Thermomigration in solder joints

Thermomigration

in

solder

joints

Chih

Chen

a,

*,

Hsiang-Yao

Hsiao

a

,

Yuan-Wei

Chang

a

,

Fanyi

Ouyang

b,

**,

K.N.

Tu

c

a_{DepartmentofMaterialsScienceandEngineering,NationalChiaoTungUniversity,Hsin-chu30010,Taiwan,ROC} b_{DepartmentofEngineeringandSystemScience,NationalTsingHuaUniversity,Hsin-chu30010,Taiwan,ROC} c

DepartmentofMaterialsScienceandEngineering,UniversityofCaliforniaatLosAngeles,LosAngeles,CA90095-1595,UnitedStates

1. Introduction

Thermomigrationhasbeenstudiedsince 1856[1].Whenan inhomogeneousbinaryalloyisannealedatanelevated tempera-ture, it will become homogenous. On the other hand, when a homogeneous binary alloy is annealed under a temperature gradient,i.e.,oneendofitishotterthantheotherend,thealloy will become inhomogeneous. This de-alloying phenomenon is calledSoreteffect,whichisacross-effectinirreversibleprocesses betweenheatconductionandatomicdiffusion[1–3].Theeffectis caused by thermomigration or atomic diffusion driven by temperaturegradient[4].

ThermomigrationoccursinapuremetalsuchasAl,Zr,Cuand Zn[5–8].WewouldexpectthatanAlutensilinkitchen,suchasa cooking pot, should expand in size after years of use. This is becauseiftheoutsideofthepotisabout500–6008Candtheinside is about 1008C due to boiling water in cooking, the thermal gradientinthewallof1mmthickofthepotwillbeapproximately 50008C/cm,Alatomswouldhavemigratedfromtheoutsidetothe

insideandthelattershouldhaveexpanded.Yet,thisdoesnotseem tohappen! The reasonis thatthe latticediffusionin Aloccurs throughvacancymechanism.Theoutsideofthepotwhichishotter will have a higher concentration of vacancies than that in the inside. The vacancy concentration gradient induces a counter atomicfluxwhichmighthavecompensatednearlyallofthefluxof Alatomsdrivenbythetemperaturegradient.Thenetchangemay betoosmalltobenoticed.

Solderistypicallyabinaryalloy[9–12],soSoreteffectcanbe observed. Actually,Soreteffecthasbeenreported in PbInalloy whichformssolidsolutionoverawiderangeofconcentration.Due to joule heating in 3D IC devices, the heat flow must induce temperaturegradientinmicrobumpsofPb-freesolders. Thermo-migration will occur, not only because Pb-free solder is a low meltingpointalloy,butalsobecausethealloyingelementsofAg, Cu,andevenNiinthePb-freesolderdiffuseinterstitiallyinSn.The fastinterstitialdiffusionwillenhancethefluxofthermomigration. Furthermore,duetojouleheating,electromigrationmayhave causedanon-uniformtemperaturedistributioninaflipchipsolder joint [13–17], thus thermomigration may occur because of electromigration.Due tocurrentcrowding,thechipside ofthe flip chipsolderjoint ishotter than thesubstrate side.In other words,electromigrationinflipchipsolderjointisaccompaniedby thermomigrationwhenalargecurrentdensityisappliedandwhen thecurrentdistributionisnon-uniforminthesolderjointdueto

ARTICLE INFO Articlehistory:

Availableonline11December2012 Keywords: Thermomigration Solder Electromigration Diffusion Packaging ABSTRACT

In3DICtechnology,theverticalinterconnectionconsistsofthrough-Si-vias(TSV)andmicrosolder bumps.Thesizeofthemicro-bumpisapproaching10mm,whichisthediameterofTSV.Sincejoule heatingis expectedto bethemost seriousissuein 3DIC, heatfluxmustbe conductedaway by temperaturegradient.Ifthereisatemperaturedifferenceof18Cacrossamicro-bump,thetemperature gradientwillbe10008C/cm,whichcancausethermomigrationatthedeviceoperationtemperature around1008C.Thusthermomigrationwillbecomeaveryseriousreliabilityproblemin3DICtechnology. Wereviewherethefundamentalsofthermomigrationofatomsinmicrobumpmaterials;bothmolten stateandsolidstatethermomigrationinsolderalloyswillbeconsidered.Thethermomigrationin Pb-containingsolderjointsisdiscussedfirst.ThePbatomsmovetothecoldendwhileSnatomsmovetothe hotend.ThenthermomigrationinPb-freeSnAgsolderjointsisreviewed.TheSnatomsmovetothehot end,buttheAgatomsmigratetothecoldend.Thermomigrationofothermetallizationelements,suchas Cu,TiandNiisalsopresentedinthispaper.Insolidstate,copperatomsdiffuserapidlyviainterstitiallyto thecoldend,formingvoidsinthehotend.Inmoltenstate,Cuthermomigrationaffectstheformationof intermetalliccompounds.

ß2012ElsevierB.V.Allrightsreserved.

*Correspondingauthor.Tel.:+88635731814;fax:+88635724724. **Correspondingauthor.Tel.:+8863715131x34321;fax:+8865720724.

E-mailaddresses:[email protected](C.Chen),[email protected]

(F.Ouyang).

ContentslistsavailableatSciVerseScienceDirect

Materials

Science

and

Engineering

R

j o urn a l hom e pa ge : ww w. e l s e v i e r. c om/ l o ca t e / ms e r

0927-796X/$–seefrontmatterß2012ElsevierB.V.Allrightsreserved.

currentcrowding.Thetemperaturegradientexistsovertheentire chip,henceitexistsforthoseunpoweredsolderjointstoo.Thiscan beregardedasanadvantageinexperimentalstudysothatwecan coupleaswellasdecoupleelectromigrationandthermomigration inourstudy.Nodoubt,wehavetoconductexperimentstostudy thermomigrationalone,withoutelectromigration.

Inadditionto3DICtechnology,thermomigrationcanoccurin solderjointsusedinSibasedsolarcelltechnology.Underthesun, therewillbeatemperaturegradientinthePb-freesolderjoints whichareusedtojointheAginterconnectsonthefrontsurfaceof thecell.ThermomigrationofAginmoltenPb-freesolderoccurs rapidly.Insolidstate,thermomigrationofAginSnwillbetwoto threeordersofmagnitudeslower evenattemperatures slightly above room temperature, because Ag is known to diffuse interstitiallyinSn.

Thermomigrationisacrosseffectorinteractionbetweenheat flowandmassflow.Intheanalysisofthermomigrationonthebasis ofirreversibleprocesses,theheatflow(JQ)drivenbytemperature

gradient and the mass flow (JM) driven by chemical potential

gradientcanbeexpressedasbelow JQ¼LQQ 1 T dT dxLQMT d dx

m

T   (1) JM¼LMQ 1 T dT dxLMMT d dx

m

T   (2) WenotethatthesecondterminEq.(1)andthefirsttermin Eq.(2)arethecrossterms.Whenasampleiskeptinatemperature gradientuntilaconcentration gradientisestablishedtobalance thetemperaturegradient,itreachesasteadystatewherethemass flowJMwillbezero.TakingJM=0,wehavefromEq.(2),

LMQ 1 T dT dx¼LMMT d dx

m

T   (3) ByeliminatingT/dx,wehave d

m

T   ¼LMQ LMM dT T2 (4)

Then,bydifferentiation,weobtain d

m

T   ¼1 Td

m

þ

m

d 1 T   ¼1 Td

m



m

1 T2dT (5)

Usingthefollowingthermodynamicrelations,

d

m

¼SdTþVdpand

m

¼HTS; (6) andsubstitutingthemintothepreviousequation,weobtain d

m

T   ¼Vdp T H dT T2¼ LMQ LMM dT T2 (7) thus Vdp T ¼ H LMQ LMM   dT T2 (8)

ForabetterunderstandingofthemeaningofLMQ/LMMinthelast

equation,weconsidertheratioofheatflowtomassflowunder isothermalcondition,thatis,whendT/dx=0.Wehave

JQ JM ¼LQM LMM ¼LMQ LMM (9) byusingOnsager’srelationthatLQM=LMQ.

TheratioofLMQ/LMMrepresentstheenergyflowassociatedwith

amassflow.DefiningQ0_=L

MQ/LMM,wehave Vdp T ¼ðHQ 0 ÞdT T2¼Q dT T2 (10)

wherewedefinetheheatoftransport,Q*=HQ0_{.Weseethatthe} heat oftransport represents thedifference betweenthe energy associatedwiththematerialsthatflows(Q0_{)andtheenthalpyof} thematerials(H)inthereservoirfromwhichtheflowstarts.Itis clear that ifH>Q0_{, the heat of transport Q*is positive, which} meansthereservoirtemperatureishigherthanthetemperatureof thediffusingatom,ortheatomisdiffusingfromhottocold.Onthe otherhand,ifQ*isnegative,atomicdiffusionwillbefromcoldto hot. In iron–carbon alloys, Shewmon showed that under a temperaturegradientcarbonmovedtothehotsideandasteady statewasestablished.ThevalueofQ*forcarbonin

a

-ironisabout 24kcal/molnear7008C.ThesignofQ*willbediscussedfurther inthenextsection.

2. Drivingforceofthermomigration

Inthermoelectriceffectwhereatemperaturegradientcandrive electrons,similarlyatemperaturegradientcanalsodriveatomsin thermomigration.Essentially,theelectronsinthehigh tempera-tureregionhavehigherenergyinscatteringforinteractionwitha diffusingatom.Ondrivingforceofatomicdiffusion,werecallFick’s firstlawthattheatomicfluxdrivenbycompositiongradientor chemicalpotentialgradientcanbegivenas[4,18,19],

J¼Ch

v

i¼CMF¼C D kT 

@m

@

x   (11) whereh

v

iisdriftvelocity,M=D/kTismobility,and

m

ischemical potentialenergy.

Consideringtemperaturegradientasthedrivingforce,wehave J¼CD kT Q  T 

@

T

@

x   (12) whereQ*isdefinedasheatoftransport.Comparingthelasttwo equations,weseethatQ*hasthesamedimensionas

m

,soitisthe energy or heat per atom. Furthermore, the sign of Q* can be determinedbyEq.(12).

We recall theFick’sfirst lawofdiffusionthat J=D(dC/dx) where theatomic flux diffuses fromhighconcentration tolow concentrationordownhilldiffusion,thediffusivityDispositive. The negative sign is conventional since the slope of dC/dx is negativeintheplotofCvs.x.Typically,wedrawastraightlineofC fromupperleftcornertolowerrightcorner.Thecoordinationofx increasesfromlefttoright,buttheCdecreasesfromlefttoright,so theslopeisnegative.Ontheotherhand,inuphilldiffusionwhere the atomic flux diffuses from low concentration to high concentration, D is negative. The same applies to Eq. (12). If atomicfluxdiffusesdownthetemperaturegradient,Q*ispositive. Butifatomicfluxdiffusesagainstthetemperaturegradient,Q*is negative.Therefore,wecanconcludethatifwefindatomicflux movesfromhottocold,theQ*ispositive.Ontheotherhand,if atomicfluxmovesfromcoldtohot,theQ*isnegative.

Hencethedrivingforceofthermomigrationisgivenas F¼Q  T

@

T

@

x   (13) Tomakeasimpleestimationofthemagnitudeofthedriving force,wetake

D

T/

D

x=1000K/cm,andconsiderthetemperature difference across an atomic jump distance and take the jump distancetobea=3108_{cm.Wehaveatemperaturechangeof}

3105_{Kacrossanatomicspacing.Sothethermalenergychange}

willbe.

3k

D

T¼31:381023

ðJ=KÞ3105_K

1:31027_J: As a comparison, we shall consider the driving force, F, of electromigration at a current density of 1104_A/cm2 _or

1108_A/m2_{,whichweknowexperimentallyhasinduced}

electro-migrationinsolderalloys.

F¼ZeE¼Ze

r

j (14) We shalltake

r

=10108

_V

_{m, Z*of theorder of10, and}

e=1.6021019_{C, and we have F=101.610}19_C10

108

_V

_m108_A/m2_=1.6

1017_CV/m=1.61017_N.

Theworkdonebytheelectricalforceinadistanceofatomic jumpof31010_mwillbe

_D

_w=4.81027_Nm=4.81027_J,

whichisclosetothethermalenergychangewehavecalculatedfor thermomigration.Thus,wecanconcludethatifacurrentdensityof 104_A/cm2 _{can induce electromigration in a solder joint, a}

temperaturegradientof10008C/cmwillinducethermomigration inasolderjoint.

Onheatoftransport,wenotethatQ*canbepositiveornegative. InFe–Csystem,Cwasfoundtomovetothehotendinterstitially witha negativeheatof transport [20]. Inalloys of SnPb,when thermomigrationdrivesPbtomovefromthehotzonetothecold zone,itmovesdownthetemperaturegradient.Butthe thermo-migrationdrivesSntomoveintheoppositedirection;itmoves againstthetemperaturegradient.TheQ*forPbispositiveorthe heatdecreases:itmeansPbatomsmovefromhotendtocoldend. ButforSn,theQ*isnegativesinceitgainsheat;itmeansSnatoms movefromcoldendtohotend.Thiscanoccurbecausewehaveone temperaturegradientinthermomigrationforbothspecies,unlike interdiffusionin a diffusion couple,in which theconcentration gradientofthetwointerdiffusingspeciesisinoppositedirection, sothechemicalpotentialchangecanbepositiveforbothspecies.It isworthmentioningwhenweanalyzedfluxmotioninatwo-phase structure of SnPb, we found that Pb is thedominant diffusing speciesanddiffusesfromthehotendtothecoldend[21,22],and owingtoconservationofmass,Snisbeingpushedbackwardandit diffuses from the cold end to the hot end. However, when thermomigrationofSnoccursinPb-free solders,itmoves from coldtohottoo,sotheheatoftransportofSnisnegative.

TomeasureQ*,ifweknowtheatomicflux,wecanusetheflux equationtodetermineQ*whendiffusivity,theaverage tempera-ture,andtemperaturegradientareknown,asdescribedbyEq.(12). Therefore,measurementoftheaveragetemperatureand temper-aturegradientarecriticaltothecalculationofQ*.Inthefollowing, wewillreviewthethermomigrationofconstituentatomsofsolder, SnandPb,aswellastheotheralloyingelements.

The thermal gradient may be created during accelerated electromigrationtests[23,24],inwhichthesolderisinthesolid state.Section3willreviewthethermomigrationbehaviorsinthe solidstate.Ontheotherhand,athermalgradientmaybegenerated duringreflow/joiningprocess,inwhichthesolderareheatedover their melting points. Thermomigration in the molten state of solderwillbepresentedinSection4.

3. Thermomigrationinsolidstatesolders

Asolderjointconsistsofmany materials,besidesthesolder alloyitself,thereareunder-bump-metallizations(UBMs)onboth sidesofthejoint,andallofthemtendtomigrateunderathermal gradient.Fig.1showstheschematicdrawingofatypicalsolder joint.AnadhesionlayerisneededbetweentheAlorCuwiring traceandtheUBMlayeronthechip.Titaniumisoftenadoptedas theadhesionlayer.TheTifilmalsoservesasa diffusionbarrier layeranditsthicknessisabout100

m

m.FortheUBMmaterials,Cu orNiorabilayerofthemischosenbecausetheyhaveexcellent wettabilitywithsolders[12].ThesoldermaybeSnPb, SnAg,or SnAgCualloys.Onthesubstrateside,thebond-padmetallization layermaybeCuorNiagain.Thereforethematerialsthatmaybe subjectedtothermomigrationare,Pb,Sn,Cu,Ni,AgandTiinthis

system.We willreview thethermomigration behavior ofthese elements.

Large thermal gradientsmaybe created in thesolder joints subjected to current stressing as well as in the neighboring unpoweredjoints.Fig.2(a)showstheschematicdrawingforthe stressingcircuit,inwhichBump2andBump3wereappliedbya directcurrent,butBump1andBump4wereunpowered.Onthe

Fig.1.Schematicdrawingshowingthecommonmaterialsusedinasolderjoints.

Fig. 2. Temperaturedistribution in solderjoints duringcurrent stressing.(a) Schematicdrawingofthetestsampleswithfoursolderbumps.Thefourbumpsare labeledasB1,B2,B3,andB4.When1.8AwasappliedthroughBump2andBump3 at1008C,thetemperaturedistribution canbesimulatedusingfiniteelement analysis.(b)Bump2;(c)Bump3;(d)Bump1;and(e)Bump4.

chip side, an Al trace connects the four bumps together. Its dimensionis2550

m

mlong,100

m

mwide,and1.5

m

mthick.In thisstructure,anasymmetricaljoule heatingtakesplaceduring thecurrentstressing.TheAlwiringtraceinthechipsidehasa smallcross-sectionalareaof100

m

m1.5

m

m.Ontheotherhand, thesolderjointandtheCulineonthesubstratesidehavea cross-sectional area of

p

40

m

m40

m

m, and 100

m

m25

m

m, respectively.Therefore,thejoule heatingeffectintheAlwiring

traceismuchhigherthanthatinthesolderjointandintheCuline. Temperaturesimulationbyfiniteelementanalysiswascarriedout tosimulatethetemperaturedistributionsinthefourbumps.The parametersusedinthissimulationarelistedinTable1.Fig.2(b)– (e)showsthetemperaturedistributions infoursolder jointsin whichBump2andBump3wereappliedby1.8Aofdirectcurrent. Temperaturegradientsbuildupacrossthesolderjointsduetothe asymmetricaljouleheating,withhotendonthechipsideandthe cold end on the substrate side. The temperature gradient is denotedasthetemperaturedifferenceacrossthesolder,dividedby the solder height, which is 50

m

m in the present case. The temperaturegradienthasbeensimulatedtobe10008C/cmand 11008C/cminBump2andBump3,respectively.Itisnoteworthy thattheasymmetricaljouleheatingalsogenerateslarge tempera-turegradientsinBump1andBump4,althoughnocurrentspassed

Table1

Theresistivityvaluesusedinthefiniteelementsimulation.

Al Cu Ni Ni3Sn4 Sn2.5Ag Resistivity(mV-cm) 3.2 1.7 6.8 28.5 12.6

Fig.3.ThermomigrationinPb-containingsolders.(a)Schematicrepresentationofexperimentalsetupforthermomigrationtest:onepairofsolderbumps(Nos.4and5)under currentstressing,andotherun-stressedbumpsundertheinfluenceoftemperaturegradient.(b)Cross-sectionalSEMimagesof2ofthestressedbumps(Nos.4and5)and4of theun-stressedbumps(Nos.2,3,6and7).ThelightercolorintheimagesisthePb-richphaseandthedarkercoloristheSn-richphases.

throughthem.ThisisbecauseSipossessesanexcellentthermal conductivityof147W/mK.Thethermalgradientis5808C/cmand 6008C/cmforBump1andBump4,respectively.Therefore,these twobumpsarequitesuitableforthermomigrationstudywithout electromigration,whereasBump 2and Bump3 canbeused to examine the combined effect of thermomigration and electro-migrationonthemicrostructurechangesofsolderjoints.

Furthermore,therealsoexistalateralthermalgradientinthe Bumpsduringcurrentstressing.Fig.2(b)showsthetemperature distributioninBump2.BecausethemajorheatingsourceistheAl tracebetweentheBump2andBump3,theupper-rightcornerof thejointappearshotterthanthatonthelower-leftcorner.Yet,for Bump3,thetemperatureontheupper-leftcornerishotterthan that on lower-right corner, as illustrated in Fig. 2(c). The temperaturedistributionin Bump 1is similar tothat inBump 2,asdepictedinFig.2(d),exceptthegradientissmaller.Fig.2(e) showsthattemperaturemapforBump4,whichissimilartothatin Bump3.Butthehot-spottemperatureandthethermalgradient arelowerthan thosein Bump3. Experimentalverification was reported by Hsiao et al. using infrared microscopy [25]. The temperature distribution will have an obvious effect on the thermomigrationofatoms.Wewilldiscussthisindetailslater. 3.1. ThermomigrationofPbatoms

ThermomigrationineutecticSnPbsolderwasfirstreportedby Yeetal.in2003[26].TheyproposedthattheSnPbsoldermigrate tothecoldendofthesolderjoints.Huangetal.reportedthatPb atomswerethedominateddiffusionspeciesforthermomigration inSnPbsolderjoints[27].Theyproposedthatitrequiresathermal gradient over 10008C/cm in order to observe thermomigration behaviorduringelectromigrationtests.Inordertomeasureheatof transport,ChungandLiuperformedathermomigrationtestina bulk sampleof eutectic SnPb solder undera constant thermal gradientof10008C/cm[28].TheyalsoobservedthatthePb-rich phasewasdepletedinthehotsideandtheheatoftransportwas calculated to be +22.16kJ/mol. Later, Ouyang et al. reported a directobservationofthermomigrationineutecticSnPbflipchip solderjoints[29].TheyfoundredistributionofSnandPboccurred, withPbmovingtothecoldend.Theyalsocalculatedtheheatof transportofPbtobe+25.3kJ/molbymeasuringthethicknessofPb accumulationatthecoldside.Moresignificantly,thetwo-phase lamellar structure was foundto become much finer than that beforethermomigration.Sincethelamellar interfacesare disor-dered, it indicates a process of large entropy generation. The findingofrefinementoflamellarstructureisadirectindicationof theeffectofentropyproductiononmicrostructureevolutiondue tothermomigration.

Fig. 3 displays backscattered scanning electron microscope (SEM) imagesof thecross-section oftherow of8 bumps after thermomigration.TheUBMthin filmsonthechipside wereAl (0.3

m

m)/Ni(V)(0.3

m

m)/Cu(0.7

m

m)depositedby sputter-ing. The bond-pad metal layers on the substrate side wereNi (5

m

m)/Au (0.05

m

m) prepared by electroplating. The arrows depicttheelectronflowdirection.Amongthe8solderbumps,only onepairofbumps,No.4/5,wascurrent-stressedof1.58104_A/

cm2 for21.5h. Electronsenteredtheleftsolderbumpfromthe bond-padon thesubstrate andexitedthebumpfromitsupper rightcorner; theyenteredtheAlinterconnectonthetopofthe bump.Theelectrons thenflowedalong theAlline andentered anothercurrent-stressedsolder bumpfromit upperleftcorner. Whenthesolderbumpswereundercurrentstressing,thejoule heatinggeneratedfromtheon-chipAlinterconnectswasgreater thanthatfromtheCubond-padsonthesubstrateside,andthusthe jouleheatingdifferencebetweensubstrateandchipestablisheda temperaturegradientacrossthesolderbumps.Thistemperature

gradient wastransferred to the un-stressed bumps because Si chips are very good heat conductors. Hence, the un-stressed neighboringbumpsintheflipchipsampleswereusedtostudythe thermomigrationinducedbyatemperaturegradient.Wecansee thataPb-richphasewasredistributedintheun-stressedbumps afterthermomigration.Forun-stressedbumps(Nos.2and7)away fromthecurrent-stressedbumps,Pb-richphasewasobservedto be accumulated on the substrate side, suggesting temperature gradient hasdriven thePb atoms moving to the cold side. In additionaltotheverticaltemperaturegradient,alateral tempera-turegradientwasfoundtobeestablishedacrossthebumps.As showninFig.3(b),aPb-richphasewasredistributedtothe upper-left-handcornerafter21.5h.Sincetheupper-left-handregionis adjacenttothecurrent-stressedbump,theaboveresultssuggest thatPbatomswerepushedtocolderside.

Itis ofinterest tofindout ifa concentration gradientof Pb exists,foreitherdown-hillorup-hilldiffusion.Theaccumulation of Pb at the cold side clearly shows that Pb moves with the temperature gradient and is the dominant diffusing species in thermomigration. If Sn wasthe dominantdiffusing element,it shouldhavebeenaccumulatedatthehotend.ThePbwouldbeleft behind and theaverage concentration of Pb inthe bulk would increase. Fig.4(a)and (b) showsrespectively theconcentration profilesofPbandSnacrossthebumpafterthermomigrationusing electronprobemicro-analyzer(EPMA).Threestraightlinesacross thebumpswerescanned.Threekindsofcurves–solid,broken,and dottedcurvesareshowninFig.4.Everylineistheaverageofthree

Fig.4.(a)and(b)ConcentrationprofilesacrossthebumpbyEPMAofPbandSn, respectively.Threeprofilelinesacrossthebumpswerescannedandeverylineisthe averageofthreesetsofdatapoints.Eachpointwastakenateach5-mmstepfrom thechipsidetothesubstrateside.

setsofdatapoints,andeachpointwastakenatevery5

m

minterval stepsfromthechipsidetothesubstrateside.Theresultsshowthat thecompositionhasastepwisedistributionacrossthesolderjoint. SincethediameteroftheEPMAprobewasofafewmicronsandis largerthanthelamellarspacing,themeasuredcompositionwasan average over several lamellae. Thus whether the Pb matrix is supersaturated of Sn or not could not be determined. In the meantime,theEPMAanalysisindicatestheaccumulated concen-trationofPbonthesubstratesideisabout73%,andintherestthe averageconcentrationofSnfromthechipsidetothesubstrateside rangesfrom70%to80%. Beyondthehigh-Pbregion,thehigher

concentrationofSnatthebottomofthesubstratesideisduetothe formationofCu6Sn5intermetalliccompounds(IMC).

WhatisunusualinFig.4isthatnoclearconcentrationgradient across thebumpwas found; excepta stepwise change froma ratheruniformregiontoahigh-Pbregion.Althoughthe distribu-tion of Pb and Snin the bulk partof thesamples shows local fluctuationduetothetwo-phasestructure,theaverage distribu-tionofPbandSnintheseregionsisstillquiteuniform.Werecall that Shewmon showeda linear concentration gradient of Cin thermomigrationofCintheFe–Csystem[13],whichisexpected fromtheSoreteffect.Toexplaintheflatconcentrationdistribution observedhere,wenotethatthermomigrationisnotdrivenbya concentrationgradient.Theconcentrationgradientobservedinthe Soreteffectisinducedbytemperaturegradient.However,inthe eutectictwo-phasestructure,thermomigrationwillnotinduceor becounteractedbyaconcentrationgradient.Thiscanbeexplained

Fig.6.Enlargedcross-sectionalSEMimagesofun-stressedbumpin(a)theregionof fineeutecticmicrostructureand(b)thePb-richphaseonthesubstrateside.

Fig.7.Cross-sectionalSEMimageforaeutecticSnPbjointbeforethermomigration tests.ThePb-richphaseandtheSn-richphasedistributeduniformlybeforecurrent stressing.Afterthermomigrationtestat1.88Aatroomtemperaturefor6h,the Pb-richphasemigratedtowardthecold.(b)Bump1;and(c)Bump4.

bythefactthatthebinaryeutecticsystemisaconstantchemical potentialwhentheisothermallineiswiththemiscibilitygapand belowtheeutectictemperature.Itmeansthatthisbinaryeutectic systemisindependentoftheconcentrationorvolumefractionof thetwoprimaryphasesaccordingtoequilibrium thermodynam-ics; therefore, the two-phase structure has no resistance to redistribution of concentration or volume fraction. Strictly speaking,wemaynotusetheconceptofequilibrium thermody-namics to explain the observation due to the presence of a temperaturegradientinoursystem.But,inourexperiment,

D

T/ T10/450issmall,sothebehaviorofthetwo-phasestructureis near-equilibrium.

ComparedtooriginalSEMimageofeutecticSnPbsolder(Fig.5), thelamellarstructureafterthermomigrationismuchfinerthan thatbeforethermomigration.Additionally,thebulkpartofthefine eutectic microstructure in thesolder jointis quiteuniform, as showninFig.6(a).Fig.6(b)showsahighermagnifiedimageofthe Pb-rich phase on the substrate side. It remains a two-phase microstructure, but has a much finer microstructure, too. In principle,whenaeutectictwo-phasemicrostructureisannealedat constant temperature,coarsening,instead ofrefinement, of the two-phaselamellarstructureshouldoccurtoreducethesurface energy.SimilarresultswerealsoobservedinhighPb/eutecticSnPb composite solder joints [27], eutectic SnPb and SnBi solders

[30,31].

Therefore,wesuggestapossiblemechanismontheformation ofstructuralrefinements(amoredisorderedstate)byathermal gradient. Onsager defined the conjugated flux and force in irreversibleprocessessothattheirproductisequaltotheproduct of temperature and entropy production per unit volume [32]. During thermomigration, the major entropy production is attributedtoheatpropagationunderatemperaturegradient,thus T V dS dt¼ 

k

dT dx   1 T dT dx   (15) whereVisvolume,andSisentropy.Ifwetakeheatconductivityin solder as

k

ffi50J/msK, dT/dx=1000K/cm, and T=400K, we obtain (T/V)(dS/dt)=1.2109J/m3s. Other source of entropy production during thermomigration would be much smaller.

Theentropyproductionbyatomicmigration,thecross-effect,can beestimatedas T V dS dt¼ C D kTF   F¼CD kT 3k dT dx  2 (16) wherethedrivingforceFwasroughlyassumedtobe3k(dT/dx)in whichkisBoltzmann’sconstant,3kT(x)–localthermal (vibration-al)energyperatom.BytakingdT/dx=1000K/cm,weobtain(T/ V)(dS/dt)=3102_J/m3_{s,whichismuchsmallerthanthatdueto}

heatpropagation.

If we take the lamellar interfacial energy to be 0.235J/m2

(235erg/cm2)obtainedfromcellularprecipitationinPb(Sn)alloy

[33–35],thetotalinterfacialenergyinthemicrostructureasshown in Fig.3 canbeestimatedabout1–10J/cm3_{.Thismeansthatit}

takeslessthan1sinentropyproductiontoproducemoreofthe energy neededtocreate thedisordered interfaces. However, in ordertorefinethemicrostructure,itrequiresatomicdiffusionin thermomigrationwhichtakestime.

Onthebasisofthe2ndlawofthermodynamics,notalltheheat suppliedtoasystemcouldbeusedtodoworkbecauseapartofit hastobewasted.Jouleheatingisakindofwasteheatinelectrical conduction.Whilealargeamountofthermalentropywaswasted, it seems that a small amount of configurational entropy was created in forming the nanoscale lamellar interfaces. While thermal entropy cannot convert into configurational entropy, theformercouldinducetremendousincreaseinthetemperature ofSichip.Sinceinterfacialdiffusionisfasterthanlatticediffusion, theformationofalargenumberoflamellarinterfacesmayhave enhancedtherateofentropyproductionduringthermomigration, in agreementwithOnsager’sprincipleofirreversible processin non-equilibriumthermodynamics.

Toseparatetheeffectofthermomigrationfrom electromigra-tion,Hsiaoetal.adoptedalternatecurrenttostresseutecticSnPb solderjoints[36].Becausethealternatecurrentgeneratesthesame ofjouleheatingasthedirectcurrentdoes,butitdoesnotintroduce electromigration.Theyalsouseinfraredmicroscopetomeasure thethermalgradientacrossthesolderbump.Inaddition,markers wereusedtomeasurethermomigrationflux,sothattheheatof transportofPbcanbemeasuredtobe+26.6kJ/mol.

Fig.8.Cross-sectionalSEMimagesshowingthemicrostructureevolutionduringthermomigrationunderathermalgradientof28298C/cm.(a)0h;(b)300h;(c)550h;and (d)800h.Tinatomswasobservedtomoveupwardtothechip,whichisthehotend.

Furthermore,thethermomigrationofPbinsolderjointscanbe alsoillustratedinFig.7.Fig.7(a)showsthecross-sectionalimage ofSEMforaeutecticSnPbjointbeforethermomigrationtests.The UBMonthechipsideis5

m

mCu/3

m

mNi.Themetallizationonthe substratesideis3

m

melectrolessNion20

m

mCulines.The Pb-richphaseandtheSn-richphasearedistributeduniformlybefore alternate current (AC) stressing. After the current stressing at 1.88AinBump2andBump3atroomtemperaturefor6h, the stressingcircuitbecameopen.NocurrentpassedthroughBump1 andBump4.Butsignificantthermalgradientwasbuiltupinthem duetothecurrentstressinginBump2andBump3.Fig.7(b)shows thecross-sectionalSEMimageforBump1.ThePb-richphasehas migratedtothelower-leftcorner,which wasthecold end.The temperature distribution for Bump 1 is similar to the one in

Fig.2(d).Yet,thePb-richphaseinBump4hasmovedtothe lower-rightcorner,which wasthecold end asshown in Fig.7(c). Its temperaturedistribution is similar tothe one in Fig.2(e).The aboveresultsdemonstratethatPbatomsmigratetothecoldend underathermalgradientinsolderjoints.

3.2. ThermomigrationofSnatoms

ItisintriguingthatSnatomsmigratetothehotendinboth Pb-containingandinPb-freesolderjoints.ThethermomigrationofSnin

eutectic SnPb solder is hard to be detected because Pb is the dominatediffusionspecies.However,thethermomigrationofSncan bestudiedinPb-freesolders.Hsiaoetal.stressedPb-freeSnAgjoints byalternatecurrentat1008C[37].TheyreportedthatSnatoms migratedtothehotendandformedSnhillocksthere.Fig.8(a)shows thecross-sectionalSEMimagefortheeutecticSnAgsolderjoints beforecurrentstressing.TheUBMonthechipsideis5

m

mCu/3

m

m Ni.Themetallizationonthesubstratesideis5

m

melectrolessNion 20

m

mCulines.Thesolderconsistsof3.5wt%ofAgand96.5wt%of Sn.Tomeasurethethermomigrationflux,arraysofmarkerswere indentedbyfocusedionbeam(FIB)onboththecoldandhotends. Thejointwasstressedby0.57Aandthejouleheatingeffectcreateda thermalgradientashighas28298C/cm,withhotendonthechip sideandcoldendonthesubstrateside.Afterstressingfor300h, hillocksofpureSnstartedtoemergeonthehotend,asillustratedin

Fig.8(b).Asthestressingtimeincreasedto550h,thehillocksgrew bigger,asdepictedinFig.8(c).TheSnhillocksbecamemoreobvious after the thermomigration test for 800h. Fig. 8(d)presents the microstructurechangeforthebumpafter800h.Thearrowsandthe dottedlinesinthefiguresindicatethepositionofthemarkers.Tin atomsmovedupwardtothechip,themarkersmoveddownwardto thesubstrateside.Therefore,theSnatomsmovetowardthehotend. By measuring the displacement of the markers and the known thermalgradient,theheatoftransportofSncanbedeterminedtobe 1.36kJ/mol.Thisvalueismuchsmallerthantheheatoftransport of Pb atoms, which is approximately +25kJ/mol [28,29,36]. Therefore,Snatomsarelesssusceptibletomigrateina thermal gradient. Ouyang and Kao performed in situ observation of thermomigration of 96.5Sn–3Ag–0.5Cu solder joints, and they confirmthatSnatomsmigratetothehotend[38].Inaddition,the molarheatoftransportoftheSnatomsismeasuredto3.38kJ/mol bymarkerdisplacementmethod.

Fig.9showstheschematicdiagramofPb-free96.5Sn–3Ag– 0.5Cuflipchipsolderjointsforthermomigrationtests.The under-bump-metallization (UBM) thinfilms onthe chip side,Ti (ca.

Fig.9.Schematicrepresentationofexperimentalsetupforthermomigrationtest: onepairofsolderbumps(Nos.1and4)undercurrentstressing,andbumpsofNo.2 andNo.3undertheinfluenceoftemperaturegradient.

Fig.10.Cross-sectionalSEMimagesofthesamesolderbump(No.2)afterinsituthermomigrationatanambienttemperatureof1508Cfor(a)0,(b)62h.(c–d)Enlarged cross-sectionalSEMimagesofbumpNo.2near(c)thechipsideafterthermomigrationfor62hand(d)thesubstratesideafterthermomigrationfor62h.

0.3

m

m)/Ni(V) (ca. 0.3

m

m)/Cu (ca. 0.7

m

m), were deposited throughsputtering.Thebond-padmetallayersonthesubstrate side,Ni (5

m

m)/Au(0.05

m

m), wereprepared through electro-plating.Theheightofthe96.5Sn–3Ag–0.5Cubumpbetweenthe UBMandthebond-padwas100

m

m.Becausethecurrentpassed behindthetopofbumpNo.1andenteredthetopofbumpNo.4, thebumpNo.2andNo.3couldbeusedtostudythermomigration.

Fig.10(a)and(b)displaystheevolutionofthemicrostructureof solder joint No. 2 at an ambient temperature of 1508C after thermomigrationfor0and62h(condition#1).Comparedwith theas-receivedsampleinFig.10(a),Fig.10(b)revealsthatamass protrusionappearedinthehighertemperatureregionafter62h, suggesting that Sn atoms were pushed to the hot side. Void formationwasalsoevidentonthesubstrateside.Toprovidea cleared view of the microstructures after thermomigration,

Fig.10(c)and(d)presentsenlargedimagesofthehotandcold regionsofbumpNo.2after62hofthermomigration,respectively. Inadditiontothetemperaturegradient,theactualtemperature ofthesampleisanotherimportantfactortotrigger thermomigra-tioninflipchipsolderjoints.Fig.11revealsthemicrostructural changesoftheun-poweredbumpNo.2underacurrentdensityof 1.4104_A/cm2_{atanambienttemperatureof1258Cbeforeand}

after 341h of thermomigration (condition #2). Notably, no significant microstructural change occurred in the un-powered bumps, even after 341h of thermomigration. Furthermore, no evidenceforvoidformationappearsintheenlargedimagesofthe substrateside(coldend)inFig.11(c).Becauseweusedthesame circuitdesignandsameDCcurrentmagnitude,thejouleheating generated under conditions #2 was the same as that under conditions #1; nevertheless, no thermomigration occurred be-causetheambienttemperaturefortheformerconditions(1258C) was much lower than that for the latter. Thus, a critical temperature existed, between ‘‘1258C+joule heating’’ and ‘‘1508C+jouleheating,’’totriggerthermomigration.Thissituation mighthavearisenbecausecurrent-inducedjouleheatingat1258C was insufficient to raise the temperature close to the critical temperature for thermomigration. Similar results were also reported in the eutectic Pb–In solders [39], showing that thermomigrationinducedfailureonlyoccurswhentemperature differenceexceeded8.58Catelevatedtemperatures.

Thereason forthis is mostprobablydue tothepresenceof stressgradient.Fora solderjointunderatemperaturegradient, thermomigrationinducedmasstransportofSnfromthecoldtothe hotendandthusthelatterwillbeincompressionandtheformerin tension,resultinginastressgradient.Sincethisstressgradientisin theoppositedirectionoftemperaturegradient,thedrivingforceof thermomigration is counteracted by this stress gradient. This reasoningissimilartothebackstressmodelofelectromigrationby Blech and Herring, in which the back stress gradient retards electromigrationandacriticallengthofinterconnectisobtained, belowwhichnoelectromigrationoccurs[40].

Thus the net driving force of Sn due to the presence of temperaturegradientandstressgradientcouldbeexpressedas

FTMFbackstress¼ Q  T 

@

T

@

x   d

sV

dx (17)

whereQ*istheheatoftransport,d

s

isstressgradient,and

V

is atomicvolume.

Note that both driving forces list in Eq. (17) are gradient dependent.AfterrearrangingEq.(17),thethresholdtemperature differenceneededtotriggerthermomigrationis

D

T T ¼exp

V

Qð

s

1

s

2Þ   1 (18)

where

s

1and

s

2aremaximumhydrostaticstressesthatmaterial

can sustain at each end of bump. Eq. (18) suggested that the threshold temperature difference is a function of temperature. Additionally,wecanseethatthethresholdtemperaturedifference willbelargeratlowerworkingtemperature,whichisconsistentto whatwehaveobservedinthePb-freesolder.

3.3. ThermomigrationofCuatoms

ThermomigrationofCuinCuhasbeenstudiedbyMeechanand Lehmanin1962[41].TheyexaminedCuthermomigrationusinga pureCudiscmaintainingoneendat12498Candtheotherendat 5308C.Thetemperaturegradientwas11948C/cm.Themeasured

Fig.11.Cross-sectionalSEMimagesofthesamesolderbump(No.2)afterinsitu thermomigrationat anambienttemperature of1258C for(a)0,(b)62h. (c) Enlarged cross-sectionalSEMimages ofbumpNo.2nearsubstratesideafter thermomigrationfor62h.

heat of transport is +53.5kcal/mol. Later, Stracke and Herzig investigatedCuthermomigrationinPbatthetemperaturerangeof 181–3038C[42].TheyalsoreportedthatCumigratedtothecoldend and obtained the heat of transport to be +5.1kcal/mol. The Cu interstitialdiffusioninSnmatrixisextremelyfastespeciallydriven

byalargethermalgradient[43,44].Basedonpreviousliterature[45], Cu atom hasthe tendency to move to the cold endin solder in thermomigration.Therefore,thermomigrationofCuinPb-freesolder maybecomea serious probleminsolder joints.Thermomigration inducedfailurewasfirstreportedbyChenetal.[46].Theyperformed

Fig.12.ThermomigrationofCuinCu/SnAg/Nisolderjoints.Directcurrentof0.55AwasappliedthroughBump2andBump3at1508C.(a)Bump1beforethe thermomigrationtest.(b)Bump4beforethethermomigrationtest.(c)Bump1afterthethermomigrationtestfor76h.(d)Bump4afterthethermomigrationtestfor76h.The Cu6Sn5IMCsdetachedfromthechipsideafterthethermomigrationtest.

Fig.13.ThermomigrationofNiinNi/SnAg/Nisolderjoints.Directcurrentof0.55AwasappliedthroughBump2andBump3at1508Cfor180h.(a)Bump1,nocurrentpassing through.(b)Bump2withdownwardelectronflow.(c)Bump3withupwardelectronflow.(d)Bump4,nocurrentpassingthrough.Nodamageduetothermomigrationwas observed.

electromigrationtestsineutecticSnAgsolderjointswitha5

m

mCu UBMonthechipside,butseriousCumigrationwasfoundonthe bumpswithoutcurrentstressing.

Fig.12(a)and(b)showsthesolderjointswith5

m

mCuUBMs beforeelectromigrationandthermomigrationtests.Thetwojoints tobetestedwereBump1andBump4,respectively.Cu6Sn5IMCs

adheredtotheCuUBMverywell.Thesolderjointswere cross-sectionedandpolishedfirsttoabouttheircenters.Similartothe stressinglayoutinFigs.2and7,electricalcurrentof0.55Awas appliedthroughBump2 and Bump3 at1508Con a hot plate, whichcorrespondstoanaveragecurrentdensityof9103_A/cm2

intheUBMopening.Therefore,theBumps1and4didnothave currentpassing through.Yet,thefourbumpshave experienced almostthesamejouleheating,becausetheSidiepossessexcellent heat conduction. The thermal gradient was approximately 10008C/cmforthesetwobumps[46].Afterthecurrentstressing for 76h, the samples were polished slightly again for SEM observation, so that the shapes of the joints changed slightly. WeobservedthattheCu6Sn5IMCsinbothbumpsmigratedtothe

cold/substrateendafterthermomigration.Fig.12(c)and(d)shows the microstructure changes in the Bump 1 and Bump 4, respectively,afterthethermomigrationtests.There wasalmost noCuUBMleftonthehot/chipendforbothbumps.Anisothermal annealingat1658Catovenwasperformedtoexaminewhetherthe agingcancausetheCumigrationtowardthesubstrate.Theresults indicate that Cu6Sn5 IMCs grew thicker after the isothermal

annealing,buttheystilladheretotheremainingCuUBMverywell

[47].Abdulhamidetal.alsoobservedthermomigrationofCutothe coldendinunstressedSnAgCusolder[48].Therefore,Cuatoms migratetothecoldendinthesolderjoints.

3.4. ThermomigrationofNiatoms

Niatomsalsomigratetowardtothecoldend[49].However, theoreticcalculationindicatesthatNiatomsmigrateslowerthan CuinSnPbsolderunderthermalgradients.Ifwetaketheeffective chargenumberofNitobe67[43],resistivityas6.4108

_V

_m,

andthe currentdensity as9.7103_A/m2_{, theelectromigration}

forceisestimatedtobe6.71017_{NusingEq.(4).Theworkdone}

by the force in an atomic jump distance of 31010_{m is}

2.011026_{J.Whenthethermomigrationforceisbalancedwith}

electromigrationforce,atemperaturedifferenceof

D

T=2.415 104_{kisneededacrossanatomicjump,whichis equivalentto}

80508C/cm.Thatis,itneedsathermalgradientover80508C/cmto observethermomigrationofNiatomsduringelectromigration.

Fig.13(a)through(d)showthecross-sectionalSEMimagesofthe fourbumpswith3

m

mNi/5

m

mCuUBMsafterstressedby0.55Aat 1508Cfor180h.TheelectricallayoutisidenticaltothatinFig.12. Whentheywerestressedby0.55A,themeasuredthermalgradient was857,1286,1429and8578C/cm[47].VoidsformedonlyinBump 3,whichhadadownwardelectronflow.Thesevoidsarecausedby electromigrationandtheyformedintheinterfaceofthesolderand theNi3Sn4IMCs.Theresistanceofthisbumpincreasedto1.5timesof

itsinitialvalue.Itisinterestingthattherewerenodamagesorvoids observedinBumps1,2,and4,exceptthatthethicknessofNi–Sn IMCsincreasedfrom0.9

m

mto1.7

m

m.Thethermalgradientsinthe fourbumpsaremuchsmallerthanthisvalueinthestudy.Therefore, migrationofNi–SncompoundswasnotobservedintheSnAgsolder joints.Weonlyobserveelectromigrationdamagesduringcurrent stressing.Thus,nothermomigrationofCuandNiwasfoundinthe jointswithNiUBMs.TheresultsalsosuggestedthattheNiUBMs serveasanexcellentdiffusionbarrierforCuthermomigration.Itis speculatedthatthe lowNisolubilityin Pb-freesolderalsoslow downtheoccurrenceofthethermomigrationofNiatoms.Zengand Tu reportedthat thesolubility ofNiis only0.28wt%in Pb-free soldersat2508C.However,thesolubilityofCuis1.54wt%inPb-free soldersat2608C[50].Therefore,thethermomigrationofNiismuch lessthanthatofCu.

3.5. ThermomigrationofAgatoms

The two of the most popular Pb-free solders are SnAg and SnAgCualloys,inwhichAgconcentrationareabout2.0–3.5wt.%. WhetherAg atomswould migrateina thermal gradient inthe solderjointisofinterests.ItisreportedthatAgatomsmigrateto thecoldendunderathermalgradient.Fig.14(a)showsthe cross-sectionalSEMimageforasolderjointbeforecurrentstressing.The UBMonthechipsideis5

m

mCu/3

m

mNi.Themetallizationonthe

Fig.14.ThermomigrationofAgatoms.(a)Cross-sectionalSEMimageshowingthemicrostructureofasolderjointbeforethermomigrationtest.(b)ThedistributionofAg atomsbyEPMAforthejointin(a).(c)Cross-sectionalSEMimageshowingthemicrostructureofasolderjointafterthermomigrationtestunderathermalgradientof28298C/ cmfor800h.(d)ThedistributionofAgatomsbyEPMAforthejointin(c).

substratesideis5

m

melectrolessNion20

m

mCulines.Thesolder consistsof3.5wt.%ofAgand96.5wt.%ofSn.Fig.14(b)showsthe distribution of Ag atoms analyzed by electron probe X-ray microanalyzer(EPMA).TheAgatomsdispersedintheSnmatrix uniformlyintheas-fabricatedsample.Thejointwasstressedby 0.57Aofanalternatecurrentandthejouleheatingeffectcreateda thermalgradientashighas28298C/cm,withhotendonthechip side and cold end on the substrate side. The samples and the stressingconditionswereidenticaltothoseinSection3.2.After stressingfor800h,somepureSnaccumulatedonthehotenddue tothermomigration,asillustratedinFig.14(c).However,theAg atomsmigratedtothecoldendaftertheACstressing,asshownby theEPMAmappingofAgatomsinFig.14(d).Theyprecipitatedas largeparticlesofAg3Snintermetalliccompoundsthere.Theresults

indicatethat theAg atoms migrate to thecold end under the thermal gradient. Nevertheless, the Ag concentration was only 3.5wt.%.ThemigrationoftheAgatomsmaynotcauseanyvoid formation.Itdeservesfurtherstudywhetherit willcauseother reliabilityproblems.

3.6. ThermomigrationofTiatoms

Tihasbeenwidelyadoptedasthediffusionbarrierbetweenthe AltraceandtheCuUBM. Itisalsoan excellentadhesionlayer betweenSiO2andAlorCufilms.ItisreportedthatTihasalarge

heatoftransportvalueof768kJ/mol(ifTimovestothecoldend,it shouldpositivevalue)[51,52]andissusceptibletomigrateundera thermalgradient.Chenetal.reportedthatTiatomsmigratetothe cold end rapidly under a thermal gradient, resulting in severe deterioration of theinterface between theCu and Al layers as showninFig.15[53].Thesamplesforthermomigrationtestswere identicalto the ones for thermomigration tests in Section 3.2, which were eutectic SnAg solder joints with 5

m

m Cu UBMs.

Fig.15(a)showsthecross-sectionaltransmissionelectron micro-scope(TEM)for theUBMstructure onthechipside. OntheAl wiringtrace,aTifilmof0.12

m

mthickwasdepositedbetweenthe Altraceandthe5

m

mCuUBMlayer, whichwaslabeledbythe dottedlinesinthefigure.ThisTilayerservedasadiffusionand adhesionlayerforCuUBManditadheredquitewelltotheAland Cufilmsbeforethermomigrationtests.Beforethetest,thesample was polished to its center first. Electromigration tests were performedat0.55Aat1508Cfor82h.ThenFIBwasadoptedto etchacrosssectionfortheobservationoftheinterfaceinBump1, which had no current passing through. After thermomigration testsatapproximately10008C/cm,themicrostructurechangesare showninFig.15(b).Coldendlocatesontheright-handofthefigure becauseof theAl traceservingthemajorheatingsource. Some Cu6Sn5IMCsstilladheredtotheAltrace.However,itisintriguing

that the Al and the Ti layers were damaged and severe void formationoccurredintheAltrace.ItisspeculatedthattheTilayer hadmigrated intotheCu andCu6Sn5 IMCsdue tothethermal

gradient because of it is very susceptible to migrate under a thermal gradient. Then the Al trace diffused into the Cu UBM becauseAlcaneasilydiffuseintotheCuUBMtoformAl–Cusolid solutionor to reactwith Cu toform intermetallic compounds, resulting in the voids in the original location of the Al trace.

Fig.15(c)presentsanothersampleafterthethermomigrationtest for82h.The5

m

mCuUBMwasmigratedtothesubstratesidedue tothermomigrationofCu.SeriousvoidsalsoformedintheAltrace afterthethermomigrationtest.Therefore,Tithermomigrationalso endangersthereliabilityofthesolderjoints.

4. Thermomigrationinmoltensolders

In theprocessingofsolder jointsinflip-chiptechnology and microbumpsin3DIC,thesolderbumpsneedtogothroughseveral

reflowsandeachofthemforabout1min.Forexample,inflipchip technologythefirstreflowisneededtotransformtheplatedsolder cylindersintosolderballsontheSichip.Then,theSichipisflipped overtoaligntoapolymersubstrate,andthentheyarereflowedfor chip-join[19].Formicrobumpfabrication,aSichipisalignedto anotherSi chipand theyare reflowedfor about1min [54,55].

Fig.15.ThermomigrationofTiinsolderjoints.(a)Cross-sectionalTEMfortheUBM structureonthechipsidebeforethermomigrationtest.TheTilayerbetweentheAl traceandtheCuUBMisofinterest.(b)Cross-sectionalFIBionimageshowingthe damageduetothermomigrationatapproximately10008C/cmat1508Cfor82h.No currentpassedthroughthisjoint.(c)Cross-sectionalFIBionimageforanother sampleafterthethermomigrationtestfor82h.Similarto(b),seriousvoidsalso formedintheAltraceafterthethermomigrationtest.

Duringthejoiningprocesses,thesolderneedstobemeltedtoreact withUBMtoformIMCs.Morereflowsmayberequiredwhenmulti chipsarejoinedtogether.Theremayexistatemperaturegradient duringreflowprocessinovenoronahotplate.Inaddition,hot compressionmethodissometimesadoptedtojoinmicrobumps

[56,57].Therewillbeathermalgradientacrossthemicrobumps forhotcompressionbecauseheatisappliedthroughoneofthe chips. The thermal gradient acrossthe solder should be much smallerthanthatduringelectromigrationtests.However,theCu andNidiffusivitiesinmoltensolderisintheorderof105_cm2_/s,

whichisseveralordersinmagnitudelargerthanthatinsolidstate. Therefore,thethermomigrationofCuandNiinmoltensoldermay occurduringreflowprocesswhenthereisasmallthermalgradient presentinthejoint.ThemigrationofNiandCuatomswillaffect thegrowthofinterfacialIMCsandthusinfluencethereliabilityof thesolderjointsandmicrobumps.

4.1. ThermomigrationofCuatomsinmoltensolders

Thesamplesusedforthermomigrationstudyinmoltensolders aredifferentfromthosedescribedaboveinsolidstate.Sandwich structuresofSi/Cu/SnAg/Cu/Siwerefabricated.TheSn2.5Agsolder of19

m

mthickwaselectroplatedonpatternedCuUBMs,whichwere 100

m

mindiameterand20

m

minthickness.Thefabricationofthe microbumpsweredescribedinourpreviouspublications[58,59]. Thewaferwasreflowedat2608Cfor1mintoformsoldercaponthe CuUBM.Tofabricatethetestsamples,aSidiewasflippedoverto alignwithanotherdieandreflowedat2608Cfor3min.Inorderto investigatetheCuthermomigrationinmoltenstate,theflip-chip samplesunderwentadditionalreflowof5,10,20,40minonahot plateorinanovenmaintainedat2608C.Thenthesampleswere cooledinairandthecoolingratewasabout58C/s.

ThermomigrationCuinmoltensolderswasfirstreportedby Guoetal.[60].Inoursamples,Fig.16(a)showsthecross-sectional

SEM imagefor theas-fabricatedsample. Thebumpheightwas approximately30

m

m. Thissampleexperienced3minreflowat 2608Conahotplate,wherethebottomdiecontactedthehotplate andthetopdiewasexposedtotheair.Therefore,thebottomdie wasthehotendandthetopdiewasthecoldend,aslabeledinthe figure. IMCsofCu6Sn5 formedatboth Cu/solderinterfaces.The

measured thickness for the interfacial IMCs was 2.3

m

m and 2.9

m

monthehotendandcoldend,respectively.Itshowsthatthe IMC on the cold end is thicker. Fig. 16(b) presents the cross-sectional SEM imagefor thesample afteran additional 10min reflowat2608C.TheCu6Sn5IMCsonthecoldendgrewto5.2

m

m,

whereas it is only 3.5

m

mon the hot end. As the reflowtime

Fig.16.ThermomigrationofCuinmoltensolder.Cross-sectionalSEMimagesshowingtheevolutionofinterfacialIMCsaftervariousreflowtimesat2608Conahotplate.The coldendlocatedatthetopSidie.(a)As-fabricatedsample.(b)After10minreflow.(c)After20minreflow.(d)After40minreflow.Cuatomsmovedtothecoldendand enhancedthegrowthofCu–SnIMCsthere.

Fig.17.PlotoftheCu6Sn5thicknessagainstreflowtimeonthehotendandcoldend. TheaverageCu6Sn5thicknessforthesamplereflowedintheovenwasalsoplotted inthefigure.

increasedto20min,asshowninFig.16(c),theIMCsoncoldend increasedtoabout6.7

m

m.YettheIMCsonthehotenddidnot grow at all, remaining about 3.4

m

m. When the reflow time increased to 40min, Fig. 16(d) shows that the asymmetrical

growthappearsmoresignificantly.TheIMCsonthecoldendgrew to12.3

m

m,yetitisstill3.6

m

monthehotend.Asacontrolled experimentforcomparison,sampleswerereflowedinanovenof uniformtemperatureforvariousperiods.Noobviousdifferencein IMCthicknesswasfoundon bothends.Fig.17summarizesthe thicknessofCu6Sn5IMCsasafunctionofreflowtimeonthehot

endandcoldend.Inaddition,theaverageIMCthicknessforthe samplereflowedin theovenwasalsoplottedinthefigure. The resultsindicatethat theIMCson thecold endhave thefastest growthand theIMCsonthehot end growslower than thatin theoven.

Thethermalgradientinthemoltensoldersappearstobemuch lowerthanthatinsolidsolderdiscussedabove.Fig.18showsthe temperaturedistributioninthemoltensolderwhenconvection coefficientwassetto15W/m2K.Thetemperaturedifferencewas 0.158Cacrossthe30-

m

m-thicksolderlayer,resultinginathermal gradientof518C/cminthemoltensolder.Becausethediffusivity ofCuinmoltensolderisashighas3.2105_cm2

/sat2608C, thermomigrationoccursinthemoltenstateunderamuchlower temperaturegradientthanthatinthesolidstate[61].Inaddition, the bump height of the microbump was only 30

m

m. The Cu thermomigrationaffectsthegrowthofinterfacialIMCsacrossthe solder joint significantly. Therefore, the Cu thermomigration will bean important reliability issue in microbumpsin 3D IC packaging.

4.2. ThermomigrationofNiatomsinmoltensolders

SandwichstructuresofSi/Ni/SnAg2.5/Ni/Siwerefabricatedfor thestudyofthermomigrationofNiinmoltensolders.TheNilayers were5

m

mthickfabricatedbyelectroplating.Thesolderthickness is closeto thatused in Cuthermomigration inmolten solders.

Fig. 19(a) shows the as-fabricated microbumps. The cold end locatesonthetopside,whereasthehotendsituatesonthebottom side.ThereisnodetectibledifferenceinNi3Sn4thicknessforthe

as-fabricatedsample. As thereflow time increasedto20minand 40minat2608C,asshowninFig.19(b)and(c),thereisnoobvious thicknessdifferencebetweentheIMCsonthebothends.Therefore, theNimigratesmuchslowerthanCuinathermalgradientand thereisnodetectiblethermomigrationofNiduringreflowprocess onahotplate.

TofurtherverifyNiwillmovetocoldendorhotendinmolten solder,thethermalgradientinthemoltensolderwasincreasedby placingablankSichipontopofthemicrobumps.Theschematic drawingfortheexperimentalsetupisshowninFig.20.SinceSiisa goodheatconductor,itwilldissipateheatawayfromthetopSidie

Fig. 18. Simulated temperature distribution in the molten solder when the convectioncoefficientwassetto15W/m2

K.Thethermalgradientwasonly518C/ cmacrossthemoltensolder.

Fig.19.ThermomigrationofNiinmoltensolder.Cross-sectionalSEM images showingtheevolutionofinterfacialIMCsaftervariousreflowtimesat2608Cona hotplate.ThecoldendlocatedatthetopSidie.(a)As-fabricatedsample.(b)After 20minreflow.(c)After40minreflow.NoasymmetricalgrowthofNi–SnIMCswas observedupto40minat2608C.

Fig.20.Schematicdrawingoftheexperimentalsetuptocreatebiggerthermal gradientinmoltensolderbyplacingalargepieceofSichipontopofthesolder joints.

of the microbump. Thermal paste of thermal conductivity of 4.5W/mKwasappliedbetweentheblankSiandthemicrobump tolowerthethermalresistanceoftheentirestructure.Bythis arrangement,thethermalgradientinthemoltensoldercanbe increased to approximately 3008C/cm. Fig. 21(a) shows the interfacial IMCs growth after 10min reflow at 2608C. The thickness of the Ni3Sn4 IMCs was 1.740.04

m

m and

1.760.03

m

m for the IMCs on cold end and on the hot end, respectively.However,thethicknessoftheIMCsonthecoldend grewthickerthanthatonthehotendafter40min,aspresentedin

Fig.21(b).Itis3.030.27

m

mand1.930.08

m

mfortheIMCson thecoldendandonthehotend,respectively.Asthereflowtime increasedto100min,thedifferencebecomesmoresignificantly,as showninFig.21(c).TheNi3Sn4IMCsgrewasthickas4.610.34

m

m

onthecoldend.Yet,itisonly2.120.06

m

mfortheNi3Sn4IMCson

thehotend.Fig.22showstheNi3Sn4IMCsthicknessasafunctionof

reflowtime for the bothends. The resultsindicate the thermo-migrationofNistartstoaffectthegrowthoftheinterfacialNi3Sn4

IMCsafter20minreflow.Inaddition,Niatomsdiffusetothecoldend underathermalgradient,althoughthediffusionrateismuchslower thanthatofCu.

5. Conclusion

Thermomigrationisexpectedtobeaseriousreliabilityissuein microbumps in3DIC technologyduetojouleheating. Thermo-migrationbehaviorsinsolderjointswerereviewedinthispaper.In Pb-containing solders, Pb atoms are the dominated diffusion speciesandtheymigratetothecoldendunderathermalgradient. The heat of transport is measured to be +22 to +26kJ/mol. However,Snatomsmigratetothehotendinthethermalgradient. Its heat of transport is measured tobe 1.36 to3.38kJ/mol. Thermomigration of Cudiffuse tothecold end very quickly in solderin bothsolidand moltensolders.Ontheotherhand,the thermomigrationofNiismuchslowerinbothsolidandmolten solders. Thermomigration of Tiis a serious issue, since it may damagethecontactinterfacebetweentheAltraceandtheCuUBM becauseitmigratestothecoldend.Agatomsalsomigratetothe coldendinsolidsolder.

Acknowledgement

The financial support from the National Science Council, Taiwan, under the contract NSC 98-2221-E-009-036-MY3 and NSC100-2221-E-007-072,isacknowledged.

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