Gabriele Boschetto

Stefania Carapezzi

Corentin Delacour

Madeleine Abernot

Thierry Gil

Aida Todri-Sanial

Ab Initio Computer Simulations on Interfacial Properties of Single-Layer MoS 2 and Au Contacts for Two-Dimensional Nanodevices

The functionality and performance of devices based on atomically thin two-dimensional (2D) materials strongly depends on the quality of the employed 2D material. Although molybdenum disulfide (MoS 2 ) is an excellent candidate for future applications in nanoelectronics, MoS 2 films have not yet reached the level of purity achieved in silicon technologies. At present, the formation of small and extended defects in the material is inevitable during the growth process, and this has a non-negligible impact on the electronic properties of MoS 2 . Furthermore, defects are also thought to affect non trivially the resistance at the MoS 2 -metal contact and the injection of carriers. In this work, we systematically and thoroughly assess the impact of some of the most commonly occurring defects in MoS 2 (such as vacancies, substitutions, and grain boundaries) not only from the point of view of the material's properties but also by looking at MoS 2 -metal contacts. To do so, we carry out ab initio computer simulations in the density functional theory (DFT) framework coupled with surface simulations based on the Green's function formalism. Our simulation approach allows us to obtain more realistic models of MoS 2 interfaces with Au. Moreover, this is the first theoretical study in which the effect of grain boundaries on the MoS 2 -Au contact properties is explored. Results suggest S vacancies to have a detrimental effect on the quality of the metal contacts, whereas Mo vacancies strongly improve the electron injection from the metal to MoS 2 . Antisite Mo defects also lead to an increased electron injection rate by acting as "conductive bridges" between the Au electrode and the 2D material. Finally, each of the grain boundaries here considered improves the quality of the contact. We expect our study to provide the necessary theoretical foundation for the design of MoS 2 -metal contacts with suitable characteristics.

Introduction

Atomically thin two-dimensional transition metal dichalcogenides (TMDs) have attracted a great deal of interest for future applications in nanoelectronics. [START_REF] Akinwande | Two-dimensional flexible nanoelectronics[END_REF][START_REF] Lee | Nanoelectronic circuits based on twodimensional atomic layer crystals[END_REF][START_REF] Dragoman | 2d materials nanoelectronics: New concepts, fabrication, characterization from microwaves up to optical spectrum[END_REF][START_REF] Jing | Engineering field effect transistors with 2d semiconducting channels: Status and prospects[END_REF][START_REF] Illarionov | Insulators for 2d nanoelectronics: the gap to bridge[END_REF] In particular, monolayer molybdenum disulfide (MoS 2 ) has been shown to display highly desirable mechanical, electronic, and optical properties due to its intrinsic reduced dimensionality, which could also enable very compact and low-power devices. For instance, MoS 2 has a very good carrier mobility at room temperature (estimated to be as high as ⇠ 400 cm 2 V 1 s 1 ), [START_REF] Radisavljevic | Single-layer MoS 2 transistors[END_REF][START_REF] Ahmed | Two-dimensional transition metal dichalcogenides and their charge carrier mobilities in fieldeffect transistors[END_REF] and chemical stability up to 1100 C. Moreover, in contrast with graphene, monolayer MoS 2 shows a direct sizeable band gap of 1.8 eV, [START_REF] Mak | Atomically thin MoS 2 : A new direct-gap semiconductor[END_REF] thus making such material suitable for a wide range of devices including field-effect transistors (FETs), memory devices, and optoelectronics. [START_REF] Lembke | Breakdown of high-performance monolayer MoS 2 transistors[END_REF][START_REF] Nourbakhsh | MoS 2 field-effect transistor with sub-10 nm channel length[END_REF][START_REF] Ge | Atomristor: Nonvolatile resistance switching in atomic sheets of transition metal dichalcogenides[END_REF][START_REF] Bhattacharjee | Insights into multilevel resistive switching in monolayer MoS 2[END_REF][START_REF] Carey | Inkjet printed circuits with 2d semiconductor inks for high-performance electronics[END_REF] Pivotal for the use of MoS 2 in electronic devices is the possibility of wafer-scale production, which nowadays is mostly achieved via chemical and/or physical vapor deposition (CVD and PVD, respectively). However, while both techniques could be suitable This document is the unedited Author's version of a Submitted Work that was subsequently accepted for publication in ACS Applied Nano Materials, copyright ©2022 American Chemical Society after peer review. To access the final edited and published work see https://doi.org/10.1021/acsanm.2c00995.

for mass production, the resulting material is often far from being pristine. Structural defects such as vacancies, substitutions, and grain boundaries are introduced in MoS 2 , and these have been shown to significantly affect the material's properties. [START_REF] Hong | Exploring atomic defects in molybdenum disulphide monolayers[END_REF][START_REF] Addou | Surface defects on natural MoS 2[END_REF][START_REF] Wang | Detailed atomic reconstruction of extended line defects in monolayer MoS 2[END_REF][START_REF] Bertolazzi | Engineering chemically active defects in monolayer MoS 2 transistors via ion-beam irradiation and their healing via vapor deposition of alkanethiols[END_REF][START_REF] Chen | Tuning electronic structure of single layer MoS 2 through defect and interface engineering[END_REF][START_REF] Mahata | Effect of intrinsic structural defects on mechanical properties of single layer MoS 2[END_REF] For instance, transistors built with CVD-and PVD-grown singlelayer MoS 2 have shown significantly lower carrier mobilities (45 cm 2 V 1 s 1 and >1 cm 2 V 1 s 1 , respectively) with respect to the ideal value cited above. [START_REF] Schmidt | Transport properties of monolayer MoS 2 grown by chemical vapor deposition[END_REF] This has been argued to be due to the high concentration of defects (typically on the order of 10 13 cm 2 ) in the material's surface. [START_REF] Li | Why chemical vapor deposition grown MoS 2 samples outperform physical vapor deposition samples: Time-domain ab initio analysis[END_REF] However, such defects may also have a positive impact on the overall functionality of nanodevices: for instance, one of the proposed working mechanisms of 2D memristors made of monolayer MoS 2 involves the migration of point defects (mainly sulfur mono-vacancies) with the formation of conductive-like channels. This would result in the modulation of the material's resistance at the interface with the metal electrode, and would explain the capability of the device to switch from its high-resistance state (HRS) to its lowresistance state (LRS). [START_REF] Ge | Atomristor: Nonvolatile resistance switching in atomic sheets of transition metal dichalcogenides[END_REF][START_REF] Kim | Zero-static power radio-frequency switches based on MoS 2 atomristors[END_REF][START_REF] Li | MoS 2 memristors exhibiting variable switching characteristics toward biorealistic synaptic emulation[END_REF] Sun et al. demonstrated how defects can also enhance the adsorption of Li on monolayer MoS 2 , therefore improving the energy storage capabilities of such material in the context of Li-ion batteries. [START_REF] Sun | Defect-mediated lithium adsorption and diffusion on monolayer molybdenum disulfide[END_REF] Grain boundaries have also been shown to be crucial for the functionality of MoS 2 -based memristors: Xu and co-authors [START_REF] Xu | Vertical MoS 2 doublelayer memristor with electrochemical metallization as an atomic-scale synapse with switching thresholds approaching 100 mv[END_REF] built a device made of bi-layer MoS 2 , and they demonstrated that its working mechanism is due to the migration of metallic ions from the Cu electrode to MoS 2 , which is facilitated by the presence of grain boundaries in the material. In addition, it was shown that grain boundaries play a crucial role for the functionality of the memristor devices built by Sangwan and co-authors. [START_REF] Sangwan | Gate-tunable memristive phenomena mediated by grain boundaries in singlelayer MoS 2[END_REF] Overall, there is clear evidence of the non-negligible impact of structural defects on the electronic properties of monolayer MoS 2 , and in turn on the performance and on the working mechanisms of 2D nanodevices. Moreover, equally important is the choice of the metal electrode: for instance, some metals can chemically react with MoS 2 , whereas others are only weakly interacting with the material via weak dispersion forces. Clearly, this has a strong impact on the contact resistance at the metal-MoS 2 junction. [START_REF] Kang | Computational study of metal contacts to monolayer transition-metal dichalcogenide semiconductors[END_REF][START_REF] Zhong | Interfacial properties of monolayer and bilayer MoS 2 contacts with metals: Beyond the energy band calculations[END_REF][START_REF] Schauble | Uncovering the effects of metal contacts on monolayer MoS 2[END_REF] Furthermore, Fermi level pinning at the MoS 2 -metal contact could also lead to large Schottky barriers and contact resistances, which are known to limit the device performance by introducing unwanted parasitic elements. [START_REF] Gong | The unusual mechanism of partial fermi level pinning at metal-MoS 2 interfaces[END_REF][START_REF] Allain | Electrical contacts to two-dimensional semiconductors[END_REF] Indeed, one of the drawbacks of TMDs is the generally higher metalsemiconductor contact resistivity with respect to other 2D materials, such as graphene. [START_REF] Xu | Contacts between twoand three-dimensional materials: Ohmic, schottky, and p-n heterojunctions[END_REF] Among the many different options, Au is perhaps one of the most commonly used elements to build electrodes in MoS 2 -based devices, due to its stability and chemical inertness. Moreover, Au can also act as the support when growing large-area monolayer MoS 2 . [START_REF] Grønborg | Synthesis of epitaxial single-layer MoS 2 on au(111)[END_REF] Clearly, a deep understanding of the physics and chemistry at the interface between Au and MoS 2 would be highly beneficial, in order to elucidate the interface energetics, carrier injection rates, and more generally to improve the design of metal contacts in 2D nanodevices. To this end, theoretical simulations based on atomistic approaches are undoubtedly useful, as in real samples different defects might be present in the material simultaneously. Thus, simulations allow us to i) assess and predict the impact of defects on the properties of both the 2D material and the interface, and ii) disentangle the effect of different defects. Indeed, the ideal defect-free Au-MoS 2 interface has been already widely studied. [START_REF] Kang | Computational study of metal contacts to monolayer transition-metal dichalcogenide semiconductors[END_REF][START_REF] Zhong | Interfacial properties of monolayer and bilayer MoS 2 contacts with metals: Beyond the energy band calculations[END_REF][START_REF] Schauble | Uncovering the effects of metal contacts on monolayer MoS 2[END_REF] However, as previously mentioned, experimentallygrown MoS 2 often presents a high number of structural defects. More recently, theoretical studies on the interaction between Au and defective MoS 2 have also been carried out: for instance, Tumino et al. combined STM images and large density functional theory (DFT) simulations to elucidate the role of point defects in single-layer MoS 2 supported on Au(111). [START_REF] Tumino | Nature of point defects in single-layer MoS 2 supported on au(111)[END_REF] Yang et al. studied the impact of sulfur vacancies in tuning the n-and p-type characteristics of MoS 2 in top contact with Au electrode. [START_REF] Yang | Electrical doping effect of vacancies on monolayer MoS 2[END_REF] Qiu and co-authors also carried out DFT simulations of defective MoS 2 -Au interfaces, mainly focusing on the role and concentration of sulfur mono-vacancies on the charge redistribution at the contact interface. [START_REF] Qiu | First-principles study of vacancy defects at interfaces between monolayer MoS 2 and au[END_REF] However, we point out that such studies focused on a limited subset of point defects, mainly sulfur vacancies and small clusters. Moreover, to the best of our knowledge, no studies have been carried out yet considering MoS 2 structures with grain boundaries in contact with Au. Therefore, in this work we perform accurate atomistic DFT simulations of defective Au-MoS 2 interfaces con-sisting of a larger set of structural defects commonly occurring with both CVD and PVD growth methods, [START_REF] Hong | Exploring atomic defects in molybdenum disulphide monolayers[END_REF] with also the inclusion of grain boundaries. Additionally, in our simulations we employ surface models based on the Green's function approach, in order to have a more realistic representation of the metal electrodes rather than carrying out simulations based on slab models. To the best of our knowledge, this is the first time that such a simulation approach has been used to study defective Au-MoS 2 interfaces.

This work consists of two parts: first, as the essential prerequisite to the following more complex simulations, we investigate the properties of point defects and grain boundaries (GBs) in freestanding MoS 2 , i.e., without the inclusion of the metal electrode. This allows us to assess the impact of defects on MoS 2 itself, and to validate our simulation approach. Then, the knowledge gained in the first part of this study is used as a starting point to carry out the main part of this work, which consists on the investigation of the chemistry and physics at the Au-MoS 2 interface. In summary, we want to thoroughly understand the properties of Au-MoS 2 contacts in realistic conditions, i.e., with a defective 2D material.

This paper is organized as follows: in the following section (Simulations Details) we describe the setup of our computer simulations and the model employed; in Results and Discussion we discuss on our simulations of defective MoS 2 and Au-MoS 2 interfaces, in the context of 2D devices. Finally, Conclusions are presented in the final section.

Simulation Details

In this work, we considered monolayer MoS 2 with either point defects or grain boundaries, in top contact with the Au electrode. Given the high number of structural defects experimentally observed in such material, we only focused on those which are the most abundant with both CVD and PVD growth techniques, as discussed by Hong et al. in their work. [START_REF] Hong | Exploring atomic defects in molybdenum disulphide monolayers[END_REF] The point defects here considered are: sulfur mono-vacancy (V S ), sulfur divacancy (V S2 ), molybdenum vacancy (V Mo ), antisite Mo filling one S mono-vacancy (Mo S ), antisite Mo filling one S di-vacancy (Mo S2 ), and two Mo atoms filling one S di-vacancy (Mo2 S2 ). These are all shown in Figure 2. Interestingly, the first three types of defects mostly occur with the CVD method, whereas the latter three with PVD. Regarding the grain boundaries, we have considered three representative cases characterized by a tilt angle of 60 : two mirror-symmetric GBs (4|4P and 4|4E), and one asymmetric GB (8|4). The 4|4P structure consists of a series of 4-fold rings connected by a shared point, whereas in 4|4E the 4-fold rings all share an edge; finally, the structure of 8|4 consists of alternating 4-and 8-fold rings. The structure of these GBs are shown in Figure 4. We point out that both 4|4P and 4|4E have been frequently observed in experimentally-grown MoS 2 samples, [START_REF] Wang | Detailed atomic reconstruction of extended line defects in monolayer MoS 2[END_REF][START_REF] Zhou | Intrinsic structural defects in monolayer molybdenum disulfide[END_REF][START_REF] Lin | Vacancy-induced formation and growth of inversion domains in transition-metal dichalcogenide monolayer[END_REF][START_REF] Van Der Zande | Grains and grain boundaries in highly crystalline monolayer molybdenum disulphide[END_REF][START_REF] Ly | Misorientationangle-dependent electrical transport across molybdenum disulfide grain boundaries[END_REF] with the former being among the most commonly occuring GBs in MoS 2 , [START_REF] Komsa | Engineering the electronic properties of two-dimensional transition metal dichalcogenides by introducing mirror twin boundaries[END_REF] . Also, 8|4 has already been discussed in the literature. [START_REF] Zhou | Intrinsic structural defects in monolayer molybdenum disulfide[END_REF][START_REF] Qiu | Dopants and grain boundary effects in monolayer MoS 2 : A first-principles study[END_REF][START_REF] Zou | An open canvas-2d materials with defects, disorder, and functionality[END_REF][START_REF] Gao | Structures and magnetic properties of MoS 2 grain boundaries with antisite defects[END_REF] We first studied the electronic properties of free-standing MoS 2 with either point defects or GBs. To study isolated structures with point defects, we considered 5⇥5 hexagonal MoS 2 supercells to obtain realistic defect concentrations, within the experimental range of ⇠10 13 cm 2 . We ensured an in-plane distance between the structure of GBs of at least 15 Å to avoid any spurious interaction. Likewise, we also included at least 20 Å of vacuum below and above the MoS 2 layer, in the out-of-plane direction.

We then coupled each of these structures with the Au(111) top electrode. We ensured that the induced strain due to the lattice mismatch between the mono-layer and the metal was as small as possible, compatibly with the feasibility of the simulations. We point out that since it is well known that the electronic properties of MoS 2 can be significantly affected by strain, [START_REF] Johari | Tuning the electronic properties of semiconducting transition metal dichalcogenides by applying mechanical strains[END_REF] only the structure of the Au electrode was strained. We note that the calculated in-plane lattice constant of MoS 2 was 3.16 Å, in very good agreement with experimental data. [START_REF] Wakabayashi | Lattice dynamics of hexagonal MoS 2 studied by neutron scattering[END_REF] When considering point defects, we started from a 3⇥3 orthorombic MoS 2 supercell, and we positioned Au(111) on top, thus obtaining an orthorombic Au-MoS 2 interface simulation cell. The resulting mean absolute strain on Au was low and ⇠3%. By choosing such a MoS 2 supercell we were able to maintain once again the concentration of defects within the typical range of values found in experiments (⇠10 13 cm 2 ). The simulation cell parameters of each Au-MoS 2 interface were a= 16.4219 Å, b= 9.4812 Å, c= 45.5679 Å, and a= 90 , b = 90 , g= 90 . From this point onward, we will refer to the defect-free interface as Au-MoS 2 , whereas if point defects are considered we will write Au-followed by the abbreviation of the defect. For instance, Au-V S refers to the interface between Au and MoS 2 with the inclusion of one S mono-vacancy.

We followed the same strategy when constructing interfaces between Au and MoS 2 with GBs, in order to minimize as much as possible the artificial strain on Au while striving to maintain the number of atoms as low as possible. Similarly with point defects, we will refer to the structures with GBs as Au-followed by the abbreviation of the GB. We obtained interfaces with an induced mean absolute strain on Au of ⇠4% in both Au-4|4E and Au-4|4P, and of ⇠2% on Au-8|4. We point out that the interface structures here constructed were not necessarily orthorombic, and the simulation cell parameters are shown in Table 1.

Atomistic simulations were carried out in the framework of density functional theory (DFT) with QuantumATK atomicscale modelling software. [START_REF] Smidstrup | Quantumatk: An integrated platform of electronic and atomic-scale modelling tools[END_REF][START_REF]QuantumATK version S[END_REF] We performed spin-polarized calculations in vacuum using the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional, [START_REF] Perdew | Generalized gradient approximation made simple[END_REF] and to model core electrons we used norm-conserving pseudopotentials from the PseudoDojo library. [START_REF] Van Setten | The pseudodojo: Training and grading a 85 element optimized norm-conserving pseudopotential table[END_REF] We employed the LCAO approach with a density-mesh Elect.

Surface Vacuum To model Au-MoS 2 interfaces we carried out Green's function surface calculations as implemented in QuantumATK: [START_REF] Smidstrup | First-princiuples green'sfunction method for surface calculations: A pseudopotential localized basis set approach[END_REF] in contrast to the widely used slab method, surface calculations within the Green's function formalism allow us to construct Au surfaces which are essentially fully periodic in one direction, and therefore with only one single surface-vacuum interface. In addition to obtaining models which are more physically realistic, simulations are also significantly less affected by the size of the surface thickness. We constructed our surface models by considering MoS 2 coupled with six atomic Au layers. We imposed Neumann boundary conditions in the vacuum direction and Dirichlet boundary conditions at the boundary with the bulk Au electrode (see Figure 1). Given the size and the computational cost associated with such systems, simulations of point defects were carried out with a 2 ⇥ 3 ⇥ 138 MP grid, whereas to compute device density of states we used an MP grid defined by a 8 ⇥ 12 ⇥ 138 k-point mesh. Geometry optimizations were converged with a maximum allowed atomic force threshold of 0.05 eV/ Å. For the interfacial GBs we used the following settings: 1 ⇥ 12 ⇥ 138 for Au-4|4P, 1 ⇥ 12 ⇥ 138 for Au-4|4E, and 1 ⇥ 7 ⇥ 128 for Au-8|4.

Results and Discussion

Electronic Properties of Defective MoS 2

The first part of this study, which serves as a prerequisite for further simulations on Au-MoS 2 interfaces, is dedicated to the analysis of the structure and the electronic properties of MoS 2 with the inclusion of either small point defects or extended defects (grain boundaries). As discussed in the previous sections, it is well known that MoS 2 grown by common methods like CVD and PVD is far from being a pristine material, as numerous defects are inevitably introduced following the growth and annealing procedures. Point defects can reach high concentrations, typically on the order of ⇠10 13 cm 2 . It is clear that with such high defect densities the electronic properties of the material could be dramatically different from the ideal defect-free case.

V S V S2 V Mo Pristine Mo S Mo S2 Mo2 S2
From the structural point of view, we found that introducing point defects (either vacancies or substitutions) leads to a small atomic rearrangement of the MoS 2 structure, as can be observed in Figure 2, where the DFT-optimized geometries of pristine and defective MoS 2 are shown. V S2 caused the three surrounding Mo atoms to move closer in order to fill the gap left by the two axial S atoms. We observed the Mo-Mo distance of such three atoms to significantly decrease from 3.17 Å to 2.85 Å. On the contrary, with V Mo the three surrounding S atoms moved slightly away from the gap left by the missing Mo atom, thus reducing the Mo-S bond length from 2.42 Å to 2.38 Å. In each Mo antisite defect the extra Mo atom occupies the position of the missing S atom, thus forming bonds with the three surrounding Mo atoms in the core of MoS 2 . The bond length between the extra substitutional Mo and the three core Mo atoms was found to be 2.58 Å, which is larger than the typical Mo-S bond length (2.42 Å). Indeed, from Figure 2 it can be observed that the antisite Mo atom sticks out slightly of the basal plane of MoS 2 . Finally, we also note that when two antisite Mo atoms are present (Mo2 S2 ) they are found to lie on the same vertical axis. Overall, given the size of the MoS 2 supercell which ensures a reasonable defect concentration of ⇠4.6⇥10 13 cm 2 , we found point defects to have a limited and rather localized effect on the MoS 2 crystal structure.

To investigate the impact of point defects on the electronic properties of MoS 2 we computed the density of states (DOS) of both the pristine and the defective material (see Figure 3), with projections onto the relevant atomic orbitals of S and Mo (S-3p and Mo-4d). As can be seen from the figure, our simulations predicted pristine MoS 2 to be a seminconductor with a band gap of 1.79 eV, in excellent agreement with the experimental value of ⇠1.8 eV. [START_REF] Mak | Atomically thin MoS 2 : A new direct-gap semiconductor[END_REF] Moreover, as expected the S-3p and Mo-4d orbitals are those with the most significant contribution to the overall DOS. Then, we found that S vacancies (V S , V S2 ) introduced localized intra-gap states, whose contribution is significantly given by the Mo-4d orbitals with respect to S-3p orbitals. These extra states are located above the Fermi level and ⇠0.57 eV from the edge of the material's conduction band. We note that this is consistent with previous DFT simulations. [START_REF] Bhattacharjee | Insights into multilevel resistive switching in monolayer MoS 2[END_REF][START_REF] Chen | Tuning electronic structure of single layer MoS 2 through defect and interface engineering[END_REF] We point out that in their work Bhattacharjee et al. [START_REF] Bhattacharjee | Insights into multilevel resistive switching in monolayer MoS 2[END_REF] found the extra states to be located ⇠0.73 eV from the edge of the conduction band, however the authors used a much larger supercell (8⇥8) to simulate defective MoS 2 . This effectively reduces the concentration of the S vacancies with respect to our study. We expect this to have a non-negligible effect on the energy of the intra-gap states, although our simulations essentially predict the same. In addition, in V S2 we observed additional states overlapping with the material's conduction band edge. Then, we found that V Mo led to a number of deep intra-gap states, some located below the Fermi level, and others above the Fermi level. Interestingly, we observed that the states below the Fermi level and closer to the valence band edge of MoS 2 are given almost exclusively by the S-3p orbitals, whereas in the states above the Fermi level both S-3p and Mo-4d show a significant contribution. From the projected DOS (PDOS) shown in Figure 3 one can also observe that vacancies do no induce any magnetic moment in the material. On the contrary, antisite Mo substitutions were all found to induce a spin magnetic moment of 1.8 µ B , 2.0 µ B , and 4.0 µ B in Mo S , Mo S2 , and Mo2 S2 , respectively. Previous theoretical studies [START_REF] Hong | Exploring atomic defects in molybdenum disulphide monolayers[END_REF][START_REF] Wang | Electronic and magnetic properties of MoS 2 monolayers with antisite defects[END_REF] on Mo S and Mo S2 antisite defects also corroborate our present findings. The presence of a non-zero magnetic moment in Mo antisite defects was explained as the result of two extra unpaired electrons on antisite Mo coming from the surrounding Mo atoms. Similarly to vacancies, each of these antisite defects was found to introduce a number of intra-gap states in MoS 2 , whose contribution to the overall DOS is given almost exclusively by the 4d orbitals of the Mo atoms.

Following the study on point defects, we then focused on the electronic properties of grain boundaries. The optimized structures are shown in Figure 4, whereas the PDOS of the GBs are shown in Figure 3, once again projected onto the 3p and 4d orbitals of S and Mo, respectively. From the same figure it is pos-sible to observe that both 4|4E and 4|4P introduced a significant number of low intra-gap states in the material, effectively leading to the vanishing of the band gap. This corroborates previous studies claiming that such GBs may lead to 1D metallic strips in MoS 2 . [START_REF] Komsa | Engineering the electronic properties of two-dimensional transition metal dichalcogenides by introducing mirror twin boundaries[END_REF][START_REF] Gibertini | Emergence of onedimensional wires of free carriers in transition-metaldichalcogenide nanostructures[END_REF] Differently from 4|4E and 4|4P, 8|4 only led to the appearance of localized deep intra-gap states, above the Fermi level. The orbital contribution on the intra-gap states in GBs is given mainly by Mo-4d orbitals, with a smaller contribution by S-3p. Finally, we also note that none of the GBs here considered showed any spin magnetic moment.

In conclusion, we found that both point and extended defects have a significant impact on the electronic and magnetic properties of MoS 2 : the appearance of either localized or diffused intra-gap states is expected to dramatically modify the material's transport properties. This in turn could have a significant impact on the performance of electronic devices based on MoS 2 . However, so far only the isolated material has been considered. In a device, the 2D material will be in contact with a metal electrode. Thus, in the next part we will focus on defective MoS 2 in contact with the Au metal electrode.

Structure and Properties of Au-MoS 2 Interfaces 3.2.1 Geometry of Interfaces

In this second and main part of our work, we focused on the structural and electronic properties of MoS 2 in contact with the Au electrode. At first, to gain a qualitative insight into the physics and chemistry at the Au-MoS 2 interface, we investigated the structure of both materials once in contact, and we calculated the average interface distance (d Au MoS 2 ) of each structure, as defined in Figure 5. Additionally, we computed the electron density difference (EDD) maps of the interfaces to visualize the redistribution of charge upon creating the contact between the two materials. EDD maps can also be used to qualitatively assess the strength of the interaction between Au and MoS 2 and the overlap between orbitals. EDD maps are shown in Figure 6. Initially, we focused on defect-free Au-MoS 2 (see Figure 1 for the optimized geometry of the system), and we found an average interface distance of 2.71 Å, in very good agreement with previous values reported in the literature. [START_REF] Kang | Computational study of metal contacts to monolayer transition-metal dichalcogenide semiconductors[END_REF][START_REF] Tumino | Nature of point defects in single-layer MoS 2 supported on au(111)[END_REF][START_REF] Popov | Designing electrical contacts to MoS 2 monolayers: A computational study[END_REF] We note that the relatively large value of d Au MoS 2 effectively limits the orbital overlap between Au and MoS 2 , and prevents any chemical bonding to occur. Indeed, our results are once again consistent with the literature: the formation of a van der Waals (vdW) gap between Au and MoS 2 was reported, as well as the interface to be characterized by weak dispersion forces. Such a weak interaction can be explained by the d-band model, as Au has fully occupied d bands. [START_REF] Zheng | Interfacial properties of bilayer and trilayer graphene on metal substrates[END_REF] Finally, we did not observe any significant structural rearrangement of the atoms of either Au or MoS 2 , confirming the weak interaction between the two materials. These findings correlate with the EDD map of the defect-free interface in Figure 6, which shows a very limited charge redistribution mainly at the surface of MoS 2 .

We then looked at defective Au-MoS 2 interfaces in the presence of small point defects. The DFT-optimized structures of such systems are shown in Figure 5. As can be seen from the figure, we found that introducing small point defects in MoS 2 caused, to some extent, the displacement of the atoms at the interface between the two materials. With both V S and V S2 such a displacement was limited, and involved mainly the atoms at the bottom-most layer of Au. Similarly, the change in d Au MoS 2 was not appreciable, its value being 2.73 Å and 2.70 Å in Au-V S and Au-V S2 , respectively. We note that the EDD maps of both structures essentially confirm the limited effect of such vacancies, as qualitatively such EDD maps do not significantly differ from that of the defect-free material. Interestingly, in the Au-V Mo interface we observed a significant variation of the crystal structure of the Au contact, presumably caused by the reactivity of the three S atoms in proximity of the Mo vacancy. Due to the lack of Mo, such S atoms change from a 3-fold coordination (typical of the defect-free material) to a 2-fold coordination, which explains the enhanced reactivity towards the Au surface. Indeed, although on average d Au MoS 2 did not vary with respect to the defect-free case, we observed the displacement of three Au atoms, which moved closer to the 2-fold S atoms with distances between 2.53 Å and 2.59 Å. The stronger orbital coupling between Au and V Mo can also be seen in Figure 6, where the charge redistribution is significant. The EDD is not limited to the interface region only but extends further into the second Au layer and throughout MoS 2 .

Au-Mo S Au-Mo2 S2 Au-Mo S2 Au-V Mo Au-V S Au-V S2 d Au-4|4E Au-4|4P Au-8|4

Pristine Au-Mo

S Au-Mo2 S2 Au-Mo S2 Au-V Mo Au-V S Au-V S2 Au-4|4E Au-4|4P Au-8|4
Regarding the interfaces with antisite Mo defects, we observed a significant displacement of both the atoms at the bottom-most Au layer and the extra Mo atom in the MoS 2 surface. As discussed in the previous section, and as can be seen from both Figure 2 and Figure 5, the substitutional Mo atoms filling the S vacancies do not lie on the same plane as the other S atoms. The bond length with the core Mo atoms of MoS 2 is longer than the typical Mo-S bond length. We predicted the average vertical separation between the antisite Mo atoms and the Au layer to be as short as 2.28 Å, 2.36 Å, and 2.22 Å in Au-Mo S , Au-Mo S2 , and Au-Mo2 S2 , respectively. Furthermore, the presence of the Au interface caused the displacement of antisite Mo atoms towards the bridge site between two Au atoms from the metal contact. In each of the Au-Mo S , Au-Mo S2 , and Au-Mo2 S2 systems we found the bond length between Mo and the two Au atoms to be 2.75-2.79 Å, a range of values comparable with the Au-Au bond length in the Au lattice (2.75 Å). This suggests a strong reactivity of Mo towards the Au surface, and most likely an enhanced orbital coupling between Au and MoS 2 . This is confirmed by looking at the EDD maps of these systems, where a significant charge redistribution around the extra Mo antisite atom occurs. Furthermore, we computed the electron localization function (ELF) of these systems, and we could confirm the formation of a chemical bond between the extra antisite Mo atom and the two Au atoms from the metal electrode. The ELF plot of the representative Au-MoS system is shown in Figure S4 in the Supporting Information.

Finally, given the widely experimentally reported abundance of V S in the material and the importance of such a defect on the functionality of 2D devices such as memristors, we additionally assessed the impact of V S concentration on the interface properties of Au-MoS 2 contacts. We point out that, by using the simulation cell described in the Simulation Details section, the initial defect concentration with one single S vacancy per unit cell was 6.4⇥10 13 cm 2 . By randomly introducing a second and a fourth S vacancy we achieved a higher defect concentration of 1.3⇥10 14 cm 2 and 2.6⇥10 14 cm 2 , respectively. Similarly to the case of a single S vacancy, we observed a small rearrangement of the Au atoms at the interface with MoS 2 , and a limited effect on the average value of d Au MoS 2 , which decreased from 2.71 Å to 2.67 Å (see Figure S1 in the Supporting Information). We expect such a decrease in d Au MoS 2 to have a limited impact on the orbital overlap between the two materials. This is corroborated by the EDD maps of both systems shown in Figure S2 (see Supporting Information). We note that this finding is in contrast with the work of Yang et al. [START_REF] Yang | Electrical doping effect of vacancies on monolayer MoS 2[END_REF] who performed similar studies on defective Au-MoS 2 interfaces and found that increasing the concentration of S vacancies led to the collapse of some Au atoms from the Au electrode to fill the S vacancies in MoS 2 . We could assume this to be an artifact of the simulation approach employed in their work, which involved a slab model of the Au interface rather than the more realistic Green's function surface model here used. Another reason could be that in their work the authors created a cluster of four S vacancies, whereas in our work we randomly introduced the S vacancies to avoid any artificial clustering or pattern.

When considering interfaces with GBs, shown in Figure 5, we observed a non-negligible decrease of the average interface distance not only with respect to the defect-free material but also to the material with point defects. Indeed, we found d Au MoS 2 = 2.43 Å, 2.50 Å, 2.63 Å in Au-4|4E, Au-4|4P, and Au-8|4, respectively. Interestingly, by looking at the DFT-optimized structures we observed a significant decrease of d Au MoS 2 in proximity of the grain boundary in both Au-4|4P and Au-8|4. Indeed, from Figure 5 it can be observed that the displacement of the Au atoms is significant above the GBs in MoS 2 . On the contrary, we found a more intimate contact (and thus an expected stronger orbital overlap) in Au-4|4E, where the interaction between MoS 2 and the Au electrode extends over the whole interface rather than being localized around the GB. This explains the shorter value of d Au MoS 2 with respect to the other two GBs here considered. The EDD maps of such systems in Figure 6 confirmed our findings: indeed, it is possible to observe a significant charge redistribution in the proximity of the 8|4 and 4|4P grain boundaries, whereas the charge redistribution in Au-4|4E is essentially delocalized over the entire MoS 2 surface.

Tunnelling Barriers

Tunnelling barriers and tunnelling probabilities are useful parameters that can be used to estimate the electron injection rate (and thus the charge transport) through the Au-MoS 2 contact. The tunnelling barrier is a consequence of the absence of covalent bonds between the 2D material and the Au electrode. A high probability of electron tunnelling suggests a strong orbital overlap between the two materials, and therefore a reduced contact resistance is expected. To extract such quantities, we computed the average effective potential (V eff ) of each interface structure, and we projected it along the direction of the Au-MoS 2 contact. By considering the shape of the potential barrier as a rectangle, the tunnelling Figure 7: Average effective potential of the defect-free Au-MoS 2 structure, projected along the direction of the interface (top). The bottom plot shows the zoomed area at the interface region. F TB is the vertical tunnelling barrier, whereas W is the barrier width. probability (T ) can then be defined as follows: 58

T = e 2 ⇣ q 2m h2 F TB ⌘ W , ( 1
)
where m is the electron mass, h is the reduced Planck's constant, F TB is the vertical tunnelling barrier, and W is the width of such barrier. As an example, Figure 7 shows the average effective potential of the defect-free Au-MoS 2 interface, in the proximity of the contact area. As can be seen from the figure, we calculated F TB as the difference between the minimum effective potential of Au and the value of the effective potential at the interface gap. [START_REF] Kang | Computational study of metal contacts to monolayer transition-metal dichalcogenide semiconductors[END_REF] A summary of the computed parameters for each Au-MoS 2 interface is shown in Table 2.

We first considered the defect-free interface, and we found a rather large tunnelling barrier (F TB = 3.54 eV), corroborating the contact between Au and MoS 2 to be weak and the orbital overlap limited. Interestingly, we note that experimental estimates of the Schottky barrier height (SBH) of Au-MoS 2 contacts range between 0.13-0.32 eV in MoS 2 -based FETs [START_REF] Kaushik | Schottky barrier heights for au and pd contacts to MoS 2[END_REF][START_REF] Kim | Fermi level pinning at electrical metal contacts of monolayer molybdenum dichalcogenides[END_REF] and 0.48±0.12 eV in MoS 2 exfoliated on template-stripped Au. [START_REF] Lee | Layer-dependent interfacial transport and optoelectrical properties of MoS 2 on ultraflat metals[END_REF] Moreover, theoretical simulations predicted this value to be higher but still within 1 eV. [START_REF] Gong | The unusual mechanism of partial fermi level pinning at metal-MoS 2 interfaces[END_REF][START_REF] Wang | A new insight for ohmic contacts to MoS 2 : by tuning MoS 2 affinity energies but not metal work-functions[END_REF] There appears to be a lot of variability in terms of SBH, which could be due to different experimental settings, a different quality of MoS 2 , and different device architectures. Nevertheless, we predicted F TB to be more than 3 times larger than the SBH obtained via simulations and also significantly larger with respect to the experimental values. This suggests F TB to have a very large contribution towards the contact resistance at the Au-MoS 2 interface, and therefore to possibly be one of the main limiting factors in the device performance. Indeed, the large tunnelling barrier resulted in a low tunnelling probabilty of 19.4%, suggesting a rather poor electron injection from the metal to the semiconductor, and therefore a high contact resistance. We point out that both values compare very well with those obtained by Wang et al. (F TB = 3.51 eV, T = 15.27%), who performed similar theoretical studies on unstrained and strained defect-free MoS 2 -metal interfaces. [START_REF] Wang | A new insight for ohmic contacts to MoS 2 : by tuning MoS 2 affinity energies but not metal work-functions[END_REF] However, in real devices to have a perfect MoS 2 sheet is very unlikely. Hence, it becomes extremely important to assess the effect of defects on tunnelling barriers and probabilities.

We then considered interfaces with the defective material, and we found that introducing sulfur mono-and di-vacancies in MoS 2 led to a slight increase of F TB , thus suggesting the worsening of the contact. Indeed, the tunnelling probability decreased to 18.5% and 18.3% in Au-V S and Au-V S2 , respectively. As previously discussed, we also increased the concentration of V S and we observed T to further decrease to 18.0% with four S vacancies. Overall, these results suggest that S vacancies have a detrimental effect on the quality of the Au-MoS 2 contact and on the electron injection rate. On the contrary, we observed the opposite effect when introducing one Mo vacancy: F TB decreased by a factor of 3 with respect to the pristine material (1.04 eV against 3.54 eV) and, as a consequence, T dramatically increased to 64.1% suggesting a significant decrease of the contact resistance. This correlates with the large atomic displacement observed at the interface discussed in the previous section due to the dangling bonds of the three S atoms surrounding the Mo vacancy. Antisite Mo defects also led to an overall decrease of the vertical tunnelling barrier, and to the increase of the tunnelling probability: we found T = 27.4%, 24.9%, and 29.4% in Au-Mo S , Au-Mo S2 , and Au-Mo2 S2 , respectively. Such an increased electron injection rate may be explained by looking at the extra Mo atom, which acts as a "connecting bridge" between the Au electrode and MoS 2 , thus facilitating the electron transfer between the two materials and also lowering the contact resistance. As previ-ously mentioned, this is confirmed by the ELF plot in Figure S4.

Overall, our results suggest that the presence of either di-or S mono-vacancies worsens the quality of the contact between Au and MoS 2 , whereas antisite Mo defects appear to bring a nonnegligible improvement. It is worth noting that vacancies (S and Mo) are generated mainly via CVD method, whereas antisite Mo defects via PVD. This means that the choice of the MoS 2 growth method is crucial, and needs to be considered extremely carefully when fabricating devices. For instance, from the point of view of the contact resistance only, PVD samples would probably be a good choice to improve the electron injection rate from the Au electrode to the 2D material. A reduced contact resistance would be undoubtedly beneficial for devices like FETs, in order to limit parasitic currents and to lower the power consumption. On the contrary, in devices like 2D memristors based on singlelayer MoS 2 , where a high-resistance state (HRS) is needed, PVD samples would probably hinder the whole device functionality, and thus we could argue that CVD-MoS 2 would be a much better choice. Mo vacancies also appear to exceptionally improve the contact between Au and MoS 2 , although we point out that in real samples the concentration of such a defect is orders of magnitude lower than that of S mono-vacancies. Thus, we expect the simulations carried out in this work to overestimate the impact of V Mo on the interface properties. Nevertheless, if Mo vacancies are desired these could also be introduced in the material via surface engineering, for instance by heavy ion irradiation [START_REF] He | Defect engineering in single-layer MoS 2 using heavy ion irradiation[END_REF] or by chemical treatment. [START_REF] Xie | Mo-vacancy induced high performance for photocatalytic hydrogen production over MoS 2 nanosheets cocatalyst[END_REF] Then, we focused on GBs and we observed that these also led to an overall non-negligible increase in the tunnelling probability (see Table 2): we found T = 27.3%, 24.8%, and 23.6% in Au-4|4E, Au-4|4P, and Au-8|4, respectively. This is once again consistent with the results discussed in the previous section: in general, the higher values of T with respect to the defect-free material correlate with the decrease of the average interface separation distance caused by the GBs, which led to the formation of some chemical bonds at the Au-MoS 2 interface. Moreover, the high tunnelling probability observed in Au-4|4E can be explained by the extended interaction between Au and MoS 2 , as previously discussed.

Overall, our results suggest that the unusual bonding of S and Mo at the boundary leads to an increased reactivity of MoS 2 towards the metal electrode. Therefore, in the context of 2D devices GBs may lead to extended areas with a locally-reduced contact resistance. GBs are inevitably formed during the material growth, and thus it is pivotal to be able to control the crystallinity of MoS 2 in order to control, in turn, the concentration and the type of GBs. As our results showed that GBs improve the electron injection, it may be beneficial to engineer such extended defects in order to increase their concentration, which could reach very high values up to 10 12 cm 2 . [START_REF] He | Engineering grain boundaries at the 2d limit for the hydrogen evolution reaction[END_REF] This could be achieved, for instance, with annealing, mechanical strain, and irradiation. [START_REF] Man | Functional grain boundaries in two-dimensional transition-metal dichalcogenides[END_REF][START_REF] Wang | Grain-boundary engineering of monolayer MoS 2 for energy-efficient lateral synaptic devices[END_REF]

Electronic Properties

Finally, we looked at the DOS of the interface structures, projected onto the 4d orbitals of the core Mo atoms of MoS 2 , as shown in Figure 8. By looking at the PDOS of the defect-free Au-MoS 2 interface it is possible to observe that the band gap of the 2D material is mostly retained, suggesting a very limited band hybridization between MoS 2 and the 5d orbitals of Au. Once again, as previously discussed, this is consistent with the formation of a weak vdW gap between Au and MoS 2 , and with the low electron injection rate. Additionally, we note a significant shift of the Fermi level towards the conduction band edge of MoS 2 , suggesting the n-type doping of the 2D material, consistently with both experiments and previous theoretical findings. [START_REF] Kang | Computational study of metal contacts to monolayer transition-metal dichalcogenide semiconductors[END_REF][START_REF] Qiu | First-principles study of vacancy defects at interfaces between monolayer MoS 2 and au[END_REF][START_REF] Fontana | Electron-hole transport and photovoltaic effect in gated MoS 2 schottky junctions[END_REF] Sulfur mono-and di-vacancies added a number of additional intra-gap states above the Fermi level of the system, as could also be seen in the free-standing material (see Figure 3). However, as the interaction between the two materials is still weak, we note that the band gap of MoS 2 is essentially retained, and its metallization limited. We found similar results when increasing the concentration of S vacancies, as can be seen in Figure S3 in the Supporting Information. Interestingly, in Au-V Mo it is possible to observe a high number of interfacial gap states, extending from the conduction band into the original material's band gap. Moreover, we note that these states cross the Fermi level of the system, suggesting a strong band hybridization and the metallization of MoS 2 . This further corroborates our previous findings on the very strong interaction between the metal contact and the 2D material with Mo vacancies. It should be noted, as previously mentioned, that the concentration of V Mo would be much lower in real samples, and therefore the impact of such a defect is most likely to be more limited.

On average, with Mo antisite defects we could observe a more significant metallization of MoS 2 with respect to both Au-V S and Au-V S2 . For each of the structures (Au-Mo S , Au-Mo S2 , Au-Mo2 S2 ) the presence of interfacial gap states induced by the Au electrode is evident. We assume this effect to be due to the presence of the extra antisite Mo atom on the MoS 2 surface: as discussed in the previous sections, such Mo atom is able to bridge the Au electrode with the 2D material, effectively facilitating the orbital overlap and increasing the electron injection rate (see Table 2). On a final note, we observed a negligible spin magnetic moment in Au-Mo S and Au-Mo S2 , differently from the free-stading material (see also Figure 3). Moreover, Au-Mo2 S2 showed a significant decrease of the spin magnetic moment from 4.0 µ B (in the free-standing material) to 0.7 µ B . This effect could be explained by the dislocation of the extra Mo atom upon contacting MoS 2 with the Au electrode. Such a dislocation leads to the loss of one Mo-Mo bond, thus removing the magnetism. Therefore, the magnetic moment in Au-Mo2 S2 derives from the second antisite Mo atom which dislocated from its original position only partially.

Among the interfaces with GBs, Au-4|4E is the structure that shows the most significant metallization, and this is the case also when compared with the systems in the presence of point defects. We could argue this to be the consequence of the extended interaction of 4|4E with the metal electrode, as our previous results suggested (see EDD maps in Figure 6). We observed a significant band hybridization between Au and MoS 2 also in Au-4|4P and Au-8|4, although somewhat less evident than in the previous case. On a final note, as we did not observe any significant spin magnetic moment in Au-4|4P, we assume the peak in the PDOS at ⇠-0.7 eV in the spin down channel to be due to some numerical error in the adopted DOS integration scheme.

Conclusions

To conclude, we used density functional theory simulations to extensively investigate the impact of both point and extended defects on the properties of MoS 2 in contact with the Au electrode. To accurately simulate realistic Au-MoS 2 interfaces we employed a surface model based on the Green's function formalism. We chose to focus mainly on the most abundant defects with either CVD (that is, V S , V S2 , V Mo ) or PVD (i.e., Mo S , Mo S2 , Mo2 S2 ) growth processes. Among the grain boundaries, we modelled three representative cases characterized by a tilt angle of 60 (4|4P, 4|4E, 8|4). See Figure 2 and Figure 4 for the optimized geometries of point defect and grain boundary structures, respectively.

First, in order to decouple the effect of the Au electrode from that of defects in MoS 2 , we investigated the impact of small point defects and grain boundaries on the electronic properties of freestanding single-layer MoS 2 . We found that each point defect caused the appearance of a number of extra states in the original material's band gap, as can be seen in Figure 3. For instance S mono-and di-vacancies led to extra gap states located above the Fermi level and near the conduction band edge of the material, whereas one single Mo vacancy introduced a higher number of deep mid-gap states both above and below the Fermi level of MoS 2 . Similarly, we observed that also antisite Mo defects introduced intra-gap states and caused a non-zero spin magnetic moment in the material. Finally, we could observe that grain boundaries 4|4P and 4|4E behave as "metallic-like strips" in MoS 2 by leading to the formation of a high number of intra-gap states extending throughout the whole original material's band gap. Contrary to such a behavior, we found 8|4 to cause extra mid-gap states located above the Fermi level of the material. Therefore, it is evident that defects have a non-negligible effect on the electronic properties of MoS 2 .

In the second and main part of this work we constructed interfaces between both pristine and defective MoS 2 and the Au(111) electrode. More specifically, we explored: i) how the structure of both materials changed upon the formation of the contact; ii) the impact of defects on the orbital overlap and the metal-to-MoS 2 tunnelling probability; iii) how the electronic properties of defected MoS 2 are affected by the presence of the metal electrode.

We started to model the defect-free interface, and we found that the contact between Au and MoS 2 is characterized by weak dispersion interactions, i.e., a van der Waals gap. From the structural point of view, we could corroborate this by the large interface separation distance (2.71 Å) between the materials (see Figure 5), and by computing the electron density difference (EDD) map of the whole system upon the formation of the contact, shown in Figure 6. Indeed, the EDD map showed that there is some limited charge redistribution mainly at the MoS 2 surface. In general, a weak vdW gap would correlate with a low electron injection rate and with a limited effect on the electronic properties of the 2D material. Our simulations confirmed such an hypothesis, as we found a low tunnelling barrier of 19.4% (shown in Table 2) and no metallization of MoS 2 (see PDOS in Figure 8).

Then we started introducing defects in the material, and we found that S vacancies led to an overall small decrease of the quality of the metal contact. On average, the interface distance between Au and MoS 2 did not change but we could observe some degree of disorder in the bottom-most Au layer, leading to a limited atomic rearrangement in the metal. Electron injection rates from the metal to the 2D material were found to slightly decrease with respect to the pristine case to 18.5-18.3%, and once again we could not observe the significant formation of interfacial gap states. Interestingly, increasing the concentration of S vacancies up to 10 14 cm 2 further decreased the tunnelling probability up to 18.0%. On the other hand, the Mo single vacancy significantly improved the quality of the contact, as we could see by the relaxed interface geometry and the EDD map, which shows a significant charge redistribution in both MoS 2 and the Au electrode. Moreover, the tunnelling probability dramatically increased to 64.1%, confirming the higher level of hybridization between the Au 5d orbitals and the 3p and 4d orbitals of S and Mo, respectively. Such an hybridization can be also observed in the PDOS of the system in Figure 8. As the PDOS crosses the Fermi level, we can also note the metallization of MoS 2 .

In the case of antisite Mo defects, we observed an overall improvement of the Au-MoS 2 contact, and our results suggest this to be due to the presence of the extra Mo atom acting as a conductive bridge between the electrode and the 2D material. EDD maps corroborate this, as a large charge redistribution can be observed on the antisite Mo. Indeed, we found this to correlate with an improved electron injection rate, which increased above ⇠25% for each of the three antisite Mo systems here considered. Also, the presence of interfacial gap states in the MoS 2 PDOS was evident.

The presence of grain boundaries led to a shorter interface separation between Au and the 2D material. This should correlate with a better electron injection rate and a strongerAu-MoS 2 interaction. Indeed, this was later confirmed by our further simulations: tunnelling probabilities increased up to 27.3%, and once again the increased orbital overlap was evident by looking at the formation of interfacial gap states in the PDOS plot of each system.

In conclusion, our results showed that defects have a significant impact on the Au-MoS 2 contact properties by either worsening or improving the quality of the MoS 2 -metal interface. Interestingly, we point out that S vacancies, which have a detrimental effect, are generated mainly via CVD, whereas Mo antisite defects, which instead improve the contact, mainly with PVD. This shows how crucial the MoS 2 growth method is, as it does not only influence the material itself but also the properties at the metal contact. Based on our results, we could argue that, from the point of view of the quality of the metal contact, PVD-MoS 2 should lead to a decrease in the contact resistance. This should be beneficial in devices like 2D-FETs to reduce the power consumption and to improve the performance. On the contrary, CVD-MoS 2 might be preferred in devices like memristors based on single-layer MoS 2 , as S vacancies appear to have a central role in the device working mechanism. Mo single vacancies, which dramatically improve the electron injection rate, are also mainly generated via CVD, however the typical Mo defect density is orders of magnitude lower than that of S mono-vacancies. Here, defect engineering might be a viable solution to increase the concentration of such a vacancy to improve the contact. The grain boundaries considered in this work were all shown to reduce the average interface distance, and therefore if the aim is to increase the metal-to-MoS 2 tunnelling probability, the engineering of the grain boundaries could also be a viable option to increase the concentration of such extended defects.

Clearly, it is worth noting that in real devices other factors may further complicate the quality of the metal-MoS 2 interaction. For instance, it is highly likely that more than a single type of defect is present in the material. Similarly, defects and grain boundaries are likely to coexist in MoS 2 . Extra adatoms deriving either from the growth or the transfer processes may also be present. Nevertheless, we expect our study to provide guidance on how to design metal contacts depending on the device application, and to which growth technique may be best suited for the purpose.

Figure 1 :

 1 Figure 1: Schematics of the Green's function surface model used in this work to simulate Au-MoS 2 interfaces. The structure here shown is the optimized interface at the PBE-D2 level between Au and pristine MoS 2 . On the left side, the fully periodic bulk Au electrode is shown, whereas on the left side the surface-vacuum interface can be seen.

Figure 2 :

 2 Figure 2: Optimized structures at the PBE level of the 5⇥5 hexagonal supercells of pristine and defective MoS 2 . Starting from the top left and following the pristine material, V S stands for sulfur mono-vacancy, V S2 for sulfur di-vacancy, and V Mo for molybdenum vacancy. Those in the bottom are all antisite Mo defects, where Mo S represents the antisite Mo atom filling one S mono-vacancy, Mo S2 the same antisite atom filling one S di-vacancy, and Mo2 S2 two Mo antisite atoms filling one S di-vacancy. For each antisite Mo defect the side view of the optimized structure is also shown for clarity.

Figure 3 :

 3 Figure 3: Projected density of states (PDOS) of pristine and defective MoS 2 with the inclusion of small point defects and grain boundaries. The projections are onto the relevant atomic orbitals of Mo and S. The plots are centered around the Fermi level of each system, and the curves were obtained with a Gaussian smearing of 0.05 eV.

Figure 4 :

 4 Figure 4: Optimized structures at the PBE level of the grain boundaries (GBs) in MoS 2 considered in this work.

Figure 5 :

 5 Figure 5: Optimized structures at the PBE-D2 level of the Au-MoS 2 interfaces with the inclusion of point defects (top) and grain boundaries (bottom). For clarity, the structures are shown in the proximity of the interface between the two materials. The parameter d is defined as the average interface separation distance.

Figure 6 :

 6 Figure 6: Electron density difference (EDD) maps of the Au-MoS 2 interfaces considered in the present study. Point defects are shown at the top, whereas GBs at the bottom. The red isosurface refers to electron enrichment, whereas the blue isosurface to electron loss. Isovalue is 0.002 eV/ Å3 .

Figure 8 :

 8 Figure 8: Projected density of states (PDOS) obtained from the Green's function surface simulations of Au-MoS 2 interfaces with the inclusion of grain boundaries, centered around the Fermi level of each system. The projections are onto the 4d orbitals of the core Mo atoms of MoS 2 .

Table 1 :

 1 Simulation cell parameters of Au-MoS 2 interfaces with the inclusion of GBs.

	Parameter Au-4|4E Au-4|4P	Au-8|4
	a ( Å)	45.9004	53.9631	53.2194
	b ( Å)	3.19013	3.16922	5.54199
	c ( Å)	49.3090	47.6598	49.3582
	a	90.0000	90.0000	90.0000
	b	90.0000	90.0000	90.0000
	g	93.3374	100.116	65.3823

Table 2 :

 2 Summary of the interface parameters of Au-MoS 2 contacts computed in this work. d Au MoS 2 is the average interface distance, F TB is the vertical tunnelling barrier, and T is the tunnelling probability. In the three antisite Mo defect structures, the average vertical separation between the extra Mo atom and the Au bottom layer is also shown in parentheses.

	Structure	d Au MoS 2 ( Å) F TB (eV) T (%)
	Pristine	2.71	3.54	19.4
	Au-V S	2.73	3.55	18.5
	Au-V S2	2.70	3.64	18.3
	Au-V Mo	2.71	1.04	64.1
	Au-Mo S	2.71 (2.28)	2.87	27.4
	Au-Mo S2	2.71 (2.36)	3.07	24.9
	Au-Mo2 S2	2.71 (2.22)	2.77	29.4
	Au-4|4P	2.50	3.19	24.8
	Au-4|4E	2.43	3.02	27.3
	Au-8|4	2.63	3.23	23.6

Acknowledgement

The authors ackowledge funding from the European Union's Horizon 2020 research and innovation programme, EU H2020 NeurONN project (www.neuronn.eu), grant agreement No. 871501. This work was granted access to the HPC/AI resources of CINES (Centre Informatique National de l'Enseignement Supérieur) under the allocation 2020-A0090811060 made by GENCI (Grand Équipement National de Calcul Intensif).


Mathieu Blot

Olivier Disson

Alexandre Leclercq

Alexandra Moura

Hélène Bracq-Dieye

Pierre Thouvenot

Guillaume Valès

Barbara Burroni

Audrey Lupo

Marc Lecuit
email: marc.lecuit@pasteur.fr

Caroline Charlier
email: caroline.charlier@pasteur.fr

Listeria-associated lymphadenitis: a series of 11 consecutive cases and review of the literature

Keywords: Listeria monocytogenes, adenitis, cancer

We studied 11 cases of culture-proven Listeria-associated lymphadenitis reported to the French National Reference Center for Listeria from 1994 to 2019, and 8 additional published cases.

Listeria-associated lymphadenitis is rare but associated with a mortality as high as for invasive listeriosis, and frequently diagnosed with concomitant neoplasia.

Introduction

Listeria monocytogenes (Lm) is responsible for listeriosis, a severe foodborne infection mostly reported in immunocompromised patients where it mostly presents as septicemia and neurolisteriosis, it is also responsible for maternal-neonatal infection. Focal infections are rare, consecutive to hematogenous seeding or direct inoculation [START_REF] Charlier | Listeria monocytogenes-associated joint and bone infections: a study of 43 consecutive cases[END_REF] . Among them, Lm-associated lymphadenitis have not been characterized. We undertook a national retrospective study of this presentation over the last 25 years and identified 11 cases, and reviewed the 8 published cases.

Patients and methods

Data collection -French surveillance of human listeriosis relies on mandatory reporting since 1999 with strains submission to the French National Reference center for Listeria (NRCL) [START_REF] Goulet | Surveillance of human listeriosis in France, 2001-2003[END_REF] .

Reporting exhaustiveness is 87% [START_REF] Morgand | Listeria monocytogenes-associated respiratory infections: a study of 38 consecutive cases[END_REF] . We retrospectively studied culture-proven Listeriaassociated lymphadenitis cases reported from January 1994 to December 2019. All cases with mention of "lymphadenitis", "lymph node infection" or "abscess" were reviewed. A confirmed case was defined as a patient from whom Listeria was isolated by culture of a lymph node.

Eleven cases were identified, their medical charts reviewed, and bacterial isolates sequenced.

Ethical evaluation Because of the observational nature of the study with all data collected as a part of French National Surveillance, it did not request patients' written consent nor formal Institutional Review Board approval, according to the French legislation.

Review of the literature -We searched the PubMed database for reports between January 1966 and December 2019, using the terms "Listeria", "listeriosis", "lymphadenitis", "lymph node" without language restriction [START_REF] Goulet | Effect of prevention measures on incidence of human listeriosis, France, 1987-1997[END_REF][START_REF] Betriu | Cervical adenitis due to Listeria monocytogenes[END_REF][START_REF] Nieman | Listeriosis in adults: a changing pattern. Report of eight cases and review of the literature, 1968-1978[END_REF][START_REF] Bojsen-Moller | Human listeriosis. Diagnostic, epidemiological and clinical studies[END_REF][START_REF] Blanche | Lymph node listeriosis in a HIV infected patient[END_REF][START_REF] Ferrer | Listeriosis in the adult: presentation of 14 cases][END_REF][START_REF] Rosenthal | Cervical lymphadenitis--a rare case of focal listeriosis[END_REF] .

L. monocytogenes characterization -Species identification was carried out with API-Listeria microgallery (bioMérieux, Marcy l'Etoile, France) before January 2017, and then MALDI-TOF mass spectrometry [START_REF] Thouvenot | MALDI-TOF mass spectrometry-based identification of Listeria species in surveillance: A prospective study[END_REF] . Genome sequencing was performed as described [START_REF] Moura | Whole genomebased population biology and epidemiological surveillance of Listeria monocytogenes[END_REF] . PSR serogrouping, Multilocus sequence types (MLST) and core genome MLST profiles were deduced from genome assemblies using the BIGSdb-Lm platform (https://bigsdb.pasteur.fr/listeria) [START_REF] Moura | Whole genomebased population biology and epidemiological surveillance of Listeria monocytogenes[END_REF] .

Histopathological analyses -We studied 2 available case-samples: 5μm-thick sections of paraffin-embedded tissue specimens were performed. Listeria was labeled by immunohistochemistry using a polyclonal rabbit antiserum (R12) that detects Lm serotype 1/2a (Listeria O I/II) or 4b and Listeria ivanovii (Listeria O V/VI antiserum Seiken kit; Denka Seiken Co., Tokyo, Japan), and a goat anti-rabbit antibody coupled to peroxidase (EnVision+, Dako), followed by hematoxylin counterstaining. Images were captured on AxioImager A2 microscope with AxioCam ICc 1 digital camera (Zeiss).

For immunofluorescence staining, paraffin-embedded tissues were deparaffinized, and antigens retrieved by citric acid buffer. Samples were stained with R12 antibody for Lm serotype I/IIa 1 or Listeria O V/VI for Listeria ivanovii and a goat anti-rabbit antibody conjugated with Alexa Fluor© 546 (Invitrogen) together with Hoechst 33342. Images were captured on a LSM710 confocal microscope (Zeiss).

Results

Clinical cohort -Among 7,643 human cases collected between 1994 and 2019 in France, 11

were Lm-associated lymphadenitis (0.14%). Eight more published cases were identified, including six with some clinical data available. The 19 cases are listed in Table 1.

Epidemiological features -Ten patients (10/18, 56%) were male. Median age [interquartile range] age was 65 years [57-79]. Four patients (4/18, 22%) were ≥ 80-year-old. Sixteen (16/18, 89%) presented 1-3 immunosuppressive comorbidities, either preexisting (n=12), or revealed by listeriosis (n=4): diabetes was reported in 12/18 (67%), alcoholism and neoplasia each in 4/18 (22%); neoplasia was diagnosed shortly before (case 8), concomitantly (cases 3 and 11), or shortly after (case 18) the diagnosis of lymphadenitis (no patient had received chemotherapy at lymphadenitis onset); myelofibrosis with chronic neutropenia and HIV infection were also reported (n=1, each).

Clinical features -Median [IQR] time from first symptom to diagnosis was 4 weeks ([3-4]

weeks, n=10). Lymphadenitis was isolated (9/15, 60%) or multiple (6/15, 40%). All involved a single unilateral area: cervical (14/19, 74%), inguinal (3/19, 16%), supraclavicular or iliac (1/19, 5% each). Lesions were bulky in 12/15 (80%). Suppuration was evidenced clinically and/or by computed tomography or ultrasound imaging in 7/16 (44%). Five patients (5/13, 38%) reported fever. No neurological involvement was reported. One patient with inguinal lymphadenitis exhibited concomitant intertrigo and lower limb cellulitis, another with cervical adenitis had concomitant upper lobe consolidation pneumonia that resolved respectively with amoxicillin/clavulanate and amoxicillin/gentamicin. Another patient with iliac lymphadenitis had confirmed Listeria-associated appendicitis.

Laboratory characteristics and microbiological features -Median leucocyte count [IQR]

was 10,150 /mm 3 [6,250-10,525] (n=6), median C-reactive protein level [IQR] was 42 mg/L [36-54] (n=5). Listeria was isolated from pus or tissue culture in 17/17 cases. In one patient (case 10, iliac lymphadenitis), samples also grew Streptococcus anginosus and anaerobic flora.

Blood cultures, when performed, were all negative (4/4). L. monocytogenes was identified in 10/11 (91%) cases, L. ivanovii in one. Distribution of Lm clonal complexes was as follows: two isolates belonged to CC2 and CC4 hypervirulent clones, two belonged to hypovirulent clones CC9 and 121, others belonged to clones with intermediate virulence (Table 1). Histopathological findings -Histopathological reports were available for 8 patients, and showed epithelioid granuloma in 6/8 (75%, including 2 with necrosis), chronic lymphadenitis or metastatic gynecological carcinoma without epithelioid granuloma (1/8, 13% each). Listeria could be identified in samples of two cases (cases 6 and 10), by immunoperoxidase staining (Figure 1A,B,E,F) and immunofluorescence (Figure 1C,D,G,H). Bacteria were localized mostly in cells having a morphology evocative of monocytes/macrophages and also in polymorphonuclear cells (Figure 1B,F).

Treatment and follow-up -Management relied on surgery in 16/16 cases (100%): puncture (6/16, 38%), surgical drainage (4/16, 25%), or excisional biopsy (6/16, 38%). Antibiotics were administered in' 11/13 (85%) and relied on amoxicillin (n=4), amoxicillin-clavulanate (n=2), amoxicillin and gentamicin (n=3), cotrimoxazole or pefloxacin (n=1, each), for a median [IQR] of 21 [15-28] days (n=10). Thirteen patients (13/17, 76%) recovered; one reported protracted recurrence requiring prolonged antibiotics (6%). Three patients (3/17, 18%) died within 3 months, immediately after surgical procedure (n=1, no autopsy performed) or as a consequence of concomitant neoplasia (n=2, including one patient for whom autopsy findings revealed myocardial ischemia and bladder carcinoma).

Discussion

We studied the detailed clinical and microbiological features of Lm-associated lymphadenitis in a cohort of 19 patients, including 11 from the French cohort and the 8 previously published cases. Several conclusions can be drawn.

First, although rare, Lm-associated lymphadenitis is a genuine disease entity, whose mortality is as high as invasive listeriosis [START_REF] Charlier | Clinical features and prognostic factors of listeriosis: the MONALISA national prospective cohort study[END_REF] . In line with this observation, most patients presented predisposing conditions associated with invasive listeriosis, namely older age and immunosuppressive comorbidities, including diabetes, alcoholism and ongoing neoplasia [START_REF] Charlier | Clinical features and prognostic factors of listeriosis: the MONALISA national prospective cohort study[END_REF] .

Lm-associated lymphadenitis and cancer were diagnosed concomitantly in four patients, in the range reported in non-maternal invasive listeriosis (22% versus 20%) [START_REF] Charlier | Clinical features and prognostic factors of listeriosis: the MONALISA national prospective cohort study[END_REF] . None had received antitumoral chemotherapy at lymphadenitis onset, possibly reflecting tumor-associated immunosuppression. Indeed, studies in a BALB/c model of mammary carcinoma have shown that Lm survives and multiplies in the tumoral microenvironment, while rapidly killed in healthy tissues [START_REF] Chandra | Myeloid-derived suppressor cells have a central role in attenuated Listeria monocytogenes-based immunotherapy against metastatic breast cancer in young and old mice[END_REF] . This selective survival and growth is linked to the recruitment of myeloid-derived suppressor cells that produce interleukin 10 and TGF-β that could help Lm escape the cellular immune response at the tumor site [START_REF] Chandra | Myeloid-derived suppressor cells have a central role in attenuated Listeria monocytogenes-based immunotherapy against metastatic breast cancer in young and old mice[END_REF] . It indicates that patients with Lm-associated lymphadenitis should be evaluated for neoplasia, mainly in the affected lymph node or loco-regionally.

Seeding from a loco-regional portal of entry is a possibility, considering the negativity of blood cultures, the absence of neurolisteriosis and the involvement of a single lymph node, even though one cannot exclude it may also result from bacteremia. The predominant cervical involvement may follow translocation in the mucosa-associated lymphoid tissue of the pharyngo-oral region. Listeria can indeed be detected in tonsils of wild animals [START_REF] Quereda | Listeria valentina sp. nov., isolated from a water trough and the faeces of healthy sheep[END_REF][START_REF] Weindl | Listeria monocytogenes in Different Specimens from Healthy Red Deer and Wild Boars[END_REF] and also in humans [START_REF] Bakulov | Listeriosis of animals: problems and research[END_REF] . The case with appendicitis likely results from Listeria translocation across the MALT tissue of the appendix (Peyer's patches).

Management should include drainage of suppurative lesions or excisional biopsy, and Listeriatargeting amoxicillin-based antimicrobial therapy, which is otherwise not recommended in suppurative lymphadenitis, where Staphylococcus aureus should be covered.

Since the review of literature was not performed according to PRISMA guidelines, some cases may have been overlooked and the total number of published cases may this be higher.

In conclusion, Listeria monocytogenes-associated lymphadenitis is rare but associated with a mortality as high as for invasive listeriosis. Patients with Lm-associated lymphadenitis should be evaluated for concomitant neoplasia.

Figure 1 .

 1 Figure 1.

Table 1 .

 1 Features of 19 patients with Listeria monocytogenes-associated lymphadenitis.

					Clinical and Imaging features
	Reference	Patient No	Age at Diagnosis, Sex, Underlying Diseases	Symptoms duration before diagnosis	Localization	Size, Number	Signs of Abscess	General and Associated Signs	Blood Cultures	Species and MLST Clonal Complex	Histopathology	Treatment, Surgery, Antibiotics	Outcome
			72-year-old man,
			Essential
			thrombocythemia,										2 recurrences
	This study	1	myelofibrosis, chronic neutropenia, unbalanced	3w	Right cervical and under the chin	Bulky, Multiple (CT-scan)	No	Pneumonia Negative	Listeria monocytogenes CC121	NP	Puncture. Amoxicillin (26d) + Gentamicin (5d)	treated with Amoxicillin (3 then 4w). Cure (4m).
			diabetes,										Death(1y).
			prednisone
			7.5mg/d
	This study	2	63-year-old man, Uncontrolled diabetes (glycated hemoglobin 17.4%), tobacco	1m	Right cervical	Bulky (6.5x8cm; CT-scan), Single	Inflammatory mass (C) and Necrotic (CT-scan)	Weight loss (12kg)	NP	Listeria monocytogenes CC4	NP	Puncture. Amoxicillin + Gentamicin.	Cure. Death (4y, hepatocellular carcinoma)
			smoke, alcoholism.
												Amoxicillin-
	This study	3	88-year-old woman. Parkinson's and Alzheimer's diseases	3w	Right inguinal	Bulky, Single (C)	No	Lower limb cellulitis	NP	Listeria monocytogenes CC2	Infiltration with gynecological carcinomatous cells	clavulanate (10d): persistence. Lymph node removal. Amoxicillin	Discovery of a metastatic gynecological carcinoma. Death (2.5m)
												6g/d.
	This study	4	82-year-old woman. II diabetes, obesity Uncontrolled type	3m	Left cervical	Bulky Single (US) (5cm, C),	No (US)	No	NP	Listeria CC9 monocytogenes	NP	Surgical antibiotic. drainage. No	Death (1d)

Acknowledgements

We thank David Hardy from Experimental Neuropathology Unit, Institut Pasteur Paris, for section preparations. We thank Dr Marie-Albane Bensussan (University Hospital, Amiens), Dr Stéphane Bland and Dr Helene Petitprez (Annecy-Genevois Hospital), Pr Karine Aubry (University Hospital, Limoges), Dr Burroni Barbara (Cochin University Hospital, Paris), Dr Jean Puyhardy (HIA Legouest hospital, Metz), Dr Barrans Alain (Bassin de Thau Hospital, Sete).

Funding: Institut Pasteur, INSERM and Santé Publique France.

Potential conflict of interest: none