第 27 卷 第 3 期
2006 年 3 月
半 导 体 学 报
C HIN ES E J O U RN AL O F S EM I CON D U C TO RS
Vol. 27 No . 3
Mar. ,2006
Influence of Interconnection Conf iguration on Thermal
Dissipation of ULSI Interconnect Systems 3
Xiao Xia1 ,g , Yao Suying1 , and Ruan Gang2
( 1 Center of A S I C , S chool of Elect ronic an d I n f ormation Engi neeri n g , Ti anj i n Uni versit y , Ti anj i n 300072 , Chi na)
( 2 S chool of I n f ormation S cience an d En gi neeri n g , Fu dan Uni versit y , S han g hai 200433 , Chi na)
Abstract : The eff ects of adjace nt met al laye rs a nd sp ace betwee n met al li nes on t he te mp e rat ure rise of multilevel
UL SI i nte rconnect li nes a re i nvestigate d by modeli ng a t h ree2laye r i nte rcon nect . The heat dissip ation of va rious
met allization tec h nologies concer ni ng t he met al a nd low2 k dielect ric e mp loyme nt is si mulate d i n det ail . The J oule
heat ge ne rated i n t he i nte rcon nect is t ra nsf e r red mai nly t h r ough t he met al li nes i n each met al layer a nd t h r ough
t he p at h wit h t he s mallest t he r mal resist a nce i n each Ield laye r . The te mp e rat ure rises of Al met allization a re ap 2
p r oxi mately ρAl /ρCu ti mes higher t ha n t h ose of Cu met allization unde r t he sa me conditions . I n a ddition , a t her mal
p r oble m i n 01 13μm globe i nte rcon nects is st udie d f or t he w orst case ,i n w hic h t he re are no met al li nes i n t he lowe r
i nte rcon nect layers . Several t yp es of dummy met al heat si n ks are i nvestigate d a nd comp a re d wit h regar d t o t her mal
eff icie ncy ,i nf lue nce on p arasitic cap acit a nce , a nd op ti mal application by combi ne d t he r mal a nd elect rical si mula2
tion .
Key words : UL SI i nte rcon nect ; heat dissip ation ; ge omet rical conf iguration
EEACC : 2570 ; 2800
CLC number : TN 4051 97 Document code : A Article ID : 025324177 ( 2006) 0320516208
1 Introduction
In advanced UL SI interco nnectio n systems ,
low dielect ric co nstant material s are adopted to
mitigate parasitic effect s such as capacitance , time
delay ,and cro ss talk noise. A s a majo r by2effect ,
t he p ro blem of heat dissipatio n beco mes more criti2
cal since t he t hermal co nductivit y of low dielect ric
co nstant material is normally very low [ 1 ] . For in2
stance , nanopo ro us silica ( aerogel or xerogel , de2
pending o n t he fabricating p rocess) is a good candi2
date for insulator s since it s effective dielect ric co n2
stant can achieve an expected value below 2 [ 2 ] .
However ,low t hermal co nductivit y causes serio us
heat t ransfer p ro blems in UL SI circuit s. The heat
generated by current p ropagatio n alo ng metal lines
(J o ule heat ) must be dissipated acro ss t he dielec2
t ric films into t he subst rate to avoid t he deteriora2
tio n of t he device perfo rmance and p remat ure de2
vice failure. Thus ,t hermal behavior in modern UL 2
SI interco nnect systems must be taken into ac2
co unt . Therefore ,analysis of t he heat dissipatio n in
t he metallizatio n system is very significant .
Shieh et al . [ 3 ] simulated t he temperat ure dis2
t ributio n of a five metal layer interco nnect st ruc2
t ure wit h different dielect ric co nfiguratio ns ( SiO2 ,
low dielect ric co nstant material , and air gap s ) .
Chiang et al . investigated t he effect of via separa2
tio n and low2k dielect ric material s o n t he t hermal
characteristics of multilevel VL SI Cu interco n2
nect s [ 4 ,5 ] . Chen et al . simulated t he temperat ure
rise of a power line to t he subst rate of t he interco n2
nectio n in t he t hree cases of a single power line ,a
power line wit h a parallel signal line in t he same
metal layer , and a power line wit h an o rt hogo nal
line array in t he lower metal layer [ 6 ] . We p ropo sed
heat sinks to imp rove heat t ransport in modern in2
terco nnectio n systems [ 7 ] . We al so simulated t he
t hermal performance of a five2multilayer UL SI in2
terco nnect [ 8 ] and deduced a set of co mpact quasi2
analytic equatio ns for estimating t he temperat ure
dist ributio n of vario us UL SI interco nnectio n st ruc2
3 Pr oject supp ort ed by t he Scie ntific Researc h Foundation f or Ret ur ned Overseas Chi nese Sc hola rs of t he Education Mi nist ry of Chi na
g Cor resp ondi ng aut hor . Email :xiaxia o @tju. edu. c n ; xiax58 @ya hoo. com
Received 13 J une 2005 , revised ma nuscrip t received 6 N ove mber 2005
ν 2006 Chi nese I nstit ute of Elect r onics
第3期
Xiao Xia et al . : Influence of Interconnection Co nfiguration o n Thermal Dissipation of UL SI …
t ures [ 9 ] .
There are many factor s t hat affect t hermal dis2
t ributio n and heat t ransfer in metallizatio n inter2
co nnectio n systems ,such as t he t hermal co nductivi2
t y of t he dielect ric material s ,resistivit y of t he met 2
al lines ,current densit y of t he metal lines ,and geo 2
met ric parameters of t he metallizatio n system.
Many researcher s have st udied t he t hermal behav2
ior of interco nnect s wit h st ruct ures who se geo met 2
ric parameters are fixed. However , t he co nfigura2
tio n of a multilevel interco nnectio n may greatly af 2
fect t he heat dissipatio n of t he system. Therefo re ,it
is important to plan caref ully t he interco nnect co n2
figuratio n. Generally ,t he heat dissipatio n of a mul2
tilevel interco nnectio n can be st udied in a simplified
st ruct ure. In t his paper ,a t hree2layer metallizatio n
interco nnect is mo deled to investigate t he influence
o n t hermal dissipatio n of adjacent metal layers ,
space bet ween metal lines , t hermal co nductivit y of
t he inter2layer dielect ric ( Ield) and int ra2layer die2
lect ric ( Iald) ,and power supply. Al and Cu metalli2
zatio ns wit h vario us interco nnect cases are st udied
in detail . The t raditio nal dielect ric SiO2 and t he low
dielect ric co nstant material aero gel are applied in
simulatio n of bot h Cu and Al metallizatio n. In addi2
tio n ,a t hermal p ro blem in 01 13μm glo be interco n2
nect s is st udied for t he wor st case ,in which t here
are no metal lines in t he lower interco nnect layers.
Several t ypes of dummy metal heat sinks are inves2
tigated and co mpared wit h regard to t hermal effi2
ciency ,influence o n parasitic capacitance ,and opti2
mal applicatio n by co mbined t hermal and elect rical
simulatio n.
517
5 T)
5 T)
5 (
5 (
kx
+
ky
+ 5x
5y
5y
5x
・
5 (
5 T)
5T
( 1)
kz
+ q = ρCp
5z
5z
5t
・
where T is t he temperat ure , q is t he heat genera2
tio n rate ,ρis t he densit y , Cp is t he heat capacit y , t
is t he time ,and k x , k y , k z are t he t hermal co nductiv2
ities in t he x , y ,and z directio ns , respectively. For
static heat t ransfer , T is independent of t .
In an interco nnect ,t he J o ule heat generated by
current in t he metal lines sho uld dissipate easily in2
to t he subst rate to avoid limitatio ns of device per2
formance and p remat ure device failure. The heat
・
generatio n rate q of t he metal lines can be calculat 2
ed by
2
・
l
1
I Rt
2
2
= ( J A ) ρmetal
×
= J ρmetal ( 2)
q =
tV
A
lA
where V is t he volume , I is t he current , R is t he re2
sistance of t he metal line , J is t he current densit y ,
ρmetal is t he met al resistivit y , a n d l a n d A a re t he
le ngt h a n d a rea of t he met al li ne , resp ectively.
Figure 1 s h ows a c r oss secti o n of t he si m ula 2
t e d i nt e rco n necti o n ,i n w hic h M a n d S a re t he dis2
t a nces bet wee n t he t w o met al li nes i n t he f i rst
met al la ye r a n d t he seco n d met al la ye r , resp ec2
tively. The t e mp e rat ure dist ri buti o n of t he i nt e r2
c o n nects dep e n ds o n ge o met ric p a ra met e rs , resis2
tivit y of t he met al , t he r mal co n ductivit y of t he di2
2 Simulation of thermal dissipation
In heat t ransfer ,t he t hermal energy of mat ter
in o ne regio n is t ransferred to mat ter in anot her re2
gio n. The t hermal analysis of a system is based o n
t he energy balance law. In t his mechanism ,molecu2
lar collisio ns cause t hermal energy to be t rans2
ferred f ro m o ne molecule to anot her . Very energet 2
ic molecules lo se energy in t he t ransfer p rocess ,and
lower energy molecules receive energy. The o nly
motio n is at t he molecular level [ 10 ] . Heat can be
co nducted t hro ugh a statio nary solid. The tempera2
t ure at any locatio n in t he system can be fo und by
solving t he heat co nductio n equatio n :
Fig. 1 Sc he matic cr oss section of t he si mulate d i nte r2
con nection st ruct ure
elect rics , a n d p owe r s up p ly. The mai n objective of
t his st udy is t o i nvestiga t e t he i nf lue nces of a dja 2
ce nt met al la ye rs a n d t he dist a nce bet wee n t he
met al li nes o n t he hea t dissip a ti o n . It is ass ume d
t hat heat f l ows o nly dow nw a r d t o t he silic o n sub2
st ra t e , w hic h is usually a t t ac he d t o a heat si n k .
518
半 导 体 学 报
The f i nit e ele me nt s of t w a re A NS YS is ap p lie d t o
si mulat e t he t he r mal dissip ati o n . Figure 2 s h ows
t he t e mp e ra t ure dist ri buti o n o n a t h ree2met al2la y2
e r Cu met allizati o n s yst e m . He re , t he cur re nt
p r op a ga tes o nly t h r ough t he t op met al li ne . The
dielect ric i nse rti o n case is SiO 2 / ae r ogel ( Iel d/
Ial d ) . I n t his st udy , t he s ubst rat e t e mp e ra t ure is
第 27 卷
p ie d by ae r ogel . The cur ves i n dicat e t hat t he mai n
t he r mal resist a nce c o mes f r o m t he ae r ogel la ye r .
O ne ae r ogel la ye r lea ds t o a t e mp e ra t ure i nc rease
of a bout 10 ℃ i n t his st r uct ure . The t he r mal resist 2
a nce of SiO 2 f il m is a bout t w o o r de rs of ma gnit ude
s malle r t ha n t hat of ae r ogel f il m of t he sa me
t hic k ness . The ref ore , s uit a bly designe d met al i n2
se rti o ns i n t he dielect ric la ye rs , esp ecially i n t he
ae r ogel la ye rs , a re desi re d f or t he heat dissip a 2
ti o n .
Fig. 2 Te mp e rat ure dist ri bution ( i n ℃) of a t h ree2
met al2laye r Cu i nte rcon nect st ruct ure ( t he Ield is SiO 2
a nd t he Iald is aer ogel )
set at 85 ℃. The t he r mal co n ductivities of SiO 2 ,
t he ae r ogel ap p lie d f or t he Iel d , a n d t he ae r ogel
[ 11 ]
ap p lie d f or t he Ial d a re 11 0 , 01 010
, a nd
[ 12 ]
01 065 W/ m K , resp ectively. Figure 3 s h ows t he
co r resp o n di ng heat f lux vect or dist ri buti o n i n t his
st r uct ure . It is o bvious t hat t he hea t t ra nsf e rs
mai nly t h r ough t he met al li nes i n eac h met al la y2
e r , a n d t h r ough t he p a t h wit h t he s mallest L / k
( t he or de r of t he t he r mal resist a nce ) i n eac h Iel d
la ye r , w he re L is t he dist a nce bet wee n t he up p e r
a n d l owe r met al li nes .
Fig. 3 Heat f lux vect or dist ributi on i n t he i nte rcon2
nection case of Fig. 2
Figure 4 s h ows t he t e mp e ra t ure dist ri buti o n
at dif f e re nt l oca ti o ns o n t he p at h of x = 0 of t he
i nt e rc o n necti o n syst e m s h ow n i n Fig. 1 . T1 , T2 ,
T3 , a n d T4 a re t he i nt e rco n nect syst e m t e mp e ra 2
t ures f or t he mat e rial i nse rti o n cases : ( 1 ) as de2
p ict e d i n Fig. 1 ; ( 2) t he seco n d met al la ye r is c o m2
p let ely occup ie d by ae r ogel , i . e . , t he re a re no
met al li nes i n t his la ye r ; ( 3 ) t he f i rst a n d sec o n d
met al la ye rs a re co mp let ely occup ie d by ae r ogel ;
a n d ( 4 ) t he f i rst met al la ye r is c o mp let ely occu2
Fig. 4 Te mp e rat ure dist ribution of t he t h ree2met al2
layer Cu i nt ercon nect st ruct ure at x = 0 ( ref e r t o
Fig. 1) f or va rious tec h nologies
Figures 5～7 s h ow t he t e mp e rat ure rises f r o m
t he subst ra t e t o t he t op met al li ne f or t he i nt e r2
c o n nect st r uct ure of Fig. 1 . V a ri ous ki n ds of met 2
alliza tio n t ec h nol ogies a re si m ula te d t o i nvestigat e
t he ef f ects of dif f e re nt f act ors ( s uc h as ge o met ric
co nf igura ti o ns , cur re nt de nsit y , met al a n d dielec2
t ric e mp l oy me nt , a n d p owe r ap p lica tio ns ) o n t he
heat dissip a tio n of i nt e rc o n nectio n s yst e ms .
These st udies i n dica t e t ha t t e mp e ra t ure rise
va ries f or dif f e re nt i nte rco n nect t ec h nologies . The
t e mp e ra t ure rises i n Fig. 5 a re f r o m t he s ubst rat e
t o t he t op met al li ne f or t he dielect ric e mp l oy2
me nt of SiO 2 / ae r ogel ( Iel d/ Ial d ) f or Al a n d Cu
met allizati o n . The t e mp e rat ure rises of Al met alli2
zati o n a re ap p r oxi mat ely ρAl /ρCu ti mes highe r t ha n
t h ose of Cu met alliza ti o n un de r t he sa me c o n di2
ti o ns . It is f oun d t hat t he seco n d met al la ye r is
m o re c ritical t ha n t he f i rst f or hea t dissip a ti o n .
For t he ( c ) a n d ( d ) cases , t he t e mp e ra t ure rise i n2
c reases f i rst wit h t he dec rease of 1 / S but suf f e rs a
dec rease w he n 1 / S = 0 , c or resp o n di ng t o t he case
i n w hic h t he re is n o met al li ne i n t he la ye r . This is
beca use t he re is no hea t s ource i n t his la ye r , a n d
第3期
Xiao Xia et al . : Influence of Interconnection Co nfiguration o n Thermal Dissipation of UL SI …
t he heat ge ne rat e d i n t he f i rst met al la ye r is easily
co n duct e d t o t he subst ra t e t h r ough t he SiO 2 f il m
un de r neat h . Te mp e rat ure rise i nc reases c o nti nu2
ously wit h t he dec rease of 1 / M . Eve n t h ough
519
t he re is n o heat s ource i n t his la ye r i n t he case of
1/ M = 0 , it is m o re dif f icult f or t he J oule hea t
ge ne ra t e d a bove t o dissip a t e i nt o t he s ubst rat e .
Fig. 5 Te mp e rat ure rises f r om t he subst rat e t o t he t op met al li ne f or dielect ric conf iguration of SiO 2 / ae r o2
gel ( Ield/ Iald ) f or Al a nd Cu met allization wit h J = 01 5 MA/ cm 2 ( a ) Al ,cur re nt t h r ough t he t op met al li ne ;
( b) Cu ,cur re nt t h r ough t he t op met al li ne ; ( c ) Al , cur re nt t h r ough all met al li nes ; ( d ) Cu ,curre nt t hr ough all
met al li nes
Figure 6 p rese nts t e mp e rat ure rises f r o m t he
s ubst rat e t o t he t op met al li ne of Cu met alliza ti o n
f o r va ri ous dielect rics e mp l oye d f or Iel d/ Ial d . Fo r
t he sa me sit uati o n , t e mp e rat ure rise is p r op orti o n2
2
al t o J . It is f oun d t hat t e mp e rat ure rises f or t he
dielect ric Iel d/ Ial d cases of SiO 2 / ae r ogel a n d ae r2
ogel/ ae r ogel a re ve ry dif f e re nt . Te mp e rat ure rises
a re l owe r w he n met al li nes a re l oca te d cl ose t o
eac h ot he r i n t he case of SiO 2 / ae r ogel but highe r
i n t he case of ae r ogel/ ae r ogel . W he n ae r ogel is
e mp l oye d as Iel d , it is dif f icult f or t he J oule hea t
t o be c o n duct e d t o t he s ubst rat e due t o t he ult ra
l ow t he r mal co n ductivit y of t he ae r ogel . The re is
muc h m ore J oule heat ge ne ra t e d p e r volume w he n
t he met al li nes a re nea r t ha n w he n t he y a re f a r .
The ref o re , t he t e mp e ra t ure rise dec reases wit h t he
i nc rease of S a n d M . Howe ve r , t he be ha vi or of
t e mp e ra t ure rises is re ve rse d w he n SiO 2 is e m2
p l oye d as Iel d beca use t he ge ne ra t e d J oule heat is
easily c o n duct e d t o t he subst rat e t h r ough t he SiO 2
f il m .
Figure 7 gives t e mp e rat ure rises f r o m t he sub2
st ra t e t o t he t op met al li ne of Cu met allizati o n f o r
va rious dielect rics e mp l oye d f o r Iel d/ Ial d . Te m2
520
半 导 体 学 报
p e ra t ure rises f or t he Iel d/ Ial d dielect ric c o nf igu2
rati o n
ae r ogel/ ae r ogel
a re
ap p r oxi ma t ely
第 27 卷
kSiO 2 / k aerogel ti mes highe r t ha n t h ose i n t he SiO 2 /
ae r ogel or SiO 2 / SiO 2 co nf igura tio ns .
Fig. 6 Te mp e rat ure rise f r om t he subst rate t o t he t op met al li ne of Cu met allization f or va rious ki nds of dielect ric e mploy2
me nt of Ield/ Iald Here t he cur re nt p rop agates t hr ough all met al li nes wit h J = 01 5 ( a , b) a nd 2 MA/ cm 2 ( c ,
d ) , resp ectively.
Fig. 7 Te mp erat ure rises f r om t he subst rate t o t he t op met al li ne of Cu met allization f or va rious ki nds of dielect ric
e mployme nt f or Ield/ Iald Here t he cur re nt p rop agates only t hr ough t he t op met al li ne wit h J = 2 MA/ cm 2 .
第3期
Xiao Xia et al . : Influence of Interconnection Co nfiguration o n Thermal Dissipation of UL SI …
The a bove si m ula ti o n i n dica tes t hat hea t dis2
sip ati o n is a c rucial asp ect of U L SI i nt e rco n nects .
This t he r mal p r oble m is m ore c ritical f or highe r
t ec h nology no de I Cs si nce t hey ha ve m uc h m ore
i nt e rc o n nect la ye rs a n d a re i nevit a bly e mp l oye d
wit h low2 k ma te rials . The si m ulat e d res ults s h ow
t hat t he vit al t he r mal p r o ble m occurs i n t he cases
i n w hic h t he re a re n o met als u n de r t he signal li ne ,
co r resp o n di ng t o 1 / M = 0 , 1/ S = 0 , a n d s o o n . Suc h
a sit ua ti o n might be t he glo be signal li ne bet wee n
[7]
f uncti o n bl oc ks . To un de rst a n d t he heat dissip a 2
ti o n i n high t ec h n ol ogy no de I Cs , t he gl obe li ne i n
t he case wit h no met al li nes un de r nea t h is i nvesti2
ga t e d f or a 01 13μm UL SI interco nnectio n. The a2
dopted geo met ric parameter s of t he interco nnectio n
are t he result s of an elect rical multi2o bjective opti2
mizatio n [ 13 ] . In t he st ruct ure ,t he glo be line is loca2
ted in t he 6t h metal layer . Figure 8 shows t he tem2
perat ure rises in t he glo be line fo r different dielec2
t rics : ( A ) ho mo geneo usly inserted aerogel ;
(B ) embedded aerogel ; ( C) ho mogeneo usly insert2
Fig. 8 Temperat ure rises on t he globe line (in t he 6t h
metal layer fo r 01 13μm ge ne rati on) i n t he case wit hout
met al li nes i n t he l owe r met al laye rs f or diff e re nt die2
lect ric conf iguration ( A ) Homoge ne ously i nse rte d
ae r ogel ; (B ) Embe dde d ae r ogel ; ( C) Homoge neously
i nserte d p olyme r low2 k material ; ( D ) De nse SiO 2
ed polymer low2k material ; and ( D ) dense SiO2 .
The gray bands cover t he range of subst rate tem2
perat ure , which is assumed to be f ro m 80 ( lower
bo und) to 150 ℃( upper bo und) . Fo ur sit uatio ns ,a ,
b ,c ,and d ,stand fo r aero gel/ aerogel ,SiO2 / aerogel ,
polymer/ polymer , and SiO2 / SiO2 employed as t he
Ield/ Iald , respectively. The t hermal co nductivit y
for polymer low2 k is aro und 01 25W/ m K. In t he fig2
ure , t he x2axis parameter of t hermal co nductance
per unit line lengt h bet ween t he heated metal line
and t he subst rate is p roportio nal to t he t hermal
co nductivit y of t he medium o n t he heat t ransfer
521
pat h and t he cro ss sectio n t hro ugh which t he heat
flow s ,and inver sely p roportio nal to t he lengt h of
t he heat t ransfer pat h [ 14 ] .
Co mpared to t he wor st case discussed above
for a lo ng glo bal line wit h no locally occupied lower
metal layers , t he act ual temperat ure of t he glo bal
interco nnect s can be locally reduced by high metal
densities in t he lower level s o r by dummy metal
lines which can reduce t he t hermal resistance be2
t ween t he glo bal lines and t he subst rate. The tem2
perat ure increase above t he densely metal2packed
area is fo und to be several degrees. Thus ,t he glo be
line temperat ure above t he unoccupied area de2
pends o n t he span distance between t he densely
packed f unctio nal blocks , as shown in Fig. 9. The
result s indicate t hat a lo ng span and poo r t hermal
co nductivit y of t he material s cause t his vital t her2
mal p ro blem in such glo be interco nnect s.
Fig. 9 Temperature dist ribution along t he global lines
above unoccupied lower metal layers between f unction
blocks of 01 5 ,1 ,2 , and 4mm distance fo r 01 5MA/ cm2
To imp rove heat t ranspo rt f ro m glo bal inter2
co nnect s downward t hro ugh t he less occupied low2
er metal layers , additio nal dummy metal lines
( metal plugs co nsisting of W in level M1 and of Cu
in t he higher level s , depending o n t he technology )
acting as heat sinks can be placed. However , dum2
my metal s simultaneo usly increase t he R C co nstant
since t hey increase t he capacitance. The optimal
co nfiguratio n and dist ributio n of dummy lines
sho uld be determined by a co mbined t hermal and e2
lect rical calculatio n. Three kinds of heat sinks de2
picted in Fig. 10 have been investigated wit h regard
to t heir t hermal efficiency and to t heir influence o n
t he parasitic line to gro und capacitance. Figure 11
© 1994-2006 China Academic Journal Electronic Publishing House. All rights reserved.
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半 导 体 学 报
522
demo nst rates t he resulting impact of dummy heat
sink insertio n o n t he t hermal co nductance and ca2
pacitance between glo bal interco nnect s and sub2
st rate for different p roperties of t he dielect rics.
Special values of co nductivit y and dielect ric co n2
Fig. 10 Different types of dummy heat sinks for cool2
ing glo bal interco nnect s
Fig. 11 Dependence of normalized t hermal co nductance
( solid line) and capacitance ( dashed line ) o n t he ratio
of t hermal conductivity and dielect ric constant s fo r dif 2
ferent types of dummy heat sinks , respectively The
quantities are no rmalized to t he correspo nding values of
a 100μm long uncoole d i nt ercon nect of level M 6
( 01 13μm ) . Horizont al li nes ref er t o uncoole d i nte r2
con nects of diff e re nt le ngt hs .
s ta nts are mar ked on t he t op edge of t he f ra me , re2
spectively. A dielect ric co nstant of 11 3 correspo nds
to a 01 01W/ m K dielect ric and 11 8 to 01 065 W/
m K[ 7 ] . To calculate t he t hermal co nductance and
capacitance of a cooled interco nnect ,t he respective
values of t he uncooled line and t he additio nal co n2
t ributio ns of t he heat sinks in Fig. 11 have to be
added. In t he case of t he ho mogeneo us insertio n
scheme ,co nductance and capacitance are increased
第 27 卷
by t he same factor . For t he embedded insertio n of
an aerogel , however , ( e. g. λIald /λIeld = 01 01 / 1 ,εIald /
εIeld = 11 3/ 41 1 ) t he t he r mal co n duct a nce of a
100μm lo ng segment of a glo bal interco nnect ,
cooled by o ne heat sink of t ype HS1 ,is increased
41 6 times ,whereas it s capacitance is increased o nly
by a factor of 11 24. The st udy finds more effective
cooling of t he same line segment by heat sink HS2
( t hermal co nductance is increased 101 2 times )
wo uld increase parasitic capacitance by 11 7 ,which
is unacceptable. Ot herwise , HS2 is efficient for t he
cooling of lo ng interco nnect s. Furt hermore ,t he re2
sistivit y of metal increases wit h t he temperat ure
rise and can be app ro ximated by ρT =ρref ( 1 +αT ( T
- Tref ) ) . He re ρT a n d ρref a re t he met al resistivities
at t e mp e ra t ure T a n d ref e re nce t e mp e ra t ure Tref ,
resp ectively. The c oef f icie nt αT is t he t e mp e rat ure
coef f icie nt of resistivit y. For Cu , αT is a r oun d
01 004/ ℃, w hic h mea ns t he resist a nce of Cu will
be i nc rease d by a r oun d 11 4 if t he te mp e rat ure i n2
c reases by 100 ℃. The ref ore , keep i ng t he t e mp e ra 2
t ure of t he met al li ne l ow is als o i mp ort a nt t o p re2
ve nt t he i nc rease of t he RC ti me dela y. A p r op e r
heat si n k designe d a t t he key l ocati o n of t he i nt e r2
c o n necti o n s yst e m is necessa ry t o a voi d un desi re d
t he r mal ef f ects s uc h as elect r o n migrati o n i n t he
met al li ne a n d degra da ti o n of t he c hip . Acc or di ng
t o t he a bove st udy , t he ef f ective c ooli ng of gl o bal
i nt e rc o n nects dep e n ds o n li ne le ngt h a n d s h oul d
be a djust e d by a c o m bi ne d t he r mal a n d elect rical
design .
3 Conclusion
Interco nnectio n co nfiguratio ns and metal line
geo met ry have a st ro ng influence o n t he heat t rans2
fer capabilit y of interco nnectio n systems. There2
fore ,very caref ul planning of t he interco nnect co n2
figuratio n is necessary. The result s o btained here
can be applied to qualitatively estimate t he t hermal
dissipatio n of t he similar st ruct ures.
The elect rical resistivities and t hermal co nduc2
tivities of Cu and Al , as well as t he t hermal co n2
ductivities of SiO2 and aerogel ,are crucial facto rs in
t he heat dissipatio n in a UL SI interco nnectio n at a
certain power level . When aerogel is employed as
Ield , t he t hermal p ro blems of interco nnectio n sys2
tems are critical due to t he ult ra low t hermal co n2
ductivit y of aero gel . It is fo und t hat temperat ure ri2
© 1994-2006 China Academic Journal Electronic Publishing House. All rights reserved.
http://www.cnki.net
第3期
Xiao Xia et al . : Influence of Interconnection Co nfiguration o n Thermal Dissipation of UL SI …
ses for t he dielect ric Ield/ Iald co nfiguratio n of aer2
ogel/ aerogel are app ro ximately kSiO2 / kaerogel times
higher t han t ho se in t he case of SiO2 / aerogel o r
SiO2 / SiO2 .
Lo nger vertical distances f ro m t he upper line
to t he subst rate and poor t hermal co nductivit y of
t he dielect rics inhibit t he dissipatio n of heat to t he
subst rate. This sit uatio n will be much mo re serio us
for a glo bal line above locally unoccupied metal
layer s ,as in t he case of glo bal lines bet ween f unc2
tio n blocks. The insertio n of dummy heat sinks is
an app rop riate means to rest rain interco nnect tem2
perat ures. Vario us t ypes of t he heat sinks differ
wit h regard to t heir t hermal efficiency and to t heir
co nt ributio n to parasitic capacitance. The optimal
choice and placement of t he different t ypes depend
o n t he p roperties of t he dielect rics and o n t he indi2
vidual interco nnect lengt h. The co mbined elect rical
and t hermal optimizatio n of t he interco nnect cool2
ing is beco ming more important for f ut ure UL SI
interco nnectio n design.
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超大规模集成电路互连系统的布线构造对散热的影响 3
肖 夏1 ,g 姚素英1 阮 刚2
(1 天津大学电子信息工程学院 专用集成电路设计中心 , 天津 300072)
(2 复旦大学信息科学与工程学院 , 上海 200433)
摘要 : 应用一个三层互连布线结构研究了诸多因素尤其是布线的几何构造对互连系统散热问题的影响 ,并对多种
不同金属与介质相结合的互连布线的散热情况进行了详细模拟 . 研究表明互连线上焦耳热的主要散热途径为金属
层内的金属线和介质层中热阻相对小的路径 . 因此互连系统的几何布线对系统散热具有重要影响 . 在相同条件下 ,
铝布线系统的温升约为铜布线的ρAl /ρCu 倍 . 此外 , 模拟了 01 13μm 工艺互连结构中连接功能块区域的信号线上的温
升情况 , 探讨了几种用于改善热问题的散热金属条对互连布线的导热和附加电容的影响 .
关键词 : UL SI 互连布线 ; 散热 ; 几何构造
EEACC : 2570 ; 2800
中图分类号 : TN4051 97 文献标识码 : A 文章编号 : 025324177 ( 2006) 0320516208
3 教育部留学归国基金资助项目
g 通信作者 . Email :xiaxiao @tju. edu. cn ; xiax58 @yahoo . co m
2005206213 收到 ,2005211206 定稿
ν 2006 中国电子学会