M A Signore

A Rizzo

D Valerini

L Tapfer

L Capodieci

A Cappello

Physical properties investigation of ion assisted-ZrN thin films deposited by RF magnetron sputtering

Ion bombardment during thin film growth is known to cause structural and morphological changes in the deposited films and thus affecting their physical properties. In this work zirconium nitride films have been deposited by ion assisted magnetron sputtering technique. The ion energy is controlled by varying the voltage applied to the substrate in the range 0 -25 V. The deposited ZrN films are characterized for their structure, surface roughness, oxygen contamination, optical reflectance and electrical resistivity. With increasing substrate voltage films cristallinity is enhanced with a preferential orientation of the ZrN grains having the (111) axis perpendicular to the substrate surface. In the same time, a decreasing in the electrical resistivity and in the oxygen contamination content is observed up to 20 V. A higher substrate voltage (25 V) causes an inversion in the observed experimental trends. The role of oxygen contamination decrease and nitrogen vacancies generation due to the ionic assistance has been considered as possible explanation of the experimental results.

Introduction

The properties of thin films grown by physical vapor deposition (PVD) processes strongly depend on the incident particles energy transferred to surface of growing films [1]. This energy available on the films surface can promote many phenomena such as the enhancement of surface atom mobility [2], modification of the cristallinity [3], variation in the composition [4], structure and Confidential: not for distribution. Submitted to IOP Publishing for peer review 21 April 2010 microstructure and, as consequence, in the physical response of the deposited material. Ion bombardment permits to obtain denser and void-free films [5] even by performing a low temperature deposition process which sometimes is more convenient and advantageous [6]. The simplest way to achieve ion bombardment on the growing film during plasma growth process is biasing the substrate during the deposition. The bias voltage applied to the substrate attracts ions (argon and nitrogen) out from the plasma towards the substrate by the potential drop in the sheath region. At a fixed process total pressure, the energy of these ions [7] will be proportional to this voltage. For small bias voltages, the sheath at the substrate will be thin enough that it will be collision free [START_REF] Chapman | Glow discharge processes: sputtering and plasma etching[END_REF]. In the present investigation RF reactive magnetron sputtering process was used to grow thin films of ZrN, a material which is remarkably stimulating the scientific interest for its wide field of applications [START_REF] Larijani | [END_REF]. During the deposition process the reactive gas mixture total pressure, the substrate temperature and the power applied to Zr target were kept constant, while a negative bias voltage was applied to the substrate in the range 0 -25 V. A (111) texture has been obtained for ZrN films and a low electrical resistivity (~160 µ •cm ) has been achieved for the 20 V-biased sample. The role of oxygen and of nitrogen vacancies has been qualitatively discussed for the experimental results interpretation. Therefore, in this work it is shown how the optimization of substrate bias can simultaneously improve ZrN films electrical conductivity and texture. The improvement of these two properties makes ZrN a good candidate as diffusion barrier in microelectronics device where low resistivity and high texturing are requested besides good adhesion, chemical inertness with copper and silicon and high thermal stability [START_REF] Abe | Proceedings of the 36th IEEE International Reliability Physics Symposium[END_REF]. An excellent diffusion barrier behavior has been found for ZrN (111)-oriented [START_REF] Chen | [END_REF] but this orientation has been gained at high deposition temperature, while in this work the application of a substrate bias leads to high texturing at room temperature.

Experimental details

ZrN films were deposited on silicon wafers (100)-oriented by reactive RF magnetron sputtering in an Ar/N 2 gas mixture. Both gases were 99.999 % pure. The working pressure was kept constant at a value of 1.12•10 -2 Torr and the nitrogen flux percentage in the mixture was fixed at 5 %. The power applied to Zr target during the deposition was 165 W. The distance between the substrates and the target was 70 mm. The substrate temperature was monitored by a thermocouple and it did not overcome 70 °C during the whole process. The only tuned process parameter was the negative bias voltage applied to the substrate in the range 0 --25 V with respect to the ground. As simplification, in the text the voltage absolute values will be indicated. Before the nitride films deposition, the target was pre-sputtered in argon atmosphere for about half an hour. The films are about 500 nmthick. The thickness was measured using a profilometer (KLA TENCOR) on steps patterned by a solid mask. The morphology and the roughness of films were investigated by atomic force microscopy (AFM). The AFM measurements were performed with a Nanoscope III from Digital Instruments. Silicon cantilevers with radius less than 10 nm was used as tip. All measurements were performed in tapping mode in air. The X-ray diffraction and reflectivity experiments were carried out by using an X-ray diffractometer in parallel beam geometry (Philips MPD PW1880, 3 kW generator) optimized for small-angle scattering measurements. For all the measurements Cu Kαradiation (λ CuKα =0.154186 nm) was used. The X-ray diffraction measurements were performed under different geometrical configurations, i.e. by performing both θ-2θ scan as well as grazing incidence (with fixed incidence angle ω i =1.0°) measurements. The grazing-incidence measurements (GIXRD) were performed by keeping the incident angle i (angle between incident beam and sample surface) fixed at 1.0°and recording the scattered X-ray beam by moving the detector and post-sample flat graphite collimator-monochromator along the goniometer circle in the 2θ range between 10°and 100°with a step size of 0.02°. The θ-2θ scan were measured in the angular 2θ range between 25°and 45°with a step size of 0.01°, because the Bragg peaks in only these angular range were intense enough to be analyzed quantitatively. Within the X-ray reflectivity (XRR) regime, we have taken specular (ω,2θ) scans (XSR) in which the grazing angle of incidence of the X-rays is equal to the exit angle (measured 2θ range between 0°and 9°with a step size of 0.01°), and transverse ω scans (XDS, diffuse scattering) in which the angular position of slit and detector (2θ angle) was fixed. DC electrical resistivity at room temperature was deduced from sheet resistance measurements using the four point-probe method. A CARY 500 spectrometer was employed to perform optical reflectance measurements in the range from 200 to 2500 nm. Standard SIMS measurements have been performed by means of a CAMECA ims4f magnetic sector instrument by using Cs + primary ions and detecting Zr + and MCs + (M = O, N) secondary ions [12].

Results

Structure and morphology of the films

Generally, for thin films with layer thickness < 1 µm and nanocrystalline structure grazing incidence diffraction measurements (GIXRD) are more appropriate for a quantitative analysis since the X-ray penetration depth is reduced and the relative Bragg peak intensity is enhanced. The grazing-incidence diffraction (GIXRD) and X-ray reflection (XSR) schemes are schematically shown in Fig. 1. Both measurements are carried out in co-planar scattering geometry. However, in the GIXRD configuration (Fig. 1a) the incidence angle i between incident X-ray beam (k 0 ) and sample surface is kept constant, while the intensity of the diffracted X-ray beam (k h ) is recorded for different 2 angles. On the contrary, for the X-ray specular reflectivity measurements (Fig. 1b) the scattered X-ray intensity is recorded keeping the angles between the sample surface and the incident and reflected X-ray beams, respectively, equal. In this case (b), the scattering vector h is parallel to the surface normal n. Figure 2 shows the GIXRD patterns of the samples deposited with a negative V bias of 0 V, 10 V and 25 V, respectively, in the 2θ angular range between 10°-100°. Several Bragg peaks are well observed and can be identified in accordance with the PDF 74-1217 [13] of the cubic phase of ZrN. The θ-2θ measurement patterns are shown in Figure 3. The 2θ as well the θ-2θ measurements show very clearly that the relative intensity of the (111) Bragg peaks increases while the width (FWHM) of the ( 111) and (200) Bragg peaks reduces with the increasing negative bias voltage V bias applied during sputtering deposition. The average ZrN particle size was estimated from the broadening of the ( 111) and (200) diffraction peaks by using a Cauchy fit of the peak profiles and applying the Scherrer's formula [START_REF] Birkholz | Thin Film Analysis by X-ray Scattering[END_REF]:

0.94 /( cos ) B D λ ω θ = ∆ ( 1
)
where D is the average crystallite size, is the X-ray wavelength, is the calculated FWHM of the diffraction peak in radians and θ B is the Bragg angle. The grain size increases linearly with increasing bias voltage V bias starting from 5.1 nm to 14.5 nm, for V bias =0 V and 25 V, respectively.

The results are depicted in Figure 4 and summarized in Table 1. In addition, the diffraction patterns in Figures 2 and3 show that the relative intensity ratio between the Bragg peaks does not correspond to the expected values as reported in the PDF 74-1217; for example the (200) Bragg peak intensity should be only slightly lower than the (111) Bragg peak intensity by about 15 % .

Furthermore, the relative (111) peak intensity increases with increasing applied bias voltage V bias .

These findings indicate a pronounced extension of the ZrN grains along the (111) crystallographic axis and a preferential orientation of the ZrN grains having the (111) axis perpendicular to the substrate surface, i.e. parallel to the deposition/growth direction. This texture of the closest packed plane is the most frequently encountered in fcc structure such as zirconium nitride [START_REF] Boxman | [END_REF]16]. A pronounced angular deviation of all the most intense Bragg peaks of the GIXRD as well as the XRD patterns is observed. In particular the angular shift of the (111) Bragg peak in Figure 3 Bragg's law and reported in Figure 5 and in Table 1. It should be noted that the value reported for c-ZrN is about 4.63Å [12]. Specular X-ray reflectivity (XSR) and transverse scan (XDS) measurements were performed in order to investigate the surface morphology, the density and the chemical compositional of the deposited ZrN films. Figure 6 shows the XSR and the transverse scans recorded for different 2θ positions of the samples assisted at V bias = 0 V and V bias = 10 V. The XSR patterns shows a very fast decay of the reflected intensity above the critical angle. The fast intensity decay observed above the critical angle θ c indicates a high surface roughness (≥ 5 nm), however, its precise value can not be determined within the Nevot-Croce model that yields typically reliable data for RMS roughness < 5 nm. The determination of the critical angle values (reported in Table 1) through the angular position of the fast intensity decay of the XSR pattern and of the )

i i c i m e A i i Z f r N M π θ ρ λ + ⋅ = ⋅ ⋅ ⋅ (2)
where r e is the classical electron radius, λ is the X-ray wavelength used, N A is the Avogadro's number, and Z i, f' i and M i are the nuclear charges, the dispersion corrections and the atomic weights of the i-th chemical element, respectively. The mass density of the deposited ZrN films as a function of the applied bias voltage V bias has been evaluated by using Eq. ( 2) and is shown in Figure 7 where it is clear that its increasing follows the voltage rise. AFM micrographs (Figure 8) give evidence of all the deposited samples topography. They exhibit a "cauliflower-like" surface which can be observed when a thin film has a columnar structure with grain size of tens of nanometers [17], as previously confirmed by XRD analysis (Fig. 4). The evaluated average root mean-square roughness (RMS) is in the range of 5-11 nm as reported in the last column of Table 1 corroborating XSR results which evaluate a surface roughness values higher than 5 nm.

Optical and electrical analyses

The characteristic feature of the reflectance spectra is a distinct minimum located in the range between 2.8 eV and 3.5 eV, followed by a sudden rise, the so called "plasma reflectance edge" [18],

at lower energies (Fig. 9). The high reflectance in the IR range is related to the high light absorption by the free electron gas (conduction electrons, described by the Drude model), while the reflectance in the UV range is related to the absorption by the interband transitions of the bounded electrons (described by the Lorentz oscillators). As a consequence, the reflectance spectra can be fitted by the use of a model including a Drude part and one or more Lorentz oscillators. The energy of the reflectance minimum, the reflectance percentage at 0.8 eV and the plasma energy of the Drude part are listed in Table 2. A detailed analysis of the optical spectra by a Drude-Lorentz model is in progress and it will be reported in a future paper.

The energy of the reflectance minimum shifts to higher energy when the voltage increases up to 20

V, then it slightly decreases for the film assisted at 25 V. At the same time, the reflectance in the low energy range also increases with the applied bias voltage until 20 V, and it slightly decreases at 25 V. Both these behaviors are reported in the inset of Fig. 9.The plasma energy value follows the same trend, as it has an increase until 20 V and a following decrease at 25 V (see Table 2).

Table 2 -Values of the energy of the reflectance minimum, the reflectance percentage at 0.8 eV, the plasma energy and the electrical resistivity as determined by optical and electrical analyses.

A similar behavior can be observed in the electrical measurements too. Indeed the general result obtained by four-point probe method measurements is that the application of a bias voltage greatly lowers the electrical resistivity down to a minimum value at 20 V, after which an inversion is observed, as reported in Figure 10 and in Table 2. In particular, the unbiased ZrN film exhibits the highest resistivity value (13240 µ •cm) that is lower than the value found by Pilloud et al. [START_REF] Boxman | [END_REF] (27000 µ •cm) evaluated by the same technique. The lowest resistivity value in our samples is 160 µ •cm, which is comparable with the lowest value found in ref. [START_REF] Boxman | [END_REF] (~150 µ •cm). However it is noteworthy that in our case this low value is obtained at a bias voltage value of 20 V, far lower than that used in [START_REF] Boxman | [END_REF] (160 V). In the analyzed negative bias voltage range (0 -25 V) the electrical resistivity of the ZrN films is at least one order of magnitude higher than that of the bulk material (13.6 µ •cm) [19], as already noted by other authors [20,21].

Oxygen contamination: SIMS analysis

Oxygen contamination is the most challenging problem for films deposition by PVD process, above all for transition metal nitrides due to the strong affinity of the metal with oxygen. To verify the oxygen incorporation, SIMS analysis was performed on all deposited samples by monitoring the CsO + molecular ion. The exact composition cannot be determined by the SIMS measurement due to a lack of a standard reference ZrN material. Therefore, the ratio of the oxygen signal number to the total signal number of the films elements (Zr, O and N) was calculated as qualitative indication. In particular these values have been normalized respect to the 20 V-assisted oxygen signal taken as reference and reported in Figure 11. Although these values do not correspond to the exact chemical composition, it is possible to compare the relative oxygen content in the different samples. They indicate that the oxygen amount is approximately the same in the first three samples (0, 5, 10 V), while it decreases biasing the substrate at 15 and 20 V, then it slightly increases again for the sample deposited at 25 V.

Discussion

The main remarkable effects related to the increasing of the substrate bias voltage observed in our study are: a pronounced preferential orientation of the ZrN grains along the (111) crystallographic axis, a rising of films density and grain size, a decreasing of lattice parameter and electrical resistivity, a shift of the reflectance minimum towards higher energy and an increasing of the reflectivity percentage in the near infrared region.

The (111) preferential orientation results from the increasing kinetic energy and momentum of incident ions with the increasing bias voltage at a constant deposition pressure [22], inducing intrinsic compressive stresses in the films through atoms substitution or vacancies generation [23].

In this case, the strain energy determines the overall energy of the films, and (111) would become the preferred orientation to minimize it [24]. It is noteworthy that the bias voltage in our films does not have any significant effect on film adhesion, while higher bias voltages (> 25 V) led to some film detachment from the substrate, probably due to the higher intrinsic compressive stress induced in the film.

The observed experimental results can be similarly attributed to two different causes: nitrogen replacement by oxygen or nitrogen vacancies generation in the ZrN lattice. Indeed, considering the lattice parameter, its decreasing down to values lower than the bulk one (4.63 Å) by rising the assistance energy, can be ascribed to stress introduced in the lattice due to nitrogen vacancies [25] or to nitrogen substitution by oxygen atoms [26]. In the first case the presence of nitrogen vacancies can influence the film lattice parameter without inducing strong structural alterations: it is known that transition metal nitrides have vacancy defect structure which are stable over a wide range of composition allowing a change in the stoichiometry without altering the NaCl crystal structure [27].

In particular, this has been noted also for nitrogen-deficient ZrN films [START_REF] Lavrenko | Powder Metall[END_REF]. In the second case, O atoms presumably tend to substitute N atoms because they are too large to be inserted into the interstitial sites of ZrN lattice causing a lattice parameter decreasing [29]. For this reason, the examination of the experimental results can help to qualitatively distinguish the respective influence of both factors.

According to the SIMS oxygen signals, the samples can be grouped into three classes: films deposited with V bias in the range 0-10 V (I) where the oxygen content is almost the same, the 15 V and 20 V-assisted samples (II) where the contamination content quickly decreases and the 25 Vassisted sample (III) where the oxygen content slightly increases again.

Although the oxygen quantity is the same for the samples belonging to the group I, their physical properties significantly change: the cristallinity is enhanced (the FWHM of ZrN(111) peak decreases) thanks to the adatom mobility enhancement related to the increased bombardment energy which allows the grain growth and the films mass density improvement [30]; the electrical resistivity decreases of about six times changing from 13240 µ •cm (0 V) to 2300 µ •cm (10 V); the reflectance minimum shifts of about 0.3 eV to higher energies from 0 V to 10 V, the reflectance percentage in the near infrared region and the plasma energy rise from ~25 % to ~36 % (measured at 0.8 eV) and from 1.8 eV to 3.2 eV, respectively. Since the oxygen content in these films is almost unchanged, these variations can be mainly attributed to the changes in the presence of nitrogen vacancies, probably due to a preferential re-sputtering of nitrogen atoms during the ion assistance.

In particular, the non-assisted sample exhibits the highest lattice parameter, even higher than the value in the bulk material, thus suggesting the lowest nitrogen vacancies content. This is in agreement with the optical and electrical measurements. Indeed the plasma energy is proportional to the square root of the free electron density, therefore the increase of its value and the corresponding shift of the reflectance minimum toward high energy indicate an increase of the free electron density. At the same time the reflectance in the low energy range, related to free electrons, increases when increasing the bias voltage from 0 to 10 V. These observations indicate an increase of the free electron density with the bias voltage, in accordance with the electrical resistivity measurements, showing a decrease of the resistivity. This can be explained considering that the formation of zirconium nitride implies the transfer of electrons from the d-band of zirconium atoms to the pstates of nitrogen ones according to the ionic model of the transition metal nitride [17], so a decrease of nitrogen content causes an increase of the number of free electrons supplied by Zr atoms since these electrons are not involved in the bonds with the missing N atoms. As a confirmation, in the literature a shift of the reflectance minimum to high energies has been observed when decreasing the nitrogen content in ZrN films [31].

The decrease of the oxygen content in samples of group II causes an additional increase of the free electron density, thus further inducing a shift of the reflectance minimum (up to 3. As already mentioned, the electrical behavior is in agreement with the optical one, since the electrical resistivity follows the same trend of the plasma energy and thus of the free electron density derived from the optical reflectance spectra. Further investigations are in progress in order to better evaluate the dependence of the resistivity on the carrier relaxation time, for example due to the grain size.

Conclusions

The negative bias voltage applied to the substrate during the sputtering deposition of zirconium nitride films has significant influence on the structural, compositional, electrical and optical properties of the ZrN films. The films exhibit a highly (111) preferred orientation due to the minimization of the strain energy. The lattice parameter decreases by rising the bias and this effect can be due to the nitrogen replacement by oxygen or to nitrogen vacancies generation caused by the ion bombardment. The simultaneous examination of the different characterizations (SIMS, optical reflectance and electrical resistance) allowed to qualitatively discriminate the influence of the two effects. The trends observed in the optical reflectance and electrical resistivity measurements are in agreement with an increase of nitrogen vacancies content with increasing the bias voltage until 20

V. A minimum resistivity value of ~160 µ •cm is obtained for the film deposited with a negative bias voltage of 20 V. The assistance by a higher bias voltage (25 V) is found to cause an inversion in the trends observed in the contamination, optical and electrical film properties.

Captions

  is clearly visible. A reliable and accurate determination of the angular peak positions (by employing a peak profile fitting) is only possible for the most intense Bragg peaks, i.e. the (111), (200), (220) and (311) peaks. The increase of the angular position of the diffraction peaks with the bias voltage corresponds to the decrease of the lattice constant, whose values have been determined from the

  Yoneda peaks positions allows us to determine the mass density (or the real part of the dielectric susceptibility) of the deposited ZrN films. The mass density is related to the critical angle θ c by the equation [13]:

  5 eV) and an increase of the reflectance intensity in the low energy range (up to ~69 %) and of the plasma energy (almost 7 eV), and a decrease of the electrical resistivity (down to ~160 µ •cm). The electrical conductivity is also improved by the decreasing of the electron scattering probability due to both the reduction of oxygen impurities and the increase of film mass density with the bias voltage.The slight inversion in the trend of the optical and electrical measurements observed for the film grown with V bias of 25 V (group III) can be ascribed to two factors: (i) the high energy bombardment can produce structural defects so that the electrons are captured in defect states, thus inducing a reduction of the free electron density, and consequently a shift of the reflectance minimum to low energy (3.3 eV), a decrease of the reflectance percentage in the IR range (~48 %) and of the plasma energy (4 eV), and an increase of the electrical resistivity (280 µ •cm); (ii) the increased ions bombardment leads to an implantation phenomenon which incorporates oxygen atoms in the films (as shown by the oxygen SIMS signal) causing the same effects mentioned above.

Figure 1 :

 1 Figure 1: Co-planar X-ray scattering geometries used for the GIXRD (a) and XSR (b)

Figure 2 :Figure 3 :

 23 Figure 2: GIXRD measurements (2θ scans) of the same samples deposited under different bias voltage V bias

Figure 4 :

 4 Figure 4: ZrN grain size as a function of the applied bias voltage V bias . An almost linear relationship is observed for the considered experimental conditions.

Figure 5 :

 5 Figure 5: Lattice parameter as a function of the applied negative bias voltage V bias . An almost linear relationship is observed for the considered experimental conditions.

Figure 6 :

 6 Figure 6: The XSR and the transverse scans recorded for different 2θ angular positions of the samples

Figure 7 :

 7 Figure 7: The mass density of the deposited ZrN films increases linearly with the increasing applied bias

Figure 8 :

 8 Figure 8: AFM micropraphs of the samples deposited at different applied substrate bias voltage as indicated in each picture. The roughness values are calculated on (2x2)µm 2 areas.

Figure 9 :

 9 Figure 9: Reflectance spectra of the films deposited at different applied substrate bias voltage. Inset:

Figure 10 :

 10 Figure 10: Dependence of the electrical resistivity (Log scale) on the substrate bias voltage.

Figure 11 :

 11 Figure 11: Relative oxygen content versus substrate voltage as derived by SIMS measurements. Each value

FigureFigure 11 (

 11 Figure 01a (Figure 1a.tif)

Table 1 -

 1 Physical parameters (lattice parameter, grain size, critical angle, mass density) as determined from XRD and XRR measurements and RMS roughness values evaluated by AFM measurements.

		negative	grain size	lattice	critical angle	Mass density	RMS
		bias voltage	D (nm)	parameter	θ c (deg)	(g/cm 3 )	roughness
		V bias (V)	(±0.5)	c (Å)	(±0.007)		(nm)
				(±0.0013)
		0	5.1	4.6768	0.30	4.82	5.5
		10	8.3	4.6232	0.32	5.48	6.7
		20	10.2	4.5855	0.335	6.00	10.8
		25	14.5	4.5921	0.35	6.56	10.8
	c-	-	-	4.63	0.364	7.09	-
	ZrN


Ph Traoré

M Daaboul

Ch Louste

Numerical simulation and PIV experimental analysis of electrohydrodynamic plumes induced by a blade electrode

In this paper, a comparative study between numerical and experimental results from PIV measurements is presented in the case of two-dimensional electrohydrodynamic plumes that arise when a sharp metallic blade, submerged in non conducting liquids, supports high electric potential. Experiments and numerical simulations have been conducted in order to confront the both approaches. A very good agreement has been found through velocity profiles and velocity fields which testifies the relevance of our numerical model. For high potentials the jet flow issued forth from the blade becomes unsteady and starts to flap on the vertical wall. Some captions of the temporal evolution of the isocontours of charge density which is not accessible from experiment are presented thanks to the numerical simulation.

Introduction

erformance of industrial systems working with liquids could be improved by using well adapted flow control devices. For instance electrohydrodynamic (EHD) devices could provide an efficient solution to control a given flow. In fact EHD apparatuses have many advantages such as: low power consumption, short response time, and good reliability. They are less subjected to failures of any kind than pure mechanical devices also utilized for flow control and they can be completely non-intrusive.

In electrohydrodynamics, the Coulomb force is the main efficient force to induce the liquid motion. In absence of thermal gradient, only two different phenomena can produce a volume charge density and then a Coulomb force.

P

The first one is the so-called charge injection process and is associated to unipolar injection of ions at a metal/liquid interface [START_REF] Chang | Two phase flow in Electrohydrodynamic" Part V[END_REF]. The second one is the conduction pumping phenomena which is based on the process of dissociation and recombination of electrolytic species. Atten & Seyed-Yagoobi [START_REF] Atten | Electrohydrodynamically induced dielectric liquid flow through pure conduction in point/plane geometry[END_REF] have demonstrated that in absence of injection this dissociation-recombination process results in the production of heterocharge layers of finite thickness in the vicinity of the electrodes. They also predict that the use of asymmetric electrodes could induce a net liquid motion. This model has been experimentally and numerically proved by Feng and Seyed-Yagoobi [START_REF] Feng | Understanding of electrohydrodynamic conduction pumping phenomenon[END_REF]. Many devices and applications based on these two phenomena have been developed. Most of them are EHD pumps or thin film devices for cooling applications. A scientific overview of numerical and experimental research on the conduction model could be found in [START_REF] Pearson | Advances in electrohydrodynamic conduction pumping[END_REF]. Although, the conduction phenomenon is better adapted for pumping applications, injection remains interesting because it induce a stronger Coulomb force. In this article, a typical blade-plane set up is used to induces ions injection in a dielectric liquid [START_REF] Atten | Injection induced electrohydrodynamic flows[END_REF] [START_REF] Huigera | Electrohydrodynamic flow of a dielectric liquid around a blade electrode[END_REF]. In such conditions, convective motion of a jet shape arises. These particular flows have been referred to as EHD plumes and are present in most of industrial devices exploiting electric forces.

In previous works it has been shown that a blade-plane geometry device generates an impinging jet which can reach a velocity of 1 m/s [7][8].

The adaptation of the Particle Image Velocimetry (PIV) technique to electrohydrodynamic flows [START_REF] Daaboul | PIV measurements on charged plumes -Influence of SiO2 seeding particles on the electrical behavior[END_REF] has permitted to obtain large velocity maps of jets. Characteristics of such flows have been studied as well as in transient or in stationary regimes [START_REF] Daaboul | PIV measurements on charged plumes -Influence of SiO2 seeding particles on the electrical behavior[END_REF] [START_REF] Louste | A study of vortex shedding induced by dielectric barrier injection[END_REF] . Although the last improvements of the PIV measurement technique some data remain non-measurable.

The analogy of EHD plumes with thermal ones has conducted many authors [START_REF] Vazquez | Dynamics of electrohydrodynamic laminar plumes: Scaling analysis and integral model[END_REF][12] [START_REF] Vazquez | Numerical modelling of EHD flows due to injectors of finite size[END_REF][14] [START_REF] Chicon | Numerical modelling of Coulomb-driven convection in insulating liquids[END_REF] to analyze EHD plumes by the mean of self-similar analysis or integral model. Under some simplifying assumptions the governing EHD equations are made tractable and the mathematical model is close to the one of thermal plumes for Pr → ∞

(where /

Pr ν α = is the Prandtl number ν is the kinematic viscosity of the fluid and α its thermal diffusivity).

Another way to obtain information on data which are not accessible experimentally, for instance the electric charge density in the device as well as the electric field at every location of space, is to require to numerical simulations.

Several attempts to model numerically the development of EHD flows and especially electro-convective flows have been made in the past. But most of the authors started their computations from an assumed velocity field and not from a real resolution of the Navier-Stokes equations [START_REF] Chicon | Numerical modelling of Coulomb-driven convection in insulating liquids[END_REF]. In [START_REF] Perez | Numerical study of an ElectroHydrodynamic plume between a blade injector and a flat plate[END_REF] the appropriate electrodynamics equations coupled with the full Navier-Stokes equations are solved numerically with the help of an efficient finite volume method to study the flow structure of EHD plumes.

In this paper, detailed comparisons between experimental results obtained from PIV measurements and numerical predictions are presented in the case of an EHD plume induced by charge injection from a blade. Velocity profiles and vector fields are correlated and the charge field in the device is extracted from the numerical results.

Experimental apparatus and techniques

Electrical Device

A schematic diagram of the system is shown in figure. The liquid used in the experiments is dielectric oil with slight electrical conductivity. The characteristics of this dielectric liquid at a temperature of 20 °C are presented in Table I.

Particle Image Velocimetry Method

The Particle Image Velocimetry method is a common technique used in experimental fluid dynamics. It consists of seeding a flow with small tracer particles and tracking these particles to determine the velocity map of the test zone.

A double pulsed laser sheet illuminates the investigation scene and a CCD camera takes 2 successive photos in order to determine the successive positions of the seeding particles (figure . 2). Special software using a correlation algorithm gives the velocity map knowing the time delay between the 2 successive images. This work was realized with a LaVision acquisition system (LaVision GmbH, Göttingen, Germany.) The images were acquired with a CCD digital camera at a spatial resolution of 1376×1040 pixels. The frames were analyzed with Davis 7.1 software. The choice of seeding particles is essential particularly in an EHD context. Addition of particles in an EHD flow has been widely studied in the context of electrostatic precipitators and essentially in air [START_REF] Atten | The electrohydrodynamic origin of turbulence in electrostatic precipitators[END_REF][18][19] [START_REF] Chun | Numerical modeling of near corona wire electrohydrodynamic flow in a wire-plate electrostatic precipitator[END_REF]. However in the case of liquids the phenomenology is rather different because of the presence of the electrical double layer at the particle surface, the liquid conductivity and its relative permittivity. Thus the behaviour of these particles in air will be different compared to the behaviour they would have in liquids. In air electrostatic precipitators, the electrostatic charge of particles could be important and thus their trajectories would be essentially driven by the electric field and only slightly affected by the air flow itself. In the case of liquids, and particularly in PIV measurements the goal sought after would be precisely that solid particles follow the trajectories of the fluid particles [START_REF] Daaboul | Etude et développements d'actionneurs électrohydrodynamiques pour le controle des écoulements[END_REF]. In order to achieve such goal and to avoid that the solid particles have their own trajectories completely driven by the electric field and roughly independently of the fluid flow, some requirements must be met. In such case it is precisely important to avoid the electrostatic precipitation of the particles on the electrodes and the charge accumulation which could modify, firstly the hydrodynamic trajectories of these particles due to the electric field and secondly the electric field itself. Daaboul [START_REF] Daaboul | Etude et développements d'actionneurs électrohydrodynamiques pour le controle des écoulements[END_REF], have demonstrated that the use of SiO 2 particles of 0.5 µm diameter with a concentration of less than 100 mg/l must be employed to have satisfactory results. In fact, with such a concentration, the electric current is not modified. Daaboul has proven that the global shape of the charged plume as well as the jet velocity profiles are not affected for these low concentrations. In this work we have used these particles with a 20mg/l concentration.

Numerical method

The problem is formulated considering the usual hypotheses of a Newtonian and incompressible fluid of dynamic viscosity µ and density ρ. The Navier-Stokes equations (mass and momentum conservation) are coupled with EHD equations and give rise to the following partial differential equations system.

. 0

U ∇ = (1)
( . )

U U U P U qE t ρ µ   ∂ + ∇ = -∇ + ∆ +   ∂   (2)
( )

. ( ) 0 q q U KE t ∂ + ∇ + = ∂ (3) q V ε ∆ = - (4)
E V = -∇ (5)
U is the fluid velocity, P the pressure, q the charge density, V the potential and E the electric field. K is the ionic mobility and ε is the dielectric constant. In the charge density transport equation (3), diffusion term has not been included since it is negligible compared to the migration term [START_REF] Perez | [END_REF]. The injection of unipolar charge of mobility K from the blade is assumed homogeneous and autonomous [START_REF] Vazquez | Characterization of injection instabilities in electrohydrodynamic by numerical modelling: Comparison of particle in cell and flux corrected transport methods for elctroconvection between two plates[END_REF] [START_REF] Vazquez | Numerical analysis of the satiability of electrohydrodynamic (EHDi) electroconvection between two plates[END_REF]; this mean that the charge density at the blade is supposed to be constant and equal to 0 q at all times since the injector and hence the injection rate are not influenced by perturbation in the bulk. We have depicted the computational domain and the boundary conditions in figure 3. 0 q and 0 V are respectively the charge density and potential applied on the blade.

Figure 3. Computational domain and boundary conditions

The numerical procedure is based on the integration of the whole system of equations by a finite volume method using a staggered grid and a semi-implicit second order in time and space accurate schemes [START_REF] Patankar | Numerical Heat Transfer and Fluid Flow[END_REF]. All details of the present numerical method can be found in [START_REF] Perez | Numerical study of an ElectroHydrodynamic plume between a blade injector and a flat plate[END_REF].

Results and discussion

The applied voltage between the blade and the plate counter electrode induces a very strong electric field at the blade tip. It is well known that in this configuration the measured current can be decomposed into a conduction current part and an injected current one which originates from the unipolar injection of charges at the blade tip. On figure 3 we have presented the current-voltage characteristic from experiments. It shows a typical behaviour associated with a space charge limited condition [START_REF] Felici | Direct Current conduction in liquid dielectrics. Part I : A survey of recent progress (Conduction en courant continu dans les liquides diélectriques)[END_REF] . The structure of the flow is composed of two main vortices on either side of the plumes which are easily identified on the figure 5 which represents the velocity field and isocontours of the velocity magnitude. For the case -5kV we obtain a stationary laminar regime while the -20kV one is fully unsteady and turbulent. In that case, the captions represent the temporal mean over all discrete times of the simulation, and over 1000 instantaneous velocity fields issued from recorded PIV images for the experiment. The comparison between experimental and numerical results shows a very good agreement. In figure 6 we have plotted the experimental and numerical longitudinal velocity profiles in x middle plane on the same graph for the both cases -5kV and -20kV. Here again the curves depicted for these two values of the applied voltage match quiet well. The little discrepancy of the profiles is only due to experimental measurements errors as well as a slight dissymmetry of the experimental apparatus that we noticed at the end of our measurements campaign. One of the most interesting features of numerical simulation is that it allows computing some quantities which are note available by measurements. The charge density is a good example of such inaccessible data by measurement means. In figure 10 we have depicted the time evolution of the dimensionless charge density in the computational domain for an applied voltage of -5kV. It is interesting to notice that the charge density is confined in a thin layer which arises from the blade until it reaches the counter electrode. The iso-values of this charge density are quite low in accordance with the relatively moderate applied voltage.

Isocontours of the charge density Time Isocontours of the charge density Time

Conclusion

PIV, experimental measurements and numerical simulations have been conducted to analyze EHD plumes arising from ions injection between a blade and a plane in a dielectric liquid under the influence of an applied voltage. Two cases have been considered: -5kV and -20kV. We have highlighted the existence of a steady and laminar regime for low applied voltage between the blade and the opposite collector electrode. A turbulent regime with the appearance of a flapping effect of the jet flow issued forth from the blade has been observed experimentally as well as numerically for -20kV applied voltage.Comparisons between experimental and numerical longitudinal velocity profiles in the x middle plane, as well as the velocity field for different values of applied voltage show a perfect agreement which testify the validity, capability and efficiency of our numerical model. The use of PIV measurements in the context of EHD flow is a real advance. Nevertheless the real effect of PIV particles in their interactions with flow through their charge catching must be more precisely investigated and determined.

1 .

 1 The test cell is composed of a 30 cm × 15 cm × 15 cm glass aquarium filled with the dielectric liquid. The electrical device is totally immerged in the liquid and fixed in a confined zone of 10 cm × 8 cm × 6 cm with flat glass surfaces in order to be able to realize PIV measurements without Laser reflections. An 8 cm long and 0.5 mm thick stainless steel blade is placed in front of a duralumin flat plane electrode. The distance d between the blade tip and the counter-electrode is set to 20 mm and the radius of curvature of the blade tip is about 7 ± 2 µm.

Figure 1 .

 1 Figure 1. Experimental apparatus

Figure 2 .

 2 Figure 2. Particle Image Velocimetry measurement system (© LaVision GmbH, Germany, http://www.lavision.de).

Figure 4 .

 4 Figure 4. Experimental current-voltage characteristic in blade-plate geometry.

Figure 5 .

 5 Figure 5. Snapshots of velocity field and isocontours of the velocity magnitude for an applied voltage of -5kV and -20kV

Figure 6 .Figure 7 .

 67 Figure 6. Comparisons of the numerical and experimental longitudinal velocity profiles in the x middle plane field for two values of the applied voltage.

Figure 8 Figure 8 .Figure 9 .

 889 Figure8presents the contour map of the dimensionless instantaneous pressure field for the two cases considered in this paper, -5kV and -20kV, at the same time of the simulation t=12.096s. At this time and for an applied voltage of -5kV the steady state is already reached while for -20kV the flow remains fully unsteady. It is clearly depicted that the maximum of pressure is logically found on the opposite counter electrode. In the case of -5kV the position of this maximum is aligned with the blade electrode on y=H/2 and the flow if fully symmetric. The value of this maximum remains stationary after a short transient period as the flow starts from rest. For -20kV, the position of this maximum, still located on the opposite wall, varies with time and also along the y axis above or below y=H/2.The flapping effect starts in the early stages of the simulation as it can be seen on figure9where the time evolution of the maximum of wall pressure values has been depicted. These fluctuations of the maximum wall pressure are indeed a characteristic of the turbulent behavior of the jet flow for this value of the applied voltage.

Figure 10 .

 10 Figure 10. Instantaneous isocontours of the dimensionless charge density at different times of the simulation.

Table 1 .

 1 Typical Characteristics of the Dielectric Oil at20 °C

	Mass density