Nouveaux concepts pour l’int egration 3D et le ... · M. Henri SCHNEIDER Maître de conférences,...

Nouveaux concepts pour l’integration 3D et le

refroidissement des semi-conducteurs de puissance a

structure verticale

Kremena Vladimirova

To cite this version:

Kremena Vladimirova. Nouveaux concepts pour l’integration 3D et le refroidissement dessemi-conducteurs de puissance a structure verticale. Autre. Universite Grenoble Alpes, 2012.Francais. <NNT : 2012GRENT049>. <tel-00738000v2>

HAL Id: tel-00738000

https://tel.archives-ouvertes.fr/tel-00738000v2

Submitted on 17 Jul 2013

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THÈSE Pour obtenir le grade de

DOCTEUR DE L’UNIVERSITÉ DE GRENOBLE Spécialité : Génie électrique Arrêté ministériel : 7 août 2006 Présentée par

Kremena VLADIMIROVA Thèse dirigée par Christian SCHAEFFER et codirigée par Jean-Christophe CREBIER et Yvan AVENAS préparée au sein du Laboratoire de Génie Electrique de Grenoble (G2Elab) dans l'École Doctorale « Electrotechnique Electronique Automatique et Traitement du Signal » Nouveaux concepts pour l’intégration 3D et le refroidissement des semi-conducteurs de puissance à structure verticale Thèse soutenue publiquement le 11 mai 2012, devant le jury composé de :

M. Thierry LEBEY Directeur de recherche, CNRS Toulouse, Président M. Hervé MOREL Directeur de recherche, CNRS Lyon, Rapporteur M. Henri SCHNEIDER Maître de conférences, INP-Toulouse, Rapporteur M. Laurent DUPONT Chargé de recherche, IFFSTAR, Versailles Membre M. Olivier LESAINT Directeur de recherche, CNRS Grenoble, Membre M. Christian SCHAEFFER Professeur des universités, INP-Grenoble, Membre M. Yvan AVENAS Maître de conférences, INP-Grenoble, Membre M. Jean-Christophe CREBIER Chargé de recherche, CNRS Grenoble, Membre

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.(AADAEEFAADCAADCEAEACADEDEFA>&+ADCCA(EAA A (EA EEA A DCA A A DDA /A EA E+AD+A DEA+A*,AAAAAEAEAAA"CA%EFAT%86HGUAAEAT%86AHU+AACAEAADEAEAADAAEA*ACACAAACAEACAAEACAEACDDEAAEADCAADCEAAFEAE(AAEEDAECADEDEFA>&ADCAAADA EAEEAA AA(EAEEA"A ;A LA A DEA A DCEA A EA A (A A EACAADAAEA"EADCDEAADEAADCEADCACAECCCA A DA A (ECAEA A (A ECCA A (EADECA CAA DECA EEDA ECA A DEA (A LECCA !C(+A EAEEAECCAADADEAEAECAA+AEAAEAWAACAEACAEA E+A EA EEA A (EA EEA A EA DCA A CA A EDA FCACDDEA E(A A EA CA EA ECA ECA 3)A 2CDA %EE4ADEA EA EA ECA 8A A CA A A EA DA A DEA +A EAEEA A DCA A #A A DCA (A DECA DCA FEEA CA CDA ACEAE(AAADEAEAEACACACEAAEAC(EACADEAADCEA"AEA A A DECA A FEA DA DCA XEXA EA CFA A C(EA ACCA CA 8(+A A CA CA ECA EECA EECA AECCCA A EA A (EA A EEFA >&A A DEA DA EA FAEE+A DDA ECA EEA ".<".*8+A A 5E+A DEA A (EA A DA ALALCADEAADCEAF=AAEADAAEDECAACACAACEAACAEADCAT").HGUA

.+ACADEACDACADEAADCEAAAADEDEFAAEAE(AACADCAFEAE(EEA*EAAAAEAECAAFAA(EAEEAADCACADCA#ADCACAADA<CACAAEDAEA(FCA:IAACADAAEAFACA:72!A:(AA(AB:7*ACA!JH6C*AJHH9AQAIHA.AT:65H>UAAAAYAA+ACAEACAEEFA>&ACEAAEECAAAA8A9EFAT9.7AHUA

*EAAFA

2CAEADEADCAECAEACAA

'FFAAA

5FA:IA,A9CAACAACAACDACA:72!A:(AB:7*ACA!JH6C*AJHH9QAIH.AT:65H>UA

&EAAD+AEA(EAEEA3CAAC4AADAAGADAAEACAACADAAEAAFA"EACAAEADDACADEAAEAADAAEAAA(ADEAEDDAECAEEA*ACCE+A(EEAECADEAA (A LECC+A A A DCA EEDA A A LCA ECA EA CA ((EA CA C(EALEFADEA.+AEAAAFCAAADAADEAEACADA>&AA DA A DCCA A T9.7AHUA :A A EA CCA DEA A EA FA3EEA CA CA DA CA A DA CA EA A FA A CA A EADC4A A EA DCA D(A EA DA A EA A (EA EEA "A (A A EA CAC+A A DD+A A EA A +A DEA DCA ECA EA CA AACADE+AA(EAADCAAA>&A"AEAAEAAEA A DA DEEA ,A EEDA A EA CA DEA 0A FA CA EA (EA EEA EA E;AEFEA DCA CA FEA >&A A ,CCA A DCEA 8A ((+A EACA A CD+A CA DEA A EA DEE+A A A DEA #A DCADEA EA DA A CCA A DA A ,A .A EA A EA A EEFA AA>&AEAACCAE(+AE(AAADEAFEAEACAAACA,CC+A EA EA A A CCA A EA ;A DDCA A EA DCA A #AECA&ACAAADECAADDADEAAFAAEACAACACACDDEAAEADCAA ACEACDCAAACAADAAEADEAEEADADEADATV-ZHIUACAA A CA A EEA 3A FEA A ECC4A A DCA EA AEEAACADA6CADCAAAAAFAABCDBBDEBAT*.!HIUAEACAEAECAADECAACAAEADCAAACE+AFABCDBBDEBT%8HJUEACAEAECAAAACAAEADCAAACEA3(FCA:J4+ACFABCDBBDEBAT:6@KUACADACAAAAAECAAEADCAAACEA&ECAEECAEECAAECCCAAEAACAEEDAEAEEAA(EAEEAADEAADCEAE(AA(EAEADAAEA>&A*ADEADAEAFAADECAACA3(FCA:K4ADDAA5EAECAEEA.%<88ADE+AAACD+AACAAEACAE(AADACAEEFADCAEA T%86HGUA*A CAA((ADDEADEAADDALEDAXDEDEFFXAALACA0E(AADEAEAAADEAADA(AD(CAAEEDA

5FA:JA,A9CAECAAEAFAA>&AFABCDBBDEBA

T%8HJUA

5FA:KA,A9CAECAAEAFAA>&AEACAAEDCDECT%86HGUA

)AECADADCACADAEADAAEAEAAC(EAADEA,CCAEACAEAE((ACACAAAAEAADCA

AEAEA(EAAEEDEAAEA(EAEEAAEADCAADE[EAAEADEEADEAAEADCAEDDDAECAA>&A*ADAEADA

DCAAEAAEDA

• "ACA<0A*D,,*DA3<**4A

*A CA EA A +A CEA A EA A A EA EADAAEAEEAACAADCEADACA(ACA(EAADEA A DCEA EA ((A ECA CA FEA DEA A A A DAEFCA F=A ECA DEA A (A A FA A (EA EEA DEA AA>&A!C(+AAEAAAT9.7AHUACAAAADEAA(AAFACA A DEA A EA DCA FEA ECA A CEA DEEA A EA EA ACEA EA A A A A EA A CA EA "A EEA 7C8EA CADCA CCA EA A ((A A A A FCA DCA D(EA A DEA ,CCAADCEAADDEAADFAFEACAACACAAA EA FA A A ,,ECA 38!%4A &EA A E+A A DA<0A*D,,*DA3<**4AEAADDAAEACEAAEECAAAA8A9EFAT9.7AHUA*ADAEAAEAEEACACAADCEADEAEACAEAAAACADCADEAADCAADCEAACACAAECA"DA A A A A DCAA A CA EEFA DCA #A A ECA DCA DAAEAACAEA3(FCA:G4A:AACACAFEADEAAAADACAAEFCA!C(+AA(ACADAACACACACCA<**A DEA EDDA ECA CA >&A ECA A A "A (A CA (EAAAACACA(EACACADCAADALCACALECADCA(ACACAACEA EACADAACAEFCAADACA EA

(FCA:GA.+ACADAEACA(A+AECADCADAADEAADCE+A CEA CA EDDEA A FEA EA A DA EEFA DA ADCAADCEA"ACEAEADEACADAACA*8%AACAFEA*ADAEADADCAAEAAEDA

5FA:GA,A9CAECACADA<**A/ACACAACEAECADCADACACAEAT9.7AHUA

"EDDEACADA<0A*D,,*DADCAEAEEACACAACEAADACAEA(FCA:@A"EAFAAEEAAA

ADAAAAADCAAEAADAADAEADA,AEADAAEAACA(EACADEAA((CADEADAADECAEAAEAA

5FA:@A,A*CAACEACEAADA<**AT9.7AHUA

.(A A D(A EA A A FC+A CA A (A A EA A DA <**AAACAEA(AAEFAEADCAEAEEAAEEFA*D,,*DADEAEDDAACAA<,<EDAECA:AEAAACEAAEECAAAA8A9EFACADCACA(EA(AAEFA3AD64AAEAEAAAACEA)A ECA DA (A CA DA <**A A A FEA DE+A A A A DAEFC+A CA A ECEA DCA A CA EA EA A A A A DA AADAAEAECCA(EAAEEFA!C(+AACAEA+ACAEA EA A EA C(EA A EA DCA A A A #A DA E(A A A DEAE((A EA CA A A CA DEA 'A A CA EA A CECA (EA A EADECA A EEDEA A DCA A DCEA DCA ECCCA A CA A AFCAEAAEEFAFEAAEA

"A DEEFEDA CEA EA A A EA DA A EA CA CA CA EA C+AEEA DCA A CEA A EECA A A E(A A D(A EA A A FCA ADEAADCEAACCAEAEAADEDEFA>&A

, /E "CF AC 2 A "CE CFC 2ACC

6CAEACAEAADEEFEDADACAADEDEFA>&ADACAAACA A CA (EA CA DEA A DCEA A CA DA DA A DAEFCACACA&EAAE+AEADAAEACAACA(EACADEAA ((CA DEA A DECA XEFXA A EA !C(+A EA DCDEA A DEA DCACA ECCCA DA A EA A A DDCA A DADEEACAAADEAEEDAAAA A"EACAACD+ACADEA A EADEE+AAADEA#ADCADEA EADAACCAADAA,AE(AAADEADEAA(ACACADEA.+AEA ;A A EA A (EA EEA A#A FA A EA;ADDCA)AECAEAEA A DECA A A CA EDDA CDA A EA DA A A EAEEACADEAADCEAAAADEDEFAE(AADCADA A.+AALACEAAADEAADCEAACADECACA(EEA((A A CA EA A EA CA DA CA CA A DEA A DCE+A A AEAAAAAAFAADDAAAADEAADCEAACCAEAE(AAEADEAAEAEAEAACCACACAEA

, BA FAACAFAAC

&CAEADDEAEDDEEAAEADDAAAA,CCAA DCEA A A A DECA DECA E(A A FEEA EA CA A ADEAACCADCA T.6@C+A"85HEUA"EADAA AECA((AAAAECA (ECA EA A C(EA A ECA ECA A A A CDA CA DCA CA EACAAACAD(AAACAEDACAADEAF(EACAAACADEEAECEAADEAEA"EACAEAAEACCAACDA A EA A DEAA A CA DCA EMA A ECEFA DECA CADEADCACAADCA(EACAEAADEAAEAADEACEA&A CA CA FCA CA DA A NA A ECEFA A C(EAA T.6@C+A "85HE+A 2."HGUA 8A A CA EA CA A DDAA EA A EA;A A EFA DEA A DDA A EA A DEA A A E(A A CA ADACACADCAFEAC(EAACAAEAACAEAECACAEDACAAC(EAAEAACACACACAEAC(EAAADDAAEAA3FAACCAC&ACA>&4A"AFAACAAADDCADCA#AAACA FEA (EA /A A FA DEEA 3EECA A FE+A DEEA C+A ADE+AAAED+ACA8B)5+A4ACAAAAEAEAECAAAFACAAAAEAEAECA3EAAEC+AE+A4A

• BCAAAFA3ACEAAC"CA A

"LFA A FA A EA A A DDCA A DA DEEA EADAACAAOAA(EEAADEACAAD(EACAEEAAAAEDDEA((EAAEACAAADEAA

!CAACAFCADEE+AAEAAAAADCAEC+AAA A A EA T.6@C+A "85HE+A 2."HG+A "8!HHUA 6CA A (A A DEA CADA ECA A CA DDA 6CA EA CA DA A DDA AEECA A FEA DCCA A EA FA EA DCA DECA 8A CA EA A DA ADEEA EA EA CA A EA CA DEA EEDA A A DEDEFA CA CAEADDADEAEACAA

"EA CA A EECA A FEA CA EECA (EA A CA A DCA EATZ.'JKUA "A DDA A A CA A EA CA EA EEA CA CA DCCA EEC+AEA A #A DA CA EA ((CA EA A CA A %'BA CA :72!+A CEA EAADDEA"EA(FCA:AHADAEDDEAAEACAAEECAAFEADCACAA<:6AA

7 CE &C

)CE-CAA"C

5FA:AHA,A!EADEE,AEECAAFEAT"85HEUA

"CAEAADDEAADEAAAEA;AAEFADEA3\*84ACAA DDA ECA A A EA CCA A EEC+A (A D+A A CA EFA EACCAACDA*EAEAA((AACA AEDACAAC(EACADEA A CA DEA A A EA A RAASA EA A DEA DCA ECA ADEA EA A A "A A EECA A ECEA DCA FEA CA EA A AECEFAAA"AAEAAEAADDEAAADAEECADCAAA EECA A ECA A DEEA CA A #A FCA A E(A AFEEAAD(EAA

8(+A A CA CA A A CA (A CFAA CA EA CA A EADDCAACAA(ECACAAECCDAEAAAFCAADEAEAA CA A DCEA *A CA EA +A A EA DEEA A EEDA ECAA A DA 0A FA EA A A EFEA DCA EA EEA AA >&A &CA DEA EA DA CA CCA A DA A EA C(EA CADEA A DCEA CA A (A EA CA A CDA A E((A EACAAACADEA&ECADEACAACAAEAAAEAEAECAAADNACACAADEEAAC(EACADEAA DA CA EA (FCA :AAA *A CA CA EA CDECA EA CAD(A EA EEA A >&+A A CA EA A CA EA ADEEFEDACCAA

)CE -CAA"C

5FA:AAA,AAEAEAECADCACAA<:6AT"85HEUA

• BCAAAFA3ACEAAACACA A

"A EA A DA RAEASA CA ECA A CA A FCA EA A CACEA A ECCCA A DCA A D(A A A (A DCEA 3A AAAADDE4AT2."HG+A"8!HHUA)A#AEAADAAA DA A A FA A EA A A DCCA EA #A AEEDAECADEAFEAFEDAAECAACAT\$.AH+AV'"HJUAA

"A DDA A A CA 3(FCA :AC4A A A EA EEA CA CDAEDDDACA AACACEA,CCA"EAEEAAEAAECAA EACA A A ECA 3EEF+A CE+A 4A EA CA A EA EAA EA CA A DA A EFA CA EECA CA .CCC+A ADDA A DA FCA A FECA A A CA &:8A 3DCA &DAEA :A 8F4A DA EA FECA A (A EA FEA (ECA A (A A EADEAA EAEA:AAAECACADCA EAEEAAADAADDAAACAACAEAEAECACAAAAEAAEAD(A3DAAE4AT<.HC+A<.H>+A&.@@+AZ.%AH+A!$8H@UA"ADDA A CCA A #A /A CA EA DEA EFA CA EDA CA AC(EAE(AAD(AAEAAAECEFAAEAADEA)AEEEFAECAAEACA A EA A EA A CA EA EEA A A DA A EADDCA DA CA EA A CA (A CA DEA EDDA ECACA EA A A EECA A FEA /A CA CA A >H]A A EA C(EAEACACEAEAAAEAAEECAAT<.H>UADCACAEADEAEAAEAAKHH9AAEAACEAAE.A

5FA:ACA,A!EADCAAEAEAECA

)A EEEFA A A CA A EA A CA A DA CA EFA ^AEDDDAADDACADEA 3(FCA:AC4A&((AEFA/AD(+AFE(+ACAEC+A+AECADEAAEEEFA,,AAEDDEA(E+ADCA#AEAA DDA A D(A "A EA DCA A A CA A A CEA A((A EFA A A EA T2."HG+A "85HE+A "8!HHUA A CA EA CA CAA A EFA A CDA D(A DCCA EA #A A DCA EDDDA DCA AEDDEA

"EFA A A RAD(ASA CA EA A CA DEA CA A EA FA <A A EAFA 6A A DA CA EA (FCA :ACA )A A EFA A A (EEA DCA EA CA AACAD(AEAADAACA(AAEDACAAC(EADEAEDDAECAEDACAACA"EAEADCAEAACADCAEACAAEFADAAFEAADEAAECAAEAA<6+ACAAEACAAEAACADEAADD+AEA;AAEFADEAEFAAAACADEAACADEA A D(A A EA CA A A DEA DCA ECA A DEA EA AA &EA A E+A EA CA CA EDA CA A C(EA 3 surfEmax_ 4A DEA

EDDA ECA EDA CA A CA 3 volEmax_ 4A DCA #A A CEA EA EA

)cos(1)sin(.max_max_θ

θvolEsurfE AAAAAAAAAAAAAAAAAAAAAAAAAA:AA

&EDAEAEA3:A4ADCAEFAA(E+ADCAAEDACAAC(EAACA:AAAEACEFAT2."HGUACAEFAD(ADEAAEAEAFEAA>H_AAJH_A"AEFADCA(EAAADADCCAACADAFEAEACACAA

6E+ACAAACCADEEAADEACAAADAAEAAEADAD(AAFAADEAAEACADCADCA A ECEFA DECA A C(EA .+A CA EA DECA A DA CA AEAADE+AEAEEACADEEAECEAAAACAEECACAE(AADAA(AEACADEAAFEEEAEACAAA"EADEEAAEAAAEAEAECAAADADAEAEACAADACA(ACAACAAFAAEADEABAEAECA

CAEFAFEAAEECACADCA#ACAEAAEA,A+AACA<B7A3DCA <DEA 7E4A &A EECA EECA A ECA EEA "..BA A 5EAT!$8H@UAACAECAEECADEAAADDAAADA2;*2CA 32*24A DCA #A CA DCA EA DA CA A EAD(AADEAECAAA

,1 FACAAA"CEA

"EA A A D(A A EA CA A EA DDCA A A EA EAECADCAD(AAEAAAFCAADEDEFA>&A.AEAAEDDAADACDADC,DEDEF+ACAEAADADEAACAE(A`EEDaAA DEA DCA CA A A FCA FEA A D(EA "EA CA CA CADDAAAADEAAAA EAA AEAEA EAEAAEA D(AA DDA CADEA)A A (FCEA DEA EA DAAE0ACADEAACADECAECA/AAEAAEACADEDEFA<**ACA CA EA DA EA A DEEFEDA CCA "EA (FCA :A>A DA EDDEA CADAAEAEAADEAADACAA<:6A

BCAA "CEA A

5FA:A>A,A!CAAEAAAEADCACAAADCEAACCAEAA

"EA CA A EEA A EA EA A A CA EDA A FECA CAEA D(A 3&:84+A CCLA A A EA D(CA A A EFA +ADADEACAEDAADEEAAEAACADEACA#A&EACAA D+A EA (A A C(EA A EA DC+A A DCA DECA EA EEA A AEECAAFEA#AEEDAA

,, BCAAECC"AACAA"CEAA9",!

.(AAA#AAEACAAEAEADCACAAAFCA>&+A CA EA A CA CA EA CA A CEA CCA EA A FA BEA"(AEAECAA((AADAAEA;AACAAAAACCAE(A"ACEACAAEACACACADDAAAADEAAADEAEAEACADEEAEADCADEC+AAAEECAAFEA3(FCA:AE4AA

BCAA "CEA&C$ FCF A

5FA:AEA,A%AAFCA>&ACAA<:6AEAEAAAEAAEAEECAAFEA

&EA A DA E+A EA CCA CA DA A CA A A DCEA A CCAEADEAAAEACAAAECEFAAKHH9ACADACADDAA A A DA EECA A FEA A CA DECA EFA A EA A DA A EA A (EAEEA "EA EA A EA C(EA A EA DCAA EADEA (CA CA CCA A EE+AFAADEACADECALDECAEEA3(FCA:AI4A"AEECACACAEAACEA EA CA DA CA bc>A E(A A DA A EA CA EECA ADEEA CA DCA EA DCA EA DEEA A DDA (EC+A L,,A A FAA<CAAEACAADEEAACEAEACAAAECAAAAEAAEDA:::AA

&C$ FCF

Diélectrique

distance variable

P+ P+P+P+ P+ P+N+

EC:;< EC:;<

CAA:;<

= >= 1?=?= 1= += 1== 1>== >= 1?=?= 1= += 1== 1>=

&C$ FCF

Diélectrique

distance variable

P+ P+P+P+ P+ P+N+

EC:;< EC:;<

CAA:;<

= >= 1?=?= 1= += 1== 1>== >= 1?=?= 1= += 1== 1>=

5FA:AIA,ABCCACA,AA<:6AEAEECAAFEA

6CAEA(EAEA EAEAAEADECAEAADAAEAA EAC(EACADEA A AHHdA A IdA 6CA EA EA CA CA A CHd+A EA DA A EA

DECAAEAE((AEACAACDAAC(EAACACAECFEAEACAEDACAAC(E+AECEADCAEADCAEAEACA

<CACAAD+AEA(FCA:AJE4ADAACEACADCAEACACAEDACAAAFACDACAEADECAEAAEAADEAAAHdAAEAC(EACADEAA

CAA:;<

= >= 1?=?= 1= += 1== 1>=

AAE4AA

CE :'@<

= >= 1?=?= 1= += 1== 1>=

5FA:AJA,A&AADCEAEAEECAAFEAE4A*CACAEDACAAFACDAA4A8CACAEDACAAEAC(EA3CAACDAAFAAEAFACFAD4AEAAEADALCAAAEACEAAEECAAFEA

'ADCAECACAEA(FCA:AJE4ACACAAEADAAEADECAAEAAAEAC(EACADEAAEECAAFEAAADCACA((AD(ACALEAACDAA EAC(EAAADDAAEADCA"AFACDAAAAAAAEAC(EA)ADEACAAAAA(ADEAAD(EACAAAACAAAA

"EA(FCA:AJ4ADAEADEEAAEACAACDACAEDACA3CAACDACAEDACA A FAA EA FACFA(FCA:AJAE44AAC(EAEAAAEACEAAEECAAEAAAEADEAAAHdAAEAC(EA'ADCAECACAEA(FCA:AJACAEADAAEADECAECAAEAC(EACADEACACADADEACAEDACAAC(EAECAECACAAEECA"AEDACAAC(EAECFAADCACAEAEACAECAAAAHdA

"EA(FCA:AKADAEA#AAADCEAACCAEAE+AA(+AEAEA CA A EA A A EA "A EA A (EA EEA A E(A AEAEC,AAEA;AACAAAA

BCA "CE

CAA:;<

= == 1== ,== >==

5FA:AKA,ABCCACA,AA<:6AEAEAAAEA

A"EA (FCA :AGA DA EA CA CA EDA CA A A FA CDACAEAAADEAAAEACAAAGHH9AA

CAA:;<

= == 1== ,== >==

CAA:;<

CE :'@

= 1= ,= *=>= = += .= ?=

5FA:AGA,A&AADCEAEAEAAAEAE4A*CACAEDACAAFACDAA4A9CAACDA3AFAAEAFACFAD4ACA

EDACAA(EABQCA

'ADCAECACAEA(FCA:AG4ACADAEACAACDACAEDACAAFAA(EABQCA3FACFA(FCA:AGE44ACEAACAAEAA+A ECA CA DECA EA AC(EA CADEA EA DEA ((A FE(A DCA AEDACA.CAE+AEADECAEACAANACADECAAEDACADAA CA A EEEFA A EDA CA A L(EA BQDEEA "EA (FCA :AGE4AA C+A EA A E+A ECA A EA CCA A FA CDA DA CA

A (EEA DCA EA CA A A CA DEA A DCEA A EA EADADCADAEAAEDA:::A'ADCAECAACAEA(FCA:AGE4ACA(AECFEACAEDACAECAECAA EFAA A*A(AECFEACAEDACAAEADEADAADAAECAECACAEECACA AEDA CA A ECEFA A DCA A CA CA CA CA 'A DCA ECA EFA CCADEEACAADAECAECAAAA

,> ("EA2FEACBAACAFAAC

)AEEEFAECAAEACAAEAAAEAACADAAAADEEAECAECAAEA;AEACADEA+AAAE+AADCAEFA FEA ADCCA DEA EA EA #A DCA "A A A CA EADDAAAACADCACAAEDACAAC(EAEAECADCAXXA ECA DEA "EA EA CA DEA A ;A EA A ECA DEA ACA DAEA CAEECA CA A CADA A FEEA EA CA AECADEAEAAA&AAEAADCAEFAFEAADCCADEA A DCEA CA A #A CEA C+A ECA CA ,CCAFAT*8H@UA"EA(FCA:A@AACACAECACADAAAAFCAADCCA DEA EA A #A CEA A CA "DA DA A A ADCEAACCAEAAEAC(EAAFEACDADEADCCAEAA

CAEACAA(EAE.

D1 D2 Dn……

MetalDielectric

5FA:A@A,A9CAECACADCACAADCEAFACAA#ACEA

ACAEAEACAAEAEA

*A (FCEA DA LEEFA A A DEDEFA DEA A CA DEA ECAECA CA 0E(A EA CA CA EDA CDDEA A EDA A "EA CAF(EACAAAACAAEEEFACAAACA<CCA DEA A A DEA A DA FCA A CA AEEFA DC+A A (EA A CA A OA (EA CA DEDEFA *A ECADCEA EEEFCA #A (CA EA A EDDEA A LCA ADCEAACAACCAAADDEAT5'HK+A".2HG+AZ8ACUA

)AEEEFAECAAACAFEACAADCCAACAA#ACEAACA EAAA((AA,CCADCA#AEADEA EDA (EA A FECA A CA D(A A DA FCA "EDDA CA CADAEAADDACACACEA ,CCADEAEAADCA (EA#AEDDCACAACEAFADACAAAEA&EAAE+AEAFECACA CA A#A EA CCLECA CEA CA A EA"EA (FCA:CHA DA CACA ECA CA DA "A CDDA ECA A DEA RAASA A #A ECAEA A EA DEA EA CA A EA <CA A (E+A EA CA A EA A #A C((EADEA 3CCA EA A d4A "A CA EFEA EA A EA A A EFACEAC,CAACACAACADAA(EAEACA0E(AACADECADEAAEA3CACA4AT286ACUACADACACAA(ADECA

5FA:CHA,A9CAECAAEACAAEAEAEAAEACACEA,CCAFA

*ACAEAADAEAEACAAEAAAE+AADEADCA(AAA>&AWAA(AAFAADEADEAA A EA A CA "A EA A A EA DA EAEEAADCCADEAAAAEADCAEACADCAECAEFACADAACACAAECADCAACACCA>&AE(AACA(CAAA A A DEA A A D(A CA A A FCA EA A CCADDEACACECA"EA(FCA:CAADACACAECAAADDADCAEACA(FCEA<0A*D,,*DA

5FA:CAA,A9CAECACADEDEFA<0A*D,,*DAAEAAEAAAEA,ADALCA+AAAAAEACAALCACADDEAA

<EA EC+A A CA EA A +A CA A DA (A A DEDEFA >&A ACAECAAA(ACA(EA'+AEACA(FCEAWACADEAADACACAEC+A A(AAACECAAACACA(EA)AA (FCEA ((A A (A EA CA DA A CA DAEFCA EA CA DA A CA CA A D(EA A A 6CAEA DA DEA EA CA EA A EDA CA EDDA FEA CA EA A ADECA"ADAAAA EACCA#ACADEAADCEAE(AAEACACDEFAAA;AACAEC+AADAAEACAAA C(EA LEFA CA "A DA EA DCA A (A A ADEA A DCEA ((A A FA A A EA E(A A DCA EA AEEFA DECA CA DA A CA EFCA CA A EEA A D(EACAA

> A AFFAAE

)A DEA A DCEA A CDDA A ECA A A EA DEA A (ACEAWACAEADCEACAADACA(AAECA"AAA(CAAECAADCAADCEADCAEADCCAEAAV,CA8A#AD+AADEAADCEAACADECAAAEEAAADEADEA"CA(A((EAAAEAE(AAFEEAAAA(AAAD(EADEA.A AAAAA(AECEADCA

EACADECAAAACAADECACAA(A"AACAAA(ADACAECAADAAECAAA((EAAAAAAEACACEAAADAAEFA6CAEAAEAADEEFEDACEACCACACADCAA(AACAA[EADEACCAEDDACAAEAAE(AAEAECAAA

> )CAAFCAFCE

&CAEAFEA A E(AAECA((CADEA AEA?ACAAAEA

"EACAA AAAE(AAECAOAECAEAADECAACADACAACALCA(CAADEADDEFEAADAADAAFACAAE+A A CA CA AA A"A (CA CA eA TVUA EEA CA A AC(EABATCUAADECA"ATUAADAEAAEAA&ADEAEAEACEA?A

TLSk ∆=Φ .. AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA3:C4A

WA DA TVQZUA A EA CA CA A f!A TZUA A EA A DECA A ACA(EAAA

.A A ((A DEEA CA A EA A DA A CA A EAECAAEAFAAEECACCAAEAECAEACAA(EACACAADEAA

"AE(AAECADEAAEDDEEMAEAA(CA:AAOAECACAADECACA(EA AE(AAECA&EA AEAWACA(CAAAEAEACADE+AEFAAECAAEADEAAA(CADCA#AACEAEAEA?A

).(. fp TTSh −=Φ AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA3:>4A

WATVQCZUAAA((AEFAAE(AAEAECAAEADEAAA(C+A!DTZUAAEADECAAEADEAA!(ATZUAAEADECAAEFACA(CA"CAACACA(CAA DADEACACAA 3DD+AEC4A EAAAA(A&EAAEAEAEAAAAA3CAEC4AA

"A DA CA A EA A A A DA A A EA CACEA A EA CA A A EA ECA A (CA )A A CA EFA EADACAAA(ADEAAEA(ADCCADEEAAA((AEF+A ADAAEFAACAADEACADAA(CAC+A A EA F+A CA FA CA A <CA EA A EA EA A CA AEA 3(CA EEA DCA A (A FCA DECA CA EA4A A A A EA A CA CA EA DA DCA A EA EA AEDA:9A

• C%

"AE(ACADEAEA((CAACADADEADEAAACA DEA CA CA EDEA ECA EA CA DEA EA AEFCA "A (CA E(A DEA EA A CA DEA DEEA 3DEAA ADEC4AA(ACEAEAE?AA

4112 .. TTSs −=Φ σε AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA3:E4A

WA 12ε AAACEAA sσ AAEAEAAB(EA

• 4FAAC

"EEFA (EA A A DA A CA A EA ECA 3A A 5C4A A A

CA CA DA CA EA A A EA CA thR (K/W)A CA

CE(A EA EA CA A EECA DDA ECA DEEFA CA (CA A ECA "EA EACADACEAEAEACE?A

Φ∆= TRth AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA3:I4A

BA A E(A A EA ECA A ((CA DEA CA A A&+A EA EA CA Ac"QDABA AE(AAEAECAA((CADEAAACA(CAACADE+A EAEACAAcAQBAA

*ACAEAA+AEAEACAAADEEAADCAA DCA A DCA CECA A CA A A (A 6CA EA EEADACCACAAAA(ACACEAACAAEEAACA(EACACADA(AA(EAE(AAA#ACADAA(AEACACAEADDADEAEACA

>1 FAAFAFEAFAAC

"A(CAAEACDAEACAECA 3A(4ACAEA 3A4A A A DCA CA CA A AADA A ECA ECA ECA A LEFCA AADEAA+AFEADCAAAA(CAAECA(CAAAHHVQCZAECA ECA A EA DCA "EA (FCA :CCA DA CA CA ECA CA CA EEA C&A3CAACEA4ACACAEAADAEAADEEFEDACAA

puceDCA

Flux de chaleur

5FA:CCA,A(AAEACACAACEAA/AEACACEAADAADECACA(CAAECA

"EA (FCA :CCA A A FA EEEFA A A CA A (A /A CA AEEFA CA DA A CA DEA 3A ECA E;A DE4A CA ADEA*EAA((ACAFEAC(EAEFAADEADECACA(CAAECAACA (EAAAECEA8AFE+A A DEAA EAACAEAAEECAAAAAE(ACAAEECADADCAFAA

EEA A CA DDA CA T9:6HGUA :A A FEA DA A ADEAA((EAACEAAECAECAEEACACACAAAT.98AHUAA

"A FA A A A CA A (A A EEFA ADCCA CA DECA A A CA CA ((A /A A (CA A ECAEAEACADACAAAAEACAAECACCLAEEAEACAECACADDACAEACAAADEEFA3(FCA:C>4AECCAA(ECAECA A EA CA A EA A ECA (EA .A EA EA CAEACAAAE;AA8ADCA#AACEAEAEACEA?A

= ajth

TTR AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA3:J4A

WA !A TZUA A EA DECA A A A EA DCA A !EA TZUA A EA DECA EEA3(FCA :CC4A :A A CA CA EA EA CA EA A DA DEA AEA CA A A DA CA EA (FCA :CCA?A A +A /A EA EACA A EA DCA A A +A A +A /A EA EA CA A A A A A(C+AA+A/AEAEACACA(CA

"AEEEFAAACAA(AAEA(EAAAAFCAAAOADEAAA.(AEAAD(EAAEECAAAAAAEAACEAAEECAEAACADDACA8A A CA A EA CA EA A EC+A A EECA A CA A CAECCA 3.64A A ECA A A CA E(A A CA EA EA CA CACEA)AEADECAAECADACAEEAAEACACAAECACACAACEAE(AACAAFEAADECAT!$8UA&EAEAEAADCA#AEEEFCAA(AACEAACAA(CA3EACADEAAAEACAAECAEAACE4A6E+AA(AAEAAAECA(EAAADCEAAECADCCAAD(EAAADEAEAEA CA CA A AA *ACA EA A A EA EACA EA CA A A EA A A CA A EA CA A ((ACACACAACAADACAEA(FCA:C>A

5FA:C>A,AEACAAECACACACAACEAA(ADEAEA

TB*$HGUA

.+A A DEEA A CA A A DCA EA A D(EA CA A AA A (A A DEA DEA EA DEA 3(A A /A(FCA :CEE44A CA EA 3(A A /A (FCA :CE4A A CA A (EACAEAECADEAADEAAEAAEACACAAE;A(EAEACAECA(CAEEAACADDACAA

AAAAAAAAAAAAAAAAAAAAAAAAAE4AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA4A

5FA:CEA,A9CAECAACAA(AE4AAA4AATB:%@JUA

8(+A CA A A A EA CA (CA A ECA +A A CA A(A A ((A CA EDDA D(EA WA CA #A ECA A ADA "A DEEFEDA CEA A A A EA DA A ((A CA A(AA

>, FAAFA

"A DA A (A CA DA EA A ((A CA A(EA CA A EA DCA A A (CA A EDDA A CA A RA(AASA,AA(CAEDCAAEAAEAAEAACAADEA6E+ACAAACAEEAAE+AAAADAAEACAAEC+AADEACCACADA(EEADCC+AEACAA(FCE+A((AD(ACADEAADEAAADCACAAEAAAD(ADCAADECACA(CAAECA.A EDDA A EA CA A (EA A A DCCA A A D(A DCA ADECA A EA ECA EA A A A EA C(EA EFA A EA CA <CADAADAE+AACAA(AAA((ACA((AEFA A A "EA (FCA :CIA DA A A FECA CA ((A EFA(A DCA ((A (CA EDCA CA DCA #A CA EA A A A(AAAECACA(A/AEAAEAEFAADEAA

5FA:CIA,A*((AEFADCA((A(CAEDCAA(AA((A

AAE(AAEAECAT%)&HAUA

:AADEAAAC+AEAAEACA(A+AA(CAEDCAA#A CA CA A A A CA (CA A CA EDA CA DCCA EA AAAD(EACAAA(A"A(CA(CEAAAFEA A DCA CA DCCA DCA A CA A DDA C+A A ACADEAEAAEECAEACAAAAEAEAAAA(AADEACATB:%@EUAA

"A (A A A DEA CA DCA #A EA DEA A ADEA EA A (CA C+A DEA A DEEA EA C(EA A DEA CA DEAEECAEAACAEA(EAEAADEA*ECAAACADCA #A EA EA CA EA EFA A DEA CA (CA CA 8A EA A EADAAAAFCAACAOAECAAAA(ADEAEDDAECACA DCA E+A A A EA A DA A (A A ACCAAEAAEAAEACA

• (AADEAA

"A(ADEAAAADFAACAADEACAEAA(CACA/AAFEACA(CA(CEATB:%@EUA&CA(FCEADCA#A CA /A (A DEA A DE(A CA E(A 3(FCA :CJ4A &EA A EA AADE+A ADEAA(AEACA`aADAA(CAEA CAAEFAA((CADEAAECA&EAAEAAAE+AA(CAAAACACAEACADDAA

AAAAAAAAAE4AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA4A

5FA:CJA,A9CAECACA(ADEAAE4ADE(AA4AE(AA

&ACACAAAAE(A(A AD(EAAA CAA(A/AAACEAAEAAECACA(AEAAEAEFAADEA T28@H+A :6*@HUA "A EA CA (A DE(A DEA A A (CA CCACAAEDEFACAEFAADEACA(CACA/AEAAEACAA(CAAECAECF+AEADECAAEADCAECFAAEDACAEAAEAEA EFA A DEA .A (CA A ECA +A EA DECA A EA DCA A EAF(EAAADEAEDDAECAEAEAEFAADEAT%)&@CUAA

.A DEA EEEFA A EA A DEA DCA CA DEA EA DCA A A (CAEDC+A EA CA A (A DEA A DA DCCA DA EADEACAEAC(EAEFACA&ADC+AEAECADEAADAAAEAADAA(ECADEACAAA<EAEC+AA(CA(CEAAAA6E+AA CAA(AEA#AADCADCCAA((A EFA A A DCA #A CA A A (A CA A CA3DAF4A.AADAEDDEAAADAA(AACCAA(AADEACA6CADCAAACA"8%A3DCA"CA8EDCEA%C4AA:2%ATB:%@IUACEAA ADEAACACA(CA(CEA5*,KCA.AAEDDAAEAADAA(ACACADEA>HHVA TB:%@JUA 8A ((+A EDA EA EC+A A CA A (A A ADCAEAADCADDADCCAADAAAAFCAAACA A DA EA A A A A EA 8(+A A CA ECAEAACEACA(AADEAAAACDECA*.-,CAT*.UA.AAEAA(ACA(CA(CE+AAEAAAEADAA(A CA DA >&A DA A DCCA CA DA &EA A D+A EADCEADADEACAC+ADAAGACAD+AAFEAAJHHVATAB:%@JUAA

• (AADEAA

"ADDACA(ADEAAADACAEA(FCA:CKA)ADECAA(AADEAA,,AAEAC(EAA(A3EADCAEAAE4A"A(AAAEAA(CAEEAADEAEAEAC(EAAEADCA:AAAA+AFA(A

3(FCA:CK4ACAA(+AECAEEAAEEEFA,,AAEDDEA(EA"AAFAAAFEA ADCACADCCAA((AEFACAADCAACAEAAEAAAAT7.@I+A!'6AAUAA

puce EF

5FA:CKA,A9CAECACA(ADEAAFA(A

"EA DDCEA A CA A (A DEA A DA CA (EA CA DAAA((AEFAADCAA3AAAVQCQZAACEAAEC4ACAEAAEACA(ADEAA6E+ADCAEAAAECACA((AEFAAACA(CAA#AADEA<CACAEACAEA DA DA CA DA A (A A CA A DCEA DEA ADEEA EA DEA &E(A BA <0A T&.6UA "CA C+A EDDA B0A<0A T'"8HJU+A A A (A A ECA ECA CA CA A A A ,CCA A A A DCA A (CA ECA ECA A EA A CA CA 3(FCA :CG4A8CAA(CAAEAACAAEEACAEAADAAAEC((AAAAAFEAADECAAFACACA:ACACADECACACAECCDADCAFADEAEAECA CAAA (AAADECAAECADEADA

AAAAAAAAAE4AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA4A

5FA:CGA,A*DAB0A<0AE4AADEEAEAACACAA4AEECACCAT'"8HJUA

A&EAAEACAB0A<0AA(AECAECACACADACEAAECA A (CA EDCA "A DA B0A <0A DA A A ((AEFAAACIHHVQCZAACADAA(ACACAADCE+AAEAEE+ADEA ADVA EA DCA EA A A EA A ECA A #A A AHQA1A %EEA A AEFA CA A (CA EDCA A CA CA CA EA A DDA CA AA CA A A EC+A A A EA #A A DCA DEA DCA EA A((AEFAC((EA"ADAB0A<0ADAECAEAA(EADA

AEFAAEACACA(CAEAADADEA3(FCA:CG44A.ADCACAAAJQAADAAEFAACAAAAID<EAA

• (AADEAEECA

"A DA A (A DEA EECA A DEA CECA A A CACACAADACAAEA&ACAAADACACA(E+ADCACAARAFASADAAEADCA/ACAAAAEECAFAEACADECA A EC+A ECA ECA A EA A CA A EA EA A CEA &2*A TB*$HGUA"#A A A DA A (A A A FEA DCCA DA A A EA(ACAFEAC(EAEFAACA((AEFAA*DEAEAADCA#AEACECAAADAAEFAC+AAFE+AAA"EAEADCAEAACAAEAECCAAEECAA(EAA AFACAAAFEAEEA"ADCAEFCAAEECAAAC+ACACAAEE+AA((AEFAAADDAECAEAECCACAEEA,AAAACADCAAEEAA(+ADCAA((AEFAAFEAEADCAADAAEFAAAECA

"A CA A (A A DEA EECA A A EA A EECAA A (EA EA A DCA CA 3A EECA EECA ,A EA A ADEEACADEAAEA4ACACACADECADEAACACAACAEDDAA(EA EA A DCA 3(FCA :C@4A 8A DA A CA EA EA CA DEAEDDAECACAECATZ)%HKUA

5FA:C@A,A9CAECACA(AADEAEECA

!CDEA A <EA T!)*GAUA A A A DA A A #A CA (AADEAEECADEAAEAGHA<CAEAAAEACAEFCAAACAACADAADCCAEECAADEEAAIHdAAEFC+AA>HHdAAECCAA A IHdA A EA A A EECA 8A CEA A ECA A (CA EDC+A AEFCA EA EDEA ECA A A A (CA A ECA A K@HVQCA EA CAcHH@_*CQVA A CA DA A CA EA A EA DECA CA DEACAAKA_*ADEAEDDAA EADECAAAECA"AAAECAEADCAEAACEAEAAHI"QAAADAAEFACACAED<EAA

.CA EEA 7C8E+A #A CA (CA RACA CASA EA A CA DEA AEECA A A A *A <A T<8HAUA "A DA A A CA EA A EAEEAAEECACACACDDAACACAEACADAA(EAEACADEACA)A(ACAAACAAEAAADEAAA(CA E(A A EA EA CA A EA ECA EA CA A (CAEDCA)AADDAEAAAEAEAAEECAEFCEAAEFCA@Hd+AD(CA>AIdAADEAAGHd+AAAAKAEECAEACACACDDAACA A CCC+A A FCCA A EECA A CA "EA EEEA DECA A A(CA EA A EA DA A DA CCLA CEHVQCA EA CA

cHCIZCQV+AACAEAAEADECACADEAAJH_*ADEAEDDAAEADECAAA ECA<CAEAA AD(EA AAA ECAEAEAAAC"QAAADAAEFACAEEAACHD<EA

"A ,(CA CA CA D+A A CA EA A +AAA(EACA3ECAACC4ACAACAECAEAA CA A DCEA A EA AE((EA A DA A (EFCA CA )A ECAEEEFAA,(CAACAACAAADCAFACAAEFCAACA )A ,(CA A CA DA EA EEA A EECA EA A ACA 3EFC+A D(C4A A CA DA A EA ECFA EA C(EAEFAAADEACAA A(CAEDCA"EAEEAAEECAA(ADAAA((AEFAAAEAADAAEFAEAAEAA ECA A FFEA A CA DCA CEA CA DDA EA CA DADEA )A ECA DA EA A (A DEA EECA EECA A CA EADECA A FACACEAACACA A FACACAADEAC(A T$8!HAUA"A EECA EECA A A FEA FA A A (CA CEA A EA A EECA FA EA ADAAAEC((AACAAAFEAADECAAFACACEACACACA

6CA EA DA EA A DEEFEDA DA A A A DA A DA AEACAE(AAFEEAA(ADEAADEACA.CCCA CA DCA FCA A A A A A A CCA ADEA,CC+ACAACAA ACCAA(CAACAAEC+A EA A A CA EC+A DEA CA DEA A ECA DEACAACAC(EAAEACA(A'+AACAEDDACDAAEA DA DCQDEDEFQ(CA DEA CA FEA DEA A A A AFE+A A D(EA C+A A DA EFCA A A(A .A CA DDA A A A ECA A CA A (AECAA

<CA E+A A EDDA A A EA CA CDEFA A A ;A A CAEC+AADAAEACAAAC(EALEFAC <CAE+ACAEA (EA A A A A DEA CA A A EA A A CA A EA DCA A A(CAEDCAEAFEAAEEACA EACCA#AA EADCADCAEAA(AAEAEA(EAEAADA8AEADAAEAAEACADEAACAA,(ADAD+ACADDAFAA(CAAEAEA;AEACADEAAACAEA((AAEECA*ADAADAEAADEEFEDACEA

/E "C F FAA FCA E AC :!)E<

"ACAA(AAEDDAA(AAEACAAEAEACAEACAAA(A6E+ADCAD(AAAEEEFAA(ECAEDA A A CA A CA CA "A CA A DCA DCAEA A (A DEA A A DEA EEC+A CA CA DEEA A CA EA A((CADEA"AA9E(A T"88@@UA:AACAC+ADCA ADA+AAA AEECACADAAAAA (CAAECA ADCA+A#AACA EA DEEA A A CA CA A DEA EA DA DCCA A(EEA((A&EAAEAACA(ADEA+ACAADEAAEA DCA EAA ((A EFA A DEA A A DA A EFAA(EA&EAAEAAEEC+AADAAEFAAAFEA#ADCACA(EA

A&ADC+AACAEAADCAEC+AEADECAADEAFACACAA

"ADACA(CAFACCAEADADEAEACADAACDACA A DA D(A A CA A (A A DA /A (EA EAC+A FEA C(EA EF+A ((A EFA A EA A (A DCA CA A(E+A(EADAAEFAACADECACA,CCAFA

"A DA EA DCA A (A A DEA A DCEA CA CADDA A A EA EA A DCCA EECA DDCEA ECA DEA A EAA <6A CA ,CCA A DCEA A CCA EA :A A EA FAA EA EA ;A EA CA DEA A DCE+A ECA DCA DA A FA WA ADAADA6CAEAEDDAADA&:%A*A3DCA&(AFA:FEA%AEA*4A"EA(FCA:>HAACACAECACADAADEACAA<:6AADA

material

material)CE

5FA:>HA,A9CAECACA(CAFA3&:%A*4AEAEA;AEACA

"AEECAAAEACADCAADEEFACA(CACAEDCACA EA EA ECA A EA EDA CCLA CA EFCA EA EEA "A EECAECAACA A (EA FCCAFEAA DECACACEAACA3AIHdAAIHHd4AACADAEAADAAEFAADCA(EACAEAAEAAEECAEECA DA EA EA DEA DA<EAEC+A A EECAEA DA ((ACA FEA C(EA EFA "A (EA EA ECCA CA A DA A EAA CAA EA (EA FCCAAEECA 3CADAA(AA((AAAAFCCAEAC4AAA(ECADEADCAEAA((AEFA A A 3DCA CA AHHHHVQCQZA EA A EA EECA EEA A EAECCA A IHd4A *A CA A +A CA ECA (A A A DA A EACA FA A EA DECA EA A DEA CA A OA A EA DEAFAAEECAAAEACACAACACA8(+ACAEEEFADDEACADA&:%A*AAACDAAACAACAACA (EA DEA A ECA CA 3CDEFA CA DA *8%A ,A C+ADEA A EA CA DEA A EDA C4A .+A ADEA EA &:%A *A DCA (A A CA A DA A EA >&A A((EA CA CA DCA EA FA CA A DCCA DEA A A A EA CA(FCEA*D,,*DA3(FCA:>A4A

Metal2)CE

5FA:>AA,A.DDEACADA&:%A*ADCAAA<:6AEACAEEFAAAA

*D,,*DA

6E+A A DCA A CA A EEEF+A A DA &:%A *A CA DCCAEADAA?AEADAAEACAADDAAEADCAADCEAAEACACACEA,AEAAAEAAEEAECE+AA((ACAEAACACEACAAEACAAEAC(EAEAADE+AA((ACAEACAA A A A CEA A (CA CA A LCA A EA ECA ECA CA DEA A+A A A CA CA (CA CA &EA A DEEFEDA CE+A CA EAEEADCAAEAECAAADA

1 /FACFAACC"!)E

.(ACA EDDEACADA&:%A*ACAEADAADACAAADCEAACCAEA3(FCA:>C4A

CC$ :"CEF A<

ACEE ACAAA

CAA A"CEAAFC

5FA:>CA,A9CAECAAEACCACAA<:6AEA&:%A*AA

"A DECEA CA ((A EA CCA CA DEA EA &:%A *A A EACCA CA DEA DCA A EA EEA DEA FECA D(A 3&:84A AEECAEEAEA;AEACADEA/AEAAADDCEAECADEAAEAA EA EA A CA ADEAADCE+ACAACACA E+AAALEACA"EAEEAFCAADEAEA&:%A*AEAEADCAAEA EA A EDA ::A *A FA DA EFA A EEA CDA 8A((+A A EECA DCA EA A A A A (A ((A 3DEA DA AE+A A A CA A EF4+A A EA EEA 3A IHdA A EHHdA EA ADA/A(A*EDA:94+ACAEFA((AACAA((AAEECAADEEAA

&EA CA A (FCE+A A A EA A DA A ;A A CDA DEA AEECAEEAE(AAEAEADAAEAEAAA&EACADAD+A CA EA (EA A A A EA EA DA A EA CA A DDA CA

DEA A DA CA EA (FCA :>CA &EA A E+A CA EECA ECA DCA #ADA DCA ECA CA EA CA A A CEA BA EA A A A A CA AEA DA LA DEA A E(EEA DCA A E(A A EA EC+A A E+A A E+A EAA CA EA CEA CA EA CA EA DEA T9.7AHUA &EA CA A(FCE+AAAEAECAEACAFACACEAEACAEAAAEADCADCCCAADAAEADCADCACAEAEACACEAAEA DDA .+A E(AA EA A CEA CCECA A A EA DC+A EA CA A ADAACAECADEACAACA(EACADEAA

8(+AEACAAAADEAEA&:%A*AAECADEAEACAAEA A A EA CA CA EA DA DCA NA EA A EDA "EAEA DDCAA EA A #A DA CA A EECA CA (A EAAEEEFAAEAEA3EFAADEAFAD(4AE(AAFEEACAFA ((EA CA EDA CA A (EA A EA ;A EA CA DEA A CA (CACA

, $FEFFE

"AACA(CAEDCADCAADA&:%A*AAADCAFEEAAEA(AAD(EACAAEACAA(AEAECAA(ACAADEA.A A(CAEDCAAEAAADDA,DCA3CACA+AECAECA+A(EAA4AEAECAAADDACA3FACAAADACA(E4ADCCA A (CA EA DEA A CA A EECA WA A EDA CA EA E;ADEA*ADAA#ACADCCAA(CAEAEAADEAAEAA<6ACADEA A DCE+A CA ECA ECA CCA FA A EDA CA EEA EA ADEA .C+A EA A EA A EFA A (A DEA A (A EAEFAADE+AA(CAAECAEACADACAA"EACACACA(CAAA#AECAAFEAECAEAEDDADEAA,CCAA

<EA EC+A A (CA A ECA #A CADEA EA CA A EECA EACAAEA#AAEA/AEADCAACAAACACA8(AA(CAA#AACAADCCAAA

)ADAEAA((A(CA3CAAAC4ACAEAAEDDEAA(AADEACAADAEAT%'$HJUA"AA A (CA EDCA EEA DCA CA EDDEA A (A A DCA#A((CAACEAAAA%C((AACAA(ADEAEAEACEA?A

ba ckMo

= AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA3:K4A

WA ρ TDFQ>UAAEAEACC+ k TVQYZUAAEACAC+A*DTQDFYZUA

AEAECAD(CAAdTDFQYUAEAAECACA(CA"A((AE+A+A+AAA DA CA A A E(A A ECA A A A A DEA A EADEATB:%HJUA

"EA F(EA CA A A %C((A A EA A (EA CA DCA CA FAA A DCA CA A D(+A A (CA EA A DCA FEA A A %C((A EAEAAECAAE(AAECAADCAA)ACADEEAEACAAAA%C((A E(A A A ECA E(A A E(A A ECA DCA ((A (CA EA AEADEATB:%HJUA"EA(FCA:>>AAEADEEACAECAE(AAE(AAECADCA ((A (CA A CH_*A EA A EA CA CA A EEA DADDA(FCA:>>E4AADCACACAEEAADDA(FCA:>>4A,AACACCADACAEAADAADAAEA((AA

E4AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA4A

5FA:>>A,A*DEEACAECAE(AAE(AAECADCA((A(CAACH_*+AAAAAAE4ACAAEEADADDAA4AADDATB:%HJUA

*A A DCA A A CA EA (FCA :>>+A A D(EA CA A (CACA 3EA A DA /A .E+A .DE+A *E+A B+A 5CE4A AADCA(EACAAAECA*EAAOAADECAACACACADCA(EACAE((AA((AEFA3FEAAHJVQZADCAECAADAAHAAAHCVQZADCAA(CAC4A)AEDAEADAEAEA(FCA:>>AAA EA CA EA A EA A CA EEA A D(EA CA A (CA(CE+ACAAADCACAEAAEDDEAC+AAADCA(EA.+A EA A EDDE+A A DEEMA DCA (CA CA ECA (CA CAAA*ECIADEADAA

.+ACA EAEAAACEAACA AAADCAEC+ACAEA(EA AACA A EA *EA CIA T8ggUA DCA EA A DA &:%A *A :A ADEAAACAAAADACAA*EACIADEAEDDAECAECA(CACAEEADCCAA(CA*EAEACAAECAADCA(EACAA ECA (CA CA A EA A DA A EFA CA EA A *EA A(CA EDCA A #A DCA (EA <CA CA E+A A EECA :A A CADEEAADDADCAAEC+ACA*EACIAALCAECA(CACA/A%ADEAEAEDDEA&:%A*A

TABLEAU I: COMPARISON DES PROPERTIES PHYSIQUES DE COOLANOL25R, MIDEL ET EAU

A !3_*4A *D3QDFYZ4A ρ 3DFQ>4A h3DFQQ4AH,>A D3VQQZ4A

ECA EAG>A @@G>A AA HJHCA

ECE *+? *1= + =,1

??= *.= +? =>>

ECA EAGIA @G>AA HIA HJI>A

ECE 1.. ??= 1 =1*

**> *> , =>

ECA EA@GA @KAKA HIA HJJ@A

ECE 111= ?+= 1 =1.

1=1, *1+ . =,*

*A EECA CA DA A A CA A (CA CA A CA CACA A EA (A DCA (EA CA A A ECA <EA EC+A A DCA *DA AEDDEA CA (A DCA DA DCA A (CA C+A EC((A A AAAADCA DEA CADEAEACAADEACADEACA"A(CACAAAAAA(CAEDCACAECA6CAAC(ACAADDAACEACADCAACA(CAEA"AACA*EA((CAADCAD(CADEAEDDAAEAACAAAAHA(ADCADACAACA%AADECAEEA&ADC+AAEC+AA*EAEA CA A CA EA EA DCA A (A A EA DECA .+A CEA CA*EA DA EA A DA A EFA EA CA A DA FEA CAEEFACAAA(EADECAECCDADCAEA

8AACAAADDACAA*EACI+AEAEACAACI_*A A FEA A CJA A EA FA CA A EHD9A DCA CA EA A A AC+EA6E+AADAEAECCAAEECACA&:%A*AADACAEEAF(EAAEAFACACA(CAAEADAACEADA EFAECACAAA AECA<CA CAADACADCAACACAECAT"8BHCUACAACAAEDAEAEDDEAAEFA CA A DCA EA CA CA EA 3CA EA A E(EC4ACACAEAAAAECFA3EAACCACADACACAFAAAE4AAAAEA(FCA:>EAA

&EA A E+A A DA A ECEFA A DEA #A ((A DCCAACA(EAQCAAAEDACAEAAEACA&:%A*AADADEA A ,CCA EA CA EA DEA DCA CA EA EA ECA A EA CAEDDEAAA(FCEA

0.001 0.01 0.1 1 10

Inception field Ei (MV/cm)

Radius of curvature rp (mm)

positivestreamers

negativestreamers

5FA:>EA/A*EDAEAEDDEAAEFADA3AE4AAFEA3A4AA(ACAEAACCAAAADEEAT"8BHCUA

*A A DCA A A CA EA (FCA :>E+A CA A A DA EA EEA ADCCA;EAADCCAEAAd+AAEDAAECEFAEAAEECACAEA#AADCCA%9QA*ACAA(EADEAACAEEADCAEDD(AEAAEAAAAEAEADCADACACAAA(CCAAEAADAACAEAAECEF+ADCCAEAAEAAEADAAA(A

EADEACAED+AEACAEAAEAAEA(FCA:>EACAACAEAC+AA EA FA A A 3A C4A DCA EA DA A EFA DEA 3ADEAFEAAEAC4ACA(AAEDA

> &CE%AFACAFAACAC"!)E

.(AADCADEAADAAD(EAADEAEA&:%A*+ADCCADDA((AAAEFA"AAA(AAEECAFAECAACADEAADCEAEAA(EAAEFEA((A(AFC+AAAECACDEA?A

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&EA A EA A A EA (CA F+A EDA A &:8A EA CA A A EA (ADCAAAEAEAADCAEAAEECAEEACADECACACEA<CAAEAEAFECAD(AEAAAACAEDA/ACADAAFECACACAAC(EADCAEAAEAEAADCAAEAFECAAEECAACACADEAAFECACACEAA(EAEACCLAAAEECAEEA8AACAAEAAFCAAAECAAFECACACAADAACEADACAAAEAEEAAAEAEAAEAD(AACAEACAEA#AAAFECAEACCAECA CA A ECCA *DEA EA FECA A CA EEA A EA E;AEFEA CA DA A CA DEA FCA A A DEA A(A A CDA A &:8A *A DEEFEDA A A A ECA DA AFECA D(A CA CA A CA A EA EEA A CA EEA CA DECA CA0E(AAACACACAEAEDDADCAEAA(A

"A DA DA ECCA CA CA A (A EEA DCA FA EA FECACEA A (A EA CA A FEA ((A A EA *A CA EA AA A DA CA A ECA DEA A (A A FECA EEA A IHdACCAEHHdA"EAAAFECAEADCAADCAADCAFEA(AAAAEECAEEAACEAACACAEAAC(A"A(FCA::AKAA::AGADA A CA DEA A D(CA A A A A FECA &:8A A(AACCAA(AAFEA*AADCAAACAEA(FCA::AKAEIAAFECACAAEAEAACAACEAACA3ICHd4ADCAA(AAEHHdAEACECA#AA A(AAIHdAAEACCAD(CAA>CHdA<EAEC+AEAAAFECAADEAEACAECAFAAEAFEC+AAADCAAECACAACADCAEAD(CAA(AECF+AAAAEA(FCA::AJAACAA(EADEAEACACADAC(AAEAFECACACAACEA

10 20 30 40100

temps(min)

v_rec4004000 x(

v_rec2002000 x(

v_rec1001000 x(

v_rec50500 x( )

v_carre1000 x( )

v_carre400 x( )

v_carre100 x( )

v_carre50 x( )

v_cercle200 x( )

v_cercle50 x( )

v_rec4004000 x(

v_rec2002000 x(

v_rec1001000 x(

v_rec50500 x( )

v_carre1000 x( )

v_carre400 x( )

v_carre100 x( )

v_carre50 x( )

v_cercle200 x( )

v_cercle50 x( )

CE1==$1===;

CE>==$>===;

CE==$===;CE=$==;

C ===;C >==;C ==;C =;

E =;E 1==;

10 20 30 40100

temps(min)

v_rec4004000 x(

v_rec2002000 x(

v_rec1001000 x(

v_rec50500 x( )

v_carre1000 x( )

v_carre400 x( )

v_carre100 x( )

v_carre50 x( )

v_cercle200 x( )

v_cercle50 x( )

v_rec4004000 x(

v_rec2002000 x(

v_rec1001000 x(

v_rec50500 x( )

v_carre1000 x( )

v_carre400 x( )

v_carre100 x( )

v_carre50 x( )

v_cercle200 x( )

v_cercle50 x( )

CE1==$1===;

CE>==$>===;

CE==$===;CE=$==;

C ===;C >==;C ==;C =;

E =;E 1==;

5F::AK,A<(CAAEAFECA&:8AA(ACADADCA((AEAA(AAFEAA

10 20 30 40 50 606

14Vitesse de gravure

temps(min)

v_rec4004000 x(

v_rec2002000 x(

v_rec1001000 x(

v_rec50500 x( )

v_carre1000 x( )

v_carre400 x( )

v_carre100 x( )

v_carre50 x( )

v_cercle200 x( )

v_cercle50 x( )

10 20 30 40 50 606

14Vitesse de gravure

temps(min)

v_rec4004000 x(

v_rec2002000 x(

v_rec1001000 x(

v_rec50500 x( )

v_carre1000 x( )

v_carre400 x( )

v_carre100 x( )

v_carre50 x( )

v_cercle200 x( )

v_cercle50 x( )

CE1==$1===;

CE>==$>===;

CE==$===;

CE=$==;

C ===;C >==;C ==;C =;

E =;E 1==;

5F::AG,A9AAEAFECA&:8AA(ACADADCA((AEAA(AAFEA

:AADAEAAICHdAAD(CADCAA(AAIHdADEADCAEAA(ECA(EA(AEAEAAFDA3DCCA;EAAC4AACAEAAEAA AEA DACADAACA (AA EAEA8A((+ADEA EA&:8+A ACEAACAA#A(A 3AAH_*4ADCAFEEA AADEAACACADA<CAEAACAAAA(EAEACACEADEA CA EA (EA EEA CA A DEEA A B5JA A A *E5GA !EA CA A CEA A DEA`DaAAADEAAFECAAFEEA.AEAWAACEAAEADEACACADCCACC+AAFE;ACAEAA(EAEEAAA(EAEAAEFA+AEAAE+AA((EAAEAFECAA(EAEE+AAAA(AA(EAEAA FEEA "EA EA A EA CA A EEA A CA CA E#ADAADAACA#AACAA(AADEA(A#AFEA)AECAEAAFEAAEDEFAAEAEACAEAAEAAEC+AL,,+ACAAAEAFECAACEAARADASAAADADACAAA0E(AA

DDA.AACARAD[EFASACACEAACAAACAECAAAEAAFE;A A EA ECA A A A ECA A CA CEA DCEA EA CCLA EACAEA

"EA CA DCA CA EA FECA CA CEA A DA A A A A 0E(A ADACACAECACDDAEA<CAAEACAEA((CAEAFECAACADEAA?AEAFECAA(EAEEACCLAAAEAD(CACCADCAAEADCAAEFAAEA(EAADACACAECA0E(AACADCACAEAFECAA(EAEACCLAAAEECAEEA"AEFAACACEAACAEAA EA A EDDCEA CA (A CA A A 3EA DCA ECA #A ((CA EA ECACAAEFAAAEAADEAD4ACAA0E(AEAACDDAACA A CEA EA A A A>H_*A CA DECA EC((EA CA A CA 0E(A A AEA.DAEADEAA&:8+AACACEAADEAAEAEAAEACAEA CA EDDDA )A A EFA A C(A DEA A DCA A FECA AFCADCCAA(ACACEAEAAEAAECCDAAD(EA)ACA EA EDDEEMA ECA A A EA DEEA A CA CEA /A CA ECA ECEA(+AEAAAACACEAAACAA((AAA&EAAEAA(ECADACCA;EAACAEAAEACADCADCAEECAEAAADEAACA0E(A"EACAEECAAEAAA#AAADCAFEEACAECCA A C(EA A EA DEA E((A ECA <EA DA EA A DA EEA ACDDAAEAAACACACACAEDDARAASACADEAAEA A DEA #A DEA EA A EA DCCEEA EA A DEA A CA 0E(AECCA EA A EECA DEA A RAASA .A A EA A EA #A A EACAADCAEDDDAA

"ACEA(EAAEA&:8AACAAEAEEAADEAEA(CAFAACACAEA(FCA::A@A

!EAE*EEAEE !EAE*EEAEE

5F::A@,A:EFA%82AADDAEAEAEAAEA(CAF

, -CAA"CFACA"CEAFAFFAC"!)E

8AACAAEADEEAAAEA&:%A*AADEDEFAD(CAAECA A [CA DCA DA EA DEEA A EA EA EA ECA AEECADCCA EA AAC(EAACADAAACAA"A<*2A EA A EA DEA A CCA DEA EA DCA FEEA CA ADEEA DEA CA A EECA A EA CCECA (A CA DEDEFA )A EDAEDEA A EA CA DEDEFA DA A CEA FA A EA DEEA 3(FCA::CH4A&EACADADAADDAEADEAEAACA+AEECADEAA#ADDACACAAFAAAEA((ADACACAAECCDAACCAEAECACAADADEA"ADAADEFAEACA A A EA A CA EA CA FA A :A A A DA A CA DEA /ADEFACADEDEFAEAACAAFE;EFAEACAEDACAADCAAEA

AAA AAAAA AE4AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA4AA

5F::CH,A<ACADEDEFAAAEA&:%A*ADEAEAACAAAAAAE4(EAEEAA4A(EAEA

> EAAA"A"(A A A EDA EA A A EA (EEA FCA A A A

DCEA A EA A A EA A EA (CA FA A A DA AACAAA(EADCACAEEA6CAEAEACAADAFCACACAADAEAA(AAEEAADAEACAAAAECAA,,AAEA(AD,DACACAEADDA6CAEAAAACAAEDAD(CAAA(ADAD+AEAEAFECAD(ACAC+AEADEEAAEAAEAEEAAA*EAAACACAEA(E+AAEAFAAAEECAADEEAAEAEAEAECA DECACAEAAC(EAA ADAADNAAAE+AAAADEAAEA A D+A (EE+A DEA FCA A CA A EECA ADDAFCACEAAAAADADEA#AAADECA*DE+A A (EAEA (EAAACAEADAEACAAFEAA AA DA CA DCA A DA A A DCA DDA A EEA (CCADEAEAADAFCA

)A DA DDA DCA A (CCA EECA FCA EA EA DA ACDA A DEA CEA EA DEA &:8A 8A ((+A A A 0E(A EA ADDACAEDADFAADDAAEAEAEAEA#ADEAAAAEAEAAECA((AAAACD+ACADECACAADAEA EA EA DCA E((A A DA CA A DEA 8A A DEEFA A EAAEEAEAEAEADFA(AEDDEAAADCA)ACADA DCEA EA #A A A A A EA FEDA CA (EA A A EA &:8A DCAEA A EA CA A CA (EA CA CE+A CA A A RAEA A EASA A CADEAAD(AEACDAADEAADEEAA((A(ADEAAEACAAEEACACAAAEFA

)AECADDACADCEAEAAEAEA(EAAADDADCEA#AEFA EA DEEA A EA EA CA CA DA A EA A DA A C(EAEEAEAACA0E(AAEDADFAAEAEA

)A A DA (CCA DCA A EA EEA A CA CA DCADEAE(AAD(AEADAAEADA&CACADCA#AEFA/AEADA A A A EFA CEA A DECA EA A EA EA A CEA ACAAEACADAACADEAACAA

8(+AACAEAAECACAAAEDAEAEEAAEAEA DCA #A (EA EDDCA ECA EA %'BA EA EA EA (A9&&%'B58!AAFEEACAAEDAEFAAAECEACAEDAAFEDA

AA&:8ACDDEAA(AADAE(AADEAAEADEEADEAAEAEAA

8A A CA A EA EEA CA &:%A *A EA A EA %'BA DEA DA3(FCA::CA4AADCA EFAA DEACACA CA ACEACACACA CA A+ACEACDEACC+ADEAAEECAEEA)ADEACAECAAC(EAEAEAEAAEA

CCEC"AC ECHC"

5F::CA,A9CAECAAEAEEACADA&:%A*AEACAEA%'BA

C &CE%A "CEFC C FACAE A

AA :CABBBBBBBBBBBBBBBBBBBBBA G@ACA &BBBBBBBBBBBBBBBBBBBA @HA>A "EAADEBBBBBBBBBBBBBBBBBBBBA @JAEA <(EACAAAADCEAAEAA

AAEABBBBBBBBBBBBBBBBBBAA@GA

EAA.EACAAEACAAABBBBBBBBBBBBBB @@AECA9EEADEBBBBBBBBBBBBBBBBBBB AHIA

ECAAEEACADEDEFBBBBBBBBBBBBBBBB AHIAECCA*EEEAECBBBBBBBBBBBBBBBB AHKAEC>A*EEEAECBBBBBBBBBBBBBBBBB AAJA

5. <(EACAAAADCEAEA&:%AA*

IAA.EACAAEACAABBBBBBBBBBBBBB ACHAICA9EEADEABBBBBBBBBBBBBBBBBBB ACIA

ICAAEEACADEDEFBBBBBBBBBBBBBBBB ACIAICCA*EEEAECBBBBBBBBBBBBBBBB ACKA

JA *CBBBBBBBBBBBBBBBBBBBBBBA A>CA

*EDA:::A?A.EAAEEADECAAD(EACA

'AEACAEAADAAAAEDACAACAAEAAAEADAA,FADCCADEAADCEAACCAEAEAEA #A DCA CA A CEA A DDA EA ,,A LEDCE+A AA A >&A A A LEA A EA ECA <CA E+A A A ((A CADA DDCA CA D(A A EA A ECEFA DECA A C(EA !C(+ADCA FEEA CA CA A A DEA DCCA DEEA EA EA EAEA A#A EEA A DA*ADEA DA A EA A EA D(CA CA A EAEFCAA EA E+AA EFAEAAADEAAA EADACADEALCAA EDA A EA C(EA kCEA ECA A EA (CA F+A CA A ECAEEA A DA((A EA FEA A EECA EEA EA ;A EACAD(A/AEAAAAECCAEAEAAEACAA+AAAECACACEAA(C+AAAEAACEAALEADEEA

8AC+AAEDADAEAAAA((AAAEEACACADACAAAADCEAAEAAAEAAEA&:%A *A "A EDA A FEA CA A A CEA DECA AEEEACACADAAEAADEAACEAAAEEAA

"EEA CA CA CA EA CA A EA CA A CEA CA ACEA CCA C&A EA A FA BEA ,A CA CECA A EAAADAA(A"ACACAABEACACAEACAA.EA A .EA .EA DA A DA A DA CA A DEA ,CCAAEACAED[CACAAEADCAAAECA(ACAD(AAA(CEAECAA(EAEAAFAACE+AAEDAC+A ADACAA.E,ADAAA ADA FCACADCAEA(EEAADEA,CCAADEE+AEA((C+AE+A A FEC+A A DFEDA A A DEA A A EA EA CCADCACACACADAFCA(A"AADCACAD(AACAEA .EA DCA CA #A CA A A A DCA .EA CA EA DA AEECACA"EAEAACACAABEADAAADEAADEEAFCACA AEECACACADEA.+ADCAAAADACAEAEAACAACEACCACAADEEAEACACAEACACADCAEA(EEAAADDA<CAEAA DEA A A ECA DEEA A *EA EA DA DEA EA CA L(A ADEEAAAAFCAAEEAADDACACAEAADA EA A EDA ::A 8(A A CEA CA A CEA CCA ADEA EA A EECA DECA A DDA A EA EEA EA A DAEA A EDA ::A "EA EEA DECA DA CA CA DA (A /A EA EEEACAECAEAEEACADEDEFAD(CAAAEACACEADAEACAECAAEECAAEAEEEAECA,AEAAAFCAADEAEAACCACAADCEA"EDA(EAAEEAAD(EAAA DDA A CA A A FCA EA CA DEDEFA A DA <0A *D,,*DAT9.7AHUAAA

*AEDADAEAAAAAAADCEAJHH9ACAADEAEACA#ARACDASAEAAEAAAEAAEA(CAFA9ACAEADEAALCACAACEAA(ABEACALEDDCACA EA(AA EACCACAAADCEAACCAEA"AAACEA CCA CA CA EA DDA A A CEA A DEA A EAEA EA A EEA A D(EA CA A A EA (CAFA A DEA EA A EA A EA A DEA (A CA DA ECA

A EA A A DDA 8(A A CEA CA A CEACCAADEAEAACADECA

"ADEAADCEACACAEAAACDDAEEAAAEEAA DA A EA A A EA A CA (CA FA A EA A ADCEAACCAEA*AADEAE(AADCEAAEACCAAAAA FCA A A DCA DA /A CA A <6A EA A CA ;A ACAA+ACA;ADDCAAEAAAACAEAECA*ADEADAEEEFA#ADCA(EAEEAEACADAFCAEADAAAAFCAAAEMA 3DEAACAAEA%'B58!ACA:72!ADEAD4A:AAECAC((EADE(AAAA(ADCADCA #A A ECA A CA DA DCCA A DA DCA A AEEAACA;AA/ACAADEFADD+AA<6+AACAEACAAECADEA,CCA

"EA A A DCEA A CA DEA A EE+A A E[EFA A A EFADEA A (A A A A DEEA )A A RAEASA A A DA ECAFACEA?A

• 2ACAAAAEACA3A+ACEAA(CA(E4A

• 5EACAAAAEADEEA

• 9AACEAA

"EAEECARAEASAAEAAADACAEA(FCA:::AE4A"ACEA:&AACA CA EA A 9&A A FEA +A +A CA A CEA :&A A A CA EAAA;A8AEA EAEECAA EAAADCNAAA CACA EA(FCA :::A4A WA A DCA FCA EDDEA CA CEA A (CA :"A A EA CA A EACAAA395m6Y:&4AAEADEEA.CAACAAA92AEAADEAAEEEA

:" b4A

5F:::AA,A*EECAECALCAAE4A*EECAE+A4A*EECADCAEA

"EADAAAACAAAAEAADAAAFA A CA A A A +A A CA A A A LEA DEEA A A A ACEA8AFE+AEA;AACAAAAA(ADECAA(EADAA CA CA CA ;A (A A DCA A DEEFA CA CEA BCA ((A A EADEEA+AEAAAAFADCA#A(ACA/ACEAAEAACA((AAAADCAACADAACAEACAAAAEA DEEA *DEA EA A E+A EA EFA DA EA EA FA EA #A A ECAEFAACACEAACA(EAAACEAT"85HEUA

"EA(EAAEAAAECADEAEEAACA;AADEFADDACA (A CA A <6A "A A A CA A DCEA DA ECA CA;A CA 6,A 3;A A CA A 4A A (EA EA A A A CAFA <A A 6+A EA DCA ECA EA CA A A CA D(A "A EECADCA A A FA <6,6A A DA A (A A EECA CAA 8A DEC+A A EECA A EA ;A EA A A A(ACAEAAACADEAEACAAEECAA;A#A<AA 6A A A DCA EEA A EDA CA ECA A A EA ;A A CA AA 3A DEEA 4A EA CA DCA (EA EA DA A EA ECA A EACA3ADEEA4AAEEACAARAASAADCAEEAT"85HEUA8C+A ADEADCADACAFA(AD+AAFA CA DA LEMA LDECA EA A EA DCA DCA EA A DCA (EA AEDCACEAEA(EEAEAFEAAAEAAAFCAA

<CA E(EA A EA A EF+A A A A EA CA CA A A AJHH9A&EAAEAAAEAEAE+A EAC(EACADCAAGGCA3AEAACEAEADEAAEAC(EAEACADEAAEAEAA(ACAAA+ACACADCC+AFAEAA#ACEAACAAEAC(EAEA A EA #A ,A GGC4A EA CA EA A CEA A A A EA EA EDA&EAAEAAAEA&:%A*AEAC(EACADCAAAEAECAAAHAHCAACDADEAAEECA"ADEEFEDACEAACADAADAEACADADAAECAAEACAAAE(AAE(EAAEAAEFA3EAAAAJHH94A&EACACADACADACAEAFEAEADEEAADEADEA

• !CAAA

"EA CA A A A CA EECA A A DEA A DCEA CAA EA CCA EA A DEA A DCEA *A (A A ECA DEACAA<6ACADEEAAADACAEA(FCA:::CAA

-xp xn

electrons librestrous libres

5FCA:::CA,AA<6ADEAAA

"EAAADEAAACAEDDEACAAA9AAEAAA CA A DA CA NA <A A FE(A DEA EDDA ECA DA CA NA 6A 8A DEEAAADCAEEA/AACACANA<AAAACANA6AADCAADEA A ECA A EA A .+A EA ;A A EFA DEA 3\*84A EFA A A EDACAAFEAADCAA"AEDAEEA8EAECAECACADEAAADCA#AACEAEAEACEA3:::A4A?A

xNdqExNaqξξξξ 00

max == AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA3:::A4A

WAAAAAAAAAAAAAAAAAA np xNdxNa .. = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA3:::C4A

WAAAEAEFAEA3A+JAH,A@*4+A6EAA6ADAADEFAAFA

6,AA<+A Siξ AAEADAEACACA3AAK4+A 0ξ AAEADACAA3GGIYAH,ACA

5,A4+AAADAEADAEAD(CAAEA\*8ADDANA6AA<A

&EAAEALCAAECDAAC+AAAAECAAACA9EDADEA EA A DEA FEA CA EDA CA A FA A EA ;A A EFA LDEA3CEA:::>4AA

xak dxxEV )max( AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA3:::>4A

"EA \*8A A EEEFA EA EA FA EA CA EA DCA (EA CA AFEA (EA DA 6A "A DEFA A A D(CA A CA FA <A A 6AA #A EA A A (E[A A A A D[EFA A DEA A EA ;A AEFADEAAAC((EAADDEAEAEAFA6,AE(AADAECAD(AA`aACAAA

"EA CCA A A EA A EA A EA CA EA A A CCA LCA DEA%'BAE+ACAAEA(AFCA9&&%'B58!A.AAAAADDADAAAAECAA((ADEEAA(AEAA(A

8A A CA A EA FA <+A A (ECA EEA AEDA CAA ;AEEA A EAECACACACAECAA<6AAC(EA8AEEACADCAADEAADCEAAEDACAADCA((AACHHD9Q+ACEA:::EADA(AEAD(CAAAEAFA<AA(AE(AAAD[EFA

AAAAAAAAAAAAAAAAAAAAAAAAAAAAA 120

)( => qEcritxNa Si

x j ξξEQCAAAAAAAAAAAAAAAAAAAAAAAAAAAAA3:::E4A

A"EAD(CAAA EAFA<AA#ACDCAA EAD(CAA EA;AAEFADEADDANA<A&EAEA(A9&&%'B58!AT%:!HIUAEAD(CAEAAEAA EA A (A A C+IdA A >dA DCA A DEFA EEA A CAHAJEQ>A AAAHAKEQ>A&EDACEA:::E+AAAEACAEAAEACAAD(CACEAACAADEACAAC(EAECCDADCAACAAHACEQCAEAACA(AAAEAA(EADACAACADEEAAEA(A9&&%'B58!A3D(CAAEAFAADAEEAEAAE4A6CAEAFEA(EAAAAADEA(AAD(CAE(AAFEEAEADEAAEA(ADADACACAEADDAEAEA(A9&&%'B58!A

"FA DCA EA EA 6EA A EA FA <A A ECA EA EEA CA AEA CA A C(EA CA DEA &A EECA EA EA A CA EA A(A CA DEFA DA A A CA EA EA A EA FA <A A #ADAAAAHAGEQ>AAIAHAGEQ>ADCAEACAAEACA"ADEFAAC(EA A EA FA <A EA A EA EA 6EcIAHAGEQ>A *A 6m+A A DCA CA CAEEA EA E+A A (+A EA CA DEFA DCA A DCA ECA EA CEA CA EACAEAAEAAC(EAALAAIAHA@EQ>A

8A A CA A DEA A EA FA 6,+A A DECA A EA EA A(AA EA AAECEFAA"EA A<6ADEAA ADACAEA(FCA:::ACADAAEACAAECDAACA/AECDADCAFAEAEEACCAADEFAACANAAEAAAACADCAFACAEA \*8A A A EA EA FA (EA DA CCLA ECEA CA EDACA EA A #A FA 3DECA A EA ;A A EFA DEA EA (CA ADECA A EA FA 6,4A *DEA DCA A DEA A DCEA 3A CA A %'B+AL:72!+A A EA DE+A EA A <:6A 4+A A DA EA ;A A CA A A ACEA CA A ECDA CA T.6GC+A "85HEUA *LA CA FA (A DA36m4+A A EDA EA FA 36,4A A CA DA A CA DECA A EA FA 6,A ADEAA EA;AAEFADEAAAAAFAADEAEA EA;A6mA WA A EDA CA A EA A ;A CA CA A CA EA CA (EA A EA (AEA"EA(FCA:::>ADADEAAEA;AACAAAEACAECAAKI]A

-xp xn

electrons librestrous libres

5FCA:::>A,AACA<6,6mADEAAA

"DECADAA EA;AACAAAV6,AEAAEADCA#AACEACEA:::IA?A

W4maxmax -N

EEVBR AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA3:::I4A

"DECAV6,AAFEAAIHdAADEA92cJHH9+AA8EcCHHD9QA

"EA EA 6cCAHAEEQ>A A EA ;A A CA A A A ECA EDA EAEA:::JA?A

−=− NSi

WqNdEEξξ .4

maxmax0

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA3:::J4A

8EAAAECADCAAACA<m+6,+6m+ALDECAEACADEAADCEAADA(EADCAA(EAEAAAFCA.C+AA0E(AACACACAEACADCAEA(EEAAADDAEEACADECAEAAIHHdADEFA 6mA A AHCHEQ>A EA CA CA DEA (EA DA 6,A A CAHAEEQ>ADECA IHdA *A A FCA CA EA A DA DEA A DA A EMAFCAACAD+ALEAAEAA(AADAEAEAAEAALEA<EAEC+AALAACAADADCADEAAAEE+ALEDDADCQCDE+ADACAADEEFALCAACACA(EAFEA((AACAECABAAACADCA#AEC+AAAACAAEECACAFAA(EACADCAD(AADAAA

• 8EADEEA

"EAA<6AADEAAACAEDDEACAAA9AAEAAACA ADACANA<AAD(ADEA EDDAECADACANA6A8ADEEA+AAEDACAAADECAA\*8AECAECAAADEAALECAADEAAEAACAAEADCAA<mQ6,AA6mQ6,AAECCDAADEACA

EAADEE+AACA(EAEA((CAADCAEEAAEAADEAAA

"EA FA <A A A CA A FEA A EA EA FA EA 6,A EA CA EAFA6mAAAAAFEAAEAEA#A;A)A(A(EAEA;AACAAAADCAEEACAA<AEAAEACADCAEAEAEAFA6,AQCA6mAWAAAAADCAADCAEAAA&AEA#AE+A A A EEA CA NA 6mA A EA EA EA FA WA A A A+ADCACAEAEAEA;A<AAEACADCAEA&CEAA DEC+A A A A A DCA A DCA EA A CA CA ((CA FEA EA EAFA 6,A CA CA A DA A CEA EA EA FA <mA :A A CA A CEA A((CAADCAXEXADEADCACADEACACEAACAEAEA A A CA DA CA ECA A DEE+A CA CEA A EFA A A EA FCCA A((CAADCAAEDACEA:::KAA

τ.DL = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA3:::K4A

WA "A A EA FCCA A ((C+A &A A A ((A A ((CA A nA A EA CA A A ADCA

<CA AAADCE+A ACEAA((CAADADEAACEAACACADCACAACEAAEFADEACACA(EACAAA 8A ((+A A A EA A A CA A EA +A A CA A A A AA A XDXA A FEA A EA EA ;A A CA A A A CA EA ACA A EA (EA CA EA A A A ;A /A DA ACEA A EA A CA DA A CAEA EA CA A A A EADEEAADEADEA"EAAAEA;A6,AEACEAAEAA

A cmN .21Ω=−ρ AEDACEA:::GAA

nN Ndq µ

1=− AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA3:::G4A

WA A A EA EFA EA 3A+JAH,A@*4+A 6A A DEFA A EA FA 6,A 3CAHAEEQ>4A A

nµ AEAAAA3AEIHCQ9ADCAA(EAEAADE4A

&EAAEAWAAAEACEAAAA cmN .3.3 Ω=−ρ DCCAEAAE?A

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=− ..1

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA3:::@4A

WAA(AHAAEAEFACCAADCAAACAAAEACA

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AACA3EIHCQ9ADCAA(EAEAADE4A

&CADAACAAEACAAAA+AEACEAAEAAEACA#AADEA*DE+ADCAE+AA(ECAAAEAAACAEDDAAEFAAACAEFAAAEFADAEAEA;AACAAAACAAA(EADEAEEA A A EA EDA A EA A <CA FA A D+A A A ACA DCA NA A QCA EA CAA A A DCA A EA T.6@K+A"85HEUA "A DCA A DEA DEA A C(A EA A CA A ADAAAEACAAAAAAEAAACEACADEA"AEECA A EA CCA ,CA A DCEA #A DA ECA ECA ACE+ACAAADEAEEEFAEAEADEAAEADEAECAADEAADCEADEAA

, C3EC

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Vka (V)

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&EAAE+ACAADEAEDAFA(AEAAEAAEFAA A A CA A A A JHH9A *DEA A CEA A EA CA AAAADAAAE;A((A/AAJHH9ACAAAEACACEAA(CAA>d.+AEACAAEHd.AAACAAACHHd.A&EDAT<.H>UAFAA A CEA A (CA DCA A A A ECA EA DE(EA A DEA A EA EAEA 3CAECADAAFECA&:84AECAECAA EA AECFCAAC(EACAACADAEAAEA!C(+AEAAEACAACAEAEAEADCADEACAAAFAAA((AADACAAAAA(EA CA CA DEEA EA A EA EA CA EDA A DFA A CA ECFAA EA DA CA DNA A DECA A DCA EA A EA EA "EA(FCA :::CEA DA CA ECA EA A EEEA A EA CA A A CA DCACAEAEAEAEAA

0,0E+00

5,0E-06

1,0E-05

1,5E-05

2,0E-05

2,5E-05

3,0E-05

3,5E-05

4,0E-05

0 200 400 600 800

Vak (V)

prototype1prototype2prototype3prototype4prototype2prototype6

Vka (V)

5FA:::CEA/A*EECAAACADCACA3DDAAAAAJ4AEAEAAAEA

&EAAEADACAEA(FCA:::CIACAEAAJAD(AEFAEAAA ECEFA EA A JHH9A EA CA CEA A (CA A (A A (CA A Ed.A A JHH9AADACAEA(FCA:::CIAA

1,0E-06

1,0E-05

1,0E-040 200 400 600 800

Vak (V)

prototype1prototype2prototype3prototype4prototype5prototype6

Vka (V)

A5FA:::CIA/A*CEAA(CAAEADCACA3DDAAAAAJ4AAEAEAA

*A CEA A A (A A DA CA A A A DECA A DCADAEEAEADEEAAEACAAAFACAFEACEAA(CAAAEA((A A EECA A CA A A EA A EA DCCA CA A DDAA EA EEEA EA A DA EA A DEEFEDA A CA A #A DAFCA A ECCA EA A DEA A EA A A ((A A DEEA A EAADAAC(EAAD(AADEAAEAEEAEAAADDAAEAEAEAA

• CCACAECACF

8A A CA A EA EEEA A A A A EA EA EADCCACAACAAECAA((CAE(AACACAAAAA6ADACACADACAADAACAADACAEAEAAADACA(EACAEACAADCADEAAFAAC(EAAADEACAA(EAEEDAAADA6CAEAAEAEAADEDEFAE(ADA EACACACEAEA AD(AAECAA ADCADA EACAACEAA(AEAAACACEADAA

"EA (FCA :::CJA A CA A A CA CEA A EEEA CA A CAEA EA A A EA "A DEDEFA 3EA E(A A (EA EA A DCCAFAA(EAEE4ACADDAAACADACAEA(FCA:::AEA

0 0,2 0,4 0,6 0,8 1 1,2 1,4

Vak (V)

5FA:::CJA/A*EECAAACAACAEAEAAAEA

"EAEACEAA+ADACAEA(FCA:::CK+AAAAAHAlAACAACACEAE(EEA#AALADCEA#AAALEAAEADEEAACACEAA

0 0.2 0.4 0.6 0.8 1 1.2 1.410

Vak [V]

5FA:::CKA/AEACEAAA

"EA(FCA:::CGADAAEECAAAACEAAEAEAEACA"ADAAAACEAAAEEADEACAEEAA EAEACEAAHAKlAAHC>lA

0 0,5 1 1,5 2

Vak (V)

(A) prototype1

prototype2prototype3prototype4

5FA:::CGA/A*EECAAAACEAAEACAEAEAAAEA

!C(+ACAAACAEAEAEA AEECAAAAAADEADEAAAFA*EAAACAEA(FCA:::C@A

0 0,5 1 1,5 2 2,5 3 3,5 4

Vak (V)

prototype1-grand rondprototype2-grand carreprototype3-grand carreprototype4-petit rond 1/4prototype5-petit carre1/4prototype6-petit carre 1/9prototype7-petit carre 1/16prototype8-petit carre 1/9prototype9-petit carre 1/16

5FA:::C@A/A*EECAAAADCCAAEAEAAAEA

*AEA(FCA:::C@AAD+AEAEAEA3DDAJAAK4AEAEAAEADEEA A A CA A DCA A AlA .CA A CEA A CA A DEA ADEAAEAEAAACEAEAC(EAEAAA3ADDAA+CAA>AACAC(EAAGGC+AADDAEAAIAACAC(EAAEECA+AADDAJAAGAACAC(EAACJCJC+AADDAKAA@AACAC(EAACCCAA4A*ACEACAAEAACDDACAEA((AEACAEECAEACAAACAEACAADE(EAAA,CCAAEAEE+AAACAECEACEAAEACAAC(E+AAAEA(EADAAEAAACACACA((CAA

6CAEACAEAEAEAEACEACAEACAA((CEACACAAECCAAEADECA3EHH_*4A8A((+ACAC(EAACACAACD(AAEDA"AAEAEE+AECCAEAACAEAAECEACEAEAABAACEAACAACAAACA

*DE+ACAAACADCAEACA((ADEAACAAECCAA #A ((CA EA CA EDA CA /A A 5FA FE;A EA CA EFAFA AH]A A E;A @H]A !C(+A DEA ECA CDA D(CA A A A+ACAEA((CAACAAECCAEACA(CACAEDAE;A<CAA E+A EEA CA EA CA CA ECA CA A ECCA EA DEA A ACEAEAAEAAAA)A(EAEEAAEADEEA;ACACCA DDA EA DCA #A A &A EA DEA A A EECA DCAEDD(AA#A((CAEAA(CCAE(AADCADADEACAAEECAADEACAECACAAECCAA

"EA(FCA:::>HADA AEECAAACAACA34AEEAAEDAACAECCA

0 0,5 1 1,5

Vak (V)

avec recuit Alsans recuit Al

5FA:::>HA/A*EECAAACAACAEEAAEDAACAAECCA

6A A EA DCA EA A EECA A A A A EAEA A AEA EA A A AA EA CA CECA DEDEFA DCAA DEA CA CA DEA LFA EA CA CA CEA EA ECA((CACACADCADA"EAEECAAACAACAAEAC(EAEAAAEAECA 3DDA(FCA:::AI4AADACA EA(FCA:::>AA,CA)ACEAAEH.AEACACAAAAA9AEADCA#ACAEAA(FCEA"EAEA CEA A EA A EA A HHAlA *A CEA DA DA A AE+ACADEAAAEACEAAD(A(ECAEAECAEACAACACACAEACA

0 0,5 1 1,5Vak (V)

5FA:::>AA/A*EECAAACAACAEAEAAAEA

6E+A A A DCA A A CA EA (FCA :::>AA ECA CA CA EA ECA ACEA3EH.4AEAEECAAAA(AFEA&AACDDEAA DCA EDD(A A #A A E(A (A EA EA A A DA AECA CA EA DEA ECA CA ECEA DA ECA <EA ECA ADAEAAEAAA+ACAEADEADCACAADADCAAEAAAEEAAADCCAEAA(CCA

>1, CCACF%C

"EA EEEA ECA A A EA EA A A EA EEA CA(ADDECA?A

• EA EA EDEA A EFA ECA CA A EA EA A AEAAECAADACACA9QAA

• ECA A DA ECA A DCA CA CA DEEFA A #ACEA A C+A A A A A CA A ECA EA EA CA AEA A AE+AA ((CEA CA AA FCA EACA CCAEAA

<CA EA EA CA A A A A EA EA A A E+A CA AAAEEEADEACAAAFCAEACACAADCEAADAECAA"(AAAAEAAEAAEACA9QAAADEAEACAACEACACAEAEACAEAAACACDCAE(AEAACA <CA E+A EA A EA EA EA EA A A A EDEEAEA CDCA DDEA 3CA EA %'B58!4A A A EA A A EA A #A(A LA A A CA A EA "EA (FCA :::>CA A CA DA CA EFADEA

)K/C(B

F)K/C(B

5FA:::>CA/A&AEAEAAAEAXXADEAEAAECAACA%'B58!ALCAECAA

"(A A A A EA ECA A EA A EA EA EA EA EDEA AEAEAECAACEAAEAEDEAAEFACAEAADCEA"EA(FCA:::>>ADA ACEACAAEA CAAA39ED4AACACEA3:ED4AAEAEAACAAA

VAK=300V

IAK=0A

VAK=446V

IAK=0A

100 ns

E4 AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA4A

5FA:::>>A/A*EECAECAAEAAEAEAEAE4A:.ZA3CH.Q4ACEAA9.ZA3AHH9Q4AAECAAAEA+A4A;AACCA

EA9QcEIH9QEHcAA+CID9QhA

BCA A CEA $5A A DEA A DA ECA EDE(A A EA ADCA #A A CA EA (FCA :::>>A DCC+A EA A (FCE+A ECCA CEA ADCEA A DCA CA A EA EA A CA A "EA A EA A CA ADADEAAAAD9QdA39Q4A

"EDA CEA A EEA DECA CA DA A A EA EA EAADCADAACACAFAEAA#ACEAACA<CA EA CA EA EFA CA A A FCA EA CA CA CA ADCEA A DA ECA DEEA EA *A EEA A DEA DCCA ACAEA[CADCAADEACHH9AEACA(CAAAHHD$;AEAAC(A A CEA EA DCA A (A A DCCA A FA EA A#A CEA "EA DFA A DA A CA A CEA A A

CEA"AEAAEADACACAEAADACAEA(FCA:::>EA*A DDA A EA DEEFEA CA FA LFEA DDA ECAEEA7C8"E+AAADCACAAAAAFACEAEAAA!ABA TB:%AAUA <CA (E+A A CCA (CA EA DEA !A BA DCA DADCAEAAA(AAA

100V DC

Monolithic integration of 3 diodeswith vertical voltage terminations

CE FA,FFA

)K/C(B !FAF

"A EACE

"A ECC

"A ECCF

FA)K/C(B

5FA:::>EA/A*CA2AEAE4AE+A4ADACACA

"EA(FCACEAAA(ACACACAEAAAEACADADA EA A A CA A 8A A EA A 9&BA ECA A A CA ACDCA A A CEA :"A+A :"C+A :">A A EA A A CEA "A EDDA CA ADEAAACHjAE(AAD(AAEEEFAAEACCACADAACACA(EFA

VDS=200V

IL1=1A IL2=1A IL3=1A

5FA:::>IA/ACEADECACA(ACACA2AEA

)A(AA(ACACAE+ACAEADEAAAAAA DEA A DCA CA EA EA EA "EA (FCA :::>JA A EADACACAEAAEA

-EFFA C"

CAA "CEA

-EFFA C"

CAA "CEA 5FA:::>JA/A<ACACA2AEAEACADCACAAAEA

"EA(FCA:::>KAAACEADECACACAADCAFCAEAA9&BAACAAE+AAFECACACEAEAAAA3:.ZA+A:.ZC+A:.Z>4AAACEAACAACEA3:"4A"ADCEAAFECADEAEADAACEAA CA A EA ECEA CEA A A CA A ECA (A CDEFAEFCACAACA

IAK=0.8A IL=0.8AVDS=150V

IAK1=0.8A IAK3=0.8AIAK2=0.8AVDS=150V

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAE4AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA4A

5FA:::>KA/ACEADECAAE4ACACAACEA,A9&BAAAECAACAE+A:"ACEAACAACEAA:.ZACEAEAEAADEAA

4A9&BAAAECAACAE+A:.ZA+A:.ZC+A:.Z>ACEAAAAEADCACA

"A (A CA CA EA A EA A (A CCLA AIH9A "A CEADAAACA ADCEAEACACA"A (AAAACAACEAACAAADEAEAAEDDADCCAACEAACEADEAEAAAEAEACECCAFCECAACEAACAEAACA*LACADAD(AAAEDDALFEACAAA

FA EA DECA A DEA A CCA CDEA DCEA A DCADACAAAFCAACACEFAA

-CAE AFAFFAFAACC"!)E

<CAEDD+AADAEA&:%*ADCAA(AAADEAADCEAAEACAFEAADCCAEECAAEAEA;AEACA DEA EA A A DDCEA A EA A <6A CA EFA A DEA ADCEAACCAEA*ADA((ADCCAEEEFADEAEACAECADEACCAEA&EAADEEFEDACACACAEADAACAEACAACEACCAACAEEAA((ADACAAD(EACAAAADCEAACCAEAAEADAAEECAEAEA;A EA &EA A DEEFEDA D+A CA EA CA CA EA EEA A EADDCA D(A A (EEA A DEA A EA CA A A CA DEA*DE+AEAEEAADCCAEECAAEAEA;AEACAD(AA #A FCA EEA A CA E(A A FEEA CA CA DEA A EADCAA(A"ECFEAA EA FCCAA EA ACAA EACDEAA ;A A CA A A ECA DEA FEA A EECA DCA EMAEA A CEA A (CA EA ECA (A EA CA CA EDA CA ACA CA DEA "A CEA CCA CA A DA DEA EA CA CADA ECA DEA A ((A DCA CA A A EECACACAAADCEAACCAEACAEA;AEAAEADEADCCAEECA"ADEEAFCAADCACACAEEAAACEA?A

• "EA EFCA A EECA ,A ECA A CA ,,A A ((A C&A CA EDACACAEAEFCACAEEAEA

• "A(ECAADEFA3EDDAAEAAEACDADEAAEECAAEAC(EAEACADE4A/AECAACA,,AAEACAAACADEACAAAAEECAADEEAEA*ADEEAECEAECAACADCEAACAEAACA,CCAAA EA A CEA 6CA (A DEA DA CA EA CA A EAC(EAEACAD(AEADADEAA(AD(EAAAECCAEFACAEAACEACADEAAEAEACAA

• 8((A A EFA A DEA A EECA /A ECA ACA ,,A CAEDACAA(EABQCACAEFAADEAEAA

8C+A CA DA A DEDEFA A A EA EEEA ECA A A EA&:%A*A"ADACEAAEAEEADEAAAAEECAECAAAEA&:%A*AADAAEA(ACADEEFEDAA

"DEA A DEA CA A CA CA EA CDA A A DEAEA EA A DA EECA A EA CA DA 6A CA #A CADAAAAD(EACAEADAEAAEDA:9A

&CE%A FECAA

*A CA EA A DA EA A EDA :+A EA CAA A DDCA AA EA &:%A *A EA ECA A DA EA A A EA &EA ADEEFED+ACAEADAACEAACEABEAE(ACAA((ADCA A FCA CA EA CA A A CA A A DCEA CCA EEAEAEA;AEAEAC(AACAEACADDCAAEA#AADCCAEAEAACAEAEADEADAAAEDA

.(A CA A A ((A DCA A FCA CA DA &:%A *A CA ADALCAACAEACAA#ADEEADCACACACAAACADCA AAA EAAEA ADEA"EA(EAA EACCACACAEA((CAE(AADAAEEAAEAFECAD(ACCLAACA EEA CA EA CA A CEA A CA A DA CA EA (FCA :::>GA "AAAAECAA#ACAEALCADA<EAEC+AEAAADA A DCA EA A FA DCCA A CA A CA EEA A ECA #ADAA

EFCA3d4

C"ACEADAC

CEFACAFCCEEC

== 1= ,= >= = += .=

A5FA:::>GA/A9CAACDAAEACCAAEAAADCEAEA&:%A*A

'ACACA EA (FCA:::>GACACAACDADEA EA;AEAA EAA 3A4AEAAEEAEEACAACEAACA3AFEC4AADAEACAEECACA3EAFAAC4A.AADEAAA(ADCAEACE+AACAAEACCALCAAEEAALCAAFACA3EA((ADEAEDDAA EA DEA D4A "EA EA CA CA EECA CA A FEA A >A E(A ADAADAACAACAEACADCAEADEEACADEAAAEEEADECAA

"EA CA A A A EA CCA A A GHH9A A EA A EA DEA A EA ADEAACAACAFEACAEEAEEACAEA;AEAAEAAEADEAAEECAAA3(FCA:::>@4A

6 >== 6,== 6 1== 6== =6==6+==6.==6?== 6>== 6,== 6 1== 6== =6==6+==6.==6?== 6>== 6,== 6 1== 6== =6==6+==6.==6?== 6>== 6,== 61== 6== =6==6+==6.==6?==

× == 6?

6 × = 6?

+ × =6 = 6=

>× =6 = 6=

6? × = 6=

9.Z 394

3.4 × == 61× =6 = 6=

× == 61 × == 6=

5FA:::>@A/A!CAAAAEAAEA&:%A*A3EEAAEFCAIHd4A

• 8((AAEFAADEAAEECA

*AEAAEAAEAE+AEAAEAADEAAEECAEA A CA CA EA CA CA EDA CA /A DCA EFA A DEA DCA AEDACAA(EABQCAACACA3EAAEAWAEFADAAEACAAEAACADEAAEAFA<AAEAFA64A"EA(FCA:::EHAAAEACA

1= >= += ?= == 1=1= >= += ?= ==*=.==,==

>> × =

>?× =

<(CAAFAA(EABQCA3d4

85º angle90º angle60º angle

5FA:::EHA/A*DEEACAEDACAA(EABQCADCA((AEFAADEAAEECAAEFCAIHdA

• "EFCACAEEAEEAACEA

6CAEAACACAEAEAEEAAEAEFCACAEEAAIHdAAEHHdAEACAEFAADEAAEECAAGI_"EA(FCACEADAEACAACDACAEDA CA A (EA BQCA CA EA AA DEAA AEA CAAEEAAHAAGHH9AA

1= >= += ?= ==1= >= += ?= *=.==,==

>> × =

>?× =

<(CAAFAA (EABQ CA3d4

==;1==;=;>==;

5FA:::EAA/A*DEEACAEDACAA(EABQCADCA((AEFCACAEEAAIHdAAEHHdA3GI_AEFAAEADE4AA

*A A DCA A A CA EA (FCA :::EAA EA ECA CA EDA EEA A A CKID9QADCA EA EFCA CA EEA A IHdA A >AHD9QA DCA EA EFCA CA EEA A EHHdA *AAF(EACAEDACAA(EABQCAAAACALEFAA EA DEA CA EEA LA DEA C((EA D1A .A EA EEA A EA EFCA CA EEACACA((ACAEDACAA(EABQCA8A((+AECFEAAEAEFCACAEEA(EAA((AC&ACAEDACACACAACAAACDAAC(EA.A EA CAAACAAECEADCAFEEACA EAEFCA CA EEA A (EA DDEA EA A EA WA EFA A DEA A DEA DAAEAAEADACAEA(FCA:::EAA

"EA (FCA:::ECA DA EADEEACAEDACAA (EABQCADCAEA#ACAAEEAAEAEFCACAEEAEAA(AEACAEFAADEAAJHjA

>==;=;1==;==;

1= >= += ?= ==1= >= += ?= ===

<(CAAFAA (EABQ CA3 d4

>> × =

>?× =

× =1 =

5FA:::ECA/A*DEEACAEDACAA(EABQCADCA((AEFCACAEEAAIHdAAEHHdA3JH_AEFAAEADE4AA

*A EC+A EA EEA CA EFA DCA DEA A DEA EA A CAEA ECA ECA CA EDA CA A (EA BQCA 3(FCA :::EC4A "AEDACAA(EAAECCDAAACAEAAEAEAEFAAGI_AA

• 5ECAADEFAA

"ADDAAACAAAFEAEA#AEFCACAEEA3IHdAEAAE4AAA(EAEAEAEFCACACEAACA,AEAAIHd+AAHHdAACHHdAACAEECA A *EA DA A EA EEA A CDEA E+A A EA AEECQAACAAAQE+AAQAHAAAQCIA3CI]+AAH]AAE]4AAACAEA(FCA:::E>A"EACCACADAGKjAEFAADEAAEECA

EFCA3d4 EFCA3d4

EC /==; EC /=;EC

/=;== 1== ,=== = 1= ,= >= === 1== ,=== = 1= ,= >= = += .=

A5FA:::E>A/A9EEAACDEAEABQEECAAAQAHA3AFEC4AAAQEA3A4A

"EA (FCA :::EEA A EA DEEA A CEA CA DCA A EDA CA A(EABQCADCA((A(ECACDEA'ADCAECACA A ACA A CEA CA A CA A EA DEA A EEA CA EDA CA A(AAA(ECA

<(CAAFAA(EABQCA3d4

25% occupation10% occupation

4% occupation

1= >= += ?= == 1=1= >= += ?=.= *== ,= =

>> × =

>?× =

A5FA:::EEA/A*DEEACAEDACAA(EABQCAADCACAEFCA

CAEEAAIHAdAA(ECAADEFACI]+AAH]AAE]A

"EA CA A A A EA A EA A A EA CDEA A EECA ADACAEA(FCA:::EIA"EACCAACAAAAGHH9AAEAAEA

AEAADEA'ADCAACAACALEEEAAEAAEAADCAACAAECALCDEAAEECAECFAACAAACAAEAAA FA ,CA A EA EA CA A A A DEA A FAEAA

9.Z 394

10% occupation25% occupation4% occupation

6 >== 6,== 6 1== 6== =6==6+==6.==6?== 6>== 6,== 6 1== 6== =6==6+==6.==6?== 6>== 6,== 6 1== 6== =6==6+==6.==6?== 6 >== 6,== 61== 6== =6==6+==6.==6?==

9.Z 394

× == 6?

6 × = 6?

+× =6 = 6*

+ × =6 = 6=

61 × = 6*

× == 6> × =6 = 6=

× == 6*1× =6 = 6

A5FA:::EIA/AA*EECAAAAEAAEA&:%A*ADCAA

CDEAAEECAACI]+AAH]AAE]A

)A(EA((AECAECACACEAA (CADCA#AACA EA (FCA:::EI+AC(AA CEAADCADEA#AAE(ADCCA EACEAADAADACAAACADEAAEAEEACACEAA(CAACAAEAEEAAEAAAEAACA8AEAEAC(EAAEAAAECCDADCADEAAAEEAEAECCDAAEA

1 'CEFC$CEA

.(AAEAACEAAAEEAC+ACAEAEAAEEEACAECAAAEA&:%A*A"AADECAAAEAEAA#AECAAEECACADA<EAECAAD+AA(AECAAAAEADEADCA#AEAEAAEAAAAAAEEAAADCCAEAA(CCA

.AEAEEEAECAAAEA&:%A*+ACAEAAACAACADADDECA?A

• EACAAAAACEAA(CAAAEA&:%A*AAEAEACAAEAAAEA

• A ((A EA EA A A CEA CA A EA CA A EA C(EA EA AAEA&:%A*A

1 CEACFCC

*A D+A EA EEEA ECA EA A A A CA DA &EA CADAD+ACAEA((CAACACADAEAAECAAEECA3!DA BA $FA <0A *CA !EA $<A >KA.4A CA 0E(A A CDA A A DEA3(FCA:::EJ4AA

5FA:::EJA/A<FEDACA0E(AAAEA&:%A*AACAAEEEACADA

5A A DA DA CA CA EA EEEA A A EAEAAAE+ACAEACAA#ADEDEFA<CAEDD+AADAEACA C(A A FA CA CA EA DDA CA D(A E(A FA ADEEFA CA CEA A ECA A FA CDDEA E(A ((CA A CA CEADA "EA DDA A EA E+A EA A CDA DEA A EECA EA A A ECACEA<*2AEAAEADEACAEACAACDAFAAAEACACA EA DDA A EA "EA CA (EA ((CA ECA DEDEF+A DAD+AAEAEEACACCAEAACEA<*2AECAECAAEECAA D(A DCA ECA CA CA CA DA C(A A DEA CA AEECA3(FCA:9EK4A

!FC"!)EDF

5FA:::EKA/A9CAECACADEDEFAAAEA&:%A* "EA(FCA:::EGAAADACADEDEFAAAEA&:%A*A

A AAAA AAAA A

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAE4AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA4AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA4A

5FA:::EGA/A<FEDACADEDEFAAAEA&:%A*AE4A(EAEE+A4A;ACAEA(EAEE+A4A(EAEA

11 CCACAC

• BA

"ADACEAACAAACAAEA&:%A*A3DDAEAAEECA EEA EA A IHdA EA CDEA A AQ@4A DEA EA EA CA A ACAAEAEEC+ACACA#A0E(AADACAEA(FCA:::E@A"ACAAAEACADAEEAEACDAAEADEEAADEA

0,E+00

5,E-05

1,E-04

2,E-04

3,E-04

4,E-04

5,E-04

0 100 200 300 400

Vak (V)

diode sansDRIM Coolerdiode avecDRIM Cooler

Vka (V)

5FA:::E@A/A*DEEAAEACAAACAAEA&:%A*AACAAEA&:%A*A

"ACADEAACACAAADCAEACAAECA*ACEAADCNACEFEADCCADCACAEACAAAFEAEAAEAADADEAAEAEEAAEECA"EAEAAD(AEAECCDADCAFEACAEAAEA A DEA EA EA A A C+A A CA A (ECA CA ECA DAFCAAECCDADCAFEA.AEAAEA&:%A*ADACACEAA(CAECCDA DCAA CA EAAEA EECAA A ADCADA EA(FCA:::IHA"AEAAADAFEADCA#ACAEAADAA A DA CA DA CA EA DEEA A A EA EA A AEECAADEACAEAAEECA

1,E-06

1,E-05

1,E-04

1,E-030 100 200 300 400

Vak (V)

diode sansDRIM coolerdiode avecDRIM cooler

Vka (V)

5FA:::IHA/A*DEEACACEAA(CACAAEA&:%A*AACAAEA&:%A*AA

"EA(FCA:::IAADAACACEACAAAEAEAEACAAACA A EA &:%A *A 3DDA EA A EECA EEA EA A IHdA EACDEAAAQ@4ACCAEEAEAEEACADEDEFAAAEADEEAA

0,00E+00

1,00E-06

2,00E-06

3,00E-06

4,00E-06

5,00E-06

6,00E-06

7,00E-06

0 100 200 300 400Vak (V)

Vka (V)

A5FA:::IAA/!CAAACAAEA&:%A*AA

"AD(AEAEACAAAECEFAA>HH9AEACACEAA(CAAAh.A%#AA A CEA A CA EEA A EA EECA A +A DEA EDDA ECA EAD+AEAACACEADEADCCAAAEA&:%A*AAA[CAEACA AAECEFACAAJHH9A"EAADEEAAEAEAAA EECA DCA C(A A ECEFA DECA EA A EECA EEA A A CADEACDDEAA#A((CAE(AAADCAAEAAADA6CA EA DCA DEA EA A A DDA EA &:%A *A EA EA EAECCA DEA A A CA CEA "A D(A (+A #A EA AECEAEEC+AAEADCACACAEDAEACDA6CAEAACAADA DEA A DCA A CA CA A EA CDA A CA A DA EA AEAEACAAEECA*EADCAACA(ACAEACDAACAEDACA CAE((AA A (A AD(A EAA A EAA AEA EA EFA CA ECA A DCA EA DEEA A (A .+A CA EAEA A EA CA DA CA 0E(A DEA EA CDA A ECEA CA (A A ECAEA)9ACAEA(EAEEA*DEAAEAA(AAD+AAEEAADEAAA(AEFAA

.AAEAACAEADECAEAEFACCA(EAEAADAFCA:AEFEAADECAAEDAAFECA&:8AADCADAAEAAEECAEEAAAEAEAEAEDAAEFAAEA(EAEEACAACDDA3EEAEDAA&:8AAEAADAEAAEDA::4AE(AACAEACACDDEAA

BCA ECA (EA EDDA A ECA DA FC+A EA (FCACEA A A CA CEA A CA A A CA A EA &:%A *A3DDAEAAEECAEEAEAAIHdAEACDEAAAQAJ4A"EACAEA((CAEEAEACDAAEADEEAADEA"AD(AEAEACAAAECEFA A EIH9A EA CA CEA A (CA E;A (EA *A CEA A CA EEAF(EAAEAEECAA+ADEAEDDAECAEADA

-6,0E-06

-5,0E-06

-4,0E-06

-3,0E-06

-2,0E-06

-1,0E-06

0,0E+00-500-400-300-200-1000

Vak (V)

DRIM Cooleroccupation 1/16

5FA:::ICA/!CAAACAAEA&:%A*A3EECAEAAIHdAEACDEAAQAJ4A

"EADEEAAEACAAACAAEA&:%A*AAACCAAEA&:%A*AEAACDEA((A3CAADEAA CACAA0E(AAC4AADACAEA(FCA:::I>A

-6,0E-06

-4,0E-06

-2,0E-06

0,0E+00-500-400-300-200-1000

Vak (V)

(A) sans DRIM Cooler

avec DRIM Cooleroccupation 1/16

5FA:::I>A/A*DEEAAEACAAACAAEA&:%A*AAAA

AEA&:%A*A3EECAEAAIHdAEACDEAAQAJ+AAQ@AAAQE4A

"A CEA DA CA EA (FCA :::I>A A CA EA ((A A EA A AECEFACAADECAADADEAAEAEEAAEECADCCAEAAEA&:%A*AEAA(ACACAAADCA(EACAAAEA&:%A*A3DDAEAEECAEAAIHdAEACDEAAQAJAAAQ@4AA

.CA(E+AEAEEAAEECACAEADEADCA#AEADEACACA (+A EA DEA A CDA EA CA A CEA (EA CA (A FEEA A EA CA AA A DEA A A A EA (FCA :::IEA :A EA EA EFA ADEAAEA((AEAA(CCA

-3,0E-05

-2,5E-05

-2,0E-05

-1,5E-05

-1,0E-05

-5,0E-06

0,0E+00-500-400-300-200-1000

Vak (V)

DRIM cooleroccupation 1/9 -avant decoupeDRIM cooleroccupation 1/9apres decoupeDRIM cooleroccupation 1/16 -avant decoupeDRIM cooleroccupation 1/16 -apres decoupe

5FA:::IEA/A*DEEAAEACAAAAAEA&:%A*AEEAAEDAEA

CDAADEA

• CCACAF

"EA (FCA :::IIA A CA DEEA A EECA A A CA A EA&:%A *A A A A A EA &:%A *A 3EECA EEA EA IHdA EA((A CDE4A CA CA #A 0E(A EEA EA CDA A A A "EA CA AAAAEA&:%A*AAFADCAADEAAEACAAAA EAAEAEECA EEA!C(+AA EAECFEAA EACAA A A DA DEA A ECFEA CA A A EECA A A A EACA A EA C(EA EA /A A DDA EA A A A EECA 3CDEA AQ@4A EA CACAAADCAACAADDAEAADCAAEECA3CDEAAQE4A.AAA((A A CA CA EA EA A ECFEA A EA CA A A A EA DEEA ADEAEA&:%A*A

0 0,2 0,4 0,6 0,8 1

Vak (V)

diode sans DRIMCooler

diode avec DRIM Cooleroccupation 1/16

5FA:::IIA/A*DEEAAEECAAACAAEA&:%A*AAAAAEA&:%A*A3EECAEEAEAIHdAEA((ACDE4A

"EA(FCACEADAAEECAA+AEDACDAADEEAEAACA+ACAAEA&:%A*A3DDAEAAEECAEEAEAAIHdAEACDEAAAQ@4A%EFAACACEADAACEAADADEAAAEA8A((+AEACAAAAEADEEAECAEAAI9ADCA:.ZcCH.AECACAA>9ACAADECA8ACA(ACAEEACDDEAA#A((CADCACA DCA A EA A DA !CA A #+A CA A A CA EA ((ADEAAACAAACAADECAADCADEA#AEAAEADAAC(EAEACAAFEAAEECAEAEADAAAAH]AAEAC(EAEACAD(A

0 1 2 3 4 5

Vak (V)

5FA:::IJA/A*EECAAACAAEA&:%A*A

*A DCA A A EA EA A A EA DEA EA A CAA CA A EA CA A A A DEA CA EA ECA A CEA 3EH.4A EAACAFEEAF(EAAEAEECAAA&AACDDEA

A#AEAE(A(A EAEAAADA<EAECAADAACAEADEADCAAEADCAAEAAAEEAAADCCAEAA(CCA

+ EAAA"A6CAEADAEAAEDA A CEAA EEA CAAA EAEEA

DECA A D(EA CA A A A DCEA EA EA A AEAAEA&:%A*A.DAEDAAAAACAEAEADCCA A EA CA A CEA CCA BEA E(A ECA (CA A EAEEAA((ADEEA*EACAEADAAACAEAEEACAEFAECAECAAEADEAAEAEAACEAAAEECAEEADAEAEACAAAADEA,CCABAACAEAEEAA(EACADCAAA+AEDDAFCADAEAAECADAMADEAADADEA6CAEAECAECA #AA ECACA A A EDA A C(EA ADEAE(A A CA EEEFA A A OA ECAEDACA.A+AADCAEFACCAAAAEDADCA#AEADEACACCAE(ACAEADACAEAAC(EAAEADCAECAECAAECAAFADCAAEDAC+AC,AEADACAEAEAD(AADDAADEA"EAD(CADEAAEAEAEAEAECAACA/AACAAEAEEACAEA((EACADCCADEAADCEAAFAEAA#ACEAACAFA8AA#ACDCAADECAAEA;AACAA A 8(+A CA DEA CEA CCA A A EA &:%A *A CA EADA A A CA A EA DEA ((A FE(A ,,A A EA CA A A CADEACAEA;AEAAEADEACAEEAA

8A A CA A EA EEEA DECA A A EA EA A AE+AACEAECAAECACAEAEDDA"EA(EAADCCADEAFAEAA#ACEAEAECAAEA6E+ACAEAEA EA ((A ECA ECA A CA DA A A ,A CEA A (CA ACAAA*ACEAAAECAEAA(CCAEAAAAEACAEAEACA EDDAAEA EAAAAEACAAEAEAEACAEDAA DCA DDA *A DD+A A EA EA EFA EA DEA A CDACAECAEA,ADEADAEADEEAA((A(ADCA#AEADEAEADEAAFECAD(AACA.CAEAEEACADEEADCARAEEDASAAEAEAEAEAEEAEAAADEAAEDAAEAEAEA"EADEEAA(EAEACAXCXAAEAAAWAAEDAAADCAAEADEADAAAACADCA#ACADA

"EAEEAAEECAECACAADEAEA&:%A*AEAECAAEAEAAEDA"ACEACAAAEAAACAFEAAEECAEEAEA;AEAAAADCEAE((EAACACAAA"EA A A ECEFA CA A DECA EA A EIH9A A A CA A A (CA A EAA A ECEFA CA 3JHH94A !C(+A A CA A A A A A EAA CA DA FCA CA A EECA A DEA "A EECAADEAFEADEAA&:%A*+ACACA#A0E(ACAADEAEA&:%A *+A EA A DCA ECEA EEA A A DDA EADCAEDDA.+AAAEADAAEEAEAA(CCACCAECAECACA DA FCA CA DCA EA A DEA EA 8A A CA A AEECA A A A DEA EA &:%A *+A A CEA CA A(AAAEA.CA(EAACEACAAACEFEADCAEAEEAAD(EACACADACACAEAAEDA:9A

C' (F"CEFCC FACA AFAFFAFAACC"!)E

AA :CABBBBBBBBBBBBBBBBBBBBBA A>IACA EDDAAAAE(AAECAAACA

CA(CBBBBBBBBBBBBBBBBBBBBBAAA>IA

CAA6AABBBBBBBBBBBBBBBBBBBBBA A>IACCA6AA<EBBBBBBBBBBBBBBBBBBBBBA A>JAC>A"FCCAEAECCAACBBBBBBBBBA A>JACEA6AA6CBBBBBBBBBBBBBBBBBBBBBA A>KACIA<AAEFAA((AA(BBBBBBBBBBBBA A>GA

>A .EACAAD(EACACADAAA(A&:%A*BBBBBBBBBBBBBA

>AA%EAEECBBBBBBBBBBBBBBBBBBBBBA AEHA>CA%EACCBBBBBBBBBBBBBBBBBBA AE>A>>A*DEEAACEABBBBBBBBBBBBBBBBBA AEGA

EA 9EEADEAAD(EACAACADAA(A&:%A*BBBBBBBBBA

EAA<EACAEAAEEEADEBBBBBBBBBA AIHAECACEACBBBBBBBBBBBBBBBBBBBBBBBA AIAAE>A<ABBBBBBBBBBBBBBBBBBBBBA AI>A

IA *CABBBBBBBBBBBBBBBBBBBBBBBBBA AIEA

*EDA:9A?A<(EACACADA&:%A*A

6CA EA CA EA A DA EDA CA A DA A (A &:%A *+AEA CA FEA CA (CA A EA EA ;A EA A DEA ADCE+A ((EA A EEEFA A A A A A FCA A A D(EA CA&EA A EDA CA EA DA EEA CA A EA EEA DECA AD(EACACADAA(A&:%A*A"EEACACACAEAADACACAA/AEECAACCA"EAAEECAAEACAAEAE(AAA((AEF+AEA((AADECAA EA DEA A EECA A A (CA A ADA A EFA .A CA [A AEDADEACAEDDAA AAAAEAACACAADAAECAADEEAAAEEAAEFAAECAAADAAEFA.(AAEAA CEA CA A A A C+A CA EA CA DA A ACCAEACAACEAEAEAAFA5!$8%A,AFACADAEACAAA>&AE(AEEAAEDACAEAECAECCAEAAEDDEAA(AEA"AEEEFACAFAAC?ADAAEAA(CAC+AEADEC+AEAAAEADACA(CAAECADACAEA C+A DA A DA A EDA ECCA 3FA CC+A EEA CAE4AA"EACAAAACCADAEEAAD(EACA DA A (EEA EA ((A DEEA /A FCA 3EA ECC+AFCCACAEE4+ACA3DCEAAD+ADDADCAAD+AA4A8(+ACADAAEAAEEEADEACACAEA[CAAEAE(A A EAA DECA A D(EA CA DA A (A&:%A *A"ADACEAACA((CAAECADAACA

1 CE A EA A F CA F CE " FCAF

*AEAEAADAEA AEDA :+A ADAA (A&:%A*AACAACA(CACAAA(AEAEFAADEA&EACAA(FCEA(ADDEAAAAEAEACACAAAEADCEAADDEFAEADCADACAEAAEFAA"A E(A CA CA (CA CA CA EA CA EEA DA A EA FA CAEE+ACAFAC+AADDAADCACA(C+AAEAAAAEADECA CA (CA .(A A A A DEE+A CA CA CEA CAA A CA A EA (A A DEA A A EA A 3EEA4A 6CA EA EEA A A A CA A CA EA A EA A EAA(AEACACA

1 4DF%EFA

"A A A A DA A A A FA A CA /A EE+ACCACAEA:ADCA#AACEAEAEACEA?A

µρ Dhv..Re = AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA3:9A4A

WA ρ TDFQ>UAA EAEACCACA(C+AdTDFQUAA EAAECACA(C+A

TQUAAEAACA(C+APSDh 4= AAAEAECCACAEEAWABAAEAA

A<AADACAAAA

<CA A (EA A A A 3iCHHH4A A (CA CA CA (A A (ADEEA ECA DEA /A A FA CA A EEA <CA A FEA A A

A 3pJHHH4A CA CA (CA DA CA EDA A A A FACA A EA CCA <CA A A A A E+A A FACAAEA

11 4DF-CFE

"AAA<EAEEAEAEDAADACAAECAAACACA(CA:ADACCAADDADCACA(CAADCA#AAEAEAEACEA?AA

kCp.Pr µ= AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA3:9C4A

WAAdATDFQUAAEAAECACA(C+A*DATQDFZUAAEAECAD(CACA(CAADATVQZUAAEACACACA(CAA

)AAA<EA3<qA4AACACAAD(AADECAEAA(CAEA(ADEACAD(AAA3EAAEA AD(AAAADDADCAEDACAAD(AADEC4A<CAAAA<EA(EA3<iA4+AAD(AAAEADCA((ACAAD(AADECA

"A EECA CEA DA A A A <EA A (A A EA DECA DCA A(CA CA *EA CI+A CA CA EA A DCA EA EEA CA DA &:%A*A

TABLEAU I: NOMBRE DE PRANDTL POUR LE FLUIDE COOLANOL 25R

B:M< -

CHA G@EJA

EHA EJ@KA

JHA >>KIA

AHHA C>>AA

&EDA A EECA:+ACAACA AAA<EAA AFEAEAAAACAF(A C+A EA A EA A A EDDE+A EA FCCA EA ECCA A DCACACA EA FCCAEACA6CAEACAEAEA ADEEFEDACEAA

1, AFACDEAA%FCE

&EA A EA CA CA EE+A EA A A CEA C(A CA A ADA A A CA CA +A ECA (CA A A CA CA AFA A A CA EE+A AD(AAADACA(ADEECA/AAAEACACAAAFAEA'AAA#ADAECAECACADDAAEACAACA"EAEEA A FCCA EA ECCA A CA A DEA E(A AA AACAEAEAEDDDADCAECAEDDEADECA6E+AAEAAADEACAECADADCCAEAEACACAACAADDAACACADDAA(EACAEAC(A"AEADADAEACAAAFECAAAFCCAEAAEAACA EA EA A (CEA ((A DCA #A CA EA EAECA *,CA CA DA A EA DCA A FCCA EA

ECCA3"4AACA3"4ACACAEACAT%)\@@UAA

"rHHI&AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA3:9>4A

"rHHI&<AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA3:9E4A

.A A DA CA DCA A A EA WA CA DCA A ACA A EA DEA EEHHAEECAEAAEAECCAIHdA3CDEAAQ@AAEAC(EAEAAEADC4+AAAAAHCK"QAACADAACADCEADAAEHHVAACAEAAEADECA QA CA (CA A IHZA &EA A EA 3DCA CA DECA CA (CA AEHj*4+AAAAAECA>AAACAACACAAAFAEEA6A CA A A A A A A (EA A ECA CA DA EA ECCA AEECA.+AEACAADACAAEADEAEAC+AAFACAEAEEA&EAAE+ACADCAECAEAFCCAEAECCACAECAAGdAEACAEAFCCAEACAECAKHHdA.AAD(AAAAEAA ACACAEEAEACA AD(AADECA AAEA CA A FACAEEA3DCAEDD+AEAFCCACAEEAAIHHd4A

A:A A DEA A A CA A ((A A A A (CA DCA A EFACA DCCA EA A ;A A FEA A DECA 3A A A ((AEFA(AEC4AADCA(A.AA((AEFAAAAAAACA EEA A EA ECA CA CCA EA CA ECA (A CA A FA A EACA

1> 4DF4AAE

"A A A 6CA EEA EFA CA A EA DEA A A (CA :A AAAECA((AEFACAADCAA(ADEAEAEACEA?A

kDhhNu .= AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA3:9I4A

WA A TVQCZUA A A ((A EF+A &A TUA A A EA ECCA CA EEA ADTVQZUAAEACACACA(CAAA

8A FA EE+A A A A 6CA A (A DEA A EA FA CACA A A EA ECA CA FA CA "CA A FA CA ACA A ECCA EA A CA A FA A D+A A A A6CA A EA A DCA #A (EA ECA A EA EA EA A (CAEECA 3DEA DA DCA CA EEA CEA 6CcE>JA EA A EA CA (CA A ECAC(A A 6Cc>JJA EA A EA A DEA A T28H>U4A &EA A EA A EECACEA A FA CA EA ECA A A CA EAC+AEAEA3:9J4A(CADEA2EAT28H>UAEAAAABEAA"ATB$.KGUADAAAAAA6CAAEAAEAADEAAAEAEA3:9K4AEAAEACA(CAAECAC(A?A

>→+<<→−

≤→−

03.0/0499.0657.303.0005.02.0615.1

005.07.0615.1

Nu AAAAAAAAAAAAAAAAAAAAAAA3:9J4A

>→+≤→=

03.0/0722.0364.403.0953.1

xxxxNu AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA3:9K4A

WAYAACAFCCAEECAEAA(ADEAPr.Re

DhLx = AWA"TU,EAFCCA

CA EE+A &TUA A EA ECC+A A A <A A A A A A A <EADA

<CAAFADCADAACAAEF+AAECACAAA6CAAAEAAAAFEAEACAA(CEADCA.AEAAEADCAAEECA A A EA CA EFCEA A CEA A DA DA 3FACAEEAECAEAACAACAE+AAECAA/ADECAADEAD4+ACAEAEAAACAAEECAAAEECAAECADEA(CADEABEAA"ATB$.KGUA"AAAEAAAADADECAADEADAAOAECA(EACAAEEAACAACAAFEACAEAACADEEAECAEEAAA(EA*EAEAACACADAACEAACEACCA

1 -AFCF

"ADAAEFAFCAFAEA((AADAAAAEAACAEEA*A((AADAACAECA(AAA3(AA(A4ACA EDDEEA CCA CA CA (CA A DEA DEA EDDA A CA ECA "A DA AEFAFCADCA#AECAEDACEA:9GA?A

2.4 2v

DhLfP ρ

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA3:9G4A

WA ρ (kg/m34AAEAEACCACA(C+AA3Q4AAEAAACA(C+A&A34A

A A EA ECCA CA EE+A "A 34A A EA FCCA CA EEA A f A A ((A A

(A "A ((A A (A DA CA A A A 8A FA E+A AECAA f cAJQADCACAAA f cAECQADCACAEAT28H>UA&EAAEACAEF+A

ADCA#AECAACEAEAEACEATB$.KGUA?A

( )5432 2537.09564.07012.19467.13553.1124 ααααα −+−+−=f AAAAAAAAAAAAAAA3:9@4A

WAsAAAEDDAAADAAAFEANACAEFA&EAAEA3AEDA::4+AAEDDAAFEAAAQAHAA f cCACQA

6E+A A DA A EFA FCA A A DEA A CA A A #A DA ADA :A A FEA A DA A EFA A ECA EA A DECA 3C+AA A EF4A EDDA DA A EFA FCA &EA A EA CA DA&:%A *+A A DEA A DCEA DCA #A CA A CA FA A EA ECACA A (CA "EA A EA A EECA EA DCA (EA CA EA A EA CADE+AA(CAECEACAADCAAEAAEECACECAEAAEADCA.+AA EA A EEA EDEFEA CA A A EA A A DEEFA CA (CA AA CA ECFEA A EA A "EA A CA EEA EA CA EFA *A CADA CAADAAEFAFCACAECAECADAAEFAFCAEA AEEA&EAAEA ADAAEFADCA#AAEA EA EA:9AHADDADEA:DAT:&8JHU?A

2².VP ρξ=∆ AAAEAAA

DhLf++= 00 .ξεξξ ϕ AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA3:9AH4A

WA ϕξ AA 00.ξε AAA((ADEAAECAADAAEFADAAA AA EA A CAEEA*A ((A A (A A CDEA AEECA A CAAAAADCA#A(AADEAEECA*DE+AACAAADEADADCAAAAA(CAACI+AEACAEAEADCDEAAAEAC+AACAAEEADEACAAAAACA.AEADA

ADAA((AAAAAADAAEFAAEADEAEADCACAAADADEAEACAEAAEDA

"AAAEAAEAEA,ECCAAAD(AEAD+ACAEAEEADAAECEAACAD(EACA

, &CE%A FA CA A F FFAA!)E

&EA A DEEFEDA CA EA DA A A EECA CA CA A DAAAD(EACACADCA#ACAEAADA&:%A*A6CAEACADAEAEDEFAACEACCACACAEACAE(A A EA A CEA EECA "CA A A EA (A CA AD(A CA DA CA DCA A CA CA DA A EECA EEA ADECA ACA A EA EEA CA &:%A *A 3(FCA :9A4A &EA A C+A AEECAAA(AEAEC(ACAACAAEA

FACEACC$

5F:9AA/A7AAEADCABADEAA&:%A*A

"AAEAACAAACEA?A

• EAC(EAAEADCAAACA

• EAFCCAAEECAAFEAADECAAEADCAIHHdA

• A A A EECA A DEEA A EA EA A CA DA A CDEAC(EAEAAEADCQC(EAAEECACAAEEA?AAQE+AAQ@+AAQAJA

• AEAECCA3&4AAEECAAEEAAIHdAAEHHdA

• A(AFCAAEECAA?AE+AAAEFA3EACAEDDAAAQAHAAN4A

• EADCEADADEAEADCAAEHHVA

• EAAEADECACA(CAAAAEAACAEEAAIHZA

• A(CAA(AA*EACIA

• DECAACA(CAEHZA

8A EEA A DDA ,DCA CA *EA CIA 3A EDA :4A A ACEACEA3:9AA4+ACADCAECACCAAkcHCKAQAEAEAEA A EA E(A ECA CA DCEA <cEHHVA EA CA EA A EA DECA

QACA(CAf!cIHZA

esTCpPQ∆

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA3:9AA4A

WA ρ TDFQ>UAAEAEACCAA*DATQDFZUAAEAECAD(CACA(CA

, (FCCE%

8ACEAAEAAAEA(AEAADEEFEDADACAEAEA A A EECA EA DCA (A A A A ((A EFA

TVQCQZU+AEA((AADECAf!D(TZUAAEADEACA,CCAAA(CAA A DA A EFA f<T<EUA A (EEA EA ((A DEEA FCA A AEA ECC+A A A A EECA A DEEA 3A A ECA A DEF4+A EA(A FCA A EECA BA *EA A A CEA A A DA EA ADAEDA&EA ADEEFEDACACACAEAADCAAEA CAACA "A ((A EFA EA A ECA A CEA A A A 6CA A A CA(A ECA tCEA 3CA A CA EA CA A EA ECC4A "EAECA CA ((A EFA A A A DCA ECA EA CA ((A EFAA<CAAECAADAAEF+ACAADAAEFAFCAAADAADA

• EFEC"CCFFC%FCE

"EA (FCA :9CA DA EA EEA CA ((A EFA A (A CA EAECCAAEECAAIHdAAEHHdAAFEEAEA#ACDEAC(EAEAAEECQC(EAEAACAAAQEA*AEACDACACAECACA A((A EFA A DCA A DCA A EA ECCA DCA (EA *A CAEA+ADCAACAEEA3(EAAA4AA((AEFA A A DDA ECA EA ECCA CA EEA .+A CA AEAECCAECF+AA((AEFACA

20 40 60 80 1004 103×

6 103×

8 103×

1 104×

1.2 104×

1.4 104×

BCFEF :F<

:D@1@E<

5F:9CA/A*((AEFAA(AAEADECACA(CADCA((AEAECCAEAEA#ACDEA3CI]4A

'ADCAECACAEA(FCA:9CACAA((AEFACAEAEAAEA DECACA(CA"EA EADCAEAA EACAA EACA CACA(CA EA ECFEA A EA DECA "A ((A EFA EA A

DDA A EA CA CA CA (C+A A CA ECA EA EA A EADECA

"AEFACADEAAA(ADEACA((AEFAEA ECA A EA C(EA EFA /A EA C(EA A DEA A EECA A EA EA A(CA .A DCA A #A ECA CDEA A EECA CA A EA ECCAECFAEAC(EAEFACA3DEADADCACACDEAACI]AACAEAECCAAIHdAEAC(EAEFAECAAHCAEACADCAEA#ACDEAADCACA EA ECCA A AHHdA EA C(EA EFA A IC4A .A EA CA A EAC(EA EFA A EA CA CA ((A EFA CEA A ECFEA CAEAECCAAACAECADCAEADECAAEADEA"EA(FCA:9>ADAEA((AADECAAEADEAAA(CADCA((AEAECCA

20 40 60 80 1000

BCFEF :F<

5F:9>A/A&((AADECADEQ(CAA(AAEADECACA(CADCA((AEAECCAEAEA#ACDEA3CI]4A

'ADCAACAEA(FCA:9>ACADEAAEAECCACDCAAAHHd+AEADECAAEADCAACDCAAEADECAEEAEADEAADEA,CCA A CA .A A A CA EA ECCA A EECA FAEA CA DCA A CA A CA A EA EEA CA &:%A *A A #A A A AECA(CAAAHHdA

"EA(FCA:9EADAADAAEFAEAA#AEACA"ADAAEFAEAADDAECAEAECCAAAECEADCA(EACAAEA ECCA A FEA :A A EA A ECA CA A (FCA EA (ADEA A DA A EFA A EA DECA CA (CA*A CA EA AEA A EDA :+A EA (EA A ECA CA *ECIA EA CA A A DCA AAAA(CAEAAEDDEA6CADCAECACAEA(FCA:9EAC+ADCAEADECA ECF+A DCA A DA A EFA CA *EA A OA ECA (EA CA EA AECA CA EA ECFEA A EA DECA /A DCA A EA ECCA AIHdAADAAEFAAAED<EADCACHj*AACACCLACD<EAAEHj*A

20 40 60 80 1000

1 103×

2 103×

3 103×

4 103×

5 103×

BCFEF :F<

5F:9EA/A<AAEFAA(AAEADECACA(CADCA((AEAECCAEAEA#ACDEA3CI]4A

• EFEC

&EAADEEFED+ACAEACA AECACACA AD(EACADA A (A &:%A *A A EA ((A (A FCA AEECA/AEAANAIHd+AAAEAIHdAAEFAEAANAAIHdAAIHHdAEAEA#ACDEAEACAAAEA

"EA(FCA:9IAACACA((AEFAA(AAEADECACA(CAEAAAEAADCAECA6CAECACAA((AEFACAEAAEACAAADCAADCAAEECACEAA

20 35 50 65 801 104×

1.1 104×

1.2 104×

1.3 104×

1.4 104×

CE=@==;

BCFEF :F<

:D@1@E<

5F:9IA/A*((AEFAA(AAEADECACA(CADCA((A(AFCAAEECAEAEA#ACDEA3CI]4A

8AACAAEAEEAAEA((AADECADEQ(CAEAAAEAAAADACAEA(FCA:9JA"EA((AECAECAAEADECAEAAAEAACAAEA((AECAECACA((AEFAA

20 40 60 80 10020

BCFEF :F<

CE=@==;

5F:9JA/A&((AADECADEQ(CAA(AAEADECACA(CADCA((A(AFCAAEECAEAEA#ACDEA3CI]4A

8(AEA(FCA:9KADAADAAEFADCAAEECAE+AAAEFA"AEAECCAEAAEAAEECAEFCEAEADCACA(ADCAFEACAEAAECAE+AADAAEFAAADCA(EA

20 40 60 80 1000

1 103×

2 103×

3 103×

4 103×

5 103×

BCFEF :F<

CE=@==;

5F:9KA/A<AAEFAA(AAEADECACA(CADCA((A(A

FCAAEECAEAEA#ACDEA3CI]4A

,1 /ECA A

*ACAEACAEAAAEEC+AAAAEECAEAAEAECCA(EACADAAD(EACAADCAEA*ADCAA EA CA CA EA A A CA CCA ECA EECA EA EA CAEA ECCA A IHdA A CA CDEA A AQEA "CA EA A EA EA A FA5!$8%A A FA DEA *EA A CEA CA A #A DA EA ADEEFEDAACACAEFAACAEAA5EA"CAT"82AHUAA

&EAACACACDDACA EAACA(CAA CAEAECAEEA.AEAFAADCA#AD(AADACAEA(FCA:9GA8ADEAADAAACAEACACAEAACAuACAEEAA

5F:9GA/A7AAEA5!$8%A3AQEACAEE4A

"AAECAADCAACEAAACE?A

• EADECACA(CAAACAEEAAA?A!cEHj*+A

• EADECACA(CAAEAA!ACAEEAAECADEAACEC+AA

• CAAECAC(EAAEEEC+A

• EADCEADAAEHHVAAC(ADEAEAAC+A

• EADAAEAACA(CACAEEAAH<E+A

• EAAACA(CAAACAEEAAC(AADEEAAEA;AEAAACADEAA(A3(FCA:9G4+A

• A DDA CA (CA (A EA A CEA A DA DCA CA

DEC?A2

sefluide

"AACAEAAAAAA?AA

• ADAAEFAECADEAACEC+A

• EADECAAAEADEA(ACEAAA;AEA?A

+=mm l

p dyzylTl

dxzlxTl

),,(1),,(1)( AAAAAAAAAAAAAAAAAAAAAAAAA3:9AC4A

• A((AEFAAAAFAAEA;AEAEAEACEA?A

( ))()()()(zTzT

zzhfp −

= ϕAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA3:9A>4A

WAAAAAAAAAAA ( ) ( ) ⋅+⋅=mm l

dyxzyll

dxyzlxl

),,(1),,(1)( ϕϕϕ AAAAAAAAAAAAAAAAAAAAAAAAAAA3:9AE4A

AEAACA(CAAECAAEAAEADEAAA

Sf dxdyzyxv

dxdyzyxvzyxTzT

),,(),,()( AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA3:9AI4A

A EA DECA A EFA CA (CA"EAFECA A DA EA EAA DEA CAEEACEA AAACAA!3+A+A;4AA3+A+A;4A A DA EA DECAA EAACA(CACEAAA+AAA;A

*AEAAEAAAEEC+ACAEA(AEADCEADAAEHHVAAEA A EA DECA QA CA (CA A IH_*A .A EA ((A A AEEC+A AACAEA5!$8%ACADAADAADA A((AACAAD(EACADA&:%A*AA

"EA(FCACEAACACA((AEFAAFACAEEA*ACAEAA+ACAAEEEFACADA&:%A*AAEA(EAFCCAA EECA EA CA CA A CA A EA A EA A E(A AECAACACAEAAEAAEECADCAFAEAA#AEAECCAA

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45 0,5

distance de l'entrée du fluide z (mm)

50µm canal

5F:9@A/A8CACA((AEFAAFACAEEA3EAECCA

IHdACDEAAQE4A

'ADCAECACAEA(FCA:9@ACAA((AEFAAEEAAACAEEA 3A A CA (4A A CA EA ECA CA A EDDEA EA +A EAC(ACDCAAGHHHVQCAQZAA

"ADAAEFAAFACAEEAEAAEAADACAEA(FCA:9AHA"CAECA A E;A (E+A CA CD<E+A A CA CA A EA A CA A CACAAECAEA

0 0,1 0,2 0,3 0,4 0,5Distance de l'entrée du fluide z (mm)

50µm canal

5F:9AHA/A<AAEFAAFACAEEA3EAECCAIHdA

CDEAAQE4A

• CFECCFCAEA6F

*AAEAAEDA:ACAAEEEFACADA&:%A*AACAEACA A EA DECA EA A ,CCA A A FA .(A A (A AED+A EA (FCA CEA DA CA A EA DECA A FA A A FA "A3ccCId4AA+A"CA3cc>Id4AA">A3ccEId4ADAAAAEA(FCA:9AAAA*AA DCA A A CA EA (FCA A FEC+A DCA CA A ;A +A A A CADA DE(E+A A DA A EA ;A A DA A A CA (C+A A EADECAEAACAAAFA"EAEEAAEADECACACAAAA EAACA(CAEA AEEAAECAE;A(EA3(CAAIj*AEAAD4A

0 0,1 0,2 0,3 0,4 0,5

Distance de l'entrée du fluide z(mm)

L1L2L3

%H1; 1;

5F:9AAA/ADEAAEADECAEAA,CCA

6E+A EA A A EA +A CA A CA EA DCEA DA AC(A EA CA EA EA A A DCEA A CCA A ECA ECA A EAAAC(EACADEA.A AA EAEEA(CAAEADEACA(CAAECADACAEADECAEAA,CCA"EA(FCA:9ACADACA DEEA A EA DECA A A EA DEA A FA A EA ;A EA A EA((A &EA A DA EA 3CA CF4+A EA CA A EA DCEA A FA

&EAACA3CAC4+ACAA(CAADAEACAFAAIHdADECAAACA(CA<CA A AEA3CA4+ACAFEAEA#AEEAA EADEA EA A A A CA A A "EACA A DEA A CAEAA EAACAEEA

H H+A H+C H+> H+E H+IAHH

ACHECEACFEC

AACFAA

!ACFEA FEF H:<

AACFAA

5F:9ACA/A8CAAEADECAAFAAEADEACAEEADCADCCACAADCEADA

.AECAAEA(ACACACACAEADECAAFAAEADEAAA DCA ((A EA A A EA 6CA DCA C(A ECA C+A EA A EA AAADAAAC(EACADE+AAEFACAAACACA (CA CA DEA A FEA ((A ECA ECA A EA DECA EEA A(ACAD(A#AACAACAEADEAAEADECAADCAC(AEAAEAWAEADEAA((CACANAAACA(CA*EAAAFAAADCAEA(CCADEACADA&:%A*A

6A CA A A CA EA A DEEFEDA EA D(A EA A A DEA DEA ADAA((AAAAACA(CAEAAEECACAECAAAAEFAACA*ACAEAADCAECAEAAED+AAFCEAAEAACACAEAECA(EAADAAEFA8AAECACACACAAEADECAAEADCADCCAEAC(EAEFAEADCAFEA*ACAADAEAADEEFEDACEA

• -AFAAFA

.(AADADAA((AAAA+A EAFACAEAA(AADACAEA(FCA:9A>A"EAFAEAEAADFACEAEA;AE(AADA A A EA A CA (CA EA A EEA "A A ECA A ACEAEAAEAAA#AAEAAEAFEADADA

:=#=#=<

5F:9A>A/A"EAFACAEA((AAAAACA(CAEAAEEA

"EA DEEA CA EA DEA A EA DECA A FA CA EEA A A DA AEFAEAAEAEAAEA((AAADACAEA(FCA:9AEA"EADECAA A CCA FA DCA (EA CA DAA DA A ((A A "A DA AEFAAECAFADCAAEAAEAEA((AA

0 0,1 0,2 0,3 0,4 0,5

!ACFENFEFH:<

sans effets d'entréeavec effets d'entrée

0,5 0,8 1,1

Distance de l'entrée du fluide z (mm)

sans effets d'entrée

avec effets d'entrée

a) b) 5F:9AEA/A*CAA((AACAE4AEADEAAEADECAAFAAEA

DEACAEEAA4AADAAEFA

&EA A DA EA DA A DA A ((A A CA DEA A CADEAECAECAADAAEFAAAEADECACA,CCA!C(+AA((AAAADEA#AFFACCAA EA FCCAAEECAA(EAADEADAAAEFAEDDEACADA&:%A*ADCAADEA,CCAADCEAACEAEA

,, CCAFAAECAFEAFCCE% FAFEA A

"A EECA ::A A CA EDCE(A A CEA CA 3A ((A EFA %OD@1@EP#ADAAEFAQ-O-CP#EADECAAAEADEB3%OMP#EA((AADECAAEADECAAAEADEAAEADECAACA(CA QB3COEP# EA EA CA OE@DP4A A CA EECA A A ACCAEA AEACADEAADCEAEA&:%A*A/AEECAEAAEAECCAIHdAEA((ACDEA"EADCEADAEAEHHVAAEAAEADECACA(CAIH_*A3AEAAHCKAQ4AEADECAACA(CAAEH_*A

TABLEAU II: COMPARAISON DES MODELES ANALYTIQUES ET NUMERIQUES

KC )FE %OD@1@EP Q-O-CP B3%OMP QB3COEP OE@DP

EECA A+CAHEA CCEA AHEA JEA HAJA

CCA @AH>AAA CHGA AAHA KHA AHAGA

(R 1 . * *

EECA A+IAHEA IAA ACGA GGA HCCA

CCA AHIAHEA EKA AEEA AHEA HCJA

(R ,, ?

EECA A+KAHE G@A AJAA ACAA H>A

CCA ACAHEA GCA AK@A A>@A H>IA

(RA 1* ? , ,

"ACEACAACAAAE;A(AAADCAAACAAEECA:A"EADCAFEACACAAEACA((AEFA8A((+ACAEAAAA>H]AAA*AAADEAAEADCCAAEAAAFEAE;ADAAACAAAACI]AAA(EAEFEA"AECAADAAEFAEA ACAEAEAA((CAADEAADA A((AAAAACA(CAEAAEECA"CAEAAEAAE;A(EA3iAH]4A*EAACA AEAA A(CEADCACADCA CAEECAAE;ADA8AACAA EAEAC+A CAA ACAAA ECA E;A (EA 8(+A A EA CA EA A A EA A A ECA E;A(EA A CA A #A CA DA &:%A *A /A CA A A DA A AEHHVQCA DCA #A ECA DCA CA DECA A A EA DEA A AAH_*A EADACADDAEAAEECAEAAEAECCAIHdACDEAAAQEAA

> 'CEFC $CE FA CA A F FFAA!)E

"EA EEEA CA CA DA &:%A *A A CA DEA A CA ADA A EFA A ECA DEA A CA EA DECA CA DEA DEA AEECAE(AACAEAEACA&EACADAD+ACAEA[CAA EACADAEAAEEEAADEACA EADEAECCA/ACAA DA A EFA A (A CA A BCA ECA CEA CA A A DADACACAACADACAEAEAACAACAEA CA EA A CA ECCA EA FEA ((CA A FE;EFA CA (CA E(AAEACAEAAA*AEDAEAADAADAAAEADAAEAEEA CA CA EA A EEEA C+A A (+A DEA ECA EA DEACA"EADAAAEAAEEEADAEACAACEACAAADAAAAEAADEEFEDACEA

> -ACFDCFCCAC$CE

"EA (FCA :9AIA A CA DFEDA CA EA A EEEA DEA ADEAEA&:%A*AA

"AEC2 "F

"AECFAA

5F:9AIA/A<ACAEAAEEEADEAADEAEA&:%A*A

"EACAECCAAACACACDDAE(AE(AA(EA ADEFAA AEFACACA"ADEFACACAA((CAEDAAFE;EFACACAACA(CA<CA E+A CA DDA A A A A A EA (A ECA CA ECCA EA FEA ECAA CA A A (CA )A (A A ECA CA A EA 3A AH,AE4+A ADEFACACAAEA.(AAEADEAAEAEAAC+AEADCDEAAEA CA 3A 4A A CA "A (CA A A A CA CA EA CADDAAFEFAAEACACAAAEAEACAAACEA"ACADAECACAEFCAADECAAECAE(AA(AA(CAEACADEAEA&:%A*A"EACAAEADECACA(CAAAAAEAACADEAEA&:%A*AA((CADEAACDACAAEAA(CA"EADACAEAADEAEA&:%A*AAEAAECCADCCAAEA#ADA CA DA EA DA A EA CA EA A A A EA A !CA A ECAEAACACEAEADACAEAEADCAAADECAECADECAE(AAEAEACACAACACA"AEACAEAADDACADEAEA&:%A*AA((CAAEDDCEACADA"EADACAEAEADCAADAACADEA CA 3DEADEACA A E4ACADACA CA CEA /A CA DA DCA A DEEFA CA (CA DEA A EECA A CA

CA DCA EA A EA A EDCA A DA "EA CA A DA A EFA AEA EA CA EDCA A DA ((A 3DEFA A CA ,>HA A >HD<E4A A AAAAEAACAD(AAEACADEADEAA&:%A*ABCAAA DA CA A CA CA EADCAA CA EA EDA A AEEC+AACAEAECAACDAEACA(A3EAAEAEA>Hd4AFACAEEAEADACAEAEADCA

8AACAAEACAAEADECAAEADC+ACAEADEAEAAEA EA DCA DCA DCA CA DEA DA CA EEA (ECFA A A EA CA A EADECA A #A EA CA EA A /A A DEA DA A CEA CADEEA ACA 3<!B4A8A((+ADCA ADEA,CC+A EAEEA A DECA EA CA DEA A DEA CA CA EECA C+A ADEA DCA A C,#A #A A EDCA A DECA 6CA EA A CA EACAAAAAEAACA(EACEAEAAAAFEAA CAA DAAAAFCA8A((+AAADAA EA EACAEA CA (EA A 3CCA EA A 94A A EA CA CEA A A (EA ECA3CCA .A A CCA EA A .4A A CA DA A A EC,EC((A A EADCA A A EEFA CA DEEA A "EA EA CA CA DA ACA EA DECA A A EA &:%A *A EA A [C+A EA A A(AEAAEA3EAAAA4AACAEFAA%EAAACEA5E;AT58AHUA

.(AACAEADECAAEA+ACAACAEA((CAEEFACADEEAA*AEDAAACAEACAAAAEAAAEACACEAACAAA(EAECA+AE+AA(AAEADECAAEAECAAACA/ADEADAAEA EADCAEACA(CA&AAEA AADAAEAEACAADEA93!4ADCADCCADECA

8CAEADCAACAAEADECAAEAAADAACAEDA/CAEDAADEACAACACAEDAACA3(FCA:9AJ4AA

AAC)A -B/

!FC"!)E

5F:9AJA/A9CAECACAEFADEAEACAAEADECAAEAA

EA&:%A*AEA<!BA

<EA EDAADEA C+A CDCA 3(FCA:9AJ4AA (AA EAAA DECCA DEA CA (A CEA 3CCA .A A CCA AH.4A <EA CA EA A CA3AHHd4A CDCA A CA 3EDDA CA A @@]4A A EA A A DECCA DEA CACEAA(E+ACAACADCAEDAEEFA/AAEAAEAA.A8C+AADAAEACAAEACAAA"EADECADEAAEAACEAEACAADEA93!4ADEEA(AA

>1 AECADA

"EA(FCA:9AKAAACEACADCAADAAEFAA(ACAACA A EA &:%A *A EECA EA IHdA CDEA AQAJA "EA (FCA AFEAEAEEAADAAEFADCADCCAECAAEADECACA(CAAEADEEAAECADECAAEECA3DAADAA((A4A"EA(FCA

:9AKAACAA(AA CEAEACAA AECACAA AECAECAACI]+AAECAECAEADCAACAAECACA"ACADCAAAECACAEAAEECACAAA((AACAEADCAEACAEADEACAADAA(AAA8ACAE+AAADAAAAAAAFECAACAAC((EADCAEA#ACADADAAAADAAEFA

101520253035404550

0 0,2 0,4 0,6 0,8 1S:E@<

FEC-:-C<

A,=MA+=M

A1=MCEE,=MCEE+=M

5F:9AKA/A<AAEFAA(ACAADCA((ADECACA(CA

3DEEACAAEC4ADCAAEECAEAIHdACDEAAQAJA

"EA(FCA:9AGAAACEAAEEFACA<!BACAAEAAEECAEA IHdA CDEA AQAJA .A DEA A DA DA A CA A CH_*+A EA CA ADEAAEACAAAAAA(AAEADECAAE;AEAEACAAADAA,C9Q_*A

110130150170190210230250270290310330350370

10 20 30 40 50 60 70 80 90 100 110 120

Température (°C)

PTS diode 1/16Extrapolation

5F:9AGA/A*CAAAAAA(AAEADECADCACAAEAA

EECAEAIHdACDEAAQAJA

<CAEACAAEADECACADEAEADE+A AACA*EAEAAH+I>IQAEACADECAAEAADEAACCj*A3EAAAA EA A EA DEA F(E(A EA A E4A "EA DCEA DA EA A CC+>VA DCA CACEAADCEAAAGKK.A

"EA5FCA:9A@ADAEACAAAECAAAEAADEAEA(#AACA3EACACEAiA.4A

A'F:'<

5FA:9A@A,A*CAAAECAAAEAADEAEACACA<!BA

&EAAE+AEACAAAECAAAEAAEAAH+CG9AACADECAA

EA DCA A ICj*A "EA EA CA EA A A EA cAEj*QV+A ECA

EFA CDCA A A ECA EcHCCj*QVA &A CA CACDDEAAA((CAAEAECCADEAACACEA"AECA A EA EA CA CA EA CCA EA A #A A A FECA6CA EA A A CA CA DEA A A CEA E;A EA :A A DAEAADEEFEDACEA

>, -DEAA

)A (A FEEA A EA A C(EA CA EA A EA &:%A *A EA AAEDACAEFACAEAAEEEACA3(FCA:9CH4AA

5FA:9CHA/A&FEEAAEAAC(EAACAAEA&:%A*A

"EA(FCA:9CHAACADAAEAEEAA(EAEAACADCAWAADCAACA ECCAA AEA/AEAACAECCAAAECA

ECAAEECA*A(AFEEAAEAEEADCACACAAFA CA CEA EA A DEA CA DCA DCA EA ECA A A EA EACAAEACAEAADADCAECA

.(AEAA(CAAEAEEACAAD(EAAA+ACAEAAECADACACECAD(ADEADA<CAE+ACAEAACA DEA EA &:%A *A CA CA DECA A CA (A CA EA (EA EA DCADCADAAEADCEAEAADEA.DAAEF+ADCCA(AAFAAAEACAEADDA.AAD(+ACAEAAAEAAFAAEACACACEAEAADEAA((CEACACEEAAEADECAA C(EA A DCA EA CA EEA (ECFA "A EA A A EA A ECFEADFAAECACACEAACCLAAI.ABCAEAADDAACEAEA DEA A CEA DCCA EA CEA CAEFA A (EA EA A EA DCA EA ECA CAFEA DEACA FAA EA DECAEA ADEA6E+A A CEADACAEA(FCA:9CAAACAEADECAEEACAADEACCAECA #A A11A *A A A EA A A DEA CA A EA A EAEEAA(EAEEAA A,CCAADEADE(E+AAA(AA(AAEACAEDDAECAD(A%#AAECCAAADECAACACAAEF+AACAAFEAADECAEEADACAEA(FCA:9CA4AACDCAAAIHj*AEACAECAADCEAEAA(EA3DAACIV4A11A

a) b) c) 5FA:9CAA/A%CAEACAEEA(ECFAAEADECAAC(EACAAEA

&:%A*AE4!EAcAGEEj*AA!AcAEA>j*+A4!EAcAIAKj*AA!AcA>Ij*AA4A!EAcACAIj*AA!AcAEECj*A

BCAAACE+ACAEAEACCA(EACADAFCAAEEA A A EA &:%A *A )A CA EA A C(EA EA A EA EA DEAECA A DA EA A EA A A +A CA EEA DEA DCA A A CEA DCADACACAADADCAECA

EAA"A6CAEADAEAAEDAEEAAD(EACACADAA

(A &:%A *A .A A A CA A CC+A CA EAACAADADDA((EAEADAECACA(CAAECAAAEACA(EAECFEAAEADECAAEADCA"EA(AACEACAEAA A EECA A CCA DCA CA EDDA A A A AE;ADA6CAEAECADA(CAA((ADEEAFCAAA((AACAAD(EACACADA&:%A*A*ACAAA CE+A CA DCA A CA A A CA &:%A *A A EAEEADAA EACAADAACACEAEA ADEA)A(CCADEA CA &:%A *A EA EA CCA A A EFA A CEA DCA A

DEA EA CA A CEA EA CA DCA (EA DECA /A CEA C(A CAE+AACAEAEAACEAAEECAADCA (EA FCCACACACAEAEAEAACAAAA

8A A CA A A CEA DEC+A A CA A DA A EFA A A(A A A E+A A #A (CA A A ECA "EA CA DECA A EADECA CA DEA EA &:%A *A EA ECA A CA EA A EDA A ADA CEA CA A A DA !C(+A A ECA A EA CACAAAA(AEFACDCAAAACA"EACEAAEEAAC(EAAEAEAECAEADCADEAAAEAACEACA A ECA EA A A DCA DEA CA A CEA A CEA (CA ACEA ECA FA A EA EA 8A DDA A EA EA A EEA CADEACADAFCAAADDAACADCAEEDAAEADAAEAEAAAADEAE(AAFEEACAACDAAC(EAAACACAFACACEAEAADEAA

*CAFEA

"AEEAAADAEAAECAEADACALCAALEEALCACECADA A (A FA DCA DEA A DCEAA CCAEA"ACA A FEA A A A EECA CA A CA A ,FADCCA DEA A DCEA DEA EA EA #A DCA ,CA ADEACAACAA(EAEA:AAAACADACAL((ALFEA DA A CA CA A EEA A EECA ADDA A (A A DE+A A FA A A FCA DCA CA(EEA ECCA A (ECA EA CA EA ECEA DCA A A ECA A EA A(EA "LFEA LCA (C+A ECA A #A A EA ;A EA LCA DEA ADCE+A DDCEA ECA DEA A A A EA DEA CA A A "A EDACA CA FA EA A +A EA ECA CA DEA A A AEECA CA DEA #A FEA A EEA CA DCA A DEA A CA AEDDA .CCLC+A LA A A ((A A CA CA L#A A EA DA AA EDD+A A A EA A A DA CA LEA A A CA (CA CACEAAAAEA*AAEEACDAEAADA(CAACAADCACA,CC+AAC+AACAADCE+AA DA FCA DCA EA EEA A DEA CA ADCEA CA EA CA DA FA A A DA FEA BA LCA DA A CAC+AAAEDDADCA#AAAEE+AA EEAAEEADEACA((ALFEAAAEEEADE+AADCAADCA((AACAEAAAFCAAAADEAADAAEFEABAIH]ACACAAEAAEADEAACEAACE+AKI]ACADA(((AAEAA(CAEAECADDAFC+AAEAAAFCAAEAEEEADEAAD(AAA[CAAEA*+AEAAADADEAACACAEADAAAAFCACADAEAACEAACEFEA.CAAACEACACAEAAEAAEA+AAEEACA A DDA DCA ECCA A DEA LCA A DCE+AEEADC+ACAAFA*LADAAL(EAAADAADACALEAAAADDA*LAADEAACAA(EACCA DEA A LECA +A LECA CA A LECA A CA DCA EMALEAAAA

"EA A EA DA +A CA EA EA LCA CA A EA A AE+A A EA DA A ,FA DCCA DEA A DCEA DEA8A EA DA A A A DEA A CA FCA A A ECA ECADA A (EEA ECA DCA DCA (ECA A EA A DEACDA L#A DA A A A EA A *LA FEA A#A CA A EA A A C+A A A FCA A LCA #A CADEA A DCE+A EA DA LEFA EA EA A EECA EEA A DEA AA *LA A A DECA A DA +A DDA ECA EECAFEA A EECA C+A CA EA DA LEFA A (EA CA CA (CACAEDCAEACAFAWA AEDACADCEAEADCCAEA A DA DEA A :A A DCEA A CA A DCA EA EAEAA

&EA AEAADEACD+A A (EA EADEEAADEAECA ECA A EA *EA DC,+A ,A #A (EA A LA CA 0E(PA 8,A EALEFA A EDA ECA A CA DEDEFFPA *A EDDA DEA LFADCCADEAADCEAACCAEAEAEA#ADCAADDAA

*CAFEA

LFEAACCACCEADEADAADCAA LEDDA<0A*D,,*DA<**AEAD,,ACAEAFCAC((EPAA

.CA ECA CA (CA F+A A CE+A LA A CEFE+A A ACEADEA8A((+ACALEADCADCACAAEADEAEC+ACA CA A EA A FCA DCCA DEA EA DCCA A((A <EA D+A A DEA A A FCA A CA DCA ECA AD(EA CA CA DA LA EEA CA EA A ECA A A IH9A .C+AEAC,A#AEDEAEAA(CCAAAAFCAADEAFEACA&:%A*ACADCEAAEA(AAEAAADEACACEAE(EEAPA<C,CAEMA EA FA A EEA DCA A A A A FCA 3CD+A DEF+ACE4ADCAAFCAACAEAAEDDPAA

*A CA A +A A A LEA EDDA A D+A EA DCNA CA A CAC+ACADCADAACACAAECA8AAACAEAEAAAD+AACAADC,CADADCAAEPAA

"LEA EA DCEA #A EA CA A A CA CA A A LALCA A A A CA E+A CA A #A A A A EA CA AFCAAEADPAA

6CADACLA(ECAFEAAAA(EACALCAADCEAAADA CEA A CLAEA CA CA D(A CA DCA A FCA"AFAAACEADACAAAACAD(A*ACACA EA A A A A DCA#A DEA A A EA CAA DCEA CAA F=A A A A EA CA DCA EMA A CDCA FCA ADCAEAAEA

ADDEC A

(AFEDCA

T.6@CUA A.C+A<A%+AEEEDCBEEBD+AAA+A8A$+AA@@CA

T.98AHUA -A.E+AEBCEDBDEEBDCBEBCEB !CCEEBEB+A$EEAA&FAA+ACACHAHA

T.98AH,CUA-A.E+A,*A*+A"A*EE+AZA9EE+AAV;+ADDCBE"DBDCBE#CDEBEBDCCBDDDCBE+A2+A<EEEA7,:6<Q*6BQ*8.+AA6jAAHQIE>AI+ACACHAHA

T2."HGUA 2AEEA2EFE+A$BB%CEDBDCED+A8ABDF+ACHHGA

T286ACAUA "A2EE+A6ACF+AAV;+A*A*+AA&E(E+A&A"E(+A9A7EC+AZA9EE+A&'CED%CED(BDE&# )C*EBECDFBEB+DB +A:B<B&ACHAC+AADEEMA

T28H>UA .A2E+A&ZAZEC+A,+CBC,B#-+A8AAVAEAB+ACHH>A

T28@HUA .8A2F+A.A2E,*+AECD*EE(EBEDCDCBED(BB+A.EAA!EA%FA(A8A*DAEAB+A9AC+A.B%8A<+A6-+ADDC>>,>EC+AA@@HAA

T2'B@EUA 2A7$+A<EAEGIIHAK)B.A+EKGEKCH)B.+AECEAHEI7E+AA@@EA

T2)!AHUA *A2CE+A#.ECEBD/D-EB0+A!CAA:FC+A&>AAJ+ACHAHA

T*.!HIUA ,6A*EEE+A,7A2E+AgA"C+AAE+A+CEBEBD-EBC%CEDBDCEDB+A:888A!EEAA.EA<EDEFF+ACG+A>+ADDAEHE,EAC+A.CFCACHHIA

T*.UA 000EA

T*8HJUA ,*A*+A(BEBDEBCEBBDEBB+A$EEAA&FAA+A:6<7+A%EACHHJA

T*8H@UA ,*A *+A &EA A DNA A A (E[EA A CA CHH@A CA1DCBEEBD+A2A*6B+A6jH@H>>JJAA

T&.6UA 000E(A

T&8"H@UA 'A&EF+A(BDEB"CEEBEBCBEDC2DBCECEBCCDBCEB(3("!AAL)ADA5CAA7+ACHH@A

(AFEDCA

T&.@@UA &A&EFC+A7A*EE+A5A%E+A<A+A4DBDCE5BDEBCEBEBEBC CBD"A:888A<FA(A*.B+AA+ADDAJK,KH+AA@@@A

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