H Koussir

Y Chernukha

C Sthioul

E Haber

N Peric

L Biadala

P Capiod

M Berthe

I Lefebvre

B. Grandidier X Wallart

P Diener

Large-area epitaxial Mott insulating 1T-TaSe 2 monolayer on GaP(111)B

Two dimensional Mott materials have recently been reported in the dichalcogenides family with high potential for Mottronics applications. Nevertheless, their widespread use as a single or few layers is hampered by their limited device integration resulting from their growth on graphene -a metallic substrate. Here, we report on the fabrication of 1T-TaSe 2 monolayers grown by molecular beam epitaxy on semiconducting gallium phosphide substrates. At the nanoscale, the charge density wave reconstruction and a Moiré pattern resulting from the monolayer interaction with the substrate are observed by scanning tunneling microscopy. The fully open gap unveiled by tunneling spectroscopy, which can be further manipulated by the proximity of a metal tip, is conrmed by transport measurements from micrometric to millimetric scales, demonstrating a robust Mott insulating phase up to 400 K.

Mott materials such as cuprates, ruthenates or nickelates exhibit an amazingly rich physics, with several competing electronic orders such as superconductivity, charge density waves (CDW) and magnetic orders. [START_REF] Perfetti | Spectroscopic Signatures of a Bandwidth-Controlled Mott Transition at the Surface of 1T-TaSe2[END_REF] In some of them, in particular the narrow gap Mott insulators, the Mott insulator-metal transitions can be triggered by optical and electric pulses with interesting perspectives for the micro and nanoelectronics industry. 47 The benchmark dichalcogenides Mott material is 1T-TaS 2 . [START_REF] Sipos | From Mott state to superconductivity in 1T-TaS2[END_REF] Just like other compounds of the MX 2 family (M=Nb, Ta, Mo, W ; X=S, Se, Te), TaS 2 exhibits a lamellar hexagonal structure, with strong in-plane interactions that favor the appearance of CDW orders. In particular, the 1T polytype exhibits a CDW which is commensurate with the lattice (C-CDW) below 190 K. At this threshold, a gap appears, which is generally attributed to a CDW-driven Mott transition: [START_REF] Ritschel | Orbital textures and charge density waves in transition metal dichalcogenides[END_REF] part of the electrons are frozen by the CDW, leaving a half lled band at the Fermi energy, splitted into lower (LHB) and upper (UHB) Hubbard bands due to electronic repulsion. The correlated metal state can be recovered upon external stimuli, [START_REF] Stojchevska | Ultrafast Switching to a Stable Hidden Quantum State in an Electronic Crystal[END_REF][START_REF] Yoshida | Memristive phase switching in two-dimensional 1T-TaS2 crystals[END_REF] but the low critical temperature limits the potential of TaS 2 for applications.

In contrast, the C-CDW survives in the selenium-based bulk compound 1T-TaSe 2 up to 437 K. [START_REF] Wilson | Charge-Density Waves in Metallic, Layered, Transition-Metal Dichalcogenides[END_REF] While this crystal does not develop a Mott-Hubbard band splitting because of stronger interlayer coupling than in TaS 2 , an insulating behavior has been found for the surface layer and single-layer grown on bilayer graphene. 1316 Angle resolved photoemission and scanning tunneling spectroscopy studies indicated the existence of a Mott gap up to 250 K for the surface layer [START_REF] Colonna | Mott Phase at the Surface of 1T-TaSe2 Observed by Scanning Tunneling Microscopy[END_REF] and up to 450 for the single-layer. [START_REF] Nakata | Robust charge-density wave strengthened by electron correlations in monolayer 1T-TaSe2 and 1T-NbSe2[END_REF] Such a high temperature is essential for the development of Mottronics devices. But the growth of 1T-TaSe 2 single layer on graphene, which has a much higher conductivity, hinders the study of electrical transport in the Mott crystal, calling for the use of more resistive substrates with reduced proximity eects. [START_REF] Chen | Visualizing the Anomalous Charge Density Wave States in Graphene/NbSe2 Heterostructures[END_REF][START_REF] Dreher | Proximity Eects on the Charge Density Wave Order and Superconductivity in Single-Layer NbSe2[END_REF] Exfoliated 1T-TaSe 2 layers reported on an insulating SiO 2 layer has recently been obtained, giving valuable informations on the thickness dependence of the Mott gap. [START_REF] Tian | Dimensionality-driven metal to Mott insulator transition in twodimensional 1T-TaSe2[END_REF] The SiO 2 surface is however known to be prone of charge trapping with strong impact on the stability of the electrical properties. [START_REF] Illarionov | The role of charge trapping in MoS2/SiO2 and MoS2/hBN eld-eect transistors[END_REF][START_REF] Illarionov | Insulators for 2D nanoelectronics: the gap to bridge[END_REF] Additionally, two keypoints must be adressed for the development of future devices. First, large TaSe 2 lms are required, and their on-wafer process must be compatible with the microelectronics industry. Second, dichalcogenide materials, in particular 1T-TaSe 2 , are known to get easily oxidized [START_REF] Tsai | Direct Synthesis of Large-Scale Multilayer TaSe2 on SiO2/Si Using Ion Beam Technology[END_REF][START_REF] Samnakay | Zone-Folded Phonons and the Commensurate-Incommensurate Charge-Density-Wave Transition in 1T-TaSe2 Thin Films[END_REF] . An eective in-situ encapsulation method at the end of the growth is thus mandatory.

In principle, the two-dimensional structure of 1T-TaSe 2 allows for a van der Waals epitaxy on passivated conventional semiconductor substrates. As a result, dichalcogenide thin lms [START_REF] Tsoutsou | Epitaxial 2D MoSe2 (HfSe2) Semiconductor/2D TaSe2 Metal van der Waals Heterostructures[END_REF] and, more recently, single layers have been grown with molecular beam epitaxy (MBE) on GaAs. 2729 Based on these achievements, we report the successful MBE growth of 1T-TaSe 2 monolayer on a Se-terminated GaP(111)B substrate. While electron diraction techniques and photoemission spectroscopy indicate the growth of the 1T polytype, the TaSe 2 /GaP heterostructure was subsequently protected with a thin Se capping layer. First, low temperature scanning tunneling microscopy (STM) performed after the sublimation of the Se cap reveals the following features: i) the expected "Star of David" (SD) superlattice caused by the C-CDW, ii) a superimposed Moiré pattern induced by the interaction of the monolayer with the GaP substrate and, iii) a Mott gap in dierential conductance spectroscopy at 77 K, which vanishes when spectroscopic measurements are acquired at smaller tip-sample distances. Then, four-point probe transport measurements of 1T-TaSe 2 monolayers grown on semi-insulating GaP substrates and still encapsulated with a resistive Se layer show a temperature-dependent characteristic of a Mott insulator up to 400 K. 1T-TaSe 2 on GaP thus offers a prolic playground for low dimensionality Mott physics, CDW and Moiré related phenomena, as well as for the development of large scale Mottronic devices at ambient temperature. S1.

The growth experiments were carried out using an ultrahigh (UHV) vacuum system consisting of MBE chambers for the growth of III-V compounds and transition metal dichalcogenides. The TaSe 2 layer was grown at 600 °C by simultaneously supplying Ta and Se on an atomically-smooth Se-treated GaP(111)B-(1x1) surface (Figure S1). Both n-type and insulating GaP substrates have been used for the following studies. The Se passivation and growth steps were monitored by in-situ reection high energy electron diraction (RHEED), as shown Figures 1a-d. The observation of a streaky RHEED pattern upon the growth of the TaSe 2 reveals the formation of a smooth and well-ordered epilayer on the GaP substrate.

The epilayer is aligned in-plane with the substrate and becomes better ordered upon annealing at 700 °C in a Se-rich atmosphere.

The low energy electron diraction (LEED) pattern measured at room temperature with an electron energy of 50 eV is displayed Figure 1e. The image has the expected hexagonal symmetry and the spots called "TaSe 2 " and "GaP" are attributed to the TaSe 2 layer and GaP(111)B surface respectively. This pattern together with the RHEED ones show that the hexagonal cell of TaSe 2 aligns with that of GaP according to the relations [0001]TaSe 2 // [ A Moiré pattern is visible and its analysis indicates the growth of a thin epilayer with a (11x11) T aSe 2 /(10x10) GaP structure, yielding a TaSe 2 lattice parameter of 3.5±0.1 Å. This value, also conrmed by X ray diraction (Supplementary Figure S2), is close to the 1T-TaSe 2 bulk lattice parameter of 3.48 Å. [START_REF] Bjerkelund | On the Structural Properties of the Ta1xSe2 Phase[END_REF] While the core level survey measured with X-ray photoelectron spectroscopy (XPS) at room temperature shows the high purity of the TaSe 2 layer (supplementary Figure S3), examination of the Ta 4f core level reveals a spin-orbit doubling of the 7/2 and 5/2 lines, which can be further decomposed into three components (Figure 1f). These triplets support the existence of three dierent Ta sites, consistent with the nonequivalent Ta atoms in the SD structure of the C-CDW phase. Moreover, the symmetry of the peaks, which diers from the asymmetry observed for the 2H-TaSe 2 phase, their position as well as their separation agree with previous XPS analysis of bulk 1T-TaSe 2 (Supplementary Table S1), further corroborating the epitaxy of the 1T-TaSe 2 polytype. [START_REF] Horiba | Charge-density wave and threedimensional Fermi surface in 1T-TaSe2 studied by photoemission spectroscopy[END_REF] Figure 2 displays typical STM images of a TaSe 2 epilayer grown on a n-type GaP substrate (doping concentration of 2×10 18 cm -3 ) after the sample transfer through air and the subsequent sublimation of the Se cap in the preparation chamber of the STM system. The large-scale image of Figure 2a shows a majority of atomic terraces with two distinct features, a quasi-periodic ower-shape pattern (evidenced by a white ower) which is superim-posed to small protrusions (green triangles). These features are reproducibly observed on the whole surface, indicating the full coverage of the GaP(111)B surface with TaSe 2 . From the height prole in Figure 2b, we measure a step height of 3.1±0.1 Å between the terraces. We note the existence of rare islands with very limited sizes, that show a height of 6.3±0.1 Å (Supplementary Figure S4). In these islands, the small protrusions are clearly visible, but the ower-shape pattern is not observed whatever the bias is. As the interlayer spacing in bulk 1T-TaSe 2 is 6.27 Å, the terraces cannot consist of stacked layers of 1T-TaSe 2 . Instead, a monoatomic step height of 3.15 Å between the GaP (111) planes [START_REF] Hattori | GaP(111)reconstructed surface studied with STM and LEED[END_REF] implies that the GaP terraces are covered with a monolayer of TaSe 2 .

Figure 2c shows a high-resolution STM image where the atoms of the top Se layer are atomically-resolved, corresponding to an atomic lattice of 3.5±0.1 Å, as expected for TaSe 2 . The Se atoms form a bright triangular pattern rotated by an angle of 13.9°from the atomic unit cell. This pattern is at the origin of the small protrusions visible in the large scale STM image of Figure 2a. Such a superstructure is due to the SD contraction of the CDW order in the 1T phase, giving rise to a superlattice [START_REF] Wilson | Charge-Density Waves in Metallic, Layered, Transition-Metal Dichalcogenides[END_REF][START_REF] Chen | Strong correlations and orbital texture in single-layer 1T-TaSe 2[END_REF] also observed in 1T-TaS 2 and 1T-NbSe 2 . [START_REF] Wu | Eect of stacking order on the electronic state of 1T-TaS2[END_REF][START_REF] Liu | Direct identication of Mott Hubbard band pattern beyond charge den-sity wave superlattice in monolayer 1T-NbSe2[END_REF] Figure 3a displays a STM image at an intermediate resolution scale, in which the additional ower-shape superstructure is highlighted. The Fast Fourier Transform (FFT) of Figure 3a, shown in Figure 3b, is composed of two series of peaks, denoted P CDW and P M oire . Their origin is revealed by applying an inverse FFT to each series of peaks. The inverse FFT of the P CDW peaks is displayed in Figure 3c, and the one corresponding to the P M oire peaks, in Figure 3d. As shown in Figure 3c, the P CDW peaks relates to a hexagonal lattice having a periodicity of 13.2±0.4 Å that is attributed to the SD lattice parameter. Two distinct domains are visible, having the same hexagonal lattice and rotated with respect to each other by an angle of 27.8°. As sketched Figure 3e, these domains correspond to the two equivalent chiral orientations of the SD lattice: the alignment of SDs on the surface can be tilted by either +13.9°or -13.9°compared to the atomic lattice. [START_REF] Song | Atomic-scale visualization of chiral charge density wave superlattices and their reversible switching[END_REF] Each chiral hexagonal domains give rise to 6 peaks in the FFT, rotated by approximately 28°with respect to the others.

Moreover, the P M oire peaks are rotated by an angle of 14°compared to both series of P CDW peaks, indicating that the Moiré pattern is aligned with the TaSe 2 atomic lattice. As shown in Figure 3d, the peaks P M oire are related to a hexagonal lattice with a periodicity of 38.6 Å. This superlattice is consistent with a Moiré lattice formed by the superposition of the TaSe 2 layer and the GaP substrate, as sketched Figure 3f. In this schematic, the top atoms of the substrate (Se passivation) have a unit cell of 3.85 Å as expected for the GaP (111) surface and the TaSe 2 layer has a unit cell of 3.50 Å similar to the measured value. The obtained Moiré unit cell of 38.5 Å corresponds to 10 unit cells for the GaP surface and 11 TaSe 2 unit cells, in quantitative agreement with the Moiré observed in the LEED pattern (Figure 1e). Surprisingly, the observed CDW lattice size of 13.2±0.4 Å is larger than the value of 12.6 Å, expected for a ( √ 13 × √ 13 R13.9°) CDW lattice commensurable with the bulk TaSe 2 atomic lattice. As shown by Lin et al. in the case of TiTe 2 on a PtTe 2 substrate, a van der Waals interaction with the substrate can be at the origin of a strong modication of the CDW order present in the TiTe 2 monolayer. [START_REF] Lin | Charge Instability in Single-Layer TiTe2 Mediated by van der Waals Bonding to Substrates[END_REF] The observed CDW lattice size of the TaSe 2 monolayer is indeed in between √ 13a 0 = 12.6 Å and √ 13b 0 = 13.9 Å with a 0 and b 0 being the in-plane TaSe 2 and GaP(111) lattice parameters respectively. It suggests a stretching of the CDW modulation in the TaSe 2 monolayer due to its proximity with the GaP substrate.

As this interaction can strongly modify the Mott gap, [START_REF] Lin | Charge Instability in Single-Layer TiTe2 Mediated by van der Waals Bonding to Substrates[END_REF][START_REF] Zhang | Reconciling the bulk metallic and surface insulating state in 1T-TaSe2[END_REF] tunneling spectroscopy was further performed. Figure 4a exhibits typical spectra. For feedback conditions with a large sample bias of -2.0 V, the dierential conductance shows a region extending between -1.0 V and +1.3 V, where the signal is below the noise level, the Fermi level being set at zero bias. Curiously, the width of this region corresponds to the theoretical band gap of GaP at 77 K (2.26 eV). Moreover the increase of the differential conductance below -1.0 V is at odd with the dispersive bands in 1T-TaSe 2 monolayers grown on bilayer graphene as found in this energy range by angle-resolved photoemis- sion spectroscopy. [START_REF] Nakata | Robust charge-density wave strengthened by electron correlations in monolayer 1T-TaSe2 and 1T-NbSe2[END_REF] Therefore, we attribute the increase of the signal below -1.0 V and above +1.3 V to the contribution of the valence and conduction bands of GaP. The position of the Fermi energy 1.3 eV below the conduction band of GaP indicates a depletion layer at the surface of the n-doped substrate, consistent with the band bending deduced from photoemission measurements (Supplementary Figures S5 andS6). Noteworthy, STM images (Figure 2c) and spectroscopic measurements on the 1T-TaSe 2 monolayer can be still performed with sample bias within the band gap of GaP. It means that the electrons predominantly propagate through the TaSe 2 monolayer to reach the collecting electrode located at the sample edge, a few millimeters away from the STM tip, as illustrated by the inset of Figure 4a. Setting the feedback condition for the sample bias at -0.5 V yields a dierential conductance with a zeroconductance region of 0.13 ± 0.02 eV. The gap is surrounded by two peaks centered at -0.22 eV and +0.21 eV, with a Fermi energy in the middle of the gap, as expected for an undoped Mott semiconductor. The energy separation between the peaks of the LHB and UHB Hubbard bands, arising from the Coulomb repulsion in the monolayer, is 0.43 eV. The observed gap amplitude and positions of the Hubbard peaks are very similar to the one reported for 1T-TaSe 2 single layers on graphene bilayer, [START_REF] Chen | Strong correlations and orbital texture in single-layer 1T-TaSe 2[END_REF][START_REF] Lin | Scanning tunneling spectroscopic study of monolayer 1T-TaS2 and 1T-TaSe2[END_REF] indicating a negligible substrate perturbation and strong electronic correlations in TaSe 2 . Based on spatially resolved tunneling spectroscopy (Figure S7), the LHB and UHB peaks are detected across the entire SD pattern. In contrast to previous results obtained at 4 K on 1T-TaSe 2 grown on bilayer graphene, [START_REF] Chen | Strong correlations and orbital texture in single-layer 1T-TaSe 2[END_REF] the amplitude of the UHB peak decreases at the center of the SD pattern but does not disappear. This could be attributed to a larger spatial extension of the electronic states at 77 K.

Interestingly, increasing the setpoint current causes a broadening of the LHB and UHB bands, which ends up with the disappearance of the Mott gap for setpoint currents higher than 250 pA (Figure 4b). In this regime, the I(V) characteristics show a metallic behavior, which strongly departs from the zero-current region measured around zero volt when the STM tip is far from the surface (Supplementary Figure S8). This result is consistent with the behavior of the Mott-Hubbard surface states of the 6H-SiC(0001), where the states do not shift but broadened upon increasing setpoint currents. [START_REF] Baou | State selective electron transport through electronic surface states of 6H-SiC(0001)-3x3[END_REF] The increasing proximity of the metallic tip modies the electron repulsion in the bands [START_REF] Nguyen | Coulomb Energy Determination of a Single Si Dangling Bond[END_REF] and, hence, gives rise to a transition between the two competing phases.

To conrm the macroscopic continuity of the TaSe 2 monolayer, four probe transport measurements have been performed at both micrometric and millimetric scales. For these experiments, an insulating GaP substrate is used to avoid an electrical conduction through the substrate. The micrometric measurements were performed with a multiple probe STM, in UHV, at room temperature, after the sublimation of the Se cap. A linear arrangement of equidistant STM tips, as seen in the SEM image of Figure 4d, yields a 4P resistance which does not signicantly vary with the tip separation (Figure 4c). Despite the roughness of the surface caused by the GaP terraces and the defects observed on each terrace, the electron conduction which is conned in the two-dimensional TaSe 2 monolayer, does not degrade over tens of micrometers. This is consistent with the low temperature STM experiments, where the electrons can only escape from the sample by reaching the few-millimetre-remote top contact applied to the TaSe 2 monolayer. This property indicates a strong robustness of transport to defects.

Temperature dependent resistance measurements have also been performed at the millimetric scale (Figure 4e-f). While the TaSe 2 epilayer is contacted with four golden probes through a 30 nm thick selenium cap in ambient air, the transport properties are further measured in a cryogenic setup under vacuum to avoid any degradation of the sample when it is overexposed to air. All measured currentvoltage characteristics exhibit an ohmic behaviour (supplementary Figure S9), from which the temperature-dependent sheet resistance R S is deduced for a four-probe square conguration. [START_REF] Miccoli | The 100th anniversary of the four-point probe technique: the role of probe geometries in isotropic and anisotropic systems[END_REF] As shown in Figure 4e, the sheet resistance R S decreases exponentially with temperature between 200 K and 400 K. Comparison of R S with a sample consisting of a selenium cap without the TaSe 2 monolayer clearly shows that the variation of R S is caused by the intrinsic property of the 1T-TaSe 2 monolayer (supplementary Fig. S8). The t with a standard activated law R ∝ exp(∆/2k B T ) gives an energy gap of ∆=136 meV. This is in remarkable agreement with the results from tunneling spectroscopy at 77 K, especially regarding the huge dierence of the probed area, from the nanoscale to the milimeter scale. Such a result demonstrates that the 1T-TaSe 2 monolayer is in the Mott insulating state not only at low temperature, but also at room temperature.

To conclude, 1T-TaSe 2 epitaxial monolayers have been grown by MBE on both doped and insulating GaP substrates. The atomic superstructure observed by STM is due to a combination of a Moiré pattern with the substrate and the CDW reconstruction in both chiral orientations. A Mott insulating gap is observed both at the nanoscale by STS and millimetric scale by four point measurements, up to 400 K. The possibility to obtain similar 2D crystals on either conducting or insulating GaP substrates, with an ecient selenium encapsulation, is suitable for both lateral and transverse electrode geometry in future device applications. Besides unveiling stimulating results on the Moiré and Mott-CDW physics, the long-range electrical transport and the manipulation of the Mott gap in tunneling spectroscopy at the local scale pave the way towards the growth of large scale 2D Mott materials and their integration in functional devices at ambient temperature.

Supporting Information

Scanning Tunneling Microscopy

Scanning tunneling microscopy has been performed at 77K with a low temperature LT-Omicron setup. To be able to study the TaSe 2 epilayer at low temperature, the GaP substrate was n-type doped at a concentration of 2-3×10 18 cm -3 . We used electrochemically etched tungsten tips, which were thoroughly cleaned in-situ by direct current heating. Prior to the STM study, the samples were bakeout in the load lock of the system at 120°C for 8 hours. Then, the protective Se layer was removed in the preparation chamber by heating the samples at 270°C for several hours. The above values lead then to the relative position of the bottom of the conduction band at the GaP surface E cs with respect to the Fermi level : E cs E f = 0.92±0.1 eV. This is in good agreement with the depletion layer deduced from the STS measurements although there is a slight dierence in the exact position of the bands with respect to the Fermi level.

Scanning Tunneling Spectroscopy

Spatially-resolved tunneling spectra were acquired across the SD pattern, as shown in Figure S7. The results obtained at dierent setpoint currents are shown Figure S8. Transport measurements in UHV Four-point probe measurements of 1T-TaSe 2 monolayers grown on semi-insulating GaP substrates were performed with a multiple STM system under the supervision of a SEM in UHV with a base pressure lower than 5x10 -10 mbar (Nanoprobe, Scienta Omicron). Prior to the experiments, the tungsten tips, obtained from electrochemical etching in NaOH, were thoroughly annealed in the UHV preparation chamber of the system to remove the thin oxide layer covering the tips and the Se cap protecting the TaSe 2 layer was sublimated. To measure the four-probe resistance of 1T-TaSe 2 , the STM tips were rst approached in the tunneling regime. The nal approach was monitored with the tunneling current. Stable electrical contacts were obtained when the current saturated, yielding electrical resistances between two tips in the range 200-300 kΩ , higher than the measured 4P resistance of the epilayer of 11±2 kΩ.

Temperature dependent transport measurements

The transport measurements have been performed on TaSe 2 monolayers grown on insulating GaP(111)B substrates. The TaSe 2 monolayers are protected from oxidation with a 30 nm-thick Se capping layer. The samples are xed at the extremity of a cryogenic insert designed for transport measurements mounted on a Janis VPF100 cryostat. The sample holder contains an insulating mounting surface and 4 xed-position tungsten probes with limited range of movements for ne scale positioning. The design of the probes includes springs that allows good mechanical stability in electrical contact for a wide range of temperatures. All 4 probes are put in contact with the sample surface (Figure S9a) and the presence of the ohmic contacts is checked by measuring current-voltage characteristics between all pairs of probes at dierent temperatures ; typical results are shown Figure S9b. The resistance of a 130 nmthick Se layer deposited on a GaAs insulating substrate was also measured as a function of temperature for comparison (black curve in Figure S9c). At high temperatures, the Se layer is at least 3 times more resistive than the TaSe 2 monolayer and becomes even more resistive

Figure 1 :

 1 Figure 1: RHEED patterns acquired along the [11-2] azimuth for (a) the clean GaP(111)B surface, (b) the Se-treated GaP(111)B surface, (c) the growth of the TaSe 2 monolayer and (d) the annealed monolayer. (e) LEED pattern of the TaSe 2 /GaP heterostructure. The diraction spots related to the GaP, TaSe 2 and Moiré lattices are highlighted in red, black and white respectively. (f) XPS spectrum of Ta 4f measured with a photon energy of 1486.7 eV. The thin lines correspond to ts obtained with the parameters given in TableS1.

Figure 2 :

 2 Figure 2: (a) Large scale STM image of the TaSe 2 monolayer. The ower-like reconstruction is highlighted in white and the CDW-related protrusions with green triangles. Feedback parameters: V S = +1.5 V, I t = 15 pA. (b) Height prole acquired along the black line in (a). (c) High resolution STM image where the top Se atoms of the TaSe 2 layer are resolved. Feedback parameters: V S = -0.5 V, I t = 70 pA. The Se and Ta positions are indicated by green and black atoms respectively and the CDW SD pattern by a blue star. The green triangles indicate the ensemble of top Se atoms corresponding to the small periodic protrusions in (a). The black and red diamonds delineate the atomic and CDW unit cells respectively.

Figure 3 :

 3 Figure 3: (a) STM image of the quasiperiodic ower-shaped superstructure observed in the 1T-TaSe 2 monolayer on GaP(111)B. Feedback parameters: V S = +3.0 V, I t = 20 pA. (b) FFT of image (a). The spots circled in red correspond to the CDW reconstruction and the spots circled in yellow are related to the Moiré pattern. (c,d) Inverse FFT corresponding to the CDW and the Moiré spots respectively. (e) Schematic of the two possible chiral CDW orientations. The CDW unit cell is indicated as a red diamond, either in continuous or dotted line for the two chiralities. (f) Schematic of the Moiré formed by the superposition of the Se terminated GaP substrate and the TaSe 2 single layer. The yellow losange gives the Moiré unit cell. The arrows in b-f underline the CDW (red) and Moiré (yellow) lattice orientations. The black and green dots in e,f are the Ta and Se atoms respectively, the blue dots in f are the atoms at the surface of the GaP substrate (Se atoms from the GaP passivation).

Figure 4 :

 4 Figure 4: (a) Tunneling spectroscopy of the 1T-TaSe 2 /GaP(111)B heterostructure. The valence and conduction band edges of the GaP substrate are indicated by vertical segments, labelled E V and E C . Feedback parameters: V S = -2.0 V, I t = 200 pA. Central inset: dI/dV spectrum acquired in a narrower energy window with dierent feedback parameters: V S = -0.5 V, I t =20 pA. The peaks related to the lower and upper Hubbard bands are respectively labelled LHB and UHB. Top inset: illustration of the measurement conguration, with the tip tunneling on the 1T-TaSe 2 layer grown on a doped GaP substrate. Both the TaSe 2 epilayer and the doped GaP substrate are in electrical contact with the ground. The arrows indicate the allowed (without cross) and forbidden (with a cross) paths for the electrons at energies below the band gap of GaP. (b) Tunneling spectroscopy performed on the same site at dierent setpoint currents indicated in the graph. (c) Room temperature four probe resistance as a function of the equidistant interelectrode distance measured in UHV. Inset: Illustration of the corresponding measurements conguration. (d) Scanning electron microscopy of the four aligned and equally spaced STM tips in contact with the TaSe 2 layer, used for (c). (e) Sheet resistance R S as a function of temperature measured in Se-capped TaSe 2 (symbols) compared to the t described in the text (line). Inset: illustration of the transport measurements conguration. The TaSe 2 monolayer grown on a semi-insulating GaP substrate is protected with a Se cap and the four electrodes are contacted across the cap. (f) Optical image of the sample and electrodes used in (e).

  Experimentalmethods and additional experimental results.

Figure S 1 :

 1 Figure S 1: 2x2 µm typical AFM image of the GaP(111)B surface after deoxidation.

Figure S 2 :

 2 Figure S 2: (a) Large 2θχ/ϕ scan of TaSe 2 along the [110] and [-211] crystal directions of GaP. (b) 2θχ/ϕ Scan on a reduced range around the (110) peak of TaSe 2 .

Figure S 4 :

 4 Figure S 4: (a) Typical STM image of a supposed bilayer nanosheet. (b) Height prole acquired along the segment seen in (a). (c) High resolution STM image of the bilayer (V sample = -2 V ; I t = 20 pA).

Figure S 6 :

 6 Figure S 6: Evolution of the binding energy of the P2p core level line from the deoxidized GaP(111)B 2×2 surface to the deposition of 1ML TaSe 2 .

Figure S 7 :Figure S 8 :

 78 Figure S 7: (a) Dierential conductance spectra measured across the SD pattern in the 1T-TaSe 2 epilayer at 77 K. Inset: the colored points in the STM image indicate the location corresponding to the spectra of the main gure. The curves have been oset for clarity. The energies of the UHB and LHB bands indicated in the Figure by vertical segments slightly shift due to potential uctuation in the epilayer.

Table S 1

 S : Fitting parameters for the Ta 4f core level in monolayer 1T-TaSe 2 measured by XPS. For all ts, the value of the full width at half maximum is constrained at 0.66 eV.

	Bond	Area (percent) Asymmetry parameter Binding energy (eV)
	Ta-Se(a)7/2	4.4	0.49	22.99
	Ta-Se(a)5/2	3.3	0.49	24.90
	Ta-Se(b)7/2	26.4	0.12	23.19
	Ta-Se(b)5/2	19.7	0.12	25.10
	Ta-Se(c)7/2	26.4	0.34	23.80
	Ta-Se(c)5/2	19.7	0.34	25.71

Acknowledgement

This work was partly funded by the RENAT-ECH network (PCMP-PCP and CMNF), I-SITE ULNE (R-20-004), Hauts-de-France region and the French National Research Agency (ANR-21-CE24-0030 Tunne2D and ANR-21-CE24-0001-01 Nanodyn). A CC-BY public copyright license has been applied by the authors to the present document and will be applied to all subsequent versions up to the Author Accepted Manuscript arising from this submission, in accordance with the grant's open access conditions.

Epitaxial growth

The GaP(111)B substrates were deoxidized in a III-V MBE reactor under cracked phosphine (PH3) and atomic hydrogen (Hat) uxes to prepare clean GaP(111)B surfaces. After deoxidization, the surface exhibited a 2x2 RHEED pattern and a morphology characterized by atomic steps whereas XPS revealed the absence of residual contamination.

The sample was then transferred under UHV in a TMD epitaxial chamber and annealed up to 600°C under a selenium ux with a Beam Equivalent Pressure in the 10 -6 Torr range to prepare a Se-terminated GaP(111) surface. During selenium passivation, the RHEED pattern turned to a 1x1 reconstruction. Atomic Force Microscopy (AFM) did not reveal any surface morphology change after selenium treatment. The TaSe 2 growth was performed at 600°C with a Ta growth rate around 0.0015 Å/s and under a selenium beam equivalent pressure of 4-5 10 -6 Torr. After growth, the layer was annealed for 10 minutes at 700°C.

XPS analysis

As the ESCA analysis chamber is connected to the MBE chambers, the samples do not suer from transfer contamination prior to their characterization by XPS. The XPS spectra have been recorded using Al Kα = 1486 eV. The high purity of the sample is conrmed by a survey in which only Ta, Se, Ga and P lines are detected.

The Ta 4f XPS core level has been tted using the software CasaXPS 1 with Doniach-Sunjic-Shirley (DSS) line shapes. 2 They consist in Doniach-Sunjic functions, 3 the only theoretically based asymmetric curves, with a cut o to avoid their area to be innite. This approach has already been used in 2H-TaSe 2 and 1T-TaS 2 . 4,5 The DSS line shapes are based on Lorentzian functions which have been convoluted with a Gaussian function to reproduce the experimental broadening of the system. S1.

The t is made with 3 doublets corresponding to the 3 inequivalent Ta atoms in the CDW in the proportion 6:6:1, each having dierent asymmetries, and based on the relative peak positions from the literature. 6 The tting parameters are as given in Table S1.

Evaluation of band-bending

We use X-ray and UV photoemission measurements to determine the surface band bending during surface passivation and upon 1 monolayer (ML) TaSe Then, on the deoxidized n-type GaP(111)B 2×2 surface, we record the position of the valence band maximum at the surface E vs with respect to the Fermi level E f (Figure S5) by a standard linear extrapolation method. 7 This leads to E f -E vs = 1.58 eV±0.05 eV. The band bending on the deoxidized GaP(111)B 2×2 surface is then dened as E vs E vb = 0.62 eV±0.05 eV. For this surface, we also record the binding energy (BE) of the P2p core level (CL) line at -129.78 eV±0.025 eV (red curve on gure S6) During the Se surface passivation and 1 ML TaSe 2 deposition, we then follow the evolution of the band bending according to the variations of the BE of the P2p CL line, as the edge of at lower temperatures. Therefore, the inuence of the Se capping layer on the resistance behavior of the TaSe 2 monolayer is negligible over the whole measured temperature range.


Quyen Van Nguyen

Pascal Martin

Jean Christophe Lacroix

Probing the Effect of the Density of Active Molecules in Large-Area Molecular Junctions

ABSTRACT:

The effect of the density of active molecules in molecular junctions (MJs) has been investigated by using a host/guest strategy. Mixed layers consisting of oligothiophene (BTB) encapsulated by β-cyclodextrin (BTB@β-CD) were generated. Cyclodextrins were then removed and the pinholes generated filled with BTB to obtain BTB@BTB films. MJs based on mixed BTB@β-CD and BTB@BTB layers, as well as single-component BTB MJs, were compared. The variation of Ln J vs thickness is similar for all systems while the J o of BTB@β-CD MJs is 20 times lower than that of BTB MJs. After -cyclodextrin has been removed, and the pinholes filled, J o increases and reaches the same value as for the BTB MJs, showing that the conductance scales with the number of active molecules. This strategy provides a unique method for investigating molecular interactions in direct tunneling MJs as well as the possibility of fabricating new functionalized MJs based on mixed layers.

Molecular electronics has been extensively investigated since the first theoretical proposal of Ratner and Aviram in 1974. 1 Since then, many researchers have attempted to generate 'reliable and robust' molecular electronics devices using various approaches ranging from single-molecule [START_REF] Xu | Measurement of Single-Molecule Resistance by Repeated Formation of Molecular Junctions[END_REF][START_REF] Xiang | Non-Exponential Length Dependence of Conductance in Iodide-Terminated Oligothiophene Single-Molecule Tunneling Junctions[END_REF][START_REF] Hybertsen | Structure-Property Relationships in Atomic-Scale Junctions: Histograms and Beyond[END_REF][START_REF] Capozzi | Length-Dependent Conductance of Oligothiophenes[END_REF][START_REF] Su | Chemical Principles of Single-Molecule Electronics[END_REF][START_REF] Xie | Single-Molecule Junction: A Reliable Platform for Monitoring Molecular Physical and Chemical Processes[END_REF][START_REF] Xin | Concepts in the Design and Engineering of Single-Molecule Electronic Devices[END_REF][START_REF] Yao | Single-Molecule Junctions with Highly Improved Stability[END_REF][START_REF] El Abbassi | Unravelling the Conductance Path through Single-Porphyrin Junctions[END_REF] to fewmolecules [START_REF] Engelkes | Length-Dependent Transport in Molecular Junctions Based on SAMs of Alkanethiols and Alkanedithiols: Effect of Metal Work Function and Applied Bias on Tunneling Efficiency and Contact Resistance[END_REF][START_REF] Kim | Correlation between HOMO Alignment and Contact Resistance in Molecular Junctions: Aromatic Thiols versus Aromatic Isocyanides[END_REF][START_REF] Smith | Length-Dependent Nanotransport and Charge Hopping Bottlenecks in Long Thiophene-Containing π-Conjugated Molecular Wires[END_REF][START_REF] Xie | Experimental and Theoretical Analysis of Nanotransport in Oligophenylene Dithiol Junctions as a Function of Molecular Length and Contact Work Function[END_REF][START_REF] Sangeeth | Comparison of DC and AC Transport in 1.5-7.5 Nm Oligophenylene Imine Molecular Wires across Two Junction Platforms: Eutectic Ga-In versus Conducting Probe Atomic Force Microscope Junctions[END_REF] or to large-area molecular junctions (MJs) [START_REF] Yan | All-Carbon Molecular Tunnel Junctions[END_REF][START_REF] Sayed | Charge Transport in Molecular Electronic Junctions: Compression of the Molecular Tunnel Barrier in the Strong Coupling Regime[END_REF][START_REF] Yuan | On the Remarkable Role of Surface Topography of the Bottom Electrodes in Blocking Leakage Currents in Molecular Diodes[END_REF][START_REF] Supur | Ion-Assisted Resonant Injection and Charge Storage in Carbon-Based Molecular Junctions[END_REF][START_REF] Hylke | Electrical Conduction through Single Molecules and Self-Assembled Monolayers[END_REF][START_REF] Akkerman | Towards Molecular Electronics with Large-Area Molecular Junctions[END_REF][START_REF] Yan | Activationless Charge Transport across 4.5 to 22 nm in Molecular Electronic Junctions[END_REF][START_REF] Yoon | The Rate of Charge Tunneling Is Insensitive to Polar Terminal Groups in Self-Assembled Monolayers in AgTSS(CH2) NM(CH2)MT//Ga2O3/EGaIn Junctions[END_REF][START_REF] Bowers | Characterizing the Metal-SAM Interface in Tunneling Junctions[END_REF][START_REF] Zhao | Rectification Inversion in Oxygen Substituted Graphyne-Graphene-Based Heterojunctions[END_REF][START_REF] Liao | Molecular Series-Tunneling Junctions[END_REF][START_REF] Liao | Tunneling across Molecular Junctions[END_REF] . Recently, molecular electronics has demonstrated improved properties in rectifiers, [START_REF] Yuan | A Molecular Diode with a Statistically Robust Rectification Ratio of Three Orders of Magnitude[END_REF][START_REF] Bayat | Control of Electronic Symmetry and Rectification through Energy Level Variations in Bilayer Molecular Junctions[END_REF][START_REF] Chen | Molecular Diodes with Rectification Ratios Exceeding 105 Driven by Electrostatic Interactions[END_REF] redox switches, [START_REF] Whalley | Reversible Switching in Molecular Electronic Devices[END_REF][START_REF] Zhang | Towards Single Molecule Switches[END_REF][START_REF] Han | Electric-Field-Driven Dual-Functional Molecular Switches in Tunnel Junctions[END_REF][START_REF] Liao | Cyclic Conductance Switching in Networks of Redox-Active Molecular Junctions[END_REF] photoswitches, [START_REF] Kumar | Mixed Monolayers of Spiropyrans Maximize Tunneling Conductance Switching by Photoisomerization at the Molecule-Electrode Interface in EGaIn Junctions[END_REF][START_REF] Jia | Covalently Bonded Single-Molecule Junctions with Stable and Reversible Photoswitched Conductivity[END_REF][START_REF] Hnid | Highly Efficient Photoswitch in Diarylethene-Based Molecular Junctions[END_REF][START_REF] Hnid | Unprecedented ON/OFF Ratios in Photoactive Diarylethene-Bisthienylbenzene Molecular Junctions[END_REF] dual-functional, [START_REF] Han | Electric-Field-Driven Dual-Functional Molecular Switches in Tunnel Junctions[END_REF][START_REF] Tefashe | Robust Bipolar Light Emission and Charge Transport in Symmetric Molecular Junctions[END_REF][START_REF] Goswami | Charge Disproportionate Molecular Redox for Discrete Memristive and Memcapacitive Switching[END_REF][START_REF] Thompson | Design Principles of Dual-Functional Molecular Switches in Solid-State Tunnel Junctions[END_REF] and high-speed devices. [START_REF] Trasobares | A 17 GHz Molecular Rectifier[END_REF][START_REF] Tan | Quantum Plasmon Resonances Controlled by Molecular Tunnel Junctions[END_REF] When the thickness of the layer is below 5 nm, the dominant transport mechanism is direct non-resonant tunneling. In this mechanism, the current density decreases exponentially with thickness and follows , where J o is the pre-𝐽 = 𝐽 0 𝑒 -𝛽𝑑 exponential factor and β is the attenuation factor. [START_REF] Li | Charge Transport in Single Au | Alkanedithiol | Au Junctions: Coordination Geometries and Conformational Degrees of Freedom[END_REF][START_REF] Li | Conductance of Single Alkanedithiols: Conduction Mechanism and Effect of Molecule-Electrode Contacts[END_REF] The attenuation factor, one of the molecular signatures of transport, estimates the impact of the molecular length, d, on the total current density. In the tunneling regime, for saturated molecules, it is around 8 -10 nm -1 while it drops to 2 -3 nm -1 for conjugated molecules. [START_REF] He | Electronic Decay Constant of Carotenoid Polyenes from Single-Molecule Measurements[END_REF][START_REF] Vilan | Large-Area, Ensemble Molecular Electronics: Motivation and Challenges[END_REF][START_REF] Jeong | High-Yield Functional Molecular Electronic Devices[END_REF] It has also been used to characterize long-distance transport (above 5 nm); for instance, the β value of unsaturated molecules changes from 2 -3 nm -1 , when the length is less than 5 nm, to 0.5 -1 nm -1 when it is above 5 nm, which indicates a transition between the direct tunneling regime and another dominant transport mechanism. [START_REF] Yan | Activationless Charge Transport across 4.5 to 22 nm in Molecular Electronic Junctions[END_REF][START_REF] Choi | Transition from Tunneling to Hopping Transport in Long, Conjugated Oligo-Imine Wires Connected to Metals[END_REF][START_REF] Nguyen | Molecular Signature and Activationless Transport in Cobalt-Terpyridine-Based Molecular Junctions[END_REF] The β values investigated by scanning tunneling microscopy (STM), conductive atomic force microscopy (C-AFM) techniques in single or few molecules devices or measured on large-area MJs are highly consistent, and a broad consensus has now been reached to state that, in the tunneling regime, they are independent of the experimental platform used and on the area of the MJ studied.

On the contrary, J 0 , is highly dependent on the experimental platform and varies considerably with the scale of the device. Akkerman et al. and later Amdursky et al. have summarized the dependence of J o on the number of molecules sandwiched. [START_REF] Hylke | Electrical Conduction through Single Molecules and Self-Assembled Monolayers[END_REF][START_REF] Amdursky | Electronic Transport via Proteins[END_REF] The J o of single-molecule devices was found to be much higher than that of large-area. [START_REF] Hybertsen | Structure-Property Relationships in Atomic-Scale Junctions: Histograms and Beyond[END_REF][START_REF] Su | Chemical Principles of Single-Molecule Electronics[END_REF] Frisbie et al. have shown that the J o value of the same few-molecules devices depend on the contact material. [START_REF] Smith | Length-Dependent Nanotransport and Charge Hopping Bottlenecks in Long Thiophene-Containing π-Conjugated Molecular Wires[END_REF][START_REF] Xie | Experimental and Theoretical Analysis of Nanotransport in Oligophenylene Dithiol Junctions as a Function of Molecular Length and Contact Work Function[END_REF] Some studies have also attributed the difference in J o to the effect of surface roughness [START_REF] Reus | Statistical Tools for Analyzing Measurements of Charge Transport[END_REF] or edge effects. [START_REF] Obersteiner | Unconventional Current Scaling and Edge Effects for Charge Transport through Molecular Clusters[END_REF] There are thus three main approaches to explain these differences: first, the atomic structure of the contacts could be different at various scales; second, the number of simultaneously active molecules could change when different fabrication procedures are used; third, cooperative effects, which are not easy to probe, could have a strong impact on device conductance. [START_REF] Selzer | Effect of Local Environment on Molecular Conduction: Isolated Molecule versus Self-Assembled Monolayer[END_REF] In this context, Ratner et al. proposed a theoretical approach, suggesting that optimal adlayer density, as well as interwire distance, could enhance the conduction, [START_REF] Reuter | Molecular Conduction through Adlayers: Cooperative Effects Can Help or Hamper Electron Transport[END_REF] and predicted that the line-shapes of the conductance histograms for single-molecule junctions could reflect cooperative effects. [START_REF] Reuter | Signatures of Cooperative Effects and Transport Mechanisms in Conductance Histograms[END_REF] Trasobares et al. experimentally determined a π-π electronic coupling parameter of 35 meV between ferrocenyl (Fc)-functionalized monolayers on nanocrystals. [START_REF] Trasobares | Estimation of π-π Electronic Couplings from Current Measurements[END_REF] Dubi proposed that intermolecular interactions could result in dephasing, leading to a substantial reduction of the current in a SAM-MJ as compared to the singlemolecule junction Cooperative effects were also recently evidenced in the tunneling rates across van der Waals-coupled binary self-assembled monolayers. [START_REF] Li | Large Cooperative Effects in Tunneling Rates across van Der Waals Coupled Binary Self-Assembled Monolayers[END_REF] Here, we report a unique strategy (Figure 1) to investigate the relationship between J o and the density of active molecules in the direct non-resonant tunneling regime without changing the size of the large-area MJ used or the electrode materials.

Firstly, a single-component layer based on oligo(bisthienylbenzene)) (BTB), was formed and investigated as a reference ,59,61 (Figure S1). Next, a mixed layer of oligo(BTB) and -cyclodextrin (called BTB@β-CD), was generated using host/guest complexation. [START_REF] Santos | Host -Guest Complexation : A Convenient Route for the Electroreduction of Diazonium Salts in Aqueous Media And[END_REF] This host/guest strategy has been widely used in selective organic syntheses of encapsulated molecular wires, [START_REF] Cacialli | Cyclodextrin-Threaded Conjugated Polyrotaxanes as Insulated Molecular Wires with Reduced Interstrand Interactions[END_REF][START_REF] Samorí | Self-Assembly of a Conjugated Polymer: From Molecular Rods to a Nanoribbon Architecture with Molecular Dimensions[END_REF][START_REF] Lagrost | Host-Guest Complexation: A Convenient Route to Polybithiophene Composites by Electrosynthesis in Aqueous Media. Synthesis and Characterization of a New Material Containing Cyclodextrins[END_REF] and for protecting atomic contacts. [START_REF] Leroux | Atomic Contacts via Electrochemistry in Water/Cyclodextrin Media: A Step Toward Protected Atomic Contacts[END_REF] In short, a 1:1 complex between β-CD and 1-(2bisthienyl)-4-aminobenzene (BTAB) was solubilized in a water/β-cyclodextrin solution (β-CD) (Figure 1). The corresponding diazonium salt was generated in situ and electroreduced. This process leads to the attachment of short encapsulated oligo(BTB) to the electrode surface. [START_REF] Santos | Host -Guest Complexation : A Convenient Route for the Electroreduction of Diazonium Salts in Aqueous Media And[END_REF] Therefore, the density of grafted oligo(BTB) wires is smaller than in the reference sample, and oligo(BTB) interchain interactions are considerably reduced. Previous XPS characterization of the layer has shown that an average of one CD molecules was incorporated for 4 BTB moieties in the generated layer. [START_REF] Santos | Host -Guest Complexation : A Convenient Route for the Electroreduction of Diazonium Salts in Aqueous Media And[END_REF] This ratio means that in a 4 nm thick oligo(BTB) layer, which consists of 3 BTB units (each BTB is 1.3 nm long), three out of four oligo(BTB) wires are statistically encapsulated by a CD. Furthermore, in this mixed layer, the β-CD moieties can be easily removed from the surface, creating pinholes (Figure 1) and a new surface labelled BTB@hole. This indicates that -CD are not trapped in the layer and that the BTB units of adjacent encapsulated wires are not widely cross-linked and do not strongly interact with each other's. These holes can be functionalized in a second diazonium electroreduction step, leading to mixed layers. [START_REF] Santos | Formation of Mixed Organic Layers by Stepwise Electrochemical Reduction of Diazonium Compounds[END_REF] In the present study, the second electroreduction is performed using again bisthienylbenzene diazonium salt, which grafts BTB wires inside the free pinholes as the second component and generates a layer labelled BTB@BTB. Finally, MJs based on single-component BTB, mixed BTB@β-CD, BTB@hole and BTB@BTB molecular layers were fabricated, and the attenuation factors, , and the pre-exponential factors, J o , of these different devices investigated to probe the effect of the density of active molecules in the junction.

The various layers were fabricated as in previous reports. [START_REF] Santos | Host -Guest Complexation : A Convenient Route for the Electroreduction of Diazonium Salts in Aqueous Media And[END_REF][START_REF] Santos | Formation of Mixed Organic Layers by Stepwise Electrochemical Reduction of Diazonium Compounds[END_REF] The thickness of the layer, measured by AFM, is controlled by the diazonium electroreduction conditions given in Table S1 and does not exceed 5 nm. (thicker BTB@β-CD layers are difficult to obtain). The thickness is given as a subscript to the layer and MJ notation in what follows. All MJs use similar Au bottom and Ti/Au top electrodes, fabricated by CMOScompatible technology (surface area = 400 µm 2 ) as shown in Figure S3. [START_REF] Martin | Organic Electrodes Based on Grafted Oligothiophene Units in Ultrathin, Large-Area Molecular Junctions[END_REF][START_REF] Nguyen | Highly Efficient Long-Range Electron Transport in a Viologen-Based Molecular Junction[END_REF] Table S2 shows the number of studied MJs, the yield of working devices and Figure S4 overlays individual JV curves measured for Au/BTB@-CD/Ti/Au of various thicknesses and Au/BTB@BTB 4.5nm /Ti/Au junctions without data selection.

Figure 2 shows average JV curves obtained for Au/BTB@β-CD /Ti/Au junctions with BTB@β-CD thicknesses of 2 and 4 nm, and compares them with those for Au/BTB/Ti/Au junctions. For mixed-layer BTB@β-CD junctions, we observe (i) a low fabrication yield (40%) when the layer is 2 nm-thick and a 90% yield for 4 nm films. These yields are close to those for the reference compact BTB layers, (ii) almost symmetrical JV curves with no significant rectification behavior in this thickness range, (iii) a strong thickness dependence of the

ACS Paragon Plus Environment

The Journal of Physical Chemistry Letters current density (Figures 2a and2b), (iv) current densities in BTB@β-CD MJs approximately 20 times smaller than those in BTB junctions (Figures 2c and2d). The very weak temperature dependence of the JV plot was determined for a 4 nm-thick Au/BTB@β-CD/Ti/Au device (Figure S6). The activation energy measured from the Arrhenius plot is 32 meV at 1 V, and can be attributed to Fermi energy broadening. [START_REF] Najarian | Robust All-Carbon Molecular Junctions on Flexible or Semi-Transparent Substrates Using "Process-Friendly" Fabrication[END_REF] This result suggests that the dominant transport mechanism is direct off-resonant tunneling between the two electrodes. [START_REF] Nguyen | Molecular Signature and Activationless Transport in Cobalt-Terpyridine-Based Molecular Junctions[END_REF] The Ln J vs thickness plots for BTB@β-CD and BTB junctions are shown in Figure 3 (blue and red curves, respectively). The attenuation factor for BTB@β-CD MJs is 2.1 nm -1 at 0.5 V which is similar to those for unsaturated molecules [START_REF] Capozzi | Length-Dependent Conductance of Oligothiophenes[END_REF][START_REF] Yan | Activationless Charge Transport across 4.5 to 22 nm in Molecular Electronic Junctions[END_REF][START_REF] Najarian | Robust All-Carbon Molecular Junctions on Flexible or Semi-Transparent Substrates Using "Process-Friendly" Fabrication[END_REF] and BTB junctions (Figures 3a,red curves). As shown by Bowers et al., inserting an alkyl chain (a saturated chain) inside the transport path of oligophenyl groups increases β from 3 nm -1 to 6.6 nm -1 . [START_REF] Bowers | Tunneling across SAMs Containing Oligophenyl Groups[END_REF] However, in the present case, inserting β-CD, a saturated molecule, does not change the β value, indicating that β-CD does not participate in transport through the MJs. On the contrary, the J o value of BTB@β-CD junctions is one order of magnitude smaller than that of simple BTB junctions. The preexponential factor, J o , of molecular electronics devices, using identical electrodes in composition (Au and Ti/Au) and areas, can thus be tuned by changing the number of active molecules while the attenuation factor does not depend on the density of active molecules in the junction. To the best of our knowledge, this is the first direct evidence of the relationship between J o and the density of active molecules sandwiched in MJs.

A simple calculation, based on geometrical considerations and explained in Figure S7, indicates that the ratio of surface concentration of oligo(BTB) wires in a single-component junction and in a mixed BTB@β-CD junction is between 7 and 15. The J o of the BTB@β-CD mixed junctions, extracted from Figure 3a, is 20 times smaller than that of simple BTB junctions. Comparing these values indicates a linear scaling of conduction properties with the number of conducting molecules in junctions and suggests that the conductance through a partially isolated BTB oligomer is close to, or slightly smaller than, that through a BTB oligomer in interaction with other BTB wires in a compact BTB film. In other words, the observed variation of J o , does not demonstrate a significant modifications of the cooperative effects between oligo(BTB) wires with the decrease of the density of active wires despite the modifications of the interchain interactions. These results agree with theoretical predictions showing a linear scaling of conduction properties with the number of conducting molecules in junctions (g(N) = Ngeff(1)) and that, in the off-resonant tunneling regime, the effective single molecule conduction (geff(1)) can be higher than the corresponding single molecule property (g(1)). [START_REF] Reuter | Molecular Conduction through Adlayers: Cooperative Effects Can Help or Hamper Electron Transport[END_REF][START_REF] Landau | Cooperative Effects in Molecular Conduction[END_REF] They also agree with recent experimental results. [START_REF] Das | Probing Matrix Effects in the Course of Electron Transfer across a Self-Assembled Monolayer[END_REF] Next β-CD molecules were removed to create holes inside the BTB@β-CD layer, to give a BTB@hole layer. BTB oligomers were then grafted into the holes by a second diazonium electroreduction to create BTB@BTB layers. The electrochemical response of an outer-sphere redox probe, FcMeOH, on a BTB@hole layer is like that for a bare electrode, as FcMeOH can reach the underlying gold electrode through the pinholes in the layer. (Figure S2) On the contrary, the electrochemical responses of FcMeOH on BTB@β-CD electrodes and BTB@BTB are close to that for a singlecomponent BTB. [START_REF] Fave | Electrochemical Switches Based on Ultrathin Organic Films: From Diode-like Behavior to Charge Transfer Transparency[END_REF] It shows a shift of the ferrocene oxidation peak towards positive potential and no reduction peak in the reverse sweep. This is due to the easily p-dopable oligo(BTB) moieties and demonstrates that BTB is grafted mostly in the pinholes generated by β-CD desorption. [START_REF] Santos | Formation of Mixed Organic Layers by Stepwise Electrochemical Reduction of Diazonium Compounds[END_REF] Moreover, measurements on 4 nm-thick BTB@hole indicate that the thickness of the BTB@BTB layer increases to 4.5 nm (Figure S8). BTB@hole and mixed-layer BTB@BTB were used in device fabrication with similar configurations: i.e. Au bottom and Ti/Au top electrodes. All the JV curves of BTB@hole devices behave as short-circuits (Figure 3b, black curve). This confirms that holes are created inside the BTB@β-CD layer by β-CD desorption, the metals deposited by evaporation go through these holes and make direct contact with the bottom electrode.

Mixed-layer BTB@BTB devices were investigated for two different layer thicknesses, 4.5 nm and 7 nm, both generated from BTB 4nm @hole electrodes. Figure 3b compares JV curves of BTB 4nm , BTB@-CD 4nm and BTB @BTB 4.5nm (generated from the BTB 4nm @hole electrode). As mentioned above, the BTB 4nm layer is more conductive than BTB@-CD 4nm . After the holes in the BTB 4nm @hole electrode have been filled, the BTB@ BTB 4.5nm JV curves can be easily recorded and none of the 24 MJs generated on a same sample shows a short circuit. This clearly confirms that the second BTB diazonium grafting takes place inside the holes. More importantly, the BTB@BTB 4.5nm MJs are much more conductive than BTB@-CD 4nm MJs and almost as conductive as BTB 4nm MJs (Figure 3b, green and purple curves). Consequently, the Ln J value at 0.5 V of a BTB@BTB MJ shifts from the BTB@-CD attenuation plot (blue curve) to that of BTB (Figure 3a, green point).

BTB@BTB 7nm MJs (generated from the BTB 4nm @hole electrode) were also compared with BTB 7nm MJs. The two devices show very similar JV curves (Figure S9). It is important to note that in both systems, the JV curves become asymmetric when the thickness increases from 4 to 7 nm, as already reported. [START_REF] Martin | Organic Electrodes Based on Grafted Oligothiophene Units in Ultrathin, Large-Area Molecular Junctions[END_REF] This behavior, fully analyzed in reference 60, indicates that the dominant transport mechanism has changed from direct non-resonant tunneling to multistep hopping. These almost identical JV curves indicate that BTB wires are deposited during the second diazonium grafting inside the free space in BTB 4nm @hole and that growth can further continue until a BTB@BTB 7nm and a BTB 7nm can no longer be distinguished.

To conclude, we have fabricated and investigated MJs based on mixed BTB@β-CD and BTB@BTB layers, thanks to an original host/guest strategy and compared their transport properties with those based on single-component BTB MJs with the same contacts. We have shown that the β values of these devices in the tunneling regime (thickness less than 5 nm) are similar for all systems. However, the preexponential factor J o changes drastically when BTB@β-CD, BTB@BTB and BTB MJs are compared. This clearly indicates that the host/guest strategy unambiguously evidences a relationship between the density of active BTB wires and J o values in large-area MJs. However, simple calculation suggests that the conductance through partially separated BTB molecules is similar to, or slightly smaller than, that in stacked strongly interacting BTB wires. This indicates either that the host guest strategy developed here is not able to separate the oligo(BTB) wires to strongly modify their cooperative effects or that no or minimal cooperative effects are observed in the investigated transport regime. Additionally, the host/guest strategy reported here can be extended in order to fabricate new functionalized MJs based on two different oligomers.

ASSOCIATED CONTENT

Supporting Information. Experimental details, electrochemical data, transport measurements at various temperature, surface coverage calculations, transport measurements on BTB@BTB 7nm MJs This material is available free of charge via the Internet at http://pubs.acs.org.

Figure 1 .

 1 Figure1. A) Scheme of BTAB, Cyclodextrine and BTAB@-CD host guest complex B) Strategy used to deposit: BTB@β-CD, BTB@hole and BTB@BTB mixed layers on Au electrode.

Figure 2 .

 2 Figure 2. (A) JV curves and (B) Ln J vs V curves for Au 50nm /BTB@β-CD/Ti 2nm /Au 50nm junctions of various thicknesses; (C) Ln J vs V comparison of BTB 2nm (red) and BTB@β-CD 2nm (green)); (D) Ln J vs V comparison of BTB 4nm (orange) and BTB@β-CD 4nm (purple).

Figure 3 .

 3 Figure 3. (A)Attenuation plots for single-component BTB (blue), mixed layer BTB@β-CD (red), and Ln J of a 4.5 nmthick BTB@BTB junction (green point) at 0.5 V applied bias; (B) JV curves of BTB@hole (black), single-component BTB 4nm (purple), BTB@-CD 4nm (orange) and BTB@BTB 4.5nm (green) MJs.BTB@hole and mixed-layer BTB@BTB were used in device fabrication with similar configurations: i.e. Au bottom and Ti/Au top electrodes. All the JV curves of BTB@hole devices behave as short-circuits (Figure3b, black curve). This confirms that holes are created inside the BTB@β-CD layer by β-CD desorption, the metals deposited by evaporation go through these holes and make direct contact with the bottom electrode.Mixed-layer BTB@BTB devices were investigated for two different layer thicknesses, 4.5 nm and 7 nm, both generated from BTB 4nm @hole electrodes. Figure3bcompares JV curves of BTB 4nm , BTB@-CD 4nm and BTB @BTB 4.5nm (generated

ACS Paragon Plus Environment

The Journal of Physical Chemistry Letters

Funding Sources

The Agence Nationale de la Recherche (France ANR-15-CE09 0001-01) and the Vietnam Academy of Science and Technology (THTEXS.03/21-24) are gratefully acknowledged for their financial support.

AUTHOR INFORMATION Corresponding Author

*lacroix@univ-paris-diderot.fr *pascal.martin@u-paris.fr

ORCID

Quyen Van Nguyen : 0000-0003-0120-0971 Pascal Martin : 0000-0003-1010-8421 Jean-Christophe Lacroix: 0000-0002-7024-4452

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. These authors contributed equally.

ACKNOWLEDGMENT

The authors thank Dr. J. S. Lomas for English editing.

ACS Paragon Plus Environment

The Journal of Physical Chemistry Letters

ACS Paragon Plus Environment

The Journal of Physical Chemistry Letters