# Nanosecond Laser Annealing: impact on superconducting Silicon on Insulator
epilayers

Y. Baron  Uni. Paris-Saclay, CNRS, Centre de Nanosciences et de
Nanotechnologies, 91120, Palaiseau, France  J. L. Lábár  Thin Film Physics
Laboratory, Institute of Technical Physics and Materials Science, Centre of
Energy Research, Konkoly Thege M. u. 29-33, H-1121 Budapest, Hungary  S.
Lequien  Uni. Grenoble Alpes, CEA,IRIG-MEM, 38000 Grenoble, France  B. Pécz
Thin Film Physics Laboratory, Institute of Technical Physics and Materials
Science, Centre of Energy Research, Konkoly Thege M. u. 29-33, H-1121
Budapest, Hungary  R. Daubriac  Univ. Grenoble Alpes, CEA,LETI, Minatec
Campus, 38000 Grenoble, France  S. Kerdilès  Univ. Grenoble Alpes, CEA,LETI,
Minatec Campus, 38000 Grenoble, France  P. Acosta ALba  Univ. Grenoble Alpes,
CEA,LETI, Minatec Campus, 38000 Grenoble, France  C. Marcenat  Univ. Grenoble
Alpes, CEA, Grenoble INP,IRIG-PHELIQS, 38000 Grenoble, France  D. Débarre
Uni. Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120,
Palaiseau, France  F. Lefloch<EMAIL_ADDRESS>Univ. Grenoble Alpes,
CEA, Grenoble INP,IRIG-PHELIQS, 38000 Grenoble, France  F. Chiodi
<EMAIL_ADDRESS>Uni. Paris-Saclay, CNRS, Centre de
Nanosciences et de Nanotechnologies, 91120, Palaiseau, France

###### Abstract

We present superconducting monocrystalline Silicon On Insulator thin 33 nm
epilayers. They are obtained by nanosecond laser annealing under ultra-high
vacuum on 300 mm wafers heavily pre-implantated with boron
($2.5\times\,10^{16}\,at/cm^{2}$, 3 keV). Superconductivity is discussed in
relation to the structural, electrical and material properties, a step towards
the integration of ultra-doped superconducting Si at large scale. In
particular, we highlight the effect of the nanosecond laser annealing energy
and the impact of multiple laser anneals. Increasing the energy leads to a
linear increase of the layer thickness, and to the increase of the
superconducting critical temperature $T_{c}$ from zero ($<35\,mK$) to
$0.5\,K$. This value is comparable to superconducting Si layers realised by
Gas Immersion Laser Doping where the dopants are incorporated without
introducing the deep defects associated to implantation. Superconductivity
only appears when the annealed depth is larger than the initial amorphous
layer induced by the boron implantation. The number of subsequent anneals
results in a more homogeneous doping with reduced amount of structural defects
and increased conductivity. The quantitative analysis of $T_{c}$ concludes on
a superconducting/ non superconducting bilayer, with an extremely low
resistance interface. This highlights the possibility to couple efficiently
superconducting Si to Si channels.

## Introduction

In the context of solid-state based quantum engineering, material science
remains a very active field of research. Recent reviews [1, 2, 3, 4] point out
the importance of controlling both the quality of materials, to prevent/reduce
quantum decoherence [5, 6], and the reproducibility, in the prospect of
scaling-up quantum technology towards a very large number of qubits. In this
quest of large scale integration, silicon and germanium can be seen as the
short-term most promising materials [7, 8]. However, they are now restricted
to spin qubits, where the rather low yield in the quantum properties has
limited the demonstration of coupled qubits to a very small number [9], as
compared to superconducting transmons qubits where operations with few tens of
qubits have been recently demonstrated [10, 11]. The possibility to fabricate
superconducting qubits with silicon would give both the advantage of a mature
technology and of superconductivity. In principle, this could be done with
superconducting silicon, obtained by combining heavily boron doping and
nanosecond laser annealing [12, 13, 14, 15, 16]. But implementation of
superconducting Si:B into quantum circuits is still at its early age [17, 18]
and a better understanding of the superconducting properties is still
required, especially with the constraints of the use of compatible large scale
integration tools. In the present study, we investigate the superconducting
properties of boron doped superconducting silicon epilayers obtained on 33 nm
thick SOI (Silicon On Insulator) 300 mm wafers after pre-implantation of boron
dopants followed by nanosecond laser annealing. Our results demonstrate a
continuous increase of the superconducting critical temperature $T_{c}$ as a
function of melted depth tuned by the laser energy, and the weak impact of
implantation-induced defects. A maximum $T_{c}$ of about $0.5\,K$ is reached
when the entire 33 nm thick silicon layer is melted, producing a crystalline
structure, while no superconductivity is observed when the annealing only
affects the surface amorphous layer induced by the strong dopant implantation.
We emphasize the role of identical multiple laser shots by comparing series of
sample having sustained 1 or 5 laser shots annealings, highlighting the
decrease of defects and better homogeneity with an increased number of shots.
The $T_{c}$ variation is well described by a two-layers model (one being
superconducting and the other not) connected through a high transparency
interface. This points out the possibility to optimally couple the
superconducting layer to silicon channels through low resistance interfaces.

### Nanosecond annealing of B implanted SOI

Figure 1:  Combined plot of Time Resolved Reflectometry $TRR$ (a), room
temperature square resistance $R_{sq}$ (b), superconducting critical
temperature $T_{c}$ (c) and measured active carriers surface density
($\mathcal{N}$) (d) as a function of the laser energy density $E_{L}$. The
dotted line at $E_{L}=445\,mJ/cm^{2}$ indicates the cross-over from a
polycrystalline boron doped layer (regime 1) to a crystalline epilayer (regime
2). The dotted line at $E_{L}=560\,mJ/cm^{2}$, where $R_{sq}$ diverges,
corresponds to the full melt of the initial silicon on insulator layer as the
annealing touches the amorphous $SiO_{2}$ BOX (regime 3). The $TRR$ color plot
scale corresponds to the measured TRR amplitude from 0.75$\,\mathcal{R}_{Si}$
(dark blue) and 2.26$\,\mathcal{R}_{Si}$ (red), and is a signature of the
layer structure: amorphous (green), polycristalline (light blue),
monocrystalline (dark blue), liquid (red). The laser pulse starts at t=10 ns.

The first step of the fabrication of superconducting SOI layers is the
implantation of a very high boron dose ($2.5\times 10^{16}\,$cm-2) at $3\,$keV
on a non-intentionally doped $300\,$mm wafer. The initial SOI wafer has a
silicon layer $33\,$nm $\pm 1\,$ nm thick on top of a SiO2 buried oxide layer
(BOX) of $20\,$nm, as in [15]. After the implantation, the SOI layer is
composed of an amorphous layer (a-Si) of $15\pm 1\,$nm on top of the remaining
silicon crystalline layer (c-Si) (see Fig.4a in [15]). CTRIM simulations show
that the dopants concentration in the underneath c-Si layer remains
significant (above $1\,at.\%$ percent) [19].
The nanosecond laser annealing process is performed with an excimer XeCl laser
of pulse duration $25\,$ns under UHV (Ultra High Vacuum) conditions
($P=10^{-9}\,$mbar) with energy density at the sample level $E_{L}=300$ to
$600\,mJ/cm^{2}$ ($E_{L}=600\,mJ/cm^{2}$ corresponding to bulk Si melting
threshold). The effect of the laser pulse is to melt the top of the implanted
silicon layer, over a $2$mm$\,\times\,2$mm surface with laser energy
homogeneity of $1.2\%$, during $\approx 15$ to $25\,$ns. This induces an
extremely fast re-crystallisation, activating the dopants up to a saturation
concentration of $n_{sat}=3\times 10^{21}\,$cm-3 (6 at.$\%$), an order of
magnitude above the solubility limit $n_{sol}\sim 4\times 10^{20}\,$cm-3 [20].
The thickness of the melted layer linearly depends on the laser energy at the
sample level. The Time Resolved Reflectometry (TRR) of a red
($\lambda=675\,$nm) laser is recorded in-situ during the nanosecond laser
annealing to follow the melting-solidification process, and its value is
compared to bare, undoped, Si reflectivity $\mathcal{R}_{Si}$ (Fig.1a).
For the present study, two series of laser spots have been generated. For the
first series, each spot has been patterned after the laser annealing, to
define Hall cross structures with Ti/Au contact pads allowing precise
measurement of the square and Hall resistances. The second series of spots
remained untreated, for X-Rays Diffraction (XRD) analysis. For both series, we
have measured the resistance as a function of temperature down to $\approx
35\,mK$ to extract the superconducting transition temperature $T_{c}$ as a
function of the laser energy $E_{L}$. We emphasize the precise control on
$E_{L}$, and the impact of the sharp, flat, few nanometer thick interface at
the bottom of the annealed layer, which allow to fine-tune with $E_{L}$ the
depth in the 33 nm deep SOI with 1-2 nm precision. The overall results for the
time resolved reflectivity $TRR$, the square resistance $R_{sq}$, the
superconducting transition temperature $T_{c}$ and the active dopants dose
$\mathcal{N}$ measured by Hall effect are shown in Fig.1 as a function of the
laser energy density $E_{L}$.
We can identify three regimes. The first regime (regime 1) is for
$E_{L}<445\,mJ/cm^{2}$ where no superconductivity is observed. The second
regime (regime 2) applies for $445\,mJ/cm^{2}<E_{L}<560\,mJ/cm^{2}$ with an
almost linear increase of $T_{c}$ up to a maximum value of $0.5\,K$. For
$E_{L}>560\,mJ/cm^{2}$ (regime 3), the entire silicon layer is full-melted,
the resistance diverges and no superconductivity is observed. We observe
important differences to the results of [15], where the annealing was
performed on the $same$ implanted layers under $N_{2}$ with a similar XeCl
excimer laser but of longer laser pulse duration (160 ns instead of 25 ns). In
the present work, we achieve a $T_{c}$ tunable up to 0.5 K, with a
superconducting phase only observed in monocrystalline layers below the full
melt threshold, as opposite to the constant $T_{c}\sim 0.18\,K$ obtained only
in a poly-crystalline layer above the full melt in [15]. Our results are
instead more similar to what was observed for the longer annealing of 160 ns
with an increased ion implantation energy, from 3 keV to 4 keV, for which
monocrystalline films were shown to be superconducting at $T_{c}=0.39\,$mK
[16]. The recrystallisation dynamics seems then to be strongly dependent on
the laser pulse duration, even for relative small changes (25 ns to 160 ns).

### Explosive crystallisation, monocrystalline SiB, full-melt

Fig.1 shows the drastically different behavior observed in the three regimes:
the explosive crystallization regime (1), the monocrystalline regime (2), and
the full melt regime (3). In regime $1$ an explosive re-crystallisation of the
doped amorphous Si (a-Si) takes place, followed by the partial melting of the
resulting poly-crystalline Si (poly-Si). In this dynamic scenario [21], even
for weak laser energy, a thin layer of the initial top a-Si melts. The
transition from solid to liquid occurs during the first nanoseconds of the
laser pulse. This thin layer re-solidifies almost instantly into poly-Si and
the latent heat released during this liquid to solid transformation is
sufficient to progressively melt the a-Si underneath. The process stops when
the entire initial a-Si is totally transformed into poly-Si, as the energy is
not sufficient to melt crystalline Si. During the remaining time of the laser
pulse, as the laser energy increases above the poly-Si melting threshold, the
just-formed poly-Si is melted over a depth that depends linearly with the
laser energy density. In regime $1$, the entire a-Si is therefore transformed
into poly-Si with a final thickness independent on the laser energy, with part
of the poly-Si having been remelted. This results in a variation of
reflectivity from the initial amorphous state at
$\mathcal{R}_{a}=$1.52$\,\mathcal{R}_{Si}$ to the polycrystalline state
$\mathcal{R}_{poly}=1.05\,\mathcal{R}_{Si}$ (Fig.1a). The square resistance
varies only slightly with the laser energy density and the small decrease
observed is due to the re-arrangement of poly-crystals and a slightly better
activation as a consequence of the poly-Si melting (Fig.1b). Correspondingly,
the active dose ($\mathcal{N}$) measured by Hall effect is nearly constant and
independent on $E_{L}$ (Fig.1c). From the laser energy density that
characterizes regime 1, we estimate the thickness of the poly-Si layer to
$\approx 18.5\,nm$, close to the initial a-Si layer thickness [15].

In regime $2$, the laser energy density is strong enough to melt the entire
poly-Si created by explosive recrystallization from the a-Si layer, plus a
thin part of the crystalline c-Si layer underneath. In that situation, the
poly-Si is entirely melted and transformed into a boron doped monocrystalline
silicon Si:B epilayer from the remaining weakly doped c-Si seed. This can be
observed in the $TRR$ map as the reflectivity first peaks as a result of the
explosive crystallisation (Fig.1a, yellow line at $t\sim 20\,$ns,
$\mathcal{R}_{ec}=1.82\,\mathcal{R}_{Si}$) then increases to the melted phase
(red, $\mathcal{R}_{melt}=2.2\,\mathcal{R}_{Si}$) to finally cool down to a
monocrystal (blue, $\mathcal{R}_{mono}=0.95\,\mathcal{R}_{Si}$). The final
thickness of Si:B layer on top of the c-Si depends linearly on the laser
energy density (Fig.S7). The active dose ($\mathcal{N}$) increases with
$E_{L}$ (Fig.1d), due to the incorporation and activation of an increasing
amount of implanted dopants in the Si:B layer. Note that the measured
$\mathcal{N}$ is always lower than the initial implanted dose (at most
38$\%$), as the Hall effect only measures the active dose. From the $TRR$ maps
identification of the full melt ($d_{melt}=d_{SOI}$) and the corresponding
dose $\mathcal{N}_{FM}$), it is possible to extract the active concentration
of the thickest monocrystalline layer, $\mathcal{N}_{FM}/d_{SOI}=2.9\times
10^{21}cm^{-3}$. The active concentration for the thinnest monocrystalline
layer is likewise calculated to $3.1\times 10^{21}cm^{-3}$. This suggests that
the layers present a nearly constant active concentration $n_{sat}\approx
3\times 10^{21}cm^{-3}$, equal within $7\,\%$ for all the layers, as also
confirmed by the nearly constant position of the Si:B XRD peak (Fig.S5).
Similarly, a saturation of the active concentration $n_{sat}=2.8-3.1\times
10^{21}cm^{-3}$ was observed in bulk Si:B layers in the same 23 to 47 nm
thickness range [20]. Those layers, realized by Gas Immersion Laser Doping
(GILD), employed nanosecond laser annealing with exactly the same laser, but
with a BCl3 gas precursor. The active concentration limit could thus be
associated not to the dopant incorporation method, but to the maximum
recrystallisation speed ($\sim 4m/s$) [22] induced by the 25 ns pulse
duration.
As the Si:B layer becomes thicker, the square resistance decreases smoothly
with $E_{L}$ (Fig.1b). One can notice that the square resistance after one
laser shot is larger than after five shots. This can be understood as, on one
side, the crystalline quality slightly improves upon repeated annealing, and,
on the other, the homogeneity of the boron is increased as the dopants
initially present in the top of the layer have more time to diffuse within the
whole melted layer. In this regime $2$, the superconducting temperature
transition grows from $T_{C}<35\,mK$ ($35\,mK$ is the minimum transition
temperature we could measure in our cryostat) to $0.5\,K$ just before reaching
the full-melt regime $3$ (Fig.1c). Contrary to the $R_{sq}$ behavior, the
$T_{c}$ difference between 1 and 5 shot(s) is less marked.

Finally, the regime $3$ is reached when the laser energy is large enough that
the entire silicon layer melts (full melt threshold) and an amorphous Si:B
layer builds up on the underneath amorphous SiO2, recovering the initial
amorphous reflectivity $R_{a}/R_{in}=1.06$ (Fig.1a). As a result, the $R_{sq}$
diverges up to 100 k$\Omega$ and superconductivity is suppressed (Fig.1b,c).

###  Superconductivity and number of laser pulses

In order to better understand the impact of multiple laser shots on both the
superconducting and the normal state, we complemented our transport
measurements and X-Ray Diffraction data with Transmission Electronic
Microscopy (TEM). We show in Fig.2 the comparison between two samples in
regime 2 having the same active dose, realised with the same laser energy
$E_{L}$=522 mJ/cm2 where nearly all the Si has been melted ($d_{melt}$=29 nm),
with 1 or 5 laser shots. The TEM images show from left to right the Si
substrate, the SiO2 BOX, the B-implanted Si layer where the laser annealing
took place, and a capping layer introduced to protect the layer during TEM
sample preparation. The interface between melted and unmelted SiB is difficult
to discern in the contrast of this particular samples as the interface is only
$\sim$2 nm away from the BOX, and as the doping increases gradually over a few
nanometers from the bottom of the SiB layer [23].

Figure 2:  TEM images of two samples realised with 1 (a,c) or 5 (b,d) laser
pulses at $E_{L}$=522 mJ/cm2 ($d_{melt}$=29 nm). From left to right are
visible the Si substrate, the SiO2 BOX, the B-implanted Si layer where the
laser annealing took place, and a capping layer for TEM. The dotted lines mark
where dislocations and stacking faults align, as a result of strain
relaxation.

The impact of performing a few laser shots as opposite to a single one is
evident in the different sublayer structure within the laser annealed SiB, and
in an increased disorder for 1 laser shot. A larger amount of structural
defects is present for a single laser annealing, with dislocations and
stacking faults starting from two interfaces situated about 10 nm and 17-21 nm
above the BOX, interfaces created between a fully strained layer on the
bottom, a partially relaxed one in the middle with a gradually increasing
deformation, and a top sublayer with a constant deformation (Fig.S8). In
comparison, the sample realised with 5 laser shots is more homogeneous, with
fewer defects starting 13 nm above the BOX, and lower deformation (Fig.S8). We
can understand this difference as stemming from an incomplete B diffusion,
from the higher implanted concentration at the top towards the bottom, during
the short ($\sim 20\,ns$) melting time for a single laser shot, as opposed to
a more homogeneous dopant concentration for 5 laser shots allowing a longer
diffusion time ($\sim 100\,ns$).
These observations are in agreement with the electrical measurements: 1 shot
samples show, systematically, a higher resistance (Fig.1) and a Residual
Resistance Ratio RRR=$R_{300K}/R_{4K}$ closer to unity, indicating that the
resistance at low temperature can be mostly attributed to impurities and
crystallographic defects as opposed to thermal scattering. As an example, the
two samples shown in Fig.2 have RRR=1.1 and RRR=1.28 for 1 shot and 5 shots
respectively. Similarly, XRD data show a better crystalline quality for the 5
shot samples, highlighted by a higher amplitude of the diffraction peak
(Fig.S5 and S6).

Figure 3:  Square conductance (inverse of $R_{sq})$ as a function of the
active dopants density $\mathcal{N}$ measured with Hall effect for both 1 and
5 shots series. The dotted line is a linear fit on the 1 shot series from
which we can extract a mobility of $12.7\,cm^{2}V^{-1}s^{-1}$. The solid line
has the exact same slope (corresponding to the same mobility) but passes
though the origin of the graph at (0,0). The negative offset corresponds to an
additional scattering mechanisms in the 1 shot series and is not present for
the 5 shots series.

In addition, we have plotted (Fig.3) the square conductance $G_{sq}$
($1/R_{sq}$) as a function of the dose $\mathcal{N}$ for two series of 1 shot
and 5 shots samples. The two series show a linear $G_{sq}(\mathcal{N})$
dependence, which is consistent with the simple Drude formula
$G_{sq}=e\mu\mathcal{N}$, where $e$ is the electronic charge and $\mu$ the
carriers mobility. The mobility obtained by the linear fit is
$\mu=12.7\,cm^{2}V^{-1}s^{-1}$, a value in agreement with past measurements
for such doping levels [24]. However, this linear fit does not extrapolate to
the x-axis origin for the 1 shot series (dotted line), whereas it does for the
5 shots series (solid line). The difference can be explained by the existence
of a bilayer (or multilayer) structure for the 1 shot series, with one layer
more disordered than the other. Indeed then
$G_{sq}^{1shot}=e\mu\mathcal{N}_{1}+e\mu^{\prime}\mathcal{N}_{2}<G_{sq}^{5shots}=e\mu\mathcal{N}$
with $\mu^{\prime}<\mu$. Plotting $G_{sq}$ vs
$\mathcal{N}=\mathcal{N}_{1}+\mathcal{N}_{2}$, gives
$G_{sq}^{1shot}=e\mu(\mathcal{N}_{1}+\mathcal{N}_{2})-e(\mu-\mu^{\prime})\mathcal{N}_{2}$,
with a negative offset such as the one observed in Fig.3. From the offset
amplitude it is also possible to roughly estimate the thickness of the poorly
conducting layer: taking the saturation active concentration in the whole
annealed layer ($n\sim 3\times 10^{21}\,$cm-3) and assuming
$\mu>>\mu^{\prime}\sim 0$, from $\Delta G_{sq}=3.9\,$mS =
$e\mu\mathcal{N}_{2}=e\mu n_{2}d_{2}$, we deduce $d_{2}\sim 6.5\,$nm. For such
rough estimation, this layer thickness is comparable, while smaller, to the 7
to 11 nm thickness of the central sublayer in 1 shot sample (Fig.2), where a
high density of stacking faults and dislocations is observed, suggesting that
the very disordered layer has a small (non-zero) $\mu^{\prime}$, while the 5
shots samples have an homogeneous mobility.

###  Superconductivity and laser energy

Figure 4:  $T_{c}$ vs laser-melted thickness $d_{melt}$ for both 1 and 5 laser
shots. The black dotted line, plotted in both the 1 and 5 laser shots panel,
shows the 2-parameter fit, in the hypothesis of $d_{S}=d_{melt}$, with
$T_{c,0}=0.52\,$K and $b=0.5$. The red continuous line shows the 3-parameter
fit with the hypothesis that the superconducting layer corresponds to the
relaxed portion of the melted layer, with $T_{c,0}=1.04\,$K, $b=0.108$ and
$d_{S}=d_{melt}-16.6\,$nm for 1 shot and $T_{c,0}=1.04\,$K, $b=0.29$ and
$d_{S}=d_{melt}-9\,$nm for 5 shots.

We now focus on the strong energy dependence of the superconducting critical
temperature. As the laser energy affects directly the melted thickness, we
plot $T_{c}$ vs. $d_{melt}$ in Fig.4. The correspondence between $d_{melt}$
and $E_{L}$ is extracted independently from the measurements of the TRR, the
dose, and the resistance, showing a good agreement and a common dependence
$d_{melt}(E_{L})$ (details in the Suppl. Mat.). For both 1 and 5 laser shots,
$T_{c}$ increases steeply with the thickness up to 0.5 K. To understand the
critical temperature dependence with thickness we recall that the melted,
ultra-doped layer is on top of the remaining, unmelted Si above the BOX, where
an implanted concentration above $\sim 1\,at.\%$ is expected. In bilayer
structures made of one superconducting (S) layer in contact with a second
normal (N) layer, a strong suppression of the $T_{c}$ can take place, if the
interface between the two layers is transparent. This is only observed when
the thickness of the S layer is smaller or of the order of the superconducting
coherence length, as is our case with $d_{melt}<33$nm$<\xi\approx 50\,$nm
[20]. This effect, known as the inverse proximity effect, was already observed
on superconducting Si layers realised in bulk Si samples [25] and is well
described with the Usadel model [26, 27, 28]:

$\displaystyle T_{c}$
$\displaystyle=T_{c0}\left[\frac{T_{c0}}{1.14\Theta_{D}}\sqrt{1+\left(\frac{k_{B}\Theta_{D}}{\tau}\right)^{2}}\right]^{\frac{bd_{N}}{d_{S}}}$
(1a) $\displaystyle\tau$
$\displaystyle=\frac{\hbar}{2\pi}\frac{v_{F,S}}{\rho_{int}}\frac{bd_{N}+d_{S}}{bd_{N}d_{S}}$
(1b) $\displaystyle b$
$\displaystyle=\frac{v_{F,S}}{v_{F,N}}=\left(\frac{n_{N}}{n_{S}}\right)^{1/3}$
(1c)

where $T_{c0}$ is the superconducting critical temperature of the single S
layer, $\Theta_{D}$ the phonon energy scale in temperature units, $d_{N}$
($d_{S}$) the thickness, $v_{F,N}$ ($v_{F,S}$) the Fermi velocity and $n_{N}$
($n_{S}$) the active dopant concentration in the normal (superconducting)
layer [14]. $\rho_{int}$ is the dimensionless interface resistance per
channel, related to the total interface resistance per unit area A by
$R_{int}A=h/2e^{2}\,(\lambda_{F,S}/2)^{2}\,\rho_{int}$.
The first noteworthy result is that it is possible to describe the
$T_{c}(d_{melt})$ dependence with zero interface resistance ($\rho_{int}=0$),
for both 1 and 5 laser shots, highlighting a very good transparency. Even
more, all the fits imposing a small but finite interface are, though in
reasonable agreement, less satisfactory than the one at zero interface. Eq.1
thus simplifies to:

$T_{c}=T_{c0}\,\left[\frac{T_{c0}}{1.14\Theta_{D}}\right]^{\frac{bd_{N}}{d_{S}}}$
(2)

To reduce the number of free fitting parameters, we fix $\Theta_{D}$, of weak
influence on the fit, to its simulated value $\Theta_{D}=650\,$K [29]. The
simplest thicknesses choice consists in associating the superconducting layer
to the melted layer. Thus, the superconducting and normal layer thicknesses
are $d_{S}=d_{melt}$ and $d_{N}=d_{SOI}-d_{melt}$. The remaining fitting
parameters are $T_{c,0}$ and the ratio of the Fermi velocities
$b=v_{F,S}/v_{F,N}$. The best fit of $T_{c}(d_{melt})$ for the whole datasets
containing 1 and 5 laser shots results is given by $T_{c,0}=0.52\,$K and
$b=0.5$ (Fig.4). The fitted $T_{c,0}$ corresponds well to the critical
temperature $T_{c}=0.5\,$K measured in GILD Si bulk samples of similar
thickness $d=30\,$nm and active doping $n_{B}=3\times 10^{21}\,$cm-3 [20].
Expressing $b$ in in the free electron model
$b=v_{F,S}/v_{F,N}=(n_{N}/n_{S})^{1/3}$, we recover a concentration in the
unmelted normal layer, underneath the melted layer, of $n_{N}=3.75\times
10^{20}cm^{-3}$. This value is remarkably close to the equilibrium solubility
limit $n_{sol}=4\times 10^{20}cm^{-3}$, suggesting that a large fraction of
the dopants present in the implantation queue ($>5.7\times 10^{20}cm^{-3}$)
would be activated, up to the equilibrium saturation concentration, by the
heat provided by the melted layer just above (the Si melting temperature being
$1683\,$K).
While this two-parameter fit provides a coherent scenario, it is interesting
to look at the results of the three parameters fit ($T_{c,0}$, $b$ and
$d_{S}$), relaxing the constraint about the superconducting thickness
corresponding to the melted thickness, maintaining $d_{N}=d_{SOI}-d_{S}$. The
fit is performed on the 1 shot samples, for which a larger range and number of
points are available (Fig. 4). A better agreement with the experimental data
is then achieved, with $T_{c,0}=1.04\,$K, $b=0.108$ and
$d_{S}=d_{melt}-16.6\,$nm (Fig.4). These fitting parameters suggest a scenario
where the superconducting layer is only the top part of the melted layer,
above the highest dislocation line, where the strain has been relaxed
(Fig.S8). In this case, the normal layer is $d_{N}=d_{SOI}-d_{melt}+16.6\,$nm,
which in the case of the samples shown in TEM analysis (Fig.2) gives
$d_{N}=20.6\,$nm, in agreement with the position of the dislocation line
$17-21\,$nm above the BOX. $T_{c,0}$ is moreover in reasonable agreement to
the maximum $T_{c}=0.9\,$K observed for $d_{melt}=300\,$nm thick bulk Si
samples, where the influence of the thin, fully strained layer, can be
neglected. In order to check if the identification of the superconducting
layer with the relaxed one is also coherent in the case of the 5 shots
samples, we have plotted in Fig.4 the $T_{c}(d_{melt})$ one parameter fit
imposing the same $T_{c,0}=1.04\,$K and $d_{N}=d_{SOI}-d_{melt}+9\,$nm, again
associating the superconducting layer to the relaxed region (for the sample in
Fig.2, this gives $d_{N}=13\,$nm in correspondence with the dislocation line
$13\,$nm above the BOX). The resulting fitted $b=0.29$ is then higher than the
one estimated from 1 shot samples fit $b=0.108$, in agreement with the larger
B concentration expected in the bottom of the sample after 5 laser shots
following the more homogeneous distribution of B for multiple laser shots.
This results highlight the importance of the structural strain relaxation in
the establishment of Si superconductivity, in agreement with recent results on
bulk Si [20, 30].

### Conclusions

In conclusion, we demonstrate superconducting monocrystalline Si epilayers
with critical temperatures up to $0.5\,$K, obtained on 33 nm thick SOI 300 mm
wafers after heavy pre-implantation of boron ($2.5\times 10^{16}\,cm^{-2})$
followed by nanosecond laser annealing with $25\,$ns pulse duration. The
analysis of the transport properties ($R$, $RRR$, dose $\mathcal{N}$,
$T_{c}$), coupled to structural measurements ($XRD$, $STEM$), have highlighted
the effect of the nanosecond laser annealing energy and the impact of multiple
laser anneals, both in the normal and superconducting phase. Increasing the
laser energy allows increasing linearly $T_{c}$, through the increase of the
melted thickness (and thus of the superconducting thickness), at a constant
saturation active concentration of $6\,at.\%$ (corresponding to the out-of-
equilibrium solubility limit attained by nanosecond laser annealing), while
also improving the overall quality of the layer, its crystallinity and
conductivity. The maximum $T_{c}$ obtained, $0.5\,K$, is comparable to the
$T_{c}$ of monocrystalline films of similar thickness obtained on bulk Si by
Gas Immersion Laser Doping, where the dopants are introduced by ’softer’
chemisorption. This implies that nanosecond laser annealing can heal
successfully the implantation-induced defects to recover a good crystallinity
from the initial amorphized phase. This supports the possibility of
transferring the fabrication of nanosecond laser annealed superconducting
layers from a laboratory environment towards more standard implantation-based
doping techniques. Performing just a few laser anneals (5) instead of a single
one reduces the amount of structural defects, such as stacking faults and
dislocations, and homogenizes the B depth distribution. Finally, the
quantitative analysis of the results in the frame of superconductor/normal
metal bilayer structures suggests the importance of the structural strain
relaxation to achieve the superconducting phase, and demonstrates an excellent
transparency between the layers, allowing the further development of
superconducting devices on SOI with compatible large scale integration tools.

##  Supplemental materials

### XRD

We have performed $\theta-2\theta$ X-Rays diffraction scans on 1 and 5 laser
shots series. The spectra obtained for 1 and 5 shots are shown in Fig.S5. From
these curves, the position, width and amplitude have been extracted using a
non-linear Gaussian fit in the vicinity of the peaks. The evolution of those
quantities is shown in Fig.S6.
A clear peak can only be observed when the melt depth exceeds the
polycrystalline layer created by explosive recrystallization at low energy.
The peak becomes sharper and higher with increasing laser energy (i.e. layer
thickness), indicating better crystalline properties resulting in a more
homogeneous layer. The position of the Si:B peaks is situated at higher
diffraction angle $2\theta_{SiB}\sim 72^{\circ}$ than Si, resulting from the
reduction of the crystal lattice due to the substitutional incorporation of B
atoms. From the peak position, we have obtained the relative variation of the
doped silicon out-of-plane lattice parameter using Bragg law:

$\frac{\Delta
a}{a}=\frac{a_{perp,SiB}-a_{Si}}{a_{Si}}=(\theta_{SiB}-\theta_{Si})\,cotan(\theta_{Si})$
(3)

where $a_{perp,SiB}$ is the Si:B lattice parameter perpendicular to the
epilayer, $a_{Si}$ that of the bare silicon and $\theta_{SiB}$ and
$\theta_{Si}$ the diffraction angles of Si:B and Si. We obtain $\Delta
a/a=-3.4$ to $-3.8\%$.

Figure 5:  Diffraction spectra of laser annealed doped silicon layers.  Figure
6:  Full width at half maximum (FWHM), amplitude and position of the Si:B XRD
diffraction peaks obtained from Gaussian fits.

### Estimating the doped depth

The estimate of the melted and correspondingly of the recrystallized SiB
thickness, is crucial to understand the superconducting properties of our
epilayers (see main text). The laser annealed thickness was determined by
several means (Fig.S7). First, the Time Resolved Reflectivity measured in-situ
during the doping allows identifying the laser energy $E_{L}$ for which the
melt begins (melting threshold, $d_{melt}=0$), for the poly-Si to
monocrystalline Si transition ($d_{poly-mono}\sim d_{a-Si}$) and for the full-
melt ($d_{melt}=d_{SOI}$). Since the melted depth is linear with $E_{L}$ (as
confirmed for different laser pulse profiles in [31]), a first estimate of
$d_{melt}(E_{L})$ is realized (stars and blue dotted line, Fig.S7). This first
study also shows that both the thinnest ($d_{poly-mono}$) and thickest
($d_{full-melt}$) monocrystalline layers display a similar concentration
$\mathcal{N}/d\approx 6at.\%=3\times 10^{21}\,at/cm^{3}$. Assuming that all
the layers have attained the same limit saturation concentration, it is
possible to plot the melted depth $d_{melt}=\mathcal{N}/n_{sat}$ from the
whole set of active dose $\mathcal{N}$ measurements, for both 1 and 5 laser
shots (Fig.1), confirming the $TRR$ estimation (black and red dots, Fig.S7).
The constant active boron concentration is also in agreement with XRD
measurements.
Additionally, the melted depth can also be extracted from the square
conductance : $d_{melt}=\rho G_{sq}$ with $\rho$ the resistivity of the
recrystallized SiB layer assuming the underneath layer has a negligible
conductance (red circles, Fig.S7). For this extraction we only use data from
the homogeneous 5 laser shots series. The value of the resistivity,
$\rho=170\,\mu\Omega cm$, is fixed from the resistivity of the full melt
sample, for which the thickness is known exactly, and whose value is coherent
with previous studies [20].
Remarkably, these estimates of the melted depth extracted from different
measurements are very consistent with each others and within 10$\%$
uncertainty. Moreover, the melted depth dependence is consistent with the
process described in sectionExplosive crystallisation, monocrystalline SiB,
full-melt: at low energy, $d_{melt}$ is almost constant and close to $18\,nm$,
while at larger energy, it increases linearly to reach $33\,nm$ at the full
melt threshold.

Figure 7:  Estimates of the melted depth using various and independent
measurements as a function of the laser energy. Blue stars and blue dotted
line: estimation from $TRR$ identification of the melt threshold, poly-Si to
c-Si transition and full melt, with $d_{melt}=aE_{L}+b$, a linear dependence
being already observed in [31]. Black and red dots:
$d_{melt}=\mathcal{N}/n_{sat}$, with $n_{sat}=3\times 10^{21}\,at/cm^{3}$
[20]. Red circles: $d_{melt}=\rho/R_{sq}$ with $\rho=170\mu\Omega cm$ [20].

### TEM - structural deformation

The in-plane and out-of-plane lattice deformations were extracted by the
Geometrical Phase Analysis (GPA) method from High Resolution Transmission
Electron Microscope (HRTEM) images. Fig.S8 shows the deformation for the two
samples shown in Fig.2. The higher density of structural disorder can be
correlated to the larger lattice deformation present in 1 shot samples.
Indeed, the in-plane and out-of-plane deformations
$\epsilon_{//}=(a_{SiB//}-a_{Si})/a_{Si}$ and
$\epsilon_{\perp}=(a_{SiB\perp}-a_{Si})/a_{Si}$ measured on the samples of
Fig.2, show $\epsilon_{//}=$1.9$\%$ (1.5$\%$) and $\epsilon_{\perp}=$2.5$\%$
(2$\%$) for 1 shot (5 shots) respectively.

Figure 8:  In plane and out-of-plane lattice deformation, obtained by GPA
method from HRTEM images [32], as a function of the distance to the BOX, for
the two samples shown in Fig.2 with 1 or 5 laser shots at $E_{L}=522mJ/cm^{2}$
($d_{melt}$=29 nm).

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