材料 外文翻译 外文文献一种精密电容测量薄膜平面扩张的第三部分导体和半导体材料.docx

材料 外文翻译 外文文献一种精密电容测量薄膜平面扩张的第三部分导体和半导体材料.docx

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材料外文翻译外文文献一种精密电容测量薄膜平面扩张的第三部分导体和半导体材料

作者：

ChadR.Snyder,MemberFrederickI.Mopsik

国籍：

America

出处：

IEEETRANSACTIONSONINSTRUMENTATIONANDMEASUREMENT

APrecisionCapacitanceCellforMeasurementofThinFilmOut-of-PlaneExpansion–PartIII:

ConductingandSemiconductingMaterials

Abstract—Thispaperdescribestheconstruction,calibration,anduseofaprecisioncapacitance-basedmetrologyforthemeasurementofthethermalandhygrothermal（swelling）expansionofthinfilms.Itisdemonstratedthatwiththisversionofourcapacitancecell,materialsranginginelectricalpropertiesfrominsulatorstoconductorscanbemeasured.Theresultsofourmeasurementsonp-type<100>-orientedsinglecrystalsiliconarecomparedtotherecommendedstandardreferencevaluesfromtheliteratureandareshowntobeinexcellentagreement.

IndexTerms—Capacitancecell,coefficientofthermalexpansion（CTE）,guardedelectrode,highsensitivitydisplacement,innerlayerdielectrics,polymers,thinfilms.

I.INTRODUCTION

THEcoefficientofthermalexpansion（CTE）isakeydesignparameterinmanyapplications.Itisusedforestimatingdimensionaltolerancesandthermalstressmismatches.Thelatterisofgreatimportancetotheelectronicsindustry,wherethermalstressescanleadtodevicefailure.Foraccuratemodelingofthesesystems,reliablevaluesareneededfortheCTE.

Traditionally,displacementgaugetechniquessuchasthermomechanicalanalysis（TMA）havebeenutilizedfordeterminingtheCTE.However,standardtestmethodsbasedonthesetechniquesarelimitedtodimensionsgreaterthan100

m[1-2].Thisisproblematicformaterialswhichcanbeformedonlyasthinlayers（suchascoatingsandcertaininnerlayerdielectrics）.Additionally,thereissomequestionastowhethervaluesobtainedonlargersamples（bulkmaterial）arethesameasthoseobtainedforthinfilms,evenwhentheeffectsoflateralconstraintsareincludedinthecalculations.

Ithaslongbeenrecognizedthatcapacitance-basedmeasurements,inprinciple,canofferthenecessaryresolutionforthesefilms.Forapairofplane-parallelplatecapacitors,ifthesampleisusedtosetthespacingoftheplates

whilebeingoutsideofthemeasurementpath,thenforaconstanteffectiveareaoftheplates

thecapacitanceinavacuum

isgivenbythewell-knownequation

（1）

where

isthepermittivityoffreespace（

）.Withthesampleoutsideofthemeasurementpathandonlyairetweentheelectrodes,thevacuumcapacitanceisobtainedromthemeasuredcapacitance

by

（2）

where

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（

）anda14-

thickinnerlayerdielectricmaterial[10].ItwasrecognizedinIIthatthedatareductionwassimpleaslongastheairfillingthegapbetweenthecapacitorplateswasdry.However,toexpandtheutilityofthecapacitancecelltohygrothermalexpansion（i.e.,swellinginahumidenvironment）,thethirdpaper（III）describedthedatareductiontechniquesnecessaryforuseofthecapacitancecellunderhumidconditions.

Fig.1.Schematicoftheelectrodes.Notethattheshadedareascorrespondtothenichromecoating.

TheresolutionoftheinstrumentwasdeterminedinIIandIII.Fordry,isothermalconditions,thecapacitancecellcanmeasurerelativechangesinthicknessontheorderof

fora0.5-mmthicksample;thiscorrespondstoaresolutionontheorderof

.Underdryconditionsinwhichthetemperatureischanged,thereproducibilityofarelativethicknesschange（e.g.,forCTEmeasurement）isontheorderof

.Finally,underhumidconditions,theultimateresolutionisprimarilyafunctionoftemperature—theactualvaluesofwhicharegiveninIII.

InII,adeficiencywasrecognizedinthedesign.Neithersemiconductingorconductingmaterialscouldbeusedasthematerialfortesting.Thiswasespeciallythecaseforsilicon,whichformsaSchottkybarrierwithnichromeandactsasavoltagerectifier.Additionally,becauseofthenatureoftheinterface,the1kHzmeasurementfrequencygeneratesultrasoundwhichresultsintheepoxycontactsbeingshakenloose.WementionedbrieflyinIIthatifthetopelectrodehadaguardringadded,thesamplecouldbeheldatzeropotentialandthiswouldnolongerbeaproblem.Todemonstratethis,weconstructedsuchacapacitancecell—thedesignandtestingofwhicharedescribedinthispaper.

II.CAPACITANCECELLDESIGN

A.ElectrodeDesign

BecausetheconstructionoftheelectrodeswasthoroughlydescribedinII,alessdetaileddescriptionwillbegivenwithemphasisonthechangesinthedesign.Theelectrodeswereconstructed,asbefore,inthefollowingmanner（seeFig.1）.

cylindricalblanksoffusedquartzweregroundandpolishedtoopticalflatness.Smallholesweredrilledthroughthecenterofeachblanksothat16gaugewirecouldbeinsertedintothem.Thewireswerethencementedwithaconductingepoxy（resistivityof

at25℃）.Asecondholeandwirewerethenaddedtoeachblankapproximately0.75cmfromtheedgeoftheblanks.Acoatingofnichromewasthenaddedsuchthatitcoveredallsurfacesexceptforasmallareaaroundthebackoftheblanks.Aguardgapwasscribedonboththetopandbottomelectrodessuchthatnomaterialwasraisedwhichcouldcauseashort.Onthebottomelectrode,theguardgapwasscribedona3cmdiameter,andonthetopelectrodeitwasscribedona6cmdiameter.Inthebottomelectrode,a1cmdiameterwellwascutintothebackoftheblankwhichextendedtowithin5mmofthefrontsurface.Thiswellwasthenfilledwithathinconductivesilverpaint.Thepaintconnectedtheouterguardring’smetallizationtotheedgeofthewell.

Fig.2.Schematicoftheassembledcapacitancecell.

B.CellAssemblyandCapacitanceMeasurements

TheholderdescribedinIIwasemployedforthemodifiedcell.Inthisversionofthecapacitancecell,bothconductorsofthesemirigidcoaxiallinewereconnectedtothetopelectrode.Thecenterconnectorandbraidwereconnectedtothecenterareaandouterguardring,respectively,byfine30gaugewirecoils.Thecoilswereterminatedwithcenterfemalecontactsfrom50

BNCconnectors,whichcouldbeeasilyconnected/disconnectedtothe16gaugetinnedcopperwirethatwasepoxiedintotheelectrodes.AschematicoftheassembledcellisshowninFig.2.ThefemaleBNCconnectoronthebrassholder（bottomelectrode）wasconnectedtothelowterminal,andthefemaleBNCconnectoronthesemirigidcoaxiallinewasconnectedtothehighterminal.AllconnectionsfromthecapacitancecelltothebridgewereperformedusingTefloninsulatedlownoisecables.

Thecapacitancemeasurementswereobtainedusingacommercialautomatedthree-terminalcapacitancebridgewhichusesanoven-stabilizedquartzcapacitorandhasacitedguaranteedrelativeresolutionofbetterthan

pF/pFfortherangeofcapacitancesusedwiththiscell（Andeen–Hagerling2500A1kHzUltra-PrecisionCapacitanceBridgewithOptionE）.（Notethatthe“useful”relativeresolutionissuggestedbythemanufacturertobetypicallyafactorof10ormorebetterthatthecitedrelativeresolution.）Thecapacitancebridge’scalibrationwasverifiedagainstaNationalInstituteofStandardsandTechnology（NIST）calibratedstandardreferencecapacitor—thedifferencebetweenthetwowaswithinthecapacitor’suncertainty.

Allmeasurementswereperformedinatemperature/humiditychamberequippedwitha90℃dewpointairpurge.Thecellwasequilibratedateachtemperatureuntiltherelativefluctuationsinthevacuumcorrectedcapacitancewerenomorethan

10pF/pF.Barometricpressurewasmonitoredusingadigitalpressuresensorwithamanufacturer’sstateduncertaintyof0.1mmHg（13Pa）.AsstatedpreviouslyinII,thetemperatureofthecellwascalibratedintermsofthechambertemperaturewitharesistancetemperaturedevice（RTD）mountedtothecellwiththermallyconductingpaste.TheRTDwascalibratedagainstaNISTcertifiedITS-90standardreferencethermometer.AsinII,becauseweareusingadryairpurge,wecanusetheidealgaslawcorrectiontodeterminethemolarvolumeoftheair

tocalculate

（3）

Where

T---absolutetemperature;

P---pessure;

R---gasconstant（

）[12].Fromthisandthevalueofthemolarpolarizationofdryairobtainedfromtheliterature,

[13],thedielectricconstantoftheairs