HAL Id: hal-00322171
https://hal.archives-ouvertes.fr/hal-00322171
Submitted on 16 Sep 2008
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Transient liquid phase bonding of titanium to aluminium nitride
Olivier Dezellus, J. Andrieux, F. Bosselet, M. Sacerdote-Peronnet, T. Baffie, F. Hodaj, N. Eustathopoulos, J.C. Viala
To cite this version:
Olivier Dezellus, J. Andrieux, F. Bosselet, M. Sacerdote-Peronnet, T. Baffie, et al.. Transient liquid phase bonding of titanium to aluminium nitride. Materials Science and Engineering: A, Elsevier, 2008, 495 (1-2), pp.254-258. �10.1016/j.msea.2007.10.104�. �hal-00322171�
24354687969:;:=<'>?A@CBED3FHGI1JLKM6N<POE?B1Q*3RTSU>A>6:;6NV?B1WX3EYPZ[6)JI1S\V#6]C^_6`J#SaGbGP6NV?BEc39RTZ8ddKe68fgBQh39ijSIEZkLlmB
n 3o"<'>CV#Z(VpESEqES1<P:;SU> lBED3srH3\tuKMZ:eZ ?
?wv
WyxBz{GEK=|P68JA>K}V#~
v"
SG Br
n
YPBEPRHI4I\<
E
GS|a69 J6
)
B
1E4tuK;:e:M6N<PJ0ZGEGE6
r6IE6OaBQUJZ8GP[6
f r"o FJ6GSP:M6B v xco n5jci v ci{B ) J0<6HIE6\>_ Z8JV JA>BP b HJ68GSP:6Hr6I68O B
Q'JgZ9G[6
l_YEx0WF^B1o
n
Y1o"oHBPr
n
YPB
E
J0<6HIE6:;ZqPKC>[K;GP6\BP
E
YPZ8K;G\V'WZ8J0VK;G4Iw=i48Jg6>hr6IE6OaB
Q'JgZ9G[6
j'L ¡)¢E£8
c_K}V#ZGEK}< ¤pEZ>ha66G>0<[[6>`>de<w:M: kSK;GP6IVS4Z:}< 4K¥GPK=<w ¦GEK}VJKMIE6F:n ZNVZV#68 qP6)JZNVC<PJ6HZ\>:;S§
Z> Eb¨ r!B1<'>K¥GE©4FH©P]r"<ªr"<>K;:M«¦[S 4 68J[KMZ9:EEJgZ87b6HZ9:;:;S 3¬XpEKe:M6J6Z[NVK=|a6§46NVMVK;G1©ZGEI
>#qEJ6ZIEK;G1©4qEJSP[66I>hZNVwVpE6Fu:
n
EJZ8796HZ9:;:;S
K;GV#68JdZ[6B[)pE6 4Ke[Z:PK¥GV#68JZ[`VK;SEG>hIE6|a6:;SaqZNV
Vp6VK}V#Z)GEK< >KeIE6Jg69GIE68JK;G1©4qPSU>A>K=P:e6HKC>S1VpE68J 4Z:'>S:;KmIaK;dKe[ZNV#K;SEG4SEdUVp6hkgSK;G\VA3c_pE6
IE6`V#68J 4K;GK;GE©dZ[NV#SaJ®K;GVpE6>gSa:;KMIaKMdKM[ZNV#K;SEGqEJSP[6\>(>*Ke>®VpE6HdZ\>V®dSaJ 4ZNV#K;SEG4SEdc*K;r"<P¯*[8J >V#Z:°>®
p6NV#68JSE©P68G6S<'>G\<[:;6ZNVK;SEG4ZGEI©EJS1§HVp4K¥GuVpE6H:¥K±\<wKMI²qEpZ1>613F>*ZH[SEG>g6±\<'6G[6B1VpE6EJgZ876
Z:;:;S K°>hIE68q:M6NV#6I²K;G4r"<ªZ9GI>SE:¥KMI4FH©²qEJg6[K=qKsV#ZNV#6\>`3FudeV#68J*Z8GEGE6Z9:MK;GE©PBVp6J6]0 46:}V#K;GE©
V#6) qP68JZNVC<PJg6SEdUVp6J6\><w:}V#K;G1©,kSK;G\V[Z8Gu6K;GE[)J6Z1>6I<PqV°SZNaS<bV
)E¨
r%§{pEKe[p4KC>*GE6Z8J:
E¨ r³pEK;©p68JVpEZ)GVpE6H 46:}V#K¥GE©4qPSEK;G\VSadwVp6>0V#Z8JCVK=G1©4EJZ)76HZ:¥:S 3
´µ`¶E·4¸
¡)¹'8º'»!¡8¢E¼®(½
µ
¼w _¾e½M¿'À½M¹ÂÁ'Ã'¢E
µ ¸
¼w¹'½M¼ÄbŽM
¸
#Ã
µ
¡Æ¢a¾
¸
¾M½e¹'½¥Ç#½e£¢1 g½
¸
¼'ÅÆ
µ
¢1¾P
¸
£ µ
¡)¢Eƽe£H¡)¢1ȽM¼ÄEÅ1jÄ1ÉÊÀ¢1¾;¾
¸\¶
Å
µ8Ë Á µ
¡)½eÆ
µ
¼w ¢1¾w À'¹
¶
Ž;¼w
µ
¡`Ç¢E£½e¢E¾'¡
µ
¢E£8 ½Ì½;
¶
ÍEÎwÏ`ÐMÐCÑ(ÒeÓÏ`ÔÕ`Ö}Ô×"ØÙ`Ú=ÛÏ`Ð#Ü Ï`Ý=ÖßÞÖ=ÑÐàÕ8Ñá(ÑÝ=ÝßÙ9Ò0âÙ)Ô8ÖßÞã;ÝßäÏ`ÔPå(àæMÐ
ç
ÑÝCÜ`è;éEê)ê(ëEì"í)î*ì8ì ï8ê*ï`ðhñòbØAóÜ8è=éê8ê`ë1ì*í8î*ì)ì"ô)ðHåï
¸ ¸
D SaK;GEK;GE©V#Sa©P6(VpE6)JVK}V#Z8GEK=< ¦SaJ'VK}V#Z8GEK=< Z\>g6HZ:e:;S >V#S4[68JZ 4KM[\>L><[p4Z\>*F:2 gBYPK n ¯ BYEK;r!B
c_K `YPKMr 3¥3;3_Z)J6K; ²qPSEJCV#Z8G\V®Ke>`><6\>V#SP6HZIEI1Jg6\>(>g6I²K;GVp6>[SEqP6HSad'qEJSPI\<[8K;G1©:;S1§4]°§j6K=©Pp\V
pEK;©PpE]L>VJ68Gb©1Vp4[SE qPSaG6G\V>><[9pjZ\>_pP6ZNV6NOa[pEZG1©P68JA>"qPZ)J°V>SaJwVC<PJ0PK;G6P:eZI6\>*dSEJ<'>6HZNV
6IEK=<w V#6 qP6)JZNVC<PJ613F/§4Z Sad'©EJ6ZNV®qES\V#68GVK;Z:dSEJ*Z[8pEKM68|PK;GE©jVp6\>A6©PSPZ8:C>*[SEG>KC>0V>*K;G
kgSK;GK;GE©VpE6aZ\>A6 j6NV#Z:1VSVpE6H[6)JZ ²KM[\>_
JZ87K;GE©²§4KsVp4ZdK;:e:M68J*Z:e:S
Ba(3
c_pE6qEJg6\>6G\V'§{SEJKC>*dS[`<'>(>6I²SEGVp6H[8pE6 KM[Z:M]0qPp >KM[Z:Z\>qP6[NV®SEd1kgSK;GEK¥GE©4q1<PJ6VKsV#Z8GEK}<
V°S>K¥GV#68J6IFu:
n
§jK}Vp>K¥:=|68Jg]#aZ\>A6IEJgZ876HZ:e:;S >`3PY1<[8p4Z:;:;S >"pPZ8|a6P66G4[8pESw>6G>K;GP[6q1<PJg6
:MKM±\<wKMI>K;:|6)J"pZ\>*Z:;J6ZI 66G<'>g6IVSkgSK;GVK}V#Z8GEK=< ¤Z:;:;S > (3W S1J6)S1|P68JB\Vp6FH©P]c"K
[Sa qPS1<PGEIw>_FH©c*KPZ9GIFH©Pc"KwZ)J6GES1Vw|P6)J >0V#Z`P:e69VpP6 IE6[S qPSw>6HZNV Z8GI ) E¨ r!B
Jg6\>qP6[`VK|6:
A31c_pE68Jg69dSEJ6BEZpEK©pVKsV#Z8GEK=<w Z[NV#K=|PK}V
K;GVpE6H:¥KM±\<KMI²dZ8|PS1<PJZNP:M6V#SdZ1>0V
Jg6Z[NVK=|P6§j6NVCVK;G1©SEd'F:n [Z9Ga6H6OqP6[NV#6Iw3b2HGVpE6,S\VCpE6)J_pPZ9GIEB\VpE6H 4K°> ZNV#[)p²K;G[SP68ddKM[9KM6G\V
SEdwVpE68J 4Z:68OEqPZG>K;SPGr!coP6`VC§466)G4chKPZGIjFu:
n
[Z8G4K;GPI\<[6VpE6HIE6`|P6:;SEq 6G\VSEd
Jg6\>K;I\<Z:>VJ6\>A>6\>gB[8JgZ[PK¥GE©SEdwVpE6H[68JgZ9 4KM[HZGEI4dZ9KM:=<wJ6,SadwVp6HZ\>(>g69 : 3 v S1§46)JK;G1©VpE6
JZ87K;GE©V#68 q68JZNVC<PJ6KM>P6 V#S4:¥K; K}VK;GE©VpE6H6dd6[NV®SEdr!co 4KC> ZNV#[8pEB11<EVK}VZ8:e>gSK¥ 4qP:eKM6\>*Z
IE6[8J6Z\>g6HSadwVp6§4SEJEK;G1©V#68 q68JZ`VC<PJ6dSaJwVp6EJZ8796IZ\>A>6 w:
VpZNV*>pS<:;I6pEK;©p
6)GES1<P©Ep²dSEJ_©ESESPI§46(VeVK;Gb©ZGIª>#qEJ6ZIEK;G1© (3bcJZ8GP>KC68GV®:¥KM±\<KMIjqPpEZ>A6PSEGEIEK¥GE©c v ^'RBaKm3}6b3
KC>gSVp68J 4Z:>gS:;KeIEK;dKM[ZNVK;SEG4SadwVp6TJZ876HZ:;:;S BKC>*ZqEJS1 KC>K¥GE© 6NVpESPIVS>gZNVKe>d aSVpjSad
Vp6\>6H[SaGVJZI1K;[NV#SEJ J6±\<K=J6 6G\V> ] L3
c_pE6)J6dSaJ6BadS1<PJ*Z8:;:;S K;GE©6:;6 6GV>VpEZNV®dSEJ ¦ZpESP SE©P68G6S<'>:¥KM±\<KMI{§jK}Vp4FH©Z`V
V#6) qP68JZNVC<PJg6\>*:;S§j68J'VpEZ8GVp6 j69:sVK;GE©4qPSaK;GV_SEd'q1<PJ6FH©pEZ8|P6669GuV#6\>0V#6INVp6\>6HZ)J6YK;BPu6B
YEG4Z)GEI4r"<®3\Fu 4SGb©jVp6 4Br"<ªpEZ\>_©PK=|6GVpE6a6\>0V®J6\><w:sV>"K;GV#6)J >*SEd_>0<[[6\>`>de<:EJgZ87K¥GE©
Z[[SE qwZGEKM6I KC>S1VpE68J 4Z:'>S:;K;IEKedKM[Z`VK;SEGw3
µ µ8Ë µ µ ¸ µ µ
¬ pE6G¤Z8|aZ9KM:MZP:M6B²Vp6 >V#Z8J°VK;Gb© ZNV#6)JLKZ9:C>.<'>6I¤K;G¤VpE6XqEJ6\>6)G\V §{SEJ §j68J6[8SE 4 6)J[KeZ:
qEJgSI\<[(V>`3^'<J6yVKsV#Z8GEK=<w c_
SEJ©EJZIE6 0q1<PJ6chK§jK}VpBK¥GX§VA3 H2
3
Q®6
3s
i 3 r 3)n 3 §jZ\>><PqEq:MKM6Ij n K;GPZNV#6[HK;GVpE6HdSaJ ¦SEd:MZ\>g68J*[N<EV*> 4Z:e:EqP:MZNV#61>
§jK}Vp ZVpEKM[PGP6\>A>,Sad 3'YK;G\V#6)J6I F:n [68JZ KM[1>§j68J6²><PqEq:MKe6Iª RHSPSw>0V#6[K;G4VpE6²dSEJ
SEdqP:MZNV#6\>_§4K}VpZVpEKM[G6\>`> Sad
3
² 3Ec_pP6Hq:MZNV#6\>*pPZIZj><PJdZ[6HJS<P©EpEG61>(> SdVp6SEJIE68J*SEd
3 ZGI Vp6K=JHJ6\>KMI\<Z:"qPSEJ#SU>K}V §4Z\>Sad! |aS:C33'c_pE6 [SaGV#ZK¥GP6I E] §uV3 SEd VCVJKMZ
2 Z8GI³S1O ©P69G%§jZ1>4qEJ6\>g69GV4Z`VHVpE6K=J >0<PJd#Z[6%IES1§{G%VS/Z.IE68qVp Sad{Z d#6N§ V#68GVp>Swd
GZGES 46`V#68J(> ) (3 n SÂ>0<PJ#dZ[6VJ6Z V 46GV*S\VpE6)JhVpZ9GªIE68©EJ6Z>K¥GE©ªZGEI²JK;Gw>K;GE©²§Z>Z)qEq:MKe6I²V#S
Fu:n §4pE6)J6Z1>_VpE6>0<PJdZ[6uSdVKsV#Z8GEK=<w §jZ\> IE6S1OPKMIaK;7b6Ij 6[pEZGEKM[Z:w©EJK¥GIaK;GE©Hk<'>0V®P6dSEJ6
JZ87K;GE©'3c_pE6 FH©P]r"<%JZ87K;GE©Z:;:;S
§²Z\>4>0<PqEqP:¥KM6I
SPSI1d6:M:;S§ K;G VpE6 dSEJL SPd
b
VpEK[ >p66NV>`3 chp6 [SaqEqP68J[)SaGV#68G\V{SEdu §uV3 0 Z`V3.r"<[8SEJ0Jg6\>qPSEGEI>V°SyVp6 FH©P]#r<
6`<EV#6[ VK[H[S qPSw>K}V#K;SaGu§4K}Vp4ZH 69:sVK;G1©4qPSK;GV_Z(V
bE¨
rH3
c*S6N|PZ:}<ZNV#6H§46NVCVK;Gb©SaGZGEI >qEJg6ZIEK¥GE©SPdVpE6jJZ8764Z:;:;S SG\V#S F:n ZGEI c"K;B_>S j6ª>g61>(>Ke:m6
I1JgSaq6NOqP68JK¥ 6G\V>_§j68J6u[Z8JJK;6IS1<1V<PGIE68J_|PZ[N<E< ) ^ZK;GZ8G68OEqP68JKe 6G\V#Z:Z8qEqPZ8JZ`VC<'>
[Sa qEJKC>K;GE© Z9G Z9:=< K;GPZ VC<EP6 pE6ZNV#6I
Z¤YKMr J6\>KC>V#S1J VpEZ`V §jZ\> Z:=Jg6ZI
IE61>[8JK=6I
6:C>6`§4pE68Jg6 E (3aR,JZ87K;G1© 68OEq68JK; 6GV>§468Jg6jJg6Z:eK;76IÂK;GZ²pSV*§4Z:;:_pESEJK=79SaGV#Z9:®±\<Z8JV7jVC<Ea6
VpZNVH§jZ\>qP:;Z[6IK;G Z [SaG1|a69GVKSaGZ9:VC<Eb<w:MZ8J4dC<PJGEZ[613*chp6 68OEqP68JKM 6GV>§j68J6 [Z)JJKe6IS<EV
<PGIE68J²|aZ[N<E< )@^Z§4K}Vp c"K,qPS§jIE68JZ\>4©PZ\>©P6NVeV#6)JVSJ6I\<[6ÂVp6 Jg6\>K;I\<Z:HS1O ©6G
qPZ)J0VK;Z:wqEJ61>(><PJ613Pc_pE6qP:MZNV#6ZN< V#68 {qP68JZNVC<PJ6H§4Z\> J68©1<P:MZNV#6I²V°Sªa6NVeV#6`J_VpEZ8G®{BVp6pP6ZNV#K;G1©
Z)GEI [SPSE:¥K;GE© JgZNV#6\>!§468Jg6Z8:C>S.[SEG\VmJSE:;:M6Iw3wxG VpE6dS:;:CS1§{K¥Gb©PB_Z:¥:Vp6²J6)qPSaJCV#6IJZ87K;G1©ÂVK; 61>
[SaJJ6\>#qPSaGIjVSVp66dd6[`VK=|P6HqP68JK;SPIdSaJ_§{pEK;[pjVp6j>gZ ²qP:M6pEZ>"P669G Z9K;GV#Z9K;GP6IZNV*[SaGP>0V#Z8GV
V#6) qP68JZNVC<PJg6BVJgZ8G>K;6GVHpP6ZNVK;Gb© Z9GI%[SPSE:¥K;GE©.VK¥ 61>46`OP[:=<IE6Iw3¬XpE6G%G6[6\>`>Z)J B[)J0<[K:M61>
:MKM±\<wKMIEJZ)76HZ:e:;S
3
FudeV#68JHp6ZNVVJ6Z V 46GV,ZGEI [SPSE:¥K;GE©ÂV#S J#SESa V#6 qP68JAZNVC<PJ6)BVpE6 >Z 4q:M6\>§j68J6[pEZ8JZ[NV#68JK=76I
Saq1VK[\Z: 6`V#Z9:;:;SE©EJZ8qPp #2TW B>A[ZGEGEK¥GE©¦6:M6[NVJ#SaG 4KM[8JSw>[SEq AYo*W Z9GI 6:M6[NVJ#SEG
qEJgSa6 4KM[8JSPZ8GEZ: >(KC> °o*^WyF `3/xG qPZ8JZ:;:M69: V#S VpE6 >0VC<I SaG K¥GV#68JdZ[6\>gB Z qEpZ>g6
[)pEZ8JZ[NV#68JK=7ZNV#K;SEG §jZ\>.[Z8JJK;6I S1<1V
]0JZ IEK¥d#d0JZ[NVKSaG
H
54B4r"<
α JgZIaKMZNVKSaG .ZGEI o*^'WF¦SEGFH©P]r"<]c*K'[S:;IE]qEJ6\>`>6IqPS§jIE68J>gZ9 {q:M6\>!p6ZNV#]°VmJ6Z(V#6I Z V®VpE6²>gZ 6HV#68 q68JZNVC<PJ6
Z)GEIdSEJhVp6j>AZ 6TV#K; 6 A31x°V®§4Z>hVp<'>"|a68JK¥d#Ke6IjVpPZNV'VpE6u[8J >V#Z:¥:;K;GP6qPpEZ\>A6>dSEJh§4pEKM[pVpP6
K;GV#68JdZ\[6%J6Z[NV#K;SEGX:eZ 68J(>SEJ qPZ8J0VK;[:M6\> ZGEZ: >6I/§68J66dd6[NVK=|a69: S11V#ZK;GE6I³<GEIE68JVp6>g6
[SaGIaK}V#K;SEG> 3
{µ (Àw¾; ¢E¼'¹¹½M(£À'A(½¸ ¼
"!#$%&')(+*,-'./*&0-1
x#GZ²dK¥JA>0V,>0V#68qPB'K}V"§jZ\>|68JK;dKM6IVpEZNV*VpE6Fu:
n
[68JZ KC[\><'>g6IÂK;GVpEKC>§jSaJ °§{K}VpK}V>u>0<PJdZ[6
S1OPK;IE6H:MZ 68J§Z>§6NVMV#6I Z:eKM±\<K;IFH©P]c"KPZ:M:;S qEJ68qPZ8Jg6I ,324 5 IEK=JA6[NV_ j69:sVK;GE©SdFu©
Z)GEIc*K'SaGVp6F:
n
>0<Pw>VJZNV#6 L>6\>A>K;:e6{I1JSaqª[SEG1dK¥©1<PJAZNVKSaG `31FuG 68OEqP68JK; 6G\V* ZIE6uZNV
EEE¨
r
6dd6[NVK=|a69: >pES1§46I©PSESPIª§j6(VeVK;G1© Sd Zª> Z:e:_Fu:n q:;Z`V#6{ :eKM±\<KMI >KM:|6)J§jK}Vp 3 ZNVA3 SEd
c_KPZIEIE6Iw3bFdeV#68J*Z)G²K;GI\<[NVKSaGqP6)JLKSI4SEd E >gB[)SaJ#J69>#qPSaGIaK;Gb©jV#SHVpE6HIEKe>`>S:s<EVK;SaGjSd_>S:;K;I4cK
K;G:eKM±\<wKMI4FH©PBZ8Gj6±\<wKM:eK=PJK=<w [SEG\V#Z[NVZ8Gb©:6HSd®
¨
§jZ\>*ZNVCV#Z8K;G6I²K;G
E
>`3\¬Xp6G² jSaJ6VpZG
3 ZNVg3 c_K"§Z\>{qEJ6\>A6G\VuK;G:MKe±\<KMIFH©PB!Z > Z:e:M68Jj[\SEG\V#Z[ V{Z8Gb©:6 E¨ §jZ1>4ZNVCV#Z8K;G6IK;GZ
>#pESEJ0V#68JVK; 6
E
> `35468qP6)GEIEK¥GE© SEG Vp6 c_K!Z[NV#K=|PK¥V B>qEJ6ZIaK;G1© SPdVpE6 :;Ke±\<KMIZ:¥:S §jZ1>
Z>(>SP[K;ZNV#6I§4K}Vp VpE64dSaJ 4Z`VK;SEGZNV*VpE6VJK=qP:M6²:MK¥GP64Sd69KsVpE68J,Z>K;GE©P:M6{VpEK;G :MZ 6)JSEdGEK}VJgSa©P68G]
qPSESEJVK}V#Z8GEKs<w GEK}VJKMIE6 #c"Kn @ 76
SEG\V°SF:n :;S1§ c"K'Z[VK=|PK}V SEJ ZIES1<EP:;6HJ6Z[NVK;SEG:MZ 68J_§4K}V#p
@
6
c_KPZ[NV#K=|PK}V
`3
6Z[NVK=|a6 §46NVCVK;Gb© §jK}Vp³VpE6dSEJL jZNVKSaGXSEdc"Kn
¯ ZNVVp6%F:n :;Ke±\<KMI K;G\V#6)JLdZ[\6 §jZ\>Z:C>S
S1w>g68J0|a6I²§4pE6Gc_
§jZ\>"JZ87b6IjV#SFu:
n
ZNV
EEE¨
rXdSEJ
4K¥G4<'>K;GE© Z
)E VpEKM[ >p66NV
SEdq1<PJ64FH©.Z\>HdKe:M:M68JH 6NV#Z:C3_YEqEJ6ZIEK;G1©.SEd!:¥KM±\<KMI Fu©.SEG >gSa:;KMI c"KB_IaKe>`>gSa:s<EVK;SEG Sad"Vp6:MZNVCV#68J
6:;6 6G\VjZNVHVpE6.c_K :eKM±\<KMI³K;G\V#68JdZ[6.ZGEI K;©EJZNV#K;SEG Sad{c"KK;G%Vp6 :eKM±\<KMIyV#S1§4Z)JI>Vp6 Fu:n
><PJdZ[6 Vp\<'> Z8qEqP6Z8J6I Z\>¦d#Z\>0VqEJSP[6\>A>6\> 3 WSaJ#6S1|P68JBSEGE[6 Z [9p6 KM[Z:³PSEGEI §jZ1>
6>0V#ZNP:;KC>pP6I ZNVHVpE6 K;G\V#68J#dZ\[6 a6NVC§j668G F:n Z9GI VpE6 FH©P]0JKM[p:eKM±\<wKMIEB"VpE6 :MZNVMV#68JJ6Z[NV#6IZ(V
EEE¨
r³§4K}V#p c"KV°S©EK=|a6²>S:;KMIFH©Pc"KFH©Pc"K' 3ßq'3
)
E¨
r `3T<K;[VpEKM[P6GEK;GE©SadVp6FH©PcK
:MZ 6)J*IE69 jSGw>0VJZ(V#6IVpE6Hd6Z1>K=PKe:MK}V Sd1kSPK¥GPK;GE©Fu:n VSc_K1§4K}V#p4FH©² VJgZ8Gw>KM69GV_:;KM±\<wKMIqPpEZ1>A6
aSaGIaK;GE©X§4K}V#p ZJ6Z>SEGEZ8P:M6yVK; 6]°V#6 qP68JgZNVC<PJ6 [ [:M613Hc_pE68Jg69dSEJ6pEZ8|PK;GE© Z8J#JLK=|6IZNV4VpEKC>
qPSEK;G\V#BwVpE6 ZNVeV#6)J§jZ\>V°S :;S§j68J!VpE6jJZ87K;GE©ÂV#6 q68JZNVC<PJ6
ZIEIEK¥GE© ZG 69:M6 6G\VV°S FH©VS
IE6[8J6Z\>g6KsV>" j69:sVK;GE©4qPSaK;GVA3
%5% % $&, 1 5 % %/2 %&./*&0-1
Q<PJ0VpE68JJZ87K;GE© 68OEqP6)JLK; 6G\V>§j68J6u[Z8J#JLK6IS1<1VZNV EE¨ r/dSaJ_ ²K;G§4K}V#pVpE6HFH©P]r"<JZ87b6
Z:;:;S
3EF> 68OEqP6[NV#6I²dCJSE qEJg6N|PK;S1<>§jSEJPB
EB _[9:M6Z)Gc*K><PJLdZ[\6>§46)J66Z\>Ke:
§6NVMV#6I
Vp6Â:;KM±\<wKMI%Z:M:;S VpPZNVuZ)qEqP6Z8J6I 68G\V#K=J6: >SP:¥KIaKMdKM6I%KeG VpE6 dSEJ Sd,q1<PJ6ÂFH© ZdeV#68Ju 4KeG
JZ87K;GE©'3xV!KC>§4SEJCVp GES1VK;G1© VpEZNVTZ [)SaGVK;G\<S1<'>uc"K
6
r"<TJ6Z[NV#K;SEG.:eZ 68J§4K}Vp.Z²VpEKM[PGE6>`>uSd
] §4Z\>ªdSaJ 46IZNVVp6%c_K Z:M:;S K;G\V#6)JLdZ[\6BJ68qP:;Z[K;GE©³VpE6 VpEK;[XFH©Pc"KH[S qPS1<PGEI
:MZ 6)J"qEJ68|PK;S1<'>: [pEZ8JZ[NV#68JK;76IZNV EEE¨ r§4pE6G4q1<PJA6FH©§jZ\>"<'>g6Iw3EuSSPI²Jg6Z[(VK|a6§j6NVCVK;G1©
Z)GEI[pE6 KM[Z:PSEGEIEK¥GE©%§jZ1>4Z:C>S S>68J|P6IZNVHVp6ÂFu:
n
>0<PJd#Z[6§jK}Vp.VpE6 dSEJL jZNVKSaGySad{Z
IES1<EP:;64:eZ 68J,chKn @
6
chKBFH©PBr"<B'F:n 3chp6\>A6J6\><w:}V>,Z)J6²K;GZ8©EJ669 6G\V*§{K}Vp qEJ6N|PK;S1<®>
S1w>g68J0|aZNVKSaGw>* 4ZIE6HZ`VFu:
nj
FH©P]#c"K;]r"< K;GV#68Jd#Z[6\>
]
)
A3
@
76
a6:;S§ qEJS 4S1V#6\>H>qEJg6ZIEK¥Gb© SPdhVp6jEJgZ87b6²Z:M:;S
SEGVpE6²Fu:
n
>0<P'>0VJZ(V#6
J6Z[NV#K=|P6§6NVMVK;G1©
+ → +
x#GjVpEKC>*J6Z[NVK;SEGEBFu:n Z9GIc"Kn @ 76
Z8J6K;GVpE6>S:;KMI>V#ZNV#6§p68J6Z\> c"KZ8GIF:'Z)J6IEKC>(>gS:=|P6IKMG
Vp6:¥KM±\<KMI²EJZ8796Z:e:;S
3FV
EbE¨
rBVp6K=Ew>!dCJ666G68J©
|PZ8JKMZNVK;SEG dSaJ*VpEKe>J6Z[NV#K;SaG KC>!GSV
|a68J G68©ZNVK=|6BSEd"VpE64SEJIE68J,SEd]EPD3} jS:@ ) (3wFu[[SEJIEK¥Gb©: BVpE6J6Z[NVK;SEG [ZGÂqEJSP[66I
SEGE: KedVp6H[pP69 4KM[Z:wZ[`VK=|PK}V Sd®c"KwK;GVpE6H:eKM±\<KMIjEJgZ9796HZ9:M:;S KC>*pEK¥©Pp6GES1<P©EppEK=©pP6)JVpEZG4
) §jK}Vp J6d68Jg69G[6VS%:;KM±\<wK;I>0V#ZNV#6 `3'chpZNVT[SEGEIEK}VKSaG.KC>dC<w:;dKM:e:M6I §4pE6GÂVp6ªJZ87b6 Z:e:;S K>
6K}Vp68J_q1<PJ6HFH© SEJ*Z8G4FH©P]0W Z:e:;S VpEZNVIESP6\>*GES\V®dSaJ# |P68J >0V#Z`P:e6Hc*K
6 W *[S {qPS<PGI>Z`VVp6
c_K
:MKe±\<KMI K;G\V#68JdZ[6 [Z\>g6³SEd r"<`3QSaJS\Vp68J Z:;:;S
K;GE© 69:M6 6G\V> VpEZNVªdSaJ# 4SEJ6 >V#ZNP:M6
[Sa qPS1<PGEIw>§4KsVpÂVK}V#Z8GEK=< ><[9p Z\>4YKB"u6 ZGEIYEGEBVpE6 Z[NVK=|PK}V Sad,c"K*K;GÂVpE6 :;Ke±\<KMI JZ87b6
Z:;:;S KC>V#SES³:;S1§ VS[8SEG\|a68J0V{F:
n
K;G\V#S/c_K
n @6
BZ> 6NOqP68JKe 6G\V#Z:;: |P68JK;dKM6I ZdeV#68J4
4KeG
JZ87K;GE© ZNV EbE¨ rH31F jSaJ6u±\<ZG\VK}V#Z`VK|6uZ8qEqEJSPZ[8p[SEG>KC>0V> K¥Gª[SE qwZ)JLK;Gb©²VpE6{69GVpEZ:;qKM6\> Swd
dSEJ 4ZNV#K;SEG4Sd®c"K;]°W PSEGEI><'>K;GE©VpE6W KM6IE6 Zß>* 4SwIE6: (3Q'JSE VpE6HJ6\><w:}V>qEJ6\>A6G\V#6I4K;G
c*ZNP:M6 BK}V*Ke> [:M6Z8J_VpEZNVFH© Z8GIr"<dSaJ VpE6§46ZP61>0VaSaGI>_§4K}Vpc"KC31xVKM>hVp6GK;G4q1<PJ6FH©
Z)GEIÂK;G VpE6²FH©P]#r < Z:e:;S >VpEZ`V"Vp6²Z[NVK=|PK}V SPdc"K®KC>VpE6²pEK;©PpE61>0V#Bw§pEK[9puk<'>0V#K;dKM6\>VpE6<®>64Z1>
JZ876HZ:M:;S Sd®6N<EV#6[NVK;[FH©P]#r <4§4KsVp
ZNVg3.r"<0
§uV3.r"<B1 3ßq'3
bE¨
r 3
W ∆i ED 4S:PSEd®ZNV#SE >
c_K=W c_K=W chK W chK
W
FH© ]
)
]0 ]
]
)
r"< ]0E ]0 ]0 ] E
YEG ]0P ]1 ]
E
]1
u6 ] ] ]1 ]E
YPK ] ] ] ]
c*ZNP:M6 3brZ:;[`<w:MZNV#6I|aZ9:=<6\>*dSEJVp6pE6ZNVSEddSEJ 4ZNV#K;SEGEB
∆iaSad®c"K;]CW [SE qPS<PGIU>hSad®dS<PJ IEK;d0d#68J6GV_[Sa qPSw>K}V#K;SEG>*Z[[SaJgIaK;G1©V°S{Vp6W K;6IE6 Z>* 4SPIE69: (3
§j6NVMVK¥Gb©ZNV'PS\VpK;G\V#6)JLdZ[61>
Vp6EJZ8796HZ9:;:;S pZ\>*6G1JKM[pE6I4K;G²FH©41<EV®K}V>*[)J >V#Z9:;:MK¥79ZNVKSaG
SP[[N<PJ#J6I<PqSaG4[SESa:;K;GE©0FH©P]r"<ª6N<EV#6[NVK;[6`VC§466)GqEJKe Z8J FH©4©EJZK;Gw>
Q®K;©'3 >#pES1§>TZc_K
FH©P]r"<P
ZNV
Fu:
n
kgSK;G\V,ZdeV#68JEJgZ87K¥GE©.dSEJ
4K;G.ZNV
EbE¨
rH3wx°V!KM>H[:M6Z8J
VpZNVZ VVpE6H6GEI4SEdUVpP6EJgZ87K¥GE©SEqP68JZNVKSaGB 4Sw>0V®SEdwVpP6EJZ87b6HZ:e:S K°>!>VK¥:M:wK;GVpE6H:eKM±\<wKMI >0V#ZNV#63
x#GEIE66IEB²Vp6 4Ke[)JSU>VJ0<[(VC<PJ6XSadÂVpEKC>yZ:¥:S 68OPpEK=K}V(>yK¥G ZG q:MZ[6\>.VpE6[pEZ8JZ[NV#68JKe>0V#KM[
jSaJqPpESE:;SE© Sd*Z>gS:;KeIEK;dKM6I FH©P]r"< 6N<EV#6[NV#K;[Z:e:S §4K}VpªIEZ8J JS1<PGEIE]L>#pPZ8qP6I [8J >0V#Z:C>!SEdr"<
6 P6IEIE6I K¥G Zj§{pEK}V#6FH©. Z`VJK=O'3 v Z8J©P64qEJK¥ Z8J FH© ©EJZK;Gw>H[Z9GpES1§j6|a68Ja6>g6\6G §pEKM[p
K;GPIEKM[ZNV#6\>Z9G6GbJLKM[pE 6G\V K¥G Fu©SdVp6²Z:M:;S I\<PJK;GE© EJZ87K;GE©'3'YPS 46F:®d0JgS F:
n
pEZ\>,Z:C>S
IEKe>`>gS:=|P6IÂK;GVp6²:;KM±\<wKMIZ9:M:;S 3az{qPSEG[SESa:;K;GE©PBFu:qEJg6[K=qKsV#ZNV#6I§4K}Vpr"<.Z)GEIc"KK;GVpE64dSaJA
SEd"Vp6dK;GP6²©EJ6 qPZ8J0V#K;[:e6>|PKC>(K=:e6²a6NVC§j668GÂVp6²qEJK; Z)J FH© ©EJZK;Gw>HGP6Z8J!VpE6Fu:
n
>0<PJdZ[6E3
2HGVpP64c"K">KMIE6B®Z[SEG\V#K;G\<S1<'>!J6Z[`VK;SEG 7SEGE6§4K}V#pZjVpEK;[PGP6\>A>HSEd ) ]0 KC>,S1'>68J|PZ8P:M613
Fu[[SaJgIaK;G1©V#So*^WyFZ8GPZ: >g61>B1VpE6J6Z[NVK;SEG²:MZ 6)J>A6±\<68GP[6HK;GVpEKC>"79SaG6KC>*c"K c"K
c"K r"<
VpEK;G:M6\>(>*VpEZG
VpEKM[ Z8GEI [SaGVK¥G<S<'> :MZ
68J Sad*c"K
n @ 76
BwK}V>g69:;d*[S1|68J6Ij§4K}VpªZ:MZ
68J Sd
©EJg6 qPZ8J0V#K;[:M6\> [SEG\V#ZK;GEK¥GE©c"KB n BFu:wZGEIr"< K=O6I§4K}Vp4 6NV#Z:;:eKM[j>KM:=|68J`3bchp6J6Z[NV#K;SEG7SEGP6
SEGVpE6Fu:
n
>KMIE6KC>*VpE6²>gZ9 6Z>"VpEZ`V*[8pZ8JZ[NV#6)JLK76I r!Z8JK; ZGI v S68pE ZG
)
§4KsVp²VC§jS
><EP:MZ 6)J(> ZX:;Z 68J SEd c"Kn
SEG F:n ZGI ZGES1VCp68J>0<PP:MZ 68J% ZK;GE: [SEGw>KC>0V#K;G1© Sad Z
±\<Z`V#68JGEZ)J qpZ\>A6c"K;B®r"<BFu: n §jpESw>64[8J >V#Z9:*>0VJC<[NVC<PJ6pEZ>66GIE6NV#68J 4K¥GP6I 5<PJ:=<
6`V_Z):C3
L3
&+ % %& ( ')0-1 ! %#$ , 1$55 %
Q®K;©'3 >pES1§>Vp6ªV qPKM[Z: 4SEJqpS:;SE© SadTZÂc"K FH© ]ur"< Z(VA3 F:n kSPK¥GVuZdeV#68J 4KeG
JZ87K;GE©ZNV Eb¨ r!B§{pEKM[p²KC> E¨ r :;S§j68JVpZ8GqEJ68|PK;Sa<'>: ZGI²SEGE: ¨ r³Z8PS1|P6Vp6 j69:sVK;GE©
qPSEK;G\VhSad'VpE6JZ876Z:M:;S
3EF²> K¥G4VpE6dSEJ 68J[Z\>A6Bwc"KUZ8GEIFu:
n
pEZ8|P6HP66G²Jg6ZIEKe:
§j6NVCV#6I
Vp6:¥KM±\<KMIFH©P]r"< Z:e:;S 32GVp6jFu:n >KMIE6B'ZVpEK;G Z8PS1<EV 3 1<EV [SaGVK¥G<S<'>!:Z 68J,Sd
VKsV#Z8GEK=<w GEK}VJK;IE6ÂpZ1>IE68|a69:SaqP6I Z:e:!S1|P68JHVpE6F:
n
>0<PJdZ[6 ZGI%Z8JS1<PGEI>S j6ÂF:
n
©EJZK;G'>
:S[Z`V#6I [:;SU>g6VS²Vp6²>0<PJ#dZ[6 °Q®K;©'3a 3EchpEKM>! 6Z9Gw>*VCpZNV_VpE6:;KM±\<KeIEJgZ876Z:;:;S pZ\>!GES1V*SEG1:
>#qEJ6ZI4SEG\V#S4F:n ><PJdZ[6Tb<EVpZ1>*Z:°>gSK;GEdKe:}VJgZNV#6I©EJZK;GjaS<PGIEZ8JKM6>hSdwVpE6>K¥GV#68J6I4[6)JZ KM[
J6Z[NVK=|6§j6NVCVK;G1©'3P2GVp6c"K_>KMIE6BZJg6Z[NV#K;SEG 7SaG646ObV#68GEIEK;GE©S|a68J jSaJ6HVpEZG Z4pEZ:ed Sd
Vp6²kSPK¥GV§{K;I\Vp KC>S'>g68J|PZ8P:M613"xG%VpEKC>4J6Z[NV#K;SaG79SaG6BVp6 :;Z 6)JÂ>6±\<69G[6 KC>c"K c"Kr"<
c_KMr"<
c"K gr < ¯ FH©
c"K;r"< ¯
FH©'3PrSP qPZ8J6I§4K}Vp§{pEZ`V_§4Z\>S'>g68J|P6I Z`V
EbE¨
r!BVpE6VC§jS]
qEpZ1>6I >0<PP]:MZ 68J,c"K
c*Kr"<.pPZ\>,IEKC>Z8qEq6Z8J6IÂZNV_VmpE64K¥GEGP6)J>KMIE64Sd_VpE6J6Z[NVKSaG 7SEGE64ZGPI
Vp6jVpEK;G c"Kr"< H:MZ 68JH:;SP[ZNV#6I ZNV!K}V>TS1<EV#6NJu>K;IE6pEZ1>a66GÂJ6)q:MZ[6IÂ Zj§4KMIE6jVC§jSP]0qEpEZ\>g6I
:MZ
6)J ZK;G:
[SEGw>K°>VK;Gb©%SPd>gS:;KMI FH©% K=O6I§4K}V#p%[J
>0V#Z:C>uSEdVp6Â[S qPS1<PGEI.c"KMr"< ¯ 3xCV,KC>
§jSEJ°Vp GS\VK¥Gb©VpZNV_VpE6|aS:}< 64SEdhVp6²:;KM±\<wKMI J6 Z9K;GEK;GE© K;GVpE6!kSK;G\VZdeV#68J 4K;G EJZ87K;GE© K>
<[p%> Z:e:M68JTZNV
E
VpZ9G ZNV
EbE¨
rH3wxG S1VpE68J!§4SEJI>gBhKC>gS\VpE68J 4Z:!>S:;KMIaK;dKM[ZNVK;SEG qEJSP[66I>
d#Z\>V#68J*ZNV Eb¨ ryVpZ8G4ZNV EbE¨ rH3
>#qEJ6ZIEK;G1©4 J6Z\[`VK|6§j6NVMVK¥Gb©ZNV'PS\VpK;G\V#6)JLdZ[61>*Z8GPIKC>S1VpE68J Z:w>SP:¥KMIEKedKM[Z`VK;SEG4SEdwVpE6
JZ876HZ:M:;S S|a68J" jSaJ6VpZ8G4ZpZ9:Md®SdK}V>®|PS:}< 6 °VpE6HIES\VMV#6I:;K;GP6>pES1§>®VpE6H:¥K±\<wKMIE]L>gS:;KeI
aS<PGIEZ8J ZNV
Eb¨
r
+ %&5 % 24 %& !%2
F4>>gSSEG Z>"VpE6Fu©P]r"< Z:e:;S 6:}V>gBVp6c"K'PZ\>g6² 68V#Z8:wP68©PK;Gw>V#SÂI1Ke>`>gS:=|P6K;GVpE6:eKM±\<KMIw3F
c_KP[pE6 KM[Z:PZ[NV#K=|PK}V ©EJZIEKe6GVwVp\<'>*Z)qEqP6Z8J(>a6NVC§j66GjVp6>0<PJdZ[\6>*SadwVp6TaZ\>6H 6NV#Z:°§4pE6)J6
Vp6c*KwZ[`VK=|PK}V KC>_VpE6pEK;©PpP6\>0V Z8GIF:
n
°§4p68J6KsV*K°>*VpE6> Z9:M:M6\>0V`3¬XpE6GVpE6uc"K'Z[`VK=|PK}V K>
><wddKM[KM69GV: pEK;©p/K;GVpE6 |PKM[K;GK}V SdVp6%c_K><PJLd#Z[6BHc_K;r"<P¯ [8J >0V#Z:e>qEJ6[K=qPK}V#ZNV#613!c_pE6 c"K
Z[NVK=|PK}V ZNVVp6F:n :;Ke±\<KMI K¥GV#68JdZ[6Z:C>S.K¥GP[)J6Z\>A6\>Z8GEIEB_ZdeV#68JTZ[68JV#Z9K;G K;GPI\<[NV#K;SEGÂqP6)JLKSIEB
a6[S j6>upEK;©PpE68JVpZ9GVpE6²Vp1Jg6\>pES:I |Z:=<6 dSaJVp6dSaJ 4ZNV#K;SEG.Sd,c"K
n @6
3'FVVpEKM> jS 69GV#B
Vp6:;KM±\<KeIa68©K;Gw>_V#S>qEJ6ZI4SaGHVpE6H[6)JZ ²KM[1>_ Jg6Z[VK=|a6§46NVCVK;Gb©'39Qw<PJVpE68J_©EJS1§HVp{Sad®c"Kn @
6
Z)GEI c"KMr"<P¯ÂVpE6)G qEJSP[66I> :eKM±\<KeI qPpEZ>6/IEKedd°<®>K;SEG Sdc*K4ZGEI r"< ZNV#SE >.IES1§GXVpP6
[)pE6 KM[Z:"qPS1V#68G\VKZ9:*©EJZIEKM6G\V>{SadTSaqEqSU>KsV#6 >K=©PG VpEZNV,pZ|a6Â6>0V#ZNP:MK°>pP6I%K¥G Vp6Â:;Ke±\<KMI JZ87b6
Z:;:;S 3'HJS1§HVpSad c"KMr"<P¯[)J >0V#Z:e>HKC>,Z[[SE qZGEKe6I VpE6qEJ6[K;qPK}V#ZNV#K;SaGSPd>gS:;KeIFH©Â©EJZK;G'>
qEpZ1>6Ic"K;r"< ¯
FH©>S:;K;I:MZ
68J 31FGKe 4qPSEJ°V#Z8GV_d6Z`VC<PJ6j>#pES1§GK;G²Q®K;©'31 Ke>_VpEZNV:MZ8J©P6uchKMr"< ¯
[)J >V#Z9:C>!©EJS1§ Z(V_VpE6PS1<PGEIPZ8J P6`VC§466GVp6ª>gS:;KMIÂFH©Â©EJgZ9K;Gw>,ZGEIVpE64:eKM±\<KeIFH©P]r"<.Z:e:S 3
c_pEKC>H 6ZGw>VpZNV,K;d[)J >0V#Z:;:eK;7bZNVK;SEG.SEd!c"KMr"< ¯ ZGEI.F©.6dd6[NVK=|a69: P6)©K;Gw>uZNV VpE6c*K>0<PJdZ[6
§{pE6)J6 VpE6 c"K Z[NVK=|PK}V K°> VpE6¤pEK;©p61>0V#B K}V qEJSEqPZN©PZ`V#6\>³ p6NV#68J#Sa©P68G6S1<'>X:¥KM±\<KMIE]L>S:;KMI
G<[:e6ZNVKSaG ZGEI ©EJS1§Vp3 xCV KM> Vp6 :MZNVCV#6)J qEJSP[6>(> VpZNVJ6\>0<:}V> K¥G JZ)qKMI KC>gSVp68J 4Z\:
>gSa:;KMIEKedKM[ZNV#K;SEG4SEdUVp6EJZ)76HZ:e:;S
ZNV:;S§XV#68 {qP68JZNVC<PJ6b3
F4>,:;SG1© Z1>,ZGÂFH©P]r"<.:MKM±\<wKMIÂKC>,qEJ6\>6GV!K;GVp6kSK;GVBwVpE6J6Z[`VK;SaG:MZ 68Ju>6±\<6GE[64S1|P68J!
Vp6HchK'>KMIE6KC> 1c"K
c*KAr <
c"K;r"<
c"K gr < ¯ FH©
c"KMr"< ¯ FH©
v 3bc_pE6u[SaJ#J6\>qSaGIaK;Gb©IEKeddC<>K;SPG
qPZ`VpÂpZ\>P669G I1JZN§jG K;GVp6²FH©P]r"<]c"K®qpZ\>A6IEK;Z8©EJAZ Z`V Eb¨ r qEJ6>6G\V#6IK¥G Q®K;©'3' mVp6
[Z9:[N<w:MZNV#6I KC>gS\VpE68J KC>PZ>6I SEG E(3Px°V,[Z8Ga6²J6) Z)JP6IVpZNV"Vp6c_Kr"< H[Sa qPS1<PGEI K>
KC>`>K¥GE©PB1§{pEKe[p4[Z9GuP6H68OEqP:MZ9K;GP6I
PK;GP6NV#K;[1>*[SEG>KCIE6)JZNVK;SEG>
(3
>gSa:;KMIEKedKM[ZNV#K;SEG4SEdUVp6:;KM±\<KeIJZ876HZ:e:S
qpZ>g6HIaKZ8©EJAZ9 ¦[Z9:M[N<:MZNV#K;SaGuZ\>6I4SEG
E
2 "%& 5 "! % &% , %&5
QSaJ*ZkSEK;G\V'EJgZ876I4ZNV Eb¨ r K¥Gu§pEKM[p4K°>gSVp68J 4Z:>gSa:MKMIaK;dKM[ZNVK;SEG4K°>Pk<'>0V[SE qP:M6NV#6IEB\VpE6
Jg6Z[NVK;SEG4:MZ 68J>6±\<69G[6HZNVwVp6HchKw>KMIE6HKC>BPchK c"Kr"< chKr < c"K r"< ¯
FH© c"K;r"< ¯ FH©
AY6[NVK;SEG4w31EB\Q®K=©'3`3Fu[[SaJI1K;Gb©jV#SHVpE6J6Z[NVK;SEG>[pE6 6©PK|6G
oJ6 46G PS6NV®Z):C3
P
SEJwVSVpE6qPZ)J°VK;Z:P:eKM±\<KeI\<'>qEJSNkA6[`VK;SEG4I1JZ`§G4K;GQK;©'3PB UVp6J6]0 j69:sVK;GE©V#68 qP68JgZNVC<PJ6
>#pES1<w:I{Vp6SEJ6NVK;[Z:M: a6
bE¨
r3xGIE66I²K;GVp6FH©P]#r<]c_K1V#68JGZ8J > >0V#6 4B1VpEZNV'|PZ:}<6
[SaJJ6\>#qPSaGI>VSVp6V#68 qP68JgZNVC<PJ6SEdwVpE6HK;G1|PZ8JKMZG\VwVJZ`G>dSEJ ZNVKSaG
+→
+
x#G²dZ[NV#Bc_K r"< ¯ §4K;:;:a6dSEJ 46I²K;GqP:MZ[6HSEd®c"Kr"< b<EVwVpE6J6]0 46:}V#K¥Gb©V#69 {qP68JZNVC<PJ6
§jK¥:M:GSV'a6|P68J IaK;dd#68J6G\VA3brSE qPZ8J6I{§jK}VpVpE6H 6:}VK;Gb©jV#6) qw6)JZNVC<PJ6,SadwVpE6FH©P]#r <4JZ876
Z:;:;S bP¨ r B1VpE6J6]0 46:}V#K¥GE©V#68 {qw68JgZNVC<PJ6Ke>*SEGE: >:eK;©Pp\V#: K;GP[8J6Z1>6I C :M6>A>VpEZG4 E¨ r `3
n S1§ K;dwVpE6_kSK;G\V®KC>* 4ZK¥GV#ZK¥GP6I²Z`VwVpE6JZ87K;GE©jV#6) qw6JZ`VC<EJ6,Sad Eb¨ r Z9deV#6)J_Ke>S1VpE68J 4Z:
>gSa:;KMIEKedKM[ZNV#K;SEG4K°>h[Sa {q:M6NV#6IEB\Vp6J6]0 j69:sVK;GE©V#6 qP68JZ8VC<PJ6§K;:e:E©EJgZI\<'Z:;:
K;GP[8J6Z\>A613xGEIE66IEB
>gSa:;KMI>0V#ZNV#6H[)pE6 4Ke[Z9:PJ6Z[NVKSaGP>§4Ke:;:PqEJSP[66I<PqPSEG4Z8G1G6Z:eK;GE©²a6NVC§j668GVp6Hc"K1PZ1>6H 6NV#Z:
Z)GEIVpE6Hc"K
6
r"<*K¥GV#68J 6NV#Z8:;:eKM[H[S {qPS<PGI>_qEJ6\>g69GVZNVVp6HchKw><PJdZ\[6HSaJ®K¥GuVpE6>SP:¥KMIEK;dKM6I²FH©
aZ1>6H 4ZNVJK=O'3bchp6H[8pE6 KM[Z:EqPSV#6)G\VK;Z:E©EJZIEKM6G\V>*SEd®S1qEqPSU>#K}V#6>K=©PG²dSEJ*c_KPZ9GI4r <4VpZNV®6NOPKC>0V
a6NVC§j66GVpE6aZ\>6H 6NV#Z:PZ9GIVpE6Fu:n [68JZ 4KM[1>EJK;G©uVpE6HI1JK=|PK¥Gb©dSEJ[6HdSaJ><[8p>gSa:;KMI>0V#ZNV#6
|aS:}< 6HIaK;ddC<'>K;SGqEJgS[6>(>6>"K;GVp6§4pESE:M6VJZ8GP>K}VKSaG79SaG613
bE¨
r³ZdeV#68J 3 PB1P
Fu[[SaJgIaK;G1©P: BPZ:e:1VpE6Hc*Ker"<P¯*K;GEK}VKMZ:;: dSEJL j6I4ZNVZpEK=©p{JZNV#6§{K¥:M:aa6H[SEG1|P68J0V#6IjdK;J(>0V®K;G\V#S
c_K r"<P¯*ZGEIVp68G4K¥GV#Sc_K;r"<ªZ9GI4chK
r < c*K
r"< KC>* 4K0>A>K¥GE©a6\[ZN<'>6>gS:;KeI>V#ZNV#6©1J#S§HVpjSaGE:
qEJgS[66I>>:;S1§: `3QK©'3 >pS§>*ZkSPK¥GVwVpEZ`VpZ\>_P66G4ZGEG6Z:e6I²Z`V Eb¨ r³dSEJ pES1<PJ(>
ZdeV#68J_pZN|PK;GE©²a66GEJZ76I²Z`V
EbE¨
rdSEJ 4K¥G312uGE: VC§{SK;G\V#68J 46`V#Z9:;:MKe[H[S qPS1<PGEI>§j68J6
[)pEZ8JZ[NV#68JK=76I o*^'W F K;GVp6VJZ8G>KsVK;SPG7SEGE6P6`VC§466)GVpE6Hc"K1Z>6H 6`V#Z9:PZ)GEIVpE6HF:n
[68JZ 4Ke[1> K*chKr <4§4KsVpqPZ)J0VK;Z:wr"< FH© >0<Pw>VKsVC<EVK;SaGuVpEZNV'dSEJ >*ZH[SEG\VK;G<S<'>*K;G\V#68J 46IaKMZNV#6
:MZ
6)J§4K}Vp4ZVpEK;[ GP6\>`>hSad
)
]
¦ZGI K;K*c"K
r"<²VpZNVZ8qEqP6Z8JA>"K;GVp6dSaJ ¦SEdd:MZP61>
K=O6I§4K}Vp4c"KPS1|P6)J*ZHIE68q1VpSEd® 4BSEd®Z>K;G1©P:e6]0qpZ1>6I4K¥GEG68J*:eZ 68J*Z8GEI4SEd'©:;SE1<:eZ)J
[)J >V#Z9:C>*K;G4[SEG\V#Z[`Vw§KsVpVpE6FH©P]0JKM[p4 4ZNVJK=O°Q®K;©'3
`3xCV®Ke>_GSV#ZNP:M6VpZNVVp6§pS:;6J6Z[NV#K;SaG
:MZ 6)J*[SaGV#ZK¥GP>*ZHd6N§¦ZNV#SE 4KM[qP68J[68GV>*SEdFu:MB§{pEKM[p²KMGEIEKM[ZNV#6\>VpZNV*>6[SaGIEZ8J J6Z[NV#K;SEG>*K;G
Jg69:ZNVKSaG§jK}VpVpE6|PKM[K;GKsV SdwVpE6Fu:n [68JgZ9 KM[\>*SP[[N<PJ(>*Z)deV#68J":SaGb©jVK; 6HZGEGE6Z:MK¥GE©'3
n
68©P:;6[NVK;G1©F:PIEKedd°<®>K;SGBVp6J68 46:}V#K;GE©V#68 q68JZNVC<PJ6!dSaJ><[8p4Z_kSK;G\V®K;G§4pEKM[p4Z:;:aVp6Hc"K;]
r"<ª[SE qPS1<PGEI>*K;GK}V#KMZ:¥: dSaJ 46I4Z8Jg6H[SaG|68J0V#6IK;G\V#S{chKMr"<ªZ8GEI4c"K r <4<PqPSEG4ZGEGE6Z:MK¥GE©KC>
[:;Sw>6V°SVpEZNVUSadwVp6K;G1|PZ)JLKMZG\VVCJZ8GP>dSaJ 4Z`VK;SEG
+
→ +
QSaJ'VpEZNVPVJZ8GP>dSaJ 4ZNV#K;SEGEB1oJg68 46G PS6NV®Z8:C3J68qPSEJCV®ZV#6` 4qP68JZNVC<PJ6,Sad
Eb¨
r P(3r!SE qPZ8J6I
§jK}VpVpE6>V#Z8JCVK¥Gb©FH©P]r"<ªZ:;:;S VpPZNV® 46:}V>*ZNV bE¨ r!B\VmpE6J6] 46:}V#K;GE©V#68 q68JZNVC<PJ6,SadwVp6
JZ876_kSK;GV_ZdeV#68J
pES1<PJ(>*Z8GbGE6Z:¥K;GE©K°>®VpE6GGE6Z8J:
E¨
r³pEK;©PpE68J 3
Q®K;©'3
3EYo*W K; Z8©P6HSEdZHc*K
FH©P]r"<P
ZNV
F:
n
kSK;G1V®Z)deV#68JEJZ)7\K;Gb©dSEJ 4K;G4ZNV
EbE¨
r Z8GI
><E'>6±\<6GV_Z)GEGE6Z:eK;GE©ZNV Eb¨ r dSaJ EE 4K;G
Ê ¸ ¼£)¾eÀ'A½¸ ¼
c_K}V#ZGEK}< ¤pEZ>ha66G>0<[[6>`>de<w:M: kSK;GP6IVS4Z:}< 4K¥GPK=<w ¦GEK}VJKMIE6 c v ^R K¥GuVpE6V#6 qP68JZ`VC<PJ6
JgZ8G1©P6 E ] EbE¨ r!B<'>K;GE©ZFH©P]r"<ªr <'>KM:M« [SP ² 68Jg[9KMZ:EEJZ87b6HZ:;:;S 3\FV EbE¨ r!B1VpE6:;KM±\<wKMI
Z:;:;S JZ8qPKMIa: >qEJg6ZI>_ Jg6\Z[NVK=|6§46NVMVK;G1©SaGVS4F:n §{pEK;:M6Hr <ª[SEG\V#ZK;GE6I²K;GVpEKC>*Z:e:;S
Jg6Z[NV>§{K}Vp4c*K1VS²dSEJ ¦dS<PJ_K;GV#68J 46NV#Z:;:eKM[H[SE qPS<PGIU> 1c_Kr"<Bc*K;r"<Bc_K r"< ¯ ZGEI4c"Kgr < 3
F4>*ZJ6>0<:}V®SEdUVpZNV®K;G\V#68JZ[NVK;SEGEB1VpE6EJgZ876HZ:;:;S KC>*Ke qPS|a68JKe>pE6I4K;Gr"<41<EVVpE6H 4ZkSaJK}V KC>
>VK;:e:wK;GVp6:;KM±\<wKMI>0V#Z`V#6HZ8deV#68J
4K;G²JZ87K;G1©'31FV
Eb¨
r!BEJ6Z[(VK=|6§46`VeVK;G1©ZGEI>qEJg6ZIEK¥GE©ZNV
Vp6F:n EJgZ876HZ:e:;S K;G\V#68Jd#Z[6HSP[[N<PJ(>gB§{pE68Jg6Z\>*KC>S1VCpE6)JL Z:'>S:;KMIaK;dKM[Z`VK;SEG4SEdwVpE6EJgZ87b6
d#Z\>V">gSa:;KMIEK¥d#Ke[ZNVKSaG4KC>*68OEqP:MZ9K;GP6I
Vp6G<[:e6ZNVKSaG4ZGPI©EJ#S§HVp4K;GVpE6:;KM±\<KeIEJZ)76HZ:¥:S
Sd
Vp6Hr"<]0JK;[p4[SP qPS<PGI4c"K;r"< ¯ 3
WSaJg6©P68GE68JgZ9:;: BPZ©PSESPI{<PGIE68J(>V#Z8GEIEK;G1©SadwVp6qEp >AKC[Z:;][p69 KM[Z:qEJSP[6\>A>6\>®VpEZNVIE6N|a69:Saq
I\<PJK;G1©aSaGIaK;GE©4pPZ\>_P66G4Z[9pEKM68|P6I²SEGVp6PZ\>KC>*SdwVmpE68J 4SPI GPZ KM[HZGEI K;G6NVK[
[SaGP>KeIE6)JZNVK;SEGw>*K¥GuVpE6FH©P]r"<]c"K1V#6)JGEZ8J > >V#69 ª3 6Z[NVK=|P6§j6NVCVK;G1©ZNVVpE6Fu:n JZ876HZ:e:S
K;GV#68JdZ\[6K;G1|PSP:|PK;GE©c"K
n @ 6
dSaJ 4Z`VK;SEG4pEZ\>_a66G4S>6J0|a6IVS²qbJSP[66ISaGE:
dSEJ*ZH[8pE6 4KM[\Z:
Z[NVK=|PK}V Sd®c"KPK;GVpE6H:;Ke±\<KMIjJZ876HZ:;:;S pEK;©p68JVpEZ)G4ZVp1J6>pES:;I|aZ9:=<6B1§{pPZNV®Ke>*K¥G
Z)©EJ66 46G\V'§4K}VpuVpE68J 4SPI GEZ KM[HIEZNV#Zb3
6Z[(VK;SEG4:eZ 68J>g6±\<68G[\6>*ZNVwVp6HchK
JZ876HZ:M:;S
K;GV#68JdZ\[6pPZ|a6P66GJ6:;ZNV#6IVSVpE6FH©P]#r <]#c"KEqEpEZ1>6HIEK;Z8©EJgZ9 <®>K;GE©VpE6HIEK¥ddC<'>K;SGqPZNVp
[SaG[68q1VA3 6] 46:}V#K¥Gb©V#69 {qP68JZNVC<PJ6>_pEZ8|P6669Gj6N|Z:<UZNV#6IdCJSE J6Z[NVK;SEG>A[pE6 6HIEZNV#Z13Q'SEJ*Z
JZ876IkSK;GVEk0<'>V">gSa:;KMIEK¥d#Ke6I²Z`V_ZJZ87K;G1©V#6 qP68JZ`VC<PJ6!Sad
E¨
r!BVp6J6]0 j69:sVK;GE©
V#6) qP68JZNVC<PJg6K°> bb¨ r!BKC3s6131:6\>`>VpEZ)G4 ¨ r³Z8aS|a6VpE6H 6:}V#K;G1©V#6 qP68JZ`VC<PJ6SEdwVpE6>0V#Z)J°VK;G1©
JZ876HZ:M:;S
b¨
r `3
n
S1§ dSEJVp6>Z 6hkgSK;G\V®de<PJ0VpE6J*Z8GbGP6Z:M6I²dSEJ
pES1<EJ(>*Z(V
Eb¨
r!B\VpE6
Jg6]0 6:}VK;Gb©jV#6 qP6)JZNVC<PJ6K;GE[)J6Z\>A6\>®V#S Eb¨ ry§{pEKM[p²KC>_G6Z8J: P¨ rpEK;©PpE68JVpZ8GVpE6
6:}V#K;GE©²qPSEK;G\V®SEdwVpE6>V#Z8J°VK;Gb©²EJgZ876HZ:;:;S 3
Fu[ GS§4:6I1©w6 6G\V> 3 c_pE6HZN<bVpESEJ(>_©EJZ(V#68de<:;: Z[ GS§4:6I1©P6VpE6Q'Jg69G[pW K;GKC>0VJ dSEJ
6\>g6Z8J[p4dSEJ_de<wGIaK;GE©VpEKC>_J6\>g6Z8J[p§jSaJ K;GVpE6HdCJZ 6N§4SEJ4SEdwVpE6©P68G68JKM[qEJSa©EJgZ8
`Y1<PqP68JA>SEGEK;±\<'6`39WZ9G VpEZG >*Z)J6HZ:e>SI\<6VSVp6>0VZdd®SdwW Ke[)JSU>g[SEq r!6G\VJ6dCJgSa
z{GEK=|68J(>K}V
v*
SG r!c
§p68J6Y1o*W S>68J|PZ`VK;SEG> Z8GIo"^'WFZGEZ:
>61>§j68J6
qP6)JdSaJ 46Iw3