中文3550字作者R.Snyder,Member FrederickI.Mopsik國籍：America出處：IEEETRANSACTIONSONINSTRUMENTATIONANDEASUREMENTAPrecisionCapacitanceCellforMeasurementofThinFilmOut-of-PlaneIII:ConductingandSemiconductingMaterialspaperdescribestheconstruction,calibration,anduseofaprecisioncapacitance-basedmetrologyforthemeasurementofthethermalandhygrothermal(swelling)expansionofthinfilms.Itisdemonstratedthatwiththisversionofourcapacitancecell,materialsranginginelectricalpropertiesfrominsulatorstoconductorscanbemeasured.Theresultsofourmeasurementsonp-type<100>-orientedsinglecrystalsiliconarecomparedtotherecommendedstandardreferencevaluesfromtheliteratureandareshowntobeinexcellentagreement.IndexTerms—Capacitancecell,coefficientofthermalexpansion(CTE),guardedelectrode,highsensitivitydisplacement,innerlayerdielectrics,polymers,thinfilms.INTRODUCTIONTHEcoefficientofthermalexpansion(CTE)isakeydesignparameterinmanyapplications.Itisusedforestimatingdimensionaltolerancesandthermalstressmismatches.Thelatterisofgreatimportancetotheelectronicsindustry,wherethermalstressescanleadtodevicefailure.Foraccuratemodelingofthesesystems,reliablevaluesareneededfortheCTE.Traditionally,displacementgaugetechniquessuchasthermomechanicalanalysis(TMA)havebeenutilizedfordeterminingtheCTE.However,standardtestmethodsbasedonthesetechniquesarelimitedtodimensionsgreaterthan100mm[1-2.]Thisisproblematicformaterialswhichcanbeformedonlyasthinlayers(suchascoatingsandcertaininnerlayerdielectrics).Additionally,thereissomequestionastowhethervaluesobtainedonlargersamples(bulkmaterial)arethesameasthoseobtainedforthinfilms,evenwhentheeffectsoflateralconstraintsareincludedinthecalculations.Ithaslongbeenrecognizedthatcapacitance-basedmeasurements,inprinciple,canofferthenecessaryresolutionforthesefilms.Forapairofplane-parallelplatecapacitors,ifthesampleisusedtosetthespacingoftheplatesd whilebeingoutsideofthemeasurementpath,thenforaconstanteffectiveareaoftheplatesA,thecapacitanceina AvacuumC

vac

isgivenbythewell-known

vac

0 (1)dwhere

isthepermittivityoffreespace8.854pFm).Withthesample0 0outsideofthemeasurementpathandonlyairetweentheelectrodes,thevacuumcapacitanceisobtainedromthemeasuredcapacitanceC byC Cvac air

(2)whereair isthedielectricconstantofair.Inthreepreviouspapers,thedesignanddatareductiontechniqueswerepresentedforourthree-terminalcapacitance-basedmetrologyforthinpolymerfilmmeasurements.Thefirstpaper(I)describedtheinitialdesignbasedongold-coatedZerodur.However,severalproblemswereencountered.ItwasdiscoveredthatZerodurdisplaysferroelectricbehavior,withanapparentCurietemperatureof206℃asdeterminedbyfittingwithaCurie–Weisslaw.TherapidchangeinthedielectricconstantoftheZeroduralongwithacouplingfromthecentralcontactthroughtheguardgaptothehighelectrodecreatedanapparentnegativethermalexpansion.Thesecondproblemwiththeinitialdesignwaswiththegoldcoating.Thiscoatinghadthetendencyto―snowplow‖whenscratchesformedinthesurfacecreatingraisedareaswhichwouldresultinshortswhenmeasurementswereperformedonthinsamples.Thesecondproblemwiththegoldwasthatitunderwentmechanicalcreepunderloading.Toresolvetheseproblems,anewelectrodewasdesignedfromfusedquartzcoatedwithnichrome.Agroovefilledwithconductivesilverpaintwasaddedtothebacksideofthebottomelectrodearoundthecentralcontacttointerceptanyfieldlinesbetweenthecentralwirecontactthroughtheguardgaptothehighelectrode.Thenewdesignwasdescribedinthesecondpaper(II)alongwiththermalexpansionmeasurementson<0001>-orientedsinglecrystalsapphire(AlO2 3

)anda14-m thickinnerlayerdielectricmaterialwasrecognizedinIIthatthedatareductionwassimpleaslongastheairfillingthegapbetweenthecapacitorplateswasdry.However,toexpandtheutilityofthecapacitancecelltohygrothermalexpansion(i.e.,swellinginahumidenvironment),thethirdpaper(III)describedthedatareductiontechniquesnecessaryforuseofthecapacitancecellunderhumidconditions.Fig.1.Schematicoftheelectrodes.Notethattheshadedareascorrespondtothenichromecoating.TheresolutionoftheinstrumentwasdeterminedinIIandIII.Fordry,isothermalconditions,thecapacitancecellcanmeasurerelativechangesinthicknessontheorderof107 ,fora0.5-mmthicksample;thiscorrespondstoaresolutionontheorderof51011m.Underdryconditionsinwhichthetemperatureischanged,thereproducibilityofarelativethicknesschange(e.g.,forCTEmeasurement)isontheorderof106

.Finally,underhumidconditions,theultimateresolutionisprimarilyafunctionoftemperature—theactualvaluesofwhicharegiveninIII.InII,adeficiencywasrecognizedinthedesign.Neithersemiconductingorconductingmaterialscouldbeusedasthematerialfortesting.Thiswasespeciallythecaseforsilicon,whichformsaSchottkybarrierwithnichromeandactsasavoltagerectifier.Additionally,becauseofthenatureoftheinterface,the1kHzmeasurementfrequencygeneratesultrasoundwhichresultsintheepoxycontactsbeingshakenloose.WementionedbrieflyinIIthatifthetopelectrodehadaguardringadded,thesamplecouldbeheldatzeropotentialandthiswouldnolongerbeaproblem.Todemonstratethis,weconstructedsuchacapacitancedesignandtestingofwhicharedescribedinthispaper.CAPACITANCECELLDESIGNElectrodeDesignBecausetheconstructionoftheelectrodeswasthoroughlydescribedinII,alessdetaileddescriptionwillbegivenwithemphasisonthechangesinthedesign.Theelectrodeswereconstructed,asbefore,inthefollowingmanner(seeFig.1).10cm2cmcylindricalblanksoffusedquartzweregroundandpolishedtoopticalflatness.Smallholesweredrilledthroughthecenterofeachblanksothat16gaugewirecouldbeinsertedintothem.Thewireswerethencementedwithaconductingepoxy(resistivityof4104cmatAsecondholeandwirewerethenaddedtoeachblankapproximately0.75cmfromtheedgeoftheblanks.Acoatingofnichromewasthenaddedsuchthatitcoveredallsurfacesexceptforasmallareaaroundthebackoftheblanks.Aguardgapwasscribedonboththetopandbottomelectrodessuchthatnomaterialwasraisedwhichcouldcauseashort.Onthebottomelectrode,theguardgapwasscribedona3cmdiameter,andonthetopelectrodeitwasscribedona6cmdiameter.Inthebottomelectrode,a1cmdiameterwellwascutintothebackoftheblankwhichextendedtowithin5mmofthefrontsurface.Thiswellwasthenfilledwithathinconductivesilverpaint.Thepaintconnectedtheouterguardring’smetallizationtotheedgeofthewell.Fig.2.Schematicoftheassembledcapacitancecell.CellAssemblyandCapacitanceMeasurementsTheholderdescribedinIIwasemployedforthemodifiedcell.Inthisversionofthecapacitancecell,bothconductorsofthesemirigidcoaxiallinewereconnectedtothetopelectrode.Thecenterconnectorandbraidwereconnectedtothecenterareaandouterguardring,respectively,byfine30gaugewirecoils.ThecoilswereterminatedwithcenterfemalecontactsfromBNCconnectors,whichcouldbeeasilyconnected/disconnectedtothe16gaugetinnedcopperwirethatwasepoxiedintotheelectrodes.AschematicoftheassembledcellisshowninFig.2.ThefemaleBNCconnectoronthebrassholder(bottomelectrode)wasconnectedtothelowterminal,andthefemaleBNCconnectoronthesemirigidcoaxiallinewasconnectedtothehighterminal.AllconnectionsfromthecapacitancecelltothebridgewereperformedusingTefloninsulatedlownoisecables.Thecapacitancemeasurementswereobtainedusingacommercialautomatedthree-terminalcapacitancebridgewhichusesanoven-stabilizedquartzcapacitorandhasacitedguaranteedrelativeresolutionofbetterthan5107

pF/pFfortherangeofcapacitancesusedwiththiscell2500A1kHzUltra-PrecisionCapacitanceBridgewithOptionE).(Notethatthe―useful‖relativeresolutionissuggestedbythemanufacturertobetypicallyafactorof10ormorebetterthatthecitedrelativeresolution.)Thecapacitancebridge’swasverifiedagainstaNationalInstitutefsdy(NIST)dderdifferencebetweenthetwowaswithinthecapacitor’suncertainty.Allmeasurementswereperformedinatemperature/humiditychamberequippedwitha90℃dewpointairpurge.Thecellwasequilibratedateachtemperatureuntiltherelativefluctuationsinthevacuumcorrectedcapacitancewerenomorethan10710pF/pF.Barometricpressurewasmonitoredusingadigitalpressuresensorwithamanufacturer’sstateduncertaintyof0.1mmHg(13Pa).AsstatedpreviouslyinII,thetemperatureofthecellwascalibratedintermsofthechambertemperaturewitharesistancetemperaturedevice(RTD)mountedtothecellwiththermallyconductingpaste.TheRTDwascalibratedagainstaNISTcertifiedITS-90standardreferencethermometer.AsinII,becauseweareusingadryairpurge,wecanusetheidealgaslawcorrectiontodeterminethemolarvolumeoftheairvtocalculateCair vacvair

RT（3）pWhereT---absolutetemperature;P---pessure;R---gasconstant(R8.314507Lkpamol1K1)[12].Fromthisandthevalueofthemolarpolarizationofdryairobtainedfromtheliterature,P4.31601103mol[13],thedielectricconstantoftheairseparatingtheelectrodesis air P air v11Pairvaieair

aie (4)MEASUREMENTSCellCalibrationTouse(1)tocalculatethethicknessofthesample,theeffectiveareamustbeknown.Todeterminethisvalueasafunctionoftemperature,asinII,wecalibratedtheareaandareaexpansionthroughtheuseofZerodurspacerswiththicknessesofapproximately2.0mm.AsinII,theactualdimensionsoftheZerodurspacersweremeasuredinaballtoplaneconfigurationwithaspeciallydesignedcaliperequippedwithalinearvoltagedisplacementtransducer(LVDT)thathadaresolutionof1104mm.ThecellwasassembledwiththeZerodurspacersusingthesamplepreparationdescribedinII.Measurementswereperformedat0℃,25℃,50℃,75℃,100℃,125C,and150℃.Thecellwascycledthroughthisrangeoftemperaturethreetimes,andthevaluesforC werevacdeterminedforeachrunafteraveragingallthepropertiesoverapproximately1husing10sincrements(atotalof360datapoints)afterequilibriumwasachieved.TheareaAwascalculatedusingtheroomtemperaturethicknessmeasurementsandthevalueforC .Allsubsequentdeterminationsof A,athigherandlowertemperatures,werevaccorrectedfortheslightexpansionandcontractionoftheZerodurasafunctionoftemperature0.05106K1).TheresultsoftheeffectiveradiusoftheelectrodeZerodurasafunctionoftemperatureareplottedinFig.3.Fig.3.EffectiveradiusofthebottomelectrodeasafunctionoftemperatureobtainedbymeasurementsusingZerodurandcorrectingforitsslightexpansion.Fig.4.Relativeexpansionofthe<100>-orientedsinglecrystalsiliconasafunctionoftemperature.Thelineisaplotofthedatafromp-TypeDoped<100>SingleCrystalSiliconTodemonstratetheabilityofthecelltomeasuresiliconandtoprovideaccuratevaluesforthermalexpansion,a0.6-mmthickwaferofsingle-sidepolished,backsidestressrelieved,p-type,<100>-orientedsinglecrystalsiliconwitharesistivityof15 cmwasn(by)oe.hescm2.ewerethencleanedwithultrapuredistilledwaterandethanol.ThecellwasassembledinthesamefashionaswasdescribedinIIandwasplacedinavacuumovenatambienttemperaturesforapproximately1htoeffectivelywringthesample.3.Measurementswereperformedat50℃,75℃,100℃,125℃,andaminimumoftwotimeseach.(Note:Nopointwastakenat0℃duetoproblemswiththecompressorintheenvironmentalchamber.)ThewaferthicknesswasdeterminedusingtheeffectiveradiusversustemperaturedatashowninFig.3.TheresultsofthisanalysisareshowninFig.4alongwiththerecommendedexpansiondataonsiliconobtainedshouldbenotedthatthestandardreferencedatawasdefinedrelativetowhereaswehavemeasured,forconvenience,relativeto25℃.Therefore,thestandardreference,relativeexpansiondatawasshiftedinFig.4byanamountSequaltoST5KwhereT istheCTEattemperatureTtakenfromItisapparentthatthetwosetsofdataagreewithintheexperimentaluncertainty.(Theerrorbarissmalleronthe25℃datapointthanonthehighertemperaturesduetothefactthatmorerepeatrunswereperformed,whichreducedtheuncertaintyforthatdatapoint.)Thisdemonstratesseveralkeyconclusionsregardingthecapacitancecell.First,thelimitationsofthepreviousdesignhavebeeneliminated;siliconandconductingsamplescanbemeasured.Second,theresultsshowthatthecapacitancecellproducesdatathatagreewithliteraturedata.Finally,wehavefurtherdemonstratedtheadvantageofourtechniqueformeasurementofthinsamplesovercommerciallyavailableTMAs.Thevalidityofthisstatementcanbeshownbyconsideringtheresultsofaroundrobinstudy.ThisstudywasperformedamongresearchersatNIST,IBMEndicott,DEC,MicroelectronicsandComputerTechnologyCorporation,NavalSurfaceWarfareDivision,CALCEElectronicProductsandSystemsCenterattheUniversityofMaryland,CornellUniversity,UniversityofTexasatAustin,PurdueUniversity,andtheSemiconductorResearchCorporation(SRC)onthemeasurementoftheCTEofsinglecrystal<100>siliconusingvariouscommercial1.1765-mmthicksampleof<100>singlecrystalsiliconwasusedbyallparticipants.AllreportedvaluesfortheCTEofsiliconwerebelowtheliteraturevaluesforthecorrespondingtemperaturerangesby15%to40%.Oursamplewasapproximatelyhalfasthickastheirsample,yetourvaluesarewithintheexperimentalerror.(Itshouldberecalledthatourtotalprecisionisindependentofactualthicknessandthemainerrorisduetoelectrode/sampleinterfacialeffects.Therefore,hadweusedthethickersample,aswasusedintheroundrobinstudy,theerrorinourresultswouldhavebeenreduced.)Inclosing,itshouldbementionedthatsincewasthe―worstcase‖scenarioforthenewcapacitancecell,itwasdeemedunnecessarytoperformmeasurementsonsinglecrystalsofametallicsamplewhichhaveamuchhigherCTE.However,asinglemeasurementwastakenonthesiliconbyconnectingthebraidsfromthehighandlowterminalstogethershortingthetwoguardringsasifitweredonebyametallicsample.Themeasuredcapacitancewasunchanged;thisthereforedemonstratedthatconductingmaterialscanbemeasured.CONCLUSIONSWehavepresentedthedesignsandimplementationofourcapacitancecellforthemeasurementofconductingandsemiconductingmaterials(aswellasdielectrics).Thethermalexpansiondata,obtainedwiththenewversionofourcapacitancecell,onp-typedopedsinglecrystalsiliconhavedemonstratedboththeabilityofthecelltomeasuresiliconandconductingsamplesandtheabilityofthecelltoprovideaccurateCTEdataonthesetypesofmaterials.Asaresult,itisapparentthatthismetrologycanalsobeappliedtothinpolymerfilmsdepositedonsiliconsubstrates.Furthermore,thiscellcanalsobeusedtostudythehygrothermalexpansion(swellingduetothepresenceofmoisture)byutilizingthedatareductiontechniquesdescribedinIII.Accordingly,thistechniqueshouldbeespeciallyusefultothemicroelectronicspackagingindustryforthecharacterizationofinnerlayerdielectricsaswellascompositestructures.ACKNOWLEDGMENTTheauthorswouldliketothankDr.J.R.EhrsteinintheSemiconductorElectronicsDivisionatNISTforprovidingthesiliconsample.一種精密電容測量薄膜平面擴張的第三部分：導(dǎo)體和半導(dǎo)體材料摘要本文介紹了設(shè)計、校準，并且使用精密電容基礎(chǔ)計量學來測量薄膜的熱、濕熱（腫脹）型<100單晶硅結(jié)果與參考文獻比較，得到了良好證明。電容、熱膨脹系數(shù)介質(zhì)、聚合物、薄膜簡介熱膨脹系數(shù)（CET）是許多應(yīng)用的一個關(guān)鍵設(shè)計參數(shù)。它是用來估算尺寸和熱應(yīng)力的錯位。熱應(yīng)力是十分重要的，它會導(dǎo)致電子行業(yè)中的設(shè)備故障。系統(tǒng)的精確建模，可靠性的測定都需要熱膨脹系數(shù)（CET）的核定。傳統(tǒng)上的位移測量方法如熱應(yīng)力分析（TMA）可以用來確定熱膨脹系數(shù)0m的基礎(chǔ)上。這些材料局限于只能作為薄層得形成（如涂料和內(nèi)層介電層）。此外，在更大的樣本（散裝材料）甚至當薄膜橫向約束的影響下所獲得的結(jié)果是否與理論值一致。人們很早就認識到，在原則上，用過電容測量可以為薄膜提供必要的參數(shù)。d，然后兩極板相互A，其真空電容量為C

0A

(1)vac d 是真空介電常數(shù)8.854pFm），只用來測量的外極板，兩極板間只0 0有空氣，空電容量C表達式為C vac

Cair

(2)式中

air

是空氣介電常數(shù)在前三篇論文，描述設(shè)計和數(shù)據(jù)還原技術(shù)的發(fā)展現(xiàn)狀，并提出了三端口電容(I)的初步設(shè)計。然而遇介電形成的表面劃傷的地區(qū)會導(dǎo)致測量誤差。第二個關(guān)于涂金的問題是它經(jīng)歷載荷下的力學蠕變。極之間的環(huán)行線接觸到任何領(lǐng)域。第二篇論文介紹了新的設(shè)計，單晶藍寶石（氧化二鋁14m為當電容極板間填充的空氣是干燥時，數(shù)據(jù)分析是簡單的。然而，電容還需測量薄膜的濕熱膨脹（例如，在一個潮濕的環(huán)境中的膨脹），論文Ⅲ中描述了電容在高溫高濕條件下數(shù)據(jù)分析的必要技術(shù)。1電極原理圖。注意陰影部分對應(yīng)的鎳鉻合金涂層在論文Ⅱ、Ⅲ中已經(jīng)確定儀器的分辨率。干燥、等溫條件下，電容對于一個10751011m條件下改變溫度，相對厚度變化（例如熱膨脹系數(shù)）大約為106。最后，在潮濕的條件下，最終解決溫度的影響——這個將在論文Ⅲ中得到