Pinhole-Seeded Lateral Epitaxy

• Pinhole epitaxy is defined as the growth mode where nanoscale openings in a graphene mask expose the substrate for direct epitaxial nucleation.
• The process involves mobile adatoms diffusing across graphene and being captured at pinholes, which control lateral overgrowth and film coalescence.
• This defect-mediated mechanism enables the formation of single-crystalline, peelable films by balancing direct bonding at pinholes with overall weak adhesion.

Pinhole epitaxy, more precisely pinhole-seeded lateral epitaxy, denotes a growth mode in which a nominally inert two-dimensional overlayer such as monolayer graphene masks a crystalline substrate except at nanoscale openings, or pinholes, where the substrate is exposed and direct epitaxial nucleation occurs. The nuclei formed at these openings inherit the substrate crystallographic registry and then overgrow laterally across the graphene until coalescing into a continuous film. In this framework, graphene functions primarily as an atomically thin mask and slip plane rather than as a remotely transmitting epitaxial template, and exfoliable single-crystalline membranes can emerge even when the decisive nucleation events occur by direct chemical contact at the pinholes (Manzo et al., 2021, Du et al., 2022, LaDuca et al., 29 Jul 2025).

1. Definition and nomenclature

In the GaSb/graphene/GaSb(001) study, the operative term is “pinhole-seeded lateral epitaxy” or “seeded lateral epitaxy at pinholes”, not a newly formalized standalone term “pinhole epitaxy.” In that usage, monolayer graphene covers GaSb(001), nanoscale openings expose the underlying GaSb, GaSb nucleates only in these pinholes in direct epitaxial registry with the exposed crystal, and subsequent growth proceeds laterally from the pinholes across the graphene surface until islands merge into a continuous film. Because most of the interfacial area remains graphene-terminated, the resulting film is mechanically weakly bound except at the pinholes and can be exfoliated as a membrane (Manzo et al., 2021).

This definition is most useful when contrasted with the two mechanisms that it can resemble macroscopically. In remote epitaxy, the graphene is ideally continuous and clean, nucleation occurs on top of graphene, and crystallographic templating is attributed to the substrate lattice potential permeating through graphene with amplitude $\Delta \phi \sim 0\text{–}40$ meV. In van der Waals epitaxy, the film aligns primarily to the two-dimensional material rather than to the bulk substrate. Pinhole epitaxy differs from both: the key registry-setting event is local and direct at exposed substrate sites, while lateral overgrowth and the small area fraction of direct bonding preserve exfoliability (Du et al., 2022).

A recurring interpretive consequence is that exfoliability and substrate-like epitaxial orientation do not uniquely diagnose remote epitaxy. They are equally expected outcomes of pinhole-seeded lateral epitaxy whenever defect openings are present and capture the mobile adatom population before nucleation occurs on intact graphene (LaDuca et al., 29 Jul 2025).

2. Interfacial origin of pinholes

The experimentally resolved prototype is transferred CVD monolayer graphene on GaSb(001). In that system, GaSb(001) initially carries a native amorphous oxide of approximately 3 nm, the graphene is transferred by a polymer-assisted wet transfer, and after transfer plus low-temperature vacuum cleaning at approximately $350\,^\circ\mathrm{C}$ the graphene appears essentially continuous in SEM, slightly bumpy in AFM with approximately 2 nm height variations, and defect-poor in Raman, with strong G and 2D bands but no detectable D peak. Despite this apparent continuity, in-situ XPS still shows an O 1s peak at approximately 531 eV and oxide satellites in Sb $3d_{3/2}$ at approximately 540 eV, indicating residual GaSb oxides trapped under graphene (Manzo et al., 2021).

The pinholes arise during the subsequent high-temperature native oxide desorption step immediately preceding MBE. Under Sb flux, annealing at $450\,^\circ\mathrm{C}$ marks the onset of oxide desorption and reveals pinholes of diameter $\sim 10$ nm in AFM height and phase contrast. By $540\,^\circ\mathrm{C}$, the density and size of small pinholes increase to approximately 10–20 nm, sparse larger holes of approximately 300 nm become visible in SEM, and Raman develops a strong D band. AFM statistics give small-pinhole spacing $L \sim 70$ nm. The reported interpretation is oxide-related etching of graphene: residual oxide “bumps” beneath graphene act as starting sites, oxygen etches graphene preferentially at strained or defective regions and edges, and oxide desorption leaves physical openings (Manzo et al., 2021).

These openings are not merely topographic defects; they define the energetically preferred nucleation sites. At approximately $500\,^\circ\mathrm{C}$, graphene is chemically inert, Ga and Sb have low sticking coefficients on graphene, and adatoms landing on graphene are highly mobile and/or desorb. By contrast, exposed GaSb at pinholes provides strong bonding sites and a large local potential well, with $\Delta \phi \sim \text{eV}$, far exceeding the weak remote modulation through graphene. This establishes the pinholes as epitaxial anchors: they impose in-plane orientation by direct contact and permit that orientation to propagate by lateral overgrowth across the masked surface (Manzo et al., 2021).

The same logic extends beyond III–V homoepitaxy. The remote-epitaxy perspective emphasizes that transferred graphene frequently contains pinholes, tears, larger openings, grain boundaries, wrinkles, and step-edge discontinuities. Whenever such defects exist at sufficiently high areal density, they become the dominant nucleation sinks and can reproduce the central observables commonly attributed to remote epitaxy (LaDuca et al., 29 Jul 2025).

3. Growth kinetics and film evolution

The GaSb case provides a monolayer-resolved growth sequence. At $0$–$350\,^\circ\mathrm{C}$0 monolayers, with one monolayer defined as half the GaSb unit cell, $350\,^\circ\mathrm{C}$1 Å, and monolayer areal density $350\,^\circ\mathrm{C}$2 for both Ga and Sb, AFM and SEM show GaSb islands only within the 10 nm and 300 nm pinholes; graphene-covered regions remain largely free of nucleation. At 2 ML, nearly all pinholes contain GaSb islands and pinholes without islands become rare. At 5 ML, the islands begin epitaxial lateral overgrowth onto the graphene, producing domes that spill out of the pinholes. By 50–100 ML, neighboring islands coalesce, and by 200 ML, approximately 60 nm, the film exhibits an atomically flat step-and-terrace morphology characteristic of GaSb(001); RHEED shows sharp streaks and the $350\,^\circ\mathrm{C}$3 superstructure of the GaSb $350\,^\circ\mathrm{C}$4 reconstruction along the $350\,^\circ\mathrm{C}$5 azimuth (Manzo et al., 2021).

The controlling kinetic variables are the adatom diffusion length $350\,^\circ\mathrm{C}$6 on the graphene-terminated surface and the average pinhole spacing $350\,^\circ\mathrm{C}$7. For the GaSb/graphene/GaSb(001) system, the argument is that $350\,^\circ\mathrm{C}$8 is plausible by analogy to prior work on metal adatoms on graphene, while AFM gives $350\,^\circ\mathrm{C}$9 nm; hence $3d_{3/2}$0. In that regime, adatoms can explore the graphene surface and are captured by pinholes before nucleating on graphene. The reported regime criterion is therefore qualitative but explicit: seeded lateral epitaxy is favored when $3d_{3/2}$1, whereas remote epitaxy could in principle emerge only when $3d_{3/2}$2 and nucleation on graphene becomes competitive (Manzo et al., 2021).

The Heusler/graphene/sapphire study reformulates the same competition in a system with much lower pinhole density. After a $3d_{3/2}$3 anneal, graphene/sapphire exhibits approximately 10 pinholes/$3d_{3/2}$4, corresponding to a characteristic spacing of order $3d_{3/2}$5 nm. For GdPtSb on graphene/sapphire, the observed temperature dependence is interpreted through the ratio of $3d_{3/2}$6 to $3d_{3/2}$7: at approximately $3d_{3/2}$8, $3d_{3/2}$9, adatoms find pinholes and nucleate directly on sapphire, and the film is predominantly in the substrate-like R0 orientation; at approximately $450\,^\circ\mathrm{C}$0, $450\,^\circ\mathrm{C}$1, nucleation occurs on clean graphene and the R30 domain increases (Du et al., 2022).

This kinetic picture implies that pinhole epitaxy is not a fixed interfacial property but a regime selected by diffusion, pinhole spacing, and defect density. A plausible implication is that graphene systems with very long adatom diffusion lengths are especially vulnerable to defect-dominated growth unless the graphene is both exceptionally continuous and characterized at the relevant length scales.

4. Structural signatures, characterization, and exfoliation

Pinhole epitaxy is diagnosed experimentally by combining interfacial spectroscopy, growth-sensitive diffraction, and post-growth microscopy. In the GaSb study, in-situ XPS tracks Sb 3d, Ga 3p, O 1s, and C 1s during oxide desorption; in-situ RHEED monitors the transition from oxide-covered to clean GaSb and later the emergence of the $450\,^\circ\mathrm{C}$2 superstructure; AFM resolves the 10–20 nm pinholes and the progression from isolated nuclei to lateral overgrowth; SEM reveals sparse larger holes and coalescence behavior; Raman tracks the appearance of the D band associated with graphene defect formation; XRD confirms only GaSb(00$450\,^\circ\mathrm{C}$3) peaks and no misoriented grains; and PL shows optical quality comparable to GaSb grown on bare GaSb (Manzo et al., 2021).

The crystallographic relationship in GaSb/GaSb across graphene is reported as

$450\,^\circ\mathrm{C}$4

with nominal lattice mismatch

$450\,^\circ\mathrm{C}$5

Because nucleation occurs at exposed GaSb(001), each pinhole seeds an island in the substrate orientation, and coalescence of equivalently oriented islands yields a single-crystal film. XRD rocking curves show broadened but still high crystalline quality: homoepitaxial GaSb gives fwhm $450\,^\circ\mathrm{C}$6 arcsec, while GaSb on graphene/GaSb shows two peaks at $450\,^\circ\mathrm{C}$7 and $450\,^\circ\mathrm{C}$8 arcsec with fwhm $450\,^\circ\mathrm{C}$9 and 12.59 arcsec. The film 006 reflection shifts slightly to lower angle, suggesting a larger out-of-plane lattice parameter, with possible contributions from thermal expansion mismatch or slight rippling on the graphene interlayer (Manzo et al., 2021).

Exfoliation demonstrates why direct bonding at pinholes does not negate membrane release. After growth, a 100 nm Ni stressor layer is deposited and the film is peeled using thermal release tape or a glass-plus-adhesive method. The underside of the exfoliated membrane is smooth, while the substrate displays sparse spalling marks. Higher-magnification SEM shows elongated marks of width approximately 300 nm and length up to several microns associated with the large holes, and smaller approximately 20 nm marks associated with the 10–20 nm pinholes. Raman after exfoliation detects G and 2D peaks on both membrane and substrate, indicating graphene tearing and residue on both sides. The interpretation is that pinholes create strong local anchors where the film is directly bonded to the substrate, but because the pinhole area fraction is small, the total adhesion remains dominated by the weak graphene interface and continuous membranes can still be peeled (Manzo et al., 2021).

The same evidence also sets a practical constraint. Too few pinholes lead to insufficient nucleation density and poor coalescence; too many or too large pinholes create too much direct chemical contact and make exfoliation difficult or impossible. In the GaSb case, the naturally generated defect size distribution appears to satisfy both requirements simultaneously (Manzo et al., 2021).

5. Relation to remote and van der Waals epitaxy

The central controversy surrounding pinhole epitaxy is interpretive rather than phenomenological: it can reproduce the same end state as remote epitaxy. In the strict remote-epitaxy picture, graphene is taken to be largely passive and transparent to the substrate lattice potential, so that adatoms on graphene experience a periodic substrate-derived modulation and nucleate epitaxially without direct substrate contact. The surface-science perspective argues that this picture is incomplete because the total potential above a graphene/substrate stack is better written schematically as

$\sim 10$0

where substrate, graphene, and reconstruction or moiré contributions can all be relevant. Under realistic screening, the remote substrate term is often not overwhelmingly larger than the graphene term (LaDuca et al., 29 Jul 2025).

The same perspective gives explicit screening estimates. In a screened Morse-model treatment, for a 3D carrier density $\sim 10$1 the Thomas–Fermi screening length is $\sim 10$2 Å; for monolayer graphene of thickness $\sim 10$3 Å, the field transmission is

$\sim 10$4

and for bilayer graphene

$\sim 10$5

The resulting screened remote potential can be of order $\sim 10$6 meV above graphene, comparable to the potential modulation from the graphene lattice itself. This supports the view that even sparse direct-contact defects can outweigh remote templating energetically (LaDuca et al., 29 Jul 2025).

The Heusler study sharpens the distinction by identifying an orientation that pinhole epitaxy cannot produce. For GdPtSb grown directly on bare sapphire, only the R0 “hexagon-on-hexagon” orientation is observed over $\sim 10$7–$\sim 10$8. On graphene/sapphire after a $\sim 10$9 graphene anneal, however, GdPtSb exhibits both R0 and an R30 domain. Because pinhole epitaxy amounts to direct epitaxy at sapphire exposed in pinholes followed by lateral overgrowth, it must reproduce the direct sapphire orientation, namely R0. It therefore cannot account for a coherent, substrate-registered R30 domain that is absent in direct epitaxy. Nor is van der Waals epitaxy on polycrystalline graphene expected to yield a single R30 lock-in; it should instead generate multiple orientations correlated with local graphene grains. In that system, the R30 superstructure is proposed as a possible experimental fingerprint of a genuine remote component, while the R0 fraction at higher temperature is assigned to pinhole epitaxy (Du et al., 2022).

This distinction also clarifies a common misconception. Substrate-like epitaxial alignment through graphene is not, by itself, evidence of remote epitaxy. Pinhole-seeded lateral epitaxy predicts exactly that outcome whenever direct nucleation at exposed substrate sites controls the orientation and lateral overgrowth completes the film (Manzo et al., 2021, LaDuca et al., 29 Jul 2025).

6. Control parameters, materials scope, and related defect-mediated phenomena

The combined studies suggest a practical regime map built around defect density, pinhole spacing, adatom diffusion length, and lattice matching. To promote pinhole epitaxy, one increases the probability that adatoms encounter reactive exposed substrate sites before they nucleate elsewhere: higher growth temperature increases $540\,^\circ\mathrm{C}$0, smaller $540\,^\circ\mathrm{C}$1 results from higher pinhole density, and strong film/substrate lattice matching makes direct nucleation especially effective. To suppress pinhole epitaxy, one seeks mechanically stable and clean graphene/substrate interfaces, low pinhole density, and growth conditions such that $540\,^\circ\mathrm{C}$2; if the substrate potential remains appreciable, this can favor remote epitaxy, whereas better lattice matching to graphene can favor van der Waals epitaxy (Du et al., 2022).

Materials choice strongly influences which regime is accessible. On graphene/GaSb(001), transferred graphene plus oxide desorption naturally creates dense pinholes and thus favors seeded lateral epitaxy. On graphene/sapphire, the substrate is an air-stable crystalline oxide rather than a III–V with thick amorphous native oxide, pinhole density after annealing is much lower, and remote and van der Waals mechanisms can therefore compete more effectively. Within the Heusler examples, GdPtSb shows remote-versus-pinhole competition, LaPtSb remains ambiguous because its R0 orientation is consistent with either remote or pinhole epitaxy, and GdAuGe instead exhibits a broad in-plane distribution interpreted as van der Waals epitaxy to graphene (Du et al., 2022).

The mechanism is presented as potentially generic. Because GaSb is chemically similar to other III–V materials, the GaSb study anticipates that the same defect-mediated route can apply more generally to other materials. The remote-epitaxy perspective extends that argument: any system in which adatoms diffuse rapidly on a two-dimensional layer but nucleate strongly at exposed substrate sites can display pinhole epitaxy, and intentional nanopatterning of graphene openings is essentially a deliberate implementation of the same principle (Manzo et al., 2021, LaDuca et al., 29 Jul 2025).

A related but distinct literature concerns pit or incipient pinhole formation during conventional epitaxy without a two-dimensional mask. In Si(100) homoepitaxy, Å-sized oxide nuclei at growth antiphase boundaries pin advancing steps, producing multilayer pits that deepen during growth and heal on annealing; this is a defect-mediated pit-formation mechanism rather than pinhole-seeded lateral epitaxy across graphene, but it illustrates the broader principle that rare chemically active defects can redirect epitaxial morphology through step pinning and heterogeneous nucleation (Yitamben et al., 2017).

Overall, pinhole epitaxy is best understood not as an anomaly but as a well-defined defect-seeded growth regime. Its decisive ingredients are local openings in the two-dimensional overlayer, direct epitaxial nucleation at those openings, lateral overgrowth across the masked surface, and a pinhole area fraction low enough to preserve exfoliation. In many transferred-graphene systems, that combination offers a sufficient explanation for single-crystalline, peelable films without invoking a remotely transparent graphene interface (Manzo et al., 2021, LaDuca et al., 29 Jul 2025).