al Ezzi, M. M.; Raghuvanshi, N.; Chung, J. Y.; Watanabe, K.; Taniguchi, T.; Garaj, S.; Adam, S.; Gradecak, S. Tunable optical properties of thin films controlled by the interface twist angle. Nano Lett. 2021, 21 (7), 2832-2839. [29] Kim, D. S.; Dominguez, R. C.; Mayorga-Luna, R.; Ye, D.; Embley, J.; Tan, T.; Ni, Y.; Liu, Z.; Ford, M.; Gao, F. ...

work page 2021

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [4]

) are calculated using the following two equations: 𝐸!=(𝐸#$#%&−𝐸’(−𝐸)*+)𝐴⁄, (1) 𝐸

Experimental Section Growth of hBN: Ge (110) substrates miscut by 4° toward [001] or [11!0] (PAM-XIAMEN) were cleaned in 20% HF solution for 3 min to remove native oxides. The Ge substrates were then loaded in a quartz tube, which was evacuated to 40 mTorr and subsequently refilled to atmospheric pressure with combinations of 99.99% H2 and 99.99% Ar. The ...

work page

[2] [6]

and excitonic insulators for exciton circuitry.[7] While single-crystalline bulk hBN flakes are mostly used for these purposes, the limited scale of bulk crystals, typically below a few tens of micrometers wide, hampers their widespread application for large-scale arrays of devices. hBN films grown by chemical vapor deposition are ideal for large-scale ap...

work page

[3] [14]

S.; Choi, S

Lee, J. S.; Choi, S. H.; Yun, S. J.; Kim, Y. I.; Boandoh, S.; Park, J.-H.; Shin, B. G.; Ko, H.; Lee, S. H.; Kim, Y.-M.; et al. Wafer-scale single-crystal hexagonal boron nitride film via self-collimated grain formation. Science 2018, 362 (6416), 817-821. [15] Bets, K. V.; Gupta, N.; Yakobson, B. I. How the complementarity at vicinal steps enables growth o...

work page 2018

[4] [28]

Y.; Al Ezzi, M

Lee, H. Y.; Al Ezzi, M. M.; Raghuvanshi, N.; Chung, J. Y.; Watanabe, K.; Taniguchi, T.; Garaj, S.; Adam, S.; Gradecak, S. Tunable optical properties of thin films controlled by the interface twist angle. Nano Lett. 2021, 21 (7), 2832-2839. [29] Kim, D. S.; Dominguez, R. C.; Mayorga-Luna, R.; Ye, D.; Embley, J.; Tan, T.; Ni, Y.; Liu, Z.; Ford, M.; Gao, F. ...

work page 2021