01-Optical-Lithography

NCheungEE243Sp2002Lec71OpticalLithography•AerialImageFormation-Fraunhoferdiffraction-ModulationTransferfunctionMTF-CoherenceFactor-DepthofFocus,LensAberration•PhotoresistExposure-DillModel,A,B,Cparameters•PhotoresistDevelopment-MackModel•LithographySimulatorsCaseStudies•PhaseShiftMask•OpticalProximityCorrection•Off-AxisIlluminationNCheungEE243Sp2002Lec72SuggestedReadingforOpticalLithographyCampbell,Chap7and8–Requirements,Opticalsystems,mechanisms•Handout-OpticalLithographyModeling(NeureutherandMack)LithographyHandbookfromSPIE,Chapter7Plummer,pp.247-277–ModelingUsefulreferences“IntroductiontoFourierOptics”byGoodman“Microlithography-ScienceandTechnology”bySheatsandSmith,Marcel&Dekker,Chapters2and3[Sheats]NCheungEE243Sp2002Lec73MethodologiesforsmallfeatureprintingNCheungEE243Sp2002Lec74FlowDiagramofLithographyModel“Dill”ModelNCheungEE243Sp2002Lec75OpticalLithographyRequirements:•CriticalDimensionresolution•LargeDepthoffocusforroughtopography•Highthroughput•Largeopticalfieldsize(large#ofpixels/field)•Defect-freeprinting•LargeprocesslatitudeNCheungEE243Sp2002Lec76PrimaryProjectionPrintingConsiderations1)Minimumfeatureresolutionlm=K1(λ/NA)2)DepthofFocusDOF=K2λ/(NA)2•LargeNAhascontradictoryeffectsNCheungEE243Sp2002Lec77Photonsources•HgArclamps436(G-line),405(H-line)and365(I-line)nm•Excimerlasers:KrF(248nm)andArF(193nm)•Laserpulsedplasma(13nm,EUV)SourceMonitoring•Filterscanbeusedtolimitexposurewavelengths•Intensityuniformityhastobebetterthanseveral%overthecollectionarea•NeedsspectralexposuremeterforroutinecalibrationduetoagingNCheungEE243Sp2002Lec78NumericalAperture•NA=(radiusoflensaperture)/(focuslength)~sinθ•Sincetheobjectivelensservesasalow-passfilterforthemaskpatternspatialfrequency,alargerNAcancollectmorediffractedbeamsfromhigherspatialfrequencies(i.e.,smallerfeatures)Note:ForalenssystemwithdemagnificationfactorM(1),theNAseenatthewaferNAW=NAlens(1+1M).NAusuallyreferstotheNAWvalue.ϑFocalPlaneApertureObjectiveLensImageNCheungEE243Sp2002Lec79•F-number=1/(2NA)•NAversusFieldsizeforcommercialopticallens:ImageFieldDiamterNA•LetLwidthbetheresolution,thepixelareawillbeLwidth2.Therefore,thenumberofpixelsperexposureallowedis(Fieldsize/Lwidth)2NCheungEE243Sp2002Lec710AerialImagesformedbyContactPrinting,ProximityPrintingandProjectionPrintingNCheungEE243Sp2002Lec711ProjectionPrintingProximityPrintingNCheungEE243Sp2002Lec712WhyResolution∝(λ/NA)xxopticalsystemImageonwaferMaskIntensityImaxONCheungEE243Sp2002Lec713waferplanegratingwithspatialfrequency1/P...,2,1,0sin±±==nnPλφ-1-2+20QualitativeExplanationofimagedegradationbylensφθMasklens+1parallelopticalbeamLLlmsinθ=NAoflensP=2LPNCheungEE243Sp2002Lec714ImageContrastCxImaskImaxImin(x)ContrastDegradesWhenPassedThroughanOpticalSystem10+−≡CIIIICminmaxminmaxNCheungEE243Sp2002Lec715SpatialCoherenceofPhotonSourceCompletelyCoherentSourcePartiallyCoherentSourceCoherencefactorσ=0Coherencefactorσ0NCheungEE243Sp2002Lec716ExampleFraunhoferDiffractionCalculationIntensityduetoapointsourceimagedthroughacircularaperture[monochromatic,coherent][SeeJ.W.Goodman,“IntroductiontoFourierOptics”forderivation.]NCheungEE243Sp2002Lec717Letthepointsourcebeatxo=0,yo=0withunityintensity.Forapupilfunction:P(x,y)≡1forx2+y2≤R≡0forx2+y2≥RTheE-fieldatxi,yiisproportionaltotheFourier-BesselTransform(i.e.Fouriertransformincylindricalcoordinates)oftheE-fieldatxo,yo.∴E(xi,yi)∝J1(s)swithS=2πNAλx2i+y2i∴I(xi,yi)=E22∝J1(s)s2“TheAiryPattern“whereJ1(s)=BesselFunctionoftheFirstKindNCheungEE243Sp2002Lec718TheI(xi,yi)hasthefirstzeroats=3.83oratr=x2i+y2i=0.61λNA∴TheAiry“disk”hasadiameterof1.2λNANCheungEE243Sp2002Lec719Rayleigh’sCriterionforimageresolution•Twopoints’imagesaredistinguishableiftheAirydisksdon’toverlap.•∴∆x≥0.61λNAfordiffractionlimitedopticsNCheungEE243Sp2002Lec720OtherFraunhoferDiffractionExamplesfx=x’/(zλ)wherezisthedistanceawayfrommaskNCheungEE243Sp2002Lec721EffectofFourierComponentsonaerialimageNCheungEE243Sp2002Lec722Off-normalIncidenceAnglePartiallyCoherentIlluminationNCheungEE243Sp2002Lec723GenericProjectionPrinterNCheungEE243Sp2002Lec724NCheungEE243Sp2002Lec725MTFAnalysisofDiffractionLimitedOpticalSystems(A)CoherentIlluminationLetusconsideranopticalsystemwithanexitapertureofradiusRandnumericalapertureNA.Foranobjectpointsourcewithunitfieldamplitudeatxo=0andyo=0,thefieldamplitudeh(xi,yi)ontheimageplaneistheFraunhoferdiffractionpattern:h(xi,yi)=(NAλR)2⌡⌠-∞+∞⌡⌠-∞+∞P(x,y)exp[-2πi(xix+yiy)(λR/NA)]dxdy[1]whichisbasicallytheFouriertransformofthepupilfunctionP(x,y):ObjectPlaneImagePlaneRProjectionLensAperturexyixyooiNCheungEE243Sp2002Lec726P(x,y)=1forx2+y2£R=0forx2+y2R[2]Directintegrationgives:h(xi,yi)=p1/2(NAl)[2J1(s)s]withs=(2pNAl)xi2+yi2[3]Thesquareofh(xi,yi)givestheintensityoftheobjectpointsourceontheimageplanewhichisanAiryfunction.AfiniteobjectwillhavefieldamplitudeEo(xo,yo)atposition(xo,yo).Atanyposition(xi,yi)ontheimageplane,thetotalfieldamplitudeEi(xi,yi)willbesummationofthecontributionsfromallpositionsoftheobject[i.e.convolutionofhandEo]:Ei(xi,yi)=õó-¥+¥õó-¥+¥h(xi-xo,yi-yo)Eo(xo,yo)dxody