REVIEW 3 major objections 8 minor 2 references
Interstitially bridged van der Waals interface enabling stacking-fault-free, layer-by-layer epitaxy
T0 review · 3 major / 8 minor · reviewed 2026-08-06 · deepseek-v4-flash
Pith's one-line read Growing bilayer MoS2 with molybdenum atoms bridging the layers locks the film into a single hexagonal stacking order that survives transfer.
desk verdict First clear experimental demonstration that Mo interstitials can steer 2H stacking in bilayer MoS2, though the mechanism is correlated rather than fully isolated from other Mo-rich-growth factors. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The carrying object is the interstitial Mo atom in the van der Waals gap, sitting on the Mo sublattice of the bottom layer and bonded to sulfur atoms from both layers. In the final structure it occupies a tetrahedral site between AA'-stacked layers (T-AA'), after passing through an octahedral configuration (O-AB') during nucleation. The interstitial acts as a nucleation seed for the second layer, lowering the barrier to forming the hexagonal phase; as the grain grows, the top layer translates into the AA' registry. Because sliding or twisting the layers would require breaking the interstitial's covalent bonds, the anchor raises the energy cost of stacking defects to roughly 1.7 eV, far above the ~1 meV per unit cell differences between polytypes without interstitials, and blocks the formation of strained solitons.
What would settle it
Grow bilayer MoS2 under Mo-rich conditions but remove or prevent the interstitials - for instance by annealing after growth to drive them out, or by using a Mo precursor that does not leave interstitial atoms - and check whether the 2H phase fraction and soliton-free transfer are preserved. If the film remains more than 99% 2H and soliton-free without interstitials, the anchor mechanism is not the active agent.
Extended reading notes
Core claim
The central claim is that Mo interstitials incorporated during layer-by-layer growth are the active agents that deterministically select and stabilize the hexagonal (2H) stacking of bilayer MoS2. Under Mo-rich growth, atomic-resolution STEM shows single Mo atoms lodged at one sublattice site, vertically aligned with Mo atoms in the bottom layer, at a density of about one interstitial per 40 unit cells. Dark-field TEM finds 159 of 160 bilayer grains in the 2H phase, with no strained solitons even after transfer; under Mo-poor growth the same measurement yields a roughly 64/36 mixture of 2H and 3R phases with abundant solitons. DFT calculations attribute this to the interstitial's large stacking-selection energy, about 1.7 eV per atom, which dwarfs the ~1 meV per unit cell energy difference between polytypes without interstitials. The paper further links the interstitials to a split, red-shifted Raman E2g1 mode, an XPS shoulder from less-oxidized Mo, a single-crystalline ARPES band structure with a strong interlayer-hybridized valence band, and field-effect transistors with an on/off ratio near $10^{9}$.
Load-bearing premise
The paper's argument depends on the claim that Mo interstitials, not some other feature of Mo-rich growth, are what determines the stacking order and its robustness.
Editorial extensions
If this is right
- Bilayer MoS2 can be grown with deterministic 2H stacking over large areas: 159 of 160 grains in the checked regions were hexagonal, compared to about 64% under Mo-poor conditions.
- The resulting films remain single-phase and free of strained solitons after transfer, indicating that the interlayer registry is locked in place.
- Transistors made from these films show stable operation with on/off ratios approaching 10^9, whereas devices from Mo-poor, mixed-stacking films are markedly worse.
- The same interstitial-guided growth can set the stacking of thicker layers (a trilayer, where the third layer takes rhombohedral order) and extends to WS2 grown under W-rich conditions, suggesting the strategy is not limited to bilayers of MoS2.
Reading between the lines
- If interstitials are the true cause, then removing them after growth, for example by annealing or electrochemical extraction, should restore stacking-fault formation and soliton mobility in the same film.
- A cleaner test of the mechanism would be to vary interstitial density at a fixed Mo:S ratio, using temperature or a secondary flux, to separate the anchor effect from other consequences of Mo-rich growth.
- The ~1.6% tensile strain implied by the Raman red-shift suggests the anchored bilayers are under built-in stress; this could shift band edges or exciton energies in ways that go beyond the paper's ARPES and transport measurements.
- The same interstitial-anchor idea might be used to stabilize other stackings, such as rhombohedral, by choosing an interstitial species or site with a different bonding preference, which would give phase-selective growth in other TMD families.
Signed reviews
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper reports the MOCVD growth of single-crystalline, 2H-stacked bilayer MoS2 on miscut c-plane sapphire under Mo-rich conditions, and attributes the stacking selectivity and post-transfer structural robustness to Mo atoms intercalated at the van der Waals gap. The authors use HAADF-STEM to identify Mo interstitials at a single sublattice site, with areal density about one per ~40 unit cells in monolayers and ~2.4e13 cm^-2 in bilayers. DF-TEM shows >99% of bilayer domains are 2H under Mo-rich growth, versus ~64% under Mo-poor growth, and the Mo-rich bilayers survive transfer without forming strained solitons. Raman shows an E2g1 doublet, XPS shows a lower-binding-energy Mo shoulder with an area fraction (~11.5%) close to the STEM interstitial fraction (~11.3%), ARPES shows a single-crystal band structure with a pronounced G1st peak, and hBN-gated FETs reach on/off ratios near 1e9. DFT calculations identify two stable interstitial configurations (O-AB' and T-AA') and predict that T-AA' becomes thermodynamically favored for islands larger than N = 11 unit cells. The manuscript acknowledges that the measured average island size per interstitial (N ~ 7) is below this threshold and hypothesizes that additional interstitials may enter after AA'-host formation.
Significance. If the causal role of interstitials is firmly established, this work offers a new route to deterministic stacking control in vdW multilayers, addressing a long-standing challenge in 2D materials synthesis. The experimental characterization is broad and internally consistent: the XPS/STEM fraction match, the ARPES single-crystal signature, and the transport on/off ratio all support the quality and phase purity of the Mo-rich bilayers. The DFT calculations are an independent theoretical input, not fitted to the stacking fractions, so the central result is not circular. However, the load-bearing causal claim - that Mo interstitials are the operative cause of 2H stacking selection and of soliton-free robustness - is not isolated from other growth covariates, and the quantitative DFT threshold (N=11) does not match the observed interstitial density (N~7). These gaps make the mechanism currently a plausible hypothesis rather than a demonstrated result. The paper would be suitable for publication after these points are addressed experimentally or the claims are appropriately qualified.
major comments (3)
- [Results and Discussion, first paragraph; Figs. 2a-b and S7] The central causal claim that Mo interstitials select 2H stacking rests on a single comparison between Mo-rich and Mo-poor growth conditions. These conditions differ simultaneously in PMo/PS (4e-2 vs 2e-3), in absolute Mo and S precursor flows, and in carrier gas flow rates (Ar 500 vs 90 sccm, H2 2 vs 4 sccm). Consequently, the observed difference in stacking ratio (99% vs 64%) could in principle be caused by changes in growth rate, nucleation density, edge termination, or carbon incorporation from Mo(CO)6 decomposition, rather than by the interstitial atoms themselves. No experiment varies the interstitial areal density while holding these other parameters fixed. The paper should either provide a dose-response experiment in which only the Mo/S ratio is varied across several intermediate values with measurement of interstitial density and stacking fraction, or directly demonstrate that the 2H selection is mediated by interstitials, for example by post-growth interstitial insertion into a Mo-poor bilayer followed by annealing and stacking characterization. Without such evidence, the causal mechanism remains correlational.
- [Results and Discussion, Growth mechanism; Fig. 3c, p. 7] The DFT prediction that T-AA' becomes thermodynamically stable only for N > 11 is not consistent with the experimentally measured interstitial density (one per ~40 unit cells, corresponding to an average N ~ 7 per interstitial in a single-island picture). The manuscript acknowledges this mismatch and hypothesizes that 'additional Mo interstitials may be introduced following the formation of the AA'-stacked host,' but provides no evidence for such post-formation insertion. This is a load-bearing point because the proposed nucleation-seed mechanism (Fig. 3d) requires the interstitial to stabilize the AA' stacking from the initial stage; if the energy crossover only occurs at larger island sizes, the mechanism cannot explain the observed highly selective 2H formation. The authors should either present a revised DFT analysis that accounts for multiple interstitials per island at the measured density, or calculate the kinetic barrier for the O-AB' to T-AA' slide to show that it is accessible under growth conditions. Merely noting the discrepancy and invoking an untested hypothesis is insufficient for the central claim.
- [Results and Discussion, Robustness after transfer; Figs. 2e-f] The absence of strained solitons after transfer is presented as evidence that interstitial covalent bonds strengthen the interlayer coupling. However, the comparison is between Mo-rich (2H, with interstitials) and Mo-poor (mixed 2H/3R, without interstitials) samples, so the suppression of solitons could equally be a consequence of the uniform 2H stacking itself rather than a direct effect of the interstitials. To support the causal inference, the authors should compare a Mo-rich bilayer that has been mechanically strained (e.g., by bending or indentation) with a Mo-poor bilayer subjected to the same strain, and show that soliton nucleation is suppressed or its onset is delayed in the interstitial-containing sample. Without such a test, the robustness claim is not specifically attributable to the interstitials.
minor comments (8)
- [Methods, DFT calculations] Please clarify the Brillouin zone sampling: the text 'Γ, K-point was used' is ambiguous; it should state the k-point grid (e.g., a Γ-centered mesh) and the number of k-points.
- [Fig. 3c caption] The caption labels the three curves as grey, orange, and red, but the y-axis label and units are not defined; please add explicit definitions of ΔEMoi, ΔEBulk, and ΔEF in the caption or in the main text.
- [Fig. S8 and text p. 7] The statement that 'AA'-MoiB is the inversion counterpart of AA'-MoiA and thus exhibits the same formation energy under free-standing conditions' should be reconciled with the earlier claim that only AA'-MoiA is kinetically accessible; please make this distinction explicit in the main text.
- [Fig. 5c and related text] The green arrow points to an extra spectral feature that is attributed to AA stacking at solitons; please clarify that this assignment is based on reference 42 and provide the calculation level, as the energy position may depend on functional and vdW correction.
- [Raman analysis, Fig. 4a] The assignment of the lower-energy Raman peak to E2g1(-) and the interpretation of the 5.7 cm^-1 red-shift as ~1.6% tensile strain should be accompanied by a reference for the strain-phonon coupling coefficient in bilayer MoS2, or a direct strain calibration.
- [XPS analysis, Fig. 4b] The fitting of the Mo 3d shoulder peaks would benefit from a description of the fitting procedure, including peak shapes, constraints, and error estimates; please also discuss why alternative assignments (e.g., MoOx or Mo-C species from the MOCVD precursor) are ruled out.
- [DF-TEM statistics, Fig. S6] Please specify the number of independently grown samples and total analyzed area for the 'over 99% (159 out of 160)' statistic, and state the criteria for classifying a domain as 2H or 3R.
- [Abstract and Conclusions] The term 'hexagonal bilayer' is used throughout to mean 2H stacking; since 'hexagonal' also refers to the crystal system, consider defining 'hexagonal phase' at first use to avoid ambiguity with the lattice symmetry.
Circularity Check
No significant circularity: the DFT mechanism is an independent theoretical input, and the acknowledged N=7 vs N=11 mismatch is a stated limitation rather than a result forced by construction.
full rationale
The paper's central derivation is not circular. The claim that Mo interstitials stabilize the 2H stacking order is supported by independent DFT calculations (Fig. 3, Methods) that compare formation energies of O-AB' and T-AA' configurations as a function of island size; these calculations are not fitted to the measured 2H/3R fractions or to the STEM interstitial density. The experimental correlation between Mo-rich growth and 2H dominance is a two-condition comparison, and the DFT N=11 versus observed N~7 mismatch is explicitly acknowledged with a speculative auxiliary hypothesis about additional interstitials entering after AA' formation. That is an untested assumption and a limitation, but it does not make the conclusion equivalent to its inputs by construction. The paper's self-citations (refs 21 and 47) are used only for known soliton/twin-boundary phenomenology and device transport context, not as load-bearing justification of the interstitial mechanism. No fitted parameter is renamed as a prediction, no uniqueness theorem is imported from the authors' prior work, and no known result is merely relabeled. The structural, spectroscopic, ARPES, and transport observations are measured independently of the DFT claim. Circularity score: 0.
Assumptions & free parameters
free parameters (1)
- Mo-rich growth condition (PMo/PS ratio) =
PMo/PS ≈ 4x10^-2 (Mo-rich); ≈ 2x10^-3 (Mo-poor)
assumptions (6)
- domain assumption DFT-PBE-D3 with vdW correction accurately describes interlayer and interstitial energetics in MoS2.
- domain assumption Chemical potentials referenced to Mo bcc metal and S orthorhombic crystal represent growth conditions.
- domain assumption HAADF-STEM contrast and simulations uniquely identify the bright sites as Mo atoms on a specific sublattice.
- domain assumption Finite-cluster DFT (triangular clusters, N up to 11) captures layer-by-layer nucleation thermodynamics.
- domain assumption The sapphire substrate and step edges do not change the relative stability of stacking orders with interstitials.
- ad hoc to paper Only the AA'-MoiA interstitial site is kinetically accessible during layer-by-layer growth.
Cite this review
Pith. "Pith review of Interstitially bridged van der Waals interface enabling stacking-fault-free, layer-by-layer epitaxy." pith.science (2026). https://pith.science/paper/5WMQPKO6
@misc{pith2026250716361,
author = {Pith},
title = {Pith review of: Interstitially bridged van der Waals interface enabling stacking-fault-free, layer-by-layer epitaxy},
year = {2026},
howpublished = {\url{https://pith.science/paper/5WMQPKO6}},
note = {Machine review of arXiv:2507.16361}
}
read the original abstract
Van der Waals (vdW) crystals are prone to twisting, sliding, and buckling due to inherently weak interlayer interactions. While thickness-controlled vdW structures have attracted considerable attention as ultrathin semiconducting channels, the deterministic synthesis of stacking-fault-free multilayers remains a persistent challenge. Here, we report the epitaxial growth of single-crystalline hexagonal bilayer MoS<sub>2</sub>, enabled by the incorporation of Mo interstitials between layers during layer-by-layer deposition. The resulting bilayers exhibit exceptional structural robustness, maintaining their crystallinity and suppressing both rotational and translational interlayer misalignments even after transfer processes. Atomic-resolution analysis reveals that the Mo interstitials are located at a single sublattice site within the hexagonal lattice, where they form tetrahedral bonds with sulfur atoms from both MoS<sub>2</sub> layers, effectively anchoring the interlayer registry. Density functional theory calculations further indicate that these Mo atoms act as nucleation centers, promoting the selective formation of the hexagonal bilayer phase. This approach offers a robust strategy for the deterministic growth of multilayer vdW crystals with precisely controlled stacking order and enhanced interlayer coupling.
Reference graph
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Reviewed August 6, 2026 · model on record in the stance chip above.
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