Multilayer CdHgTe-based infrared detector: 2D/3D microtomography, synchrotron emission and finite element modelling with stress distribution at room temperature and 100 K

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Anne-Laure LEBAUDY, Raphaël PESCI, Boris PIOTROWSKI - Multilayer CdHgTe-based infrared

detector: 2D/3D microtomography, synchrotron emission and finite element modelling with stress

distribution at room temperature and 100 K - Materialia - Vol. 9, p.100511 - 2020

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Multilayer

CdHgTe-based

infrared

detector:

2D/3D

microtomography,

synchrotron

emission

and

ﬁnite

element

modelling

with

stress

distribution

at

room

temperature

and

100 K

A.L.

Lebaudy

∗

_,

_R.

_Pesci

_,

_B.

_Piotrowski

ENSAM-Arts et Métiers ParisTech, LEM3 UMR CNRS 7239, 4 rue Augustin Fresnel, 57078 Metz Cedex 3, France

a

b

s

t

r

a

c

t

ThemechanicalbehaviourofaCdHgTe-basedinfrareddetectorwasevaluatedafterprocessingatseveral temper-aturestodeterminetheimpactofthermomechanicalloadingonresidualstressandreliability.Thearchitecture ofthedetectorwasfirstentirelycharacterized,relyingonSEM,X-raymicrotomographyanddiffractionanalysis, inordertogetthenature,themorphologyandthecrystallographicorientationofalltheconstitutivelayers, andinparticulartheindiumsolderbumps.Theresultsnotablyshowedtheunexpectedsinglecrystalaspectof theindiumbumpswitharepeatabletruncatedconegeometry.Toobtainthethermomechanicalresponseofthe structureafterprocessingandintherangeofoperatingtemperatures(from430Kto100K),a3DFiniteElement modelwasthendeveloped.Asexpected,thenumericalresultsshowedastressgradientevolutioninthe struc-turefromhightolowtemperatures,withhighlocanjvvlstressaround30MPaintheCdHgTeat100K,mainly duetothethermalexpansioncoefficientmismatchbetweenthedifferentlayers.Theyhighlightedthesignificant influenceofthegeometryandthesinglecrystalnatureofthebumpsaswellasthebehaviourlawofthedifferent materials.

1. Introduction

Thedemandtoincreasefunctionalityandperformanceofelectronic deviceshasledtothegradualminiaturizationofelectronicpackaging. Theflipchipprocesswherethechipisassembledfacedownontothe circuitboardisidealforsizeconsiderations[1]:thisarchitecturedoes notneedextracontactareaonthesidesofthecomponentandthe con-nectionlengthisminimised,whichisrelevantforhighfrequency ap-plications.Intheinfrareddetection field,theflipchiptechnologyis exploitedforseveralphotodiodecircuitsin InSb,GaN, CdHgTe dedi-catedtodifferentcutoff wavelengths.Thepackagingiscomplexand con-tainsseveralmaterialssuchasmetal,semi-conductororunderfillresin, whichhaveverydifferentmechanicalbehaviours(thermalexpansion, elasticconstants,amongothers).Theinterconnectsizedecreasingand theglobalarchitecturecomplexificationleadtosevere thermomechan-icalloadingsduringthemanufacturingstepsandrunningconditions: theycaninduceresidualstress,mainlycomingfromthemismatchin thethermalexpansioncoefficient(CTE)ofthevariousmaterialsused

[2],warpageormechanicalfailure[3]inthemicroelectronic assem-bliesandaﬀecttheirreliability.Suchresidualstresseshaveoftenbeen observedandquantiﬁedinthinorthickplates,forexampleafter weld-ing[4,5],withagreatimpactoftensilevaluesonthestructureintegrity

orfatiguelimit,sothattheyshouldberationalised.Byapproximating thestructuretoathinfilmandtheStoneyformulation[6]usingthe curvatureofthesubstrate,itispossibletocalculatetheresidualstresses inthechipabovebyneglectingtheinterconnectionlayer.Thismethod isverylimitedanddoesnotallowforanestimationoftheevolution ofstressthroughallthelayers.Someexperimentaltechniquessuchas Ramanspectroscopy[7], X-raydiffraction[8]orKossel Microdiffrac-tion[9]can alsobe used, buttheyarelimitedin scopedue tolocal heating,lowelectrical conductionorthethicknessofthelayers.The mostcommonapproachtoestimatethestressvaluesistouseFinite El-ementMethod(FEM)andsimulatethestackofchipandconnections underthermalloading.Ifliteraturepresentssomepapersabout2D rep-resentations[10,11],theincreasingnumberofsolderbumpsinthe as-sembliesledtothedevelopmentof3Dmodels[12].Theresultsenable toobserveastressgradientthroughoutthearchitectureandinall di-rections.However,manyhypothesesareoftenformulatedconcerning thematerialproperties,withthedifferentlayersincludingsingle crys-tals usuallyassumedtobe isotropic,andeitherplanestressorplane strainconditionsareconsidered[13].Inthecaseoftheinterconnection zone,theshapeofthesolderbumpscanberoughlyassimilatedto cylin-dersor truncatedspheres whilethematerialanisotropyisneglected, andtolimitthenumberofelementsinmodels,manyauthorspropose toreplacetheinterconnectionlayerwithahomogeneouslyequivalent material[14].Theseassumptionshelptodecreasethecomputingtime andtomodelthewholeassembly,butitmakesitimpossibletorender

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Fig.1.ArchitectureoftheIRdetectorconsidered.

astressgradientineachlayer[15]andtheycanleadtoa misestima-tionof thestressvalues.Today, themainchallengeforstress analy-sisinflipchippackagesisthesignificantgradientatthemicrometric scale.Theinterconnectionlayercanbeverythincomparedtothetwo interconnectedcircuitswhich canintroducehighstrain inthesolder bumps.Moreover,themechanicalbehaviouroftheconstitutive materi-alsisoftennotwellknown.Themodellingscalehastobeadaptedto therequiredobservationsandtheimpactoftheinputdataontheresults mustbeevaluatedtodeterminewhatthemostinfluentialparameters are.

Thepresentstudyaimsatestimatingthelevelofstressthatappears inaninfraredCdHgTe-baseddetectorafterprocessingatroom temper-atureandat100Kduringservicelife.A3DFEMmodelisdeveloped toprovide abetterunderstandingofthestrain/stressgradientinthe structureunderthermalloadingandtoimprovethereliability.The rel-evanceofsuchamodelatalocalscalestronglydependsontheaccurate knowledgeoftheactualarchitectureofthecomponent.First,a charac-terisationsteprelyingonSEMcoupledtoEDSandEBSD,X-ray microto-mographyandsynchrotronemissionhasbeencarriedouttoapprehend thegeometry,thechemicalcompositionandthecrystallographyofall thelayersofthestructure,especiallytheindiumsolderbumpsinthe in-terconnectionlayer,whichseemstobethemostcriticalinthestructure, consideringtheobservedfailuremodes.Fromtheseconsiderations,a3D FEMmodelwasdevelopedandthermalloadingsrepresentativeofthe componentlifecyclewereapplied.Thesesimulationsmadeitpossibleto showthestressgradientsarisingintheseverallayersatroom tempera-turebutalsoatoperatingtemperature(77K).Aparametricstudyonthe inputparameterswasthencarriedouttodeterminethemostinﬂuential variablesonthestressvalues.Finally,thestressdistributionwas com-paredtoexperimentalvaluesobtainedat77Kduringapreviouswork usinganX-raydiﬀractionmethodforsinglecrystal.

2. Experimental procedure

2.1. Presentationofthedetectorarchitecture

Thisworkconsidersaﬂipchipinfrareddetector(midwave-infrared MWIR)witha30μmpitch320×256I/OpixelsIRfocalplanearray.The correspondingarchitectureispresentedinFig.1:aCdHgTethinlayer (detectorcircuit)isinterconnectedtoasiliconsubstrate(readout cir-cuit)throughindiumbumpsandanepoxyunderﬁll.

Thisarchitectureleadstosomesymmetrywithorthotropic proper-ties:theindiumsolderbumpsarealignedparallel/perpendiculartothe edgesofthedetectioncircuit.Fourmainprocessstepsarenecessaryto manufacturethedetector(allstepsaredescribedin[16]):theindium bumpdepositingonthesiliconcircuit,thehybridisationoftheCdHgTe detection circuit,theunderfilling stepandthefinaldetectioncircuit thinning.Duringthehybridisationstep,heatinguntil430Kisapplied (aboveindiummeltingtemperature);thenbothmechanicaland chemi-calpolishingsofthedetectorcircuitareperformedtokeeptheactive de-tectionCdHgTelayerverythincomparedtothethicknessofthesilicon circuit.Duringmanufacturingandservicelife,thecomponentis there-foresubjectedtointensetemperaturevariationsfrom430Kto77K.The CTEmismatchbetweentheCdHgTedetectorchip,theinterconnection layerandthesiliconcircuitismainlyresponsibleforresidualstress initi-ationandwarpageintheassemblythatcanleadtoseveralfailuremodes suchassolderbumpdamageorcracksintheCdHgTechip.Inorderto better understandtheappearanceof residualstress,especiallyin the detectioncircuitandthesolderbumps,thegeometryandthematerials constitutiveofthedifferentlayershadtobepreciselyknowntobuild thefiniteelementmodel.Acompletecharacterisationoftheassembly wasthereforecarriedoutandparticularemphasiswasputonthe inter-connectionlayerandthesolderbumps.

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Fig.2. (a)Solderbumpsvisualisationbymicrotomography(b)Exampleofapost-processingofthestackwithImageJ® (c)Solderbumprepresentedasatruncated cone.

Table1

Indiumsolderbumpaveragethicknessinboththecentreandtheedgesofthecomponent.

Mean value Standard deviation Solder bump thickness (μm) Component centre 6.52 6.54

Component edge 0.11 0.13 Diameter in contact with CdHgTe (μm) Component centre 17.4 0.16 Component edge 16.8 0.19 Diameter in contact with silicon (μm) Component centre 12.8 0.12 Component edge 12.3 0.14 2.2. Geometricalcharacterisation

WhilethegeometryofthesiliconandCdHgTecircuitsiswellknown, themorphologyoftheinterconnectionlayercomposedofsolderbumps inanepoxymatrixstillremainstobe confirmedafterthe hybridisa-tionstepbecausevisuallyinaccessible.Inordertoaccuratelymodelthe structure,effortshavebeenmadeinX-raymicrotomographytoobtain theprecise3Ddescriptionofthesolderbumpsinthecentreandonthe edgesoftheassembly.Ithastheadvantageofbeingnon-destructive, whileachievingaveryacceptablespatialresolution.Thismethod ex-ploitstheselectiveabsorption propertiesof theX-raysbythematter toobservethe sampleinside[17]: ina tomograph,thesampleis il-luminatedwithanX-raysourceandtheintensitymodulationsofthe transmittedbeamarerecoveredas animagebya 2Ddetector. Dur-ingan acquisition cyclewhose duration varies from a fraction of a secondtoseveral hours,some projectionsarecollected accordingto differentangularpositions ofthesampleinrotation.Thedistanceto thedetector,thechoiceoftheacquiredimagenumberaswellasthe anglesteparerealisedaccordingtothedesiredresolution.The recon-structionof3D objectsismadefrom theangularprojections:a grey levelis associatedwitheach voxelof thevolume,whichinforms on theattenuationcoefficientof thematter. Theanalyses wererealised

using aPhoenixv|tome|xm 300/180tomographfromGeneral Elec-tricMeasurementandControlequippedwitha16 megapixel Dyn41-100 detector.Thetubeof thesetup canreach anacceleration volt-age of 180kV andgenerate anX-ray beamallowinga veryﬁne de-tail detection (downto0.5μmvoxel size).Without any cutting,the analyses wereperformed witha1μm3 _resolution _and_led _to_a_good

estimation of the solder morphology andrepartition. To be statisti-cally representative, a large volume of thesample, approximatively 2.0×2.0×1.0mm3 _was _analysed,_{corresponding} _to _a _ﬁeld _of _about

4500soldersbumps,bothinthecentreandattheedges ofthe com-ponent.Afterthresholdapplication,the3Dvisualisationofthesolder bumpswiththesoftwareMyVgl® wasveryprecise,asshowninFig.2

(a).

TheopensourceimageJ® softwarepresentedin[18]wasusedfor partofthepost-processingintheinterconnectionzone:anexampleis giveninFig.2(b).Byaveragingsolderdiametersinallimages,itwas possibletovisualizethetypicalgeometryofanindiumsolderbump:the detaileddimensionsaregiveninTable1,withsimilarresultsinboththe centreandtheedgesoftheIRdetector.Theﬁnal3Drepresentationcan beeasilyassimilatedtoatruncatedcone(Fig.2(c)),withmaximumand minimumdiametersincontactwiththeCdHgTecircuitandthesilicon substrate,respectively.

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Fig.3.CrystallographicorientationofthesiliconandCdHgTesinglecrystals.

2.3. Crystallographicanalyses

Afterthegeometriccharacterisationoftheindiumsolderbumps,it wasnecessarytodeterminethecrystallographicnature ofeach crys-tallinelayerof thestructurein order toidentifytherelevant consti-tutiverelation of each material tosupply theﬁnite element model. ElectronBackscattereddiﬀraction(EBSD)analyseswereperformed us-ingaJEOL7001F FEGSEMequippedwitha CCDcamera from Ox-fordInstruments.The CdHgTeandthesilicon wereeasily accessible withtheelectronbeambecausetheyhademergentsurfaces.The anal-ysesestablished that they weretwo single crystals(111) and (100) oriented,respectively,asshowedinFig.3,withamisorientationless than1°.

Somecomponentswerecutandpreparedwithspecifictechniquesin ordertoaccesstheinterconnectionzone,especiallytheindiumsolder bumps.Thesectionswerefirstcarefullyprepared(sawingand polish-ing)usingaLeicaEMTXPfollowedbyionicpolishingwithaLeicaEM TIC3X.Thislastpolishingtechniqueprovidedidealsurfaceconditions forperformingEBSDmappingswithoptimalindexingrate.The equip-mentusedallowedioncross-sectioncuttingatroomtemperatureorat lowtemperaturewhenthesetupwassuppliedwithliquidnitrogen.Due tothelowmeltingtemperatureofindiumanditsdiffusionproperties, theionicpolishingwascarriedoutat153Kwithanacceleration volt-ageof10kVandperformedinthecentreoftheassembly.Then,phase andorientationmappingswereconductedonseveralsolderbumpsin theionicpolishedarea.EBSDmappingswereperformedwithabeam energyof20kV,withastepsizeofroughly0.5μm;theywerethen post-processedusing theChannel5suite. Intotal,adozen indiumsolder bumpsweremapped,showingthattheywereallsinglecrystalswith randomorientation,asshowninFig.4.TheEBSDorientationimages arecolour-codedtoindicatethegrainorientationgivenbythestandard triangle(tetragonallattice).

Inordertoconﬁrmtheseobservationsconsideringagreater num-berofsolderbumps,ringdiﬀractionexperimentswerecarriedouton thebeamlineID11attheESRF(EuropeanSynchrotronRadiation Facil-ity)inGrenoble,France.Asexploitedby[19,20],thismethodallowsto identifytheseveralphasespresentinasample.Themeasurementswere performedwitha78.5keV(𝜆=0.158Å)monochromaticX-raybeamin transmissionmode.Aschematicrepresentationoftheexperimental de-viceisshowninFig.5(a).The0.2×0.2mm2_incident_beam

correspond-ingtoaﬁeldof about40 indiumsolderbumpsentered normallyto thespecimens,formingcompleteDebye–Scherrerringsfromtheseveral crystallographicphasesofthestructure.The2Ddiﬀractionringswere recordedbyaFrelon2DCCDcamerawitharesolutionof2048×2048 pixels (47.2×47.2 μm2 _pixel _size). _A _distance _{sample/camera} _of

288.2mmwaschosentorecoveramaximumofdiﬀractionringswhile keepinganacceptableresolutionfortheirproperindexing.Thesamples

Fig.4. EBSDmappingsshowingthemeancrystallographicorientationofthree indiumsolderbumps.

wereplacedinsuchawaythatthebeamwasfocusedinthecentreofthe assembly,"full-chip"zone,toacquirethediffractionringsofthe detec-tioncircuit,theinterconnectionzoneandthereadingcircuit simultane-ously.TheideawastopenetratefirstthesiliconsubstratewiththeX-ray beamandexitthroughthethinneddetectioncircuitsidetominimizethe amountofmaterialcrossedbythediffractedbeamcomingfromindium soldersandlimitthediffractionringattenuation.Anexampleofa gen-erateddiffractionpatternacquiredbythecameraisshowninFig.5(b). The diffraction patternsobtained haveboth diffraction spotsand completerings.Eachringcorrespondstodiffractingplanes{hkl}ofa definitephase:itiscomposedofseveralindividualspotsdiffractedat thesameBraggangle,eachspotbeinggeneratedbyagrainina diffrac-tionposition.Itisthereforepossibletoidentifythephasespresentinthe assembly,theircrystallographicstructureaswellastheirpolycrystalline ormonocrystallinenature.Giventhesmallbeamsizeused,acomplete ring willbe characteristicofapolycrystallinephasewithsmallgrain size.InFig.5(b),theveryintensespotscorrespondtosiliconand Cd-HgTesinglecrystals;othersareduetoremainingphases.Inorderto in-dexthediffractionringsandassociatethemtotheirrespectivephases,it isnecessarytoproceedtoapreliminarysteptodeterminetheir associ-ateddiffractionangles.TheFit2Dsoftwarewasusedforpost-processing tointegratetheDebye–Scherrerringsandgeneratetheequivalentofa 2𝜃 scan[21].Theinputdataincludethepixelsizeofthecamera,the wavelengthoftheradiationconsideredaswellasthecamera-to-sample distance.Theseparametersarethenrefined;theuserhasthepossibility tomanuallycorrectthecentreofthebeamandthenon-orthogonality ofthedetectorwithrespecttotheincomingbeam.Thisstepcanalso be performedmoreaccuratelyusing acalibrationmaterialsuchasa nanocrystallinepowder[22].Inourcase,thecalibrationisbasedon diffraction peaksof thesilicon,thelessstrainedlayer(becausevery thickcomparedtoothers).AsshowninFig.6,severaldiffuse continu-ousdiffractionlines/diffractionringscanbeattributedtoverythin poly-crystallinelayersintheassemblysuchastheUnderBumpMetallization (UBM).Thediffractionringsofindiumhavealsobeenidentified accord-ingtotheirdiffractionangle𝜃 associatedtothe{hkl}diffractingplanes (surroundedlines/diffractionringsinthe2𝜃 scanpresentedFig.6):they arediscontinuous,showingthepresenceofonlyafewgrainswith dif-ferentorientations.

This resultconﬁrmstheconclusions from EBSDmappingson the cross sectionsanalysed:each indiumsolderbumpis asinglecrystal. Thiscanbeofcrucialimportancesincethetetragonalcrystalofindium leadstoahighlyanisotropicthermomechanicalbehaviouralongthe dif-ferentcrystallographicaxes.Thefactthatitispresentinasinglecrystal

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Fig.5. (a)Diﬀractionringsetup(b)Diﬀractionpatternofthecomponentacquiredbythe2Ddetector.

Fig.6. Ringdiffraction:identificationofthediscontinuousdiffractionringsof indium.

formwithrandomorientationsintheIRdetectorcangeneratea me-chanicalresponsethatcandiﬀergreatlyfromoneindiumsolderbump toanother(onepixelofthedetectortoanother).Consideringthese var-iousgeometricandcrystallographicobservations,a3Dﬁniteelement modellingwasbuilttosimulatethecompletestressdistributioninthe IRdetector.

3. Finite element modelling 3.1. Architectureandmeshing

The3DFEMmodeldevelopedinthisworkaimstoshow,atthescale ofthelayerorofasolder(thatisapixeloftheIRdetector),thepresence ofstrain/stressgradientsunderthermalloadingsandthereforeto eval-uatetheimpactoftemperaturevariationsonthestresslevelreached

Fig.7. Boundariesconditionsconsideredforthe3Dmodel.

inCdHgTe,indiumandsilicon.Itmustbeasrepresentativeofthe ac-tualgeometryoftheassemblyaspossiblewithoutnecessarilymodelling theentirestructure,inordertohighlighttheeﬀectofstressgradients onaverylocalscalebyconsideringmaterialswithveryhigh hetero-geneousproperties.Theunderbumpsmetallizationbetweenthe detec-tion/readoutcircuitsandindiumsolderwasignoredinordertosimplify themodelandanidealbondingalongthematerialinterfaceswas as-sumed.Onlythethreemainlayersoftheassemblywereconsideredin thesimulations:

- ThedetectioncircuitinCdHgTe.

- The interconnection zone consisting of a ﬁeld of indium solder bumpsembeddedinanepoxymatrix.

- Thesiliconsubstrate.

Thesolderbumpsweremodelledastruncatedconesasobservedin theX-raymicrotomographyreconstructions.

ThemeshoftheCdHgTelayerandtheinterconnectionzone(solders andepoxymatrix)wasrealisedusinglinearhexahedralelements.Atthe interfacewiththeinterconnectionzone,theﬁrst50μmofsiliconwere alsoﬁnelymeshedwithlinearhexahedralelements;then,adecreasing meshwasappliedusingquadratictetrahedralelementsinorderto de-creasethecalculationtime.Thismeshallowedtoobtainreliablestress

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50 100 150 200 250 300 350 400 450

Epoxy element

deactivation

Epoxy element

activation

« strain free »

Underill step

Underill

temperature

er

ut

ar

e

p

m

e

T)

K(

Room temperature

Melting temperature

of indium

Hybridisation

100 K

Operating

temperature

Fig.8. Thermalloadingsconsideredinthemodel.

distributionatthesiliconsurface:indeed,this layerismore than40 timesthickerthanthecombineddetectioncircuitandinterconnection layer,sothatitisrelevanttoconsiderthatitisonlyunderloadingat itsextremesurface.Ameshconvergenceanalysisshowedthatasizeof 1.3μmisnecessarynottoinﬂuencethestressvalues.

3.2. Geometrichypotheses,boundaryconditionsandthermalloadings

Duringhybridisation,beforethinning,thedetectioncircuitconsists oftwomainlayers,theCdHgTeepitaxiallayerandaCdZnTesubstrate

[16].Inordertominimisethenumberofnodesinthemodel,the pres-enceoftheCdZnTelayerwasnottakenintoaccountintheassembly. Thethermalcycleisthereforeappliedtothegeometryofthefinal detec-tioncircuit,sowithonlytheactivelayerofCdHgTe.Thisisarequired assumptiontodecreasethenumberofelementstomeshthesilicon sub-strate,whichissignificantlythickerthantheCdHgTe.Theboundary conditionsofthemodelareshowninFig.7.Thestructurehastwoplanes ofsymmetry:conditionsUx=0andUy=0respectivelyappliedontwo facesofthemodel(allthelayersconsidered).Then,theunderfillstep inducestheformationofanepoxy"beading"surroundingandrisingon theflanksofthedetectioncircuit:inordertotakeitintoaccount (con-sideringitsthicknessandthehighdifferenceofthermalexpansionwith theCdHgTe layer),thedisplacements of thelatterwerealsolimited (Ux-CdHgTe=0andUy-CdHgTe=0).

Althoughthethermalconductivityisdiﬀerentforalltheconstitutive materials,theassemblyisassumedtohaveahomogeneoustemperature ateachcomputationtime.TheadoptedthermalcycleisshowninFig.8. Inordertosimulatetheunderﬁllstep,itwasdecidedtodeactivatethe epoxyelements("strainfree")atthebeginningofthecalculationandto reactivatethemat353K(Abaqusoption),theglasstransition temper-atureofepoxy,abovewhichitwasconsideredthatepoxydidn’thave anyimpactonthemechanicalbehaviourofthestructure.

Table2

ElasticconstantsofCdTeandHgTe.

References C 11 C 12 C 44 Uncertainty Temperature (K) CdTe [25] 53.51 36.81 19.94 + / − 0.2% 298 [26] 61.5 43.0 19.6 + / − 18% 77 [24] 53.8 37.4 20.2 + / − 3% 298 56.2 39.3 20.6 + / − 3% 77 HgTe [27] 54.8 38.1 20.4 + / − 0.5% 290 58.7 41.0 21.7 77 [28] 53.61 36.60 21.23 + / − 0.8% 298 58.63 40.59 22.41 78 [29] 50.8 35.8 20.5 200 3.3. Materialproperties

Thedetectioncircuitconsistsofa(111)-orientedCdHgTesingle crys-tal.WhileCdHgTehashighperformanceinthefieldofinfrared detec-tionduetoitsopticalandelectricalproperties,ithasmuchlower me-chanicalpropertiesthanothermaterialsusedforthisapplication.Itis generallyconsideredasa"soft"material[23],withaverylow mechan-icalstrength.Duetothedifficultyinmeasuringtheelasticproperties of athin-film material,fewdataaboutthemechanicalbehaviourare availableinliterature:onlyvaluesfortheCdTeandHgTemanufactured withmethodsallowingtoobtainlargesinglecrystalscanbefound.In thisstudy,thestiffnesstensorsatroomtemperatureand77Kproposed by[24]fortheCdTehavebeenused(Table2).

TheplasticbehaviourofCdHgTeisalsonotwellknown.Theyield stresshasbeenestimatedat12MPabyBalletetal.[30].Thisvaluecan beimpactedbyapossiblediﬀusionofthezincpresentintheCdZnTe epitaxialsubstratetotheCdHgTeactivelayerbeforethinning.With4% zincintheCdHgTe[31],theyieldstresscanbemultipliedby4for ex-ample,leadingtoavalueofabout60MPa;ithasbeenﬁxedat30MPa inourmodel.TheCTEproposedbyWilliamsetal.[32]andBagotetal.

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Fig.9. EvolutionoftheCTEforindiumsinglecrystalasafunctionoftemperature[36].

Table3

Elasticconstantsofindiumsinglecrystalaccordingto[37,38,39].

[37] [38] [39] Elastic constants 300 K 77 K 298 K 300 K 351 K 371 K 391 K 412 K 422 K 429.7 K C 11 45.35 52.6 445 45.1 43.3 425 42.1 41.4 41.1 40.9 C 33 45.15 50.8 444 45.3 43.5 42.9 42.3 41.7 41.3 41.1 C 44 6.51 7.6 6.55 6.53 6.3 6.17 6.03 5.89 5.83 5.78 C 66 12.07 16 12.2 11.9 10.7 10.3 9.88 9.46 9.21 9.05 C 12 40.01 40.6 39.5 39.7 39.8 39.6 39.5 39.1 39.2 39.1 C 13 41.51 44.6 40.5 41.1 40.9 40.4 40.3 40.1 39.9 39.5

[33]correspondingtoatemperaturerangefrom293Kto693Kandfrom 0Kto80Krespectively,havealsobeenused.Indiumischaracterised byalowmeltingpoint,asmallyieldstressandaveryhighductility at293Kand77K.ThesepropertiescombinedwithitshighCTE com-paredtoCdHgTeandsiliconareveryinterestingfortheinterconnection layerwhenoperatingatlowtemperature.Themechanicalpropertiesof polycrystallineindiumarewellknown:thebehaviourlawsfrom4Kto 295KhavebeendeterminedbyReedetal.[34],confirmingthehigh levelofplasticityandtheCTEgivenbyTouloukian[35].Onthe con-trary,fewdataaboutindiumunderitssinglecrystalformareavailable, buttheypointtoaconsiderableanisotropyduetothetetragonallattice withanotable ratiobetween thetwolatticeparameterscanda.For example,Collinsetal.[36]showedthattheCTEisverydifferentalong theaxisofthecrystalconsidered.Fig.9presentstheresultsobtained fordifferentauthors,withIn(ǁ),theCTEmeasuredalongthequadratic axisofindium,In(⊥),thatmeasuredaccordingtoaplanenormaltothe quadraticaxis,andIn(av),theaverageCTE.

The6elasticconstantsofindiumforseveraltemperatureswerealso determinedbyseveralauthors(Table3).Severalsimulationswerethen

Table4

MechanicalpropertiesofEpotek301–2asafunctionoftemperature.

Temperature (K) Young modulus (MPa) Poisson’s ratio

293 3664 0.358

250 4109 0.365

200 4474 0.349

150 5745 0.334

100 6993 0.350

launchedtocomparetheresultsconsideringthepropertiesofindiumas bothpolycrystalandsinglecrystal.

Epoxypolymers(commonlyknownasepoxies)arewidelyusedin microelectronicsforthemanufactureofflipchipassembliestofillthe interconnectionzonebetweenthechipanditssubstrate,thatistosayto fillthegapbetweenthesolderbumps.ThegradeusedintheIRdetector isEpotek301–2andwascharacterisedbyCeaseetal.[40]for temper-aturesrangingfrom300Kto100K.ThevaluesofYoung’smodulusE andPoisson’sratioobtainedarepresentedinTable4.

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Fig.10. Sectionalviewofthestressdistributioninthediﬀerentlayersoftheassemblyat293K.Therightpartisazoomoftheframedzonewithaﬁnerscale.

Atroomtemperature,Epotek301–2hasapurelyelasticbehaviour withayieldstress/strength around40MPa.Itwillthenvary signiﬁ-cantlywithtemperature,asmostofthermoplastics,withaglass transi-tiontemperatureTg=213K;themanufacturerindicatesthattheCTEis 61.10−6_K−1_below_this_temperature_and_180.10−6_K−1_beyond_it.

Thesubstrateofthecomponentisanorientedsiliconsinglecrystal (100),thebehaviourof whichis elastic,witha yieldstress/strength closeto130MPa.TheCijklelasticityconstantsconsideredforthemodel

camefrom[41]andtheCTEasafunctionoftemperaturefrom[42]. Forallthesinglecrystalmaterials,theelasticconstantsare imple-mentedintheFiniteElementmodelinatwo-step-process.First,basing ontheexperimentalresults,thecrystallographicorientationofCdHgTe, siliconandtheindiumbumpsareidentiﬁedandtheelasticconstantsare giveninthecrystalbasisforeachmaterial.Then,theorientationofeach crystalisintroducedintheFiniteElementmodel(whereaglobal coor-dinatesystemimposestheglobalorientation)throughaspeciﬁc calcu-lationthatactsasatransfermatrixbetweeneachcrystalandtheglobal coordinatesystem.

4. Results and discussion

4.1. Simulationswithpolycrystallineindiumsolderbumps

The3Dmodellingstrategyallowstovisualizethestressgradients alongthethickness,inallthelayersoftheassembly,througha well-deﬁned cuttingplane.Themaindrawbackof theFEMsimulationsis thecomputationaltime.Toseethestrain/stressgradientatthesolder scale,itisnotpossibletomodelthetotalityofthestructure(morethan 80,000solderbumps).Firstsimulationswith36,144,324and1296 solder bumps werelaunched andshowed that144 were representa-tiveofthewholeassembly,withconvergingresults.Inthispaper,all therepresentations ofthestress variationappearingintheassembly werevisualizedusingdiagonalsections.Onlyhalfofthearchitecture is presented in thefollowing ﬁguresshowing theedgeandthe cen-treofthestructureduetothesymmetryconditions.At293K,we no-ticethatintheCdHgTelayer,thecomponentsofthestresstensor tak-ingthehighestvaluesare𝜎xxand𝜎yy,closeto30MPatheedgesand

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zz yy yz xz xy

100 K

xx 10 MPa 30 MPa 20 MPa -20 MPa -10 MPa -30 MPa 0 MPa 10 MPa 30 MPa 20 MPa -20 MPa -10 MPa -30 MPa 0 MPa 10 MPa 30 MPa 20 MPa -20 MPa -10 MPa -30 MPa 0 MPa 10 MPa 30 MPa 20 MPa -20 MPa -10 MPa -30 MPa 0 MPa 10 MPa 30 MPa 20 MPa -20 MPa -10 MPa -30 MPa 0 MPa 10 MPa 30 MPa 20 MPa -20 MPa -10 MPa -30 MPa 0 MPa 4 MPa 12 MPa 8 MPa -8 MPa -4 MPa -12 MPa 0 MPa 4 MPa 12 MPa 8 MPa -8 MPa -4 MPa -12 MPa 0 MPa 4 MPa 12 MPa 8 MPa -8 MPa -4 MPa -12 MPa 0 MPa 4 MPa 12 MPa 8 MPa -8 MPa -4 MPa -12 MPa 0 MPa 4 MPa 12 MPa 8 MPa -8 MPa -4 MPa -12 MPa 0 MPa 4 MPa 12 MPa 8 MPa -8 MPa -4 MPa -12 MPa 0 MPa

Component edge

Component centre

Fig.11. Sectionalviewofthestressdistributioninthediﬀerentlayersoftheassemblyat100K.Therightpartisazoomoftheframedzonewithaﬁnestscale.

Component edge

Purely elastic polycristalline indium σyy

σxx

Component edge Component centre

σyy

Reference model

20 MPa 60 MPa 40 MPa -40 MPa -20 MPa -60 MPa 0 MPa

CdHgTe with a yield stress of 60 MPa

10 MPa 30 MPa 20 MPa -20 MPa -10 MPa -30 MPa 0 MPa 10 MPa 30 MPa 20 MPa -20 MPa -10 MPa -30 MPa 0 MPa Out of scale

Out of scale Out of scale

a) c) b) Component centre σxx σxx σyy

Fig.12. Comparisonofthenumericalresults(a)Standardmodel(reference)(b)CdHgTewithayieldstressof60MPa(c)Polycrystallineindiumwithapurelyelastic behaviour.

around10MPainthecentre(Fig.10);azoomoncertainzonesmakes itpossible tohighlightgreater tensile values inthe areasin contact withthesolderbumps.Theepoxyisinuniformbiaxialtensionaround 15MPaandtheindiumsolderbumpsarealsoinslighttensionfor𝜎xx

and𝜎yy(2MPa);thesiliconisinbiaxialtensionwithvaluesranging from4MPato12MPaundertheindiumsolderbumps.Finally,itcanbe notedthattheaﬀectedsilicondepthunderthesolderisapproximately 8μm.

Whencoolingat100K,interestingresultscanbenoted(Fig.11):

- Biaxialtensionisintensiﬁedalong𝜎xxand𝜎yyintheCdHgTe,with valuesfrom30MPaabovethesolderbumpsto18MPainthe inter-solderareas;theepoxy shows somevalues outsidethescale pre-sented(greyarea:35MPaonaveragefor𝜎xxand𝜎yy).Thisis con-sistentwiththeexperimentalstressvaluesobtainedin[43],inwhich theauthorsusedX-RayDiﬀraction(XRD)witha0.8mm2_beam_to

makesome mappingsfromthecentretotheedgeoftheCdHgTe chip:inparticular,themeasurementsat77Kshowedtensionstress valuesuptoabout30MPa.

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3 MPa 9 MPa 6 MPa -6 MPa -3 MPa -9 MPa 0 MPa

Single crystal indium local stress scale

One single crystal indium solder (orientation 1)

10 MPa 30 MPa 20 MPa -20 MPa -10 MPa -30 MPa 0 MPa Out of scale 3 MPa 9 MPa 6 MPa -6 MPa -3 MPa -9 MPa 0 MPa

Single crystal indium local stress scale σxx

σxx

Reference model: elasto-plastic polycristalline indium

10 MPa 30 MPa 20 MPa -20 MPa -10 MPa -30 MPa 0 MPa Out of scale

One single crystal indium solder (orientation 3)

Single crystal indium local stress scale σyy X Y Z Global Abaqus coordinate system

Crystallographic orientation of one single crystal indium solder bump surrounded by polycrystalline solder bumps

Orientation 1 Orientation 2 Orientation 3

c a b c a b

Orientation 2 with a 45 rotation around a axis σyy

One crystal indium solder (orientation 2)

Single crystal indium local stress scale σxx

σyy

Fig.13. Influenceofoneindiumsolderbumpmodelledassinglecrystal:differentcrystallographicorientationsandthermalexpansioncoefficientsconsidered (100K).

- Thesolderbumpsattheedgeoftheassemblyareintension,while thoseinthecentreareincompressionwithtensionintheirperiphery (forboth𝜎xxand𝜎yy).Thisparticularstressstateisrelatedtothe diﬀerenceintheCTEbetweentheepoxymatrixandindium(61.10−6

K−1_and_30.10−6_K−1_,_{respectively).}

- Thestressvariationsinthesiliconareenhancedwiththeapparition ofcompressionvaluesofabout−7MPaaccordingto𝜎xxand𝜎yyin thezonesundertheepoxy.

- Thelayerwiththemostimportantvaluesin𝜎zzisthe interconnec-tionzone,withsolderbumpsincompressionandtheepoxyin ten-sion.

- Thevaluesof𝜎yzand𝜎xzareampliﬁed,especiallyintheCdHgTe andthesiliconbetweenthesolderbumps.Theepoxyisalsoslightly aﬀected.

- Finally,thevaluesof𝜎xyaregenerallylow:onlytheepoxylocally reachescompressionlevelsaround−12MPaintheareasincontact withtheindiumsolderbumps.

Theresultsshowthegreatinfluenceof themechanicalproperties andtheCTEmismatchbetweeneachlayerofthestructureonthestress values.Thestressgradientscanbeappreciatedattwoscales:between theedgeandthecentreoftheassembly,andatthelocalscale consid-eringonesolderbump/pixeloftheIRdetector.Thedifferencebetween theedgeandthecentreistypicallyduetotheCTEmismatchbetween theCdHgTeandthesilicon.Indeed,theCdHgTedetectioncircuitcanbe assimilatedtoathinfilmcomparedtothesiliconcircuitthickness.The CdHgTehasaCTEtwicesmallerthanthesilicon,whichexplainsthe in-ducedtensilestressstateappearingduringcoolingfrom430Kto100K. Thestressgradientishigherat293Kthanat100KbecausetheCdHgTe hasstarted toyield,sothatthebiaxialtensile stateof CdHgTetends tobeuniformatlowtemperature(around30MPaaccordingto𝜎xxand

𝜎yy).Tokeepthestaticequilibriumofthestructureundertheincreasing tensilestateoftheCdHgTelayer,alowcompressivemeanstateappears

inthesiliconsubstrate.Moreover,stressheterogeneitiesinthesolder zoneappearat293Kandareenhancedat100K:thisphenomenon cor-respondstothemismatchbetweentheCTEofCdHgTe,indium,epoxy andsilicon.Thesiliconisincompressionundertheepoxy(−10MPato −20MPa)andintensionunderthesolders(8–18MPa)withinadepth of afewmicrons.Thus,usingapolycrystallinebehaviourlawfor in-dium,heterogeneitiescanalreadybeobservedunderthermalloading, whetheritispixelbypixelorbetweenthecentreandtheedgeofthe detector.

4.2. Inﬂuenceoftheinputparameters

Inthissection,thefocusismadeontheinfluenceoftheinput pa-rameters ofthemodelonthenumericalresults.Asexplainedin2.4, oneofthesourcesofuncertaintiestopredictthestressdistributionin theIRdetectoristhelackofknowledgeabouttheCdHgTe thermome-chanicalproperties.Severalsimulationsconsideringthedifferentelastic constantsproposedbyalltheauthors(Table3)haveshownaverylow impactonthestressvaluesinallthelayersat100K(<1%).Thequestion oftheplasticityoftheCdHgTeisalsoveryimportant,especiallydueto thepossiblediffusionofZncomingfromtheCdZnTesubstratebefore thinning.IntheresultspresentedinSection3.1(Fig.12(a)),theyield stressoftheCdHgTewasfixedat30MPa,avalueestimatedfrom lit-eratureandtheresidualstressmeasurementspresentedin[43].Other simulationswithayieldstressof 60MPa werelaunched (Fig.12(b)) andshowedthegreatimpactonthenumericalresultssincethe max-imal stressvalues observedwereof thesameorder ofmagnitude.A strongerstressgradientwasalsoobservedintheCdHgTelayerbetween theedgeandthecentreoftheassembly.Onthecontrary,neither sili-connorindiumwasreallyaffected,duetotheirthicknessandtheirhigh plasticity,respectively.Itisthereforeveryimportanttowelldefinethe mechanicalbehaviouroftheCdHgTeinordertogetstressvaluesas rep-resentativeaspossiblewiththemodel.IntheflipchipFEMfield,most

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ofthe authorsmadethehypothesisthat circuitandsoldermaterials couldbeconsideredaspurelyelastic[11,14].Thematerialproperties ofindiumannouncedbyPlötneretal.[44]showedavery lowyield stresswithhighplasticity.Apureelasticlawforindiumwasalso imple-mentedinthemodelforcomparison(Fig.12(c)).Thevaluesof𝜎xxand

𝜎yyinthiscasewerethusverydiﬀerent:thesiliconbelowtheindium solderswasmorestressedwithnegativevaluesoutoftherepresented scale(−30MPa),whiletheCdHgTejustabovewasincompression con-trarytothepreviousresults.Asforindium,itwasinhightensionwith stressvaluesoutofscale.Theseresultswerethedirectconsequenceof theabsenceofplasticityinindium:thestressvaluesincreasedwithout anylimitation.

4.3. Inﬂuenceofcrystallographicorientationforindiumsolderbumpsas singlecrystals

SincetheEBSDandXRDresults showedthateach indiumsolder bumpwasasinglecrystal,complementarysimulationswerelaunched consideringthisparticularaspect.Morespecifically,theaimwastosee ifthegreatanisotropyofthecrystallographicorientationandtheCTE ofindiumpresentedbyCollinsetal.[36]couldincreasethestress gra-dientsintheassembly,especiallyatlowtemperature,sincethesolder expansion/contractionunder thermalloadingwassupposedtoaffect thelevelofstressintheotherlayers.Severalsimulationswerelaunched consideringonlyoneindiumsolderbumpasasinglecrystalandthe othersaspolycrystalline.Fig.13presentstheresultsobtainedforthree differentorientationsofonesolderbumpat100K,inparticularthosefor whichthedifferenceismaximised(anisotropyenhancedformechanical propertiesandCTE),whenconsideringthedifferentaxesofthe tetrago-nallatticeofindium.Theyshowaweakimpactonthestressdistribution intheCdHgTejustabove,andiftheindiumsolderbumpsaremostlyin tensionwithlowcompressioninthecentreat293Kand100K,when polycrystallineorsinglecrystalswithorientation1or3,someofthem canbefullyincompressionwithhigherstressvaluesduetotheir crystal-lographicorientationandtheparticularevolutionoftheCTE(especially fororientation2).Itshouldnotedthatthiseffectissimilarwhen consid-eringallthesolderbumpsassinglecrystals,withorientationscloseto orientation2alwaysinducinghigherstress/deformationinthebump. Theselocalvariationsinthestressvalues canleadtopossiblesolder cracksattheinterfacewiththeCdHgTeand/orsiliconlayersand ex-plainthe“randomlysupposed” apparitionofdefectssuchasdeadpixels inthedetector.

5. Conclusions

Inthiswork,thestrain/stressevolutioninanIRdetectorsubjected tothermalloadingsduringitscyclelifehasbeennumericallystudied. Conclusionsofthisstudycanbesummedupasfollows:

- Theexperimentalresultsgaveaverydetaileddescriptionofthe de-tectorstructure.Thetomographyanalysesledtoanexcellent defini-tionofthe3Dsolderbumpgeometryafterthelastprocessstep.EBSD andringdiffractionprovidedafirsttwo-dimensionaldescriptionof thenatureandcrystallographyofthedifferentlayers.Themost im-portantpointsarethepresenceofCdHgTeandsiliconsinglecrystals aswellasthesinglecrystalnatureofindiumsoldersandtherandom repartitionoftheircrystallographicorientation,afeaturethatuntil nowwascompletelyunknown.Theycouldsubsequentlybe imple-mentedinthefiniteelementmodelwiththeiranisotropic mechan-icalproperties,whichwasessentialforthemodeldevelopmentto simulatestrain/stressheterogeneitiesatthescaleofonepixelofthe detector.

- Theﬁniteelementmodelwasveryusefultoobservelocal hetero-geneitiesinsidetheCdHgTeandsiliconlayersandtoestimatethe stresslevelineachindiumsolderbump.Heterogeneitiesappeared atthescaleofthesolderbumpat293Kandwereampliﬁedat100K.

WhereasthebiaxialtensilestateofCdHgTetendedtobeuniformat lowtemperature(around30MPaaccordingto𝜎xxand𝜎yyconsistent withthevaluesobtainedexperimentallyat77K[43]),siliconwasin compressionunderepoxy(−10a−20MPa)andintensionunderthe solderbumps(8–18MPa)withinadepthofafewmicrons.Thus, us-ingapolycrystallinebehaviourlawforindium,heterogeneitiescan alreadybeseenpixelbypixelwhenapplyingthermalfieldsbetween thecentreandtheedgeofthedetector.Inordertohaveamore pre-ciseestimationofthestressstateineachpixelofthedetector,other simulationswerelaunchedconsideringthesinglecrystalnatureof eachsolderbumpaswellastheinfluenceofthecrystallographic ori-entationandtheanisotropicCTEofindium.Thenumericalresults showedthattheCdHgTelawwasaweakimpacted,butaccording totheircrystallographicorientation,theindiumsolderbumpscould bemoreincompressionat293Kand100K:thisdifferenceinthe stress/deformationcouldleadtopossiblecracksattheinterfacewith theCdHgTeand/orsiliconlayersandexplainsomedefectssuchas thedeadpixelsappearinginthedetectorduringelaborationand ser-vicelife.

Declaration of Competing Interest

Theauthorsdeclarethattheyhavenoknowncompetingﬁnancial interestsorpersonalrelationshipsthatcouldhaveappearedtoinﬂuence theworkreportedinthispaper.

Acknowledgements

ThisworkwassupportedbyRegionLorraineinFrancein collabora-tionwithCEA(Commissariatà l’EnergieAtomique).

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