Brice Le Borgne
email: b.h.leborgne@surrey.ac.uk

Aurélie Girard

Christophe Cardinaud

Anne-Claire Salaün

Laurent Pichon
email: laurent.pichon@univ-rennes1.fr

Florence Geneste
email: florence.geneste@univ-rennes1.fr

Covalent functionalization of polycrystalline silicon nanoribbons applied to Pb(II) electrical detection

Keywords: Silicon nanoribbons, Aryl-diazonium salts, Functionalization, Chemical sensors

Although recent studies in the field of nanomaterials have allowed the realization of highly sensitive sensors, research regarding new types of functionalization of nanostructures to reach high selectivity are still missing. Here, a simple electronic device based on polycrystalline

silicon (poly-Si) nanoribbons used for lead detection is presented. This device is functionalized by reduction of aryl diazonium salts in order to detect heavy metals. The effectiveness of the grafting process and thickness homogeneity of the coating layer were evaluated by XPS and NanoSIMS techniques. The preconcentration of lead (Pb 2+ ) at the surface of the functionalized nanostructures was substantially verified. Finally, electrical characterization of the resistors based on the functionalized nanoribbons, showed that the sensitivity to these species is increased in the concentration ranging from 10 -7 to 10 -5 mol L -1 . This technique could pave the way for use of complexing agents to enhance heavy metal detection.

Introduction

Lead is one of the heavy metals, of which its presence in water at high concentrations has become a growing concern. Heavy metals form an important class of pollutants [1]. They can be found in water naturally but also due to mining, agriculture and industry. Detecting and eliminating heavy metals is of concern because they are highly persistent and not generally degraded by bacteria. They are toxic and their accumulation in living cells leads to serious pathologies [2]. Some heavy metals have been subject to severe regulations due to high levels of toxicity even in trace amounts. Thus, exposure to heavy metals may result in cancer, damage to the kidneys and even death in some cases where concentration levels are very high [3].

The mass production of silicon based components allows the realization of low-cost, easy to process and fully embeddable electronic raw material. Polycrystalline silicon (poly-Si) is one of the many forms of silicon, which is composed of a combination of silicon crystals and solar cells [START_REF] Dore | Progress in laser-crystallized thinfilm polycrystalline silicon solar cells: intermediate layers, light trapping, and metallization[END_REF][START_REF] Becker | Polycrystalline silicon thin-film solar cells: Status and perspectives[END_REF], strain gauges [START_REF] French | Piezoresistance in polysilicon and its applications to strain gauges[END_REF][START_REF] Mosser | Piezoresistive pressure sensors based on polycrystalline silicon[END_REF] or diodes [START_REF] Card | Studies of tunnel MOS diodes I. Interface effects in silicon Schottky diodes[END_REF]. One of its deposition technique is Low-Pressure Chemical Vapor Deposition (LPCVD) which can provide good homogeneity of the silicon in terms of thickness, doping concentration and stability.

Most electronic sensors are based on field effect transistors (FETs) which have proven high sensitivity and electrical performances [START_REF] Estrela | Chemical and biological sensors using polycrystalline silicon TFTs[END_REF][START_REF] Knopfmacher | Highly stable organic polymer field-effect transistor sensor for selective detection in the marine environment[END_REF][START_REF] Chen | Sensitivity and detection limit analysis of silicon nanowire bio (chemical) sensors[END_REF]. However, they require several photolithography processes, plasma etching and deposition steps that can provide reproducibility drawbacks. In contrast, new passive devices such as resistors have recently shown that they enable chemical species detection, exhibiting low detection limits (e.g. for gases [START_REF] Frazier | Fully-drawn carbon-based chemical sensors on organic and inorganic surfaces[END_REF] or biological materials [START_REF] Nikolaides | Silicon-on-Insulator Based Thin-Film Resistor for Chemical and Biological Sensor Applications[END_REF]). More specifically, poly-Si is very sensitive to charged species although its fabrication process is less demanding and cheaper.

Nanostructures such as nanowires [START_REF] Irvine | Single-electron effects in heavily doped polycrystalline silicon nanowires[END_REF][START_REF] Yen | Label-free and real-time detection of ferritin using a horn-like polycrystalline-silicon nanowire field-effect transistor biosensor[END_REF][START_REF] Hakim | Thin film polycrystalline silicon nanowire biosensors[END_REF] or nanoribbons [START_REF] Zeimpekis | Dual-gate polysilicon nanoribbon biosensors enable high sensitivity detection of proteins[END_REF][START_REF] Sun | Effect of subthreshold slope on the sensitivity of nanoribbon sensors[END_REF] can be obtained from few nanometers thick poly-Si layers by LPCVD at low temperature (< 600°C) [START_REF] Pichon | Thin film transistors fabricated by in situ doped unhydrogenated polysilicon films obtained by solid phase crystallization[END_REF][START_REF] Matsuyama | Highquality polycrystalline silicon thin film prepared by a solid phase crystallization method[END_REF]. These nanostructures offer interesting potential for chemical species detection so far as their high surface/volume ratio enables them to have a high exchange surface between analyte and sensitive material. Furthermore, they can be easily functionalized using miscellaneous materials such as antibodies [START_REF] Stern | Label-free immunodetection with CMOScompatible semiconducting nanowires[END_REF] or DNA [START_REF] Godem-Wenga | Polysilicon nanowires based field effect transistor compatible with MOS technology for integrated labelfree direct detection of DNA hybridization[END_REF] in order to reach selectivity to targeted species.

Aryl-diazonium salts are frequently used to functionalize semiconductors [START_REF] Pinson | Attachment of organic layers to conductive or semiconductive surfaces by reduction of diazonium salts[END_REF], particularly crystallized silicon-based surfaces [START_REF] Stewart | Direct covalent grafting of conjugated molecules onto Si, GaAs, and Pd surfaces from aryldiazonium salts[END_REF] and their spontaneous grafting on poly-Si layers has been previously demonstrated [START_REF] Girard | Effect of doping on the modification of polycrystalline silicon by spontaneous reduction of diazonium salts[END_REF]. This efficient and fast grafting process leads to a strong covalent bond and monolayers or thin films, can be obtained in well-controlled conditions [START_REF] Allongue | Organic monolayers on Si (111) by electrochemical method[END_REF][START_REF] Allongue | Structural characterization of organic monolayers on Si <111> from capacitance measurements[END_REF]. Nevertheless, the potential of aryl diazonium grafting at the nanostructures surface has been marginally investigated to date [START_REF] Haight | Controlling the electronic properties of silicon nanowires with functional molecular groups[END_REF][START_REF] Balasubramanian | Chemically functionalized carbon nanotubes[END_REF].

A C C E P T E D M A N U S C R I P T
The interest of a complexing agent to accumulate heavy metal ions at the surface of sensors has been previously demonstrated. Indeed, some complexing agents for Cd [START_REF] Fan | Determination of Cd2+ and Pb2+ on glassy carbon electrode modified by electrochemical reduction of aromatic diazonium salts[END_REF], Pd [START_REF] Roglans | Diazonium salts as substrates in palladium-catalyzed cross-coupling reactions[END_REF] and Pb [START_REF] Fan | Determination of Cd2+ and Pb2+ on glassy carbon electrode modified by electrochemical reduction of aromatic diazonium salts[END_REF] ions have been already immobilized on surfaces by reduction of their diazonium salts.

The use of complexing agents to accumulate ions (i.e. in aqueous solution) at the surface of a resistor based on poly-Si nanostructures has not been investigated and requires exploration.

The coating layer would be expected to give a higher sensitivity to the sensors.

In this work, we present a simple resistor based on poly-Si nanoribbons for heavy metal detection. The presented device is formed by a row of nanoribbons which is fully compatible with CMOS technology and enables direct in-situ measurement. These nanoribbons were functionalized with aryl diazonium salts containing complexing groups in view of using this type of structure for heavy metal detection. The effectiveness of the grafting process is evaluated. After which, the preconcentration of lead ions (Pb 2+ ), chosen as an example of heavy metal ion, at the surface of the functionalized nanostructures is checked. Finally, an electrical characterization of the sensor shows that the coating layer increases the detection capabilities.

Materials and methods

Devices fabrication

Silicon nanostructures were formed on a cleaned silicon wafer and native oxide was removed by chemical etching using a diluted HF solution (2%). A 1.2 µm thick SiO2 insulating layer was deposited by Atmospheric Pressure Chemical Vapor Deposition (APCVD) technique at 420°C using silane (SiH4) and dioxygen (O2) gas sources. Amorphous silicon was deposited by LPCVD at 550°C at 90 Pa using SiH4 source and crystallized during an annealing step at 600°C for 12 hours in order to obtain a 50 nm thick poly-Si layer. The layer underwent photolithography and was etched using SF6 plasma reactive ion etching (RIE). Thus, 500 parallel nanoribbons (Fig. 1a) were formed. The length (L) and width (W) of these

A C C E P T E D M A N U S C R I P T
nanoribbons were 8 µm and 5 µm, respectively. A protective 100 nm thick SiO2 layer was deposited following APCVD. SiO2 was etched in order to open a window on each side of the nanoribbons (Fig. 1b). This layer enabled the deposition of heavily in-situ doped N-type poly-Si layer using SiH4 and phosphine (PH3) sources for the formation of contact electrodes. This last layer was etched by SF6 plasma RIE. Finally, the protective layer was etched using HF (2%) (Fig. 1c). Fig. 1d presents a SEM image of the obtained device.

Chemical

The resistor was functionalized by spontaneous grafting of aryl diazonium salts (Fig. 2) according to the following protocol, described in previous studies [START_REF] Bourdillon | Immobilization of glucose oxidase on a carbon surface derivatized by electrochemical reduction of diazonium salts[END_REF]. All manipulations were carried out under argon using a Schlenk line with standard airless techniques. A 2% hydrofluoric acid solution was cannulated into a reactor cell, which contained the samples under argon, in order to remove the native Si oxide. After 15 seconds of immersion, the HF solution was eliminated. A solution of 4-carboxymethyl-benzenediazonium salts or 4-iodobenzenediazonium salts was prepared by addition of 0.25 mL of isopentyl nitrite to 17 mg of 2-(4-aminophenyl)acetic acid or 20 mg of 4-iodoaniline dissolved in 120 mL of deoxygenated acetonitrile (HPLC grade) at 0°C for 15 minutes. This solution was then cannulated into the reactor cell. The samples were kept in the solution at 0°C for 15, 30, 60 or 180 minutes. The devices were then washed in three successive baths of acetonitrile of 5 minutes each. The solutions of lead for electrical tests were prepared from Pb(NO3)2 in ultrapure water.

Instrumentation

Layers thicknesses were obtained using HORIBA Uvisel 2 Ellipsometer. The swept spectral range was from 200 nm to 2100 nm and with the incident angle on the sample fixed at 70°.

The following values were taken for poly-Si base layer: n = 3.85, k = 0.016 at 632 nm. The X-ray photoelectron spectroscopy (XPS) has been carried out with a Kratos Axis Nova HSA spectrometer using a monochromatic Al Kα excitation (1486.6 eV), with magnetic confinement charge neutralization. The lens low magnification mode was used with the slot aperture resulting in an analysed area of 700 per 300 μm 2 . Charge stabilization was achieved by using the Kratos Axis internal device. Survey scans were recorded with an energy step of 0.5 eV and a pass energy (PE) of 80 eV. High resolution spectra were acquired at 20 eV PE and a step of 0.1 eV. In these conditions, the energy resolution gives a full width at half maximum (FWHM) of the Ag3d5/2 peak of about 0.55 ± 0.02 eV. The photoelectron take-off angle was 90° with respect to the sample plane, which provides an integrated sampling depth of approximately 15 nm. Chemical images were recorded at 80 eV PE using the small spot aperture and high-resolution iris settings leading to 400 per 400 μm 2 images with a pixel resolution of ~2 µm. Data analysis was done with the CasaXPS software [START_REF]CasaXPS software[END_REF].

It is worth noting that the grafted layer was still observed in XPS when the samples were sonicated 3 times in acetonitrile for 5 minutes.

NanoSIMS analyses were performed on a NanoSIMS 50 standard ion microprobe (Cameca).

The samples were cut and directly introduced into the chamber. An oxygen primary ionic source was used for the measurement of 208 Pb. A 17 keV O-beam (~30 pA) was focused and raster-scanned on the surface sample. Sputtered positive secondary ions were extracted for mass analysis and collected in an electron multiplier. A mass resolving power of ~5500 (M/ΔM) was enabled to remove potential mass interferences. All 208 Pb images (50µm

A C C E P T E D M A N U S C R I P T
50µm) of the same set were recorded under the same primary ion current and with the same parameters (diaphragms, slits, time/pixel). The spatial resolution for all images was 400 nm.

Results and discussion

Ellipsometry

The working principle of the sensor is based on the ions charges influence on the semiconductor (poly-Si). Consequently, it is crucial to ensure that the coating film thickness does not exceed a few nanometers, as it would lead to charge screening, which would prevent charge detection. Thus, the thickness of the coating film was measured by ellipsometry. This was performed on a 50 nm thick poly-Si layer. Fig. 3 shows that thickness increases with the grafting time. During the first hour of grafting, the deposition rate was about 6 nm/hour whereas during the two following hours, this rate decreased to about 0.5 nm/hour, showing a saturation of the thickness. These observations are in accordance with existing literature [START_REF] Chen | Molecular grafting to silicon surfaces in air using organic triazenes as stable diazonium sources and HF as a constant hydride-passivation source[END_REF].

XPS analyses

XPS analysis was performed to ensure that the grafting of diazonium salts was effective. In this view 4-iodo-benzenediazonium salts were used in which, iodine was used as a specific chemical XPS marker. The protocol for the grafting process was similar to those of the carboxylate layer. 50 nm thick polycrystalline silicon layers were prepared and grafted (see experimental section) with an immersion time of 30 minutes (thickness 3.5 nm) and 1 hour (thickness 6 nm). Analysis were done on a non-grafted poly-Si layer and different parts of processed devices. Fig. 4a presents grafting results on poly-Si part of the grafted device for 30min and 1 hour, compared to a poly-Si non-grafted sample. For the device, sample analysis was carried out at the centre of a nanoribbon connection pad (800 800 µm). As shown on the figure, no iodine is detected on the non-grafted poly-Si, whereas a significant I 3d signal is observed for the grafted surfaces. Moreover, the signal intensity follows the grafting time.

Fig. 4b compares iodine I 3d signal for the 30 minutes grafted device on the poly-Si pad and the SiO2 base layer. It seems that the grafting process preferentially takes place on the poly-Si, whereas an organic layer was probably also formed on the SiO2 area. Indeed, after treatment with diluted HF, the SiO2 surface give some Si-H bonds that are known to spontaneously react with diazonium salts [START_REF] Pichon | Thin film transistors fabricated by in situ doped unhydrogenated polysilicon films obtained by solid phase crystallization[END_REF]. To confirm the efficiency of the grafting process at the micrometric level, XPS images were performed on the same device. Analysis was carried out on a poly-Si cross pattern of 30 μm width and comb-like structures on SiO2 whose width was 5 μm, corresponding to the width of the nanoribbons (see Fig. 5a). Indeed, the nanoribbons have not been directly imaged because they remain difficult to spot, using this technique. However, it has been achieved on structures of comparable dimensions. XPS imaging of a surface consisted of choosing a binding energy representing a core level from the element of interest (here, poly-Si (Si 2p at 99.3 eV), SiO2

(Si 2p at 103.3 eV) and iodine (I 3d5/2 at 621.2 eV)), acquiring an image then taking a second image at an energy representative of the background signal for the photoelectron peak previously measured. Once the peak and background images are done, interpretation of the results was based on the difference in counts per second between the peak and the background images. The XPS images obtained from the analysis of silicon, silicon oxide and iodine

A C C E P T E D M A N U S C R I P T
compounds after grafting are given in Fig. 5b, 5c and 5d, respectively. On the part of the pattern with poly-Si, the signal intensity related to the iodine compound is significantly higher than on the silicon oxide probably because of the higher effectiveness of the grafting process on poly-Si. Fig. 5d shows that the presence of iodine on the comb structures of 5 µm width and on the cross, is noted. The intensity of the signal is strong and relatively homogeneous along these structures. This confirms the efficiency of the grafting and its homogeneity along nanostructures of poly-Si of 50 nm thickness.

These analyses show that a simple dip coating process in a solution of diazonium salts allows the homogeneous functionalization of nanostructures composed of polycrystalline silicon thin films (50 nm thick). Note that to our knowledge, this is the first study reporting the covalent grafting of aryl-diazonium salts on non-intentionally-doped thin silicon layers. Further experiments were then carried out to check the efficiency of the carboxylate-modified layer deposited on the nanoribbons to complex lead ions.

NanoSIMS analysis

A comparison of non-grafted and grafted structures was performed by the analysis of the isotope 12 of carbon ( 12 C) by NanoSIMS imagery. The results are presented in Fig. 6; these measurements have been performed simultaneously. Consequently, the samples have been exposed to the same level of ion beam, which means that the intensities were comparable.

Before the grafting process (Fig 6a), the signal intensity was low, showing that the sample contained a very small amount of carbon on its surface. After functionalization (Fig 6b), the signal intensity drastically increased. Interestingly, a red colour was observed on all the samples, including i) nanoribbons, ii) contact electrodes and iii) SiO2 zones between each nanoribbon. Owning to the high sensitivity of this imaging technique, no difference in the effectiveness of the grafting process according to the nature of the surface (poly-Si or SiO2) was observed. These results underline the effectiveness of the grafting process to modify the poly-Si nanostructures, confirming XPS analyses.

To ensure that immobilized carboxylate groups are able to trap lead ions, unmodified and modified samples were exposed to a Pb 2+ solution (10 -3 mol L -1 ) for 15 minutes, corresponding to a thickness of 2.5 nm. The samples were then rinsed by immersion in isopropanol and dried. The analysis of the device was done targeting isotope 128 of lead ( 128 Pb). For the non-grafted device (Fig. 6c), the signal was low, highlighting that the amount of lead on its surface was negligible. Conversely, the signal intensity was high on the grafted structure (Fig. 6d). These results underline the role of the carboxylate groups to preconcentrate lead ions on the surface by complexation, as it has been observed previously [START_REF] Liu | Diazonium salts: Stable monolayers on gold electrodes for sensing applications[END_REF].

Electrical characterization

Electrical analysis of the nanoribbons-based resistors has been performed in order to highlight any interesting grafting effects on the lead detection. It is worth noting that during the set of experiments, the coating layer has been chosen as thin as possible to avoid any charge screening effect, due to the insulating nature of diazonium salts [START_REF] Allongue | Structural characterization of organic monolayers on Si <111> from capacitance measurements[END_REF]. Consequently, the , where q is the charge and i is the current. Indeed, the influence of ions on silicon is related to the supply of surface charges and therefore, it has been considered as interesting and should be evaluated.

For an easier comparison of the performances of the different devices, the measured charges were normalized by the first charge value Q0 measured at t0 = 1 s from the initial current I0.

Since the measurement time step Δt was set to 1 s, the value of the normalized load is thus obtained by making a discrete sum as follows:

(1) Firstly, normalized charge was recorded as a function of time after exposure of the modified nanoribbons to different concentrations of analytes. As shown in Fig. 7, the functionalized devices were exposed to deionized water and to different concentrations of lead solutions, ranging from 10 -7 to 10 -3 mol L -1 . These solutions were prepared following the protocol detailed in the experimental section. Before the analyte deposition, the normalized charge of all devices increased linearly in the same way whereas the current remains constant. After the deposition, the higher the concentration of Pb 2+ was, the more the normalized charge increased. For the sample exposed to water, no slope change was noted. These results show that the detection of ions is effective and depends on solution concentration. Moreover, the detection of ions is effective and depends on the solution concentration. It also highlights that such a sensor could be used for real-time on-site measurements, its response showing sufficient slope changes depending on the concentration after 10 minutes exposure time. different devices, tested one by one, at room temperature. The insulation of the contact electrodes was checked (Fig. S1). For periods of less than 10 minutes exposure, no clear increase of the charge was observed (Fig. 8a). The normalized charge significantly increased with concentration when the time of exposure to the ions was greater than 10 minutes, showing an influence of the Pb 2+ charges on the poly-Si.

We consequently studied the sensor response for an exposure time ranging from 10 to 50 minutes and checked the influence of the carboxylate layer on the measured charge. The In zone A, ranging from 10 -8 to 2 10 -7 mol L -1 , there is no noticeable difference between the response of the sensor in the grafted and non-grafted configurations, probably because the sensor is not sensitive enough to detect Pb 2+ ions at concentrations lower than 2 10 -7 mol L -1 .

The error bars confirm that there is no clear trend. We observe the same uncertainty in zone C, ranging from 7 10 -6 to 10 -4 mol L -1 , where the dispersion of the measured data points becomes substantial, especially with the poly-Si device. This is probably due to the high concentration of the analysed solutions, leading to saturation of the carboxylate groups by lead ions and important unselective adsorption of ions on the surface. In contrast, in zone B (from to 2 10 -7 to 7 10 -6 mol L -1 ) a significant difference is obtained, highlighting a higher clearly enhances the difference between the charges obtained on unmodified and modified devices, as shown after 30 and 50 minutes of exposure to lead solutions (Fig. 8c and8d). This behaviour, showing that modification of the surface is necessary and exacerbates detection in a well-defined range of concentrations has been frequently reported in literature with sensors based on a preconcentration of ions on their surface [START_REF] Liu | Graphene wrapped Cu2O nanocubes: non-enzymatic electrochemical sensors for the detection of glucose and hydrogen peroxide with enhanced stability[END_REF]. Note that no interference studies were performed in this work. However, one can assume that using molecules with termination such as 1,4,8-tri(carbamoylmethyl) hydroiodide (TETRAM), such a sensor could show selectivity to lead. Indeed, this compound has already proven selectivity to Pb 2+ trapping [START_REF] Nasraoui | Improvement in performance of a flow electrochemical sensor by using carbamoyl-arms polyazamacrocycle for the preconcentration of lead ions onto the electrode[END_REF].

Thus, the coating layer could be tuned to reach selective detection of a specific targeted species.

Conclusion

In this proof of concept study, a lead sensor based on polycrystalline silicon nanoribbons fabricated in a fully compatible CMOS silicon technology is demonstrated. The small volume of solution required for the analysis and the low dimensions of the device, combined with the benefits of nanoscale and microtechnology, make these devices promising as embeddable sensors in an autonomous system to monitor contamination on site. Lead detection was checked by electrical measurements due to the influence of the lead on the electrical conductivity of Si-poly nanoribbons. Functionalization improves the accuracy of the sensor and increased its sensitivity. The lowest concentration where a noticeable difference exists between non-grafted and grafted devices (zone B) is 10 -7 mol L -1 , which is very encouraging for this type of device, far from having reached maturity.

  grain boundaries that are formed during crystallization process. Poly-Si is prepared by layer deposition and is used in a variety of applications, such as thin film transistors (TFTs) [4,5],

Fig. 1

 1 Fig. 1 3-dimensional sketches of the fabrication process. (a) Deposition and formation of 500

Fig. 2

 2 Fig. 2 Spontaneous grafting of carboxylate-terminated aryl diazonium salts at the surface of

  optical constants of the layer were determined using the classical Lorentz oscillator dispersion formula. The values were measured on clean surfaces before grafting and the layers thicknesses were determined from the same plates after modification, taking n = 1.65, k = 0 for the layer. Measurements reported are the average of five data points across the substrate.

Fig. 3

 3 Fig. 3 Film thicknesses measured by ellipsometry as a function of grafting time. Each

Fig. 4

 4 Fig. 4 Grafting efficiency verification. (a) XPS iodine I 3d spectral region (range 616 eV to

Fig. 5

 5 Fig. 5 XPS imaging of the cross pattern based device. (a) Cross and combs shapes used for

Fig. 6 .

 6 Fig. 6. NanoSIMS imaging of the nanoribbons-based device. 12 C element tracking before (a) and after (b) grafting process. Inset is a corresponding SEM view of the device. 208 Pb tracking

  grafting step was performed during 15 minutes (thickness 2.5 nm). The analysis is based on the measurement of the charge quantity flowing through the resistor (biased at 1V) and calculated in real-time by integrating current as a function of time:

Fig. 7

 7 Fig. 7 Normalized charge measurement as a function of time on modified poly-Si

  characterization of the devices, with and without functionalization of the nanoribbons, was performed to ascertain if the preconcentration of lead ions on the surface significantly impacts the quality of the detection. The normalized charge for 10, 30 and 50 minutes for concentrations ranging from 10 -8 to 10 -4 mol L -1 is presented in Fig.8b, 8c and 8d, respectively.The red curve, corresponding to the non-grafted structures, does not seem to show any real trend. The charge decreases when the concentration increases to the middle of the measured range (around 10 -6 mol L -1 ) and then increases with the concentration up to 10 -4 mol L -1 . For the grafted structures (black curve), the quantity of charges increases with the concentration. This phenomenon can be explained by the presence of Pb 2+ charges, preconcentrated at the surface by complexation with the carboxylate groups, which influence the conduction in the semiconductor. The resistivity of the overall material (poly-Si/salts/Pb 2+ ) decreases and the calculated charge increases. When the grafted and non-grafted structures are compared, three zones corresponding to different electrical behaviours can be distinguished. These zones are denoted as A, B and C.

  amount of charges for the coated device. Such an observation seems to show that in this concentration range, the preconcentration of the lead ions (II) on the surface of the functionalized poly-Si nanoribbons affects the charge of the device. A longer exposure time

Fig. 8

 8 Fig. 8 Normalized charge measurement for different Pb 2+ concentrations (a) and exposure

  Nanoribbons used as sensitive units are functionalized with an organic layer deposited by spontaneous grafting of diazonium salts. While this reaction is well-known on silicon, there are few studies on the grafting of diazonium salts on polycrystalline silicon nano-objects. The efficiency of the functionalization of these structures is underlined due to surface characterization techniques (ellipsometry, XPS and NanoSIMS). The functionalization made possible the preconcentration of ions contained in the analyte at the surface of the sensitive elements of the device.

[ 1 ]

 1 H. Yongming, D. Peixuan, C. Junji, E.S. Posmentier, Multivariate analysis of heavy metal contamination in urban dusts of Xi'an, Central China. Sci. Total Environ. 355 (2006) 176-186. [2] D.T. Dexter, F.R. Wells, A.J. Lee, F. Agid, Y. Agid, P. Jenner, C.D. Marsden, Increased nigral iron content and alterations in other metal ions occurring in brain in Parkinson's disease. J. Neurochem. 52 (1989) 1830-1836. [3] R.C Patra, D. Swarup, S.K. Dwivedi, Antioxidant effects of α tocopherol, ascorbic acid and L-methionine on lead induced oxidative stress to the liver, kidney and brain in rats. Toxicology. 162 (2001) 81-88. [4] R.E. Proano, R.S. Misage, D.G. Ast, Development and electrical properties of undoped polycrystalline silicon thin-film transistors. IEEE T. Electron. Dev. 36.9 (1989) 1915-1922. [5] R. A. Sporea, M. Trainor, N. Young, J.M. Shannon, S.R.P. Silva, Temperature effects in complementary inverters made with polysilicon source-gated transistors. IEEE T. Electron. Dev., 62 (2015) 1498-1503.


Amine Achour

Dr Mohammad Islam

Iftikhar Ahmad

Laurent Le Brizoual

Abdou Djouadi

Thierry Brousse
email: thierry.brousse@univ-nantes.fr

Prof Thierry Brousse

Influence of Surface Chemistry and Point Defects in TiN based Electrodes on Electrochemical Capacitive Storage Activity

Keywords: Titanium nitride, surface defects, electrochemical capacitor, XPS, Cyclic voltammetry

The effect of surface chemistry of reactive sputtered TiN electrodes in the electrochemical capacitors (ECs) was investigated. The TiN films were produced on vertically aligned carbon nanotubes. X-ray photoelectron spectroscopy analysis revealed surface defects generation with no effect on morphology. Cyclic voltammetry experiments were performed in aqueous 0.5 M K 2 SO 4 solution and 1 M Et4NBF4 ((tetraethylammonium tetrafluoroborate)) organic electrolyte. The presence of oxygen vacancies and Ti interstitials on the top surface layer lead to enhanced electrochemical capacitive charge storage. Such findings open the way to design nitride films with optimized surface chemistry for use in the ECs.

It is a well-known fact that the specific capacitance of electrochemical capacitors (ECs) is an electrochemical surface-confined process and, therefore, both the surface area and surface chemistry of the active material determine its capacitance value. Although research efforts are focused at surface area enhancement for super-capacitor development, the effect of surface chemistry of different active materials including oxides, nitrides and carbides remains relatively less explored [1-3]. Indeed, understanding the effect of surface chemistry is important in order to develop high performance materials for ECs.

Recently, transition metal nitrides (TMNs) are attracting attention for their use in electrochemical capacitors or micro-supercapacitors because of their good electrical conductivity, chemical inertness and thermal stability [4-10]. Among these TMNs, titanium nitride (TiN) [5-7] has been explored extensively due to its high electrochemical stability, good power density as well as interesting specific capacitance. Previously, we reported the effect of surface modification of TiN films through vacuum annealing in order to improve the specific capacitance [10].

In this communication, we provide an evidence that presence of surface defects on the TiN film electrodes are responsible for the electrochemical storage. In case of defect-free TiN electrodes or with very low defect density on the surface, high surface area TiN becomes inactive for electrochemical capacitive charge storage.

The carbon nanotubes (CNT) were grown over amorphous carbon (a-C)/Si substrate via microwave plasma-enhanced chemical-vapor deposition process using in acetylene and ammonia mixture with a NH 3 /C 2 H 2 ratio of 0.2. The chamber pressure, microwave power, temperature and time were maintained at 0.2 Pa, 120 W, 600 °C and 60 min, respectively. More details of the CNT growth procedure are described elsewhere [11].

Following vertically aligned CNT array growth, titanium nitride (TiN) films were produced through reactive direct-current (DC) plasma sputter deposition. The details of the sputtering system can be found elsewhere [10]. The TiN films were deposited under different conditions of applied power and plasma gas mixture in order to induce different surface chemistries. In one case, the argon (Ar) and nitrogen (N 2 ) gas volumetric flow ratio was maintained at 18:2 (sccm) at 120 W power. The sample was designated as TiN1-CNT. The other sample referred to as TiN2-CNT was obtained when the respective values of Ar:N 2 and P values were 20:1 and 80 W. In both samples, the TiN film thickness was kept to be ~100 nm as determined from the reference samples that used flat, polished silicon wafers as substrates.

The surface and cross-section of the TiN@CNT electrodes were examined under scanning electron microscope (SEM; JEOL JSM 7600F) by operating at 5 kV. The phase analysis was performed by means of X-ray diffraction (XRD) studies using a Siemens D5000 diffractometer with CuKα1 monochromatic radiation in the Bragg Brentano configuration.

The surface analysis was carried out through XPS measurements on a Kratos Axis Ultra apparatus. The high-resolution spectra were recorded using AlKα (1486.6 eV) beam at 20 eV pass energy and 0.9 eV energy resolution. Any charge energy shift in the binding energy (BE) was compensated by setting the C 1s line of the contamination peak to 284.4 eV. For both TiN1-CNT and TiN2-CNT, the XPS measurements were performed ex-situ with the samples stored in the same environment for similar time periods. In case of TiN2-CNT electrode, a slight shift to higher 2θ values by 0.1 o in the diffraction peaks was noticed that may be attributed to the stress effect within the TiN deposit [12]. The CNT exhibit presence of the diffraction peaks at 2θ values of 25.9° and 42.7° that correspond to the (002) and (100) graphite reflections (JCPDS No. 01-0646), respectively. However, in our case, the vertically aligned CNTs have an average length of about 2 μm and a relatively low area density of 10 9 cm -2 . Therefore, it is difficult to evidence the CNT diffraction peaks using X-Ray diffraction. The peak at 44.5° is attributed to fcc Ni phase [11] that was used as catalyst for CNT growth. The other weak diffraction peaks present in all the three samples maybe ascribed to the substrate.

The XPS deconvolution of the Ti 2p core level high resolution spectra for the TiN1-CNT and TiN2-CNTelectrodes are represented in Fig. 2a and Fig. 2d, respectively. The peak deconvolutions show that the TiN1-CNT exhibit major components mixture of Ti-N-O, Ti-N and Ti-O chemical bonds. The intense peak located at 458.2 eV can be related to Ti 2p 3/2 and can be assigned to TiO 2 (Ti 4+ oxidation state) while the weak peak at lower binding energies (∼454.6 eV) can be assigned to TiN [13,14]. Between these two peaks, there are two other peaks that can be attributed to the oxynitride (TiO x N y ) and Ti 2 O 3 which have an oxidation state between those of TiN and TiO 2 [13,14]. According to literature, one doublet can be related to Ti (Ti 3+ oxidation state) in Ti 2 O 3 . The Ti 3+ oxidation state is usually attributed to the defects in TiO 2 [15,16]. In case of Ti 2p core level spectrum of TiN2-CNT electrode (Fig. 2d), there is no peak related to Ti 2 O 3 suggesting that the TiO x layer that built up on the TiN surface has very few or no defects at all. The amount of Ti 2 O 3 is related to the number of oxygen vacancies generated due to nitrogen doping of TiO x layer at the top surface of TiN.

The absence of Ti 2 O 3 phase (Ti 3+ ) may be accounted for the low density or absence of oxygen vacancies in the TiO x layer of this electrode. On the other hand, β-N (the nitrogen that substitutes oxygen in the TiO x layer) introduces these oxygen vacancies, as reported in our previous work [5].

In order to confirm the absence of defect on the surface of TiN2-CNT electrodes, one can compare the N 1s core level spectra of both electrodes, as shown in Fig. 2b and Fig. 2e.

The deconvoluted N 1s peak of TiN1-CNT electrode contains four peaks (Fig. 2b). The peak located in the 396.1-396.9 eV range can be attributed to titanium nitride in agreement with Ref [18]. Two or three other peaks at higher energies can be resolved and may result from superposition of peaks corresponding to the oxynitride (TiN x O y ) and nitrogen-oxygen adsorbed species (NO x = NO or NO 2 ) or Ti-NO x [19-20] compounds at the surface. The intense peak at lower energy side (395.2-395.9 eV) is attributed to β-N which is associated with oxygen substitution by nitrogen in the TiO x layer. The peak related to β-N does not appear in the deconvoluted N 1s spectrum of TiN2-CNTs (Fig. 2e). As mentioned above, this kind of substituted nitrogen atoms are believed to create oxygen vacancies. Therefore, the lack of β-N species at the surface of TiN2-CNTs sample is in a good agreement with the absence of Ti 2 O 3 band on the electrode surface.

Another way to examine the presence of defects on the surface of TiO x layer is by looking at the valence band (V B ). In Fig. 2c and 2f are presented the V B of TiN1-CNT and TiN2-CNT electrodes, respectively. In case of TiN1-CNT electrode (Fig. 2e), the band located at about 0.84 eV can be assigned to Ti 3d (Ti +3 ) defect states related to oxygen vacancies or Ti interstitial defects in TiO 2 [21][22][23]. In contrast, the case of the XPS band characteristic of the Ti 3d (Ti +3 ) defect states located at 0.84 eV [20] is absent from the surface of TiN2-CNT electrode (Fig. 2c), thus indicating the lack of oxygen vacancies and/or Ti interstitial defects in TiO 2 . Again, this is in a good agreement with absence of the bands assigned to the Ti 2 O 3 bonding and β-N arising from substitutional-insertion nitrogen doping on the surface of this electrode. Therefore, the detailed XPS analysis of the TiN2-CNT electrode demonstrates prevalence of very low defects density on the surface of this electrode.

Based on our previous works, such different surface chemistry should have an impact on the electrochemical capacitive storage of such materials [5, 8, 10]. It is noteworthy that the oxide layers at the TiN surface may be a by-product that is formed during film deposition and/or aging as it is not possible to avoid oxidation of the surface of transition metal nitrides once they are exposed to air.

In order to assess the surface chemistry effect on the electrochemical behaviour of the two electrodes, cyclic voltammetry (CV) was used to investigate the electrochemical behavior of the two samples in different types of electrolytes. The cyclic voltammograms of the TiN1-CNT electrode after testing in 0.5 M K 2 SO 4 aqueous solution and 1.0 M Net 4 BF 4 organic electrolyte at 200 mV.s -1 are showcased in Fig. 3a and Fig. 3b, , respectively. The CV exhibits a near symmetrical rectangular shape in 0.5 M K 2 SO 4 electrolyte solution that indicates quasiideal capacitive behavior. On the other hand, the capacitive current was found to decrease in 1 M Net 4 BF 4 organic electrolyte because of the absence of protons in this kind of electrolyte, as discussed earlier [5]. In contrast with this behavior, the CVs for the TiN2-CNT electrode (Fig. 4 c,d) exhibit a completely distorted shape and a very low capacitive current in both electrolytic solutions. This indicates that the TiN2-CNT film does not store as much charges as TiN1-CNT sample even it exhibits the same high surface area. The absence or scarcity of point defects on the surface as qualitatively determined from XPS analyses (absence of β-N, Ti 2 O 3 phase and Ti +3 d band) may account for this trend. The electrical double layer (EDL) capacitance of the TiN2-CNT electrode in 0.5 M K 2 SO 4 aqueous electrolyte in the 0 to 0.15 V vs Ag/AgCl potential window was calculated to be 10 µF.cm -2 which is a standard EDL capacitance value for carbon based electrodes. Furthermore, it seems that hydrogen evolution reaction is promoted in this electrolyte since it occurs below 0 V vs Ag/AgCl. The oxidation current at more positive potentials can be related to oxidation processes occurring at the TiN surface. Further research is required to investigate the nature of these electrochemical processes, as this is outside the scope of this communication.

Moreover, it is believed that the loss of electrochemical character of the TiN film as ECs electrode is not merely related to the absence of oxygen vacancies in the TiO x layer at the top surface of this electrode. In fact, the absence of the Ti 3+ d band (shown in Fig. 3b) can also indicate the absence of other types of defects such as interstitials Ti atoms, which in turn, can also have an impact on the electrochemical charge storage properties of the TiN2-CNT electrode. Therefore, it can be suggested that both type of defects i.e. oxygen vacancies and interstitial Ti in the top TiO x layer formed at the TiN surface may contribute to the electrochemical charge storage in the TiN electrode. The research findings presented here highlight the role of surface defects in the TiN based electrodes towards electrochemical charge storage properties.

A very thin TiN film (100 nm thick) was produced over vertically aligned carbon nanotubes using two different deposition conditions to obtain EC electrodes with similar high surface area and surface morphology, albeit different surface chemistry. The electrode surface resulting from higher plasma power (120 W) and less degree of nitrogen gas dilution (Ar:N 2 of 18:2) had point defects generated due to top layer oxidation. The surface chemistry of this electrode comprised of β-N, Ti 2 O 3 as well as Ti 3+ d as probed with X-ray photoelectron spectroscopy (XPS). Thus, XPS analyses confirm the presence of surface defects such as oxygen vacancies and Ti interstitials on the surface of this electrode. During EC measurements, such electrode exhibited the highest performance in terms of electrochemical charge storage in both aqueous and organic-based electrolytes. The TiN film deposited under a different set of processing conditions (80 W power, Ar:N 2 of 1:20), however, indicated absence of β-N, Ti 2 O 3 phases and the Ti +3 d band in the valence band as figured out from the XPS analysis. The lack of these chemical moieties may be ascribed to the absence of surface defects that led to the loss of capacitive/pseudo capacitive charge storage behavior. To the best to our knowledge, these findings are the first evidence of the effect of surface chemistry on the energy storage characteristics of transition metal nitrides. Our results highlight the effect of the surface defects on the electrochemical behavior of TiN thin films and pave the way to design enhanced nitride-based electrodes for electrochemical capacitors.

  The electrochemical measurements were performed in two different electrolytes namely an aqueous solution of 0.5 M K 2 SO 4 and an organic solution of 1.0 M Et 4 NBF 4 (tetraethylammonium tetrafluoroborate) in HPLC grade acetonitrile. The high purity chemicals procured from Alfa Aesar were used without any further purification. For electrochemical characterization, a cell in three-electrode configuration was used with Ag/AgCl and a platinum gauze as reference and counter electrodes, respectively. The measurements were recorded using a VMP 3 multi potentiostat-galvanostat (Biologic, France) with EC-Lab software for monitoring. The surface area of the working electrode was defined by means of a Teflon TM cell holder. For cycling voltammetry studies, ten cyclic voltammograms (CVs) were obtained prior to those presented in this work in order to ensure that the CV data were representative of each electrode.The top view and cross section of the TiN film deposited on to the vertically aligned CNTs were examined under SEM, as shown in Fig.1. Since there was no noticeable difference in morphologies of the two TiN electrodes although the sputter deposition conditions were different, only the SEM results for the TiN1-CNT electrode are presented.The microstructures revealed that the TiN nanostructures anchored to the outer surfaces of the individual CNTs at their tips and length segments near their top ends, thus causing an increase in the outer diameter of the CNTs by few tens of nanometers. The XRD patterns (Fig.1c) confirm the presence of TiN phase (JCPDS file: 87-0633)in both samples with diffraction peaks at 36.7° and 42.5° assigned to the (111) and (200) crystallographic orientations [5, 8].

Fig. 1

 1 Fig. 1 Vertically aligned CNT array coated with a 100-nm TiN film used as electrode: (a, b) SEM microstructures revealing surface and cross-section growth morphologies, and (c) X-ray diffraction patterns of the two samples and CNT without TiN deposit.

Fig. 2

 2 Fig. 2 XPS spectra of the two different TiN coated CNT electrodes: For TiN1-CNT electrode, high resolution, deconvoluted spectra for the (a) Ti 2p band, (b) N 1s band high resolution spectrum, and (c) XPS valence band are shown. For the TiN2-CNT sample, high resolution, deconvoluted spectra for the (d) Ti 2pband, (e) N 1s band high resolution spectrum, and (f) XPS valence band are presented.

Fig. 3

 3 Fig. 3 Cyclic voltamograms of TiN/CNT-A electrode in (a) 0.5 M K 2 SO 4 aqueous electrolyte solution and (b) in 1 M Net 4 BF 4 organic electrolyte at a scan rate of 200 mV.s -1 . Cyclic voltamogramms of TiN/CNT-B electrode in (a) 0.5 M K 2 SO 4 aqueous electrolyte solution and (b) in 1 M Net 4 BF 4 organic electrolyte at a scan rate of 200 mV.s -1 .

The authors would like to extend their sincere appreciation to the Deanship of Scientific Research at King Saud University for its funding of this research through the Research Group Project no. RGP-283.


J P Echeverry

B Urbaszek

T Amand

X Marie

I C Gerber

Splitting between Bright and Dark excitons in Transition Metal Dichalcogenide Monolayers

Keywords:

The optical properties of transition metal dichalcogenide monolayers such as the two-dimensional semiconductors MoS2 and WSe2 are dominated by excitons, Coulomb bound electron-hole pairs. The light emission yield depends on whether the electron-hole transitions are optically allowed (bright) or forbidden (dark). By solving the Bethe Salpeter Equation on top of GW wave functions in density functional theory calculations, we determine the sign and amplitude of the splitting between bright and dark exciton states. We evaluate the influence of the spin-orbit coupling on the optical spectra and clearly demonstrate the strong impact of the intra-valley Coulomb exchange term on the dark-bright exciton fine structure splitting.

Introduction.-Transition metal dichalcogenide (TMDC) monolayers (MLs), with chemical formula MX 2 , with M=Mo or W and X=S, Se or Te, are semiconductors with a direct bandgap in the visible region situated at the K-point of the Brillouin zone [1,2]. In these 2D systems the broken inversion symmetry of the crystal lattice allows for optical control of the valley degree of freedom [3][4][5][6]. Combined with strong spin-orbit coupling (SOC) this leads to valley-spin locking [7], opening exciting avenues for original applications in optoelectronics and spintronics. Tightly bound excitons [8][9][10][11], with binding energies around 0.5 eV, originate from the direct term of the electron-hole (e-h) Coulomb interaction, enhanced by the strong 2D quantum confinement, the large effective masses, and the reduced dielectric screening in 2D systems. While the energy spectra of these excitons have been intensively studied by combining both experimental and theoretical technics in the last years [12][13][14][15][16][17], little is known about their fine structure.

For optoelectronics based on TMDC MLs it is important to clarify if the lowest energy transition is optically bright or optically dark (i.e. spin forbidden) [18]. This bright-dark exciton fine structure splitting governs the optical properties also of 2D semiconductor nanostructures such as III-V and II-VI quantum wells [19][20][21][22][23] as well as CdSe nanocrystals [24]. In particular, the measured low photo-or electro-luminescence yield and its increase with the temperature in monolayer WSe 2 has been interpreted recently in terms of dark excitons lying at lower energy compared to the bright ones [25][26][27][28][29]. This will also affect the efficiency of recently demonstrated WSe 2 or WS 2 light emitting devices [30,31]. For fundamental physics experiments an optically dark ground state can be an advantage, as it allows to study exciton quantum fluids in Bose-Einstein exciton condensates [32]. It is thus crucial to determine both the amplitude and sign of this bright-dark exciton splitting in TMDC MLs.

Figure 1b) presents the schematics of a typical TMDC ML band structure in a single particle picture. In addition to the large spin-orbit splitting ∆ v between A and B valence bands (VBs), the interplay between inversion asymmetry and spin-orbit interaction also yields a smaller spin-splitting (∆ c ) between the lowest energy conduction bands (CBs) [33][34][35][36]. First let us consider A-excitons, with the transitions involving only the highest VB energy (A) and the two lowest CBs (↑ or ↓), see Figure 1a). Here Ω ↑↓ represents dark (spin forbidden) transitions, and Ω ↑↑ shows bright transitions. As a first approximation, one could consider that the energy splitting ∆ Dark-Bright = Ω ↑↓ -Ω ↑↑ between bright and dark excitons is mainly due to the CB splitting ∆ c = E CB↓ -E CB↑ induced by SOC. Depending on the material, ∆ c can either be negative for WX 2 or positive for MoX 2 systems (X=S, Se), as standard functional theory (DFT) and tight-binding calculations have shown [33,34,[37][38][39][40]. However, this single particle approach misses a key ingredient for the accurate determination of the dark-bright exciton splitting: the short-range part of the e-h Coulomb exchange interaction for the exciton [19,21,41]. So far in the context of TMDC MLs only the effects of the long-range exciton exchange interaction on the valley dynamics of bright exciton states in TMDC monolayers have been studied [42][43][44][45].

Here we demonstrate that the e-h exchange interaction within the exciton causes a splitting between the low energy optically bright and dark excitons in TMDC MLs. We find a giant exchange term of the order of 20 meV, more than 100 times larger than in GaAs quantum wells for instance [19,21,41]. For all the investigated MoX 2 and WX 2 MLs, this local field effect due to the exchange interaction is added algebraically to the CB spin-orbit term ∆ c , yielding a splitting ∆ Dark-Bright between bright and dark exciton that differs significantly from ∆ c , see comparison in Figure 1a). We find that for MoX 2 systems, A-exciton dark states are higher in energy than bright ones, whereas this order is reversed for WX 2 MLs. Interestingly for WSe 2 ML we obtain ∆ Dark-Bright = -16 meV, a value in good agreement with a first experimentally derived value [28]. Importantly, we also report results on the exciton states involving the B valence band, which are fully consistent when compared to ∆ Dark-Bright for the A exciton, since the conduction band splitting contributes with the opposite sign. Moreover we show that the determination of the CB spin-orbit splitting ∆ c requires to perform DFTbased calculations within the GW approach [46,47]. Significant changes compared to standard DFT level calculations [12,13,33,39] are obtained for all TMDC MLs.

Computational Details.-The atomic structures, the quasi-particle band structures and optical spectra are obtained from DFT calculations using the VASP package [48,49].

Heyd-Scuseria-Ernzerhof (HSE) hybrid functional [50][51][52] is used as approximation of the exchange-correlation electronic term, as well as the Perdew-Burke-Ernzerhof (PBE) one [53]. It uses the plane-augmented wave scheme [54,55] to treat core electrons. Fourteen electrons for Mo, W atoms and six for S, Se ones are explicitly included in the valence states. All atoms are allowed to relax with a force convergence criterion below 0.005 eV/ Å. After primitive cell relaxation at the PBE level, the optimized lattice parameters, given in Table I are in good agreement (1%) with previous calculations [56] with all values slightly larger than the bulk experimental ones. A grid of 12×12×1 k-points has been used, in conjunction with a vacuum height of 17 Å, to take benefit of error's cancellation in the band gap estimates [57], and to provide absorption spectra in reasonable agreement with experiments as suggested in different works [58,59]. A gaussian smearing with a width of 0.05 eV is used for partial occupancies, when a tight electronic minimization tolerance of 10 -8 eV is set to determine with a good precision the corresponding derivative of the orbitals with respect to k needed in quasi-particle band structure calculations. Spin-orbit coupling was also included non-self-consistently to determine eigenvalues and wave functions as input for the full-frequency-dependent GW calculations [60] performed at the G 0 W 0 level but also at GW 0 level with 3 iterations of the G term, when necessary. The total number of states included in the GW procedure is set to 600, after a careful check of the direct band gap convergence, to be smaller than 0.1 eV. All optical excitonic transitions have been calculated by solving the Bethe-Salpeter Equation as follows [61,62]:

ε QP c -ε QP v A vc + v c vc|K eh |v c A v c = ΩA vc , (1)
where Ω are the resulting e-h excitation energies. A vc are the corresponding eigenvectors, when ε QP are the singlequasiparticle energies obtained at the G 0 W 0 level, and K eh being the CB electron-VB hole interaction kernel. This term consists in a first attractive screened direct term and a repulsive exchange part. Practically we have included the six highest valence bands and the eight lowest conduction bands to obtain eigenvalues and oscillator strengths on all systems. Dark excitons are characterized by oscillator strengths around one thousand times smaller than bright ones [63].

Results and Discussion.-Figure 1a) and Table I present the calculated values of the splittings ∆ Dark-Bright between non-optically active 1s exciton transitions Ω ↑↓ and active ones Ω ↑↑ . This splitting is positive for A exciton in the cases of MoSe 2 and MoTe 2 MLs. These re- sults are compatible with the measured dependence of the photoluminescence (PL) intensity with respect to the temperature [26][27][28][29]. If we assume, that the direct contribution terms of the K eh kernel are very close for the two distinct spins orientations for one particular ML, the effect of the e-h exchange term is to partially compensate the conduction band splitting, by substracting roughly 20 meV for those two systems from ∆ c to obtain the exciton dark-bright splittings, see Figure 1a). In other words, the CB spin-orbit splitting and the exciton exchange term have opposite signs. Interestingly the exciton exchange contribution seems to be an invariant quantity for the entire family, at least for the tested TMDC MLs, and agrees well with the single available value of this term in the literature, coming from calculations of a freestanding MoS 2 ML [17]. For the particular MoSe 2 and MoTe 2 cases, since the conduction band splitting is larger than the exciton exchange term, ∆ Dark-Bright is positive, as shown in Figure 1a). Local-field effects (exciton exchange term) also act on the B exciton, accordingly to the sign change of ∆ c for the transition involving the B valence band series but with almost the same repulsive exchange term, now the Ω B ↑↓ transition appears below the Ω B ↑↑ one. Note that for those two systems, there is also a change in the direct term, since it appears less attractive than in the A case, this is particularly true for MoTe 2 .

The MoS 2 ML is very intriguing, our calculations show that the CB spin-orbit splitting and the exciton exchange term almost cancel each other yielding a very small bright-dark exciton separations. As a consequence, ∆ Dark-Bright is negative for PBE-based calculations (-5 meV) and 0 meV when HSE orbitals are used. This is in line with the previous determination of Qiu et al [17] for the same system, since Ω A ↑↓ is lower in energy than Ω A ↑↑ by approximatively 17 meV and Ω B ↑↓ by around 23 meV with respect to Ω B ↑↑ . We observe the same trend, the difference being certainly due to our larger ∆ c values obtained at the GW level, see below. On the B exciton, we also observe a small decrease of the direct contribution that makes the absolute energy difference between the parallel and anti-parallel spins slightly smaller that the simple addition of the conduction band splitting and the exciton exchange term. For WS 2 and WSe 2 MLs, since ∆ c is very small in both cases, see Figure 1a) and Supplemental Material [68], the exchange term contribution dictates the bright-dark exciton splitting inducing the bright exciton to lie at lower energy compared to the dark one. The corresponding energy separations remain very modest when compared to the binding energy, but at the same time allow to actively populate the bright excitons when increasing the sample temperature. To be more specific for WSe 2 , we propose here an estimate of the dark-bright energy splitting smaller than 20 meV, in good agreement with the indirect determination based on a recent fit procedure of experimental data [28].

DFT-PBE DFT-HSE

G 0 W 0 -PBE G 0 W 0 -
The determination of the bright and dark exciton splitting in TMDC MLs, requires very high accuracy in the calculations of spin-orbit splitting in the conduction bands. It is well documented that standard DFT fails predicting band structure parameters like band gap or effective masses. Due to the ground state character of the DFT, conduction band splittings need to be more accurately described by means of many-body based calculations. Here our GW -based calculations provide more accurate band structure parameters compared to standard DFT, as it has been shown for similar systems [56,58,59,69] Here we compare the SOC effects on both valence and conductions bands, by means of standard DFT with our results from more advanced GW schemes. All data corresponding to VB energy splittings ∆ v values are reported in Supplemental Material [68]. Those values agree very well with previous DFT-based reports [33,38,39,56]. It clearly shows that adding a partial exact exchange contribution to the electronic exchange-correlation functional significantly enlarges ∆ v for all TMDC MLs. This trend is directly observable in the computed absorption spectra and more specifically in the ∆ B ex -A ex results of Table I which include contributions both from ∆ v and ∆ c but also e-h interaction effects. HSE-based calculations always give larger A-B splittings than the experimental estimates, but still remain in a reasonable agreement with them. Considering ∆ c , at the DFT level, our results are similar to previous reports [33,39]: for the MoX 2 family, when going from a semi-local to a hybrid approximation of the electronic exchange-correlation term, the splittings between spin-↑ and ↓ CB states are enhanced, see Figure 2 and Supplemental Material [68]. Interestingly for the WS 2 and WSe 2 cases, if now ↓-CB is the lowest unoccupied state, the energy separation is significantly reduced in hybrid functional calculations, meaning that short-range Hartree-Fock term strongly influence both atomic SOC contributions from the transition metal and from the chalcogen, to make them competitive with opposite signs [33]. For the MoS 2 and MoSe 2 cases, our G 0 W 0 calculations based on PBE or HSE wave functions provide similar ∆ c splittings suggesting a non-dependence band splitting on the ground state orbitals in contrast with MoTe 2 ML, probably due to an overestimation of the chalcogen contribution using HSE-based orbitals, which leaves ∆ c 40% larger even after applying a single shot GW correction. Remarkably for W-based systems the GW scheme reduces drastically ∆ c starting from PBE orbitals, and even reverses again the spin-up and spin-down conduction bands ordering in HSE-based calculations. This clearly indicates that ↑ and ↓ CB states are almost degenerate at the GW level, contrary to standard DFT predictions.

The G 0 W 0 results reveal further interesting details: as it has been already reported [56] and mentioned in the present letter, all the extracted values of GW calculations, namely ∆ v , ∆ c and E g (free carrier gap value) are sensitive to the choice of starting set of orbitals. Larger values of E g are yielded and a better agreement with previous calculations of the exciton binding energies are obtained when HSE wave functions are used, as shown in the Supplemental Material [68]. Unexpectedly, PBE-based calculations give an indirect band gap in K + -Λ, with values smaller by 0.03 and 0.05 eV respectively when compared to direct K + -K + gaps for WS 2 and WSe 2 . However these surprising results agree with a recent experimental result [70]. The choice of lattice parameter value is also important for the resulting band structure properties: using the experimental lattice parameter results in different values for ∆ c mainly. Preeminently most of the systems have an indirect band-gap with this particular choice of the lattice parameter [68], even after the use of partially self-consistent GW 0 scheme. This conforts us in our particular choices of exchange-correlation functional (HSE) at the DFT level and of the lattice parameter values (optimized ones), for which all MLs have direct band-gaps in good agreement with previous studies.

Conclusions.-Our calculations demonstrate that the bright to dark exciton energy splitting in MoX 2 and WX 2 monolayers depends in both sign and amplitude on the electron-hole short range Coulomb exchange within the exciton. In addition to this exchange energy, the conduction band spin-orbit splitting ∆ c needs to be taken into account, which has initially been put forward as the main origin of the dark-bright exciton splitting. To measure the splitting between ∆ c between electron spin states in the absence of holes, techniques like angle resolved photoemission spectroscopy (ARPES) [71] or electron spin resonance would be desirable, as pure optical spectroscopy techniques (absorption, emission) cannot separate this contribution from the strong electron-hole Coulomb exchange effects.

We thank Misha Glazov for fruitful discussions and ANR MoS2ValleyControl and Programme Investissements d'Avenir ANR-11-IDEX-0002-02, reference ANR-10-LABX-0037-NEXT for financial support. The authors also acknowledge the CALMIP initiative for the generous allocation of computational times, through the project p0812, as well as the GENCI-CINES, GENCI-IDRIS and GENCI-CCRT for the grant x2014096649. I. C. Gerber also thanks the CNRS for his financial support. X. M. acknowledges the Institut Universitaire de France. B.U. is supported by ERC Grant No. 306719.

FIG. 1 :

 1 FIG.1: a) Dark-bright energy splittings of the A 1s state excitons in the MoX2 and WX2 systems at G0W0+BSE level of theory, the bright exciton energy being set to 0, in comparison with the conduction band splitting induced by spin-orbit coupling ∆c. The sign of the e-h exchange contribution is negative. Insets are the corresponding qualitative band structure of the excitons in MoX2 (left) and WX2 (right), with bright and dark excitons in red and dotted gray respectively. b) Schematics of the one particle band structure of systems like MoX2 ML in the K+ valley, the K-valley can be obtained by time-reversal symmetry. The spin-orbit induced splittings for valence (∆v) and conduction bands (∆c) are shown.

TABLE I :

 I ∆Bex-Aex : calculated energy splitting between 1s A and B bright excitons, ∆ Dark-Bright : calculated dark-bright energy separation for various TMDC MLs of the 1s state excitons at the G0W0+BSE level using HSE orbitals, the values in parentheses are extracted from G0W0-PBE calculations.

  Evolution of the calculated conduction band splittings with respect to the level of theory for five TMDC monolayers. The data are extracted from Table SI-1.

		80
		60
		40
	c (meV) ∆	20 0	MoS 2
		-20	MoSe 2
			MoTe 2
		-40	WS 2
			WSe 2
		-60	HSE
	FIG. 2: