# Control over epitaxy and the role of the InAs/Al interface in hybrid two-
dimensional electron gas systems

Erik Cheah<EMAIL_ADDRESS>Solid State Physics Laboratory, ETH Zurich,
8093 Zurich, Switzerland  Daniel Z. Haxell  IBM Research Europe - Zurich, 8803
Rüschlikon, Switzerland  Rüdiger Schott  Solid State Physics Laboratory, ETH
Zurich, 8093 Zurich, Switzerland  Peng Zeng  ScopeM, ETH Zurich, 8093 Zurich,
Switzerland  Ekaterina Paysen  Paul-Drude-Institut für Festkörperelektronik,
Leibniz-Institut im Forschungsverbund Berlin e. V., 10117 Berlin, Germany
Sofieke C. ten Kate  IBM Research Europe - Zurich, 8803 Rüschlikon,
Switzerland  Marco Coraiola  IBM Research Europe - Zurich, 8803 Rüschlikon,
Switzerland  Max Landstetter  Solid State Physics Laboratory, ETH Zurich, 8093
Zurich, Switzerland  Ali B. Zadeh  ScopeM, ETH Zurich, 8093 Zurich,
Switzerland  Achim Trampert  Paul-Drude-Institut für Festkörperelektronik,
Leibniz-Institut im Forschungsverbund Berlin e. V., 10117 Berlin, Germany
Marilyne Sousa  IBM Research Europe - Zurich, 8803 Rüschlikon, Switzerland
Heike Riel  IBM Research Europe - Zurich, 8803 Rüschlikon, Switzerland
Fabrizio Nichele  IBM Research Europe - Zurich, 8803 Rüschlikon, Switzerland
Werner Wegscheider  Solid State Physics Laboratory, ETH Zurich, 8093 Zurich,
Switzerland  Quantum Center, ETH Zurich, 8093 Zurich, Switzerland  Filip
Krizek  Solid State Physics Laboratory, ETH Zurich, 8093 Zurich, Switzerland
IBM Research Europe - Zurich, 8803 Rüschlikon, Switzerland  Institute of
Physics, Czech Academy of Sciences, 162 00 Prague, Czech Republic

(August 30, 2024)

###### Abstract

In-situ synthesised semiconductor/superconductor hybrid structures became an
important material platform in condensed matter physics. Their development
enabled a plethora of novel quantum transport experiments with focus on
Andreev and Majorana physics. The combination of InAs and Al has become the
workhorse material and has been successfully implemented in the form of one-
dimensional structures and two-dimensional electron gases. In contrast to the
well-developed semiconductor parts of the hybrid materials, the direct effect
of the crystal nanotexture of Al films on the electron transport still remains
unclear. This is mainly due to the complex epitaxial relation between Al and
the semiconductor. We present a study of Al films on shallow InAs two-
dimensional electron gas systems grown by molecular beam epitaxy, with focus
on control of the Al crystal structure. We identify the dominant grain types
present in our Al films and show that the formation of grain boundaries can be
significantly reduced by controlled roughening of the epitaxial interface.
Finally, we demonstrate that the implemented roughening does not negatively
impact either the electron mobility of the two-dimensional electron gas or the
basic superconducting properties of the proximitized system.

##  I Introduction

Material systems that combine semiconductors (SEs) and superconductors (SCs)
have recently prompted novel research directions in condensed matter physics.
The main motivation to study these systems are different approaches to quantum
computing, e.g. Andreev Hays  _et al._ (2021) and Transmon qubits Larsen  _et
al._ (2015); Casparis  _et al._ (2018) or topological systems hosting Majorana
bound states Sarma  _et al._ (2015).

The combination of InAs and in-situ deposited Al has become an established
material platform, either in the form of proximitized quasi one-dimensional
hybrid nanowires or shallow two-dimensional electron gas (2DEG) systems
Krogstrup  _et al._ (2015); Shabani  _et al._ (2016). The choice of InAs as
the semiconducting part is due to its relatively high spin-orbit coupling and
advantageous band alignment at the shallow SE/SC interface Mikkelsen  _et al._
(2018). Furthermore, it exhibits good etching selectivity and chemical
stability in device fabrication processes. The choice of Al is motivated by
the possibility to achieve a high degree of epitaxial order on InAs Krogstrup
_et al._ (2015), as well as by the fact that Al and InAs are mutually
compatible with in-situ deposition in typical III-V Molecular Beam Epitaxy
(MBE) systems, which often contain both the In and Al sources.

It was shown that the crystal structure of epitaxial Al films differs,
depending on the implemented SE system. Krogstrup, et al. have shown in Ref.
Krogstrup  _et al._ (2015) that in-situ Al deposition on specific nanowire
facets results in the formation of a single crystal Al film with thicknesses
down to a few nanometers. Improving the interface between the materials
resulted in a break-through, where a so-called "hard" superconducting gap was
induced into the hybrid system, meaning that no sub-gap states were observed
in tunneling spectroscopy measurements. This is in contrast to materials with
ex-situ deposited Al, where sup-gap states are typically present Chang  _et
al._ (2015).

Nanowire-based systems have shown great promise as a platform for
investigating transport phenomena Mourik  _et al._ (2012); Vaitiekėnas  _et
al._ (2020); Kurtossy  _et al._ (2021), however the lack of reliable schemes
for scaling up to large device arrays limits their perspective for industrial
applications. To address the scaling issue, growth of larger scale nanowire
networks via selective area growth was recently developed Friedl  _et al._
(2018); Krizek  _et al._ (2018). Yet, the complementary 2DEG systems show more
promise for large-scale applications, due to their compatibility with top-down
fabrication techniques Aghaee  _et al._ (2022).

In comparison to nanowires, the 2D systems reduce the spatial degrees of
freedom for relaxation of the Al layer. This promotes the formation and co-
existence of Al grains with various orientations after in-situ Al deposition,
as previously reported in literature Sarney  _et al._ (2018, 2020); Wang  _et
al._ (2020). Such grains in the Al film determine the local epitaxial
relations to the underlying SE crystal and induce sharp grain boundaries into
the system. There are strong indications that the formation of grain
boundaries has a significant effect on the properties of superconducting thin
films. For example, it was shown that the superconducting properties (e.g.
critical temperature and critical magnetic field) of thin Al films can
significantly exceed typical bulk values Ferguson  _et al._ (2007), where
extreme cases are found in granular aluminum films consisting of nano-sized Al
grains Pracht  _et al._ (2016). A different study has shown that the presence
of grain boundaries modifies the oxidation dynamics of Al films Nguyen  _et
al._ (2018), which can cause oxidation beyond the thickness of native oxide
(around 3 nm). This effect is not restricted to thin Al layers only, as the
presence of grain boundaries in combination with strain have reportedly
altered the SC properties of Nb thin films David Henry  _et al._ (2014).
Despite the presence of grain boundaries, a hard superconducting gap was also
reported for Al in-situ deposited on shallow InAs 2DEG structures Kjærgaard
_et al._ (2016).

In terms of hybrid materials, the direct effect of these local
crystallographic changes in thin Al remains vastly unexplored, but recent
studies have suggested that local disorder in superconducting films could play
a key role in the functionality of superconducting qubits Richardson  _et al._
(2016); de Leon  _et al._ (2021) and proximitized SE/SC structures Cole  _et
al._ (2016); Thomas  _et al._ (2022). Therefore, the nanotexturing of the Al
thin films should be investigated in more detail, with particular emphasis on
the growth of grain-free materials.

The direct way to improve the crystalline quality of the Al is to control the
Al orientation on top of the SE 2DEG. This can be done either by the
modification of the surface chemistry by capping the SE surface with different
materials, where Sb-based interlayers have shown most promising results in
promoting the growth of single crystalline Al films in recent studies Sarney
_et al._ (2018, 2020). A disadvantage in this case is that presence of Sb
often causes problems with the stability of the interface and device
fabrication Thomas  _et al._ (2019); Moehle  _et al._ (2021). Another approach
is to control the orientation of the Al by modifying the lattice constant of
the underlying SE Wang  _et al._ (2020). In that case, the engineered
modification of the lattice constant within the quantum well region is
necessarily related to a change in the electronic properties of the 2DEG,
which may affect the desired balance between electron mobility and
proximitized superconductivity.

Figure 1: (a) ADF-STEM image of the shallow InAs 2DEG structure. The red line
highlights locations of the images used for the lattice constant evaluation.
An illustration of the structure is shown in the right panel. (b) HAADF-STEM
image of a single misfit dislocation. (c) ADF-STEM image of an extended twin
defect, with a higher magnification image in the inset (scalebar is 1 nm). (d)
The deviation of the measured lattice constant as a function of the distance
from the substrate (extracted from HAADF-STEM images taken in the center of
each grown layer) from the bulk lattice constant for the individual layers.
The lattice constant is evaluated from the spacings of both the (001) and
(110) planes. BB stands for bottom barrier, QW for quantum well and TB for top
barrier, which are plotted in the green shaded area. (e) Same dependency, but
for the lattice constant of each individual layer in the structure. The blue
line shows the bulk lattice constant of each layer.

Here, we introduce a novel approach to control thin Al film crystallinity.
First, we give a detailed description of the growth of shallow InAs 2DEGs and
analyse the strain evolution in the structure. This allows us to identify the
most abundant defects responsible for relaxation within the metamorphic buffer
layer and show that the lateral lattice spacing remains stable within the QW
region of the 2DEG. Next, we identify the two dominant grain orientations
responsible for grain boundaries in our in-situ grown epitaxial Al films.
Furthermore, we demonstrate that controlled roughening of the SE surface can
be implemented to grow grain-boundary-free Al films over scales of at least
5$\mu$m. Finally, we find that the roughening does not negatively affect the
mobility and electron density in the 2DEG, while preserving the functionality
of the material in hybrid Josephson junctions (JJs).

Figure 2: (a) HAADF-STEM image of the interface between an Al:$A$(112) grain
and the semiconductor, showing Al(112) to SE(110) lateral matching. Both the
image and the model (top right panel) show an undisturbed epitaxial matching.
The red line highlights coherent matching over a step on the SE surface. (b)
HAADF-STEM image of a grain of the same orientation (Al:$A$), but rotated by
90∘ around the [111] axis, i.e., showing Al(110) to SE(110) matching
(Al:$A$(110)). The Bragg-filtered image (bottom right panel) shows that the
lattice mismatch along this direction is relaxed by networks of misfit
dislocations with AlxSE 5x3 periodicity. Figure 3: (a) HAADF-STEM image of the
interface between an Al:$B$(001) grain and the semiconductor, showing Al(001)
to SE(110) lateral matching. The Bragg-filtered image (bottom right panel),
shows that the strain along this direction is relaxed by the typical formation
of misfit dislocations (highlighted by red circles). (b) HAADF-STEM image of a
grain of the same orientation (Al:$B$), but rotated by 90∘ around the [011]
axis, i.e., showing Al(110) to SE(110) matching (Al:$B$(110)). Both the image
and the model (top right panel) show significant mismatch. The Bragg-filtered
image (bottom right) shows that the lattice mismatch along this direction is
relaxed by networks of misfit dislocations with AlxSE 3x2 periodicity.

##  II Growth of the semiconductor

The epitaxial Al films, which are the main focus of this work, were deposited
on shallow InAs-based 2DEG structures Shabani  _et al._ (2016). The InAs QWs
were grown on semi-insulating Fe-doped (001) InP substrates by MBE. The native
oxide of InP was desorbed at 530∘C for 3 minutes (growth temperature was
measured by optical monitoring of the InP band edge Weilmeier  _et al._
(1991)). The first lattice-matched 100 nm thick layer (x = 0.52) was grown at
$\sim$ 510∘C, with a V/III ratio of 3.5 and at 1 Å/s. For the purpose of this
work, the V/III ratio corresponds to the ratio of As4 and group III growth
rate (details given in Methods sup ).

The lattice mismatch between the InP and InAs was compensated by growth of a
step-graded metamorphic InxAl1-xAs buffer layer. The buffer consists of 20
steps with thicknesses of 50 nm, where x increases from 0.52 to 0.89 and was
grown at $\sim$ 460∘C. We found the lowest semiconductor surface roughness for
samples where the growth rate was increased from 1 to 1.5 Å/s and the V/III
ratio was reduced from 2.3 to 1.8 when reaching x = 0.705. After the
metamorphic buffer, a step-back step with x = 0.82 and a thickness of 8 nm was
grown while maintaining the other growth conditions.

To further smoothen the surface before growth of the QW, a 50 nm thick virtual
substrate was grown at 480∘C, using growth rate of 1.5 Å/s and V/III ratio of
3. The QW region consists of a 6.3 nm thick bottom In0.75Ga0.25As barrier,
grown with V/III ratio of 2.75 while maintaining the growth rate of 1.5 Å/s
and growth temperature of 480∘C. The 8.5 nm thick QW is grown at 1.125 Å/s and
V/III ratio of 3.25. The In0.75Ga0.25As top barrier was grown under the same
conditions as the bottom barrier. The full structure is illustrated and shown
in the Annular Dark Field (ADF) Scanning Transmission Electron Microscope
(STEM) image in Fig. 1a.

For the purpose of this study, we fixed the top barrier thickness to 13.4 nm,
as this material configuration provided us with a good ratio of as-grown
mobility and strength of the induced proximity effect, as discussed below. In
our standard samples, the surface is capped with 2 mono-layers (MLs) of GaAs
(at 0.375 Å/s), which provide a barrier for In diffusion into the Al film and
improve chemical stability during device fabrication.

Adjustment of the growth conditions of the metamorphic buffer layer typically
results in semiconductor surface without pronounced cross-hatching, isotropic
cross-hatching or anisotropic cross-hatching, as shown in the Supplemental
Material sup . For the optimized samples with strongly anisotropic cross-
hatching, grown as described above, we measured electron mobilities around 50
000 cm2/(V$\cdot$s) at electron densities around 4$\cdot$1011 cm-2 at 4.2 K
(measured in van der Pauw configuration on a 5x5 mm2 sample).

The structure of the SE is partially adapted from Ref. Shabani  _et al._
(2016). In our case, we grew a thicker bottom barrier, upper barrier and QW.
Yet, the SE/SC coupling in such a structure remained on a scale relevant for
our transport experiments Haxell  _et al._ (2022a, b); Hinderling  _et al._
(2022); sup . We observed that the behaviour of our proximitized devices
exceeds the theoretical limits given for specific barrier thicknesses in Ref.
Shabani  _et al._ (2016). This should be thoroughly investigated in future
works, as the proximity effect in hybrid materials is expected to be affected
by the interplay of strain, material composition of the barrier, QW
dimensions, quality of the Al film and the epitaxial interface.

One of the important aspects of the SE structure is strain, which can strongly
affect its transport properties, but also the epitaxial relation to the Al
film. Strain fields related to defect formation and lattice relaxation in the
InxAl1-xAs metamorphic buffer are clearly visible in the ADF STEM image in
Fig. 1a. Importantly, they do not extend into the QW region, which remains
defect free. The most abundant defects which dominate the relaxation and
generate the strain fields are shown in High Angle Annular Dark Field (HAADF)
STEM images in Fig. 1b and c. The first type, shown in b, are isolated misfit
dislocations. The second type are single twin planes extending over tenths of
nanometers, shown in c. Both defect types are randomly distributed throughout
the strain relaxation region.

To further understand the strain distribution within the structure, we
extracted the lateral and vertical lattice constants from STEM images by
measuring the (1$\bar{1}$0) and (001) lattice plane spacings (details are
given in the Supplemental Material sup ) in the center of each layer along the
red dashed line in Fig 1a. A percentual deviation from the bulk lattice
constant is plotted as a function of distance from the substrate in Fig. 1d.
As expected, the (110) lattice spacing is rather stable, while the (001)
spacing expands and varies throughout the buffer layer. The (001) spacing
shows two local minima, which overlap with the most strained regions visible
in Fig. 1a. The measured lattice spacing is shown in Fig. 1d, showing that the
lateral (110) lattice spacing remains almost constant in the QW region, as
expected for growth on a relaxed virtual substrate. The average spacing and
deviation is 6.00 $\pm$ 0.02 Å for the bottom barrier, QW and top barrier,
which yields 0.9 $\%$ compressive strain compared to InAs. This negligible
variation of the lattice constant is important, as the strain can be
considered as fixed between the SE and Al. We observed a similar relaxation
behaviour in multiple samples.

Figure 4:  (a) ADF-STEM images of high grain density (top panel) and a single
orientation (bottom panel) Al thin films. The red arrows highlight regions
with strong changes in contrast. (b) A higher magnification and contrast
normalized HAADF image showing structure of one of the possible grain
boundaries, highlighted by red arrows in (a). (c) Contrast normalized HAADF-
STEM image of an Al film deposited on a roughened surface. (d) Schematic of
the possible orientations of different Al films on a heavily anisotropically
roughened surface. (e) HAADF-STEM images of two perpendicular projections
([110] and [1$\bar{1}$0]) of the top interface of the semiconductor,
demonstrating the anisotropy and scale of the intentional roughening.

##  III Al thin films

For the in-situ Al deposition, the wafer was moved to an ultra-high vacuum
buffer chamber (1$\times$10-11 mbar) directly after growth of the shallow InAs
2DEG, and re-transferred when the pressure in the growth chamber reached
1$\times$10-10 mbar, i.e., once the As background dropped after closing the As
valve. The manipulator was rotated towards the liquid nitrogen shroud. No
active cooling was involved and therefore the cooling power is only related to
the MBE system being set to idle state and the sample holder going towards
thermal equilibrium with LN2 cooled cryo-shrouds (in our system for at least
12 hours to reach approximately -30∘C). The Al films (12 nm thick in samples
used in the presented transport experiments) were deposited at a rate of 1Å/s
at a pressure of 3-5$\times$10-11 mbar in the growth chamber. We note that the
sample surface must remain cold during the deposition. Therefore, the used
growth rate (controlled by the cell temperature) needs to be optimized for
each specific MBE system geometry, as it determines heat delivered to the
surface of the sample during growth. After the deposition, the wafer was moved
to the load lock chamber (below 5$\times$10-10 mbar). In order to prevent
thermal dewetting of the Al film, we transferred the sample as fast as
possible to the load lock, i.e., it remained cold until controlled oxidation.
In our case, the sample was oxidized and brought to room temperature in the
load lock by slowly venting with an Ar/O2 (90/10 %) mixture over the course of
15 minutes (at 25∘C). An AFM image of the oxidized surface for both the
controlled oxidation and venting into atmosphere is shown in the Supplemental
Material sup . The samples that were unloaded via controlled oxidation shown
lower surface roughness and reduced formation of large AlOx grains than what
we observed in samples directly unloaded into ambient atmosphere.

Figure 5:  (a) BF-STEM image of Al films deposited on a surface capped with 4
MLs of GaAs showing a change of contrast in the center. The HAADF image in the
inset shows the orientation of the Al film. (b) ADF-STEM image, showing the
origin of the contrast in (a). The fast Fourier transform in the inset shows
that the Al crystal is mirrored over the boundary. (c) Contrast normalized
HAADF image of the crystal around the boundary. (d) BF-STEM image of Al films
deposited on a surface capped with 5 MLs of GaAs. The HAADF-STEM image in the
inset shows the orientation of the Al film. (e) ADF-STEM image, showing an
abrupt change in contrast in the same film as in the lower panel of Fig. 4 a.
(f) HAADF-STEM image of the same area. The Fast Fourier Transform does not
show a detectable change in the crystal structure. Figure 6: (a) Hall
resistance (green) and longitudinal resistance (blue) as a function of
magnetic field for the InAs 2DEG on standard (full line) and intentionally
roughened (dashed line) SE surface, after removal of the epitaxial Al. (b)
Electron mobility and carrier density as a function of top barrier thickness
(for standard structures 2 MLs of GaAs cap and after Al wet etching).

In our standard samples, where the surface was capped by depositing 2 MLs of
GaAs and grown as described above, we mainly observe the presence of two
distinctly oriented grains of Al. The first type is shown in Fig. 2. In this
case, the Al with (111) out-of-plane orientation adapts either (112) in (a) or
(110) in (b) lateral matching to the (110) planes of the semiconductor (here
labeled as Al:$A$(112) and Al:$A$(110)). Therefore in STEM, it is possible to
observe two distinct projections and epitaxial relations of the Al:$A$
crystal, depending on its alignment to the substrate. For the Al:$A$(112)
orientation shown in Fig. 2a, we observe a clean, fully epitaxial interface,
with apparent (and ordered) intermixing within the first matching monolayers.
For the Al:$A$(110) orientation shown in Fig. 2b, we observe 5x3 matching,
i.e., there are two misfit dislocations at the interface per 3 planes in the
substrate.

The second grain type is shown in Fig. 3, where the Al adapts (011) out-of-
plane orientation and lateral matching as either (001) in (a) or (110) in (b)
to the (110) planes of the semiconductor (here labeled as Al:$B$(001) and
Al:$B$(110)). For this grain, we observe formation of misfit dislocations for
both alignments to the (110) planes of the semiconductor. For the Al:$B$(001)
matching, the film relaxes by the formation of periodic arrays of misfit
dislocations with larger spacing. In contrast, there is a single misfit
dislocation per 2 planes in the substrate, i.e., a 3x2 match for the
Al:$B$(110) orientation. We observed that both grain types were equally
present in the samples and often adapted small tilts (e.g. the slight tilt
visible in Fig. 3a). A larger scale ADF-STEM overview of such a sample is
shown in the top panel of Fig. 4a. The changing ADF contrast indicates a high
density of grains with different orientation. The contrast can originate from
the two different types of grains, mutual tilt of grains with the same
orientation and/or from the two possible projections (i.e. 90∘ grain
rotation). An example of a boundary between the two different grain types is
shown in Fig. 4b. The smoothness of the SE surface in the HAADF STEM image
indicates that the presence of the boundary is not associated with neither a
surface step nor a crystallographic defect in the semiconductor.

These partially polycrystalline Al films performed consistently with previous
reports in literature in our transport experiments which rely on the combined
SE/SC system Haxell  _et al._ (2022a, b); Hinderling  _et al._ (2022); sup .
On the other hand, consistent results were achieved only when processing
temperatures did not exceed 175∘C. This is due to degradation of both the Al
film and the SE/Al interface, which was investigated by in-situ annealing of a
lamella prepared from the standard material in a scanning transmission
electron microscope. While ramping the temperature up to 225∘C, we observed
degradation of individual grains into amorphous Al, diffusion grain boundaries
and also intermixing of Al at the interface and even local recrystallization
into a zinc-blende structure, as reported in the Supplemental Material sup .
Reaching such high temperatures during device fabrication had a negative
impact on the transport properties of the material and the fabricated devices
could not be further utilized in our experiments. The observed degradation is
also expected to happen in the smallest features of our devices, since their
dimensions are often comparable to the lamella (5 micrometers in length and
below 50 nm thick). Importantly, the observed recrystallization was selective
to the specific grain type and some of the investigated grains remained
crystalline and their interface to the SE was stable even at 225∘C. This
difference in thermal energy necessary do dissolve the interface for specific
grain types needs to be considered during development of fabrication processes
and is one of the motivations to develop growth of single crystalline Al films
on InAs 2DEGs.

##  IV Effect of roughening on crystallography

The Al film is locked into a single orientation using intentional roughening
of the In0.75Ga0.25As surface by deposition of more GaAs on the InGaAs top
barrier. This is shown for a sample capped with 5 MLs of GaAs in the bottom
panel of Fig. 4a. In such films, we did not detect the presence of any grain
boundaries, i.e., grains with different orientations over a range of 5 $\mu$m,
the typical size of our investigated lamellae.

We found that nanoscale surface roughening of the SE induced by GaAs
deposition is anisotropic along the [110] and [1$\bar{1}$0] directions, as
shown in the STEM images in Fig. 4e and as investigated by STEM tomography
Nicolai  _et al._ (2021) in the Supplemental Material sup . This is likely
related to highly anisotropic diffusion of Ga atoms during deposition at
elevated temperatures Ohta  _et al._ (1989) and a large mismatch between the
In0.75Ga0.25As top barrier and GaAs cap Dieguez  _et al._ (1997).

The nanoscale roughening of the SE surface seems to affect the orientation of
the Al in two ways, summarized in Fig. 4c. Firstly, it leads to a selectivity
of the out-of-plane grain orientation and reduced formation of grain
boundaries. Similarly, growth on roughened or nano-patterned substrates, i.e.
nano-heteroepitaxy, was previously used to reduce formation of threading
dislocations and residual strain in heterostructures with highly mismatched
materials Chen  _et al._ (2018); Feng  _et al._ (2016). Secondly, the
modulation of the SE surface locks the in-plane orientation into either the
Al:$A$ or Al:$B$ grains, so that the $\\{$110$\\}$ planes of the Al align with
the (1$\bar{1}$0) planes of the SE. Both effects are likely related to the
enhanced 3D character of the roughened surface, which gives the Al layer an
additional degree of freedom for strain relaxation.

We observed this behaviour in samples where the InGaAs top barrier was capped
with more than 3 MLs of GaAs. An example is shown in Fig 5, where the Al layer
is locked in 5a as Al:$A$(110) after capping with 4 MLs of GaAs and 5b as
Al:$B$(110) after capping with 5 MLs of GaAs. For the sample capped with 4 MLs
GaAs in Fig. 5a, we observed that the Al only adapted the Al:$A$(110)
orientation. Surprisingly, we observed regions with abruptly changing Bright
Field (BF) and ADF contrast in the STEM images. Yet, this contrast was not
related to a major change in the crystal orientation, but to mirroring with
respect to the Al(111) planes, as shown in Fig. 5b. This is apparent from the
mirroring of the fast Fourier transform spectra and the atomic arrangement in
the HAADF-STEM zoom-in in Fig. 5c. This implies that even when the whole Al
film is locked as Al:$A${110}, the Al:$A$($\bar{1}$10) and Al:$A$(1$\bar{1}$0)
are not degenerate in this grain orientation. Hence, the Al film in this
crystal orientation is naturally prone to twinning and the related formation
of incoherent grain boundaries.

This is different for a sample capped with 5 MLs of GaAs, shown in Fig. 5d,
where the crystal orientation was locked into Al:$B$(100). Similarly to the
previous case, the lateral matching to the substrate was fixed as Al(110) to
SE(110) for the whole layer. In this case, we detected only subtle differences
in ADF and BF contrast, as shown in Fig. 5e. Such a detail in the acquired
image of the Al layer corresponds to the region of the film with a change in
contrast shown in the lower panel of Fig. 4a. These changes of contrast were
sparse in the films and are likely related to subtle tilts of the crystal, as
no apparent crystallographic change was seen in neither the HAADF-STEM image
nor the fast Fourier transform in Fig. 5f. Compared to Al:$A$, the symmetry of
Al:$B$ type grain with respect to the {110} in-plane direction results in the
formation of a fully single crystalline film. The subtle observed tilts might
be related to relaxation of the strain induced by natural bending of the
lamella for samples incorporating metamorphic buffer layers. We note that the
differences in the capping layer thickness used in this study are at the
experimental limits even with the utilized MBE technique. A consistent study
of the capping layer thickness is needed in future works to gain full control
over the Al grain growth selectivity.

In addition, we observed that the grain distribution in the films was affected
by various additional factors, such as lamella preparation, strain, oxidation
etc., which complicated the capability to perform consistent studies. Also,
the Al film degraded and new grains appeared if the lamella was stored in
ambient conditions for more over one month, indicating room temperature
recrystallization in the films, as shown in the Supplemental Material sup .

##  V Effect of roughening on transport properties

Figure 7: (a) False-colored SEM image of the measured Josephson junction,
highlighting the top-gate (gold) and the epitaxial Al leads of the JJ (blue).
The terminals for the bias current $I$ = $I_{\mathrm{SD}}$ \+
$I_{\mathrm{AC}}$, measured 4-probe voltage $V_{\mathrm{DC}}$ and
$V_{\mathrm{AC}}$ and gate voltage $V_{\mathrm{G}}$ are highlighted. (b)
Differential resistance $R$ = $V_{\mathrm{AC}}$/$I_{\mathrm{AC}}$ of the JJ as
a function of source-drain current $I_{\mathrm{SD}}$ and gate voltage
$V_{\mathrm{G}}$. (c) Dependence of $R$ of the JJ as a function of
$I_{\mathrm{SD}}$ and out-of-plane magnetic field $B_{\perp}$. (d) Dependence
of $V_{\mathrm{DC}}$ (red, left axis) and differential resistance $R$ (blue,
right axis) on $I_{\mathrm{SD}}$, measured at a base temperature of 18 mK. The
black dashed line shows a linear fit to the I-V trace above $\sim$ 0.4 mV. The
individual MAR peaks in $R$ are labeled by $n$. They are related to the
measured voltage via the I-V trace (grey dotted lines). The black arrows point
to the position of the switching and excess current, respectively. (e)
Temperature dependence of $R$ as function of bias current $I_{\mathrm{SD}}$.
For clarity, each temperature trace is offset by 50 $\Omega$. Extracted
$V_{\mathrm{DC}}$ positions of the MAR peaks in $R$ for $n$ = 1, 2, 3 as a
function of temperature are shown in the inset. The dashed lines correspond to
fits to the BCS theory for the nominal Al superconducting gap.

Even though the reduction of grain boundaries by surface roughening offers
many benefits in terms of the crystal structure of the Al films, as discussed
above, it is crucial to maintain the transport properties of the 2DEG. In Fig.
6a, we compare magneto-transport measurements of the roughened and standard
materials. The measurements were performed in a van der Pauw configuration at
4 K on 5x5 mm as-grown samples after the Al film was removed by wet-etching.
For the standard non-roughened surface we measured an electron mobility of 53
000 cm2/(V$\cdot$s) at an electron density of 4.0$\cdot 10^{11}$ cm-2. For the
sample with the same structure but intentionally roughened surface (5 MLs of
GaAs) we measured 51 000 cm2/(V$\cdot$s) at an electron density of 3.5$\cdot
10^{11}$ cm-2. The Drude mobility and charge carrier density do not
significantly change for the roughened sample. We consider this difference to
be negligible, since the properties and chemistry of the surface were reported
to have a strong effect on the transport in shallow InAs 2DEGs Pauka  _et al._
(2020); Hatke  _et al._ (2017). We observed clear quantum Hall and Shubnikov-
de Haas transport features at higher magnetic fields in both samples. The
variation in quantum Hall behaviour at higher magnetic fields can be related
to the difference in electron density and sample geometry, for example. In
practical applications of the hybrid material, the rather low critical
magnetic field of the superconducting aluminium typically limits the magnetic
field range in transport experiments to below 1.5 T in a parallel field and
tens of mT in a perpendicular field, where the behaviour of the compared
materials is almost identical.

To further investigate the effect of the near-surface structure on the
electron mobility, we grew a series of standard samples (capped with 2 MLs of
GaAs) with the In0.75Ga0.25As top barrier thickness varying from 5 to 20 nm.
The electron mobility increased almost linearly from 5 000 up to 100 000
cm2/(V$\cdot$s) while the density remained between 3$\cdot 10^{11}$ and
4$\cdot 10^{11}$ cm-2, as shown in Fig. 6b. This demonstrates that the effect
of the intentional roughening of the surface on the electron mobility is
indeed negligible in comparison to the effect of other growth parameters and
changes in the structural design. An enhancement in mobility is desirable, but
an increase in the top barrier thickness can also affect the strength of the
proximitized superconductivity, as will be discussed below and in the
Supplemental Material sup .

Finally, to assess the influence of the intentional roughening of the SE/SC
interface on the superconducting properties of the proximitized system, we
investigated the basic characteristics of a top-gated SC-normal-SC (SNS)
planar Josephson junction (JJ) device, shown in Fig. 7a. The JJ device was
defined by selectively etching Al (blue) to expose the III-V semiconductor
below, which was controlled via an electrostatic gate (gold). The differential
resistance $R$ = $V_{\mathrm{AC}}$/$I_{\mathrm{AC}}$ as a function of bias
current $I_{\mathrm{SD}}$ and top gate voltage $V_{\mathrm{G}}$, is shown in
Fig. 7b. The transition from superconducting to the resistive state (at the
switching current $I_{\mathrm{sw}}$) was tuned by sweeping $V_{\mathrm{G}}$,
where full suppression of the supercurrent appeared around $V_{\mathrm{G}}$ =
-1.8 V. For all following experiments we set $V_{\mathrm{G}}$ = -1.1 V where
we expected the SE segment to be tuned to the single sub-band regime.

Next, we investigated the SC-to-normal transition as a function of the out-of-
plane magnetic field $B_{\perp}$. We observed a Fraunhofer pattern typical for
planar JJs, shown in Fig. 7c. The suppression of the switching current occurs
when the flux penetrating the junction area equals the magnetic flux quantum,
as further discussed in the Supplemental Material sup . For large current bias
the junction resistance attained a normal state value $R_{\mathrm{n}}$ = 150
$\Omega$ (the same as above the critical temperature of $T_{\mathrm{c}}$
$\approx$ 1.38 K).

At zero magnetic field we found a maximum switching current $I_{\mathrm{sw}}$
$\approx$ 1 $\mu$A, and excess current $I_{\mathrm{exc}}$ $\approx$ 1.7
$\mu$A, as shown in Fig. 7d. Both the products $I_{\mathrm{sw}}R_{\mathrm{n}}$
and $I_{\mathrm{exc}}R_{\mathrm{n}}$ can be related to the interface
transparency and the induced superconducting gap energy Flensberg  _et al._
(1988); Kjærgaard  _et al._ (2017). This is consistent with other reports in
literature and discussed in more detail in the Supplementary Material sup .

The induced gap energy can also be extracted by analysing the modulation of
the differential resistance in the resistive state. This originates from
multiple Andreev reflection (MAR) and became apparent when the current bias
was larger than the switching current for both the gate and magnetic field
dependencies. The MAR is a signature of coherent charge transport at finite
bias within the induced superconducting gap, $\Delta$*, i.e., at sub-gap
voltages $V_{\mathrm{DC}}<2\Delta_{\mathrm{Al}}$/$e$ ($\Delta_{\mathrm{Al}}$ =
$1.76\cdot k_{\mathrm{B}}\cdot T_{\mathrm{c}}$ $\approx$ 210 $\mu$eV)
Flensberg  _et al._ (1988); Kjærgaard  _et al._ (2017). The position in
$V_{\mathrm{DC}}$ of individual MAR peaks is related to the size of the
induced gap, as shown in Fig. 7d-e. The induced gap $\Delta$* is given via
$e\cdot V_{\mathrm{DC}}$ = 2 ${\Delta}^{*}/{n}$, where $n$ = 1, 2, 3, … This
is highlighted in Fig. 7d for a measurement at 18 mK. By averaging the value
extracted for n = 1, 2 and 3, we found $\Delta$* = 197 $\pm$ 2 $\mu$eV which
is close to the nominal $\Delta_{\mathrm{Al}}$. This value of $\Delta$*
remains almost constant up to 700 mK, as apparent from the dependency of
$V_{\mathrm{DC}}$ assigned to different $n$ on temperature shown 7e. Above 700
mK, $\Delta$* starts to change and follows the BCS relation Waldram (1996) for
the Al gap energy $\Delta_{\mathrm{Al}}(T,n)$ =
2/$n\cdot\Delta_{\mathrm{Al}}(0)\cdot\textrm{tanh}(1.74\sqrt{T/T_{\mathrm{c}}-1})$.

To demonstrate the quality of the intentionally roughened material, we
compared the measurements to a nominally identical JJ device fabricated from
the standard non-roughened material (2 MLs of GaAs). The same analysis of MAR
as introduced above yields $\Delta$*r = 197 $\pm$ 1 $\mu$eV for the roughened
material and $\Delta$*s = 184 $\pm$ 6 $\mu$eV for the standard material, both
at 500 mK. The similar values of $\Delta$* together with the no apparent
change in electron mobility, show that the quality of the hybrid material is
not significantly affected by the implemented roughening.

Furthermore, we investigated a JJ fabricated from the standard material where
the top barrier thickness was increased from 13.4 nm to 20 nm (20 nm top
barrier thickness and 2ML GaAs cap). In this case, we observed a reduced
number of clear MAR features which complicated the correct assignment of $n$,
as shown in the Supplemental Material. The analysis yields an upper bound of
$\Delta$*20nm = 170 $\mu$eV for $n$ = 2 at 550 mK, which is lower but still
comparable to the samples with a thinner barrier and unexpected in comparison
to theoretical predictions Shabani  _et al._ (2016). The possibility to
increase the electron mobility (i.e. tune the top barrier thickness), while
preserving the induced gap size can be advantageous in future device designs.
More importantly, it was recently suggested by Awoga et al. Awoga  _et al._
(2022), that a weaker coupling between the SE and SC can mitigate influence of
local disorder, which is expected to be one of the significant factors that
can impair device performance. More detailed analysis of the MAR data for all
the investigate samples is given in the Supplemental Material sup . Our
results show that more experimental investigations of growth series with
consistent change of parameters are necessary to relate the material
properties to current theoretical description of hybrid devices.

Overall, we found that all three material designs exhibited a highly
transparent interface, gap size comparable to the BCS theory and other reports
in literature, signatures of coherent ballistic transport through a JJ and a
good performance in our other experiments focused on InAs/Al hybrids Haxell
_et al._ (2022a, b); Hinderling  _et al._ (2022). In addition, studying
differently designed material structures implemented into hybrid devices is
important for further understanding of the influence of individual material
parameters on transport properties.

##  VI Conclusion

This work provides a full description of the growth of shallow high-quality
InAs 2DEGs with epitaxial Al films by MBE. We have demonstrated that
deposition of 5 MLs of GaAs on the top barrier anisotropically roughens the
surface. Subsequent in-situ deposition of a thin epitaxial Al film results in
the formation of an Al layer with a single crystal orientation, which remains
free of grain boundaries on at least a 5 $\mu$m scale. Our results also
indicate that the intentional roughening can be further optimized to achieve
full control over the crystallographic orientation of the Al film.

We found that the introduced roughening did not impair the electron mobility
and carrier density of the shallow 2DEG. In addition, the material showed
qualities comparable to state-of-the-art SE/SC hybrid JJ-based devices in
transport experiments. This implies that local nanotexturing of the
semiconductor surface (likely at scales below the Fermi wavelength) does not
negatively impact the transport properties of the proximitized system, and
provides new experimental insight into the requirements on quality of the
interface in hybrid materials, which were recently subject of extensive debate
Cole  _et al._ (2016); Thomas  _et al._ (2022).

Apart from the possibility of extending the enhanced epitaxy on roughened
surfaces to other materials, control over the Al orientation has implications
for interface engineering and chemical stability of the well-established
hybrid InAs/Al structures. Most importantly, the removal of grain boundaries
from the Al film allows for the possibility to form more complex and still
fully epitaxial heterostructures on top of the Al. Finally, we hope that the
extensive details of material synthesis provided in this work allows for
reproducible growth of the material and make it widely accessible to the
scientific community.

##  VII Acknowledgement

We thank Christian Reichl, Stefan Fält and Mattias Beck for technical support.
We also thank Sjoerd Telkamp, Clemens Todt and Tilman Tröster for fruitful
discussions. We thank the IBM Quantum Academic Network for financial support.
We acknowledge the support of the Cleanroom Operations Team of the Binnig and
Rohrer Nanotechnology Center (BRNC). This work was supported by the Swiss
National Center of Competence in Research Quantum Science and Technology,
QSIT, together with the European Union and the state of Berlin within the
frame of the European Regional Development Fund (ERDF) under project number
2016011843 and by Czech Science Foundation grant number 22-22000M. F. N.
acknowledges support from the European Research Council grant number 804273
and the Swiss National Science Foundation grant number 200021 201082.

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