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

Laplace

Laurent Boudou Laplace

Duvan Mendoza-Lopez

Laurent Berquez
email: laurent.boudou@laplace.univ-tlse.fr

Christian Laurent Laplace
email: christian.laurent@laplace.univ-tlse.fr

Feihu Zheng
email: feihuzheng@tongji.edu.cn

Charge Trap Spectroscopies in Polymer Dielectrics: Application to BOPP

Keywords: trap spectroscopy, detrapping, deep traps, bioriented polypropylene

Polymer dielectrics are in use in a variety of applications in active or passive electrical components. Their propensity to store electrical charges is used e.g. to form electrets but is a drawback when insulation properties are looked for. It is therefore essential to investigate the traps characteristic for a given material because trapping phenomena control the transport properties and therefore the field distribution. Different trap spectroscopies are available to infer the nature of traps, their energy depth and their amount. In the first part of this communication, we briefly review the different methods for traps characterization, emphasizing on strength and weaknesses of the methods. In a second part, results obtained on bioriented polypropylene are used to illustrate the difference in trap depth estimation obtained using thermal and optical excitation to release charges from traps. The differences are discussed with introducing results from luminescence induced by charge recombination.

I. INTRODUCTION

Traps control the electrical properties of the material through their energy depth distribution and their density. The presence of a large density of shallow traps can constitute an explanation to the relatively low barrier to injection inferred from apparent conduction currents in polymeric materials. Indeed, a Schottky barrier of several eVs is anticipated considering it as wide band gap materials, leading to extremely small theoretical current. The possibility of having a direct transfer of charges to localized states, which would act as springboard for injection, would provide a justification to measured currents.

Different methods have been implemented over the years to get insight into fundamental properties of traps that are the physical-chemical nature, the energy depth, and the amount. Methods can be with or without stimulation of charge detrapping and are based on either pure electrical response such as surface potential decay, coupled thermal-electrical effects as with thermally stimulated discharge current (TSDC) or couple electrical-optical effects as in photostimulated discharge (PSD) for example, as reviewed recently [START_REF] Teyssedre | Charge trap spectroscopy in polymer dielectrics: A critical review[END_REF].

Important questions are still open on the equivalence of the methods. As example, TSDC and PSD give substantially different trap depths and it is not clear if discharge proceeds in a way different from pure detrapping, if the probed levels are not the same or if the way energy provided to occupied levels is different.

In the first part of this contribution we briefly review these different methods available for traps characterization. In a second part, we present results obtained on bioriented polypropylene (BOPP), a material used extensively in power capacitor application of its high breakdown field, using three of the previously described methods. The differences in the results are discussed.

II. TRAP SPECTROSCOPIES: OVERLOOK

The methods that will be discussed here mainly concern the energetic aspects of traps. Their nature is to be probed using physico-chemical methods while their density is extremely difficult to catch without an exhaustive view of the fraction of occupied levels among all potential sites available.

Trap spectroscopies rely on a pre-charging step followed by a stimulation for charge detrapping during which a quantity related to the stored charge is recorded. The precharging step can be ionizing, including electron, irrradiation, contact with a gas discharge discharge, application of a DC field, etc. The stimulation can be thermal or optical giving an estimate of the trap depth when charge detrapping is observed -see Fig. 1.

Among the different available spectroscopies, the thermally stimulated discharge current (TSDC) [START_REF] Kojima | Thermally stimulated currents from polyethylene terephthalate due to injected charges[END_REF][3] is probably the most well-known where the external current is recorded upon thermal stimulation. Quite often, the luminescence due to charge recombination following the detrapping -see Fig. 1, is recorded at the same time as the current leading to thermally stimulated luminescence (TL) [START_REF] Blake | Simultaneous thermoluminescence and thermally stimulated conductivity in polyethylene[END_REF]. An alternative to the thermal stimulation is to stimulate charge detrapping by an optical excitation giving a spectroscopy called photostimulated discharge (PSD) when the current is recorded [START_REF] Mellinger | Photostimulated discharge in electret polymers: an alternative approach for investigating deep traps[END_REF] [START_REF] Ma | Investigation of surface and bulk charge traps of polyimide film by using the photo-stimulated discharge method[END_REF].

In all the cases, the trap depth is inferred from the energy provided to overcome the barrier between the trapping level and the conduction level. This simple interpretation is however a rough approximation because other physical processes may be active as we will be shown later on. Generally, extracting the trap energy distribution is not a simple task.

The characteristics of the main techniques used for trap spectroscopy in dielectrics are depicted in Table 1. Besides methods involving optical or thermal excitation advocated above, a variety of techniques are based on the spontaneous decay of charge (through space charge, current, potential measurement). The probe signal is either of optical or electrical nature. The provided information, advantages and drawbacks are discussed in the next section.

The methods are sorted by splitting them between those that need an excitation and. those that do not.

A. Methods without stimulation

The analysis of the spontaneous decay of the charge has been achieved based on isothermal current decay [START_REF] Simmons | Theory of isothermal currents and the direct determination of trap parameters in semiconductors and insulators containing arbitrary trap distributions[END_REF] [START_REF] Watson | The energy distribution of localized states in polystyrene, based on isothermal discharge measurements[END_REF], or, more often, surface potential decay [START_REF] Molinié | A review of mechanisms and models accounting for surface potential decay[END_REF][10] measurements. The decrease in time of the potential results from the detrapping of charges followed by their drift in the insulation. The field induced by the charges is a driving process As the probe provides an integral signal, a physical model is needed, with suppositions about the nature of charges, the way it is released. In addition, hypotheses on the mechanisms at play at the charging step need to be taken. It leads to a complex picture involving several physical phenomena.

On the one hand, three mechanisms can be at play in surface charge release, being transport in the insulation bulk, which is the process of interest for traps characterization, neutralization by ions existing in the environing gaseous medium, and surface leakage since samples have generally a limited size.. A comprehensive picture of these different contributions has been provided recently by Zhang [START_REF] Zhang | Interpretation of the surface charge decay kinetics on insulators with different neutralization mechanisms[END_REF].

On the other hand, SPD can be due not only to charge motions, also to orientation polarisation. It is not straightforward to discriminate between the two effects.

Finally, the charging step is to be modelled: mainly ions are deposited charges by corona discharge. There are underlying charge exchange processes between deposited ions and electrons or holes carriers, that subsequently drift and get trapped in the volume of the insulation. However, in most of the works except of a few [START_REF] Hogue | Triboelectric, corona, and induction charging of insulators as a function of pressure[END_REF], this charge exchange step is forgotten: the source charge is continuously 'injected' into the insulation and considered as a finite reservoir during the discharge [START_REF] Chen | A new model for surface potential decay of corona-charged polymers[END_REF] [START_REF] Coelho | On the natural decay of corona charged insulating sheets[END_REF] or it is considered that the charges directly occupy deep surface states [START_REF] Li | The energy distribution of trapped charges in polymers based on isothermal surface potential decay model[END_REF].

Besides the behaviour of the source term, handling detrapping and transport is puzzling. To simplify the problem and being able to infer the trap distribution, it is generally supposed that the transport of charges is fast compared to the detrapping process, i.e. charges immediately disappear once detrapped. The potential decat then gives an image of the trap distribution N(E) with:

𝑡𝑑𝑉/𝑑𝑡 ∝ 𝑘 𝑏 𝑇𝑁(𝐸 𝑡 (𝑡)) (1)
and

𝐸 𝑡 = 𝑘 𝑏 𝑇𝑙𝑛(𝜈𝑡) ( 2
)
where T is the temperature, Et the trap depth, t the time in the potential decay. ν is the attempt-to escape frequency and kb is the Boltzmann's constant.

Sophistication of the charge distribution measurement techniques has allowed to refine the analysis of the kinetics of charge release and therefore of the trap depth distribution. Hence, it is in principle possible to distinguish injected charges from orientation polarization charges, to check if different types of charges are injected, and to support hypotheses on charge localization. The original analysis was proposed by Dissado et al. [START_REF] Dissado | Space charge injection and extraction in high divergent fields[END_REF]. Refinements and variants of the model have been provided the questioning about the charge distribution [START_REF] Mazzanti | A space charge based method for the estimation of apparent mobility and trap depth as markers for insulation degradation-theoretical basis and experimental validation[END_REF] [START_REF] Dissado | Decay of space charge in a glassy epoxy resin following voltage removal[END_REF]. With considering as input data the total net stored charge amount QM(t) function of time after charging, the limits min and max. of the top-hat occupied trap distribution, the initial charge QM0 or the charge release rate can be obtained:

𝑄 𝑀 (𝑡 = 0) = 𝑄 𝑀0 = 𝑒𝑁 0 [∆ 𝑚𝑎𝑥 -∆ 𝑚𝑖𝑛 ] (3)
𝑠 = 1 𝑄 𝑀0 𝑑𝑄 𝑀 (𝑡) 𝑑𝑙𝑜𝑔(𝑡) = -𝑘 𝑏 𝑇 ∆ 𝑚𝑎𝑥 -∆ 𝑚𝑖𝑛 𝑙𝑛10 (4)
Here, s is for the charge resorption rate, given in % per decade in time. The trap depth obtained with this method are consistent with those obtained in SPD, pointing to thermal activation of the charges.

Another technique without stimulation consists in recording the luminescence due to charge recombination immediately after bi-polar charging [START_REF] Laurent | Optical emission due to space charge effects in electrically stressed polymers[END_REF], so-called chargerecombination induced luminescence (RIL). The charging can be achieved with an AC discharge in contact with the surface of a film, or by irradiating the sample with ionizing radiation generating pairs of charges [START_REF] Massines | On the nature of the luminescence emitted by a polypropylene film after interaction with a cold plasma at low temperature[END_REF] [START_REF] Teyssedre | Spectral analysis of optical emission due to isothermal charge recombination in polyolefins[END_REF]. With this method, the nature of chemical groups involved in charge recombination and the kinetics of charge release are most specifically investigated.

The technique is simple to implement and does not require any hypothesis on charge transport. It was applied using a variety of irradiation sources, particularly γ-rays [START_REF] George | The isothermal luminescence and thermoluminescence of gamma-irradiated polyethylene at 77 K[END_REF] [START_REF] Hama | Studies of the recombination of cation-electron pairs by long-range tunneling, as studied by ITL measurement in irradiated polymers[END_REF]. When using contact with a plasma discharge, i.e. plasma-induced luminescence (PIL), only the surface of the material is charged. We will illustrate the input of this technique for the identification of trapping centres in BOPP.

B. Methods with stimulated detrapping

Stimulating the discharge using either optical or thermal excitation provides an alternative to the methods described in Part A. There are however fundamental differences between the two excitation ways and the derived quantities are often far from each other. The reasons for these differences are discussed below.

Optical excitation is attractive since by scanning the light irradiation wavelength, a direct estimation of the trap depth can be obtained, at the onset of discharge current increase. (Figure 1, path 2). Hence, photostimulated discharge (PSD) potentially provides a direct estimate of trap depth without signal conditioning. However, things are far from being that simple mainly due to the photoconduction processes involving not only photo-detrapping of carriers but also photo-injection from the electrodes, or excitation of π electrons in conjugated groups [START_REF] He | Influence of photoconductivity on the study of trap levels in polyimide by photo-stimulated discharge[END_REF]. It has been shown that the nature, through the work function, and shape of the electrodes significantly impact the response. For example, a shift of the position of the PSD peak of polypropylene films to longer wavelengths was reported when the electrode irradiated by light is changed from gold (work function Φ = 5.1 eV) to aluminium (Φ = 4.28 eV) for [START_REF] Ma | Analysis and interpretation of photo-stimulated discharge spectrum for polypropylene films under different electric and geometrical conditions[END_REF]. Also, the use of fingered electrodes improved the PSD signal presumably by avoiding light to be absorbed by metallic electrodes. However, using fingered electrode can have an important side effect which is the enhancement of the electric at the electrode edges. Charge injection and trapping can be substantially increased at these "hot points" [START_REF] Ma | Analysis and interpretation of photo-stimulated discharge spectrum for polypropylene films under different electric and geometrical conditions[END_REF].

In photoconduction phenomena, excitation by light can be with different contribution as carriers photo-injection at the dielectric-electrode interface, detrapping of carriers, or carriers creation by excitation of conjugated groups followed by field-aide exciton dissociation. In PSD, the expected main mechanism is carrier detrapping. However, the other contributing processes to photoconduction can be at play as well [START_REF] He | Influence of photoconductivity on the study of trap levels in polyimide by photo-stimulated discharge[END_REF]. At short excitation wavelength (<260nm), i.e. energy (>4.8eV) it was shown that external photo-effects cannot be neglected in various polymer electrets when using pressed electrodes [START_REF] Mellinger | Photostimulated discharge in electret polymers: an alternative approach for investigating deep traps[END_REF].

The TSDC method consists in bringing the material to a high temperature, then charging e.g. by applying a dc field and then cooling to low temperature with maintaining the field in order to freeze the charge state. After short-circuiting the sample, a linear heating rate of a few °C/min is applied while the discharge current is recorded as a function of temperature. For TSL the precharging step does not necessarily involve field application. Ionization radiation is a typical charging means.

In comparison to isothermal decay methods, the experimental time is thermally stimulated methods (TL or TSDC) is substantially shortened. In addition, a series of relaxation modes can be analysed in a single spectrum when isothermal methods would require measurements at different temperature to reach time characteristic of the process compatible with the method. Besides, a charged state can be frozen by cooling such that the charges in shall levels can be retained when they would be quickly released in isothermal cases.

A kinetic analysis must be developed when using thermal stimulation for obtaining a trap depth. The current collected externally in short-circuit conditions represents the spaceaveraged transport current. It depends on the initial position of trapped charges and on the local field that drives the charges to the collecting electrode. Compared to TL, it represents a major difference as TL reflects charge recombination phenomena that don't necessarily involve long-range transport.

In TSDC either charge detrapping or dipoles relaxation may lead to a signal. The most simplified model and equation of the TSDC glow curve is the one (5) describing relaxation from dipoles in a homogeneously polarized dielectric. The current density with shorted electrodes is.

𝐽(𝑇) = 𝑃 0 𝜏 0 𝑒𝑥𝑝 - 𝐸 𝑎 𝑘 𝑏 𝑇 × 𝑒𝑥𝑝 [- 1 𝛿𝜏 0 ∫ 𝑒𝑥𝑝 - 𝐸 𝑎 𝑘 𝑏 𝑇′ 𝑑𝑇 ′ 𝑇 𝑇 0 ] ( 5
)
where P0 is the frozen polarization (C/m²) and δ is the heating rate. τ(T) is the relaxation time, with Arrhenius temperature dependence:

𝜏(𝑇) = 𝜏 0 𝑒𝑥𝑝 𝐸 𝑎 𝑘 𝑏 𝑇 (6)
where Ea the activation energy, τo is the frequency factor, and kb the Boltzmann's constant. For TSDC resulting from moving charges, the resolution in general cannot be achieved analytically rigorously. The initial charge distribution in the material controls the discharge current. In very specific situations the TSDC has the same form as [START_REF] Mellinger | Photostimulated discharge in electret polymers: an alternative approach for investigating deep traps[END_REF]. One of them is for charges initially trapped in a region close to the surface without contacting it. The discharge is controlled by the charges mobility and by the space charge induced field. The equation is approximately valid up to the time internal charges reach one of the electrodes [25][26]. Charge detrapping with fast retrapping seems to be another such case [START_REF] Van Turnhout | Thermally stimulated discharge of electrets[END_REF]. For other initial distributions and hypotheses, there is no simple expression.

TL can be viewed as a complementary method to TSDC. Inconsistencies can be explained by the fact that the first is sensitive mainly to charge relaxation followed by their recombination while the latter probes both dipole and charge relaxation. TL may be complemented by the analysis of the emission spectrum: The information from TL completes that from TSDC as it reveals recombination events and the chemical nature of recombination centres.

Like for TSDC, with simple hypotheses as electrons escaping from a single trap level, followed by recombination on trapped holes, a simple equation holds for the TL glow [START_REF] Ambrico | Thermoluminescence study of the trapped charge at an alumina surface electrode in different dielectric barrier discharge regimes[END_REF]. Figure 2 details the hypotheses taken. The escape rate of electrons from the traps is governed by the vibrational frequency S for trapped electrons interacting with the lattice and by the trap depth Et. The overall escape rate is proportional to 𝑆 exp -𝐸 𝑡 /𝑘𝑇. With an excess of accessible holes (m>>n) and a strong recombination probability (Am>>An), the TL spectrum is described by first order kinetics and matches exactly to [START_REF] Mellinger | Photostimulated discharge in electret polymers: an alternative approach for investigating deep traps[END_REF] with replacing P0 by n0, τo by S -1 and Ea by Et.

III. MATERIALS AND METHODS

We report below on traps identification and detrapping processes in bioriented polypropylene (BOPP), a material with outstanding breakdown strength largely used in power capacitors application. Three among methods described above were implemented, namely TSDC, PSD and RIL in order to explore different principles for traps characterization.

A. Samples

BOPP films, 17 µm in thickness were provided by Copafilm, Germany. The surface of the films is with smooth craters produced to improve impregnation of the films. Some of the properties of such films were already investigated, notably through luminescence experiments [START_REF] Qiao | Evidence of exciton formation in thin polypropylene films under AC and DC fields and relationship to electrical degradation[END_REF]. Disks of 8 cm diameter were used in all the experiments. For RIL measurements, samples were used directly without electrode deposition. For TSDC experiments, circular gold electrodes of 30 nm in thickness and 20 mm in diameter were sputtered on each face of the samples. For PSD experiments gold electrodes were also deposited by sputtering. The front side (irradiated by light) electrode was processed as a fingered electrode of 50 nm thickness and 4 cm diameter [START_REF] Boudou | Photo-stimulated discharge current measurements on biaxially oriented polypropylene thin films (BOPP)[END_REF]. The back electrode (collecting the current) is a full electrode of 50 nm thickness.

B. Recombination-Induced Luminescence

The principle of the experiment consists in exciting/charging the surface of the sample using a acpowered dielectric barrier discharge (5.5 kHz) produced in helium gas at low temperature (about -110°C) at atmospheric pressure. Details of the set-up are available in [START_REF] Massines | On the nature of the luminescence emitted by a polypropylene film after interaction with a cold plasma at low temperature[END_REF] [START_REF] Teyssedre | Spectral analysis of optical emission due to isothermal charge recombination in polyolefins[END_REF]. A typical interaction time of 5 s is used in order to avoid N total trap density n occupied electron traps (initially no) m hole states density available for recombination Et :trap energy An retrapping probability Am recombination probability Fig. 3. Processes involved in a simple thermoluminescence model.

Adapted from [START_REF] Ambrico | Thermoluminescence study of the trapped charge at an alumina surface electrode in different dielectric barrier discharge regimes[END_REF]. modification of the surface by the discharge. After switching off the discharge, the light emitted by the sample is analysed in isothermal conditions. Several mechanisms are at the origin of the delayed light emission, an example being long-lived photoluminescence (phosphorescence) due to UV excitation by the discharge. We have shown that the long-lasting signal (at times beyond ≈30s) is triggered by charge recombination and the spectral features of the signal is in principle relevant to the trapping centre. In order to detect light, either a photomultiplier working in photon counting mode or a CCD camera associated to a dispersive system are used. In this way the kinetic of total light decay and the emission spectrum in different time windows can be obtained.

C. Photo-Stimulated Discharge

The diagram of electrical circuit for PSD method is shown in Fig 4a . The stimulating light is produced by a 150 W Xenon arc lamp associated with a grating monochromator (300nm-blaze grating, 1200g/mm). The bandwidth of the monochromatic light is controlled by adjusting the input and output slits. Details of device characteristics are given in [START_REF] Boudou | Photo-stimulated discharge current measurements on biaxially oriented polypropylene thin films (BOPP)[END_REF]. The samples are previously charged under DC voltage. The experimental protocol used is represented in Fig. 4b. The charge and discharge currents are recorded using a Keithley 617 ammeter during the conditioning phases as well as during irradiation. For the results shown here, the polarization voltage was from 1 to 3 kV and the polarization time 30 min. After polarization the sample was short-circuited during 30 min before the light irradiation starts in order to relax fast processes. In this way, the PSD spectrum is initiated with a small 'dark' current that does not interfere with the PSD current. The PSD spectrum is recorded while scanning the light from low to high energy (590 nm to200 nm) at a scanning rate of 24 nm/min. Experiments were realized in air atmosphere and at room temperature.

D. Thermally Stimulated Depolarization Current

TSDC measurements were performed in a thermally controlled chamber, in a helium atmosphere. The samples were first polarized with a DC voltage VP in the range 0.5 to 2.5 kV at a constant temperature TP (80°C), for a time tP = 30 min. After cooling under applied voltage, the samples were reheated from -60 °C temperature up to 140 °C, using a constant heating rate δ = 3 °C/min, under short-circuit conditions. The discharge current was recorded using a Keithley-617 electrometer during all the cycle, with as main objective to exploit the current obtained during the ramp-up.

IV. RESULTS

A. Recombination-Induced Luminescence

Fig. 5a shows the decay of the total light (Plasma-Induced Luminescence, PIL) measured using a photomultiplier immediately after switch off of the discharge. The discharge was previously produced for a short time (5 s) to avoid surface modification. The dwelling time for PM signal counting was 1 s. According to the decay, there are two processes of light emission. In the short time range, the decay is approximately exponential and may result from chemiluminescence and/or UV-induced phosphorescence induced by the discharge [START_REF] Massines | On the nature of the luminescence emitted by a polypropylene film after interaction with a cold plasma at low temperature[END_REF]. Then it, switches to a power law decay at long time, which is considered as representative of radiative charges recombination. The PIL decay has been fitted to the following equation: (a) Integral light decay and fit to Eq. ( 11) with drawing of the decaying functions (red: exponential; green: power law).

𝑃𝐼𝐿(𝑡) = 𝐼 1 𝑒𝑥𝑝 - 𝑡 𝜏 1 + 𝐼 1 𝑡 -𝛼 (7)
(b) Spectra obtained in different time intervals during the decay. The RIL spectrum (in blue) peaks a 500 nm. with τ1 =4.5 s and α=0.87. The second process, i.e. RIL, becomes dominant after about 15 s.

Several spectra were recorded during the decay, using an integration time with the CCD of 5 s and increasing to 30 s for integrating more signal as the decay progresses. Fig. 5b shows three spectra obtained in different time intervals along the decay. In the first seconds after the discharge, the peak is found at about 420 nm with a shoulder at 500 nm. In the second spectrum (6-11 s in the decay), the two contributions appear clearly. Based on these results, it can be considered that the luminescence fingerprint of centres excited upon charge recombination in BOPP is at 500 nm (2.48 eV). Such results are in-line with previous results on PP [START_REF] Teyssedre | Spectral analysis of optical emission due to isothermal charge recombination in polyolefins[END_REF]. The recombining centres were considered to be polyenone sequences.

B. Photo-Stimulated Discharge

Fig. 6 shows typical results from PSD on BOPP obtained with different pre-applied voltages. The reference spectrum corresponds to the blank, i.e. current measured on illuminating without pre-applied voltage, revealing no appreciable signal. For the spectra obtained with pre-applied voltage, a decrease of the current from the long wavelength side is observed, corresponding to the tail of the isotherm discharge.

Two main regions are visible in the spectrum. A narrow peak is observed in the region 200 to 250 nm. The position of the peak seems dependent on the pre-applied voltage, being at about 230 nm for 1 kV applied and moving to 200 nm for 3 kV. It is not clear if it corresponds to a shift or to the appearance of 2 contributions. BOPP has strong absorption in this wavelength range, with notably π→π* transitions in defects such as C=C double bonds. The corresponding energy, about 6 eV is very large to be considered for a trap level. The UV-vis absorption spectrum of BOPP has no feature that would match with the other characteristic peak at 400 nm (3.1 eV) in the PSD spectrum. Polyolefins in general don't have absoption bands in this region.

C. Thermally Stimulated Discharge Current

Fig. 7 shows TSDC spectra obtained with different polarization voltages, between 1 kV and 2.5 kV. Two regions of discharge appear, consistently with literature reports. The peak observed below room temperature (0°C) appears related to the β-relaxation of PP. The discharge current is grossly linear with applied voltage, and its origin might be dipolar, and does not necessarily involve charge detrapping. In the higher temperature range, the response is qualitatively dependent on the charging field. In the results presented here, when positive, the discharge current is anomalous current, i.e. of the same sign as the charging current. A positive current peak is found with maximum at 70°C, and a negative one with maximum at about 110°C. Because the higher temperature peak is revealed even at low applied field, a dipolar origin cannot be discarded. With increasing voltage, the first peak (70°C) grows substantially, and counter-balances the higher temperature one.

Because of the overlapping currents, analysis of the TSDC peak is not straightforward. A way could be to consider that the red curve is characteristic of a single process and that qualitatively, the shape does not change with applied field. By removing a fraction of this peak (normally in proportion of voltage ratio) from the ones obtained at high voltage, then the anomalous discharge peak might be isolated.

A rough estimate of the energy for the TSDC peaks was obtained, just considering first order kinetics and single trap level for each of them. From ( 5), [START_REF] Ma | Investigation of surface and bulk charge traps of polyimide film by using the photo-stimulated discharge method[END_REF]

The relation between Tm and Ea is very close to linearity, being for δ=5°C/min Ea (eV)=-0.039+0.00308×Tm (K) with a correlation coefficient better than 0.999 in the Tm range 100-450 K. According to [START_REF] Molinié | A review of mechanisms and models accounting for surface potential decay[END_REF], the activation energy for the peaks at 70 and 110°C are 1.02 and 1.14 eV. It would reflect the energy of relatively deep traps in BOPP, but much less than those obtained by PSD.

V. DISCUSSION

A large difference in trap energies for polyethylene, obtained from thermal (0.8 eV) vs. optical excitation (4.0 eV) excitation, was reported recently by He et al [START_REF] He | Study on the detrapping of charge carriers in polyethylene films[END_REF] although the same distribution of traps is apparently active in the discharge process. The interpretation of the differences was based on "thermal erosion" of traps in the case of thermal (TSC) method. Hence, it was concluded that PSD could provide more representative information on the intrinsic properties of traps in the polymer. The term "erosion" is somewhat vague; it probably corresponds to the 'wet dog effect', i.e. the disappearance of traps by polymer chains motion. Partial heating, like photo-bleaching are methods used to neutralize charges trapped in shallow levels. Suzuoki et al [START_REF] Suzuoki | Investigation of carrier traps in polyethylene by PSDC and TSC[END_REF] investigated the differences between thermal and optical excitation by making PSD measurements combined with partial heating technique. Again, the energy obtained by thermal excitation appeared lower than by optical excitation. The differences in activation energy obtained by PSD and initial rise method in TSDC were interpreted by direct traps modification induced by molecular motions. Such molecular motions are induced by temperature rise while a frozen configuration is probed by optical methods.

The analysis of TSDC peak poses the problem of solving the case of distributed processes. Different results showed that in presence of a distribution of trap depths, an underestimate of the activation energy is obtained [START_REF] Teyssedre | Charge trap spectroscopy in polymer dielectrics: A critical review[END_REF]. However, in general, energies found in TSDC tend to match those found in isothermal decay. Besides, trap depths obtained for various defects using molecular modelling are of the order of 1 eV and seem more consistent with results obtained by thermal stimulation than by optical.

For these reasons, the mechanism of optically stimulated discharge should be reconsidered in order to reconcile the different aspects of charge excitation (and de-excitation). Given the peak wavelength in PSD (at 3.1eV), it can be thought that the energy provided to extract the charge from the trap is in part released through light emission when the charges recombine (or get retrapped). This would give consistency between RIL (emission peak at 2.5eV) and PSD data in terms of energy. However, this would not explain the apparent mismatch in trap depth between thermal and optical excitation.

A way to explore is the one with optical excitation producing charge detrapping indirectly. Indeed, instead of devising a mechanism with direct transfer of the optical energy to the potential energy of the charge, an excited state of the charged centre could be involved. In this scheme, light beam would excite the charged centre, which upon release to the ground state would produce thermal vibration and possibly light emission. Thermal vibration could produce charge detrapping followed by recombination (giving luminescence in RIL) or current (PSD).

In this scheme, light could be produced at two steps: during relaxation of the excited charged centre and upon charge recombination, without necessarily the same energy.

The energy peaks obtained in PSD would then be characteristic of the excitation of the charged state, and would therefore constitute a fingerprint of the trapping center without representing the trap depth. Still the method could be selective. The UV-vis absorption spectrum of BOPP reveal a peak in absorption at 200 nm and a shoulder at 230 nm. This region of the spectrum is associated to π→π* transitions of C=C bonds. A second shoulder at 280 nm is associated to the n →π* transition in carbonyl compounds. The photoluminescence of polyolefins [START_REF] Boudou | Photo-stimulated discharge current measurements on biaxially oriented polypropylene thin films (BOPP)[END_REF] has maxima in the excitation spectrum in these two regions, with distinct emission bands. However, 280 nm is not present in the PSD of BOPP.

VI. CONCLUSION

Various methods for trap distribution characterisation in polymer dielectrics have been briefly reviewed. The differences in trap depth estimated from optical and thermal methods are highlighted. Luminescence techniques bring complementary information compared to other methods through the emission spectrum of chemical groups interacting with charges. RIL exploits a response based on detrapping/retrapping/recombination of charges on active centres. In some way this goes against the schemes of analysing discharge decay in TSDC that neglects retrapping and suppose direct disappearance of the charges.

Three methods have been implemented for characterization traps in BOPP and obtained differences in results tentatively explained. The RIL spectrum of BOPP is consistent with that obtained previously on PP and seems reflecting charge recombination on polyenone sequences. PSD reveals two main peaks at 220 and 400 nm (respectively 5.6 eV and 3.1 eV) while the energies obtained from two peaks by TSDC are 1.02 and 1.14eV). The larger trap depth obtained by PSD could be due to an indirect process of charge detrapping under light excitation involving an excited level of the trapping centre.

Fig. 1 .

 1 Fig. 1. Sketch of mechanisms involved in (deep) trap spectroscopy techniques on dielectric materials: (1) detrapping by thermal excitation; (2) detrapping by optical excitation; (3) recombination of charges; (4, 5) charge recombination not involving passage through the extended states, being resonant tunneling from an excited state of the recombining center.

Fig. 2 .

 2 Fig. 2. Image of the surface of BOPP film showing crater-like structure for favoring impregnation

Fig. 4 .

 4 Fig. 4. Principle of PSD tests

Fig. 5 .

 5 Fig. 5. Results from PIL obtained on BOPP.

Fig. 6 .

 6 Fig. 6. PSD spectra obtained for different pre-charging voltages.

Fig. 7 .

 7 Fig. 7. TSDC spectra obtained for different pre-charging voltages. -40 0 40 80 120

  , the relation between escape time and peak temperature is as follows:

	𝜏 0 . 𝑒𝑥𝑝	𝐸 𝑎 𝑘 𝑏 . 𝑇 𝑚	=	𝑘 𝑏 . 𝑇 𝑚 ² 𝛿. 𝐸 𝑎	(8)
	Taking τo as the reciprocal of the fundamental frequency
	kbT/h, where h is the Planck's constant, a transcendental
	relation between activation energy and peak temperature is
	obtained:
	𝑇 𝑚	2 =	𝛿. ℎ. 𝐸 𝑎 𝑘 𝑏 2 . 𝑇 𝑚	. 𝑒𝑥𝑝	𝐸 𝑎 𝑘 𝑏 . 𝑇 𝑚

ACKNOWLEDGMENT

We are thankful to Prof Len Dissado for his advises. G. Teyssedre is grateful to Tongji University for the position of invited researcher awarded during this project.


T T N Vu

G Teyssedre

S Le Roy

C Laurent

Space Charge Criteria in the Assessment of Insulation Materials for HVDC

Keywords: HVDC insulation, space charge, materials assessment, LDPE, XLPE

The purpose of this work is to present and to discuss a methodology for the assessment of materials intended to be used as insulation in HVDC cables, particularly as regards the evaluation of the effects of material formulation on space charge accumulation within the insulation. Sample design, testing method and protocol and criteria used for the material evaluation are specifically considered. The criteria being put forward are based on available models of insulation life vs. stress with consideration of polarity reversal effects. It is shown through several examples using low density polyethylene and crosslinked polyethylene materials that criteria such as the Field Enhancement Factor and the space-averaged residual charge density are indeed sensitive to material formulation and especially to the presence of crosslinking by-products. When using a crosslinking process that does not produce residues, the material tends to behave like low density polyethylene regarding space charge features. Finally, the question of the representativeness of tests performed on flat specimens vs. model or full cables is discussed.

INTRODUCTION

THE number of HVDC links installed and in projects is experiencing an unprecedented growth due to the superiority of DC over the traditional HVAC energy transport with latest developments in converter technologies [START_REF] Mazzanti | Extruded Cables for High-voltage Direct-Current Rransmission[END_REF][START_REF] Chen | Review of high voltage direct current cables[END_REF]. Further, the development of cable manufacturing with synthetic insulations is encouraged, as it provides advantages in terms of cost, operating temperature, the risk of pollution or maintenance in comparison to impregnated paper-based insulation [START_REF] Hanley | A general review of polymeric insulation for use in HVDC cables[END_REF]. These evolutions of HVDC energy networks have impacts on insulating materials: design rules as well as material quality assessment criteria are not necessarily anymore the same as with HVAC systems [START_REF] Ghorbani | HVDC cable systems-highlighting extruded technology[END_REF][START_REF] Jeroense | Technical challenges linked to HVDC cable development[END_REF]. Material conductivity, the nonlinear response in field and space charge effects are among key features for HVDC with challenges for full control and modelling. Indeed, the switch from a capacitive-shaped to a resistive-shaped field distribution on going from AC to DC faces the much stronger dependence of conductivity than permittivity on temperature, field, and even material nature. Impact on design can be viewed at least in three practical situations: in HVDC cables under temperature gradient, in piece parts with materials of different nature, and in designs imposing a large geometrical field enhancement.

In cables under thermal gradient, the consequence is a reduction of the field at the inner semiconductor (semicon) of the cable and a strengthening of the field to the outer one [START_REF] Fabiani | HVDC cable design and space charge accumulation. Part 3: Effect of temperature gradient[END_REF].

So, this could be viewed as a trend to field homogenization in the bulk. However, depending on the actual field and temperature dependencies of the conductivity, a stress inversion phenomenon can be obtained, i.e. field being maximum at outer semicon [START_REF] Boggs | Effect of insulation properties on the field grading of solid dielectric DC cable[END_REF], with consequences on accessories reliability. Therefore, from the standpoint of field homogenization, the targeted properties for materials would be a relatively low activation energy for conductivity (i.e. weak dependence of conductivity on temperature) and effective nonlinear conductivity with field [START_REF] Boggs | Effect of insulation properties on the field grading of solid dielectric DC cable[END_REF].

In association of dielectrics, the stress can move from one material to the other, with changing field or temperature and experimental measurements on field distribution on flat specimen are consistent with field distribution expected from conductivity data [START_REF] Vu | Correlating conductivity and space charge measurements in multidielectrics under various electrical and thermal stresses[END_REF]. The association of insulating materials of different nature, as in joints and cable terminations [START_REF] Morshuis | Dielectric interfaces in DC constructions: space charge and polarization phenomena[END_REF], coupled to these non-linear effects and to thermal gradients, may make the prediction of field distributions in service conditions substantially more difficult. Out of the cable applications, the association of solid and gaseous insulations as with spacers in gas-insulated systems constitutes another situation where it is impossible to anticipate which of the three field distribution states: capacitive, resistive or transient, will be most critical [START_REF] Vu-Cong | Time constant evaluation of transient AC -DC field distribution[END_REF].

Finally, in HVDC cables with thick insulations, thermal runaway in the insulation could eventually occur at high temperature: the resistivity of the material must be sufficiently high to avoid these effects [START_REF] Olsson | Modelling of thermal behaviour of polymer insulation at high electric dc field[END_REF][START_REF] Hjertberg | Materials for HVDC cables[END_REF].

All the features addressed above can in principle be handled at the design step if the materials properties are known at any field/temperature. Here much could be said about the appropriate determination method of conductivity, as most often it is extremely hypothetical to obtain a steady state DC current and the measurement can be sensitive to the electrodes being used and do not necessarily represent intrinsic properties of materials [START_REF] Jeroense | Technical challenges linked to HVDC cable development[END_REF][START_REF] Nilsson | The role and measurement of dc conductivity for HVDC cable insulation materials[END_REF].

The other main properties to be assessed for application of insulating materials to HVDC is that concerning space charge features, which are suspected to lead to the reduction of the cable performance and/or lifetime. A direct effect of the space charge is the distortion of the electric field distribution in the insulation, therefore hampering the modelling of field distribution that can be done based on conductivity data. This concerns the generation and storage of charges into the insulation, in principle by process other than conductivity gradient: the conductivity gradient found in cables under thermal gradient on its own generates a space charge [START_REF] Aladenize | On the intrinsic space charge in a DC power cable[END_REF] and early field distortions found in HVDC cables have been interpreted by McAllister et al. [START_REF] Mcallister | Charge accumulation in DC cables: A macroscopic approach[END_REF] as a consequence of nonuniform conductivity. A second harmful consequence of space charges is the possibility to trigger ageing phenomena into the insulation though potential or kinetic energy associated with the release of these charges.

The propensity of insulations made for HVAC cables, especially crosslinked polyethylene, to generate space charges has led to the development of new generation of materials providing fewer charges, with emphasis on the improved physical and chemical cleanliness of materials [START_REF] Hjertberg | Materials for HVDC cables[END_REF].

Whatever their origin, depending on their position in the bulk of the insulation, on their nature (polarity, homo-vs. hetero-charges, etc.), the consequences of the presence of charges may not be the same. Besides, the space charge distribution patterns can be substantially different from one material to the other and therefore, there is a need for reducing the amount of data available into relevant quantities for materials assessment. Space charges measurement in dielectrics has become rather common practice for investigating charge accumulation processes under electrical stress. A wealth of measurement system exists with their respective merit in terms of sensitivity, sample geometry, measurement dynamics, etc. They represent interesting tools in the perspective of optimizing semicon / insulation materials formulation intended to HVDC cables provided adequate criteria are identified. The aim of the present work is to present a methodology for cable materials screening, including:

 Manufacturing of plaque samples;  Field and temperature testing conditions;  Measurement technique;  Criteria for materials assessment. In a first section of this contribution, we present the approach we have developed for space charge criteria [START_REF] Vissouvanadin | A methodology for the assessment of HVDC-XLPE cable insulation[END_REF], based on models for materials endurance under DC stress. The analysis provides figures for the relative merit of materials for the purpose of materials screening. In a second section, we show how the so-developed analysis can be implemented on polyethylene materials of different nature.

ASSESSMENT METHODOLOGY

LIFE MODELS VS. SPACE CHARGE

2.1.1

WITHOUT POLARITY INVERSION When a cable is intended to work with Voltage Source Converters -VSC system, the inversion of power flux is achieved by changing the current direction without inverting the voltage polarity. In that case, the insulation life is generally estimated through the well-known Inverse Power Law -a semi-empirical relationship giving the time to breakdown as a function of the maximum stress level through the insulation:

N F C L          max 1 . ( 1
)
where Fmax accounts for the maximum electrical stress through the insulating material, N is the aging parameter also known as the Voltage Endurance Coefficient (VEC) and C is a constant.

Space charge accumulation under DC stress leads to local field enhancement within the insulating material hence decreasing the time to breakdown. Furthermore, it has been pointed out that space charge is likely to take part in the ageing process through the modification of the material structure [START_REF] Dissado | The role of trapped space charges in the electrical aging of insulating materials[END_REF] and may act to increase the VEC. Considering a value of VEC of 10, in accordance with the Cigré recommendations for HV extruded cables [START_REF]Recommendations for testing DC extruded Cable systems for power transmission at rated voltage up to 250 kV[END_REF], a field enhancement of 10% of the Laplacian field leads to a life reduction by a factor about 3. For non-optimized insulation, the amount of space charge (and thus the field distortion factor) mostly increases with the applied voltage. In order to keep an acceptable cable life, the design stress has then to be limited reducing thereby the power transmission efficiency (power per unit of the cable weight).

WITH POLARITY INVERSION

Line Commutated Converters -LCC cable system requires voltage polarity reversals for changing the power flux. Hence cables have to be designed to withstand such kind of stress. In that case, it has been demonstrated [START_REF] Montanari | Evaluation of dc insulation performance based on space-charge measurements and accelerated life tests[END_REF] through accelerated life tests coupled to space charge measurements that the insulation life depends not only on the electrical stress level but also on different parameters related to the charge accumulation among which the quantity of charge (QM) obtained after a polarization procedure under an applied field Fapp, the charge depletion rate during depolarization (s) and the frequency of polarity inversion (f). According to the model proposed by Cavallini et al [START_REF] Cavallini | Life model based on space-charge quantities for HVDC polymeric cables subjected to voltage-polarity inversions[END_REF], the ratio between life with and without voltage inversion is given by:

2 1 ). ( . 1 1 a app a I f F Q s K L L    (2)
where K, a1 and a2 are correlation coefficients. According to the above relationship, it can be emphasized that the insulation life decreases with the frequency of inversion and the amount of trapped charge (QM). For polymeric materials, QM is generally assumed to evolve as a power function of the applied field Fapp [START_REF] Montanari | Evaluation of dc insulation performance based on space-charge measurements and accelerated life tests[END_REF][START_REF] Cavallini | Life model based on space-charge quantities for HVDC polymeric cables subjected to voltage-polarity inversions[END_REF] for electrical stresses above the ohmic regime, namely

b app M F Q  , with b
characterizing the charge accumulation rate versus the applied stress.

It is worth mentioning that, according to the model, the insulation life in the presence of inversions (LI) decreases inversely with the charge depletion rate. It means that in the presence of inversion, the material should be able to expel trapped charges as fast as possible during short-circuit. As a consequence, the presence of deep traps within the insulating material introduced by chemical additives may be harmful with regard to the material endurance.

ASSESSMENT BASED ON SHORT TERM TESTS

According to the model presented above, qualification of additives relevant to crosslinked materials (antioxidants, crosslinking agents, etc.) may be performed by deriving relevant parameters from space charge measurements. For a given case study (i.e. XLPE), it can be assumed that the correlation coefficients (K, a1 and a2) involved in the expression of the insulation life (LI) are not modified by changing the nature of additives and only the parameters related to space charges that are the field reinforcement factor, the trapped charges density and the depletion rate during voltoff are modified. These parameters may be derived using short term testing under proper conditions of electrical stress and temperature. Moreover, when several formulations are investigated, quality comparison could be done on the basis of space charge parameters assuming that the best formulation is the one which exhibits an optimized set of properties, say the lowest amount of space charge (implying in general weak field amplification) and a high rate of charge release during voltoff.

TEST CONDITIONS

SPACE CHARGE MEASUREMENT TECHNIQUE

For the current analysis, we have selected the pulsed electro-acoustic -PEAmethod for space charge measurement [START_REF] Maeno | Measurement of spatial charge distribution in thick dielectric using the pulsed electro-acoustic method[END_REF] first because of its simplicity of use and second because of its flexibility insofar as a wide range of material thicknesses can be measured, typically from 100 µm to several millimeters for XLPE materials. This can be achieved by adapting the device characteristics such as the pulse width or the piezoelectric sensor thickness. Another advantage of the PEA method is that measurements are easy to perform both in Volton and Volt-off because of the nature of the excitation (electrical pulse) and through the use of a decoupling capacitor. The PEA system also provides an excellent time resolution (typically 1 profile/s for plaque specimen) and therefore enables to detect fast time-varying phenomena such as the so-called fast charge packets [START_REF] Delpino | Fast charge packet dynamics in XLPE insulated cable models[END_REF].

The method can also be adapted to coaxial geometry which is advantageous for taking into account the thermal gradient existing in cables and to fit to the cylindrical geometry of real cables. However, signal processing is somewhat trickier due to the impact of thermal gradient and the need to account for the cylindrical geometry and the attenuation of the acoustic waves in the deconvolution of raw PEA signal [START_REF] Fu | Space charge measurement in polymer insulated power cables using flat ground electrode PEA system[END_REF][START_REF] Vissouvanadin | Deconvolution techniques for space charge recovery using pulsed electroacoustic method in coaxial geometry[END_REF].

SAMPLES PROCESSING

Rough products were LDPE -low density polyethyleneand semiconducting materials-SC, in the form of granules, both being cross-linkable, i.e. containing peroxide. Plaques of LDPE and SC materials were processed by press-molding at 120 °C. Then, disks of SC material, 12 mm in diameter, were cut. The final samples were obtained, with structure described in Figure 1, by cross-linking the 3 layers altogether at 180 °C for 15 min under a press. The upper semiconducting electrode (in contact with the PEA electrode to which voltage is applied) is chosen thicker (typically 600 µm) than the lower one (in contact with the PEA electrode connected to the acoustic sensor) to attenuate possible reflection of the acoustic waves that may occur at the interfaces between the sample and the metallic electrodes of the PEA cell due to acoustic impedance mismatch between these materials. The lower semiconducting electrode is chosen as thin as possible (typically 200 µm) to keep a reasonable spatial resolution. The insulation layer was limited to 500 μm for the purpose of reaching high level of electrical stress (up to 40 kV/mm) taking into account the maximum voltage than can stand the PEA test cell (30 kV). This is also advantageous because it reduces attenuation and dispersion of the acoustic waves.

The picture of Figure 2 shows an example of cross-section of such samples (showing distinctly the three different layers). Typical sample geometry is 200 µm / 500 µm /600 µm for SC/Insulation/SC structures. For evaluating the impact of insulating material formulation (base resin, antioxidants or different cross-linking agents), gold electrodes were used instead of semicon. In that case, electrodes are deposited onto the insulating samples by sputtering of a gold target. Deposited gold layers have to be thick enough (typically thicker than 30 nm) to avoid possible influence of the electrodes of the PEA cell.

OUTGASSING ISSUES

Cross-linking by-products are known to promote space charge formation under DC field. Predominantly heterocharge build-up, i.e. charge of polarity opposite to that of the adjacent electrode was reported [START_REF] Lau | Simultaneous space charge and conduction current measurements in solid dielectrics under high dc electric field[END_REF][START_REF] Fu | Influence of thermal treatment and residues on space charge accumulation in XLPE for DC power cable application[END_REF][START_REF] Fu | Space charge formation and its modified electric field under applied voltage reversal and temperature gradient in XLPE cable[END_REF]. This phenomenon is generally attributed to charge mobility enhancement due to the presence of by-products (mainly cumyl alcohol, acetophenone and alpha-methyl styrene when using dicumyl peroxide as a cross-linking agent) and the blocking nature of electrodes. Heterocharges enhance electric stress in the vicinity of the electrodes leading to a premature failure of the specimen according to the Inverse Power Law. The amount of heterocharges can be reduced by degassing the sample [START_REF] Vissouvanadin | Impact of concentration gradient of polarizable species on the electric field distribution in polymeric insulating material for HVDC cable[END_REF]. Actually, fully degassing a real cable may require long time and considerable energy, becoming economically unsustainable. For this reason, cables are partially degassed for the purpose of eliminating low boiling point species such as methane and ethane.

To be as close as possible to the real condition in cables, by-products concentration in plaque samples should be adjusted to the one contained in real cable. However, in general, plaque samples exhibit a very high rate of degassing due to their shape and thickness making it difficult to control the amount of by-products. For that reason, all samples were degassed, at 50 °C for 2 days to constitute a baseline for comparison of material formulation.

TEST PROTOCOL

For plaque specimens, the typical test procedure is depicted in Figure 3, consisting in polarization/depolarization at -10, -20, -30 kV/mm, each step lasting 3 h, up to -40 kV/mm step followed by polarity inversion to +40 kV/mm lasting for 3h, and finally depolarization measurement for 3 h. Applied field ramps-up and ramps-down were 1 kV/mm/s. Cycles of 3 h/3 h polarization/depolarization were chosen as a compromise between a quasi-steady state behavior and reasonable measurement time.

Ideally, plaque sample should be stressed with temperature gradient as in cable. This requires setting two different temperatures at each face of the plaque. This kind of set-up has already been developed [START_REF] Chen | Space charge measurement in LDPE films under temperature gradient and DC stress[END_REF][START_REF] Lv | Mechanism of space charge formation in cross linked polyethylene (XLPE) under temperature gradient[END_REF]. Given the thickness of sample and the PEA cell configuration, such heating system is however difficult to set-up with accurate thermal control. Hence measurements were carried out in isothermal conditions in the range of 25 to 50 °C as the maximum allowable temperature is limited to 70 °C by the electronic part of the measuring system.

Space charge profiles were acquired all along the cycle at a frequency of 1 profile/s. Spatio-temporal evolution of space charge can be pictured by means of a cartography using a color code for representing the net charge density. This representation enables to identify the global behavior of the material regarding space charge accumulation under different levels of field. From the observation of the cartography, one can also make a first idea about charge depletion rate during Volt-off. Furthermore, such representation is suitable to identify particular phenomena such as charge injection or heterocharges build-up. Hence, cartography of space charge can be used as a starting point for comparison between different formulations.

An example of charge pattern for gold-metalized commercial HVAC-XLPE is given in Figure 4. The measurement is done at 40 °C using the protocol of Figure 3. The time is given on X-axis (each step lasts 3 h); the thickness is along the vertical axis (anode is to the top, cathode to the bottom before polarity reversal) and the color scale represents charge density, negative and positive polarity being represented by cool (blue) and warm (yellow) colors, respectively.

For -10 kV/mm, charges are injected at both anode and cathode forming homocharges adjacent to the electrodes. A large fraction of these charges still remains after 3 h in Voltoff, suggesting the presence of deep traps within the bulk of the material.

For higher stress level (from -20 to -40 kV/mm), the bulk of the insulation is mainly dominated by negative charges that appear injected from the cathode and transported into the bulk. Negative charges enhance the field at the anode triggering an injection of positive charges as it can be seen at the beginning of the Volt-on step at -40 kV/mm. This phenomenon is even more spectacular after polarity reversal where positive charges are injected from the anode.

One has to realize here that the PEA technique as well as the other methods for space charge measurements is only sensitive to the net space charge density. A domain appearing as negatively (respectively positively) charged is a domain where the negative (positive) carriers dominate over the positive ones. One therefore has to think in terms of majority vs. minority carriers. The Field Enhancement Factor (FEF) is defined as the ratio between the internal field and the Laplacian field. The FEF is rigorously equal to 1 along the sample thickness if no space charge is present. If charges accumulate in the dielectric, the FEF takes necessarily a value higher than the unity somewhere within the dielectric (and, conversely, a value lower than the unity somewhere else). Hence, it seems relevant to consider the evolution in time of the position where the FEF is at maximum. Also its position during a polarization step could bring interesting information. As an example, a maximum FEF in the vicinity of an electrode could be attributed to a possible presence of charges of opposite polarity to that electrode. Similarly, a maximum FEF located in the bulk is mostly due to homocharges.

CRITERIA DEFINITION

FIELD ENHANCEMENT FACTOR

Figure 5 portrays the evolution vs. time of the FEFmax for different electrical stresses in the case of the HVAC-XLPE sample (left column). The evolution of its position is represented on the right column. The evolution of the position of the FEF is interesting to follow, as it can be considered that interfaces constitute weak points of the system: if heterocharges are present, the FEF will be positioned close to the interfaces and this can be considered as a negative feature. For -10 kV/mm, the highest value of the field is located in the bulk (closer to the anode) as a consequence of homocharges. For higher stress (-20 and -30 kV/mm), a FEFmax of about 1.2 is reached after 3 h of polarization and is located next to the anode due to negative charges in the bulk. The injection of positive charges occurring at -40 kV/mm leads to a displacement of the maximum stress from the anode to the bulk of the insulation.

DYNAMIC OF SPACE CHARGE RELAXATION

The total amount of trapped charges cannot be fully quantified by the FEF value. Consider, for example, successive layers of negative and positive charges. In this case the FEF can take a small value throughout the bulk of insulation whereas the amount of charge could be relatively high and may accelerate the material aging through the storage of electromechanical energy [START_REF] Dissado | The role of trapped space charges in the electrical aging of insulating materials[END_REF]. A more relevant way to quantify the amount of trapped charges is to compute the space averaged charge density (x) along the sample depth:

  d M dx t x d t Q 0 ) , ( 1 ) (  ( 3
)
where d is the inter-electrodes distance. The value estimated immediately after grounding (in volt-off) could be considered as the amount of accumulated charges during the volt-on procedure.

Figure 6 shows the different curves of QM(t) obtained during depolarization in the case of the HVAC-XLPE sample. One can notice that before polarity reversal, the amount of charges (at the beginning of depolarization) increases with the applied field. However, the value of QM (t = 0, +40 kV/mm) after polarity reversal falls below the one obtained after -30 kV/mm. This is due to the complex reorganization of space charges controlled by the voltage inversion, e.g. recombination between the bulk negative majority carriers and the injected positive charges following the polarity reversal (see Figure 4).

The temporal evolution of QM(t) is directly related to charge detrapping. Using a proper detrapping model [START_REF] Dissado | Space charge injection and extraction in high divergent fields[END_REF], relevant parameters related to the traps (density, apparent depth in energy) can be extracted from such curves.

For analyzing the charge decay, we consider the ensemble of charges irrespective of their nature. Charge detrapping is supposed to occur through thermal activation from traps to the conduction band and valence band, respectively for electrons the Fermi level, it is possible as initially proposed by Dissado et al [START_REF] Dissado | Space charge injection and extraction in high divergent fields[END_REF][START_REF] Dissado | The decay of space charge in a glassy epoxy resin following voltage removal[END_REF] to relate the residual charge in depolarization to the minimum and maximum trap depths and to the trap density:

  ) . ( ) . ( . . . ) ( max 1 min 1 0 t E t E T k e N t Q B M     (4)
where e is the elementary charge. Quantities min and max are linked to the emission frequency from traps (T) and to trap depths:

                      T k T T T k T T B B . exp ). ( ) ( . exp ). ( ) ( max max min min     (5)
E1 is the integral exponential function defined as:

    x du u u x E ) exp( ) ( 1 (6)
Fitting the experimental curves of QM(t) through equation 4provides quantities N0, min and max. An example of fit of decay curve so obtained is plotted in Figure 8. In general, acceptable fits are obtained through this procedure, whatever the material, charging conditions and temperature. It can be expected that the charge decay rate depends on the charge density since the field induced by space charge aids the transport. However, with the hypotheses taken herein, the rate limiting step in sample discharge is considered as being detrapping of charges and not their drift to the electrodes. Combining equations 4 through 6 gives:

  min max 0 0 . . ) 0 (       N e Q t Q M M (7)
The charge resorption rate, expressed in % per decade in time depends on the trap depth range:

) 10 ln( ) log( ) ( . 1 min max 0       T k t d t Q d Q s B M M (8)
Among the above quantities, the effect of the charge relaxation rate is worth discussing. A slow relaxation of charges implies that at polarity reversal the residual field will add to the applied field. If homocharges were present before field inversion, it means that field reinforcement on the interfaces, which are considered as weak points, will be present at polarity reversion. Improvement of XLPE withstanding to polarity inversion stresses was observed with incorporation of tree-retardant additives [START_REF] Abou-Dakka | Space charge evolution in XLPE with long-term aging under DC voltage -the effect of temperature and polarity reversals[END_REF]. The effect was explained by the dissipation of injected charges away from the injecting electrode and hence to the mitigation of field intensification effect at polarity inversion. Lifetime measurements carried out by Cavallini et al. on different materials [START_REF] Cavallini | Life model based on space-charge quantities for HVDC polymeric cables subjected to voltage-polarity inversions[END_REF] point along that direction, with an inverse correlation of charge release rate with life.

On another respect, it can be argued that fast space charge relaxation can trigger the release of energetic carriers and

Time (h)

produce some ageing effects to the insulation. Resorting to long term degradation and life models, generally static processes involving electrostatic or electromechanical energy are considered [START_REF] Dissado | The incorporation of space charge degradation in the life model for electrical insulating materials[END_REF][START_REF] Mazzanti | Electrical aging and life models: the role of space charge[END_REF]; however, under fast varying voltages, carriers accelerated in defective/lower density region of the material may trigger defects growth and contribute to life reduction [START_REF] Montanari | Bringing an insulation to failure: the role of space charge[END_REF][START_REF] Laurent | Charge dynamics and its energetic features in polymeric materials[END_REF]. Therefore, the interpretation of the criterion has to be appreciated depending on whether polarity inversion has to be applied and on expected switching rates of the system.

Combining equations ( 2), ( 7) and ( 8) one gets the following relation between quantities extracted from space charge measurements and lifetime with polarity inversion, for a given applied stress:

                      2 1 . . . 1 1 1 min max 0 max a B a B O N I f T k T k N a FEF L ( 9
)
where N0, a0, a1 and a2 are positive quantities. This expression highlights the detrimental effect of field distortion, charge quantity and apparent trap depth on expected lifetime. In practice, considering data obtained on various materials, variations in the decay rate are mainly due to variations in the maximum trap depth. To sum up, the spatio-temporal charge distribution obtained on flat specimen under charging and discharging steps with various voltages are analyzed considering as main output parameters:

 the FEF obtained in volts-on for typical polarization time of 3 h: a single parameter extracted can be the maximum of FEF obtained during the step;

 the initial quantity of charges when switching off the voltage;

 the maximum in trap depth, that represents the capability of the material to permanently store the charges. Eventually the position in the insulation where the FEF is at maximum and the minimum trap depth are worth considering. In the following we show examples of the application of such criteria for a comparison of the performance of different materials that are candidate for insulation in HVDC.

APPLICATION TO MATERIALS SCREENING

The screening procedure is illustrated below through a comparison of different materials involved in DC insulation development. In a first step, we compare space charge features on the LDPE resin serving as basis for DC-XLPE to the same material soaked into acetophenone, reaching a concentration of 1 wt.%, which is the order of magnitude of the concentration found in peroxide-crosslinked materials. In a second step, we compare the features obtained on AC-XLPE (XLPE-1) previously described to those obtained on peroxidecrosslinked XLPE (XLPE-2) providing similar features to a commercial grade HVDC product and that obtained with a crosslinking process based on the use of co-agents of crosslinking with allylic functions (XLPE-3) [START_REF] Gard | Development of a XLPE insulating with low peroxide by-products[END_REF]. The process requires a much lesser amount of peroxide and is virtually without by-products. No thermal treatment was achieved in the latter case before measurements.

LOW DENSITY POLYETHYLENES

Figure 9 shows the space charge patterns obtained on LDPE and acetophenone-soaked LDPE, with initially 1% wt. concentration. Both samples were gold-coated and measurements were carried out at 40°C. A relatively small amount of charges is detected on LDPE with the current stressing conditions. These are essentially negative charges detected, still visible after polarity reversal. The residual charge density at the beginning of the Volt-off step is given in Table 1. It increases only slightly with the applied stress.

Comparatively, the acetophenone soaked sample reveals a much larger amount of negative charges occupying the whole volume and tending to accumulate at the anode. At polarity reversal, a front of positive charges is detected in the first minutes, and then negative charges dominate again. The buildup of this negative space charge may correspond to trapping of electronic carriers by the molecule or to field-induced ionization effects. A FEFmax as high as 1.5 has been found for this material whichever the stress, cf. Table 1. 4), the patterns in Figure 10 clearly reveal fewer charges and are somewhat less complex. In XLPE-1, the charge switches from homocharge to heterocharge, depending on stress conditions, as if there were competition between injection and dissociation. For XLPE-2 (Figure 10a), carriers appear mainly due to injection at the electrodes, with a nearly symmetrical density and position at low field and with positive charges dominating over negative ones at higher field. For XLPE-3 (Figure 10b), the charge tends to be negative before polarity reversal (as for LDPE-1). Positive charges appear next to the bottom electrode after inversion, presumably due to the field amplification resulting from to the previously stored negative charges. The residual charge densities after switching off the voltage are particularly low for XLPE-3, being of the order of 0.1 C/m³ for the first 3 levels of stress and of 0.3 C/m³ for the last one. Also, the FEF is low.

DISCUSSION

OUTPUTS FOR MATERIALS ASSESSMENT

Considering the parameter values of FEFmax and QM0 extracted for LDPE samples, it appears obvious that acetophenone exhibits a considerable role on the space charge response, especially with promoting the formation of negative heterocharges whatever the applied field, and with as consequence an increase in the local field by about 50% in respect to the applied field. The features appear consistent with earlier reports [START_REF] Maeno | Effects of crosslinking byproducts on space charge formation in crosslinked polyethylene[END_REF].

The AC-grade XLPE has really poor performances comparatively to the other two materials and the features support the efforts put along the years to develop crosslinked materials with improved properties in terms of space charge features [START_REF] Hjertberg | Materials for HVDC cables[END_REF][START_REF] Fabiani | Polymeric HVDC cable design and space charge accumulation. Part 1: insulation/semicon interface[END_REF][START_REF] Smedberg | Effect of molecular structure and topology on network formation in peroxide crosslinked polyethylene[END_REF]. Comparing features for XLPE-2 and 3, both the FEFmax and the residual charge QM0 appear lower for the latter before polarity inversion at 40 kV/mm. Quantities approach here those obtained for LDPE-1. After polarity inversion, XLPE-3 performs as well as XLPE-2. Only the charge dissipation rate, reflected by the value of max, is larger for XLPE-3, for all stress levels. The very fact that charge density is less might be one of the reasons for the slower charge release and hence larger apparent trap depth. Indeed, the residual field that controls charge transport is not taken into account in the detrapping kinetic model. Overall, XLPE-3, which was crosslinked without by-products, exhibits better performances. This is all the more remarkable that it was obtained without thermal conditioning of the material, which could also evacuate volatile residues like water.

The effects of by-products, among which acetophenone incorporated into LDPE or present as cross-linking residue within XLPE, are investigated for long for their detrimental properties to charge accumulation. Nevertheless, there is no general agreement on the details of the mechanisms at play. When acetophenone is incorporated into LDPE, space charge accumulation is observed, sometimes as heterocharge features, and electrical conductivity is increased. Three processes can be envisaged, being injection-assisted process for electronic carriers [START_REF] Li | Influence on spatial charge distribution of cross-linking agent residues in XLPE[END_REF], transport-assisted process for these charges [START_REF] Hussin | The Effect of acetophenone and alphamethylstyrene on the space charge properties of low density polyethylene[END_REF], and promotion of ionic transport either by direct ionization of acetophenone under the field or indirectly through ion solvation effects. As an example, Hozumi et al [START_REF] Hozumi | Carrier mobility in acetophenone-soaked polyethylene estimated by transient space charge[END_REF] have shown that saturation of acetophenone into LDPE favors the injection of negative charges. Charge packets can be formed by solvation of impurities into acetophenone [START_REF] Hozumi | Space charge behavior in XLPE cable insulation under 0.2-1.2 MV/cm dc fields[END_REF]. Finally according to Kobayashi et al [START_REF] Kobayashi | Effect of acetophenone on the space charge evolution in LDPE and LLDPE[END_REF], the conduction into acetophenone-containing LDPE is of ionic type.

In results presented above, acetophenone clearly promotes the formation of a negative space charge into LDPE. The same effects are observed at all fields in XLPE-1 and at moderate fields (10-20 kV/mm) in XLPE-2. For high fields (40 kV/mm), positive and negative charges coexist. The behavior of by-products into XLPE is more complex, owing to the presence of several species and on possible interactions with antioxidants. The new feature is that through a crosslinking process that does not lead to by-products, materials with much less pronounced space charge phenomena can be produced, which points on the very effects of byproducts when dealing with peroxide crosslinked materials.

At the present time such alternative crosslinking scheme has not been transferred to the industrial scale. Therefore, peroxide crosslinking is still used. Obviously, though the trend is to reduce the amount of peroxide, crosslinked cables have to be degassed, at least partially, in order to reduce heterocharges. However, the degassing process consumes considerable amounts of energy. For instance, 43 days at 60 °C are required to remove 50% of the initial concentration of acetophenone contained in the middle of the insulation for a 18 mm-thick XLPE insulated HV power cable [START_REF] Andrews | The role of degassing in XLPE power cable manufacture[END_REF]. Thus developing processes leading to less charge accumulation are highly desirable.

REPRESENTATIVENESS FOR DC CABLES

The extension of the above approaches to model cables and to full size cables would be of course desirable for guaranteeing the validity of the method, this, all the more that devices for measurement on full size cables become available [START_REF] Castellon | Electric field and space charge measurements in thick power cable insulation[END_REF][START_REF] Tzimas | Space charge evolution in XLPE HVDC cable with Thermal-Step-Method and Pulse-Electro-Acoustic[END_REF]. However, at the stage of materials screening and particularly for formulation purpose this would be very heavy to implement as optimization concerns not only the insulation (nature of base resin, crosslinking agent and antioxidant) but also the semicon (matrix, carbon black and processing agents). As the possibilities for changing composition are far larger for the later, the sampling matrix for the full study would require a large number of cables to be produced. At the stage of materials selection, flat specimens certainly constitute a lighter approach and also may provide the possibility of carrying out a deeper investigation.

Some comments are worth giving on the transposition of results from flat specimen to cable scale. The association of semicon and insulation can be checked applying the PEA technique on sandwich structures processed as described in section 2.2. An example of space charge pattern obtained in commercial materials crosslinked altogether is shown in Figure 11. The pattern reveals the formation of heterocharges (in relatively low amount) and a substantial positive charge injection upon polarity reversal. The geometry itself (cable vs. flat geometry) does not constitute an obstacle for screening since if materials are well characterized in plaque form, with the relevant field range, then it should be possible to anticipate their behavior in case of non-uniform field. The reciprocal is not true however. Indeed, features for cables response, including space charge response, are brought about by nonlinear conduction and thermal gradients, as addressed in the introduction. In many instances, it becomes extremely difficult to discriminate for example charge build up due to ion migration from that relevant to conductivity gradient. So for pure material approaches, homogeneous field is preferable.

Sample thickness (about 500 µm herein vs. several cm within full size cables) and conditioning probably constitute more debatable aspects. Concerning thickness, it is generally observed that charge release after DC stressing decreases when the material thickness increases. For example, Fu et al [START_REF] Fu | Space charge formation and its modified electric field under applied voltage reversal and temperature gradient in XLPE cable[END_REF] showed that, in MV cables with 4 mm thick insulation, the heterocharge build up under a given polarity subsists after stressing for more than 30 min under the reverse polarity. Also, we have observed that pre-stressed MV cables may retain their charge for months in Volt-off and ambient conditions. Such features are usually not observed in thin samples. This can be understood since charge redistribution implies transit over longer distances.

Outgassing is another key point in the space charge behavior. Clearly it is extremely difficult to test plaque samples or even miniature cable samples pretending to be in conditions representative of HV cables regarding by-products concentrations [START_REF] Nilsson | The role and measurement of dc conductivity for HVDC cable insulation materials[END_REF][START_REF] Vissouvanadin | Impact of concentration gradient of polarizable species on the electric field distribution in polymeric insulating material for HVDC cable[END_REF]. Expelling is a relatively fast process in plaque samples, and as DC testing necessarily requires long testing times, combined with thermal stress, initially freshly crosslinked samples necessarily evolve during the testing time. For these reasons, thermal annealing is most always achieved prior to testing. Even though thermal treatment was achieved, present results have confirmed, in line with earlier works, that crosslinking by-products are detrimental to materials performance regarding space charge criteria. Therefore, there is no more real challenge regarding the effect of crosslinking residues.

CONCLUSION

We have presented a methodology for assessing insulation as well as semicon materials for use in HVDC cables application from the standpoint of space charge characteristics. Materials figures of merit are defined in line with life models of insulations under DC stress, which encompass materials endurance under polarity reversal. Quantities of interest are maximum field distortion, residual charge density after DC stressing and parameters related to the kinetics of charge release. The use of such quantities, though resulting in a coarser picture of material response than space charge patterns may provide, has the advantage of permitting a direct material-to-material comparison, including comparison of materials association. Though the examples are given for flat specimen, in principle the procedure can be extended to cable geometry samples. Using this methodology, we confirm earlier reports on the detrimental effects of crosslinking byproducts regarding space charge features considering crosslinking of LDPE initiated by peroxide radicals.

Figure 1 .

 1 Figure 1. Typical geometry of plaque samples.

Figure 2 .

 2 Figure 2. Cross-section of a SC/XLPE/SC sandwich.

Figure 3 .

 3 Figure 3. Stress cycle applied for space charge measurements on flat specimens.

Figure 5 .

 5 Figure 5. Left column: Evolution of the FEFmax vs. time. Right column: evolution of the FEFmax position vs. time under various fields for the gold-metalized HVAC-XLPE sample. Before polarity inversion, x=0 is the cathode, x=d the anode.

Figure 4 .

 4 Figure 4. Space charge pattern for a gold-metalized HVAC-XLPE sample obtained using the protocol of Figure 3. The color bar represents charge density in C/m 3 .

Figure 8 .

 8 Figure 8. Example of fit of QM(t) to equation 4 for a XLPE sample prepolarized under 40 kV/mm at 40°C for 3h. Fit parameters are: N0=10 19 m -3 .eV -1 , min =0.93 eV and max=1.1 eV. The slope of the curve provides the charge decrease rate per decade of time.

Figure 7 .

 7 Figure 7. Model of charge detrapping by thermal activation without retrapping. Electrons only in this example.

Figure 6 .

 6 Figure 6. Time evolution of the space-averaged charge density obtained during 3 h in volts-off after 3h polarization steps under fields indicated in the caption.

  and holesas depicted in Figure7. Neglecting retrapping phenomena and hypothesizing a constant trap density N0 per unit energy within a range of trap depths [min -max ] close to

  (a) LDPE (b) LDPE + 1% wt. acetophenone

Figure 9 .

 9 Figure 9. Space charge pattern obtained on LDPE (a) and acetophenonesoaked LDPE (b) using the stress cycle shown in Fig. 3. The color bar provides charge density in C/m 3 .

3 Figure 10 .

 310 Figure 10. Space charge patterns obtained on peroxide-crosslinked material (a) and crosslinking process without by-products (b) with the same stress conditions and representation of data as in Figure 9.

3. 2

 2 CROSSLINKED POLYETHYLENES Space charge patterns for the crosslinked polyethylenes are shown in Figures 4 and 10. Compared to the AC-XLPE (Figure

Figure 11 .

 11 Figure 11. Space charge pattern obtained applying the stress cycle of Figure 3 on a sandwich structure SC/XLPE/SC crosslinked altogether.

Table 1 .

 1 Sum-up of space charge data for some of the tested insulations.

	F	app (kV/mm)	-10	-20	-30	-40	40
	LDPE-1	FEF max M0 (C/m³) 0.08 0.08 0.12 1.06 1.05 1.07 1.09 1.09 Q --0.13
			FEF max	1.50 1.53 1.53 1.53 1.47
	LDPE-2 (1%	Q M0 (C/m³) 0.25 0.63 0.97	--	1.45
	acetophenone)	 min (eV)	1.04 1.00 0.92	--	0.96
			 max (eV)	1.14 1.14 1.13	--	1.07
			FEF max	1.02 1.25 1.30 1.23 1.15
	XLPE-1 (AC-XLPE,	Q M0 (C/m³) 0.13 0.52 0.78	--	0.67
	peroxide, outgassed)	 min (eV)	1.02 0.98 0.97	--	0.95
			 max (eV)	1.13 1.10 1.11	--	1.11
			FEFmax	1.10 1.13 1.10 1.05 1.15
	XLPE-2 (peroxide,	Q M0 (C/m³) 0.26 0.45 0.75	--	0.35
	outgassed)	min (eV)	1.05 1.03 1.02	--	1.05
			max (eV)	1.14 1.19 1.17	--	1.13
			FEF max	1.07 1.05 1.05 1.06 1.02
	XLPE-3 (without	Q M0 (C/m³) 0.10 0.09 0.09	--	0.33
	by-products)	 min (eV)	1.01 1.02 1.04	--	1.03
			 max (eV)	1.16 1.21 1.22	--	1.17

ACKNOWLEDGMENTS

We are greatly indebted to Dr M. Mammeri, I. Denizet and J.C. Gard from Silec Cable for their support of this study.

Center" where he studied plasma-polymerized thin films. Back in Toulouse he developed an approach to electrical ageing in polymeric materials based on luminescence analysis. He is now dealing with experimental and modeling activity relating to charge transport and ageing. He is currently Research Director at CNRS and was until recently Director of the Laboratory of Plasma and Energy Conversion -LAPLACE-in Toulouse.