# Room temperature donor incorporation for quantum devices: arsine on
germanium

Emily V. S. Hofmann  Department of Electronic and Electrical Engineering,
University College London, WC1E 6BT, London, UK  London Centre for
Nanotechnology, University College London, WC1H 0AH, London, UK  IHP –
Leibniz-Institut für Innovative Mikroelektronik, Im Technologiepark 25,
D-15236 Frankfurt (Oder), Germany  Taylor J. Z. Stock  London Centre for
Nanotechnology, University College London, WC1H 0AH, London, UK  Oliver
Warschkow  London Centre for Nanotechnology, University College London, WC1H
0AH, London, UK  Rebecca Conybeare  London Centre for Nanotechnology,
University College London, WC1H 0AH, London, UK  Department of Physics and
Astronomy, University College London, WC1E 6BT, London, UK  Neil J. Curson
Department of Electronic and Electrical Engineering, University College
London, WC1E 6BT, London, UK  London Centre for Nanotechnology, University
College London, WC1H 0AH, London, UK  Steven R. Schofield  London Centre for
Nanotechnology, University College London, WC1H 0AH, London, UK  Department of
Physics and Astronomy, University College London, WC1E 6BT, London, UK
<EMAIL_ADDRESS>
###### Abstract

Germanium has emerged as an exceptionally promising material for spintronics
and quantum information applications, with significant fundamental advantages
over silicon. However, efforts to create atomic-scale devices using donor
atoms as qubits have largely focussed on phosphorus in silicon. Positioning
phosphorus in silicon with atomic-scale precision requires a thermal
incorporation anneal, but the low success rate for this step has been shown to
be a fundamental limitation prohibiting the scale-up to large-scale devices.
Here, we present a comprehensive study of arsine (AsH3) on the germanium (001)
surface. We show that, unlike any previously studied dopant precursor on
silicon or germanium, arsenic atoms fully incorporate into substitutional
surface lattice sites at room temperature. Our results pave the way for the
next generation of atomic-scale donor devices combining the superior
electronic properties of germanium with the enhanced properties of
arsine/germanium chemistry that promises scale-up to large numbers of
deterministically-placed qubits.

scanning tunnelling microscopy, density functional theory, atomic fabrication,
germanium (001), arsenic, arsine, dopant

Germanium is experiencing a strong resurgence of interest for the fabrication
of (opto)-electronic, spintronic, and quantum technological devices Scappucci
_et al._ (2021); Hendrickx  _et al._ (2021). Compared to silicon, germanium
has a higher electron mobility Lee  _et al._ (2005), stronger spin-orbit
coupling Liu (1962), larger Bohr radius Liu (1962), larger Stark effect
Sigillito  _et al._ (2016), and is relatively insensitive to exchange coupling
oscillations Pica and Lovett (2016); Koiller  _et al._ (2002). In addition,
germanium can be made free of nuclear spin by isotopic enrichment Itoh  _et
al._ (1993), donors in germanium have long coherence times Tyryshkin  _et al._
(2012); Sigillito  _et al._ (2015), and germanium is already used in high-
performance electronics.

Electron spins localized on donor atoms in semiconductors form excellent two-
level quantum systems (qubits) Muhonen  _et al._ (2014). Assembling individual
donors to form devices requires the positioning of potentially thousands of
donors with atomic-scale precision de Leon  _et al._ (2021). This necessitates
a detailed understanding of the chemical processes involved, and the ability
to produce substitutional donor atoms at atomically-precise locations with
extremely high fidelity. The most successful approach to date is phosphorus in
silicon using phosphine (PH3) as the donor precursor, and an atomically-
patterned hydrogen resist Schofield  _et al._ (2003, 2006); Warschkow  _et
al._ (2016). Among the many devices that have been fabricated using this
technique are the celebrated single-atom transistor Fuechsle  _et al._ (2012),
and a few donor device where two-qubit operations were demonstrated via
exchange coupling He  _et al._ (2019).

A critical step in the scale up to large numbers of donor qubits is
incorporating the donor atoms into the surface layer Schofield  _et al._
(2003). For all of the systems investigated to date—phosphine on silicon
Schofield  _et al._ (2003); Bennett  _et al._ (2009) and germanium Scappucci
_et al._ (2012), and arsine (AsH3) on silicon Stock  _et al._ (2020)—a thermal
anneal is required to achieve this surface incorporation. However, this anneal
can also provide an opportunity for the donor species to desorb. The
probability of successfully incorporating phosphorus into silicon using a
hydrogen resist was studied by two independent groups and determined to be
$P_{\text{incorp.}}\sim 70$% Ivie  _et al._ (2021); Füchsle (2011). Since the
probability for successfully fabricating $N$ qubits scales as
$(P_{\text{incorp.}})^{N}$, this means that even for a modest 50 qubit device,
the success rate using phosphorus in silicon can be anticipated to be as low
as 1 in $10^{8}$.

Here, we show that at room temperature, arsenic atoms fully incorporate into
the germanium surface layer from adsorbed arsine molecules. Remarkably, and
unlike all previously studied systems, no thermal anneal is required for the
incorporation of arsenic into germanium. Thus, the donor incorporation
probability is unity, suggesting that arsine on germanium offers a path to the
creation of large scale quantum devices consisting of many thousands of
donors.

## Results

### The room temperature dosed surface

Figure 1a shows an overview STM image of a Ge(001) surface dosed with arsine
at room temperature. Rows of germanium dimers run horizontally across the
image and form either a buckled c$(4\times 2)$ configuration or a more
symmetric appearing $2\times 1$ configuration Zandvliet (2003). Features
related to arsine dosing are highlighted by boxes. The brightest features that
we observe present a single protrusion on top of a dimer row and in the
position mid-way between two neighbouring dimers (Fig. 1b). This feature does
not conform to any of the anticipated arsine adsorbate [AsH${}_{x}+(3-x)$H]
configurations Schofield  _et al._ (2006); Warschkow  _et al._ (2016);
Scappucci  _et al._ (2012); Stock  _et al._ (2020) (see Supplementary
Information), but is an excellent match to a germanium ad-dimer in a “B” site
configuration Zandvliet  _et al._ (2000); Zoethout  _et al._ (1998) (Fig. 1c).
Moreover, we occasionally observe these features shifting position on the
surface (see white and black arrows on Figs. 1j–m), which is another known
characteristic of germanium ad-dimers at room temperature Zandvliet  _et al._
(2000); Zoethout  _et al._ (1998); Huijben  _et al._ (2006). The existence of
germanium ad-dimers implies that arsenic atoms have incorporated into the
surface from the adsorbed arsine molecules, displacing germanium atoms onto
the surface in the process.

Figure 1: a, Overview STM image of arsine (AsH3) on Ge(001) at room
temperature. b,c, Germanium B-site ad-dimer image and schematic. d,e, STM
image and schematic of an m1 feature. f, Images of t1 feature that is three
dimers wide and spans two dimer rows. g, STM image of a h1 feature. h-m, five
images of the same region of the surface where one feature undergoes
transitions between h1, h2, h3, g1, and t1 features, and n-s, the
corresponding structural schematics. Calculated DFT energies are quoted for
each structure. Orange circles on panels (n-s) provide a guide-to-the-eye to
highlight the location of the brightly-imaging portions of the STM images. STM
image parameters: all images $-1.5$ V, 200 pA. Image (a) z-range 190 pm,
images (b-m) z-range 140 pm; the colour scheme is shown top right. (a)
$30\times 22$ nm2, (b,f,g) $5.7\times 3.8$ nm2, (d) $6.9\times 3.8$ nm2,(h-m)
$8.0\times 6.1$ nm2.

We next turn our attention to the most abundant feature after arsine dosing:
this feature appears as two adjacent dark dimers, and two examples are
highlighted in Fig. 1d. Close inspection reveals that this feature is not
perfectly symmetric, but instead it appears slightly less dark in one corner.
We assign this feature to a fully dissociated arsine molecule, resulting in a
surface-incorporated arsenic atom and three adsorbed hydrogen atoms forming a
hydrogen-terminated arsenic-germanium heterodimer (As–Ge–H) and a germanium
monohydride dimer (H–Ge–Ge–H). This structure is illustrated in Fig. 1e and we
label it m1. This feature images less brightly than the surrounding clean
germanium dimers due to the absence of the germanium dimer $\pi$-bonds caused
by the adsorption of the three hydrogen atoms, and the formation of a lone
pair on the arsenic atom. The slightly less-dark site in one corner of the
feature can be attributed to the arsenic atom.

In Figs. 1f,g we highlight two other arsine features that we label t1 and h1.
Both of these features are three dimers wide. The t1 feature exhibits a
complicated appearance and spans two dimer rows (Fig. 1f), while the h1
feature exhibits a single dark dimer adjacent to two protrusions positioned
asymmetrically about the dimer row (Fig. 1g). We observe transitions between
these, and several other three-dimer wide features, as shown in Figs. 1h–m. By
analogy with the m1 feature, we readily assign the h1 feature to a hydrogen-
terminated arsenic-germanium heterodimer (As–Ge–H) and two adsorbed hydrogen
atoms; however, in this case, the two hydrogen atoms are adsorbed to the ends
of two neighbouring dimers to form two germanium hemihydride dimers (Ge–Ge–H),
rather than to a single dimer as was the case for m1. The two protrusions
observed in the STM image are produced by the two clean germanium atoms of the
hemihydride dimers, as highlighted by the orange circles in structural
schematic in Fig. 1n.

In the next image, Fig. 1i, one of the two asymmetric protrusions has changed
from the top of the dimer row to the bottom. We attribute this change to one
hydrogen atom moving from one side of the germanium dimer to the other, as
illustrated by structure h2 in Fig. 1p. Similarly, in Fig. 1j we see that the
second asymmetric protrusion has now also changed sides, which can be
attributed to the second hydrogen moving to the other side of its germanium
dimer as shown in structure h3 (Fig. 1q).

The subsequent transition, observed in Fig. 1k is, at first consideration,
rather unexpected. Here the two protrusions of the two clean germanium atoms
of the hemihydride dimers of structure h3 merge together to form a single
protrusion. We explain this change as being caused by the capture of a single
germanium monomer at the clean germanium ends of the two hemihydride dimers in
an end-bridge bonding configuration, as shown schematically in Fig. 1r and
labelled g1.

Figure 1m shows the final transition in the set, where the feature has now
become the two-dimer row spanning feature t1 already mentioned (Fig. 1f).
Here, it appears that the protrusion produced by the monomer of the g1 feature
observed in Fig. 1k has increased in size and intensity, and that our feature
has now locally pinned a phason defect (i.e., a defect where two neighbouring
dimers become statically buckled in the same direction Van Houselt  _et al._
(2006); Sweetman  _et al._ (2011)) on the adjacent dimer row. However, we do
not expect the spontaneous local pinning of a phason except at very low
temperatures Sweetman  _et al._ (2011); Saedi  _et al._ (2009) Thus, we
propose a chemical origin for this pinning, specifically the capture of a
second germanium monomer to form a dimer-trough bridging germanium dimer, as
shown in Fig. 1s. This structure explains both the enlargement of the
protrusion at the site of the monomer in structure g1, and also the dimer
pinning that causes the phason-like defect. We further note that the
appearance of the trough-bridging dimer of this feature very closely matches
that observed in germanium deposition experiments Zandvliet  _et al._ (2000);
Zoethout  _et al._ (1998).

Figure 2: Exchange of a germanium monomer between two As-Ge-H heterodimer
features (t1 and g1). a, STM image where a t1 feature is seen to the centre-
left of the image and a g1 feature is seen centre-right, as indicated. b, A
subsequent STM image of the same region of the surface shown in panel (a);
here we see that the t1 feature has changed to g1, and the g1 feature has
changed to t1. c, Schematic diagram showing the arrangement and positioning of
the t1 and g1 features as they appear in panel (a). d,e, Two successive STM
images where another such monomer exchange was observed between t1 and g1
features. Image parameters: (a,b,d,e) $-1.5$ V, 200 pA, z-range: 140 pm, (a,b)
$8\times 5$ nm2, (d,e) $21\times 5$ nm2.

The transitions $\text{h3}\rightarrow\text{g1}$ and
$\text{g1}\rightarrow\text{t1}$ involve the dynamic capture of germanium
monomers. These monomers are bound in g1 or t1 features, but are occasionally
able to overcome the diffusion barriers at room temperature to leave one
feature and be captured at another. Two examples of such transitions where we
identify both the source and the destination of a transiting germanium monomer
are shown in Fig. 2. Figure 2a shows an STM image where a t1 and g1 feature
are separated by a space of three dimers in the horizontal direction, and a
single germanium dimer row in the vertical direction, as illustrated in Fig.
2c. Figure 2b shows a subsequent image of the same area of the surface, where
we see the t1 feature has become a g1 feature and vice versa, mediated by the
exchange of a germanium monomer between them. We observed this exchange
several times back and forth in successive STM images, confirming the
reversibility of these transitions. Another example of such an exchange is
shown in Figs. 2d,e. These observations demonstrate that germanium monomers
are highly mobile along the direction of the dimer rows at room temperature in
agreement with previous reports Zandvliet  _et al._ (2000); Zoethout  _et al._
(1998); Swartzentruber (1997); and that monomer capture at a g1 site (to
convert it to t1) occurs where the g1 feature exists on the neighbouring row
with its monomer directed toward the row on which the mobile monomer is
diffusing.

We gain further insight into the dynamics of the surface by counting the
feature transitions between successive STM images. Table 1 shows a count of
transitions observed within a $50\times 50$ nm2 scan over a period of 12
hours. There is a strong symmetry to the table about the diagonal, as expected
for reversible transitions. The largest number of transitions, 56% of the
total number of observed transitions (129 out of 231), involve the shifting of
hydrogen atoms across the dimer row to cause transitions among h1, h2, and h3
features. The next largest category are the monomer exchange transitions
$\text{g1}\leftrightarrow\text{t1}$, which account for 35% of the total.
Transitions between h1–h3 and g1 were relatively rare, accounting for 9% of
all transitions; this demonstrates that the majority of monomer transitions
are exchanges between dimer t1 and monomer g1 configurations. No transitions
were observed between the h1–h3 and t1 structures, which can be understood
since the g1 structure is intermediate between h1–h3 and t1. Also notable is
the absence of transitions $\text{g1}\leftrightarrow\text{g1}$ or
$\text{t1}\leftrightarrow\text{t1}$: experimentally these would appear as a
mirror symmetry transition about the dimer row, but such transitions are
extremely unlikely given our structural assignments.

Table 1: Transitions between features in successive STM images over a 12 hour period. The average time between images was 9 minutes, and the imaging parameters were $-1.5$ V, 200 pA. We group h1 and h3 into a single feature classification, since experimentally it can be very difficult to delineate between them; transitions between h1 and h3 involve the shifting of both hydrogen atoms of the two hemihydride dimers to the opposite side of the dimer row. Similarly, we note that an alternate configuration of structure h2 exists, where the positions of the two hydrogen atoms are reversed to the opposite side of the dimer row, and we denote this configuration h2∗ (see Supplementary Figure S1). From: To: |  h1/h3 |  h2/h2∗ |  g1 |  t1
---|---|---|---|---
h1/h3 | 15 | 36 | 8 | 0
h2/h2∗ | 36 | 42 | 1 | 0
g1 | 11 | 1 | 0 | 40
t1 | 0 | 0 | 41 | 0

We support these compelling experimental observations with DFT calculated
formation energies. We calculate each of the experimentally observed
structures and find that the formation energies for h1–h3 are all equal at
$-2.8$ eV, and structure g1 is nearly equal at $-2.9$ eV. The closeness of
these energies suggests the possibility of reversible transitions between
these structures, exactly of the sort that we have already described above.
Structure m1 is slightly more stable at $-3.1$ eV. In addition, we have
calculated the energies for a wide range of AsH${}_{x}+(3-x)$H adsorption
configurations; the most stable of these are an AsH${}+2$H configuration that
we label e1 (see Supplementary Figure S1) and an As${}+3$H configuration that
we label f1; both have formation energies of $-2.2$ eV. Thus, we see there is
a large energy gain ($0.6$ eV) for the incorporation of arsenic into the top
surface layer, and a very large overall energy gain for surface incorporation
($\sim 3$ eV) compared to arsine in the gas phase. These large energy gains
are the driving force underpinning the surface incorporation of arsenic into
Ge(001) at room temperature.

As a further confirmation of our interpretation, we check that the densities
of ejected germanium and incorporated arsenic are equal. Feature t1 is one of
the most common features that we observe and this accounts for $30\pm 11$% of
all arsenic-germanium heterodimer features (m1, h1-h3, g1, and t1) that we
observe. The g1 features occur less frequently, accounting for $9\pm 4$% of
heterodimer features, while the number of B site germanium ad-dimers is
equivalent to $15\pm 5$% of the number of heterodimer features. Thus, noting
that each t1 and ad-dimer feature contains two germanium atoms, we account for
$99\pm 35$% of the germanium atoms ejected onto the surface results from the
incorporation of arsenic.

### Thermal annealing

Figure 3: a, STM image of arsine dosed Ge(001) after annealing to 140∘C. b,
Epitaxial germanium. c, m2 feature. d, Schematic of a h2 feature highlighting
the conversion to e, an m1 feature, and f, a m2 feature. g, Plot of the
feature count of all h1, h2, h3, g1, and t1 features, m1 features, and m2
features as a function of temperature up to 300∘C. Image parameters: (a,b)
$29\times 25$ nm2, (c) $6\times 4$ nm2, (a,b,c) $-1.5$ V, 200 pA. z-range: (a)
190 pm (b) 280 pm (c) 110 pm.

Figure 3a shows an image of a dosed surface after annealing to 140∘C. Almost
all of the room temperature features have disappeared, except the m1 features.
In their place, we find small isolated patches of epitaxial germanium (Fig.
3b), and features that appear as two dark dimers separated by a single clean
germanium dimer (Fig. 3c). The presence of epitaxial germanium is evidence
that the $140^{\circ}$C anneal provides sufficient energy for dimer diffusion
and the formation of small epitaxial islands, consistent with previous reports
Li and Altman (2002); Scappucci  _et al._ (2009).

The absence of all h1–h3 features demonstrates that this temperature is
sufficient for isolated hydrogen atoms in hemihydride (Ge-Ge-H) configurations
to shift from one dimer to the next. If we consider the h2 structure,
illustrated in Fig. 3d, we see two possibilities for such shifts indicated by
the red and blue arrows, resulting in the conversion to an m1 feature (Fig.
3e) or to a new structure, m2, shown schematically in Fig. 3f. This structure
(m2) has a Ge-As-H heterodimer and a single monohydride dimer, making it
chemically similar to the m1 feature; however in this case there is a single
clean germanium dimer that separates the heterodimer and the monohydride
dimer. The m2 structure has precisely the characteristics of the new features
observed in our STM images after 140∘C annealing (Fig. 3c), i.e., two dark
dimers separated by a clean germanium dimer.

Our DFT calculated energy for the m2 structure is $-3.1$ eV, which is the same
as the m1 feature. Thus, the m1 and m2 features are both 0.3 eV more stable
than any of the h1–h3 features; this means the reverse barrier for conversion
of m1 and m2 back to h1–h3 is necessarily 0.3 eV larger than the forward
barrier to form m1 and m2, explaining the conversion of the h1–h3 structures
into m1 and m2.

In Fig. 3g we show a plot of the density of features between room temperature
and 300∘C. We have grouped the features h1–h3, g1, and t1 into a single curve
and plot m1 and m2 separately. The m1 features are the most common feature on
the room temperature surface, accounting for $37\pm 8$% of all As-Ge-H
features. After the first anneal (140∘C) we see the number of h1–h3, g1, and
t1 features has fallen almost to zero, while there has been a rise in m1
features and a dramatic rise in m2 features. Upon annealing to higher
temperatures up to 300∘C we see the gradual disappearance of both m1 and m2
from the surface, which can be understood as the process where the hydrogen
begins to diffuse away from the m1 and m2 features to form isolated
monohydride dimers, leaving hydrogen-free arsenic-germanium heterodimers (As-
Ge), as discussed below.

Figure 4a shows an STM image of the surface after annealing to 250∘C. In this
image we no longer see any of the features from either the room temperature or
the 140∘C annealed surface. Instead, we see features that appear to be a
single dark dimer, highlighted in Fig. 4c, and features that look like a
single dimer that is strongly buckled, as highlighted in Fig. 4d. These
features are readily identifiable as monohydride dimers, and hydrogen-free
arsenic-germanium heterodimers, respectively Stock  _et al._ (2020); Curson
_et al._ (2004).

Figure 4: STM images of the arsine dosed Ge(001) surface after annealing to a,
250∘C and b, 420∘C. Boxes on panel (a) highlight a monohydride dimer and
arsenic-germanium heterodimer, respectively. c, Structure and STM image of a
monohydride dimer. d, Structure and STM image of a hydrogen-free arsenic-
germanium heterodimer. e, Plot of the feature count of all hydrogen-terminated
As-Ge-H heterodimer features (i.e., h1–h3, g1, t1, m1, and m2), mono-hydride
features, and hydrogen-free As-Ge heterodimers features up to 800∘C. Image
parameters: (a,b) $27\times 19$ nm2, (c,d) $3\times 4$ nm2. (a,c,d) $-1.5$ V,
200 pA. (b) $-1.5$ V, 200 pA. Z-range: (a,c,d) 120 pm, (b) 190 pm

Figure 4b shows an STM image of the surface after annealing to 420∘C, and here
we find the only surviving features are hydrogen-free arsenic-germanium
heterodimers. The absence of hydrogen from this surface is consistent with the
known desorption temperature of hydrogen from the monohydride phase on Ge(001)
of 330∘C Shimokawa  _et al._ (2000).

We show in Fig. 4e another plot of the density of features (c.f. Fig. 3f) on
the surface as a function of anneal temperature up to 800∘C. Here, we group
together all of the features that include a hydrogen-terminated As-Ge-H
heterodimer (i.e., h1–h3, m1, m2, g1, t1) into a single curve. We also plot
the density of hydrogen-free arsenic-germanium heterodimers and monohydride.
The density of As-Ge-H heterodimers diminishes rapidly as we anneal the
surface to above $200^{\circ}$C. Concomitant with their decrease is a rapid
rise in the density of bare arsenic-germanium heterodimers and isolated
monohydride. It is notable that the ratio of hydrogen to arsenic in the range
250–300∘C is equal to the expected stoichiometric ratio of 3:1 to within our
experimental uncertainties (accounting for two hydrogen atoms per
monohydride). The density of bare arsenic-germanium heterodimers remains
constant up to at least 500∘C, but is strongly reduced at our highest anneal
temperature (800∘C), which can be attributed to arsenic diffusion into the
bulk Stock  _et al._ (2020); Solmi and Nobili (1998); Pitters  _et al._
(2012), or arsenic desorption from the surface, or a combination of both. In
the case of desorption, this is likely to be in the form of As2 molecules, as
is known to occur for desorption of P2 molecules from the silicon (001)
surface between 670 and 820∘C Bennett  _et al._ (2010).

## Discussion

Our results show arsine on germanium represents a marked departure from all
previously studied donor precursors on silicon and germanium. In all
previously studied systems an incorporation anneal (typically 350∘C) is
required in order for the donor atoms to adopt substitutional lattice sites in
the surface Schofield  _et al._ (2003); Scappucci  _et al._ (2011); Stock  _et
al._ (2020). However, this anneal is highly undesirable as it provides a route
for the desorption of the donors from the surface, and presents a major
obstacle to the scale up to large-scale quantum technological devices Ivie
_et al._ (2021); Füchsle (2011). Arsine on germanium solves this problem,
since the donor atoms are completely substitutionally incorporated into the
surface spontaneously upon adsorption at room temperature, and no
incorporation anneal is required.

Furthermore, we note that the incorporation of arsenic is rapid. We have
performed arsine dosing in-situ, allowing us to restart imaging $<15$ minutes
after arsine exposure. We have not observed evidence for arsenic in any
configuration other than As-Ge-H heterodimers. Moreover, in all cases, each
As-Ge-H heterodimer is accompanied by two additional hydrogen atoms in the
form of either a monohydride dimer, or two hemihydride dimers. This suggests
that arsine dissociates and incorporates immediately on adsorption, without
any surface diffusion. Thus, it can be anticipated that arsine will fully
dissociate and incorporate into suitably defined lithographic patches with
extremely high fidelity, as required for the fabrication of large-scale
quantum technological devices, e.g., those involving large numbers of qubits.

We have presented a comprehensive understanding of the incorporation of
arsenic into the germanium (001) surface due to the exposure to arsine at room
temperature. We have demonstrated that arsine fully dissociates on the Ge(001)
surface at room temperature, and results in the substitutional incorporation
of arsenic into the surface layer. Our results are extremely significant in
the context of atomic-scale donor device fabrication as they provide a
solution to the donor incorporation probability problem that currently
severely limits the scale-up of phosphorus in silicon devices to large numbers
of qubits.

## Methods

### Scanning tunnelling microscopy

Scanning tunnelling microscopy (STM) experiments were performed in a Scienta
Omicron GmbH low-temperature STM system operating at room temperature and
under ultrahigh vaccuum $<5\times 10^{-10}$ mbar. High resistivity (1–100
$\Omega$cm antimony doped) germanium 001-oriented samples were degassed
overnight at 200∘C, then heated to $760^{\circ}$C by direct current heating
for 1 hour. The samples were subsequently cleaned by repeated cycles of
sputtering (1.2 kV, 10 mA, 30 min) and direct current annealing (700∘C, 30
min). Sample preparation was then completed with three 30 s anneals to
$760^{\circ}$C, with a 25∘C/min cool down from 600∘C. An infrared pyrometer
(IMPAC IGA50-LO plus) was used to measure the sample temperature, providing
absolute temperature measurements accurate to $\pm 30^{\circ}$C. Arsine dosing
was performed in-situ with the STM tip macroscopically retracted. The samples
were exposed to 99.999% purity arsine (ATMI Inc.) with a total chamber
pressure of $1\times 10^{-10}$ mbar. After arsine dosing, the tip was
reapproached and imaging started within 15 minutes of dosing.

### Density functional theory

Density functional theory (DFT) calculations were performed using the B3LYP
hybrid exact-exchange functional Becke (1988); Lee  _et al._ (1988), atom-
centred Gaussian-type orbital basis sets, and methods of energy computations
and structure optimisation as implemented in the Gaussian 16 software Frisch
_et al._ (2016). A compact Ge21H20 cluster model was used to represent the
Ge(001) surface, describing three Ge-Ge dimers in the surface-closest atomic
layer, and eight, four, and three atoms in the second, third, and fourth
atomic layer, respectively. The twenty hydrogen atoms of the cluster provide a
chemical termination for all germanium atoms other than those of the surface
layer. These cluster-terminating hydrogen atoms were held in fixed positions
during all geometry optimisations in order to simulate the strain that would
be imposed by the surrounding surface and bulk atoms of an extended surface.
All other atoms were fully relaxed during geometry optimisation.

In our calculations two types of composite basis set were used, referred to in
the following as large and small. Geometry optimisations and vibrational
frequency calculations were conducted using the small basis, which is composed
of the standard 6-311++G(d,p) basis set for all atoms of the adsorbate and the
top surface layer of the cluster (i.e. the dimer atoms), a 6-311G(d,p) basis
set for second layer atoms, and the core-pseudopotential LANL2DZ basis set for
third and fourth layer atoms as well as the cluster-terminating hydrogen
atoms. Following geometry optimisation, a single-point energy is calculated at
the optimised structure using the large basis set, which is composed of the
6-311++G(2df,2pd) basis set for the adsorbate atoms and top surface layer and
a 6-311G(2df,2pd) basis set for all other atoms. Thus, using quantum-chemical
notation, the total energy, $E$, of a given structure is calculated as
$E_{\text{SCF}}(\text{B3LYP/large//B3LYP/small})+\text{ZPE}(\text{B3LYP/small})$.

Adsorption energies, $\Delta E$, of surface structures arising from the
adsorption and dissociation of arsine on Ge(001) were calculated as formation
energies of adsorption as follows

$\Delta E=E_{(\text{cluster+AsH}_{3})}-E_{\text{cluster}}-E_{\text{AsH}_{3}},$
(1)

where $E_{\text{cluster}}$ is the total energy of the bare germanium cluster,
$E_{(\text{cluster+AsH}_{3})}$ is the total energy of the cluster with an
adsorbed or dissociated arsine molecule, and $E_{\text{AsH}_{3}}$ is the total
energy of a gas phase arsine molecule.

In some of the adsorption structures considered here, a germanium atom has
been displaced away from the adsorption site to a location further away than
can be accommodated by our three-dimer cluster. In this case, the adsorption
energy is calculated as follows,

$\Delta
E=\frac{2E_{(\text{cluster+AsH}_{3}-\text{Ge})}+E_{(\text{cluster}+2\text{Ge})}-3E_{\text{cluster}}-2E_{\text{AsH}_{3}}}{2},$
(2)

where $E_{(\text{cluster+AsH}_{3}-\text{Ge})}$ is the total energy of the
cluster with a dissociated arsine molecule and one missing Ge atom and
$E_{\text{cluster}+2\text{Ge}}$ is the total energy of a cluster with a Ge-Ge
ad-dimer, bridging perpendicular between two surface dimers. These ad-dimers
are directly observed in our experiments and are therefore the correct
reference to account for the displaced germanium atoms in our calculations.

## acknowledgement

This project has been supported by the EPSRC project Atomically Deterministic
Doping and Readout For Semiconductor Solotronics (EP/M009564/1). EVSH was
partly supported by the EPSRC Centre for Doctoral Training in Advanced
Characterisation of Materials (EP/L015277/1), and IHP Leibniz-Institut fur̈
Innovative Mikroelektronik. RC was supported by the EPSRC and SFI Centre for
Doctoral Training in Advanced Characterisation of Materials (EP/L015277/1).
TJZS was partly supported by the JSPS/ESPRC core-to-core scheme under project
Defect Functionalized Sustainable Energy Materials: From Design to Device
Application (EP/R034540/1). SRS acknowledges the use of the UCL Myriad High
Performance Computing Facility (Myriad@UCL).

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