resultssoftmod

1Room-temperaturesoftmodeandferroelectriclikepolarizationinSrTiO3ultrathinfilms:InfraredandabinitiostudyWei-weiPeng1,RobertTétot1,2,GangNiu3,EmilieAmzallag2,BertrandVilquin4,Jean-BlaiseBrubach1&PascaleRoy1Duetotheremarkablepossibilitiesofepitaxiallygrowingstrontiumtitanate(SrTiO3orSTO)onsilicon,thisoxideiswidelyusedasabufferlayerforintegratingotherperovskiteoxideswhichallowsforthedevelopmentofvariousfunctionalelectronicdevicesonsilicon.
Moreover,STOisknowntobeanincipientferroelectricinbulkbutmaybecomeferroelectricwhenintheformofstrainedultrathinfilms.
Giventheimportanceofthepotentialapplicationsforelectronicsifthispropertyisdemonstrated,weperformedaspectroscopicstudyofSTOonSi(001)templatescouplingexperimentalandabinitioinvestigations.
Weselectedsixsamplesofultrathinfilms:threestrainedsamples(ofthickness4,9and48nm)andthreerelaxedsamples(ofequivalentthickness).
Theirinfraredspectrashowthatboththemechanicalstressandthethicknessplaymajorroles:higherenergymodesevolveassoftmodesinthinnerstrainedfilms.
Inordertosupporttheseobservations,thedynamicalabinitiocalculationsallowedderivingtheconditionsforSTOfilmstobecomeferroelectricatroomtemperatureasshownbythedevelopmentofasoftmodeandthedivergenceofthein-planedielectricconstant.
Perovskiteoxidesformaclassofelectronicmaterialswhichcoversawiderangeofelectricalpropertiessuchassuperconductivity,piezoelectricity,ferroelectricityandferromagnetism.
Variousfunctionaldevices,likeelectro-mechaniccaptors,electro-opticcouplers,ferroelectricnon-volatilememories,radio-frequencyfiltersetc.
,basedonperovskiteoxidethinfilmsgrownonSrTiO3/Silicon(STO/Si)templatesaredevelopedaroundtheseproper-ties1,2.
Substrate-likeSTO/Si(001)hasbeenthesubjectofseveralstudiesmotivatedbyitspotentialapplicationasatemplatetointegratefunctionaloxideswithperovskitestructureonsilicon3–6.
Indeed,veryrecentworkshaveshownthatSTO/SicrystallinetemplatescouldbeusedforthemonolithicintegrationofIII–Vsemiconductorsonsilicon,duetothepropertiesofthesemiconductor/STOheterointerfaces7–9.
Concurrently,STOitselfisveryattractivefortechnologicalandfundamentalresearchasasystemcombiningstructuralandferroelectricinstabilities10.
STOundergoesacubictotetragonal(I4/mcm-D4h)phasetransitionataround105K,withasmalltetragonaldistortion(c/a=1.
0015)at10K11,connectedwithanantiferrodistorsivesoftphononmode.
STOalsoundergoesapressure-inducedcubictotetragonaltransitionat10GPaatroomtemper-ature12.
Ontheotherhand,STObulkpresentsaremarkablyhighstaticdielectricconstantatroomtemperature(~300K)whichincreasesbyaboutafactorof102at4K.
However,thephononmoderesponsibleforthisferroelectric(FE)behaviordoesnotcondensateatanytemperatureduetoquantumfluctuations,whichmakesSTOaso-calledincipientferroelectric,withacriticaltemperatureTc~32K13–15.
Nevertheless,ithasbeenshownthattheFEphasecanbeinducedinbulkSTObychemicalpressure(18Osubstitution16,17,Cadoping18)orsurfaceeffects19.
Unfortunately,inSTOthinfilms,thedielectricconstanttendstobesignificantlyreduced,therebylimitingtheirapplications.
Thissizeeffectisnotfullyunderstoodandmaybedue,accordingtotheauthors,toadeadlayereffect20,21,internalstress22or/andaprofoundchangeofthelatticedynamicalpropertiesresultinginthehardeningofthesoftmode23–26.
In1SynchrotronSOLEIL,L'OrmedesMerisiers,Saint-Aubin,BP48,F-91192,Gif-sur-Yvette,France.
2CNRS-Universitéparis-Sud,ICMMO(SP2M)UMR8182,Bt410,F-91405,OrsayCedex,France.
3ElectronicMaterialsResearchLaboratory,KeyLaboratoryoftheMinistryofEducation&InternationalCenterforDielectricResearch,Xi'anJiaotongUniversity,Xi'an,710049,China.
4EcoleCentraledeLyon,InstitutdesNanotechnologiesdeLyon(INL),UniversitédeLyon,CNRS-UMR5270,36AvenueGuydeCollongue,F-69134,Ecully,France.
CorrespondenceandrequestsformaterialsshouldbeaddressedtoG.
N.
(email:gangniu@mail.
xjtu.
edu.
cn)orP.
R.
(email:roy@synchrotron-soleil.
fr)Received:28November2016Accepted:5April2017Published:xxxxxxxxOPEN2contrast,manytheoreticalandexperimentalstudieshaveshownthatitispossibletoproduceFEinSTOultra-thinfilmsbyamisfit-strainevenatroomtemperature27–32.
Noticehoweverthat,thevaluesofcriticalstrainandtemper-aturereportedinthesestudiesarenotconsistentamongsteachotherandthatthefilmthicknesswhichcansignifi-cantlyaffectthemechanicalstressofthefilmisnotalwaysspecifiedinthesestudies.
Obviously,determiningtheconditionsforobtainingferroelectricSTOthinfilmsdirectlyonsiliconatroomtemperatureiscrucialfortechnologicalapplications.
Veryinterestingly,Warusawithanaetal.
30observed,bymeansofpiezoresponseforcemicroscopy(PFM),FEnanodomainsattemperatureashighas400KinSTOultrathinfilms(2to4nm)grownonSi(001)substrates,whilesuchdomainswerenolongerobservedforthicker8nmfilms.
PFMiswidelyusedtostudyferroelectricityinthinfilmsasitallowstowrite,readandreversiblyswitchpolardomains.
Suchdomainstructurescanbeobservedusingconventionalscanningprobetechniquesofopticalsecondharmonicgeneration(SHG)30,32–34.
Alternatively,inthispaper,weinvestigatetheferroelectricityinstrainedSTObymeansofthespectroscopicstudyofthesoftmode.
ThesoftmodeconceptwasproposedbyCochran35in1960andithassincebeenusedasanon-ambiguoussignatureofFEtransitions13,23–26.
InordertodefinethespecificrolesofstrainandthicknessfordevelopingFEpropertiesatroomtemperatureinSTO/Si(001)ultrathinfilms,wereporthere(i)thefirstobservationsofthephononsandsoftmodesonsuchnanometerthicksampleswhereferroelectrictransitionisexpected36and(ii)DFTcalculationsofthedielectricconstantandpho-nonmodesfor1.
2,2.
0,2.
5nmthinfilmsforvariousstrainvalues.
Absorbancemeasurementshavebeencarriedoutbetween20–600cm1onsixSTO/Si(001)ultrathinfilms(twoseriesofthreefilms4,10and50nm).
Oneseriesunderwentanannealingafterdepositiontopartiallyrelaxthestraininducedbythe1.
69%mismatchbetweenthecubicSTOparameter(a[100]=3.
905)andtheSi(001)parameter(a[110]=3.
840).
Theotherserieswasas-grownonSiandmayretainsomestraininducedbytheSTO/Si(001)mismatch.
Thestrainoftheas-grownandunstrainedsamplesweredeterminedbyRHEED,XRD(inplaneandoutofplane)andTEM.
Inshort,thein-planestrainoftheas-grownfilmsof4nm,10nmand50nmcanbeestimatedas1.
69%,1.
4%and0%respectivelywhileallunstrainedsamplespresentnodetectablein-planestrain.
Thesynthesisoffilms,straindeterminationanddetailsofIRspectrameasurementsandDFTcalculationsarereportedinMethods.
ExperimentalandcalculatedIRspectraThemeasuredIRspectrumofthethreeunstrainedandofthethreestrainedSTO/Si(001)filmsarepresentedinFig.
1aandb,respectively.
Itcanbeobservedfirstthattheexperimentalspectraappeartobestronglystraindependent,especiallyforthetwothinnerlayers(10and5nm).
Allsixfilmsshowthreemainphononmodes.
Figure1.
MeasuredandcalculatedabsorbanceofSTOthinfilmswithvariousthicknessesandstrainstates.
(a)IRabsorbanceoftheunstrainedSTO/Si(001)filmsofthickness50,10and4nm.
ThethreephononstructuresTO1,TO2andTO4correspondtotheclassificationofthebulkphononmodes.
(b)IRabsorbanceofthestrained(as-grownonSi)STO/Si(001)filmsofthickness48,9and5nm.
ThefourmainstructuresoftheintermediatefilmarelabelledSM,T1,T2,T3,whereSMdesignatessurfaceand/orsoftmodeandT1,T2,T3bulk-likemodes(seedetailsinthetext).
Differencesinthespectraofthetwothickerfilmsmayberelatedtothedifferenceintheirrelaxationmechanism(Seerefs40and41).
Theplasticrelaxationoftheas-grown48nmfilmcausessmalldomainsborderedbydislocationsattheinterface.
(c)CalculatedabsorbanceofSTObulkandfullyrelaxedSTOslabsof7layers(2.
5nm),5layers(2nm)and3layers(1.
2nm).
Thepresenceofmodesatnegativevalues(imaginarymodes)demonstratesthatallslabsaremetastable.
(d)CalculatedabsorbanceofSTOslabsof7,5and3layerswith1.
69%straincorrespondingtothelatticemismatchbetweenSTOandSi(001).
Modesarelabelledasin(b).
In(c–d)sticksareproportionaltooscillatorstrength(maximumintensitynormalizedat1)andlinesrepresentthesumof30cm1wideGaussianseachcenteredatthemodesfrequencies.
3Theunstrainedandstrainedthickestfilms(50nm)presenttheso-calledTO1,TO2andTO4peaksasobservedforbulk13–15,37(SeeTable1).
Forbulkmodes,theassignmentscanberesumedasfollows:TO4andTO2areTi-Ostretchingandbendingmodesrespectively,whiletheSr-TiO3latticevibrationgivesrisetoTO137.
Meanwhile,twoweakerbandsappearonthethinneststrainedfilmat58and81cm1andanintensebandisclearlypresentonthestrained9nmfilmat~40cm1.
Inshort,thestrainedthinnerlayers(5and9nm)presentphononsstruc-turesshiftedathigherfrequencyandextraphononatlowfrequency(probablyduetosurfacemodes)comparedtobulkortothickerrelaxedfilms.
Figure1cpresentsthecalculatedphononstructuresforbulk(bottom),andunstrainedslabsof7,5and3STOlayers(2.
5,2.
0and1.
2nmrespectively).
Notethatthe7layersfilmpresentsathickness(2.
5nm)comparabletoourthinnestmeasuredfilms(4nm).
Thisthicknesswaschosenasitallowedareasonabledurationofthecalculations.
Asamatteroffact,thelossofsymmetryinthedirectionperpendiculartotheslabmakesthecalculationsofIRspectraextremelyCPUtimeconsuming.
Thesimulatedspectrashowanexcellentagreementwithmeasurementsforbulk13–15,37aswellasforthethickerfilms(SeeFig.
1aandbandTable1).
Certainly,intermsofphononpositionsandrelativeintensitiesbothexperimentalandsimulatedspectraincludethreephononstructures,twoweakeraround200cm1and550–600cm1andastrongeronearound100cm1.
Indeed,thenumerousmodesforthevariousslabsresultfromtheappearanceofsurfacemodes.
Itisworthhighlightingthatthecalculatedspectraoffreeslabsexhibitanintenseimaginarymode(140i),showingthatunstrainedslabsaremetastable.
Figure1dpresentsequivalentcalculationsonslabsofthesamethicknessunder1.
69%strain.
NoticethatimaginarymodesofFig.
1carenolongerpresentinthecalculatedspectrashowingthatstrainhasstabilizedtheseslabs.
Comparedtorelaxedslabs,themainspectralfeaturesappearquali-tativelyinthesameenergyrangebutintensephononsarepresentatlowfrequencies.
Mostpeaks,under400cm1,resultfromtheloweringofthesymmetryofslabscomparedtobulkwhichgeneratesmultiplecomponentsfromTO1andTO2modes.
Thislargernumberofmodesisingoodagreementwiththerichexperimental5and9nmstrainedfilmsspectraalthoughnoneofthesimulatedspectrapresentsmodeunder50cm1.
CalculatedspectraanddielectricconstantofSTOultrathinfilmsaccordingtothestrain.
Inthesearchfortheconditionsfordevelopingasoftmode(andtheFEstate),weunderwentsystematiccalculationsonSTOslabforvariousstrainlevelsunder1.
69%(wherenoimaginarymodeisobserved)downtotheoccurrenceofanimaginarymode.
TheresultsarepresentedinFig.
2afortheslabof7layers(resultsfor3and5layersshowthesametrendandarenotshownhere).
This7layersslabcorrespondstoathicknessof2.
5nm,avalueofthesameorderasthe4nmsamplesmeasuredhere,allowingthereforeaqualitativecomparisonbetweenthecalcu-latedandmeasuredspectra.
Indeed,theloweringoftheparallelstrainfrom1.
69%to1.
305%causesaprogressivemodificationofthesim-ulatedspectra:thefrequencyoftheSMmodetendstozeroasthestraindecreasesdownto1.
305%andbecomesimaginaryfor1.
30%,whileT1,T2andT3modesareindependentofstrain.
Notice,however,thatattemptstoevaluatethespectraatintermediatestrainfailedbecausethestructureoscillatesbetweenbeingstableandmetastable.
VibrationalmodesMeasuredFrequency(cm1)CalculatedFrequency(cm1)MainAssignment(fromcalculations)Film4nmFilm10nmFilm50nmBulk(Petzelt14)Bulk7slabsBulk7slabsrelaxedstrainedrelaxedstrainedrelaxedstrainedrelaxedstrained(1305%)relaxedstrained(1.
305%)TiO2SurfaceTransverse/LongitudinalmodesSM505842…28…(S)Ti-O6581…45…(S)Ti-O…141i62…(S)Ti-O(B)O-Ti-OSrOSurfaceTransverse/LongitudinalmodesSM80164/…(B)Sr-O-Sr(B)Sr-O-Sr234260/…(B)O-Ti-O(B)O-Ti-OTransverse/Longitudinalmodes(Bulklike)T114315513314313310593112/846185171(S)Sr-OTi(B)O-Ti-O(B)O-Sr-O(B)O-Sr-OT2187203189191189179176183/171282230/5700(B)Ti-O-Ti(B)Sr-O-Sr(B)O-Ti-OT3544555547553547542548562/489609620(S)Ti-O(B)Sr-O-Ti(B)Ti-Sr-Ti(S)Ti-OTable1.
MeasuredandCalculatedFrequenciesofthemainmodesforultrathinfilmsandBulktogetherwithsomeassignment.
Left:MeasuredfrequenciesofthemainopticalmodesforstrainedandrelaxedSTOthinfilmsofvariousthicknesses(~50,10and4nm)togetherwithexperimentalbulkfrequenciesfromtheliterature37.
Center:Calculatedfrequenciesofthemainopticalmodesfor1.
305%strainedandrelaxedSTOslabof7layerstogetherwithcalculatedbulkfrequencies.
AllmodesaredividedintoTransverseModesT1,T2andT3andSurface/SoftModes(SM).
SMareclassifiedaccordingtoSTOterminatedsurface:SrOorTiO2.
Thepresenceofimaginarymodeat141i(inbold)showsthattherelaxedslabismetastable.
Themodescontributingtothelargedielectricconstantforstrainedslabs(surfacemodesandthelargeLO/TOsplittingT2mode)alsoappearinbold.
Right:Theassignmentbasedoncalculationsofthemainopticalmodesforstrainedandrelaxedtogetherwithcalculatedbulkfrequenciesarepresentedinthethreelastcolumns.
4WithintheCRYSTALcode,thestaticin-planedielectricconstantε(0)//,canbeevaluatedforslabsundercon-strainsasfollows.
First,thepolarisabilityα//(paralleltothesurface)andα⊥(normaltothesurfaces)aredeter-minedasthesecondderivativesoftheenergyoftheslabasafunctionofanexternalelectricfield(//or⊥)accordingtotherelationship:α=EEFF(0)2,iiiii2whereistandsfor//or⊥and=)iEF0iandα=)iiEF0i22.
Thenthetensorε(∞)iiscalculatedbymeansoftherelationshipε∞=πα()()1iV4ii,whereVisthevolumeoftheunitcelloftheslab.
Thetensorε(0)iaswellasthelongitudinalopticalmodes(LO)arefinallycalculatedwiththeCRYSTALcodeusingtheε(∞)itensor.
TheresultsareshowninTable2forbulkandstrainedslabs(1.
69%and1.
305%).
Asthestrainislowered,ε(0)//increaseswhileε(0)⊥remainsconstant.
Thevariationsofε(0)//arereportedinFig.
2btogetherwiththesoftmodefre-quencydependenceonthestrain.
Onecanreadilynoticethatε(0)//tendstoinfinityandthesoftmodefrequencytendstozerobetweenstrainsof1.
305and1.
30%,whichdenotesaFEstate.
Wenowfocusontheoriginofthedivergenceofε(0)//instrainedslabs.
ForacrystalwithNIR-activeopticalmodes,theLyddane-Sachs-Tellerrelation(LST)connectsthedielectricconstanttotheopticalphononfrequencies:∏∏ωωω∞==+shift(0)()1,jNLOTOjNjTO22jjjFigure2.
ResultsofDFTcalculationsforaSTOslabof7layersundervariousin-planestrainsbetween1.
69%and1.
30%.
(a)Simulatedspectraforvariousstrains.
AverystrongdependenceoftheSurface/Softmode(SM)passingfrom~100cm1toanimaginaryvalueasthestraindecreasesisobserved.
At1.
305%strain,theSMislocatedat40cm1whileitbecomesimaginaryforstrainof1.
3%.
(b)VariationsoftheSoftModefrequencyandofthestaticdielectricconstantparalleltotheslabasafunctionofthestrain.
Thevaluesofboththesoftmodeandthein-planestaticdielectricconstantdivergesforstrainvaluesunder1.
305%.
5whereωLOjandωTOjarelongitudinalandtransversalopticalfrequencies,respectively,andωω=shiftjLOTOjj.
Thisrelationappliedtotheslabof7layersspectrumfor1.
305%strainyields=∞2795(0)(),tobecomparedwiththevalue=∞2747(0)()////ofTable2,whichshowsthatthedielectricconstantoftheslabismainlyduetothein-planecomponent.
FromtheLSTrelation,averyhighvalueofε(0)mayarisefromtwoeffects;(i)whenaparticularωTOjtendstozerowithanon-zeroLO-TOshift,(ii)whenaparticularLO-TOshifttendstoinfinity.
Inthepresentcase,botheffectscontributeandtheveryhighvalueofε(0)(13267)ismainlyobtainedfromthecontributionoffourpeaks:thethreepeaksofthesurface/softmodes(SM)andthepeakat220cm1(SeeFig.
3).
InFig.
3,themaincontributionstothestaticdielectricconstantareillustratedforthebulk(topofthefigure)andforthe1.
305%strainedslabof7layers(bottomofthefigure).
Inthebulk,thelowestfrequencyphononTO1-LO1at112cm1–846cm1isthemaincontributiontothestaticdielectriccon-stant.
Theothertwo(TO2-LO2andTO4-LO4)contributeonlymarginally.
Inthestrainedslab,thetransversemodesbetween100and200cm1andat~600cm1arecausedrespectivelybythetransformationofTO1andTO2(mixedcontributionofSr-TiO3stretchingandO-Ti-Obendingforatomslocatedinthemiddleoftheslab),andTO4(mainlyTi-Ostretchingforatomslocatedinthemiddleoftheslab).
Atlowerfrequencies(under100cm1),themodescanbeassignedtosurfacecomponentsofmixedTi-ObendingandstretchingcontributionsparalleltotheTiO2-terminatedsurfacewhilethelowestfrequencymodeisapurebendingofO-Ti-Oatthissurface.
TheBulkV/4π(bohr3)α(bohr3)ε(∞)ε(0)ε(0)/ε(∞)31.
7424.
494.
416637.
3StrainedSlabof7layersStrainV/4π(bohr3)α//(bohr3)α⊥(bohr3)ε(∞)//ε(∞)⊥ε(0)//ε(0)⊥ε(0)///ε(∞)//1.
69%27.
9621.
9223.
54.
636.
3467218.
110091.
31%28.
1622.
3423.
74.
836.
31326718.
12747Table2.
CalculateddielectricpropertiesofSTObulkandslabof7layersfor1.
69%and1.
305%strains.
Thebulkcalculatedvaluesε(∞)=4.
4andε(0)=166canbecomparedtotheexperimentalvalueof5.
6,ontheonehand,andtotheexperimentalvalueof300andtotheLSTbasedvalueof280fromref.
15,ontheotherhand.
Figure3.
MainopticalmodescontributingtothelargestaticdielectricconstantforSTObulk(top)andforaslabof7layersunder1.
305%strain(bottom).
ThebulkTOmodesarerepresentedasblackandredsticks.
Meanwhile,onlythelargeLO-TOshiftfortheTO1mode(shift~700cm)isillustratedwitharedarrow.
Atthebottomofthefigure,themainopticalmodesfora7layersslabunder1.
305%strainarepresented.
Theblacksticksrepresentmodeswhichderivetheirintensitiesfromatomsfurtherfromthesurfaces(bulklikemodes).
ThebluesticksaretransversemodesfromatomsattheTiO2-terminatedsurface.
Theredstickat210cm1correspondstoaTOmodefromTi-Obending(bulklikemode).
TheverylargeLO-TOshiftofthe210cm1mode(indicatedbyaredarrow)contributesstronglytothehighvalueofε(0)//.
Insetstopandbottom:theelementarycellforbulkandfor7layersslab(Sr:biggreensphere,Ti:mediumbluesphere,O:smallredsphere).
6highvalueofε(0)//isduetotheLO-TOshiftofthe220cm1mode(strainindependent)andasmallercontribu-tioncomesfromtheLO-TOshiftsofthethreesurface/softmodes(between3and15),however,thiscontributionincreasesasthestrainapproaches1.
3%whiletheTOfrequenciestendtozero.
ThissecondcontributionisclearlyattheoriginoftheFEtransitioninducedbystrain.
StraindependentCurielawforSTOultrathinfilms.
WhenaferroelectriciscooledtowardsthecriticaltemperatureTc,thesoftmodefrequencytendstozero,accordingtotheCurielaw:ω=*.
.
TconstTT()TOc05SMSincethefrequenciesofallotherphononsarealmosttemperatureindependent,theLSTequationcanbesim-plifiedintoεω∝TT(0)()()TO2SMresultingin:ε=*.
TconstTT(0)()c1Supposingnowthatthelinearthermallatticeexpansionαisaconstant,thelatticeparameterafollowsalinearlaw:α=+aaT(1)0andthestrainα==STaaa00isproportionaltoT.
Hence,thepreviousCurielawappliesaccordingtothestrain:ω=*.
SconstSS()TOc05SMandε=*SconstSS(0)()c1whereScisthecriticalstrain.
ThiscanbeverifiedintheFig.
4(aandb)forSTOslabof3and7layers.
CalculatedpolarizationoftheTiO2-terminatedsurface.
Ourcalculationon1.
305%strainedSTOslabof7layersshowsthattheterminationspresentafirst-layerpuckering,withoxygenionsbeingpulledoutofthesurfacesbyquantitiess(Ti)=0.
058,inqualitativeagreementwiththeexperimentaldataofBickeletal.
19(0.
08±0.
08).
Inparallel,thefirsttwointerlayersdistancesdecreasebyabout0.
1(d0=1.
81insteadof1.
92inthebulk).
FollowingBickeletal.
19wecanevaluatethepolarizationoftheTiO2surface,P=qs/V,whereq(Ti)~2.
5andV=a2*d0.
WeobtainP(Ti)=9.
106C/cm2tobecomparedwiththevalueof24.
106C/cm2fortheexem-plaryroomtemperatureferroelectricBaTiO3,whichconfirmstheferroelectriccharacteroftheslab.
Inconclusion,wedemonstratedbymeansofIRmeasurements,DFTcalculationsandasoftmodeanalysis,thepossibilityofobtainingferroelectricultrathinfilmofSrTiO3directlyonSi(001)atroomtemperature.
TheseresultscorroboratethosebyWarusawithanaetal.
30obtainedbymeansofpiezoresponseforcemicroscopyonsimilarsamples.
WefoundthattheferroelectricityismainlyduetothesoftO-Ti-ObendingmodewhichdevelopsattheTiO2-terminatedsurfaceofthefilm.
Twocriticalparametersmaybecontrolledtoobtainthisresult:thethicknessofthefilmandthein-planestrain.
Toillustrateourresults,weproposetheschematicphasediagramrepresentedinFig.
5.
Thethickerthefilm,thelargerthe(compressive)strainneededtodevelopferroelectricity.
Concerningthethickness,IRspectrashowSMmodesinfilmsofthickness9and5nmwhilethethickerfilmof48nmonlypresentshigherfrequencyfeatures.
SuchlackofSMsuggeststhatthethickerfilmissomewhattoorelaxedtodevelopFEwhichisinqualitativeagreementwiththenon-ferroelectricfilmof8nmthicknessreportedbyWarusawithanaetal.
30.
Noticethatifoneextrapolatesthecalculatedferroelectrictransitionatthefullcom-pressivestraininducedbythemismatchbetweenSTOandSi(001),1.
69%,theFEshoulddevelopforthicknessof~6nm.
Thisstudydemonstratesforthefirsttime,thatalargein-planedielectricconstantcandevelopinultra-thinfilmsforstrainsbetweenacriticalvalue(~1.
23%forathicknessof1.
2nm)upto1.
69%.
Figure4.
RepresentationoftheferroelectricCurielawasafunctionofstrainforSTOslabsof3and7layers.
(a)Softmodefrequencydependenceonthesquarerootofstrain.
(b)Staticparalleldielectricconstantdependenceontheinverseofstrain.
ThedashedlinesaretherepresentationsoftheCurielaw.
OneobservesthattheCurielawisfollowedinamuchlargerstrainrangeforslabof3layerswhichcanbeexplainedbythemuchlargerroleofsurfacesinthiscase.
7MethodsSrTiO3/Si(001)filmssynthesis.
Forthisstudy,sixSTOthinfilmsonp-typeSi(001)substratesweredevel-opedbymolecularbeamepitaxy(MBE)asdescribedindetailinourpreviousstudies38–41.
Wesummarizethemainstepshere.
SrandTimetaleffusioncellsandaneedlevalvecontrolledhigh-puritymolecularoxygensourcewereused.
In-situRHEEDwasemployedtomonitorthefilmsurfacestructuralpropertiesinrealtimeduringthegrowth.
ThesiliconsubstratewaspreparedbyaSr-assistedpassivationmethodleadingtoa1/2monolayer(ML)-coveredSisurface39forthesubsequentSTOgrowth.
TheSTOfilmswerethendepositedonSi(001)atwellcon-trolledtemperatures(360and600°C)andunderaprecisecontroloftheoxygenpartialpressure.
ThecrystallinepropertiesoftheSTOfilmwerecharacterizedusingahighresolutionRigakufour-circlediffractometer.
Avac-uumscienceworkshop(VSW)XPSchamberequippedwithafocusedunpolarisedmonochromaticAlKαX-raysource(υ=1486.
6eV)andanacceptanceanglearound2°wasusedtostudythefilmandtheinterfacestructure.
WedeterminethethicknessoftheSTOfilmsusingHighResolutionX-RayReflectometry(HRXRR),followedbyafastFourierTransform(FFT)analysisfrominterferencefringesmeasurements.
Inref.
38,typical2θ/ωscanaroundSTO(002)Braggreflectionconditionarereported.
STOpossessesaperovskite-typestructure(Pm3m)andthelatticemismatchbetweenSTO(a=3.
905)andSi(001)(a=5.
431/rac(2)=3.
84)is1.
69%withSTOunitcellrotated45°aroundSisurface[001]axis.
TheSTO(002)peakappearsalongwiththeSi(004)peak,confirmingtheout-of-planeepitaxialrelationshipSTO(001)//Si(001).
Furthermore,thePendellsungfringesattheshoulderoftheprincipalSTO(002)peak,atteststhegoodcrystallinityandflatnessoftheSTOepitaxialfilms.
Figure3ofref.
38dis-playsthehighresolutiontransmissionelectronmicroscopycross-sectionalviewimagesofthe4nmSTO/Sisamplesgrownat360°C.
Asexpected42,theepitaxialrelationshipbetweenSTOandSiis[100]STO(001)//[110]Si(001)andthefilmpresentsagoodstructuralqualityandanatomicallyabruptinterfacewithsilicon.
Atotalofsixsampleshavebeenretained:threestrainedsamples(ofthickness4nm,9nmand48nm)obtainedthroughagrowingat360°Candthreerelaxedsamples(ofthickness4nm,10nmand50nm)grownfollowingatwo-stepprocess.
Forstrainedsamples,thetemperatureof360°CwasselectedasitallowsforSTOdepositionwithagoodcrystallizationwithouttheformationofSioxidesattheinterface38.
Concerningthetwostepprocess,twomonolayersofSTOwerefirstlydepositedat360°CtoobtainadirectSTO-Siinterface;then,theepitaxialtemperaturewasincreasedto600°Callowingforabettercrystallizationandsmallerlatticemismatch.
Indeed,allSrTiO3/Si(001)filmspresentgoodcrystallization,andsharpinterface.
Thestraindetailsoftheas-grownsample(strainedsample)wereobtainedbyRHEED,XRD(in-planeandout-of-plane)andTEM.
Thein-planestrainof4,10,50nmwereestimatedas1.
69%,1.
4%and0%respectivelyasdescribedbyNiuetal.
41whileallunstrainedsamplespresentnodetectablein-planestrain38,40.
ThecationandoxygenstoichiometryforallsixsampleswasconfirmedusingRutherfordbackscatteringmethodwhichisbulksensitive,andXPSwhichissurfacesensitive.
Figures6and7presentexamplesofsuchmeasurementsforthe10nmsamples.
Indeed,Rutherfordcharacterization(Fig.
1)onthe10nmfilmgrownat360°Cdidnotdetectanydifferencesinthebulkstoichiometrycomparedtotheidealstoichiometry.
Similarly,XPScharacterizationdidnotdetectanydifferencesinoxygensurfacestoichiometrybetweenthesamplesgrownat360°Candat600°C.
Moreover,theTi2ppeaksintheXPSspectra(Fig.
2b)confirmedthatthetitaniumatoms(moredifficulttooxidizedcomparedtothanSr)arefullyoxidized(i.
e.
thesamplecontainsanegligibleamountofoxygenvacancies).
Clearly,theabsenceofshoulderontherightsideofTi2p3/2peakdemonstratestheabsenceofoxygenvacancies.
InfraredandTHzspectroscopy.
ThefilmsvibrationalstructureswereprobedusingIRtransmissionmeas-urementsattheinfraredbeamlineAILES(AdvancedInfraredLineExploitedforSpectroscopy),SynchrotronFigure5.
Schematicthickness-strainphasediagrambasedonDFTanalysisforSTOultrathinfilmsatroomtemperature.
Thestrainisvariedbetween1.
69%(Si(001)inducedstrain)and0%(fullyrelaxed)andthicknessbetween0.
5and2.
5nm.
Theferroelectricstransitioncorrespondstothezeroingofasoftmode.
Themetastablephasecorrespondstothedevelopmentofanimaginarymode.
8SOLEIL43,44.
Exploitingthehighbrightnessoftheedgesynchrotronradiation45,IRspectrainthe20–600cm1range(1cm1resolution)wereobtainedusingaBrukerE55Fouriertransformspectrometerequippedwitha6micronsMylarbeamsplitterandcombinedwithabolometer(IRLab).
Theinterferometerandthebeamlinewereevacuatedat104mbar(orbetter)toavoidabsorptionbywaterandresidualgas.
ThespectraofthesixSTOfilmswereobtainedbymeasuringthesignaltransmittedinthefarinfrared(FIR)andTHzdividedbyanaccuraterefer-enceprovidedbythesignalthroughanequivalentSisubstrateusingtherelationTfilm=Tsubstrate+film/Tsubstrate46,withTthetransmission.
Theabsorbance,A,wasthenevaluatedusingtherelationA=logT.
Forallfilmsmeasure-ments,ahighprecisionsampleholderallowedplacingthesampleandthereferenceatthesamepositionrelativetotheincidentbeamwhichresultedinacompletecompensationofthefringingfromthesubstrate.
Anexampleoftheincidentbeammeasurement(nosample),Si(001)substrateonlytransmissionandSTOonSi(001)50nmfilmispresentedinFig.
8togetherwiththeresultingabsorbance.
DFTcalculations.
TheequilibriumstructuralparametersandthephononmodesoftheIRspectrawerecalculatedusingabinitiocalculationsattheDFTlevelbymeansoftheCRYSTAL09code47wherethecrystallineorbitalsareexpandedintermsoflocalizedatomicGaussianbasisset.
TheB3PWfunctional,basedonBecke'sthreeparametersadiabaticconnectionexchangefunctional48incombinationwiththenon-localcorrelationPWGGA49,hasbeenusedinthiswork.
Titaniumandoxygenweretreatedatanall-electronlevelandthestandardbasissetHAYWSC311(1d)GforstrontiumwereusedfororbitalexpansionwhensolvingtheDFT-SCFequationiteratively.
ThenumberofkpointsinthefirstirreducibleBrillouinzone(Pack–Monkorstlattice)50atwhichtheHamiltonianmatrixisdiago-nalizedisequalto40.
Inoptimizingthegeometry,weallowedtherelaxationofallatoms.
Amodifiedconjugatedgradientalgorithm51hasbeenimplementedintheCRYSTALcodetooptimizecellparametersandfractionaryatomiccoordinates.
Ingeometryoptimization,thecriterionforconvergenceonthetotalenergyissetto108Hartree.
Γ-pointvibrationalfrequenciesandabsorbancearecalculatedwithaprecisionof10cm1onthefre-quencyand30%ontherelativeabsorbance.
Figure6.
Rutherfordbackscatteringspectraonthe10nmthinfilmsynthetizedat360°C.
Theexperiment(blackcurve)showsthesamestoichiometryasthesimulatedidealSTO(redcurve).
Figure7.
XPSspectraon10nmthicksamplessynthetizedat360°C(blackcurve)and600°C(redcurves).
(a)zoomontheSr3Pregion,(b)zoomontheTi2pregion.
9Thefulloptimizationofthebulkcellgeometryleadstothelatticeparametera=3.
9212(0.
4%greaterthantheexperimentalvaluesa=3.
905)andadensityof5.
06g.
cm3(1.
2%greaterthanexperimentalvalue).
Theinterionicdistance,dSr-O=2.
773anddTi-O=1.
961areingoodagreement(+0.
4%)withexperimentalvalues(2.
761and1.
952respectively).
TheMullikenchargesarerespectivelyQSr=1.
856,QTi=2.
486andQO=1.
449.
TheabsorbancespectrumforbulkcubicSTOwascalculatedusingtherelaxedstructuredescribedpreviously.
Absorbancecalculationshavealsobeenperformedforslabsof3,5and7SrTiO3layersalongthe[001]direction(periodicboundaryconditionsareimposedinthe[100]and[010]directions).
Inthiscase,theperiodicsimulationboxcontainsa50nmemptyspacebetweentwoadjacentslabsinordertoavoidsurfaceinteraction.
Ourresultsmaybecomparedwithprevioustheoreticalstudies52–54.
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AcknowledgementsThiswork,partlyrealizedonNanolyonplatform,wassupportedbytheFrenchAgenceNationaledelaRecherche(ANR,ProjectNo.
ANR-07-BLAN-0312MINOS)andJSPS-EGIDESakuraproject.
WethankK.
Raderforacriticalreadingofthemanuscript.
11AuthorContributionsG.
N.
andB.
V.
preparedthesamples,W.
P.
,J.
B.
andP.
R.
performedtheIRmeasurements,E.
A.
andR.
T.
performedDFTcalculations.
R.
T.
andP.
R.
wrotethepaperandsupervisedtheresearch.
AdditionalInformationCompetingInterests:Theauthorsdeclarethattheyhavenocompetinginterests.
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