domain: spi phys

text:
C Villeneuve-Faure

K Makasheva

L Boudou

G Teyssedre

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

Charge injection and retention in thin dielectric layers remain critical issues for the reliability of many electronic devices because of their association to a large number of failure mechanisms. To overcome this drawback a deep understanding of the mechanisms leading to charge injection close to the injection area is highly demanded. Even though the charge injection is extensively studied and reported in the literature to characterize the charge storage capability of dielectric materials, questions about charge injection mechanisms when using Atomic Force Microscopy (AFM) remain open. In this paper, a thorough study of charge injection by using AFM in thin plasma processed amorphous silicon oxynitride layers with properties close to that of thermal silica layers is presented. The study considers the impact of applied voltage polarity, work function of the AFM tip coating and tip curvature radius. A simple theoretical model was developed and used to analyze the obtained experimental results. The electric field distribution is computed as a function of tip geometry. The obtained experimental results highlight that after injection in the dielectric layer the charge lateral spreading is mainly controlled by the radial electric field component independently on the carrier polarity. The injected charge density is influenced by the nature of electrode metal coating (work function) and its geometry (tip curvature radius). The electron injection is mainly ruled by the Schottky injection barrier through field electron emission mechanism enhanced by thermionic electron emission. The hole injection mechanism seems to differ from the electron one in the dependence on the work function of the metal coating. Based on the performed analysis, it is suggested that for hole injection by AFM, pinning of the metal Fermi level with the metal-induced gap states in the studied silicon oxynitride layers starts playing a role in the injection mechanisms.

Introduction

Charging effect in thin dielectric materials was extensively studied since the 60's of the last century because of the large scientific and technological interest to this physical phenomenon.

Presently, the dielectric charging phenomenon is exploited in numerous applications, particularly in electret-based and non-volatile memory devices [START_REF] Normand | Effects of annealing conditions on charge storage of Si nanocrystal memory devices obtained by low-energy ion beam synthesis[END_REF]. Charges accumulation in dielectric materials induces adverse effects on the response of the media, such as electric field strengthening, breakdown or electrostatic discharges, which represent failure issues for numerous systems. It is the case for example of radio-frequency MicroElectroMechanical Systems (RF-MEMS) [START_REF] Witvrouw | Materials issues in the processing, the operation and the reliability of[END_REF]. Dielectric charging of RF-MEMS switches is the main cause of failure and low reliability of capacitive switches with electrostatic actuation. Due to the trapping of electrical charges on the surface and/or in the volume of the dielectric layer, the values of applied voltage for switch actuation are modified in a way that after a certain number of events the switch is out of control. Different strategies, related mainly to the nature of the dielectric layer (silica, silicon nitride, hafnium dioxide, tantalum pentoxide, etc.), have been adopted to overcome this yet resisting drawback. However, deep understanding of the mechanisms involved in charge injection and retention is crucial to improve reliability of devices and systems, and consequently to limit or even to avoid, their failure. Charge storage in insulating materials has received considerable attention during many years but it still represents great scientific challenges, largely due to the lack of knowledge on the specific mechanisms related to generation, transport and trapping of charges. Furthermore, when the layer thickness scales down below micrometer dimension, specific issues are superimposed [START_REF] Rezende | Detection of charge distribution in insulator surfaces[END_REF]. For bringing new information on these processes, development of diagnostic means of charging state, adapted to characterization of thin layers (thickness of few tens of nanometers), is highly demanded. Classical space charges measurement techniques, based on acoustic [START_REF] Maeno | High-resolution PEA charge distribution measurement system[END_REF] or thermal [START_REF] Mellinger | Three-dimensional mapping of polarization profiles with thermal pulses[END_REF] perturbation, fail to characterize thin dielectric films (thickness of less than a few microns) due to their limited in-depth spatial resolution which is of the order of a few microns at most. To attain the nanoscale level, techniques derived from Atomic Force Microscopy (AFM) have naturally emerged offering the possibility to localize injected charges and to probe the resulting modifications in the electrostatic field.

During the past decade Electrostatic Force Microscopy [START_REF] Stern | Exposition and imaging of localized charge on insulator surfaces using force microscope[END_REF][START_REF] Marchi | Characterisation of trapped electric charge carriers behaviour 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] (EFM) and Kelvin Force Microscopy [START_REF] Rezende | Detection of charge distribution in insulator surfaces[END_REF][START_REF] Marchi | Characterisation of trapped electric charge carriers behaviour at nanometer scale by electrostatic force microscopy[END_REF][START_REF] Morita | Microscale contact charging on silicon oxide NATO Science Series II[END_REF] (KFM) were extensively used to study charge injection and retention in thin dielectric films. From experimental point of view, the charge injection phenomenon is strongly influenced by the injection conditions: injection in contact or dynamic mode [START_REF] Neves | Charge injection on insulators via SPM techniques: towards data storage devices[END_REF], environment (humidity or gas nature) [START_REF] Rezende | Detection of charge distribution in insulator surfaces[END_REF][START_REF] Marchi | Characterisation of trapped electric charge carriers behaviour at nanometer scale by electrostatic force microscopy[END_REF], surface treatment [START_REF] Neves | Charge injection on insulators via SPM techniques: towards data storage devices[END_REF], and measurement distance [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 case of lift mode). Even though the dielectric charging effects were extensively investigated experimentally, the underlying physical phenomena are still marginally discussed in the literature. The difficulties often stem from the fact that the electric field is very high and highly diverging, and that the charging procedures are quite difficult to model, e.g. charging achieved in taping mode. Up to now only few mechanisms were proposed to explain the charge injection in thin dielectric films. Injection by corona discharge [START_REF] Morita | Atomic Force Microscope combined with scanning tunneling microscope[END_REF] is commonly evoked in the literature as the main mechanism in analogy with the most widely applied technique for dielectric charging. However, recent theoretical calculations, and the following analysis, demonstrate that corona discharge cannot develop in so small tip-to-sample distances, making it impossible to be considered as mechanism at the origin of charge injection in AFM [START_REF] Makasheva | Dielectric charging by AFM in tip-to-sample space mode: overview and challenges in revealing the appropriate mechanisms[END_REF]. It is rather an electric field dependent mechanism to be seek to explain the dielectric charging by AFM, in particular the field electron emission enhanced by thermionic electron emission [START_REF] Makasheva | Dielectric charging by AFM in tip-to-sample space mode: overview and challenges in revealing the appropriate mechanisms[END_REF]. Moreover, current measurements during charge injection reveal a behavior close to Fowler-Nordheim mechanism [START_REF] Fowler | Electron emission in intense electric fields[END_REF][START_REF] Ando | Conducting atomic force microscopy studies on local electrical properties of ultrathin SiO 2 films[END_REF]. Most of the studies on dielectric charging by AFM focus on the charges retention capabilities of materials [START_REF] Rezende | Detection of charge distribution in insulator surfaces[END_REF][START_REF] Morita | Atomic Force Microscope combined with scanning tunneling microscope[END_REF].

The influence of tip characteristics (geometry of the tip and work function of the coating material) is rarely taken into account to better understand the charge injection mechanisms.

Sun et al [START_REF] Sun | A research on the Surface Charge with Different Coating Tip by Electrostatic Force Microscope[END_REF] briefly addressed the influence of the material work function of the AFM tip on the charge injection, by comparing features from two tips with different coatings. However there was no consideration of the tip geometry (which actually controls the electric field) or the voltage polarity. Indeed, the AFM tip geometry is an important parameter which indicates that different mechanisms [START_REF] Makasheva | Dielectric charging by AFM in tip-to-sample space mode: overview and challenges in revealing the appropriate mechanisms[END_REF] are involved in the charge injection process since electrons and holes exhibit different injection and decay rates [START_REF] Morita | Microscopic contact charging and dissipation[END_REF].

This study addresses the physical phenomena involved during AFM charge injection in thin dielectric layers. Particularly, it reveals the influence of tip radius and tip work function on the electron and hole injection through KFM measurements. After a quick presentation of the experimental conditions, electric field simulation, using Finite Element Model (FEM), is presented. Then, the experimental results obtained by KFM on plasmaprocessed amorphous silicon oxynitride thin layers exploring AFM tips with different geometries and metal coatings, i.e. different work functions, are presented and discussed using the results from the electric field simulation to identify the mechanisms involved in electron/hole injection and their lateral spreading.

Experimental part

To investigate charge injection in thin dielectric layers, a structurally well characterized material is needed. Amorphous silicon oxynitride layers (a-SiO x N y :H, x < 2, y < 1) with very low nitrogen content (only 4 at.% for all samples) and structural and electrical properties close to a thermal silica layer were selected for this study. They were elaborated by Pulsed Plasma Enhanced Chemical Vapor Deposition (PPECVD) [START_REF] Makasheva | Dielectric layers for RF-MEMS switches: Design and study of appropriate structures preventing electrostatic charging[END_REF]. Our choice to probe plasma deposited thin layers is based on the versatility of the plasma process and its compatibility with microelectronic technology, which makes the study useful for many different applications. The a-SiO x N y :H layers were deposited on Au/Ti metallized Si (100) 4"-wafers in the plasma sustained by a capacitively-coupled radiofrequency (RF) discharge at frequency of f = 13.56 MHz with power of 5 W. In the so-described structure the Ti-layer was used as adhesive layer between the Au-layer and the Si-substrate. The RF discharge was modulated with square pulses of period T p = 400 ms and pulse width of 100 ms. The gas mixture contained SiH 4 (1.2 sccm, where sccm stands for standard cubic centimeters per minute at standard temperature and pressure), N 2 O (120 sccm) and He (80 sccm, equivalent to 40% of the total gas flow). The total gas pressure used for deposition was p = 65 Pa. The substrate temperature was kept to 300°C during the deposition process.

The layer thickness and its optical properties were determined by spectroscopic ellipsometry measurements in the spectral range 250-850 nm. A Sopra GES-5 ellipsometer was used. Detailed description of the applied procedure to acquire the spectra is given in reference [START_REF] Villeneuve-Faure | Kelvin force microscopy characterization of charging effect in thin a-SiO x N y :H layers deposited in pulsed plasma enhanced chemical vapor deposition process by tuning the silicon environment[END_REF]. Simulation of the recorded spectra was performed with Winelli software [20] provided by Sopra. Forouhi-Bloomer dispersion law [START_REF] Forouhi | Optical dispersion relations for amorphous semiconductors and amorphous dielectrics[END_REF] was applied for spectra processing.

This approximation provides information on the layer thickness and its optical properties (nrefractive index and kextinction coefficient). To study the charge injection we have used 40 nm-thick a-SiO x N y :H layers (refractive index, n = 1.49 ± 0.01 at  = 632.8 nm and relative dielectric permittivity,  r = 3.90 ± 0.05 at 1 kHz and room temperature determined by spectroscopic ellipsometry and dielectric spectroscopy measurements, respectively). More information on the structural and electrical characterization of these dielectric layers is given 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-SiO x N y :H layers deposited in pulsed plasma enhanced chemical vapor deposition process by tuning the silicon environment[END_REF]. AFM measurements were performed using a Bruker Multimode 8 apparatus. Charges implantation protocol and ambient environment were well controlled in order to ensure results repeatability. AFM silicon tips with different coating materials, as provided by Bruker and NanoSensor, were used to investigate the influence of injection conditions, especially the influence of tip work function and geometry on the injected charges. The charging step was achieved in contact mode (contact force set to 20nN) by applying positive or negative DC bias between ±5V and ±25V to the AFM tip during 1min, the silicon wafer back side being grounded. The Au/Ti layer between the silicon substrate and the dielectric layer remains at floating potential. Moreover, a controlled environment, without humidity and under N 2 atmosphere, was used avoiding thus charge dissipation due to water layer adsorbed on the sample surface. After the charging step, the same AFM tip was used to probe the surface potential by Amplitude Modulation KFM with 5nm-lift. The spring constant was estimated using Thermal Tune mode and was monitored during measurements to control accurately the contact force during injection. As the tip properties are crucial for our study, each tip was previously characterized using Scanning Electron Microscopy (SEM) to determine the tip curvature radius. Figure 1 shows SEM images of AFM silicon tips with different coatings emphasizing important differences in terms of surface morphology and curvature radius. The characteristics of all tips used in this study are summarized in Table 1.

Electric field modeling

To identify physical mechanisms involved in charge injection using AFM tip, electric field modeling is required. A simple model describing the AFM tip as a truncated cone of 10µmheight with 14° degrees aperture angle, and ending with a semi-spherical apex (of curvature radius R c ) was used. It corresponds to classical AFM tip shape used for modeling [START_REF] Boularas | Multidimensional modelling of electrostatic force distance curve over dielectric surface: Influence of tip geometry and correlation with experiment[END_REF]. The tip is supposed to be surrounded by air box (of dimensions large enough to avoid edge effects) and in contact with the dielectric a-SiO x N y :H layer, of 40 nm in thickness. The relative dielectric permittivity of a-SiO x N y :H equals 3.9, as measured by dielectric spectroscopy [START_REF] Makasheva | Dielectric layers for RF-MEMS switches: Design and study of appropriate structures preventing electrostatic charging[END_REF] and that of the air is taken as 1. The potential is applied on the tip surface and the dielectric back side is supposed at reference potential.

In order to compute the electric field distribution in air and in the dielectric layer, a 2Daxisymmetric finite-element model using COMSOL Multiphysics® was developed. Mesh was refined and optimized close to the contact point to improve calculation accuracy. The dielectric layer was supposed free from electrical charges. The Poisson's equation was solved in air and in the dielectric layer to determine the potential distribution. Without charges, it is in the form:

0 divE  r . ( 1
)
The electric field E r derives from the potential:

E grad V  r . (2)
Typical boundary conditions for the described configuration were applied. No charge conditions (zero potential) are applied on the free boundaries of the simulation box. These conditions ensure no edge effects. . This field intensification increases when the tip curvature radius is smaller. The ratio between electric field intensity at the tip and that at the ground varies with factors from about 3.5 to 1.6 when the tip curvature radius changes from 27 to 120nm. The calculated electric field strengths at the contact point are not far from the highest applied electric field (1.5  10 8 V/m) in current measurements performed on Metal/Insulator/Metal capacitors containing the studied oxynitride layers where no breakdown appeared [START_REF] Makasheva | Dielectric layers for RF-MEMS switches: Design and study of appropriate structures preventing electrostatic charging[END_REF].

Besides, KFM measurements performed at the same location after charges dissipation exhibit no modifications either of the surface topography or of the surface potential, whereas this should be the case when local breakdown occurs [START_REF] Porti | Atomic force microscope topographical artifacts after the dielectric breakdown of ultrathin SiO 2 films[END_REF].

The radial contribution of the electric field E r is depicted in figure 2

Experimental results

Charge injection was performed under tip bias varying from -25V to 25V in 5V steps applied for 1min. For each new value of the bias voltage the charge injection was achieved on a new position on the a-SiO x N y :H layer away from a previously charged point not to suffer any influence. KFM profiles were recorded immediately after voltage application, along a line crossing the injection point. Figure 3 represents classical cross-section over bell-like shape potential, which is obtained after local charging of the thin dielectric layer [START_REF] Villeneuve-Faure | Kelvin force microscopy characterization of charging effect in thin a-SiO x N y :H layers deposited in pulsed plasma enhanced chemical vapor deposition process by tuning the silicon environment[END_REF]. This profile exhibits Gaussian shape and is exploited for extraction of three parameters relevant to our study: (i) the maximum potential, V m , in respect to surface reference potential which is measured at the injection point; (ii) the peak full width at half maximum (FWHM) which reflects the lateral spreading of injected charges; and (iii) the area under the potential profile I s , which represents to a first approximation the quantity of stored charges in the dielectric layer [START_REF] Stevens | Nano-and Meso-measurement methods in the study of dielectric[END_REF]. In the following, the impact of AFM tip geometry, tip coating and applied bias on these three parameters is studied aiming at an identification of the charge injection mechanisms. Indeed, the FWHM of the potential spot increases when the radial electric field increases. The charge spot broadening is less pronounced for tips with large curvature radii, which most probably is linked to the degradation of the lateral resolution for these tips. The tip diameter in this case approaches the potential spot dimensions. These results emphasize that charge lateral spreading is mainly driven by the radial electric field, independently from the charges nature.

To go deeper into the understanding of this phenomenon a more detailed theoretical model taking into account the radial electric field modifications induced by the injected charges and description of the available charge traps in the dielectric thin film is required. However, as a first approximation our results show that the broadening of the potential profile is mainly driven by the radial electric field. Most likely the trapping of the injected charges prevents from further lateral spreading.

The FWHM vs. bias curves appear symmetrical with bias polarity, cf. figure 4(a). This is not a necessarily expected behavior since the dispersion of positive and negative charges on the sample surface might be different. Reports on other materials like SiO 2 or PMMA [START_REF] Neves | Charge injection on insulators via SPM techniques: towards data storage devices[END_REF] with non-symmetric FWHM point towards surface carrier conductivity which can be affected by surface pollution (water layer for example). In the dry atmosphere conditions of our study, surface conductivity is avoided and the behavior should be linked to the intrinsic properties of the a-SiO x N y :H dielectric layer. Consequently, in the studied a-SiO x N y :H thin layers, for high electric fields (>10 8 V/m), positive and negative carriers exhibit quite the same lateral transport features.

Charge injection efficiency

To investigate charge injection efficiency in thin dielectric layers two parameters are considered: (i) AFM tip (electrode) metallic coating (metal work function) and (ii) tip curvature radius. These two parameters are involved in the theory of field emission in intense electric fields established by Fowler and Nordheim [START_REF] Fowler | Electron emission in intense electric fields[END_REF]. Figure 5 emphasizes the influence of tip curvature radius on the variation of the measured KFM maximum potential (V m ) and on the integrated potential (I s , the area of KFM profile considered as a measure of the density of stored charges) as a function of applied bias for Pt-coated tip. As shown on figure 5(a), the maximum potential increases linearly with the applied bias. The maximum potential is higher for smaller tip curvature radius. Figure 5(b) confirms the increase in stored charge amount with decreasing the tip curvature radius. The integrated potential is symmetrical when the bias polarity is reversed. Consequently, for Pt-coated electrode, the injected charge amount is independent from the bias polarity. The increase in tip curvature radius induces significant decrease in the injected charge amount. linearly with the applied bias but its behavior strongly depends on the bias polarity. Indeed, for positive bias on the tip, the maximum potential scales up linearly without being influenced by the metal coating nature whereas, for negative applied bias, the maximum potential evolution depends substantially on the metal coating determining a steeper slope of the curve for Co-compared to the Pt-coated tip. Figure 6(b), confirms the above observations and points out that, contrary to the Pt-coated tip, the integrated potential profile obtained with the Co-coated tip is not symmetric with respect to the positive and negative applied bias polarities. For positive applied bias, the injected charge density is independent on the metal coating, whereas for negative bias, the injected charges amount is larger for the Co-than for the Pt-tip. The origin of this effect can be found in the difference of the work functions between the two metal coatings of the AFM tip. To confirm this evolution a more systematic study on the influence of electrode work function on the charges density is proposed in the next section. The electrostatic modeling presented in section 3 shows that the axial electric field represents the main contribution to the electric field. Therefore, the integrated potential profile I s for different metal coatings and tip radii obtained for negative applied bias to the tip is presented in figure 7(a) as a function of the axial electric field computed at the injection point.

The integrated potential profile I s appears roughly proportional to the electric field strength at the injection point and the slope of this dependence is steeper when the work function of the metallic coating is lower. The proportionality between I s and applied bias V is probably fortuitous since injection laws in general are non-linear in field and the field is diverging in the analyzed situation, with the existence of a triple point around the injection point. In addition, the radial component of the electric field favors lateral spreading of the injected charges. The greatest contribution of the radial electric field appears at a finite distance from the injection point (r = 0) and the position of the maximum along with the magnitude are substantially dependent on the tip curvature radius (figure 2(e)). For these reasons, it is difficult to evaluate charge amount vs. applied bias for inferring injection mechanism.

However, the impact of the metal work function is addressed in the discussion.

The shape of the I s vs V curves is different for positive applied injection bias to the AFM tip. Indeed, as shown on figure 7 showing a tendency to invert. Exception is observed for the PtSi-coated tip only which is most probably related to the kind and doping degree of Si in the alloy, unfortunately not reported in the AFM tip data sheet. However, the results shown in figure 7 confirm that the electric field has quite the same influence on the hole injection height barrier as on the electron one, but the dependence on the metal work function differs. To clarify this last point we have performed an analysis treating the studied silicon oxynitride layers as wide-band-gap semiconductors.

Discussion

The physical situation that arises in this study is a contact between metal and dielectric layers. The transport properties at the metal-semiconductor (dielectric) interface, usually called MS-interface, are generally considered in terms of Schottky barrier height (SBH).

Accordingly, the density of injected charges is determined by the SBH. When a negative bias is applied to the tip, one considers that electrons are injected in the silicon oxynitride layer.

The injection barrier height ϕ e is given by [START_REF] Kao | Electrical transport in solids[END_REF]:

3 0 4 em r eE          , (3)
where ϕ m is the metal work function, χ is dielectric layer electron affinity, e is the elementary charge, ε r is the relative permittivity of the dielectric layer and ε 0 is the vacuum permittivity.

Given the constant character of parameters related to the silicon oxynitride layer, a-SiO x N y :H, relation [START_REF] Rezende | Detection of charge distribution in insulator surfaces[END_REF] predicts that the injection barrier decreases when the electric field increases and/or the metal work function decreases. Considering the measured for the a-SiO x N y :H relative dielectric permittivity ε r = 3.9 [START_REF] Makasheva | Dielectric layers for RF-MEMS switches: Design and study of appropriate structures preventing electrostatic charging[END_REF] and electron affinity of silica layers as reported in the literature  = 0.9 eV [START_REF] Robertson | Band offset of wide-band-gap oxides and implication for future electronic devices[END_REF] we estimate from relation (3) a reduction of the injection barrier height of 0.27 eV for the lowest applied field of 2.0  10 8 V/m and of 0.74 eV for the highest applied field of 1.5  10 9 V/m. For a given value of the electric field the reduction of the injection barrier height leads to an easier injection of the electrons in the dielectric layer. This results in a higher density of injected charges as observed in this study (figure 7(a)). When the metal coating has lower metal work function, i.e. Co-coated tip versus Pt-coated tip, the injection is further enhanced. As far as the injection mechanism is concerned its identification requires analysis considering also the temperature as the injection barrier is involved in different injection mechanisms like thermionic emission or field electron emission, or the mutual action of both emissions [START_REF] Murphy | Thermionic Emission, Field emission, and the Transition Region[END_REF]. For the range of electric field variation studied in this work and based on the methodology described by Murphy and Good [START_REF] Murphy | Thermionic Emission, Field emission, and the Transition Region[END_REF], the domains of action of thermionic and field electron emissions, the intermediate region and their limits were studied and reported for Co-and Pt-coatings in reference [START_REF] Makasheva | Dielectric charging by AFM in tip-to-sample space mode: overview and challenges in revealing the appropriate mechanisms[END_REF]. While the electric field dependence acts on the shape of the injection barrier at the surface, the temperature dependence occurs at the Fermi distribution function of the free electron gas in the metal. The charge injection in this work was performed at room temperature. For electric field strengths up to 6.4  10 8 V/m the electrons are injected in the silicon oxynitride layer due to the mutual action of thermionic and field electron emissions. The domain of pure field electron emission applies for higher electric fields. As predicted earlier [START_REF] Murphy | Thermionic Emission, Field emission, and the Transition Region[END_REF] and observed here the transition between different injection mechanisms is smooth (figure 7(a)). However, application of a positive bias cannot be analyzed only on the basis of pure Schottky injection mechanism although the electric field strength is high. The region created on the MS-interface should also be considered. Without loss of generality, when a positive bias is applied to the AFM tip (figure 7(b)) the charge injection barrier height at the metaloxide interface is rather described in the literature by the theory of metal-induced gap states (MIGS) [START_REF] Heine | Theory of Surface States[END_REF]. These states are predominant donorlike if they are close to the dielectric valence band -E V and acceptorlike when they are close to the conduction band -E C (figure 8). The energy level in the band gap where the inversion occurs is called charge neutrality level -E CNL . Generally though, when a metal and semiconductor (oxide layer) are in contact they form an interface where charge transfer arises between the metal and interface states lying in the semiconductor/dielectric band gap. The charge transfer creates a dipole which reduces the SBH and consequently modulates the influence of the metal on injection. As shown in figure 8, when the metal Fermi level is close to the E V and MIGS are close to the E C the electron injection will be driven by the metal work function and the hole injection by MIGS.

Using the MIGS model the potential barrier height ϕ h for hole injection can be expressed by the following relation:

    h g m CNL CNL ES           , (4)
where E g is the electronic gap of the dielectric layer and ϕ CNL is the charge neutrality level measured from vacuum level which depends on the dielectric material properties. S is a dimensionless slope of barrier height to metal work function. It is related to the density of MIGS and their extension in the dielectric gap describing thus the pinning of the Fermi level of the metal with the MIGS and the degree of screening induced by the interfacial states [START_REF] Kao | Electrical transport in solids[END_REF].

It was shown previously that the pinning parameter S correlates with the electronic part of the dielectric constant (  ) [START_REF] Tersoff | Schottky Barrier Heights and the Continuum of Gap States[END_REF] and empirically obeys the relation [START_REF] Mönch | Role of Virtual Gap States and Defects in Metal-Semiconductor Contacts[END_REF]:

  2 1 1 0 1 1 S .      , (5)
where   is the high frequency limit of the dielectric constant. For S equals 1, MIGS have no influence on hole injection and for S equals 0, injection is ruled only by MIGS [START_REF] Yeo | Metal-dielectric band alignment and its implications for metal gate complementary metal-oxide-semiconductor technology[END_REF].

Concerning the a-SiO x N y :H layer under study the measured by ellipsometric spectroscopy value of the electronic part of the dielectric constant is   = 2.24. Applying the relation [START_REF] Mellinger | Three-dimensional mapping of polarization profiles with thermal pulses[END_REF] one finds the pinning parameter S equals 0.867. This value is consistent with values reported in the literature for silica layers [START_REF] Robertson | Band offset of wide-band-gap oxides and implication for future electronic devices[END_REF][START_REF] Tersoff | Schottky Barrier Heights and the Continuum of Gap States[END_REF][START_REF] Mönch | Role of Virtual Gap States and Defects in Metal-Semiconductor Contacts[END_REF][START_REF] Yeo | Metal-dielectric band alignment and its implications for metal gate complementary metal-oxide-semiconductor technology[END_REF] as the used a-SiO x N y :H layer has dielectric properties close to thermal silica. The obtained value for the pinning parameter indicates rather low influence of the interfacial states on the hole injection, i.e. the work function dependence is not screened by the interfacial states, which actually does not explain the results obtained when a positive bias is applied on the AFM tip (figure 7(b)). Although physically sound, the MIGS theory has some drawbacks, like for example the point that it describes the semiconductor (dielectric) part without considering the image charge created in the metal. The CNL does not apply to the entire interface region. It rather refers to the semiconducting part only. It assumes that the net charge due to the occupation of surface states is determined only by the position of the Fermi level at the surface. The CNL is defined as the one that coincides with the Fermi level position, no distribution is assumed.

A recent theory [START_REF] Tung | Formation of an electric dipole at metal-semiconductor interfaces[END_REF][START_REF] Tung | The physics and chemistry of the Schottky barrier height[END_REF] based on the polarization of the chemical bonds at metal semiconductor interfaces could quantitatively account for the experimentally observed strength of Fermi level pinning (S parameter) without regard to the actual distribution of gap states. It goes beyond the MIGS theory, considering formation of a dipole, called Schottky dipole, which is formed from the net charge resulting from the gap states and its image charge in the metal. Only considering a chemical bonding at the MS-interface a coherent explanation of the Fermi level pinning effect, on the one hand, and the experimentally observed dependence of the SBH on interface structure, on the other hand, can be provided.

Conclusion

Influence of AFM tip geometry (curvature radius of the tip

Figure 1 .

 1 Figure 1. SEM images of silicon AFM tips with (a) Pt and (b) diamond coating.

Figure 2 (

 2 Figure 2(a) represents the equipotential lines and the electric field intensity for 10V applied on a 27nm-radius tip. The distribution of the axial component of electric field E z is depicted in figure 2(b). As expected, the electric field is enhanced close to the AFM apex. The evolution of E z as a function of the position in depth of the dielectric layer (along the vertical axis for r = 0) is represented in figure 2(d) for different tip curvature radii and applied potential of 10V. Close to the dielectric surface, the electric field is substantially enhanced compared to a plane-plane configuration (2.5 × 10 8 V/m for the above given conditions, represented by the dot line in figure 2(d)). This field intensification increases when the tip curvature radius is

Figure 2 .

 2 Figure 2. Spatial distribution of the computed electric field: (a) equipotential lines and electric field intensity; (b) axial contribution E z and (c) radial contribution E r of the electric field for 10V applied on 27nm-curvature radius AFM tip. Impact of tip curvature radius on the field distribution: comparison of (d) E z (r=0) and (e) E r (z=0) cross sections with 10V applied to AFM tips of different curvature radii.

Figure 3 .

 3 Figure 3. KFM profile obtained on 40nm-thick a-SiO x N y :H layer after charging for 1min at 25V using Pt-coated AFM tip with curvature radius R c = 27nm.

Figure 4 :

 4 Figure 4: Evolution of the FWHM of KFM profile as function of (a) injection bias and (b) lateral electric field for different AFM tips.

Figure 4 (

 4 Figure 4(b) represents the variation of FWHM as a function of the maximum value of the radial electric field component computed according to the model presented in the previous section for each one of the couples: applied bias to the tip and its curvature radius. A good correlation is observed between the FWHM and the maximum of the radial electric field.

Figure 5 .

 5 Figure 5. Evolution of (a) maximum potential V m and (b) integrated potential profile I s as a function of injection bias for Pt-coated AFM tips with different curvature radii.

Figure 6

 6 Figure 6 emphasizes the influence of metallic coating (metal work function) on the evolution of maximum potential and integrated potential profile as a function of applied bias for a 46nm-curvature radius tip. As shown on figure 6(a), the maximum potential increases

Figure 6 .

 6 Figure 6. Evolution of (a) the maximum potential V m and (b) the integrated potential profile I s as function of the injection bias for Pt-and Co-coated AFM-tips (curvature radius fixed to 46nm).

  (b), for Co-and Pt-coatings the integrated potential profile scales up linearly with the electrical field offering a reduced influence of the tip coating. The dependencies on the metal coating work function get closer to each other, even

Figure 7 .

 7 Figure 7. Evolution of the area under the potential profile I s as function of the computed axial electric field component for different metal work functions for (a) negative injection bias and (b) positive injection bias in a-SiO x N y :H thin layer. The lines in the graph are shown as guide to the eye.

Figure 8 .

 8 Figure 8. Energy band diagram for metal-dielectric interface. The metal is described by its Fermi level (E Fm ) and its work function ϕ m . MIGS are described by the charge neutrality level ϕ CNL . The dielectric is described by its valence E V and conduction E C levels.

  ) and metal coating (work function) on the charge injection in thin dielectric amorphous silicon oxynitride layers was investigated experimentally. A theoretical model was developed to support the analysis of the obtained results. Results emphasize that the charge lateral spreading is driven by the radial contribution of the electric field. Moreover, it was shown that in a-SiO x N y :H thin layers both carriers, electrons and holes, obey the same lateral transport processes. Concerning charge injection mechanisms, the injected charge amount is influenced by the nature of electrode metal coating (work function) and its geometry (tip curvature radius) which modify the applied electric field. The charge behavior varies as a function of the carrier nature. The electron injection is mainly ruled by the Schottky injection barrier through field electron emission mechanism enhanced by thermionic electron emission. The amount of injected charges increases with increasing the electric field intensity and decreasing the work function of the AFM tip metal coating. It is larger when the charge injection is performed with AFM tips with smaller curvature radii. However the hole injection mechanism seems to differ from the electron one in the dependence on the work function of the metal coating. The MIGS theory fails to describe correctly the charge injection mechanism for hole carriers in the studied a-SiO x N y :H thin layers expressing an experimentally obtained pinning parameter not much lower than unity. Further studies will be directed to elucidation of this last observation to better understand the charge transfer at the interface between two very thin metal/dielectric layers

Table 1 .

 1 AFM tip characteristics

	Item	Pt	Co	PtSi	D
	Coating on silicon	Platinum	Cobalt	PtSi alloy	Diamond
	Work function - m	5.64 eV [22]	5.00 eV [22]	4.80 eV [23]	Depends on doping (around 5.5eV)
	Curvature radius -R c	27 nm	×	27 nm	×

Acknowledgments

The authors acknowledge support from the UMS Raymond Castaing of the University of Toulouse and Mr. Stéphane Le Blond du Plouy for the SEM observations. This work is financially supported by the Agence Nationale de la Recherche in France, project ANR-InTail under contract ANR-AA-PBLI-II-2011 and the Région Midi-Pyrénées.

when using AFM. A direction to explore is the recently developed theory based on the polarization of the chemical bonds at metal semiconductor interfaces.


Laurent Millière

Kremena Makasheva

Christian Laurent

Bernard Despax

Laurent Boudou

G Teyssedre
email: gilbert.teyssedre@laplace.univ-tlse.fr

L Milliere

Silver nanoparticles as a key feature of a plasma polymer composite layer in mitigation of charge injection into polyethylene under DC stress

Keywords: polyethylene, nanocomposites, silver nanoparticles, plasma processes, HVDC, charge injection, space charge mitigation

come

Silver nanoparticles as a key feature of a plasma polymer composite layer in mitigation of charge injection into polyethylene under dc stress

INTRODUCTION

Optimization and valorization of green electrical energy production is one of the most important economic development concerns in the world. However, as energy production sites are often far from consumption sites, there is a need to transport energy over long distances, including sometimes undersea connections. In this context High Voltage Direct Current (HVDC) links represent several advantages over HVAC lines like the reduction in energy losses along with the absence of reactive power compensation stations [START_REF] Mazzanti | Extruded Cables for High-Voltage Direct-Current Transmission[END_REF]. Polyethylene-based materials are used for long in the insulation of HVAC extruded cables and accessories where they gradually replaced oil-paper insulations. In spite of this experience in the field, HVDC extruded cables still suffer from reliability problems due to the accumulation of electric charges forming internal space charge in the polymer bulk [START_REF] Hanley | A general review of polymeric insulation for use in HVDC cables[END_REF][START_REF] Khalil | International research and development trends and problems of HVDC cables with polymeric insulation[END_REF]. This phenomenon creates an internal electric field distribution different from the design field that can trigger local damages to the structure which leads ultimately to breakdown [START_REF] Montanari | Space charge phenomenology in polymeric insulating materials[END_REF][START_REF] Laurent | Charge dynamics and its energetic features in polymeric materials[END_REF]. In theory, polyethylene with its wide band gap of 8.8 eV [START_REF] Less | Intrinsic photoconduction and photoemission in polyethylene[END_REF] should prevent charge injection from any conducting or semi-conducting electrodes. In reality, electronic carriers of positive and negative polarities are injected from the contact electrode/polymer and are detected as space charge using space charge measurement techniques [START_REF] Thomas | Space-charge dynamic in polyethylene: from dc to ac stress[END_REF]. Charge injection has been reported both in laboratory experiments carried out on flat samples with semi-conducting (SC) contacts to mimic the situation in cables and in real cables where a semi-conducting screen (carbon black doped thermoplastic) is in contact with the polymer [START_REF] Fabiani | Polymeric HVDC cable design and space charge accumulation. Part 1 : insulation/semicon interface[END_REF]. This charge injection process is presumably due to energy states enabling carriers to bypass the potential barrier at the SC/dielectric interface [START_REF] Taleb | Modelling of Charge Injection and Extraction in a Metal/Polymer Interface through an Exponential Distribution of Surface States[END_REF]. Moreover, extruded cables production is mainly based on cross-linked polyethylene (XLPE) owing to its outstanding thermo-mechanical stability. The crosslinking process generally uses peroxides as initiator, leading to the formation of byproducts which substantially contribute to space charge features of the material when compared to low density polyethylene (LDPE) [START_REF] Vissouvanadin | Impact of concentration gradient of polarizable species on the electric field distribution in polymeric insulating material for HVDC cable[END_REF]. Many papers have been published over the last two decades on the impact of additives and residues on space charge in polyethylene materials, especially in XLPE. In going from LDPE to XLPE a switch from homocharge-dominated to heterocharge-dominated space charge profiles occurs, which can be roughly understood as a switch from injection-dominated charge build-up to ionic charge build-up originating from crosslinking residues.

Several methods for improving the performances of polyethylene-based insulation of HVDC cables by reducing space charge build-up have been investigated. Strategies are envisaged either at the source of the charges or at the level of their dispersion in the material. Expelling cross-linking by-products, which are volatile molecules, by heating the system is in principle one of the solutions to reduce the amount of ionic carriers in XLPE. However it may become very demanding energetically for thick insulations as in high voltage cables. So, ongoing researches address the development of processes limiting the amount of by-products. Most of the attempts for reducing the amount of space charge concern the modification/improvement of the bulk material. Dispersion of nano-fillers into the polymer bulk is being deeply investigated nowadays [START_REF] Tanaka | Advances in nanodielectric materials over the past 50 years[END_REF], for example in LDPE with dispersion of nano TiO2 [START_REF] Zhao | Effects of LDPE/nanofilled LDPE interface on Space Charge Formation[END_REF], Al2O3 [START_REF] Zheng | Morphology related packet-like space charge behavior in LLDPE doped with Al2O3 nano-particles[END_REF], montmorillonite [START_REF] Liao | Improved Electric strength and Space Charge Characterization in LDPE Composites with Montmorillonite Fillers[END_REF] and MgO [START_REF] Murata | Investigation of space charge distribution and volume resistivity of XLPE/MgO nanocomposite material under DC voltage application[END_REF] particles. The general trend is a mitigation effect of the amount of space charge without clear evidence on the mechanism due to the complexity of the nanocomposite materials and the variability of results [START_REF] Nelson | Nanodielectricsthe first decade and beyond International Symposium on Electrical insulating Materials[END_REF]. To our knowledge, few studies focus on the polymer/electrodes interface properties to tune charge injection effect. Tailoring the interfacial properties of the insulation could be a way to control the generation of electronic carriers. The most common studies consist in a modification of the polymer sample interface by fluorination with a F2/N2 mixture [START_REF] An | Suppression effect of surface fluorination on charge injection into linear low density polyethylene[END_REF]. Charge injection mitigation was reported to be due to the presence of deep traps into the fluorinated layer that can block or shield further charge injection.

Following a different strategy, we recently reported [START_REF] Milliere | Silver nanoclusters containing layer as an efficient barrier for charge injection in polyethylene[END_REF] on charge injection mitigation when a thin composite layer containing silver nanoparticles (AgNPs) was deposited on the surface of polyethylene as shown in Figure 1. A drastic effect was observed and attributed to the presence of AgNPs acting as deep traps. In this paper, we extend the analysis in order to find out which features of the nanocomposite layer are playing key role in charge injection mitigation. The paper is organized along the following lines. We first give the experimental details describing the substrate preparation, plasma deposition process and methods for physico-chemical and electrical characterization. We discuss in a second part the impact of the process parameters on the distribution of the size and density of the AgNPs contained in the composite layer. Space charge patterns under different protocols for DC voltage application are discussed in a third part by changing the characteristics of the composite layers. Results are discussed in a fourth part of the paper.

EXPERIMENTAL DETAILS

Substrate preparation

Polymer substrates of LDPE were produced from antioxidant-free pellets, as specified by BOREALIS, molded at 155°C under 3 bars for 20 minutes. The final samples were disks of 7 cm in diameter and 300 ± 10 µm in thickness. The LDPE substrates were subsequently outgassed for 12 h under vacuum (0.06 Pa) at 23°C for removing volatiles molecules and water. Indeed it has been shown that even using antioxidant-free polyethylene films, space charge can be detected originating from the material bulk and giving rise to spurious effect when investigating charge injection from the electrodes. When conditioning the samples under vacuum for a given time, injection phenomena can be revealed

LDPE substrate 300 µm 50 nm

AgNPs

SiO x C y :H matrix through the detection of homocharge (charge of the same sign as the nearby electrode) above a field level of the order of 10 to 15 kV/mm using conventional space charge detection techniques [START_REF] Roy | Description of charge transport in polyethylene using a fluid model with a constant mobility: fitting model and experiments[END_REF]. The vacuum pretreatment conditions also conform to the low pressure plasma deposition process described below.

RF plasma process

The nanocomposite layer is synthetized in a low pressure plasma reactor enabling sputtering from a silver target and plasma polymerization of hexamethyldisiloxane (HMDSO -[CH3]6Si2O) as two independent steps in the same chamber. Details of the process can be found elsewhere [START_REF] Makasheva | Silver nanoparticles embedded in dielectric matrix: charge transport analysis with application to control of space charge formation[END_REF][START_REF] Despax | Deposition of polysiloxane thin films containing silver particles by an RF asymmetrical discharge Plasma Process[END_REF]. The plasma reactor is schematized in

Physico-chemical characterization methods

The chemical structure of the layers was analyzed through Fourier Transform Infra-Red spectroscopy in Attenuated Total Reflectance mode (ATR-FTIR) in the range 400-4000 cm -1 using a Brucker Vertex 70 spectrometer. Images of the nanocomposite layers were obtained by Scanning Electron Microscopy (SEM). The thicknesses of the nanocomposite layers were inferred from SEM observations of the samples in Energy Dispersive X-ray spectrometry mode (EDX) in a cross-section view. Some of samples were produced with the AgNPs layer only, without SiOxCy:H coating in order to observe the silver clusters and determine their parameters. The surface density, covered area (fraction of LDPE sample area covered by AgNPs) and size distribution were deduced after image processing. The latter was performed with Gatan DigitalMicrograph® software by application of filters associated with a selective numeral analysis.

Space Charge Measurements Method and Protocol

The Pulsed Electro Acoustic (PEA) technique was used for space charge measurements. The principle of the PEA technique consists in detecting acoustic waves generated by internal charges under the Coulombic influence of a pulsed electric field [START_REF] Fukunaga | Internal space charge measurement for the study of the electrostatic phenomena[END_REF]. The equipment is composed of a high voltage direct current supply connected to a semi-conducting (SC) electrode made of carbon black-doped polymer. The pulse generator is also connected to the high voltage through a decoupling capacitance.

An aluminum electrode is used as the ground electrode where the acoustic waves are detected.

Samples are sandwiched between the two electrodes of the PEA system without further metallization.

The PEA cell is installed in a thermo-stated oven and all measurements were realized at 25°C. To obtain an exploitable signal, the acoustic response to excitation by 600 V amplitude pulses at 1 kHz frequency is averaged for 60 s. The spatial resolution of the set-up is 25 µm. Deconvolution of the signal was done by using software developed in our laboratory. The samples were tested following a protocol depicted in Figure 3. It consists of different steps of polarization, each followed by a depolarization period. In a short term protocol (Figure 3(a)) the DC field is increased from 10 kV/mm to 50 kV/mm by steps of 5 kV/mm (corresponding to a positive voltage applied to the HV electrode).

The voltage is maintained at each step for 20 min, followed by a depolarization step for 20 min. After the last positive step at 50 kV/mm (positive voltage applied to the SC electrode), the applied stress was reversed to -40 kV/mm with a subsequent increase to -50 kV/mm. PEA profiles were recorded every 60 s in the polarization and depolarization steps at each voltage level. In a longer term protocol (Figure 3(b)) we used two steps of 20 kV/mm and 40 kV/mm applied for 12 hours each (positive voltage applied to the SC electrode). Each step is followed by a depolarization period lasting for 5 hours. PEA profiles were recorded every 150 s. The dynamics of the space charge is revealed through color maps showing the measured charge density (color scale) in a 2D-representation where the x-axis is the time (associated with the applied voltage through the experimental protocol) and the y-axis the position between anode and cathode.

Surface potential measurements

Electrical properties of the samples were investigated by surface potential measurements following charging of the material by corona discharge. Charging was achieved applying a DC voltage of 3500 V during 10 s on a needle electrode installed at 5 mm from the sample surface. Potential profiles were measured using a Kelvin probe by scanning the surface along different axes in steps of 5 mm at different times after charging: 0, 3, 15 and 60 minutes. All measurements were carried out in air at room temperature.

PHYSICO-CHEMICAL CHARACTERIZATION

Nanoparticles size and surface density as a function of experimental parameters

The plasma operation conditions along with the results from the analysis of size, surface density and organization of sputtered AgNPs on the LDPE samples are summarized in Table I. Three values of the input power (40, 60 and 80 W) and two values of the argon pressure (8.00 and 5.33 Pa) were used in this experiment. The corresponding self-bias voltages are also given. The self-bias voltage is related to the asymmetric nature of capacitively-coupled discharges [START_REF] Köhler | Plasma potentials of 13.56-MHz rf argon glow discharges in a planar system[END_REF]. It is set up at the driven electrode and results from the DC voltage drop between the bulk plasma and the electrodes across the plasma sheaths connecting the driven electrode to the ground. It is negative in the usual case and since the voltage drop across the sheaths is inversely proportional to the sheath capacitances, the sheath with smaller area (smaller electrode) has smaller capacitance and therefore a larger voltage drop. It scales up with the injected power, at a constant pressure, as confirmed in this experiment (Table I), and is at the origin of the acceleration of argon ions towards the silver target, finally bombarding it. As the ion dynamic is strongly involved in the sputtering process, the gas pressure is the second important parameter after the injected power in this process. A gas pressure increase might influence the silver sputtering in the following ways: (i) through an increase of the plasma density, thus the ion density, if quasi-neutrality of the plasma is considered; (ii) through the plasma sheath close to the smaller electrode, mainly through its width and its nature (collisional or collisionless) and (iii) through the effect of scattering of sputtered atoms. Our results show that for a fixed injected power the self-bias voltage decreases when increasing the gas pressure. It is due to the thinner plasma sheath close to the powered electrode, when the gas pressure is increased, that will have a larger capacitance per unit area, thus setting up a smaller self-bias voltage. The most appropriate way to follow the plasma behavior in order to relate it to the plasma deposition process is through optical emission spectroscopy of the plasma glow emission, as performed in this work. The evolution of line intensity ratio of IAg(546.6nm) to IAr(549.6nm) gives an image of the Ag-amount in the plasma which can be related to the Ag-volume fraction deposited on the substrate. The higher the line intensity ratio, the higher the Ag-volume fraction is. The variation of the line intensity ratio (IAg(546.6nm)/IAr(549.6nm)) as a function of the injected power or the gas pressure is recorded for each deposition, since this kind of charts constitutes useful data to obtain reproducible results. According to the performed analysis three main categories of AgNPs can be identified (Table I): (i) small isolated AgNPs; (ii) large isolated AgNPs; and (iii) large coalesced AgNPs. This classification will be used hereafter. All the samples used for space charge measurements were covered by an organosilicon SiOxCy:H thin layer after the deposition of the layer of AgNPs. Figure 4 shows examples of each of the above identified categories of as-deposited AgNPs on the LDPE surface without SiOxCy:H cover layer, referred as to S1 (large isolated AgNPs), S2 (small isolated AgNPs) and S5 (large coalesced AgNPs). A cross-section view image of the AgNPs/SiOxCy:H nanocomposite stack on the LDPE surface, containing the large isolated AgNPs presented on S1 image, is also shown in EDX mode (bottom right panel, referred as to S1t in Figure 4). For sample S1, the AgNPs size span from 5 to 25 nm with an average size of 15 nm, the particles surface density being 6.4 × 10 11 NP/cm 2 giving a surface covered area of 65%. Particles appear with irregular shape however, well isolated from each other. Sample S2, which has been prepared under a lower pressure (p = 5.33 Pa) for the same discharge power (P = 40 W), exhibits AgNPs of much smaller diameters (<10 nm) with larger surface density of 7.1 × 10 11 NP/cm 2 and covered surface area of the same order as in sample S1. Sample S5 which has been prepared under the same pressure (p = 8.0 Pa) as sample S1 but for a higher discharge power (P = 80 W) exhibits much larger particles size spanning from 20 to 40 nm, with a density of 1.8 × 10 11 NP/cm 2 and a covered surface area of 88%. The clusters appear coalesced with wormlike shape. The later feature has already been reported for other type of metal clusters (gold and/or cobalt clusters) embedded in fluorocarbon [START_REF] Perrin | Optical properties and microstructure of gold-fluorocarbonpolymer composite films[END_REF] or hydrocarbon matrices [START_REF] Laurent | Properties of metal clusters in polymerized hydrocarbon versus fluorocarbon matrices[END_REF].

These features of the AgNPs are in agreement with the fact that, for a given deposition time, the amount of deposited silver increases with the discharge power or the gas pressure. The cross-section view shown in S1t allows a precise measure of the thickness of the nanocomposite layer (54 nm in the present example) which has been confirmed by profilometer measurements. Considering a size of 15 nm for the AgNPs, as deduced from the SEM image (upper left panel -S1), the nanocomposite layer can be represented by two regions with the first one consisting of AgNPs embedded in organosilicon matrix of thickness of 15 nm, and the second region of only organosilicon layer with thickness estimated to 35 nm. Silver nanoparticles were not directly detected by ATR-FTIR analysis but their presence on LDPE surface contributes to the intensity decrease of CH2 and CH3 peaks (Figure 5(b)) by the exerted light filtering effect. The intensity of LDPE vibrational peaks is inversely proportional to the size and the surface covered by AgNPs (Table I). The highest intensity is recorded for the LDPE sample alone, than for the LDPE sample covered with only organosilicon layer. The peak intensity decreases with increasing the AgNPs mean size. In presence of AgNPs, when they are coalesced as for sample S5, the intensity ICH2(LDPE) at 1462 cm -1 is twice smaller as compared to the intensity of the same band for the S2 sample (small isolated AgNPs). For the same surface covered area, the CH2 peak intensity increases when the particle size is smaller. begin to be injected at 20 kV/mm with an increasing density up to the maximum applied field (50 kV/mm). Negative charge injection from the aluminum electrode is not detected (position at 0 µm on Figure 6(a)). This is in accordance with the results reported in the literature [START_REF] Xiao | Interface electric field of carbon black loaded electrode and its significant influence on charge injection into polyethylene[END_REF] as regards the efficiency for charge injection of various contacts. The Al/polyethylene contact is weekly injecting for negative charges when compared to the SC/polyethylene contact for positive charges. Also, it was shown experimentally that the mobility of negative charge is much lower than that of positive carriers in LDPE [START_REF] Thomas | Space-charge dynamic in polyethylene: from dc to ac stress[END_REF]. For these reasons the space charge patterns are dominated by positive carriers. Models describing bipolar charge transport account for this behavior [START_REF] Xiao | Interface electric field of carbon black loaded electrode and its significant influence on charge injection into polyethylene[END_REF]. Al electrode is visible. One should keep in mind that in any space charge measurement, the apparent charge density, would it be zero charge density, can be the result of a net value of overlapping positive and negative charge distributions. The origin of negative charges seen after polarity reversal near the SC electrode is not straightforward. It seems to be due to a negative charge injection from the SC cathode all the more that the cathode field is intensified as mentioned above.

Physico-chemical characterization of the composite layer

SPACE CHARGE MEASUREMENTS

Space charge in reference LDPE sample

Figure 6(b) shows the example of the charge dynamics at 50 kV/mm before and after the polarity inversion, in polarization and depolarization. The build-up of the positive charge during polarization at 50 kV/mm is clearly revealed as well as the positive charge decay during depolarization. Upon polarity reversal, the build-up of the bipolar space charge is evidenced under polarization as well as its decay in depolarization. In order to be more quantitative and for comparison purpose, we have represented in Figure 6(c) the evolution of the absolute value of the internal charge along the voltage protocol. To this aim, we have integrated the charge over the insulation thickness, differentiating positively (Eq. 1) and negatively (Eq. 2) charged regions, according to:

  m Q d 1 x dx d        , (1)
  m Q d 1 x dx d        . ( 2
)
Charge integration does not include the influence charge on the electrodes of width , estimated to be 40 m. Figure 6(c) represents quantitative data of the apparent amount of positive and negative charges in the sample bulk as derived from this procedure. For each polarization step, the measurement starts with a significant preexisting charge whose density increases with the rank of stress step. Overall, the space charge distribution is dominated by positive charges whatever the polarity of the applied voltage.

Space charge in tailored LDPE sample S1 (large isolated AgNPs)

Sample S1, a LDPE tailored with AgNPs/SiOxCy:H nanocomposite stack on one face only (AgNPs of mean size 15 ± 10 nm in diameter), was put into contact with the SC electrode of the PEA system.

Space charge in tailored LDPE samples S2 (small isolated AgNPs) and S5 (large coalesced AgNPs)

Tailored LDPE samples S2 and S5 were subsequently tested (AgNPs average sizes <10 nm and 30 nm, respectively) as representatives of small and large average size distribution and organization of the AgNPs, the latter being isolated for S2 and coalesced for S5. Experimental conditions for space charge measurements were otherwise identical to those for S1 sample. The space charge dynamics is shown in Figure 8(a) and 8(b) respectively. When compared to the space charge distribution in sample S1 (large isolated AgNPs) (Figure 7), one can note a less efficient barrier effect for positive space charge formation, in particular in the case of sample S2 (Figure 8(a)). This conclusion relies on the following analysis. Space charge distribution in sample S2 shows a positive space charge accumulation near the Al cathode during polarization and this accumulation is visible at low electric field (10 kV/mm). Taking into account the analysis of space charge distribution in sample S1, this positive space charge can only be due to a weak injection level at the SC anode followed by a migration of the positive charge towards the cathode where it accumulates and forms a heterocharge layer. The positive space charge density increases with the applied voltage although its spatial extension from the cathode decreases when increasing the voltage. This is due to the negative charge injection from the Al cathode with migration to the SC anode and accumulation nearby as demonstrated by the negative charge build-up near the SC electrode that appears at 40 kV/mm. Overall, both electrodes inject charges and one observes a distribution due to the overlap of the two distributions with heterocharge formation at each electrode. This is typical of situation where the electrodes are partially blocking leading to an unbalance between the incoming charges and the extracted charges at the electrode [START_REF] Roy | Relative Importance of Trapping and Extraction in the Simulation of Space Charge Distribution[END_REF]. The predominance of positive charge near the cathode (at least up to 40 kV/mm) denotes a higher charge injection from the SC anode. A similar analysis can be done in the case of sample S0 (Figure 8(c)) although the positive injection is mitigated when compared to the behavior in sample S1. Heterocharge accumulation following injection and migration of charges of both polarities is also observed although the positive space charge accumulation is less visible, denoting a lower density of positive space charge due to a weaker positive injection. The barrier effect observed in sample S1 (large isolated AgNPs) is therefore also observed in samples S2 (small isolated AgNPs) and S5 (large coalesced AgNPs) but with a lower efficiency, sample S5 having an intermediate behavior between samples S1 and S2. The space charge dynamics and distribution observed after polarity reversal confirm the previous analysis with a higher density of positive charge injected from the Al anode in the case of S5 (which is due to a higher field at the anode when compared to S2). Overall, the integration of the charge density accumulated during polarization under positive voltage between positions 40 m and 100 m from the cathode (arbitrary chosen for rejecting the image charge at the cathode but taking into account the charge density accumulated in its vicinity) can provide a ranking criterion for the barrier effect for charge injection at each voltage level and for each sample type: the higher density of positive charge the higher efficiency for positive charge injection is. When the space charge integrated within the same limits is negative, the barrier effect is all the more efficient that the charge density is high, and is more efficient than when a net positive charge is measured. A plot of the space charge integrated within these limits at each voltage level during polarization is shown in Figure 9(a) for the samples S1, S2 and S5. It confirms a higher efficiency of the barrier effect in sample S1, followed by sample S5 and sample S2.

DISCUSSION

The above reported results raise several questions. Even if an effect of the silver nanoclusters characteristics is observed, one has to discuss the effect of the SiOxCy:H layer by itself. We therefore prepared a LDPE substrate covered with the organosilicon layer without AgNPs (sample S0) in order to investigate the possible effect on charge injection. Another important feature of the results is the apparent barrier effect of the nanocomposite layer on both positive and negative charge injection. To strengthen the analysis, we investigated space charge in a sample tailored on both faces with identical electrodes. Then, the mechanism of charge injection mitigation has to be investigated in order to understand which features of the AgNPs are controlling the charge mitigation. For that purpose, we have performed surface potential measurements on samples with large isolated and coalesced AgNPs.

Finally, the barrier effect has to be assessed using a protocol involving longer polarization period (defined as "longer term protocol").

Space charge distribution in tailored sample with SiOxCy:H layer.

A sample has been prepared with the deposition of the SiOxCy:H layer on one face and using the same protocol for plasma deposition as in the other tested samples. Thickness and characteristics of the organosilicon layer are the same as for samples containing AgNPs. Figure 8(c) shows the space charge injection is mitigated in sample S0 when compared to the reference sample but to a lower extent when compared to samples S1 and S5. This is evidenced by the representation of Fig. 9(a) where the integrated charge vs. field plot of sample S0 lies between the curves relative to S5 and S2. It can therefore be concluded that charge injection mitigation is also observed with the organosilicon layer but the barrier effect is greatly enhanced in sample containing AgNPs when the particle size is larger than 10 nm.

Polarity dependence of the barrier effect on charge injection

In order to investigate precisely this effect, we used a sample tailored on the two faces by AgNPs containing organosilicon layers prepared in the conditions of sample S1 (silver particles having an average size of 15 nm). To avoid the complexity in the analysis of the space charge distribution due to the difference in the nature of the electrodes of the PEA set-up, we used a SC electrode in contact with the Al electrode. The configuration under study is therefore symmetrical with the two faces of the sample being identical in terms of the nature of the contact. Figures 10(a

Barrier effect and influential features of the Ag NPs

At least three features of the AgNPs have to be considered for interpretation of charge injection mitigation: the average size of the NPs, their surface density and the fact they can be isolated or percolated. Owing to the experimental results, to the least inter-connection and size of particles appear more influential in the range of densities investigated here. The average particles size seems influential with less mitigation effect when it is lower than 10 nm (S2) when compared to 15 nm (S1) or 14 nm (S4). AgNPs in sample S3 (22 nm, isolated clusters) and S5 (30 nm, percolated clusters) have a higher average size and appear also as less efficient in mitigating charge injection than in S1 (15 nm) and S4 (14 nm). It seems therefore that the AgNPs optimum size for charge injection mitigation is about 15 nm. AgNPs in sample S5 are percolated. The electrical properties of a population of NPs in a dielectric matrix change drastically at the percolation threshold [START_REF] Abeles | Structural and electrical properties of granular metal films[END_REF][START_REF] Ping | Electronic transport in granular metal films Phil[END_REF] where Ag islands form an infinite metallic cluster which spans the whole sample. This can obviously be influential in the mitigation of charge injection. We have investigated the change in electrical properties going from sample S1 (isolated AgNPs) to S5 (percolated AgNPs) by surface potential measurements. The experimental results are shown in Figure 11. An efficient mitigation of charge injection appears therefore as a characteristic of isolated AgNPs with a size distribution of the order of 15 nm. The question to be discussed is the cluster size effect observed from sample S1 (AgNPs mean size of 15 nm) to sample S2 (AgNPs mean size is less than 10 nm). Among possible explanation, quantum effects due to the reduction of the number of atoms in the metallic cluster could be evoked. Indeed metal clusters are congregates of atoms that have properties different from both a single atom and the bulk metal. However, as the size of a cluster increases, its

properties evolve to those of the bulk. For example, the ionization potential (and electron affinity) of a single atom of Ag will decrease (respectively increase) gradually with an increasing number of silver atoms to reach the metal work function of bulk silver (4.64 eV) [START_REF]CRC Handbook on Chemistry and Physics[END_REF]. The size dependence of the ionization potentials and electron affinities of metallic clusters varies as R -1 , R being the cluster radius [START_REF] Harbola | Theoretical study of the size dependence of ionization potential and electron affinity of metallic clusters[END_REF]. Quantum effects will be stronger for small cluster size and therefore more operant in sample S2

(small isolated AgNPs) when compared to sample S1 (large isolated AgNPs). It is not consistent with experimental data. Another experimental fact is that the charge mitigation by the NPs is observed under both polarities of the applied voltage. Quantum effects due to the size reduction would hardly give an interpretation for the polarity effect. An alternative would be to consider the stability of charged clusters. By using different metal cluster generation and ionization methods, it has been

Conclusion

Charge injection from a semi-conducting electrode into low density polyethylene submitted to a DC field has been investigated up to 50 kV/mm through space charge dynamics. A comparison between charge injection efficiency has been achieved when the polyethylene sample was tailored with a SiOxCy:H nanocomposite layer containing a plane of silver nanoparticles having different characteristics. With reference to a polyethylene sample, charge injection mitigation was observed with an increasing intensity upon deposition of the SiOxCy:H layer without AgNPs, with percolated AgNPs and with non-percolated AgNPs of 15 nm. Charge injection is suppressed in the latter case even under high field (50 kV/mm) and the effect is observed for both polarities of the voltage and for longer polarization duration (24 hours). AgNPs appear therefore as a key feature for charge injection suppression. The ability of silver clusters to stabilize electrical charges thereby counterbalancing the injecting field seems to be a key factor in explaining charge injection mitigation.

Figure 1 .

 1 Figure 1. Schema of polymer surface tailored by a AgNPs/SiOxCy:H nanocomposite layer.

Figure 2 .

 2 The asymmetrical electrodes configuration of this capacitively coupled radio-frequency (RF, f = 13.56 MHz) driven discharge leads to a self-bias of the smaller electrode. The LDPE substrate is clamped on a temperature-controlled substrate holder (bottom electrode) connected to the ground. The RF power is transmitted to a silver target (smaller electrode) located 4 cm above the sample. The plasma is initiated in pure argon at pressure of 5.33 Pa after pumping the chamber for 12 hours at very low pressure of 0.06 Pa. Owing to the asymmetrical design of the electrodes, argon ions of the discharge are accelerated by the self-bias voltage towards the silver electrode where they sputter silver atoms forming nanoclusters on the LDPE sample surface.The size distribution and surface density of the AgNPs can be controlled by changing the experimental parameters: power of the discharge (i.e. self-bias voltage), discharge pressure and sputtering time. A range of parameters were chosen for our study as being 40, 60 and 80 W for the discharge power (corresponding to self-bias voltages -725, -850 and -970 V, at 8.00 Pa), 5.33 and 8.00 Pa for the gas pressure, the deposition time being constant (5 s). In a second step, HMDSO is introduced into the chamber with the plasma powered on. This implies that the silver electrode is quickly totally covered by a thin polymer layer therefore preventing from silver sputtering. HMDSO partial pressure is controlled through a pulsed flow, argon partial pressure is maintained at 5.33 Pa and the RF power is maintained at 80 W. The thickness of the SiOxCy:H layer deposited on top of the AgNPs previously formed at the LDPE surface is controlled by the deposition time fixed at 60 s in our study. The LDPE samples are hidden behind a mask for the time of plasma process stabilization and then exposed to the plasma during the deposition time by removing the mask. It allows controlling the short deposition times used in this experiment. The processes of silver sputtering and SiOxCy:H deposition are monitored by optical emission spectroscopy through the intensity ratio of the emission lines of silver and argon excited atoms (λAg = 546.6 nm and λAr = 549.6 nm, respectively)[START_REF] Despax | Deposition of polysiloxane thin films containing silver particles by an RF asymmetrical discharge Plasma Process[END_REF].

Figure 2 .

 2 Figure 2. Schema of plasma reactor.

Figure 3 .

 3 Figure 3. Short (a) and longer (b) term protocols for space charge measurements.

Figure 4 .

 4 Figure 4. SEM images in plan-view of the AgNPs layers deposited on LDPE substrate S1 (large isolated), S2 (small isolated) and S5 (large coalesced). SEM cross-section image in EDX mode of the AgNPs/SiOxCy:H composite layer on the LDPE substrate S1t, containing the large isolated AgNPs presented on S1 image.

Figure 5 (

 5 Figure5(a) represents FTIR spectra of LDPE sample with and without any coating. Typical for LDPE surface chemical bonds[START_REF] Gulmine | Polyethylene characterization by FTIR[END_REF], the four main peaks (see TableII): rocking r(CH2) at 714cm -1 , bending (CH3) at 1374cm -1 and (CH3) 1462cm -1 , and the two stretching g(CH2) at 2843cm -1 and a(CH2) at 2916cm -1 are identified on the LDPE reference spectrum. No oxidized groups have been recorded after the vacuum preconditioning. The samples tailored with AgNPs/SiOxCy:H plasma polymer stack have many broad bands attributed to various chemical bonds in the range 800 cm -1 to 1263 cm -1 such as Si-O, Si-C, O-C and O-H. The band at 1042 cm -1 is associated with Si-O-Si asymmetric stretching mode in a silicon suboxide environment. The contribution at 1020 cm -1 is more probably ascribed to CHx(x<2)-Si wagging mode[START_REF] Makasheva | Silver nanoparticles embedded in dielectric matrix: charge transport analysis with application to control of space charge formation[END_REF][START_REF] Despax | Deposition of polysiloxane thin films containing silver particles by an RF asymmetrical discharge Plasma Process[END_REF].

Figure 5 .

 5 Figure 5. ATR-FTIR spectra of samples: (a) reference LDPE and sample S1 (plane of AgNPs covered by an organosilicon layer); (b) focus on δ(CH2) bond at 1462 cm -1 for LDPE reference sample, samples S0 (LDPE covered with only organosilicon layer), S1 (large isolated AgNPs covered by SiOxCy:H), S2 (small isolated AgNPs covered by SiOxCy:H) and S5 (large coalesced AgNPs covered by SiOxCy:H).

Figure 6 (

 6 Figure 6(a) shows the space charge density along the protocol defined in Figure 3(a) for a 300 mthick degassed bare LDPE sample. It is typical of the behavior of treated-LDPE sample with a distribution dominated by charge injection and a space charge density below 10 C/m 3 [19]. For a positive voltage polarity, the distribution is dominated by charge injection from the SC electrode (position 300 µm in Figure 6(a)) and a bulk space charge density below 2 C/m 3 . The positive charges

Figure 6 .

 6 Figure 6. Space charge dynamics in reference LDPE sample along the short term protocol: (a) 3D plot of space charge dynamics, (b) charge density profiles during polarization (left) and depolarization (right) for the steps at 50 kV/mm under positive (top) and negative (bottom) applied voltages, and (c) averaged positive and negative charge densities along the protocol.

Figure 7

 7 Figure7gives the charge dynamics along the short term protocol. It is strikingly different from the charge dynamics in the reference sample. There is no evidence of positive charge injection from the SC/plasma polymer stack contact up to the end of the polarization period under positive voltage (50 kV/mm). The space charge in the bulk is negative and is due to the migration of the charge injected from the Al/polymer contact. Space charge profiles at 50 kV/mm are shown at different times in Figure 7(b) in polarization and depolarization steps. The presence of negative charge distribution throughout the bulk is confirmed without signs of positive space charge build-up. The AgNPs/SiOxCy:H nanocomposite layer appears efficient to block the formation of positive space charge. Upon polarity reversal, massive space charge formation following injection of positive charge

Figure 7 .

 7 Figure 7. Space charge dynamics in sample S1 (LDPE tailored with AgNPs/SiOxCy:H nanocomposite stack on one face only) along the short term protocol: (a) 3D plot of space charge dynamics, (b) charge density profiles during polarization (left) and depolarization (right) for the steps at 50 kV/mm under positive (top) and negative (bottom) applied voltages, and (c) averaged positive and negative charge densities along the protocol.

Figure 8 .

 8 Figure 8. Space charge dynamics in LDPE tailored (with AgNPs/SiOxCy:H nanocomposite stack on one face only) samples along the short term protocol: (a) S2 (small isolated AgNPs), (b) S5 (large coalesced AgNPs), and (c) S0 (organosilicon matrix only).

Figure 9 .

 9 Figure 9. Ranking of the efficiency of the barrier effect to charge injection in each tested sample. Each point represents the space charge integrated over the region 40 µm to 100 µm from the cathode: (a) along the short term protocol during polarization (space charge at the end of each voltage step), and (b) along the longer term protocol at three characteristic times (17, 23 and 28 hours) at 40 kV/mm

  dynamics where it can be seen, by comparison with the space charge distribution shown in Figures6, 7, 8(a) and 8(b) (respectively LDPE reference sample; LDPE tailored samples S1; S2 and S5) that the

  ) and 10(b) show the charge distribution dynamics for the LDPE sample and the field distribution at different times during polarization and depolarization. Field enhancement is observed at the cathode for both polarities of the applied voltage due to the fact that the positive space charge originating from injection at the SC anode dominates the space charge distribution. A field intensification of 5.8 kV/mm at the cathode and a field decrease of 8.8 kV/mm at the anode are derived from the space charge distribution at the end of the positive voltage step at 50 kV/mm. It is worth emphasizing small differences between the space charge dynamics of one-and two-faces tailored samples (see respectively Figures6(a) and 10(a)). This is due to the difference of the contact at the cathode being Al/LDPE and SC/LDPE respectively for one-and two-faces tailored samples. One should note a higher electron injection from the cathode in case of the SC/LDPE contact reducing the net positive charge accumulated near the cathode. Figures10(c) and 10(d) shows the charge distribution dynamics for the two-faces tailored sample and the field distribution at different times during polarization and depolarization. The barrier effect is clearly revealed at both electrodes without evolution of the electric field distribution. The barrier effect mechanisms are therefore operant for positive and negative charges.

Figure 10 .

 10 Figure 10. Space charge dynamics along the short term protocol and field distribution in polarization and depolarization under different applied voltages: (a) and (b) in reference LDPE sample, and (c) and (d) in twofaces tailored S1 sample (large isolated AgNPs). Note the symmetrical SC/sample contact at anode and cathode.

  When the AgNPs are percolated (Figure11(a)), the surface potential appears constant along the scanning lines above the surface of the sample: AgNPs charging is uniform like in a bulk metal and the surface potential decay is rather slow. Percolated AgNPs behave like a metal sheet most probably because charging at one favorable site under the needle leads to charging of the AgNPs belonging to the infinite clusters, i.e. local charging affects the global structure. When the AgNPs are isolated, the surface potential is not uniform along the scanning lines and the surface potential decay is much faster.Charging is inhomogeneous along the sample surface because each cluster has to be charged individually through direct charging by the corona or through lateral conduction from clusters to clusters. This would take time after corona contact and could explain the decay of the surface potential.

Figure 11 .

 11 Figure 11. Surface potential measurements on (a) S5 (large coalesced AgNPs) and (b) S1 (large isolated AgNPs) samples. Blue lines indicate the edges of the composite layer. Measurements are carried out at different times after charging as indicated.

Figure 12 .

 12 Figure 12. Space charge dynamics in (a) reference LDPE, (b) S1 (large isolated AgNPs), (c) S2 (small isolated AgNPs), and (d) S5 (large coalesced AgNPs) samples along the longer term protocol.

RF electrode cooling Mask LDPE sample Water cooling Bottom electrode

		RF generator
		(13.56 MHz)
		Match box
		Silver target
		Gas
		distribution
	Optical emission	ring	Vacuum pump
	spectroscopy
			Pressure
			measurement
			(Baratron gauge)

Table I .

 I Experimental parameters for silver sputtering and characteristics of deposited AgNPs.

	Sample	Input power P (W)	Self-bias Vdc (V)	Argon pressure p (Pa)	Line ratio IAg/IAr	Density of AgNPs (NPs/cm²)	Covered area	Size (nm) distribution	Organization
	S1	40	-725	8.00	1.0	6.1×10 11	65%	15 ± 10 nm large isolated
	S2	40	-785	5.33	0.4	7.7×10 11	64%	< 10 nm	small isolated
	S3	60	-850	8.00	1.2	2.0×10 11	74%	22 ± 15 nm large isolated
	S4	60	-955	5.33	0.5	6.3×10 11	75%	14 ± 10 nm large isolated
	S5	80	-968	8.00	1.7	1.8×10 11	88%	30 ± 10 nm large coalesced
	S6	80	-1025	5.33	0.5	4.4×10 11	85%	21 ± 10 nm large isolated

Table II .

 II Band assignment of the FTIR spectra of LDPE and LDPE-AgNPs/SiOxCy:H samples.

	Bond	Wavenumber (cm -1 )	Vibrational assignment
	γr(CH2)	714	rocking
	CH3 in SiCH3	796	symmetrical stretching
	SiOC in SiOCH3	800-850	rocking
	Si-H	800-950	stretching
	Si-O-Si	1042	asymmetrical stretching
	Si-CHx(x<2)-Si	1020	wagging
	C-H in SiCH3	1263	symmetrical deformation
	δ(CH3)	1374	bending
	C-H in SiCH3	1410	rocking
	δ(CH2)	1462	bending
	C-C=O and C=O	1630-1720	stretching
	νg(CH2)	2843	stretching
	C-H in CH3	2904	asymmetrical stretching
	νa(CH2)	2916	stretching
	O-H (free and associated)	3200-3600	stretching

ACKNOWLEDGMENT

This work was financially supported by the Agence Nationale de la Recherche in France, project ANR-InTail under Contract No. ANR-AA-PBLI-II-2011. 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.

shown that some charged clusters are more stable than others depending on the number of constituting atoms [START_REF] Rabin | Shell effects in singly and multiply charged silver and gold clusters[END_REF]. These so-called "magic numbers" were successfully explained by shell like arrangement of electrons in the cluster, so that the cluster achieves a higher stability at shell closing. Little is known about the stability of multiple charged clusters, even if stable triple charged silver ions (Agn 3+ ) have been observed for specific values of n. In each case, the higher stability was explained by the electronic occupation of shells. Both silver clusters anions [START_REF] Herlerta | Observation of multiply charged silver-cluster anions[END_REF] and cations [START_REF] Rabin | Shell effects in singly and multiply charged silver and gold clusters[END_REF] have been observed and this could give a basis for the interpretation of the barrier to injection effect observed under both voltage polarities. However, the average size of the Ag clusters in our nanocomposite (estimated to be 3 × 10 4 atoms and 1 × 10 5 atoms for 10 nm and 15 nm cluster diameter, respectively) is much higher than the upper limit of a few hundreds of atoms for conventional DFT quantum computation though it might become tractable in the future using developing algorithms [START_REF] Hine | Linear-scaling densityfunctional theory with tens of thousands of atoms: Expanding the scope and scale of calculations with ONETEP Computer[END_REF][START_REF] Bowler | Calculations for millions of atoms with density functional theory: linear scaling shows its potential[END_REF]. But the possibility that they stabilize positive and negative charge has to be considered. A simple field calculation assuming a single charge state of each cluster in the case of sample S2 leads to a field value at the surface of the electrode adjacent to the charged layer of 63 kV/mm (with a AgNP density of 7.7 × 10 11 cm -2 , a relative permittivity of 2.2 for LDPE and the distance to the adjacent electrode small in comparison to the total dielectric thickness as is the case in our configuration). Such space-charge induced field is actually of the order of magnitude of the applied field. Besides, if every AgNP accommodates more than one charge, the barrier effect is magnified. A reasonable interpretation of the barrier effect could therefore be a field reduction at the injecting electrode due to AgNPs charging.

Checking the barrier effect on the longer term

Finally, the mechanism of charge injection mitigation by the presence of AgNPs in the composite layer has to be checked on the longer term. We have used the "longer term protocol" for voltage application as described in paragraph 2.4. The space charge dynamics is shown for reference LDPE, S1, S2 and S5 samples in Figures 12(a which strengthens the results obtained with the short term protocol, and the ranking between the different samples is the same as regards the efficiency of the barrier to injection.