# Boron distribution in two-phase superconducting silicon-on-insulator by atom probe tomography

P. Dumas, S. Duguay, D. Blavette, M. Opprecht, S. Kerdilès, F. Lefloch, F.

Nemouchi

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P. Dumas, S. Duguay, D. Blavette, M. Opprecht, S. Kerdilès, et al., Boron distribution in two-phase superconducting silicon-on-insulator by atom probe tomography. Journal of Applied Physics, 2025, 138 (5), pp.053901. 10.1063/5.0264354. hal-05201223

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# Boron distribution in two-phase superconducting silicon-on-insulator by atom probe tomography

P. Dumas ⚙️ ; S. Duguay ⚙️ ; D. Blavette; M. Opprecht; S. Kerdilès ⚙️ ; F. Lefloch ⚙️ ; F. Nemouchi ⚙️

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J. Appl. Phys. 138, 053901 (2025)

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# Boron distribution in two-phase superconducting silicon-on-insulator by atom probe tomography

Cite as: J. Appl. Phys. **138**, 053901 (2025); doi: 10.1063/5.0264354

Submitted: 10 February 2025 · Accepted: 11 July 2025 ·

Published Online: 1 August 2025

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P. Dumas,<fnref n="1" />,ª ID S. Duguay,<fnref n="2" /> ID D. Blavette,<fnref n="2" /> M. Opprecht,<fnref n="1" /> S. Kerdilès,<fnref n="1" /> ID F. Lefloch,<fnref n="3" /> ID and F. Nemouchi<fnref n="1" /> ID

## AFFILIATIONS

## ABSTRACT

We investigate with Atom Probe Tomography (APT) the distribution of boron in a thin superconducting Silicon-On-Insulator film (33 nm) obtained by high-dose ion implantation (2.5 × 10¹⁶ at/cm<fnref n="2" />) and single-pulse laser melting (160 ns). Only 40% of the target dose was found in the superconducting film, indicating a severe loss of dopants upon fabrication. Besides, the extremely rapid growth of SiB₃ precipitates during laser melting impedes the incorporation of active boron in the silicon lattice. Overall, SiB₃ precipitates and hyperdoped silicon account for 5.0 × 10¹⁵ at/cm<fnref n="2" /> and 1.0 × 10¹⁶ at/cm<fnref n="2" /> of the retained dose, respectively. This partitioning of boron between the two phases is supported by the “isolated active dopants model,” which allowed to trace back the sheet resistance of the film from APT data. Lastly, the superconducting critical temperature of the present film (0.39 K) is relatively high in view of the computed concentration of active boron (2.3 × 10²<fnref n="1" /> cm⁻<fnref n="3" />). This highlights the interplay between doping and strain relaxation in the establishment of superconductivity.

© 2025 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0264354

## I. INTRODUCTION

In the fields of semiconductors, hyperdoping is the process of introducing impurities beyond their solubility limit with the aim of achieving new properties in host materials. In silicon andgermanium, one can cite the use of chalcogens (S, Se, and Te) for improving the sub-bandgap photoelectric response<fnref n="1" />,<fnref n="2" /> and that of dopants (B, Al, Ga) for turning semiconductors into superconductors.<fnref n="3" />,⁴ In particular, the discovery of superconductivity in boron-hyperdoped silicon has opened the way to the fabrication of quantum devices with the mature processes of the silicon technology. So far, however, only proofs of concept have been achieved in an academic environment,⁵ but the ultimate goal remains to fabricate such devices on wafers using CMOS compatible processes.

Regarding the mere fabrication of superconducting silicon, the objective of large-scale integration implies to switch from the original Gas Immersion Laser Doping (GILD) technique,⁶ performed under ultra-vacuum with multiple-pulse laser melting, to a simplified approach based on high-dose boron implantation and single-pulse laser melting under N₂ atmosphere. This process,

called Pulsed Laser Induced Epitaxy (PLIE), has been recently applied on 300 mm Silicon-On-Insulator (SOI) wafers using a large laser beam (1.5 × 1.5 cm<fnref n="2" />).⁷,⁸ The main result of these studies is the evidence of superconductivity in both polycrystalline and monocrystalline SOI layers hyperdoped over approximately 30 nm. However, in order to enhance the superconducting critical temperature of these films, one has to identify the mechanisms limiting the hyperdoping in terms of dopant deactivation and dose loss. In particular, we are willing to identify the nature of boron precipitates recently evidenced on electron microscopy images.⁸ Such precipitates are thought to consume a considerable amount of boron dose, and therefore to be detrimental for the establishment of superconductivity in hyperdoped silicon.

In this work, we investigate with Atom Probe Tomography (APT) the atomic-scale distribution of boron in a thin superconducting SOI film obtained by PLIE on a 300 mm platform. APT is an advanced microscopy technique capable of imaging in 3D the distribution of impurities inside clusters/precipitates or in the form of segregation at defects/interfaces.⁹,¹⁰ Here, we are able to treat separately the boron atoms incorporated as dopants in the silicon

<footnote n="1">¹Université Grenoble ALPES, CEA LETI, 38000 Grenoble, France</footnote>

<footnote n="2">²Univ. Rouen Normandie, CNRS, INSA Rouen Normandie, Groupe de Physique des Matériaux UMR 6634, F-76000 Rouen, France</footnote>

<footnote n="3">³Université Grenoble ALPES, CEA IRIG, 38000 Grenoble, France</footnote>

<footnote>ªAuthor to whom correspondence should be addressed: paul.dumas2@cea.fr</footnote>
lattice from those trapped in nanoscale precipitates and to quantify
the contribution of each phase. Lastly, the electrical properties of
the film are correlated to phase composition and discussed in
terms of process conditions (pulse duration, implant parameters).

II. MATERIALS AND METHODS

We started with a 300 mm SOI wafer featuring a 15 nm thick undoped silicon film on top of a 20 nm thick buried oxide (BOX). First, a 18 nm thick epitaxial silicon layer was deposited to thicken the original SOI layer, resulting in a 33 nm thick silicon film. Then, after HF cleaning, $^{11}$B⁺ ions were implanted at a dose of 2.5 × 10¹⁶ at/cm², an acceleration energy of 4 keV, a tilt angle of 7°, and a twist angle of 22°. After another HF cleaning, the wafer was introduced into a SCREEN LT-3100 equipment equipped with a UV laser (λ = 308 nm). Pulses of 160 ns duration were shot at the surface of 21 square fields of dimensions 1.5 × 1.5 cm², under N₂ atmosphere. The purpose of N₂ is to minimize oxygen penetration and oxide formation during laser irradiation. Each field received one single pulse carrying an energy density ranging from 1.0 to 1.5 J/cm² (a step of 0.025 J/cm²). Previous characterizations have shown that the energy at which the SOI starts melting is 1.0 J/cm², and the energy leading to its full melt is 1.325 J/cm².⁸ At 300 K, the smallest sheet resistance was found in the film irradiated just below the full melt threshold, namely, 1.3 J/cm². This energy led to the regrowth of a film of monocrystalline quality, hyperdoped down to the BOX, and exhibiting superconductivity below 0.39 K. After deposition of a 100 nm thick protective amorphous silicon layer by Plasma Enhanced Chemical Vapor Deposition (PECVD), the same film has been further characterized by electron microscopy (Fig. 1).⁸ White arrows indicate boron precipitates of around 2 nm radius. Note that the PECVD temperature was kept small (150 °C) to preserve the microstructure of the laser-annealed state.

Regarding the APT analysis made in the present work, a small
volume of material was lifted-out and attached to a tungsten needle
using a G4 CXe DualBeam plasma focused ion beam. Afterward, a
sharp tip of around 30 nm diameter was obtained by ion beam
milling and then cleaned at low acceleration voltage. Lastly, this tip
was field-evaporated at a baseline temperature of 80 K on a
CAMECA LAWATAP instrument equipped with an amplified
ytterbium-doped laser of 343 nm wavelength, delivering an energy
of 10 nJ during 350 fs, with a spot size of 0.3 mm and a repetition
rate of 100 kHz.¹¹ APT data were treated with the home-built
GPM3D software.

III. RESULTS AND DISCUSSION

A. A two-phase SOI film

Figure 2 highlights the mass spectrum related to the APT
analysis of the superconducting SOI film. One can first notice the
high Charge-State Ratio (CSR) of silicon ions (Si⁺⁺/Si⁺ ~ 20). This
ratio provides a qualitative indication of the strength of the electric
field at the tip apex, which, combined with the thermal energy of
laser pulses, gives rise to the field evaporation of atoms. For the
analysis of boron-doped silicon, a CSR higher than 10 is preferred
for keeping the laser power at a low value, and hence limiting the
thermal migration of boron and related artifacts.¹² Concerning the

evaporation of boron, the dominant ions are B⁺ and B⁺⁺ with a
small proportion of BO⁺, BO₂⁺, B₂⁺, and B₃⁺. These latter might origi-
nate from the evaporation of doped oxides and precipitates, respec-
tively. Finally, unshaded peaks of Fig. 2 correspond to hydrogen
ions (H⁺, H₂⁺, H₃⁺), oxygen ions (O⁺, O₂⁺), and water ions (H₂O⁺,
H₂O⁺⁺).

Figure 3(a) shows the 3D distribution of elements within the SOI film after reconstruction of the evaporated volume. Each colored dot represents one atom: green for boron, transparent red for silicon, and black for oxygen. The black appearing layers on either side of the reconstructed volume are the surface native oxide and BOX, respectively. Unfortunately, only the first nanometers of the BOX layer have been evaporated before the rupture of the tip. Nevertheless, the 3D image of the superconducting SOI layer is complete and shows two phases: one enriched in silicon (α phase) and a second one enriched in boron (precipitates β¹ to β⁴). The combined thickness of surface oxide and platelet β¹ is around 4 nm, which corresponds to the thickness of the surface layer appearing in black in Fig. 1. Therefore, we conclude that β¹ exceeds the lateral dimensions of the 3D volume so as to form a continuous line of precipitates at the surface. As for β² and β³, both have an elliptical/spherical shape with a mean radius of around 4 and 3 nm, respectively. These sizes are larger than those observed by electron microscopy (~2 nm, Fig. 1), hence constituting the first evidence for the existence of artifacts in APT data. Lastly, the dimensions of β⁴ cannot be properly determined as the precipitate is truncated.

Below the 3D image of Fig. 3(a) is shown the corresponding
boron profile expressed in atomic fraction (X₀ = n<sup>B</sup>/n<sup>B</sup> + n<sup>Si</sup> + n<sup>O</sup>).

<figure><img src="image_13.png" /><figcaption>**FIG. 1.** Cross-sectional transmission electron microscopy image of the superconducting SOI film obtained by PLIE on a 300 mm platform. From bottom to top, the substrate, the BOX layer (20 nm), the SOI film (31 nm), a surface oxidized layer (4 nm), and the protective amorphous film (a-Si). The image was taken in the high-angle angular dark-field imaging technique. The arrows indicate the regions of low atomic number that have been interpreted as boron precipitates (~2 nm radius). The monocrystalline quality of hyperdoped silicon was demonstrated by fast Fourier transform images.⁸</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>FIG. 2. Mass spectrum related to the APT analysis of the hyperdoped superconducting SOI film. Ions originating from the protective layer (a-Si) are not shown.</figcaption></figure>

The concentration varies from about 25 at. % close to the surface down to 5 at. % at the interface with the BOX, where a small segregation peak can be observed. There are also three peaks of concentration 22, 12, and 10 at. % whose depth coincides with the position of precipitates as shown above. However, from the perspective of measuring the exact composition of precipitates, one has to analyze each phase separately. For this purpose, a procedure that consists in sorting the boron atoms by phase was carried out. It consists in measuring the composition ($X_0$) inside a sphere of radius 2 nm around each boron atom. If $X_0$ exceeds a threshold $X_T$ with a number of atoms higher than $N_{MIN}$, the sphere atoms are assigned to precipitates. Otherwise, atoms are considered belonging to the $\alpha$ phase. Using $X_T = 10$ at. % and $N_{MIN} = 5$, a good agreement was found between the position and size of precipitates as shown in Fig. 3(a) with those resulting from the phase assignment [Fig. 3(c)]. Following this procedure, we created two files: one with the total number of atoms and one with atoms of the $\alpha$ phase only. Finally, one can remark that the interfaces between matrix and precipitates look sharper in Fig. 3(c) relatively to Fig. 3(a). This increased sharpness is artificial and exaggerated by the fact that not all atoms are shown in Fig. 3(c). This is in contrast with Fig. 3(a) where no special treatment was applied.

## B. Boron distribution in each phase

Let us now proceed with the separate analysis of phases. The atomic fraction of boron in the $\alpha$ phase is plotted as a function of depth in Fig. 4(a). $X_\alpha$ decreases almost linearly over 31 nm, from around 8 at. % down to 4 at. %. These values correspond to doping concentrations of $4 \times 10^{21}$ and $2 \times 10^{21}$ cm$^{-3}$ with respect to the silicon lattice. Naturally, these concentrations greatly exceed the solubility limit of boron at the melting point ($\sim 5 \times 10^{20}$ cm$^{-3}$), as expected after laser melting. What is more surprising is the fact that the doping concentration varies with depth. This is in contrast with the flat/box-shaped profiles obtained with GILD.⁶ This high homogeneity of dopant distribution with GILD can be explained in part by the multi-pulse treatment (few hundreds of laser shots),

allowing the dopant concentration to flatten progressively upon each pulse in the melt phase. Also, the “close to one” segregation coefficient ($k \sim 1$) enables the transfer of the homogeneity of the dopant concentration from the melt to the recrystallized phase. In our case, the single-pulse treatment is surely too short for flattening the as-implanted distribution in the melt. Besides, the melt is cooled at a slower rate because of the longer pulse of the present laser system (160 ns vs 25 ns for GILD). This leads to a reduced segregation coefficient ($k < 1$), and hence to a pileup of dopants at the surface.

In order to ensure that the $\alpha$ phase is indeed hyperdoped, one has to check the absence of tiny clusters in its midst. This can be done with the so-called “1NN method,” which consists in evaluating the distribution of First Nearest Neighbor (1NN) distances between boron atoms.¹³ The analysis has been restricted to the upper part of the $\alpha$ phase (5–19 nm) because the composition has to be relatively constant for applying the method. As shown in Fig. 4(b), the experimental distribution of 1NN distances is well fitted if one assumes that $\alpha$ is a single phase with a random repartition of boron atoms. This result supports the commonly accepted picture that boron atoms occupy the substitutional sites of the hyperdoped lattice without concomitant formation of clusters.¹⁴,¹⁵

Concerning the $\beta$ phase, the atomic fraction of boron was measured at different locations in $\beta^1$, $\beta^2$, and $\beta^3$ using a cylindrical probe of 4 nm diameter. Concentration profiles are shown in Fig. 5, where the vertical black lines indicate the position of $\alpha/\beta$ interfaces as defined in Fig. 3(c). These interfaces are, in fact, quite diffuse ($\sim 2$ nm), as shown by the slow increase of $X_\beta$ toward the core of precipitates. The existence of diffuse interfaces combined with the observation of precipitates with overestimated sizes (Fig. 3) is a clear manifestation of local magnification effects.¹⁶,¹⁷ While these latter may bias the concentration close to interfaces, the concentration in the core remains unaffected and is representative of the true precipitate composition. The averaged core concentration is equal to 78 at. % in $\beta^1$, 80 at. % in $\beta^2$, and 70 at. % in $\beta^3$. These values are consistent with the composition of $SiB_3$, a metastable boride whose
<figure><img src="image_15.png" /><figcaption>FIG. 3. (a) 3D distribution of boron, silicon, and oxygen in the reconstructed volume (from left to right, 1.5 nm of SiO$_{2}$, 34 nm of α + β, and the first 3 nm of BOX). Each atom is represented by a colored dot: green for boron, black for oxygen, and transparent red for silicon. Curved lines in precipitates are due to the curvature of the tip. (b) Atomic fraction of boron (X$_{0}$) relatively to silicon and oxygen as a function of depth and related error bars (σ = 1.96[X$_{0}$ (1 − X$_{0}$) /N]$^{1/2}$, N = number of atoms). The atomic fraction of boron is represented every 1 nm. (c) 3D distribution of atoms after the phase assignment procedure. The color code remains the same for atoms belonging to β phase. For α phase, silicon atoms are not represented while boron atoms are shown in transparent green. Finally, the three figures share the same depth scale as shown in (b).</figcaption></figure>

composition ranges from 74 to 80 at. %. This observation of mature precipitates after such short annealing (160 ns) is puzzling and indicates that the growth of SiB$_{3}$ in the liquid phase is even faster than previously thought. 18

C. Quantification of boron dose

The retained boron dose (at/cm$^{2}$) can be assessed in the two-phase SOI film knowing the overall composition (X$_{0}$), the composition in each phase (X$_{α}$ and X$_{β}$) as well as their respective atomic density (ρ$_{α}$ and ρ$_{β}$). The overall composition X$_{0}$ is not affected by local magnification effects and can be simply obtained by dividing the total number of boron atoms (n$_{B}$) by the total number of boron and silicon atoms (n),

$$
X_0 = \frac{n^B}{n} = \frac{\sum_i X_0^i n^i}{\sum_i n^i}. \qquad (1)
$$

Here, the sum is made over the whole thickness of the two-phase film with slices i = {1,2...34} of 1 nm. All values are known from APT data, leading to X₀ ~ 8.5 at. %. As discussed earlier, the concentration within diffuse α/β interfaces is biased by local magnification effects. However, these interfaces have been fully assigned to the β phase (Fig. 5), leaving unaffected the composition of the α phase. Therefore, Xα was computed in the same way as for X₀,

$$
X_{\alpha} = \frac{n_{\alpha}^{B}}{n_{\alpha}} = \frac{\sum_{i} X_{\alpha}^{i} n_{\alpha}^{i}}{\sum_{i} n_{\alpha}^{i}}. \qquad (2)
$$

This yields X_α ~ 5.9 at. %, which is very close to the average between the surface and bottom concentration as shown in Fig. 4(a). As for X_β, we considered that SiB_3 precipitates have the same composition of 75 at. %. Regarding atomic densities, ρ_α was taken equal to 5 × 10^22 at/cm^3 for the sake of simplicity. We could have used Vegards' law to account for the deformation induced by boron atoms but the lattice parameter of cubic boron is poorly known and anyway, the effect is small (few %).¹⁹ Besides, we found ρ_β = 9.55 × 10^22 at/cm^3 from the crystallographic data of SiB₃.¹⁸ Using conservation of mass laws, one ends up with the following expression:

$$
\varphi_{\alpha + \beta} = \frac{X_0 t_{\alpha + \beta}}{f_{\beta} / \rho_{\beta} + (1 - f_{\beta}) / \rho_{\alpha}}, \quad (3)
$$

where f_β = (X₀ - X_α)/(X_β - X_α) is the molar fraction of precipitates (3.7%) as given by the lever rule and t_α+β is the thickness of the two-phase SOI film (34 nm). The data listed in Table I lead to φ_α +β ~ 1.5 × 10¹⁶ at/cm². To this must be added the dose in oxides (~10¹⁵ at/cm²). This value was directly assessed from the 3D image by comparing the volume of oxides with the corresponding number of boron atoms. Lastly, one can assess the dose present in the non-analyzed part of the BOX by assuming a linear decrease in the concentration down to zero at the interface with silicon. One finds another 1 × 10¹⁵ at/cm². Thus, the total retained dose is evaluated at around 1.7 × 10¹⁶ at/cm², meaning that around 30% of the targeted dose is missing.

The main source of dose loss likely originates from ion implantation and laser annealing processes. During low-energy/ high-dose boron implants, elastic backscattering of ions combined with self-sputtering can lead to an appreciable loss of around 15%.20,21 There is also the issue of boron evaporation, or out- diffusion, during laser melting. All in all, dose losses of around
<figure><img src="image_16.png" /><figcaption>FIG. 4. (a) Depth distribution of boron in α phase over 31 nm. Error bars represent sampling errors σ = 1.96 [X$_{α}$(1 − X$_{α}$)/N]1/2 made in estimating the concentration from a limited number of atoms N. (b) Distribution of 1NN distances between boron atoms located in the upper part of α phase (5–19 nm) where X$_{α}$ ~ 7.5 at. %.</figcaption></figure>

30% have been reported in laser-annealed boron-implanted silicon.²² This is quite consistent with the dose loss observed here. One also has to mention the past issues related to the incomplete detection of boron by APT. Indeed, significant losses have been observed because of the miscount of “multiple events,” when several ions strike the detector nearly simultaneously and close to each other. Nevertheless, major advances in detector capabilities have considerably improved the detection of such events on this particular atom probe.²³ Still, some events originating from highly concentrated regions (borides) might still be undetected, leading to a small underestimation of the precipitate composition. However, this phenomenon is thought to be negligible here as we identified the phase that was expected after such short precipitation, namely, SiB₃.¹⁸

In order to check the validity of boron quantification, we wish to evaluate the sheet resistance of the film at room temperature (R_S) from APT data. Concerning the β phase, we assume that its conductivity is comparable to that of SiB₆ (~500 S/m²⁴) and, therefore, negligible with respect to the hyperdoped α phase. In boron-doped silicon, it has been shown in a recent study that the formation of inactive substitutional complexes (B₂, B₃) limits the

generation of holes.⁶ Hence, the carrier concentration shall not be taken equal to the total substitutional concentration, but to the concentration of isolated boron. The term “isolated” refers to substitutional boron atoms sharing their four bonds with silicon atoms. Since boron is randomly distributed in the silicon lattice, the concentration of isolated boron at a given depth is given by this simple probabilistic formula $C_α^I = ρ_α X_α (1 - X_α)^4$. In addition, because the α phase does not occupy the whole volume of SOI, $C_α^I$ must be scaled by the volume fraction of phase ($f_α^V$). A mean value of $f_α^V$ can be derived from previous data: $f_α^V = (1 - f_β)/[1 - f_β \times (1 - ρ_α/ρ_β)] \sim 98\%$. Finally, using the expression of multiple resistors in parallel,

$$R_S = \frac{1}{e f_\alpha^V \int C_\alpha^I \mu(C_\alpha^I) dx}, \quad (4)$$

where e is the elementary charge and μ(C_α^I) is the mobility as a function of carrier concentration as given by Masetti et al.²⁵ After numerical integration, Eq. (4) yields 47 Ω/sq, a value in close agreement with the experimental R_S (51 Ω/sq⁸). This result supports the quantification made in this section.

<figure><img src="image_17.png" /><figcaption>FIG. 5. Atomic fraction of boron in precipitates β¹, β², and β³. Each profile was obtained by measuring the concentration in slices of 0.5 nm thickness and 4 nm diameter. Error bars represent sampling errors σ = 1.96[X_β (1 − X_β)/N]1/2, while vertical black lines indicate the position of α/β interfaces as defined in Fig. 3(c).</figcaption></figure>
<table><caption>TABLE I. Parameters enabling boron quantification in Sec. II ($\alpha + \beta$).</caption><thead><tr><th>n<sup>B</sup></th><th>n</th><th>X<sub>0</sub> (%)</th><th>n<sub>α</sub><sup>B</sup></th><th>n<sub>α</sub></th><th>X<sub>α</sub> (%)</th><th>ρ<sub>α</sub> (cm<sup>-3</sup>)</th><th>X<sub>β</sub> (%)</th><th>ρ<sub>β</sub> (cm<sup>-3</sup>)</th></tr></thead><tbody><tr><td>25 783</td><td>302 593</td><td>8.52</td><td>14 669</td><td>247 012</td><td>5.94</td><td>5.0 × 10<sup>22</sup></td><td>75</td><td>9.55 × 10<sup>22</sup></td></tr></tbody></table>

## D. Process conditions and superconductivity in PLIE samples

According to recent studies, the onset of superconductivity in silicon is shown to occur at a threshold concentration of active boron ($C_T$), above which the critical temperature ($T_C$) increases linearly.⁶ Interestingly, $C_T$ has a structural meaning. It is the concentration above which the layer starts relaxing. Having this in mind, let us compute the active concentration of boron in the present film. Assuming again that hole carriers are provided by isolated boron atoms in $\alpha$ phase, one finds an active dose of $7.3 \times 10^{15} \text{ cm}^{-2}$, which corresponds to an averaged concentration of $2.3 \times 10^{21} \text{ cm}^{-3}$ for 31 nm. This value is smaller than the $3 \times 10^{21} \text{ cm}^{-3}$ reported in a superconducting SOI film of the same thickness, pre-implanted with the same dose of $2.5 \times 10^{16} \text{ at/cm}^2$, but laser-melted with a shorter pulse (25 ns).²⁶ Despite this difference in active concentrations, both films feature the same $T_C \sim 0.4$ K. Perhaps the longer laser pulse here employed (160 ns) induces a higher state of relaxation in SOI, leading to similar $T_C$'s with a smaller amount of hole carriers.

At the same time, the drawback of using longer pulses is they activate mechanisms that go against dopant activation. The first one reminds that around 30% of the dose was lost during ion implantation and laser annealing process. Part of this loss is due to dopant out-diffusion during melting, a mechanism promoted by longer pulses. Second, among the $1.5 \times 10^{16} \text{ B/cm}^2$ retained in the two-phase SOI film, one calculates that one third is trapped in $SiB_3$. This is a considerable amount. The origin of precipitation during laser melting has been discussed in a previous work.⁸ Basically, precipitates are thought to grow from a saturated liquid solution whose boron content is higher than the solubility limit ($\sim 14$ at. %). Then, naturally, the longer the melt lasts, the more dopants are trapped in $SiB_3$. However, solutions exist for attenuating both issues. For instance, the implant energy can be increased to generate broader profiles with reduced concentration peaks. This has proven to be efficient for reducing precipitation and triggering superconductivity in the film under study.⁸ Implanting less dopants close to the surface is also expected to reduce the amount of out-diffused boron atoms during laser melting. Finally, implanting the dose in several steps with different energies might help in generating box-shaped profiles, like those obtained with the GILD technique.

## IV. CONCLUSION

In summary, a superconducting SOI film obtained by high-dose boron ion implantation ($2.5 \times 10^{16} \text{ at/cm}^2$) and single-pulse laser melting (160 ns) has been investigated by APT. Two phases were evidenced: an hyperdoped silicon matrix in which boron is randomly distributed, and a nanoscale precipitates having the $SiB_3$ composition. Contrary to GILD samples, the concentration of

boron in the hyperdoped phase is not constant with depth and increases by a factor of two between the bottom of the film ($2 \times 10^{21} \text{ cm}^{-3}$) and the surface ($4 \times 10^{21} \text{ cm}^{-3}$). This non-uniform concentration can be explained by an insufficient mixing in the liquid phase and by segregation during recrystallization.

The dose retained in SOI was evaluated at $1.5 \times 10^{16} \text{ cm}^{-2}$, implying a significant loss of dopant during ion implantation and laser melting. In addition, $SiB_3$ precipitates account for one third of the dose, leaving $1 \times 10^{16} \text{ cm}^{-2}$ in the hyperdoped phase. This partitioning of boron between the two phases is supported by the “isolated active dopants” model, which allowed to trace back the sheet resistance of the film from APT data. Lastly, the relatively high superconducting critical temperature of the present film (0.39 K) was discussed in relation with the active concentration and the onset of strain relaxation. Ion implantation engineering might also help in increasing the superconducting critical temperature of thin SOI films.

## ACKNOWLEDGMENTS

The authors thank Sumitomo Heavy Industries and its French subsidiary LASSE for helping in operating and maintaining the LT-3100 laser annealing system. This work was founded by European projects MATQu and SIQUOS (Grant Agreement Nos. 101007322 and 101017733) and supported by the CNRS Federation IRMA-FR 3095.

## AUTHOR DECLARATIONS

### Conflict of Interest

The authors have no conflicts to disclose.

### Author Contributions

**P. Dumas:** Data curation (equal); Formal analysis (lead); Investigation (lead); Methodology (lead); Writing – original draft (lead); Writing – review & editing (lead). **S. Duguay:** Data curation (equal); Formal analysis (equal); Writing – original draft (supporting); Writing – review & editing (equal). **D. Blavette:** Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (supporting); Writing – review & editing (equal). **M. Opprecht:** Data curation (lead); Formal analysis (equal); Writing – original draft (supporting); Writing – review & editing (equal). **S. Kerdilès:** Data curation (equal); Resources (lead); Writing – original draft (supporting); Writing – review & editing (equal). **F. Lefloch:** Project administration (lead); Resources (lead); Supervision (lead). **F. Nemouchi:** Project administration (lead); Resources (lead); Supervision (lead).
DATA AVAILABILITY

The data that support the findings of this study are available
within the article.

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