Thru-Hole Epitaxy: Mechanisms and Applications

• Thru-Hole Epitaxy (THE) is an epitaxial growth mode where the 3D film nucleates through exposed substrate openings in a 2D mask, enabling lateral overgrowth.
• THE controls film morphology by exploiting pinhole and percolative pathways, which affect nucleation delays and crystallographic orientations.
• Quantitative studies and simulations show that defect topology and engineered perforations critically govern nucleation kinetics and the survival of connected areas.

Thru-Hole Epitaxy (THE) denotes an epitaxial growth mode on 2D-material-covered substrates in which the 3D film nucleates at exposed spots in the mask—holes, pinholes, openings, or uncovered regions of the underlying substrate—and then grows laterally across the 2D material. In this framing, THE is a form of pinhole-seeded lateral epitaxy or connectedness-initiated epitaxial lateral overgrowth, and its defining feature is direct epitaxial connectedness between film and substrate through at least one thru-hole rather than crystallographic alignment mediated solely through an intact spacer (Jang et al., 2021, Lee et al., 2023).

1. Definition and physical basis

In THE, the substrate is partially covered by a 2D layer such as graphene or $h$-BN, and the 2D layer is not fully continuous. GaN begins by directly nucleating on exposed substrate regions inside holes or openings, and the resulting domains then expand laterally over the 2D-covered regions. The term “thru-hole” is used for a hole that is connected all the way from the top-most 2D layer to the substrate, thereby establishing what has been called epitaxial connectedness (Lee et al., 2022).

This definition accommodates both deliberately opened masks and disordered masks with random transport pathways. A thru-hole need not be a simple vertical aperture. It may be vertical, meandering, crooked, or maze-like, provided that it forms a continuous connection from the top layer to the substrate. In stacked 2D-mask systems, the physically relevant quantity is therefore not merely nominal mask coverage but the survival of connected openings through the entire stack (Lee et al., 2022).

The mechanism is correspondingly local. Atoms arriving on the mask can diffuse to connected openings, reach the crystalline substrate, nucleate directly on that substrate, and then overgrow laterally. In more recent solution-processed implementations, this same logic is extended from explicit holes to percolative nanoscale transport pathways inside a disordered 2D network, so that precursor access and epitaxial nucleation occur beneath an apparently blocking overlayer (Ha et al., 16 May 2025).

2. Relationship to remote epitaxy and van der Waals epitaxy

THE is central to an ongoing interpretive dispute about growth on 2D interlayers. In one formulation, remote epitaxy requires crystallographic alignment, easy detachability, and no thru-holes anywhere under the domain, whereas THE requires alignment, detachability, and at least one thru-hole connecting film to substrate. On this basis, alignment and easy lift-off are not unique signatures of remote epitaxy, because the same observables can arise from connectedness-initiated lateral overgrowth after direct nucleation at exposed substrate sites (Jang et al., 2021).

This distinction matters because much of the evidentiary burden falls on proving the absence of connected openings across the entire interface, not merely in a single cross-sectional transmission electron microscopy field of view. The critique advanced in the THE literature is that a single hole-free TEM image does not establish the absence of holes everywhere under a domain. The same logic is strengthened experimentally by growth through thick and symmetrically incompatible spacer layers, and even through a $50 \, \text{nm}$ SiO$_2$ interlayer in which nanoscale holes intentionally expose the substrate; if aligned GaN still forms under those conditions, the operative mechanism is through-hole-mediated direct epitaxy plus lateral overgrowth rather than remote transmission through an intact spacer (Jang et al., 2021).

The contrast with van der Waals epitaxy is also specific. Van der Waals epitaxy is associated with weak interaction between film and substrate, often with less stringent substrate-imposed alignment. In the THE interpretation of growth on partly masked sapphire, however, experimentally observed orientation selectivity in the presence of exposed sapphire openings points to nucleation-controlled growth at the openings rather than purely weak-interaction overlayer growth (Lee et al., 2023).

A further argument against strong remote-field control comes from surface-potential calculations. In the reported DFT analysis, the seed potential difference $\Delta V$ on a monolayer overlayer is only about $1$–$2\%$ of that on bare sapphire, and with $n \ge 2$ layers the potential becomes almost like isolated 2D material. Within that framework, connectedness rather than long-range field transmission becomes the primary control parameter (Jang et al., 2021).

3. Crystallographic orientation disparity and the reinterpretation of THE

A particularly important result for THE comes from GaN growth on bare and partly graphene-covered $m$-plane sapphire under identical growth conditions. The study intentionally omitted a low-temperature buffer layer so that GaN formed isolated domains or islands with well-defined facet shapes rather than a continuous flat film. This made domain morphology and reciprocal-space mapping directly useful for identifying preferred crystallographic orientation (Lee et al., 2023).

On bare $m$-plane sapphire, GaN domains were reported as $(100)$-oriented. On partly graphene-covered $50 \, \text{nm}$0-plane sapphire, with graphene coverage fraction about $50 \, \text{nm}$1 from AFM/ImageJ analysis, GaN domains were instead $50 \, \text{nm}$2-oriented. Reciprocal-space maps on the bare substrate showed only the GaN $50 \, \text{nm}$3 Bragg peak at $50 \, \text{nm}$4 and the GaN $50 \, \text{nm}$5 Bragg peak at $50 \, \text{nm}$6, confirming exclusive $50 \, \text{nm}$7 orientation. Reciprocal-space maps on the partly graphene-covered substrate showed only the GaN $50 \, \text{nm}$8 Bragg peak at $50 \, \text{nm}$9; that peak was split into two components attributed to two twin variants tilted in opposite directions, with tilt of about $_2$0, consistent with prior reports (Lee et al., 2023).

Substrate	Reported GaN orientation	Key structural evidence
Bare $_2$1-plane sapphire	$_2$2	SEM morphology; XRD peaks at $_2$3 and $_2$4
Partly graphene-covered $_2$5-plane sapphire	$_2$6	SEM morphology; XRD peak at $_2$7 with twin-variant splitting

High-resolution cross-sectional TEM provided the decisive mechanistic evidence. For GaN grown on the partly graphene-covered substrate, GaN was seen in direct contact with the $_2$8-plane sapphire, graphene was not observed at the specific nucleation interface in the high-resolution image, and the data indicated that GaN started nucleating on the exposed sapphire surface and then laterally grew over the graphene. The resulting conclusion was that orientation disparity does not rule out thru-hole epitaxy, even when growth conditions are identical. More narrowly, the commonly invoked inference that different preferred orientations under identical conditions must exclude pinhole-seeded lateral epitaxy is not valid in general (Lee et al., 2023).

4. Epitaxial connectedness in stacked masks

The survival of thru-holes across multiple stacked 2D layers is a central mechanistic issue for THE. If holes in each layer were isolated and randomly distributed, stacking would rapidly seal them, making connected access to the substrate improbable. The multistacking analysis addressed this by modeling each 2D layer as a $_2$9 grid of hexagonal unit cells, each cell being either open or closed, and by considering seven hole configurations, HC1 through HC7, designed to represent different hole sizes, anisotropies, and directional crack-like morphologies. Layers were stacked up to $\Delta V$0 with hole areal fractions $\Delta V$1, and the surviving thru-hole areal fraction $\Delta V$2 was computed using a breadth-first search over 1600 Monte Carlo samples for each parameter set (Lee et al., 2022).

The geometric result is that laterally extended or anisotropic holes survive stacking much more effectively than compact isolated holes. For the two-layer case at $\Delta V$3, the reported surviving thru-hole fractions were $\Delta V$4, $\Delta V$5, $\Delta V$6, $\Delta V$7 for HC4, $\Delta V$8 for HC5, $\Delta V$9 for HC6, and $1$0 for HC7. The contrast between HC2 and HC3 is especially instructive: although HC3 had larger holes on average, HC2 produced slightly larger surviving thru-hole area because its holes were more irregular and elongated. With fixed total hole area, increased shape anisotropy and a larger number of individual holes improve interlayer overlap (Lee et al., 2022).

Across stack number $1$1, the decay of surviving connected area was described approximately by

$1$2

where $1$3 is the survival rate per stack. For HC1 at $1$4, the fitted value was $1$5, larger than the intuitive $1$6 because even HC1 occasionally formed larger-than-one-cell holes. The anisotropic crack-like cases decayed much more slowly; at 10 stacks, $1$7 for HC7 was about five orders of magnitude larger than for HC1. When $1$8 was varied from $1$9 to $2\%$0, the fitted $2\%$1 values ranged from $2\%$2 to $2\%$3 for HC1 and from $2\%$4 to $2\%$5 for HC7. Fitting earlier experimental GaN domain-area data to the same form yielded an experimental survival rate $2\%$6, which the simulations matched with $2\%$7 for HC1 and $2\%$8 for HC7. The broader implication is that THE in multistacked masks depends not simply on defect density but on the topology of connected defects (Lee et al., 2022).

5. Nucleation landscapes in spin-coated GO and rGO nanosieves

Solution-processed graphene oxide has been used to realize a nanosieve version of THE. In that approach, a $2\%$9-plane sapphire wafer was coated with $n \ge 2$0 SiO$n \ge 2$1, patterned with a hexagonal array of circular openings of $n \ge 2$2 diameter, spin-coated with GO, annealed at $n \ge 2$3 in N$n \ge 2$4 to form reduced graphene oxide, and then subjected to GaN growth by HVPE at $n \ge 2$5 for 1 min without a low-temperature GaN buffer layer. Three precursor solutions were compared: $n \ge 2$6 GO without TBA, $n \ge 2$7 GO without TBA, and $n \ge 2$8 GO with TBA; in the TBA case, $n \ge 2$9 of $m$0 TBAOH was added to $m$1 of $m$2 GO and diluted to $m$3, yielding a final TBAOH level of only $m$4 (Beak et al., 7 May 2025).

The annealed rGO films produced three distinct local nucleation outcomes. First, ELOG-like nucleation occurred on exposed substrate regions where the mask locally failed to cover sapphire. Second, THE-like nucleation occurred through appropriately thin areas, nanoscale voids, or percolative regions of the rGO stack. Third, complete nucleation suppression occurred on thickly stacked zones where precursor diffusion through the film was strongly hindered. In the no-TBA samples, all three behaviors coexisted because sparse regions and overstacked regions both persisted; increasing GO concentration shifted the average Raman G-band intensity upward but did not remove the low-intensity tail that signaled sparse coverage. By contrast, TBA improved flake dispersion, suppressed strong interflake aggregation, and yielded a narrower G-intensity distribution without the low-intensity tail, corresponding to a more uniform, moderately stacked rGO morphology that suppressed both ELOG-like and no-nucleation modes while expanding THE-like regions (Beak et al., 7 May 2025).

Within this framework, THE is governed by percolative transport pathways in a mask that is continuous enough to block large-scale direct exposure but porous enough to permit limited precursor access. The reported morphological signatures were consistent with this assignment: low G intensity and sparse AFM coverage correlated with ELOG-like nucleation and large merged GaN domains, intermediate uniform coverage with percolative gaps correlated with smaller, more sharply faceted domains and reduced coalescence, and high G intensity or overstacked zones correlated with empty openings after growth (Beak et al., 7 May 2025).

6. Self-adjusting $m$5-BN masks and scalable selective-area growth

A distinct development is the use of spin-coated, solution-processed $m$6-BN fragment stacks as self-adjusting masks for THE. In that implementation, chemically or mechanically exfoliated $m$7-BN flakes were redispersed in ethanol and spin-coated on $m$8-plane sapphire at 2400 rpm for 2 minutes, producing a thick, disordered, loosely stacked $m$9-BN fragment layer with thickness on the order of several hundred nanometers. GaN growth was then carried out with NH$m$0 at 1 slm and HCl at 10 sccm at $m$1 for 10 min (Ha et al., 16 May 2025).

Here the mask is not treated as rigid. “Self-adjusting” refers to localized structural reconfiguration of loosely stacked $m$2-BN fragments—shifting, lifting, or reorienting—in response to GaN growth. The mechanistic sequence is that precursors percolate through nanoscale interconnected voids within the thick fragment network, reach sapphire, nucleate epitaxial GaN beneath the mask, and then drive local rearrangement of the $m$3-BN as growth proceeds. Some nuclei remain buried as composite GaN/$m$4-BN regions, whereas others grow upward and emerge as isolated, faceted domains (Ha et al., 16 May 2025).

Structural evidence was assembled from SEM, Raman mapping, HR-TEM, SAED, and EDS. Plan-view SEM showed a small number of isolated GaN domains that were well aligned in orientation, while Raman mapping showed $m$5-BN signal around $m$6–$m$7 and GaN signal around $m$8, including GaN-related peaks in regions where SEM did not reveal obvious exposed GaN domains. Cross-sectional HR-TEM showed a several-hundred-nanometer-thick inhomogeneous composite layer between sapphire and the surface, and SAED showed identical crystallographic orientations for sapphire, interfacial GaN, composite regions, and pure GaN domains, with additional diffraction spots from randomly oriented embedded $m$9-BN fragments. EDS confirmed the presence of Ga and N even beneath regions without exposed surface domains (Ha et al., 16 May 2025).

The paper presents indirect evidence that threading dislocation propagation is suppressed, including well-faceted isolated domains, absence of clear vertical threading-like contrast beneath isolated domains in TEM, preserved crystallographic alignment in SAED, and the resemblance of the self-adjusting multilayer-like masking to dislocation-filtering strategies used in ELOG. At the same time, it explicitly notes that TDD was not directly quantified over a statistically large area because HRTEM samples are too local. The practical significance claimed for this route is selective-area GaN growth without transfer or lithography, with relevance to micro-LEDs and photonic integration platforms (Ha et al., 16 May 2025).

7. Quantitative control of THE by engineered perforation

THE has also been cast into a quantitatively tunable form using O$(100)$0-plasma-perforated graphene on $(100)$1-plane sapphire. In this case, atomically thin graphene functions as a nanoscale mask, O$(100)$2 plasma creates controlled perforations, and the perforated-area fraction $(100)$3 becomes the central process variable. The physical picture is direct: intact graphene inhibits direct nucleation, whereas the plasma-opened areas expose sapphire and act as epitaxial access points for GaN nucleation (An et al., 10 Sep 2025).

The reported kinetic trends are correspondingly simple. The nucleation-site density scales with $(100)$4, while the nucleation-delay time decreases approximately as $(100)$5. Time-resolved areal coverage and domain counts exhibit systematic $(100)$6-dependent trends: low $(100)$7 gives a long nucleation delay, few domains, and slow coverage increase; larger $(100)$8 yields earlier nucleation, faster domain-count increase, and earlier coalescence. A coarse-grained kinetic Monte Carlo model reproduced these trends using adatom arrival, surface diffusion, attachment at exposed sapphire within perforations, and coalescence as the first front-front contact between laterally growing domains. Fitting the simulation data yielded onset times $(100)$9 that closely matched independently observed no-growth thresholds, specifically 28.5 s versus $50 \, \text{nm}$00 s for Set 1 and 38 s versus $50 \, \text{nm}$01 s for Set 2 (An et al., 10 Sep 2025).

This establishes a process-window interpretation of THE masks. Too little plasma exposure leaves $50 \, \text{nm}$02 too low for efficient nucleation; sufficient plasma exposure activates through-hole formation and gives predictable nucleation density and growth timing; excessive exposure risks loss of selectivity by over-damaging the mask. In that sense, THE can be treated not only as a mechanistic explanation for growth on imperfect 2D masks but also as a quantitatively engineerable selective-epitaxy workflow in which connected exposed area governs early-stage GaN nucleation statistics (An et al., 10 Sep 2025).