Thermoelectronic breakdown with pressure and space charge effects in polyethyleneN. Zebouchi, T. G. Hoang, and Bui Ai Citation: Journal of Applied Physics 81, 2363 (1997); doi: 10.1063/1.364241 View online: http://dx.doi.org/10.1063/1.364241 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/81/5?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Effect of temperature on trap depth formation in multi-layer insulation: Low density polyethylene and fluorinatedethylene propylene Appl. Phys. Lett. 104, 031605 (2014); 10.1063/1.4862061 Dielectric properties and effect of electrical aging on space charge accumulation in polyimide/ TiO 2nanocomposite films J. Appl. Phys. 108, 094113 (2010); 10.1063/1.3506715 Effect of metal-polymer interface on the breakdown electric field of poly(vinylidene fluoride-trifluoroethylene-chlorofluoroethylene) terpolymer Appl. Phys. Lett. 91, 062907 (2007); 10.1063/1.2768205 ac aging and space-charge characteristics in low-density polyethylene polymeric insulation J. Appl. Phys. 97, 083713 (2005); 10.1063/1.1868880 Combination of thermal and electromechanical breakdown mechanisms to analyze the dielectric breakdown inpolyethylene terephthalate J. Appl. Phys. 83, 6190 (1998); 10.1063/1.367495

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Thermoelectronic breakdown with pressure and space charge effectsin polyethylene

N. Zebouchi, T. G. Hoang, and Bui AiLaboratoire Genie Electrique, Universite´ Paul Sabatier, 118 Route de Narbonne 31062 Toulouse, France

~Received 4 June 1996; accepted for publication 19 November 1996!

The electrical breakdown of low density polyethylene films 100mm thick was investigatedexperimentally and theoretically under high hydrostatic pressure~1 to 500 bar! at temperatures of20, 70, and 90 °C. The theoretical analysis was based on combining the two basic mechanisms ofthermal and electronic breakdowns by introducing a new parameter, pressure. This model mainlytakes into account the transient current using the hopping transport phenomenon and local electricfield distortion due to the presence of space charges in the material. The results of simulation showgood agreement with experiments compared to our previous works on the modeling of electricalbreakdown in which the effect of space charges was neglected. ©1997 American Institute ofPhysics.@S0021-8979~97!00505-7#

I. INTRODUCTION

The behavior of the dielectric breakdown obtained withthe combined effects of temperature,T, and pressure,P, ondifferent kinds of polyethylene, such as polyethyleneterephthalate~PET!,1 high density polyethylene~HDPE!,2,3

cross linked polyethylene~XLPE!,4 and low density polyeth-ylene ~LDPE!,5 has been explained by means of classicalelectrical breakdown models: thermal breakdown,6 electro-mechanical breakdown,7 and electronic breakdown in amor-phous materials8 by considering mainly that the electric fieldthroughout the entire insulator was uniform, i.e., containedno space charge distributions.

Although our modeling9–12 has given successful agree-ment with experiments, space charge cannot be neglected,since it is known to distort the local electrical field in thedielectric and affect the high field conduction and breakdownphenomena. Several authors have shown its important role indielectric failure, both indirectly through dc prestressingeffects13–15 and directly by space charge measurements.16,17

The latter used recently developed nondestructive techniquessuch as the laser-induced pressure pulse~LIPP!,18,19 the pi-ezoelectrically induced-pressure step~PIPS!,20 the pulsedelectroacoustic~PEA!,21,22 and the thermal pulse~TP!methods.23,24 A striking example of the influence of spacecharges on electrical breakdown is given in our previouswork25 using the thermal step method.26 The application, forseveral hours, of a high electric field, gradually increasingfrom 50 to 130 kV/mm, to LDPE samples with semiconduct-ing electrodes at 50 and 60 °C led to the presence of a spacecharge distribution and the development of injected charges.

To take the combination of these effects into account inthe explanation of our experimental results obtained underhigh pressure, a theoretical model was proposed which con-sidered the injection and the kinetics of space charge devel-opment leading to breakdown, pressure being considered as anew parameter.

The objective of the present work is first to present theexperimental results of electrical breakdown in 100-mm-thick LDPE films cut from submarine dc power cables, overthe hydrostatic pressure range of 1–500 bar for temperatures

of 20, 70, and 90 °C, and, second, to give the theoreticalresults deduced from the numerical analysis of combinedthermal and electronic breakdown models considering thetransient phenomena of charge transport and taking into ac-count the distortion of the internal field in the material underpressure.

II. EXPERIMENTAL APPARATUS

Evaluating the breakdown voltage of polymers underhigh hydrostatic pressure is one of the main technologicalproblems in the domain of dielectric studies. The experimen-tal apparatus,27 consisted of a high-pressure bomb~9500cm3! in which was placed a measuring cell, a pressure gen-erator, and a breakdown detector system. The pressure in thebomb was obtained by a diaphragm compressor using gas-eous nitrogen as the transmitting fluid. A maximum dc volt-age of 100 kV could be applied successively to eightsamples, via high-voltage relays placed in the measuringcell. LDPE sample films 100mm thick were inserted into thestainless-steel electrode system with a Rogowsky profile.The desired temperature was obtained with a stability of 1 °Cby the use of heating resistors. When breakdown occurred ina sample, the detector system was triggered and the break-down voltage was immediately recorded and removed. Themost complex technological problem to be solved for thesemeasurements was the reliability of the electrical lead, whichhad to withstand the combined effects of different stresses:pressure~50–1000 bar!, temperature~20–100 °C!, and highvoltage, up to 100 kV.

III. EXPERIMENTAL RESULTS

The breakdown field,Fb , of the samples was measuredat pressures of 1, 50, 150, 300, and 500 bar and at tempera-tures of 20, 70, and 90 °C. The applied dc voltage was raisedat a constant ratea55 kV/s until breakdown occurred. Sinceelectrical breakdown is a statistical phenomenon, all the re-sults were studied using the cumulative Weibull distributionfunction28 defined as

2363J. Appl. Phys. 81 (5), 1 March 1997 0021-8979/97/81(5)/2363/7/$10.00 © 1997 American Institute of Physics [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

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P~F !512expF2S FFbD bG , ~1!

whereP(F) is the probability of failure.Fb.0 andb.0 arethe scale and shape parameters, respectively. The randomvariableF is the breakdown field. The scale parameterFb

indicates the breakdown field for whichP(Fb)5(12e21),at which 63.2% of the events have occurred.

An example is given in Fig. 1 showing the Weibull prob-ability plots of the breakdown data forT570 °C with differ-ent pressures. Straight lines represent the best fit of relation~1! through the experimental points.Fb values versus pres-sure and temperature are listed in Table I.

It can be seen thatFb increases with pressure for a giventemperature. For example, at 70 °C,Fb52.83 MV/cm at 1

bar and 4.57 MV/cm at 500 bar. The breakdown field varia-tion coefficient dFb/dP in this pressure range is about3.4831023 MV/cm bar.

It can be also seen from Table I and Fig. 2 thatFb

decreases with rising temperature at a given pressure. Forexample,Fb decreases from 4.68 MV/cm at 20 °C to 2.25MV/cm at 90 °C for P51 bar. The corresponding break-down field variation coefficient dFb/dT is about23.4731022 MV/cm °C.

These kinds of increase in dielectric strength with pres-sure and decrease with temperature were already found ex-perimentally in our previous works for PET1 and polyethyl-ene~PE! films.2–5 The principal qualitative explanations forthe negative temperature dependence of the dielectric break-down strength concerned the effects of mechanical stressfrom a consideration of the behavior of Young’s modulus,which falls with temperature, thermal breakdown, and elec-tronic breakdown in amorphous materials as presented byFrohlich.

The positive hydrostatic pressure dependence ofFb wasqualitatively interpreted as being due first to the electrome-chanical breakdown process since Young’s modulus in-creases with increasing hydrostatic pressure;29 second to thedecrease of the mean free pathl of electrons, caused bycompression involving an increase of the electric breakdownfield according to Von Hippel’s avalanche breakdownmodel,30 which depends inversely onl; and finally to an

FIG. 1. Weibull diagram obtained with LDPE samples, 100mm in thick-ness, in the pressure range of 1–500 bar for the temperature of 70 °C.

FIG. 2. Variations of experimental breakdown fieldFb exp of LDPE films vspressure for different temperatures and for 90% confidence limits withWeibull’s statistical method.

TABLE I. Breakdown fieldFb values obtained from experimental values for different pressures and tempera-tures using Weibull’s statistical method with 90% confidence bounds represented in parentheses.

P ~bar!

1 50 150 300 500

20 4.68~4.49–4.89!

5~4.85–5.17!

5.49~5.22–5.79!

6.01~5.54–6.55!

6.22~6.03–6.41!

T ~°C! 70 2.83~2.73–2.92!

3.15~3.00–3.30!

3.57~3.31–3.86!

3.98~3.57–4.45!

4.57~4.16–5.06!

90 2.25~2.11–2.41!

2.78~2.62–2.95!

3.18~2.99–3.39!

3.38~3.18–3.60!

3.66~3.54–3.80!

Fb exp ~MV/cm!

2364 J. Appl. Phys., Vol. 81, No. 5, 1 March 1997 Zebouchi, Hoang, and Ai [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

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increase in the material density with pressure. Hikita31 ob-served the same effect in a study of the dependence of thedielectric strength on polyethylene density at atmosphericpressure.

We attempted to base our theoretical explanation of theP andT dependence in our previous experimental results forPET9,10 and PE11,12 films on thermal breakdown, electrome-chanical breakdown, and a combination of these two. Weassumed a steady state for current conduction and a uniforminternal field.

The numerical analysis of these models was qualitativelyin good agreement with experiments. However, from thequantitative point of view, a difference remained betweenexperimental measurements and theoretical values. This wasattributed to the presence of space charge in the materialsstudied. So, to improve later results and for a better under-standing of the electrical breakdown field variations withpressure and temperature investigated experimentally in thepresent work on LDPE films, the following model is pro-posed.

IV. BREAKDOWN MODEL WITH COMBINEDPARAMETERS T AND P

A. Formulation and calculation

This model is a combination of two basic mechanisms:~i! Thermal breakdown, which is governed by the fol-

lowing fundamental heat balance equation6 into which weintroduce the parameterP:

CvS dTdt D2div~K gradT!5J~P,T,F !F, ~2!

whereCv is the specific heat per unit volume,K the thermalconductivity,J the current density, andF the electric field.This breakdown mechanism occurs when a local temperaturein the bulk reaches the melting temperatureTf .

By assuming that the width and breadth are much largerthan the thicknessd, the problem can be reduced to a one-dimensional problem. The fundamental equation of thermalbreakdown becomes

CvS dTdt D2d

dx SK dT

dxD5J~P,T,F !F, ~3!

where thex axis is in the direction of the sample thickness.~ii ! Electronic breakdown, which occurs when any one

of the mean local fields,Fm(xd), over a relevant distancexdwithin the bulk is defined as

Fm~xd!51

xdE0

xdF~x!dx, ~4!

reaches the electronic breakdown field,Fb elec, for which thedistance dependence in dielectric films32 is given by

Fb elec~xd!5Bxd2n~P,T!, ~5!

whereB is a constant. The parametern depends on experi-mental conditions ofP andT.

To determine the theoretical breakdown field using thecombination of these two models in our numerical analysisprocedure, it is necessary to evaluate the temperature and the

electric field in the dielectric for each time,t, and each po-sition, x. We then compare the temperature to the meltingpoint valueTf @Eq. ~2!# and the mean electric field for adistance corresponding to positionx with the electronicbreakdown fieldFb elec @Eq. ~5!#. If either of the two condi-tions is satisfied, material failure occurs.

The principal hypotheses used for this modeling are asfollows.

~1! Thermal conduction can be neglected here, ordiv~K gradT!50. So, Eq.~2! is reduced to

vS dTdt D5J~P,T,F !F. ~6!

~2! The transport phenomenon during the transient stateresults from electrode-injected carriers~Schottky process!and carriers generated in the bulk material by the hoppingmechanism~Fig. 3!. This model has been largely applied inthe study of space charge limited current, electronic conduc-tion in insulators, ionic transient currents, and so on.33–40

The interface current and the bulk current can then be repre-sented by the following relations:

Schottky model

J~P,T,F !5A T2 expFbF1/22Wc

kBTG ~7!

with b5[e3/4pe(P)] 1/2;Hopping model

J~P,T,F !5el~P!nN expFeFl~P!

2kBTGexpS 2W

kBTD , ~8!

whereA is a constant,Wc the potential barrier for injectedelectrons at the cathode,kB the Boltzmann’s constant,e thecharge of the electron,n the vibration constant of the carrier,N the number of charges transported per unit volume,W thebarrier height of the hopping process,e the dielectric permit-tivity, and l the hopping distance depending onP.

~3! The polarity of transported and injected carriers isnegative. This assumption is supported theoretically by thestudy of electrical conduction in LDPE.41,42 As we can ob-

FIG. 3. Transport phenomenon by hopping process after Iwamoto and Fu-kuma.Nk , Ek , Tk are the number of electrons per unit area, the electricfield, and the temperature at divisionk, respectively.Jk is the current den-sity across divisionk, l the hopping distance, andSl the division width withS the number of hopping distances in each division.

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serve from Fig. 3, after Fukuma,36 electrons are injectedfrom the cathode over the potential barrierWc by theSchottky process. Carriers are assumed to transit to only oneof two adjacent wells with one jump over the potential bar-rierW, and to be transported over a long range in successivejumps. At the anode, they are neutralized or extracted overthe potential barrierWa .

~4! Under initial conditions att50, no charges arepresent in the bulk of the dielectric and the internal field isuniform.

Based on the different charge transport processes givenin Fig. 3, the simulation procedure is to calculate the localtemperatureTk and fieldFk for each division and each time,from the current density due to injected carriers and bulkgenerated carriers. Then, the set of equations used in ourcalculation are as follows.

The local temperature for each division given by Eq.~6!can be written as

dTkdt

5U~Jk211Jk!Fk

2CvU. ~9!

Taking into account the possibility for the carrier tomove in the same or the opposite direction to the electricfield, the expression of current densityJk across thekthboundary division can be expressed according to the hoppingmodel ~Fig. 3! by

Jk~P,T,F !5el~P!nNk

sl~P!expH 2W

kBTkJ expH eFkl ~P!

2kBTkJ

2el~P!nNk11

sl~P!expH 2W

kBTk11J

3expH 2eFk11l ~P!

2kBTk11J , ~10!

whereTk , Nk , andFk are the temperature, the number ofcarriers per unit area, and the electric field at divisionk,respectively;l the hopping distance ands the number ofhopping distances in the division. The sample thicknessd isdivided intom divisions andk varies from 1~at the cathode!to m ~at the anode!.

The current density at the cathodeJc(x50) and the an-odeJa ~x5d, sample thickness! are, respectively,

Jc~P,T,F !5AT12 expH b~2F1!

1/22Wc

kBT1J

2el~P!nN1

sl~P!expH 2Wc

kBT1J

3expH 2eF1l ~P!

2kBT1J , ~11!

Ja~P,T,F !5el~P!nNm

sl~P!expH 2Wa

kBTmJ

3expH eFml ~P!

2kBTmJ . ~12!

The detailed steps for establishing these current densityequations are given mainly in the reported works of

Iwamoto.33–35 Iwamoto principally considers that the poten-tial and the carrier density are linear in the division.

To determine the time variation of the number of carriersper unit area at thekth division, the current continuity equa-tion in the bulk is applied

dNk

dt5~Jk212Jk!/e. ~13!

The electric field value in thekth division is given by thePoisson equation

Fk5e

me H (i51

k S i2 1

2DNi2(i5k

m Sm2 i11

2DNiJ 2V

d,

~14!

whereV is the applied voltage.Since a ramp voltagea is applied to the material, we

have

V~ t !5at. ~15!

According to Eq.~4!, the mean local electric field can beexpressed as

Fmk5F(i51

k

Fi G Y k ~16!

From Eq.~5!, the electronic breakdown field for a rel-evant distancexk in the material is

Fb eleck5B~xk!

2n~P,T!. ~17!

B. Results of simulation

The theoretical breakdown field values of the simulation,given together with the experimental values in Table II, wereobtained in the following conditions:

~i! Physical constants:A50.1 Am22 K22, n51011 Hz,W50.4 eV, Wa50.4 eV, Wc50.5 eV, B52.453108,d5100 mm, a55 kV/s, Cv51.743106 JK21 m23, andTf5383 K. The constantsCv and Tf were given by themanufacturer.B was reported from electrical breakdown

TABLE II. Experimental and theoretical values of electrical breakdownfield determined for different temperatures and pressures for the combinedelectronic and thermal breakdown models.

P ~bar! T ~°C! Fb exp ~MV/cm! Fb theo ~MV/cm!

1 20 4.68 4.9370 2.83 2.9890 2.25 2.37

50 20 5.00 5.2570 3.15 3.3290 2.78 2.93

150 20 5.49 5.7770 3.57 3.7590 3.18 3.31

300 20 6.01 6.3270 3.98 4.1890 3.38 3.46

500 20 6.22 6.5470 4.57 4.8090 3.66 3.74

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measurements on polypropylene~PP!.36,37The values of dif-ferent parametersW, Wc , Wa , n, andA were chosen fromthose used by other authors.40,43,44

~ii ! For the combination of the temperature and pressureeffects, we assume that the relative permittivitye and thejump distancel depend onP ~1–500 bar! and that theirvariations withT can be neglected in the range of tempera-tures studied~20–90 °C!.

In our previous studies on the modelling of conductionphenomena in polymers under combined pressure and tem-perature parameters45,41 and in other works,46–48 it has beenshown that the volume of the material is reduced by thehydrostatic pressure effect. Thus, if we consider the hoppingmodel as the principal transport process in the bulk, from thetheoretical calculation based on the previous hypotheses, thehopping distance 1 is reduced from 4 to 2.85 Å when thepressure is increased from 1 to 500 bar. The permittivitye (P) varies from 2.30 to 2.39 in this pressure range.

~iii ! For the electronic breakdown, the parametern in-creases with temperature and decreases with pressure byabout 3% from the initial value of 0.08 atT520 °C andP51 bar. This estimated value is reasonable since it hasbeen found experimentally in electrical breakdown of poly-propylene atT525 °C and atmospheric pressure thatn isequal to 0.11.36,37

C. Discussion

From the qualitative point of view, these experimentaland theoretical results have shown that the breakdown fieldshave negative temperature dependence (dFb/dT,0) andpositive pressure dependence (dFb/dP.0). These charac-teristics have often been obtained in our results and pub-lished in several articles resulting from experimental andtheoretical studies on electrical breakdown inpolymers.1–5,9–12 Furthermore, quantitatively, it seems thatthe theoretical results are greatly improved if the distortionof the electrical field in the material is taken into account~Fig. 4! as shown in this proposed model. For example, therelative variations of experimental and theoretical values arefor T590 °C

dFb exp/dP52.8231023 MV/cm bar,

dFb theo/dP52.7431023 MV/cm bar,

and forP5300 bar

dFb exp/dT523.7531022 MV/cm °C,

dFb theo/dT524.0831022 MV/cm °C.

The magnitude of the theoretical external current densityfound by numerical analysis for this temperature and pres-sure range is in agreement with the experimental data onexternal current density investigated in our previous works49

on LDPE samples under hydrostatic pressure up to 300 barfor temperatures of 25 and 70 °C for applied fields rangingfrom 0.4 to 2.0 MV/cm.

Furthermore, this modelling shows that the electricalbreakdown in LDPE is affected by the formation of negativespace charges near the cathode~Fig. 5!. These negative car-

riers could be due either to a decrease of the cathode field~Fig. 6!, which would reduce the mobility of electrons, or toa drift of some bulk electrons.

This homospace charge accumulation in front of thecathode was confirmed by our results obtained with the ther-mal step method in the study of the role of space charges inprecursor phenomena of the electrical breakdown in the samekind of material.25 In this study, we observed that, at 60 °Cand atmospheric pressure with an applied field of 130 kV/mm, a strong accumulation of electrons took place near thecathode just before the failure of the material. This led to anenhancement of the electric field close to the anode, creatingan internal field of about 30 kV/mm which was, in this case,added to the applied field. So the sample was really submit-ted to a resulting field of about 160 kV/mm.

On the other hand, from both experiments and numericalcalculation of electronic avalanche current breakdown inpoly-p-xylylene ~PPX! thin polymer film which included

FIG. 4. Variations of experimental breakdown fieldFb exp and theoreticalFb theo obtained from the combination of the thermal and the electronicbreakdown processes of LDPE films under pressure forT590 °C.

FIG. 5. Calculated charge density distribution up to electrical breakdown,for T570 °C and 1 bar, in LDPE film 100mm thick.

2367J. Appl. Phys., Vol. 81, No. 5, 1 March 1997 Zebouchi, Hoang, and Ai [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

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various factors controlling the transient conduction~chargeinjection from metal electrodes, field distortion, carrier trap-ping, carrier recombination etc.!, Takaiet al.50,51 observed asignificant accumulation of electrons and a continuous de-crease in the internal field in the cathode region after appli-cation of a voltage pulse, while the anode field increasedonly gradually until current instability or negative resistanceoccurred.

Although this model appears to successfully explain thebreakdown field variations withP andT, some experimentswill be needed in the future in order to confirm the validityof the theoretical results:

~i! evaluation of the space charge and its evolution withpressure using the pressure wave propagation~PWP!technique which we have set up recently in our labo-ratory and

~ii ! complementary measurements of electrical break-down under the combined effects of pressure and tem-perature for different thicknesses in order to deter-mine the electronic breakdown parameter variationsnvs P andT.

V. CONCLUSION

Electrical breakdown of low density polyethylene filmswas investigated experimentally at temperatures of 20, 70,and 90 °C under hydrostatic pressure ranging from 1 to 500bar. The theoretical simulation of experimental results de-pending on both pressure and temperature parameters is pro-posed on the basis of a breakdown model in which we intro-duce the electronic breakdown, which depends on thedielectric thickness, into the thermal breakdown process,which is due to the transient conduction current. This model,taking into account the effects of the distortion of the internalelectric field, caused by the formation of space charges in thematerial, seems to be applicable for the explanation of ourstudy on the electrical breakdown of LDPE samples underthe combined effects of pressure and temperature.

ACKNOWLEDGMENTS

We would like to thank the Fonds International pour laCooperation Universitaire FICU, the Ministe`re Franc¸ais desAffaires etrangeres ~DCSTE!, and the Ministe`re AlgerienDelegue aux Universite´s et a la Recherche Scientifique~CST! for their financial support, and to Dr. M. Fukuma forthe valuable discussions.

1N. Zebouchi, R. Essolbi, D. Malec, T. G. Hoang, B. Ai, and M. Bendaoud,J. Appl. Phys.76, 8218~1994!.

2M. Fark, T. G. Hoang, R. E. Hayani, B. Ai, B. Dalle, J. Perret, C. Simon,and J. Berdala, J. Phys. D22, 566 ~1989!.

3F. Benlizidia, M. Farkh, T. G. Hoang, B. Ai, B. Dalle, F. Duchateau, D.Roy, and J. Berdala, in Proceedings of the Third International Conferenceon Insulated Power Cables, Versailles, France, 1991~unpublished!, p.570.

4T. G. Hoang, R. Essolbi, D. Roy, F. Ballon, and M. Pays, in Proceedingsof the Third International Conference on Insulated Power Cables, Ver-sailles, France, 1991~unpublished!, p. 573.

5P. Guerin, T. G. Hoang, B. Ai, and P. Destruel, J. Appl. Phys.57, 10~1985!.

6K. Wagner, Trans. AIEE41, 288 ~1922!.7K. H. Stark and C. G. Garton, Nature~London! 176, 1225~1955!.8H. Frohlich, Proc. R. Soc. London, Ser. A188, 532 ~1947!.9N. Zebouchi, Magister thesis, University of Science and Technology, Al-giers, 1992.

10N. Zebouchi, M. Bendaoud, R. Essolbi, D. Malec, B. Ai, and T. G. Hoang,J. Appl. Phys.79, 2497~1996!.

11D. Malec and R. Essolbi, J. Phys.~France! III 3, 1083~1993!.12D. Malec, R. Essolbi, M. Farkh, T. G. Hoang, B. Ai, N. Zebouchi, and M.Bendaoud, J. Phys. D27, 360 ~1994!.

13I. Kitani and K. Arii, Jpn. J. Appl. Phys.22, 857 ~1983!.14T. Mori, T. Matsuoka, and T. Mizutani, IEEE Trans. Electr. Insul.1, 71

~1994!.15A. Bradwell, R. Cooper, and B. Varlow, Proc. IEEE188, 247 ~1971!.16Y. Zhang, J. Lewiner, C. Alquie, and N. Hampton, in Proceedings of theFourth International Conference on Insulated Power Cables, Versailles,France, 1995~unpublished!, p. 697.

17T. Mizutani, in Proceedings of the Eighth International Symposium onElectrets, Paris, France, 1994~unpublished!, p. 163.

18P. Laurenceau, G. Dreyfus, and J. Lewiner, Phys. Rev. Lett.38, 46 ~1977!.19R. G. Multhaupt, Phys. Rev. B27, 2494~1983!.20M. Haardt and N. Eisenmenger, Ann. Rept. Con. Electr. Insul. Dielect.Phenom.46, ~1982!.

21T. Takada, T. Maeno, and H. Kushibe, IEEE Trans. Electr. Insul.22, 497~1987!.

22R. Liu, T. Takada, and N. Takasu, J. Phys. D26, 986 ~1993!.23R. E. Collins, J. Appl. Phys.47, 4404~1976!.24Y. Suzuoki, H. Muto, T. Mizutani, and M. Ieda, Jpn. J. Appl. Phys.24,604 ~1985!.

25N. Vella, A. Toureille, N. Zebouchi, and T. G. Hoang, in Proceedings ofthe Third International Conference on Insulated Power Cables, Versailles,France, 1995~unpublished!, p. 701.

26A. Toureille, J. Electrostatique32, 277 ~1994!.27T. G. Hoang, P. Guerin, and R. Lacoste, in Proceeding of the First Inter-national Conference on Conduction and Breakdown in Solid Dielectrics,Toulouse, France, 1983~unpublished!, p. 390.

28E. Occhini, IEEE Trans. Power Appl. Syst.PAS-90, 2671~1971!.29A. Ainbinder, Mekh. Pol.1, 65 ~1965!.30A. Von Hippel, Z. Fur Phys.75, 145 ~1932!.31M. Hikita, Ph.D. thesis, Nagoya University, 1982.32F. Forlani and Minnaja, Phys. Status Solidi4, 311 ~1964!.33M. Iwamoto and T. Hino, Electr. Eng. Jpn.100, 9 ~1980!.34M. Iwamoto and T. Hino, Electr. Eng. Jpn.100, 1 ~1980!.35M. Iwamoto and T. Hino, Electr. Eng. Jpn.100, 25 ~1980!.36M. Fukuma, M. Nagao, and M. Kosaki, in Proceeding of the Third Inter-national Conference on Properties and Applications of Dielectric Materi-als, Tokyo, Japan, 1991~unpublished!, p. 1052.

37M. Fukuma, M. Nagao, and M. Kosaki, in Proceedings of the EighthInternational Symposium on High Voltage Engineering Yokohama, Japan,1993 ~unpublished!, p. 183.

FIG. 6. Calculated electric field profile up to electrical breakdown in LDPEfor T570 °C andP51 bar.

2368 J. Appl. Phys., Vol. 81, No. 5, 1 March 1997 Zebouchi, Hoang, and Ai [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

141.217.58.222 On: Wed, 26 Nov 2014 16:43:21

38K. Yamashita, M. Iwamoto, and T. Hino, Jpn. J. Appl. Phys.20, 1429~1981!.

39M. Iwamoto, in Proceedings of the Second International Conference onProperties and Applications of Dielectric Materials, Beijing, China, 1988~unpublished!, p. 351.

40H. J. Neuhaus, Ph.D. thesis, Massachusetts Institute of Technology, 1989.41M. Saidi, N. Amroun, M. Bendaoud, R. Essolbi, A. Antoniou, and T. G.Hoang, High Pressure Res.9, 355 ~1992!.

42D. K. Das Gupta and M. K. Barbarez, J. Phys. D6, 867 ~1973!.43M. Fukuma, M. Nagao, and M. Kosaki, in Proceedings of the FourthInternational Conference on Properties and Applications of Dielectric Ma-terials, Brisbane, Australia, 1994~unpublished!, p. 24.

44M. Iwamoto, J. Appl. Phys.79, 7936~1996!.45N. Zebouchi, R. Essolbi, D. Malec, T. G. Hoang, and B. Ai, in Proceed-

ings of the Eighth International Symposium on Electrets, Paris, France,1994 ~unpublished!, p. 61.

46N. Fuhs, Phys. Status Solidi A10, 201 ~1972!.47F. Yong, L. Qingquan, and S. Shufa, in Proceedings of the Third Interna-tional Conference on Properties and Applications of Dielectric Materials,1991 ~unpublished!, p. 1014.

48J. Gollewski, P. Mondalski, and J. Kalinowski, High Pressure Res.9, 268~1992!.

49R. El-Hayani, 3emeCycle thesis, University Paul Sabatier, Toulouse, 1987.50Y. Takai, M. Kobayashi, T. Mizutani, and M. Ieda, J. Phys. D21, 1151

~1988!.51Y. Takai, M. Kobayashi, T. Mizutani, and M. Ieda, J. Phys. D21, 1159

~1988!.

2369J. Appl. Phys., Vol. 81, No. 5, 1 March 1997 Zebouchi, Hoang, and Ai [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

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