††thanks: These authors contributed equally: Dongsoo Jang, Chulwoo Ahn,
Youngjun Lee††thanks: These authors contributed equally: Dongsoo Jang, Chulwoo
Ahn, Youngjun Lee††thanks: These authors contributed equally: Dongsoo Jang,
Chulwoo Ahn, Youngjun Lee††thanks: email<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>email<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>email<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
# Thru-Hole Epitaxy: Is Remote Epitaxy Really Remote?

Dongsoo Jang  Department of Physics, Kyung Hee University, Seoul 02447, Korea
Chulwoo Ahn  Department of Information Display, Kyung Hee University, Seoul
02447, Korea  Youngjun Lee  Department of Physics, Kyung Hee University, Seoul
02447, Korea  Seungjun Lee  Department of Physics, Kyung Hee University, Seoul
02447, Korea  Hyunkyu Lee  Department of Information Display, Kyung Hee
University, Seoul 02447, Korea  Donghoi Kim  Department of Information
Display, Kyung Hee University, Seoul 02447, Korea  Young-Kyun Kwon∗,
Department of Physics, Kyung Hee University, Seoul 02447, Korea  Department of
Information Display, Kyung Hee University, Seoul 02447, Korea  Jaewu Choi∗,
Department of Information Display, Kyung Hee University, Seoul 02447, Korea
Chinkyo Kim∗, Department of Physics, Kyung Hee University, Seoul 02447, Korea
Department of Information Display, Kyung Hee University, Seoul 02447, Korea

###### Abstract

The remote epitaxy was originally proposed to grow a film, which is not in
contact but crystallographically aligned with a substrate and easily
detachable due to a van der Waals material as a space layer. Here we show that
the claimed remote epitaxy is more likely to be nonremote ‘thru-hole’ epitaxy.
On a substrate with thick and symmetrically incompatible van der Waals space
layer or even with a three-dimensional amorphous oxide film in-between, we
demonstratively grew GaN domains through thru-holes via connectedness-
initiated epitaxial lateral overgrowth, not only readily detachable but also
crystallographically aligned with a substrate. Our proposed nonremote thru-
hole epitaxy, which is embarrassingly straightforward and undemanding, can
provide wider applicability of the benefits known to be only available by the
claimed remote epitaxy.

## Introduction

It is a golden rule that epitaxial growth of a crystalline film is allowed
only by direct bonding to a crystalline substrate. Extremely surprising
studies reported that a crystalline film was epitaxially grown remotely
without direct bonding to an underlying substrate despite an ultrathin defect-
free 2D overlayer placed in-between, which was named as remote
epitaxy.Kim_Nature_544_340 ; Kong_NM_17_999 ; Jeong_SA_6_eaaz5180  An earlier
study, for instance, claimed that GaN can be remotely grown through only up to
two layers of graphene but not even a single layer of $h$-BN on underlying
GaN.Kong_NM_17_999  This result was explained by the teleported influence of
the GaN substrate that was not completely screened.Kong_NM_17_999  Once the
thickness of an inserted 2D material becomes above a critical value, the grown
film is no longer crystallographically aligned with the underlying
substrate.Kong_NM_17_999 ; Jeong_SA_6_eaaz5180

The remote epitaxy strictly requires not only the defect-free growth of 2D
material but also the state-of-the-art transfer with precise layer-number
control. Nevertheless, great attention has been paid to remote epitaxy since
it has been believed to provide the great benefit of easy separation of the
film, which is crystallographically aligned with a substrate.Kong_NM_17_999 ;
Kim_Nature_544_340 ; Jeong_SA_6_eaaz5180  Several other studies have also
demonstrated the facile detachment of a film taken as evidence of remote
epitaxy.Jeong_Nanoscale_10_22970 ; Jeong_APL_113_233103 ; Guo_NL_20_33 ;
Jeong_ACSANM_3_8920 ; Bae_NM_18_550  Strictly speaking, however, the easy
detachability may not necessarily originate from the ‘remoteness’ of the
remote epitaxy, but simply indicates that the binding between the film and
space layer/substrate is weaker than the adhesion of the film to a detacher
such as a thermal release tape. In fact, the entire remoteness of the remote
epitaxy across the interface has never been rigorously verified yet. The
estimated potential fluctuation across the surface of 2D material/substrate
given as theoretical evidence of remote epitaxy was only one-tenth of thermal
energy at growth temperature, and more importantly, the corresponding
potential profile is essentially uncorrelated to that of the bare
substrate.Kong_NM_17_999  Moreover, it turned out that the overlooked
connectedness directly to the substrate through the space layer (Extended Data
Fig. 7 of Ref. [1]) should not have been neglected. Thus, it is physically
more reasonable to presume that the claimed remote epitaxy is not likely to be
remote.

Figure 1: Logic flow chart of growth types categorization. Five different
growth types are categorized on basis of alignment, easy detachability, and
the existence of thru-holes in a 2D insertion layer beneath the grown domain.
Performed processes or flows are denoted by solid boxes or lines, whereas
dashed boxes or lines indicate unperformed processes or flows. Note that
remote epitaxy was claimed as a growth type in a farfetched manner on basis of
insufficient experimental evidence by which [GT1] or [GT2] cannot be
specified.

In order to support our argument above, we elaborate on the logic related to
growth types categorization. Let us consider a single domain grown on a 2D
layer transferred onto a single crystalline substrate. The growth type [GT]
for this domain can be categorized into one of the following five as shown in
Fig. 1: [GT1] remote epitaxy, [GT2] growth type X, [GT3] epitaxial lateral
overgrowth (ELOG), [GT4] van der Waals epitaxy, and [GT5] growth with
misaligned orientation. These GT’s were categorized on basis of alignment (A
or A′), easy detachability (B), and the existence of at least one thru-hole in
the 2D insertion layer beneath the grown domain (C). The presence of at least
one thru-hole in the $i$-th region of the 2D insertion layer beneath the
growth domain is labeled as (Ci). Thus, (C) is equivalent to $C_{1}\vee
C_{2}\vee\cdots\vee C_{N}$ where $N$ is the number required for the union of
1-st, 2-nd, $\cdots$, $N$-th region to fully cover the _entire_ region of 2D
insertion layer beneath the growth domain. On the other hand, the logical
negation of (Ci) or NOT (Ci), denoted as $(\overline{\mathrm{C}_{i}})$, is the
complete absence of thru-hole in the $i$-th region of 2D insertion layer
beneath the growth domain. Likewise, $(\overline{\mathrm{C}})$, indicating NOT
(C), is the complete absence of thru-hole in the _entire_ region of 2D
insertion layer beneath the growth domain. Of course, these growth types are
not necessarily exclusive to one another, and under certain circumstances,
mixed growth types may be observed among various domains or within a merged
film. However, for the simplicity of discussion, we assume that one growth
type is associated with one single domain.

The necessary and sufficient condition for [GT1] remote epitaxy is the
combination of (A) and $(\overline{\mathrm{C}})$. The verification of
$(\overline{\mathrm{C}})$ requires a full series of high-resolution cross-
sectional transmission electron microscopy (HR-TEM) images all across the
interface, which has never been given yet. This kind of extensive HR-TEM
measurements is, however, impractical even for micro-sized domains, so that
the verification of $(\overline{\mathrm{C}_{1}})$, which was typically shown
by a single HR-TEM image in the previous papers on remote epitaxy, was
provided as evidence for remote epitaxy instead of $(\overline{\mathrm{C}})$.
On the other hand, we named any growth type, which satisfies (A), (B), and
(C), as [GT2] growth type X, which is definitely not [GT1] remote epitaxy. As
can be readily inferred from Fig. 1, however, a connectedness-initiated
epitaxy through very small thru-holes can be a candidate for [GT2] growth type
X because HR-TEM in the thru-hole-free region of the domain grown by [GT2]
growth type X can reveal that $(\overline{\mathrm{C}_{i}})$ is satisfied and
only a few small thru-holes may allow easy detachability. In our manuscript,
the existence of growth type X was explicitly verified and we identified this
growth type X as thru-hole epitaxy. [GT2] Thru-hole epitaxy distinctively
refers to the case in which grown domains are not only aligned with a
substrate but also easily detached. Easy detachability is the main distinction
of [GT2] thru-hole epitaxy differentiating from conventional [GT3] ELOG. As
can be seen from Fig. 1, we would like to emphasize that the combination of
(A), (B) and $(\overline{\mathrm{C}_{1}})$ is not enough to specify either
[GT1] remote epitaxy or [GT2] growth type X, i.e., thru-hole epitaxy. In other
words, the combination of (A), (B) and $(\overline{\mathrm{C}_{1}})$ is not
sufficient enough to verify the existence of [GT1] remote epitaxy. Note that
remote epitaxy was claimed as a growth type in a farfetched manner on basis of
insufficient experimental evidence by which [GT1] or [GT2] cannot be
specified.

Furthermore, we show that all the other claimed evidences of remote epitaxy
are also evidences of thru-hole epitaxy. (See Supplementary Note1 for more
detailed explanation.) Thus, either remote epitaxy or thru-hole epitaxy cannot
be specified on basis of all the combined experimental evidences, claimed by
remote epitaxy, which are just necessary conditions of remote epitaxy. Only if
$(\overline{\mathrm{C}_{1}})\wedge(\overline{\mathrm{C}_{2}})\wedge\cdots\land(\overline{\mathrm{C}_{N}})$
equivalent to $(\overline{\mathrm{C}})$ were verified, the existence of [GT1]
remote epitaxy would be verified. The flaw of logic in the previous papers on
remote epitaxy is that the existence of [GT1] remote epitaxy was claimed to be
confirmed only by $(\overline{\mathrm{C}_{1}})$ instead of
$(\overline{\mathrm{C}})$ although other evidences were given. Moreover, our
computational simulation revealed that the theoretical evidence of [GT1]
remote epitaxy is questionable as described below. With appropriate
justification ((i) logic flow chart, (ii) our experimental results, and (iii)
our computational simulation), we claim that the existence of remote epitaxy
has not been verified yet and is questionable.

It appears that the original proposers of remote epitaxy recently realized the
existence of thru-holes and recognized that the previous experimental
evidences for remote epitaxy may not be enough to specify either [GT1] remote
epitaxy or [GT2] thru-hole epitaxy.Kim_ACSNano_15_10587  In order to find out
the role of thru-holes and specify either remote epitaxy or thru-hole epitaxy,
they designed and carried out experiments, but they reached a hasty conclusion
in which [GT2] was excluded even in the presence of thru-
holes.Kim_ACSNano_15_10587  (See Supplementary Note2 for the more detailed
explanation.)

## Results and discussion

Based on the argument made above, we hypothesized that the claimed remote
epitaxy may simply be ‘thru-hole’ epitaxy composed of two processes through
nanoscale holes sparsely distributed in the space layer: nucleation on the
exposed substrate and lateral growthNam_APL_71_2638  over the space layer. To
verify our proposed hypothesis, we demonstratively grew epitaxial GaN domains
under various et mediocri conditions, which are far from those required by the
state-of-the-art growth and transfer indispensable in the claimed remote
epitaxy. By doing so, we reveal that our proposed nonremote thru-hole epitaxy
can equally well provide in an unprecedentedly straightforward manner the
benefits, which are supposedly accompanied only by the claimed remote epitaxy,
such as facile detachability and crystallographic alignment with a substrate.
In the following, we first provide computational results showing the
unfeasibility of remote epitaxy and then experimental results verifying thru-
hole epitaxy.

### Computational evidence questioning remote epitaxy

Figure 2: Structural configurations and surface potential profiles of sapphire
with and without graphene or hBN overlayer. a–c Structural configurations of
(a) bare $r$-sapphire, (b) graphene, and (c) $h$-BN monolayer on the
$r$-sapphire, and their surface potential profiles evaluated at a distance $d$
from the respective top surfaces. The distance $d$ was chosen to be 2.0 Å and
3.0 Å on the bare $r$-sapphire and each of the overlayers, which are
approximately bonding distances between GaN and the respective surfaces. d
Side views of bilayers of graphene and h-BN on the $r$-sapphire. e The maximum
potential differences $\Delta V$ observed between the Ga and N sites of a Ga-N
dimer considered as an initial seed depicted in (a–c). The infinity indicates
the 2D overlayer without the $r$-sapphire substrate. The topmost atomic layer
overlaid on each color-coded potential profile is a guide for the eyes. The
color bars indicate the potential variation relative to the average potential
value set to be zero. Note that the potential variations on the overlayers
were color-coded within a much narrower range. Each 2D space
layer/$r$-sapphire is composed of a $2\times 3$ rectangular cell of the
$r$-sapphire and a rectangular cell modified from a
$(\sqrt{13}\times\sqrt{13})R13.9^{\circ}$ cell of a 2D overlayer, which
somewhat mimics a naturally-occurring incommensurate stacking.

The remote epitaxy proposed by earlier studiesKong_NM_17_999 ;
Kim_Nature_544_340 ; Jeong_SA_6_eaaz5180 ; Jeong_Nanoscale_10_22970 ;
Jeong_APL_113_233103 ; Guo_NL_20_33 ; Jeong_ACSANM_3_8920 ; Bae_NM_18_550  was
validated mainly by the surface potential distribution calculated over a space
layer complying with that of a substrate. We discussed some questions raised
from the previous calculations in Supplementary Note3. To verify whether such
validation is indeed valid, we evaluated the electrostatic potential
distributions on various surfaces including not only bare substrates such as
sapphire, Si, GaAs, GaN, and LiF but also those substrates with a 2D graphene
or $h$-BN overlayer, which will later be denoted as ‘overlayer/substrate’,
using the first-principles density functional theory (DFT) calculations. As an
exemplary demonstration, we display the surface structures of the bare
$r$-sapphire, graphene/$r$-sapphire, and $h$-BN/$r$-sapphire in the top view
and their calculated surface potential profiles in Figs. 2(a–c), respectively.
Here we emphasize that a computationally-convenient small commensurate
stacking configuration introduced to resolve the lattice mismatch between the
substrate and the 2D overlayer instigates an artificially periodic potential
fluctuation, which would lead to a misinterpretation, as discussed later. To
mimic a naturally-occurring incommensurate stacking, we thus constructed
relatively a large supercell structure composed of 2D overlayer/$r$-sapphire.

As shown in the lower part of Fig. 2a, the bare $r$-sapphire without a space
layer generates a huge potential variation, which is attributed to both a
strong ionic characteristic of Al-O bonds and an uneven surface configuration
of the substrate. When a monolayer ($n=1$) of the 2D space overlayer, either
graphene or $h$-BN, covers the $r$-sapphire, not only is the surface potential
variation drastically reduced due to the screening of the space layer, but it
does not reflect the shape of the potential profile on the $r$-sapphire
substrate, as shown in the lower parts of Figs. 2b and c. With one more layer
($n=2$) of the overlayer material, not to mention the complete dissimilarity
between its surface potential distribution and that on the bare substrate, the
surface potential variation becomes much smaller, being almost close to that
over the overlayer itself without the substrate, since the second layer is
essentially flat as shown in Fig. 2d. Furthermore, the potential variations
for $n{\geq}3$ cases were found to be almost the same as that of either
isolated graphene or $h$-BN, as shown in Supplementary Fig. 1.

To examine whether the remote epitaxy would indeed have been eventuated on
defect-free 2D space materials, we estimated the potential difference $\Delta
V$ undergone by a Ga-N dimer regarded as a primordial growth seed that should
anchor on the 2D overlayer with a similar orientation to on the bare substrate
to guarantee the remote epitaxy. Figure. 2e shows $\Delta V$ as a function of
the layer numbers $n$ of 2D graphene and $h$-BN overlayers. Even with $n=1$,
$\Delta V$ was calculated to be only $1\sim 2$ % of that on the bare sapphire,
and rapidly converged to the value on the 2D overlayer without the substrate
when $n{\geq}2$. For comparison, over other substrates, such as Si, GaAs, GaN,
and LiF, we evaluated their potential variations at $d=3.0$ Å, near which the
2D space layer would locate, above their surfaces, to know over which
substrate the potential variations emerge through a 2D space layer. As shown
in Supplementary Fig. 2, the magnitude of the evaluated potential variation
only over the GaN substrate is similar to that over the $r$-sapphire, but
those over the other substrates are much smaller. Thus, the teleportation of
substrate potential variations through a 2D space layer is not likely to occur
over any kind of substrates as seen in Fig. 2 for $r$-sapphire.

We further investigated the potential variations on the $c$\- and $m$-sapphire
substrates while increasing the layer number $n$ of the $h$-BN space material
from $n=0$ to $n=3$, whose trends are essentially identical to that on the
$r$-sapphire case, as shown in Supplementary Fig. 3. To verify the effect of
an artificially-generated periodicity caused by the strain applied to forcibly
match the lattice mismatch between the substrate and the space layer as
mentioned above, we evaluated the surface potential profiles over various
stacking configurations of $h$-BN/$c$-sapphire, the combination of which
clearly evinces such stacking effect. As displayed in Supplementary Fig. 4,
the calculated potential variations are very sensitive to a choice of stacking
configurations. Especially, in small supercell configurations, local potential
variations look as if that of the substrate would be reflected over the 2D
space layer, but this is a misleading artifact caused by such a forcibly
matched stacking to make it commensurate. Therefore, the potential fluctuation
of 2D material/substrate does not truly reflect the orientation and
periodicity of the underlying substrate if the artifact originating from
artificial stacking configurations is simply excluded. For a detailed
explanation, see Supplementary Note4.

Based on our calculations, the remoteness of the claimed remote
epitaxyKong_NM_17_999 ; Kim_Nature_544_340 ; Jeong_SA_6_eaaz5180 ;
Jeong_Nanoscale_10_22970 ; Jeong_APL_113_233103 ; Guo_NL_20_33 ;
Jeong_ACSANM_3_8920 ; Bae_NM_18_550  is conceptually and strongly
questionable, and thus it should be replaced by a genuine growth mechanism,
nonremote thru-hole epitaxy. The proposed thru-hole epitaxy enabled us to grow
epitaxial GaN domains, which still exhibit all the benefits from the seemingly
remote epitaxy, in the growth regime even prohibited by the claimed remote
epitaxy.

### Thru-hole epitaxy enabled by connectedness

Figure 3: Crystallographic alignment of GaN domains grown on
$h$-BN/$r$-sapphire verified by SEI and XRD. a An SEI of typical GaN domains
grown on $h$-BN/$r$-sapphire. The garble-roof-shaped GaN
domainsShin_JAC_46_443  are aligned in parallel. b–c X-ray scattering
intensity of GaN and $r$-sapphire in (b) $\theta$-2$\theta$ and (c) $\phi$
scan. The observed [112̄0]-oriented GaN domains are exactly aligned with
$r$-sapphire as if they were grown on the bare $r$-sapphire substrate as
indicated by $\Delta\phi_{r1}$=180∘ and
$\Delta\phi_{r2}$=133∘.Chen_JJAP_42_L818 ; Imer_JCG_306_330

To verify our proposed growth mechanism, we grew GaN domains on a thick and
polycrystalline $h$-BN space layer transferred onto $r$-, $m$\- and
$c$-oriented sapphire substrates. The thickness of $h$-BN was deliberately
chosen by multiple transfers to make the influence of a substrate completely
negligible and to entirely exclude the remoteness of the claimed remote
epitaxy. It was surprisingly observed that those GaN domains grown on a
$h$-BN/$r$-sapphire substrate exhibit the [112̄0]-orientation with a garble-
roof-shape as if directly grown on the bare $r$-sapphire substrate, as shown
in a secondary electron image (SEI) of Fig. 3a. Even more surprisingly, those
[112̄0]-oriented GaN domains were all in-plane aligned with one another on the
thick and randomly-oriented polycrystalline $h$-BN layer, (Supplementary Fig.
5) clearly indicating that the growth result is not what is expected in van
der Waals epitaxy but exactly what would be expected in the claimed remote
epitaxy. The crystallographic alignment of those GaN domains with the
$r$-sapphire substrate is confirmed by X-ray scattering measurement as shown
in Figs. 3b and c. Likewise, similar results were observed on $h$-BN/$c$\- and
$m$-sapphire. (Supplementary Fig. 6) We observed the exact one-to-one
correspondence in Bragg peaks of GaN domains respectively grown on
$h$-BN/sapphire and on bare sapphire. (Supplementary Fig. 7) It seemed that we
dramatically extended the applicable growth regime of the claimed remote
epitaxy, resulting from the crystallographic information of sapphire
teleported to GaN even across a thick $h$-BN space layer.

Figure 4: TEM and FFT verifying the connectedness. a High-resolution cross-
sectional TEM image, taken from the region enclosed by a dashed cyan box shown
in Supplementary Fig. 8a and b. b–c The fast Fourier transforms (FFTs) of
[112̄0]-oriented GaN and $r$-sapphire enclosed respectively by the (b) orange
and (c) green boxes marked in (a). d High-resolution cross-sectional TEM
image, taken from the region enclosed by a dashed yellow box shown in
Supplementary Fig. 8b. e–f GaN is seen to be grown directly on $r$-sapphire
indicating the connectedness achieved, (Supplementary Fig. 9a) and their
crystallographic alignment was verified by FFTs in (e) and (f). Note that
there are crystalline $h$-BN layers, marked in (a), which embed carbon-based
amorphous materials. (Supplementary Fig. 9b) They are thought to originate
from the residue of PMMA used for $h$-BN transfer and do not make any
influence on the thru-hole epitaxy. The slight tilt of a line along the
laterally aligned Bragg peaks of [112̄0]-oriented GaN with respect to that of
$r$-sapphire shown in FFT is due to the characteristics of crystallographic
orientation of $r$-sapphire, not due to the stress relaxation.

Then, what caused this astonishing crystallographic alignment of GaN domains
with underlying sapphire substrates even covered by the thick and
polycrystalline $h$-BN? To answer this question, we extensively performed TEM
measurement. Figure 4a shows a high-resolution cross-sectional TEM image
revealing the interfacial region of GaN and $r$-sapphire with a thick $h$-BN
space layer in-between. (Supplementary Fig. 8) Enigmatically, the fast Fourier
transformation (FFT) analysis shown in Figs. 4b and c revealed that GaN, which
is [112̄0]-oriented, right above thick $h$-BN was aligned with $r$-sapphire
consistent with XRD measurements shown in Figs. 3b and c. It was unveiled that
the origin of this striking crystallographic alignment of GaN is thru-hole
epitaxy. As shown in Fig. 4d, [112̄0]-oriented GaN was directly connected to
the $r$-sapphire substrate through thru-holes in $h$-BN in spite of multiple
transfers of $h$-BN. (Supplementary Fig. 9) As shown in Fig. 4e and f, FFTs
near thru-holes through which GaN and sapphire are connected show the
crystallographic alignment of GaN with underlying sapphire. It can be
naturally inferred that GaN nucleated on exposed sapphire through thru-holes
must have laterally grown over a thick $h$-BN space layer as seen in Fig. 4a.
Our experimental results, absolutely unexpected by the claimed remote epitaxy,
were made possible not because the remoteness was mysteriously enhanced but
because the connectedness was securely established.

It is the first direct evidence of our proposed thru-hole epitaxy, which is
applicable to any systems and also even to the claimed remote epitaxy. It is
farfetched that the claimed remote epitaxy was attributed to remoteness, but
it is rather reasonable to connectedness secured by thru-hole epitaxy, as
verified by our computational results described above. In a previous study, as
a matter of fact, this same kind of connectedness was also observed on small
areas but unfortunately disregarded as a minor effect.Kim_Nature_544_340
Being above the critical layer thickness or losing the connectedness is the
reason why the claimed remote epitaxy fails. Thus, we claim that the
connectedness serving as a control parameter is utilized as a true criterion
not only for the claimed remote epitaxy but also for the thru-hole epitaxy. We
showed how to control the extent of the connectedness by intentionally
adjusting the thickness of and deliberately not improving the quality of a 2D
space layer. (Supplementary Fig. 10) We emphasize that the better the quality
of a 2D space layer the lower the density of thru-holes. As a result, the
weaker the connectedness the smaller the critical value of the thickness,
above which the claimed remote epitaxy or the thru-hole epitaxy is
forbidden.Kong_NM_17_999 ; Jeong_Nanoscale_10_22970  Therefore, the thru-hole
epitaxy of crystallographically aligned GaN on $h$-BN/sapphire does not
require the state-of-the-art perfection of $h$-BN at all.

The readily facile detachability of a grown film crystallographically aligned
with an underlying substrate is the exclusive benefit of the claimed remote
epitaxy. To check whether the grown film by thru-hole epitaxy is readily
detachable as well, we carried out the detachability experiment. Supplementary
Fig. 11 shows that GaN domains were readily detached simply by using a thermal
release tape although they were connected to the substrate by thru-holes.
(Supplementary Fig. 12) We emphasize that there is a critical connectedness
below which all the benefits of the claimed remote epitaxy can be obtainable.
Unlike the stringent requirement imposed by the claimed remote epitaxy, the
connectedness below such critical connectedness is readily achievable.
(Supplementary Fig. 13)

### Extended demonstration of thru-hole epitaxy

Figure 5: Compelling evidences of thru-hole epitaxy through a SiO2 space
layer. a SEI of in-parallel aligned GaN domains with garble-roof shape grown
on $h$-BN/SiO2/$r$-sapphire. b–c X-ray scattering intensity of GaN and
$r$-sapphire in (b) $\theta$-2$\theta$ and (c) $\phi$ scan. Those
[112̄0]-oriented GaN domains are still crystallographically aligned with
$r$-sapphire in spite of 50-nm-thick SiO2 space layer verified by
$\Delta\phi_{r3}$=94∘, $\Delta\phi_{r4}$=86∘, and $\Delta\phi_{r5}$=5∘. d
High-resolution cross-sectional TEM image, taken from the region enclosed by a
dashed red box in Supplementary Fig. 14a and b, and FFTs for various regions.
TEM and FFTs of the regions enclosed by the orange, blue, and green boxes
confirm the connectedness by thru-hole epitaxy (shaded in red) and
crystallographic alignment.

Our experimental results showed that the connectedness by thru-holes is
crucial to achieving the crystallographic alignment of a film with a 2D-layer-
covered substrate. As long as the connectedness is maintained, the thru-hole
epitaxy was found to be valid regardless of either the type or the thickness
of a space layer. Our proposed mechanism might, however, be challenged by the
speculation that the growth was partly initiated over the $h$-BN regions the
thickness of which was less than a critical value of the claimed remote
epitaxy. To unambiguously exclude the speculation, we introduced an additional
50-nm-thick SiO2 space layer between $h$-BN and $r$-sapphire to form
SiO2/$r$-sapphire with and without $h$-BN overlayer, which should completely
suppress the remoteness. Subsequently, nanoscale openings were produced in
SiO2 to achieve connectedness. This experimental configuration fully
guarantees the thru-hole epitaxy but completely eliminates the possibility of
the remote epitaxy. As expected from the thru-hole epitaxy, GaN domains grown
in these experimental configurations were crystallographically aligned with
$r$-sapphire as shown in Figs. 5(a–c). This result indicates that we
successfully achieved the connectedness by intentionally creating nanoscale
openings, (See Methods section) verified by TEM analysis as shown in Fig. 5d
and Supplementary Fig. 14. The thru-hole epitaxy is robustly manifested even
with a SiO2 space layer.

Moreover, we also successfully detached those [112̄0]-oriented GaN domains
from $h$-BN/SiO2/$r$-sapphire simply by using a thermal release tape as shown
in Supplementary Fig. 15. Here we would like to emphasize that the
crystallographic alignment is associated with the connectedness, whereas
$h$-BN or any 2D van der Waals space layer plays a role in not transferring
the crystallographic information through but only in allowing the film grown
above to be readily detachable.

We have shown that ostensibly ‘remote’ epitaxy based on remoteness is evinced
by the nonremote thru-hole epitaxy originating from connectedness. Our
proposed thru-hole epitaxy mechanism maintains every advantage (e.g.,
undemanding detachability, crystallographical alignment with an underlying
substrate, independence of space layer symmetry) of the remote epitaxy in an
embarrassingly straightforward and undemanding manner. It was also
demonstrated that our method can be readily extended to hBN/substrate even
with a thick SiO2 film in-between without compromising the advantages
described above. This growth behavior can open possibilities for the great
advantage of detachable heteroepitaxial film growth with no constraint on the
state-of-the-art transfer perfection of 2D materials and the thickness of
which should be less than a few layers imposed by the claimed remote epitaxy.

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## Methods

Processes of the thru-hole epitaxy.

The thru-hole epitaxy consists of the following processes, growth and transfer
of $h$-BN, and growth of GaN, which were carried out with no special
optimization. Despite no optimization, we were able to accomplish the thru-
hole epitaxy to the extent demanded, indicating that state-of-the-art
perfection is not necessary for the thru-hole epitaxy.

Growth of $h$-BN.

A polycrystalline $h$-BN thin film was grown on a Cu foil by chemical vapor
deposition (CVD) at 1000∘C with hydrogen (50 sccm) and argon (100 sccm) as a
carrier gas as shown in Supplementary Fig. 5. Growth was carried out with
ammonia borane (NH3BH3) as a precursor for two hours after two-hour annealing
of the Cu foil. The thickness of $h$-BN was roughly estimated to be 2–4
nanometer by transmission electron microscopy. The chemical identification of
$h$-BN is shown in Supplementary Fig. 9.

Transfer of $h$-BN.

This CVD-grown $h$-BN was transferred onto $r$-, $c$-, and $m$-sapphire
substrates by applying a wet transfer method with poly (methyl methacrylate)
(PMMA). PMMA was spin-coated over $h$-BN grown on a Cu foil, which was then
etched with FeCl3. PMMA/$h$-BN was transferred onto the desired substrate, and
then that was rinsed twice with deionized water. After that, the PMMA was
removed by acetone, and $h$-BN/substrate was cleaned by isopropyl alcohol. The
extent of the connectedness was intentionally controlled by changing the
number of transfers made. For multiple transfers of $h$-BN, the transfer steps
listed above were simply repeated.

Creation of thru-holes in SiO2.

We intentionally created the connectedness by introducing thru-holes in a SiO2
space layer. Thru-holes were produced in SiO2 during the pre-heating step of
the GaN growth by utilizing FeCl3, which is known to thermally decompose
SiO2.Jang_CAP_16_93

Growth of GaN.

GaN was grown on $h$-BN/sapphire or $h$-BN/SiO2/sapphire by using hydride
vapor phase epitaxy at 960∘C with HCl (10 sccm) flown over metal Ga and NH3
(1500 sccm) carried by N2.

Electron microscopy, focused ion beam, and EDS.

Transmission electron microscopy (TEM) and selected area diffraction (SAD)
measurements were performed by using a Thermo Fisher TitanTM80-300 microscope
operated at 300 kV. The available point resolution is better than 1 Å at the
operating acceleration voltage. TEM images were recorded by using a charge-
coupled camera (Gatan, Oneview095). Scanning TEM (STEM) & energy dispersive
spectroscopy (EDS) analysis with Super-X EDS was made by using a Thermo Fisher
Talos F200X at 200 kV with a probe size of $\sim$1 nm. Secondary electron
images (SEIs) were taken by using Hitachi S-4700. For the preparation of TEM
samples, focused ion beam (Hitachi, NX5000) was utilized.

Computational simulation.

First-principles calculations were performed using the density functional
theoryKohn1965  as implemented in Vienna ab initio simulation package
(VASP)Kresse1996 . The electronic wavefunctions were expanded by plane wave
basis with a kinetic energy cutoff of 520 eV. We employed the projector-
augmented wave pseudopotentialsBlochl1994 ; Kresse1999  to describe the
valence electrons, and treated exchange-correlation functional within the
generalized gradient approximation of Perdew-Burke-Ernzerhof.Perdew1996
Interlayer interactions were incorporated with Grimme-D2 van der Waals
correction.grimme-d2  To reduce long-range interactions from neighboring cells
located along the out-of-plane or growth direction, we included a sufficiently
large vacuum region of 20 Å. The Brillouin zone (BZ) of each structure was
sampled using a separation of 0.04 Å-1 $k$-point mesh according to the
Monkhost-Pack scheme.MP  The structures were relaxed until all forces became
smaller than 0.02 eV/Å. The exchange-correlation potential was excluded in
potential fluctuation maps because exchange-correlation potential on a long
distance from the surface is incorrect within standard DFT.Kong_NM_17_999 ;
LVTOT  Various 2D overlayer/sapphire supercell structures were constructed to
avoid artificially generated periodic potentials.

## Acknowledgments

We gratefully acknowledge financial support from the Korean government (MSIT,
MOE) through the National Research Foundation (NRF) of Korea
(NRF-2019R1A2C1005417, NRF-2019R1F1A1063643, NRF-2020R1F1A1050725,
NRF-2020R1A5A6017701,
NRF-2021R1A5A1032996, BK21 FOUR Program). Some portion of our computational
work was done using the resources of the KISTI Supercomputing Center
(KSC-2020-CRE-0011).

## Author Contributions

Y.L. and S.L. carried out the computational simulation, supervised by Y.-K.K.
C.A. performed the growth and transfer of $h$-BN, supervised by J.C. D.J
carried out the growth and transfer of GaN with assistance from H.L. and D.K.,
supervised by C.K. Data analysis and figure preparation of XRD and TEM were
performed by D.J. and C.K. The manuscript was written by Y.-K.K., J.C., and
C.K. with assistance from all the authors.

## Competing interests

The authors declare no competing interests.

## Data availability

All data are available in the main text or the supplementary information.

See pages ,- of SI.pdf