††thanks: These two authors contributed equally ††thanks: These two authors
contributed equally

# Te-doped selective-area grown InAs nanowires for superconducting hybrid
devices

Pujitha Perla  Peter Grünberg Institut (PGI-9), Forschungszentrum Jülich,
52425 Jülich, Germany  JARA-Fundamentals of Future Information Technology,
Jülich-Aachen Research Alliance, Forschungszentrum Jülich and RWTH Aachen
University, Germany  Anton Faustmann  Peter Grünberg Institut (PGI-9),
Forschungszentrum Jülich, 52425 Jülich, Germany  JARA-Fundamentals of Future
Information Technology, Jülich-Aachen Research Alliance, Forschungszentrum
Jülich and RWTH Aachen University, Germany  Sebastian Kölling  Department of
Engineering Physics, École Polytechnique de Montréal, C.P. 6079, Succ. Centre-
Ville, Montréal, Québec, Canada H3C 3A7  Patrick Zellekens  Peter Grünberg
Institut (PGI-9), Forschungszentrum Jülich, 52425 Jülich, Germany  JARA-
Fundamentals of Future Information Technology, Jülich-Aachen Research
Alliance, Forschungszentrum Jülich and RWTH Aachen University, Germany
Russell Deacon  RIKEN Center for Emergent Matter Science and Advanced Device
Laboratory, 351-0198 Saitama, Japan  H. Aruni Fonseka  Department of Physics,
University of Warwick, Coventry CV4 7AL, UK  Jonas Kölzer  Peter Grünberg
Institut (PGI-9), Forschungszentrum Jülich, 52425 Jülich, Germany  JARA-
Fundamentals of Future Information Technology, Jülich-Aachen Research
Alliance, Forschungszentrum Jülich and RWTH Aachen University, Germany  Yuki
Sato  Peter Grünberg Institut (PGI-9), Forschungszentrum Jülich, 52425 Jülich,
Germany  JARA-Fundamentals of Future Information Technology, Jülich-Aachen
Research Alliance, Forschungszentrum Jülich and RWTH Aachen University,
Germany  Faculty of Science and Engineering Department of Electronics,
Doshisha University, Doshisha University, Kyotanabe, Kyoto 610-0321, Japan
Ana M. Sanchez  Department of Physics, University of Warwick, Coventry CV4
7AL, UK  Oussama Moutanabbir  Department of Engineering Physics, École
Polytechnique de Montréal, C.P. 6079, Succ. Centre-Ville, Montréal, Québec,
Canada H3C 3A7  Koji Ishibashi  RIKEN Center for Emergent Matter Science and
Advanced Device Laboratory, 351-0198 Saitama, Japan  Detlev Grützmacher  Peter
Grünberg Institut (PGI-9), Forschungszentrum Jülich, 52425 Jülich, Germany
Peter Grünberg Institut (PGI-10), Forschungszentrum Jülich, 52425 Jülich,
Germany  JARA-Fundamentals of Future Information Technology, Jülich-Aachen
Research Alliance, Forschungszentrum Jülich and RWTH Aachen University,
Germany  Mihail Ion Lepsa  Peter Grünberg Institut (PGI-10), Forschungszentrum
Jülich, 52425 Jülich, Germany  JARA-Fundamentals of Future Information
Technology, Jülich-Aachen Research Alliance, Forschungszentrum Jülich and RWTH
Aachen University, Germany  Thomas Schäpers<EMAIL_ADDRESS>Peter
Grünberg Institut (PGI-9), Forschungszentrum Jülich, 52425 Jülich, Germany
JARA-Fundamentals of Future Information Technology, Jülich-Aachen Research
Alliance, Forschungszentrum Jülich and RWTH Aachen University, Germany

###### Abstract

Semiconductor nanowires have emerged as versatile components in
superconducting hybrid devices for Majorana physics and quantum computing. The
transport properties of nanowires can be tuned either by field-effect or
doping. We investigated a series of InAs nanowires which conductivity has been
modified by $n$-type doping using tellurium. In addition to electron
microscopy studies, the wires were also examined with atomic probe tomography
to obtain information about the local incorporation of Te atoms. It was found
that the Te atoms mainly accumulate in the core of the nanowire and at the
corners of the {110} side facets. The efficiency of $n$-type doping was also
confirmed by transport measurements. As a demonstrator hybrid device, a
Josephson junction was fabricated using a nanowire as a weak link. The
corresponding measurements showed a clear increase of the critical current
with increase of the dopant concentration.

InAs nanowire, Te doping, selective-area growth, molecular beam epitaxy,
Josephson junctions

##  I Introduction

InAs nanowires have proven to be suitable consituents for various electronic
devicesDayeh  _et al._ (2007); Tomioka  _et al._ (2007); Thelander  _et al._
(2008); Burke  _et al._ (2015) and also for studying fundamental quantum
physics phenomena in nanoscale structures.Fasth  _et al._ (2005); Fuhrer  _et
al._ (2007); Heedt  _et al._ (2016, 2017); Iorio  _et al._ (2019); Bordoloi
_et al._ (2020) Recently, InAs nanowires attracted attention by their
integration in semiconductor-superconductor hybrid structures. A prominent
example is the effort regarding the realization of Majorana fermions for
topological quantum computing.Mourik  _et al._ (2012); Aguado (2017) In
addition, InAs nanowires can serve as a weak link in gate-controlled Josephson
junctionsDoh  _et al._ (2005); Günel  _et al._ (2012) for superconducting
qubits such as transmonsLarsen  _et al._ (2015); de Lange  _et al._ (2015) or
Andreev level qubits.Zazunov  _et al._ (2003)

Due to the Fermi level pinning within the conduction band in InAs, a surface
accumulation layer forms naturally,Wieder (1974) ensuring that the nanowire is
conductive even without doping. In some cases, however, the ability to control
conductivity through doping is desired, e.g. for adjusting the channel
conductance in field-effect transistors. Nanowire conductivity has also a
great impact on the critical current of Josephson junctions based on InAs
nanowiresGünel  _et al._ (2012) and therefore it is a crucial design parameter
for the aforementioned qubit circuits.

In most cases, Si is employed as an $n$-type dopant in InAs nanowires.Sladek
_et al._ (2010); Wirths  _et al._ (2011); Ghoneim  _et al._ (2012); Dimakis
_et al._ (2013); Park  _et al._ (2015) Using Si doping, densities in the order
of $10^{19}$ cm-3 are achieved.Wirths  _et al._ (2011); Ghoneim  _et al._
(2012) However, apart from the increase of the carrier concentration in the
nanowire, Si doping affects the growth kinetics as well as the nanowire
dimensions.Wirths  _et al._ (2011); Dimakis  _et al._ (2013) In GaAs, Te is
known as a very effective $n$-type dopant.Sankaran (1980); Kamp  _et al._
(1994); Bennett  _et al._ (2003) As a group VI element Te shows no amphoteric
behavior as it is the case for Si in GaAs. As a matter of fact, Te doping
already found its applications in $n$-type doped GaAs nanowires.Wallentin and
Borgström (2011); Orrù  _et al._ (2016); Goktas  _et al._ (2018); Hakkarainen
_et al._ (2019) Recently, it was demonstrated that Te is also a very efficient
dopant in InAs nanowires.Güsken  _et al._ (2019)

To explore the suitability of Te-doped nanowires in superconductor/nanowire
hybrid structures, we have grown a series of nanowires with different doping
using selective-area molecular beam epitaxy (MBE). The structural properties
are investigated by electron microscopy. Detailed information about the dopant
distribution in the nanowires is obtained by atom probe tomography (APT).
Electrical transport measurements are performed both at room temperature and
at 4 K to determine the doping efficiency. Finally, the properties of the
doped nanowires for superconducting hybrid structures are investigated by
fabricating and measuring nanowire-based Josephson junctions.

##  II Growth and Device Fabrication

The InAs nanowires were grown by MBE using selective area growth on a Si(111)
wafer covered by a 20-nm-thick thermally oxidized SiO2 layer.Koblmüller  _et
al._ (2010); Perla  _et al._ (2021) By means of electron beam lithography,
hole arrays with a pitch of 1 $\mu$m and hole diameter of 80 nm are patterned.
The holes are etched by reactive ion etching to a depth of roughly 16 nm
followed by cleaning in piranha solution (H2SO4:H2O${}_{2}=3:1$). Immediately
before growth, an etching step of 60 s in HF is performed in order to remove
the remaining SiO2 in the holes without damaging the Si(111) surface below.

The InAs nanowires are grown without any catalyst via the vapor-solid
mechanism ∘C.Rieger  _et al._ (2013) The tellurium is supplied by a GaTe cell.
For the first $10\,$min, a substrate temperature of 480 ∘C, an In growth rate
of $0.08\,\mu$m/h and an As beam equivalent pressure (BEP) of $4\times
10^{-5}$ mbar are used to sustain the nanowire self-seeding. The nanowire
growth is then proceeded with a lower substrate temperature of
$460\,^{\circ}$C and In growth rate of $0.03\,\mu$m/h. For growth runs A to D
the As4 BEP varied between $3-3.5\times 10^{-5}$ mbar for $3.5$ h depending on
the Te doping concentration to avoid changes in the morphology of the
nanowires.Güsken  _et al._ (2019) Here, the Te concentration has been varied
between $5\times 10^{17}$ and $1\times 10^{19}$ cm-3 by varying the GaTe cell
temperature between $420\,^{\circ}$C and $497\,^{\circ}$C based on
calibrations conducted on Te-doped GaAs layers via Hall-measurements. In
addition, two samples were grown with a lower As4 BEP of $2.5\times 10^{-5}$
torr (growth runs E and F) with a nominal doping of $5\times 10^{18}$ and
$2.5\times 10^{19}$ cm-3, respectively. The parameters of the Te-doped InAs
nanowires are summarized in table 1.

Table 1: Growth runs for InAs nanowires: growth run, nominal doping concentration, GeTe cell temperature, As4 BEP, length, diameter, resistivity, and carrier concentration from transport measurements at room temperature.  growth run | Te-doping | GeTe cell | As4 BEP | length | diameter | $\rho$ | $n_{\mathrm{3D}}$
---|---|---|---|---|---|---|---
| ($\mathrm{cm}^{-3}$) | (∘C) | (torr) | ($\mu$m) | (nm) | ($\Omega\mathrm{cm}$) | ($\mathrm{cm}^{-3}$)
A | $5\times 10^{17}$ | 420 | $3\times 10^{-5}$ | $4-5$ | $100\pm 5$ | $18.4\times 10^{-3}$ | $(0.75\pm 0.23)\times 10^{18}$
B | $1\times 10^{18}$ | 437 | $3\times 10^{-5}$ | $5-6.5$ | $103\pm 5$ | n.a. | $(1.15\pm 0.80)\times 10^{18}$
C | $5\times 10^{18}$ | 478 | $3.5\times 10^{-5}$ | $3.5-4.5$ | $111\pm 5$ | $4.3\times 10^{-3}$ | $(2.76\pm 2.50)\times 10^{18}$
D | $1\times 10^{19}$ | 497 | $3.5\times 10^{-5}$ | $4-5$ | $113\pm 3$ | $2.7\times 10^{-3}$ | $(9.04\pm 2.29)\times 10^{18}$
E | $5\times 10^{18}$ | 478 | $2.5\times 10^{-5}$ | $3.5-5$ | $121\pm 7$ | $10.0\times 10^{-3}$ | $(1.27\pm 0.45)\times 10^{18}$
F | $2.5\times 10^{19}$ | 520 | $2.5\times 10^{-5}$ | $3.5-5$ | $140\pm 8$ | $1.2\times 10^{-3}$ | $(5.86\pm 2.21)\times 10^{18}$
Figure 1: (a) Scanning electron micrograph of selectively grown Te-doped InAs
nanowires with a nominal doping concentration of $1\times 10^{18}$ cm-3. The
nanowires grow in 80-nm-wide holes with 1 $\mu$m pitch. Close-up of nanowires
with different Te-concentrations: (b) $1\times 10^{18}$ cm-3 (growth run B),
(c) $1\times 10^{19}$ cm-3 (growth run D), (d) $2.5\times 10^{19}$ cm-3
(growth run F), respectively. (e) Zoom-in of (d) showing additional facets
forming an irregular dodecagonal shape.

For the APT measurements discussed below, we also prepared InAs nanowires with
different doping concentrations, which are covered by a 50-nm-thick GaSb shell
(cf. Table 2). The GaSb shell ensures that all atoms of the cross section of
the InAs nanowire are gathered by the APT detector.

Table 2: Growth runs for InAs/GaSb core/shell nanowires with their corresponding nominal doping concentration and the doping concentration determined by APT.  Growth run | Te-doping | Te (APT)
---|---|---
| ($\mathrm{cm}^{-3}$) | ($\mathrm{cm}^{-3}$)
H | $1\times 10^{18}$ | $(1.47-1.92)\times 10^{18}$
I | $7.5\times 10^{18}$ | $(2.45-4.95)\times 10^{18}$
J | $2.5\times 10^{19}$ | $(0.39-1.38)\times 10^{19}$

Specific devices with ohmic contacts have been fabricated for electrical
characterisation of InAs nanowires with varying Te-doping levels from growth
runs A-F. The nanowires have been transferred mechanically using a clean paper
tip to highly doped Si substrates covered by a 200 nm thick thermal SiO2 layer
in order to provide a global back gate. On top of the SiO2 layer, metallic
contact pads and alignment markers have been placed using optical lithography
and lift-off processes. Electrical contacts were defined in a four-terminal
configuration by electron beam lithography. The contacts consisted of non-
alloyed Ti/Au metal layers, 80 nm and 50 nm thickness respectively, deposited
by electron beam evaporation. An Ar+ sputtering step of 90 s was included
before metallization in order to remove the native oxide and to provide a
clean semiconductor surface.

The shunted Josephson junctions were processed with nanowires from growth runs
A, B, and D. The AuGe shunt resistor is defined by electron beam lithography.
It consists of a 10-nm-thick, 1-$\mu$m-wide and 7-$\mu$m-long AuGe stripe with
a resistance $R_{\mathrm{shunt}}=80-140\,\Omega$. The InAs nanowires are
transferred individually onto a Si substrate containing a 5 nm/10 nm thick
Ti/Pt gate pad covered with a 3 nm/12 nm thick stack of Al2O3/HfO2. The NbTi
electrodes that connect the nanowire with the shunt resistor and the
surrounding TiN circuit are fabricated by means of Ar ion milling ($\sim 180$
s) and the subsequent sputter deposition of 80 nm NbTi via DC magnetron. Here,
the average junction length is in the range of 100 nm and mainly limited by
the e-beam lithography. Junctions were fabricated in the center of the
transferred nanowires.

##  III Results and Discussion

###  III.1 Nanowire structure

Figure 1 (a) shows a scanning electron microscopy (SEM) image of an array of
Te-doped ($1\times 10^{18}$ cm-3) nanowires (growth run B). The yield is about
95%. The image confirms the uniformity of length and diameter. In Figs. 1 (b)
and (c), close-ups of a nanowire from growth runs B and D are shown. Up to a
Te concentration of $1\times 10^{-19}$ cm-3 the nanowires show a hexagonal
cross section with $\\{$110$\\}$ facets as well as a comparable diameter of
around 110 nm. However, for the nanowires with the highest Te concentration of
$2.5\times 10^{-19}$ cm-3 we observe that diameter increased visibly.
Furthermore, as can be clearly seen in Figs. 1 (d) and (e), the sidewalls of
the nanowire developed additional {112} facets, forming an irregular
dodecagonal shape.

Tellurium atoms have a surfactant effect accumulating on the side facets and
decreasing the diffusion length of the host indium atoms.Wixom  _et al._
(2004); Sáfar  _et al._ (1997); Neves  _et al._ (1998) As a result, an
increase of the nanowire diameter is expected, which was observed also in our
experiments (cf. table 1). A similar behavior has Sb in InAs(Sb) nanowires,
where with increasing Sb supply the nanowire radius increases
accordingly.Anyebe  _et al._ (2015); Potts  _et al._ (2016)

###  III.2 Transmissions Electron Microscopy

The crystal structure of the nanowires from all the growths is mainly formed
by wurtzite (WZ) region containing inclusions of zinc blende (ZB) segments and
twining planes, as shown in Fig. 2 (a) for a nanowire from growth run C. In
contrast to the previous study on randomly positioned Te-doped InAs
nanowires,Güsken  _et al._ (2019) in these nanowires, no clear clear change in
crystal structure was observed with the increase of the Te doping level.

Figure 2: (a) A high magnification annular dark field (ADF) image of a
nanowire from growth run C showing the typical crystal structure of the Te
doped nanowires. WZ regions containing stacking faults are marked in blue and
red, respectively, and ZB inclusions are marked in yellow. The region used for
the magnified image is indicated in the inset bright field (BF) low
magnification image. (b) Higher magnification ADF image of the tip region. It
appears to consist of multiple facets with the top (111) facet being smaller
in diameter ($\approx 26$ nm) compared to the nanowire.

Figure 2 (b) shows a higher magnification image of the tip of the nanowire.
Assuming similar facets are maintained during growth, the top (111) growth
facet is of smaller diameter than the rest of the nanowire. Therefore, it can
be safely assumed that the nanowire growth takes place by adatom deposition on
multiple facets on the tip region.

###  III.3 Atomic Probe Tomography

For APT, single InAs nanowires with different Te doping levels and a GaSb
shell are isolated using a method described in detail in Ref. [Koelling  _et
al._ , 2017]. They are analyzed in a LEAP4000X HR equipment. We imaged the
distribution of Te in the InAs nanowires utilizing the same methods for noise
level suppression and background correction as in Ref. [Koelling  _et al._ ,
2017]. The APT analyses reveal four notable findings. First, as can be seen in
Fig. 3, Te accumulates at the core of the wire and at the corners of the
hexagonal {110} facets for all investigated Te doping concentrations.

Figure 3: Two-dimensional map of the Te concentration determined by APT from
samples of growth runs H (a), I (b), and J(c).

Second, the measured Te dopant incorporation increases with the corresponding
nominal doping (cf. Figs. 3 and 4). Third, the Te concentration increases
towards the bottom of the nanowires typically reaching a factor of $2-3$
higher concentration near the bottom with respect to the top (cf. Fig. 4).
Forth, as depicted in Fig. 5, with the increase of Te nominal doping, the
facets of the hexagonal InAs nanowires become unstable and the nanowires with
the highest doping have locally dodecagonal cross sections. This observation
is confirmed by TEM cross sectional images, as shown in Supplemental Material
Fig. S1.

Figure 4: (a) APT 3D map of an exemplary InAs/GaSb core/shell nanowire. The
elements are displayed with different colors. (b) Axial atomic Te
concentration profiles of samples from growth runs H, I, and J. The nominal
Te-doping concentration is given in brackets.  Figure 5: Cross section of InAs
nanowires with different doping as obtained from 10 nm slices of APT
measurements. The shape of the core is marked using 40% Indium iso-
concentration surfacesHellman  _et al._ (2003) and facets/corners are then
marked manually. (a) Wires with low doping concentration (growth run H) always
show hexagonal facets. (b) As the doping increases (growth run I) extra facets
start appearing locally. (c) In highly doped samples (growth run J), there are
sections with length of hundreds of nanometers which have dodecagonal shape.

We interpret these findings as follows. Te diffuses along the sidewall of the
nanowire, a contribution coming also from the substrate surface, and
incorporates via the small (111) growth facet on the top of the nanowire (Fig.
2 (b)) and on the corners of the hexagonal facets. Note that the diameters of
the top (111) facet in Fig. 2 (b) and the Te rich core in Fig. 3 (c) are
comparable. As the wire grows, the diffusion contribution of the substrate
surface disappear and Te incorporation at top decreases. Due to the large
covalent radius of Te atoms, they accumulate on the corners between facets.
The accumulation at the corners promotes the formation of (112) facets and
hence the dodecagonal segments. One can presume that the surfactant Te
incorporates easier into the solid on (111) and (112) surfaces than (110).

###  III.4 Electrical Characterization

In Fig. 6 the resistance at room temperature from nanowires with different
doping levels are plotted function of the ratio of nominal distance between
the contacts and the cross sectional area $d_{\mathrm{nom}}/S$.

Figure 6: Four-terminal resistance $R$ of doped nanowires at room temperature
plotted function of the ratio between nominal contact distance
$d_{\mathrm{nom}}$ and mean nanowire cross sectional area $S$. The solid lines
represent the linear fits to determine the resistivity. For the samples of
growth run B no reliable linear fit was possible.

Here, $S$ was determined for each growth series by average the diameters of
the measured nanowires assuming a regular hexagonal shape. The transport
measurements have been carried out in a four-terminal scheme in order to
eliminate the effect of contact resistances. For each growth run with a
specific doping concentration, one finds a linear increase of resistance with
the contact separation length verifying the ohmic behavior of the transport in
the wire. The doping effect of Te is confirmed by the decrease of the slope,
i.e. decreased resistivity $\rho$, with increasing doping concentration (c.f.
Table 1). In Fig. 6 one observes that there is a spread of the resistance of
different nanowires with identical contact separation. The effect is less
pronounced for higher doping levels. One reason for the varying conductance
could be found in non-uniform cross section $S$. Although the nanowires were
grown in a selective-area epitaxy scheme, fluctuations of the cross sectional
area can not be avoided.

Charge carrier concentrations of nanowires with different doping levels were
extracted from field-effect measurements by biasing a global back gate. We
found that the conductance is reduced for negative gate voltages, confirming
the $n$-type doping character. Quantitative information about charge carrier
concentration was obtained using the threshold voltage $V_{\mathrm{th}}$ at
pinch-off. Since nanowires with a Te doping concentration larger than $5\times
10^{18}\,\mathrm{cm}^{-3}$ did not reach pinch-off at accessible back-gate
voltages, $V_{\mathrm{th}}$ was in this case obtained by extrapolating the
approximately linear dependence towards positive voltages. Example of traces
including a linear fit are given in the Supplemental Material in Figs. S2 -
S4. Some nanowire samples showed a gate hysteresis behavior, which was
reproducible during several cycles. In that case, $V_{\mathrm{th}}$ was
determined by taking the average of the threshold voltages for up- and down-
sweeps. Details of the determination of $V_{\mathrm{th}}$ and the calculation
of the charge carrier concentration $n_{\mathrm{3D}}$ are given in the
Supplemental Material.

Figure 7: (a) Extracted charge carrier concentrations $n_{\mathrm{3D}}$ from
gate pinch-off curves at room temperature for nanowires with different nominal
Te-doping concentrations (growth runs A to F). (b) $n_{\mathrm{3D}}$ at 4.2 K
for growth runs A to D.

The field-effect measurements on nanowires grown with different Te doping
concentrations were carried out at room temperature and at 4.2 K. The
corresponding charge carrier concentrations at different nominal doping
concentrations are depicted in Fig. 7. The graphs confirm that the
experimentally determined charge carrier concentration values increase with
the nominal doping of the nanowires.

For sample C and D, one finds that at room temperature, the measured carrier
concentrations are close to the nominal Te doping concentrations demonstrating
the efficient dopant incorporation. However, for samples E and F grown with
the low As4 flux the doping efficiency is somewhat lower, the obtained charge
carrier concentrations being lower than expected from the previous growth runs
A to D. This could be explained by a modified Te incorporation due to altered
growth conditions by decreased As4 flux. The measured charge carrier
concentrations are found to be generally higher at room temperature compared
with 4.2 K, which represents the expected behavior in semiconductors.

A relatively large spread of $n_{\mathrm{3D}}$ for the investigated nanowires
from identical batches is observed. A possible explanation for that is the
imprecise character of the method to determine the charge carrier
concentration from the gate pinch-off threshold voltage. Defects within the
oxide and at the interface with the semiconductor effectively alter the
capacitance used to determine the carrier concentration (see section II-B in
the Supplemental Material) leading to scattered results. Furthermore, it was
shown in Fig. 4 that the Te incorporation along the nanowire axis is not
uniform, resulting in different effective doping depending on the length of
the particular nanowire. Therefore, one must be careful to directly compare
the obtained results with measurements from APT. However, it can be concluded
that the charge carrier concentration strongly depends on the nominal dopant
concentration, suggesting an effective $n$-type doping of InAs by Te.

###  III.5 Josephson junctions

In order to demonstrate the suitability of Te-doped nanowires for
superconducting hybrid structures the properties of gate-controlled Josephson
junctions are investigated. The measurements have been performed in a 3He/4He
dilution refrigerator with a base temperature of 15 mK. The measured junctions
JJ-A, JJ-B, and JJ-D were fabricated from nanowires from growth series A, B,
and D, respectively. A typical structure is shown in Fig. 8 (a), in which the
nanowire-based Josephson junction is shunted by an AuGe resistor.

Figure 8: (a) SEM micrograph of a nanowire Josephson junction that is
connected in parallel to an extrinsic on-chip shunt resistor. The
superconducting leads consist of a 80-nm-thick NbTi layer. The electrostatic
tuning is realized by means of a global bottom gate pad. (b) Gate- and
current-dependent differential resistance map of a nanowire Josephson junction
of growth run B. The measurements were taken at 15 mK. (c) Single voltage-
current characteristics taken from (a) at gate voltages of
$V_{\mathrm{g}}=0\,$V and 7 V. The calibrated characteristics for
$V_{\mathrm{g}}=7\,$V after subtracting the conductance of the shunt is also
given. (d) Gate-dependent critical current for junctions JJ-A, JJ-B, and JJ-D
at 15 mK.

The shunt was included to suppress hysteretic effects in the current-voltage
characteristics and to improve the performance of the device in measurements
of the ac-Josephson effect Joyez  _et al._ (1999); Chauvin (2005). In Fig. 8
(b) the color-coded differential resistance vs. bias current is plotted in the
gate voltage range from $V_{\mathrm{g}}=-1$ V to 7 V for junction JJ-B made
from a nanowire having a doping nominal concentration of $1\times 10^{18}$
cm-3. One finds that for gate voltages below $1\,$V the nanowire is pinched
off, with the remaining resistance of 80 $\Omega$ given by the shunt resistor.
Between $V_{\mathrm{g}}$=$1\,$V and $2.5\,$V the device shows signatures of
Coulomb blockade which can be attributed to the presence of an intrinsic
quantum dot.Zellekens  _et al._ (2020) At gate voltages above $2.5\,$V, the
nanowire channel is open and exhibits gate-tunable supercurrent, i.e., an
important requirement for hybrid superconducting circuit applications. The
critical current shows some superimposed fluctuations due to interference
effects.Doh  _et al._ (2005); Günel  _et al._ (2012) From Fig. 8 (c) showing a
single voltage-current ($I-V$) trace at $V_{\mathrm{g}}=7$ V (red curve) a
critical current of $I_{\mathrm{c}}=140\,$nA is extracted. The $I-V$
characteristics contains the contribution of the shunt resistor, which needs
to be subtracted to gain the actual current through the junction. Indeed, the
resistance of the shunt can be determined directly from the measurement at
zero gate voltage (cf. Fig. 8 (c)), where the junction is pinched-off
completely. After the calibration of the junction response by means of a
point-wise combination of the traces at $7$ V and $0$ V, it is possible to
extract the unperturbed characteristics of the device (cf. Fig. 8 (c), dark
red trace). Junctions JJ-A and JJ-B could be pinched-off completely so that
the normal state resistance $R_{\mathrm{N}}$ could be extracted. At a gate
bias of $7$ V we determined $I_{\mathrm{c}}R_{\mathrm{N}}$ products of 65
$\mu$V and $188\,\mu$V for sample JJ-A and JJ-B, respectively.

The critical current as a function of gate voltage for all investigated
Josephson junctions are shown in Fig. 8 (d). The junction containing a
nanowire with the highest doping level only shows a weak relation between
$V_{\mathrm{g}}$ and the measured $I_{\mathrm{c}}$. In contrast, the wires
with the lower carrier concentrations exhibit a transistor-like behavior with
pronounced pinch-off and saturation regions. All critical currents shown some
fluctuations due to inference effects in the nanowire channel.Doh  _et al._
(2005); Günel  _et al._ (2012) The difference in the threshold voltage between
junction JJ-A and JJ-B are attributed to Coulomb resonances which dominate the
transport at low gate values.Zellekens  _et al._ (2020) A comparison of the
critical current at $V_{\mathrm{g}}=6\,$V reveals increase by a factor of 10
between JJ-A and JJ-B and a factor of five between JJ-B and JJ-D, which
confirms the impact of the doping concentration on $I_{\mathrm{c}}$.

A reliable way to confirm that nanowire-based junction do indeed carry a
Josephson supercurrent is to perform measurements under microwave irradiation.
Here, the application of a microwave signal results in Shapiro steps of height
$n\cdot V_{0}$, with $V_{0}=hf/(2e)$, $h$ Planck constant and $n=1,2,3,\dots$.
Figure 9 (a) shows a set of current–voltage traces of junction JJ-D for $f=5$
GHz and different microwave powers at $V_{\mathrm{g}}=7$ V.

Figure 9: (a) Current-voltage characteristics of junction JJ-D for different
microwave powers. (b) Measurements of Shapiro steps as a function of power.
The color scale corresponds to the number of measurement points at normalized
voltages $V/V_{0}$ with $V_{0}=hf/(2e)$.

At low power, i.e. $-20$ dB, the curve basically mimics the behavior of a
purely DC-driven junction. However, if the power is increased to $-10$ dB and
further to $0$ dB, the zero voltage state is gradually suppressed and
equidistant voltage plateaus, i.e. Shapiro steps, appear. In Fig. 9 (b) the
presence of Shapiro steps at multiples of $V_{0}$ for $f=6$ GHz is shown as a
function of microwave power. The color scale gives the number of counts as a
function of voltage, i.e. large number of count corresponds to the appearance
of a step. The regular oscillating pattern without any subharmonic features
indicates a sinusoidal current-phase relation of the Josephson junction.

##  IV Conclusions

We demonstrate that Te is an efficient dopant for MBE-grown InAs nanowires. At
very high dopant concentrations, above $1\times 10^{19}$ cm-3, a change in
wire morphology was observed, where the hexagonal cross section changes to a
dodecagonal one. The side facets have also a great influence on the
distribution of Te dopant, which accumulates at the corners of the hexagonal
(111) facets,as APT revealed. In addition, the APT showed that in the center
of the wire the Te concentration is higher and that the total Te concentration
increases toward the bottom of the nanowire. The effective doping was
confirmed by electrical measurements at room temperature and 4 K, where a
systematic increase in the conductivity of the wire with the doping
concentration was observed. Indeed, a significant increase in the critical
current was obtained in Josephson junctions with a nanowire weak link. At
moderate doping concentrations, even gate control was maintained. Since InAs
nanowires are often used in hybrid structures for Majorana physics or quantum
computing, Te doping provides a very efficient method to tailor the nanowire
properties for devices in these applications.

## Acknowledgements

We thank Tobias Ziegler, Patrick Liebisch, Patrick Pilch, Bram Aarts and Abbas
Espiari for their assistance during sample preparation and Michael
Schleenvoigt for the metal deposition, Marvin Jansen for initial assistance
with TEM, Benjamin Bennemann, Christoph Krause, and Herbert Kertz for
technical assistance. Dr. Florian Lentz and Dr. Stefan Trellenkamp are
gratefully acknowledged for electron beam lithography. Dr. Elmar Neumann and
Stephany Bunte for their assistance with the focused ion beam setup and
scanning electron microscopy. Dr. Gianluigi Catelani is gratefully
acknowledged for theory support regarding the magnetic field measurements. All
samples have been prepared at the Helmholtz Nano Facility.Forschungszentrum
Jülich GmbH (2017) The work at Forschungszentrum Jülich was partly supported
by the project ”Scalable solid state quantum computing”, financed by the
Initiative and Networking Fund of the Helmholtz Association, by the Deutsche
Forschungsgemeinschaft (DFG, German Research Foundation) Project: ”Coupling of
quantum dots with superconductors”, (SCHA 835/9-1), UK EPSRC is acknowledged
for funding through grant No. EP/P000916/1. The APT work was supported by
NSERC Canada (Discovery, SPG, and CRD Grants), Canada Research Chairs, Canada
Foundation for Innovation, Mitacs, PRIMA Québec, and Defence Canada
(Innovation for Defence Excellence and Security, IDEaS). The work at RIKEN was
partially supported by Grant-in-Aid for Scientific Research (B) (No.
19H02548), Grants-in-Aid for Scientific Research (S) (No. 19H05610), and
Scientific Research on Innovative Areas ”Science of hybrid quantum systems”
(No. 15H05867).

## References

  * Dayeh  _et al._ (2007) S. Dayeh, D. P. Aplin, X. Zhou, P. K. Yu, E. Yu, and D. Wang, Small 3, 326 (2007).
  * Tomioka  _et al._ (2007) K. Tomioka, P. Mohan, J. Noborisaka, S. Hara, J. Motohisa, and T. Fukui, J. Cryst. Growth 298, 644 (2007).
  * Thelander  _et al._ (2008) C. Thelander, C. Rehnstedt, L. E. Froberg, E. Lind, T. Martensson, P. Caroff, T. Lowgren, B. J. Ohlsson, L. Samuelson, and L.-E. Wernersson, Electron Devices, IEEE Transactions on 55, 3030 (2008).
  * Burke  _et al._ (2015) A. M. Burke, D. J. Carrad, J. G. Gluschke, K. Storm, S. Fahlvik Svensson, H. Linke, L. Samuelson, and A. P. Micolich, Nano Letters 15, 2836 (2015).
  * Fasth  _et al._ (2005) C. Fasth, A. Fuhrer, M. T. Bjork, and L. Samuelson, Nanoletters 5, 1487 (2005).
  * Fuhrer  _et al._ (2007) A. Fuhrer, L. E. Fröberg, J. N. Pedersen, M. W. Larsson, A. Wacker, M.-E. Pistol, and L. Samuelson, Nano Letters 7, 243 (2007).
  * Heedt  _et al._ (2016) S. Heedt, A. Manolescu, G. A. Nemnes, W. Prost, J. Schubert, D. Grützmacher, and T. Schäpers, Nano Letters 16, 4569 (2016).
  * Heedt  _et al._ (2017) S. Heedt, N. T. Ziani, F. Crépin, W. Prost, J. Schubert, D. Grützmacher, B. Trauzettel, T. Schäpers, _et al._ , Nature Physics 13, 563 (2017).
  * Iorio  _et al._ (2019) A. Iorio, M. Rocci, L. Bours, M. Carrega, V. Zannier, L. Sorba, S. Roddaro, F. Giazotto, and E. Strambini, Nano Letters 19, 652 (2019).
  * Bordoloi  _et al._ (2020) A. Bordoloi, V. Zannier, L. Sorba, C. Schönenberger, and A. Baumgartner, Communications Physics 3, 1 (2020).
  * Mourik  _et al._ (2012) V. Mourik, K. Zuo, S. M. Frolov, S. R. Plissard, E. P. A. M. Bakkers, and L. P. Kouwenhoven, Science 336, 1003 (2012).
  * Aguado (2017) R. Aguado, Rivista del Nuova Cimento 40, 523 (2017).
  * Doh  _et al._ (2005) Y.-J. Doh, J. A. van Dam, A. L. Roest, E. P. A. M. Bakkers, L. P. Kouwenhoven, and S. D. Franceschi, Science 309, 272 (2005).
  * Günel  _et al._ (2012) H. Y. Günel, I. E. Batov, H. Hardtdegen, K. Sladek, A. Winden, K. Weis, G. Panaitov, D. Grützmacher, and T. Schäpers, Journal of Applied Physics 112, 034316 (2012).
  * Larsen  _et al._ (2015) T. W. Larsen, K. D. Petersson, F. Kuemmeth, T. S. Jespersen, P. Krogstrup, J. Nygård, and C. M. Marcus, Phys. Rev. Lett. 115, 127001 (2015).
  * de Lange  _et al._ (2015) G. de Lange, B. van Heck, A. Bruno, D. J. van Woerkom, A. Geresdi, S. R. Plissard, E. P. A. M. Bakkers, A. R. Akhmerov, and L. DiCarlo, Phys. Rev. Lett. 115, 127002 (2015).
  * Zazunov  _et al._ (2003) A. Zazunov, V. S., Shumeiko, E. N. Bratus, J. Lantz, and G. Wendin, Phys. Rev. Lett. 90, 087003 (2003).
  * Wieder (1974) H. H. Wieder, Applied Physics Letters 25, 206 (1974).
  * Sladek  _et al._ (2010) K. Sladek, V. Klinger, J. Wensorra, M. Akabori, H. Hardtdegen, and D. Grützmacher, Journal of Crystal Growth 312, 635 (2010).
  * Wirths  _et al._ (2011) S. Wirths, K. Weis, A. Winden, K. Sladek, C. Volk, S. Alagha, T. E. Weirich, M. von der Ahe, H. Hardtdegen, H. Lüth, N. Demarina, D. Grützmacher, and T. Schäpers, Journal of Applied Physics 110, 053709 (2011).
  * Ghoneim  _et al._ (2012) H. Ghoneim, P. Mensch, H. Schmid, C. D. Bessire, R. Rhyner, A. Schenk, C. Rettner, S. Karg, K. E. Moselund, H. Riel, and M. T. Björk, Nanotechnology 23, 505708 (2012).
  * Dimakis  _et al._ (2013) E. Dimakis, M. Ramsteiner, C.-N. Huang, A. Trampert, A. Davydok, A. Biermanns, U. Pietsch, H. Riechert, and L. Geelhaar, Applied Physics Letters 103, 143121 (2013).
  * Park  _et al._ (2015) D. W. Park, S. G. Jeon, C.-R. Lee, S. J. Lee, J. Y. Song, J. O. Kim, S. K. Noh, J.-Y. Leem, and J. S. Kim, Scientific Reports 5 (2015), 10.1038/srep16652.
  * Sankaran (1980) R. Sankaran, Journal of Crystal Growth 50, 859 (1980).
  * Kamp  _et al._ (1994) M. Kamp, G. Mörsch, J. Gräber, and H. Lüth, Journal of Applied Physics 76, 1974 (1994).
  * Bennett  _et al._ (2003) B. R. Bennett, R. Magno, and N. Papanicolaou, Journal of crystal growth 251, 532 (2003).
  * Wallentin and Borgström (2011) J. Wallentin and M. T. Borgström, Journal of Materials Research 26, 2142 (2011).
  * Orrù  _et al._ (2016) M. Orrù, E. Repiso, S. Carapezzi, A. Henning, S. Roddaro, A. Franciosi, Y. Rosenwaks, A. Cavallini, F. Martelli, and S. Rubini, Advanced Functional Materials 26, 2836 (2016).
  * Goktas  _et al._ (2018) N. I. Goktas, E. M. Fiordaliso, and R. R. LaPierre, Nanotechnology 29, 234001 (2018).
  * Hakkarainen  _et al._ (2019) T. Hakkarainen, M. Rizzo Piton, E. M. Fiordaliso, E. D. Leshchenko, S. Koelling, J. Bettini, H. Vinicius Avan ço Galeti, E. Koivusalo, Y. G. a. Gobato, A. de Giovanni Rodrigues, D. Lupo, P. M. Koenraad, E. R. Leite, V. G. Dubrovskii, and M. Guina, Phys. Rev. Materials 3, 086001 (2019).
  * Güsken  _et al._ (2019) N. A. Güsken, T. Rieger, G. Mussler, M. I. Lepsa, and D. Grützmacher, Nanoscale Research Letters 14, 179 (2019).
  * Koblmüller  _et al._ (2010) G. Koblmüller, S. Hertenberger, K. Vizbaras, M. Bichler, F. Bao, J.-P. Zhang, and G. Abstreiter, Nanotechnology 21, 365602 (2010).
  * Perla  _et al._ (2021) P. Perla, H. A. Fonseka, P. Zellekens, R. Deacon, Y. Han, J. Kölzer, T. Mörstedt, B. Bennemann, A. Espiari, K. Ishibashi, _et al._ , Nanoscale Advances 3, 1413 (2021).
  * Rieger  _et al._ (2013) T. Rieger, D. Grützmacher, and M. I. Lepsa, physica status solidi (RRL)–Rapid Research Letters 7, 840 (2013).
  * Wixom  _et al._ (2004) R. Wixom, L. Rieth, and G. Stringfellow, Journal of crystal growth 269, 276 (2004).
  * Sáfar  _et al._ (1997) G. A. M. Sáfar, W. N. Rodrigues, L. A. Cury, H. Chacham, M. V. B. Moreira, S. L. S. Freire, and A. G. de Oliveira, Applied Physics Letters 71, 521 (1997).
  * Neves  _et al._ (1998) B. R. A. Neves, M. S. Andrade, W. N. Rodrigues, G. A. M. Sáfar, M. V. B. Moreira, and A. G. de Oliveira, Applied Physics Letters 72, 1712 (1998).
  * Anyebe  _et al._ (2015) E. Anyebe, M. K. Rajpalke, T. D. Veal, C. Jin, Z. Wang, and Q. Zhuang, Nano Research 8, 1309 (2015).
  * Potts  _et al._ (2016) H. Potts, M. Friedl, F. Amaduzzi, K. Tang, G. Tütüncüoglu, F. Matteini, E. Alarcon Lladó, P. C. McIntyre, and A. Fontcuberta i Morral, Nano letters 16, 637 (2016).
  * Koelling  _et al._ (2017) S. Koelling, A. Li, A. Cavalli, S. Assali, D. Car, S. Gazibegovic, E. P. A. M. Bakkers, and P. M. Koenraad, Nano Letters 17, 599 (2017).
  * Hellman  _et al._ (2003) O. C. Hellman, J. B. du Rivage, and D. N. Seidman, Ultramicroscopy 95, 199 (2003), iFES 2001.
  * Joyez  _et al._ (1999) P. Joyez, D. Vion, M. Götz, M. Devoret, and D. Esteve, Journal of superconductivity 12, 757 (1999).
  * Chauvin (2005) M. Chauvin,  _The Josephson effect in atomic contacts_ , Ph.D. thesis, Université Pierre et Marie Curie-Paris VI (2005).
  * Zellekens  _et al._ (2020) P. Zellekens, R. Deacon, P. Perla, H. A. Fonseka, T. Mörstedt, S. A. Hindmarsh, B. Bennemann, F. Lentz, M. I. Lepsa, A. M. Sanchez, D. Grützmacher, K. Ishibashi, and T. Schäpers, Phys. Rev. Applied 14, 054019 (2020).
  * Forschungszentrum Jülich GmbH (2017) Forschungszentrum Jülich GmbH, Journal of large-scale facilities 3, A112 (2017).

Te-doped selective-area grown InAs nanowires for superconducting hybrid
devices (Supplemental Material)

##  SI TEM cross-section images showing nanowires facets

In Fig. S1 a cross section of a nanowire from growth run F is depicted.

Supplementary Figure S1: A cross section taken from the middle of a nanowire
core with the highest doping concentration ($2.5\times
10^{19}\,\mathrm{cm}^{-3}$) of growth run F, showing formation of multiple
facets of $\\{110\\}$ and $\\{112\\}$ (11 in this case) leading to the
dodecagonal shape.

##  SII Electrical Characterization

###  A Electrical characterization of Te-doped nanowires

Electrical characterisation of nanowires with varying Te-doping levels were
performed at room temperature as well as at 4.2 K. Room temperature
measurements without back gate were done using a Keithley SCS-4200
semiconductor characterisation system connected to a 4-point probe station.
Measurements at low temperature were performed in a Lakeshore liquid 4He flow-
cryostat capable of cooling down to approximately 4.0 K. Nanowires were
investigated in two- and four-terminal configurations with and without
applying a voltage to the back gate. A Keithley 2636B source-measurement unit
was used for the application of the bias current. Potential differences in
four-terminal configuration were measured using a Keysight 34461A multimeter
with input impedance of 10 M$\Omega$.

###  B Determination of carrier concentration

In order to obtain information on charge carrier density in the nanowires, the
source-drain conductance was investigated depending on voltage
$V_{\mathrm{g}}$ applied to the global back-gate electrode. The threshold
voltage $V_{\mathrm{th}}$ was extracted by extrapolating from the linear
behavior at positive gate voltages (cf. Fig. S2). Some gate-dependent
measurements showed an hysteresis effect, i.e. the results for gate up- and
down-sweep were slightly shifted. In these cases, the average value was used
for further evaluation (c.f. Figs. S3 and S4). Gate-dependent measurements
were achieved on two ways. On the one hand, the gate was swept by directly
taking the source-drain current at constant $V_{sd}$. Alternatively, the
conductance was extracted from $IV$ sweeps at different fixed gate voltages.
This was preferred in cases with a small gate hysteresis, in order to reduce
uncertainties in conductance from offsets of the measurement devices. In Fig.
S4 an example measurement for the latter case is shown.

Supplementary Figure S2: Representative source-drain conductance $G_{sd}$ of a
nanowire with nominal doping $1\times 10^{18}\,\mathrm{cm}^{-3}$ (growth run
B) depending on back-gate voltage. Threshold voltage $V_{\mathrm{th}}$ is
extrapolated from the approximately linear behaviour at positive gate
voltages. Supplementary Figure S3: Representative source-drain conductance
$G_{sd}$ of a nanowire with nominal doping $5\times 10^{18}\,\mathrm{cm}^{-3}$
(growth run E) depending on back-gate voltage $V_{\mathrm{g}}$. The threshold
voltage $V_{\mathrm{th}}$ is extrapolated from the approximately linear
behaviour at positive gate voltages. The observed conductance shows a
hysteresis effect in between gate up- and down-sweep, resulting in different
obtained threshold voltages. For further analysis the mean value from up- and
down-sweep was used. Supplementary Figure S4: Representative source-drain
conductance $G_{sd}$ for a nanowire with nominal doping $5\times
10^{18}\,\mathrm{cm}^{-3}$ (growth run C), extracted from $IV$ measurements at
varying back-gate voltages for both gate up- and down sweep. Threshold
voltages Vth are extrapolated from the approximately linear behaviour at
positive gate voltages.

For calculating the charge carrier concentration from the threshold voltages
the following relation was usedDayeh  _et al._ (2007)

$\displaystyle
n_{\text{3d}}=\frac{C\left|V_{\mathrm{th}}\right|}{el_{\mathrm{NW}}\pi
r_{\mathrm{NW}}^{2}}\,,$ (S1)

with $e$ the electron charge, $l_{\mathrm{NW}}$ the nanowire length between
the contacts, $r_{\mathrm{NW}}$ its radius. $C$ denotes the capacitance
between the nanowire and the global back-gate electrode. It is given byDayeh
_et al._ (2007)

$C=\frac{2\pi\epsilon_{0}\epsilon
l_{\mathrm{NW}}}{\ln\left[\left(2h+d+2\sqrt{h^{2}+hd}\right)/d\right]}\,.$
(S2)

Here, $\epsilon_{0}$ is the dielectric constant, $\epsilon$ is the relative
dielectricity of the gate oxide, i.e. $\epsilon=3.9$ for SiO2, $h$ denotes the
thickness of the oxide between back-gate and nanowire and $d=2r_{\text{NW}}$
the diameter of the nanowire.

##  SIII Extrinsically shunted Josephson junctions

Supplementary Figure S5: Shapiro response of samples JJ-A at (a) f = 4.1 GHz
and (b) f = 6.0 GHz and JJ-D at (c) f = 1.5 GHz and (d) f = 3.8 GHz for a gate
voltage of Vg=7 V [(a),(b)] and Vg=0 V [(c),(d)].

In Josephson junctions the dissipationless supercurrent arises from the
coherent tunneling of Cooper pairs between two superconducting electrodes,
driven by the phase difference $\delta$. In tunnel junctions with large
spatial extensions, the phase can be considered as a quasistatic parameter due
to the damping effect of the large capacitance associated with it. The large
time constant suppresses sudden changes of the voltage
$V\propto\partial\delta/\partial t$, which stabilizes the system with respect
to thermal and quantum fluctuations. However,if one assumes a nanowire
Josephson junction, the phase dynamics are not longer purely determined by the
superconductor/nanowire/superconductor stack itself. Instead, the
superconducting leads and the circuit environment, modeled as a admittance
$Y(\omega)$, with $\omega$ the frequency, start to influence the
electromagnetic properties of the device. Thus, the phase difference $\delta$
between the two superconducting electrodes of the junction is not a simple
parameter anymore rather than the combination of all phase fluctuation
contributionsJoyez  _et al._ (1999); Chauvin (2005)

$\sqrt{\langle\delta^{2}\rangle}\propto\frac{Z_{s}(\omega)}{R_{\mathrm{K}}\left(1+e^{-\hbar\omega/k_{B}T}\right)}\,.$
(S3)

Here, $R_{K}$ corresponds to the von-Klitzing constant ($h/e^{2}$), $T$ is the
electron temperature and $Z_{s}(\omega)$ is the total impedance. The latter is
thereby determined by the junction inductance $L_{0}$, the junction
capacitance $C_{0}$ and the impedance of the external circuit. In case of a
small junction, $L_{0}$ and $C_{0}$ are small, too, and $Z_{s}(\omega)$ is
dominated by the external circuit admittance $Y(\omega)$. Such a scenario is
usually associated with large phase fluctuations, which ultimately lead to a
stochastic behavior of the corresponding supercurrent:

$I(\omega)=\langle
I_{0}\rangle=I_{0}\langle\sin{\left(\delta\right)}\rangle\,,$ (S4)

e.g. a widely spread distribution of the switching current or the occurrence
of a hysteresis in the zero-voltage state. The latter is especially important
in the case of large supercurrents, for which the actual electron temperature
deviates significantly from the bath temperature due to overheating
effects.Courtois  _et al._ (2008)

The most simple way to limit both phase noise as well as phase diffusion is
the implementation of an on-chip shunt resistor in close proximity to the
nanowire Josephson junctions.Joyez  _et al._ (1999); Chauvin (2005) In our
case, the InAs/Al half-shell nanowire Josephson junction is shunted by an on-
chip AuGe stripe (cf. Fig. 8 (a) in the main text) Both elements are connected
by superconducting TiN electrodes. The normal conducting shunt resistor causes
as suppression of the pronounced and abrupt switch between zero voltage state
and dissipative transport. Instead, there is a smooth and continuous
transition between both branches, effectively providing experimental access to
the full voltage range. After the subtraction of the shunt resistance, the
remaining trace exhibits the typical decrease of the current above a critical
value, which is a clear signature for the suppression of the Cooper pair
driven transport. By extracting the turning point of the supercurrent peak, as
shown in, it is then possible to obtain the maximum junction current
$I_{0}$.Joyez  _et al._ (1999); Chauvin (2005)

The full calibration procedure is as follows: First, the gate dependency of
the supercurrent is investigated in order to measure the shunt resistor
independently. Thus, the nanowire has to be pushed into pinch-off by applying
a sufficiently large negative gate voltage. Now, by applying a linear fit
within the range of the supercurrent branch to every individual $I$-$V$
characteristics, it is possible to obtain the combined resistance of the
parallel circuit. For negative voltages, i.e. when the nanowire is pinched-
off, the circuit resistance becomes equal to the normal conducting shunt
resistance. In order to limit the influence of noise and measurement
uncertainties, the whole saturation region is used to calculate an average
value for the resistor. The contribution of the normal conducting shunt
resistor, which acts as an additive and linear contribution, can then be
removed by a point-wise extraction of the junction resistance
$R_{\mathrm{JJ}}$ and calibration of the measured voltage $V$

$\displaystyle R_{\mathrm{JJ}}$ $\displaystyle=$
$\displaystyle\frac{VR_{\mathrm{s}}}{I_{\mathrm{bias}}R_{\mathrm{s}}-V}\,,$
(S5) $\displaystyle I_{\mathrm{JJ}}$ $\displaystyle=$
$\displaystyle\frac{V}{R_{\mathrm{JJ}}}\,,$ (S6)

with $I_{\mathrm{bias}}$ as the externally applied current.

##  SIV Shapiro measurements on nanowire Josephson junctions with different
doping concentrations

Figure S5 provides an overview of the power-dependent Shapiro response for the
junctions JJ-A and JJ-D in the main manuscript. For the undoped nanowires, a
pronounced spectrum can be observed for both measurements, i.e. f = 4.1 GHz
(cf. Fig. S5 (a)) and f = 6.0 GHz (cf. Fig. S5 (b)), respectively. Thus, even
though the nanowire have a low carrier concentration and despite the
comparably poor quality of the ex-situ contacts, a clear supercurrent without
any resistive contribution can be observed if a sufficiently large gate
voltage (V${}_{\mathrm{g}}>$4 V) is applied. The same holds for the wires with
the highest doping level in Figs. S5 (c) and (d), respectively, proving that
the large supercurrent of I${}_{\mathrm{s}}>$200 nA is really carried by a
Josephson junction rather than just a metallic short.

## References

  * Dayeh  _et al._ (2007) S. Dayeh, D. P. Aplin, X. Zhou, P. K. Yu, E. Yu, and D. Wang, Small 3, 326 (2007).
  * Joyez  _et al._ (1999) P. Joyez, D. Vion, M. Götz, M. Devoret, and D. Esteve, Journal of superconductivity 12, 757 (1999).
  * Chauvin (2005) M. Chauvin,  _The Josephson effect in atomic contacts_ , Ph.D. thesis, Université Pierre et Marie Curie-Paris VI (2005).
  * Courtois  _et al._ (2008) H. Courtois, M. Meschke, J. T. Peltonen, and J. P. Pekola, Physical Review Letters 101, 067002 (2008).