Chemical defects are of deleterious nature for the electrical properties of insulating polymers and can largely degrade their performance. Although these defects usually leave spectroscopic signatures in terms of characteristic luminescence peaks, it is nontrivial to assign, in an unambiguous way, the peaks to specific groups of defects because of the low intensity of the signal. In this work, we go beyond the traditional electroluminescence technique to record spectroscopic features of insulating polymers. By introducing a single plan of silver nanoparticles (AgNPs) at the near-surface of thin polypropylene films, the electroluminescent signal is enhanced by plasmon-related process. The latter leads much higher intensity and phasestabilization of the recorded spectra, thus improving the assignment of characteristic luminescence peaks.

I. INTRODUCTION

Insulating polymers are widely used in electrical engineering applications, such as high voltage direct current (HVDC) electrical cables, generators, transformers, capacitors, etc. [START_REF] Dissado | Electrical Degradation and Breakdown in Polymers[END_REF]. However, their service life in systems is limited by the stresses (electrical, thermal, mechanical, etc.) they undergo. Knowledge on the response of insulation materials, and in particular insulating polymers to the applied electrical stresses is essential to determine their safety limits. These materials should sustain very high electric fields. For example, the typical service fields for HVDC cables are in the order of 20 kV/mm. With time the ability of insulating polymers to sustain high electric fields decreases. It is mainly due to gradual degradation of the insulating materials and often leads to electrical breakdown. However, the degradation process takes certain time and is accompanied by modification in the response of the materials to the electrical stress. Moreover, the prebreakdown patterns may differ depending on the situation and the environmental factors (humidity, oxygen, radiation, corrosive agents, etc.) Electrical aging and degradation of insulating polymers therefore represent a constant interest in order to understand the fundamental mechanisms behind these effects, originating from evolving in time defects of the materials, and to contribute to the design and engineering of highly-performant electrical systems.

Electrical aging in insulators results from the induced thermal and higher energy chemical reactions after interaction of charged carriers with the dielectric material [2 -4] stress can partially be assigned to the space charges effect in the material. Different diagnostic methods are currently available to probe space charge, like wave propagation techniques (either pressure-wave -PIPWPor pulsed electroacoustic -PEAmethods) or thermal methods (Laser Induced Modulation Method -LIMMor Thermal Pulse -TP-) [START_REF] Fleming | Space charge profile measurement techniques: recent advances and future directions[END_REF]. In the last few years, electrical modes derived from Atomic Force Microscopy (AFM), like Kelvin Force Microscopy (KPFM) [START_REF] Palleau | Numerical simulations for a quantitative analysis of AFM electrostatic nanopatterning on PMMA by Kelvin force microscopy[END_REF][START_REF] Villeneuve-Faure | Methodology for extraction of space charge density profiles at nanoscale from Kelvin probe force microscopy measurements[END_REF] and Electrostatic Force Distance Curve (EFDC) [START_REF] Villeneuve-Faure | Towards 3D charge localization by a method derived from atomic force microscopy: the electrostatic force distance curve[END_REF] advanced on the subject by revealing information on the charge injection and transport processes at nanoscale level. However, given the principle of operation, the above mentioned methods can reveal the presence of space charge but they are not sensitive to the energetics of charge carriers.

As demonstrated previously, the electroluminescence (EL) appears appropriate diagnostic tool to address the aging problem of insulating polymers because the degradation process involves energy dissipation in the chemical bond energy range (of a few eV) that corresponds to the UV-vis range of the optical spectrum [9 -15]. EL is the excitation of luminescence as a result of the existence of an applied potential difference in the probed material. Basically the EL emission is a dynamic response of charges transport in the polymer material. The appearance of EL can be considered as a sign for the beginning of aging of polyolefin polymers under electrical stress. Spectroscopic analyses thus give indication on the nature of the transition process, i.e., on the dissociative versus non-dissociative excited states relaxation, defining in that way the energy decay mechanism: chemical versus physical one.

The EL of insulating polymers, such as polyethylene and polypropylene, is a specific response of the material which shows charge-structure interactions including the relaxation of kinetic energy by hot carriers, or modifications in their potential energy during radiative recombination of charges [11 -15]. However, one of the challenges to meet when applying EL to probe aging mechanisms of polyolefin polymers is the low intensity of the obtained signal [START_REF] Qiao | Electroluminescence and cathodoluminescence from polyethylene and polypropylene films: Spectra reconstruction from elementary components and underlying mechanisms[END_REF][START_REF] Qiao | Evidence of Exciton Formation in Thin Polypropylene Films under AC and DC Fields and Relationship to Electrical Degradation[END_REF]. This problem is even more complex in the case of polyethylene and polypropylene, as these are weakly emitting materials under electrical field. As a result, the resolution of recorded spectra does not allow fine interpretation. To overcome this problem, we present in this paper a study on the possibility to analyze the The authors are with LAPLACE laboratory, Université de Toulouse; CNRS, UPS, INPT; 118 route de Narbonne, F-31062 Toulouse, France (corresponding authors: kremena.makasheva@laplace.univ-tlse.fr and gilbert.teyssedre@laplace.univ-tlse.fr).

Plasmon induced enhancement of the electroluminescence signal of thin insulating polypropylene films*

K. Makasheva, Member, IEEE, L. Montanari, A. Scarangella, and G. Teyssedre, Senior Member, IEEE spectroscopic signature of insulating polypropylene films by plasmon induced enhancement of their characteristic EL spectra.

II. EXPERIMENTAL PART

A. Description of the structure and the plasma process

The insulating polymer material under study was a thin bi-oriented polypropylene (BOPP) film (thickness of 17.8 µm). The BOPP film, provided by KOPAFILM, Germany, was with different roughness for the two faces.

A very thin nanocomposite layer, consisting of a single layer of silver nanoparticles (AgNPs) embedded in a very thin organosilicon (SiOC:H) matrix, was deposited on the side of larger roughness of the BOPP film by a plasma process. To perform the EL-measurements the structure was both sides covered by 100 nm-thick ITO layers with 90% transparency and resistivity of 16 × 10 -3 Ω/cm 2 . A schematic cross-view of the structure is shown in Figure 1(a) and an optical image on top of the final sample is given on Figure 1(b).

The nanocomposite layer was deposited in two steps process: 1-plasma sputtering to create the layer of AgNPs and 2-plasma polymerization of hexamethyldisiloxane (HMDSO) precursor to cover the AgNPs by an organosilicon layer. The plasma deposition was performed in an axially-asymmetric capacitively-coupled RF (f = 13.56 MHz) discharge that successfully combines sputtering of a metal target and plasma polymerization. Details about the plasma process are given elsewhere [START_REF] Makasheva | Dielectric engineering of nanostructured layers to control the transport of injected charges in thin dielectrics[END_REF]. The discharge powered electrode (smaller electrode) was Ag-made target to bear the sputtering. For the sputtering step the plasma was maintained in pure argon at low pressure (p = 5.4 Pa) with RF power of P = 20, 40 and 80 W (Vdc = -546, -750 and -1000 V, respectively). The sputtering time was fixed to 5 s or to 12 s. [START_REF] Makasheva | Dielectric engineering of nanostructured layers to control the transport of injected charges in thin dielectrics[END_REF][START_REF] Milliere | Silver nanoparticles as a key feature of a plasma polymer composite layer in mitigation of charge injection into polyethylene under dc stress[END_REF].

The very thin SiOC:H cover layer was deposited in the same reactor after decomposition in the plasma of HMDSO at total pressure of ptot = 6.6 Pa. The power injected in the Ar-HMDSO plasma for this second step was P = 80 W which induced a bias voltage of Vdc = -900 V.

B. Structural and optical characterizations

At each step of the elaboration process the samples were structurally and optically characterized. The size and surface density of AgNPs were determined after processing of Scanning Electron Microscopy (SEM) images. Optical transmittance spectra were recorded using a Hewlett Packard HP8452A Diode Array Spectrophotometer in the UV-vis-NIR range (190-820 nm) to obtain the position of the AgNPs Local Surface Plasmon Resonance (LSPR). A Semilab 2000 spectroscopic ellipsometer was used to determine the thickness of the SiOC:H cover layer.

C. Electroluminescence characterization

EL measurements [13 -15] were achieved under secondary vacuum (<10 -6 mbar) in order to avoid electrical discharges in the ambient. They were performed under ac voltage with variable frequency and electric field, up to 180 kV/mm, using cooled detectors; being a photomultiplier in photon counting mode for EL-field intensity and phase patterns, and a CCD camera coupled to a dispersive system for spectra acquisition.

III. RESULTS AND DISCUSSION

A. AgNPs Localized Surface Plasmon Resonance -LSPR

The mean size of the obtained AgNPs is smaller than 10 nm for the lowest applied power of 20 W and of 15 ± 10 nm and 20 ± 10 nm for the 40 W and 80 W, respectively. The AgNPs are organized in the plane in a single layer. Depending on the time of sputtering the size and density of AgNPs are different and the single plan can be discrete for short sputtering times (5 s) or percolated for longer sputtering times (12 s) at fixed power and pressure. The resultant organosilicon cover layer is conformal to the AgNPs. It is with thickness of only 6.5 nm. UV-vis-NIR transmission spectra of the elaborated samples containing AgNPs are presented in Figure 2. The spectra for layers of discrete and percolated AgNPs are shown in Figure 2(a). One observes the LSPR of AgNPs (20 ± 10 nm size and surface density of 2 × 10 11 NPs/cm -2 ) of the discrete structure at 505 nm. The LSPR disappears when the AgNPs are percolated in the layer. When elaborated with lower plasma power the AgNPs are smaller in size and their LSPR is blue shifted as shown in Figure 2(b). However, the AgNPs size variation gives the possibility to probe different chemical bonds in the BOPP structure. The influence of the conductive ITO electrodes is also shown in Figure 2(b). One can notice that the conductive ITO electrodes limit the analyses to the visible range, which is in accordance with the targeted energies.

B. Enhancement of the electroluminescence intensity

EL-intensities of bare BOPP sample and of the AgNPs/SiOC:H tailored one as function of the applied electric field are shown in Figure 3. One can clearly notice the very strong enhancement of the EL-signal in presence of AgNPs. Actually, the plasmon induced enhancement of the EL spectrum can be more than 3 orders of magnitude. Moreover, the detection threshold is much lower. Even with a field of 10 kV/mm the BOPP signature becomes readable. It was previously shown that switching form gold to ITO electrodes produced a decrease in the EL emission from BOPP along with a change in the shape of the EL-field characteristic in which the bump-like shape obtained for Au-electrodes disappears with ITO. This was explained by the contribution from surface plasmon (SP) emission in the red domain [START_REF] Teyssedre | Ac and dc electroluminescence in insulating polymers and implication for electrical ageing[END_REF][START_REF] Qiao | Electroluminescence and cathodoluminescence from polyethylene and polypropylene films: Spectra reconstruction from elementary components and underlying mechanisms[END_REF][START_REF] Qiao | Evidence of Exciton Formation in Thin Polypropylene Films under AC and DC Fields and Relationship to Electrical Degradation[END_REF] in case of gold; such emission being dominating at low ac field.

There are indeed different possibilities for the enhancement of the EL intensity: (i) stronger excitation, meaning larger number of recombination events; (ii) larger quantum yield (larger probability for radiative recombination); (iii) AgNPs contribution to the emission signal. To get further into the underlying process, complementary information is achieved through phaseresolved EL patterns and EL emission spectra. Figure 4 compares the EL phase patterns obtained without and with the AgNPs/SiOC:H nanocomposite stack. Data are obtained at different applied electric fields owing to the strong difference in the EL yield (Figure 3). One can clearly see that there is no strong dependence of the shape of the pattern on the electric field and that the advance of phase is not largely pronounced in presence of AgNPs. This appears to be a quite distinct behavior compared to results obtained with Au electrodes where in general the advance of phase is larger when the SP emission is dominant [START_REF] Qiao | Evidence of Exciton Formation in Thin Polypropylene Films under AC and DC Fields and Relationship to Electrical Degradation[END_REF].

We have shown previously that the EL spectrum of BOPP, and more generally of polyolefins, can be deconvoluted into different contributions peaking at 415, 505 and 570 nm, all of these bands being characteristic of existing defects or created chemical functions into the material [START_REF] Teyssedre | Ac and dc electroluminescence in insulating polymers and implication for electrical ageing[END_REF][START_REF] Qiao | Electroluminescence and cathodoluminescence from polyethylene and polypropylene films: Spectra reconstruction from elementary components and underlying mechanisms[END_REF][START_REF] Qiao | Evidence of Exciton Formation in Thin Polypropylene Films under AC and DC Fields and Relationship to Electrical Degradation[END_REF]. Combined with the absorbance spectrum of the AgNPs/SiOC:H tailored BOPP film (Figure 5) one can realize the strong coupling at the same energy (2.45 eV or  = 505 nm) between the LSPR of the AgNPs and the contribution of recombination-induced luminescence involving conjugated CC bonds bound to CO species [START_REF] Qiao | Electroluminescence and cathodoluminescence from polyethylene and polypropylene films: Spectra reconstruction from elementary components and underlying mechanisms[END_REF]. Moreover, the spectrum obtained for tailored with AgNPs BOPP films (Figure 5) reveals the presence of an additional band at about 650 nm that does not appear in the spectra obtained on bare BOPP (not shown here). In case of Au-electrodes an extra broad emission at 700-750 nm was attributed to the SP emission [START_REF] Qiao | Electroluminescence and cathodoluminescence from polyethylene and polypropylene films: Spectra reconstruction from elementary components and underlying mechanisms[END_REF]. The additional band at 650 nm can be attributed to the SP emission from the AgNPs in SiOC:H environment. However, this does not constitute the only explanation to light enhancement. Other possibilities are to be considered. Firstly, the AgNPs/SiOC:H layer may favor charge injection, and then charge trapping on the AgNPs. The number of recombination events might be amplified by combining the enhanced charge injection efficiency and the capability of AgNPs to stabilize injected charges [START_REF] Makasheva | Dielectric engineering of nanostructured layers to control the transport of injected charges in thin dielectrics[END_REF]. Second, a sensitization of the PP due to the presence of AgNPs may occur, either through the formation of oxidized groups in the AgNPs environment, or through metal enhanced luminescence processes, that involve the LSPR in presence of metallic nanoparticles. This later process, complex indeed, has been recently reported in different nanoscience fields [START_REF] Jeong | Metal enhanced fluorescence (MEF) for biosensors: General approaches and a review of recent developments[END_REF][START_REF] Scarangella | Detection of the conformational changes of Discosoma red fluorescent proteins adhered on silver nanoparticles-based nanocomposites via surface-enhanced Raman scattering[END_REF].

IV. CONCLUSION

Evidences on the possibility to change energetics of the charge carriers near the interface is brought by electroluminescence measurements on tailored by AgNPs interfaces of capacitor films. Not only the light intensity is found much stronger in presence of AgNPs, but the detection of light emission starts at lower field. Such strong emission is most likely due to a radiative surface plasmon relaxation from the AgNPs in organosilicon environment. Depending on the size and density of AgNPs one can obtain different levels of energy absorption at the LSPR, thus providing flexibility for further enhancement of the response, according to probed material. Further work will be directed to explore the metal enhanced electroluminescence process by considering the localized surface plasmon resonance in presence of AgNPs in order to probe structural modifications and subsequent aging of polymeric insulations.

  . The aging of insulating polymers under electrical *Research supported by the program IDEX Actions Thématiques Stratégiques -ATS 2015 of the Université de Toulouse under project SEPHIR (2016-066-CIF-D-DRVD). The authors acknowledge support from the UMS Raymond Castaing of the University of Toulouse and thank Mr Stéphane Le Blond du Plouy for the SEM observations.

Figure 1 .Figure 2 .

 12 Figure 1. (a) Schematic of the studied structure in cross-section view and (b) Optical image of the final sample taken on the top.

Figure 3 .Figure 4 .

 34 Figure 3. Electroluminescence vs. electric field under 50 Hz ac stress of bare and tailored BOPP films.

Figure 5 .

 5 Figure 5. Absorbance and ac-EL spectrum of an one side tailored BOPP by an AgNPs/SiOC:H nanocomposite stack. The EL spectrum is obtained with an ac crest field of 90 kV/mm. The spectrum is deconvoluted into the sum of different Gaussian functions with peak wavelength indicated in the figure.

ACKNOWLEDGMENT

The authors acknowledge fruitful discussions with Dr. Christian Laurent.


Rémi Bérard

Kremena Makasheva

Hassan Sabbah

Karine Demyk

Christine Joblin

Using cold plasma to investigate the mechanisms involved in cosmic dust formation: role of the C/O ratio and metals

Keywords: astrochemistry, dust, stars: AGB and post-AGB, methods: laboratory, plasmas

Using a cold plasma reactor in which we inject an organosilicon molecular precursor, we investigate chemical mechanisms that can be involved in dust formation in evolved stars. By injecting metal atoms into the gas-phase, we investigate the role of metals on dust composition. We show the formation of composite particles made of pure metal (silver) nanoparticles embedded in an organosilicon dust. We study the impact of oxygen and show that it can inhibit dust formation, likely through the destruction of nucleation seeds.

Introduction

The processes related to nucleation, growth and processing of dust particles are of interest for both laboratory cold plasmas and astrochemistry. At the end of their life, evolved stars expel elements, in particular hydrogen, carbon, oxygen, silicon as well as metals such as titanium, magnesium and iron. The presence of these elements in an environment with favourable temperature and density conditions, results in dust formation. It is admitted that the gas-phase composition, in particular the C/O ratio has an impact on the type of formed dust (Ebel 2000). Metals also have a role as they are found to be involved in the final dust composition. Our objective is to get insights into the underlying mechanisms by using a dusty cold plasma.

Synthesis of the cosmic dust analogues

Our experiment is based on a capacitively-coupled axially-asymmetric radiofrequency (RF, 13.56 MHz) argon (p=5.3 Pa) discharge. A complete description of the set-up can be found elsewhere (Despax & Raynaud 2007). The plasma is ignited between two different in size parallel electrodes. The top electrode (smaller) is the driving one. The bottom electrode and reactor walls are grounded. Consequently, a self bias voltage is created on the top electrode allowing for sputtering of a metallic target (silver). The used molecular precursor is hexamethyldisiloxane (HMDSO, Si 2 C 6 OH 18 ). From its decomposition, we expect to have fragments containing Si, C, O and H, which are key elements to build cosmic dust analogues. HMDSO is pulse injected in the reactor. For our experiments, the pulse period (5 s) and the amplitude (1 V) are fixed. The amount of HMDSO is controlled by the pulse duration. The plasma is monitored by optical emission spectroscopy (OES). More specifically we perform a time-resolved analysis on two spectral lines: the argon line at 549.6 nm and the silver line at 546.5 nm. When HMDSO is injected inside the argon plasma, we observe oscillations of the argon line intensity at two frequencies (Fig. 1 (a)). The higher frequency corresponds to the pulsed injection of HMDSO whereas the lower frequency is related to dust formation in the plasma. The correlation between the argon line variation and dust formation have been demonstrated by light scattering studies (Despax et al. 2012). On the other hand, one can observe that the silver line disappears after HMDSO injection (Fig. 1 (a)). This is due to the growing deposit of the molecular precursor on the target, which prevents the sputtering of the metal. We however successfully manage to create dust with silver by increasing the RF power and reducing the HMDSO average flow, by reducing the pulse duration (Fig. 1 (b)).

Dust is collected and observed by scanning electron microscopy (SEM). An exemple is presented in Fig. 2. Dust particles have a round shape with a reproducible average size and dispersion, which depend on the experimental conditions. We should note here that the dust particles are connected by a matrix made of the same elements as the dust. Plasma cosmic dust analogues 3

Impact of metal atoms

The IR spectrum of the collected dust (Fig. 3) has been studied using the ESPOIRS set-up (Demyk et al. 2017). Without silver, the dust has a typical organosilicon structure with a characteristic band at around 10 µm corresponding to SiOSi (+SiOCH x , x=[2,3]) bonds. Bands of SiCH x are also evidenced around 3.4 µm and at 8 µm.

In presence of silver atoms, the IR spectrum reveals an organosilicon structure and new bands involving silver. We observe the formation of silver carbonate which indicates an interaction of the metal with CO species in the gas phase. In addition, the AgOSi vibration is an indication of an organosilicon-silver interaction inside the dust. We note changes in the aliphatic bands indicating a modification of the carbonaceous structure of the dust. Using in addition TEM analysis, we conclude that the addition of metal atoms in the plasma leads to the formation of silver crystalline nanoparticules embedded in the organosilicon dust. We also investigated the molecular content associated with the collected dust using the laser desorption ionisation mass spectrometry available on the AROMA set-up (Sabbah et al. 2017). We found the presence of numerous hydrocarbon species including aromatics, which are not observed in the sample without silver. This suggests a role of silver atoms in the formation of these species in the gas phase.

Impact of oxygen

In relation with the C/O ratio, we investigate the impact of oxygen on dust formation by progressively adding O 2 , which dissociates in the plasma. The experiment is followed by OES and presented in Fig. 4. In the presence of dust in the plasma, we progressively increase the oxygen flow. At a certain amount of oxygen, dust formation is not observed anymore. When the oxygen flow is decreased, dust formation reappears again. This shows a correlation between the oxygen amount and dust formation in the plasma. We identify a transition regime between the presence and absence of dust. Oxygen can either affect nucleation seeds or dust growth. The injection of another compound that would serve as nucleation seeds may help further progress in addressing this issue.

Conclusion and perspectives

In this exploratory work, we successfully use a cold plasma reactor to investigate the impact of gas-phase composition on the formation of dust containing key elements involved in stardust (C, O, Si, H, metal). We show that a large amount of oxygen in the mixture prevents dust formation. When metal atoms are injected in the plasma, different chemical mechanisms enter into competition leading to the formation of crystalline metallic nanoparticles embedded in the amorphous organosilicon dust. This also impacts the gas-phase carbon chemistry with the formation of new molecular species including aromatic molecules. Further investigation is needed to fully understand the role of silver on the molecular composition. Other, more astrophysically relevant metals such as iron will be considered in future experiments.

Figure 1 .

 1 Figure 1. Time-resolved OES of argon (549.6 nm) and silver (546.5 nm) lines. Dust synthesis (a) without silver sputtering (P=10 W, HMDSO average flow = 0.28 sccm), and (b) with silver sputtering (P=30W, HMDSO average flow = 0.12 sccm).

Figure 2 .

 2 Figure 2. SEM image of collected dust (P=10 W, HMDSO average flow = 0.28 sccm).

Figure 3 .

 3 Figure 3. Infrared spectra of collected organosilicon dust with and without silver.

Figure 4 .

 4 Figure 4. Time resolved OES following the impact of oxygen flow on dust formation.

Acknowledgements We acknowledge support from the European Research Council FP7 ERC-2013-SyG NANOCOSMOS (G.A. no. 610256). Rémi Bérard acknowledges a travel grant from the Programme National "Physique et Chimie du Milieu Interstellaire" (PCMI) of CNRS/INSU with INC/INP co-funded by CEA and CNES.


F Mortreuil

L Boudou

K Makasheva

G Teyssedre

C Villeneuve-Faure

Influence of dielectric layer thickness on charge injection, accumulation and transport phenomena in thin silicon oxynitride layers: a nanoscale study

Keywords: thin film, dielectric, plasma deposition, charge injection, Kelvin Probe Force Microscopy, space charge

Charge injection and retention in thin dielectric layers remain critical issues due to the great number of failure mechanisms they inflict. Achieving a better understanding and control of charge injection, trapping and transport phenomena in thin dielectric films is of high priority aiming at increasing lifetime and improving reliability of dielectric parts in electronic and electrical devices. Thermal silica is an excellent dielectric but for many of the current technological developments more flexible processes are required for synthesizing high quality dielectric materials such as amorphous silicon oxynitride layers using plasma methods. In this article, the studied dielectric layers are plasma deposited SiOxNy. Independently on the layer thickness, they are structurally identical: optically transparent, having the same refractive index, equal to the one of thermal silica. Influence of the dielectric film thickness on charging phenomena in such layers is investigated at nanoscale using Kelvin Probe Force Microscopy (KPFM) and Conductive Atomic Force Microscopy (C-AFM). The main effect of the dielectric film thickness variation concerns the charge flow in the layer during the charge injection step.

According to the SiOxNy layer thickness two distinct trends of the measured surface potential and current are found, thus defining ultrathin (up to 15 nm thickness) and thin (15 nm -150 nm thickness) layers. Nevertheless, analyses of KPFM surface potential measurements associated with results from Finite Element Modelling of the structures show that the dielectric layer thickness has weak influence on the amount of injected charge and on the decay dynamics, meaning that pretty homogeneous layers can be processed. The charge penetration depth in such dielectric layers is evaluated to 10 nm regardless the dielectric thickness.

Introduction

Common property of the dielectric materials is to accumulate charges under external stress, either electric field or particle beam irradiation. Charge accumulation phenomena occur in any dielectric regardless its dimensions (centimeter or nanometer scale) inducing inhomogeneous internal electric field. Even though this effect lies down the principle of operation of a large number of applications as non-volatile memory devices [START_REF] Rao | Silicon nanocrystal based memory devices for NVM and DRAM applications[END_REF][START_REF] Perret-Tran-Van | Controlled fabrication of Si-nanocrystals embedded in thin SiON layers by PPECVD followed by oxidizing annealing[END_REF] it causes dielectric troubleshoots in other devices like electrostatic adhesion in MicroElectroMechanical System (MEMS) [START_REF] Witvrouw | Materials issues in the processing, the operation and the reliability of[END_REF] or induces damages in electronic devices through uncontrolled electrostatic discharges [4]. Thus, the dielectric charging phenomenon appears as one of the major challenges to meet for many electrical systems. The mechanisms of charge injection and accumulation in dielectric layers remain constantly a subject of scientific research aiming at a better managing of this phenomenon and controlling the level of electrostatic charging of the dielectric layers [START_REF] Rao | Silicon nanocrystal based memory devices for NVM and DRAM applications[END_REF][START_REF] Perret-Tran-Van | Controlled fabrication of Si-nanocrystals embedded in thin SiON layers by PPECVD followed by oxidizing annealing[END_REF][START_REF] Rezende | Detection of charge distribution in insulator surfaces[END_REF][START_REF] Lamhamdi | Voltage and temperature effect on dielectric charging for RF-MEMS capacitive switches reliability investigation[END_REF][START_REF] Zhang | Stability, nonlinearity and reliability of electrostatically actuated MEMS devices[END_REF]. However, major advances on the matter can be expected after development of appropriate diagnostic to probe charge injection and decay in thin dielectric layers.

During the past decades, a lot of experimental techniques have been developed to measure space charge distribution as function of the depth in the dielectric and the question of their adaptation to thin dielectrics was raised [START_REF] Teyssedre | Challenges in probing space charge at sub-micrometer scale[END_REF][START_REF] Hamidouche | Very high spatial resolution space charge measurement using electro-acoustic reflectometry[END_REF]. These techniques, based on acoustic or thermal interaction with electrical charges, provide charge density distribution in thick polymer films (thickness from few tens up to few cents of micrometers) with spatial resolution approaching 1µm but they fail to probe charge injection and decay mechanisms in thin dielectric films (thickness in the nanoscale range) used in electronic or microsystems components.

Moreover, when the layer thickness scales down the micrometer range, specific issues like interfaces or transition between amorphous and crystalline domains in the dielectric, especially for insulating polymers, are superimposed [START_REF] Arita | A method for detection and visualization of charge trapping sites in amorphous parts in crystalline polymers[END_REF].

Aiming at a study of the charges distribution in thin dielectric films, techniques derived from Scanning Probe Microscopy (SPM) have naturally emerged to inject locally charges and to image the resulting surface potential modification. In this case, the Atomic Force Microscope (AFM) tip is used to perform local charge injection in dielectric materials, followed by measurements of the induced resonance frequency shift by Electrostatic Force Microscopy (EFM) [START_REF] Stern | Exposition and imaging of localized charge on insulator surfaces using force microscope[END_REF][START_REF] Marchi | Characterization of trapped electric charge carriers behavior at nanometer scale by electrostatic force microscopy[END_REF][START_REF] Lambert | Dispersive charge transport along the surface of an insulating layer observed by electrostatic force microscopy[END_REF][START_REF] Tzeng | Charge trapping properties at silicon nitride/silicon oxide interface studied by variable-temperature electrostatic force microscopy[END_REF] or by the resulting surface potential in Kelvin Probe Force Microscopy (KPFM) [START_REF] Rezende | Detection of charge distribution in insulator surfaces[END_REF][START_REF] Stern | Exposition and imaging of localized charge on insulator surfaces using force microscope[END_REF][START_REF] Morita | Microscale contact charging on silicon oxide Characterization[END_REF]. Literature overview emphasizes that charge injection and decay in thin dielectric films were extensively studied by EFM and KPFM focusing on charge density determination [START_REF] Charrier D S H, Kemerink | Real versus measured surface potentials in scanning Kelvin[END_REF][START_REF] Borowik | Calculating Kelvin force microscopy signals from static force fields[END_REF], influence of the experimental conditions (humidity [START_REF] Rezende | Detection of charge distribution in insulator surfaces[END_REF][START_REF] Stern | Exposition and imaging of localized charge on insulator surfaces using force microscope[END_REF][START_REF] Ishii | Static states and dynamic behaviour of charges: observation and control by scanning probe microscopy[END_REF], lift height [START_REF] Zaghloul | On the influence of environment gases, relative humidity and gas purification on dielectric charging/discharging processes in electrostatically driven MEMS[END_REF] or perturbation introduced by the electrostatic forces [START_REF] Zaghloul | A systematic reliability investigation of the dielectric charging process in electrostatically actuated MEMS based on Kelvin Force Microscopy[END_REF][START_REF] Ziegler | Feed-forward compensation of surface potential in atomic force microscopy[END_REF]), or charge dynamics [START_REF] Stern | Exposition and imaging of localized charge on insulator surfaces using force microscope[END_REF][START_REF] Zaghloul | On the influence of environment gases, relative humidity and gas purification on dielectric charging/discharging processes in electrostatically driven MEMS[END_REF]. In spite of the numerous investigations on the problem, many aspects as charges distribution within the layer, mechanisms occurring at the metal/dielectric interface or charge injection mechanisms remain currently ill described. Besides, the AFM techniques can bring complementary information on the dielectric charging phenomenon. For example, low-current measurements in thin dielectric layers can be performed by conductive-AFM (C-AFM) or Tunneling AFM (TUNA) [START_REF] Lanza | Conductive Atomic Force Microscopy: Applications in Nanomaterials[END_REF]. Two aspects can be thus investigated: (i) dielectric reliability in terms of breakdown [START_REF] Foissac | A relationship between statistical time to breakdown distributions and pre-breakdown negative differential resistance at nanometric scale[END_REF] or leakage current [START_REF] Seko | Behavior of Local current leakage in stressed gate SiO2 films analyzed by Conductive Atomic Force Microscopy[END_REF] and (ii) mechanisms occurring during charge injection and transport. It was demonstrated for ultrathin SiO2 layer (less than 4 nm) that Fowler-Nordheim mechanism [START_REF] Foissac | A relationship between statistical time to breakdown distributions and pre-breakdown negative differential resistance at nanometric scale[END_REF][START_REF] Frammelsberger | C-AFM-based thickness determination of thin and ultra-thin SiO2 films by use of different conductive-coated probe tips[END_REF] can be extracted from current versus voltage curves.

However, determination of some physical parameters as energy barrier or in-depth charge distribution remains strongly correlated to the tip-sample surface contact estimation [START_REF] Frammelsberger | C-AFM-based thickness determination of thin and ultra-thin SiO2 films by use of different conductive-coated probe tips[END_REF][START_REF] Frammelsberger | Simplified tunnelling current calculation for MOS structures with ultra-thin oxides for conductive atomic force microscopy investigations[END_REF][START_REF] Olbrich | Nanoscale electrical characterization of thin oxides with conductive atomic force microscopy 36[END_REF][START_REF] Porti | Nanometer-scale electrical characterization of stressed ultra-thin SiO2 film using conducting atomic force microscopy[END_REF][START_REF] Olbrich | A new AFM-based tool for testing dielectric quality and reliability on a nanometer scale[END_REF] and requires alternative approaches. This paper is dedicated to an experimental study of the influence of dielectric layer thickness on charge injection and transport in thin amorphous silicon oxynitride layers. This well-characterized material [START_REF] Makasheva | Dielectric layers for RF-MEMS switches: design and study of appropriate structures preventing electrostatic charging[END_REF][START_REF] Villeneuve-Faure | Kelvin force microscopy characterization of charging effect in thin a-SiOxNy:H layers deposited in pulsed plasma enhanced chemical vapor deposition process by tuning the silicon environment[END_REF], elaborated by plasma process, presents electrical properties very close to those of thermal silica which makes it perfect model material. Surface potential measurements achieved by KPFM and current measurements performed by C-AFM are combined to better understand charge injection mechanisms in thin dielectric films. The paper is organized as follows: the experimental details are presented in section 2. Section 3 is dedicated to results and discussion focusing successively on the SiOxNy layers characterization, the influence of dielectric thickness on charge injection mechanism and the amount of injected charges, the current versus voltage characteristics recorded by C-AFM, and the charge dynamics after injection. Finally, Section 4 summarizes the main conclusions.

Experimental

Plasma processed amorphous silicon oxynitride layers (SiOxNy) with very low N-content (of only 4 at. %) have been chosen for this study because of their outstanding electrical properties, close to those of thermal silica, and the possibility to well-control their thickness [START_REF] Makasheva | Dielectric layers for RF-MEMS switches: design and study of appropriate structures preventing electrostatic charging[END_REF]. The dielectric layers were deposited by Pulsed Plasma Enhanced Chemical Vapor Deposition (PPECVD) in a radio-frequency (RF) capacitively coupled discharge sustained at low gas pressure. The parameters of the plasma process are summarized in Table 1. The gas mixture was of He, SiH4 and N2O, with helium as a vector gas (39.7% of the total gas flow). The N2O content was high, in order to achieve good quality silica layers. The RF discharge was modulated with square pulses to avoid dust formation in the plasma and to improve quality of the deposited layers, thus their dielectric properties. The arrangement of the dielectric matrix, and accordingly the quality of deposited silica layers was further improved by the very slow deposition process and the high temperature of the substrate during deposition. More details on the plasma process are presented elsewhere [START_REF] Makasheva | Dielectric layers for RF-MEMS switches: design and study of appropriate structures preventing electrostatic charging[END_REF][START_REF] Villeneuve-Faure | Kelvin force microscopy characterization of charging effect in thin a-SiOxNy:H layers deposited in pulsed plasma enhanced chemical vapor deposition process by tuning the silicon environment[END_REF]. The structure of the studied devices is shown in figure 1. The basis consists of a 50 nmthick SiO2 layer thermally grown on Si (100) intrinsic substrates by dry oxidation. The parameters of the dry oxidation process are given in Table 1. Spectroscopic ellipsometry was used to measure the dielectric layer thicknesses according to the procedure developed earlier [START_REF] Villeneuve-Faure | Kelvin force microscopy characterization of charging effect in thin a-SiOxNy:H layers deposited in pulsed plasma enhanced chemical vapor deposition process by tuning the silicon environment[END_REF]. A SOPRA GES-5 ellipsometer with a rotating polarizer and a fixed analyzer was used in the spectral range 250-850 nm. The simulation of the recorded spectra was performed with Winelli software provided by SOPRA LAB [32]. Forouhi-Bloomer dispersion law was applied for the spectra processing [START_REF] Forouhi | I Optical dispersion relations for amorphous semiconductors and amorphous dielectrics[END_REF]. This approximation applies for dielectric and semiconducting thin layers and provides information on the layer thickness and optical properties (n -refractive index and k -extinction coefficient).

AFM measurements were performed using a Bruker Multimode 8 apparatus under controlled environment (without humidity since under N2 atmosphere) to avoid charge dissipation due to the presence of water layer on the sample surface [START_REF] Villeneuve-Faure | Kelvin force microscopy characterization of charging effect in thin a-SiOxNy:H layers deposited in pulsed plasma enhanced chemical vapor deposition process by tuning the silicon environment[END_REF]. A silicon AFM tip with PtIr coating (curvature radius Rc = 25 nm and spring constant ks = 2.4 N/m) was used for the charge injection protocol and for the surface potential measurements by KPFM. The dielectric charging was achieved in contact mode (contact force set to 90 nN) by applying positive DC bias (V0 = +5 to +15 V) to the AFM tip for different time durations, the sample back side being grounded (figure 1(a)). After the charging step, the same tip was used to probe the surface potential in Amplitude Modulation KPFM mode using a 10 nm-lift.

Current measurements were performed with a diamond coated highly doped Si tip (Rc = 125 nm and ks = 2 N/m) using C-AFM mode (figure 1(b)). A bias varying between +1 V and +20 V was applied to the Au-electrode. In order to adapt the noise detection level, the current measurements were performed owing to a low noise amplifier module, with 20 pAsensitivity for the dielectric layers thicker than 15 nm and 10 nA-sensitivity for lower thicknesses. Current was acquired during 60 s for each bias.

Results and discussion

Dielectric layer characterization

The thickness and optical parameters of the plasma deposited SiOxNy layers were systematically measured by spectroscopic ellipsometry. The SiOxNy-layers span in the thickness range from ultrathin, i.e. up to 15 nm (5.9 ± 0.4 nm and 11.1 ± 0.9 nm) to thin, 15 nm < d < 150 nm (15.6 ± 0.4 nm, 31.1 ± 0.2 nm, 50.0 ± 0.2 nm, 68.0 ± 0.3 nm, 129.7 ± 0.8 nm), layers. They are all transparent with extinction coefficient k < 0.002 in the investigated spectral range, having refractive index n = 1.45 ± 0.1 at wavelength  = 632.8 nm (figure 2) which qualifies them as layers with optical properties very close to thermal silica layers. Using the Forouhi-Bloomer dispersion law for spectra processing allows for extraction of the layer thickness and the optical properties in a consistent way. It avoids overestimation of the layer thickness when the refractive index of bulk silica is applied for simulation of the recorded ellipsometric spectra [START_REF]Consistent refractive index parameters for ultrathin SiO2 films[END_REF]. Regardless the SiOxNy-layer thickness the refractive index remains the same (figure 2(a)).

We do not observe departure in the optical properties, towards higher refractive index, for the ultrathin SiOxNy-layers as reported for ultrathin SiO2 thermal layers [START_REF]Consistent refractive index parameters for ultrathin SiO2 films[END_REF]. Conservation of the refractive index for the SiOxNy-layers is most likely due to the plasma deposition process for which the layer growth results from deposition of plasma generated radicals, issued from the injected precursors. The applied for this study pulsed mode of operation of the PPECVD process improved the quality of the deposited layer. It leads to homogeneous distribution of the gas precursors in the reactor between the pulses, before each plasma ignition, which prevents from plasma deposition under O-related by-products exhaust [START_REF] Radouane | RF discharge modelling in a N2O/SiH4 mixture for SiO2 deposition and comparison with experiment[END_REF]. Thus the PPECVD process allows for better control of the layer stoichiometry (O / Si = 2), avoiding modifications in the layer composition and structure. The spectral response of the SiOxNy-layers is closely related to the dielectric structure of the layer. It also gives information on the energy gap and the different charge traps [START_REF] Robertson | Band offsets of high K gate oxides on III-V semiconductors[END_REF].

After processing of the ellipsometry spectra, for all studied here SiOxNy-layers, we have found an electronic part of the dielectric constant of  = 2.13 (n = 1.46). The later provides a Schottky pinning parameter of Sp = 0.887 and defines the charge state in the SiOxNy dielectric interface as slightly pinned when in contact with a metal electrode [START_REF] Robertson | Band offsets of high K gate oxides on III-V semiconductors[END_REF][START_REF] Villeneuve-Faure | Charge injection in thin dielectric layers by atomic force microscopy: influence of geometry and material work function of the AFM tip on the injection process[END_REF]. A small increase of the refractive index is observed in the Mid-UV and Near-UV range for the thickest SiOxNy layer (d = 129.7 nm, in figure 2(b)). In addition to the normal dispersion of the refractive index in that spectral region, the refractive index increase is most likely due to the limited, but present small N-content (4 at. %) in the SiOxNy-layer.

Impact of the dielectric thickness on the charge injection: KPFM study

For each SiOxNy layer, charge injection was done under tip bias V0 varying from +5 V to +15 V during various times (from 1 min to 10 min). Immediately after charge injection, the KPFM -Dielectric layers with thickness less than 15 nm (ultrathin layers): FWHM and area IS increase with the dielectric layer thickness even though the electric field decreases (constant bias voltage). The same evolution of the surface potential profile is observed when increasing the injection bias for a fixed injection time (results not shown). Indeed, the Vm and IS are insensitive to the injection bias increase for charge injection in the 11 nm-thick film, whereas these two parameters increase with increasing the bias for charge injection in the 130 nm-thick dielectric film. Concerning the 31 nm-thick film, again a two steps behavior is observed: the increase of Vm and IS with increasing the injection bias is followed by saturation (for applied bias larger than +8 V). However, the relationship between the area and the amount of injected charges is not straightforward in this case because of the dielectric layer thickness. This aspect will be discussed in detail in the following sections.

Electric field influence on the charge injection: modeling approach

Results presented in the previous part show different fate of the injected charges depending on the dielectric layer thickness. To better understand the underlying mechanisms, we have performed an electrostatic modelling of the system aiming at identification of the relative contribution of the electric field components during charge injection and the influence of dielectric layer thickness on the surface potential profile.

The electric field is computed using a simple model consisting in a truncated cone of 10 µm-height with 14° aperture angle, ending with a semi-spherical apex of Rc = 25 nm or Rc = 125 nm. The considered geometry corresponds to a classical AFM tip shape used for modelling [START_REF] Boularas | Multidimensional modelling of electrostatic force distance curve over dielectric surface: Influence of tip geometry and correlation with experiment[END_REF]. It accounts for the macroscopic shape of the tip, rather than the nanoscopic shape of the tip apex due to the long range nature of the electrostatic forces [START_REF] Sacha | Influence of the macroscopic shape of the tip on the contrast in scanning polarization force microscopy images[END_REF]. This tip is surrounded by an air box (dimensions large enough to avoid edge effects). It is in contact with the dielectric SiOxNy layer (figure 5(a)). The Au-electrode is considered at floating potential.

Potential and electric field are computed in air, SiOxNy, SiO2 layers and in the intrinsic Sisubstrate. The electric field is supposed capacitively distributed considering the relatively short polarization times used here and the large dielectric time constant for the dielectric layers. The relative dielectric permittivity of the SiOxNy layer is taken r = 3.9, as measured by dielectric spectroscopy for the very same dielectric layers [START_REF] Makasheva | Dielectric layers for RF-MEMS switches: design and study of appropriate structures preventing electrostatic charging[END_REF]. For the thermal SiO2 and the Si-substrate it is r = 3.9 and 12, respectively. The model is 2D-axisymmetric based on Finite-Element Model (FEM) developed on COMSOL Multiphysics. The mesh is refined and optimized close to the contact point to improve calculation accuracy. The potential is applied on the tip and the ground is taken at the silicon substrate backside (charge injection configuration). The dielectric is supposed free from charges at the initial state. The boundary conditions are selected to ensure no edge effect and no charges (zero potential) on the free boundaries of the simulation box.

The Poisson's equation is solved in air and in the dielectric layers to determine the potential V.

∇ ⃗ ⃗ • (𝜀 0 𝜀 𝑟 𝐸 ⃗ ) = 𝜌 ( 1
)
where ρ is the charge density and ε0 is the vacuum permittivity.

The electric field 𝐸 ⃗ is derived from the potential V: distribution of the electric field in the 11 nm-thick layer is explained by the fact that for dielectric layers with thicknesses smaller than the AFM tip radius, the configuration gets closer to a planeplane one. In our configuration this effect is ensured by the Au layer, which screens the electric field, and diminishes the influence of the thermal SiO2 layer and the intrinsic Si bulk. The evolution of the lateral Er-component of the electric field along the dielectric surface is represented in figure 5(d) for the 130 nm-thick and the 11 nm-thick (insert of figure 5(d)) dielectric layers. One can notice that the maximum lateral electric field is less influenced by the thickness of the dielectric layer whereas a profile broadening is observed for the thinner layer. This high lateral electric field drives the charges spreading in radial direction. The strong inhomogeneity of the electric field, especially for thin SiOxNy-layers (d > 15 nm) prevents from correct interpretation of the measured surface potential on films of different thicknesses, as the electric field at the contact point is different. For comparison reasons figure 6 represents the variation of the surface potential maximum Vm and FWHM as function of the film thickness for the same initial electric field at the injection point, as calculated from the above described model. The FWHM does not vary significantly with the dielectric layer thickness. This is most probably related to the fact that the lateral electric field maximum is weakly influenced by the dielectric layer thickness (figure 5(d)). In addition, it is of the order of 0.5 µm, i.e. significantly larger than the distance from the axis providing maximum radial field.

𝐸 ⃗ = -∇ ⃗ ⃗ 𝑉 (2)
So, the space-charge induced field probably drives the charge spreading more significantly than the geometric field.

The potential maximum Vm and consequently the area under the peak Is increases with the film thickness. However, to conclude about possible relation between the charge storage capability and the film thickness, the relation between charge amount and surface potential should be determined.

Estimation of the injected charge density

In order to identify the impact of the dielectric layer thickness on the probed surface potential, the previous finite element model was modified. Space charge distribution 𝜌 was introduced in the Poisson's equation. The Gaussian shape of the measured surface potential profile was adopted for the lateral distribution of the injected charges. Nevertheless, different hypotheses can be made for the in-depth distribution of the injected in the dielectric layer charges. Here we have investigated two different in-depth charge distributions:

1) In the first case, the in-depth charge density distribution was supposed constant over a thickness dp. The same hypothesis was made by E. Palleau et al. [START_REF] Palleau | Numerical simulations for a quantitative analysis of AFM electrostatic nanopatterning on PMMA by Kelvin force microscopy[END_REF]. The resulting charge density profile 𝜌 𝐻 is called 2D, depicted on the insert in Figure 7(a), and can be given by the following expression:

𝜌 𝐻 (𝑟, 𝑧) = 𝑄 𝑑 𝑝 1 𝜎 𝑟 √2𝜋 𝑒𝑥𝑝 (- 𝑟² 2𝜎 𝑟 ² ) 0 ≤ z ≤ dp ( 3
)
where Q is the injected charge quantity, dp is the charge penetration depth in the dielectric and σr is a parameter corresponding to the lateral extension of the charge distribution (related to the FWHM, Wr = 2.35 σr). The penetration depth dp could be smaller or equal to the dielectric layer thickness. Figure 7(a) illustrates the charge density distribution in a 130 nm-thick dielectric layer for Q = 1.25 × 10 -16 C, dp = 11 nm and Wr = 250 nm.

2) In the second case, the in-depth distribution of injected charges is with half-Gaussian shape. The resulting 3D charge density profile 𝜌 𝐺 , depicted on the insert in figure 7(b), can be given by the following expression:

𝜌 𝐺 (𝑟, 𝑧) = 2𝑄 1 𝜋𝜎 𝑟 𝜎 𝑧 𝑒𝑥𝑝 (- 𝑟 2 2𝜎 𝑟 2 - 𝑧² 2𝜎 𝑧 ² ) 0 ≤ z ≤ d ( 4
)
where σz is related to the in-depth distribution of injected charges (related to FWHM Wz of the full Gaussian with Wz=2.35σz). The insert in figure 7 To obtain the surface potential profile, the electrostatic force Fe induced on the tip by the charge cloud was computed using the following equation:

𝐹 𝑒 = ∬ 𝜀 0 𝜀 𝑟 2 ‖𝐸 ⃗ ‖²𝑑𝑆 𝑡𝑖𝑝 ( 5
)
where E is the electric field, r = 1 is the air relative dielectric permittivity and dS is an elementary surface. At each point, the electrostatic force Fe is computed as function of the applied bias V0. Thus a parabolic curve, as the one shown in figure 7(c), is obtained and the related surface potential corresponds to the electrostatic force minimum [START_REF] Charrier D S H, Kemerink | Real versus measured surface potentials in scanning Kelvin[END_REF]. Therefore, independently on the considered space charge distribution, for fixed charge distributions, the maximum surface potential increases with the dielectric layer thickness.

Concerning the 2D-charge distribution

Moreover, the increase in potential vs. layer thickness obtained in simulation with the 2D or 3Dcharge distribution reproduces the trends in the experimental results presented in figure 6.

According to these simulation results, the increase in potential with the dielectric thickness for fixed injection conditions (field and time) would be explained mainly by electrostatic features and not by a variation in the amount of injected charges. The electric field at the contact point actually determines the charge amount to be injected in the dielectric.

Charges dynamic during injection: current measurements

To go further in the description of charge dynamic during injection, the study on charge injection and surface potential measurements was completed with C-AFM measurements. The C-AFM measurements were performed by using the second device structure (figure 1(b)) and a diamond coated highly-doped Si tip with curvature radius of Rc = 125 nm. For comparison purposes, the current measurements performed on dielectric films with different thicknesses are presented as function of the electric field at the contact point (figure 8). The electric field at contact point is computed using a FEM model, similar to the one already described in Section 3.3. The main difference is that the bias is applied on the Au-electrode (figure 1(b)) and the tip is grounded, in order to remain consistent with the experimental situation.

As previously noticed, different responses are observed for the ultrathin (d < 15 nm) and the thin (15 nm < d < 150 nm) SiOxNy films. The measured current for ultrathin layers remains at low current level (0.14 pA) and almost constant for a large range of variation of the electric field up to a threshold value after which a very quick current increase (5 orders of magnitude) is observed (figure 8). The thin layers are characterized by a rather slow increase of the current with the electric field, starting at halved current level (0.07 pA) for a fixed electric field and increasing by an order of magnitude for the same range of variation of the electric field. The 16 nm-thick SiOxNy film appears intermediate with a mixed response. No topography modifications were observed on the surface of the studied dielectric layers after the C-AFM measurements. With respect to the current measurements, one can say that Fowler-Nordheim conduction is most likely the mechanism controlling the current in ultrathin layers [START_REF] Foissac | A relationship between statistical time to breakdown distributions and pre-breakdown negative differential resistance at nanometric scale[END_REF][START_REF] Frammelsberger | C-AFM-based thickness determination of thin and ultra-thin SiO2 films by use of different conductive-coated probe tips[END_REF][START_REF] Olbrich | Nanoscale electrical characterization of thin oxides with conductive atomic force microscopy 36[END_REF][START_REF] Porti | Nanometer-scale electrical characterization of stressed ultra-thin SiO2 film using conducting atomic force microscopy[END_REF]. However, for the interpretation of these results, in term of transport laws, the current density needs to be computed, which requires estimation of the current collection area. Indeed, assessment of the current collection area is the main bottleneck in the analysis of the C-AFM results. In C-AFM mode, the measurement response is closely linked to the physical properties of the contact between the nano-sized tip and the dielectric surface. This interaction was demonstrated for ultrathin inorganic (ceramic) dielectric films and thin organic semiconductor films, by using the Fowler-Nordheim [START_REF] Charrier D S H, Kemerink | Real versus measured surface potentials in scanning Kelvin[END_REF][START_REF] Foissac | A relationship between statistical time to breakdown distributions and pre-breakdown negative differential resistance at nanometric scale[END_REF][START_REF] Frammelsberger | C-AFM-based thickness determination of thin and ultra-thin SiO2 films by use of different conductive-coated probe tips[END_REF][START_REF] Villeneuve-Faure | Charge injection in thin dielectric layers by atomic force microscopy: influence of geometry and material work function of the AFM tip on the injection process[END_REF][START_REF] Boularas | Multidimensional modelling of electrostatic force distance curve over dielectric surface: Influence of tip geometry and correlation with experiment[END_REF][START_REF] Palleau | Numerical simulations for a quantitative analysis of AFM electrostatic nanopatterning on PMMA by Kelvin force microscopy[END_REF] and the Space Charge Limited Current law [START_REF] Reid | Space charge limited current measurements on conjugated polymer films using Conductive[END_REF],

respectively. We also split the analysis here in two, for ultrathin and thin SiOxNy layers [START_REF] Hebert | Measurement of the refractive index of thin SiO2 films using tunneling current, oscillations and ellipsometry[END_REF].

-Ultrathin dielectric layers (d < 15 nm)

Concerning the ultrathin dielectric layers, the collection area is typically determined by using one of the three main approaches: (i) The contact area is computed using the Hertz approach and corresponds to the mechanical contact area [START_REF] Ruskell | High-resolution Fowler-Nordheim field emission map of thin silicon oxide layers[END_REF], (ii) The effective contact surface is determined by fitting the current-voltage experimental curve. This assessment depends on the following parameters: AFM-tip work function, contact force and dielectric thickness, and leads a broad range of obtained values, from 10 nm² to 100 nm² or even more if the curvature radius of the AFM-tip is large, and (iii) The contact area is estimated after SEM observations of the AFM tip after measurements [START_REF] Celano | Evaluation of the electrical contact area in contact-mode scanning probe microscopy[END_REF].

In order to better estimate the effective contact surface for the current measurements we have used a fourth approach. The current versus electric field curve obtained for the 6 nm-thick SiOxNy layer was fitted using the Fowler-Nordheim Tunneling (FNT) theory. In the frame of FNT the current is given by:

𝐼 = 𝑆𝛼𝐸 2 𝑒𝑥𝑝(- 𝛽 𝐸 ) (6)
with

𝛼 = 𝑞 3 8𝜋ℎ 𝑚 𝑒 𝑚 𝑜𝑥 1  𝐵 and 𝛽 = 8𝜋 3 √2𝑚 𝑜𝑥 𝑞ℎ  𝐵 3/2 .
In equation ( 6) E is the applied field to the dielectric layer, S is the area of the electrodes (when considering a symmetric metal/insulator/metal (MIM) structure; with Rc = 125 nm >> d = 6 nm, the hypothesis for a symmetric MIM structure is fulfilled), mox is the effective electron mass in the band gap of the dielectric (mox = 0.37me for SiO2 [START_REF] Frammelsberger | Simplified tunnelling current calculation for MOS structures with ultra-thin oxides for conductive atomic force microscopy investigations[END_REF]), me is the free electron mass, h is the Planck's constant, q is the electron charge and B is the energy barrier height. Figure 9 represents the FNT plot for the 6 nm-thick SiOxNy sample after fitting the experimental data at high electric field to equation ( 6). This procedure permits to extract parameters as injection barrier B and contact surface. Accordingly, an energy barrier B of 3.28 eV was found. It is in agreement with values reported in the literature, from 2.25 to 3.34 eV for SiO2 layers [START_REF] Frammelsberger | Simplified tunnelling current calculation for MOS structures with ultra-thin oxides for conductive atomic force microscopy investigations[END_REF]. For comparison purposes, the Schottky barrier height (SBH) was calculated in the frame of the metal-induced gap states theory accounting for the charge transfer at the metal-dielectric contact [START_REF] Robertson | Band offsets of high K gate oxides on III-V semiconductors[END_REF][START_REF] Villeneuve-Faure | Charge injection in thin dielectric layers by atomic force microscopy: influence of geometry and material work function of the AFM tip on the injection process[END_REF]. By applying the Schottky pinning parameter Sp = 0.887, as obtained after considering the extracted from spectroscopic ellipsometry measurements electronic part of the dielectric permittivity ( § 3.1), the SBH for electrons was found 3.87 eV.

(I/E 2 ) (A/(V/m) 2 ) 1/E ((V/m) -1 ) 1.0x10 -9 2.0x10 -9 -72 -68 -64 -60 -56 Experimental data FNT Ln
However, the achieved correlation coefficient of the FNT fit is poor, of only 0.92. It leads to a quite high error interval for the contact surface, ranging from 2.4 × 10 4 nm² to 3.7 × 10 7 nm², when taking into account the standard deviation of the intercept. Considering the effective surface as Seff =  Rc 2 , the corresponding collection surface ranges from 0.5 × Seff to 760 × Seff.

Neither of the above presented approaches is really convincing in our case. Indeed, the effective contact surface seems to be an adjustment parameter whose physical significance is not straightforward. Considering only mechanical contact is a limitation because it does not take into account the possibility to collect charges by "proximity", that is to say through air by the curvature of the AFM-tip. Such situation was already demonstrated. Dielectric layers can be charged in "tip-to-sample" space mode, i.e. charges are injected without contact between the tip and the dielectric surface over a distance of around 50 nm [START_REF] Ressier | Electrostatic nanopatterning of PMMA by AFM charge writing for directed nano-assembly[END_REF][START_REF] Makasheva | Dielectric charging by AFM in tip-to-sample space mode: overview and challenges in revealing the appropriate mechanisms[END_REF]. However, the charge collection efficiency strongly depends on the distance to contact point. The latter is in agreement with the presented experimental results.

-Thin dielectric layers (15 nm < d < 150 nm)

To analyze the results for thin SiOxNy-layers (15 nm < d < 150 nm), the current measured in a classical MIM configuration is completed by the C-AFM results. The MIM measurements were performed under controlled atmosphere. The potential Vdc was applied by steps and the current was measured for 1000 s on a 116.8 nm thick SiOxNy layer. The C-AFM measurements were performed on the 50 nm-thick SiOxNy-layer and the current density was obtained after dividing the measured current by an effective contact area (Seff). The upper electrode (probe), is represented by a disk with radius equal to the curvature radius of the tip (Rc = 125 nm). To test the reliability of the procedure and to account for the uncertainty in the effective collection area, the estimation of the current density is completed in the hypothesis of a collection surface 10 and 100 times larger than the Seff. The obtained results are presented in figure 10. Comparison between C-AFM and classical MIM configuration is tough, as applied electric field in the two cases are very different; homogeneous versus inhomogeneous one, with strongly pronounced strengthening at the AFM tip. However, the measured current densities seem consistent with transport mechanisms described by an ohmic behavior at low field, a threshold field of 10 8 V/m which is represented by a change in slope in the log-log diagram, and a high field region where the C-AFM points appear rational with the overall. However, measurements for electric fields in-between these two extremities must be performed to complete and confirm the described trend. Even though the overall picture seems consistent, taking into account of different Seff raises the problem of the effective contact surface between the AFM-tip and the sample. The contact surface can then be used as an adjustable parameter for each experiment. Indeed, studies reported in the literature show that for C-AFM measurements, the contact surfaces should be taken several order greater than the presumed one, a disk with a radius equal to the AFM-tip curvature radius [START_REF] Olbrich | Nanoscale electrical characterization of thin oxides with conductive atomic force microscopy 36[END_REF][START_REF] Porti | Nanometer-scale electrical characterization of stressed ultra-thin SiO2 film using conducting atomic force microscopy[END_REF][START_REF] Olbrich | A new AFM-based tool for testing dielectric quality and reliability on a nanometer scale[END_REF]. Despite the simplicity of the above presented approach, the obtained results underline that a quantitative interpretation of the C-AFM measurements of inorganic thin dielectric layers requires assessment of the collecting surface and consideration of the current density heterogeneity. The same outcome was reached in the case of organic semiconductors [START_REF] Reid | Space charge limited current measurements on conjugated polymer films using Conductive[END_REF].

Present results suggest further complexity brought by charge trapping near the AFM tip. The electric field near the tip is obviously modified by the stored charge, by amounts of the order of the applied field by considering the electrostatic modelling made with 2D or 3D charge clouds.

Because of these charge trapping effects, injected charges can flow radially over reasonable distance before being collected in the bulk. It means that the apparent collecting surface would have a dynamic character in addition to the uncertainty about its extension.

Charge dissipation after injection: time evolution for ultrathin and thin SiOxNy-layers

We finally consider how the potential profiles evolve in time after charge storage to approach charge dissipation processes. Figure 11 represents the evolution of the potential profile, recorded at different times after injection. Again the ultrathin and thin SiOxNy-layers behave differently.

For the ultrathin SiOxNy-layers the surface potential baseline at the end of the injection process is at higher level compared to the surface potential before the charging step. Then a rapid decrease of the reference baseline of the surface potential is observed in time, as shown for the These results actually provide information about the charges penetration depth. Indeed, the penetration depth is one of the key parameters to know aiming at extraction of the charges density from surface potential measurement [START_REF] Palleau | Numerical simulations for a quantitative analysis of AFM electrostatic nanopatterning on PMMA by Kelvin force microscopy[END_REF]. According to the obtained results on the reference surface potential, one can conclude that the charge penetration depth is limited to the thickness of ultrathin dielectric layers (d < 15 nm), thus confirming the assumption made in Section 3.4 for charge penetration depth of 10 nm. The invariance of the reference surface potential for thin layers (15 nm < d < 150 nm) validates the hypothesis of in-depth charge spreading independent from the layer thickness.

Conclusion

The influence of the thickness of thin plasma deposited silicon oxynitride SiOxNy layers on the charge injection mechanisms was investigated in KPFM mode at nanoscale for different applied The SiOxNy layers are well structured, optically transparent, and having refractive index n = 1.45, equal to the one of silica. Analysis of the recorded surface potential profiles, after performed charge injection, shows distinguished behavior for ultrathin (d < 15 nm) and thin (15 nm < d < 150 nm) dielectric layers. The same is observed for both increased bias voltage and increased injection time. To explain the observed trends a 2D-axisymetric electrostatic model is developed on FEM basis. The FEM modelling emphasizes that during the charge injection step the electric field in the dielectric layer is divergent and strongly enhanced close to the injection point. This enhancement is less pronounced for the ultra-thin dielectric layers for which the dielectric thickness becomes comparable to the curvature radius of the AFM tip. The electric field decreases exponentially in the dielectric layer. The radial electric field component is strong, giving rise to charge spreading in radial direction. The electric field at the contact point determines the amount of injected charges in the dielectric layer. The injected charges are localized close to the injection point. Their penetration depth in the oxynitride dielectric layer in the order of 10 nm. Current versus voltage curves were obtained locally in C-AFM mode. An injection barrier of 3.28 eV has been extracted from FNT plots. Again the ultra-thin and the thin SiOxNy layers behave differently, with mixed behavior for the dielectric layer with thickness in the transition between the two groups. The fast increase in current at high field could be related to Fowler-Nordheim effect. However, incertitude about effective collection surface in C-AFM, configuration of divergent field and probable space charge induced modification of the local field make quantitative assessment tricky. The collection surface seems to have a dynamic character in addition to the uncertainty about its extension. Analysis of charge dissipation in the dielectric layers confirms the second hypothesis for bell-shape distribution of the amount of injected charges in both axial and radial directions and the considered in the model charge penetration depth. Further work will be directed to edge effects induced by the discontinuity of the metal electrode and to analyses of energetics of injected charges, and description of charge trapping and transport in these silica-like SiOxNy layers.

  70 nm-thick Au/Ti-electrodes (60 nm of Au and 10 nm of Ti with the Ti-layer used as adhesion layer) were processed by sputtering on top of the basis SiO2 by sputtering. Two kinds of metal electrodes were designed: large square plate (4 × 4 mm 2 ) floating electrode for charge injection study (figure 1(a)) and small wire (40 µm width and 1 mm long) localized electrode for current measurements (figure 1(b)). Top view of the wire electrode is shown on the Scanning Electron Microscopy image (figure 1(c)). To embed the metal electrodes at different depths the structures were covered by SiOxNy dielectric layers with different thicknesses as top layers. The thickness of the dielectric top SiOxNy-layers was controlled by the deposition time according to the characteristic for the system low deposition rate. After the SiOxNy deposition a small opening in the top dielectric layer was made to reach the Au-electrode for the current measurements (figures 1(b) and 1(c)).

Figure 1 .

 1 Figure 1. The studied device is composed of thermal SiO2 base, Au electrode and SiOxNy-layer over Si substrate. Device configuration for (a) charge injection and decay measurements and (b) C-AFM measurement; (c) Scanning Electron Microscopy top view image of the Au-electrode embedded at 31 nm for the current measurements.

Figure 2 .

 2 Figure 2. (a) Refractive index and extinction coefficient of the studied SiOxNy thin dielectric layers as obtained from spectroscopic ellipsometry at  = 632.8 nm, (b) Variation of the refractive index and the extinction coefficient in the studied wavelength range for one ultrathin SiOxNy layer (d = 11.1 nm) and one thin layer (d = 129.7 nm).

  were recorded along a line crossing the injection point (figure3)[START_REF] Villeneuve-Faure | Kelvin force microscopy characterization of charging effect in thin a-SiOxNy:H layers deposited in pulsed plasma enhanced chemical vapor deposition process by tuning the silicon environment[END_REF].

Figure 3 (

 3 Figure 3(a) represents the surface potential induced by the injected charges. The potential distribution is of round shape. AFM mapping of the SiOxNy-surface in the region of charge injection shows no modification of the SiOxNy-surface topography (figure 3(b)). A classical Gaussian shape of the potential profile is observed (figure 3(c)). Three relevant parameters were extracted from this profile: (i) The maximum potential Vm, with respect to surface reference potential, which is measured at the injection point; (ii) The Full Width at Half Maximum (FWHM) which reflects the charges lateral spreading and (iii) The area IS under the potential profile which is considered to represent, to a first approximation, the quantity of stored charges. The later assumption is considered valid even for thin dielectric films because the injected charges remain close to the surface. The evolution of these three parameters, as function of the charge injection conditions, was investigated to follow the charge injection and transport dynamics. The reference potential in figure 3(c) corresponds to the potential of the surface prior to charge injection. Reproducibility measurements show very low variation in the probed values of the potential profile, thus the extracted parameters. Standard deviation of the potential maximum does not exceed 8% and the one of FWHM of the potential profile is limited to 4%. For clarity issues errors bars are not represented on the figures later on.

Figure 3 .

 3 Figure 3. AFM mapping of the SiOxNy-surface in the region of charge injection (2 min at V0 = +12 V) for the 130 nm-thick layer: (a) potential distribution and (b) SiOxNy surface topography. (c) KPFM surface potential profile.

Figure 4

 4 Figure 4(a) represents the evolution of the surface potential profile as function of the film thickness for charge injection at +12 V during 2 min. One can distinguish two different trends with respect to the dielectric layer thickness.

-

  Dielectric layers with thickness larger than 15 nm (thin layers): FWHM and area IS are insensitive to the dielectric layer thickness. The influence of the dielectric thickness on the evolution of the maximum potential Vm and area IS as function of the injection time for different SiOxNy-layer thicknesses is presented in figure 4(b). As previously, different behaviors are observed as function of the dielectric layer thickness for ultrathin and thin layers. For the 11 nm-thick SiOxNy-layer, IS and Vm remain relatively constant regardless the injection time. The 31 nm-thick SiOxNy behaves differently for short and longer injection times. For short times (less than 5 min), Vm and IS increase with injection time.For longer injection times a saturation in the two parameters is observed. As for the 130 nmthick SiOxNy-layer, the Vm and IS increase with the injection time but the FWHM (not shown vs.charging time) of the potential profile is slightly influenced by the injection time. It increases by only 0.1 µm, from 0.4 µm for 1 min charging time to 0.5 µm for 10 min.

Figure 4 .

 4 Figure 4. (a) Evolution of the surface potential profile FWHM and area IS as function of the SiOxNy-layer thickness for constant injection time and bias (2 min at V0 = +12 V); (b) Evolution of the surface potential maximum Vm and the area IS under peak as function of the injection time for SiOxNy-layers with different thicknesses (applied bias of V0 = +12 V).

Figure 5 .

 5 Figure 5. (a) Scheme of the AFM tip and the sample system, (b) Spatial distribution of computed electric field modulus for V0 = +10 V applied to the tip during charging protocol (Rc = 25 nm) for the 130 nm-thick dielectric layer, (c) Related Ez electric field in-depth distribution of the 130 nm-thick dielectric layer. In insert, the Ez indepth distribution of the 130 nm-thick and the 11 nm-thick dielectric layer for the same V0 and (d) the lateral Er electric field distribution at the dielectric/air interface of the 130 nm-thick dielectric layer. In insert, the lateral Er distribution of the 130 nm-thick and the 11 nm-thick dielectric layer for the same V0.

Figure 6 .

 6 Figure 6. Evolution of surface potential maximum Vm and FWHM as function of the SiOxNy film thickness for an electric field at the injection point of 4.7 × 10 7 V/m (injection time of 2 min).

  (b) illustrates the 3D-charge density distribution in the same 130 nm-thick dielectric layer for Q = 1.25 × 10 -16 C, Wz = 10 nm (representing the in-depth charge spreading dp) and Wr = 250 nm.

Figure 7 .

 7 Figure 7. Charge distribution in the FEM model for (a) 2D 𝜌 𝐻 and (b) 3D 𝜌 𝐺 charge density distributions, AFM probe is lifted at 10 nm as for KPFM measurements. (c) Evolution of electrostatic force as function of the applied bias on the tip for 130 nm-thick SiOxNy layer and 2D charge density 𝜌 𝐻 (Q = 1.25 × 10 -16 C, dp = 11 nm and Wr = 250 nm), (d) Evolution of computed maximum potential and FWHM of the potential profile as function of the SiOxNy-layer thickness for the two charge density profiles 2D 𝜌 𝐻 and 3D 𝜌 𝐺 ( Wz = 10 nm and Wr = 250 nm).

  figure7(d). As previously, the results emphasize that the resulting surface potential maximum increases with dielectric film thickness, whereas the FWHM remains constant. The FWHM is identical for the two charge density profiles 2D 𝜌 𝐻 and 3D 𝜌 𝐺 .

Figure 8 .

 8 Figure 8. Current versus electric field characteristics for SiOxNy layers with different thicknesses.

  the tip (V/m)

Figure 9 .

 9 Figure 9. FNT plot for the 6 nm-thick SiOxNy sample.

Figure 10 .

 10 Figure 10. Current density variation for low and high electric fields: I) classical MIM measurements on 116.8 nm thick layer, II) C-AFM measurements on 50 nm thick layer.

  thick SiOxNy-layer (figure11(a)). The surface potential baseline reaches a level close to the initial one, i.e. that the surface potential before charge injection, after 500 s.The thin dielectric layers are characterized by no modifications of the reference surface potential at the end of the injection with respect to the values before injection. The reference surface potential remains at the same level after injection too, whereas a decrease of the surface potential maximum of the profile occurs, as given for the 31 nm-thick SiOxNy-layer (figure11(b)).

Figure 11 .

 11 Figure 11. Evolution of potential profiles with time after injection for (a) ultrathin (11 nm-thick SiOxNy) and (b) thin (31 nm-thick SiOxNy) dielectric layers (injection at V0 = +12 V during 4 min).

Figure 12 .

 12 Figure 12. (a) Reference surface potential evolution in time after charge injection for ultrathin and thin SiOxNy films (11 nm-thick and 31 nm-thick SiOxNy films), (b) Evolution in time after charge injection of the FWHM and the surface potential profile normalized area, with respect to its initial value, for different film thicknesses. The same charge injection conditions are used in each case: 2 min at V0 = + 5 V.

  and injection times. The SiOxNy layers are structurally identical for all thicknesses.

Table 1 .

 1 Parameters of the plasma process for deposition of SiOxNy-layers and the dry oxidation process for growth of thermal SiO2-base.

	Plasma conditions for deposition of SiOxNy-layers
	RF frequency	13.56 MHz
	Applied power	5 W
	Pulse period	400 ms
	Pulse width	100 ms
	Total pressure	65 Pa
	Total gas flow	201.2 sccm
	He flow	80 sccm
	N2O flow	120 sccm
	SiH4 flow	1.2 sccm
	Precursor ratio,  = [N2O]/[SiH4] 100
	Deposition rate	3.9 nm/min
	Substrate temperature	300°C
	Dry oxidation conditions for growth of thermal
	SiO2-base
	Total pressure	1030 hPa
	Gas mixture	N2-O2
	O2-content	1%
	Temperature	1100°C

Acknowledgments

This work has been supported by Région Midi-Pyrénées under contract Reference 10051265 and by the program IDEX Actions Thématiques Stratégiques -ATS 2015 of the Université de Toulouse under project SEPHIR (2016-066-CIF-D-DRVD).