E Eustache

M A Mahjoub

Y Guerfi

S Labau

J Aubin

J M Hartmann

F Bassani

S David

B Salem

Smooth plasma etching of GeSn nanowires for gate-all-around field effect transistors Q1 Q2 Q3

Keywords: germanium-tin nanowire, GAA-FET, plasma etching, XPS

We report on the nanopatterning of horizontal and vertical germanium-tin (Ge 1-x Sn x or GeSn) nanowires by inductively coupled plasma reactive ion etching for gate-all-around field effect transistors. First, a chlorine based chemistry has been investigated and optimal conditions identified for GeSn 6% alloys. Then, plasma etching was optimized to etch high Sn content GeSn alloys (up to 15%) with a high anisotropy, smooth sidewalls and a high selectivity versus a hydrogen silsesquioxane hard mask. We have shown that, in order to obtain smooth surfaces after plasma etching, a HCl pre-treatment was mandatory to eliminate the native Sn and Ge oxides. This behavior was even more pronounced for high Sn contents. Finally, we succeeded in patterning 20 nm wide suspended beams from GeSn layers with Sn concentrations up to 15% Sn.

Introduction

Germanium tin alloys (Ge 1-x Sn x ) are promising candidates for next-generation complementary metal oxide semiconductor (CMOS) circuits, low power consumption devices and Si-photonics [START_REF] Soref | Enabling 2 µm communications[END_REF]. The energy bandgap of the GeSn alloys can indeed be controlled by changing the Sn content [START_REF] Jenkins | Electronic properties of metastable GexSn 1-x alloys[END_REF][START_REF] Ghetmiri | Direct-bandgap GeSn grown on silicon with 2230 nm photoluminescence[END_REF]. For Sn contents 8% and above, unstrained GeSn exhibits a low and direct band gap, with an increase of carrier mobility and electron injection velocity compared to pure Ge [START_REF] Wirths | Si-Ge-Sn alloys: from growth to applications[END_REF]. For those reasons, GeSn alloys are currently being investigated as channel materials in next generation devices. Indeed, combining direct band-to-band tunneling and low bandgap should yield efficient tunnel field effect transistors [START_REF] Schulze | Vertical Ge and GeSn heterojunction gate-all-around tunneling field effect transistors[END_REF]. Moreover, as a group IV alloy, GeSn is an ideal semiconductor for the co-integration of high speed CMOS transistors and Si photonic devices in the * Author to whom any correspondence should be addressed. short-wave infrared range [START_REF] Zhang | Theoretical investigation of tensile strained GeSn waveguide with Si 3 N 4 liner stressor for mid-infrared detector and modulator applications[END_REF][START_REF] Su | GeSn p-i-n photodetector for all telecommunication bands detection[END_REF][START_REF] Wang | High-performance GeSn photodetector and fin field-effect transistor (FinFET) on an advanced GeSn-on-insulator platform[END_REF]. Gate-all-around field effect transistors (GAA-FETs) are considered as being the 'ultimate' devices to continue the downscaling of transistors. Such an architecture yields the best electrostatic control over the channel by the gate, limiting short-channel effects and significantly reducing the off-state leakage current (I OFF ). Vertical nanowires [START_REF] Guerfi | Vertical silicon nanowire field effect transistors with nanoscale gate-all-around[END_REF] and stacked nano-sheets [START_REF] Loubet | Stacked nanosheet gate-all-around transistor to enable scaling beyond FinFET Dig[END_REF], which have low footprints, are attractive candidates to integrate GAA-FETs in electronic circuits. GeSn nanowires patterning by inductively coupled plasma reactive ion etching (ICP-RIE) will then be key. Indeed, it will define the channel, one of the most crucial parts of such transistors.

Because of the low Sn solubility in Ge (less than 1% at thermal equilibrium), it is difficult to grow (and process) high Sn content GeSn layers. The Sn concentration should be high enough to have the desirable electrical properties, but not too high, to minimize process complexity. The thermal processing window is indeed substantially reduced as the Sn concentration increases (Sn surface segregation/precipitation) [START_REF] Wirths | Ni(SiGeSn) metal contact formation on low bandgap strained (Si)Ge[END_REF]. The fabrication of gate stacks [START_REF] Schulte-Braucks | Low temperature deposition of high-k/metal gate stacks on high-Sn content (Si)GeSn-alloys[END_REF] or ohmic contacts [START_REF] Wang | Metal stanogermanide contacts with enhanced thermal stability for high mobility germanium-tin field-effect transistor[END_REF][START_REF] Schulte-Braucks | Schottky barrier tuning via dopant segregation in NiGeSn-GeSn contacts[END_REF] on GeSn was investigated. However, data are scarce concerning the plasma etching of GeSn. As the current study will show, different etching behaviors happen when the Sn content changes. Gupta et al [START_REF] Gupta | Highly selective dry etching of germanium over germanium-Tin (Ge 1-x Snx): a novel route for Ge 1-x Snx nanostructure fabrication[END_REF] found Sn-F bonds on the GeSn surface after CF 4 plasma exposition. This study suggested that a SnF x passivation layer was formed, preventing CF 4 plasma etching. After exposure to ambient air, there was SnO y F x on a GeSn surface exposed to a CF 4 plasma which can be removed thanks to a dip in diluted HCl. Shang et al [START_REF] Shang | Dry-wet digital etching of Ge 1-x Snx[END_REF] used this behavior for their digital dry-wet etching of GeSn. By alternating CF 4 plasma etchings and dips in HCl, they were indeed able to etch 1.5-3.2 nm of GeSn per cycle. This type of process is very effective to precisely define a pattern (fin or nanowire). It is however unsuitable for the anisotropic etching of patterns from as-grown GeSn films. Although a Cl 2 chemistry was mentioned [START_REF] Lei | The first GeSn FinFET on a novel GeSnOI substrate achieving lowest S of 79 mV/decade and record high Gm, int of 807 µS/µm for GeSn P-FETs[END_REF], plasma etching processes were not reported in recent studies on nanoscale patterned GeSn transistors [START_REF] Schulze | Vertical Ge and GeSn heterojunction gate-all-around tunneling field effect transistors[END_REF][START_REF] Lei | The first GeSn FinFET on a novel GeSnOI substrate achieving lowest S of 79 mV/decade and record high Gm, int of 807 µS/µm for GeSn P-FETs[END_REF]. Milord et al [START_REF] Guerfi | Vertical silicon nanowire field effect transistors with nanoscale gate-all-around[END_REF] used a fast etching process (340 nm min -1 ) to fabricate micrometer scale disks. They were able to vertically etch hundreds of nm thick GeSn layers thanks to the addition of O 2 in a Cl 2 /N 2 mixture. O 2 may have allowed the formation of weakly volatile species, which passivated the sidewalls, while ions brought enough energy to assist desorption or remove these species horizontally by physical sputtering [START_REF] Cardinaud | Plasma etching: principles, mechanisms, application to micro-and nano-technologies[END_REF]. However, 10 nm range patterns would require a slower and more precise process.

This article focuses on nanopatterning by ICP-RIE of GeSn alloys with Sn contents in the 6%-15% range. The morphology of nanowires and the chemical composition of the surface have been analyzed by scanning electron microscopy and x-ray photoelectron spectroscopy. We show that, in order to obtain smooth surfaces after plasma etching, HCl pretreatment is mandatory to eliminate the native Sn and Ge oxides.

Experimental details

The GeSn samples used in this study were grown in the 300 • C-350 • C range on Ge strain-relaxed buffers, themselves on 200 mm Si (100) substrates, by reduced pressure chemical vapor deposition. The 50 nm thick GeSn 6%, 10% and 15% layers were fully strained, as confirmed by x-ray diffraction [START_REF] Aubin | Very low temperature epitaxy of heavily in situ phosphorous doped Ge layers and high Sn content GeSn layers[END_REF]. Etching masks were defined by e-beam lithography (JOEL6300FS system) using a 60 nm thick hydrogen silsesquioxane (HSQ) resist. Two types of patterns were studied: dots with a diameter ranging from 10 to 110 nm for vertical GAA-FETs and fins with line widths ranging from 10 to 100 nm and a pitch of 50-100 nm for horizontal suspended GAA-FETs (after further removal of the under layer). The 1 cm 2 samples were bonded on 4 inches silicon wafers using poly methyl methacrylate and loaded in an Oxford Plasma Lab 100 ICP-RIE plasma etching chamber for fins and dots patterning. Samples were characterized by scanning electron microscopy (SEM) in tilted view at 85 • from the surface using a ZEISS ULTRA + microscope in order to evaluate the fins profile and etching rates. XPS analysis of the GeSn surface was carried out immediately after etching (a few minutes in ambient air only) in a customized thermo electron theta 300 spectrometer, using a high resolution monochromatic Al Kα source at 1486.6 eV. The detection angle was fixed at 21 • to the normal of the wafer. XPS spectra were calibrated according to the C1s binding energy of 285 eV. Pass energy for narrow scan windows was set as 23.5 eV with a scan step size of 0.2 eV. The data were fitted using a Shirley function for the background and a pseudo-Voigt function with a Lorentzian contribution of 30% for the peaks. All parameters were left free during fitting, except for the full widths at half maximum that were kept the same for the different contributions of one element.

Results and discussion

Patterning of Ge 0.94 Sn 0.06

We studied the etching process of GeSn 6% Sn with a Cl 2 /O 2 /N 2 chemistry. To obtain a precise control and low etching rates, ICP and platen radio-frequency powers were limited to 100 W. Figure 1 shows the influence of the Cl 2 /O 2 /N 2 gas flows. Varying these parameters is a straightforward method to adjust the ratio between etching and passivation. The resulting etching rate and verticality are severely impacted by chemistry changes. The starting Cl 2 /O 2 /N 2 gas mixture was fixed at 25/10/25 sccm. It resulted in the formation of so-called 'grass', as shown figure 1(a). This behavior usually occurs when an etch product is re-deposited, or, more probably in our case, when passivation is too strong against etching, generating needles all over the etched surface. Increasing the chlorine flow to 100 sccm results in a faster etching rate of ≈10 nm s -1 , which is not desirable for the fabrication of nanoscale GeSn fins and dots (figure 1(b)). Reducing the chlorine flow to a moderate value of 50 sccm reduced the etching rate to 3 nm s -1 and yielded smooth sidewalls. There was however an overetching of GeSn below the HSQ patterns (i.e. an undercut), while dots were conically shaped (figure 1(c)). This was likely due to a poor surface passivation of the GeSn sidewalls. Figure 1(d) shows the best result obtained with optimized parameters: the ICP power was reduced to 50 W to decrease the plasma density and the platen power was kept to 50 W. The overall gas flow was reduced and the O 2 and N 2 flows increased, proportionally, to improve sidewall passivation: Cl 2 /O 2 /N 2 flows of 18/5/13 sccm were then used, with a 10 mTorr etch pressure. The over-etching of GeSn below the HSQ patterns was then totally suppressed. With such process, sidewalls were vertical and smooth while the etching rate was limited to ≈3.4 nm s -1 .

3.2.

Transfer of the process to Ge 0.9 Sn 0.1 and Ge 0.85 Sn 0.15

The optimized etching recipes were used on GeSn layers with higher Sn contents (10% and 15%). The etch rate decreased to ≈1.5 nm s -1 for 10% of Sn, with a reduced notching in the GeSn layer, as seen in figure 2(a). Decreasing the etch pressure from 10 mTorr down to 5 mTorr (figure 2(b)) restored the verticality of the sidewalls.

For 15% of Sn, the notch was still present even at 5 mTorr in figure 2(c). There was also unwanted needles on the bottom surface. A decrease of the pressure to 3 mTorr, which is the lowest pressure achievable within our equipment with these gases flows and pumping unit, restored the verticality of the sidewalls, but needles remained (not shown here). As needles in an etching process with passivation gas usually originate from too much passivation, we tried to remove oxygen from the recipe. As shown in figure 2(d), needles indeed disappeared, but the verticality of the patterns was lost, with a large etching of the GeSn layer under the HSQ mask.

XPS study of the etching process

To determine the origin of the needles, XPS analyses were carried out.

The top row of figure 3 shows the fitted Ge3d and Sn4d XPS spectra of the Ge 0.94 Sn 0.06 surface (figure 3 For S6ref and S15ref, the XPS spectra shows the presence of an additional doublet at 24.4 and 23.7 and a broad peak at 25.65 eV attributed to the Sn4d 5/2 and Sn4d 3/2 doublet and to Sn oxide (Sn-O), respectively. The intensity of the Sn-O peak is higher in the S15ref case, probably due to the higher Sn concentration. After 15 s of etch, the Sn-O peak is completely removed for S6-15 and S15-15. Moreover, the XPS spectra show an important decrease of the Ge-O peak in the S6ref case. This is not the case for the S15-15, with an almost steady Ge-O peak. This can be explained by a segregation of Sn-O compounds at the surface of GeSn, resulting in some micro-masking and therefore high surface roughness and/or the presence of needles, since the Sn-O etching seems to be faster.

After 60 s of etch, the GeSn layer was completely etched for S6-60 and S15-60 surfaces.

To confirm these hypotheses, the atomic percentages (%) of the different chemical compound detected on the GeSn surface were calculated with the Thermo Avantage ® software. Table 1 gives the atomic percentages of Ge and Sn compounds. For a better understanding, three additional parameters were defined:

St Sn (%) = Sn% Sn% + Ge% × 100 (1)
P Ge-O (%) = Ge -O% Ge -Ge% + Ge -O% × 100 (2)
P Sn-O (%) = Sn -O% Sn -Sn% + Sn -O% × 100 (3)
where St Sn (%) is the Sn percentage in the GeSn alloy, P Ge-O represents the Ge-O (%) in the total Ge compound and P Sn-O represent the Sn-O (%) in the total Sn compound. Sn concentrations close to the surface were higher than bulk values in Ge 0.94 Sn 0.06 (S6ref) and Ge 0.85 Sn 0.15 (S15ref) samples. They were indeed equal to 9.5% and 22.5% instead of 6% and 15% for Ge 0.94 Sn 0.06 and Ge 0.85 Sn 0.15 , respectively. There was thus some Sn surface segregation, all the more so for high Sn content layers.

After 15 s of etching, the P Sn-O (%) was 0 for Ge 0.94 Sn 0.06 and Ge 0.85 Sn 0.15 surfaces, showing that Sn-O was completely removed. Meanwhile, P Ge-O (%) decreased, after 15 s of etching, from 31.9% down to 17.3% for Ge 0.94 Sn 0.06 , at variance with Ge 0.85 Sn 0.15 , with a P Ge-O (%) staying more or less constant at 30% (table 1). All of this confirms that Sn-O etching was faster and the micro-masking hypothesis. Indeed, the Sn-O percentage was lower in the Ge 0.94 Sn 0.06 case, resulting in its complete removal before the 15 s of etching, some removal of Ge-O and a Sn surface concentration closer to its bulk value, then (6.5% instead of 6%). This was not the case for Ge 0.85 Sn 0.15 , as the starting percentage of Sn-O was much higher. The Ge-O percentage stayed constant, then, while the Sn surface concentration remained definitely higher than in bulk value (19.4% instead of 15%). XPS has thus shown that oxidized Sn on the GeSn surface was the origin of the micro-masking of GeSn, notably for high Sn contents. For that, samples were thus dipped in a 10% HCl solution prior to plasma etching, in order to remove the Ge and Sn surface oxide. Figure 4 shows a 15% Sn sample etched with the optimized process at 5 mTorr. Thanks to this process, needles have disappeared, sidewalls are perfectly smooth and the GeSn notch was removed.

GeSn horizontal nanowire formation for GAA MOSFET

In this last section, a process sequence for the fabrication of Q5 horizontal suspended Ge 0.9 Sn 0.1 nanowires for next generation GAA-FETs based on sequential GeSn and Ge plasma etching 50 nm is presented. The first step consists in the definition of the HSQ hard mask by electron beam lithography. Nanowires with diameters ranging from 5 to 100 nm were targeted. We focus here on single fins 25 nm wide (figure 5(a)) and on networks of 5 fins 20 nm wide (figure 5(b)). GeSn/Ge fins were then patterned by anisotropic plasma etching using the developed recipe (not shown). After that, Ge was selectively removed thanks to CF 4 isotropic ICP plasma etching, liberating the Ge 0.9 Sn 0.1 nanowires. Figures 5(c) and (d) show a single and a network of 10 GeSn suspended nanowires. Thanks to the oxygen passivation during etching with our optimized recipe, the GeSn nanowires were perfectly protected during the Ge underetching step. Finally, the residual HSQ resist was etched in hydrofluoric acid, the sample surface rinsed in deionized water and dried with a N 2 flow. Suspended GeSn nanowires with such small diameters are highly desirable in ultimate GAA-FETs.

Conclusion

A process flow for the fabrication of GeSn nanowires for next generation GAA-FETs was evaluated. An anisotropic plasma etching that used a Cl 2 /O 2 /N 2 gas mixture was optimized in an ICP-RIE etching equipment. Gas flow, pressure and ICP power were adjusted to have a smooth and anisotropic etching of a GeSn 6% layer. The optimized etching process was then performed on GeSn layers with higher Sn concentrations. Etching parameters were adapted to avoid the presence of a notch in the GeSn layer (on top of Ge). Thanks to a pressure decrease and a better passivation capability, we were able to anisotropically etch GeSn alloys with up to 15% of Sn, with no notch anymore, smooth sidewalls and a high selectivity with respect to the HSQ hard mask. Finally, a process flow for the fabrication of horizontal suspended nanowires was successfully developed. The later could be used for the realization of next generation GeSn GAA-FETs.

Figure 1 .

 1 Figure 1. 85 • tilted SEM images of Ge 0.94 Sn 0.06 /Ge after 60 s plasma etching with (a) 25/10/25, (b) 100/10/25, (c) 50/10/25, and (d) 18/5/13 sccm of Cl 2 /O 2 /N 2 .

Figure 2 .

 2 Figure 2. 85 • tilted SEM images of etched samples: Ge 0.9 Sn 0.1 /Ge at (a) 10 mTorr and (b) 5 mTorr; Ge 085 Sn 0.15 /Ge at (c) 5 mTorr and (d) 5 mTorr without O 2 .

  S6-ref) and the same surface after 15 s (figure 3 S6-15) and 60 s (figure 3 S6-60) of etching. The bottom row shows XPS spectra of the Ge 0.85 Sn 0.15 surface (figure 3 S15ref) and the same surface after 15 s (figure 3 S15-15) and 60 s (figure 3 S15-60) of etching. Regardless the sample, XPS spectra show a doublet at 22.4 and 24.4 eV, attributed to the Ge Ge3d 5/2 and Ge3d 3/2 and a board peak at 31.88 eV attributed to Ge oxide (Ge-O).

Figure 3 .

 3 Figure 3. XPS spectra of Ge3d and Sn4d for (top row) the Ge 0.94 Sn 0.06 reference sample and the same sample after 15 and 60 s of etching and (bottom row) the Ge 0.85 Sn 0.15 reference sample and the same sample after 15 and 60 s of etching.

Figure 4 .

 4 Figure 4. 85 • tilted SEM image of a Ge 085 Sn 0.15 sample after a dip in HCl prior to ICP-RIE.

Figure 5 .

 5 Figure 5. Process technology for the fabrication of suspended GeSn nanowires: (a) and (b) single and network of HSQ hard mask fins obtained by electron beam lithography. (c) and (d) Single and network of suspended GeSn nanowires with HSQ resist still present.

Table 1 .

 1 Chemical composition of Ge 0.96 Sn 0.06 and Ge 0.85 Sn 0.15 surfaces before and after 15 s of etching.

		Ge-Ge (%)	Ge-O (%)	Sn-Sn (%)	Sn-O (%)	P Ge-O (%)	P Sn-O (%)	St Sn (%)
	S6ref	31.8	14.9	3.6	0.8	31.9	17.9	9.5
	S6ref@15 s	49.7	10.4	4.5	0	17.3	0	6.5
	etch
	S15ref	29.9	12.9	5.9	3.8	30.1	39	22.5
	S15ref@15 s	29.9	12.8	8.4	0	29.9	0	19.4
	etch

Acknowledgments

This work was partly supported by the French RENATECH network through the PTA technological platforms in Grenoble and by the EquipEx IMPACT program, managed by the ANR French agency (ANR-10-EQPX-33).

ORCID iDs

J M Hartmann  https://orcid.org/0000-0001-7006-8586 F Bassani  https://orcid.org/0000-0001-8688-1328 B Salem  https://orcid.org/0000-0001-8038-3205

Data availability statement

All data that support the findings of this study are included within the article (and any supplementary files). Q6


Hadi Hijazi
email: hijazi@itmo.ru

Mohammed Zeghouane

Franck Bassani

Pascal Gentile

Bassem Salem

Vladimir G Dubrovskii

Impact of the droplet composition on the nucleation rate and morphology of vapor-liquid-solid GeSn nanowires

Keywords: Vapor-liquid-solid growth, GeSn nanowires, droplet composition, nucleation rate

It is well-known that chemical potential driving the vapor-liquid-solid growth of semiconductor nanowires is strongly affected by the liquid phase composition. Here, we investigate theoretically how the droplet composition influences the nucleation of Au-catalyzed GeSn nanowires on Ge(111) and Si(111) substrates. We compare chemical potentials in an Au-Ge-Sn catalyst droplet before and after adding Ga and/or Si atoms. It is found that the presence of these atoms enhances the nucleation rate of nanowires on both substrates. Theoretical results are compared to experimental data on GeSn nanowires grown in hot-wall reduced pressure chemical vapor deposition reactor. It is shown that the intentional addition of Ga in the de-wetting step improves the uniformity of the nanowire dimensions and yields higher density of nanowires over Ge(111) substrates. The nanowire growth on Si(111) substrate occurs only when Ga and/or Si are added to Au droplets. These results show that controlling the composition of the catalyst droplet is crucial for improving the quality of GeSn nanowires.

Introduction

Semiconductor nanowires (NWs) have attracted much interest as fundamental building blocks for nanoscience and nanotechnology. Particularly elemental and binary group IV-based NWs have shown great promise for different applications. [START_REF] Le | Axial SiGe heteronanowire tunneling field-effect transistors[END_REF][START_REF] Wu | Block-by-block growth of single-crystalline Si/SiGe superlattice nanowires[END_REF][START_REF] Zaima | Growth and applications of GeSn-related group-IV semiconductor materials[END_REF][START_REF] Wen | Formation of compositionally abrupt axial heterojunctions in silicon-germanium nanowires[END_REF][START_REF] Rosaz | Vertically integrated silicon-germanium nanowire field-effect transistor[END_REF] Bottom-up NWs are usually grown by the vapor-liquid-solid (VLS) method with a metal droplet which can be made either of one of the growth constituencies in the self-catalyzed approach [START_REF] Yu | Defect-free GeSn[END_REF][START_REF] Sun | Au-Sn catalysed growth of Ge 1-x Sn x nanowires: growth direction[END_REF] or of a foreign element such as Au [START_REF] Azrak | Growth of in-plane Ge 1-x Sn x nanowires with 22 at. % Sn using a solidliquid-solid mechanism[END_REF][START_REF] Meng | Core-shell germanium/germanium-tin nanowires exhibiting roomtemperature direct-and indirect-gap photoluminescence[END_REF][START_REF] Biswas | Non-equilibrium induction of tin in germanium: towards direct bandgap Ge 1-x Sn x nanowires[END_REF]. Different growth techniques are used to grow NWs, including molecular beam epitaxy [START_REF] Han | Analysis of Raman scattering from inclined GeSn/Ge dual-nanowire heterostructure on Ge(111) substrate[END_REF][12][START_REF] Zhu | Vapor-solidsolid grown Ge nanowires at integrated circuit compatible temperature by molecular beam epitaxy[END_REF] and chemical vapor deposition (CVD). [START_REF] Periwal | composition-dependent interfacial abruptness in Aucatalyzed Si 1-x Ge x /Si/Si 1-x Ge x nanowire heterostrucures[END_REF][START_REF] Albani | Critical strain for Sn incorporation in spontaneously graded Ge/GeSn core/shell nanowires[END_REF] One of the most interesting binary material within group IV-based semiconductor family is Ge 1-x Sn x , which opens up a possibility for achieving direct bandgap in group IV semiconductors. [START_REF] Kouvetakis | Tin-based group IV semiconductors: new platforms for opto-and microelectronics on silicon[END_REF][START_REF] Soref | Silicon photonics: a review of recent literature[END_REF][START_REF] Zhang | Computational design of directbandgap semiconductors that lattice-match silicon[END_REF][START_REF] Wirths | Lasing in direct-bandgap GeSn alloy grown on[END_REF][START_REF] Stange | Optical transitions in direct-bandgap Ge 1-x Sn x alloys[END_REF] NWs have been proven efficient for growing GeSn material with a high Sn concentration of ~9 % needed to achieve direct bandgap despite a low equilibrium solubility of Sn in Ge (~1 %) and a large lattice mismatch (14 %). [START_REF] Meng | Core-shell germanium/germanium-tin nanowires exhibiting roomtemperature direct-and indirect-gap photoluminescence[END_REF][START_REF] Biswas | Non-equilibrium induction of tin in germanium: towards direct bandgap Ge 1-x Sn x nanowires[END_REF][START_REF] Haffner | Growth of Ge 1-x Sn x nanowires by chemical vapour deposition via[END_REF][START_REF] Assali | Growth and optical properties of direct band gap Ge/ Ge 0.87 Sn 0.13 core/shell nanowire arrays[END_REF] This may enable monolithic integration of direct bandgap group IV semiconductor with Si electronic platform and pave new ways for fabrication of cheap and highly efficient nanooptoelectronic devices. [START_REF] Von Den Driesch N Stange | Direct bandgap group IV epitaxy on Si for laser applications[END_REF][START_REF] Sau | Possibility of increased mobility in Ge-Sn alloy system[END_REF] It is well-known that the composition of a catalyst droplet influences many properties of VLS semiconductor NWs, including their crystal phase, [START_REF] Glas | Why does wurtzite form in nanowires of III-V zinc blende semiconductors?[END_REF][START_REF] Gil | Record pure zincblende phase in GaAs nanowires down to 5 nm in radius[END_REF] doping, [START_REF] Hijazi | Si doping vapor-liquid-solid GaAs nanowires : n-type or p-type ?[END_REF] growth rate, [START_REF] Dubrovskii | Influence of the group V element on the chemical potential and crystal structure of Au-catalyzed III-V nanowires[END_REF] chemical composition, [START_REF] Leshchenko | Nucleation-limited composition of ternary III-V nanowires forming from quaternary gold based liquid alloys[END_REF] growth direction [START_REF] Panciera | Phase selection in self-catalyzed GaAs nanowires[END_REF] and morphology [START_REF] Pan | Dimension engeneering of hoghquality InAs nanostructures on a wafer scale[END_REF][START_REF] Jia | Foreign metal ions to control the morphology of solution-liquid-solid reaction[END_REF]. In addition to the growth species (atoms to be transferred from vapor to the solid state through liquid), the droplet often contains impurities that may affect the nucleation rate and further growth of NWs. The driving force for NW growth is the chemical potential difference A c c e p t e d M a n u s c r i p t ∆μ between the liquid and solid phase. This ∆μ depends on the growth temperature and atom-fractions of different species dissolved in a catalyst droplet. Interatomic interactions between different species in liquid are described by the corresponding binary and higher order interaction parameters. [START_REF] Glas | Chemical potentials for Au-assisted vapour-liquid-solid growth of III-V nanowires[END_REF][START_REF] Hijazi | Influence of Si on the nucleation rate of GaAs nanowires on Si substrates[END_REF] Therefore, each atom present in the droplet must be accounted for when describing nucleation and growth of NWs.

Foreign atoms may be added to the droplet prior to growth in the de-wetting step. Unintentional impurities may originate from the substrate, especially when the sample is heated up to a high temperature. [START_REF] Hijazi | Influence of Si on the nucleation rate of GaAs nanowires on Si substrates[END_REF][START_REF] Hijazi | Dynamics of Au droplet formation on SiO 2 /Si(111) surface[END_REF][START_REF] André | Vapor liquid solid-hydride vapour phase epitaxy (VLS-HVPE) growth of ultra-long defect-free GaAs nanowires: Ab initio simulations supporting center nucleation[END_REF] For example, the nucleation rate of GaAs NWs on GaAs substrates is enhanced due to the absorption of additional Ga atoms evaporated from the substrate. [START_REF] André | Vapor liquid solid-hydride vapour phase epitaxy (VLS-HVPE) growth of ultra-long defect-free GaAs nanowires: Ab initio simulations supporting center nucleation[END_REF] When GaAs NWs are grown on Si substrates, Si atoms evaporating from the substrate in the de-wetting step may completely suppress nucleation of NWs. [START_REF] Hijazi | Influence of Si on the nucleation rate of GaAs nanowires on Si substrates[END_REF] Foreign atoms can also be added intentionally by predeposing different metals to form an alloyed rather than pure Au catalyst droplet. [START_REF] Hijazi | HVPE-Grown GaAs Nanowires : Growth Modeling, Passivation and Transport Properties[END_REF] It is paramount therefore to have the full appreciation of the influence of the alloy composition on the nucleation, growth and resulting properties of NWs.

Consequently, here we develop a thermodynamic model to quantify how adding Ga and/or Si atoms to Au droplets influences the VLS growth of GeSn NWs. Our approach is based on the calculation of chemical potential for a mixture of different species present in the droplet, with the solid phase consisting of pure GeSn. We compare the model predictions with experimental data on GeSn NWs grown by Au-catalyzed CVD on Ge(111) and Si(111) substrates and show a good quantitative correlation. The model can be further used to study the influence of foreign impurities on the VLS growth of different semiconductor NWs on different substrates. Such calculation enables, first, to avoid pregrowth annealing of samples when the absorption of atoms from the substrate inhibits the NWs growth, and second, to deposit suitable thin films before the dewetting step.

Experimental

GeSn NWs were grown in hot-wall reduced pressure CVD reactor (Easy Tube 3000 First Nano). Two types of substrates were used, Ge(111) (system I) and Si(111) (system II). Prior to growth, all samples were chemically etched in an aqueous hydrofluoric solution to remove native oxides. Then, five different samples were prepared with different catalyst droplets compositions: pure Au on Ge(111) substrate (sample S1), Au-Ga on Ge(111) substrate (sample S2), pure Au on Si(111) substrate (sample S3), Au-Si on Si(111) substrate (sample S4), and Au-Ga-Si on Si(111) substrate (sample S5). Au and Au-Ga droplets were obtained by depositing 3 nm thick Au and 5 nm thick Au + 3 nm thick Ga thin films, respectively, at room temperature, followed by the annealing step at a temperature of 350 °C which serves for thermal de-wetting of thin films into droplets. Si atoms were added to the droplets of samples S4 and S5 by annealing at 550 °C for 10 minutes before cooling down and initiating the NW growth. This high temperature annealing activated the diffusion of Si from the substrate into the droplets, as in Refs. [START_REF] Hijazi | Influence of Si on the nucleation rate of GaAs nanowires on Si substrates[END_REF][START_REF] Hijazi | Dynamics of Au droplet formation on SiO 2 /Si(111) surface[END_REF]. Germane (GeH 4 ) and tin tetrachloride (SnCl 4 ) gases were used as Ge and Sn precursors, respectively. An additional HCl flow was maintained at 20 sccm to improve the NWs morphology and suppress the parasitic nucleation on the substrates. Hydrogen was used as a carrier gas and the total pressure was fixed at 4.5 Torr. The morphologies of as-grown GeSn NWs were characterized by scanning electron microscopy (SEM).

Model

We consider a NW of a given semiconductor material growing in the VLS mode from a supersaturated liquid droplet which contains n species. Initially, the droplet contains no foreign atoms. We will now add N ε atoms of one foreign element to this droplet and study the change of the chemical potential difference Δμ between the liquid and solid phase induced by this process. We assume that the solid phase remains pure and hence the incorporation of foreign atoms into the NW is not accounted for. In this case, the chemical potential change depends only on the state of liquid. The shift ρ I of Δμ from its initial value Δμ 0 without any foreign atoms can be written as:

ρ I = ∑ μ ε x,L -μ 0 x,L x . (1)
Here, x represents the growth species, while μ 0 x,L and μ ε x,L are their chemical potentials in liquid before and after adding N ε foreign atoms to the catalyst droplet, respectively. These chemical potentials are calculated using the regular solution model: [START_REF] Glas | Chemical potentials for Au-assisted vapour-liquid-solid growth of III-V nanowires[END_REF]

μ x,L = μ x,PL + k B T ln(c x ) + 1 2 ∑ c i n+1 i,j=1 c j (ω ix + ω jx -ω ij ) , (2)
where μ x,PL is the chemical potential of element x in pure liquid, k B is the Boltzmann constant and T is the absolute temperature. The c q = N q /N tot is the atomic fraction of element q, with N q as the number of atoms of A c c e p t e d M a n u s c r i p t element q in the droplet containing the total number of atoms N tot . These c q are obtained simply by noting that adding N ε foreign atoms to the droplet increases N tot , and therefore reduces the initial atomic fractions c q 0 of all other species. [START_REF] Hijazi | Influence of Si on the nucleation rate of GaAs nanowires on Si substrates[END_REF] This gives:

c q = c q 0 . (1 -c ε ) , (3)
where c ε = N ε N tot ⁄ is the atomic fraction of foreign atoms in the droplet.

The concentration-dependent parameters ω ij describing binary interactions between elements i and j in the liquid phase are given by: [START_REF] Stringfellow | calculation of ternary phase diagrams of III-V systems[END_REF]

ω ij = 1 N A V i V j c i V i +c j V j [(δ i -δ j ) 2 -C (χ i -χ j ) 2 (V i V j ) 1/2 ] . (4)
Here, V q , χ q and δ q = √(ΔH at,q -RT) V q ⁄ are respectively the molar volume, the Pauling electronegativity and the Hildebrand solubility parameter of element q, where ΔH at is the enthalpy of atomization and R is the ideal gas constant. N A is the Avogadro number, and C is a constant which equals 1.256 × 10 5 if all quantities are in SI units. After some calculation, the liquid chemical potential of element x upon adding N ε foreign atoms can be rewritten as:

μ ε x,L = 2k B T ln(1 -c ε ) + ξ x c ε + λ x c ε 2 + γ x , (5a)
with

ξ x = -∑ c i 0 n i,j=1 c j 0 (ω i,x + ω j,x -ω i,j ) + ∑ c i 0 n i=1 (ω i,x + ω ε,x -ω i,ε ), (5b) λ x = 1 2 ∑ c i 0 n i,j=1 c j 0 (ω i,x + ω j,x -ω i,j ) - ∑ c i 0 n i=1 (ω i,x + ω ε,x -ω i,ε ) + ω ε,x , (5c)
γ x = 1 2 ∑ c i 0 n i,j=1 c j 0 (ω i,x + ω j,x -ω i,j ) . ( 5d
)
Using these expressions, Eq. ( 1) can be rewritten as:

ρ I = 2k B T ln(1 -c ε ) + Ωc ε + Λc ε 2 , ( 6
)
where Λ = ∑ λ x x and Ω = ∑ ξ x x . This generalizes the result of Ref. [START_REF] Hijazi | Influence of Si on the nucleation rate of GaAs nanowires on Si substrates[END_REF] to the case of arbitrary composition of a droplet containing n species and 1 type of foreign atoms.

The same calculation can be done to describe system II in which two foreign elements (Ga and Si) with the numbers of atoms N ε1 and N ε2 are added to the liquid droplet. The corresponding atomic fractions of the two elements in liquid equal c ε1 and c ε2 , respectively. In this case, the atomic fractions of the other species in liquid should be modified to:

c q = c q 0 . (1 -c ε1 -c ε2 ). (7)
Following the same method, the change of chemical potential is obtained in the form:

ρ II = 2k B T ln(1 -c ε1 -c ε2 ) + Λ 1 c ε1 2 + Λ 2 c ε2 2 + σc ε1 c ε2 + Ω 1 c ε1 + Ω 2 c ε2 , (8a)
with

Λ q = ∑ { 1 2 ∑ c i 0 n i,j=1 c j 0 (ω i,x + ω j,x -ω i,j ) - x ∑ c i 0 n i=1 (ω i,x + ω εq,x -ω i,εq ) + ω εq,x } , ( 8b
) σ = ∑ c i 0 n i,j=1 c j 0 (ω i,x + ω j,x -ω i,j ) - ∑ c i 0 n i=1 (2ω i,x + ω ε1,x + ω ε2,x - ω i,ε1 -ω i,ε2 ) + (ω ε1,x + ω ε2,x -ω ε1,ε2 ), (8c)
Ω q = ∑ {-∑ c i 0 n i,j=1 c j 0 (ω i,x + ω j,x -ω i,j ) + x ∑ c i 0 n i=1 (ω i,x + ω εq,x -ω i,εq )}. (8d)
According to Ref. [START_REF] Hijazi | Influence of Si on the nucleation rate of GaAs nanowires on Si substrates[END_REF], the NW nucleation rate rapidly increases with increasing the chemical potential of the liquid phase. Therefore, positive chemical potential difference ρ eases and negative ρ suppresses nucleation of VLS NWs by adding one or two foreign elements to the catalyst droplet.

Results and discussion

We will now apply the model to study the growth systems presented above. Parameters of different elements used in calculations are summarized in table 1. We first consider GeSn NWs grown on Ge(111) substrate (system I). The initial liquid phase is a ternary Au-Ge-Sn alloy, to which we add Ga atoms (ε = Ga). Adding foreign elements, such as Ga in this case, to the droplet can increase the degree of supersaturation and provide an effective method to enhance the NW nucleation rate. In addition, binary phase diagrams of Sn or Ge with Ga indicate the existence of low eutectic temperatures (from 20 to 29 °C), which may allow for lowering the growth temperatures of GeSn NWs. Figure 1 (a) shows the evolution of ρ I with c Ga . The curves are obtained from Eq. ( 6) for different c Ge 0 and c Sn 0 , in Aucatalyzed VLS growth processes at a fixed growth temperature T of 350 °C. These c Ge 0 and c Sn 0 were estimated from the Au-Sn-Ge ternary phase diagram. [START_REF] Wang | Thermodynamic modelling of the Au-Ge-Sn ternary system[END_REF] Positive values of ρ I obtained in a wide range of concentrations reveal that the presence of Ga always enhances the nucleation and growth rates of Aucatalyzed GeSn NWs. For self-catalyzed process where c Sn 0 is fixed at 0.95, [START_REF] Olesinski | The Ge-Sn (germanium-tin) system[END_REF] ρ I also increases at low c Ga but starts to decrease below zero when c Ga is greater than 0.1. This value is however hardly reachable because the solubility of Ga in Sn droplet is almost zero at the growth temperature. [START_REF] Anderson | The Ga-Sn (gallium-tin) system[END_REF] We can see that lower Sn concentrations in the catalyst droplet enhance the chemical potential difference. More quantitatively, an increase of the chemical potential difference up to ~ 150 meV can occur in Au-rich droplets. This will lead to rising the NW nucleation rate by several orders of magnitude, because the nucleation probability depends exponentially on ρ. [START_REF] Hijazi | Influence of Si on the nucleation rate of GaAs nanowires on Si substrates[END_REF][START_REF] Dubrovskii | Zeldovich nucleation rate, self-consistency renormalization, and crystal phase of Au-catalyzed GaAs nanowires[END_REF] Let us now compare these results with experimental observations. Figures 1 (b) and (c) show tilted-view SEM images of samples S1 and S2, respectively. In both cases, GeSn NWs grow preferentially along the [111] direction perpendicular to the substrate surface. The NW diameter is relatively uniform along its entire length. This can be attributed to the passivation of the NW sidewalls by chlorine atoms as previously discussed in Ref. [START_REF] Guilloy | Uniform phosphorus doping of untampered germanium nanowires[END_REF]. However, random nucleation of Au-catalyzed NWs on the substrate surface in sample S1 is revealed by the broad distribution of diameters within the NW ensemble. The largest NWs are surrounded by the depleted zones where no other NWs or droplets are observed. On the other hand, NWs catalyzed by Au-Ga droplets in sample S2 show a much narrower distribution of diameters, larger surface density and more uniform A c c e p t e d M a n u s c r i p t spatial distribution over the substrate surface, revealing their synchronized nucleation. Note that both samples were grown under the same conditions: a growth temperature of 350 °C, a growth time of 60 minutes and a GeH 4 / SnCl 4 flux ratio of 10 -3 . The growth temperature employed corresponds to the optimal conditions for the Au-catalyzed VLS growth of GeSn NWs determined in our previous work. [START_REF] Haffner | Growth of Ge 1-x Sn x nanowires by chemical vapour deposition via[END_REF] As shown in the inserts of figures 1 (b) and (c), the NW growth rate is reduced by a factor ~ 1.75 in the presence of Ga in the droplet.

Based on these data, we propose the following explanations for the observed difference in the morphology of GeSn NWs obtained with pure Au or Au-Ga droplets.

(1) Due to a lower nucleation probability of NWs emerging from pure Au droplets following from figure 1 (a), the incubation time required to start the NWs from the substrate is longer in sample S1. This allows larger droplets to collect the surrounding smaller ones by the Ostwald ripening process and increase their sizes before initiating the NW growth, similarly to Ref. [START_REF] Hijazi | Dynamics of Au droplet formation on SiO 2 /Si(111) surface[END_REF]. This results in the depletion zones observed around the largest NWs in figure 1 (b).

(2) For NWs catalyzed by Au-Ga droplets, the initial nucleation is easier according to figure 1 (a). This effect leads to more synchronized nucleation of NWs in sample S2 and explains their larger surface density, smaller diameters and higher degree of spatial uniformity seen in figure 1 (c). This trend was systematically observed for different Au and Ga films thicknesses tested (not shown).

(3) Due to a difficult nucleation of NWs emerging from pure Au droplets, these droplets remain in contact with Ge substrate for a longer time. Consequently, NWs of sample S1 receive more Ge atoms from the substrate compared to sample S2. Higher Ge concentration in the droplets after nucleation enhances the growth rate of these NWs, [START_REF] Hajjar | Morphology and composition of Au catalysts on Ge(111) obtained b thermal dewetting[END_REF] as is seen from figure 1 (a). This explains why the NWs in sample S1 are longer than in sample S2.

A c c e p t e d M a n u s c r i p t

It is important to note that the variation in chemical potential driving the NW nucleation is sensitive to the vapor phase composition. For example, it was experimentally demonstrated that increasing the P SnCl 4 /P GeH 4 partial pressure ratio results in a reduced growth of Au-catalyzed GeSn NW on Ge(111) substrates. [START_REF] Haffner | Growth of Ge 1-x Sn x nanowires by chemical vapour deposition via[END_REF] In other words, the NW nucleation and growth rates are decreased by depositing more Sn and less Ge onto the Au droplet. This property also clearly follows from the graphs in figure 1 (a). We now consider system II which corresponds to GeSn NWs grown on Si(111) substrates, where Si can be transferred to the droplets in the high temperature annealing step. The initial droplet is a ternary Au-Ge-Sn alloy, to which we add Ga and Si (𝜀 1 = Ga, 𝜀 2 = Si). Figure 2 (a) shows three-dimensional map of the chemical potential difference ρ II versus c Ga and c Si , obtained from Eq. 8 with c Ge 0 and c 𝑆𝑛 0 fixed at 0.05 and 0.5, respectively. The growth temperature is the same as in system I. Considering first the dependence of ρ II on c Ga at a fixed c Si , we can see that the presence of Ga is always favorable for the NW nucleation. This is confirmed experimentally in figures 2 (b) and (d), where the NWs emerge only in the presence of Ga. The nucleation rate and hence the incubation time required to start the NWs from the substrate is now different for different concentrations of Si in the droplet. Considering the evolution of ρ II with c Si at a fixed c Ga , figure 2 (a) shows that ρ II monotonically increases with c Si even at c Ga = 0. This explains the presence of GeSn NWs in the annealed sample S5 [figure 2 (c)] and their absence in sample S3 where the droplets consist of pure Au [figure 2 (b)]. Overall, these results show that GeSn NWs cannot be grown on Si(111) substrates with pure Au catalyst. Adding only Si atoms in the high temperature annealing step, as in sample S4, allows the VLS growth of NWs with random position, size and orientation. The NW morphology is largely improved by adding Ga to the Au-Si droplets. However, this growth is much less regular than on Ge(111) substrates with Au-Ga droplets and needs to be further optimized with respect to other conditions such as temperature, total pressure and composition of the vapor phase.

The Sn concentration in our GeSn NWs grown on both Ge(111) and Si(111) substrates, estimated by energy dispersive X-ray spectroscopy, is relatively low, in the range from 1 to 2 %, which is only slightly beyond the equilibrium solubility. Previous study has shown that a lower growth temperature is required to achieve Snrich GeSn NWs, with up to 10 % total concentration of of Sn and a limited Sn segregation. [START_REF] Dou | Investigation of GeSn strain relaxation and spontaneous composition gradient for low-defect and high-Sn alloy growth[END_REF] Another work revealed an important role of the axial NW growth rate in the non-equilibrium incorporation of Sn into Ge. [START_REF] Grzybowsk | Next generation of Ge 1-𝑦 Sn 𝑦 (y = 0.01-0.09) alloys grown on Si(100) via Ge 3 H 3 and SnD 4 : reaction kinetics and tunable emission[END_REF] Even more delicate dependence of the Sn incorporation may arise due to variable compositions in Au-Ge-Sn-Ga or Au-Ge-Sn-Ga-Si alloy droplets. This study is beyond the scope of this work and will be presented elsewhere. However, our model and data reveal in a consistent manner the impact of the liquid phase composition on the nucleation rate of GeSn NWs influencing their size homogeneity, surface density and morphology on different substrates. The model is not specific for GeSn material and should work in a wide range of materialsubstrate combinations for controlling the properties of different semiconductor NWs by tuning the catalyst composition.

Conclusions

A model has been developed which allows one to quantify how chemical potential in a catalyst droplet is modified by adding one or two types of foreign elements before the VLS growth of NWs. Au-catalyzed growth of GeSn NWs on Ge(111) and Si(111) substrates from Au-Ge-Sn droplets with added Ga and/or Si atoms have been analyzed. For Ge(111) substrates, it has been shown that nucleation of GeSn NWs is easier when Ga atoms are added to Au catalysts in the de-wetting step. This leads to a higher surface density and enhanced size uniformity within the NW ensembles. For Si(111) substrates, the VLS growth of GeSn NWs can only be achieved with adding Si or both Si and Ga atoms to Au droplets. Adding Ga improves the homogeneity of the NW morphology which, however, remains less regular than on Ge(111) substrates. Overall, these results can be used for optimizing nucleation and growth of semiconductor NWs on different substrates by adding suitable foreign atoms to the catalyst droplets.

Figure 1 :

 1 Figure 1: (a) Evolution of the chemical potential change ρ I versus atomic fraction of Ga added to the droplets of different composition. The growth temperature is 350 °C. Blue full line corresponds to the Sn-catalyzed vapor-liquid-solid process without any Au. The other curves correspond to the Au-catalyzed vapor-liquid-solid process with different initial atomic fractions of Sn c Sn 0 . Full and dashed lines represent initial atomic fraction of Ge c Ge 0 = 0.05 and 0.1, respectively. Panels (b) and (c) show scanning electron microscopy images of GeSn NWs grown on Ge(111) substrates with pure Au (S1) and Au-Ga (S2) catalyst droplets, respectively. The inserts show cross-section views with the measured NW lengths. Scale bars correspond to 1 µm.

Figure 2 :

 2 Figure 2: (a) Three-dimensional map showing the chemical potential change ρ II versus the atomic fractions of Ga and Si in the catalyst droplet. The initial atomic fractions c Ge 0 and c Sn 0 are fixed at 0.05 and 0.5, respectively. The growth temperature is 350 °C. (b-d) Scanning electron microscopy images of GeSn NWs grown on Si(111) substrates under the following conditions: (b) deposition of Au without annealing, (c) deposition of Au followed by annealing at 550 °C for 10 minutes, (d) deposition of Au and Ga followed by annealing at 550 °C for 10 minutes. Scale bars correspond to 1 µm.

  A c c e p t e d M a n u s c r i p t A c c e p t e d M a n u s c r i p t

Table 1 :

 1 Parameters used in calculations of the binary interaction parameters ω ij .

	Element	V (𝐜𝐦 𝟑 . 𝐦𝐨𝐥 -𝟏 )	(𝟏𝟎 𝟐𝟒 𝐞𝐕. 𝐦𝐨𝐥 -𝟏 ) 𝚫𝐇 𝐚𝐭	𝛘
	Au	11.3790	2.285	2.54
	Ga	11.8095	1.729	1.81
	Ge	12.9696	2.353	1.90
	Sn	16.2394	1.885	1.96
	Si	11.2724	2.846	2.01

Acknowledgments: H.H. and V.G.D. are grateful to the Russian Science Foundation for financial support under the Grant 19-72-30004.

Conflicts of interest:

The authors declare no conflict of interest.


Léo Garnier

Benjamin Verlhac
email: verlhac@ipcms.unistra.fr

Paula Abufager

Nicolás Lorente

Maider Ormaza
email: ormaza@ipcms.unistra.fr

Laurent Limot
email: limot@ipcms.unistra.fr

The Kondo effect of a molecular tip as a magnetic sensor

A single molecule offers to tailor and control the probing capability of a scanning tunneling microscope when placed on the tip. With the help of first-principles calculations, we show that on-tip spin sensitivity is possible through the Kondo ground state of a spin S = 1/2 cobaltocene molecule. When attached to the tip apex, we observe a reproducible Kondo resonance, which splits apart upon tuning the exchange coupling of cobaltocene to an iron atom on the surface. The spin-split Kondo resonance provides quantitative information on the exchange field and on the spin polarization of the iron atom. We also demonstrate that molecular vibrations cause the emergence of Kondo side peaks, which, unlike the Kondo resonance, are sensitive to cobaltocene adsorption.

Introduction. The decoration of metal probe-tips by a molecule intentionally picked up from a surface has proven to be a powerful method to improve the measurement capabilities of a scanning tunneling microscope (STM). The degrees of freedom of the molecule introduce tip-surface interactions across the vacuum gap that are usually absent when using a metallic apex. These interactions can endow STM with an enhanced sub-molecular resolution, [START_REF] Temirov | A novel method achieving ultra-high geometrical resolution in scanning tunnelling microscopy[END_REF][START_REF] Gross | The Chemical Structure of a Molecule Resolved by Atomic Force Microscopy[END_REF][START_REF] Weiss | Imaging Pauli Repulsion in Scanning Tunneling Microscopy[END_REF] and provide new chemical insight. [START_REF] Gross | Bond-Order Discrimination by Atomic Force Microscopy[END_REF][START_REF] Chiang | Real-space imaging of molecular structure and chemical bonding by single-molecule inelastic tunneling probe[END_REF][START_REF] Wagner | Scanning Quantum Dot Microscopy[END_REF][START_REF] Guo | Nuclear quantum effects of hydrogen bonds probed by tipenhanced inelastic electron tunneling[END_REF] Detailed information can be gathered about single molecules on a surface and the way they interact among each other, which is of interest to chemistry and biology. [START_REF] Jelínek | High resolution SPM imaging of organic molecules with functionalized tips[END_REF] To probe magnetic effects with a molecular tip it is necessary to have a magnetic molecule at the tip apex. Recently, a tip decorated with a nickelocene molecule [START_REF] Ormaza | Efficient Spin-Flip Excitation of a Nickelocene Molecule[END_REF] [Ni(C 5 H 5 ) 2 ] was used to monitor surface magnetism through the inelastic component of the tunneling current, [START_REF] Czap | Probing and imaging spin interactions with a magnetic single-molecule sensor[END_REF][START_REF] Verlhac | Atomic-scale spin sensing with a single molecule at the apex of a scanning tunneling microscope[END_REF] which provides an electrical access to the nickelocene spin states. [START_REF] Heinrich | Single-Atom Spin-Flip Spectroscopy[END_REF] An exciting alternative could consist in using a magnetic molecule undergoing a Kondo effect, which is quite common for magnetic molecules adsorbed on metal surfaces. [START_REF] Scott | Resonances in Molecular Devices[END_REF] This ubiquitous quantum phenomenon occurs when a magnetic impurity -molecule or atom-couples to a non-magnetic host metal. [START_REF] Hewson | The Kondo Problem to Heavy Fermions[END_REF] The conduction electrons of the metal spin-screen the impurity to form a singlet below a temperature T K . The screening occurs coherently causing the emergence of a narrow resonance at the Fermi energy in the molecular conductance. Interestingly, this so-called Kondo resonance changes when the Kondo impurity magnetically couples to its local environment. By closely monitoring the resonance line shape, magnetic information can be gathered through the impurity. Kondo atoms and molecules have been widely used in STM for this purpose, [START_REF] Wahl | Exchange Interaction between Single Magnetic Adatoms[END_REF][START_REF] Otte | Spin Excitations of a Kondo-Screened Atom Coupled to a Second Magnetic Atom[END_REF][START_REF] Tsukahara | Evolution of Kondo Resonance from a Single Impurity Molecule to the Two-Dimensional Lattice[END_REF][START_REF] Néel | Two-Site Kondo Effect in Atomic Chains[END_REF][START_REF] Fu | Spin-resolved splitting of Kondo resonances in the presence of RKKY-type coupling[END_REF][START_REF] Von Bergmann | Spin Polarization of the Split Kondo State[END_REF][START_REF] Spinelli | Exploring the phase diagram of the two-impurity Kondo problem[END_REF][START_REF] Khajetoorians | Tailoring the chiral magnetic interaction between two individual atoms[END_REF] but the discrete interatomic separations imposed by the substrate lattice prevent a detailed investigation. In a seminal work to circumvent this limitation, 23 a tip was decorated with a Kondo atom and its separation from another Kondo atom on the surface was continuously changed. This study, however, suffered from the poor structural and magnetic knowledge of the tip apex. To improve tip-control and simplify the procedure, a Kondo effect carried by a molecular tip would be preferable, but its experimental realization has remained elusive.

To build a molecular Kondo tip, we resort here to cobaltocene [Co(C 5 H 5 ) 2 , noted Cc] -a molecule of the metallocene family, which in vacuum has a spin S = 1/2 due to a singlyoccupied doublet (π xz , π yz ). We show that Cc can be sublimated onto a metal surface and subsequently picked up by the STM tip to produce reproducible Kondo physics at the tip apex. With the help of first-principles calculations and dynamical correlations, we describe the Kondo ground state and demonstrate magnetic tip-sensitivity across the vacuum gap.

We also show that the Kondo signature is intertwined with molecular vibrational modes that depend on how cobaltocene is contacted to its metallic environment. The Cc-tip shows great potential for probing surface magnetism besides displaying fascinating many-body vibrational features.

Adsorption on Cu(100).

After shortly exposing Cu(100) to a molecular flux (see Supporting Information), single Cc molecules were found on terraces and on step edges of the surface (Figure 1a). The Cc molecules on the terraces exhibited a ring-like pattern (inset of Figure 1b) that we assign to a cyclopentadienyl group (C 5 H 5 , Cp hereafter) being exposed to vacuum. The ring-like pattern observed and the apparent height of 400 ± 50 pm (Figure 1b) are typical for metallocenes, [START_REF] Ormaza | Assembly of Ferrocene Molecules on Metal Surfaces Revisited[END_REF][START_REF] Bachellier | Unveiling nickelocene bonding to a noble metal surface[END_REF] and point to a Cc adsorbed with its molecular axis parallel to the surface normal. We found that isolated Cc was preferentially adsorbed with the bottom Cp ring centered on the hollow site of Cu(100) (see Figure S1 in Supporting Information).

Our density functional theory (DFT) calculations point to a bottom Cp ring positioned at a distance of 259 pm from the surface (Figure 1c) with a 0.16 e -charge transfer from the molecule to the substrate, which corresponds to a moderate chemisorption. The projected density of states (PDOS, Figure S2) indicates that the mixing of C(sp), Co(d xz ) and Co(d yz ) orbitals results in the partially-populated π xz and π yz frontier molecular orbitals, giving a magnetic character to cobaltocene on Cu(100). The computed magnetic moment of Cc is carried by the Co atom and is 0.75 µ B , which corresponds to an effective spin of S = 1/2. The π orbitals are nearly degenerate and spatially add up to yield the ring-like shape of Cc (Figure 1d). These properties are similar to those of a nickelocene molecule that is adsorbed on a surface [START_REF] Bachellier | Unveiling nickelocene bonding to a noble metal surface[END_REF] or on a tip. 26

Cc-tip and Kondo resonance. To prepare a Cc-tip with atomic control, we transferred a Cc from Cu(100) to the tip apex of the STM. The transfer process, which was analogous to other metallocene molecules, [START_REF] Ormaza | Efficient Spin-Flip Excitation of a Nickelocene Molecule[END_REF][START_REF] Ormaza | Controlled spin switching in a metallocene molecular junction[END_REF][START_REF] Ormaza | On-Surface Engineering of a Magnetic Organometallic Nanowire[END_REF] consisted in approaching the tip towards the Cc molecule within 100 pm from point contact at a bias of -20 mV or lower (see supporting information).

The presence of Cc on the tip apex produced a molecular pattern when imaging an adatom (Figure 2a), which was otherwise featureless when using a metallic tip apex (Figure S1). The molecular pattern is attributed to a Cc that is adsorbed on the tip apex with its molecular axis tilted with respect to the surface normal. Three configurations were observed: a twolobe pattern with one lobe brighter than the other (noted 1), a two-lobe pattern with equal intensities on the lobes ( 2), and a one-lobe pattern (3).

We used DFT to compute the structure of the Cc-tip. We mimicked the molecular tip by considering a Cc molecule adsorbed on a Cu adatom on Cu(100) (Figure 2b) and calculated the relaxed structure (see Supporting Information). We found an excellent agreement between the experimental and the simulated STM images (Figure 2c). The relaxed structures correspond to three stable configurations close in energy (Table S1). Configuration The computed magnetic moment of Cc on the tip shows negligible dependence on adsorption configuration (Table S1). In the case of configuration 1, for instance, the magnetic moment is 0.89 µ B , the projection on the Co atom giving 0.83 µ B -the charge transfer of Cc to the metal tip is 0.12 e -. The spin-polarized PDOS (Figure S2) changes compared to Cc on the copper surface. The effective spin S = 1/2 of the Cc-tip is now carried by an unpaired electron in the π yz orbital, which corresponds to a singly occupied molecular orbital. The π xz orbital lies above the Fermi energy and corresponds to the lowest unoccupied molecular orbital. The π yz orbital possesses a nodal plane perpendicular to the Cp ring (Figure 1d)

and produces the two-lobe pattern seen in the STM images of the Cc-tip. This behavior is common to other cobaltocene derivatives. [START_REF] Knaak | Ligand-Induced Energy Shift and Localization of Kondo Resonances in Cobalt-Based Complexes on Cu(111)[END_REF] Figure 2d presents a typical differential conductance (dI/dV ) spectrum that was acquired with Cc-tip 2 positioned above a Cu(100) terrace. The spectrum exhibited a sharp peak near zero-bias and was flanked by peaks nearly symmetric with bias polarity (solid black lines in Figure 2d). The dominant zero-bias peak is assigned to a Kondo resonance resulting from the spin-flip scattering of tip conduction electrons by the S = 1/2 spin of Cc. The nearly symmetric shape of the peak indicates that the quantum interference with the continuum of the tip electrons is negligible. [START_REF] Fano | Effects of Configuration Interaction on Intensities and Phase Shifts[END_REF] The spatial distribution of the Kondo resonance in the molecule (inset of Figure 2d) follows the two-lobe pattern of the π yz orbital, revealing that the Kondo effect is carried by this orbital.

The side peaks are assigned to a Kondo effect where tunneling electrons have their spin flipped when elastically scattering off the Cc spin, but with sufficient energy to activate a vibrational mode in the molecule. [START_REF] Paaske | Vibrational Sidebands and the Kondo Effect in Molecular Transistors[END_REF] These peaks fall at biases corresponding to the vibrational excitation energies of the cobaltocene molecule. [START_REF] Yu | Inelastic Electron Tunneling via Molecular Vibrations in Single-Molecule Transistors[END_REF][START_REF] Parks | Tuning the Kondo Effect with a Mechanically Controllable Break Junction[END_REF][START_REF] Fernández-Torrente | Vibrational Kondo Effect in Pure Organic Charge-Transfer Assemblies[END_REF][START_REF] Choi | A Single Molecule Kondo Switch: Multistability of Tetracyanoethylene on Cu(111)[END_REF][START_REF] Rakhmilevitch | Electron-Vibration Interaction in the Presence of a Switchable Kondo Resonance Realized in a Molecular Junction[END_REF] Their intensity is higher at negative bias compared to positive bias. Additionally, while the Kondo resonance showed little dependence on tip configuration (Figure S3), the intensity of these side peaks changed from tip to tip. For simplicity, in the following we restrain the presentation to Cc-tip 2 without loss of generality. To enrich the discussion of the Kondo line shape, we include in our analysis the Cc molecules that are adsorbed at the bottom of the edge of Cu(100) steps (inset of Figure 1a; see also Figure S1). Remarkably, these Cc have same experimental markers as the Cc-tip. They have a two-lobe pattern when imaged and their dI/dV spectrum is nearly mirror symmetric in bias to the spectrum acquired with a Cc-tip (Figure 2e). 2). (c) Set of dI/dV spectra acquired with the Cc-tip positioned above a Fe for various tip-atom distances; for clarity, the spectra were shifted vertically from one another by 1 µS. The distance z = 0 corresponds to point contact (Figure S4). The solid red lines are a line shape simulation based on a dynamical scattering model. [START_REF] Zhang | Temperature and magnetic field dependence of a Kondo system in the weak coupling regime[END_REF][START_REF] Ternes | Spin excitations and correlations in scanning tunneling spectroscopy[END_REF] We used the third-order formulas to include Kondo physics and set the potential scattering U to zero. Inset: Sketch of the experimental setup. (d) Distance dependence of the excitation threshold |eV 0 | (y-axis: left) and of the exchange field (y-axis: right). The exponential fit described in the text is plotted as a solid red line.

Cc-tip: Kondo effect.

To validate the Kondo nature of the zero-bias peak, we probed the temperature dependence of the dI/dV spectrum of the Cc-tip and that of the Cc at the step edge. A set of spectra is presented Figure 3a. The peak broadened progressively with temperature, which is a signature of a Kondo system. The dI/dV spectra were simulated using a Frota function (solid red line in Figure 3a) [START_REF] Frota | Shape of the Kondo resonance[END_REF][START_REF] Pruser | Long-range Kondo signature of a single magnetic impurity[END_REF] σ(eV,

Γ) = h * ℜ [ √ iΓ/(iΓ + eV -ϵ K ) ] + σ 0 , ( 1
)
where ℜ indicates the real part, while σ 0 , h and ϵ K are constants. The thermal smearing introduced by the tunneling mechanism and the smearing of the lock-in detection were also accounted for in the simulation. [START_REF] Crampin | Resonator design for use in scanning tunneling spectroscopy studies of surface electron lifetimes[END_REF] As shown in Figure 3b, the evolution of Γ(T ) with temperature is well reproduced by 42

Γ(T ) = 1.455/2 √ (2k B T K ) 2 + (αk B T ) 2 , ( 2
)
where k B is the Boltzmann constant. We obtain T K = 4.3 ± 1.3 K and α = 5.0 ± 0.3 (solid line in Figure 3b). This asymptotic slope is close to the predicted value for a spin-1/2 Kondo system in the strong coupling regime, [START_REF] Nagaoka | Temperature Dependence of a Single Kondo Impurity[END_REF] while the relatively small value of T K indicates a weak coupling of Cc to the metal tip apex. Similar findings were reported for other Kondo systems. [START_REF] Otte | The role of magnetic anisotropy in the Kondo effect[END_REF][START_REF] Dubout | Controlling the Spin of Co Atoms on Pt(111) by Hydrogen Adsorption[END_REF] To further evidence the Kondo nature the zero-bias peak, we magnetically coupled the Cc-tip to a Fe atom on Cu(100) across the vacuum gap. The magnetic coupling of a Kondo atom to another magnetic atom, [START_REF] Otte | Spin Excitations of a Kondo-Screened Atom Coupled to a Second Magnetic Atom[END_REF][START_REF] Bork | A tunable two-impurity Kondo system in an atomic point contact[END_REF] or a magnetic electrode, [START_REF] Fu | Spin-resolved splitting of Kondo resonances in the presence of RKKY-type coupling[END_REF][START_REF] Choi | Resonance of a Co Atom Exchange Coupled to a Ferromagnetic Tip[END_REF] is known to split the Kondo resonance into two peaks. A typical set of dI/dV spectra recorded above the Fe atom at different tip-atom distances z is presented in Figure 3c (z = 0 corresponds to point contact, Figure S4). The spectra were acquired with one of the lobes of the Cc-tip centered on the atom. While the z = 150 pm spectrum was indistinguishable from the one acquired above the bare Cu(100), for smaller distances a splitting of the peak was apparent. The splitting became increasingly stronger as z was decreased, the median energy position of the two peaks remaining unchanged within experimental resolution. However, the intensity of the two peaks was asymmetric for opposite voltage polarities.

To rationalize these observations, we follow our previous work on the nickelocene-terminated tip, [START_REF] Verlhac | Atomic-scale spin sensing with a single molecule at the apex of a scanning tunneling microscope[END_REF] and use a simplified spin Hamiltonian to describe the magnetically coupled Cc-Fe system (see supporting information and Figure S5):

Ĥ = -gµ B B ex Ŝz , (3)
where the z-axis corresponds to the out-of-surface direction -for simplicity, we neglect the small tilt of Cc. Even though Kondo correlations are not explicitly accounted for in Eq. ( 3), similar spin Hamiltonians have been shown to quantitatively describe the energies of spin-split Kondo peaks. [START_REF] Otte | Spin Excitations of a Kondo-Screened Atom Coupled to a Second Magnetic Atom[END_REF][START_REF] Von Bergmann | Spin Polarization of the Split Kondo State[END_REF][START_REF] Zhang | Temperature and magnetic field dependence of a Kondo system in the weak coupling regime[END_REF][START_REF] Otte | The role of magnetic anisotropy in the Kondo effect[END_REF] This effective Zeeman Hamiltonian consists of the gyromagnetic factor (g = 2), the Bohr magneton (µ B = 57.9 µeV/T), and the exchange field (B ex ) produced by the Fe atom and acting on Cc along the z-axis. Within mean-field theory, B ex = |J|⟨S z,Fe ⟩/gµ B , where ⟨S z,Fe ⟩ ≈ 3/2 is the effective spin of Fe on copper [START_REF] Verlhac | Atomic-scale spin sensing with a single molecule at the apex of a scanning tunneling microscope[END_REF][START_REF] Khajetoorians | Itinerant Nature of Atom-Magnetization Excitation by Tunneling Electrons[END_REF] and J is the magnetic coupling between Cc and Fe -we take the coupling to be Ising-like. The spin-split zero-bias peak is then ascribed to a pair of conductance steps placed symmetrically about zero bias. The steps in Figure 3c are associated to inelastic tunneling events in which tunneling electrons excite Cc from its magnetic ground state |m = +1/2⟩, with m as the magnetic quantum number, to the excited state |m = -1/2⟩. They are located at a bias |eV 0 | = gµ B B ex corresponding to the energy separating the two Zeeman levels.

A line shape simulation based on Eq. ( 3) and on a dynamical scattering model [START_REF] Zhang | Temperature and magnetic field dependence of a Kondo system in the weak coupling regime[END_REF][START_REF] Ternes | Spin excitations and correlations in scanning tunneling spectroscopy[END_REF] is presented as a solid red line in Figure 3c. The simulated line closely reproduces the experimental spectra. Figure 3d presents quantitative estimates for B ex as extracted from the simulations carried out at various distances z. The exchange field is an exponential function of z of the form exp (-z/λ) (Figure 3d) with a decay length of λ = (23 ± 1) pm, which is characteristic of an exchange interaction across a vacuum gap. [START_REF] Czap | Probing and imaging spin interactions with a magnetic single-molecule sensor[END_REF][START_REF] Verlhac | Atomic-scale spin sensing with a single molecule at the apex of a scanning tunneling microscope[END_REF][START_REF] Schmidt | Quantitative Measurement of the Magnetic Exchange Interaction across a Vacuum Gap[END_REF][START_REF] Yan | Control of quantum magnets by atomic exchange bias[END_REF][START_REF] Yang | Tuning the Exchange Bias on a Single Atom from 1 mT to 10 T[END_REF] The coupling is |J| ≈ 1.3 meV at the shortest probed Fe-Cc distance, similar to other exchange coupled systems. [START_REF] Choi | Resonance of a Co Atom Exchange Coupled to a Ferromagnetic Tip[END_REF][START_REF] Muenks | Correlation-driven transport asymmetries through coupled spins in a tunnel junction[END_REF] Our simulations also capture the line shape asymmetry observed experimentally.

This asymmetry η = (h + -h -)/(h + + h -), which stems from a selection rule for spin excitations, [START_REF] Ternes | Spin excitations and correlations in scanning tunneling spectroscopy[END_REF][START_REF] Loth | Controlling the state of quantum spins with electric currents[END_REF] reflects changes in the inelastic step height at positive and negative voltage (h + and h -). From our simulations, we found a constant value of η = 20 ± 5% for the shortest tip-sample distances (solid lines in Figure 3c). Although this value must be handled with care as the potential scattering was set to zero in our simulations, [START_REF] Von Bergmann | Spin Polarization of the Split Kondo State[END_REF] η provides a measure for the adsorbate-related spin polarization owing to the Kondo nature of the Cc-tip. [START_REF] Von Bergmann | Spin Polarization of the Split Kondo State[END_REF][START_REF] Pasupathy | The Kondo Effect in the Presence of Ferromagnetism[END_REF] With the help of an external magnetic field, the information gathered at the atomic-scale with a Cc-tip, either through the exchange interaction or the spin polarization, should prove sufficient for obtaining a magnetic contrast in STM images. needed to understand this behavior. [START_REF] Reecht | Vibrational Excitation Mechanism in Tunneling Spectroscopy beyond the Franck-Condon Model[END_REF] For a complete picture of the Kondo effect of cobaltocene, we present in Figure 4d a typical dI/dV spectrum of single-Cc on a Cu(100) terrace. Compared to previous Cc-tip spectra, the line shape has a more complex pattern. It is much broader with a dominant peak located at 25 mV and a second peak at 125 mV, with a reproducible shoulder centered at zero-bias.

Cc

The Kondo spectral function can be again computed assuming that molecular vibrations are still present when cobaltocene is adsorbed on the terrace (Figure 4e). The calculation was performed with the computed vibrational frequencies, using the Kondo temperature and the electron-vibration couplings as fitting parameters. The Kondo temperature was fixed to that of the Cc-tip, implicitly assuming that the Kondo effect is still carried by a single molecular orbital. The spectrum is broad showing two characteristic peaks at 30 mV and at 120 mV.

Despite the large number of parameters, the calculation conclusively shows the prevalence of vibrational signatures in the spectrum. Unlike the Cc-tip, all possible vibrational modes of Cc are excited in the range from 2 meV to 395 meV. This leads to a quasi-continuum of excitations that are packed in two regions, one at 30 meV and the other at 120 meV, corresponding to the distribution of modes in the molecule. The low-energy features in the dI/dV can then be unambiguously assigned to a Kondo effect in the presence of strong electron-vibration coupling in the Cc molecule.

Conclusion.

We have shown that by decorating a STM tip with a cobaltocene molecule it is possible to routinely produce a Kondo resonance at the tip apex, which is flanked by side peaks resulting from vibrational excitations. The Kondo resonance can be used to probe a magnetic exchange interaction across the vacuum gap and to determine a samplerelated spin-polarization. These results open the exciting perspective of obtaining a magnetic contrast in the STM images by monitoring the changes in the Kondo resonance. A variety of magnetic systems can be investigated in this way, ranging from simple ones, e.g. atoms and molecules, to magnetic surfaces, complementing other spin-polarized scanning probe techniques. [START_REF] Serrate | Imaging and manipulating the spin direction of individual atoms[END_REF][START_REF] Baumann | Electron paramagnetic resonance of individual atoms on a surface[END_REF] The physics of two Kondo impurities may also be thoroughly explored with

Figure 1 :

 1 Figure 1: (a) Cobaltocene on Cu(100) (image size: 20 × 15 nm 2 , sample bias: 20 mV, tunneling current: 30 pA). Inset: ×1.6 zoom of Cc molecules at a step edge. (b) Line profile of a Cc on copper terrace. The profile was taken along the white line in panel (a). Inset: Close-up view of Cc on a terrace (2 × 2 nm 2 , -70 mV, 20 pA). (c) Side view of the relaxed structure of Cc on Cu(100) as computed by DFT. (d) Calculated wave-function density of the π xz and π yz orbitals of Cc in vacuum and their linear combination.

1 and 3

 3 correspond to a Cc bound to the Cu adatom trough two C atoms of the Cp ring, resulting in a tilt angle of 16 • with respect to the surface normal. Configuration 2 corresponds to a Cc bound to the Cu adatom through one C atom of the Cp ring, resulting in a tilt angle of 4 • . We note that similar stable configurations, where a Cu atom either interacts with a C-C bond or a with C atom, are also observed in point contact measurements of a Cu-tip with a C 60 molecule.[START_REF] Schull | Charge Injection through Single and Double Carbon Bonds[END_REF]

Figure 2 :

 2 Figure 2: (a) Fe atom on Cu(100) imaged with three different Cc-tips noted 1 to 3 from left to right (1.8 × 1.8 nm 2 , 60 mV, 30 pA). (b) DFT-computed relaxed structures for the Cc-tip, and, (c) corresponding simulated STM images (0.8 × 0.8 nm 2 , isovalue: 0.004 nm -3 ). (d) dI/dV spectrum taken with a Cc-tip above the bare Cu(100) surface (feedback loop opened at -70 mV, 200 pA). Inset: Constant-height dI/dV image acquired with the Cc-tip above a Fe atom (1.6 × 1.6 nm 2 , sample bias: -2 mV). The feedback loop was opened at distance of z = 0.4 nm above the center of the Fe atom. (e) dI/dV spectrum of a Cc adsorbed at a step edge of Cu(100) surface acquired with a Cu-terminated tip (-75 mV and 200 pA). Inset: Constant-height dI/dV image acquired above a Cc adsorbed at a step edge (2.5 × 2.5 nm 2 , sample bias: +4 mV). The feedback loop was opened at distance of z = 0.4 nm above one of the Cc lobes. The vertical lines in panels (d) and (e) mark the position of Kondo side peaks due to molecular vibrations.

Figure 3 :

 3 Figure3: (a) dI/dV spectra of Cc adsorbed on a step-edge of Cu(100) for different temperatures (feedback loop opened at -70 mV, 300 pA). For clarity, the middle and top spectra are shifted vertically by 4 and 8 nS, respectively. The solid red lines are simulated line shapes using Eq. (1) with ϵ K = 0.5 ± 0.1 meV. (b) Temperature-dependence of Γ extracted from the dI/dV spectra. The solid line correspond to the curve calculated using Eq. (2). (c) Set of dI/dV spectra acquired with the Cc-tip positioned above a Fe for various tip-atom distances; for clarity, the spectra were shifted vertically from one another by 1 µS. The distance z = 0 corresponds to point contact (FigureS4). The solid red lines are a line shape simulation based on a dynamical scattering model.[START_REF] Zhang | Temperature and magnetic field dependence of a Kondo system in the weak coupling regime[END_REF][START_REF] Ternes | Spin excitations and correlations in scanning tunneling spectroscopy[END_REF] We used the third-order formulas to include Kondo physics and set the potential scattering U to zero. Inset: Sketch of the experimental setup. (d) Distance dependence of the excitation threshold |eV 0 | (y-axis: left) and of the exchange field (y-axis: right). The exponential fit described in the text is plotted as a solid red line.

Figure 4 :

 4 Figure 4: (a) d 2 I/dV 2 spectrum of a Cc-tip in configuration 2 (feedback loop opened at -70 mV and 2 nA). (b) Experimental (x-axis: top) and DFT-computed (x-axis: bottom) vibrational energies. The experimental energies comprise those of the Cc-tip (blue lines) and of Cc at the step edge (red lines). (c) Computed spectral function of a Cc-tip in configuration 2 (top panel) and its derivative (bottom panel). (d) dI/dV spectrum of Cc adsorbed on a terrace of Cu(100). The feedback loop was opened at -175 mV, 200 pA. (e) Computed spectral function of Cc with a quasi-continuum of vibrational excitations (see text).

Acknowledgement

The authors thank the Agence Nationale de la Recherche (grants No. ANR-13-BS10-0016, ANR-11-LABX-0058 NIE and ANR-10-LABX-0026 CSC) and the MICINN (project RTI2018-097895-B-C44) for financial support.

a Cc-tip, adding control to previous work by Bork et al. [START_REF] Bork | A tunable two-impurity Kondo system in an atomic point contact[END_REF] and extending it to single Kondo molecules.

Supporting Information Available

Information is provided concerning tip/sample preparation and DFT calculations. Additional experimental and computational data are presented that support the main conclusions of the article (Figures S1-S8). This material is available free of charge via the Internet at http://pubs.acs.org/.