Ines Abid

Patricio Benzo

Béatrice Pécassou

Shuai Jia

Jing Zhang

Jiangtan Yuan

Jean Baptiste Dory

Olivier Gauthier Lafaye

Renaud Péchou

Adnen Mlayah

Jun Lou

Plasmon damping and charge transfer pathways in Au@MoSe 2 nanostructures

Keywords: hybrid plasmonic, 2D materials, charge transfer, Plasmon damping, Photoluminescence quenching

Hybridization of plasmonic and excitonic elementary excitations provides an efficient mean of enhancing the optical absorption and emission properties of metal/semiconductor nanostructures and is a key concept for the design of novel efficient optoelectronic devices.

Here we investigate the optical properties of 2D MoSe 2 quantum well flakes covered with Au nanoparticles supporting plasmonic resonances. Using spatially resolved confocal spectroscopy, we report the observation of a quenching phenomenon of the Raman scattering and photoluminescence emission of both the MoSe 2 layer and the Au nanoparticles. We found that the quenching of the photoluminescence emission from the Au nanoparticles is partial and measurable unlike the one observed for the Au-covered MoSe 2 layers, which is total. Its dependence on the thickness of the MoSe 2 layer is determined experimentally. Based on electro-dynamics calculations and on the electronic band alignment at the Au/ MoSe 2 interface, the results are interpreted in terms of i) damping of the plasmonic resonance of the Au nanoparticles due to the optical absorption by the MoSe 2 layer ii) a two-pathways charge transfer scheme where the photo-excited electrons leak from the MoSe 2 layer to the Au NPs whereas the photo-excited holes flow in the opposite direction i.e., from the Au NPs to the MoSe 2 layer. The two combined mechanisms account well for the experimental observations and complements the interpretations proposed in the literature for similar metal nanoparticles/transition metal dichalcogenide systems.

Introduction

Combining two-dimensional (2D) semiconductor quantum wells (QWs) made of single layers of transition metal dichalcogenides (TMDs) and plasmonic nanomaterials opens up new routes to investigate plasmon-exciton interaction [1][2][3][4][5] and to engineer highly efficient and functional hybrid nanodevices in the field of electronics [6][7][8], photovoltaics [9], sensing [10][11], integrated photonic-electronic circuit [START_REF] Zhu | Excitonic Resonant Emission-Absorption of Surface Plasmons in Transition Metal Dichalcogenides for Chip-Level Electronic-Photonic Integrated Circuits[END_REF] and photocatalysis [START_REF] Yin | Au Nanoparticle-Modified MoS 2 Nanosheet-Based Photoelectrochemical Cells for Water Splitting[END_REF][START_REF] Li | Active Light Control of the MoS 2 Monolayer Exciton Binding Energy[END_REF][START_REF] Jiang | Metal/Semiconductor Hybrid Nanostructures for Plasmon-Enhanced Applications[END_REF]. In this context, exploring the contact interface between the metal nanostructures and the TMD layers is crucial to understand the optical, structural and mechanical properties of these hybrid systems. Recent studies proved that the deposition of metal nanoparticles on TMDs may modify the electronic, optical and vibrational properties of the TMD layer [START_REF] Gong | Metal Contacts on Physical Vapor Deposited Monolayer MoS 2[END_REF][START_REF] Zhang | Probing thermal expansion coefficients of monolayers using surface enhanced Raman scattering[END_REF][START_REF] Zhang | Surface enhanced Raman scattering of monolayer MX2 with metallic nano particles[END_REF][START_REF] Deng | Thickness-dependent morphologies of Ag on nlayer MoS2 and its surface-enhanced Raman scattering[END_REF][START_REF] Shankar Singha | Tuning the photoluminescence and ultrasensitive trace detection properties of few-layer MoS 2 by decoration with gold nanoparticles[END_REF][START_REF] Bhanu | Photoluminescence quenching in gold -MoS2 hybrid nanoflakes[END_REF][START_REF] Sun | Probing Local Strain at MX 2 -Metal Boundaries with Surface Plasmon-Enhanced Raman Scattering[END_REF]. Gong et al [START_REF] Gong | Metal Contacts on Physical Vapor Deposited Monolayer MoS 2[END_REF] showed that the optical phonons are very sensitive to the nature of the deposited metal NPs and to the surface coverage. Using surface enhanced raman scattering (SERS), Sun et al [START_REF] Sun | Probing Local Strain at MX 2 -Metal Boundaries with Surface Plasmon-Enhanced Raman Scattering[END_REF] and Zhang et al [START_REF] Zhang | Surface enhanced Raman scattering of monolayer MX2 with metallic nano particles[END_REF] pointed out strain effects induced by the metallic nanoparticles deposited on MoS 2 layers. A quenching phenomenon of the PL emission in monolayer TMDs has been first reported by Bhanu et al [START_REF] Bhanu | Photoluminescence quenching in gold -MoS2 hybrid nanoflakes[END_REF] in Au/MoS 2 flake. They showed that because the electron affinity of MoS 2 is lower than the work function of Au, the photoexcited electron in the MoS 2 layer readily transfer to the Au, leaving the hole behind. This Charge Transfer (CT) mechanism strongly reduces the probability for radiative recombination and causes PL quenching. Actually, the phenomenon of PL quenching in monolayers of transition metal dichalcogenides has various origins. i) Kang et al [START_REF] Kang | Photoluminescence Quenching in Single-Layer MoS 2 via Oxygen Plasma Treatment[END_REF] investigated the effect of plasma oxygen treatment on the optical properties of single layer MoS 2 and have demonstrated the creation of MoO3 defect sites controlled by the plasma exposure time. They showed that such defects are responsible for lattice distortion and local direct-toindirect band gap transition causing phonon assisted exciton recombination and PL quenching. ii) Yuan et al [START_REF] Yuan | Photoluminescence Quenching and Charge Transfer in Artificial Heterostacks of Monolayer Transition Metal Dichalcogenides and Few-Layer Black Phosphorus[END_REF] studied the interlayer coupling behaviour of bilayer stacked MoS 2 , WS 2 and MoS 2 /WS 2 heterostructures with varied stacking order. They demonstrated that the strong PL quenching is due to the exciton splitting and to the subsequent reduction of the radiative recombination probability due to both the type-II band alignment and the build-in electric field in these heterostacks. iii) Kim et al [START_REF] Kim | Photoluminescence quenching in monolayer transition metal dichalcogenides by Al2O3 encapsulation[END_REF] studied the PL quenching in Al 2 O 3 encapsulated MoS 2 , MoSe 2 , WS 2 and WSe2 monolayers. Using bottom gated photo-transistors, they showed that the photo-current and the responsivity were increased after Al 2 O 3 encapsulation. These experimental findings were interpreted in terms of hole transfer from the TMD layer to encapsulation-induced trap states. iv) Recently Zhang et al [START_REF] Zhang | Modulated interlayer charge transfer dynamics in a monolayer TMD/metal junction[END_REF] reported giant PL quenching factors of nearly 3.5 and 10 in respectively MoS 2 /Au and MoS 2 /Pd heterolayers at liquid nitrogen temperature. The quenching phenomenon was interpreted in terms of interlayer CT governed by temperature and by Van der Waals interlayer interaction along the lines proposed by Bhanu et al [START_REF] Bhanu | Photoluminescence quenching in gold -MoS2 hybrid nanoflakes[END_REF]. The PL quenching phenomenon in hybrid metal/TMD nanostructures may have a strong impact on future applications and can even be put to good use in novel optoelectronic designs. For instance, one may seek for total suppression of the radiative recombination of electron-hole pairs in monolayer TMDs for optimum lightto-current conversion and enhanced responsivity of photodetectors. On the other hand, from a fundamental point of view, understanding the dynamics of the CT between plasmonic metal nanoparticles and TMDs layers and its impact on the optical properties is still on the way and requires further experimental and theoretical studies. In this work, we systematically investigate the optical properties of MoSe 2 layers covered with Au nanoparticles. Among the family of 2D TMD materials, MoSe 2 has the advantage of a fundamental excitonic absorption around 800 nm (A exciton) [START_REF] Tonndorf | Photoluminescence emission and Raman response of monolayer MoS 2, MoSe 2, and WSe 2[END_REF][START_REF] Zhang | Direct observation of the transition from indirect to direct bandgap in atomically thin epitaxial MoSe2[END_REF], red-shifted with respect to the interband absorption of Au, thus minimizing the excitation transfer from the TMD layer to the Au NPs and the resulting dissipation effects. Using spatially resolved PL and Raman measurements, we investigate the phenomenon of PL emission and Raman scattering quenchings of both the MoSe 2 layer and the Au NPs. The study is however focused on the quenching of the PL emission from the Au NPs. Indeed, to the best of our knowledge, up to now, only the PL quenching of TMD layers combined with various metallic materials has been addressed in the literature [START_REF] Bhanu | Photoluminescence quenching in gold -MoS2 hybrid nanoflakes[END_REF][START_REF] Kang | Photoluminescence Quenching in Single-Layer MoS 2 via Oxygen Plasma Treatment[END_REF][START_REF] Yuan | Photoluminescence Quenching and Charge Transfer in Artificial Heterostacks of Monolayer Transition Metal Dichalcogenides and Few-Layer Black Phosphorus[END_REF][START_REF] Kim | Photoluminescence quenching in monolayer transition metal dichalcogenides by Al2O3 encapsulation[END_REF][START_REF] Zhang | Modulated interlayer charge transfer dynamics in a monolayer TMD/metal junction[END_REF], as stated above, and interpreted in terms of CT across the metal/semiconductor interface. Here, we show that the analysis of the PL signal emitted by both the MoSe 2 layer and the Au NPs brings valuable information which allows for a deeper understanding of the optical properties of this hybrid nanostructure and of the CT mechanisms taking place at the metal/semiconductor interface.

Sample preparation

The MoSe 2 flakes were grown by chemical vapor deposition (CVD) on a SiO 2 (90 nm)/Si substrate. The latter was exposed to MoO3 and pure selenium powder at high temperature (750 °C), thus leading to the nucleation and the growth of large crystalline area of multilayer and monolayer MoSe 2 flakes [START_REF] Xia | CVD synthesis of large-area, highly crystalline MoSe 2 atomic layers on diverse substrates and application to photodetectors[END_REF][START_REF] Shaw | Chemical vapor deposition growth of monolayer MoSe2 nanosheets[END_REF]. The Au NPs were deposited at a deposition rate of 0.027 nm/s on the MoSe 2 layers by magnetron sputtering of a pure gold target in ultra-high-vacuum at 600°C. Part of the SiO 2 /Si substrate supporting the MoSe 2 flakes was protected from the sputtered Au atoms flow by a mask and has been later used as a reference for the uncovered MoSe 2 flakes, and to investigate the change of the optical properties with Au NPs density (i.e., with surface coverage). Indeed, in the transition zone between Au-covered and bare regions of MoSe 2 , the Au NPs density progressively decreases as will be shown later. In this study, two equivalent thicknesses of Au (i.e., the thickness of a 2D layer with same volume) were investigated: 4.8 and 0.8 nm. The average size of the Au NPs obtained with 4.8 and 0.8 nm equivalent thicknesses are, respectively, 17 and 7 nm as determined by Scanning Electron Microscopy (SEM) imaging (Figure A1 Appendix).

Results and discussion

Scanning Electron Microscopy (SEM) and Atomic Force Microscopy (AFM) images (Figure 1) show that the Au nanoparticles form separated clusters, when deposited either on SiO 2 or on MoSe 2 . This suggests a Volmer-Weber growth mode of Au on both surfaces, in agreement with previously reported works on Au and Ag NPs deposited on MoS 2 [START_REF] Gong | Metal Contacts on Physical Vapor Deposited Monolayer MoS 2[END_REF][START_REF] Deng | Thickness-dependent morphologies of Ag on nlayer MoS2 and its surface-enhanced Raman scattering[END_REF]. As a matter of fact, it has been shown earlier that Au grows epitaxially on MoS 2 [START_REF] Honjo | On cluster mobilities in nucleation and growth processes of epitaxial thin films[END_REF] and as a result the Au NPs display a flat surface [START_REF] Maurel | Electrical behavior of the Au/MoS2 interface studied by light emission induced by scanning tunneling microscopy[END_REF][START_REF] Carladous | Light emission from spectral analysis of Au/MoS 2 nanocontacts stimulated by scanning tunneling microscopy[END_REF][START_REF] Darby | Growth of gold films on air-and vacuum-cleaved molybdenite[END_REF]. One can also notice (Figure 1C,E) that the size and density of the NPs depend on the nature of the supporting surface. Indeed, the nanoparticles formed on MoSe 2 are larger and denser than those formed on SiO 2 . The estimated surface coverage is 62% for Au NPs on monolayer MoSe 2 and only 40 % on SiO 2 . This difference in surface coverage can be attributed to the amorphous nature of the SiO 2 substrate which prevents the growth and coalescence of adjacent Au seeds required to form large metallic Au nanoparticles and to increase the surface coverage. Moreover, Figure 1C, E show that the NPs size and density depend on the thickness of the MoSe 2 layer as well. Indeed, they both increase with increasing MoSe 2 layer thickness as already reported by Deng et al [START_REF] Deng | Thickness-dependent morphologies of Ag on nlayer MoS2 and its surface-enhanced Raman scattering[END_REF] for Ag NPs on MoS 2 . Optical absorption measurements under confocal microscope were performed on the MoSe 2 @ SiO 2 and Au@ SiO 2 samples. A surface plasmon (SP) resonance is observed around 580 nm on both Au@ SiO 2 samples deposited with 4.8 and 0.8 nm equivalent thicknesses (Figure A2 Appendix). Its large spectral width (around 150 nm at half maximum) is due to the size-dependent broadening of the SP resonance and to the near-field electromagnetic interaction between the Au NPs separated by nanometer gaps [START_REF] Chen | Shape-and Size-Dependent Refractive Index Sensitivity of Gold Nanoparticles[END_REF]. The optical absorption spectrum of MoSe 2 @ SiO 2 exhibits two maxima around 800 and 700 nm (Figure A2, Appendix) due to the A and B exciton transitions, respectively [START_REF] Tonndorf | Photoluminescence emission and Raman response of monolayer MoS 2, MoSe 2, and WSe 2[END_REF][START_REF] Zhang | Direct observation of the transition from indirect to direct bandgap in atomically thin epitaxial MoSe2[END_REF]. To investigate the effect of the deposited Au NPs on the optical properties of the MoSe 2 layer, we have performed spatially resolved PL measurements. The PL signal from the bare MoSe 2 region is used as a reference. As shown in Figure 2A, the PL emission from the bare MoSe 2 region is characterized by a strong emission peak at 820 nm, due to the radiative recombination of the lower energy A excitons, and is very typical of a direct-band gap MoSe 2 monolayer [START_REF] Tonndorf | Photoluminescence emission and Raman response of monolayer MoS 2, MoSe 2, and WSe 2[END_REF][START_REF] Zhang | Direct observation of the transition from indirect to direct bandgap in atomically thin epitaxial MoSe2[END_REF][START_REF] Xia | CVD synthesis of large-area, highly crystalline MoSe 2 atomic layers on diverse substrates and application to photodetectors[END_REF][START_REF] Shaw | Chemical vapor deposition growth of monolayer MoSe2 nanosheets[END_REF]. Interestingly, this prominent PL emission completely disappeared in the case of MoSe 2 monolayer covered with Au NPs, suggesting a strong PL quenching phenomenon (Figure 2A). In order to determine the origin of this remarkable effect, three main hypotheses can be invoked: i) the absorption of the MoSe 2 luminescence emission by the Au NPs, ii) the possible presence of a tensile strain generated by the growth of the Au NPs on the MoSe 2 layer, iii) the separation of the photo-generated electrons and holes due to CT between the MoSe 2 layer and the Au NPs. To investigate the role of the optical absorption by the Au NPs, the measurements were reproduced for a smaller deposited Au thickness (0.8 nm equivalent thickness, i.e., 7 nm average NPs size), in order to reduce the overall optical density of the Au NPs. As shown in Figure A3A (Appendix), no PL emission from the MoSe 2 monolayer covered with Au NPs was detected in this case and the quenching effect remained total. Moreover, the excitation laser intensity has been increased by a factor 100 to enhance the photo-generation of electron-hole pairs in the MoSe 2 layer. Even so, no PL emission was detected at all (Figure A3B) which points out the high efficiency of the mechanism responsible for the PL quenching. The latter being independent of the Au NPs optical density, the absorption of the MoSe 2 PL emission by the Au NPs can be ruled out to account for the observed PL quenching of MoSe 2 . Several studies [START_REF] Gong | Metal Contacts on Physical Vapor Deposited Monolayer MoS 2[END_REF][START_REF] Zhang | Phonon and Raman scattering of two-dimensional transition metal dichalcogenides from monolayer, multilayer to bulk material[END_REF][START_REF] Horzum | Phonon softening and direct to indirect band gap crossover in strained single-layer MoSe 2[END_REF][START_REF] Island | Precise and reversible band gap tuning in single-layer MoSe 2 by uniaxial strain[END_REF][START_REF] Zhu | Strain tuning of optical emission energy and polarization in monolayer and bilayer MoS 2[END_REF][START_REF] Wang | Strain-induced direct-indirect bandgap transition and phonon modulation in monolayer WS2[END_REF][START_REF] Morales-Garcia | Tuning the electronic properties of monolayer and bilayer transition metal dichalcogenide compounds under direct outof-plane compression[END_REF][START_REF] Conley | Bandgap Engineering of Strained Monolayer and Bilayer MoS 2[END_REF][START_REF] He | Experimental Demonstration of Continuous Electronic Structure Tuning via Strain in Atomically Thin MoS 2[END_REF][START_REF] Sortino | Dielectric Nanoantennas for Strain Engineering in Atomically Thin Two-Dimensional Semiconductors[END_REF] showed that the strain imposed by the metal NPs to the TMD layer may strongly modify its electronic band structure and can be responsible for a strong quenching of the PL emission. In particular, tensile strain may induce a direct-to-indirect band gap transition [START_REF] Horzum | Phonon softening and direct to indirect band gap crossover in strained single-layer MoSe 2[END_REF][START_REF] Morales-Garcia | Tuning the electronic properties of monolayer and bilayer transition metal dichalcogenide compounds under direct outof-plane compression[END_REF][START_REF] Conley | Bandgap Engineering of Strained Monolayer and Bilayer MoS 2[END_REF] which leads to a red shift of the PL peak and to a drastic decrease of the PL intensity [START_REF] Island | Precise and reversible band gap tuning in single-layer MoSe 2 by uniaxial strain[END_REF][START_REF] Zhu | Strain tuning of optical emission energy and polarization in monolayer and bilayer MoS 2[END_REF][START_REF] Conley | Bandgap Engineering of Strained Monolayer and Bilayer MoS 2[END_REF][START_REF] He | Experimental Demonstration of Continuous Electronic Structure Tuning via Strain in Atomically Thin MoS 2[END_REF]. Using calculations based on Density Functional Theory (DFT), Horzum et al [START_REF] Horzum | Phonon softening and direct to indirect band gap crossover in strained single-layer MoSe 2[END_REF] showed that monolayer MoSe 2 undergoes a direct-to-indirect band gap crossover under ∼3% biaxial tensile strain. In our samples, strain could be generated for two main reasons: i) the 24% lattice mismatch between MoSe 2 and Au, and/or ii) the cooling of the sample from the rather high growth temperature (600°C) of the Au NPs down to room temperature, which may generate tensile stress and strain in the MoSe 2 layer because of the different thermal expansion coefficients of Au and MoSe 2 @ SiO 2 substrate. To track the presence of strain in our Au@ MoSe 2 layers, we have performed Raman spectroscopy measurements. As shown in Figure A4 (Appendix), the intensity of the MoSe 2 Raman peaks due to the A' 1 phonons vanishes for 4.8 nm equivalent thickness Au@ MoSe 2 sample. However, for 0.8 nm deposited thickness, the Raman signature of the A' 1 mode remains visible and red-shifted by 5.7 cm -1 . According to the calculations performed by Horzum et al [START_REF] Horzum | Phonon softening and direct to indirect band gap crossover in strained single-layer MoSe 2[END_REF], the A' 1 vibration frequency is lowered by 9 cm -1 for a 1% biaxial tensile strain. The 5.7 cm -1 red-shift measured in our samples corresponds thus to 0.6% strain which is a rather moderate value consistent with the slow cooling rate of the sample (24°/min in the initial 20 min and 1.3°/min at longer times) after Au NP deposition at 600°C. This value is well below the 3% minimum strain required for the direct-to-indirect band-gap transition in monolayer MoSe 2 . Nevertheless, the PL of monolayer MoSe 2 is totally quenched in our samples. Therefore, it is unlikely that, although present, the tensile strain plays a significant role in the total quenching of the PL emission.

The quenching of the PL emission from the metal/TMD nanostructures has already been reported in the literature [START_REF] Bhanu | Photoluminescence quenching in gold -MoS2 hybrid nanoflakes[END_REF][START_REF] Zhang | Modulated interlayer charge transfer dynamics in a monolayer TMD/metal junction[END_REF] and was interpreted as due to the transfer of photo-excited electrons from the TMD layer to the metal NPs. In our MoSe 2 /Au nanostructures, the observed quenching is so strong that it is not even measurable as no PL emission from the monolayer MoSe 2 could be detected even at liquid nitrogen operation temperature and at high optical pumping rate (Figure A3 Appendix).

In order to further reduce the density of Au NPs and force the emergence of the PL emission from the MoSe 2 layer, we have performed spatially resolved PL measurements on MoSe 2 flakes partly covered by a mask prior to the deposition of Au (0.8 nm equivalent thickness). In this way, the density of the deposited Au NPs decreases continuously across the transition area between Au-covered and bare regions of the MoSe 2 flake (Figure A5, Appendix). As expected, the PL emission of the monolayer MoSe 2 and the Raman scattering by A' 1 phonons emerge with decreasing density of Au NPs (Figure A6 Appendix), i.e., density of trap sites for the photogenerated electrons. It is worth to underline that quenchings of both PL emission and Raman scattering are observed (Figures A5 andA6 Appendix) on Au NPs-covered MoSe 2 monolayer which suggests a common fundamental mechanism as will be discussed below.

The transfer of photo-excited electrons from the TMD layer to the metal NPs gives a satisfactory interpretation of the quenching of the PL emission of the MoSe 2 monolayer and will be discussed below in more detail. However, so far, the investigations were focused on the PL emission of the TMD layer solely. The PL emission of the Au NPs has been disregarded up to now. Although much weaker than the PL emission of the TMD layer, the PL emission of the Au NPs brings valuable information on the CT phenomena as will be seen now.

The PL emission of Au NPs is due to radiative recombinations of the photogenerated conduction electrons above the Fermi level with holes mainly in the d valence band which is characterized by a large density of states. The PL emission is very broad: it spans from 550 to 770 nm [START_REF] Etchegoin | An analytic model for the optical properties of gold[END_REF][START_REF] Zheng | Different sized luminescent gold nanoparticles[END_REF][START_REF] Zhang | Photoluminescence of a single complex plasmonic nanoparticle[END_REF] as observed in the spectrum of the Au NPs deposited on SiO 2 (Figure 2B). This is due to the electronic band structure of gold and to the convolution of the emitted spectrum by the broad SP resonance of the Au NPs (Figure A2 Appendix).

Surprisingly, the PL emission intensity (integrated over the entire spectral range and excluding the Raman peaks) of the Au NPs covering the MoSe 2 flake is around 34% of that observed for the Au NPs supported by the SiO 2 surface (Figure 2B). This quenching is only partial and not total as the one observed for the emission of monolayer MoSe 2 (Figure 2A). It is measurable and thus can be exploited to investigate the PL quenching mechanism.

Figure 3A displays an optical microscope image of a multilayer MoSe 2 flake covered with Au NPs (4.8 nm equivalent film thickness). The thickness of the flake increases from region b to f as shown by the increasing optical contrast. Region a, where the Au NPs cover the SiO 2 substrate, is used as a reference. As shown in Figure 3B, the PL emission is reduced by nearly a factor 3 in region b (monolayer MoSe 2 ) and by a factor 100 in region f (bulk-like MoSe 2 ). This indicates that the PL quenching of the Au NPs is strongly influenced by the thickness of the MoSe2 supporting layer. We here define a quenching factor of the PL emission of the Au NPs as

Q (x,y )=1- I PLAu@MoSe 2 ( x,y ) ⟨ I PLAu@SiO 2 ⟩ (1)
Where I PLAu@MoSe 2 (x, y ) is the measured local PL intensity of the Au NPs covering the MoSe 2 flake integrated in the 550-720 nm spectral range. ⟨ I PLAu@ SiO 2 ⟩ is the spatially averaged PL intensity of the Au NPs covering the SiO 2 surface integrated in the same spectral range and used as a reference. As defined, the quenching factor Q is equal to 1 when the PL of the Au NPs on MoSe 2 is completely quenched, and 0 when the photoluminescence of Au NPs on MoSe 2 and on SiO 2 are identical. It is worth to mention that the quenching factor as defined by Eq.1 is obtained from the raw PL data regardless of the different density (i.e., surface coverage) and surface morphology of Au NPs deposited on MoSe 2 and on SiO 2 (Figure 1C,E). Knowing that the photoluminescence of Au NPs films similar, to those studied here, strongly depends on the surface roughness and grain boundaries formed on the nanoparticle surface46 and keeping in mind that the average NPs density are larger on MoSe 2 than on SiO 2 (Figure 1C, E), the actual quenching factor is larger than the one estimated using Eq.1. For instance, the quenching factor for Au NPs deposited on one monolayer MoSe 2 is 66% (Figure 2B) but reaches 78% when corrected for the different surface coverages (62% for Au NPs on MoSe 2 and 40% for Au on SiO 2 , Figure 1C,E). As shown in Figure 1C, the surface coverage, Au NPs size, and surface roughness and morphology also depend on the thickness of the MoSe 2 layer supporting the nanoparticles. In order to avoid uncertainties in the estimation of the quenching factor which may arise from corrections due to thickness dependent surface coverage and surface roughness inhomogeneities, we use the definition of the quenching factor given by Eq.1.

To investigate the dependence of the quenching on the MoSe 2 layer thickness, we present in Figure 3D a systematic mapping of the quenching factor generated from spatially resolved PL measurements performed on another multilayer MoSe 2 flake covered with Au NPs and displayed in Figure 3C. The map of the quenching factor Q (Figure 3D) clearly matches the optical image of Figure 3C and confirms the increase of the quenching efficiency with increasing thickness of the MoSe 2 layer flake.

It is worth to mention that because of the presence of Au NPs on the MoSe 2 flake, the AFM height profile cannot provide the thickness of the MoSe 2 flake. Indeed, typical size of the Au NPs is around 17 nm whereas the thickness of a MoSe 2 single layer is 0.8 nm [START_REF] Xia | CVD synthesis of large-area, highly crystalline MoSe 2 atomic layers on diverse substrates and application to photodetectors[END_REF]. Therefore, it is impossible to extract the layer thickness from AFM profiles due to the large height fluctuations. To determine the thickness of covered MoSe 2 flakes we rather rely on optical methods. Indeed, to determine the thickness of MoSe 2 flakes, we exploit the Raman signal of the Si phonons from the Si/ SiO 2 substrate. The number of MoSe 2 monolayers has been evaluated by using Beer-Lambert's law which accounts for the laser absorption by the MoSe 2 flake and for the subsequent decrease of the Si Raman peak intensity with increasing flake thickness. We also assumed that the region with the minimum optical contrast (region b in Figure 3A) is a monolayer thick MoSe 2 as shown by the strong PL emission exhibited by regions of similar optical contrast. Figure 4 displays, now quantitatively, the dependence of the quenching factor Q on the thickness of the MoSe 2 multilayer flake. It increases from 66% for Au NPs on monolayer MoSe 2 to 96% when the nanoparticles are supported by approximately 40 monolayers thick MoSe 2 . The measured maximum value 99.6% is reached for Au NPs supported by bulk-like MoSe 2 (around 143 monolayers thick as estimated from Beer-Lambert's law). Obviously, the presence of the MoSe 2 layer strongly impacts the PL emission of the Au NPs which, to the best of our knowledge, was not reported up to now. This experimental finding has to be correlated with the quenchings of the PL emission and Raman scattering of monolayer MoSe 2 (Figure 2), and any explanation has to account for the PL quenching of both the monolayer MoSe 2 and of the Au NPs.

First, let's discuss how the optical properties of the Au NPs may be affected by the presence of the supporting MoSe 2 layer and in particular, to what extent the change in their optical absorption and emission rates can explain the quenching of their PL emission.

To address this point, we have performed electrodynamics simulations based on the discrete dipole approximation (DDA) method (Appendix) applied to a model system consisting of a hemispherical Au nanoparticle (17 nm in diameter corresponding to the average size revealed in Figure 1C) on top of a MoSe 2 / SiO 2 layer. Figure 5 displays electric near-field intensity maps generated at the laser excitation wavelength (532 nm) for an Au NP deposited on SiO 2 and on 1, 4 and 10 monolayers thick MoSe 2 / SiO 2 . The numerical simulations clearly show that the electric near-field around and inside the nanoparticle is damped when the latter is supported by a MoSe 2 layer. The damping is more pronounced with increasing thickness of the MoSe 2 layer. It is due to the imaginary part of the complex dielectric function of MoSe 2 , i.e., to the decay of the excited surface plasmons into electron-hole pairs (including excitons) in the MoSe2 layer. The electric near-field enhancement has been integrated over the Au nanoparticle volume and the optical absorption of the laser energy by the nanoparticle has been estimated. The so-calculated optical absorption spectra point to plasmon damping indeed and to plasmonic-excitonic hybridization visible through absorption dips produced by the Fano-type interaction [4,5] between the red-shifted plasmonic resonance and the excitonic transitions (A and B) of the MoSe 2 layer (Figure A7A Appendix). Moreover, according to the calculations, the absorption of the laser light (producing the PL emission) of the Au NP is reduced by 39.2% in the case of Au NP on monolayer MoSe 2 compared to the situation where the nanoparticle is supported by SiO 2 . Therefore, one expects that the PL emission of the Au NP on MoSe 2 is reduced by the same factor. Indeed, to take into account this plasmon damping effect, let's write the quenching factor as Eq.2:

Q=1-A ( λ ex , t ) (2)
where A(λex, t) is the DDA-calculated optical absorption, at the laser excitation wavelength λex = 532 nm, of the Au NP on MoSe 2 / SiO 2 , normalized to that of the same NP on SiO 2 ; As mentioned above Q depends on the thickness t of the MoSe 2 layer (Figures 5,A7). For Au NPs on monolayer MoSe 2 , the calculated Plasmon Damping (PD) induced PL quenching factor is around 40% (Figure 4), a significant value which is however lower than the 66% observed experimentally. The calculated PD-induced quenching increases with increasing thickness of the MoSe 2 layer (Figures 5 andA7) and reaches a maximum value of 70 % for Au nanoparticle on a bulk-like MoSe 2 layer (150 monolayers, Figure 4). This value is still lower than the measured one (99.6%). It is worth to mention that the electron-hole pairs generated in the MoSe 2 layer by plasmon damping is submitted to charge transfer as well: the photogenerated electrons are transferred to the Au NPs and thus plasmon damping is not expected to increase the PL emission from the MoSe 2 layer. Another possible reason for the quenching of the PL emission from the Au NPs could be the excitation transfer mechanism: the light emitted by radiative recombinations of electron-hole pairs localized into the Au NPs can be absorbed by the MoSe 2 layer, thus regenerating electron-hole pairs into the MoSe 2 layer. To account for this excitation transfer mechanism we assume that roughly half of the photons emitted by the Au NP is absorbed by the underlying MoSe 2 layer, whereas the other half is emitted towards the superior half-space and is collected by the microscope objective. In that case the quenching factor Q (Eq.2) becomes Eq.3.

Q=1-A ( λ ex , t ) (1-e -2 α ( λ em )t ) 2 (3)
Where α(λ em ) is the absorption coefficient of the MoSe 2 layer at the emission wavelength λem of the Au NP. As a first approximation, we assume that the path of the light emitted by the Au NP into the MoSe 2 layer is 2t (t being the MoSe 2 layer thickness) in order to consider back reflection at the SiO 2 /Si interface. This of course leads to overestimation of optical absorption and excitation transfer in the case of MoSe 2 layer much thicker than the light penetration α-1. Figure 4 shows the quenching factor calculated according to Eq. 3 and using λ em = 625 nm as the average PL emission wavelength of the Au NPs. Strictly speaking, because of the change of the electronic band structure induced by inter-layer Van der Walls interactions, the absorption coefficient α of a multi-layer MoSe 2 depends on its thickness t. For this reason, calculations of the ET contribution to the quenching factor were performed assuming the absorption coefficient of monolayer MoSe 2 [START_REF] Liu | Optical properties of monolayer transition metal dichalcogenides probed by spectroscopic ellipsometry[END_REF] and of bulk MoSe 2 [START_REF] Niu | Thickness-Dependent Differential Reflectance Spectra of Monolayer and Few-Layer MoS2, MoSe2, WS2 and WSe2[END_REF]. As can be noticed (Figure 4), whatever the absorption coefficient used in the calculations, the contribution of the excitation transfer mechanism to the quenching of the PL emission of the Au NPs is negligible in the case of few-layers MoSe 2 (up to 7 monolayers) because of their weak optical absorption. However, it increases with increasing layer thickness and reaches a maximum of 15% for bulk-like MoSe 2 (150 monolayers). As mentioned above, this value is certainly overestimated but it quantitatively indicates that the excitation transfer mechanism contributes significantly to the quenching of the Au NP PL emission in the case of bulk-like MoSe 2 .

An additional reason for the reduced PL signal from the Au NPs on MoSe 2 layer could be the different interference effects experienced by the light emitted and reflected back at the SiO 2 /Si interface as the 90 nm SiO 2 layer forms a low-Q optical cavity. However, comparison of the calculated optical reflection properties of MoSe 2 / SiO 2 /Si and SiO 2 /Si stacks showed that, given the large numerical aperture of the collection objective and the unpolarized character of the PL emission from the Au NPs, such interference effects have only a weak impact (Figure A8 Appendix). Furthermore, the presence of Au NPs on the MoSe 2 layer surface does not lead to a decrease of the optical absorption by the MoSe 2 layer, as shown by the DDA numerical simulations (Figure A7B Appendix). On the contrary, the optical absorption by the MoSe 2 layer is rather enhanced by the electric near-field produced by the hybrid plasmonic-excitonic resonances, particularly at the A and B exciton wavelengths (Figures A7B andC Appendix) in agreement with published works [START_REF] Najmaei | Plasmonic Pumping of Excitonic Photoluminescence in Hybrid MoS 2 -Au Nanostructures[END_REF].

According to the difference between the measured quenching factor and the one calculated assuming PD + ET mechanisms (Figure 4) it appears that around 15% (in the case of thick MoSe 2 ) to 30% (in the case of few-layer MoSe 2 ) of the measured of quenching the PL emission of the Au NPs does not have an optical origin. A possible source of quenching of the PL emission and Raman scattering observed for Au NPs deposited on MoSe 2 can be found in the electronic band alignment of the Au/ MoSe 2 system and in the CT phenomena taking place at the metal/semiconductor interface, which we now discuss. . According to photo-electron spectroscopy measurements, the electron affinity χ of MoSe 2 and the work function Φ m of Au are respectively 4.2 and 5.1 eV [START_REF] Kang | Band offsets and heterostructures of twodimensional semiconductors[END_REF][START_REF] Chang | Monolayer MoSe 2 Grown by Chemical Vapor Deposition for Fast Photodetection[END_REF]. Once the two materials are in contact, a Schottky junction with height Φ s = Φ m -χ is formed at the metal/semiconductor interface, in the absence of inter-mixing, impurities or defects which may pin the Fermi level. In the case of a thick MoSe 2 layer, the Φs = 0.9 eV band offset between the Fermi level of Au and the conduction band of MoSe 2 leads to band bending and to the formation of a barrier with height Φs, and a depletion layer which thickness is determined by the built-in potential V in and the doping level of the semiconductor Typical depletion thicknesses W range from few nanometers, for heavily doped semiconductors, to few hundreds of micrometers for non-intentionally doped ones. In a thick semiconductor layer, the charge carriers are repelled away from the interface, but can possibly transfer to the metal by quantum tunnelling through the so-called Schottky barrier. In the case of monolayer MoSe 2 /Au interface, the 2D semiconductor is much thinner (sub-nm thick) than the depletion layer. Hence, there is no depletion layer to consider in this case. Electrons in the conduction band of the monolayer MoSe 2 experience no Schottky barrier as shown in the band alignment diagram of Figure 6. They rather feel a Schottky well with depth Φs and can therefore readily transfer to the unoccupied states above the Fermi level of the Au NPs. In the case of electron-hole pairs generated by an optical excitation, the electrons in the conduction band of MoSe 2 are transferred to the Au NPs leaving behind the holes in the valence band. Electrons and holes are thus spatially separated, with almost no wavefunction overlapping which drops down the probability for radiative recombination and leads to a quenching of the PL emission of the monolayer MoSe 2 as observed experimentally (Figure 2A). This CT quenching mechanism has already been discussed in several published papers [10,[START_REF] Bhanu | Photoluminescence quenching in gold -MoS2 hybrid nanoflakes[END_REF][START_REF] Kim | Photoluminescence quenching in monolayer transition metal dichalcogenides by Al2O3 encapsulation[END_REF][START_REF] Zhang | Modulated interlayer charge transfer dynamics in a monolayer TMD/metal junction[END_REF].

It is worth to mention that, in contrast with the PL quenching phenomenon discussed here, several studies reported, on the contrary, a rather strong enhancement of the PL from monolayer MoS 2 and MoSe 2 either transferred onto metal nanoparticles [5,[START_REF] Najmaei | Plasmonic Pumping of Excitonic Photoluminescence in Hybrid MoS 2 -Au Nanostructures[END_REF][START_REF] Chen | Manipulation of photoluminescence of two-dimensional MoSe 2 by gold nanoantennas[END_REF], using lift-off/transfer techniques [START_REF] Wang | Location-specific growth and transfer of arrayed MoS 2 monolayers with controllable size[END_REF], or supporting metal nanoparticles formed by e-beam lithography [START_REF] Butun | Enhanced Light Emission from Large-Area Monolayer MoS2 Using Plasmonic Nanodisc Arrays[END_REF][START_REF] Palacios | Enhanced radiative emission from monolayer MoS2 films using a single plasmonic dimer nanoantenna[END_REF][START_REF] Lee | Fano Resonance and Spectrally Modified Photoluminescence Enhancement in Monolayer MoS2 Integrated with Plasmonic Nanoantenna Array[END_REF]. Because of the low operation temperature of these processes, it is unlikely that a Schottky metal/semiconductor interface is formed and hence no efficient CT from the TMD layer to the metal NP could take place. The interaction between the TMD layer and the metal nanoparticles is rather weak [START_REF] Alamri | Plasmonic Au Nanoparticles on 2D MoS 2 /Graphene van der Waals Heterostructures for High-Sensitivity Surface-Enhanced Raman Spectroscopy[END_REF]. In that case, the strong plasmonic enhancement is responsible for increased PL emission from the TMD layer and may counterbalance a possible moderate PL quenching due to CT from the TMD layer to the metal NPs. In our samples, because the Au NPs grow on the MoSe 2 layer at high temperature, it is likely that hybridization of electronic states at the MoSe 2 /Au interface occurs thus leading to the formation of a Schottky interface [START_REF] Huang | Tunable Schottky Barrier at MoSe 2 /Metal Interfaces with a Buffer Layer[END_REF][START_REF] Gong | The Unusual Mechanism of Partial Fermi Level Pinning at Metal-MoS 2 Interfaces[END_REF][START_REF] Popov | Designing Electrical Contacts to MoS 2 Monolayers: A Computational Study[END_REF]. Therefore, electrons may efficiently transfer from the MoSe 2 layer to the Au NPs, which is responsible for the quenching of the PL emission of MoSe 2 . In addition, the latter cannot be counterbalanced by any plasmonic enhancement because of the large broadening of the SP resonance in our Au NPs (Figures A2-A7 Appendix).

Let's comment on the fact that the PL emission of the MoSe 2 layer is totally quenched in the samples deposited with 4.8 and 0.8 nm equivalent thicknesses, under high optical pumping at liquid nitrogen temperature (Figure A1). As a matter of fact, the decay time of the PL emission measured in monolayer MoSe 2 is of the order of 1 nanosecond [START_REF] Robert | Exciton radiative lifetime in transition metal dichalcogenide monolayers[END_REF] at room temperature. We here suggest that the transfer of the photoexcited electrons from the MoSe 2 layer to the Au NPs is much faster; under this condition, the formation and recombination of excitons becomes highly unlikely thus leading to strong quenching of the PL emission from the MoSe 2 layer.

Moreover, the quenching of the Raman scattering by MoSe 2 phonons observed for MoSe 2 layers covered with Au NPs (Figures A4 andA6 Appendix), gives an additional indication for an even faster (than 1 nanosecond time scale) electron transfer. Indeed, Shree et al [START_REF] Shree | Observation of exciton-phonon coupling in MoSe 2 monolayers[END_REF] have investigated the temperature dependence of the exciton linewidth in monolayer MoSe 2 and have estimated the exciton-phonon scattering time. Using the acoustic and optical exciton-phonon coupling strengths reported in ref [START_REF] Shree | Observation of exciton-phonon coupling in MoSe 2 monolayers[END_REF], we found that the exciton-phonon scattering time is in the 15-20 femtoseconds (fs) range, at room temperature. Hence, providing that the electron transfer time from the MoSe 2 layer to the Au NPs is smaller than 15-20 fs, the photoexcited electron could leave the MoSe 2 layer before it emits a phonon. In other words, the electron transfer may quench the exciton-phonon interaction, thus leading to a lower Raman efficiency (Figures A4 andA6) and to a total quenching of the PL emission in MoSe 2 layer covered with Au NPs compared to bare MoSe 2 (Figures 2 and3).

We now focus on the quenching of the PL emission of the Au NPs not explained by the PD and ET mechanisms. As shown in the energy diagram of Figure 4, gold has an optical absorption band edge around Ed ~ 2.4 eV due to transitions of electrons from the d-band to the unoccupied states of the s-band above the Fermi level [START_REF] Johnson | Optical Constants of the Noble Metals[END_REF]. The d-band is characterized by a large bandwidth due to the density of states associated with the dispersion curves in the different directions of the Brillouin zone. The optical excitation energy used in our experiments (532 nm, i.e., 2.33 eV) is nearly resonant with the d-s transition, and, as mentioned above, the electron-hole pairs photo-generated in the Au NPs may recombine radiatively giving rise to the broad PL emission observed in Figures 2B and3B. Because of the electron transfer from the monolayer MoSe 2 to the Au NPs discussed above, one would expect an enhancement, rather than a quenching, of the PL emission from the Au NPs grown on MoSe 2 . Indeed, since the MoSe 2 layer acts as an electron source, the electron density in the Au NPs should increase and so the probability of their radiative recombination with the holes photo-generated in the dband of the Au NPs. This is however opposite to the experimental findings (Figures 2,3) which indicate a partial quenching of the PL emission of the Au NPs grown on MoSe 2 layer.

The energy diagram in Figure 6 shows that the d-band of Au is at a lower energy than the valence band of MoSe 2 . The MoSe 2 /Au valence band offset is ΔEv,d = Φs + (Ed -Egap); Egap being the band gap energy of the MoSe 2 layer. Using the values quoted in Figure 6, one obtains ΔEv,d ≈ 1.9 eV. This large valence band offset constitutes a deep well for the holes photo-generated in the d-band of the Au NP. It is thus energetically favorable for such a hole to transfer to the valence band of MoSe 2 , i.e., for an electron in the valence band of MoSe 2 to transfer to a free d-electron state of the Au NP. Consequently, the probability for electrons at the Fermi level of the Au NP to recombine radiatively is decreased due to the leakage of the photo-generated holes from the Au NP to the MoSe 2 layer. This second CT pathway of holes from the Au NPs to the MoSe 2 layer is here introduced as a possible origin of the difference between the measured overall quenching of the PL emission of the Au NP and the one calculated by considering both PD and ET contributions. To complement Eq 3., the quenching factor can be now expressed as

Q=1-A ( λ ex , t ) (1-e -2 α ( λ em )t ) 2 η CT (t) (4)
Where η CT (t) accounts for the contribution of the CT mechanism to the quenching of the PL emission of the Au NPs. It depends on the thickness t of the MoSe 2 layer as shown in Figure 4: it contributes for around 30% to the overall quenching in the case of monolayer MoSe 2 and 15% in the case of bulk-like MoSe 2 . Unlike the one observed for the MoSe 2 layer (Figure 2A), the quenching of the PL emission of the Au NPs is not total (Figure 2B). We suggest that this difference lies in the different temporal dynamics of the PL emission of the MoSe 2 layer and of the Au NPs. Indeed, because there is a large density of electrons below the Fermi level in the metallic NP, the electrons recombine radiatively with the photo-generated holes and emit light on a sub-picosecond time scale [START_REF] Sakat | Time-Resolved Photoluminescence in Gold Nanoantennas[END_REF] in agreement with the large spectral width of the PL emission (Figure 3B). Therefore, electron-hole pairs photo-excited in an Au NP may partly recombine radiatively before the holes escape to the MoSe 2 layer. In other words, the transfer of holes from the Au NPs to the MoSe 2 and the radiative recombination of electron-hole pairs within the Au NPs may occur on the same time scale and counterbalance each other, leading thus to only a partial PL quenching. Finally, Figures 3 and4 clearly show that the measured quenching of the PL emission from the Au NPs increases towards its maximum value (Q=1) with increasing thickness of the MoSe 2 layer. This behavior is well accounted for by the calculated PD and ET quenching mechanisms (Figure 4). It also indicates that the CT mechanism contributes to the total quenching by an additional 30% in the case of few-layers MoSe 2 (up to 7 monolayers) a value which decreases to around 15% in the case of bulk-like MoSe 2 layer (Figure 4). The fact that the CT rate is slowed down with increasing MoSe 2 layer thickness can be understood in terms of Schottky barrier and depletion zone formation at the bulk-like MoSe 2 /Au interface which may prevent the photo-generated holes to escape from the Au NPs to the MoSe 2 layer.

Conclusions

We have investigated the optical properties of hybrid MoSe 2 /Au nanostructures formed by sputtering of gold nanoparticles on CVD grown single-and multilayer MoSe 2 . We reported the observation of a complete quenching of the photoluminescence emission of monolayer MoSe 2 . We have verified that this complete quenching was not due to the strain caused by the growth of Au on MoSe 2 , nor to excitation transfer due to optical absorption by the Au NPs. It is interpreted in terms of electron transfer from the monolayer MoSe 2 to the Au NPs, which corroborates previously reported results and interpretations. In addition, we have exploited the photoluminescence emission of the Au NPs deposited on the MoSe 2 layer. Using spatially resolved photoluminescence, a partial quenching of the PL emission of the Au NPs was pointed out and measured as a function of the MoSe 2 flake thickness. These results are explained by i) Plasmon damping and subsequent reduced optical absorption of the laser light by the Au NPs which can be understood in terms of surface plasmons decay into electron-hole pair excitations of the MoSe 2 layer, ii) An excitation transfer mechanism in which the photon emitted by radiative recombinations of electron-hole pairs localized into the Au NPs is absorbed by the MoSe 2 layer and converted into an electron-hole pair into the TMD sheet iii) Charge transfer of the holes photo-generated in the Au NPs due to the band alignment diagram at the semiconductor/metal interface which allows the holes in the Au NPs to leak towards the MoSe 2 layer. The plasmon damping, the energy transfer mechanisms and the two-pathways CT mechanism of electrons from the MoSe 2 layer to the Au NPs, and vice versa of holes from the Au NPs to the MoSe 2 layer, explain well the quenching of the photoluminescence of both the MoSe 2 layers and the Au nanoparticles when they are put in contact and form a Schottky junction. This work complements the interpretations proposed in the literature and contributes to the understanding of the complex properties of the metal/TMD interface. Moreover, the presented results may be useful for applications in highly sensitive photo-detectors since radiative losses are eliminated by PL quenching and CT to high mobility materials may improve the overall performances of nano-optical devices.

Numerical simulations based on the Discrete Dipole Approximation method

Discrete Dipole Approximation (DDA) method has been used to calculate the electric near-field distribution generated by excitation (532 nm laser wavelength) of a hemispherical Au nanoparticle (17 nm in diameter) supported either by a 20 nm thick SiO2 substrate or by a MoSe2/SiO2 layer with thickness increasing from 1 to 150 monolayers (i.e., bulk like MoSe2) as shown in Figure 5. The calculations were implemented in DDSCAT 7.3.3 software [2][3][4][5]. The inter-dipole distance was set to 0.5 nm to ensure full convergence of the calculations while keeping within reasonable computation time. The optical index of Au was taken from ref [6] and those of MoSe2 monolayer and SiO2 from refs [7] and [8], respectively. The optical index of monolayer MoSe2 was assumed in all the calculations and only the thickness of the layer was increased. This means that the effect of Van der Waals interlayer interaction on the electronic band structure and on the optical index of multilayer MoSe2 was not taken into account.

Calculations of the optical reflection properties of MoSe2/SiO2/Si and SiO2/Si stacks

To estimate the impact of the MoSe2 layer on the optical properties of the substrate, the optical reflection properties of MoSe2/SiO2/Si and SiO2/Si 2D stacks were calculated using the scattering matrix method [9]. The latter is well adapted to the analysis of interference effects in layered 2D systems. Since the PL emission from the Au NP involves d-to-s transition dipole momentum and that the deposited Au nano-crystals are randomly oriented, we assume that the emission of the hemispherical Au nanoparticle is isotropic (random orientation of the transition dipole) and that half of the light intensity is emitted by the air-exposed surface and directly collected by the objective. The other half (directed towards the substrate) is subject to interference effects produced by the optical cavity formed by the (0.8 nm) MoSe2/(90 nm)SiO2/Si stack (Figure A8). We used complex refractive indexes from literature for MoSe2 [7], SiO2 [8] and Si [10] To match the experimental conditions, we considered the average reflection of the emitted light for incident angles between 0° (normal incidence) and 65° corresponding to 0.9 numerical aperture of the collection objective of our setup. As the light emitted by the Au NPs is not polarized, we also averaged the reflected spectra over the transverse electric (TE) and transverse magnetic (TM) polarizations. Figure A8 shows the spectrum of the ratio of the reflection coefficients calculated with and without the MoSe 2 layer. The average value of this ratio is below 1 which indicates that the addition of the MoSe 2 layer decreases the amount of the light reflected by the substrate. This reduction in reflectivity (between 0.94 and 0.97 in the PL emission range of the Au NPs) is rather weak which indicates that interference effects do not play a major role, mainly because of the large numerical aperture of the objective which operates an angular averaging of the collected signal.

Figure A8: a) and b) reflectivity spectra of MoSe 2 /SiO 2 /Si (full lines) and SiO 2 /Si (dotted lines) stacks (right figure) calculated using the scattering matrix method. The spectra were integrated over the angular dispersion for numerical aperture NA=0.9 and TE/TM polarizations. c) and d) are reflectivity spectra corrected assuming that 50% of the emitted light is reflected by the substrate. The other 50% is directly collected by the objective. The dashed line shows the ratio d/c of spectra d) and c).

Figure 1 :

 1 Figure 1: A) Cross-section drawing of the sample. B) Optical microscopy image C) SEM and D) AFM topography images of a MoSe 2 flake covered by Au NPs deposited with 4.8 nm Au equivalent thickness. E) SEM image of a MoSe 2 flake covered by Au NPs deposited with 0.8 nm Au equivalent thickness.The optical absorption spectrum of MoSe 2 @ SiO 2 exhibits two maxima around 800 and 700 nm (FigureA2, Appendix) due to the A and B exciton transitions, respectively[START_REF] Tonndorf | Photoluminescence emission and Raman response of monolayer MoS 2, MoSe 2, and WSe 2[END_REF][START_REF] Zhang | Direct observation of the transition from indirect to direct bandgap in atomically thin epitaxial MoSe2[END_REF]. To investigate the effect of the deposited Au NPs on the optical properties of the MoSe 2 layer, we have performed spatially resolved PL measurements. The PL signal from the bare MoSe 2 region is used as a reference. As shown in Figure2A, the PL emission from the bare MoSe 2 region is characterized by a strong emission peak at 820 nm, due to the radiative recombination of the lower energy A excitons, and is very typical of a direct-band gap MoSe 2 monolayer[START_REF] Tonndorf | Photoluminescence emission and Raman response of monolayer MoS 2, MoSe 2, and WSe 2[END_REF][START_REF] Zhang | Direct observation of the transition from indirect to direct bandgap in atomically thin epitaxial MoSe2[END_REF][START_REF] Xia | CVD synthesis of large-area, highly crystalline MoSe 2 atomic layers on diverse substrates and application to photodetectors[END_REF][START_REF] Shaw | Chemical vapor deposition growth of monolayer MoSe2 nanosheets[END_REF]. Interestingly, this prominent PL emission completely disappeared in the case of MoSe 2 monolayer covered with Au NPs, suggesting a strong PL quenching phenomenon (Figure2A). In order to determine the origin of this remarkable effect, three main hypotheses can be invoked: i) the absorption of the MoSe 2 luminescence emission by the Au NPs, ii) the possible presence of a tensile strain generated by the growth of the Au NPs on the MoSe 2 layer, iii) the separation of the photo-generated electrons and holes due to CT between the MoSe 2 layer and the Au NPs.

Figure 2 :

 2 Figure 2: A) Room-temperature PL spectra of bare (red) and 4.8 nm equivalent thickness Au NPs-covered MoSe 2 monolayer (black). B) PL spectra of 4.8 nm equivalent thickness Au NPs deposited on SiO 2 (red) and on MoSe 2 (black). The PL emission was excited by a 532 nm laser.To investigate the role of the optical absorption by the Au NPs, the measurements were reproduced for a smaller deposited Au thickness (0.8 nm equivalent thickness, i.e., 7 nm average NPs size), in order to reduce the overall optical density of the Au NPs. As shown in FigureA3A(Appendix), no PL emission from the MoSe 2 monolayer covered with Au NPs was detected in this case and the quenching effect remained total. Moreover, the excitation laser intensity has been increased by a factor 100 to enhance the photo-generation of electron-hole pairs in the MoSe 2 layer. Even so, no PL emission was detected at all (FigureA3B) which points out the high efficiency of the mechanism responsible for the PL quenching. The latter being independent of the Au NPs optical density, the absorption of the MoSe 2 PL emission by the Au NPs can be ruled out to account for the observed PL quenching of MoSe 2 . Several studies[START_REF] Gong | Metal Contacts on Physical Vapor Deposited Monolayer MoS 2[END_REF][START_REF] Zhang | Phonon and Raman scattering of two-dimensional transition metal dichalcogenides from monolayer, multilayer to bulk material[END_REF][START_REF] Horzum | Phonon softening and direct to indirect band gap crossover in strained single-layer MoSe 2[END_REF][START_REF] Island | Precise and reversible band gap tuning in single-layer MoSe 2 by uniaxial strain[END_REF][START_REF] Zhu | Strain tuning of optical emission energy and polarization in monolayer and bilayer MoS 2[END_REF][START_REF] Wang | Strain-induced direct-indirect bandgap transition and phonon modulation in monolayer WS2[END_REF][START_REF] Morales-Garcia | Tuning the electronic properties of monolayer and bilayer transition metal dichalcogenide compounds under direct outof-plane compression[END_REF][START_REF] Conley | Bandgap Engineering of Strained Monolayer and Bilayer MoS 2[END_REF][START_REF] He | Experimental Demonstration of Continuous Electronic Structure Tuning via Strain in Atomically Thin MoS 2[END_REF][START_REF] Sortino | Dielectric Nanoantennas for Strain Engineering in Atomically Thin Two-Dimensional Semiconductors[END_REF] showed that the strain imposed by the metal NPs to the TMD layer may strongly modify its electronic band structure and can be responsible for a strong quenching of the PL emission. In particular, tensile strain may induce a direct-to-indirect band gap transition[START_REF] Horzum | Phonon softening and direct to indirect band gap crossover in strained single-layer MoSe 2[END_REF][START_REF] Morales-Garcia | Tuning the electronic properties of monolayer and bilayer transition metal dichalcogenide compounds under direct outof-plane compression[END_REF][START_REF] Conley | Bandgap Engineering of Strained Monolayer and Bilayer MoS 2[END_REF] which leads to a red shift of the PL peak and to a drastic decrease of the PL intensity[START_REF] Island | Precise and reversible band gap tuning in single-layer MoSe 2 by uniaxial strain[END_REF][START_REF] Zhu | Strain tuning of optical emission energy and polarization in monolayer and bilayer MoS 2[END_REF][START_REF] Conley | Bandgap Engineering of Strained Monolayer and Bilayer MoS 2[END_REF][START_REF] He | Experimental Demonstration of Continuous Electronic Structure Tuning via Strain in Atomically Thin MoS 2[END_REF]. Using calculations based on Density Functional Theory (DFT), Horzum et al[START_REF] Horzum | Phonon softening and direct to indirect band gap crossover in strained single-layer MoSe 2[END_REF] showed that monolayer MoSe 2 undergoes a direct-to-indirect band gap crossover under ∼3% biaxial tensile strain. In our samples, strain could be generated for two main reasons: i) the 24% lattice mismatch between MoSe 2 and Au, and/or ii) the cooling of the sample from the rather high growth temperature (600°C) of the Au NPs down to room temperature, which may generate tensile stress and strain in the MoSe 2 layer because of the different thermal expansion coefficients of Au and MoSe 2 @ SiO 2 substrate. To track the presence of strain in our Au@ MoSe 2 layers, we have performed Raman spectroscopy measurements. As shown in FigureA4(Appendix), the intensity of the MoSe 2 Raman peaks due to the A' 1 phonons vanishes for 4.8 nm equivalent thickness Au@ MoSe 2 sample. However, for 0.8 nm deposited thickness, the Raman signature of the A' 1 mode remains visible and red-shifted by 5.7 cm -1 . According to the calculations performed by Horzum et al[START_REF] Horzum | Phonon softening and direct to indirect band gap crossover in strained single-layer MoSe 2[END_REF], the A' 1 vibration frequency is lowered by 9 cm -1 for a 1% biaxial tensile strain. The 5.7 cm -1 red-shift measured in our samples corresponds thus to 0.6% strain which is a rather moderate value consistent with the slow cooling rate of the sample (24°/min in the initial 20 min and 1.3°/min at longer times) after Au NP deposition at 600°C. This value is well below the 3% minimum strain required for the direct-to-indirect band-gap transition in monolayer MoSe 2 . Nevertheless, the PL of monolayer MoSe 2 is totally quenched in our samples. Therefore, it is unlikely that,

Figure 3 :

 3 Figure 3: A, C) Bright field optical microscopy images of two multilayer MoSe 2 flakes covered by Au NPs with 17 nm average size (i.e., 4.8 nm equivalent thickness). B) PL spectra of the Au NPs recorded in the regions labelled a to f in A. The sharp peaks below 550 nm correspond to the Raman scattering by the Si optical phonon of the SiO 2 /Si substrate and by the A ' 1 optical phonons of the MoSe 2 layer. D) Map of the quenching factor Q of the PL emission of the Au NPs in the region delimited by the square shown in C.

Figure 4 :

 4 Figure 4: Quenching factor Q of the PL emission of the Au NPs as a function of the thickness (in monolayers) of the supporting MoSe 2 flake. The experimental values (red squares) are shown with error bars estimated assuming 10% relative uncertainty on the number of MoSe 2 monolayers. The contribution of solely plasmon damping (PD) to the calculated quenching factor is shown with black dots. The triangles show the calculated quenching factor when excitation transfer (ET) is taken into account in addition to the PD. Triangles up and down are obtained assuming the optical absorption of a monolayer MoSe 2 and bulk MoSe 2 , respectively. The difference between measured PL quenching and calculated quenching is assigned to charge transfer (CT) quenching. Dashed lines are guides to the eye.Obviously, the presence of the MoSe 2 layer strongly impacts the PL emission of the Au NPs which, to the best of our knowledge, was not reported up to now. This experimental finding has to be correlated with the quenchings of the PL emission and Raman scattering of monolayer MoSe 2 (Figure2), and any explanation has to account for the PL quenching of both the monolayer MoSe 2 and of the Au NPs.First, let's discuss how the optical properties of the Au NPs may be affected by the presence of the supporting MoSe 2 layer and in particular, to what extent the change in their optical absorption and emission rates can explain the quenching of their PL emission.To address this point, we have performed electrodynamics simulations based on the discrete dipole approximation (DDA) method (Appendix) applied to a model system consisting of a hemispherical Au nanoparticle (17 nm in diameter corresponding to the average size revealed in Figure1C) on top of a MoSe 2 / SiO 2 layer. Figure5displays electric near-field intensity maps generated at the laser excitation wavelength (532 nm) for an Au NP deposited on SiO 2 and on 1, 4 and 10 monolayers thick MoSe 2 / SiO 2 . The numerical simulations clearly show that the electric near-field around and inside the nanoparticle is damped when the latter is supported by a MoSe 2 layer. The damping is more pronounced with increasing thickness of the MoSe 2 layer. It is due to the imaginary part of the complex dielectric function of MoSe 2 , i.e., to the decay of the excited surface plasmons into electron-hole pairs (including excitons) in the MoSe2 layer. The electric near-field enhancement has been integrated over the Au

Figure 5 :

 5 Figure 5: Electro-dynamics simulations, based on the discrete dipole approximation (DDA) method, of the optical electric field intensity enhancement | E|2/|E0|2 (E0 being the amplitude of the incident excitation field). The latter is displayed in log scale (red color corresponds to a factor 10 enhancement). Calculations were performed for the 532 nm laser wavelength used to excite the PL emission. The arrows indicate the polarization of the incident wave impinging a hemi-spherical Au nanoparticle (17 nm diameter) supported either directly by a 20 nm thick SiO 2 layer (A) or by a MoSe 2 layer with thickness of 1 (B), 4 (C) and 10 (D) monolayers. The lateral dimensions (130 x 130 nm²) were made sufficiently

Figure 6 :

 6 Figure 6: Energy level diagram of contacted a MoSe 2 /Au Schottky interface. The arrows indicate the electrons and holes transfer between the MoSe 2 and Au. The green arrow represents the optical excitation energy (2.33 eV). Φ m is the work function of Au, χ is the electron affinity of MoSe 2 and Φ s = Φ m -χ is the Schottky band offset at the MoSe 2 /Au interface. BC and BV stand, respectively, for the conduction and valence band edges of MoSe 2 . ED ~ 2.4 eV is the d-to-s bands transition energy edge in bulk Au.According to photo-electron spectroscopy measurements, the electron affinity χ of MoSe 2 and the work function Φ m of Au are respectively 4.2 and 5.1 eV[START_REF] Kang | Band offsets and heterostructures of twodimensional semiconductors[END_REF][START_REF] Chang | Monolayer MoSe 2 Grown by Chemical Vapor Deposition for Fast Photodetection[END_REF]. Once the two materials are in contact, a Schottky junction with height Φ s = Φ m -χ is formed at the metal/semiconductor interface, in the absence of inter-mixing, impurities or defects which may pin the Fermi level. In the case of a thick MoSe 2 layer, the Φs = 0.9 eV band offset between the Fermi level of Au and the conduction band of MoSe 2 leads to band bending and to the formation of a barrier with height Φs, and a depletion layer which thickness is determined by the built-in potential V in and the doping level of the

Figure A2 :

 A2 Figure A2: Absorbance spectra of Au nanoparticles deposited on SiO2 (black) for 4.8 (A) and 0.8 nm (B) deposited equivalent thicknesses and of bare monolayer MoSe2 grown by CVD on SiO2 substrate (red). The absorbance spectrum of Au NPs on SiO2 is much weaker in B compared to A because of the much lower Au NPs density and size (see Figure A1). The spectrum of MoSe2/SiO2 is the same in A and B and has been rescaled for comparison with the absorption spectrum of the Au NPs. The vertical dashed line shows the laser excitation wavelength 532 nm used to excite the photoluminescence emission.

Figure

  Figure A3: A) Room temperature photoluminescence spectra of bare MoSe2 (red) and MoSe2 covered with Au NPs (0.8 nm equivalent thickness) (black) excited with 532 nm laser wavelength. B) Liquid Nitrogen temperature photoluminescence spectra of MoSe2 covered with Au NPs (4.8 nm equivalent thickness) excited at 532 nm laser wavelength with laser intensity increasing from 1% to 100% of the maximum value 10 6 W/cm 2 . The increase of the detected signal, with increasing laser intensity, is due to the long-wavelengths tail of the PL emission of the Au NPs. The PL emission of the MoSe 2 layer is totally quenched.

Figure A4 :

 A4 Figure A4: Raman scattering spectra of bare monolayer MoSe2 (red) and of Au NPs-covered monolayer MoSe2 (black) for (A, C) 4.8 nm and (B, D) 0.8 nm deposited equivalent thicknesses. (C) and (D) show the 200-270 cm -1 spectral region of Figures A and B, centered on the A ' 1 phonon wavenumber. The spectra of MoSe2 covered with Au NPs are multiplied by a factor 5 in C and D.

Figure A5: The SiO 2 /

 2 Figure A5: The SiO 2 /Si substrate supporting the MoSe 2 flakes was partly masked prior to the deposition of Au (0.8 nm nominal thickness). Due to the rounded shape of the mask edge, the sputtered Au atoms slightly penetrate underneath the mask which is responsible for a nonabrupt transition from Au-covered to bare MoSe 2 regions. Left figure: Scanning Electron Microscopy (SEM) image (×156 magnification) in the transition area between Au-covered and bare MoSe 2 regions of the sample. An isolated triangular MoSe 2 flake located in this area was selected for optical spectroscopy investigations. Right figure: A) Dark field optical image (x50 magnification) of the selected MoSe 2 flake. B, C, D, E) SEM images (× 350000 magnification) recorded in the square delimited areas shown in A. The Au NPs are visible in the SEM images and their density clearly increases from left to right : 0.2 ± 0.1 % (C), 0.4 ± 0.1 % (D) and 0.7 ± 0.1 % (E)

Figure A7 :

 A7 Figure A7: Discrete Dipole Approximation (DDA) based numerical simulations:A) Optical absorption spectra of a hemispherical Au nanoparticle (17 nm in diameter) supported either by a 20 nm-thick SiO2 substrate (spectrum labeled 0) or by a MoSe2 multilayer flake stacked on a 20 nm-thick SiO2 substrate. The thickness of the MoSe2 flake is 1, 4, 10 and 20 monolayers. The absorption by the Au nanoparticle is calculated using a spatial integration of the electric field intensity enhancement (Figure5) inside the nanoparticle and the imaginary part of the dielectric function of gold. The spectra are normalized to the maximum absorption of the Au nanoparticle on SiO 2. The dashed vertical lines indicate the A (796 nm) and B (694 nm) exciton wavelengths and the laser excitation wavelength (532 nm). The surface plasmon resonance of the Au nanoparticle on SiO2 is strongly red-shifted, damped and hybridized with the excitonic transitions when the nanoparticle is supported by MoSe2. The dips at the exciton wavelengths indicate a Fano type interaction between the plasmonic resonance and the A and B excitonic transitions. B) Optical absorption spectrum of a monolayer MoSe2 supporting a 17 nm hemispherical Au NP The absorption is calculated using a spatial integration of the electric field intensity enhancement inside the MoSe2 layer and the imaginary part of the dielectric function of monolayer MoSe2. The optical absorption spectrum is normalized with respect to the spectrum calculated for a bare monolayer MoSe2. As the vertical axis scale starts at 1, the optical absorption of the MoSe2 layer is clearly enhanced by the Au NP, particularly around the dips formed by the Fano interference between the plasmonic resonance and the A and B excitonic transitions. C) Electric field intensity enhancement |E| 2 /|E 0 | 2 calculated for a hemispherical 17 nm diameter Au NP on monolayer MoSe 2 /SiO 2 and for bare monolayer MoSe 2 /SiO 2 . The thickness of the SiO 2 substrate is 20 nm. The scale bar is 10 nm long and the arrow indicates the polarization of the incident electric field. Calculations were performed for 532 nm wavelength corresponding to the laser wavelength used to excite the PL emission. The intensity is in log scale and the maximum intensity (red) is for 0.4.

  ). The density of Au NPs and MoSe2 surface coverage increases continuously from left to right (see FigureA5). As a consequence, the PL intensity increases (i.e., PL quenching is suppressed) with decreasing density of the Au NPs. Also, the PL emission wavelength blue shifts and its line width decreases due to weaker disorder effects caused by the Au NPs. E) Peak wavenumber and F) intensity of Raman scattering by A'1 phonons mapped in the region delimited by the rectangular dotted line in Figure A. The quenching of both Raman scattering and PL emission are clearly correlated. The intensity of the Raman peak progressively increases (by approximately a factor 3) and its position blue shifts to its nominal value in monolayer MoSe2 (around 241 cm -1 ) with decreasing density of Au NPs. Both quenchings of the Raman scattering and PL emission are interpreted in terms of transfer of the photo-excited electron from the MoSe2 layer to the Au NPs; the latter acting as traps for the photo-generated electrons.

Nanosheets, J. Phys. Chem. C. 124 (2020) 20350-20358. https://doi.org/10.1021/acs.jpcc.0c04664.

Acknowledgements

This work was granted access to the HPC resources of CALMIP supercomputing center under the allocation 2020-P0996. The work has been supported by the EUR grant NanoX n° ANR-17-EURE-0009 in the framework of the "Programme des Investissements d'Avenir"

Data availability

The raw/processed data required to reproduce these findings cannot be shared at this time due to technical or time limitations.

Appendix