扫描微波显微镜导纳校准测量规范指南 Good practice guide for calibrated admittance measurements using scanning microwave microscopy (SMM)

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Goodpracticeguideforcalibratedadmittancemeasurementsusing

scanningmicrowavemicroscopy

Abstract

Themeasurementofelectricalpropertiesatthenanoscaleallowsevaluatingtheperformanceofnanomaterialsdevelopedforconsumerelectronics,innovativequantumtechnologies,IoTapplicationsandlifescienceresearch.LocalDCresistancesandhighfrequency(HF)impedancesareamongthemostprominentpropertiestomeasurefornowadaysadvanceddevices.Currently,ConductiveprobeAtomicForceMicroscopy(C-AFM)andScanningMicrowaveMicroscopy(SMM)aretwomaintechniquesusedforthecharacterizationoftheseproperties.Althoughpowerful,thesetwotechniquessufferfrommajordrawbacks:costly,complicatedimplementation,andlackoftraceability.Measurementsarethusunreliable.The20IND12EMPIRprojectELENAaimsatpioneeringthetraceabilityofsuchmeasurements,withstateduncertaintiesandincreasingtheaffordabilityofthesemethods.

Withinthisproject,METASandLNEwithsupportfromJKU,PTBandULILLE,jointlyproposeagoodpracticeguide(GPG)onthecalibrationofSMMformeasurementatthenanoscale,coveringHFadmittancefrom100nSto100mS,foruseinindustrialapplicationsformeasurementatthenanoscale.ThisGPGreliesonrobustcalibrationmethods,referencesamplesandsimplifieduncertaintybudgets.

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Content

1.Introduction 3

2.Experimentalsection 3

2.1.SMMmeasurementprinciple 3

2.2.Environmentalconditions 4

2.2.1.NationalMetrologyInstituteenvironments 4

2.2.2.“OutoftheLab”environment 4

2.3.Calibrationsample 5

2.3.1.VerticalMOScapacitor 5

3.MeasurementProcedure 8

3.1.Imagingconditions 8

3.2.CalibrationofSMM 8

3.3.Simplifieduncertaintybudgets 9

3.3.1.SMMcalibrationforcapacitancemeasurements 10

3.3.2.SoftwareforSMMcalibration 10

4.Calibrationresults 11

4.1.CalibrationofSMMforcapacitancemeasurementsinNMI 11

4.2.CalibratedSMMmeasurementsofdielectricconstantonhigh-κmaterials 12

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1.Introduction

Thescanningmicrowavemicroscopy(SMM)isapowerfulnanoscaletechniquetomeasuretheadmittanceofdielectricthinfilmsornanocapacitors.SMMthusallowsthemeasurementofthenanoscalecapacitanceandconductancegivingaccesstothedielectricconstant,lossangletangentanddopantconcentrationofmaterials.

Thethree-yearsELENAproject:Electricalnanoscalemetrologyinindustry(startdate:1stSept2021)

[

1

]aimsatestablishingaEuropeanmetrologicalinfrastructureandcost-effectivetechnologiesforbothtechniquesC-AFMandtheScanningMicrowaveMicroscopy(SMM)providingmeansforindustriestoconducttraceablenanoscalemeasurementsofmaterialsanddeviceselectricalproperties.OnepartoftheprojectfocusedonthedevelopmentofreferencesamplesandcalibrationmethodsforSMMwhiledrawingupsimplifieduncertaintybudgets,alloftheseforuseinindustrialapplications.

Thisgoodpracticeguide(GPG)summarizestheuseofSMMasarelevanttechniqueforcarryingoutnanoscaleadmittance(capacitanceandconductance)measurementswithademonstratedtraceabilitytotheinternationalsystemofunits(SI).ThisGPGwasestablishedbyMETASandLNE,withthesupportofJKU,PTBandULILLE.

ThecalibrationofSMMforadmittancemeasurementsreliesontheuseofacalibrationkitsuchasdevelopedbyMC2Technologies[

1

],[

2

]orMETAS[

3

][

4

].TheMC2technologiescalibrationkitiscomposedofMOScapacitorsrangingfrom0.3fFto9.8fFwhilethestandardsproposedbyMETASshowsacoplanarcapacitorstructureonatrilayermembrane(SiN/SiO2/SiN)withcapacitancerangingfrom1.3fFto10.1fF.

Inthefollowingsections,wegiveageneraldescriptionoftheexperimentalset-up(SMMprinciple,environmentalconditions,referencesamples)detailthecalibrationmethodsdevelopedfornanoscaleadmittancemeasurementsusingSMM,describethesoftwareusedtocalculateuncertaintyandpresentcalibrationresultsonSMMsystemswithsimplifieduncertaintybudgets.

2.Experimentalsection

2.1.SMMmeasurementprinciple

SMMconsistsofascanningprobemicroscope(SPM)interfacedwithavectornetworkanalyzer(VNA).TheSPMincludesanatomicforcemicroscope(AFM)(inbothNMIs)orascanningtunnelingmicroscope.Basically,theconductivetipoftheSMMisconnectedtothemicrowavesource/meterofVNA(seeFig.1)viaaimpedancematchingnetwork.

Whilethetipscansoverthesamplesurface,itirradiatesthemicrowavesignal,highlylocalizedattheapex,overalocalregionofthesample,allowingsimultaneoustopographicandelectricalcharacterizationofthesampleunderstudy.

Figure1.SchematicdiagramoftheAFM-basedSMMsetup,showingthematchingnetworkbetweentheVNAandthesampleunderstudy

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Dependingonthemismatchbetweenthecharacteristicimpedance(Z0)andthelocalimpedanceofthetip−samplesystem(Zs),onepartoftheincidentmicrowavesignalisreflectedbacktravellingfromthetip-samplecontactpointtotheVNAandtheotherpartistransmittedthroughoutthesample.

Theratiobetweenthereflectedandincidentsignalsatthetip-sampleinterfaceistheso-calledS11scatteringparameter.Nevertheless,theVNAmeasurethescatteringparameterS11matthereferenceplane(verticalbluedashedlineinFigure1),whichisaffectedbythe“matchingnetwork”.Followingtheone-portVNAcalibrationprocedure[

5

],S11mmeasurementsrecordedbyVNAareconvertedintocompleximpedancevalues.

2.2.Environmentalconditions

2.2.1.NationalMetrologyInstituteenvironments

ThefollowingenvironmentalconditionssupportstableoperationoftheSMMwithminimummechanical,thermal,electricaldriftandensuresveryaccuratemeasurements:

●Ensurestablelabclimate(temperature,humidity)toenablestableoperationoftheSMMwithminimummechanical,thermal,andelectricaldrift;

●InthebestcasetheC-AFMmicroscopeshallbeinstalledinagloveboxunderadrynitrogenatmosphere(RH<1%)andthecompleteset-up(glovebox,measurementcircuit,etc)locatedinanelectromagneticallyshieldedenvironment(Faradaycage)understabilizedroomtemperature(airconditioningsystem)at20°Cor23°Cwithatemperatureregulationof±0.3°Corbetter;

●Avoidopeningwindows,directsunlightontheexperiment,andotherthermalsourcesinfluencingtemperatureandhumiditynearbythemeasurementsetup.

Figure2.GloveboxatLNE,wheretheAFMpartislocatedinside.

Loghumidity,temperature,typeofatmosphere,andpressureinthelaboratoryorthegloveboxtoallowtracingbackimplausibleC-AFMmeasurementsandcheckpossibleinfluencesofoneoftheseparameters.

2.2.2.“OutoftheLab”environment

Inlessrestrictedenvironmentalconditions,generallymetinIndustryorAcademia,accuratetraceableadmittancemeasurementsusingSMMcanstillbeperformed.Ifthefollowingconditionsaresatisfied:

RH=(40±10)%andT=(23±3)°C,

thentheuserwilleasilydrawupasimplifieduncertaintybudgetasexplainedlaterinthisGPG.Notemperatureorrelativehumiditycorrectionwillneedtobeappliedbytheuseronthemeasuredvaluesiftheseconditionsarerespected.

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2.3.Calibrationsample

2.3.1.VerticalMOScapacitor

AfirstversionofcalibrationkitfabricatedbyMC2TechnologiesisusedtocalibratetheSMM.AsshowninFig.3,each45×45mm2substratehas144identical140×140µm2patterns.Eachpatternshas4identicalsetsof48microcapacitors.Eachcapacitorconsistsofacirculargoldelectrode(goldpadheight=281nm)depositedonsilicondioxidewithdifferentthicknessesandaSi(100)substratestronglydopedwithboronatoms(p-type)(Fig.4).

Figure3.Top:atopviewopticalimageofoneoftheusedcalibrationsample.Inthisimage,thepad,wherethedevicesetwereusedforthecalibration,islabelledandmarked.Below:azoominopticalimageofthesamepadandthechosensetisframedinredsquare.

Figure4.Top:AFMimageofanareawhereall48microcapacitorsstay.Below:crosssectionviewtakenalongthedashedlineshowninthetoppanel.Thescaleisnotproportional.

ThedopingconcentrationNaofthesubstratewasextractedfromresistivitymeasurements(Na=8.2×1018atoms/cm3),thisquitehighvaluemakestheparasiticdepletioncapacitanceCdnegligiblecomparedtoitsdielectriccapacitanceCox.BecauseofthevariationofSiO2thickness(from50nmto220nmwithabout50nmsteps)andthelateralsizeofthegoldelectrode(withdiametersvaryingfrom1µmto4µm),capacitancevaluesoffabricatedmicrocapacitorsvaryfrom300aFto10fF.Moredetailsaboutthefabricationprocessofcalibrationsamplearedescribedelsewhere[

1

].

Itmustbenotedherethattheknowledgeofthecapacitancevaluesresultsfromcalculationusingthemeasuredvaluesofthedimensionalparametersofthecapacitors(thicknessofthedielectriclayerandtheareaofthetopelectrode).TheseparameterscanbemeasuredwithcertainuncertaintybyAFMorscanningelectronmicroscope(SEM)techniques.Thecapacitancecalculationsalsodependonthe

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relativepermittivityεrvalueofthesilicondioxide,usuallysetto3.9asnominalvalue[

8

][

9

].Thesecalculations,relyingonananalyticalapproachorusingafiniteelementmodeling,considertheeffectsoffringingfields.

Theuncertaintyassociatedwiththiscalibrationstructurewasreportedin[

10

].ThesearecomposedoftheuncertaintiesondimensionalmeasurementoftheMOScapacitors(topelectrodeareasanddielectriclayerthickness),thoseonthedielectricconstantoftheSiO2layerandtheuncertaintiesonthedepletioncapacitance.Forclaritypurpose,atypicaluncertaintybudgetacquiredontheMC2calibrationkitispresentedinTab.1.

Table1.UncertaintybudgetforthecalculationofthecapacitanceofthefirstversionofMC2calibrationkit

Uncertaintybudget(%)

Type

Topelectroderadius=2µmSiO2layerthickness=50nm

Topelectroderadius=0.5µmSiO2layerthickness=200nm

Areameasurement

A,B

0.9

2.4

Thicknessmeasurement

A,B

1.3

0.7

Permittivityεr(SiO2)

B

1.0

1.0

Depletioncapacitance

B

2.0

0.8

Capacitancevalues(fF)

9.472±0.263

0.272±0.009

Usingthisuncertaintybudget,asecondversionofthecapacitancecalibrationkitwasproposedandmanufactured(Fig.5).

Figure5.Atopviewopticalimageofoneofthesecondversionofthecalibrationstructure.

Itiscomposedof400identicalpatternscomposedof20MOScapacitorsrangingfrom0.30fFto39.38fF.ItexhibitslargertopelectrodesandthickerSiO2layerstoimprovetheuncertaintyassociatedwithdimensionalmeasurement.Thedopingdensityofthesubstratewasalsoincreasedtoreducetheuncertaintycontributionofthedepletioncapacitance.Thedopingdensityamountsto(2.00±0.04)·1020atoms/cm3.TheuncertaintybudgetassociatedwiththesecondversionofthecalibrationkitisshowninTab.2.

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Table2.Uncertaintybudgetforthecalculationofthecapacitanceofthesecondversionofcalibrationkit.

Uncertaintybudget(%)

Type

Topelectroderadius=10µmSiO2layerthickness=300nm

Topelectroderadius=1µmSiO2layerthickness=1200nm

Areameasurement

A,B

0.16

1.53

Thicknessmeasurement

A,B

0.60

0.44

Permittivityεr(SiO2)

B

1

1

Depletioncapacitance

B

0.06

0.04

Capacitancevalues(fF)

39.38±0.47

0.30±0.01

2.4.Samplepreparationmethod

ToreducetheimpactofparasiticcapacitancesduringSMMmeasurements,thesampletobemeasuredshouldbelocatedclosetothecapacitancecalibrationkitandtheconductivebackelectrodeofallsampleshouldbeconnectedtoground.InSMMsystemswheretheverticalpositionoftheSMMheadisnotmaintainedfixed,itisnecessarytoadjusttheheightofsamplesatasameverticallevel,within±20µmofdifference,toguarantythesamereferenceplane(verticalbluedashedline,Fig.1).

Ifthesampleunderstudyconsistsofabaredielectricfilm,itisnecessarythedepositionofsmallgoldelectrodesonthesamplesurface.Thus,werespectthesameverticalMOScapacitorconfigurationduringSMMmeasurements.

AgoodelectriccontactmustbeestablishedbetweentheSMMtipandthetopelectrodeoftheMOScapacitortoenableacorrectreadingoftheS11parameter.Itistypicallydonebyapplyingarelativelystrongcontactforce(≈2μN).Severalscanmayberequiredtofullycleanthearea.ItcanbeseeninFigure6wherethesamepatternofthesecondversionoftheMC2calibrationsampleisscannedovermultipletimeswithastrongappliedforce.

Figure6.S11amplitudecontrastoverthesecondversionoftheMC2calibrationsampleacquiredwithanimportanttip-sampleinterfaceforce(5µN).left:firstimage;center:5thimage;right:8thimage

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3.MeasurementProcedure

3.1.Imagingconditions

Imagingconditions-SMMimagesarebestacquiredincontactmode,wherethetipremainsincontactwithmeasuredsurfaceduringthewholemeasurementprocessandensuresahomogenouselectricalcontact.Recordedsignalsconsistsoftopographyandelectricaldata(S11,m-MagnitudeandS11,m-Phase).

ChoiceoftheVNAoperatingfrequency-BeforelandingtheSMMprobeonthesamplesurface,afullfrequencysweepoftheVNAsignalisperformedoveritsoperationfrequencyrangewithatiphoveringabovethesamplesurfacebutnotincontactyet.ThemicrowavefrequencywiththelowestS11,m-Magnitudesignalischosenforresonancebasedimpedancematchingsystems.

Imageprocessing–DuringSMMscanning,artifactscommonlyseeninAFMimagingliketiltandscanlineartifactsarepresent.Thosecanbecorrectedbythefollowingalgorithmon

●Firstorderpolynomialbackgroundremoval(surfacefeaturesmasked)

●Meanbackgroundsubstraction

●PolynomialalignrowalgorithmappliedtotheSiO2surface(Topelectrodesmasked)

Inadditiontothis“classical”AFMdatatreatment,ifanunshieldedSMMprobeisused,itisrequiredtodealwiththeparasiticcapacitancebetweentheAFMconeandsampleandtheAFMcantileverandsample.Pratically,itisdonebymeanbackgroundsubstractionandzerolevelingofeachSiO2terraces.

3.2.CalibrationofSMM

ThecalibrationofSMMrequiresatleastthreecapacitorswithknowncapacitancevalues.ApoorandarbitraryselectionofthesethreecapacitorswithoutestablishedcriteriacanleadtoobtainerroneousresultsoncapacitancemeasurementsafterSMMcalibration.Thecapacitorsofthereferencedeviceareselectedaccordingtothefollowingcriteria:

●theypresentacleansurfaceconfirmedbyAFM,

●theyensureagoodandhomogeneouselectricalcontactbetweentheSMMtipandtheirtopelectrode,

●theycoverthefulldesiredcalibrationrange,

●theircapacitancessatisfyapproximatelytheinequality|Ci–Cj|≥ΔCmax/2,

whereiandj(≠i)rangingfrom1to48andΔCmaxisthedifferencebetweenthehighestandlowestcapacitancevaluesΔCmax=Cmax–Cmin.Dependingonthecapacitancevalueofthedeviceundertest(DUT),itisimportanttochooseatripletofcapacitors,therangeofwhichcoverstheexpectedvalueoftheDUT.Forexample,fortheDUTwithacapacitancearound0.8fF,atripletwithcapacitancesaround0.3fF,1fFand10fFwouldbemoresuitablethantheonewithcapacitancesaround1fF,5fFand10fF.

ThecalibrationoftheSMMconsistsinconvertingtherawmeasuredreflectioncoefficientS11,mintothecompleximpedanceofthesampleunderstudyZsusingthemodifiedShortOpenLoad(SOL)calibrationmethodproposedbyHoffmannetal.[

5

].ThequantitiesS11,mandZsarerelatedbytwoequations:

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whereS11istheexpectedreflectioncoefficientande00,e01,ande11arethreecomplexparameters(alsoknownaserrorparameters)tobedeterminedfromS11,mmeasurementsonthreereferencestructureswithknowncapacitancevalues.Zrisanon-zeroreferenceimpedance,whichistypicallysetat50Ω.Itisimportanttonotethatthiscalibrationrequiresallmeasurements(forreferenceandDUTdevices)tobeperformedwiththesametipandatthesameRFfrequency.ThewholecalibrationprocessneedstoberepeatedtocalibratetheSMMmeasurementatotherfrequencies.

3.3.Simplifieduncertaintybudgets

ThecombinedstandarduncertaintiesresultfromthemainuncertaintycontributionsthataresummarizedinTab.3forthefirstversionofMC2referencesample.Asexpected,thelargestcontributioncomesfromtheSMMcalibrationuncertainty.Detailsaregivenbelow.Nochangeoftheerrorparameters(e00,e01,ande11)hasbeendetectedfromthemeasurementscarriedoutonthereferencepattern.TherepeatabilitylevelsobservedonthemeasurementsofCref-09,Cref-21,andCref-40havebeenfoundbetween0.2%and1.1%.Theuncertaintycontributionfromparasiticcapacitancesbecomesnonnegligibleforthesmallestcapacitance,reaching0.7%.

Table3.Mainuncertaintycontributionsfor3valuesmeasuredonMC2calibrationkit–firstversion(A61sample):C05(8.79fF),C23(1.36fF),C32(0.33fF).

UncertaintybudgetforCi(%)

Type

C09

C21

C40

Histogram

A

0.1

0.6

2.1

Repeatability

A

0.5

1.1

0.2

SMMcalibration

B

2.1

2.9

2.5

Parasiticcapacitances

B

0.02

0.18

0.72

Watermeniscus

B

0.2

0.2

0.2

CombineduncertaintyuCm

2.2

3.2

3.3

TheSMMcalibrationuncertaintyisestimatedfromtheuncertaintiesofcapacitancecalculationoftheselectedcapacitorsCref-09,Cref-21,andCref-40weretakenfromTab.2.

Similarly,theuncertaintybudgetassociatedwithcapacitancemeasurementbySMMcalibratedonthesecondversionofthecalibrationsampleisshowninTab.4.

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Table4.Mainuncertaintycontributionsfor2valuesmeasuredonMC2calibrationkit–secondversion(B03sample):C01(39.37fF),C16(11.11fF).

UncertaintybudgetforCi(%)

Type

C01

C16

Histogram

A

0.17

0.13

Repeatability

A

TBD

TBD

SMMcalibration

B

0.68

064

Parasiticcapacitances

B

0.01

0.03

Watermeniscus

B

0.2

0.2

CombineduncertaintyuCm

0.73

0.7

Anonnegligibleimprovementcanbeobservedwhencomparedtothecalibrationperformedwiththefirstversionofthecalibrationsample.

3.3.1.SMMcalibrationforcapacitancemeasurements

Therobustandsimplifieduncertaintybudgetdrawn-upbelowrequirestofulfiltwoconditionsforuseinanindustrialenvironment:

●Environmentalcondition

RH=(40±10)%andT=(23±3)°C.

Thisconditionallowstheusertodonotapplycorrectiononthemeasuredvaluesfromtemperatureandrelativehumidityeffects.

●SMMtip

Asmentionedbefore,iftheSMMmeasurementisperformedwithanunshieldedtip,asubtractionmethodshouldbeusedtodealwiththeparasiticcapacitances.TheperformanceofthistreatmentisimprovedwhenanAFMtipwithalargeformfactorastheparasiticcapacitancesarelessproneto

changeoverlocationinthisconfiguration.

3.3.2.SoftwareforSMMcalibration

ThesoftwaredevelopedbyMETASdedicatedtoSMMCalibrationcanbeused.ThemeasurementmodelisbasedontheOne-PortcalibrationalgorithmwellknownfromVNAmetrology.TheuserwillbeguidedthroughthemainstepsfromS11mrawdatatocorrectedS11data.AsdirectedbythemSOLtechnique[

5

],theuserselectsatleastthreestandardregions/patternsusingmasks.Itisthennecessarytoassignthereferencesstandardstothesemasks.Tocomputetheerrorterms,twosourcesofuncertaintiescanappearhere.Theonecomingfromthedefinitionofthestandards,theotherfromthemeasurementsystemitself.ThemathematicalpropagationoftheuncertaintiesisprovidedbythelibraryUncLib[

11

],alsodevelopedatMETAS.OncetheS11measurementsarecorrected,itisthen

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possibletodisplayvariousinformation,suchastheequivalentimpedance,resistance,andcapacitance,permittivityordopantdensity.Resultsaredisplayedintheformofmapscansofthecorrectedvaluesandassociateduncertainties.

4.Calibrationresults

ThecalibratedSMMwasusedtoperformelectricpropertiesmeasurementonvarioussamples.

4.1.CalibrationofSMMforcapacitancemeasurementsinNMI

TwoversionsofthecalibrationstructuresweremeasuredbytheSMM.AnSMMimagewasacquiredoverthefirstversion(A64)ofthecalibrationsampletoperformthecalibration,thenonthesecondversion(B03)whichservesastestsample,andfinallybackontheA64sampletochecktheinstrumentcalibration.Infigure7,theaveragerelativedeviationbetweenthecomputedandmeasuredcapacitanceofthetestsampleusingthecalibratedSMM.

Figure7.AveragerelativedeviationbetweenthecomputedandmeasuredcapacitanceofthetestsampleusingthecalibratedSMM.

Asystemicconstanterrorof8%isobservedbetweenthetwostructures.ItisbelievedthatadifferenceinthedielectricconstantoftheSiO2layerinbothstructures.Moreover,parasiticcapacitancemaystillbeunaccountedforinthefirstcalibrationsample.Additionalmeasurementsareplannedtobetterunderstandtheoriginofthisdeviation.

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4.2.CalibratedSMMmeasurementsofdielectricconstantonhigh-κmaterials

TheSMMcalibratedonthefirstversionofMC2calibrationkit(A64)wasusedtoperformcapacitancemeasurementovertwohigh-κsamples,namelyPZTandPMN-PT.ThosetwosampleswereprovidedtoLNEbyElectrosciencesLtd.Goldpadofvariousdiametersweredepositedontopofthehigh-κlayertoserveastopelectrodeofacapacitorinwhichthedielectricmaterialisthehigh-κlayer.Thecapacitancevalueassociatedwitheachgoldpadonthetestsamplesweremeasuredbythecalibratedsample.Thedimensionofthetopelectrodeandthicknessofthehigh-κlayerwasmeasuredwithacontrolleduncertaintyusingSEM(forthicknessmeasurement)andAFM(fortopelectrodearea)images.Numericalsimulationswereconductedtoestimatethedielectricconstantofthehigh-κlayerwithanuncertaintyof3.5%forthePZTsampleandof10.6%forthePMN-PTsampleduetodifficultyintheareadeterminationcausedbyaroughsurface.TheevolutionofthedielectricconstantofthePZTlayerasafunctionoftheexcitationfrequencywa