OpticalCrosstalkPreventioninCMOSImageSensorsCMOS图像传感器的光学串扰预防

OpticalCrosstalkinCMOSImageSensors

Introduction

Siliconphotodiode

Spectralcrosstalk

Electroniccrosstalk

Spatialcrosstalk

Inter-layer

Dielectric

Colorfilters

Fig.1.IllustrationofthethreetypesofcrosstalkinaCMOSimagesensor.

Methods

Finite-DifferenceTime-Domain(FDTD)Simulation

Tosimulatethepropagationoflightinsidetheimagesensor,weusedFinite-DifferenceTime-Domain(FDTD)simulation.FDTDiswell-suitedforsimulationofthebehavioroflightonasub-wavelengthscale,aregimewherediffractionandothercomplexphenomenadominate.Givenalayout,materialparameters(refractiveindex),andalightsource,thistechniqueexplicitlysolvesMaxwell’sequationsforelectricandmagneticfieldsatfinelyspaced(~10nm)gridpoints.Itthenmovesforwardintimebyaverysmallamount(~10-17sec,aboutthetimeittakeslighttotravelafewnanometers)andsolvestheequationsagainusingthepreviouslysolvedvalues.

Afteranumberoftimestepsdeemedsufficientforconvergencetoasteady-statesolution,theenergyflow,knownasthePoyntingvector,iscomputedanddisplayedasinFigure2.Inaddition,thepowerfluxfallingonanarbitrarysurface,suchastheactivepixelarea,iscalculated.TheconstructionoftheFDTDlayoutsanddisplayofthePoyntingvectorwiththepixelstructureoutlinedwasfacilitatedbyMatlabscriptsthatChrishadwritteninthecourseofhisresearchassistantship.

Fig.2.AsampleFDTDresult,showingthemagnitudeofthePoyntingvectorintheverticaldirectionasafunctionofpositioninthepixel.Thepixellayoutwasadaptedfromthescanningelectronmicroscopy(SEM)imagefromRhodes

ADDINEN.CITE<EndNote><Cite><Author>Rhodes</Author><Year>2004</Year><RecNum>8</RecNum><record><rec-number>8</rec-number><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Rhodes,H.</author><author>Agranov,G.</author><author>Hong,C.</author><author>Boettiger,U.</author><author>Mauritzson,R.</author><author>Ladd,J.</author><author>Karasev,I.</author><author>McKee,J.</author><author>Jenkins,E.</author><author>Quinlin,W.</author></authors></contributors><titles><title>CMOSimagertechnologyshrinksandimageperformance</title><secondary-title>MicroelectronicsandElectronDevices,2004IEEEWorkshopon</secondary-title></titles><periodical><full-title>MicroelectronicsandElectronDevices,2004IEEEWorkshopon</full-title></periodical><pages>7-18</pages><dates><year>2004</year></dates><urls></urls></record></Cite></EndNote>

[1]

.

FDTDPixelSimulation

Thespecificsoftwarepackagethatweused,OptiFDTD,iscapableoffullthree-dimensionalsimulation,butprocessingtimerestrictedourworktotwodimensions.TheparticulartypeofFDTDsimulationweusedwascontinuouswave,meaningthatonlyonewavelengthoflightisused.Sinceeachsimulationwasataspecificwavelength,werestrictedourworktothreewavelengthsrepresentativeofthecolorfiltersinaCMOSimagesensor:450nm(blue),555nm(green),and650nm(red).Thisalsomeansthatweonlyneededtoknowthematerials’characteristicsatthesewavelengths,althoughwesacrificeknowledgeaboutthebehavioroftheimagesensoratthein-betweenwavelengths.WeobtainedrefractiveindexdataforsomematerialsfromPalik

ADDINEN.CITE<EndNote><Cite><Author>Palik</Author><Year>1985</Year><RecNum>5</RecNum><record><rec-number>5</rec-number><ref-typename="Book">6</ref-type><contributors><authors><author>Palik,E.D.</author></authors></contributors><titles><title>Handbookofopticalconstantsofsolids</title></titles><dates><year>1985</year></dates><publisher>AcademicPressOrlando</publisher><urls></urls></record></Cite></EndNote>

[2]

andmadeapproximationsforothers.

Sinceweworkedintwodimensions,thesimulationsareacross-sectionalapproximationofanactualpixel.Giventhatwearemodelingafinitearea,itisimportanttodefinethesimulationbehaviorattheedgesofthedomain.Inthedirectionparalleltotheimagesensorplane,weusedperiodicboundaryconditionsthatwouldeffectively“wraparound”anyelectromagneticwavetotheotherside.Inthedirectionnormaltotheimagesensorplane,wesetabsorbingboundaryconditionssothatlightthatwasincidentontheseedgeswouldleavethedomain.

Evenwitharobustsimulationtool,theevaluationofcrosstalkisnotstraightforwardbecauseitisimpossibletoseparatethelightthatisintendedforonepixelfromthelightintendedforanotherpixel.Whileitissimpletorestricttheincominglighttothewidthofasinglepixel,thewavewillquicklyspreadoutduetodiffraction.AsaresultoftestsdonebyChrisduringhisresearchassistantship,itwasdecidedthatstronglyabsorbing“black”colorfilterswouldbeusedasthecolorfilteroftheneighboringpixel.Whilediffractionwouldstilloccurafterthecolorfilters,itwouldbelessdrasticandtakeplacefurtherdowntheopticalpath,reducingitsinfluence.

PixelStructure

Thepixelstructuresweremadetobegenericrepresentationsofcurrentexamplesinliterature.Althoughthestructurehasbeensignificantlysimplified,theoverallopticalcharacteristicsofthepixelarethesame.Thepixel,aslaidoutinOptiFDTD,isshowninFigure3anddescribedbelow.

Microlens

SiO2

Colorfilter

Si3N4

SiO2

Si

Fig.3.Two-pixelstructureasdefinedinOptiFDTD.Notethedifferentshadesofthecolorfiltersofthepixels.

Thelightfirsttravelsthroughair(n=1)andentersasphericalmicrolensofrefractiveindex≈1.6.Belowthelensisasilicondioxide(n≈1.46)layerthatactsasapassivationlayer.Nextisthecolorfilterlayerthatvariedaccordingtothesimulation,althoughforsimplicity,itisalwaysthesamethickness.Belowthisisasiliconnitride(n≈2.0)passivationlayer,followedbythethicksilicondioxideinterlayerdielectric(ILD).Thislayerwouldnormallycontainseverallayersofmetalinterconnects,buttheywereomittedduetowidevariationsinmetallayoutsamongdesigns,aswellastheirunpredictableelectromagneticeffects.Atthebottomofthepixelisthesilicon(n≈4.0)substratewheretheincidentlightisconvertedintoelectricalcurrent.

TomorepreciselyreproducethecharacteristicsofarealCMOSimagesensor,wherepixelcircuitryoftenoccupiesasignificantportionofthepixelspace,welimitedthelightcollectingareaofthesiliconsubstrate.Thisisrepresentedbythefillfactorofadesign,whichisthefractionofthepixelareadedicatedtocollectinglight.

DetailedMethodsforSpatialCrosstalkReduction

Forsimulationsofthecrosstalkreductionmethods,the1.75µmpixelpitchwaschosenasatechnologynodewhenopticalcrosstalklimitstheperformanceofthesensorandtheproposedmethodsmayfirstbeimplemented.Tolimitthenumberofsimulationsnecessary,alltestswereat650nm(red)light.Itwasexpectedthatthispartofthevisualspectrumwouldhavetheworstcrosstalkproblemsduetoincreaseddiffractionatlongerwavelengths.Theactive(light-collecting)portionofthesiliconsubstratewaslimitedtothecenter1.2µmofthepixel,afillfactorof47%.Toprovideparitybetweeneachlightguidingdesign,thespaceabovetheremaining0.55µmwasreservedformetalinterconnects,althoughtheywerenotincludedinthedesignforreasonsdiscussedearlier.

Forsimulationswherelightentersnormaltotheimagesensor,atwo-pixellayoutwasused,onepixelwitharedfilter,theotherblack.Takingtheperiodicboundaryconditionsintoaccount,thismimicsastructureofaninfinitelineofalternatingredandblackpixels.Unfortunately,two-pixelsimulationsforangledincidencewerenotsatisfactoryduetothenon-idealbehavioroftheperiodicboundaryconditionsforoff-axislight.Forthisreason,simulationsofoff-axisincidenceweredoneusingafour-pixelperiodicstructureandtheresultsforeachpixeltype(intendedorunintendedlightrecipient)representtheaveragevalueofthetwopixels.Previoussimulationshaveshownthattheresultsforon-axistwo-andfour-pixelsimulationsarenearlyidentical,sothecomparisonbetweenthetwoissound.Intheinterestoftime,thetwo-pixelon-axissimulationswereperformedwith5nmgridspacing,whilethefour-pixeloff-axissimulationsused10nmgridspacing.

Foroff-axissimulationsitwasnecessarytolaterallyshiftthemicrolensesandcolorfilterstoguidethelightontothecorrectphotodiode.Thisisdoneinrealimagesensorsaswell.Theoptimalshiftwasapproximatedthroughseveraltrialsandkeptconstantforallthelightguidingsimulations,exceptforthereferencepixel,whichrequiredalargershift.

Atotalofsixdifferentpixeldesigns(includingabaselinereferencedesign)weresimulatedatthreeangles(0,15,and25degrees)toobservetheperformanceofthecrosstalkpreventionmethods.Inthefollowingsections,wewillgiveashortoverviewoftotalinternalreflection(TIR)anditsimplicationsforthesedesigns,discusseachdesignindividually,andthenfollowwithaperformancecomparisonbetweenthetechniques.

TotalInternalReflection

Inordertounderstandhowtwoofthesetechniquesfunction,itisnecessarytomentiontotalinternalreflection.Whenlightisincidentonamaterialinterface,itisrefractedatanangleaccordingtoSnell’slaw:

(1)

Whengoingfromahighrefractiveindexmaterialtoalowerone,thereisanangleabovewhichthelightisreflectedinsteadofrefracted;thisiscalledthecriticalangle.Usingsimplegeometry,wecancalculatetheexpressionfortheincidentanglebelowwhichlightwillundergoTIR(heredefinedastheanglemeasuredfromthenormaloftheimagesensorplane)as

(2)

Accordingtothisequation,plottedinFigure4,ahigherindexcontrast(definedassoitisalwaysgreaterthanonewhenTIRispossible)yieldsahighermaximumincidenceangleforTIR,whichwewouldliketomakeashighaspossible.Thisequationisverysensitivetoevenasmallindexcontrast,asshownbythesharpriseinTIRangleastheindexcontrastincreases.

Fig.4.RelationshipbetweenthemaximumangleofincidenceforwhichTIRoccursandtheindexcontrast.

AirGap

ThistechniquetoconfinetheincidentlightreliesonTIRattheboundarybetweentheILD,inthiscasesilicondioxide,andanairvoidthatisformedattheedgeoftheactivepixelarea.Thismethodhasbeenrecentlydemonstratedinliterature

ADDINEN.CITE<EndNote><Cite><Author>Hsu</Author><Year>2005</Year><RecNum>2</RecNum><record><rec-number>2</rec-number><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Hsu,T.H.</author><author>Fang,Y.K.</author><author>Yaung,D.N.</author><author>Wuu,S.G.</author><author>Chien,H.C.</author><author>Tseng,C.H.</author><author>Yao,L.L.</author><author>Wang,W.D.</author><author>Wang,C.S.</author><author>Chen,S.F.</author></authors></contributors><titles><title><styleface="normal"font="default"size="100%">Ahigh-efficiencyCMOSimagesensorwithairgapinsituMicroLens(AGML)fabricatedby0.18-</style><styleface="normal"font="default"charset="161"size="100%">μ</style><styleface="normal"font="default"size="100%">mCMOStechnology</style></title><secondary-title>ElectronDeviceLetters,IEEE</secondary-title></titles><periodical><full-title>ElectronDeviceLetters,IEEE</full-title></periodical><pages>634-636</pages><volume>26</volume><number>9</number><dates><year>2005</year></dates><urls></urls></record></Cite><Cite><Author>Yaung</Author><Year>2003</Year><RecNum>4</RecNum><record><rec-number>4</rec-number><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Yaung,D.N.</author><author>Wuu,S.G.</author><author>Chien,H.C.</author><author>Hsu,T.H.</author><author>Tseng,C.H.</author><author>Lin,J.S.</author><author>Chen,J.J.</author><author>Lo,C.H.</author><author>Yu,C.Y.</author><author>Tsai,C.S.</author></authors></contributors><titles><title>Air-gapguardringforpixelsensitivityandcrosstalkimprovementindeepsub-micronCMOSimagesensor</title><secondary-title>IEDMTech.Dig</secondary-title></titles><periodical><full-title>IEDMTech.Dig</full-title></periodical><pages>1–16.5</pages><dates><year>2003</year></dates><urls></urls></record></Cite><Cite><Author>Hsu</Author><Year>2004</Year><RecNum>3</RecNum><record><rec-number>3</rec-number><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Hsu,T.H.</author><author>Fang,Y.K.</author><author>Yaung,D.N.</author><author>Wuu,S.G.</author><author>Chien,H.C.</author><author>Wang,C.S.</author><author>Lin,J.S.</author><author>Tseng,C.H.</author><author>Chen,S.F.</author><author>Lin,C.S.</author></authors></contributors><titles><title>Dramaticreductionofopticalcrosstalkindeep-submicrometerCMOSimagerwithairgapguardring</title><secondary-title>ElectronDeviceLetters,IEEE</secondary-title></titles><periodical><full-title>ElectronDeviceLetters,IEEE</full-title></periodical><pages>375-377</pages><volume>25</volume><number>6</number><dates><year>2004</year></dates><urls></urls></record></Cite><Cite><Author>Hsu</Author><Year>2005</Year><RecNum>7</RecNum><record><rec-number>7</rec-number><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Hsu,T.H.</author><author>Fang,Y.K.</author><author>Yaung,D.N.</author><author>Wuu,S.G.</author><author>Chien,H.C.</author><author>Wang,C.S.</author><author>Lin,J.S.</author><author>Tseng,C.H.</author><author>Chen,S.F.</author><author>Lin,C.S.</author></authors></contributors><titles><title>ColormixingimprovementofCMOSimagesensorwithair-gap-guardringindeep-submicrometerCMOStechnology</title><secondary-title>ElectronDeviceLetters,IEEE</secondary-title></titles><periodical><full-title>ElectronDeviceLetters,IEEE</full-title></periodical><pages>301-303</pages><volume>26</volume><number>5</number><dates><year>2005</year></dates><urls></urls></record></Cite></EndNote>

[3-6]

byengineersattheTaiwanSemiconductorManufacturingCompany(TSMC),whofoundthatitcouldsignificantlyincreaselighttransmissionandreducecrosstalk.ASEMimageofoneoftheirteststructuresisshowninFigure5(a)andanillustrationoftheairgapconceptisshowninFigure5(b).

(a)

(b)

Fig.5.SEMimage(a)andillustration(b)oftheairgapconcept,courtesyofHsuetal.

ADDINEN.CITE<EndNote><Cite><Author>Hsu</Author><Year>2005</Year><RecNum>2</RecNum><record><rec-number>2</rec-number><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Hsu,T.H.</author><author>Fang,Y.K.</author><author>Yaung,D.N.</author><author>Wuu,S.G.</author><author>Chien,H.C.</author><author>Tseng,C.H.</author><author>Yao,L.L.</author><author>Wang,W.D.</author><author>Wang,C.S.</author><author>Chen,S.F.</author></authors></contributors><titles><title><styleface="normal"font="default"size="100%">Ahigh-efficiencyCMOSimagesensorwithairgapinsituMicroLens(AGML)fabricatedby0.18-</style><styleface="normal"font="default"charset="161"size="100%">μ</style><styleface="normal"font="default"size="100%">mCMOStechnology</style></title><secondary-title>ElectronDeviceLetters,IEEE</secondary-title></titles><periodical><full-title>ElectronDeviceLetters,IEEE</full-title></periodical><pages>634-636</pages><volume>26</volume><number>9</number><dates><year>2005</year></dates><urls></urls></record></Cite></EndNote>

[3]

Notethespaceinbetweentheairgapstoallowthemetalinterconnectstorunthroughthestructure.AGGRstandsforAirGapGuardRing.

Thebenefitofsuchadesignistwo-fold.First,lightinsidethepixellighttunnelatananglelessthanthecriticalangleoftheoxide-airinterfaceshouldbereflectedandlandonthephotodiode.Second,anylightthatdoesnotundergoTIRattheoxide-airinterfaceisrefractedatamoreverticalangle,meaningthatitwilltravellessdistancelaterallyandhavelesslikelihoodofreachingtheactiveareaoftheadjacentpixel.Givenanindexcontrastbetweensilicondioxideandairof1.46,wewouldexpectacriticalangleofover46°,morethansufficientformostsensors.Inrealsituations,thisairgapwouldhavearoundedshape,butwasapproximatedasrectangularforsimplicity.

Theairgapsareformedbyselectivelyetchingawayanearlyverticallineofoxidewheretheairgapsshouldbe.Thenafilmisdepositedontopthatpinchesofftheholeandsealstheairgap.Whilethisseemssimple,theprocessisquitedifficultandcaremustbetakentoensurethatothermaterialsdonotresideinthevoids.

Otherthanthespacingoftheairgaps,whichwaspresetforthisstudytokeepthecomparisonbetweenthetechniquesfair,thereistheadditionaldegreeoffreedomofthewidthofthegaps.Forverynarrowairgaps,itispossiblethatlightmay“leak”throughthegapevenwhenitshouldbereflected.Totestthiseffect,twoairgapwidthsof0.1µmand0.2µmweresimulated.

LightGuide

Thelightguidemethodoperatesonaprincipleverysimilartotheairgapmethod.Insteadofcreatingalow-indexareabetweenthepixels,therefractiveindexofthepixelcentermaterialisincreased.Thistechniquehasbeenrecentlyexplored

ADDINEN.CITE<EndNote><Cite><Author>Hsu</Author><Year>2004</Year><RecNum>1</RecNum><record><rec-number>1</rec-number><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Hsu,T.H.</author><author>Fang,Y.K.</author><author>Lin,C.Y.</author><author>Chen,S.F.</author><author>Lin,C.S.</author><author>Yaung,D.N.</author><author>Wuu,S.G.</author><author>Chien,H.C.</author><author>Tseng,C.H.</author><author>Lin,J.S.</author></authors></contributors><titles><title>LightguideforpixelcrosstalkimprovementindeepsubmicronCMOSimagesensor</title><secondary-title>ElectronDeviceLetters,IEEE</secondary-title></titles><periodical><full-title>ElectronDeviceLetters,IEEE</full-title></periodical><pages>22-24</pages><volume>25</volume><number>1</number><dates><year>2004</year></dates><urls></urls></record></Cite></EndNote>

[7]

bythesamegroupatTSMCwithsomesuccess,althoughthelimitedindexcontrastachieved(1.02)wouldonlycauseTIRforangleslessthanabout10°.

(a)

(b)

Fig.6.IllustrationsdescribingthebenefitsofTIR(a),wherelightispreventedfromleavingtheintendedpixel,andrefraction(b),wherethelateraltravelofnon-reflectedlightisreduced,forthelightguidemethod.CourtesyHsuetal.

ADDINEN.CITE<EndNote><Cite><Author>Hsu</Author><Year>2004</Year><RecNum>1</RecNum><record><rec-number>1</rec-number><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Hsu,T.H.</author><author>Fang,Y.K.</author><author>Lin,C.Y.</author><author>Chen,S.F.</author><author>Lin,C.S.</author><author>Yaung,D.N.</author><author>Wuu,S.G.</author><author>Chien,H.C.</author><author>Tseng,C.H.</author><author>Lin,J.S.</author></authors></contributors><titles><title>LightguideforpixelcrosstalkimprovementindeepsubmicronCMOSimagesensor</title><secondary-title>ElectronDeviceLetters,IEEE</secondary-title></titles><periodical><full-title>ElectronDeviceLetters,IEEE</full-title></periodical><pages>22-24</pages><volume>25</volume><number>1</number><dates><year>2004</year></dates><urls></urls></record></Cite></EndNote>

[7]

Thisstructureisformedbysimplyetchingawaythematerialovertheactivepixelareaanddepositingahigher-indextransparentmaterial.Themaindifficultyhereisthatthereplacementmaterialmustsatisfyseveralrequirements.First,itmustbeopticallytransparent,otherwiseitwillabsorblightandthesensorlightsensitivitywilldecrease.Second,itmustbeelectricallyandmechanicallycompatiblewiththeothermaterials.Finally,itmusthavearefractiveindexhighenoughtopromoteTIRofasufficientrangeofangles.Itisalsoimportanttoconsiderthatachangeinrefractiveindexofthelighttunnelmaterialwillaffecttheopticalpropertiesofthepixelevenforperfectlynormalincidence.

Simulationswereperformedusingtwolightguidematerialswithrefractiveindicesof1.6and1.8,correspondingtocriticalanglesof24.1°and35.8°.Theserepresentcaseswherethereissignificantindexcontrastandnoabsorption.Thewidthofthelightguideisequaltothewidthoftheactivepixelarea(1.2µm).

MetalMirrors

Thismethodrepresentsanear-idealcasewheremirrorsreflectallincidentlight,regardlessofincidentangle,confiningittothepixelcenter.Themirrorswouldbemadeofaluminum,thesamematerialusedforthemetalwires.Therehavenotbeenanypublicationsofthistechniquetodate,whichisnotsurprisinggiventhepotentialdifficultiesinfabricatingit,aswellasadverseelectricalandmechanicaleffectsassociatedwithagreatamountofadditionalmetal.

Simulationsofthemetalmirrortechniqueused0.1µmthickwallsofmetalplacedsimilartotheairgaplayout.

Results/Discussion

ReferencePixel

AsthePoyntingvectorplotsshow,thereisasignificantamountofdiffractionthatcausesthelighttospreadout,evenatnormalincidence.Thespreadingisamplifiedatoff-axisincidence,ascanbeseeninFigure8.AllPoyntingvectorplotshavebeenenhancedtobringoutdetail;althoughitmayappearthatlightisleakingthroughtheblackfilter,theactualpowerisnegligible.Notethatthetransmissiondecreasesandcrosstalkincreasessignificantlywithincreasingangle,evenwitharoughoptimizationofthemicrolensandcolorfiltershift.

Fig.7.Poyntingvectorplotforthereferencepixelfornormalincidence.

Fig.8.Poyntingvectorplotforthereferencepixelat25°incidence.

(a)

(b)

Fig.9.Transmission(a)andcrosstalk(b)versusincidentangleforthereferencepixel.

AirGap

Theairgapresultsdemonstrateastrongdependenceonthethicknessofthegap.Forthe0.1μmvoid,thereisasignificantamountofcouplingtotheothersideofthegap.Inthe0.2μmcase,thereislesscoupling,buttheincreasedwidthofthegapsallowsasmallerapertureforthelighttoenter.Thelattereffectdominatesatnormalincidence,wherethethinnervoidshaveahighertransmissionandlowercrosstalk.Atanangle,however,thecouplingthroughthegapisenhanced,leadingtodecliningtransmissionandincreasingcrosstalk.AsFigures11and12show,thewiderairgapisabletoconfinethelightmoreefficientlyandthereforeperformsbetterforoff-axisincidence.

(a)

(b)

Fig.10.Poyntingvectorplotsforthe0.1μmairgap(a)and0.2μmairgap(b)designsfornormalincidence.

Fig.11.Poyntingvectorplotforthe0.1μmairgapdesignat25°incidence.

Fig.12.Poyntingvectorplotforthe0.2μmairgapdesignat25°incidence.

(a)

(b)

Fig.12.Transmission(a)andcrosstalk(b)versusincidentangleforthetwoairgapandreferencepixels.

LightGuide

Thelightguidedesignsshowsimilartradeoffsastheairgapdesigns.Atnormalincidence,bothsuppressthecrosstalk,butthen=1.8designtransmitslesslightbecauseitshigherrefractiveindexcausesincreasedreflection,whichwasverifiedinthesimulations.Foroff-axisincidence,however,thehigher-indexlightguideconfinesthelightmuchmoreeffectively,leadingtovastlyhighertransmissionandlowercrosstalk.TheimprovedopticalconfinementcanbeseeninthePoyntingvectorplotsbygenerallylowervaluesoutsideofthelightguideofthetargetpixel.

(a)

(b)

Fig.13.Poyntingvectorplotsforthen=1.6lightguide(a)andn=1.8lightguide(b)designsfornormalincidence.

Fig.13.Poyntingvectorplotforthen=1.6lightguidedesignat25°incidence.

Fig.14.Poyntingvectorplotforthen=1.8lightguidedesignat25°incidence.

(a)

(b)

Fig.15.Transmission(a)andcrosstalk(b)versusincidentangleforthetwolightguideandreferencepixels.

MetalMirrors

Asexpected,themetalmirrordesignperformedverywellduetoitsabilitytoreflectlightatanyangle.Aluminumisaverygoodreflector,asdemonstratedbythelackoffieldpenetrationintothemetal,sothelossintransmissionathigheranglesisnotduetoabsorptionbuttolightmissingthetopaperture.Astheresultsshow,crosstalkisincrediblylow,lessthan0.03%forallangles.

Fig.16.Poyntingvectorplotforthemetalmirrordesignfornormalincidence.

Fig.17.Poyntingvectorplotforthemetalmirrordesignat25°incidence.

(a)

(b)

Fig.18.Transmission(a)andcrosstalk(b)versusincidentangleforthemetalmirrorandreferencepixels.

Comparison

Lookingattheresults,itisevidentthatthebestsolutionfortheon-axiscase,then=1.6lightguidedesign,wasamongtheworstperformersathighanglesofincidence.Themostrobustcrosstalkpreventionmethods,meaningthosethatperformedwellregardlessofangle,werethehigh-indexlightguideandmetalmirrordesigns.Notethatthereisawiderangeoftransmissionandcrosstalkvaluesamongthedifferenttests,especiallyforthe25degreecase.Itisalsoimportanttoobservethatsomedesignsperformedworsethanthebaselineincertainsituations.

(a)

(b)

Fig.19.Plotsofthetransmission(a)andcrosstalk(b)foralltesteddesigns.

Asafurthercommentonthemethodstested,itisimpor