Strengthening ultrathin Si3N4 membranes by compressive surface stress

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ContentslistsavailableatScienceDirect

Sensors

and

Actuators

A:

Physical

j o u r n a l ho me p a g e :w w w . e l s e v i e r . c o m / l o c a t e / s n a

Strengthening

ultrathin

Si

3

N

4

membranes

by

compressive

surface

stress

A. Shaﬁkov

a,∗

_,

_B.

_Schurink

a

_,

_R.W.E.

_van

_de

_Kruijs

a

_,

_J.

_Benschop

a,b

_,

_W.T.E.

_van

_den

_Beld

a

_,

Z.S.

Houweling

b

_,

_F.

_Bijkerk

a

a_Industrial_Focus_Group_XUV_Optics,_MESA₊_Institute_of_{Nanotechnology,}_University_of_Twente,_{Drienerlolaan}_5,₇₅₂₂_NB,_Enschede,_the_Netherlands1

b_ASML_Netherlands_B.V.,_Veldhoven,_the_Netherlands

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received21August2020

Receivedinrevisedform

10November2020

Accepted19November2020

Availableonline23November2020

Keywords: Bulgetesting Residualstress Fracturestrength Siliconnitride Membrane

a

b

s

t

r

a

c

t

Inthiswork,theeffectofcompressivesurfacestressonthinﬁlmmembranefracturewasstudiedbybulge test.Inordertocreatemembraneswithcompressiveresidualstressatthesurface,low-pressurechemical

vapordeposition(LPCVD)Si3N4membraneswerecoatedwitha1−8nmcompressiveSiNxadlayeror

subjectedtoAr-ionbombardment.Fracturestrengthanalysis,doneusingﬁniteelementmethodand

Weibulldistribution,andmicroscopeinspectionoffailedmembranesshowedthatthepressurelimit

ofthemembranesisdeterminedbytheintrinsicfracturemode,causedbyhighstressinducedatthe

membraneedgenearthetopsurface.Bycreatingcompressiveresidualstressatthemembranesurface, themaximumstressinducedbytheappliedpressurewasreducedandthefracturestrengthoftheSi3N4

wasincreasedfrom17.3GPato18.3GPa.Asaresult,membraneswithacompressivesurfaceshoweda

50%increaseinpressurelimit,from5kPa/nmto7.5kPa/nm.

1. Introduction

Thinfreestandingfilms(membranes)havebeenreceivingmore andmoreinterestduetotheiruseinawiderangeofapplications includingpelliclesforextremeultravioletlithography(EUVL)[1], X-rayand electrontransparent windows[2] and micro-electro-mechanical systems(MEMS).Oftentheapplicationsrequirethe freestandingfilmstobeextremelythin(downtotensofnm),as aresultsuchmembranescanbeextremelyfragile–thesmallest forceappliedtothethinfilmcancreatelargemechanicalstresses andleadtofailureofthemembrane.Hencemechanicalstrengthof thethinfilmsisofessentialimportance.

Aparticularmaterialthathasbeenreceivingalotofattention due to its excellent mechanical properties, is thin film amor-phous silicon nitride grown by chemical vapor deposition. In additiontohighmechanicalstrength,suchfilmshavehigh elec-trontransparencyduetothelowatomicmassofSiandNatoms andrandomizedelectronscatteringduetotheamorphous struc-ture.Combinationof thesepropertiesmakesamorphoussilicon nitridethinfilmsespeciallyattractiveforelectrontransparent

win-∗ Correspondingauthor.

E-mailaddress:a.shaﬁkov@utwente.nl(A.Shaﬁkov).

1 _{www.utwente.nl/xuv}_.

dowsusedingascells for environmentaltransmissionelectron microscopy(ETEM),which allowsin-situobservationof biolog-icalsamplesandprocesses occurringat highpressures,suchas metalhydrogenation,oxidationandothers[2–4].Thisisachieved byusingtwothinﬁlmmembranestoformawindowedgascell, whichenclosessamplesinasmallvolumeunderhighpressures insideaTEM.Thepressurethatcanbecreatedinsidesuchgascells islimitedbythestrengthofthemembranes–ifthestressesinduced bytheappliedpressuredifferenceexceedthestrengthofthe mate-rial,themembranewillrupturereleasingthegasandpotentially damagingtheelectronsource.Improvingtherobustnessof win-dowedgascellswouldallowtostudyprocessesathigherpressures thancurrentlyachievable.

One way to increase the pressure limit is to improve the mechanical strength ofthe thin ﬁlm.Silicon nitrideis a brittle materialanditsstrengthisusuallylimitedbythedefectspresent in the material [5]. Therefore, reducing the amount of defects resultsin a strength increase. Thiscan bedoneby better con-trolandoptimizationofprocessconditions.Furthermore,onecan minimizethedefectsbyusingthesizeeffect–thesmallerthe sam-ple,thefewerdefectsitwillcontain.Forexample,Alanetal.[6] usedthesizeeffecttofabricateSi3N4 membraneswithstrength approachingthetheoreticallimit:15nmthickﬁlmscould with-standstressesas highas19.5GPa.Anotherwaytoincreasethe pressure limit is toreduce themaximum stress createdin the https://doi.org/10.1016/j.sna.2020.112456

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thefieldofnanometer-scalethinfilmmembranes.Tothebestof ourknowledge,nostudieshavebeendoneoncompressivesurface strengtheningforsuchmembranesdespitetheirgreatpotentialfor useinapplicationssuchasETEMgascellsorthinfilmsensorsand actuators.

Therefore, the objectiveof this studywasto investigatethe effect of surface compressive stress on failure of ultrathin sil-icon nitride membranesunder appliedpressure. Using Weibull analysis and post-mortem inspection of membrane frames, we foundthattheultimatepressurelimitisdeterminedbythestress at themembrane edgenearthe ﬁlmsurface.Next, we demon-strated the strengthening effect of surface compressive stress using two different experimental approaches: 1) by adding a compressivelayeratopthemembrane surface,and 2)by alter-ing the surface of the membrane by ion bombardment to add compression. By using ﬁnite element method (FEM) to model stress distributions and analyzing the stresses at fracture as a function of the compressive surface layer thickness, we found thatfractureoriginateseitherfromthefreesurfaceofthe mem-braneorneartheinterfacebetweenthecompressivesurfacelayer and themain tensilemembrane layer,dependingonthe thick-ness.

2. Membranefabricationandmechanicaltesting 2.1. Fabrication

For the fabricationof thesilicon nitridemembranes, single-sidepolishedp-type,(100)-orientedsiliconsubstrates(Okmetic, Finland) with a thickness of 525±25␮m were used. A nomi-nally stoichiometric silicon nitride(Si3N4) layerof 47nm thick wasgrownbymeansoflowpressurechemicalvapordeposition (LPCVD).Next,frontandbacksideofthesubstratearespin-coated withpositivephotoresist,thebacksideisUVexposed througha Cr-mask containing6×6arrayof30 circlesof1750␮m diame-terand6circlesof3750␮mdiameter.Afterdevelopmentofthe photoresist,theexposedSi3N4(circularholes)onthebacksideis etchedbymeansofreactiveionetch(RIE)usingaSF6plasma chem-istry.Oncethe47nmofSi3N4isselectivelyetched,thephotoresist andetchresiduesareremovedinaUV-ozonesurfacecleaning sys-tem.Theherebyproducedchemicaloxidethinlayerisremovedin bufferedhydroﬂuoricacid(30s)andsubsequentlytheexposed sil-iconisetchedanisotropicallyintetramethylammoniumhydroxide (TMAH)(25%,90◦C,800min)throughoutthesubstratetorelease thesquareSi3N4 membranes.Anisotropicetchingterminateson theSi{111}planesandthesidesoftheetchedcavityinthesilicon waferhaveaslopeof54.7◦.Asresult,theSi3N4freestanding win-dowsformedonthefrontsideofthewaferhavesquareshapewith thesidesorientedalongtheSi<110>directionsandaresmallerthan thepatternedcircularopeningsintheSi3N4layeronthebackside ofthewafer.Theﬁnalreleasedmembraneshaveawindowsizeof 1.04×1.04mm2_and_a_thickness_of_21.4_±_0.2_nm,_which_is_lower

X-rayreflectometry(XRR)afterreleaseandaftermodification,viz., coatingwithanadlayerorsubjectingthemembranetoanAr bom-bardment. Grazing incidence X-raydiffractometry (GIXRD)was performedonthemembranesand showedthat thelayershave anamorphousstructure.Roughnessofas-releasedandmodified membraneswasmeasuredbyatomicforcemicroscopy(AFM).All thesampleshadsmoothsurfacemorphologyandlowroughness withrootmeansquare valueof∼0.3nm.TypicalAFMscanning imagesarepresented in a Fig.1, showingsimilar surface mor-phologybetweennon-modified,Arbombardedmembranes and membranesovercoatedwitha8.3nmSiNxadlayer.Thereforethe effectofthesurfaceroughnessonfracturestrengthisexpectedto belowandthesameforallofthestudiedsamples.

2.2. Mechanicaltesting

Mechanicalpropertiesofthethinﬁlmmembraneswerestudied usingabulgetestsetup(Fig.2)consistingofamembranemounting stagewithnitrogengassupply,apressuresensorandascanning whitelightinterferometer(WLI).

InordertodetermineYoung’smodulusandresidualstressin thinfilmmembranespressurevs.deflectioncurvesweremeasured. Forthatapressurewasappliedfromthemembranecavitysideas shownonFig.2(a),andaheightmapofthemembranewindow andframewasobtainedwithWLI.Thedeflectionwascalculatedas theheightdifferencebetweentheflatframeandthecenterofthe membrane.Thepressurewasincreasedstepwiseandletto stabi-lizebeforeeachWLImeasurement.Atypicalpressurestepbetween themeasurements was7kPa, with a pressure increase rate of roughly1kPa/s.ThevaluesofYoung’smodulusandresidualstress weredeterminedbyfittingtheexperimentallymeasured pressure-deflectioncurveswiththebulgeequationforN-layermembrane(1) [8]: P=3.41

n=1..N 0,ntnh a2 +

n=1...N (1.981−0.585

v

n) En 1−

v

ntn h3 a4 (1) wherePistheappliedpressuredifference,histhedeﬂection,ais thehalf-widthofthesquaremembranewindowandtn,

v

n,En,0,n arethickness,Poissonratio,Young’smodulusandresidualstress ofthen-thlayer,respectively.ThePoissonratiowasassumedto be0.25forboththeSi3N4membranelayersandtheSiNxadlayers, whichiswithintherangeofvaluesthataretypicallyreportedfor siliconnitridethinﬁlms[5,9,10].

Todeterminethestrengthofthemembranes,burstpressures weremeasuredusingthesamebulgesetup.Pressurewas continu-ouslyincreasedwithanaveragerateofabout5kPa/s.Incontrastto pressure-deflectionmeasurements,themembraneburstpressure wasmeasuredbyapplyingpressurefromtheflatsideasshownon theFig.2(b).Itisknown,thatifamembraneispressurizedfrom thecavityside,asingularstressfieldformedatthesharpcorner betweentheframeandthefilmcancausedelaminationandearly failure[11].Therefore,pressurizationfromtheflatsideispreferred forapplicationswheremembranesneedtowithstandhighpressure

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Fig.1.AFMscansof(a)as-releasedSi3N4membranes,(b)ArbombardedSi3N4membranes,and(c)membranescoatedwith8.3nmSiNxadlayer.

Fig.2. Bulgesetup.(a)Configurationusedduringpressure-deflectionmeasurements,pressureappliedfromthecavityside.(b)Configurationusedduringburstpressure

measurements,pressureappliedfromtheﬂatsideofthemembrane.

differencesandformeasuringstrengthofthethinfilmasfracturein thatcaseinitiatesfromthefilm,ratherthantheinterfacebetween thefilmandtheframe.Thestressdistributionsinthepressurized membranesweremodelledbyFEMusingtheComsolMultiphysics softwarepackage[12].Thefracturedmembraneswereinspected usinganopticalmicroscopetodetermineifthefractureoriginated fromthecentralfreestandingareaofthemembraneortheedgeof thewindow,wherethehigheststressinthethinfilmislocated.

3. Failureofsingleuniformlayermembranes

Fractureinbrittlematerials,suchasthesiliconnitridethinfilms usedinthisstudy,occursduetolocalstressconcentrationsatthe defectspresentinthematerial.Thelocalstressfieldaroundadefect dependsonitsshapeandsize.Generallylargerdefectscreatemore intensestressconcentrationsandinitiatefailureatlowervaluesof appliedstress.Therefore,failureofabrittlematerialisa statisti-calprocessanddependsonthedefectdistributioninthematerial. Thedefectsmayhaveextrinsicorigin,suchasa surfacecrack,a pinholeora dustparticleembeddedinthethin film.However, theyalsocanhaveintrinsicnature,forexampleagrainboundary inapolycrystallinematerialoratomicsizedeviationsfromshort rangeorderinamorphousglass-likematerials.Whereasintrinsic nanoscale defectsareexpected tobeabundantin thematerial, extrinsiconesarelargerandcanbesparselydistributed.Therefore, thesmallerthesamplevolume,thehighertheprobabilitythatit containsonlytheintrinsicdefects.Asaresult,thestrengthofthe sufficientlysmallsamplesis determinedbytheintrinsicdefects (intrinsicstrength),whilelargersamplesaremorelikelytofaildue toextrinsicones(extrinsicstrength).

LetusnowconsiderstressdistributioninthepressurizedSi3N4 membraneandpossiblefailureorigins.OntheFig.3,whichpresents anexampleofsuchstressdistributionobtainedbyFEM,wecan distinguishtwopartsofthemembranewithverydifferentstress states.Firstisthenarrowregionalongthemembraneedges,where

bendingcausesahighstress,whichhasamaximumatthetopside ofthethinﬁlminthemiddleofthemembraneedge.Thesecond isthecentralfreestandingpartofthemembrane,wherethestress isaboutthreetimeslowerthanthemaxstressattheedge.Letus nowassume,thattheSi3N4containstwodifferentpopulationsof defects:atomicallysmallintrinsicdefectsthatareabundantinthe layer,andlarger,butsparselydistributedextrinsicones.In that case,thenarrowregionalong theedgewould containonlythe smallintrinsicdefectsandexhibitrelativelyhighstrength (intrin-sicstrength),whereas thelargefreestandingregion wouldalso containlargerextrinsicdefectsandhavelowerstrength (extrin-sicstrength).Insummary,ifourassumptionaboutthetwodefect populationspresentinthelayersiscorrect,weshouldexpectthat pressurizedmembranescanexhibittwofailuremodes:1)intrinsic failureinitiatedfromtheedgeofthemembrane,2)extrinsicfailure initiatedfromanextrinsicdefectinthecentralfreestandingregion. Asnotedearlier,brittlestrengthdependsonthedefect distribu-tioninthematerial.Therefore,strengthofbrittlematerialshasto beanalyzedstatistically.Whenfailureofthematerialiscausedby asingledefectpopulation(singlefailuremode),strengthanalysis iscommonlydonebyﬁttingtheexperimentallymeasuredfailure probabilityasafunctionoftheappliedstressusingaunimodal Weibulldistribution[13]: F=1−S=1−exp

−

m

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WhereFistheprobabilityoffailure(Sistheprobabilityofsurvival) atgivenvalueofappliedstress(maximumstress,ifloadingisnot uniform).TheparametersmandarerespectivelytheWeibull modulusandthecharacteristicstrengthforthisloadinggeometry. Assuming,thatthetwoproposedfailuremodesareindependent (i.e.,eventsofmembranesurvivingagainsteachfailuremodeare

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Fig.3.StressdistributioninapressurizedmembraneobtainedwithFEM.Stressconcentrationispresentatthemembraneedge,whichcanleadtofailure.Simulation

parameters:E=225GPa,0=850MPa,v=0.25,windowsize2a=1.04mm,thicknesst=21.4nm,appliedpressureP=108.6kPa.

statisticallyindependent),failureprobabilitycanbedescribedbya multiplicativebimodalWeibulldistribution[13]:

F=1−SiSe=1−exp

−

center(P)_e

me −

edge(P) i

mi

(3) WhereSiandSeareprobabilitiesofamembranesurviving intrin-sicandextrinsicfailuremodesunderappliedpressureP,edge(P) andcenter(P)arevaluesofmaximumstressthatcanbefoundat theedgestressconcentrationandinthecentralareaofthe mem-brane(maximummembranestress).Theparameterse,me and i,miarecharacteristicstrengthandWeibullmodulusfor extrin-sicandintrinsicfailuremodes,respectively.Assumingthatedge(P) andcenter(P)canbeapproximatedaspowerfunctionsofapplied pressureP(e.g.∼P2/3_for_a_circular_membrane_[₈_])_we_can_further rewritethebulgeequationwithappliedpressureasanargument, yielding: F=1−exp

−

_PP i

m_i −

_PP e

me

(4) WherePiandPearethecharacteristicburstpressuresforintrinsic andextrinsicfailuremodescorrespondingto63.2%failure proba-bilityfortherespectivemode,andm_i,m_eareshapeparameters.This finalformoftheWeibullequationismoreconvenientforfitting theexperimentallymeasureddata(burstpressures)than distri-bution(3),since itusespressure assingleargument,insteadof edge(P)andcenter(P).Afterfittingtheexperimentallymeasured membranefailureprobabilitieswithdistribution(4),intrinsicand extrinsicstrengthscanbefinallycalculatedasi=edge(Pi) (maxi-mumstressattheedgeatPi)ande=center(Pe)(maximumstress inthecentralareaofthemembrane,i.e.membranestress,atPe) usingFEM.

3.1. Experimentalresults

To determine the strength of the Si3N4 layer, bulge test-ingwasperformedonas-releasedmembranes.Young’smodulus and residual stress in the membranes are determined by ﬁt-tingpressure-deﬂectiondatatothebulgeEq.(1),whichdataare 225±6GPaand850±30MParespectively.Fig.4presentsthe fail-ureprobabilityplotforas-releasedSi3N4membranesasafunction oftheappliedpressure.Theplotconsistsoftwodifferentslopes:a steepslopecontainingdataofsamplesthatfailedatpressuresinthe rangeof100–110kPaandashallowslopewithsamplesfailingat lowerpressures.Theexistenceoftwosuchvisuallydistinctparts ofthedistributionsuggeststhattheyhavedifferentphysical ori-gins,i.e.theyarecausedbydifferentdefectpopulations.Tosupport thissuggestion,thefailedmembranesarecategorizedaccordingto theirappearanceafterfailure.Inmoredetail,theresidual mem-branepiecesstillattachedtotheedgeoftheframearepresentedin twodistinctivemanners.Themajorityofthesampleshavespikes

Fig.4. CumulativefailureprobabilityFof1.04×1.04mm2_21.4_±_0.2_nm_thick_Si

3N4

membranes.ThebottomhorizontalaxisrepresentsthevalueofappliedpressureP,

whereasthetophorizontalaxiscorrespondswiththevalueofmaximalstressatthe

membraneedgeedge(P).Solidsquaresaremembranesfracturedattheedge,while

hollowonesaremembranesthatfracturedinthecentralarea.Thedataisﬁtted

(solidline)withabimodalWeibulldistribution(4).Fittedparametersandnumber

oftestedsamplesaregivenastextinsertontheplot.

pointingtothemiddleofoneofthefourmembraneedges,asshown onFig.5(a).Thissuggeststhatinthesesamplesfailureoriginated atthemembrane edgeandhappenedthroughtheintrinsic fail-uremode.Notethatintheverymiddleoftheedge,closetothe fractureorigin,membraneresidueisalwaysabsent,becauseofthe cracksthatpropagatealongtheedgefromtheorigin.Apartfrom thesesamples,membranesarefoundwithspikespointingtothe membranecenter,which arepresentonallfouredges,as illus-tratedonFig.5(b).Thesesuggestthatthefractureoriginatedfrom anextrinsicdefectinthefreestandingpartofthemembrane.Based ontheappearanceoftheresidualmembranepieces,allfailed sam-pleswerecategorizedintotwogroups:thosethatfracturedatthe edgeandthosethatfracturedinthecenter.Afailedmembranewas categorizedasfailedattheedgeifitmetthefollowingcriteria: (1)ifthecrackpaths,indicatedbythedirectiontheresidualﬁlms piecesonallfouredgesarepointingto,canbetracedtoapointon oneofthefouredges;(2)anapproximately50␮mwideareaatthe edge,containingthesuspectedgefractureorigin,doesn’thaveany residualmembranepieces;(3)nexttothatarea,frombothsides, thereareresidualmembranepiecesorientedtowardstheareaata shallow<45◦anglerelativetotheframe.Samplesthatdidnotmeet thecriteriagivenabovewereclassiﬁedasfracturedinthecenter. Usingthesecriteria,itwaspossibletounambiguouslycategorize eachsampleinoneofthetwogroups.Thecategorizedsamples

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Fig.5.Schematicandopticaldarkﬁeldmicroscopeimagesofmembranesfailedthroughdifferentmodesshowingdistributionofﬁlmpiecesattachedtotheframe.The

redcrossandwhitedashedarrowsindicatetheexpectedlocationofthefractureoriginandthedirectionsofcrackpropagationinferredfromtheshapeofthemembrane

residualsleftontheframe.(a)Intrinsicfracturemode,spikespointingorcurvedtowardsthemiddleofthebottomedge(b)Extrinsicfailuremode,spikesonallfouredges

arepointingtowardscenterofthemembrane.

arelabeledinFig.4,wheresamplesfailedattheedgeandinthe centralareaareindicatedwithopenandﬁlleddots,respectively. Fromthiswecanconﬁrmourhypothesis,thatthetwoslopesof thefailureprobabilitydistributionhavedifferentphysicalorigins, namelytheshallowslopeofthefailuredistributioncorresponding totheextrinsicfailuremode,whilethesteepslopecorrespondsto theintrinsicmode.

Takingintoaccounttheexistenceofthetwoindependent fail-uremodes,theexperimentalfailureprobabilitydistributionwas fittedwiththebimodalmultiplicativeWeibulldistribution(4).The fitted distribution(solid line)and values of thefitting parame-tersare shownontheFig.4.Theherebyintrinsic andextrinsic layerstrength, foundfromFEM, arerespectively:i=17.3GPa ande=11GPa.Theobtainedvalueofiiscloseto19.5GPavalue reportedby[6],whichistothebestofourknowledgethe high-estexperimentallymeasuredstrengthvalueforsiliconnitridethin films.Furthermore,iisapproachingtheruleofthumbvalueof theoreticalstrengthE/10=22.5GPa,whichsupportsthenotion thatitisnotlimitedbyextrinsicdefectsandrepresentsthe intrin-sicfilmproperty.Ontheotherhandtheextrinsicstrengthislower thanintrinsicstrength,duetothelargersizeoftheextrinsicdefects. Inaddition,theextrinsicfailuremodeshowsalowervalueofthe Weibullmodulusm_e(i.e.largerspreadinsamplestrengthvalues)

thantheintrinsicmodem_i,whichreﬂectsthefactthattheextrinsic defectshavealargervariationinsize.

Insummary,weobservedandidentifiedtheexistencetwo fail-uremodesinthepressurizedSi3N4thinfilmmembranes:intrinsic failure,i.e.failureinitiated fromtheedgeofthemembrane,the locationofthehighestappliedstress,andextrinsicfailure,i.e. fail-ureinitiatedfromthecentralfreestandingregionofthemembrane andcausedbytheextrinsicdefects.Reducingtheamountof extrin-sicdefectsbyoptimizingthefabricationprocess,i.e.byfindingthe source(s)ofdefectsorusingimprovedsubstratecleaning proce-dures,willhelptomakemorereliablemembranes,whichwould failinanarrowrangeofappliedpressures.However,toincrease theultimatepressurelimitofthemembranesoneneedstoeither increasetheintrinsicstrengthofthematerialorreducethe max-imumstressappliedtothethinfilm.Inthenextsectionwewill demonstratethatthemaximumstresscanbereducedbyadding compressivestressinthethintoplayerofthemembrane. 4. Improvedfracturestrengthandpressurelimitof membraneswithcompressivestressatthesurface

Intheprevioussectionweexplainedthattheultimatepressure thatamembraneisabletowithstandisdeterminedbythe

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intrin-acttheinducedstressandincreasethepressurelimitofavessel. Theeffectofcompressionatthemembranesurfacewithrespectto failureisstudiedanddiscussedinthefollowingsections.

4.1. Elasticpropertiesofmembraneswithsurfacecompression Inthisworkwedemonstratetwomethodstoproduce mem-branes with residual compressive stress at the surface: 1) depositionofthinadlayerswithresidualcompressivestressand 2)exposingthemembranesurfacetoanAr-ionbombardment.

Intheﬁrstmethod,anadditionalthinSiNxlayer,oradlayer,is depositedbyreactivemagnetronsputteringontopofpre-released Si3N4membranes,themainlayer.ThesputteredSiNxlayerhasa compressiveresidualstressthatiscausedbytherelativelyhigh energyofatomsduringdeposition,typicallyintheorderof sev-eraleV.Tostudytheeffectofadlayerthicknessonthemembrane strength,SiNxadlayerswiththicknessesintherangeof1.4–8.3nm weredepositedontopofSi3N4membranes.Themaximum thick-nessof8.3nmisbasedontheconditionthattheaveragestressin themembraneremainstensileafteradlayerdeposition,toavoid wrinklingofthemembranewhichwouldcomplicatethe interpre-tationofthebulgetestresults.

InordertodetermineresidualstressandYoung’smodulusof theadlayers,pressure-deflectiondatawasmeasuredontheSi3N4 membranes withSiNx adlayers and fitted tothe bulge Eq. (1) for abilayermembrane withN=2.Fig.6shows thechangein theobtainedvalues accordingtothefitting parameters, includ-ing thetotal lineforce

t=0,mtm+0,ata and thestiffness

Et=Emtm+Eataofmembranesasafunctionofthethicknessof theadlayerta.Thelineforceandstiffnessshowalineardependence inthisrangeofthicknesses,thereforeitisassumedthatYoung’s modulusEaandresidualstress0,aoftheadlayersareuniformand independentoftheadlayer thickness.ThevaluesoftheYoung’s modulus and residual stress in theSiNx adlayers are obtained fromlinearfitting:Ea=208±11GPaand0,a=−1908±64MPa. Despitethebendingmomentcausedbythedifferenceinresidual stressatthebottomandtopsideofthemembraneswith adlay-ers,nosignificantchangeinresidualdeflection(withoutpressure applied)ofthemembraneswasobserved.Instead,allmembranes showedsimilarresidualwarpageof∼50nm,causedbytheresidual strainsandwarpageoftheSiframe.

Alternatively,thecompressivestresscanbegeneratedinthe Si3N4layeritself.Itisknownthatalowenergy(sub-keV)ion bom-bardment cangenerateseveralGPaofcompressivestressinthe ﬁrstfewnanometersofmaterialduetoionimplantationand sur-faceatomrepositioningordensiﬁcation[14].Tostudytheeffectof compressivestressgeneratedbyionbombardmentonthepressure limit,membraneswereexposedforashorttime(10s)toanArion beamwithnominalionenergyandcurrentdensityof130eVand 0.2mA/cm2_,_{respectively,}_amounting_to_a_total_dose_of_∼1.3*1016 ions/cm2_._From_XRR_measurements_before_and_after_exposure,_the changeinSi3N4membranethicknesswasdeterminedtobe approx-imatelytm−t_m=1.65nm.Valuesofaverageresidualstressand Young’smodulusinthemembranesbombardedbyArionswere

_0,m t_m−0,m tm−tAr

tAr =−2.77GPa,whichiscomparabletothestress

intheadlayers.However,sincetheactualresidualstress distribu-tionisunknown,wecannotcalculatethefracturestrength,whereas thisis possiblefor membraneswithadlayersand thereforethe preferredroutetostudyinmoredetail.

4.2. Fracturestrengthandpressurelimit

The failure probabilities for membranes with added surface compressionareplottedasafunctionoftheappliedpressurein Fig.7.

Similarlytoas-releasedmembranesinSection3,membranes withSiNxadlayersandbombardedbyanArionbeamexhibittwo failuremodes:intrinsic–strongersamplesfracturedattheedge, andextrinsic–weaksamplesfracturedinthemembranecenter. Theappearanceoftheresidualfilmpiecesontheframesoffailed membraneswassimilartothecaseofas-releasedmembranes,with theonlynotableexceptionthattheresidualfilmpiecestendedcurl, becauseofthebendingmomentcausedbythedifferenceinstress onthetwosidesof thefilm.Comparedtomembraneswithout addedsurfacecompression,alargerfractionofmembraneswith adlayersfracturedthroughextrinsicmechanism,ascanbeseen whencomparingFigs.4and7.Theriseoftheextrinsicmodeis likelycontributedtobyanincreasedamountofdefectsinthe mem-braneintroducedbysputterdepositionoftheadlayer.Inaddition, inthepresenceofanadlayer,theintrinsicmodeoffracturewill occurathigherpressuresandasaresultthemembranestresses (i.e.stressincentralarea)willreachhighervalues.Hence,thereis anincreasedprobabilityofmembranesfailingthroughtheextrinsic mode.Furthermore,onecannotethepoorfitqualitywiththe mul-tiplicativebimodalWeibulldistribution,whichbecomesespecially apparentformembraneswiththickadlayersforwhichamore sig-nificantfractionofsamplesfailsthroughtheextrinsicmode.This suggeststhattheextrinsicdefectsarenotdistributeduniformlyin thesamplepopulation(i.e.onepartofthewaferismore defec-tivethantheother),inwhichcaseanalternativebimodalWeibull distribution,e.g.additive[16],wouldbebettersuited.However, a more extensivestudy of theeffect of adlayers ondefectivity andextrinsicfailuremodewasbeyondthescopeof thispaper. Instead,wewillbefocusing ontheintrinsicmechanism of fail-ure,whichhappensattheedgeduetoconcentrationofbending stress.

Letusconsidertheintrinsicfailuremechanism-thesteeppart oftheWeibulldistribution.Ar-ionbombardedmembranes,despite theirlowerthickness(19.8nmvs.21.4nm),haveahigherintrinsic burstpressurethanas-releasedmembranes(134kPavs.109kPa). Thisincreaseiscausedbythereducedstressatthetopsurface,after beingbombardedbytheArions.However,asnotedbefore,the fracturestresscannotbecalculatedforArbombardedmembranes, astheresidualstressdistributionisunknown.

Intrinsicburst pressuresfor membranes withSiNx adlayers, normalizedtothetotalthickness,arepresentedonFig.8(a). Nor-malizationis donetoaccountfor anincrease inburst pressure

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Fig.6.(a)Changeintotalline-force

tand(b)stiffness

Etofmembraneswithincreasingthicknessoftheadlayer.

Fig.7.ThecumulativeprobabilityoffailureFformembraneswithsurfacecompression.(a)-(e)21.4±0.2nmSi3N4membraneswith1.4-8.3nmthickSiNxadlayers.(f)

19.75±0.3nmmembranesafterArbombardment(initialthickness21.4nm).ThebottomhorizontalaxisrepresentsthevalueofappliedpressureP,whereasthetop

horizontalaxiscorrespondswiththevalueofmaximalstressatthemembraneedgeinthemainSi3N4layermain_edge(P).Solidsquaresaremembranesfracturedattheedge,

whilehollowonesaremembranesthatfracturedinthecentralarea.Dataareﬁtted(solidline)withabimodalWeibulldistribution(4).Fittedparametersandnumberof

testedsamplesaregivenastextinsertontheplot.

causedsolelybytheincreaseinmembranethickness.Compared toas-releasedmembranes,membraneswithadlayershaveupto 50%highervaluesofnormalizedintrinsicburstpressure,which isanadvantageforsuchapplicationsasgascellsfor environmen-talTEMandEUVpellicles,whereacombinationofhighstrength andtransparency(smallthickness)isrequired.Itappearsthatthe normalizedburstpressuredoesnotchangemonotonouslyandthat theoptimalthicknessoftheadlayerisaround4nm.Tounderstand whatcausesthisnon-monotonouschangeofburstpressureletus assumethattheintrinsicfracturecaninitiatefromthelocationof

thehigheststresseitherin themainSi3N4 layerorin theSiNx adlayer.For each adlayerthickness,themaximum stressinthe mainlayerandadlayerwithanappliedpressureequalto intrin-sicburstpressure(main

edge(Pi)and ad

edge(Pi))werecalculatedusing FEM,theobtainedvaluesareplottedinFig.8(b).Itcanbeobserved thatad

edge(Pi)steadilyincreasesuntiltheadlayerreachesa thick-nessof4nmandthenstopsatabout17.3GPa.Thestressinthemain layermain

edge (Pi) alsoinitiallyshowsaslightincreasefrom17.3GPato 18.2GPa,butthen,asad_edge(Pi)startstosaturate,mainedge(Pi) decreases andreduceseventobelow17.3GPa,thestrengthofanadlayer-free

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Fig.8.(a)Intrinsicburstpressureof21.4nmSi3N4membraneswithSiNxadlayersasfunctionofadlayerthicknessta.PressurePiisnormalizedtoaccountforsheerincrease

intotalmembranethicknesst.(b)Maximumstressedge(Pi) foundinthemainlayerandadlayercorrespondingtointrinsicburstpressure.Dashedlinesonbothgraphsshow

expectedvaluesassumingconstantintrinsicstrengthof17.3GPaformainSi3N4layerandSiNxadlayers.

Fig.9.Diagramsshowingfracturebytheintrinsicmodeinmembranes(a)withoutadlayer,(b)withthinadlayer,(c)withthickadlayer.Diagramsinthebottomrow

qualitativelyillustratestressdistributionsinmain(blue)andadlayers(green)atthemomentoffracture,redcrossindicateslocationoffracture.

membrane.Thissuggeststhatwithincreaseoftheadlayer thick-ness, thelocationof thefracture originchangesfrom themain layertotheadlayer.Inas-releasedmembraneswithoutadlayerthe intrinsicfailureinitiatesfromthefreesurfaceofthemainlayerat 17.3GPa(Fig.9(a)).Assuch,anincreaseinadlayerthicknessalso increasestheratiobetweentensilestressintheadlayerandstress inthemainlayerofthepressurizedmembrane.Hence,whilein themembraneswithathinadlayerthefailureisstilldetermined bythestressinthemainlayer(Fig.9(b)),inthemembraneswith thickeradlayersthestressintheadlayerreachestheadlayer ten-silestrengthbeforethestressinthemainlayerleadstofailure. Asaresult,thefracturestartsfromthefreesurfaceoftheadlayer (Fig.9(c)).Theadlayerthicknesscorrespondingtothistransition from thesituationdescribed inFig.8(b) tothesituationin the Fig. 8(c) appearsto betheoptimalthickness, which allowsfor highestPi/t.Forapracticalpurposeitisdesirabletodelaythis tran-sition,i.e.tohaveaneventhickeradlayerwithfracturestillbeing limitedbythestressinthemainlayer.Inordertoachievethis,it willbeusefultouseadlayerswithevenlowerstress(more com-pressive)or/andhigherfracturestrength,whichmaybedoneby tuningthecompositionoftheadlayeranddepositionconditions.

Similarly,inthecaseofArbombardment,thedepthdistribution andmagnitude ofthecreatedcompressivestresswillinfluence thepressure limit ofthe membrane. Henceit shouldbe possi-bletofindmoreoptimalparametersfortheionbeamtreatment thantheonesusedinthiswork,andachievehigherincreaseofthe pressurelimit.Althoughitisdifficulttopredictwhichexact param-etersofthebeamwouldbeoptimal,weexpectthatmoreenergetic beamwouldleadtolargerimplantationdepthandhigher magni-tudeofthecompressivestresscreated,whichshouldresultina strongermembrane,aslongasthedamagecausedby implanta-tiondoesn’tcompromisethefracturestrengthofthebombarded layer.

Asnotedearlier,main

edge (Pi) initiallyincreaseswithadlayer thick-ness,inotherwordsthestrengthofthemainlayercoveredbythe adlayerishigherthanthefracturestressoftheas-released mem-brane.Comparedtocracksstartingfromafreesurface(Fig.9(a)), cracksoriginatingfromavolumeundertheadlayer(Fig.9(b))will requireahigheractingstressforgrowth[17].Hence,thestrength ofthemainlayerincreaseswhenitiscoveredbyanadlayerandthe fractureoriginismovedawayfromthefreesurfaceofthe

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mem-brane.Themagnitudeofthecompressivestressintheadlayerand theadlayerthicknessshouldhaveaninﬂuenceonthe strengthen-ingeffectoftheadlayer,i.e.,anextremelythinadlayerwillprovide littleresistancetothecracksgrowingunderit,whileathickadlayer withlargecompressivestressshouldbemoreeffectiveat hinder-ingcrackgrowth.Howeverincreaseoftheadlayerthicknessquickly causesthefractureorigintomovetothefreesurfaceoftheadlayer, whichdoesn’tallowtostudythestrengtheningeffectindetailin thisexperiment andcompareitwiththetheoreticalmodel pro-posedbyGreen[17].

Insummary,membraneswithcompressiveresidualstressatthe topsurfaceinducedbyArionbeambombardmentorthedeposition ofthinadlayerscanwithstandahigherpressurebeforeintrinsic failureisinitiated.Compressivestressatthetopsurfacereduces themaximumstresscausedbybendingnearthemembraneedge andcausesthefractureorigintomoveunderthesurface,which leadstoincreasedfracturestrength.

5. Conclusion

In this work westudied thefailure ofthin film membranes withandwithoutsurfacecompressionunderanexternallyapplied pressure. By analyzing the failure probability distributions and inspecting the frames of failed membranes, we identified and quantified two distinct failure modes: intrinsic, corresponding to a failure initiated in the small highly stressed region along the membrane edge, and extrinsic, a failure mode caused by theextrinsicdefectsin thelargefreestandingpartofthe mem-brane.

Usingargon-ionbombardmentorthedepositionofadlayersto createmembraneswithcompressivetoplayers,wehave demon-stratedthatresidualcompressivestressatthesurfacemitigatesthe intrinsicfailuremode,whichallowsstrongermembranesthatare abletowithstandupto50%higherappliedpressures.Thisresult canbeusedtowidentherangeofapplicationsforthinﬁlm mem-branes,especiallyintheareaswheremembranetransparencyfor electronsorX-raysiskey.

Analysisofthestressinmembraneswithadlayerssuggeststhat whenthecompressivesurfacelayerissufﬁcientlythin,the frac-tureoriginatesfromtheinterfacebetweenthecompressivesurface layerandthemaintensilelayer,whileinmembraneswithathicker compressivelayerfailurestartsfromthefreesurfaceofthe mem-brane.Stressrequiredforfracturetoinitiatefromunderneaththe compressivelayerwasfoundtobeslightlyhigherthanforfracture thatstartsfromthefreesurface.

CRediTauthorshipcontributionstatement

A. Shaﬁkov: Methodology, Investigation, Writing - original draft.B.Schurink:Methodology,Investigation,Writing-review &editing.R.W.E.vandeKruijs:Methodology,Supervision, Writ-ing-review&editing.J.Benschop:Supervision,Writing-review &editing.W.T.E.vandenBeld:Methodology,Writing-review& editing.Z.S.Houweling:Supervision,Writing-review&editing. F.Bijkerk:Supervision,Fundingacquisition,Writing-review& editing.

DeclarationofCompetingInterest

Theauthorsreportnodeclarationsofinterest. Acknowledgements

ThisworkispartofresearchprogrammeoftheIndustrialFocus GroupXUV Optics, beingpartof theMESA+Institutefor

Nano-technologyandtheUniversityofTwente,(www.utwente.nl/xuv) andtheIndustrialPartnershipProgramme“X-tools”(projectNo. 741.018.301).TheworkwasﬁnanciallysupportedbytheDutch ResearchCouncil(NWO),ASML,CarlZeissSMT,MalvernPanalytical andtheProvinceOverijssel.

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Biographies

AiratShaﬁkovreceivedhisB.Sc.andM.Sc.(withhonors)degreesfromMoscow

InstituteofPhysicsandTechnology,in2015and2017,respectively.Heiscurrently

workingtowardsthePh.D.degreeinIndustrialFocusGroupXUVOpticsindustrial

focusgroupoftheMesa+instituteattheUniversityofTwente.Hisresearchinterests

includesynthesisandstudyofmechanicalpropertiesofnanoscale-thinfreestanding

ﬁlms.

BartSchurinkhasabothaB.Sc.(SaxionUniversity,Enschede,2006)andM.Sc.

degree(UniversityofTwente,Enschede,2011)inBioMedicalsciences.APh.D.degree

(UniversityofTwente,Enschede,2016)inmicrotechnologyandﬂuidicsfora

brain-on-chip.FollowedbyworkingasaPostdoctoralResearcher(UniversityofTwente,

Enschede,2016)onfreestandingceramicthinﬁlmsaspellicleforEUVL.Since2020,

heisworkingasSeniorProcessEngineeratMicronitMicrotechnologies(Enschede).

RobbertvandeKruijshasbeeninvolvedinthedevelopmentofthinﬁlmcoatingsfor

mainlyx-rayandneutronapplicationsforover20years.Hisﬁeldofinterestranges

fromfundamentallayergrowthandatomicscaleinteractionstowardsapplication

relevanttopicssuchasthermaldamage,opticscontaminationandspectral

ﬁlter-ing.CurrentlyheisinvolvedinvariousEUVLrelatedR&DprojectswithintheXUV

focusgroupoftheMESA+instituteattheUniversityofTwente,exploring

industri-allyrelevanttopicssuchasopticslifetime,protectivepelliclesandadvancedreticle

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graphene.Thescientiﬁcchallengethathetakesistorevealtheunderlying

funda-mentalphysicalmechanismsforthesechemicalprocesses.

SilvesterHouwelingreceivedaM.Sc.inPhysics(2007)fromUniversiteitUtrecht

onsiliconnitridethinﬁlmsforphotovoltaicsandthinﬁlmtransistors.Heobtained

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