ferroelectric thin-film waveguides in integrated optics and optoelectronics

title: FerroelectricThin-filmWaveguidesinIntegratedOpticsandOptoelectronics

author: Prokhorov,A.M.;Khachaturian,O.A.publisher: CambridgeInternationalSciencePublishing

isbn10|asin: 189832610Xprintisbn13: 9781898326106ebookisbn13: 9780585119229

language: English

subject Ferroelectricthinfilms,Integratedoptics,Opticalwaveguides.

publicationdate: 1996lcc: TA1520.P761996ebddc: 548.8

subject:Ferroelectricthinfilms,Integratedoptics,Opticalwaveguides.

FerroelectricThin-FilmWaveguidesinIntegratedOpticsandOptoelectronics

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FerroelectricThin-FilmWaveguidesinIntegratedOpticsandOptoelectronics

AMProkhorov,YuSKuz'minov,OAKhachaturyan(GeneralPhysicsInstitute,RussianAcademyofSciences,Moscow)

TranslatedfromtheRussianbyMariannaTsaplina

CAMBRIDGEINTERNATIONALSCIENCEPUBLISHING

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PublishedbyCambridgeInternationalSciencePublishing7MeadowWalk,GreatAbington.CambridgeCB16AZ,England

FirstpublishedApril1996

ConditionsofsaleAllrightsreserved.Nopartofthispublicationmaybereproducedortransmittedinanyformorbyanymeans,electronicormechanical,includingphotocopy,recording,oranyinformationstorageandretrievalsystem,withoutpermissioninwritingfromthepublisher

BritishLibraryCataloguinginPublicationDataAcataloguerecordforthisbookisavailablefromtheBritishLibrary

ISBN189832610X

ProductionIrinaStupakPrintedbyStEdmundsburyPress,BuryStEdmunds,Suffolk,England

ContentsPreface ix

Symbols xi

Introduction xiii

1Epitaxialfilmsofcomplexoxidecompounds

1.1Vacuumepitaxy 2

1.2Gas-transportepitaxy 4

1.3Filmsdepositedbyifsputtering 8

1.3.1ThinfilmsofLiNbO3depositedonasapphiresubstrate

1.3.2TungstenbronzeferroelectricK3Li2Nb5O15 13

1.3.3KNbO3thinfilms 14

1.3.4KTaxNb1-xO3thinfilms 16

1.3.5.Thinfilmsbypulsedlaserdeposition 17

1.3.6.WaveguidesbyMeVHeionimplantation 20

1.3.7Stripwaveguides 21

1.3.8Doublewaveguide 23

1.4Autodiffusedlayersinlithiumniobateandlithiumtantalate

1.4.1Out-diffusionkinetics 27

1.5Thediffusionmethodformetalsandoxides 33

1.5.1Diffusionoftransitionmetals 37

1.5.2Titaniumdiffusion 41

1.5.3Copperdiffusion 49

1.6Proton-exchangedLiNbO3waveguides 51

1.6.1Ion-exchangeprocessesinLiNbO3 53

1.6.2Samplepreparationandexperimentalmethods 54

1.6.3Annealedproton-exchangedwaveguides 56

1.6.4Waveguidesfabricatedusingbufferedmelts 59

1.6.5Protondiffusion 63

1.6.6Waveguidesusingcinnamicacid 64

1.6.7Proton-exchangewaveguidesofMgO-dopedandNd:MgO-dopedLiNbO3

1.7Planarion-exchangedKTiOPO4waveguides 69

2Liquid-phaseepitaxyofferrolelectrics

2.1Theepitaxialgrowthbymelting(EGM) 74

2.2Thecapillaryliquidepitaxial(CLE)technique 78

2.2.1CLEgrowthprocedure 79

2.2.2.CLEgrowthandcrystalquality 80

2.3Theliquid-phaseepitaxy(LPE)technique 83

2.4Physico-chemicalbasisofcapillaryliquid-phaseepitaxy

2.4.1ThephasediagramofLiVO3-LiNbO3 91

2.4.2PhasediagramofLiVO3-Li(Nb,Ta)O3pseudobinarysystem

2.4.3Theschemeofthegrowthcell 95

2.5KineticsofepitaxialgrowthofLiNbO3 97

2.5.1Thestationarycrystallizationmodel 97

2.5.2Epitaxyundernon-isothermicconditions 100

2.5.3DeterminationofsupersaturationUanddiffusioncoefficientD

2.5.4Epitaxyunderisothermalconditions 106

2.6CrystallizationoffilmsfromLiNb1-yTayO3solidsolutions

2.6.1Liquid-phaseepitaxialgrowthofLi(Nb,Ta)O3films

2.7ThinfilmsofLiNbO3dopedwithdifferentelements

2.8Epitaxialferroelectricfilmswithperovskitestructure

2.8.1Liquid-phaseepitaxyofpotassiumniobate 119

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2.8.2Growthofpotassiumlithiumniobatefilmsonpotassiumbismuthniobatesinglecrystals

2.9Diffusionliquid-phasemethodofgrowingimmersedwaveguidechannels

2.9.1Striplinestructures 124

2.9.2Symmetricwaveguides 124

2.10GrowthofepitaxialfilmsintheKTiOPO4familyofcrystals

3Influenceofelectriccurrentuponliquid-phaseepitaxyofferroelectrics

3.1.Electricfieldandcrystallization 131

3.1.1Bulkcrystallization 131

3.1.2Thinfilms 134

3.1.3Liquid-phaseelectroepitaxy 136

3.2Physicalbasisofliquid-phaseelectroepitaxy(Thetheoryofthemethod)

3.2.1Temperaturedistributioninasystemundertheactionofanelectriccurrent

3.2.2Filmgrowthrate 141

3.2.3Chemicalcompositioncontrolofthefilm 142

3.2.4Initialstagesofnucleation 143

3.3Theroleofthermoelectriceffectsinthecourseofliquid-phaseelectroepitaxyofferroelectrics

3.4Electro-LPEgrowthoflithiumniobate-tantalatefilms

3.4.1Epitaxialgrowth 152

3.4.2Electrochemicalprocessesintheliquidphase 152

3.4.3Growthkineticsofelectro-LPEgrownlithiumniobate-tantalatefilms

3.5OptimizationofconditionsofepitaxialgrowthoflithiumniobatefilmswithallowanceforJouleheat

4Structureandcompositionoflightguidingfilms

4.1Structureandphysico-chemicalpropertiesoflithiumniobateandtantalatecrystals

4.2X-raydiffractionanalysisoffilms 173

4.2.1Layercomposition 174

4.2.2Monocrystallinityandinterplanardistances 175

4.2.3Measurementofstrainsinthediffusedlayer 178

4.2.4Tidistributionindiffusedlayers 181

4.2.5Thestructureofproton-exchangedLiNbO3 182

4.2.6Orientationrelations 184

4.3Morphologyandperfectionoflayers 185

4.3.1Micromorphologyoffilmsurfacefordifferentcrystallographicorientationsofthesubstrate

4.3.2Diffusion-induceddefectsinfilms 188

4.4Substrate-filminterfaceandtransitionregion 190

4.5Dislocationstructure 191

4.6Domainstructure 196

4.6.1Epitaxialfilmonadomainboundaryofthesubstrate

4.6.2Domainconfigurationsinfilms 198

4.6.3Microdomainsinsubstratesandinepitaxiallayers

4.6.4PeriodicallyinverteddomainstructuresinLiTaO3andLiNbO3usingprotonexchange

4.6.5Waveguideperiodicallypoledbyapplyinganexternalfield

4.6.6DomaininversioninLiNbO3usingdirectelectron-beamwriting

4.7Annealing-inducedvariationofthephasecompositionandcrystallinestructureofthelithiumniobatecrystalsurface

4.7.1Annealing-inducedvariationofthecrystallinestructureofthelithiumniobatecrystalsurface

4.7.2Annealing-inducedvariationofthephasecompositionofthelithiumniobatecrystalsurface

5Physicalpropertiesofwaveguidelayers

5.1Opticalpropertiesoflithiumniobateandtantalatesinglecrystals

5.2Opticalwaveguidemodesinsingle-crystalfilms 215

5.2.1Waveguideandradiationmodes 216

5.2.2Waveequationandfielddistribution 221

5.2.3OpticalmodesinepitaxialLi(NbTa)O3waveguides

5.2.4Characteristicsofout-diffusedwaveguides 229

5.2.5Propertiesofdiffusedwaveguides 234

5.3Secondharmonicgenerationinwaveguides 237

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5.3.1Phasematchinginanopticalwaveguide 239

5.3.2Overlapoffieldsofinteractingmodes 240

5.3.3Angularmatching 241

5.3.4Temperaturematching 244

5.3.5Second-harmonicgenerationinawaveguidewithperiodicallydomain-invertedregions

5.3.6Effectofprotonexchangeonthenonlinearopticalproperties

5.3.7Sum-frequencygenerationinwaveguides 253

5.4SecondharmonicgenerationintheformofCherenkovradiation

5.5Electro-opticeffectsinopticalwaveguides 258

5.6Lightresistanceoflightguides 260

5.7Photorefractivepropertiesoflightguides 264

5.7.1Holographicformationofgratingsinopticalwaveguidelayers

5.7.2PhotorefractiveeffectinplanarTi-diffusedguides

5.7.3Relaxationofindexchange 274

5.7.4Photorefractiveeffectinannealedproton-exchangedLiNbO3waveguides

5.8Energylossinwaveguides. 279

5.8.1LossesinTi-diffusedLiNbO3waveguides 279

5.8.2Absorptionlossinstripguides 282

5.8.3Lossinepitaxialwaveguides 284

5.9Ferroelectricpropertiesofwaveguides 285

5.9.1Dielectricproperties 285

5.9.2Pyroelectricproperties 287

5.9.2.1Thelow-frequencysinusoidaltemperaturemodulationmethod

5.9.2.2Thethermalpulsemethod 287

5.10Temperaturedependenceofthermoelectriccoefficientsoflithiumniobateandlithiumtantalate

6Thin-filmstructureinintegratedoptics

6.1Principalcharacteristicsofwaveguidingelectro-opticmodulators

6.1.1Controlvoltage 293

6.1.2Bandwidth 295

6.1.3Modulationdepthandinsertionlosses 297

6.2Photoinducedpolarizationconversion 298

6.3WaveguidemodulatorsonthebasisofTi:LiNbO3 300

6.3.1Electro-opticmodulatoroncoupledchannelwaveguideswithavariableDb

6.3.2Interferometricandperfectinnerreflectionmodulators

6.4Practicalexamplesofwaveguideelectro-opticmodulators

6.4.1Opticalwaveguideswitchmodulator 308

6.4.2Thin-filmelectro-opticlightmodulator 311

6.4.3Braggdiffractionmodulator 315

6.4.4Ridgewaveguidemodulator 317

6.4.5Ti-diffuseddiffractionmodulator 320

6.4.6InterferometricMach-Zehndermodulator 326

6.4.7Electro-opticphotorefractivemodulator 328

6.4.8KNbO3inducedwaveguidecut-offmodulator 331

6.5Waveguideelectro-opticpolarizationtransformer 334

6.6Lightbeamscanninganddeflectioninelectro-opticwaveguides

6.7Electro-opticallytunablewavelengthfilter 342

6.8Flip-chipcouplingbetweenfibresandchannelwaveguides

6.9KTiOPO4waveguidedevicesandapplications 349

6.9.1PhasematchinginperiodicallysegmentedKTiOPO4waveguides

Conclusions 356

References 357

Index 371

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PrefaceThisbookisalogicalcontinuationofthetwopreviousbooksbytheauthors1whichwerepublishedintheAdamHilgerseries.Altogether,thesethreebooksprovideacompleteenoughpictureofapplicationofferroelectriccrystalsandfilmsinlaserradiationcontrol.Thisvolumeisdevotedtoferroelectricthin-filmwaveguidesforintegratedopticsandoptoelectronics.Wedealherewiththemostwell-knownmethodsofobtainingthin-filmstructures.Ourprimeconcernisliquid-phaseepitaxyfromalimitedmeltbulkwithandwithoutapplicationofanelectricfield.Amethodispresentedwhichcombinesliquid-phaseanddiffusiontechniquesforobtainingstructureswithaprescribedconfigurationofwaveguidechannels.Adetainedconsiderationisgiventophysico-chemicalpropertiesofthinferroelectriclayers,suchasmorphology,domainstructureofatransitionlayerandferroelectricproperties.Animportantroleforpracticaluseaselectro-opticmodulators,deflectorsandtransducersisplayedbytheopticalproperties,modecompositionofpropagatingradiation,secondharmonicgeneration,electro-opticproperties,photorefraction,destructionthresholdandlightloss.Alltheseaspectshavefoundreflectioninthebook.Examplesofpracticaluseofopticalwaveguidesaregiven.

Thebookmaybeinstructiveforexpertsinthefieldofintegratedopticsandoptoelectronics,aswellasforstudentsinterestedinthecorrespondingtopics.

A.M.PROKHOROVYU.S.KUZ'MINOVO.A.KHACHATURYANMOSCOW1995

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ListofSymbolsAH,CH -latticeparameters

Bij -dielectricimpermeabilitytensorrC -electrodecapacitancec -thermalconductivityc -concentrationd -interelectrodegapdij -nonlinearopticalcoefficientd -thicknessds -elementofthelightpathD -diameterD -diffusioncoefficientD -electricinductivitye -electronchargeE -electricfieldstrengthEx,Ey -electricfieldcomponentsgij -componentsofquadraticelectrooptic

coefficientG -electrodewidthh -heightI -lightintensityj -chargedparticleflowJv -concentrationgradientJ -currentdensityJr -nthorderBesselfunctionk -coefficientofsegregationk=2pn/l.

-propagationconstant

k -thermalconductivity

K(k) -completeellipticintegralKTP -KTiOPO4l -lengthL -pathlengthL -interactionlengthM -molecularweightM -numberofmodesno,ne -ordinaryandextraordinaryrefractive

indicesNi -molarfractionPL -Langmuirvapourpressurep -pressurePo -saturatedvapourpressureP -poweroflightPout -outputpowerPin -inputpowerP -dielectricpolarisationPs -spontaneouspolarisationPijml -photoelastictytensorq -kineticcoefficientQD -activationenergyfordiffusionQv -activationenergyforvaporisationQij -electrostrictivecoefficientr -radiusrij -linearelectroopticcoefficientR -resistanceRi -reflectivitys -distanceS -complianceS -areaSi -principalstrainSAW -surfaceacousticwavest -time

T -temperatureTEi -wavemodesU -supersaturationn -velocityofzonemotionV -voltagebetweenelectrodesW -electrodewidthzef -effectiveparticlechargea -energyofformationofunitsurfacea -coolingratea -insertionlossai -electronicpolarisabilitya -evaporationcoefficienta0 -inverseaccommodationcoefficienta -numberofatomsperunitvolumea -overlapparameterb -propagationconstantintheguidebi -wavevectorsG -normalisedoverlapintegraldij -KroneckersymbolDn -refractiveindexchangeDm -variationofchemicalpotentialDlr -shiftofthecentrewavelengthe -dielectricpermitivitye0 -dielectricpermitivityinavacuumx -appliedelectricfieldh -phasemodulationindexq -diffractedangleqB -Bragganglel -wavelengthl0 -free-spacewavelengthlL.S -heatconductivitiesofsourceandliquidl -specificheatofcrystallisationL -gratingperiodicity

m -mobilityn -molefractionP -Peltiercoefficientr -liquid-phaseresistivity

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r -density

s -surfacetensions -supersaturations -stresst -diffusiontimetp -precipitationtimet -switchingtimetT -Thomsoncoefficientt -thicknessj -phaseshiftj -overallphasefactork -couplingconstantw -modefieldwidth

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IntroductionAnincreasednumberofcomplicatedelectronandopticalsystemsstimulatesthedevelopmentofoptoelectronics.Theanalysisoftendenciesinthedevelopmentofappliedphysicspointsouttheimportantrolethedielectricmaterialsand,firstofall,non-centrosymmetricpiezo-andferroelectricsplayintheformationofnewtrendsinelectronics(LinesandGlass1981).

Aninevitableincreaseinthevarietyofthin-filmferroelectricstructuresthatarewidelyusedinthenewtrendsofappliedphysicsbringsaboutimprovementintechnologyanddetailedstudiesofthevariousphysico-chemicalpropertiesofsubstances.Thispromotesfurthercreationofmaterialswithpredeterminedphysicalpropertiesthatareoptimumforconcreteapplicationsinengineering(Miyazawa1980;Tomashpol'sky1984;Khachaturyanetal.1984).

Singlecrystalsofactivedielectricsandferroelectricspossessinganinterestingcombinationofelectro-,acousto-andnonlinearopticalpropertiesarepromisingmaterialsfordesigninghighlyefficientdiscreteelementsofintegratedoptics(modulators,deflectors,switches,etc.)andquick-operatingschemesforcomputation,andcanunderliethecreationofhybridopticalintegratedschemes(Kuz'minov1975;Smolenskyetal.1971;Marcuse1974;BurfootandTaylor1979;Smolenskyetal.1985).

TheprincipalapplicationsofferroelectricmaterialsarepresentedinFig.1.Asisseenfromthefigure,thewidestrangeofapplicationofferroelectricsisoptics.Ferroelectriccrystals,usuallyclearandmeasuringfrom0.35to4mm(ed.byShaskol'sky1982)areappliedasphaseandamplitudemodulatorsoflaserradiation,transducers,deflectors,etc.

Ferroelectricfilmshavebeenintensivelyinvestigatedforthelast15yearsduetothegeneraltendencyofmicrominiaturization,decreaseinpowercapacityandincreaseinthesensitivityofdevices.Anumberofphenomena(e.g.lightswitch-overinstriplinewaveguides)donothavebulkanaloguesatall.Thepossibilityofusingthin-filmstructuresascontrolelementshasledtothedevelopmentofalargenumberofmethodsforobtainingfilmsandcoverings.

Dependingonaconcretedomainofapplicability,thin-filmferroelectricsofdifferentstructuralperfectionareused,forinstance,ferroelectricceramics,polycrystallineandepitaxialsingle-crystalfilms.Forsmall-sizecondensers,polycrystallineferroelectricfilmswithahighdielectricpermittivityandlowdielectricloss(BaTiO3,SrTiO3,(Ba,Sr)TiO3)areused,animportantrolebeingplayedbythedependencesoftheseparametersontemperature,frequencyand

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Fig.1Recentadvancesinmaterialsforcommunicationdevices(Miyazawa1980).

electricfieldstrength(Photonics,editedbyBalkanski1975).Forstoichiometricpolycrystallinefilmscloseto1mminthickness,thelow-frequency(1kHz)dielectricpermittivityexceeds1000andthehigh-frequencydielectricabsorptionleadstoastrongfrequencydependenceofdielectricpermittivityandthelosstangent.Slightviolationsfromstoichiometrycustomarilyinduceadecreaseofdielectricpermittivityandanincreaseoflosses.(Ba,Sr)Nb2O6,(Ba,Sr)TiO3andLiTaO3filmsofsolidsolutionsofPbTiO3andPbZrO3withlanthanum(PLZT)andtriglycinesulphate(TGS)aresuccessfullyusedforhigh-frequencypiezoelectricfilters,transducersandpyroelectricthermaldetectors.Therequirementoftheseapplicationsisahighelectromechanicalcouplingorpyroelectriccoefficient,aswellaslowdielectriclosses.Polycrystallinefilmsaresuitableprovidedthecrystallographicaxesareappropriatelyorientedduringfilmdepositionorsubsequentpolarization.Butthebestcharacteristics

canbeexpectedfromsingle-crystalfilmswithorientedpyroelectricandpiezoelectricaxesbecauseoftheirhighcouplingcoefficientandtheabsenceofinfluenceofpolarisationofintercrystallayersinpolycrystallinefilms.

TheuseofferroelectricfilmsforrecordingIRradiationisofinterest.Severalpapersaredevotedtothestudyofpyroelectriceffectinferroelectricfilms(Okuyamaetal.1981;Nakagama1979;Mukhortovetal.1981;Petrossoetal.1983;Schittetal.1984;Antsyginetal.1986).Okuyamaetal.(1981)described

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Fig.2Examplesoftheuseofthin-filmferroelectrics(Okuyama,Hamakawa1986).

athin-filmpyroelectricdetectormadeoftheferroelectricPbTiO3.

Antsyginetal.(1986)investigatedthin-filmstructuresofferroelectricbarium-strontiumniobate.Theexperimentsestablishedthatpyroelectric,electro-opticandelectrophysicalpropertiesofthebarium-strontiumniobate(BSN)filmsarewelldescribedbythephenomenologicalrelationstypicalofbulkferroelectricswithasmearedphasetransition.ItwasfoundthatontheBSN-electrodeboundarythelengthofanon-ferroelectriclayerdoesnotexceedabout3×10-8m.ThestudiesofBSNfilmrepolarisationcausedbyanappliedelectricfield,carriedoutbypyroelectricmeasurementsusingthethermalpulsemethod,repolarizationcurrentsandpulsedelectro-optics,showedthattherepolarizationofBSNfilmsisdeterminedbynucleationnearapositiveelectrode.Quick-operatingandmultielementradiationdetectorsemployingBSNfilmsasanactivepyroelectriclayerwerecreated.

Thus,alreadyearlyworksontheapplicationofthinferroelectricfilms

forIRradiationrecordingindicatedthattheirsensitivityisclosetothatofpyroelectriccrystals,althoughitshouldbenotedthatferroelectricfilmsweremostlypolycrystalline.

Geary(1979)andLemonsetal.(1978)pointedtothepossibilityofemployingferroelectricsPb5Ge3O11andGd2(MoO4)3indeviceswithamovingdomainboundary.Theydescribedopticalshuttersandanalogueelements.Figure2givesexamplesofapplicationofthin-filmferroelectricstructures(OkayamaandHamakawa1986).Inthemetal-ferroelectric-semiconductor(MFES)structure,thesurface

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potentialofthesemiconductorcancontrolthepolarizationoftheferroelectricfilm.WhentheMFESstructureisusedasashutterofafield-effecttransistor(FET),theoutletcurrentofthetransistorcanbemodulatedbythesurfacepotentialduetofilmpolarization.Forexample,PbTiO3filmspossessadielectrichysteresisloopandahighremanentpolarizationandcanthereforebeusedinMFESFET-typememorycellspossessingstablestatesillustratedinFig.2a.

Sinceathinferroelectricfilmhasaveryhighdielectricconstant,theappliedvoltageindevicescanbeloweredappreciablybyusingaferroelectricratherthanadielectricfilm.Thin-filmelectroluminescent(EL)devicestypicallyhaveasandwichstructureconsistingofZnSfilmsanddielectricY2O3films.AnELdeviceusingPbTiO3insteadofY2O3films(Fig.2b)hasalowcontrolvoltage.ThethresholdvoltageofanELdeviceisloweredfrom210to50V.

FilmsofPbTiO3depositedontothinSiO2orSimembranesasstripsseveraltensorhundredmicrometersinlengthwereusedforthefabricationofultrasonictransducers(Fig.2c).Thinmembranesweremadebyseedingboron-dopedsiliconwiththeuseofaqueoussolutionsofethylenediamineandpyrocatecholwhichetchedwellthe(100)and(110)facetsbuthadaweakeffectuponthe(111)facets.Electrodesweredepositedbyphotolithography.Anultrasonicwaveinducedmechanicaloscillationsofthemembraneatseveralresonancefrequencies,theshearstressinthefilmcausedpiezoelectricstress.Inthe300-690mmdevice,thesecondresonanceharmonichadafrequencyof30-150Hz.

VariousIRtransducerscanbemadeinPbTiO3filmsonthebasisofthepyroelectriceffect.MFESFETwithanelectrodeabsorbingIRlightaresensitivetransistors(Fig.2e).InfraredlightincreasesthePbTiO3filmtemperatureandthusmodulatesthesurfacepotentialofSiwhichaffectstheoutletcurrentofthetransistor.Theoutletvoltage

isinverselyproportionaltothelightmodulationfrequency.TheresponsetoIRradiationisveryquickandforaCO2laserthetimeofpulseincreasemakesup3.5ms.Thesensitivityofasiliconmonolithictransducercanbeincreasedbyremovingthesiliconsubstratefromthesensitivearea.

Thepropertiesandthewayofpreparationofthinfilmsusedinopticaldevicesmustsatisfyhigherdemands.

Thefirstexperimentalandtheoreticalstudiesofthin-filmopticalwaveguidesusedinintegratedopticswereperformedinthesixties(Deryuginetal.1967;Goncharenko1967;Goncharenkoetal.1969;Tien1971).Thesepapersinvestigatedthemainpropertiesofthin-filmdielectricwaveguidesofopticalrangeandshowedprospectsoftheirapplication.Someprogressmadeinthisfieldinrecentyearsisindicativeofthenecessityofgrowingthinsinglecrystalepitaxialfilmsforthispurpose.Infilmsofthicknesscomparablewiththewavelength,onecanobtainhighintensitiesevenwithmediumlaserpowers.Furthermore,thephasevelocityofalightwaveinathin-filmwaveguidedependsonthefilmthicknessandtheorderofthewavemode,whichsuggestsnewprospectsforcreationofdevices.

Thetheoryofplanardielectricwaveguides,whichunderliethecreationofthemainelementsforradiationcontrol,isdescribedindetailinanumberofpapersandmonographs(Tien1971;Zolotovetal.1974;Kogelnik1977;Tamir1979;Hunsperger1984;House1988).

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Therequirementsofintegratedopticsinperfectthin-filmstructuresnecessitatedawideuseofvariousmethodsoffabricatinglow-losswaveguidelayers.Alltheknownmethodscanbeconditionallydividedintotwogroups:

1.Refractiveindexincreaseinthenear-surfacelayerofabulkcrystal.

2.Growthofathinfilmwithahigherrefractiveindexonthesubstratesurface.

Thefirstgroupincludesthethermaldiffusionoftransitionmetalions,out-diffusion,ionimplantationandion-exchangeddiffusion.Thesecondinvolvesmainlyepitaxialfilmgrowth.

Untilrecently,theliquid-phaseheteroepitaxyhasbeen,infact,theonlyleaderinproducingheterostructureswithpredeterminedphysicalcharacteristics,whichwasparticularlyclearlyseenonanexampleofawiderangeofA3B5compounds.Foranumberofdevices,thissituationwillremainunchangedinthenearfuture.Amongtheknownliquid-phaseepitaxymethodsthemostpromisingforcomposition,thicknessandstructurecontrolistheliquid-phaseelectroepitaxyoffilms.

Theexistenceofelectro-,piezo-andnonlinearopticalpropertiesoffersnewopportunitiesforpracticaluseofferroelectricfilms.Theuseofepitaxialfilmsofoxideferroelectricsonthebasisofniobatesofalkalinemetalsintheelementalbasisofoptoelectronicsshowstheirnoticeableadvantagesoverbulkanalogues,firstofallfromtheviewpointofminiaturization,loweringofconsumedenergyandintensityofcontrolfields.Lithiumniobateandtantalatearewidelyusedinintegralelectro-opticelementsandincommunicationsystems.Bothpassiveintegro-opticcomponents(polarizers,couplers,filters)andactivecomponents(modulators,switchers,frequencyshift,etc.)havefoundtheirapplicationincommunicationsystems.Theabove-

mentionedferroelectricsposseshighelectro-opticcoefficientsascomparedwithsemiconductingcompoundsoftheA3B5groupwidelyusedforcreatingradiationsourcesanddetectorsaswellasvariouselectronicdevices.Aspecialplaceinintegro-opticdevicesistakenby'dipped'opticalwaveguidechannels.Obtainingsymmetricwaveguidechannelsbythefilmdiffusionmethodprovidesasimpleandconvenientmatchingbetweenthechannelwaveguideandopticalfibres.

Wehaveanalyzedtheepitaxialgrowthofferroelectricsfromaliquidphase,whichmadeitpossibletooptimizetheconditionsforobtainingstructurallyperfectlayersandfilmpropertycontrol.Theperformedstudiesmadeitpossibletoimprovetechnologytosuchanextentthattheproblemsofverticalintegrationofmultilayerferroelectricstructuresforintegro-opticdevicescanbesolvedcompletelyusingliquid-phaseepitaxyandliquid-phaseelectroepitaxy.Thesetechniquescanalsobeappliedtootheroxideferroelectricsandtohigh-temperaturesuperconductors.

Chapter1presentsthemainmethodsoffabricatingopticalwaveguides,exceptliquid-phaseepitaxy,whichisanalyzedinchapter2.

Epitaxialmethods,whichcannowbeusedtoproducelayerswithmaximumproximityintheirstructuralperfectiontobulkcrystals,arediscussedinchapter2.

Attentioninthischapterisalsogiventothecapillarymethodofliquid-phaseepitaxyofferroelectrics,tothegrowthkineticsoflithiumniobate,potassium

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niobateandsolidsolutionsoflithiumniobate-tantalate.Thecrystallizationmodels,describingthenatureofmasstransferintheliquidphaseforisothermalandnon-isothermalepitaxyconditions,areconsidered.Analyticalexpressionsarederivedlinkingthefilmthicknesswiththegrowthsystemparameters.Thefilmdiffusionmethodofgrowingimmersedwaveguidechannelsinferroelectricsisdiscussed.

Chapter3dealswiththeoreticalandexperimentalresultsofinvestigatingtheinfluenceofadirectelectriccurrentontheliquid-phaseepitaxyprocesses.Materialsoftheoriginalstudiesoftheauthorsongrowingthin-filmferroelectricstructuresarepresentedonanexampleoflithiumniobateandsolidsolutionsoflithiumniobate-tantalate.Anappliedelectricfieldinducingelectriccurrentisshowntohaveanappreciableeffectoncrystallizationconditions,whichguaranteescontrolofthepropertiesofthegrowingstructures.

Chapter4isprimarilyconcernedwiththeresultsofinvestigatingepitaxialferroelectricfilms:crystallinestructure,composition,orientation,micromorphologyofthesurfaceandofthesubstrate-filmboundary,domainanddislocationstructures.

Chapter5isdevotedtoinvestigationsoftheferroelectric,opticalandwaveguidepropertiesofepitaxialfilmsoflithiumniobate,lithiumtantalateandsolidsolutionsoflithiumniobate-tantalate.Thedielectricandpyroelectriccharacteristicsoflayersandthetemperaturedependenceofthermoelectriccoefficientsarepresented.Opticalresistancetolaserradiationisexamined.Refractiveindicesandthemodestructureofradiationthroughepitaxialfilmsaredetermined.Lightattenuationunderwaveguidepropagationandtheelectro-opticpropertiesofstructuresareinvestigated.

Thesubjectofchapter6istheapplicationofopticalplanarandchannelwaveguidestolaserradiationcontrol.Theparametersof

variousthin-filmintegro-opticalmodulators,deflectorsandtransducersofradiationarepresented.

1EpitaxialFilmsofComplexOxideCompoundsThepresent-daydevelopmentofsolidstateelectronicsisassociatedtoagreatextentwiththedevelopmentofthegrowthtechniqueofsinglecrystalsandsingle-crystalfilms.Thisisconnectedwiththefactthatemploymentofsinglecrystalsandsingle-crystallayersexcludestheinfluenceofgrainboundariesandstructuraldefectstypicalofpolycrystalsandthusprovidesamoreeffectiveuseofthephysicalpropertiesinherentinamaterial.

Inrecentyears,increasingattentionhasbeenpaidtotheproblemsoforientedgrowthofasingle-crystalferroelectriclayerontoasingle-crystalsubstrate,epitaxy,sincetheferroelectricpropertiesaremostofallpronouncedinsingle-crystallayers.

Epitaxyofoxideferroelectricsisnowunderparticularlyintensestudy,andinthischapterweexaminethisproblem.Thenumberofknownferroelectricsisincreasinglylarge,reachingnowseveralhundred.Particularlyfruitfulhasbeenthesearchfornewferroelectricsamongtheperovskite-typestructures(LinesandGlass1977).Thegrowthofperfectepitaxialferroelectricfilmsofagiventhickness,withacontrolledcompositionandanecessaryimpurityconcentration,isoneofthemaintasksofthin-filmtechnologyandisstimulatedbytherequirementsofintegratedoptics.

Single-crystalfilmsarecustomarilyobtainedeitherbyepitaxialgrowthontoorientedsubstratesorbystimulatingorientedcrystallizationonnon-orientedinsulatingsubstrates(Chernovetal.1980;Sheftal1983).

Table1.1givesalistofadvantagesanddisadvantagesofthemain

methodsforobtainingfilms(ed.byPoate1978).Comparativeanalysisofthemethodsforobtainingheterostructuresshowstheadvantageofepitaxialmethods.

Thedegreeoffilmperfectionisdetermined,inthefirstplace,bythespecificitiesofeachmethodand,inthesecondplace,byconcretefilmgrowthconditions(thedegreeofvacuum,temperatureregimes,growthrates,impuritycontent).

Therearenowthreebasicwaysofepitaxialgrowthofsingle-crystalfilms:

1.Vacuumepitaxy(involvingmolecularbeam),

2.Gas-transportepitaxy(involvingdecompositionofvolatilecompoundsandtransportchemicalreactions),

Table1.1Methodsofproducingfilms

Method Advantages Shortcomings

Vacuumdepositionwithresistiveheatingofevaporator

Simpleequipmentforfusiblematerials

Fusionwithevaporatormaterials

Vacuumdepositionwithelectron-beamevaporator

Fitformostofthesingle-elementmetalsandsemiconductors

Refractorymetals,carbonandoxidesaredifficulttoevaporate

Ionsputtering Fitforbothconductingandinsulatingmaterials;compositionisdeterminedbythatofthetarget.Permitsobtainingamorphousfilmsofmetalsandsemiconductors.readilyadmitsbiasfield

Arorotheratomsandmoleculesofsputteredgasereinsertedintosubstrate,substrateistypicallystronglyheated,filmmaterialismixedwithsubstratematerialandsubstratesurfacecanbedamaged

Chemicalprecipitationfromthevapourphase

Giveshigh-qualitydevices,epitaxiallayersforactivedevices,polycrystallinelayerscanbedeposited

Equipmentismoresophisticated.requiresexactprescriptionofgasflowvelocity;highsubstratetemperature

Epitaxial Guaranteeshigh- Sophisticatedequipment

growthfrommolecularbeams

qualityfilmsofcompounds

Electrochemicalprecipitation

Awiderangeoffilms;uniformlythicklargearea

Canonlybeappliedformetalfilms;problemofimpurities

Epitaxialgrowthfromtheliquidphase

High-qualityfilmsofcompounds

Itisdifficulttocontrolconcentrationandguaranteereproducibility

Ion-beammethod

Strictcontroloverprecipitationparameters

Lowprecipitationrateandsophisticatedequipment

3.Crystallizationfromaliquidphaseorliquid-phaseepitaxy.

Weshallnowconsidereachoftheseepitaxymethods.

1.1Vacuumepitaxy

Epitaxyfrommolecularbeamssuggestsgrowthofanepitaxiallayerwhenmolecularbeamsoratomsfallontoaheatedsubstratesurfaceinaultrahighvacuum.Abeamisgeneratedbysourceslocatedintheso-calledeffusivefurnacesinwhichthermalequilibriumismaintained.Thecharacteristicfeatureofthismethodismaintenanceofaconstantcompositionoftheevaporatingsubstanceanditseffusionrate.Theprocesstypicallyproceedsinhighvacuum,whichguaranteesasufficientpurityofepitaxiallayergrowth.Themethodiscommonlycharacterizedbyrelativelylowtemperaturesandgrowthrates.Alayeronasubstrateisformedundercrystallizationofcomponentscomingfromdifferentindependentbeamsand,therefore,thecompositionofthegrowinglayerandthelevelofitsdopingareeasilycontrolled.Thismakesthemethodsuitableforobtainingstructureswithasharpvariationinthecompositionandimpurityconcentration.Alowgrowthrateenablesthelayerthicknesstoberatheraccurately

controlled.Lowgrowthtemperaturessuppresstheinfluenceofthediffusionprocesseswhichlevelupthecompositionsofneighbouringlayers.

Duringcrystallizationfromamolecular(atomic)beam,vacuuminthereactorismaintainedatsuchalevelthatthefreepathofthemolecules(atoms)exceeds

greatlythedistancefromthesourcetothesubstrate.Supersaturationabovethesubstrateisdeterminedbythepressureofthevapourofthecrystallizingcomponentandbythesubstratetemperature.Regulationofthesourceandsubstratetemperaturescontrolssupersaturationand,therefore,thegrowthrate.

Layergrowthbythismethodproceedsinthefollowingsteps:

1.transportofthecomponentvapourtothesubstratesurface;

2.accommodationofatoms(molecules)onthesubstrate;

3.atommigrationonthesubstratesurface,re-evaporation;

4.building-inofmigratingatomsinactivegrowthcentres,stablenucleation;

5.coalescenceofnuclei.

Amolecular(oratomic)beam,emittedbythesource,isdirectedontoasubstrate.Thevapourpressureabovethesource,Psour,inthecaseofone-componentvapourisequalto

whereP0isthesaturatedvapourpressureatthesourcetemperature,a0istheinverseaccommodationcoefficientequaltotheratioofthenumberofevaporatedatomstothenumberofatomscollidedwiththesourcesurface.

Inthecaseofatwo-component(AandB)vapour,itspressureabovethesourcecontainingbothcomponentsisequalto(accordingtotheRaoultlaw):

wherePAandPBarethevapourpressuresofthecomponentsAandB,a0Aanda0Bareinverseaccommodationcoefficientsofthe

componentsAandB,P0AandP0BaresaturatedvapourpressuresofthecomponentsAandBforTsour,NAandNBaremolarfractionsofthecomponentsAandB(NA+NB=1).

Incrystallizationofatwo-componentvapour,specialmeasuresaretakentopreserveitsconstantcomposition.Sometimes,evaporationiscarriedoutfromseparateone-componentsources.Thevapourpressureofthecrystallizingcomponentiscontrolledbythesourcetemperature.

Itshouldbenotedthatevenasmalldifferenceintheelasticityofvapoursofthecomponentsofdissociatingcompoundscanhaveanappreciableeffectonboththestructureandthepropertiesofthecondensates.Thelatterplaysagreatroleforferroelectricmaterials.Thecondensatecompositionalsodependsonthesubstratetemperature,whichisexplainedbyselectivere-evaporationofcomponents(Shimaoka1985;Tomashpol'sky1982).

Inrecentyears,themethodofpulsedlaserdeposition(PLD)hasbeenintenselydeveloped(GaponovandSalashchenko1976;Firtsaketal.1984;Lushkaetal.1982).Theideaofusinglaserradiationforsubstanceevaporationinavacuumforthepurposeofthin-filmsputteringappearedwiththeconstructionofinitialpowerfullasers.

VariousresearchesusingPLNhavebeencarriedoutforobtainingorientedfilmsofnearlytwentysemiconductingcompounds,suchasgermanium,silicon,galliumarsenidefilms,aswellasfilmsofoxygen-freeferroelectricsofthetype

ofantimonysulphoiodideandtinthiohypodiphosphate(GaponovandSalashchenko1976;Firtsaketal.1984;Lukshaetal.1982).Insomecases,orientedgrowthoflasercondensatesexhibitsatemperatureloweringascomparedwithwhatweobserveinthermaldepositionmethods.Thisfactcannotbeexplainedconsistentlybythequantitativeanalysisofthelayerformationmechanism.Onthequalitativelevel,thespecificfeaturesofepitaxialfilmgrowthunderQ-modelaserdepositioncanbeexplainedbybombardingthesubstratebyhigh-energyions(102-103eV)oflaser-inducedplasma,whichstrengthenthepotentialreliefofthesurfaceandprovideanorientedgrowthalreadyunderinsignificantatommotions,thatis,atalowersubstratetemperature.

Therelationshipsbetweenmatterandenergytransferprocessesandphaseandintraphasetransformationsinthecondensateallowustodistinguishbetweentwoprincipalcondensationmechanisms:vapour-liquid-amorphousmetastable(glass-like)phaseandvapour-amorphousmetastablephase(withsubdomainsofpolyamorphousmodificationsandtheircondensationthroughamorphouslabilephases)whicharetypicaloflaserdeposition(Firtsaketal.1984).

Vacuumepitaxy,includinghigh-frequencycathodesputtering(Takadaetal.1974),suggestsaneasycontroloftheprocessandenablespurefilmswithaclearlypronouncedinterfacetobeproduced.Butinsomecases,inparticular,forferroelectrics,theseadvantagesareratherdifficulttorealize.Violationsofstoichiometry,occurringwhencomplexoxidefilmscontainingvolatilecomponentsareformedinvacuum,restrictsubstantiallytheefficiencyofthemethod.Thefilmsthusobtainedareasarulepolycrystallineorhaveanimperfectstructure,forexample,filmsofbismuthtitanate(Takeietal.1969),leadtitanate-zirconate(Philips1971),lead-lanthanumtitanate-zirconate(Ishidaetal.1977;Takadaetal.1974),BaTiO3andBaxSr1-xTiO3(Mukhortovetal.1981),lithiumtantalate(D'Amicoetal.

1984)andlithiumniobate(Takadaetal.1974;Meeketal.1986;Postnikovetal.1973;Foster1971;Ninomukaetal.1978).

Lithiumniobatefilmsonasapphiresubstratewereobtainedbysputteringinvacuum(Foster1971;Takadaetal.1974).Films1800Åthickweretransparentandsmoothbutexhibitedhighopticallosses,upto9dB/cm.Itisnoteworthythatthelossesinfilmsincreasedwithincreasingmismatchbetweenthefilmandsubstratelatticeparameters.

Usingvacuumepitaxy,Ninomukaetal.(1978)precipitatedz-LiNbO3filmsontoasubstrateofasingle-crystalMgOorientedalongthe[111]axis.Suchanorientationalrelationshipisduetotheidenticalpositionofoxygenionsintheindicatedplanes(thelatticeparametermismatchwasabout0.2%).Filmswereprecipitatedatarateof0.1mm/hatasubstratetemperatureof620-660°C.Thisexperiomentgavesingle-crystallayers6000Åthickwithasurfaceroughnessof100Å.Nevertheless,lossesinthefilmswereinthiscasealsoanorderofmagnitudelargerthanindiffusionfilms(~10dB/cm).

1.2Gas-transportepitaxy

Epitaxialfilmgrowthviaachemicalreactionincludesprocessesinwhichthecrystallizingphaseisduetoreactionsproceedinginavapour-gasmixture.

Thecrystallizationprocess,asanyphasetransition,isdrivenbythedifferenceinthethermodynamicpotentialsofphasesundergoingtransformations,but

inthecaseofcrystallizationbymeansofchemicalreactionsthegasphasesupersaturationcannotbedeterminedsincethechemicalreactionproceedsatthecrystallizationfronttheelementaryactsofchemicaltransformationsandtheelementaryactsofcrystallizationarecloselyconnected.

Theepitaxialgrowthrateisdeterminedbytheyieldofthechemicalreactionsresultingintheformationofacrystallizingsubstanceanddepends,therefore,ontheconcentrationofinteractingphasesinthegasmixture,thespeedofgasmixturepassageoverthesubstrate,thecatalyticactivityandthesubstratetemperature.Theseparameterscanbecontrolledintheepitaxialgrowthprocess.Thecatalyticactivityofthesubstrate,whichdependsonthemethodofsurfacetreatment,iscustomarilyassumedtobefixedineachseriesofexperiments.

Filmgrowthbymeansofchemicalreactionsundergoesthefollowingstages:

1.transportofstartingcompoundstothesubstratesurface;

2.chemicalreactionresultingintheformationofmoleculesofthegrowingcrystal;

3.migrationofmoleculesaboutthesubstratesurfaceduetoreactionheatrelease,aswellasspontaneousmigration;

4.desorptionofunreactedmolecules;

5.building-inofmigratingatomsintoactivegrowthcentres,formationofstablenuclei;

6.coalescenceofnuclei.

Oneofthemodificationsoftheprocessesdescribedaboveisthegas-transportreaction.Itsmaindifferencefromthechemicalreactionisthatachemicalcompoundcontainingacrystallizingsubstanceis

formedstraightinthereactorandthentransportedinacertainwayontoaheatedsubstratewhereitisdecomposedandcrystallized.

Thesysteminwhichtheepitaxialfilmgrowthproceedsthroughgas-transportreactionsmusthaveatleasttwotemperaturezones.Inoneofthem,thetransportinggasreactswiththesubstancesourcetoformavolatilecompoundtransportedtothesecondzonewherethesubstrateislocatedandwherethesubstanceorcompoundissegregatedandcrystallized.Thestagesoftheprocessproceedinginthesecondtemperaturezonearesimilartothestagesoffilmgrowthbymeansofchemicalreactions.

Awidespreadandconstructiveversionofthegas-transportepitaxyistheso-called'sandwichmethod'inwhichthesubstrateandthesourceareplatespositionedfractionsofamillimetrefromoneanotherandhavedifferenttemperatures(Dorfman1974).

Inspiteofthedifficultiesincreatingsteeptemperaturegradients,the'sandwichmethod'hasthefollowingadvantages:

a)thespacewherethereactionproceedsisseparatedfromtheremainingspaceofthereactorand,therefore,thepurityoftheprecipitatinglayerisdeterminedbythepurityofthestartingmaterialonly;

b)ahighefficiency(90-98%)ofmasstransfer(theratioofthesubstrateweightgaintothesourceweightloss);

c)ahighcrystallizationrate(hundredsofmicronsperhour).

Thechemicaltransportreactionunderlyingepitaxyfromthegasphasecanberepresentedinthefollowingwayonanexampleofasemiconductingcompound

where(AB)solisamaterialsynthesizedinadvance,theso-calledsolid-statesource,whichisinmostcasesmadeofapolycrystallinepowder;Cvapisagaseoussubstance,theso-calledtransporter;(AB)vapandBvaparegaseousproductsofaforwardchemicalreaction.

Substance(AB)solisinthesourcezoneatthetemperatureTsourandthesubstrateisinthecrystallizationzoneatthetemperatureTcryst,whereTcryst<Tsour.Whenthesourceinteractswiththetransporters,gaseousproductsinthedirectreactions(AB)vapandBvapgoovertothecrystallizationzonewherethereversedreaction(fromrighttoleft)proceedsandresultsintheformationofanepitaxialABlayeronthesubstrate.ThetransporterCvaprevealedinthereversereactiongoesovertothesourcezone,whereitisagaininvolvedinaforwardreaction.

Whenepitaxialfilmsaregrownbycrystallizationfromagasphase,uniformlydopedlayerscanbeobtainedquiteeasily.Adopingimpurityisintroducedintotheoperatingspaceeitherintheformofahighlyvolatilecompoundorintheelementalstate.Theimpurityconcentrationinthegasphaseiscontrolledinthiscasebythegasmixturecomposition,andinthecaseofelementaladditionsbythesourcetemperature.

Themethodofchemicalgas-transportreactionshassomeadvantages:theinitialreagentscanbesubjectedtopurification,thecrystallizationprocessisreadilycontrolled,thedevicesusedinthemethodaresimplerthanthoseusedinthemolecularbeammethod(e.g.nodevicesforhighvacuumareneeded).

Theshortcomingsofthemethodareasfollows:

a)difficultiesinmaintainingaconstantconcentrationofgaseousreagentsinthesubstratezone;

b)rapidcompositionmodulationcannotbecarriedoutduetothediffusioncharacterofgaseousreagentmotiontowardsthesubstrate;

c)theabsenceofaclearlypronouncedboundarybetweenlayers.

CurtiesandBrunner(1975)reportedobtainingLiNbO3filmsonaLiTaO3substrateusinggas-transportepitaxy.Thepropagationlossreachedavalueof40dB/cm,whichisexplainedbythepresenceofscatteringcentresinthefilms.Single-crystalfilmsobtainedbythegas-transportepitaxyevenunderoptimumconditionsusuallyhavealowstructuralperfectionwithnumerouspointdefectsofpackageanddislocations(CurtiesandBrunner1975;Aleksandrov1972;Nelson1963).

FushimiandSugh(1974)reportedonastudyofthegrowthofLiNbO3singlecrystalsbytheclosed-tubevapourtransporttechniqueanditsapplicationtotheepitaxialgrowthofthinfilmsofLiNbO3singlecrystals.

ThetransportexperimentsforLiNbO3werecarriedoutusingsealed,evacuatedtransparentquartztubes.LiNbO3powderandatransportagentwereloadedatoneendofthetube,whichwasthenevacuatedto10-5mmHgandsealedwithatorch.Theampouleswithstartingmaterialswereheatedinanelectricfurnace.Thetemperatureofbothendsofeachampoulewascontrolled,and

theendcontainingthestartingmaterialswasalwaysmaintainedatthehighertemperature.Theheatingtemperaturesexaminedrangedbetween650and1500°C.ThecoolendproductswereexaminedbyX-raydiffractometrywithCuKaradiation.

Transportagentsexaminedinthisstudyincludedsulphur,iodine,andamixtureoftheseelements.LiNbO3couldbetransportedbysulphur,butnotbyiodine.TransportofLiNbO3bysulphurwasretardedbyaddingiodinetothereactionsystem.Thecomparisonwasmadebetweenthestartingcompositionof1.00gLiNbO3and0.40gsulphurandthatof1.00gLiNbO3,0.40gsulphur,and0.40giodineloadedintheampoules12mmindiameterand100mmlong.Thehotandcoolendtemperatureswere1000°Cand910°C,andtheheatingperiodwassevendays.ThetransportratesofLiNbO3were0.125g/dayforsulphurand0.012g/dayforthemixtureofsulphurandiodine.

TherelationsbetweenthetransportrateofLiNbO3andtheamountofthesulphurtransportagentwereexaminedat1000°Chotendand910°CcoolendtemperaturesandaresummarizedinFig.1.1.Althoughthemeasuredtransportratesareslightlyscattered,theresultwasexpressedas

wherebwasfoundtobe2.0-2.5.

LiNbO3transportedbysulphur,accompaniednoby-productsandcrystallizedinfairlywellshapedtinyrhombs,coveredbythefacetsparalleltothe planes,withdimensionsupto0.5×0.5×0.5mm.The

planescorrespondtotheperfectcleavageplaneofLiNbO3.ThecrystalhabitwasexaminedinaprecessioncamerawithMoKaradiation.

Eventhoughthevapourtransporttechniquewasnotsuitablefor

obtainingbulkLiNbO3singlecrystals,thetechniquewasappliedtotheepitaxialgrowthofLiNbO3ontheLiTaO3substrate.Opticallyflat

,(010)and(001)platesofLiTaO3wereusedassubstratesforepitaxialgrowth.TheconditionsforepitaxialgrowtharelistedinTable1.2.Thoughthedepositedlayerthicknesswasnotuniform,2-10mmthickLiNbO3crystallayerswereformedontheLiTaO3substrates.ThesurfacesoftheLiNbO3layersdepositedontheLiTaO3platesweresmooth,whilethosedepositedonthe(010)andthe(001)plateswereroughbecausetheywerecoveredbythefacets.Fairlygoodcrystal

Table1.2ConditionsfortheepitaxialgrowthofLiNbO3(Fushimi,Sugh1974)

Ampoulesize 15mmdiam.,170mmlong,20mmdiam.,210mmlong

Initialcharge LiNbO3:1.00-1.40g,S:0.40-2.00g

Substrate LiTaO3 ,(010),(001)plate

Substrate-sourcedistance

8.3-11.0cm

Sourcetemperature 950-1000°C

Substratetemperature 900-910°C

Heatingperiod 3-17h

Coolingrate Furnacecooling,60°C/h

Fig.1.1RelationsbetweenthetransportrateofLiNbO3andtheamontofsulphur(FushimiandSugh1974).

Fig.1.2(right)RockingcurveoftheLiNbO3layerdepositedonaLiTaO3(001)plate(FushimiandSugh1974).

qualityoftheLiNbO3layersandtheirexcellentepitaxyontheLiTaO3substratesoverthewholedepositionareawererevealedbyX-raytopography.Figure1.2showsarockingcurveoftheLiNbO3film

depositedonaLiTaO3(001)plate,whereKa1andKa2reflectionsfromLiNbO3andLiTaO3areclearlyseparated.

1.3Filmsdepositedbyrfsputtering

Papershavebeenpublishedonionimplantationfortreatmentoflithiumniobatecrystalsurfaces,inparticular,forproducinglightguidinglayers.Townsend(1984)reportedobtainingplanarlightguidesinlithiumniobatebyimplantingN+,B+,He+andNe+ions.HealsodeterminedthedependenceoftherefractiveindexvariationAnonirradiationdosesforeachoftheseionsandshowedthepossibilityofproducinglightguideswithPn>0.1atlowsubstratetemperaturesandirradiationdosesexceeding1022cm-3.Itisnoteworthythatwaveguidesobtainedbytheion-implantationmethodtypicallyexhibithighlosses.Sampleannealingreducesthelosses,butoverannealingreducesthedifferencebetweentherefractiveindicesofthewaveguideandthesubstrate.Furthermore,underionimplantation,thesurfacelayerofthesinglecrystalbecomesamorphous.Inlithiumniobate,implantationofAr+andNe+leadstodistortionsinthesurfacelayerofthecrystallatticeupto10%.Damageinwaveguidelayersalsoimpairstheelectro-opticalpropertiesofcrystals.Thisessentialshortcomingoftheion-implantationmethodmakesiteffectiveonlyforproducingpassiveelementsofintegratedoptics.

Theadvantagesofthismethodovertheothermethodsofthinfilmprecipitationarewellknown:thepossibilityoffabricatingmulticomponentcompounds

(thechemicalelementsinthecompoundcompositioncanbequalitativelycharacterizedbyvariousphysicalproperties,forexample,partialvapourpressure);maintenanceofalowgrowthrate(0.01-5Å/s)duringthewholefilmformationprocessunderintensebombardmentbysecondaryelectronsandions,whichisintheendresponsibleforthehighqualityofitsstructure.ButthemainadvantageofHF-sputtering,particularlyimportantforproducingmultilayerstructures,isthesynthesisofgrain-orientedandevensingle-crystalfilmsonanon-orientingsurface.Thiscanberealizedwhenthefilmissynthesizedbythemechanismoffinalgrowthorientation(Bauer1969).Filmcondensationinthiscasewastheresultofcompetinggrowthofdifferentlyorientedcrystalsratherthanofthetendencytoformationofconfigurationswithaminimumoffreeenergy,asisthecasewhentheinitialorientation(e.g.orientationcausedbytheinfluenceofthesubstratenature)determinesnucleationandsubsequentcondensategrowth.Atdifferentcrystalsurfaces,adifferentnumberofmoleculesiscondensedperunittime,whichdeterminesthepredominantgrowthofcrystalswithoneoftheorientations.IthasbeenestablishedthatunderHF-sputteringthedeterminingfactorinthisgrowthmechanismisthedifferenceinthere-evaporationratesofdifferentcrystallinegrainfacetsundertheactionofelectronandionbombardmentofthesamplesurfaceduringferroelectriclayersynthesis(Margolinetal.1983).Naturally,suchmechanismisonlypossibleatlowgrowthratescomparablewiththeratesofparticlere-evaporationfromthecrystalsurface.HF-sputteringprovidestheindicatedrelationbetweenthespeedatwhichthematerialisfedtothecondensationzoneandthecontrolledspeedofitsremoval.Choosingthetarget-substratedistanceandtheoxygenpressurecreatesconditionsforplasmochemicalreactionsforoxidemoleculeformationduetotwo(andmore)vapouratomcollisionsinthepresenceofionizingelectrons.Undersuchconditions,filmthicknessincreaseswithincreasingsubstratetemperatureTs,which

agreeswithexperiment.Samplesthusobtainedhaveahighdegreeofstructureperfectionandpreserveinitialstoichiometry.

Sapphireandsiliconwereusedassubstratesinsuchexperiments.Theferroelectricfilmswere1-9mmthick.Thesubstratetemperaturemaintainedinthecourseofgrain-orientedfilmsynthesiswasestablishedtodeterminethegrainsize,whichproducesaqualitativeeffectontheprincipalelectrophysicalpropertiesofsamples.Forexample,agrainsizeof~3mmsuggeststheoccurrenceofferroelectricproperties.

1.3.1ThinfilmsofLiNbO3depositedonasapphiresubstrate

Takadaetal.(1974)werethefirsttosucceedinfeedingalaserbeamintoasingle-crystalLiNbO3thinfilmdepositedonasapphiresubstratebytherfsputteringmethod.Theauthorsbelievethatthesuccessisduetotheuseofanextremelylowsputteringrate.Itshouldbeemphasizedthat,intheirwork,theabove-mentionedpolishingprocesswasnotessentialtotherf-sputteredthinfilm,andthelightbeamcouldbeeasilyfedintothefilm.

Anrfdiodesputteringapparatuswasusedtofabricatethethinfilm.Thetargetusedintheexperimentwaspreparedinthefollowingway:First,lithium-enrichedpulledLiNbO3singlecrystalswerecrashedintograins.Then,adisc9cmindiameterand8mmthickwasformedbythegrains.Finally,thedisc

Table1.3LatticeparametersandordinaryandextraordinaryrefractiveindicesofLiNbO3andsapphireatroomtemperatures(Takadaetal.1974)

Crystal aH(Å) cH(Å) no ne

(l=6328Å)

LiNbO3* 5.149 13.862 2.289 2.201

Sapphire** 4.758 12.991 1.766 1.758

*KNassau,HJLevinsteinandGMLoiacono,J.Phys.ChemSolids,27,989(1966);

**AMyronandJJeppesen,J.Opt.Sec.Am.,48,629(1958).

Table1.4Atypicalsputteringadoptedintheexperiment(Takadaetal.1974)

Target-substratespacing 4cm

Gascontents Ar(60%)+O2(40%)

Gaspressure 2×10-2Torr

rfpower 50W

Magneticfield 100G

Substratetemperature 500°C

Fig.1.3(a)Laserbeaminasingle-crystalLiNbO3filmdepositedbytherfsputteringmethod,and(b)correspondingsample

configuration(Takadaetal.1974).

wassintered.Thec-planeofsapphirewasusedassubstrate.Table1.3showsthelatticeparametersandordinaryandextraordinaryrefractiveindicesofLiNbO3andsapphire.

AtypicalgrowthconditionofthefilmisshowninTable1.4.ThedepositionrateundertheconditionofTable1.4is250Å/h,whichisextremelylowcomparedwiththevalueusedintheusualsputteringprocess.Filmsobtainedaretransparentandsmooth,andshowahomogeneousinterferencecolour.

Figure1.3showsaphotographofafilmwithathicknessof1800Åandatraceofthe6328ÅHe-Nelaserbeamfedintothefilmbyarutileprismcouplerattheleft-handside.Thelossofthefilmislessthan9dB/cm,whichiscomparablewiththelossmeasuredinanepitaxialZnOfilm.Theexperimentalvaluewasobtainedbyusinganopticalfibrewithadiameterof0.5ram.Oneendofthefibrewasplacednearthefilmsurfaceandtheotherendwasconnectedwithaphotodiodeinordertomeasurethelightintensityscatteredbythesurface.AnexampleofexperimentalresultsisshowninFig.1.4.ThemodeusedinthisexperimentwasTM0.Intheexperiment,thelossoftheTE0modewasusuallylargerthanthatoftheTM0mode.

TheordinaryandextraordinaryrefractiveindicesofthefilmwereobtainedfromthemeasuredvaluesofthecouplinganglesfortheTE0andTM0modesandthethicknessofthefilmbyusingtheformulasfromthepaperbyP.K.Tien.Theresultsare andwherenoandnearetheordinaryandextraordinaryrefractiveindices,respectively.ThesevaluesareclosetothoseofthebulkLiNbO3showninTable1.3.

Itisverydifficulttoidentifythefilmthicknesslessthan1umtobeasingle-crystalLiNbO3filmbecausethefilmistoothintobeinvestigatedbymeansofX-rayanalysis.Thefilmswerethereforemadethickerthan1um,andthefollowingpatternsfromthefilms

wereanalyzed:(i)electrondiffractionpattern,(ii)X-raydiffractionpatternbyadiffractometer,(iii)X-rayLauepattern,and(iv)pseudo-KosselpatternbyadivergentX-raybeam.Analysisshowedthat

Fig.1.4Surface-scatteredlightintensityasafunctionofdistancealongthelaserbeaminthefilm.Theslopeindicates

thatthelossofthefilmat6328Åislessthan9dB/cm.Thethicknessofthefilmis1800ÅTM0modeisused

(Takadaetal.1974).

Fig.1.5(right)Propagationlossoflight

asafunctionofthelatticeconstantcHofdepositedfilms(Takadaetal.1974).

single-crystalLiNbO3wasreallydepositedepitaxiallyonthesapphiresubstrateoverawideareasothatthec-planeofthefilmwasparalleltothec-planeofthesubstrate.

Figure1.5showsthepropagationlossasafunctionofthelatticeconstantofdepositedfilms.Itcanbeseenthatthepropagationlossoflightinthefilmisstronglyrelatedtotheincreaseofthediscrepancyinthelatticeconstantofthefilmfromthatofthesubstrate.

Theoriginofthepropagationlossoflightisnotclearinthegivensample.Itis,however,expectedthatthelosscouldbedecreaseduptoaboutone-tenthofthatofthepresentsamplesbypurifyingthetargetmaterialandsputteringgasesandbyfindingoutamoreadequatesputteringcondition,eventhoughtheinternalstressinthefilmcausedbymisfitinthelatticeconstantbetweenthefilmandthesubstratecouldnotbecompletelyeliminated.

IntheworkbyN.F.Foster(1969),lithiumniobatewasdepositedbytriodesputteringinanargon-oxygengasmixturecontaining5-10%oxygen.TheapparatususedisshowninFig.1.6.Thesubstrateholderassemblywasmountedsothatthesubstratecouldbelocatedabovepositionsfortheevaporationofmetalfilmsorforthesputteringoflithiumniobatewithoutbreakingvacuum.

Thesubstratesusedwere1/4in.squareby1/2in.longbarsoffusedquartz,orsapphirewiththec-axiscoincidentwiththebaraxis.Afterchemicalcleaning,thebarswereclampedinthesubstrateholder,heatedto~150°Cinvacuum,andplatedwithathinchromiumunderlayerfollowedbyabout1000Åofgold.Thesubstratetemperaturewasthenincreasedtotheinitialdepositiontemperature,thesputteringgaswasadmittedatadynamicpressureofabout2m,andtheprimarydischargewasstruckandadjustedto1.5Aat60V.Thetargetvoltagewasappliedandthesubstrateswungintoplaceoverthetarget.Withatargetvoltageof1kV,thetargetcurrentwas12

mA.Amagneticfieldparalleltotheprimarybeamwasproducedbypassingacurrentof2Athroughthe100turncoilsmountedonthefilamentandanodehousings.Undertheseconditions,thesubstratetemperatureincreasedduringdepositionto30-50°Cabovetheinitialtemperature.Topermitopticalratemonitoring,thesubstratewastiltedat45°tothetarget,andundertheseconditionsthefilmgrowthratewasapproximately3/4m/h.Films2-4umthickweredeposited.Thelithiumniobatetargetwasmadeofapowderpressedintoa2.5cmdiameterx3mmthickdiscand

Fig.1.6Triodesputteringunit(Forster1971).

subsequentlyfiredinairat1200°C.Initially,thediscwaswhiteandhighlyinsulatingandsputteringwasveryslow.Asthetargetbecameheated,however,itdarkened,presumablythroughthelossofoxygen,andbecamesufficientlyconductingforthedcsputteringprocesstoproceedreadily.Theoxygenpresentinthesputteringgasassuredthatthedepositedfilmswereinsulating.

14filmsweredepositedduringthisstudy.Forthefirstfourdepositionstheinitialsubstratetemperatureswerebetween100and300°C.ThesefilmswereclearandadherentbutshowednoX-raystructureorpiezoelectricactivity.Theremainingtenfilmsweregrownatinitialsubstratetemperaturesof325-380°C.TheseexhibitedwelldefinedX-raypatternscorrespondingtotrigonallithiumniobate.AtypicalX-rayDebye-Scherrerpatternshowsthatthefilmispartiallyoriented.Althoughthedegreeandthetypeoforientationvariedfromfilmtofilm,the(00.1)and/or(01.2)planesshowedsometendencytoalignparalleltothesubstratesurface.

1.3.2TungstenbronzeferroelectricK3Li2Nb5O15

Amongvariousfamiliesofferroelectricmaterials,thetungstenbronzefamilyisofinterestforopticalwaveguidesandSAWapplications.K3Li2Nb5O15(KLN)isatetragonalcrystalwiththepointgroup4mmandistypicalofcompletelyfilledtungstenbronzeferroelectrics.Single-crystalKLNhasalargeelectromechanicalcouplingfactor

, andk33=0.52andalsohasreducedzero-temperaturecoefficientsofdelayforSAWs.However,itisverydifficulttoobtainhighqualityandlargeKLNcrystals.AnapproachtothesolutionofthisproblemistogrowepitaxialKLNfilms(ProkhorovandKuz'minov,1990).

Anrfsputteringapparatus(ANELVAFP-21)wasusedbyShiosakietal.(1982)tofabricateKLNthinfilms.Thetargetusedintheexperimentwaspreparedbysinteringthepressedpowderwitha

potassium-andlithium-enrichedcompositionof33mol.%K2CO3,22mol.%K2CO3and45mol.%Nb2O5.Theoptimumgrowthconditionsforhigh-qualityKLNsingle-crystalthinfilmssputteredonbothK3Bi2Nb5O15(KBN)andsapphiresubstratesarea50%Ar-50%O2atmosphereatapressureof9.0×10-2torr,anrfpowerinputbelow150Wand500-630°Csubstratetemperature.Thedepositionrateundertheseconditionsis~800Åh-1atanrfpowerof100W.

BoththeKLNfilmsepitaxiallygrownonKBNandthosegrownonsapphiresubstratesweretransparentandtheirsurfacesweresmooth.AnalysisoftheseKLNfilmsbyX-raydiffractionandREDmeasurementsshowedthattheKLNfilmsobtainedweresinglecrystalsoffairlygoodquality.

AHe-NelaserbeamwassuccessfullyfedintoKLNfilmssputteredontheKBN(001)andsapphire substrates,usingaprismcoupler.BymeasuringcouplinganglesforthreedifferentTEmodes,theeffectiverefractiveindexb/k0inaKLNfilm2.1mmthicksputteredontheKBN(001)substratewasdeterminedtobe2.26,2.25and2.23fortheTE0,TE1andTE2modes,respectively.TherefractiveindexnointhisKLNfilmwascalculatedtobe2.27fromtheeffectiverefractiveindicesgivenabove.MeasurementsoftheopticalpropagationlossintheKLNfilmgrownontheKBNsubstratewerenotattempted.TherefractiveindexnoinaKLNfilm~2.7mmthicksputteredonasapphire

substratewasalsodeterminedtobe2.27bymeasuringthecouplinganglesforelevenTEmodes.Thevalueof2.27obtainedaboveisclosetothatforabulkKLNcrystal.Furthermore,theTE0modepropagationlossintheKLNfilmonsapphirewasmeasuredbytheopticalfibreprobemethod.Theopticalpropagationlossinthisfilmwasdeterminedtobe7.8dBcm-1.

SomeexperimentswerecarriedoutontheSAWpropertiesofthelayeredKLN/sapphirestructure.ThesampleusedinthisstudywasaKLNfilm9mmthicksputteredonasapphire substrateatasubstratetemperatureof520±C.Interdigitaltransducers(IDTs)werenormalelectrodeswith25fingerpairsanda100mmspatialperiod,whichwereevaporatedonthefilmsurface.Thecentre-to-centrepropagationpathlengthwas12.5mm.Accordingly,thevalueofKHforthissamplewas0.6.SincethedelaytimeofSAWpropagationis2.3ms,theSAWvelocityonthisKLNfilmwasdeterminedtobe5430ms-1whichisincloseagreementwiththecalculatedvalue,5500ms-1atKH=0.6.

1.3.3KNbO3thinfilms

TheKNbO3filmsweregrowninarf-diodesputteringsysteminwhichthecathodeformsthebottomelectrode.Thesystem,describedindetailbyS.SchwynandH.W.Lehmann(1992),isequippedwithaload-lockandheatedsubstrateplatform(mountedonthetopplateofthesystem),whichallowssubstratesurfacetemperaturesupto700°C(Thonyetal.1992).Thissputterupdesignturnedouttoberatherusefulsincethisconfigurationalsoallowstheuseofhomemadetargetswhichdonotalwayshavethedesiredhighdensityandcohesion.

Themostimportantparameterintheseexperimentsisthecompositionofthetarget.SputteringfrompureKNbO3targetresultedinfilmswhichwereseverelydeficientinpotassium.Inordertoevaluate

whichcompositionisappropriatetoobtainstoichiometricfilms,K2CO3andKNbO3powdersweremixedindifferentmolarratios.Subsequently,thepowderwaspressedatroomtemperatureatapressureof5.6×107N/m2.Thediscsobtainedweresolidenoughtobetransferredintoavacuumchamber.Althoughoutgassingismuchstrongercomparedtosinteredmaterial,thehomemadetargetsprovedtobeusefuliftheyarepumpedandpresputteredforasufficientlylongperiodoftime(approximately10h).Atargetcompositionof1:1moleK2CO3andKNbO3finallyyieldedstoichiometricfilms.Thismeansthatthepotassiumconcentrationinthetargetwasthreetimeshigherthanthefinalconcentrationinthesputteredfilms.Table1.5summarizestheparameterswithwhichcrystallinestoichiometricKNbO3filmsweregrown.

Theopticalpropertiesarestronglyrelatedtothecrystalstructureandthecrystallinityofthelayers.Toprovidefavourableconditionsforthegrowthofhighlyorderedfilms,arelativelyhighsubstratetemperature(610°C)andaverylowdepositionrate(6Å/min)werechosen.Thetypicalthicknessofthelayersobtainedusingtheseparametersis200nm.

Furthermore,lattice-matchedsubstrateshadtobefoundinordertoobtaincrystallinefilms.Thetwocrystallinematerials(MgO)(A12O3)2.5spinelandMgOwereconsideredtobewellsuitedassubstratesforthinfilmsofKNbO3bulkcrystals.Moreover,therefractiveindexofthesematerialsisconsiderablylower

thanthatofKNbO3allowingmonomodewaveguidinginlayersofonly100nmthickness.TheMgOsubstrateshadatomiclayerpolishedsurfacesandbothsubstrateswerenotspeciallycleanedpriortouse.

ThecompositionofthelayerswasdeterminedbyRBSusingHe4+ionswithanenergyof2MeV.Thesemeasurementsshowedthatstoichiometricfilmscouldbegrownfroma(KNbO3)(K2CO3)targetsputteredinpureargon(Fig.1.7).Theadditionofoxygenresultsinapotassiumdeficiencyofthefilms.Ascanbeseen,themeasurementresultsareinexcellentagreementwiththesolidlineofthesimulatedspectrumofastoichiometricfilmwithathicknessof190nm.Furthermore,theprofileisflattoppedindicatingconstantcompositionacrossthefilmthickness.Theoxygenstoichiometrywasinvestigatedusingnuclearreactionanalysisanddidnotshowanyoxygendeficiency.

TheX-raydiffractionspectrastronglydependonthecompositionofthefilmsanddepositiontemperature.Layerswithapproximatelystoichiometriccomposition(19.2-20at%)depositedonMgOatatemperatureof500°Corbelowonlyshowweaklinesinthex-rayspectrum.Someofthesmallpeakscouldbeidentifiedasthe(110)and(220)reflectionoforthorhombicKNbO3,whereasitwasnotpossibletoidentifytheothersunambiguously.

Whenthetemperaturewasincreasedto580-610°C,thefilmbecamesinglecrystallineandonbothsubstratestwolineswereobtainedwhichwereclosetothe(0001)and(002)reflectionsoftetragonalKNbO3(Fig.1.8).Thelatticeconstantsobtainedfromthex-raydiffractionmeasurementsforallthethreelatticedirectionsyieldeda=b=4.16parallelandc=4.10perpendiculartothesubstrateplaneforlayersdepositedonMgO.Thismeansthatthefilmistetragonalwithinthemeasurementaccuracy.Therefore,thetetragonalcoordinatesystemwillbeusedinthefollowing.Comparedwiththelattice

constantsofthetetragonalphase(extrapolatedtoroomtemperature)ofa=b=3.985Åandc=4.075Åthisindicatedalatticemismatchof4%and0.7%,respectively.Tetragonalsymmetrywhichinbulkmaterialisassignedtothestructuralphaseinthetemperaturerange22-440°Ccanbeexplainedbythefactthatthesubstrateiscubicand,therefore,forcesthegrowinglayerinbothdirectionsoftheinterfaceplanetothesamelatticeconstant.Thex-raydatashowedthatthereisaclosecorrelationbetweenfilmstoichiometryandx-rayintensity:asthestoichiometryimproves,thediffractedlinesbecomenarrowerandtheirintensityincreases.

Table1.5rf-sputteringparametersforgrowingstoichiometriccrystallineKNbO3films(Thonyetal.1992)

Targetcomposition

K2CO3:KNbO3 1:1 mol

Gas 100% Ar

Temperature 610 °C

Power 50 W

Processpressure 2×10-2 mbar

Gasflow 20 cm/min

Fig.1.7RBSspectrumofaKNbO3thinfilmofthicknessd=188nmdepositedonMgOsubstratefrom

targetcompositionof(KNbO3)(K2CO3)at610°C(Schwynetal.1992).

1.3.4KTaxNb1-xO3thinfilms

APerkinElmer4400sputteringmachinewasusedforfilmdeposition.A4in.diametersputteringtarget(nominalcomposition:KTa0.5Nb0.5O3)witha15at%excessKandpressedto90%oftheoreticaldensity,waspreparedbystandardceramicprocedures.Substratesusedforfilmdeopositionwere(a)Ptcoated(3000Åsputteredlayer)Siwaferswitha1500AthickintermediatelayerofSiO2and(b)GaAs(100)waferswithaheavilydoped(n=1018-1019/cm2)surfacelayer.Anexcellentlatticematch,within0.3%,existsbetweenKTNandGaAssurfacesublattice(Sashitaletal.1993).

Underanychosensetofsputteringconditions,filmsweresimultaneouslydepositedonPt/SiO2/Si,GaAsandsapphiresubstrates.TheKTNsynthesisconditionsaresimilartothoseforKNbO3,seeTable1.5.Filmsthussputteredwerecompletelycolourlessandtransparent.CompositionofaKTNfilmonsapphirewasdeterminedbyRutherfordbackscatteringspectroscopy(RBS).RBSsimulationspectrayieldedafilmcompositionofK0.94Ta0.68Nb0.4O3.X-raydiffractionanalysisoftheKTNfilmon

sapphireshowsonlyasingle(100)peakanditstwohigherorders.Thepeaksharpness,referredtothatofthe(1012)sapphiresubstrate,indicatesnearlysinglecrystalepitaxialgrowthoftheKTNlayer.BraggpeaksfromaKTNfilmonGaAsshowonlyasinglenarrow(200)KTNreflection,indicativeoflargegrainswithahigh(100)preferredorientation.Thetwoweakpeaksonthelow20sideoftheGaAsreflectioncouldnotbeattributedtoanyoftheKTNrelatedreflections.

TheCurietemperatureplot(evsT)foraKTNfilmonaPt/SiO2/Sisubstrate(measuredat1kHz,Fig.1.9a)peakssharplyat6°Cwithamaximumeof2090,indicatingalmostabulksinglecrystal-likebehaviour.Figure1.9bshowsthecapacitance(at1kHz)versustemperaturebehaviourofaPt/KTNfilm/GaAstestcapacitor.Again,thesharppeakat3°Cexhibitsabulksinglecrystal-likeCurie-Weissbehaviour.ReflectancespectraofKTNfilmsyieldedrefractiveindicesfrom2.06at0.6mmto1.975at1.1mmandlowabsorptioncharacteristics.ThesearesmallerthanbulkKTNrefractiveindices,from2.15to2.3.ThequadraticEOeffectinKTNfilmsonSiandGaAssubstrateswasmeasuredasthechangeinreflectanceunderanappliedelectricfieldatnearly5°CaboveTc.Thelock-insignal,correspondingtotheelectricfieldinducedreflectivity

Fig.1.8X-raydiffractionspectrumofsingle-crystalline

filmdepositedonMgOshowingthe(001)and(002)reflectionoftetragonalKNbO3(Schwynetal.1992).

changeversusappliedfield,isshowninFig.1.10.ThedifferencesintheplotsforGaAsandSisubstratesareapparentlyduetothoseofcrystallinityandstoichiometrydeviationsofthetwofilms.

Thepeakeforthesefilms(~2090)issignificantlylowerthanthatofbulksinglecrystalvalues.ForameasuredTc=3°C,thecorrespondingfilmcompositionshouldbeKTa0.63Nb0.37O3.

1.3.5.Thinfilmsbypulsedlaserdeposition

ThelasersputteringmethodisdemonstratedonanexampleofLiTaO3(J.A.Agostinelli,G.H.Braunstein1993).Thefilmswereproducedon(0001)-sapphiresubstratesbypulsedlaserdeposition(PLD)usingKrFexcimerlaserradiationat248nm.Typicalpulseenergieswere400mJwithpulsedurationsofabout30ns.Thebeamwasweaklyfocusedontoarotatingtarget,givingafluencebetween1.0and2.0J/cm2.ThetargetwasasinteredpolycrystallinebulkceramicdiscofLiTaO3preparedfrommixedpowdersofLiOH.H2OandTa2O5.ThetargetwasproducedwithanexcessLicontentsuchthattheLi/Taatomicratiowas1.1/1.Thediscwasmountedhavingthenormaltoitssurfaceatanangleof10°withrespecttotherotationaxisinordertoimprovetheuniformityofdepositedfilmthickness.Theanglewas

chosensothatthenormaltothetargetsurfacesweepsoutacircleatthesubstanceplanetogiveanoptimumuniformityfortheselectedsubstrate-to-targetdistance,whichwas6cm.Thesubstratewasmountedontheheaterblockusingsilverpainttoprovidegoodthermalcontact.Areactiveambientof85mtorrofO2wasused.Thethicknessofdepositedfilmsrangedfromabout100to800Åbutmostfilmswerepreparedwithathicknessof4000Å.Filmdepositionratesinthevicinityof1A/pulsewerefoundandlaserrepratesof4Hzwerecommonlyused.

Filmsgrownatsubstrate-heatertemperaturesof500°Cwerefoundtobeamorphouswhereasthosegrownat525°Candabovewerecrystalline.Filmswerefoundtoimprovewithincreasingtemperatureandsubstrate-heatertemperatureintherange650-700°C,theproducedfilmshavingexcellentcrystallineproperties.Figure1.11isacoupledXRDscanofaLiTaO3filmdepositedon(0001)sapphireat650°C.Thedataindicatethatthefilmissingle-phase,single-orientationLiTaO3.Thepresenceofonlythe(001)linesofLiTaO3showsthattheentirefilmisc-oriented,allowingeasyuseofthed33coefficient.

Fig.1.9a)Curie-WeissbehaviourofKTNonPt/SiO2/Siandb)Curie-WeissbehaviourofKTNonGaAs(Sashital

etal.1993).

Fig.1.10Electro-opticeffectofKTNfilms(Sashital

etal.1993).

Fig.1.11(right)Coupledx-raydiffractionscanofa4000

AthinfilmofLiTiO3on(0001)sapphirepreparedat650°C(AgostinelliandBrainstein1993).

Suchanorientationisequivalentto'z-cut'LiTaO3inthebulk.Themeasuredc-latticeconstantof13.73isclosetothevalueof13.755Å

forbulkLiTaO3.ICPanalysisofthesefilmsindicatedaLi/Taatomicratioof48.5/51.5withanuncertaintyofabout2at%.In-planeorientationwasstudiedbyx-raypolefigureanalysisusingthe(012)planeofLiTaO3.Forallsubstratetemperaturesusedbetween525and750°C,thefilmswerefoundtobetwinned.Atthelowertemperatures,roughlyequalproportionsofeachorientationwereobserved.Forsubstrate-heatertemperaturesof650°Candabove,amajororientation(>90%)inexactalignmentwiththesubstratewasobserved.

Thedegreeofcrystallineperfectionwasexaminedusingionchannelling.Fromtheseinvestigationsitfollowsthatthequalityofthefilmimprovesasafunctionofheightabovetheinterface.Thelowerqualityofthenear-interfaceregionislikelytoberelatedtoahighdensityofmisfitdislocationsarisingfromaratherlargelatticemismatchofabout8%.

Althoughafilmthatisstrictlysinglecrystalwouldbedesirable,itissufficientfornonlinearopticalapplicationsthattheLiTaO3filmbec-oriented.Becausethec-axisdirectionistheopticalaxisdirectioninthisbirefringentmaterial,theeffectiveindexforlightthatispropagatinginsuchathin-filmwaveguideaseitheratransversemagnetic(TM)waveoratransverseelectric(TE)wavewillbeindependentofthepropagationdirectionintheplanarwaveguide.Thus,

ac-orientedfilmofLiTaO3withnoin-planeorientationcaninprinciplegiveanopticalwaveguidehavinglowscatteringloss.Itisalsoofinterestthattheconditionofc-orientationissufficienttogiveasingled33coefficientfortheentirefilm.Thus,thewell-orientedbutsomewhattwinedfilmsofLiTaO3meetthecriteriaforcrystallinequalityrequiredfornonlinearoptical/electro-opticaldevices.Althoughsinglecrystallinityisnotanecessaryrequirementfortheseapplications,asingleorcontrolledferroelectricdomainstructureisessential.Someeffortwasmadetoelucidatetheas-growndomainstructureofthefilmsbyetchinginhotHF:HNO3withasubsequentexaminationbyscanningelectronmicroscopy.Thefilmsappearedtoetchuniformly,whichsuggeststhatthefilmsaresingledomainasgrown.

MeasurementsoftheopticalpropagationlossforaLiTaO3film,~3400Åthick,grownat650°C,areshowninFig.1.12.Abeamof633nmradiationwascoupledintothefilmusingarutileprism.ThedatacorrespondtoscatteredlightintensityfortheTM0mode.Thebestfitlinethroughthedataindicatesalossofabout0.6dB/cm.However,thelargescatterinthedataplacesaconsiderableuncertaintyinthelossfactor.Itisbelievedthatthelargedeviationsfromthelinearfitaretheresultofpoorsamplingstatisticsfromasmallnumberofstrongscatteringcentresthataresamplingthewaveguideintensity.Thesecentresarelikelytobetheparticulatefeaturesdiscussedabove.Itis,however,apparentthatthesecentresdonotproduceanyseriouswaveguideloss.

Moreover,therearesignificantobstaclesforthegrowthofepitaxialLiNbO3andLiTaO3filmsonGaAsforthebluelightgeneration,becauseofthefollowingreasons:(a)GaAshasthezincblendestructurewithalatticeparameterof0.5673nm,whileLiTaO3hasthetrigonalstructurewitha=0.5153nmandc=1.3755nm,(b)LiTaO3isreactivewithGaAsandproducedundesirablephasesatinterfaces,

and(c)anintermediateoxidelayerwithlowrefractiveindexisrequiredtoformawaveguide.

L.S.Hungetal.(1993)reportepitaxialgrowthofaLiTaO3layeronaGaAswithaMgObufferlayer.TheMgOlayeractsasadiffusionbarriertoimpedefilm-substrateinteractions,andformsawaveguidestructurewiththeoverlyingLiTaO3.

(NH4)2Sx-treated(111)GaAswaferswereusedassubstratesforepitaxialgrowthofMgOfilms.MgOwasdepositeddirectlyonGaAsbyelectron-beamevaporation.Thedepositionprocesswascarriedoutat3×10-8torrwithoutintroducingadditionaloxygenintothesystem,ensuringanundisturbedGaAssurfacetothegrowthofepitaxialMgOfilms.Thesubstratewasheatedbyaradiativeheater.Thegrowthtemperaturewas450-550°Candmonitoredbyaninfraredpyrometer.Thedepositionratewas0.05-0.15nm/s,andthethicknessoftheMgOfilmswasabout100-500nm.

LiTaO3filmsweregrownbypulsedlaserdeposition.Theparametersofthesputteringlaserarepresentedabove.Depositionwascarriedoutatarateof0.1nm/pulse,thesamplewascooledtoroomtemperatureinoxygenatapressureof150torr.

ThethicknessandcompositionoftheresultingMgOandLiTaO3filmsweredeterminedbyRutherfordbackscatteringspectrometry.Thespectrumcanbebestfittedbyasimulationofabilayeredstructurewiththestoichiometricratio

ofMg:O=1.0:1.0andLi:Ta:O=1.15:0.97:3.TherearedgeoftheTaprofileandthefrontedgeoftheGaAsprofileareabrupt,indicatinglimitedinterfacialreaction.

Thestandard0-20diffractionpatterntakenfromaMgOfilmonGaAsrevealsonlytheMgO(111)andGaAs(111)diffractionpeaks.ThefullwidthathalfmaximumoftheMgO(111)rockingcurvemeasuredatabout1.8°,indicatingahighly[111]-axisorientedfilm.EpitaxialgrowthofMgOonGaAswasverifiedbyx-raypolefigureanalysis.AcomparisonoftheresultsobtainedfromMgOandthatfromtheunderlyingGaAsindicatesthatasingle-crystal[111]-orientedMgOfilmisgrownon(111)GaAs,andthattheMgOlatticeisrotatedby180°aboutthe[111]surfacenormalwithrespecttotheGaAssubstrate.

ThecrystalqualityofLiTaO3canbesubstantiallyimprovedbyincreasingthegrowthtemperatureof600-650°C.

1.3.6.WaveguidesbyMeVHeionimplantation

PlanarwaveguidesinKNbO3byMeVHeionimplantationforopticalwaveswithpolarizationparalleltothecrystallographicb-axiswereproducedbyF.P.Strohkendletal.(1991).Theseguidesconsistedoftheessentiallyundamagedsurfacelayerwhichisseparatedfromthebulkbyaburiedlayerofareducedrefractiveindex.TheionicendofthedamagerangeoftheincidentHeionswasfoundtopartiallyamorphizethecrystallattice(R.Irmscheretal.1991).Thewaveguidesareleaky,aslightwhichispropagatingintheundamagedsurfacelayercantunnelthroughthebarrierwithaloweredindexintothesubstrate.Thewaveguidesshowedaminimumpropagationlossforanimplantationdoseof5×1014cm-2.ThisdosewasatleastoneorderofmagnitudebelowthedoseswhichhavebeenusedsofartoproducewaveguidesinKNbO3(T.Bremeretal.1988andL.Zhangetal.1988).

F.P.Strohkendletal.(1991)reportedonacriterionofplanarwaveguidesforopticalwaveswithpolarizationparalleltothecrystallographicc-axiswithevenlowerimplantationdoses,thatis,withdosesofabout1014cm-2.Prismcoupling,aswellasend-firecouplingofaHeNelaserbeamwithawavelengthof632.8nmwasusedtocharacterizetheTEmodespropagatingalongthea-axisintheionimplantedplanarwaveguides.

KNbO3crystalsampleswerecutperpendiculartotheb-axisandhaddimen-

Fig.1.12IntensityasafunctionofpropagationdistanceforlightscatteredoutoftheTM0modeLiTaO3thinfilmwaveguideonsapphire(Agostinelliand

Braunstein1993).

sionsoftypically7×2×9mm3.ThesampleswereirradiatedatroomtemperaturewithHeionsofeither1or2MeVanddosesintherange5×1013to5×1014cm-2.TheangleofincidenceoftheHeionswasslightlyoffnormaltoavoidchannelling.Thecrystalsampleswereheatsinkedandtheionfluxwaskeptbelow5×1015cm-2h-1topreventthecrystalsfromheating.ThedoseswerekeptdeliberatelylowbecauseionimplantationisaninherentlydestructiveprocessandleadsinKNbO3alreadyatdosesoftheorderof2×1015cm-2tostrongwaveguidelosses.

Afterimplantation,thesamplesexhibitedplanarwaveguiding.PrismcouplingofanHe-Nelaserwithawavelengthof632.8nmwasusedtomeasurethemodespectraoftheplanarwaveguidesbydarklineandbrightlinespectroscopy.Figure1.13showstwoexamplesofdarklinespectrawhichweretakenbymeasuringthebeampowerreflectedfromtheright-anglecouplingprismasafunctionofthemodeeffectiveindexNeffnpcosa,whereistherefractiveindexofthecouplingprismatawavelengthof632.8nm.Thepronouncedreflectivitydipinthedarklinespectrumofthesampleirradiatedwith1MeVHeionsandadoseof5×1013cm-2indicatesthesuccessfulproductionofawaveguidingstructureandoccursduetoresonantexcitationofthelowestmode.Thedeeperthemediainthedarklinespectrathelesslightisreflectedbackfromthecouplingpoint,andhence,thebetteristhecouplingofthelaserbeamtothewaveguidemode.FromthenormalizedintensityinthedipoftheTE0modeofthe1MeVwaveguide,Strohkendletal.(1991)calculatedacouplingefficiencyof~33%.TheTE0modeofthe2MeVguidewasonlydetectedinthebrigthlinespectrumthatistakenbymeasuringthepoweratthewaveguideexitasafunctionofthecouplingangle.Theabsenceofapronouncedreflectivitydipinthecorrespondingdarklinespectrum(Fig.1.13)indicatesthatthecouplingefficiencyoftheincidentlaserbeamtotheTE0modewaslessthan~1%.

Thedarklineandbrightlinespectraofthewaveguidesimplantedwithdoseshigherthan1×1014cm-2exhibitedseveralreflectivitydips.

Notethatforadoseofuptol×1014cm-2nonleakymonomodewaveguideswereproducedinKNbO3.Themuchweakercouplingefficiencyforthe2MeVguidegivesevidencethatthewaveguidinglayerwithanincreasedrefractiveindexislocateddeeperbelowthecrystalsurfacethanforthe1MeVguide.Therefore,Strohkendletal.(1991)havefoundthationimplantationcreatesalayerofincreasedrefractiveindexburiedbelowthecrystalsurface.Therehavebeenseveralreportsonso-called'anomalous'increasesoftheextraordinaryrefractiveindexinbirefringentcrystals(L.Changetal.1988).

1.3.7Stripwaveguides

Integratedopticsapplications,suchasmodulatorsorfrequencydoublers,whichwouldbenefitfromthehighfiguresofmeritofKNbO3demandforthefabricationofstripwaveguides.Baumertetal.(1985)havereportedforthefirsttimeonstripwaveguidesinKNbO3.Theyachievedopticalwaveguidingandcut-offmodulationbyusingtheelectro-opticeffectforwaveguideformationandmodulation.

Flucketal.(1991)reportedforthefirsttimeonpermanentopticalstrip

waveguidesinKNbO3.Theone-dimensionalwaveguidingstructureswereproducedbyMeVionimplantationandappropriatemasking.

TheKNbO3crystalswerecutperpendiculartothecrystallographicb-axis.Thesizeofthecrystalsampleswas9.95×l.97×8.04mm3.Thesurfaceandthetwoend-facesperpendiculartothea-axiswerecarefullypolishedinordertoallowefficientend-firecouplingofalaserbeam.ThefabricationofstripwaveguidesusingHeionimplantationwascarriedoutbyfirstproducingaplanarguideandthenapplyinganimplantationmasktoformtheverticalsidewalls(Fig.1.14).Theplanarwaveguidewasformedbyirradiatingthesamplesatroomtemperaturewith3.2MeVHeionsandadoseof7.5×1014cm-2.Theincidenceoftheionswasslightlyoffnormaltoavoidchanneling.Thedosewaschosendeliberatelylowbecausefortheseconditionslowattenuationplanarwaveguideshavebeenproduced.Thethicknessoftheplanarwaveguidesisgivenbytheaverageionpenetrationdepth,whichwascalculatedwiththeMonteCarlomethodtobe7.7mmfor3.2MeVHeionsinKNbO3.

Toformone-dimensionalwaveguides,Flucketal.(1991)maskedthesamplesforfurtherimplantationbyasetofparalleltungstenwires13mmindiameterandwithaspacingof400mm(Fig.1.14).ThewireswereusedasasimplemaskofsufficientthicknesstocompletelyshieldstripsoftheplanarwaveguidesfromfurtherHeionbombardment,hencefromfurtherrefractiveindexmodification.TheverticalsidewallswereformedwithHeionsof2.9MeVandvaryingangleimplantation,respectively.Ideally,theimplantationmaskwouldpossessverticalwallsanduniformthickness.Butbecauseofusingwires,thereareionswhichpassthroughtheouterthinnerpartofthewires,thereforereducingtheeffectivewidthofthestrips.Becausetheseionslosepartoftheirenergybeforereachingthecrystalsurface,theypenetratelessdeeplyintothecrystal,hencethesidewalldamagelayerswillcontinuouslyrisetothesurface,reducingthewaveguide

widthespeciallynearthesurface.Thelateralstragglingoftheincidentionswhichisduetotheinteractionwiththetargetionsleadsalsotonarrowingofthewidthofthestripguides.Theactualwidthofthestripwaveguidesformedbyusingtungstenwires13mmindiameterasanimplantationmaskisreducedto11.4mm.

Fig.1.13ReflectivityasafunctionofeffectiverefractiveindexNeffforwaveguidescreatedwith1and2MeVionsandadoseof5×1013cm-2.

(Strohkendletal.1991).

Fig.1.14a)Creationofaplanarwaveguidinglayer,

b)formationoftheopticalstripwaveguidesbyfurtherimplantationwithappropriatemaskingof

thesamplewhichproducesthesidewalls(Flucketal.1991).

TheopticalcharacteristicsofthestripwaveguidesfabricatedbytheionimplantationprocessasdescribedabovearegiveninTable1.6.

1.3.8Doublewaveguide

Planarburieddoublewaveguideswereproducedincrystallinequartzandtheirconvolutedprofilesweredeterminedbymodeindexmeasurements(Chandleretal.1988).LiNbO3isofmuchgreaterinterestandapplicationthanquartzandionimplantationisquiteabletoproducelow-lossguidesinthismaterial(Al-Chalabi1985).Itisimportant,however,nottoassumeasimpleprofilesummationprocessinLiNbO3.Astheiondamagehasbeenshowntoannealatalowertemperature(<400°C)(Glavasetal.1988),itisquitelikelytosufferpartialannealingduringsuccessiveirradiations,duetotheirthermalorionizationeffects.Anassessmentoftheseriousnessofthisproblemisanimportantprerequisitetotheconsiderationofanymultiplewaveguideconstruction.

Themethodofdeterminingthedouble-waveguideprofileisnotimmediatelyobvious.Simplewaveguidesarenormallycharacterizedbythespacingoftheirresonantmodespectra(brightordarklines)usingaquantummechanicalanalogysuchasperturbationtheory,aphase-integralapproximation,(Wentzel-Kramers-Brillouin),orafiniteelementmethod.Onlythelatterwouldbeapplicabletoadoubleguide,anditsimplementationwouldbelaborious.

Chandleretal.(1989)usedLiNbO3samplesobtainedfrom1mmthicky-cutwafers.Theywereclampedingoodthermalcontactwithanaluminiumblockheldattherequiredtemperature.Beamheatingwasminimizedbyrestrictingthecurrenttoabout0.5mAandthiswasscannedoveranareaofnearly0.5cm2(foruniformityofdose).Theshallowbarrierwasproducedwith1.1MeVHe+toadoseof1.5×1016ion/cm2andthedeepbarrierwith2.2MeVHe+toadoseof3.0×1016ion/cm2.Theenergyratiogaveopticalwellsofapproximatelyequalwidthsandthedoseratiowasnecessaryforequalheightbarriers,becauseofthehigherdamageefficiencyfortheshallowerimplant.Theimplantareasforthetwoenergieswereoverlappingbutdisplacedfromeachotherbyseveral

Table1.6CharacteristicsoftheopticalstripwaveguidesinKNbO3formedbyHeionimplantation(Flucketal.1991)

Planarimplantation

Energy 3.2MeV

Dose 7.5×1014cm-2

Sidewallimplantation

Energy 2.9MeV

Angie 5/22/34/45°

Totaldose 3.5×1015cm-2

Sizeofstripwaveguide(mm)

Width 11.4

Depth 7.7

Propagationlosses(dB/cm),wavelengthinnm

514.5 4.3

632.8 1.4

860.1 2.9

millimetresinordertogivethreedistinctregionsforprofilemeasurements-shallowbarrier,deepbarrier,andthecompositeguide.Foreachregion,darkmodepositionsweremeasuredwithTEpolarizationusingthezdirectionofpropagationforbothred(0.6328mm)andblue(0.488mm)light.Allvisiblemodesweremeasured-thesharpguidingmodeswithinthewells,andthebroad'substratemodes'notconfinedbytheguides.Thesewereallusedbythecomputerreflectivitysimulationprogramtogivetherefractiveindexprofilesinthedifferentcases.Theanalyticfunctionchosentodescribe

eachrefractiveindexbarrierconsistedofanexponential/Gaussiannucleardamagepeaksuperimposedonaflatelectronicplateau.Thisfunctionischaracterizedbyfourvariableparametersandhasbeenfoundtodescribeadequatelytheexperimentalresultsforsingle-barrierprofilesinLiNbO3(Glavasetal.1988).Forsingle-barrierimplantsthemodeswerespacedfairlyevenly,butinthecaseofthedoubleguidesthespacingwasveryuneven,andalsothelineintensitiesvariedconsiderably.Theuseoftwowavelengthshadtheadvantageofactingasacheckagainstmissinganyoftheveryfaintmodes.

Thefirstsamplewasimplantedwithahigh-energydose(2.2MeV,3.0×1016ions/cm2)followedbythelow-energydose(1.1MeV,1.5×1016ions/cm2)bothat300K(Chandleretal.1989).

Figure1.15showsthecompositeindexprofilesforthissamplemeasuredat0.488and0.6238mmtogetherwiththerealmodevalue.Bothbarriersarerepresentedfunctionallybyexponential/Gaussiannucleardamagepeaksonflatplateaux.Itappearsthat,ingeneral,adirectsummationofthedamagehasoccurredfromthetwoimplants,withafewexceptions.Thehigh-energypeak(whichwasimplantedfirst)hasbeenreduced,possiblybyannealingduringthesecondimplant:thelowenergypeakheightisnotasummationbecauseitisclosetosaturationandthelow-energypeakpositionhasbeenshiftedtogreaterdepth.Thislattereffectmaybeattributedtoanincreasedionrange

Fig.1.15Fittedprofilesofexperimentaldatameasuredat0.488mm(upper)and0.6328mm(lower).Themodelevelsandnormalizedmodecurves

areshown(0.488mmdotted)(Chandleretal.1989).

(~4%)forthesecondimplant(lowenergy)duetoanoverallreductionindensityoftheregionduringthefirstimplant(highenergy).

LiNbO3hasbeenshowntobeagoodsubstrateforion-implanteddoublewaveguides.Theprofilesofthenucleardamagebarriersareessentiallyadditive,providedthataccountistakenofpossibleannealingduringirradiationandionrangemodificationduetodensitychanges.Forbarriersofequalheight,itmustalsoberememberedthatthedamageefficiencyfallsalmostinverselywiththeionrange.

1.4Autodiffusedlayersinlithiumniobateandlithiumtantalate

KaminowandCarruthers(1974)developedanovelandsimpleout-diffusiontechniqueforachievingthinpositiveindexlayersinLiNbO3orLiTaO3withoutdegradingtheoriginalsurface.Theauthorsuseddiffusionofcomponentsoutofacrystal.Inthismethod,stoichiometricdeparturesnearthesurfaceoflithiumniobateandlithiumtantalatecrystalswereachievedbyvacuumheatingthecrystalscausingout-diffusionofLi2O.Itisknownfromprevious

workonbulkmaterialsthatextraordinaryrefractiveindexneincreasesasLi2Oisremovedfromthecrystalbuttheordinaryindexisnotaffected(Carruthersetal.1974).For

inthe0.48<n<0.50range;andfor

wherethemolarfractionv=0.5forastoichiometriccrystal.Thus,theout-diffusionproducesarefractiveindexgradientthathasamaximumpositiveindexchangeatthesurfaceandgraduallyapproachesthebulkindexintheinteriorofthespecimen.Theseout-diffusedlayersserveasexcellentlow-loss

opticalwaveguidesthatpossessallthecharacteristicsofthebulkcrystal.

Theout-diffusedlayershavethefollowingadvantagesoverepitaxiallayers:(a)theprocessingismuchsimpler;(b)thesurfaceremainssmoothandneednotberefinished;(c)theopticalqualityandpropertiesofthelayerareidenticalwiththoseofthebulkcrystal;(d)thereisnoabruptlatticemismatchorimperfectionatthefilm-substrateboundarytoproducescattering;and(e)forout-diffusionbelowCurietemperature,thelayersneednotbepoled.However,theout-diffusedlayersmaybedisadvantageousinsomeapplicationsunlesstheindexprofileparameterscanbecontrolledindependently.Thus,thepeakindexchangeatthesurface,a,andthecharacteristicdiffusiondepth,b,determinethenumberofmodestheguidewillsupportandthedegreeofconfinementofopticalenergytothesurface.

Thetransmissioninterferencemicroscopemethodwasemployedtomeasuretheout-diffusionindexprofilesonalargenumberofspecimenspreparedundervariousconditions.

Refractive-indexprofilesnormaltothesurfacesweremeasuredwithaLeitzinterferencemicroscope.Withthisinstrument,interferencefringes,inpolarizedlight,canbeobservedwitharesolutionofabout2mm.Interferogramsthroughthe(a,c)facetof(1,2)areshowninFig.1.16.TheedgeinFig.1.16aisnormaltotheaxis,andthelight(aHglamp)isanordinarywave.OnlyaverysmallordinaryindexchangeDnoisobserved.TheindexchangeDnisgivenbyDn=pl/d,wherepisthenumberoffringesbywhichtheinterferencepatterninthegradedregionisshiftedfromtheunperturbedpattern,listhewavelength(0.546mm),anddisthesamethickness(2000mm).Thefringeshiftdepictstheindexprofiledirectly.AsubstantialpositiveindexchangeisobservedwithextraordinarylightasinFig.1.16b,

wheretheedgeisagainnormaltothec-axiscorrespondingtoout-diffusionalongthec-axis.TheextraordinaryindexchangeisgreaterthaninFig.1.16c,wheretheedgeisparalleltothec-axiscorrespondingtoout-diffusionnormaltothec-axis.TheinterferogramofFig.1.16d

Fig.1.16Interferograms:a)ordinarywave,diffusionalongc,

b)extraordinarywave,diffusionalongc,c)extraordinarywave,diffusionnormaltoc,d)extraordinarywave,diffusionnormaltoc(KaminovandCarruthers1973).

illustratesthestillgreaterout-diffusionexperiencedby(1-3)underobservationconditionscomparabletothoseinFig.1.16cfor(1-2).

1.4.1Out-diffusionkinetics

Theout-diffusioncomponentsfromthesurfaceofasolidcrystalinvolvethreebasicreactionsteps:(i)diffusionofgaseousmoleculesawayfromthesurface;(ii)desorptionofmoleculesfromthecrystalsurface;and(iii)diffusionofmoleculesthroughthecrystaltothesurface.Thesimpleerrorfunctioncomplement(erfc)solutiontothediffusionequationtowhichtheextraordinaryindexcurveswerefittedintheworkbyKaminowandCarruthers(1973)isonlyvalidforaconstantsurfaceconcentration.Morerefinedboundaryconditionscanbeusedtoexaminethenatureoftheseapproximations.

Inthecrystal,Fick'ssecondlawgoverningthediffusionis

andisvalidforcaseswherethediffusioncoefficientDisindependentoftandx.HereCistheconcentrationdeficitofLi2Oingcm-3atadistancexintothesurfaceafterdiffusiontimet.

Theunitsofconcentrationarerelatedtonby

whereMisthemolecularweightandpthedensity(whichvariesslightlywithnitself).Theinitialconditionis

ThediffusionconstantvarieswithT

whereQDistheactivationenergyfordiffusion,R=1.99calK-1mol-1.

Theboundaryconditionatthecrystalsurfaceequatesthevaporizationflux,Jv,totheconcentrationgradientatthesurfaceas

Thisassumesimplicitlythatthesolid-vapourinterfaceisstationarywithrespecttothediffusiondistance(i.e.thereisnovapouretchingofthecrystalsurface)andthattheflux,Jv,doesnotchangewithsurfaceconcentration.Fortheout-diffusionproblem,thesurfaceconcentrationchangesbyverysmallamounts,soboththeseassumptionsarevalid,andthesolutiontoequation(1.5)is(CarslawandJaeger,1971)

whereierfcistheintegraloftheerrorfunctioncomplementandisevaluatedbyCarslawandJaeger(1971)andCrank(1970).Thesurfaceconcentrationcanbewrittenas

Thenormalizedfunctionserfc(x/b')andp1/2erfc(x/b)areplottedinFig.1.17andcanbeseentobesimilar.Theexponentialfunctionexp(-x/b'')isalsoincludedforcomparison.

ThequantitiesDneandCarerelatedbyequation(1.5)andequation(1.7)sothatforLiNbO3:

Thenequation(1.11)canberewrittenas

ThevaporizationfluxisrelatedtotheequilibriumvapourpressureofLi2Oover(Li2O)v(Nb2O5)(1-v)bytheLangmuirrelation

orforcomputationalpurposes,

Fig.1.17Diffusionprofiles-analyticalcurvesforp½ierfc(x/b),erfc(x/b')andexp(x/b'').Atypicalsetofexperimentaldataisfitted

asshownwitha=a'=a"andb=1.36b'=1.97b"(Carruthersetal.1974).

wheretheLangmuirvapourpressurePLisrelatedtotheequilibriumsaturationvapourpressurePeqby

whereQvistheactivationenergyforvaporization.Heretheevaporationcoefficient,a,mayvaryfromunity,whenmoleculesevaporateintoavacuumattheequilibriumrate,tonearzero,whenmoleculesevaporateatakineticallydeterminedratewithsignificantenergyorentropybarriers.Experimentally,theevaporatinggeometry,totalpressureandpumpingspeedinfluenceJvbecauseofthepartialconfinementofthespecimensurfacebythefurnacetube.Thisdeparturefromidealfreeevaporationwillinfluencethevalueofainanundeterminedmannerthatdoesnotdependontemperature.Consequently,thistemperaturedependenceofaisignoredhere,andtheassumptionwillbejustifiedlater.Thetotalsurfaceconcentrationchangesby (seeCarruthersandPeterson,1971),sowemayregardJvasconstantatanygiventemperature.

Theout-diffusedspecimensareobservedbyKaminowandCarruthers(1973)undertheinterferencemicroscopeandthefringedisplacementsyielded ThedataarefittedtotheierfcdistributionatDne(0),Vand InFig.1.17itcanbeseenthatDn(0)=aandDn(x)=0.5awhenx=0.36b,whichyieldsvaluesforaandb.Atypicalsetofdata,measuredbytheintersectionofeachfringewithalinenormaltothesurface,isplottedinFig.1.17usingthecalculatednormalizationparametersaandbtoobtainacomparisonwiththeanalyticalcurveforierfc.Tocomparethesamedatawiththeerfcandexpfunctions,newparametersa',b'anda",b",respectively,arecalculatedtoobtain

afitat , and asbefore.Then

ItcanbeseeninFig.1.17thatthedataarebestrepresentedbytheierfccurveasexpectedbutthattheerfcandexpcurvesgivefairapproximationstothedata.Theexpfunctionisaconvenientapproximationfordeterminingthewaveguidingpropertiesofthesegradedindexlayers.Whenthecharacteristicdepth,b,obtainedfromsuchcurvefittingisplottedagainstt1/2,theslopeis2(D)1/2,allowinganaccuratedeterminationofD(T)forthetemperatureatwhichthespecimenwastreated.

Thevaporizationfluxcanbecomputedfromtherefractiveindexgradientatthesurface.Fromequations(1.5a),(1.7)and(1.10)wehave

Itmaybeseenfromequation(1.14)that

Thus,Jvmaybecomputedfromtheparametersaandborfromthegradientitself.Notefromequations(1.15),(1.16)and(1.22)thatthesurfacerefractiveindexgradientisindependentoft.

Fromequations(1.9),(1.17)and(1.20)wehave

where Takingthelogarithmofequation(1.23)anddifferentiatingwithrespecttol/T,wecometo

WehaveignoredtheslighttemperaturedependenceofG0overtherangeofTemployed.Itcanthenbeseenthatthedifferencebetweentheactivationenergiesforvaporizationandsolidstatediffusiondeterminesthetemperaturedependenceoftherefractiveindexgradientatthesurface.

Theactualvaporizationflux,Jv,canbecalculatedfromequation(1.21)andprovidesacheckagainstthemeasuredweightloss.

ThediffusioncoefficientsfoundexperimentallybyCarruthers(1974)areplottedagainstl/TinFig.1.18fordiffusionnormalandparalleltothec-axis.

Fig.1.18Variationofdiffusioncoefficientswithtemperatureas1/Tinlithiumniobatefordiffusionnormalandparalleltothec-axis.Straightlineshavebeenfittedbyleast

squaresregressionanalysis-seeTable1.7(Carruthersetal.1974).

Table1.7Diffusionequationparameters(Carruthers,Kaminow,Stulz,1974)

D0,cm2s-1 QD,kcalmol-1

LiNbO3

^c-axis (3.21±0.44)×102 68.21±0.48

||c-axis (3.32±1.19)×102 68.17±1.24

LiTaO3

^c-axis (2.8^0.8)×10-2 50.1±4.3

||c-axis (6.6±2.5)×10-2 52.1±7.0

Table1.8Refractiveindexgradientequationparametersfromregressionanalysis(Carruthers,KaminowandStulz,1974)

G0(m-1) (Qv-QD)(kcal/mol) Qv(kcal/mol)

LiNbO3

^c-axis 3.69×10-5 2.38 70.6

||c-axis 2.2×10-7 9.15 59.0

LiTaO3

^c-axis 3.0^10-3 13.6 64

||c-axis 1.5×10-3 11.2 63

Thestraightlineswerecalculatedbytheleastsquaresregressionanalysis.TheresidualvariancesareshownasparallellinesandcanbeseentoencompassthecentroidoftheD-valuesbutnottheerrorrangeinallcases.AlsotheresidualvarianceismuchlargerforD||thanforD^fornotquiteclearreasons.ThecalculatedvaluesofD0andQDare

showninTable1.7.Itcanbeseenthatboththepre-exponentialfactorsandtheactivationenergiesaresimilartoeachother,withinexperimentalerror,fordiffusionnormal.

Thegradientoftherefractiveindexchangeatthesurface(givenbyp1/2a/b)maybeverysensitivetoanumberofexperimentalvariablessuchassurfacecondition,pumpingspeed,andpressure.

Thegradientswereaveragedateachtemperatureandplottedagainst1/TinFig.1.19.Thestraightlinesweredrawnfromaleastsquaresregressionanalysisoftheaveragevaluesoftherefractiveindexgradientsateachtemperature.ThepertinentparametersareshowninTable1.8.

ThevaluesoftheactivationenergyforvaporizationinTable1.7canbecomparedwiththevaluesobtainedforthevaporizationofLi2O.(Berkowizetal.1959;NesmeyanovandBelykh,1969).Forthereaction

avaluefor ofabout155kcal/(moleLi2O)hasbeenestimated.Thisgivesanactivationenergyforvaporizationofabout74kcal/(moleLiNbO3),

Fig.1.19Variationofthegradientoftherefractiveindexchangeatthesurfaceoflithiumniobategiven

asp1/2a/bwithtemperatureas1/T,seeTable1.8(Carruthersetal.1974).

whichisquiteclosedtothemeasuredvaluesinTable1.8forv=0.48andconfirmsthisreactionasaprobablerealizationmechanism.

TherehavebeennoequilibriumvapourpressuremeasurementsofLi2Ooverlithiumniobate,soitisnotpossibletodetermineaatthistime.However,acomparisonofthevaluesofPLcalculatedfromequations(1.15)and(1.18)andshowninTable1.9withtherangeofequilibriumvapourpressuresofpureLi2Ooverthesametemperaturerange(Berkowizetal.1959;NesmeyanovandBelykh,1960)suggeststhat andthat Suchanisotropicandlowvaluesoftheevaporationcoefficientsuggestthatevaporationoccursatakineticallydeterminedratewithsignificantsurfaceenergyorentropybarriers.

Thediffusiondataforlithiumtantalatewereobtainedbyout-diffusingonespecimenateachofninetemperaturesrangingfrom930°Cto1400°C.Thediffusioncoefficientswerecalculatedfromtheslopesofthebversust1/2relationshipsasbefore.

Sincefewerspecimenswereused,thesedataarenotasaccurateasthoseforlithiumniobate.Asinthecaseoflithiumniobate,thedatafordiffusionnormaltothec-axisshowlessscatterthanthosefordiffusionparalleltothec-axis.Thediffusioncoefficientsareplotted

againstl/TinFig.1.20fordiffusionnormalandparalleltothec-axis.Thestraightlineswerecalculatedbyleastsquaresregressionanalyses,andtheresultingvaluesofD0andQDaregiveninTable1.7.Asforlithiumniobate,thepre-exponentialfactorsandactivationenergiesaresimilar,withinexperimentalerror,fordiffusionnormalandparalleltothec-axis.However,thedifferencesbetweenlithiumniobateandlithiumtantalatearesignificant;thevaluesofD0arelowerbyfourordersofmagnitudeandQDisslightlysmallerforlithiumtantalate.Thegreaterdifficultyofdiffusioninlithiumtantalatemaybeassociatedwiththemorecovalentnatureofthebonding(asreflected,forexample,inthehighermeltingpoint).

Thegradientoftherefractive-indexchangeatthesurface(givenbyD½a/b)isshowninFig.1.21.Thescatterisquitelarge,especiallyfordiffusionparalleltothec-axis.Thestraightlineswerecalculatedbyleastsquaresregressionanalyses,andtheresultingvaluesofG0andQv-QDareshowninTable1.8.Thecomputedactivationenergiesforvaporizationarequitesimilartothoseforlithiumniobateandagainsuggestthatthesamevaporizationreactionisoccurring.Unlikelithiumniobate,however,thegradientofthesurfacerefractive-indexchangebecomeshigherathighertemperatures.Thisisadesirable

Table1.9ulatedevaporationfluxesandkineticvapourpressureforLiNbO3(Carruthers,Kaminow,Stulz,1974)

Jv(gcm-2s) PL(atm)

T(°C) ^c-axis ||c-axis ^c-axis ^c-axis

930 1.95×10-11 0.828×10-11 0.279×10-11 0.118×10-11

1000 6.04×l0-11 2.42×10-11 0.888×10-11 0.356×10-11

1050 1.24×10-10 2.57×10-11 1.86×10-11 0.385×10-11

1100 2.01×10-10 5.18×10-11 3.07×10-11 0.791×10-11

1125 4.04×10-10 2.63×10-10 6.22×l0-11 4.05×10-11

Fig.1.20Variationofdiffusioncoefficientswith

temperatureas1/Tinlithiumtantalatefordiffusionnormalandparalleltothec-axis.Straightlineshavebeenfittedbyleast

squaresregressionanalysis,seeTable1.7(Carruthersetal.1974).

Fig.1.21(right)Variationofthegradientoftherefractiveindex

changeatthesurfaceoflithiumtantalategivenasp1/2a/bwithtemperatureas1/T,seeTable1.7(Carruthersetal.1974).

featureforobtainingsteeperindexprofilesandthinnerwaveguidinglayers,providedtherequireddiffusiontimesat1400°Ccanbekeptsufficientlyshort.

Theevaporationcoefficients,º,arecomparablewiththoseforlithiumniobate andagainsuggestthatevaporationisthekineticallyrate-limitingreaction.

1.5Thediffusionmethodformetalsandoxides

Amongthemostthoroughlyinvestigatedmethodsisnowthediffusionmethodwhichiswidelyusedforfabricationofplanarandchannellightguidesonlithiumniobateandlithiumtantalateplates.However,thisonlyrefersinfullmeasuretotitaniumdiffusion.Themethodconsistsindepositingafilmorastripofmetaloritsoxideontothesubstratesurface,afterwhichthecrystalisdiffusionallydistilledordopedinoneorseveralstages.Thecharacteristicdiffusiontimerangesbetween1and10h,thetemperaturebeing800-1100°Cforlithium

niobateand800-1300°Cforlithiumtantalate.Thediffusiontypicallyproceedsinamediumofinertgasesargonandhydrogenandinsomecasesintheair,inanoxygenfluxorinitsmixturewithargon.Inthepresenceofoxygen,processestypicallyproceedintwostageswithapreliminarymetaloxidation.Transitionmetalsaremostoftenemployedasdopingimpurities.

Thestudiesofmetaldiffusionmethodcarriedoutinrecentyearsinthetechnologyoflightguidefabricationinvolvinglithiumniobateandlithiumtantalatehaveshownthatinpractice,titaniumdiffusionismoresuccessfulasbeingmoreintensiveandprovidinghigherDnoandDnevaluesascomparedtoothermetals.

Whenthismethodisappliedtocreatingchannelandsingle-modeplanarstructuresinlithiumniobateandtantalate,allowanceshouldbemadeforLi2Oout-diffusionintheregionsadjoiningthoseofchannelformation.Theout-diffusionprocessisknowntocauseanincreaseinne.Electro-opticdevicesaremostoftenintendedformodesofjustthispolarizationsincetheelementr33(associatedwithne)ofthetensorofelectro-opticcoefficientsoflithiumniobateandtantalatecrystalsisthelargest.Li2Oout-diffusionmayleadtoincreasinglossesandtonon-reproducibilityofthemodecompositioninthechannelstructureandisthereforeundesirable.

Thespecificfeaturesofbackgroundout-diffusionintheformationofTi:LiNbO3lightguidesandthewaysofitssuppressionaredescribedbyChenandPastor(1977),Jackeletal.(1981)andNodaetal.(1980).ChenandPastorshowthatasaresultoftitaniumdiffusion(themetalfilmthickness20mm,preliminaryoxidationtime1hatatemperatureof600°C,andthediffusionproperlastssixhoursat900°C)one'titanium'mode(theeffectivelightguidedepthis4mm)andtwo'out-diffusion'modes(15mm)areexcited.Thelattermodeswerethenremovedbysampleannealinginthepowdermixtureof

Li2CO3+Nb205.Componentsofthemixturewith99%ofthemainsubstanceweretakeninproportioncorrespondingtoLiNbO3compositionwithaccounttakenoflithiumcarbonate.Sampleswereannealedat900°Cfor1-4hours,andthe'titanium'modewasnotsuppressed.

Weshallpointouttwowaysofout-diffusionsuppression:metaldiffusionfromfilmsinamediumoflithiumoxideorcorrespondingchemicalcompoundsandlight-guidechannelformationinagasfluxcontainingwatervapour.

TheefficiencyofthistechniquewasprovedbyJackeletal.(1981)usingIRspectroscopyintheregionof3480cm-1(bond-O-H-)ofspecimenswhichhadundergonedifferenttreatment.Titaniumdiffusioninwetargonleadstoarelativeincreaseofhydrogenconcentrationinthesurfacelayerofsubstratesascomparedtotheoriginalcrystal.TheauthorsbelievethatthisinducesLi+ionmigrationsuppressioninthecrystalandpromotesthedecreaseoftheout-diffusionrate.

Zilingetal.(1980)showedthatassoonasTi4+issubstitutedforNb5+,thereoccurschargenonequilibriumwhichcanbecompensatedbypositioningtheLiionintheinterstice.RefractiveindexvariationinaLiNbO3crystaluponthesubstitutionoftitaniumforniobiumcan,dependingontheconcentrationofthelatter,becausedbythedifferenceinionreactionsandinnerstressesduetodiffusion.TakingintoaccountalimitedplasticityofLiNbO3crystalsatthediffusiontemperature,wecanexpectthattheinnerstresseswillcausemicrocrackingandrelaxpartiallywithincreasingdislocationdensityinthe

near-surfacelayer.Bothtypesofdefectswereobservedexperimentallyandarelikelytobethemainfactordeterminingopticallossesofwaveguidinglayers.SimilarresultswereobtainedbyGolubenkoetal.(1980)andZolotovetal.(1989)inthestudyofTidiffusionintoz-cutLiNbO3crystalsinAratmospherewithacompensationofthebackLi2Odiffusion.

AtthesametimeitshouldbenotedthatoneofthemostessentialdefectsofTi:LiNbO3-waveguidesistheirliabilitytolaser-induceddamageknownas'optical'(HolmanandCressman,1982).

Animportantroleisplayedbythediscussionofpossiblemechanismsoftherefractiveindexincreaseonthecrystalsurfaceduetodiffusion.Zilingetal.(1980),Sugiietal.(1978),Canalietal.(1986)andFejeretal.(1986)pointoutthreemechanismsofrefractiveindexincrease:

1.duetothephotoelasticeffect;

2.duetoincreaseofelectronpolarizability;

3.duetodecreaseofspontaneouspolarizationinthedopingregion.

Mechanism1

Therelativedielectricimpermittivitytensor andthestraintensorareknowntoberelatedthroughthephotoelasticitytensor

Thecomponentsofthedielectricimpermittivitytensorareequalto

Thecomponentsofthetensors and arerelatedas

where istheKroneckersymbol.

Differentiatingtheexpression(1.27),multiplyingtheresultby andmakinguseof(1.26),wecometo

InthecaseofthinlayersitturnsouttobesufficientonlytoconsiderthemainstrainsSx,SyandSzalongthex-,y-andz-axes,respectively.Makingallowanceforthisandalsofortheestimate

weobtain

wherePimisanabbreviatednotationofthecoefficientsPijmm.

Sugiietal.(1978)carriedoutadetailedcalculationandreportedDn0andDnotobeatleasthalftheobservedvaluesand,besides,toexhibitastrongertemperaturedependence.

Mechanism2

Herethedirectcauseoftherefractiveindexincreaseisarelativelyhighpolarizabilityoftheimpurityionsimplantedintothecompositionofthemedium.TherelationbetweenelectronpolarizabilityandtherefractiveindexofthesubstanceisgivenbytheLorentz-Lorenzformula

whereNiisthenumberofi-typeatomsinaunitvolumeandaiistheelectronpolarizabilityoftheseatoms.

AccordingtoZilingetal.(1980),HolmanandCressman(1982)andSugiietal.(1978),titaniumiondiffusioninlithiumniobateproceedsmostlythroughLi+andNb+5sitesofthecrystallattice.ThecrystallochemicalradiiofTi4+,Li+andNb5+ionsarerespectivelyequalto0.061,0.068and0.064nm(HolmanandCressman1982),andtheircoordinationnumberinlithiumniobateisequalto6.Theconcentrationofsubstitutionaltitaniumionsunderusualdiffusionconditionsamountstoapproximately1021cm-3.Toprovidetherefractiveindexincreaseoftheorderof0.001forsuchconcentrations,theai,valuesofTi4+ionsmustexceedthecorrespondingvaluesforthesubstitutedionsbyapproximately0.0410-24cm3.Thisrequirementisinprinciplemetbythesubstitution .AsfarastheNb5+ionisconcerned,itsai,valuesarehigherthanthoseofTi4+

sinceithasanadditionaloccupiedelectronshellanditsradiusexceedsthatoftheTi4+ion.Inthequalitativerespect,theactionofthismechanismshouldobviouslybethoughtofasdisputable.

Mechanism3

Thismechanismreflectstherelationbetweenspontaneouspolarizationofadielectricanditsrefractiveindex(theKerreffect).Thisrelationcanbeexpressedintheform(Sugiietal.1978)

whereDPsisvariationofthequantityPsduetoimpuritydiffusion,g13andg33aretensorcomponentsofthequadraticelectro-opticeffect.

Calculationsshow(Sugiietal.1978)that and .

Ontheotherhand,itshouldbetakenintoconsiderationthatpolarizationreversalinthebulkcrystalinducesdeformationsalongthex-,y-andz-axesduetotheelectrostrictioneffect

whereQyareelectrostrictioncoefficients.

AnincreaseofneandnoisonlypossibleprovidedthatDPs<0,andasaresultofsuchpolarizationreversalwehave

Thesignsoftherequireddeformationsareoppositetothoseobservedinexperiment.

Thus,theonlysatisfactorydescriptionofthefactorsresponsiblefortherefractiveindexincreaseinthesurfacelayeroflithiumniobateduetotitaniumdiffusioncanbegivenexclusivelyintheframeworkofmechanism1.

1.5.1DiffusionofTransitionMetals

ThreedifferenttransitionmetalionshavebeendiffusedintocrystalsofLiNbO3toformlow-lossTEandTMmodeopticalwaveguidesthatconfinethelighttowithinafewmicronsofthesurface.AthinlayerofmetalofthicknesstisfirstevaporatedontoasurfaceofthecrystalandthenthecrystalisheatedattemperatureTinanonreactiveatmosphereforatimet.Theimportantwaveguideparameters-thenumberofmodesM,themaximumindexchangea,andtheeffectiveguidethicknessbcanbeindependentlycontrolledbythediffusionparameterst,T,andt.

SchmidtandKaminow(1974)haveshownthatawidevarietyofmetalsmaybediffusedintoLiNbO3andLiTaO3toformguidinglayers.Onepromisingclassofmetals,whichtheystudied,wasthetransitionelements.Theyareknown(McClure,1959)tocontaind-electronorbitalsthatarepolarizableinthevisiblespectrum.RepresentativemembersareTi,V,andNicontainingrespectively2,3,and8electronsintheunfilleddshellsoftheatoms.Thenumberofd

electronsinaniondependsuponitsvalencestate.

Thinlayers(200-800Å)ofthemetalswereevaporatedontothe(010)or(001)facetsofLiNbO3fordiffusionperpendicularorparalleltothec-axis,respectively.ThesampleswereheatedinflowingAr(topreventoxidationofthemetal)totemperaturesintherange850-1000°C(belowtheCurietemperature)inatimelessthan1h,andthediffusiontimetwasmeasuredfromthatpoint.Aftertimet,flowingoxygenwasadmitted(toreoxidizeLiNbO3)andtheovenswitchedoff.Forsufficientlylongdiffusiontimes,allthemetaldisappearsfromthesurface.Ifthediffusionisstoppedbeforeallthemetalentersthecrystal,anoxideresidueformsonthesurfacewhichisremovedbyverylightlyhandpolishingthesurface.

Observationsoftheindexprofilebytheinterferencemicroscopeindicatethepresenceofpositive-indexlayersforbothnoandnefordiffusionofeachofthethreemetals.Mostofthelayers,however,aretoothin(1-3mm)topermitmeasurementsofthefunctionalfromtheindexprofile.Electronmicroprobemeasurementsalsolacktheresolutiontomeasurethemetalconcentrationprofilesofthethinlayers.However,themicroprobewasemployedtomeasuretherelativeconcentrationprofilefortwothickNi-diffusedguides(Fig.1.22).

Fig.1.22Electronmicroprobemeasurementofwaveguidesformedbydiffusionofa400Å,Nifilm:Ni/Nb

countratiovsdepthx.aremeasuredpointsfor6hdiffusionat850°C.aremeasuredpointsfor6hdiffusionat950°C.ThesolidlineisfitoftheGaussianfunction.Thedashedlineisfitof

theerfcfunction(SchmidtandKaminow,1974).

Fordiffusiontimeslongcomparedtothetimerequiredforthemetalfilmtocompletelyenterthecrystal,theconcentrationprofileshouldapproachtheGaussianfunction(Shewmon1963)

wherexisthedepthbelowthesurface,athenumberofatomsperunitvolumeinthedepositedfilmofthicknesst,

andthediffusionconstant

(Strictlyspeaking,tin(1.35)shouldincludeacorrectionforthewarm-uptime.)Forshortdiffusiontimes,wherethemetalisnotcompletelydiffusedintothecrystal,theconcentrationprofileshould

beacomplementaryerrorfunction(erfc)withthesurfaceconcentrationindependentoftime(Shewmon1963).Fordiffusiontimescomparablewiththetimerequiredforallthemetaltoenterthecrystal,theconcentrationprofilewillbeintermediatebetweentheGaussiananderfcprofiles.

ThisbehaviourisillustratedinFig.1.22wheretheNi/Nbcountratiosareplottedasfunctionsofdepthfordiffusionperpendiculartothec-axisintwowaveguides.TheactualNi/Nbconcentrationratioisproportionaltothecountratiowithaproportionalityfactorgreaterthanunity.Thedatawereobtainedbyprobingpointsonaplanenormaltotheplaneoftheevaporatedlayer.Measurements

ofsurfaceconcentrationc(0,t)weremadeontheevaporatedfacetitself.GaussiananderfcprofilesarefittedtothedataatDn(x)=aand(1/2)ainFig.l.22.Thewaveguideformedbyheatinga400Åthickfilmat850°Cfor6hhasafunctionalshapewelldescribedboyacomplementaryerrorfunction.Thewaveguideformedbyheatinga400Åthickfilmat950°Cfor6hhasthelong-tailcharacteristicofacomplementaryerrorfunctionbutitalsohasthebell-likeshapenearthesurfacecharacteristicofaGaussianfunction.Inbothcasesthemetalfilmappearedtobecompletelydiffusedintothecrystal,butthediffusionrateismuchgreateratthehighertemperature.

ThevaluesofbobtainedforthetwoGaussianprofilesinFig.1.22showthatthesurfaceconcentrationc(0,t)isqualitativelyproportionaltot/b,asrequiredby(1.34).Inaddition,thesurfacecountratioforathirdsamplewitht=250Å,whichwastreatedfor6hat950°C,wasalsoinagreementwiththeexpectedt/bdependence.

Itisreasonabletoassumethattherefractive-indexchangeDn(t)isproportionaltoc(x)forsmallDn.ThenmakingallowancefortheGaussianprofile(1.34),wehave

Itisclearfrom(1.37)thatacanbecontrolledbyadjustingtandfrom(1.35)and(1.36)thatbcanbecontrolledbyvaryingtandT.Byanalogywithaslaborexponentialguide,thenumberofmodesMshouldbeproportionalto(CarruthersandKaminow1974)

Thus,asingle-modeguidecanbefabricatedwithb/aand,hence,theopticalmodedepthquitesmall.Incontrast,theb/aratioforout-diffusedguideswasfoundtoberelativelyinsensitivetotheavailablediffusionparameterstandT(CarruthersandKaminow,1974).

Severalmetal-diffusedwaveguideshavebeenexamined.Thenumberofmodesandtheirprismcouplinganglesweremeasuredand,fromthesemeasurements,thediffusiondepthbandtheindexchangeatthesurfacetn(O)wereestimatedbycomparingtheeffectiveindicesofthemodeswiththoseexpectedforanexponentialwaveguide(CarruthersandKaminow1974;Conwell1973).TheaverageresultsofthesemeasurementsforanumberofTi-,V-,andNi-diffusedsamplesaregiveninTable1.10.Itshouldbeemphasizedthatsincetheprofileisnotexponential,alltheeffectivemodeindicesinanexperimentalmultimodeguidecouldnotbemadecoincidentwiththosewithanexponentialguideforanysetofa,bparameters.Thehighest-andlowest-ordermodeswerematchedfortheestimatesofTable1.10,anditwasassumedthatbisaboutthesameforTEandTMmodes.Itmaybeseenthataisaslargeas0.04andbassmallas1mmfortheTiguides.ThediffusiondepthsbarelargerandtheindexchangesaaresmallerforNiandVthanforTiforgiventandT;however,reducingtand/orTwouldbringaandbforNiandVmoreintothelinewiththevaluesfor

Ti.ThechangeinrefractiveindexwithconcentrationmaybecalculatedusingthedataofTable1.10,equation(1.37)andthestandarddensitiesofthemetals:forexample,forTi,dno/dc=l.6×10-23cm3;forV,dno/dc=0.8×10-23cm3;andforNi,dno/dc=0.6×10-23cm3.

Thedominantsourcesofwaveguidelossarescatteringfromcrystalsurfaceimperfectionsand,possibly,absorptionbythemetalions.Thelossesat0.63mmareestimatedtobeabout1dB/cm.

Thewaveguidesaresuperiortoout-diffusedguidesinthataandbcanbecontrolledseparatelytoyieldverythinsingle-modelayers.TheyhavetheadvantageoverguidesformedbydiffusionofNbintoLiTaO3at1100°CthatthecrystalsarenotdepoledsincetheCurietemperatureofLiNbO31125°Ccomparedto600°CforLiTaO3.DiffusionintoLiTaO3attemperaturesbelow600°Cisfeasiblebutveryslow.

Itseemslikelythatmanyothermetalswillproduceeffectiveguideswhendiffusedintoavarietyofinsulatingcrystals.SchmidtandKaminow(1974)havemadepreliminarytestsusingvariousotherelementsondifferentsubstrates.

Table1.10Averageresultsformetal-diffusedguides(SchmidtandKaminow,1974)

MetalThicknesst(Å)

Timet(h)

Temperat.T(°C)

Diffusiondirection

Numberofmodes(M)

Effectiveb(mm)

EffectiveDn0(0)

EffectiveDne

Ti 500 6 960 1TM 1.1 0.01 ...

4TE 1.1 ... 0.04

1TE 1.6 0.006 ...

5TM 1.6 ... 0.025

V 250 6 950 1TM 6.5 0.0005 ...

4TE 6.5 ... 0.002

V 500 6 970 1TM 6.2 0.0005 ...

4TE 6.2 ... 0.004

Ni 270 6 800 2TM 2.9 0.007 ...

2TE 2.9 ... 0.004

2TE 2.6 0.007 ...

2TM 2.6 ... 0.006

Ni 270 6 960 3TM 6.6 0.002 ...

0TE 6.6 ... ...

2TE 5.5 0.0015 ...

0TM 5.5 ... ...

Ni 500 6 800 3TM 2.8 0.0095 ...

2TE 2.8 ... 0.006

3TE 3.1 0.0085 ...

2TM 3.1 ... 0.0045

Ni 500 6 960 7TM 11.6 0.0025 ...

0TE 11.6 ... ...

4TE 4.5 0.0045 ...

0TM 4.5 ... ...

Ithasbeenfound,forexample,thatAu-,Ag-,Fe-,Co-,Nb-,andGe-diffusedLiNbO3andTi-diffusedLiTaO3allyieldgoodwaveguides.Apparently,anyvalenceelectronscontributedbytheseelementsincreasetheopticalpolarizabilitywithoutacompensatingincreaseinthelatticevolume.Then,ifthemetalionsdonotintroduceexcessiveabsorptionattheoperatingwavelength,asatisfactorywaveguideisproduced.

1.5.2Titaniumdiffusion

Inthepaperscitedabove,thebackdiffusionofLi2Ohasnotbeenused.Butthisdiffusionisnecessaryforcreatingactiveelementsofintegratedoptics(modulators,switches,etc.)onthebasisofstriplinewaveguidessincealongwithstriplinewaveguidesthebackdiffusionprovidesthecreationofaplanarwaveguideforanextraordinarywave.ThedataonthereversediffusioncompensationisduetoBurnsetal.(1978),RanganathandWang(1973)andChenandPastor(1977)andMiyasawaetal.(1977).Theseauthorsmainlyconsidereddiffusioniny-cutcrystals.Atpresent,z-cutLiNbO3crystalsareofincreasingimportanceforintegratedoptics,firstofallbecausethiscutallowsaparticularlysimple'Cobra'typeelectrodeconfigurationtobeusedformodulatorsandswitches(PapuchonandCombemale1975)and,second,becausetheTidiffusionrateintheAratmospherealongthez-axisofaLiNbO3crystalisseveraltimesgreaterthantheratealongthey-axis(Fukudaetal.1978).Inviewofthis,z-cutLiNbO3crystalsareveryconvenientforcreatingdevicesonthebasisofstriplinewaveguides.

Golubenkoetal.(1980)investigatedTidiffusioninz-cutLiNbO3crystalsinanargonatmospherewithabackLi2Odiffusioncompensation.Themethodsofsamplepreparationareofpracticalinterest.Polishedz-cutLiNbO3sampleswerepreliminarilyannealedat1000°Cinanoxygenatmospheretoremovethesurfacelayer

damagedundermechanicalpolishingofcrystals.Titaniumlayersofdifferentthickness(200-600Å)weredepositedontoannealedplatesbymagnetronsputtering.ThespecimenswereplacedintoaplatinumcruciblefilledwithLiNbO3powderpreparedfromshavingsofthesamecrystals.TheconcentrationofLi2Ovapoursformedbythepowderandthesampleisinequilibrium,andthusthereisnoneedchoosingthetimewhenthebackdiffusioncompensationmuststart.Diffusionwascarriedoutinafurnacewithanargonatmosphere.Theheatingratewas50°C/min.Assoonasthenecessarytemperaturewasestablished,theamountofArwasdecreasedlestthefluxshouldcarryawayLi2Ovapours.Whenthediffusionwasover,thespecimenswerecooledinthesameArfluxatarateof5°C/min.Thewaveguidesobtainedinthisprocesshadlosseslessthan1dB/cmanditwasnotnecessarytocoolthespecimensinanoxygenatmosphere.

TheEPRstudiescarriedoutbyZilingetal.(1980)showedthatLiNbO3specimensthatwerenotspeciallydopedwithtitaniumexhibitedFe+3andMn+2ionspectra.Afterthespecimenswereannealedinavacuumat1000°Cfor2h,theFe+3linedisappearedwhiletheMn+2lineremainedunaltered.Intheregion thereappearedasinglelinewithananisotropicg-factor.AnalysisoftheorientationaldependenceofthespectrumrevealedthattheparamagneticcentreobservedhassymmetryC3v.

Inspecimenscoveredwithatitaniumlayer100nmthick,forwhichthediffusionannealingwascarriedoutinvacuuminregimesprovidingaTiconcentration

Fig.1.23EPRspectraof(1)Ti-dopedand(2)originalvacuum-annealedcrystals(Zilingetal.1980).

of(0.5-2)×10-2cm-3,thelineintensityincreasesbymorethananorderofmagnitude(Fig.l.23)andcorrespondstothenumberofcentres,6.5×1015.TheparamagneticcentreresponsiblefortheappearanceofthislinehasanelectronspinS=1/2andg-factorstypicalofthe3d-ionwhichinthiscaseistitaniuminthestateTi3+.EPRspectraofpairwiseTi3+ionswerenotobserved.

Whenspecimensareannealedintheair,thenumberofTi3+centresdecreasesrapidlywithincreasingtemperature.Att>600°Cthecorrespondinglinedisappears.NonewlinesexceptthosebelongingtoFe3+wereobserved,whichsuggeststitaniumtransitiontothenon-paramagneticstateTi4+.ThesymmetryC3visindicativeofthefactthataTiioncanbeinthepositionofeitherlithiumorniobium,butthevalenceoftheTiionandthechangeofthisvalencetestifyinfavourofniobiumsubstitution.Forconcentrationslessthanabout6×1019cm-3,theconclusionofthepositionofTiintheLiNbO3latticeisconfirmedbytheresultsreportedbyPearsalletal.(1976).

Thesesubstitutionalatomsalsohaveactivationenergiesofabout3.7eVwhicharemuchhigherthanthoseofinterstitialatoms,suchasLiandCu,ofabout1eV.Therefore,boththemarkedlatticecontraction

andthehighactivationenergyfoundintheTidiffusionintoLiNbO3implythatTidiffusessubstitutionallyintotheLiNbO3crystal.Recently,ithasbeenshownthatTidiffusedintoLiNbO3isall+4valenceandTiionssitnotonvacanciesordefectsbutonwelldefinedsites(Pearsalletal.1976).InLiNbO3,twopossiblesitesremainforsubstitutionalimpurities,aLisiteandaNbsite.ThelatticecontractionwouldoccurifTiionsreplacedeithertheLisiteortheNbsite,sincetheeffectiveionicradiusofTi+4,0.605Å,issmallerthanthoseofLi+1andNb+5of0.68and0.64Å,respectively,whenthecoordinationnumberofallofthemissix.However,thereplacementofNbionsbyTiionsismorefavourablefromthepointofviewofchargecompensation,soitisassumedthatTiisdiffusedassubstitutionalionsfortheNbsiteinLiNbO3.

Armeniseetal.(1983)discussedthefirststepoftheinteractionbetweenTiandLiNbO3,occurringbefore,andsubsequentlyleadingtotheformationofthe(Ti0.65Nb0.35)O2compoundlayer.Inparticular,theystartedwiththestresseseventuallyinducedbyTideposition,thendescribedthekineticsoftheTioxidationanditsinteractionwiththeOatomsoftheannealingatmosphereandofthesubstrate.So,theyshowedtheformationofLiNb3O8and(Ti0.65Nb035)O2compoundsandthedissolutionofTiO2andLiNb3O8phases,leadingtoacompleteformationofthe(Ti0.65Nb0.35)O2layer.

Opticalgradeandopticallypolishedy-andz-cutLiNbO3single-crystalsubstrateswereused.Tifilmswiththicknessesrangingfrom150to600Å,weredcsputterdepositedonsubstratesfromapure(99.99%purity)TitargetinapureAratmosphere(10-3torr)withadepositionrateofabout80Å/min.BeforeTidepositiontheTitargetwassputteretched,whilenosputteretchingwasperformedonthecrystalsubstrates.Onfewsamples,Tiwasdepositedinanevaporatorequippedwithanelectrongun.Sampleswerethenannealedinaflowing(120litre/h)dryoxygenatmosphereatdifferenttemperaturesandtimes.Theheatingandcoolingratewas30°C/min.

Samplemorphology,compoundformation,atomiccompositionprofiles,andstructuralcharacterizationoftheformedphaseswereanalyzedbyascanningelectronmicroscope(SEM),equippedwithanenergydispersiveX-rayanalysis,Rutherfordback-scatteringspectroscopy(RBS),byusinga1.8-MeV4He+beam,Augerelectronspectroscopy(AES),secondaryionmassspectrometry(SIMS),andglancingangleX-raydiffractionperformedwithaWallace-Wardcylindricaltexturecamera.ThepeculiaritiesandthereasonsforthechoiceofthesemicroanalyticaltechniqueswerediscussedbyArmeniseetal.(1982).NondestructiveRBSanddestructiveAESandSIMSin-depthatomiccompositionprofilingtechniqueswereusedtoobtaincomplementaryinformationandtoensurethatmeasured

compositionswithAESandSIMSwerenotfalsifiedbytheeventualdriftofmobilespecies,inducedinthesampleduringtheionmilling.Inparticular,toavoidelectricalchargeupduringanalyses,sampleswerecoatedwithabout50-100Åofcarbonorgold.

TheTioxidationprocessstartsattemperatureshigherthan300°Candmaybedirectlyobservedfromthecolourofthespecimensurfacelayerwhichchangesfrommetallic-gray(300°C,4h)towhitetranslucentin500°C,4hannealedsamples.Microanalyticaltechniquescanhelptounderstandtheoxidationmechanismsandkinetics.

Withincreasesintheannealingtemperature,thecompleteformationofTiO2,whichoccursat500°C,4h,isfollowedfirstbythegrowthoftheLiNb3O8phase,andthenbytheformationofthe(Ti0.65Nb0.35)O2phase.

TheLiNb3O8compoundcanbeclearlydetectedandidentifiedbyglancingangleX-raydiffractionpatternstakenwiththeWallace-Wardcylindricaltexturecamera.

Thesurfacemorphologyofthesampleannealedat750°Cfor2hwasexaminedinaSEM,operatingwithsecondaryelectrons.Onthesurface,manywhitezonesmorethan100mmindiameterappearandcoverabout10%ofthewholesurface.TheirtypicalshapesandmorphologiesareshowninthemicrographinFig.1.24.

Asalreadymentionedabove,thegrowthofLiNb3O8isfollowedbythe

Fig.1.24SEMmicrographsofwhitezonesappearingonaz-cutsample,coatedwitha400ÅthickTifilmandannealed

indryO2at750°Cfor2h(Armeniseetal.1983).

appearanceoftheternarycompound(Ti0.65Nb0.35)O2whosespotsbecomeevidentinglancingangleX-raydiffractionpatterntakenwiththeWallace-Wardcylindricaltexturecameraforannealingtemperatureshigherthan700°Candincreasecontinuouslyinintensityupto950°Cfor30minthermalannealing,whentheLiNb3O8phaseisalreadycompletelyconsumedanddecomposed.

Armeniseetal.(1983)fullycharacterizedthisternarycompoundandidentifieditastherealsourceforTidiffusioninLiNbO3.Itgrowsepitaxiallyonbothy-andz-cutsubstrates.

DifferentmicroanalyticaltechniqueswerethusemployedtostudythefirststepsoftheinteractionbetweenTiandLiNbO3crystalsoccurringduringthefabricationofTiindiffusedopticalwaveguides.Theresultsobtainedcanbesummarizedasfollows.

TisputteredorevaporatedfilmsgroworientedontheplanesoftheLiNbO3substrateforallobservedcrystallineorientations.The

crystallinequalityofboththefilmandthesubstratedoesnotdependonthedepositiontechniques(evaporationorsputtering)iflowvoltageandsputteringrateareused.

ThestressesinducedbytheTifilmarethusfoundtobeindependentofthedepositiontechnique.

Forlow-temperaturethermaltreatments(300-500°C)theTifilmwillformanamorphousTioxidelayer.TheoxidationmechanismwasclearlydeterminedasacaptureofOatomsbothfromthesurroundingatmosphereandfromtheLiNbO3substrate.ThislasteffectgivesrisetoanaccumulationofNbattheTi/LiNbO3boundarywhile,duetoitshighionicability,LidoesnotaccumulatebutdiffusesthroughtheTiorTi-oxidefilm.Thechangeoftheoxygenconcentrationintheannealingatmosphere(dryO2ordryAr)willonlyproduceanincreaseordecreaseintheamountoftheOatomscapturedbyTifrom

thebulk.Therefore,thefirststepofTiin-diffusedopticalwaveguidefabricationconsistsoftheformationofaTiO2layeratabout500°C.TheseresultscanalsoexplaintheformationofwaveguidesobtainedbydiffusingTiatabout1000°CfromdepositedTiO2films(Nodaetal.1975).

Atincreasingannealingtemperature(greaterthanorequalto600°C),theformationoftheLiNb3O8phasewasobservedonbothTicoatedanduncoatedLiNbO3substrates.AssketchedinFig.1.25,ontheTicoatedsamplesthiscompoundgrowsaslargecrystallitescharacterizedbyawell-definedorientationrelationshipwithrespecttotheunderlyingy-andz-cutsubstrates.FromRBSspectratheepitaxialqualityoftheLiNb3O8phaseshowsupbetteronTiuncoatedsamples.

TheLiNb3O8compoundcontinuestogrowwithincreasingannealingtemperatureupto750°C,whileforhigherannealingtemperatureitdecomposesandfinallyvanishes(T>900°C).Fukumaetal.(1978)didnotdetectthepresenceoftheLiNb3O8compoundinsamplesannealedathightemperatures.Thiscompoundisstillpresentandclearlydetectablealsoinrapidly(>30°C/min)cooledsamples,whenannealedattemperatureslessthanorequalto800°C;nevertheless,thepresenceofflowingoxygencannotinhibitthephaseseparationandtheLiNb3O8growth.Moreover,LiNb3O8formationanddissolutionappearnottobeaffectedbythepresenceofTi.Armeniseetal.(1983)attributetheformationofthiscompoundtoLiorLi2Oout-diffusionandtotheconsequentgrowthofaLi-deficienttoplayer.LiNb3O8isreportedtobeproblematic:infact,wheneverthisphasewasdetectedtheamountoftheopticaldamageinwaveguidesincreaseddramatically(Holmanetal.1978).Thisphasewasnolongerdetectedinsamplesannealedattemperatureshigherthan850°C,itsformationinduceslargestressandmicrofracturesinTiO2films(seeFig.l.25)andmaybeasourceofTiprofileinhomogeneitiesinthediffusedlayers.

ThegrowthofLiNb3O8isfollowedbytheappearanceofthe(Ti0.65Nb0.35)O2compoundwhichgrowscontinuouslyupto900-950°C,leadingtoacompleteconsumptionoftheTiO2layer(Fig.1.25).Thisternarycompoundistheonlyphasepresentat900-950°C;itformsauniformlayerontopoftheLiNbO3substrateandconstitutestherealsourceforTiin-diffusionwhichtakesplaceforlongerannealing,asreportedbyArmeniseetal.(1983).ItshouldbepointedoutthatadecompositionofLiNb3O8occursalsoinTiuncoatedsamples,andconsequentlyitappearsasanintrinsicstepoftheLiNbO3annealingprocess.

ResultssimilartothosediscussedaboveforannealinginadryO2atmospherewereobtainedinLiNbO3samplesannealedindryN,Ar,andstaticair.ExperimentsareinprogressonthepresenceandgrowthkineticsoftheLiNb3O8phaseinsamplesthermallytreatedwithprocessessuchasannealinginanatmosphererichinLiorinagasflowingthroughH2O,whichwereallreportedascapableofpreventingLiout-diffusion(Jackel,1982).

Sugiietal.(1978)investigatedthemechanismforgenerationofmisfitdislocationsandcracks.ThediffusionofTiintoLiNbO3createdstressessufficienttogeneratebothmisfitdislocationsandcrackswithinthediffusedlayer.Inevaluatingstresses,apositivesignfortensilestressandanegativeoneforcompressivestresswereused.Byassumingthatthestresssyonthediffusedlayerinthedirectionnormaltothesurfaceplaneiszero,themaximumimpurity-inducedstressesalongthecrystalsurfaceinsidethediffusedlayer

Fig.1.25SchematicofLiNb3O8and(Ti065Nb035)O2growthinLiNbO3aftertheformationoftheTiO2toplayer.

Temperaturesandtimesareonlyindicativefora400ÅthickoriginalTifilm(Armeniseetal.1983).

canbeexpressedasfollows:

whereSisthecomplianceofLiNbO3(Warneretal.1967)andeisthestressalongthex-,y-andx-axes.ThecalculatedstressesforthesamplesaregiveninTable4.3.Thesestresseswerepartiallyrelievedbythegenerationofmisfitdislocationsneartheboundarybetweenthediffusedandsubstrateregions,butthepresenceofcracksindicates

thatthedensityofthemisfitdislocationswasmuchlowerthantheoneneededforcompleteaccommodationoftheimpurity-inducedstresses.Anisotropyofstresses,(sx)max>(sz)max,resultedinpreferentialgenerationofcracks.

Thesameauthorsalsoconsideredthemechanismcausingrefractive-indexchangesinthediffusedlayer.Thereareatleastthreepossiblemechanismsforrefractive-indexchangesinthediffusedlayer:(i)duetoaphotoelasticeffect

bydiffusion-inducedstrains,(ii)duetoanincreaseoftheelectronicpolarizabilitybythein-diffusionofTi,(iii)duetoadecreaseofthespontaneouspolarizationofLiNbO3,Pdp,byTidiffusion.

Therefractiveindexofacrystalisspecifiedbytheindicatrix,thatis,anellipsoidwhosecoefficientsarethecomponentsoftherelativedielectricimpermittivitytensorBij,namely,

StrainsSndeformtheindicatrixthroughthephotoelectriceffect,andthechangeinBijisgivenby

wherepijisthephotoelasticcoefficient.

Inthecaseofathindiffusionlayer,itissufficienttoconsideronlyprincipalstrainsS1,S2,andS3,inthex-,y-,andz-axes,respectively.Thenequation(1.42)turnsinto

whereallthesuffixesareabbreviatedinthematrixform(Nye1957).Withallowancefor ,thechangesintherefractiveindicesatthesurfaceareapproximatedby

Forno=2.306,ne=2.220(refractiveindicesforNaD-lines)(Midwinter1968),andp11=0.034,p12=0.072andp13=0.178(O'Brienetal.1970),thecalculatedvaluesforthesampleswerecomparedwiththevaluesobservedbyNodaetal.(1975).Itwasfoundthattherefractiveindexchangesduetothephotoelasticeffectcontributetoabouthalfoftheobservedchanges.

Thesecondpossiblemechanismforindexchangesisbydiffusionofimpurityionshavinglargerelectronicpolarizabilitythanthatofthehostionstobesubstituted.Asinmostsolids,therefractiveindexofaferroelectriccrystalshouldoriginatefromelectronicpolarization.Therelationbetweentherefractiveindex,n,andelectronicpolarizability,a,isgivenas

whereN1isthenumberofionsoftypeiperunitvolumeandatistheelectronicpolarizabilityoftheion.ItwasfoundthatTiionsreplacedNbionsofatomicfractionofabout1021cm-3intheLiNbO3crystal.InordertoproducearefractiveindexchangeDn=10-3,theelectronicpolarizabilityofTiion,a(Ti),shouldbelargerby0.04×10-24cm3thanthatoftheNbion,a(Nb).However,itisunreasonablesincetheelectronicpolarizabilityofionshasatendencytodecreaseastheionicradiusbecomessmall(Kittel1956).

Thepossibilityofathirdmechanismisnowdiscussed.IntheferroelectricphaseinLiNbO3,oneofthecharacteristicfeaturesisthemarkeddecreaseintherefractiveindexduetospontaneouspolarizationPsthroughtheKerreffect.Theyaregivenby

fortherefractiveindicesnoandne,respectively,wheregoisthequadraticelectro-opticcoefficient.IfTi-diffusionintoLiNbO3changedthespontaneouspolarizationbyDps,Dpswouldproducerefractive-indexchangesgivenas

wheng13=0.043m4C-2,g33--0.16m4C-2(Ivasakietal.1966)andPs=0.50Cm-2(Savage,1966),DPsof-0.005Cm-2willcauserefractive-indexchangesof and Ontheotherhand,achangeofthespontaneouspolarizationwillatthesametimecauselatticestrainsinthea-andc-axesthroughtheelectrostrictiveeffect.Then,thestrainsduetoDPs,Snaregivenby

whereQ31=-0.0036m4C-2,andQ33=0.067m4C-2istheelectrostrictivecoefficientforLiNbO3(Iwasakietal.1968).IfDPs<0asrequiredtoincreasetherefractiveindices,itshouldproducestrainsS2>0andS3<0.ThesignsofS2andS3are,however,oppositetothoseoftheobservedstrainseyandez'respectively.Thus,itisunlikelythattherefractiveindexincrementsarecausedbydecreasingthespontaneouspolarization.

Itisconcludedthatthefirstmechanismproposedforrefractive-indexchangesismorelikelythanthesecondandthird.

1.5.3Copperdiffusion

Nodaetal.(1974)attemptedtodiffusemanykindsofmetals,suchasCu,A1,Ge,Cr,Fe,Nb,andTiintoLiTaO3.Amongthem,Cuwaseasilydiffusedatrelativelylowtemperatures,andasaresultalargerefractiveindexchangewasobservedintheCu-diffusedlayer.TheauthorsreportedtheexperimentalresultsonCudiffusioninLiTaO3.

Twokindsofdiffusionprocesseswereexamined:thermaldiffusion,anddiffusionunderanelectricfield(electrodiffusion).

PolishedLiTaO3Y-platesweredepositedwithCuabout5000ÅthickandwereheatedinairandinanAratmosphere.Forthespecimenstreatedinair,thedepositedCuwasoxidizedduringtheheattreatment,anddiffusionproceededremarkably,whileforthespecimentreatedinanAratmospherediffusionscarcelyoccurred.TheseresultsindicatethatCumustbeionizedinordertodiffuseintothespecimenandthationizationfromthecopperoxideiseasierthanthatfromthepuremetal.

AninterferencefringeprofileoftheCu-diffusedlayerobservedalongthex-axisisshowninFig.1.26.Diffusiontookplaceat800°Cfor10hinair.Theedgewasnormaltothey-axisandthelight(aNalamp)wasanordinarywave.Themaximumincreaseinnois3×10-3andthediffusiondepthisabout120mm.Theprofilefortheextraordinarywavewasthesameasthatfortheordinarywave,andthediffusedlayersupportedbothTEandTMmodes.Apeakoftherefractiveindexwasalwaysobservedbeneaththesurfaceforallspecimensdiffusedunderdifferentconditions.Thereasonforthephenomenonisnotclearyet.Inthethermaldiffusionmethod,itisdifficulttocontroltherefractiveindexchangeandthediffusiondepth.Moreover,therequiredtemperatureishigherthantheCurietemperatureofLiNbO3.Therefore,thermaldiffusionisnotsuitableforfabricatingtheactiveandthinsingle-modewaveguidinglayer.

TheauthorsthenexaminedthediffusionofCuintoLiTaO3underanelectricfieldusingthedepositedCuorCuOaselectrodes.Byapplyinganelectricfield,Cuiondiffusedeasilyfromtheanodesideinthelower-temperatureregion,thatis,500°C,atwhichnothermaldiffusionwasobserved.Figure1.27showsan

Fig.1.26InterferencefringepatternontheCu-diffused

layer,indicatingthechangeoftherefractiveindexn0.CuwasthermallydiffusedintoaLiTaO3Y-plate

at800°Cfor10h(Nodaetal.1974).

Fig.1.27(right)InterferencefringepatternoftheCu

electrodiffusedlayerinLiTaO3indicatingthechangeofrefractiveindexn0.Diffusionwascarriedoutat500°Cfor1hinairandan

electricfieldof10V/mmwasapplied(Nodaetal.1974).

interferencestructurefortheY-platespecimendiffusedat550°Cfor1hunderanelectricfieldof10V/mm.Thestructurewasobservedalongthex-axisusingtheordinarilypolarizedlight.Theprofilefornewasalmostthesameasthatfornointhiscasealso.Therefractiveindexatthesurfaceincreasesbyabout5×10-3,andthediffusiondepthis25mm.Theincreaseintherefractiveindexwasfoundtobeproportionaltotheappliedfield.Withelectricfieldsstrongerthan30V/mm,microcracksoccurredatthesurfaceofthediffusedlayer,andsuchalayerwasnotsuitableforthewaveguide.

Figure1.28showstherelationbetweenthediffusiondepthandthediffusiontimeforthespecimensdiffusedinairat550°Cunderanelectricfieldof10V/mm.Thechangesintherefractiveindexwerealmostconstantforthevariationofthediffusiontime.Whenthediffusiontimewaslongerthan1h,thecrystallinityofLiTaO3wasdegraded.TheelectrodiffusioninanAratmospherewasalsoexaminedforthespecimensdepositedwithCuO,anddiffusionwasfoundtoproceedmoreslowlythanthatmadeinair.

Nodaetal.fabricatedsuccessfullythewaveguidinglayersupportingonlythefundamentalmodesTE0andTM0bythefollowingconditions:temperature550°C,electricfield10V/mm,diffusiontime10rain,andinanArgasflow.Thethicknessofthediffusedlayerwasabout4mm.AHe-Nelaserbeamwasfedintothelayerwithaprismcouplerandpropagatedalongthex-axisofLiTaO3.AphotographoftheoutputspotsofTE0andTM0modesdecoupledwithagasprismisshowninFig.1.29.Thephotographshowsthatthespotshavewell-definedshapesandthemlinespassingthroughthespotsarefaint.Furthermore,onlyaslightdecaywasobservedinthestrengthofthescatteredlightoverthe1cmlengthofalightstreakalongthelayer,anditcanbeconcludedthattheopticalqualityofthelayerwassatisfactoryat0.633mm.However,aweakabsorptionpeakwasobservedatawavelengthof1mm,andtheuseofthelayerinthis

wavelengthregionmaybesomewhatlimited.

Fig.1.28RelationbetweendiffusiondepthanddiffusiontimeinCu-diffusedLiTaO3.Diffusionwascarriedoutat500°Cinairunderanelectricfieldof10V/mm

(Nodaetal.1974).

Fig.1.29(right)Outputspotswithfaintmline

decoupledwithaGaPprismforTE0andTM0modes.AHe-NelaserbeamisfedintotheCuelectrodiffusedlayerwiththeprism

coupler,andispropagatedalongthex-axisofLiTaO3(Nodaetal.1974).

1.6Proton-exchangedLiNbO3waveguides

Theionexchangemethodisbasedontreatmentofaspecimeninasaltmeltorsaltmixturesothatasaresultofchemicaldiffusionthereoccursapartialreplacementofmobileionsfromthesurfaceregionofthespecimenbyionsfromthemelt.Themostintensiveion-exchangeprocessesproceedamongunivalentionsofalkalinemetalsLi+,Na+,K+,Cs+,Rb+,aswellasTi4+,Ag+,Cu+and,possibly,Cu2+ions.Theprincipalfactorsaffectingtheion-exchangeprocessaretemperature,time,thestateofthesamplesurface,thechemicalcompositionandthemeltproperties.Toformalightguide,itisnecessarytoprovidearefractiveindexincreaseonthesamplesurface,andthereforethechoiceofappropriateion-exchangedpairsistypicallycarriedoutbycomparingtheelectronpolarizabilitiesofionsorbyestablishingtheratioofelectronpolarizabilitiestothecubesoftheirradii.Thehigherthevaluesofelectronpolarizability,thelargertherefractiveindexincrease.Thisisinmostcasesvalidfortheionexchangeprocessinglasses.Wealsonotethatindevelopingthismethodoneshouldnotneglectapossibleoccurrenceofsomebackgroundprocesses,suchassamplesurfaceseeding,phaseseparationandothers.

Lithiumniobateandtantalatearethefirstcrystallineobjectsforwhichion-exchangeddopingwasfirstrealized.SubstitutionalionsintheseprocessesareofcourseLi+ions.

Manyrecentreportsaredevotedtofabricationandinvestigationofthepropertiesoflightguidesformedbythe exchangemethod.AsthesourceofH+ions,Jackeletal.(1982)usedameltofbenzoicacidC6H5COOHat160-250°C.Toavoidacidevaporationanddecomposition,x-andz-cutlithiumniobateplatesweredopedinaclosedvesselwithoutreachofair.ThelightguidesamplesexhibitedpropagationofTE-modesonly,thedistributionfunctionofthe

refractiveindexofthelightguidebeingastepfunctionwithDne=0.12.Thevaluesoftheioninterdiffusioncoefficientswere3.8×10-12and1.0×10-12cm-2/sat244and217°C,respectively.Theproton-lithiumexchangewasobservedtoproceedsomewhatsloweralongzthanalongxdirection.Thelightlossinlightguideswasapproximately0.5dB/cm.Channellightguidesfabricatedusingmasks(chromiumfilms10nmthickandgoldfilms50nmthick)were1-20mmthick(Jackeletal.1982).Attemptstodopey-cutLiNbO3platefailedduetoastrongdestructionofthesurface.

Thepossibilityofobtainingwaveguidelayersonaz-cutLiTaO3usingtheion-exchangereactioninabenzoicacidmeltwasreportedbyAtuginandZakharyan(1984)andKopylovetal.(1983).Theprofileoftherefractiveindexincreasen(x)atelevatedtemperatureswasinvestigatedbyanumericalmethod(Kolosovskyetal.1981)whichallowedtheauthorstoreconstructtheprofilefromalimitedsetofdatabothforasharp(exponential)andasmooth(Gaussian)profilevariation.SurfaceopticalvariationsshowedthattheinvestigatedinteractionofLiTaO3withbenzoicacidstimulatesanincreaseoftheextraordinaryrefractiveindexonly.TheprofilesofDn(x)areclosetostep-likeones,thedepthofthewaveguideregionmakesupabout2.5mm.TheobservedjumpintherefractiveindexvariationislikelytobecausedbythephasetransitioninLi1-xHxTaO3typecompoundsduetoanincreaseoftheorderparameterx(RiceandJackel1982).

Theexperimentalresults(Reachetal.1985;Boikoetal.1985;Bashkirovetal.1985;Gan'shinetal.1985)suggestthefollowingschemeofproton-exchangeddoping:

1.Proton-lithiumexchangecausestheformationonacrystalsurfaceofanearlyconstanthydrogenconcentration,whichisapparentlyduetoastrongdependenceoftheinterdiffusioncoefficientDonionconcentrationinthesurfacelayer.

2.Experimentalstudiesshowthattonucleationandafurtherannealing-stimulateddevelopmentinannealingthecrystallinephasesn-Nb2O5andLiNb3O8therecorrespondsadefiniteH+-to-Li+concentrationratiointhedopedregion.Thisratiocanbeattainedwiththehighestprobabilityattheionexchangefront.Theformationoftheindicatedphasesisinevitablyassociatedwiththeoccurrenceofsignificantstructuraldistortions.Thisaccounts,inparticular,fortheloweringoftherefractiveindexDno=0.04whichislargerthanintherestoftheproton-exchangeregion.

3.Mismatchofthelatticeparametersofn-Nb2O5,LiNb3O8andLiNbO3leadstoconsiderablestresses,andthesurfaceregiongoesovertoametastablestate.

Reportshaveappearedonthedevelopmentandsuccessfulapplicationofacombinedwayoflightguidefabricationonthebasisoflithiumniobate-theso-calledTIPE(titanium-in-diffused-proton-exchange)process(Becker1983).Theprocessproceedsasfollows:titaniumdiffusionformsaTi:LiNbO3lightguideinwhichmodesofbothordinaryandextraordinaryrayscanbeexcited.Afterthis,thesampleistreatedinabenzoic-acidorinsomeothermeltsuitableforaproton-lithiumexchange.TheTIPEpromotestheformationofstructureswithahighnonx-,y-andz-cutsofacrystal(aftertitaniumdiffusiontheLiNbO3(Y)surfaceisnotpronetodestructionundertheactionofbenzoicacid).TIPElightguidesmayhave,dependingonthe

preparationconditions,rathercomplicatedrefractiveindexprofiles.Obviously,theTidiffusioninTIPEstructuresshouldonlybecarriedoutattemperatureshigherthan950°C.DiffusionatlowertemperaturesisfraughtwithariskofformationonthecrystalsurfaceofachemicalcompoundcontainingTiandNboxideswhichblocklithiumdiffusionthroughtheinterface.Thismayresultinblockingasubsequentproton-lithiumexchange.

Beingresistanttoinducedlaserradiation,proton-exchangedwaveguidesexhibittheloweringoftheelectro-opticeffectandahighinstabilityoftherefractiveindex.Ti-diffusedwaveguidesdegradewithtime,whileproton-exchangedwaveguidesage.Moreover,theypossessatypicalshortcoming-aweakrestrictionofthelightwave,whichisduetoanessentialimpossibilityofobtainingasharprefractiveindexvariationatthesubstrate-layerboundary.

1.6.1Ion-exchangeprocessesinLiNbO3

Theproton-exchangetechniqueinvolveschemicalreactionbetweensinglecrystallithiumniobate(LiNbO3)andasuitableprotonicsource,mostcommonlybenzoicacid(C6H5CO2H,m.p.=122°C),attemperaturesfrom150°Cto300°C(Jackeletal.1982).Theoverallreactioncanberepresentedbytheequation

Hydrogenisincorporatedwithinthecrystalintheformofhydroxylgroups

astheresultofbondingbetweenH+andO2-inthelattice.Theextentofprotonexchangedependsonthereactiontimeandtemperature,andonlypartialexchangeisnecessaryforwaveguideformation(Jackeletal.1983;Rice1986;RiceandJackel1984).AcompleteexchangecanbeobservedinLiNbO3powderandresultsintheformationofthecompoundLiNbO3,causingastructural(hexagonaltocubic)transformation(RiceandJackel1982;Fourquetetal.1983;WellerandDickens1985).Itisonlytheextraordinaryrefractiveindexthatisincreasedbyprotonexchange,whiletheordinaryindexisslightlydecreased(Jackeletal.1982).ThenatureofthesinglepolarizationmeansthatTEmodesaresupportedinx-andy-cutwaveguidesandTMmodesaresupportedinz-cutwaveguides.

Theopticalpropertiesofprotonexchangewaveguideshavebeendeterminedfromprism-couplingdata(Clarketal.1983;Wongetal.1986)andinfraredspectroscopyhasbeenusedtofollowtheincorporationofhydrogenashydroxylgroups(JackelandRice1981;Lonietal.1987).ThisapproachhasbeenextendedtodeterminerelationshipsbetweentheextentofformationofOHgroupsandwaveguidedepthsforx-andz-cutsingle-crystallithiumniobate.Improvedopticalpropertiesforannealedwaveguidesandwaveguidesproducedusingbufferedmeltswerereportedmanytimes(Jackeletal.1983;JackelandRice1984;Wong1985;Minakata1986),theterm'buffered'referringtypicallytobenzoicacidcontainingsmallamountsoflithiumbenzonate.Asystematicstudyofannealedandbufferedmeltwaveguideswascarriedoutinordertounderstandwhythepropertiesareimproved.Theroom-temperaturehydrogenisotopicexchangewasshowntooccurinproton-exchangeswaveguides(DeLaRueetal.1987;Lonietal.1987)indicatingthatthesewaveguidesreactwithatmosphericwatervapour.Theisotopicexchangetechniquewasusedtoinvestigatethebehaviourofbothannealedandbufferedmeltproton-exchangedwaveguidestowardsatmosphericwatervapour

attemperaturesupto375°C.

High-indexchanges(Dn=0.12)werereportedforionexchangeofLiNbO3inmeltsofAgNO3(ManharandShah1975)andTlNO3(Jackel1980)Unfortunately,thehigh-indexchangeisnotconsistentlyreproducibleandwasfoundtobedisconnectedwiththeintroductionoftheheavyAg+andTl3.4+ions(Griffiths1981;Chenetal.1982).RatheritresultsfromaprotonexchangeprocesssimilartothatreportedbyJackeletal.(1982),withwaterimpuritiesinthemeltactingasthesourceofhydrogen(JackelandRice1982).Sincetheseprocessescannotgiveconsistentresults,theyarenotasusefulashadpreviouslybeenhoped.Thus,protonexchangeinbenzoicacidfillstheneedforameansofproducinglargeindexchangesinLiNbO3.

JackelandRice(1982)showedthatimmersionofLiNbO3inhotacids,orincertainhydratemelts,resultsinprotonexchange,inwhichlithiumionsarelostfromthecrystalandaresubstitutedbyanequalnumberofprotons(JackelandRice,1981;RiceandJackel,1982).Instrongacids,suchasHNO3orH2SO4,thesubstitutioniscompleteandthenewcompoundHNbO3isacubicperovskite.ThelargestructuralandbulkchangefromthetwistedperovskiteLiNbO3structureprecludestheformationofasurfacelayerontheLiNbO3substrate.However,inlessacidicenvironments,suchasMg(NO3)26H2OorbenzoicacidC6H5COOH),anincompleteexchangeoccurs.Studiesofsingle-phasepowdersamplesshowthatatleastasmuchas50%ofthelithiumcanbereplacedby

protonswithoutamajorstructuralchange.OnmacroscopicLiNbO3crystals,partiallyexchangedlayersthickerthan10mmhavebeenformedusingbenzoicacid.

JackelandRice(1982)choosebenzoicacidasthemostpromisingoftheprotonsourceswhichproducepartialexchange,primarilybecauseofitshighboilingpoint(249°C)andstabilitythroughoutitsliquidrange.Thehighboilingpointpermittedworkingattemperaturesforwhichdiffusionwasrapid.Stabilityofthecompoundpermittedobtainingconsistentresults.Secondaryargumentsinfavourofbenzoicacidwereitslowtoxicityandlowprice.

Benzoicaciddoesnotattackmostmetals,sometalmaskscanbeusedtodefinechannelwaveguidesorothersmallfeatures,suchasgratings.Usingamaskofapproximately100ÅCrand500ÅAu,Jackeletal.(1982)havemadeaseriesofchannelwaveguides1-20S0109>mwide.Theuseofasimilarmaskingtechniqueformakinghigh-efficiencygratingsisnowunderinvestigation.

Clarketal.(1983)confirmedthattheuseofy-cutsubstratesrendersthesurfaceofthesubstrateliabletosevereetching.However,theproblemcanbeovercomebyusingprotonexchangeinconjunctionwithTiin-diffusiontoproducewaveguidesony-cutsubstrateswhichguidebothTEandTMmodes(DeMichellietal.1982).Bothactiveandpassiveopticalwaveguidedevicescanbefabricatedusingthistechnique;highefficiencybeamdeflectors(Punetal.1982),opticalfrequencytranslators(Wongetal.1982),andsecondharmonicgenerators(DeMichellietal.1983)havebeendemonstrated(seechapters5and6).

1.6.2Samplepreparationandexperimentalmethods

Lonietal.(1989)proposedthefollowingwayofpreparationoflight-guidinglayers.Nominallyidenticalcongruent-compositionx-andz-

cutlithiumniobatesubstrates(dimensions:1cm×1.5cm×0.1cm)werepolishedonbothfacetsforIRspectroscopicexperiments.Thesamplesinholderswereplacedinindividualcoveredsilicaglassbeakerswhichcontainedaccuratelyweighedquantitiesofmoltenbenzoicacid.Theheatingsourcewasahigh-temperatureoilbathwhichwascontrolledto±0.25°C.TemperaturesweremeasuredusingaPt-13%Rh/Ptthermocouple.The'neatmelt'x-andz-cutwaveguideswerefabricatedattemperaturesbetween167°Cand211°C,fortimesrangingfrom0.12to6h.Thefabricationprocedureforthex-cutbufferedmeltproton-exchangedwaveguideswasidentical,exceptthatthewaveguideswerefabricatedat215°Cand135°Cfortimesrangingfrom1to8.5h.ThequantityoflithiumbenzoateaddedtothebenzoicacidmeltswasdefinedintermsoftheLi+molarfraction,thatis,[molesoflithiumbenzoate]/([molesoflithiumbenzoate]+[molesofbenzoicacid]).Themolarfractionsoflithiumbenzoate,forfabricationofthebufferedmeltwaveguides,werebetween0.28×10-2and1.12×10-2.

SampleswereannealedinaPyrextubemountedinafurnacewhosetemperaturewascontrolledto±2°C.Theatmosphereusedwasdioxygensaturatedwithwater,obtainedbybubblingO2throughacolumnofwarm(60°C)water.Thewaveguidesweremountedinastainlesssteelboatthatallowedauniformflowofgasoverthesurfaceofeachwaveguide.Toavoidthermalshockatinletandoutlet,thewaveguidesweremovedslowlyalongthefurnacetubeoveraperiodofapproximatelyoneminute.Theannealingtimewasdefinedastheintervalbetween

thesamplereachingthefurnacehotspotanditssubsequentremoval.ThewetO2flowwasmaintainedthroughouttheentranceandremovalperiods.

Afterprocessing,thewaveguidesweremountedinevacuablePyrexinfraredcellsfittedwithcalciumfluoridewindowsforH/Dhydrogenisotopicexchangestudies.High-temperaturehydrogenisotopicexchangewascarriedoutbyannealingthewaveguidesasabove,exceptthatD2O(99.8percent)wasusedinsteadofH2O.Theinfraredspectrawererecordedusingaspectrometeranddatastation.Theopticalpropertiesoftheplanarwaveguideswereassessedat)l=0.6328mmusingtheprismcouplingtechniqueandassumingnormalizedstep-indexequations(TienandUlrich1970).TherefractiveindexprofilesoftheannealedwaveguideswerecalculatedusingtheIWKBmethod(Finaketal.1982),amethodparticularlyusefulforwaveguideswithagraded-indexprofile.

ProtondiffusionwascontrolledbytheIRspectra.Thex-cutspectraconsistoftwooverlappingbandsintheOHstretchingregion:abroad-bandatvmax=3250cm-1duetohydrogen-bondedOHgroups,andasharpbandatvmax=3505cm-1dueto'free'OHgroups.PolarizationmeasurementsindicatethatfreeOHisconstrainedtovibrateinthe(x,y)-planeofthewaveguide.Abandatvmax=3505cm-1isalsoobservedinthespectraofz-cutwaveguides.However,theabsorptionduetohydrogen-bondedOHgroupsisdiscernibleonlyasashoulderonthelow-frequencysiteofthesharpbandatvmax=3505cm-1.

Thedifferentspectraarepresumablyduetothedifferentcrystalorientation.

Thex-andz-cutinfraredspectra,Fig.1.30(a,b),indicatethattheOHabsorbanceincreaseswiththewaveguidefabricationtime.Itwasreported(Wongetal.1986)thatforx-cutlithiumniobate,therelationshipbetweentheOHabsorbanceat3505cm-1wasnonlinear

withtemperatureandtime.TheresultsduetoLonietal.(1989)wereinagreementwiththeseobservations.However,todeterminetheextentofproton-exchange,theareaoftheOHbandsshouldbeused.Therelationshipbetweentheabsorptionbandareaandwaveguidefabricationtemperatureislinear,asdepictedinFig.1.31(a,b)forx-andz-cutproton-exchangedwaveguides,respectively.Theobservedtemperaturedependenceindicatedthatthereisaminimumtemperaturerequiredforproton-exchange,thevaluesbeingT=(140.6±3.3)°Cforz-cutmaterialsandT=(131±8.3)°Cforx-cutmaterials.Correspondingvaluesobtainedbyplottingthewaveguidedepth(determinedfromprismcouplingdata)asafunctionoftemperaturewereT=(148.5±7.5)°Cforz-cutmaterialsandT=(145.4±3.4)°Cforx-cutmaterials.Thedatasuggestthattheminimumexchangetemperatureisslightlyhigherforz-cutmaterials.

TherelationshipbetweentheOHabsorptionbandareaand(time)1/2forx-andz-cutproton-exchangedwaveguidesislinear(thez-cutcaseinFig.1.32(a)),whichisconsistentwithaprocessinwhichtheextentofOHgroupformationinthewaveguidelayerisgovernedbydiffusion.Thenaturallogarithmoftheslopeofeachline(areaversust1/2)wasplottedasafunctionof1/TandtheobservedArrheniusbehaviourenabledapparentactivationenergiesfortheproton-exchangeprocesstobecalculated.ThevaluesobtainedwereQx=60.4kJmol-1andQz=81.2kJmol-1.

Sinceboththeabsorptionbandareaandwaveguidedepthshowat1/2dependence,thetwoquantitiescanbelinearlyrelated.Thiswasverifiedbyplottingthebandareaasafunctionofdepthforthex-andz-cutwaveguides,illustrated

inFig.1.32(b)forthez-cutwaveguides.Therefore,thedepthofaproton-exchangedwaveguidecanbeestimatedbycalculatingtheareaundertheinfraredabsorptionbands.Withsuitablerecalibration,themethodcanalsobeusedforwaveguidesproducedusingbufferedmelts.Themethodisparticularlysuitedforsingle-modeproton-exchangedwaveguides,wheretheusualIWKBandstep-indexmethodscannotbeused.

1.6.3Annealedproton-exchangedwaveguides

Theeffectofannealingontherefractiveindexprofileofanx-cutproton-exchangedwaveguide(Table1.11)isshowninFig.l.33a.Althoughtheinitialstep-likeindexprofileissubstantiallypreservedafterashortannealingtime,ataileventuallyformsatthewaveguide-substrateboundary,indicatingachangetoamoregraded-indexprofile.Thewaveguide(surface)indexofthesampledecreasedby0.04(atl=0.6328mm)afterannealingat320°Cfor3h11min(Fig.1.33a),andthedepthoftheguidingregionincreasedby1.30°m(Table1.11).Asaconsequence,thenumberofmodessupportedincreasedfromthreebeforeannealing,tofive.Afterfurtherannealingat400°Cfor30min,thetailonthestep-likerefractiveindexprofilewasmoreprominent.

Theeffectofannealingontheeffectivemodeindices(at)l=0.6328mm)andwaveguidedepthofthesamesampleisillustratedinFig.1.33b.Thesecond-ordermode(m=1)andthethird-ordermode(m=2)hadmaximumeffectiveindicesafterannealingtimesofapproximately10and15rain,respectively.Thefourth-ordermode(m=3)reachedamaximumafterapproximately1h.Afterthis,theeffectivemodeindicesalldecreasedgraduallywithincreasingannealingtime.Noinitialincreasewasobservedforthefundamentalmode(m=0).TheresultsobtainedforthesamplesinTable1.11indicatethatmostofthechangesintherefractiveindexprofileoccur,

approximately,withinthe

Fig.1.30infraredspectraofproton-exchangedwaveguides.a)x-cut,T=198°C:i)4.42h,ii)3h,iii)2h,iv)1h,

v)0.25h.b)z-cut,T=211°C:i)6h,ii)4.42h,iii)3h,iv)2h,v)1h,vi)0.42h,vii)0.12h

(Lonietal.1989).

Fig.1.31Absorbancebandareavstemperature:a)x-cut,b)z-cut(Lonietal.1989).

firsthalftoonehourofannealingandthesmallervariationsareobservedafterannealingformuchlongerperiods.

Afterannealingthex-cutproton-exchangedwaveguideat250°Cfor0.5h,therewasasignificantdecreaseintheintensityoftheinfraredabsorptionbandduetothehydrogen-bondedOHgroupsinthesample,butthebandat3505cm-1wasunchanged.Aprolongedannealingatthesametemperatureproducedfurther,butsmaller,variationsinthebroad-band.Thisbehaviourcanbecorrelatedwiththeobservationthatthemajorchangesintherefractiveindex

Fig.1.32a)Absorbancebandvst1/2(z-cutproton-exchangedwaveguides).b)Absorbancebandareavsdepth

(z-cutproton-exchangedwaveguides)(Lonietal.1989).

profileofsampleX3occurredwithinthefirst0.5hofannealing.Nodecreaseintheeffectivemodeindiceswasobservedatroomtemperature(afterannealing)overameasurementperiodofoneyear,inagreementwithJackelandRice(1984).

Thehydrogenisotopicexchangetechniquewasusedtotestwhetherannealedproton-exchangewaveguidesreactwithatmosphericwatervapourinasimilarmannertoannealedwaveguides,atroomtemperature.Theinfraredabsorptionspectraindicatedthat,unlikeinunannealedproton-exchangewaveguides,nohydrogenisotopicexchangetookplaceinthematerial.However,whenthex-cutwaveguidesweresubsequentlyannealedat320°Cfor0.5hinawet(D2O)/O2atmosphere,therewasanuptakeofdeuterium.Fromtheinfraredabsorptionspectrumofthesampleitcanbeseenthatthehydrogen-bondedOHwasmarkedlyreducedbyannealing.Thesharpbandatvmax=3505cm-1decreasedsignificantly,withthegrowthofanODcounterpartatvmax=2590cm-1.Thespectraoftheabsorptionbandstructuresindicatedthat,afterannealing,thewaveguides

Table1.11Opticalwaveguidemeasurements(l=0.6328mm)andannealingconditionsfor'neatmelt'x-cutproton-exchangedwaveguides(Loni,Hay,DeLaRue,Winfield,1989)

Diffusiontime,h

Annealingtemperature,°C

Annealingtime,h

Waveguide(surface)index

Depth(mm)

1 - - 2.3281 0.40

250 0.5 2.3082 0.70

250 1 2.3081 0.70

250 2.62 2.3036 0.72

3 - - 2.3295 0.73

250 0.5 2.3168 1.14

250 1 2.3151 1.19

250 2.62 2.3098 1.27

6(T=168°C)

- - 2.3307 1.09

250 0.5 2.3231 1.41

250 1 2.3168 1.61

250 2.62 2.3153 1.63

1 - - 2.3244 0.63

320 0.25 2.3072 1.02

320 1 2.2862 1.34

320 3.18 2.2763 1.50

3 - - 2.3286 1.12

320 0.25 2.3137 1.85

320 1 2.3026 2.02

320 3.18 2.2882 2.42

6(T=175°C)

- - 2.3281 1.60

320 0.25 2.3191 2.35

320 1 2.3021 2.72

320 3.18 2.2992 2.54

Fig.1.33a)Refractiveindexprofile(l=0.6328mm)asafunctionofwaveguideannealing;thesamesamplewasproton-exchangedat175°Cfor3h.b)Variationineffective

modeindiceswithannealingtime(thesamplewasannealedat320°c)(Lonietal.1989).

didnotreactwithatmosphericwateratroomtemperature.Similarresultswereobservedwhenpreviouslyannealed(O2/H2atmosphere)waveguideswerereannealedusingD2Oatahighertemperatureof375°C,althoughhydrogenisotopicexchangewasnotobservedinthesewaveguides(beforereannealing)atroomtemperature.

1.6.4Waveguidesfabricatedusingbufferedmelts

Theopticalpropertiesofwaveguidespreparedinbenzoicacidwithaddedlithiumbenzoateweredeterminedfromprismcouplingdata,viamodeanglemeasurementsandcalculationsusingthestep-indexmodel.Theresultingwaveguidedepthswerelinearlyrelatedtothesquarerootofthefabricationtime.Asthemolarfractionoflithiumbenzoateincreases,theeffectivediffusioncoefficient(estimatedfromthedepthversust1/2curves)decreases(Fig.1.34)indicatingthattheextenttowhichproton-exchangeoccursdependsstronglyonthepresenceoflithiuminthemelt.Asimilareffectmightbeexpected,intheabsenceoflithiumbenzoate,duetothepresenceoflithiuminthemeltresultingfromtheLi+-H+exchangeprocess.

However,thelithiumconcentrationsinbenzoicaciddeterminedbyatomicabsorptionspectroscopyafterprotonexchange,aresufficientlysmall(Lonietal.1987)andtheequivalentlithiumbenzoatemolarfractionisoftheorderof0.02×10-1.Therefore,theeffectivediffusioncoefficientremainsapproximatelyconstantthroughouttheexchangeperiod.

Thedegreeofopticalstabilityinaproton-exchangedwaveguidedependsonthemolarfractionoftheaddedlithiumion(Fig.l.35a,x-cut).Forexample,thedecreaseinthefundamentalmode(m=0)indexoveraperiodof410hwas0.0045forasamplecontainingLi+molarfraction=0.09×10-2,and0.001forasamplecontainingLi+molarfraction=1.10×10-2.JackelandRice(1984)showedthatnomeasurabledecreaseintheeffectivemodeindexcanbeobservedforwaveguidesproducedfrommeltscontainingmolarfractionsoflithiumiongreaterthan3.40×10-2.

Althoughtherefractiveindexprofilesarestep-like,thevalueofDne

decreasesasthelithiumbenzoatemolarfractionincreases(Fig.l.35b).ThelowestvaluemeasuredbyLonietal.(1989)wasDne=0.085forawaveguideproducedusingLi+molarfractionequalto2.42×10-2.InfraredspectraofwaveguidespreparedinbenzoicacidwithaddedlithiumbenzoateareshowninFig.l.36.AlthoughtheOHabsorptionbandsatvmax=3505cm-1andvmax=3250cm-1arebothpresent,therelativeintensityofthelatterbandismuchsmallerthanthatforwaveguidesproducedusingbenzoicacidaloneundernormallyidenticalconditions.ThelargerLi+molarfraction,thesmallertherelativemagnitudeoftheabsorptionatvmax=3250cm-1,indicatingthatthehydrogen-bondedOHgroupsarepresenttoalesserextent.Noroomtemperaturehydrogenisotopicexchangewasobservedinthewaveguideswhichwerefabricatedusingbufferedmelts(uptoLi+molarfraction=1.04×10-2),indicatingthat,likeannealedproton-exchangedwaveguides,theydonotreactwithatmosphericwatervapour.

Annealingthebufferedmeltwaveguidesinawet(H2O)dioxygenatmospherehadrelativelylittleeffect.Forexample,nomeasurablechangesintheinfraredabsorptionspectrawereobservedafterthebufferedmeltwaveguideswereannealed.Smallchangeswere,however,observedintherefractiveindexprofiles,butthesewereofthesamemagnitudeastheonesobservedduringthelaterstagesofannealingneatmeltproton-exchangedwaveguides.

Sincethepresenceofhydrogen-bondedOHinbufferedmeltwaveguidesisverymuchreduced,thechangesintherefractiveindexprofilesasaconsequenceofannealingmustarise,inthemain,fromthediffusionofprotonsoriginatingfrom'free'OHintothesubstrate.Itisunlikelythat'free'OHout-diffusesintotheatmospheresincetherewouldbeanassociatedreductionintheabsorptionband.

Thelossofhydrogenduringtheannealingprocesscouldariseby

migrationofthehydrogen-bondedOHtothesurfaceoftheguidingregionfollowedbyreactionofsurfacehydroxylgroupstogivesurfaceoxidesandwater.Thelatterprocesscaneithertakeplaceviaroute2,orviaroute4followedbyroute5,inthescheme:

Fig.1.34Effectivediffusioncoefficientsat215°Cand235°CversusLi+molefraction(x-cut)(Lonietal1989).

Fig.1.35a)VariationineffectivemodeindexwithtimefordifferentLi+molefractions(x-cut).b)Stepindexchange versusLi+mole

fraction(x-cut)(Lonietal.1989).

(where representshydrogen-bondedOH).Theprocessisreversible,sinceithasbeenshownthatDisincorporatedintoproton-exchangedwaveguidesfromD2Oduringannealing.Thiscouldoccureitherdirectly,viaroute6,orviaroute1followedbyroute4.Thelatterrouterequireshydrogen-bondedOHtobepresentandislikelytobeimportantonlyduringtheearlystagesofannealing.Lonietal.(1989)demonstratedreversibleHDexchangeatroomtemperature.However,thisisnotobservedwithannealedorbufferedmeltwaveguides,arguingthatHDroomtemperatureexchangeinvolvesroute1thenroute4androute3thenroute2,ratherthanthedirectroutes5or6.Thedirectroutes5and6dooccurathightemperaturessince,asmentionedabove,Dcanbeincorporatedathightemperatureswithoutthepresenceofhydrogen-bondedhydroxylgroups( ).Itis

Fig.1.36Infraredabsorptionspectraofx-cutprotonexchangedwaveguidesfabricatedusingbufferedmelts,at215°C:i)neatbenzoicacid,ii)Li+molefraction=0.28×10-2,iii)Li+molefraction=1.04×10-2(Lonietal.1989).

suggestedthattheannealingprocesscanberepresentedbythefollowingreactionsteps:

Theremovalofhydrogen-bondedOHgroupsasH2Opreservedchargeneutralityinthecrystalandcantakeplaceviareaction(1.54)followedbyreaction(1.55).Reaction(1.55)wasfirstsuggestedbyBollmann(1987),althoughforadifferentsituation.

Lonietal.(1989)believethathydrogen-bondedOHgroupsarelikelytoberesponsible,toasubstantialdegree,fortheundesirableeffectsassociatedwithproton-exchangedwaveguides;forexample,deviceinstabilities,suchasdcdrift(Wongetal.1982).Wongetal.(1982)reportedthatapplyingadcvoltageofapproximately5V(eitherpolarity)toaproton-exchangedstripwaveguidephasemodulatorresultedintheextinctionoftheguidedmode,withatime-constantoftheorderof1min.Removingthedcvoltageledtoaslowrecoverywhereasvoltagereversalledtoamuchmorerapidrecovery.Suchaneffectmaywellbecausedbythemovementofhydrogen-bondedOH(protons)undertheinfluenceofanappliedelectricfield.Thedistributionofhydrogen-bondedOHis,initially,likelytobeapproximatelyuniformwithintheguidinglayer.However,onapplyinganelectricfieldtheelectrostaticforceswouldredistributetheprotons.Protonswhicharehydrogen-bondedwillbemorestronglyattractedbyanegativepotential,sincetheyarethemoremobilehydroxylgroups.Theconsequentredistributionoftheprotonscouldresultinamajormodificationinthewaveguiderefractiveindexprofile.Removaloftheelectricfieldwouldgiveachargeimbalanceandtheprotonswouldtendtomigratebacktomorefavourablesites,recoveringtheoriginalwaveguiderefractiveindexprofile.

Inadditiontotheremovalofhydrogen-bondedOHandthediffusion

of'free'OHintothesubstrate,theannealingprocessmayalsoinvolvemigrationoflithiumionsfromadjacentregionsofthesubstrateintothewaveguideregion.Inthissituation,thedistortedunitcellstructureinthewaveguidemaytendtochangebacktothatofvirginLiNbO3.Asaconsequence,theelectro-opticeffectwouldberestoredandpropagationlossesreduced.Itiswidelyacceptedthatthediamond(parallelogram)whichappearsinthe(012)plane,basedontherhombicsystem,isrelatedtothestrongelectro-opticeffectintheLiNbO3crystal,asshowninFig.1.37.Aftertheexchange,thefigureisslightlyclosetothesquare(perovskite,thecubicsystem)causedbythestrainDc/c.Sincethesquarehasthecentreofsymmetry,thelinearelectro-opticconstantdoesnotgenerallyexist.Thus,itisestimatedthatr33reducesbecauseofthedeformationofthediamond.However,inspiteofnophasetransitionintheexchangedlayer,thevalueofr33seemstobeverysmall.ItissuggestedthattheHNbO3(system)compositionoftheexchangedlayershouldhaveapoorelectro-opticeffect.

1.6.5Protondiffusion

Usingtheprismcouplingtechnique,Clarketal.(1983)calculatedtheeffective

refractiveindexofeachobservedmode.ThevaluesofeffectiverefractiveindiceswerethenusedastheinputforacomputerprogrambasedonnormalizedstepindexequationsgivenbyKogel'nikandRomaswamy(1974),tocalculatethesurfacerefractiveindexandthedepthoftheplanarwaveguide.Thestep-indexassumptionwasverifiedbymodellingthediffusionprofileoftheplanarwaveguidebyafinitedifferencesolutionoftheone-dimensionalionexchange(equation(1.56))(WilkinsonandWalker1979)

where ;Daisthein-diffusioncoefficientforprotons,Dbtheout-diffusioncoefficientforLi+ions,andutheconcentrationofprotonstothetotalconcentrationofions.

Theequationtakesintoaccounttheratioofthediffusioncoefficientsofthespeciesdiffusinginandoutofthesubstrate.Itwasfoundthattherateofprotonsdiffusinginwasverymuchsmallerthanthatofthelithiumionsdiffusingout.Fromthemodel,theoreticalvaluesofthediffusioncoefficientsforlithiumandprotonionswerefoundtobe1.62and0.08mm-2/hat200°C,respectively.Clarketal.(1983)usedtheabovemodelinconjunctionwithavariationalsolutionofthewaveequation(Walker1981)tocalculatemodeeffectiveindices.Theparameterainequation(1.56)wassystematicallyvariedtoobtainabestfittomeasuredeffectiveindexvalues.Thebest-fitprofileoccurredwhen indicatingthatthesolutionofequation(1.56)wasastepfunction.

Plotsofthediffusiondepthversus(time)1/2forvarioustemperaturesareshowninFig.1.32(b).Fromthegradientofthecurves,thevaluesforthediffusioncoefficientwerecalculatedassumingthattheprotonsourceconcentrationdidnotvaryduringtheexchangeprocess.ThisgivesvaluesofthediffusioncoefficientD(T),asshowninTable1.12.

Thevalueswerecalculatedassumingthediffusiondepthdtovaryasfollows(Crank1970):

Fig.1.37Deformationofdiamondappearsinthe planeofLiNbO3

beforeandafterexchange(Minakataetal.1986).

wheretistheexchangetime.Inequation(1.57),thetemperaturedependenceofDisgivenbytheArrheniuslaw:

whereD0isaconstantfortheprotonexchangeprocessinz-cutLiNbO3,Rtheuniversalgasconstant,Ttheabsolutemelttemperature,andQtheactivationenergyfortheexchangeprocess.Figure1.38illustratestherelationshipbetween1/TandInD(T).Fromthisplot,theQandD0valueshavebeenobtained:Q=94kJ/mol,D0=1.84×109mm2/h.Equation(1.57)canthereforeberewrittenas(1.59) exp(-5.65×103T)mm.FromFig.1.38onecanreadoffthevalueofthediffusioncoefficientwithintheworkingrangeforbenzoicacid(150-230°C).

1.6.6Waveguidesusingcinnamicacid

Punetal.(1991)havedemonstratedtheuseofcinnamicacid(C6H5CH:CHCOOH)andinparticulartranscinnamicacid,asanewprotonsourceforthefabricationofhigh-indexproton-exchanged(PE)waveguidesinz-cutLiNbO3.TherefractiveindexprofileofthePEwaveguidesusingthisacidisagradedindexfunctionandisdifferentfromthoseobtainedusingorganicacidswhichhavestepindexprofiles.

Z-cuty-propagatingPEplanarwaveguideswerefabricatedinintegratedopticsgradeLiNbO3substratesthatwerepolishedononeface.Thesubstrateswereprecleanedthoroughlyusingaseriesoforganicsolventsandpreheatedbeforeimmersingintotheacidmelt.Theanalyticalgradetranscinnamicacidwascontainedinacoveredquartzcrucibleandmaintainedatthesettemperatureforfabrication.Aftertheexchangeprocess,anyresidualacidwasrinsedawaywithacetone.Forannealingexperiments,thewaveguideswerepostbakedinahorizontalfurnaceat350°Cfortimesbetween6minand5h.A

dryoxygenatmosphereflowingat500ml/minwasusedtopreventdeoxidizationofthewaveguides.

Thewaveguidedepthsandindexprofileswerecomputedfromthemeasureddatausingthecontinuouseffectiveindexfunctionmethod(Chiang1985).

Figure1.39showsthevariationofwaveguidedepthdwithexchangetimetfordifferentfabricationtemperaturesT.Assuming ,theeffectivediffusioncoefficientD(T)canbecalculatedforeachfabricationtemperature.ThetemperaturedependenceofD(T)followstheArrheniuslaw,thatis, ,whereD0isthediffusionconstant,Qistheactivation

Table1.12Diffusioncoefficientswithrespecttotemperature(Clarc,Nutt,Wongetal.1985)

T D(T)

(°C) mm2/h

180 0.027

200 0.081

220 0.207

Fig.1.38PlotofInD(T)versus1/T(gradientofline=Q/R)(Clark,etal.1983).

energyandRistheuniversalgasconstant.FromtheArrheniusplot,thatis,In[D(T)]versus1/T,thevaluesofD0andQwerefoundtobe9.78×107mm2/hand77.15kJ/mol,respectively.HencethediffusiondepthofaPEwaveguideusingtranscinnamicacidcanbeexpressedas

Figure1.40showsatypicalvariationoftheindexprofileofthePEwaveguidewithannealingtimeasaparameter.Thewaveguidewasinitiallyexchangedat235°Cfor2h.Theindexprofilechangesfromatruncated-parabolicfunctiontoastepfunctionafterannealingfor16min.Withfurtherannealing,anindextailformsattheguidesubstrateboundaryandtheprofileisGaussian-like.Figure1.41showstheeffectofannealingonthesurfaceindexchangeDnandthewaveguidedepthincrease ,whered0istheinitialwaveguidedepthbeforeannealing.ThelineardependenceindicatesthatbothDnandDdfollowapower-lawrelationshipwithannealingtimeta,andcouldbegivenby

wherec1andc2areconstants.Fromthemeasureddata,c1andc2havevaluesof0.082and1.81respectively.Otherwaveguidespreparedusingdifferentinitialexchangetimesandtemperatureshavesimilarcurvesafterannealing,butwithdifferentvaluesofc1andc2.Annealedsingle-modewaveguidesalsoexhibitalowerpropagationloss(0.33dB/cm)comparedtothatoftheunannealedcounterpart(0.81dB/cm).

1.6.7Proton-exchangewaveguidesofMgO-dopedandNd:MgO-dopedLiNbO3

Ithasbeenreportedthatproton-exchangewaveguidesformedinMgO-doped

Fig.1.39Waveguidedepthdasafunctionofexchange

timetusingtranscinnamicacid(Punetal.1991).

LiNbO3haveahigherdamagethresholdthanwaveguidesfabricatedinundopedmaterial(Digonnetetal.1985).Inordertousehigherpumppowerswhileavoidingeffectsassociatedwithphotorefractivedamage,LiNbO3substratesdopedwithbothneodymium(toprovidethelasingmedium)andmagnesiumoxide(tosuppressphotorefractiveeffects)canbeused.

BothJackelandDigoneetetal.(1985)haveindependentlycharacterizedproton-exchangewaveguidesfabricatedinx-(DigonnetM.etal.1985;JackelJ.L.1985)andy-cut(DigonnetM.etal.1985)LiNbO3dopedwith5%MgO,whilstLietal.(1988)characterizedwaveguidesfabricatedinx-cutLiNbO3dopedwithapproximately1%Nd.Jackelusedneatbenzoicacidmeltsforwaveguidefabricationat150and250°CandDigonnettetal.usedneatandbufferedbenzoic-acidmelts(1and2mol.%lithiumbenzoate)at249°C,whereasLietal.useda'double-exchange'technique(requiring1mol%followedby3mol%lithiumbenzoate)at300°C.Lonietal.(1990)reportedthefirstcharacterizationofneat-melt,proton-exchangedwaveguidesinthex-cutsubstratedopedsimultaneouslywithMgOandNd.

Planarwaveguideswerefabricatedonx-cutNdMgO-doped(0.1-0.2%:4.5%)LiNbO3andonx-andz-cutMgO-doped(4.5%)LiNbO3.PlanarwaveguideswerealsoproducedincongruentLiNbO3andwereusedasareferenceforthewaveguidesfabricatedinthedopedsubstrates.Thewaveguideswerefabricatedbyimmersioninneatbenzoicacidattemperatureswithintherangeof182-235°C,withfabricationtimesrangingbetween1and12.5h.Allthewaveguidesweremultimode.Lightpropagationwasalongthey-direction.

ThecharacteristicOHabsorptionbandswereobservedintheinfraredspectraofalltheMgO-dopedand(Nd:Mg)-dopedsubstratesandproton-exchangedwaveguides.Therelativeintensititesofthebandsweredependentonthewaveguidefabricationparameters,inamannersimilartothatobservedforwaveguidesproducedincongruentsubstrates,andtheinfraredspectraofwaveguidesproducedinbothtypesofdopedsubstrateswereidentical.Theonlyobviousdif-

Fig.1.40IndexprofileofPEwaveguideasafunctionof

annealingtime(T=235°C,t=2.0h,Tc=350°c)(Punetal.1991).

Fig.1.41SurfaceindexchangeDnandwaveguide

depthincreaseDdasafunctionofannealingtimeta(Punetal.1991).

ferencesintheinfraredabsorptionspectra,comparedtothoseofwaveguidesformedbyprotonexchangeincongruentLiNbO3,wereinthepositionsoftheOHpeaksbeforeandafterprotonexchange.

InagreementwiththeresultsreportedbyJackel(1985),theslightlydifferentOHenvironmentsandbehaviourbeforeandafterprotonexchangemaybeindicativeofslightlydifferentwaveguidematerialstructures.

Byplottingtheexponentialrelationshipbetweenwaveguidedepthand

,andassuming ,effectivediffusioncoefficients,D(T),fortheproton-exchangeprocesswereestimated.Figure1.42showstherelationship

Table1.13Diffusionparameters(QandD0)forprotonexchangeindoped(d)andundoped(c)LiNbO3(Lonietal1990)

Sampledescription Diffusionparameters

Q(kJmol-1) D0(mm2h-1)×109

x-cut,H+:LiNbO3(c) 81.24 0.234

x-cut,H+:LiNbO3(d) 91.54 1.41

(H+:Nd:MgO:LiNbO3)(d)

z-cut,H+:LiNbO3(c) 90.40 1.472

z-cut,H+:MgO:LiNbO3(d) 99.36 5.037

H+:Nd.MgO:LiNbO3(d)

obtainedbetweentheeffectivediffusioncoefficientsandtemperatureforproton-exchangedwaveguidesfabricatedinboththedopedandundopedsubstrates.ItcanbeseenfromtherelationshipsdepictedinFig.1.42thatthediffusionprocessincongruentLiNbO3isslowerforz-cutsubstratesthanforx-cutsubstrates.ThisrelativeslownessisalsothecasefortheMgO-dopedsubstratesand,presumably,fortheNd:MgO-dopedsubstrates.

AlthoughaccordingtoFig.1.42,theprotonexchangeprocessproceedsmoreslowlyinMgO:LiNbO3thanincongruentmaterialofthesameorientation,inagreementwiththeresultsofJackel(1985),thereappeartobenomeasurabledifferencesbetweentheeffectivediffusioncoefficientsforproton-exchangeinNd:MgO:LiNbO3andMgO:LiNbO3.ThepresenceofMgOandNd:MgOLiNbO3singlecrystalshasalsobeenshowntoreducethediffusioncoefficientsfortitaniumin-diffusion(Bulmer1984).ForprotonexchangeincongruentLiNbO3dopedwith5%MgO,theeffectivediffusioncoefficientestimatedbyJackel(1985)forawaveguidefabricationtemperatureof250°Cwas0.81m2h-1.Extrapolatingthecurveforthex-cutproton-exchangewaveguidesinMgO:LiNbO3to250°C,Fig.1.42,yieldsasapproximatelyidenticaldiffusioncoefficientof0.80m2h-1.Thissimilarityisreasonable,giventheprobablelevelofprecisioninobtaininguniformMgOdopantconcentrationsinthesolid.TakingtheeffectivediffusioncoefficientsforprotonexchangeinMgO:LiNbO3(Nd:MgO:LiNbO3)asapercentageofthecorrespondingvaluesforcongruent,onefindsthatthereductionisoftheorderof50±5%forx-cutwaveguidesand37±4%forz-cutwaveguides(Table1.13).

TheobservedArrhenius-typerelationshipsbetweenD(T)andT(Fig.1.42),aretypicaloftheproton-exchangeprocess.ByplottingInD(T)asafunctionofT-1,acomparisonofboththeactivationenergyandpreexponentialfactorwasobtainedforthewaveguidesfabricated

inthedopedandundopedsubstrates,Table1.13.IncongruentLiNbO3,boththeactivationenergyandthepreexponentialfactorarelowerforx-cutsubstratesthanforz-cutsubstratesandhighereffectivediffusioncoefficientsareevidentforx-cutsubstrates(Lonietal.1989,Clarketal.1983).ThisrelationshipalsoappliesforNd:MgO-dopedandMgO-dopedsubstratesofx-andz-cutorientations.Comparingthewaveguidesproducedindopedandundopedsubstrates(Table1.13),onefindsthatlowereffectivediffusioncoefficientsareobtainedforprotonexchangeindopedsubstrates.Inaddition,theactivationenergyandpreexponentialfactorarehigherforMgO-doped(Nd:MgO-doped)substrates.ThesedifferencesareprobablyrelatedtoslightdifferencesbetweenthebulkandwaveguidecrystallinestructuresofcongruentandMgO-doped(Nd:MgO-doped)LiNbO3.

1.7Planarion-exchangedKTiOPO4waveguides

Potassiumtitanylphosphate(KTiOPO4,abbreviatedasKTPbelow)haslongbeenrecognizedasanoutstandingmaterialformanyimportantopticalandelectro-opticalapplications(Zumstegetal.1976,Liuetal.1984,Liuetal.1986).Itshighdamagethreshold,goodmechanicalandthermalstability,largeopticalnonlinearity,andbroadtemperaturebandwidthhavemadeitarguablythebestmaterialforfrequencyconversioninthevisibleandnearinfraredranges.KTPalsoshowsgreatpromiseinelectro-opticapplicationsduetoits

Fig.1.42Relationshipsbetweeneffectivediffusioncoefficientandtemperatureforaseriesofx-andc-cutproton

exchangedwaveguidesfabricatedindopedandundopedLiNbO3(Lonietal.1990).

lowdielectricconstantsandlargePockelscoefficients(BierleinandArweiler1986).

Despitetheinitialsuccesses,theion-exchangeprocesshasitsdrawbacks.Specifically,theionicconductivityvariessignificantlywithcrystalgrowthmethodsandwithimpurities,makingthedevicefabricationprocessdifficultandwithpooryields.Thisinherentlydiffusiveandstronglyanisotropicion-exchangeprocessoftenproduces (whereMisT1orRb)guideswithabroadpoorlydefinedrefractiveindexprofilealongthec-axis,andwasbelievedtoberesponsiblefortheobservedvariationsintheperformanceofthesedevices.BetterunderstandingofthemechanismofionicconductionandtheunderlyingdefectsinKTPpromisestoreducethisproblem(Morrisetal.1991).

TheionexchangeconditionsandwaveguidingresultsaresummarizedinTable1.14,wheredisthediffusiondepthandDntheincreaseinthesurfacerefractiveindex.Anerrorfunctiondistributionisassumed

fortherefractiveindexprofilesintheionexchangedregions,adistributionwhichagreeswellwiththeionconcentrationprofileandisshowninFig.1.43foratypicalRb-exchangedsample.Themaximumincreaseinthesurfacerefractiveindexobservedforrubidium(Dn=0.02)isclosetothevaluethatwouldresultinnearlycompleteionexchangeformingaRbTiOPO4surfaceonaKTPsubstrate(Zumstegetal.1976).Theincreaseinthesurfacerefractiveindexforalltheseionexchangedguidesgenerallyscaleswiththeelectronicpolarizabilitiesoftheexchangedionsrelativetopotassium.

Theionexchangedwaveguidesarestablebothatroomtemperatureand,providedthediffusiontemperatureremainsbelowabout450°C,theexchangeprocessdoesnotintroduceanynoticeablesurfacedefects.Nearandabove450°C,slightsurfaceetchingoccursinsomesamplesduringtheexchange.

TheresultsgiveninTable1.14showtheiondiffusioninKTPtobehighlyanisotropic,beingmuchgreateralongthez-axis(corpolardirection)andbeing

Fig.1.43DepthprofileforRbionexchangeinKTP

(BierleinandFerretti1987).

higheronanegativez-surface(positivepyroelectriccoefficient)thanonapositivez-surface.Thediffusionanisotropycorrelateswellwiththelargeanisotropyofionicconductivitiesanddielectricproperties(BierleinandArweiler1986).Thevariationsindiffusionintothedifferentpolarsurfacesresultfromdifferencesinsurfaceadsorptionandreactivities.Additionalvariationsindiffusionkineticsareobservedalongthez-axisfromchangesinlocalionicproperties.Somecrystalshadregionsofvaryingpyroelectricanddielectricpropertiesdependingoncrystaldefects,incorporatedO-H,etc.Thediffusionrategenerallyscaleswithionicconductivity,aresultwhichisexpectedsinceionicconductivityanddiffusionarecloselyrelated.

DiffusionconstantsandactivationenergiesindicatethattheRb-K-exchangeprocessdoesnotobeysimplediffusionkinetics.TheeffectivewaveguidethicknessandDnwerefoundtobenearlyindependentofdiffusiontimefrom0.25to4hatatypicaldiffusiontemperatureof350°Candalsonearlyindependentofdiffusion

temperaturefrom350to400°C.Also,post-annealingaRb-exchangedguideinairfrom300to350°Cfor30minto2hdidnotsignificantlychangedorDn.TheseresultsindicatethattheeffectiveexchangeorthediffusionratefortheRbKsystemisinitiallyhighandthendecreasessignificantlyaftersomepointintheexchangeprocess.ThislargechangeinexchangeordiffusionratecanbeexplainedbyassumingaverylowdiffusionconstantforRbandKinRb-rich

andahighconstantinKTP.Single-crystalRbTiOPO4(RTP)showsamuchlower(~100times)ionicconductivitythanKTPandhenceionicdiffusionisalsoexpectedtobemuchlower.ExchangingKwiththelargerRbioninaKTPsurfacelayerwillalsotendtoblockconductionchannelswhichfurtherlowersionicconductivity.Hence,duringionexchange,asthe

Table1.14KTPwaveguidecharacteristics(Bierlein,Ferretti,Brixner,Hsu1987)

Ion Surfacetype

Temperature(°C)

Time(h)

Numberofmodes

Modetype

d(mm) Dn

Rb x 450 3.3 0 TE

1 TM 1.3 0.02

Rb z(+) 350 4 3 TE 4 0.019

3 TM 4 0.018

Rb z(-) 350 4 3 TE 6.5 0.008

2 TM 6.5 0.008

Cs z 450 4 11 TE 13 0.028

8 TM 13 0.019

T1 z 335 4 4 TE 1.6 0.23

4 TM 1.6 0.18

surfacerubidiumconcentrationincreases,thediffusionconstantsatthesurfacedecreasewhichwillsuppressfurtherionexchangeandresultintheequilibriumiondistributionshowninFig.1.43.Althoughsuchanequilibriumdistributionisunusual,itisconsistentwithdiffusiontheory.Thistypeofbehaviourisanadvantageforopticalwaveguidedevicessinceitallowstospeedupwaveguidefabricationatrelativelylowtemperaturesandalsopermitsthermallystableproperties.

Planarwaveguideswerefabricatedonthez-surfaces(crystallographiccdirection)ofhydrothermallygrownKTPcrystalsbyimmersingtheminamoltenmixtureofRbNO3(80mol%)andBa(NO3)2(20mol%).Diffusiontimesrangedfrom2to20minat350°C.

Followingdiffusion,633nmlightfromahelium-neonlaserwascoupledintothewaveguideusingaprism.Theeffectiveindicesofthewaveguidemodestravellingalongthey-axisoftheKTPcrystalweremeasuredandtherefractiveindexprofileofthewaveguidewasobtainedbytheinverseWKBmethod(Risk1991).

AtypicalrefractiveindexprofileobtainedinthismannerisshowninFig.1.44forTEmodes.ThesolidcurvesinFig.1.44arethebestfitsoftherefractiveindexprofile,n(z)=ns+Dnerfc(z/d),wherensistherefractiveindexoftheKTPsubstrate,Dnistherefractiveindexchangeatthesurface(z=0)ofthesubstrate,erfcisthecomplementaryerrorfunction,anddisthedepthofthewaveguide.Theexperimentallymeasuredrefractiveindexdistributioniswelldescribedbyanerfcprofile,asmightbeexpectedforsimplediffusion,andthisagreeswiththemicroprobemeasurementsofRb-ionconcentrationreportedbyBierleinetal.(1987).IthasbeenmentionedabovethatDnanddaremarkedlydifferentdependingonwhetherthe+cor-csideofthesubstrateisused(Bierleinetal.1987).WiththeadditionofBaions,thewaveguidepropertiesareessentiallythesameonboththe+cand-csides.

ThewaveguidedepthdandsurfacerefractiveindexchangeDnweremeasuredforseveraldiffusiontimes.Thedepthofthewaveguidewasfoundtodepend

Fig.1.44RefractiveindexprofileofKTPwaveguideformedbyionexchange.PointswereobtainedbyinverseWKBfrommeasuredmodeindices.Thesolid

curvesarebestfitsoftheprofilen(z)=Dns+Dnerfc(z/d)(Risk1991).

Fig.1.45EffectofpostbakingtheKTPcrystal.Solid

curveshowsrefractiveindexprofileofwaveguidefabricatedaccordingtotemperaturecycledescribed.

Dashedcurveshowsrefractiveindexprofileofthesamewaveguideafterheatinginairto350°C

for10min(Risk1991).

ondiffusiontimetas .ThedepthobtainedforagivendiffusiontimewassimilarforbothTEandTMmodes.ThesurfaceindexchangeDnobtainedforTMmodeswassomewhathigherthanforTEmodes.ThisispossiblyaconsequenceofinferringDnfromthemode

indicesusingasimpleWKBmodelthatdoesnotincludetheeffectofthebiaxialnatureofthesubstrateontheTMmodes.However,theTMmodeindicesareaccuratelymodelledusingthissimpleWKBapproachwiththevaluesofDnanddgiven,andthissufficesforpredictingthephase-matchingcharacteristicsforfrequencydoubling.

ItisimportanttocontrolthetemperatureoftheKTPcrystalbeforeandafterdiffusiontopreventcrackingofthesubstrateandunwantedmigrationoftheRbions.ItwasfoundthatimmersingtheKTPcrystalsdirectlyintothemeltfromroomtemperaturecausedthemtocrack,sothesubstrateswerefirstgraduallyheatedinairtonearthetemperatureofthemeltbeforebeingimmersed.ThisphenomenonisaresultoftheparticularthermalandmechanicalpropertiesofKTP.TheKTPcrystalwasheldinapreheatingfurnaceforabout1h,toensurethatthetemperatureofthecrystalhadequilibratedtothefurnacetemperature.Thenthecrystalwasdippedinthemelt.Aftertheprescribeddiffusiontime,theKTPcrystalwasremovedfromthemeltandallowedtocoolrapidlydowntoroomtemperature.BecausethediffusionoftheRbionsissofastforthisRb/Baprocess,unwantedmigrationoftheRbionsfurtherintotheKTPcrystal

canoccurifthesubstrateisnotcooledrapidly,resultinginchangesintherefractiveindexprofile.ThisisillustratedinFig.1.45,whichshowstherefractiveindexprofileofaplanarKTPwaveguideimmediatelyafterthediffusionprocessandafteranadditional10minofbakinginairat350°C.Itisevidentthattheadditionalheattreatmenthasresultedinasignificantdecreaseinsurfaceindexchangeandanincreaseinthedepthofthewaveguide,andthattherefractiveindexdistributionnolongerhasanerfcprofile.

2Liquid-PhaseEpitaxyofFerroelectricsThemethodofliquid-phaseepitaxyfromthefluxisbasedonthefollowingprocedure(Nelson1963;Andreevetal.1975).Thedissolvedsubstancecancrystallizeonthesubstrateimmersedinasupersaturatedconstant-temperatureflux.Inthecourseofcrystallization,supersaturationofthesolutiondecreasesandthegrowthratetendstozero.Themaximumamountofthecrystallizedsubstanceisproportionaltothemassofsolutionandthemagnitudeofsupersaturation.

Theliquid-phaseepitaxyhassomeadvantagesoverothermethods.Stoichiometryneednotbemaintainedduringgrowthfromthemelt,whichpermitsanycombinationoftemperaturesandcompositionsneartheliquiduslineofthephasediagram.Inmanycases,acorrectchoiceofthesolventallowscrystallizationatatemperaturelowerbyseveraldegreesthanthemeltingpointofthecompound.Thishelpstolowertheconcentrationofchemicalandstructuraldefectsascomparedtothatinacrystalgrownfromanearlystoichiometricmelt.Thelowerthetemperature,thelessthepossibilityofcontaminationofthefluxbyimpuritiesfromthecontainer(Alferov1976;Dolginoveta1.1976).

Thereareseveralmodificationsoftheliquid-phaseepitaxyofferroelectrics,themostpopularofwhichareepitaxialgrowthbymelting(Miyazawa1973;Adachietal.1979),liquid-phaseepitaxyfromtheflux(Kondoetal.1975;Baudrantetal.1978(a);Baudrantetal.1978(b);Ballmanetal.1975);KhachaturyanandMadoyan1978;Miyazawaetal.1978;Kondoetal.1979;KhachaturyanandMadoyan1980),capillaryliquid-phaseepitaxy(Khachaturyanetal.

1984;FukudaandHirano1976;FukudaandHirano1980),andliquid-phaseepitaxyfromalimitedvolume(Madoyanetal.1983;Madoyanetal.1985).

Theapplicationofliquid-phaseepitaxymethodsprovidesaclearlypronouncedsubstratefilmboundarywithstep-likerefractiveindicesandarelativelysmoothsurfaceofthestructure.

2.1Theepitaxialgrowthbymelting(EGM)

ToobtainferroelectricsinglecrystalLiNbO3films,Miyazawa(1973)proposedthemethodofepitaxialgrowthbymeltingonLiTaO3substrates.Forsubstrates,LiTaO3singlecrystalswereusedbecausethepointgroupofLiNbO3and

LiTaO3hasthesameclass, ,andthemeltingpointofLiTaO3ishigherbyabout300°CthanthatofLiNbO3.ThisdifferenceinthemeltingpointisthekeypointfortheEGMmethod,wherethemeltingpointofthesubstratehastobehigherthanthatofthefilmmaterial,aswillbedescribedlater.

Fortunately,itisobviousfrommanypreviousinvestigationsontherefractiveindicesofLiNbO3singlecrystals(Tien1972)thatrefractiveindicesforordinaryandextraordinaryraysofLiNbO3singlecrystalswithanysolid-solutioncompositionarelargerthanthoseofLiTaO3atroomtemperature.TherefractiveindicesofLiNbO3andLiTaO3aregiveninchapter5,indicatingthataLiNbO3filmonaLiTaO3substrateactsasadielectriclightwaveguide.

TheLiTaO3substrate,whichwaspreparedfromasingle-crystalboulegrownbypullingfromameltwithacongruentmeltingcompositionofLi/Ta=0.951inmoleratio(Miyazawa1971)was10×15×4mminsizeinthex,y,andcdirections,respectively.Thec-planewaslappedandpolishedoptically,andLiNbO3ceramicscrushedintopowderwerelaidonthepolishedc-planeofthesubstrate.Thesubstratewiththepowderonitstopsurfacewasheatedto~1300°CinaresistancefurnaceinordertomelttheLiNbO3crushedpowderalone,anditwasthencooledslowlyat~20°C/hthroughthemeltingpointofLiNbO3(1250°C).Inthisway,aLiNbO3filmcrystallizedepitaxiallyontheLiTaO3substrate.Asamatterofcourse,thesubstrateisnotinasingleferroelectricdomain.(ThenameEGMoriginatesfromtheprocessdescribedabove.)ForthecompositionoftheLiNbO3ceramicsacongruentmeltingcompositionofLi/Nb=0.942inmoleratio(Lerneretal.1968)wasused,sinceacompositionalfluctuationdidnotoccurduringthegrowthrun.Consequently,afluctuationoftherefractiveindexdoesnotexistinthegrownfilm.TherefractiveindicesofcongruentLiNbO3are and at6328Å.

ThelatticeparametersofcongruentLiNbO3andLiTaO3singlecrystalsatroomtemperaturearegiveninchapter4.ThemismatchofthelatticeparametersatroomtemperaturebetweentheLiNbO3filmandtheLiTaO3substrateisabout0.08%and0.57%foraHandcH,respectively.ThefilmthicknesswasmeasuredbylineanalysisusinganX-raymicroanalyzer.AnintensitydistributionprofileofcharacteristicX-rayspectraforNbandTa,asshowninFig.2.1,wasobtainedbyscanningtheelectronbeamperpendiculartothefilmsubstrateboundaryoverthecrosssectionofthespecimen.FromFig.2.1thefilmthicknesswasmeasuredtobeabout6mm.Thec-planeofthefilmwasetchedwithasolutionofaHF+2HNO3mixtureatitsboilingpointfor2mintodeterminewhethertheLiNbO3single-crystalfilmwasgrownornot.

TheferroelectricdomainofaLiNbO3singlecrystalisrevealedmoreeasilybychemicaletchingthanthatofLiTaO3.Theetchedtopsurface,showninFig.2.2,indicatestheferroelectricmultidomainstructure,whichisveryclosetothatofaLiNbO3singlecrystalwheretheareaswithtrigonalhillocks(blackincolour)areatthenegativeendofspontaneouspolarizationandthosewithouthillocksareatthepositiveone.ItwasconcludedthattheLiNbO3single-crystalfilmwasgrownontheLiTaO3substrate,sinceitiswellknownthattheferroelectricdomainstructure,asshowninFig.2.2,isnotrevealedinaLiTaO3singlecrystalunderthesameetchingcondition.X-rayexaminationresults

Fig.2.1Intensitydistributionprofileof

characteristicsX-rayspectraforNbandTa,perpendiculartothefilmsubstrate

boundary(Miyazawa1973).

Fig.2.2(right)Etchfigureofthefilmsurface,indicating

theferroelectricmodulationpattern(Miyazawa1973).

indicatethattheLiNbO3single-crystalfilmwasepitaxiallygrownonthesubstrate.

Asthetopsurfaceoftheas-grownfilmwasrelativelyrough,itwashandpolishedfirstwithdiamondpasteandthenwith0.05mmA12O3powderinordertodemonstratelightwavepropagationinthe

epitaxiallygrownfilm.Figure2.3showsa6328-ÅHeNelaserbeamwhichwasfedintothefilmattheright-handsidebyaprismcoupler.Arutileprismwasusedastheinputcoupler.Thelightbeampropagatedthroughtheentirelengthinsidethefilmandthenradiatedintofreespaceattheleft-handedgeofthespecimen,leavingabrightareawhichindicatesthenear-fieldstructure.Afewspecksoflightareobservedalongthelightstreak,andalargespotisobservedneartheleft-handedge.Inotherexperiments,thesingle-crystalfilmwasgrownonthex-andy-planesofthesubstrate.Thefilmgrownonthex-planeincludedseveralcracksrunningalongtheperfectcleavageplane ofLiNbO3,Fromdetailedobservationsofthefilmsurfaceunderadifferentialmicroscope,itwasfoundthatweaklyobservedscatteringalongthepropagatinglightbeamwascausedbytheroughnessofthefilmsurface.

Ballmanetal.(1975)havemodifiedthemethoddevelopedbyMiyazawa.EvidenceispresentedwhichsuggeststhattheepitaxialgrowthbymeltinginvolvesadiffusionmechanismbetweenthemeltingliquidandtheLiTaO3substrate.AlthoughthegrowthprocessinvolvessimplemeltingofLiNbO3powderonthesurfaceofLiTaO3substrates,thesuccessfulproductionofahighqualityfilmisespeciallydependentuponthemannerinwhichthepowderisappliedtothesubstrate.

Ifthepowderedlayeristoothickorifthethicknessvariesappreciablyoverthesurfacearea,puddlesofLiNbO3formduringthemeltingprocess.Theyproduceaveryunevensurfaceafterrecrystallizationandmakethefabricationofanopticalwaveguidequitedifficult.

Fig.2.3Lightbeampropagatinginthefilmgrownontothec-plane,whichwas

fedbyaprismcouplerattheright-handside(Miyazawa1973).

LiNbO3powdersofabout30mmparticlesizeweresuspendedinalacquer.ThisLiNbO3-lacquersuspensionwasthen'painted'ontheLiTaO3substrates.Thesepaintedlayerswerepracticallyflat,andwhendry,thesuspendedpowderswerefirmlyfixedtothesubstrate.Thespecimenswerethenbroughtuptothedesiredfiringtemperature(1260°Cand1320°C)inaresistancefurnace.Duringthewarm-upperiod,theorganiclacqueriscompletelydecomposedandleavesaveryuniformlayerofLiNbO3powderreadyforthemeltphaseepitaxialreaction.Aftera30minsoakperiodatthefiringtemperaturethesampleswerecooleddowntoroomtemperatureatarateof20deg/h.

ThefilmthicknesscanbecontrolledbyvaryingtheconcentrationoftheLiNbO3-lacquersuspension.Similarly,thicknesscanbebuiltupbyadditionalpaintingandfirings.Thefilmsrequiredlightsurfacepolishorbuffinginordertocouplelaserlightinoroutviaarutileprism-filmcoupler.Figure2.4showsthephasediagramforLiNbO3(film)andLiTaO3(substrate)astothetwoendmembers(Petersonetal.1967).Theshadedarearepresentsthetemperaturerangecoveredinthisstudyanditincludesthereactiontemperature(1300°C)

reportedbyMiyazawainhiswork.

Fig.2.4LiNbO3-LiTaO3phasediagram

(Petersonetal.1970).

Itisevidentthatinameltphaseepitaxialprocessseveralfactorscombinetodeterminethefinalcompositionofthefilm.Thephasediagramitselfpredictsthefilmcompositiononecouldobtainasafunctionofthereactiontemperature.Anadditional,andimportantconsiderationistherateatwhichLiTaO3-lacquerwilldissolveinthemoltenLiNbO3-lacquerduringthesoakperiod.Afurthercompositionalgradingcanoccurduetosegregationwhichtakesplaceasthemoltenlayercrystallizesinaccordancewiththephasediagram.Thereisthenthesolidsoliddiffusionprocesswhichoccursasthegrownfilmisslowlycooledtoroomtemperature.

Thefilmthicknessmeasurementswereobtainedbyusinganelectronmicroprobeandtrackingacrossthecleavededgeofaspecimen.Theelectronbeamtrackedacrossthesurfaceofthefilmandcontinuedacrossthefilmsubstrateboundary.Asthebeamfirstentersthefilm,boththeniobiumandtantalumcountsriseandthisisindicativeofthesolidsolutionnatureofthefilm.Asthebeamleavesthefilmandentersthesubstrateregion,theniobiumintensitydiminishes.Thedistancetrackedwhiletheniobiumintensityiselevatedisequaltothefilmthickness.Figure2.5showstheeffectinafilm~3mmthick.

TheroleofsolidsoliddiffusionandhowitmaybeusedtoalterthepropertiesofagrownfilmisshowninFig.2.6.CurveArepresentstheindexoftherefractionprofileforasolidsolutionfilm.CurveBrepresentstheindexprofileforthesamecrystallinefilmafterithasundergoneanannealat1200°Cfor48h.Itisclearfromtheloweringoftherefractionindexandtheincreasedfilmthickness(3.7mmto~10mm)thatextensivediffusionhasoccurredinthesolidstateduringtheanneal.

Thelossofthefundamental(m=0)waveguidemodewasdeterminedbymeasuringthelightlostintransmissionbetweentheinputandtheoutputcoupler.Solidsolutionfilmsofthetypeshownheregavelosses

ofabout5dB/cm.Thesamemethodwasalsousedtoobtain(K,Li)LiNbO3films(Adachietal.1979)uptoseveralmicronsthick.Thequalityofthefilmdependsonthechoiceofsubstratesandthewayinwhichtheceramicpowderisdepositedontothesubstratesurface.

2.2Thecapillaryliquidepitaxial(CLE)technique

Thecapillaryliquidepitaxialtechniqueisoneofthenewmethodsforobtaining

Fig.2.5Nb+andTa+intensityaselectronbeamtracksoffilmsurfaceandfilmsubstrate

interface(Ballmanetal.1975).

ferroelectricfilms.Themethodisamodificationofthewell-knownStepanov'stechnique(Stepanov1963;Maslov1977)whichgivessinglecrystalsintheformofthinfilms(FukudaandHirano1976;FukudaandHirano1980).

2.2.1CLEgrowthprocedure

ThegrowthsetupusedforCLEgrowthisthesameasusedinthepreparationofLiNbO3ribboncrystals(FukudaandHirano1975).Thegrowthsetupcomprisesa50mmdiameter×30mmlongPtcrucible,agap-shapedPtcapillarywitha0.5mmwidthand30-50mmheight,aconicalPtafterheater,ceramicinsulatorsandasubstratepullingmechanism.ThegrowthgeometryisshowninFig.2.7.Growthisinitiatedwhenthetipofthesubstratetouchestheliquidinthecrucible,withabout0.5mmseparationbetweenthesubstrateandthecapillaryplate.Whenthesubstrateispulled,thesolutionismixedwiththatinthecapillarygap,onthetopofthedie.Therefore,thecapillarydieisusedasareservoirtofeedthelayerofliquidbetweentheexteriorofthedieandanadjacentsubstrate.Temperatureadjustmentisaccomplishedbymonitoringtheliquidtemperature.

Figure2.8showsthegeometryforanimprovedCLEtechniqueandamultilayergrowthtechnique,proposedbyFukudaandHirano(1980).IntheimprovedCLEtechnique,thecapillarydiecomprisestwoparallelverticalplatesofdifferentlengthsuitablyspacedtoprovidethecapillaryaction(seeFig.2.8a).Theliquidrisesthroughthecapillarydietopandgrowthistheninitiated.Thesubstrateplateconstitutesthediewallcomplementingthelowerendportionoftheshortercapillaryplate.Figure2.8bshowsthatafilm(LiNbO3)oraribbon(LiTaO3)crystalcanbegrownusingtheimprovedCLEandEFGtechniquessimultaneously.

LiNbO3thinfilmsweregrownfromaLiNbO3-LiVO3moltensolution.Amixtureof50mol%Li2CO3,10mol%Nb2O5and40

mol%V2O5wasusedasastartingmaterial.ThemixturewasheatedinaPtcruciblebyrfheatingandthesolutiontemperaturewasadjustedtoavaluesuitableforgrowth(850-900°C).Thefilmthicknesswascontrolledbysolutiontemperatureandpullingspeed.Afterterminatinggrowth,thefurnacewascooledtoroomtemperatureatarateofabout200°C/h.ForLiTaO3substratesmirror-polishedplates(typicaldimensions15×30×2mm)werefabricatedfromCzochralskigrownboules.Thefollowingorientationswereused:(001)<100>,(100),<210>,(130°rotatedYplate)<210>and(170°rotatedYplate)<210>,where()and<>showtheplateplaneandpullingdirection,respectively.

LiTaO3thinfilmsweregrownfromaLiTaO3-LiVO3moltensolution,aswereLiNbO3filmsfromaLiNbO3-LiVO3moltensolution.Forsubstrates,LiNbO3platecrystalswerefabricatedfromCzochralskigrownboules.Orientationswere(001)<100>,(131°rotatedYplate)<210>,and(210)<112.1°rotatedY>.

Forseveraladvancedexperiments,basedontheCLEtechnique,multiple-layerstructurefilmsorstripedfilmsonsubstratesandmultipleribbonsweregrown.Thefollowingsubstrateswereused:LiNbO3filmson(001)<100>LiTaO3plates,LiTaO3filmson(001)<100>LiNbO3plates,and(001)<100>LiTaO3substrateswith200or25mmwidthand0.75mmdepthalong<100>

Fig.2.6Indexofrefractionprofileversusthicknessforafilmbeforeandafter1200°anneal(Ballman

etal.1975).

Fig.2.7(right)GeometryofCLEgrowth(Fukuda

andHirano1980).

direction,asshowninFig.2.9(madebyionbeametching).LiNbO3thickfilmsweregrownon(001)<100>LiTaO3platesoras-grownribbons,fromaLiNbO3meltinsteadofaLiNbO3-LiVO3solution.ThefilmgrowthconditionsarepresentedinTable2.1.

2.2.2.CLEgrowthandcrystalquality

LiNbO3epitaxialthinfilmshavebeensuccessfullygrownontoLiTaO3substrates.Thefilmthickness,whengrownat970°Canda3mm/minpullingrate,wasabout2mmandalmostconstant,exceptnearthefilmedge.Thefilmsurfacewassmooth,clearandmirror-polished.Thesideviewofthefilmsubstrateboundaryobservedbyopticalmicroscopywasverysharp.AnX-rayrockingcurvefromthe

(006)reflectionshowedclearlyseparatedfourpeaksofCuKalandCuKa2radiationfromthefilmandsubstrate(FukudaandHirano1976).

Fig.2.8GeometryforimprovedvariationsoftheCLEtechnique(a)andmultiple-layergrowthtechnique(b)(Fukudaand

Hirano1980).

Table2.1LiTaO3andLiNbO3thin-filmgrowthconditions(Fukuda,Hirano1976)

Film Substrate Solutiontemperature

Pullingrate(mm/min)

Filmthickness(mm)

LiTaO3 LiNbO3 1026 2 2

LiNbO3 LiTaO3 995 1.8 0

LiNbO3 LiTaO3 975 2.3 3.5

LiNbO3 LiTaO3 970 3 3

LiNbO3 LiTaO3 965 2.3 4.5

Fig.2.9A(001)<100>LiTaO3substratewith20mmwideand0.75mmdeepgroovesetchedwithanionbeam,alongthe<100>direction(FukudaandHirano1980).

Theseresultssuggestthatthefilmsobtainedwereofhighquality.

Thethicknessofthefilmisafunctionofthesolutiontemperatureandpullingrate,ashasbeenreportedindetail(FukudaandHirano1976).Thelowerthesolutiontemperature,thethickerthefilmobtained.But

asthetemperaturebecamelower,manysmallhillocksappearedonthefilmsurfaceandslipboundariesweredetectedneartheedge.Rapidpullingproducedagradualdecreaseinthicknesswithinthecrystal,whileslowerpullingproducedagradualincreaseinthickness.

LiNbO3films,whichweregrownontothe(100)<210>,(131°rotatedYplate)<210>,and(170°rotatedYplate)<210>usingthesamegrowthconditionsasemployedonthe(001)<100>plates,wereofpoorqualityhavingroughsurfacesandmanydefects.Thefilmqualitywasremarkablyimprovedbyadjustingtheinitiatedtemperatureusingdiesofdifferentlengths.Itisassumedthattheappropriategrowthtemperaturewasachievedaftercarvingquicklythesolutionontothesubstrateusingcapillaryactionsothatthefilmdidnotsufferbadeffectsoflargesupercoolingbyloweringthesolutiontemperature.

Theimprovementwasobservedastheresultofchangingthedielength(l)(wherelmeansthepartofagap-shapedcapillary0.5mmwide)forgrowthonthe(170°rotatedYplate)<210>plate.

Figure2.10showstypicaletchpatternsforLiNbO3filmsgrownonplates(+Z)LiNbO3platesand(+Z)LiTaO3plate

crystals,respectively.Etchingwascarriedoutfor15minutesattheboilingpointoftheetchant(HF:HNO3=2:1).Forthecrystalsexamined,itwasobservedthatthefilmsurfacesidewasalways(-Z)planeoverthewholeplateirrespectiveofsubstrateorientation.ItissuggestedthatthefilmgrownbytheCLEtechniqueisofthesingledomaintype.Thismaybeattributedtothefactthatgrowthisinitiatedintheferroelectricphase.

Thelatticeconstantc0ofa filmona(001)<100>LiTaO3plate,whichwasgrownusingthemixtureofLiNbO3(10mol%),LiTaO3(10mol%)andV2O5(80mol%),wasmeasuredbyX-raydiffraction.Thevalueofcowas13.80Å,whichwasnearlythesameasthatofthebulk crystal(Swartzetal.1975).Thissuggeststhat oftheCLEgrownfilmfromthesesystemsapproachedunity,asisindicatedinEFGgrowth(FukudaandHirano1975).

LiTaO3thinfilmscouldbealsogrownwithgoodepitaxyontoLiNbO3substrates,whosemeltingpointwasabout400°Clowerthanthatofthefilm

Fig.2.10TypicaletchpatternsforaLiNbO3film(a)(-Z)LiNbO3plate(b)(+Z)

LiNbO3plateand(c)(-Z)LiTaO3plate,respectively(FukudaandHirano1980).

material.Thethicknessofthefilmsgrownat1026°Catapullingrateof2mm/min,wasabout2mm.ThefilmsurfaceandqualityobservedandmeasuredbyopticalmicroscopyandX-raydiffractionwerenearlythesameasthatofLiNbO3filmsonLiTaO3substrates.

Figure2.11showstheas-grownfilmsurfaceandsideviewofLiTaO3andLiNbO3multiple-layerstructurefilmson(001)<100>LiTaO3substrates.Thefilmsurfaceflatnessisalmostthesameasthatofthesinglelayerfilmsusedasasubstrate(seethedottedlineinFig.2.11).Thefilmareabout5mmthick.Inparticular,itischaracteristicthatthefilm-to-filmboundaryobservedbyapolarizedmicroscopeisverysharp.

LiNbO3filmsweregrownonto(001)<100>LiTaO3substratesinwhichstripedditches200or25mminwidthand0.75mmindepthalongthepullingdirectionhadbeenprepared(seeFig.2.9).Itshouldbenotedthatstripedditcheswerecompletelyburiedunderfilmsandthatthefilmsurfacewasalmostflat.

FromtheconsiderationoftheCLEcharacteristicsmentionedaboveitissuggestedthataburiedfilmorlayerstructurefilm,asdepictedinFig.2.12,canbegrownbycombiningtheCLEtechniquewithetchingandpolishing.Shapedfilmscanalsobegrownusingashapeddie.

UsingthedieasshowninFig.2.8,LiNbO3thinfilmsandLiNbO3thickfilmsweregrownon(001)<100>LiTaO3substrates.ThinfilmsgrownfromtheLiNbO3-LiVO3systemwereessentiallythesameasthosegrownusingthedieshowninFig.2.7.ThefilmgrownfromaLiNbO3meltwas200mmthick.(001)<100>LiNbO3onLiTaO3multipleribbonswerealsogrown.WhengrownfromtheLiNbO3melt,thesurfacewasnotsmoothandcontainedstriationsandripples,aswasseenintheEFGgrownribbon(FukudaandHirano1975).ThecompositionprofilesperpendiculartothefilmsubstrateboundaryweredeterminedusinganX-rayprobemicroanalyzer.Asshownin

Fig.2.13,thereisasharptransitionfromtheNb-totheTa-containinglayer.

CapillaryliquidepitaxywasusedtogrowferroelectricfilmsofLiNbO3(Khachaturyanetal.1984;FukudaandHirano1976;FukudaandHirano1980),Li(Nb,Ta)O3andLiTaO3(FukudaandHirano1976;FukudaandHirano1980),andKNbO3(KhachaturyanandMadoyan1980;KhachaturyanandMadoyan1984).Thecapillaryliquidepitaxymethodhasthefollowingadvantages:thepossibilityofobtainingfilmsfromahigh-temperaturematerialonsubstratesfrommaterialswithalowermeltingtemperature,asmoothfilmsurfaceandaclearlypronouncedfilmsubstrateboundary.

2.3Theliquid-phaseepitaxy(LPE)technique

Analysisofexperimentalstudiesofthegrowthofthin-filmferroelectricstructuresshowsthatthemostperfectepitaxiallayersofLiNbO3,Li(Nb,Ta)O3,KNbO3wereobtainedbytheliquid-phaseepitaxytechnique.Theopticallossesinlightpropagationthroughtheindicatedstructuresliewithintherange0.5-3dB/cm.

Thelowgrowthratetypicalofliquid-phaseepitaxymakesitpossibletocontrolthesizeofepitaxiallayerstoanaccuracymuchhigherthanthatattained

Fig.2.11As-grownfilmsurfaceflatnessandsideviewofaLiTaO3

andLiNbO3multiple-layerstructurefilmona(001)<100>LiTaO3substrate(FukudaandHirano1980).

indiffusionprocesses.

Kondoetal.(1975)appliedtheliquid-phaseepitaxymethodtogrowingLiNbO3films.Amixtureof50mol%Li2O,10mol%Nb2O5and40mol%V2O5waschosenasastartingcompositionforLPEgrowth.Thecompositionisequivalentto20mol%LiNbO3inthepseudobinarysystem.AfterweighingtheappropriateamountofLi2CO3,Nb2O5,andV2O5,themixturewasheatedat1200-1250°Cformorethan3hinaresistancefurnace.APtcrucible50mmindiameter,40mminheight,and1mminwallthicknesswasused.Thefurnacewasdividedintothreeheatingzones.Eachzonewascontrolledindependentlywithinanaccuracyof±0.5°C,sothattheverticaltemperaturedistributionwasalmostuniformupto200mmabovethecruciblebase.

Afterachievingcompletemelthomogeneity,themoltensolutionwascooledtoabout850°Catarateof30°C/h,andwasheldmorethan3hatthistemperature.

Ac-cutLiTaO3substrate,positionedslightlyabovethemoltensolutiontobeequilibratedwiththesolutiontemperature,wasdippedinthemoltensolution.Anappropriatedippingtemperaturewas825-850°C.Thesubstratewasthenremovedfromthemoltensolutionandslowlybroughttoroomtemperature.

Fig.2.12Aburiedfilmorlayeredstructurefilmareshown,

whichcanbegrownbycombiningtheCLEtechnique,etchingandpolishing(FukudaandHirano1980).

Fig.2.13CompositionprofilesdeterminedbyX-ray

probemicroanalyser(FukudaandHirano1980).

Thegrowthrateoftheepifilmwasexaminedbychangingthedippingtime,anditwasestimatedtobeapproximately0.1mm/min.Oneendofthesubstratewascutobliquelyinordertodraintheflux,andthefluxwasfoundtodrainfromthespecimenuponremovalfromthemoltensolution.Theresidueofthefluxadheringtotheas-grownspecimenwaswashedawaywithwater.

Theas-grownspecimenthusobtainedisshowninFig.2.14a.Thesurfaceappearsclearandsmooth,andthefilmseemstransparentandcolourless.Figure2.14bindicatesacross-sectionalprofileofthespecimennearthefilmsubstrateboundary.Thefilmthicknesswasmeasuredtobe~3.1mm,exceptneartheboundary.Protuberanceattheboundarymaybecausedby'wetting'ofthemoltensolutionontothesubstrate.

Theroughnessoftheas-grownsurfacedependsonthefilmthickness.Smallhillocks,whichappearonthesurface,aresurroundedbyfacetsofLiNbO3.Thehillocksonthegrowingsurfaceareadjacenttoaconstitutionalsupercooledsolution,andapreferentialgrowthofthehillocksoccurs.Asaresult,theymaybecomelargerandgrowfasterasthegrowthproceeds.Consequently,thefilmsurfacebecomesrougher.

Fig.2.14a)As-grownLiNbO3filmontheLiTaO3substrate.b)cross-sectionalprofilenearthefilmsubstrateedge.Film

thicknesswasabout3.1mm(Kondoetal.1975).

Fig.2.15X-rayrockingcurvetakenfor(006)reflection(Kondoetal.1975).

ThecrystallinityofthefilmwasinvestigatedbytakingX-rayrockingcurves.Figure2.15showsa(006)rockingcurve.Thefourpeaks,correspondingtoCuKa1andCuKa2radiationsfromthefilmandthesubstrate,arewellseparated.Thischaracteristicfeatureindicatesthatthefilmhasahighsinglecrystallinitywithgoodepitaxy.

Thefilmwasalsogrownontothey-platesubstrate.Thegrowthratewas3-5timesfasterthanontothec-plane.However,thefilmsurfacewasroughercomparedtothec-plane,andanX-rayrockingcurverevealedthatthefilmhadpoorepitaxywithmanymicrocracks.ThismaybecloselyrelatedtothelatticeparametermismatchbetweenLiNbO3andLiTaO3.Themismatchforthec-anda-axeswasabout0.7and0.1%,respectively.Theanisotropyofthelatticemismatchinthey-planeresultsinthenonuniformgrowthofthefilmcausedbymismatchdislocations.

Baudrantetal.(1978)hasalsousedLiTaO3substratesforliquid-phaseepitaxyoflithiumniobate.

LiTaO3waferswerepolishedtoahighdegreeofperfection,mounted

horizontallyonaplatinumsubstrate-holderandslowlyintroducedintotheverticalfurnaceforepitaxy.Asolutionobtainedfromatypicalchargeof27wt%Li2CO3-20wt%Nb205-53wt%V2O5hadasaturationtemperatureofabout950ºC.Growthtemperatureswerechosebetween940and945ºC.Undertheseconditions,thegrowthratewasabout0.5mm/min.

Inordertoobtainsmoothmonolayer-typeepitaxialfilmsratherthanisland-typefilms,severalcrystallographicorientationsofthesubstrateweretested.Symmetryconsiderationsandagoodfitbetweentheparameterssuggestedanattempttotryfirstepitaxialgrowthonthe(00.1)basalplanes.

SeveralLiNbO3filmswereisothermicallygrownfromundercooledsolutionsduringdifferentgrowthperiodsinordertofollowthesuccessivegrowthstepsofanepitaxiallayer.The[00.1]orientedfilmsbecomerapidlycontinuous

andfromthicknessofabout2mmareperfectlysmoothanddirectlyusableforlightpropagationexperiments.

Infact,theprofileofthetransitionlayercouldbedeterminedboyionicanalyserchemicalcontrol.Thisprofileshowstheexistenceofan~2000Åthicktransientlayer.Thiscanbeexplainedeitherbyaninterdiffusion ontheLiTaO3matrixor,moreprobably,byaslightdissolutionofthesubstratebeforegrowth.Thus,thefirstgrowinglayerswillhavecompositionofthetypeLiTaxNb1-xO3varyingrapidlyfrom1to0.

Fromanopticalpointofview,thisLPEfilmprofilecan,however,beconsideredasastepinterfacecomparedtothemeltphaseepitaxialfilmprofilewhichexhibitsagradedindex(Takadaetal.1974).Itshouldbenotedthattoofastacoolingrateafterepitaxyinvolvedcrackformationbothinthefilmandinthesubstrateparalleltothecleavageplanes(01.2).

Intheirearlierpaper,Baudrantetal.(1975)usedasubstrateoflithiumniobatecrystalswithorientation^c.Thepreparationandtechnologyofepitaxiallayerswereidenticalwiththosedescribedabove.

Themethodofliquid-phaseepitaxyfromalimitedvolumeofsolutioninamelthasbeenproposedrecentlybyMadoyanetal.(1983)andMadoyanetal.(1985).Crystallizationproceedsherefromalimitedvolumeofflux(solutioninmelt)containedinacapillaryformedbytwoparallelsubstrates.Whenthegapbetweenthesubstratesissmall,theliquid-phaseconvectionisabsentandthegrowingsurfaceisfedbydiffusionofthedissolvedcomponent.Thefilmthicknessdependsonthedistancebetweenthesubstrates(thecapillarywidth),epitaxytemperatureregime,materialandsubstrateorientation.Lowcoolingratesprovideprecipitationofthelayerontothesubstratesurfacewithoutcrystallizationintheflux.

Theliquid-phaseepitaxymethodiseconomicalowingtothepossibilityofusingthesolventmaterialrepeatedly.Thebasicshortcomingofthemethod,whenappliedtolithiumniobate,iscomplicatedcontrolofobtaininglayerswithprescribedparameters.Thetendencyofthesolutioninmelttosuper-cooling(to70-80ºC)hampersapreciselocationoftheliquiduscurve(theinitialepitaxytemperature).Chemicalactivityoftheliquidphaserestrictsstronglythechoiceofconstructionalmaterialforcruciblesandsubstrate-holders.

2.4Physico-chemicalbasisofcapillaryliquid-phaseepitaxy

Crystallizationfromabufferedmeltexhibitsfunctionsofboththesolutionandmeltmethods,whichaccountsforthewiderangeofcompositionsemployed,includingthemajorityofmeltingcompounds.Liquid-phaseepitaxyisdeterminedbythermodynamics,kineticsandtechnology(Andreevetal.1975).Thefirstofthesefactorsisresponsibleforthecharacterofphaseequilibriuminthesubstrate-bufferedmelt-vapoursystem.Thesefactorscompletelydeterminetheprocessunderequilibriumconditionsonly.Thekineticfactorshaveasubstantialeffectupontheepitaxyprocessundernonequilibriumconditions.Thegrowthkineticsaredeterminedbythefeedofthegrowingsurfaceandbytheactivationenergyoftheprocessatthephaseboundaries.Themethodicalfactorsincludethoseconnectedwithprocesstechnology.

Phaseequilibriuminthesubstrate-solutionsystemdeterminesthenatureofcrystallization.Asaturatedliquidphase(i.e.asaturatedsolutionofthecompoundundercrystallizationinameltofanothermaterial)isbroughtincontactwiththesubstrate,andundersubsequentsupersaturation(duetocoolingoradditionalfeedfromthesolidorgasphase)theepitaxiallayerprecipitatesontothesubstrate.Theliquid-phasecompositionandtheslopeoftheliquiduscurvedeterminethecomposition,growthrateandthicknessofthefilm.Inreality,theprocessproceedsinnonequilibriumconditionsforasimplereasonthatcrystallizationrequiressupersaturation,whichinitselfisadeviationfromequilibrium.Thisexplainswhythecrystallizationprocessandtheepitaxiallayerparametersarecharacterizedbyotherfactors,namely,byalimitedspeedatwhichcomponentsapproachthegrowingsurface(typically,inanon-mixingandisothermicsolution),bysupersaturationofthesolutionduringgrowth,bynucleationandthegrowthmechanismonthesurfaceandbyconvectionduetotemperatureandcompositiongradients.Inaddition,atanearlystageofanewheterostructurallayer,thatis,intheheterotransitionphase,therealwaysexistsathermodynamicinstabilitybetweenthesolutionandthecrystalsurface.

Thermodynamicinstabilitybetweenthecrystalsurfaceandtheliquidphasemustexistprovidedthesolidstatecomposition,wheninequilibriumwiththeliquidphase,differsfromthecompositionofthecrystalwhichisincontactwiththesolution(BolkhovityanovandChikichev1982).Furthermore,thecrystallizationprocessdependsontherelationbetweenthecrystallizationrateofagivensubstanceandthecoolingrateofthesolutionforadefinitestateofthesubstratesurface,ontheinitiallevelofsolutionsaturationandonotherfactors.Thefollowingversionsofthisrelationshiparepossible.Ifthecrystallizationrateexceedsappreciablythefeedrate,theactsofcrystallizationandsolutioncanalternateduetoinsignificantthermal

fluctuations.Thus,theepitaxyprocesswillhaveafluctuationalcharacter,whichcancauseadistortionofthecrystallizationfrontshape.Thiseffectisobservedatminimumratesofinducedcoolingofthesystem.

Underepitaxy,thesolutioninmeltisincontactwiththesubstrateontowhichthelayeriscrystallized.Theepitaxyprocessandthepropertiesoftheprecipitatedlayerarethereforealsodeterminedbythepropertiesofthesubstrate.Thesubstrateonlyhasadirecteffectuponthecrystallizationofthefirstlayer(withthethicknessofseverallatticeconstants),whentheepitaxyprocessisdeterminedbythecharacterofphaseequilibriumatthesubstrate-solutionboundaryandbythekineticsofsurfaceprocesses.Althoughthefurthergrowthproceedsontheepitaxiallayer,partofthesubstrateparametersaffectthecrystallizationduringthewholeprocess(e.g.thesubstrateorientation).Inthisconnection,inthechoiceofmaterialforasubstrate,alongwithphysicalparameters,suchastherefractiveindex,opticalcoefficients,etc.,thecrystallochemicalspecificitiesshouldbetakenintoaccount.Themostimportantconditionforobtainingperfectlayersisuniformityofthecrystallinestructureofthefilmandsubstratewithadifferencebetweenthelatticeconstantsnothigherthan1%.Thesubstratemustbechemicallyneutralwithrespecttotheliquidphaseanditssolubilityinthemeltinsignificant.Finally,substrate-filmpairsshouldbechosentohaveclosethermalcoefficientsofexpansionlesttemperature

variationsshouldinducestrongtensionsalongtheinterface.

Theclosevaluesofthefeedratesandcrystallizationpromoteconditionsofapproximateconstancyofthebufferedmeltsupersaturation.Thisprovidesahigheruniformityofcrystallizationlayers.Whenthesubstanceapproachesthecrystallizationfrontatarateexceedingthecrystallizationrate,thesupersaturationofthesolutioninthemeltgraduallyincreases.Undertheseconditions,thevariousactivecentreshaveanincreasingeffectuponthelayergrowth.Theroleofsuchcentresismostoftenplayedbydefectsofthesubstratesurfaceandatomsofimpuritiesinthesolution.Whentheinducedcoolingrateofthesystemdiffersonlyslightlyfromtheoptimumepitaxyconditions,thepredominantsubstancecrystallizationonthesecentrescanbeseenasaslightworseningofthestructuralperfectionofthelayers.Afastercoolingofthesystemleadstoastrongerpredominantroleofdefectsoftheorientingsurfaceinthecrystallizationprocess.Theextrememanifestationofthiseffectisthepolycrystallinelayergrowthwhichtakesplaceatconsiderableratesofinducedcoolingofthesystem.Thus,forthegrowthoflayerswithaperfectenoughstructureandmorphologyofthesurface,thesolution-substratesystemshouldbesocooledthatastrictlydefiniteandconstantamountofsubstanceisfedtothecrystallizationfrontperunittime.

Thebasicrequirementsonsolventsusedinliquid-phaseepitaxyareasfollows(Andreevetal.1975):

1.alowmeltingtemperatureofthesolventandalowvapourpressureattheepitaxytemperature;

2.ahighsolubilityofmaterialundercrystallization,whichmakesitpossibletoobtainepitaxiallayersatlowtemperatures;

3.stabilityofthesolidphaseofthedissolvingsubstanceundergrowth

conditions;

4.solventneutralitytothecruciblematerial;

5.alowsolventsolubilityinthecrystallizedlayer(thesolventcontaminatesthefilmlessifthefilmandsolventmaterialhaveidenticalions).

UnderLPEofferroelectrics,theconstituentliquidofthesolutionismostoftenoneofthebasiccomponentsofthesolidstate,andphaseequilibriumsaresuchthattheliquidsolutionfromwhichprecipitationoccursisdilutewithrespecttoallthecomponentsexceptone.

Forinstance,forgrowingferroelectricfilmsoflithiumniobatefromasolutioninmelt,thesolventshouldbenonvolatileandnonviscous,withawiderangeofsupercooling,andmustnotformcompoundsandsolidsolutionswiththedissolvedsubstance.Thethermalcoefficientofsolubilitymusthavevaluesoftheorderof0.1%g/gradinorderthatthesolutioninmeltcouldbecooledslowly.Toobtainfilmsofhighopticalqualityandstructuralperfection,itisnecessarytooptimizesimultaneouslyallthetechnologicalparameters,namely,supersaturationandviscosityofthesolution,saturationtemperature,etc.

Foranadequatechoiceofsolvent,thesolubilityoflithiumniobatewasinvestigatedinvariousinorganiclayers:PbO-PbF2,Li2O-MoO3,Li2O-V2O5(Kondoetal.1975;Baudrantetal.1975),Li2O-B2O3,Li2O-WO3(Kondoetal.1975;Ballmanetal.1975),LiF,LiCl(Kondoetal.1975),KCl(Baudrantetal.1975),K2WO4andWO3(KhachaturyanandMadoyan1978).Thepossibility

ofLiNbO3precipitationfrombufferedmeltsLi2O-V2O5,Li2O-B2O3andLi2O-WO3wasrevealed.Allthethreesystemsexhibitedprecipitationoflithiumniobatewithouttheformationofotherphasesinawiderangeofconcentrations.

Beforeanyliquid-phaseepitaxialtechniquewasappliedtofilmgrowth,severalsystemsofinterest,K2WO4-LiNbO3,KVO3-LiNbO3,NaVO3-LiNbO3andLi1-xNaxVO3-LiNbO3,wereinvestigated(Neurgaonkaretal.1980)andthetemperatureandcompositionalboundariesoverwhichLiNbO3crystallizeswereestablishedbythedifferentialthermalanalysistechnique.

ExaminationofthephasediagramsinFig.2.16showsthattheLiNbO3phasecrystallizesinallthethreesystemswhentheconcentrationofLiNbO3isabove50mol%and,hence,thedippingtemperaturehadtobeinthe1100to1150ºCrange.TheLPEgrowthoftheNb-richfilmswassuccessfulontheY-cutLiNbO3substratesfromtheK2WO4-LiNbO3andKVO3-LiNbO3systems,andtheunitcellavariedfrom5.148ÅforLiNbO3substrateto5.153ÅfortheNb-richLiNbO3films.Ballmanetal.(1975)alsostudiedtheK2WO4-LiNbO3system,andtheirresultswereinexcellentagreementwiththoseofNeurgaonkarandStaples(1981).AccordingtoNeurgaonkaretal.(1978),K+doesnotpreferthesixfoldcoordinatedLi+-siteintheLiNbO3structure;thechangesintheunitcellaarethereforeconsideredtobeduetochangesintheLi:Nbratio.

Inthethirdsystem,NaVO3-LiNbO3,thesituationiscompletelydifferent.Crystalchemistry(Neurgaonkaretal.1980)showsthatabout7mol%sodiumdissolvesintheLiNbO3structureand,forthisadditionofsodium,theunitcellachangedfrom5.148ÅforLiNbO3to5.179ÅforLi0.93Na0.07NbO3.This

Fig.2.16Partialphasediagram:a)K2WO4-LiNbO3;b)KVO3-LiNbO3;c)NaVO3-LiNbO3

(NeurgaonkarandStaples1981).

createdalargelatticemismatchbetweentheLiNbO3orLiTaO3substrateandthefilm,andtheLPEgrowthwasthereforeunsuccessful.

2.4.1ThephasediagramofLiVO3-LiNbO3

Theanalysisoftheresultspresentedaboveshowsthatobtainingfilmsismuchmoredifficultfromtheborateandtungstensystemsthanfromthevanadiumone.ThemostsuitablesolventforLiNbO3appearedtobethecompositionLi2O-V2O5whichsatisfiestheabove-mentionedrequirements.Theexcessivesolventiseasilyremovedfromtheepitaxialstructuresurfacebyboilingindistilledwater.

Tochooseoptimumgrowthconditionsandtostudythegrowthkinetics,exactdataarerequiredonthephasediagramofthesolvent-precipitatesystem.Sincethedataintheliteratureareverydiverse,itbecamenecessarytocarryoutsystematicphysico-chemicalstudiesofthepseudobinarysystemLiVO3-LiNbO3.

ThecharacteroftheinteractionbetweenLiNbO3andthefluxLi2O-V2O5waspreliminarilyinvestigated.Coolingthemeltedmixturewith10to100mol%LiNbO3atarateofabout1grad/minresultedintheformationofsmallcrystalswhichcouldbeeasilyseparatedfromtherestofthebufferedmeltbywashingindistilledwater.X-raydiffractionexaminationshowedthattheprecipitatedcrystalpowdercorrespondedtolithiumniobate.Itshouldbenotedthat,insomecases(LiNbO3concentrationfrom30to50mol%),thecrystalsizereached5mm.So,thepossibilityofLiNbO3crystalgrowthbythespontaneouscrystallizationmethodhasbeenshown.

Figure2.17ashowstheusefulpartofthepseudobinaryphasediagraminvestigatedbydifferentialthermalanalysis(DTA),directobservationsofthemeltandX-rayanalysis(Baudrantetal.1978).

Usingheatingandcoolingratesof10or5ºC/min,thermaleffectsdue

todissolutionandcrystallizationcanbedetected.Thus,theappearanceoftheLiNbO3solidphasefromvariousconcentratedsolutionsiseasilydetectableandisrepresentedbythedarkline2inFig.2.17awhichis,infact,thecriticalnucleationcurve.Endothermalphenomenaduetodissolutionarelessdiscernibleatalowsolutionconcentrationandmustoftenbecompletedbymicroscopicandweighingobservationsduringliquid-phaseepitaxyexperiments.ItisthuspossibletodrawthedottedlineinFig.2.17awhichrepresentstheliquiduscurve.

Theeutecticpointhasbeenlocalizedatabout4mol%ofLiNbO3byaccurateX-rayinvestigationsoftheprimarylargestcrystalsfoundinthebulksolid'residue'.TheprimarycrystalshavebeenidentifiedasLiVO3ononesideoftheeutecticpointandLiNbO3,ontheotherside.ThisdiagramshowsthatLiNbO3canbecrystallizedoverawidecompositionrange.Finally,Baudrantetal.(1978)pointoutthatthedomainoftheslowgrowthrateisverynarrow,extendingnomorethan10ºCundertheliquiduscurve.

TheliquiduscurvewascalculatedusingtheSchröderequation:

Fig.2.17a)PseudobinaryLiNbO3-LiVO3phasediagram,(1)-liquiduscurve.(2)-criticalnucleationcurve(Baudrantetal.1978);b)Dependence

ofthemolefractionlogarithmoninversetemperature(Madoyanetal.1979).

whereN1isthemolarfractionofthedissolvedcomponent.Thelineardependenceofthelogarithmofthemolarfractionontheinversetemperature(Fig.2.17b)suggestsanidealnatureofthesystemsolutions.ThemeltingheatofanindividualLiNbO3,determinedfromtheslopeangle,isequalto13.2kcal/mole.

Analysisofthephasediagramshowsthepossibilityofobtainingfilmsandcrystalsoflithiumniobatewithinawidetemperaturerangeof700to1200ºC.Withintherangeof750-950ºC(15-30mol%LiNbO3),theslopeoftheliquiduscurvepermitsaneasygrowthcontrolsinceaslighttemperaturevariationdoesnotentailavariationofthesolutioncomposition.Thegrowthrateofthelayercanbeestimatedfromthevariationofthesolutionconcentrationatagivencoolingrate.

2.4.2PhasediagramofLiVO3-Li(Nb,Ta)O3pseudobinarysystem

PhasediagramsoftheLiVO3-Li(Nb1-xTax)O3pseudobinarysystem,rangingfrom0to1,wereinvestigated,wherexisthemoleratioofTa2O5/(Ta2O5+Nb2O5)(Kondoetal.1979).Thetemperature-compositionrange,inwhichLi(Nb,Ta)O3solidsolutioncrystallizes,wasdeterminedbydifferentialthermalanalysis(DTA).Phase

diagramsforLi2O-Nb2O5,Li2O-V2O5andV2O5-Nb2O5pseudobinarysystemswerereportedonbyReismanandHolzberg(1965),ReismanandMineo(1962)andWaringandRoth(1965),respectively.

SamplesforDTAexperimentswerepreparedbymixingchemicalreagentgradeLiCO3,Nb2O5,Ta2O5andV2O5powderinthedesiredratios.Themixtureswereplacedinaplatinumcell.DTAmeasurementswereconductedinahigh-temperaturethermoanalyzerusinga-Al2O3asareference.Heating-coolingcycleswerecarriedoutatarateof20ºC/min,andwererepeatedseveraltimes.Heatingorcoolingratesbelow20ºC/minoftenresultedinaveryweakresponsecorrespondingtothermaleffectsduetodissolutionandcrystallization.ThetemperaturecorrectionofDTAmeasurementswasmadebyusingLiVO3(616ºC),NaCl(800ºC)andLiNbO3(1250ºC)asreferencesatthesameheating-coolingrate.Liquidustemperaturesweredeterminedfromtheheatingcurves,because

theheatingcurvesdidnotindicatesignificantoverheatingeffects,whilethecoolingcurvesoftenindicatedlargesupercoolingeffects.Furthermore,liquidustemperatureswerealsorecognizedbysaturationtemperatures.Thesaturationtemperatureisdeterminedasthetemperaturewhereneitherdissolutionnorcrystallizationoccurswhenasubstrateisdippedinthesolution.Theliquidustemperaturefromtheheatingcycleagreedwiththesaturationtemperaturewithin±10ºC.

TheresultsaregiveninFig.2.18,wheretheendmembersarestoichiometricLiVO3andspecificsolid-solutioncompositionsofthepseudobinarysystemLi(Nb1-xTax)O3,andliquidustemperaturesforseveralvaluesofxareshown.OnthephasediagramoftheLiVO3-LiNbO3pseudobinarysystem,x=0.0intheFig.2.18,theliquidustemperaturedecreasesfrom1250ºC,themeltingpointofLiNbO3to960ºCat20mol%LiNbO3.Apseudoeutecticoccursatabout3mol%LiNbO3.

Theliquiduslinesbecomehigherandtheirslopessteeperastheparameterxincreases.Figure2.18showsthattheprimaryphaseLi(Nb,Ta)O3cancrystallizeatpercentageshigherthan3mol%Li(Nb1-xTax)O3foreachxvalue.

Tamadaetal.(1991)reportedaLiNbO3thin-filmopticalwaveguidegrownbyliquidphaseepitaxy(LPE)usingLi2O-V2O5fluxanda5mol%MgO-dopedZ-plateLiNbO3substrate.Unfortunately,therewasalargeopticallossatblue-greenwavelengthsinspiteofitshighcrystallinityandgoodsurfacemorphology.Thisopticalabsorptionwhichcouldnotbecompletelyremovedbytheheattreatmentinaflowingoxygenwithlessthanafewvol.%ozoneafterfabrication,wasduetothe crystalfieldtransitionofV3+ionswhichwereincorporatedintotheLiNbO3filmfromtheLi2O-V2O5flux.Therefore,inordertorealizeaLi2O-V2O5thinfilmopticalwaveguideforbluewave-

Fig.2.18PhasediagramofLiVO3-Li(Nb1-xTax)O3pseudobinarysystem(Kondoetal.1979).

lengths,anotherfluxsystemwhichisfreefromtransitionmetalsmustbedeveloped.

Li2O-B2O5wastargetedasalikelycandidateforthisfluxsystemforseveralreasons.First,itdoesnotcontaintransitionmetals,sothatopticalabsorptioncentresmightnotbeintroducedevenifboronwereincorporatedintothefilm.Second,thereportedeutecticreactiontemperatureof800ºContheLiNbO3-LiBO2pseudobinarysystem(Ballmanetal.1975)issufficientlylowascomparedwiththeCurietemperatureofLiNbO3(1050-1200ºC).Moreover,MgO-dopedLiNbO3wasconsideredtobemoresuitableasasubstrateforobtainingaLiNbO3thinfilmwithhighcrystallinity,becausefilmpropertiesweredrasticallyimprovedwhenaMgO-dopedLiNbO3substratewasusedwithLi2O-V2O5flux(Tamadaetal.1991).

YamadaandTamada(1992)reportedLPEgrowthofLiNbO3thinfilmsona5mol%MgO-dopedZ-plateLiNbO3substrateusingLi2O-B2O3fluxandpresentedadetailedcharacterizationofthefilmproperties.

LPEgrowthwastriedfrommetalsofvariouscompositionsintheLiNbO3-LiBO2pseudobinarysystem.Meltcompositionsappropriateforobtainingfilmswithaperfectmirrorsurfacewerearound20mol%LiNbO3intheLiNbO3-LiBO2pseudobinarysystemwhichcorrespondstothepointof50mol%Li2O,10mol%Nb2O5and40mol%B2O3intheternarysystem.Thus,theLi2O/Nb2O5compositionwasalsovariedalongtheB2O340mol%fixedlineintheternarysystem.Thegrowthtemperaturewaschosentobeabout5ºClowerthanthesaturationtemperature,whichresultsinagrowthrateof1mm/min.Inthisway,aLiNbOsingle-crystalthinfilmwithasuitablethicknessforanopticalwaveguidecanbeobtainedbydippingthesubstrateintothemeltfor3-4min.

Thefilmcrystallinitywasinvestigatedbythex-raydoublecrystal

method.Afilmgrownfrom52mol%Li2O,8mol%Nb2O5and40mol%B2O3meltwasused.Thefullwidthathalf-maximumof11.4arcsecforapeakcorrespondingtothefilmiscomparableto10.2arcsecforthesubstratepeak,whichindicatesthatthisfilmhasextremelyhighcrystallinity.Thedifferenceofthediffractionanglebetweenthefilmandthesubstratewas249arcsec.Thelatticemismatchalongtheaaxis,Da,calculatedfromthisvalue,is41.4×10-5nm,whereYamadaandTamada(1992)definedthesubstratelatticeconstantminusthefilmlatticeconstant.ThevalueofDawassomewhatlargerthanthatoffilmsgrownfromLi2O-V2O5flux(3.7×10-5-40.3×10-5nm),whichsuggeststhatthisfilmhasacompositionricherinLi.Thereexistsanapproximately400nmthicktransientlayerformedbyMgdiffusionfromthesubstratetothefilm.However,ifthethicknessofapracticalopticalwaveguide(typically4-5mm)istakenintoaccount,itcanbesaidthattheprofileofthisLPEfilmisalmoststep-shaped.Thoughboroncouldnotbedetectedatallinthismeasurement,averysmallamountmightbeincluded.

Theferroelectricdomainstructurewasalsoinvestigatedusingaconventionaletchingmethod.Thecross-section,whichcorrespondstothe-Ysurfaceofthesubstrate,wasopticallypolishedandthenetchedina1HF+4HNO3solutionat90ºCfor1min.Polishedsurfaceswereexaminedusingadifferentialinterferencemicroscope.Thisshowedthatsingle-poledfilmsweregrownonboththe+Zand-Zsurfaceofthesubstrate.Butthedirectionofspontaneouspolarizationofthefilmgrownonthe-Zsurfaceisoppositetothatofthe

substrate,whereasfilmsgrownonthe+Zsurfaceweresingle-poledalongthesamedirectionasthesubstrate.Thesephenomenaformastrikingcontrasttothedomaininversionatthe+ZsurfacewhentheLi2O-V2O5fluxisused(TamadaandYamada,1991)andcanbeexplainedbyaninternalself-polingfieldproducedbythedifferenceofthespontaneouspolarizationbetweenafilmandasubstrate(Miyazawa,1979;PeuzinandMiyazawa,1986).Thatistosay,duetotheLi-richcompositionofthefilm,therelationshipofthespontaneouspolarizationofasubstrateandafilmatthegrowthtemperatureiscontrarytothatofthecaseusingLi2O-V2O5flux.

2.4.3Theschemeofthegrowthcell

FourbasicwaysoffilmcrystallizationfromafluxontoasubstrateareillustratedinFig.2.19onanexampleoftheLiVO3-LiNbO3system:

1.growthbyaslowsolutioncooling(thestraightlineA-B);

2.growthonasubstratelocatedinthecoldpartofthecrucibleatatemperatureTcold,theexcessivecrystallizingsubstancebeingincontactwiththesolventinahotterzoneatatemperatureThot.

Convectionanddiffusionthattakeplaceinthismethodcausemassexchangewhichallowsanexcessivedissolvedsubstanceprecipitateonthesubstrate.Inthefilmgrowthregion,theconditionsaredeterminedbythevalueoftheconstanttemperaturegradientandbythesubstrategrowthregime(thestraightlineC-E);

3.growthundertheconditionofsupersaturationduetosolventevaporation(thestraightlineA-D);

4.filmgrowthbymeansofspontaneouscrystallizationfromasupersaturatedsolutionataconstanttemperature.

Solutionsaturationisachievedbypreliminaryslowsaturationofthesolution.Themethodisbasedontheabilityofthesolutionofsome

compoundstoreachastableandstrongsupersaturationwithinawidetemperaturerangeandwithalowtemperaturegradient,whichpermitsrapidgrowthofepitaxial

Fig.2.19Phasediagramillustratingthemethods

ofgrowingsingle-crystalfilmsfromsolutioninmelt(onanexampleoftheLiVO3-LiNbO3

system).

filmsbyspontaneouscrystallizationfromasupersaturatedsolution.

TheadvantagesofLPEareclearlyseenonanexampleofobtainingalargeseriesofsemiconductorA3B5typecompounds.Togrowoxideferroelectricfilms,thismethodshouldbemodified.

Themostpromisingisthemethodofcapillaryliquid-phaseepitaxialgrowthofferroelectrics,proposedbyKhachaturyanandMadoyan(1985),whichprovidesimprovementofplanarityandthequalityoflayersurfacesgrownfromathinplane-parallelvolumeofameltandpermitssomecontroloverthegrowthparameters.Thismethodalsomakesitpossibletodefinewithahighaccuracytheparametersdeterminingthefilmthicknessandgrowthrate.CombinationofthewideoperationallatitudeofthecapillarytechniquewiththegeneralproceduralmeritsofLPEmakesitthemostpromisingmethodofobtainingintegro-opticalelements.

Inageneralcase,theliquid-phasecapillary(LPC)technique(PanishandSumski1971;Bolkhovityanov1977;MalininandNevski1978)suggestsfilmgrowthfromabufferedmeltlimitedtotwoparallelsubstrates.

Figure2.20givestheschemeofsubstratepositionsandthetemperatureregimefortheliquidcapillaryepitaxymethod.

Substratesaremoundedverticallyoveracruciblefilledwithaliquid,andatastartingepitaxytemperatureT0areimmersedinthebufferedmeltwhichispulledintothegapbetweenthesubstratesduetotheactionofcapillaryforces.Thewettedsubstratesarethenmoundedhorizontallyintheoperatingzoneofthereactionvessel,andthetemperatureinthecrystallizationcellstartstodecrease.Filmsgrowontheinnersurfacesofthesubstrates,asshowninFig.2.20.Aftertheepitaxialthin-filmstructureisformed,theliquidphaseissuckedofffromthecapillarygapbymeansofaliquid-phaseabsorber(Dudkin

andKhachaturyan1988).Theliquid-phaseabsorberwasmadeofmicrochannelslabsorkaolincotton.

Thetemperatureregimeoftheprocessisdeterminedbytheslopeoftheliquiduscurve.Forprecipitationofperfectlayersatahigh-temperaturecoefficientofsolubility,thecoolingrateshouldbeverylow.

Fig,2.20Temperatureregimeduringtheepitaxyprocess(left)

andtemperaturedistributionundercapillarytechnology(right)(KhachaturyanandMadoyan1984).

Animportantadvantageoftheliquid-phasecapillary(LPC)techniqueisaconstantthicknessoftheliquidzoneoverthewholesubstratesurface.Thismakesitpossibletoremovethewedgeshapeandobtainequallythicklayers.Themaximumgapisdeterminedbythefluxviscosityandbythewettingofthesubstratesurface.

TheLPCtechniquepermitseasycontrolofthegrowthrateandthelayercomposition:theprecipitationrateisdeterminedbysupersaturationnearthefront,whichdependsondiffusionandthetemperaturevariationrate.

2.5KineticsofepitaxialgrowthofLiNbO3

Masstransferplaysanimportantroleinthecrystalandfilmgrowth.Havingadirecteffectuponthethicknessandgrowthrate,theseprocessesdeterminethestructuralperfectionandpropertiesofthegrowncrystalsandfilms.Thestudyoftheregularitiesofprocessesintheliquidphaseandattheinterfacesuggestsoptimumversionsofcontrolovergrowthandobtainingepitaxiallayerswithprescribedproperties.

Themajorityofpapersdevotedtokineticsofepitaxialfilmgrowthfromabufferedmeltarebasedonthediffusionapproximationinwhichthefilmgrowthrateislimitedbythediffusionmasstransferofthedissolvedcomponenttothecrystallizationfront.

WehavealsoconsideredthegrowthkineticsofLiNbO3filmsinthediffusionapproximationandestablishedthedomainofitsapplicabilitywithinwhichtheinfluenceofconvectiveprocessesisinessential.Calculationshavebeencarriedoutwithallowanceforspecificitiesofagrowingsystemforthecapillaryversionofepitaxy,whichpermitsahighlyaccuratereproductionofthecalculatedconditionsofepitaxy(MadoyanandKhachaturyan1983).

2.5.1Thestationarycrystallizationmodel

Weshallconsideracrystallizationsystemintheformoftwoparallelsubstrateswithabufferedmeltbetweenthem.Thegapbetweenthesubstratesismuchlessthantheirsize,whichcorrespondstotherealconditionsandallowsustoproceedtoaone-dimensionalproblem.Thesystemisassumedtobeisothermalwithoutlocalsupercooling,andtheinitialconcentrationC0isthesamethroughouttheentirethicknessofthesolution.

Inrealsystems,phaseandchemicalequilibriumaredisplacedinorientedcrystallization.Thesolutionconcentrationdiffersfromtheequilibriumvalue,variesfromonecrystallographicfacetorientationtoanother,andisconnectedwiththepropertiesofthisfacet.So,inourmodeltheconcentrationnearthesubstratesurfacemustbehigherthantheequilibriumonebyacertainquantityUdependentonthematerialandsubstrateorientation.

Weshallexaminetheconcentrationvariationinacapillaryconsistinginthegeneralcaseofdifferentsubstrates(Fig.2.21).Coolingofthesystemleadstotheformationofaconcentrationprofileandtolayerprecipitationontothesubstrates.Atapointx=0,whichcorrespondstothemaximumsupersaturationofthesolution,theconcentrationgradientisequaltozeroand,therefore,theparticleflowsthroughtheplanex=0areequalonbothsides.Then,fortheliquid-phaseregiontrappedbetweentheplanex=0andthefirstsubstrate,

Fig.2.21Schematicofdistributionofconcentrationsinacapillarysystem:a)precipitationontodifferentsubstrates;b)precipitationonto

identicalsubstrates;c)concentrationvariationduringcrystallizationinthebulk;d)dependenceoftheeffectivethickness

oftheliquidphaseonthesizeoftheopeninginacapillary.

theconcentrationdistributionsatisfiesthediffusionequationwiththeboundaryconditions

whereC0istheinitialsolutionconcentration,C1(x,t)istheconcentrationofthecomponentbetweenthefirstsubstrateandtheplanex=0,mistheslopeoftheliquiduscurve,tistime,aisthecoolingrate,U1issupersaturationnearthesubstratesurface,(m=tanj)istheslopeangleoftheliquiduscurve.

Introductionofsupersaturationdoesnotalterthecharacterofdistributionbutonlyleadstoitsdisplacementintime(retardation)byu1m/a.Thesolutionofthediffusionequationgivestheexpressionforconcentrationvariation(Moon1974):

where ,Disthediffusioncoefficient.

Underquasistationaryconditions(for ),integratingtheexpression(2.2),weobtainthevalueofthemaximumrelativesupersaturationDCm1:

WesimilarlyobtainexpressionsfordC2/dxandDCm2intheregionbetweentheplanex=0andthesecondsubstrate.Theresultingsupersaturationinthesolutionisequaltothesumoftherelativesupersaturationandthesupersaturationatthesubstratesurface.Sincethetemperaturesofbothsubstratesarethesame,itfollowsthatintheabsenceofnucleationintheliquid-phasevolume,theremustholdthecondition

From(2.4)wecanreadilyderivetheexpressionfor and :

whereU21=U2-U1and isthegapbetweenthesubstrates.Thus,filmprecipitationontodifferentsubstratesinacapillarycomesfromtheliquidlayerwhosethicknessisdeterminedbytheexpressions(2.5)and(2.6).

Nowweshallconsiderprecipitationontosimilarsubstrates,whenU1=U2.IftheresultingsupersaturationexceedsthecriticalsupersaturationDCm0underwhichcrystallizationoccursinthebulk,precipitationintoeachsubstratecomesfromalayerthickness(Fig.2.21(b)).Supersaturationintheliquidphaseincreases,DCm+U,withincreasinggapsizeanddappearstobeequaltothecriticalvalue.From(2.3)itfollowsthat

Undersuchconditionsnucleationoccursinthemiddleofthecapillary,andanewcrystallizationfrontthereappears.Atthisfront,thesupersaturationUcanbeassumedequaltozerosincespontaneousnon-orientedcrystallizationproceeds.Inthecentreofthecapillarythe

concentrationbecomesequaltotheequilibriumoneatagiventemperature,andanewconcentrationdistributionoccurs(Fig.2.21c).Precipitationontothesubstratecomesfromthelayer

Afurtherincreaseofdleadstoanincreaseof uptothecriticalvalueatwhichintheregionbetweenthesubstrateandthemiddleofthegapacrystallizationfrontoccursagain.Figure2.21dshowsthethicknessvariationoftheliquid-phaselayerfromwhichincreasedprecipitationcomesontothesubstrate.Thus,intheabsenceofconvectiveflowsandaninducedmixtureofthe

solution,precipitationofthelayercomesfromalimitedvolumeoftheliquidphase.

2.5.2Epitaxyundernon-isothermicconditions

Animportanttaskoftheoreticalestimationsisfindingtheepitaxialfilmthicknesssincethisis,infact,theonlymeasurableparameterofthefilms.Typically,thethicknessisevaluatedfromtheamountofprecipitateusingthephasediagramanddisregardingmasstransfer.

Underthecondition (Fig.2.20),thelayerthicknesshisdefinedbytheexpression(Moon1974)

Ifwesubstituteheretheexpressionforconcentrationvariation(Madoyanetal.1988)

and ,whereCsisthedissolvedcomponentconcentrationinthesolidphaseandkisthesegregationcoefficient,thenreplacingtby

weobtain

Thewholecrystallizationprocesscanbedividedintotwostages:nonstationarywhichformstheconcentrationprofile,andstationaryunderwhichtheprofileremainsunchanged(ZhovnirandMaronchuk

1980).Theefficiencydeterminedastheexperimental-to-calculatedthicknessratioincreaseswithincreasingcoolingtimeorwithdecreasinggapsize.ToobtainLiNbO3filmswithathicknesscorrespondingtotheequilibriumone,wecanincreasethesoakingtimeataconstanttemperatureafterthecoolingprocessisover.TheconcentrationinthesolutionlevelsupandbecomesequaltoU+Ck,whereUissupersaturationatthecrystallizationfrontandCkisthesaturationconcentrationcorresponding,accordingtotheliquiduscurve,tothefinalepitaxytemperature.Intheformula

C1=U1+Ck,andinsteadofd/2wehaveusedthe valuefromEq.(2.5).

2.5.3DeterminationofsupersaturationUanddiffusioncoefficientD

LetacapillarywithagapdconsistoftwosimilarsubstrateswithacharacteristicsupersaturationU.

Theexpression(2.9)determinesthedependenceofthefilmthicknessonthefinalsolutionconcentration.Substitutingexperimentalfilmthicknessvalues,wecanfindthefinalconcentrationvalueCk+U.Thedifferencebetweenthevalueobtainedand isequaltothecharacteristicsupersaturation.

ForanexactdeterminationoftheUvalueitisnecessary,asmentionedabove,toproceedtosoakingaftercoolingisover.Asthesoakingtimeincreases,thethicknessincrementmustdecreaseduetoconcentrationlevelling.

Inanumberofpapers,diffusionwasinvestigatedonsingle-crystalsampleswithinclusionsofdropsfromthemotherliquor(Timofeeva1978).

Wehaveevaluatedthediffusioncoefficientonthebasisofexperimentallyestablishedfilmparameters.

Whenepitaxyproceedsontodifferentsubstrates,thefilmthicknessdependsonthepositionofthepointofmaximumsupersaturation.From(2.5)itfollowsthat

Thevalues and aredeterminedfrom(2.9)onthebasisofexperimentallymeasuredlayerthicknesses(substituting ford/2).

Inexaminingtherelationshipbetweenthegrowthparametersandthemasstransfercharacter,ithasbeenestablishedthat,inbufferedmeltsystems,thecontributionofconvectiveflowsisinsignificantifthegapbetweensubstratesissmallandincreasessharplywithincreasingd(LitvinandMaronchuk1977;Mil'vidskyetal.1980).Thefilmgrowthrateisreadilydeterminedfrom(2.8)or(2.9).Thelineardependencev=f(d)testifiestothefactthatundertheseconditionsmasstransferislimitedtomoleculardiffusion.Asdincreases,adeviationfromlinearityinthesolutionisobservedasaresultofnaturalconvectionduetogravitationandthedifferenceinthedensitiesofthedissolvedsubstanceandthesolvent.Inthesolution,crystallizationcentresmayoccurwhicharedistributedthroughouttheentireliquid-phasevolumebyconvectiveflows.

Inadditiontothevalueofthecriticalgapd*determiningthediffusionregion,animportantfactoristhestationarity .Thetimeofappearanceofaconstantconcentrationprofileforthegap isdefinedbythecondition .

Astheprocesstime increases,theprocessapproachesthestationaryone.

Fig.2.22Filmthicknessandgrowthrateasfunctionsofgrowthsystemparameters:a,d:

1)a=0.2grad/min,2)a=0.4grad/min,3)a=0.6grad/min.b:1)calculatedvalues,2)(0001)isorientationofLiTaO3,3)(1120)isorientation

ofLiTaO3.

TocalculatethethicknessandthegrowthrateofaLiNbO3film,weshouldknowthevaluesofthediffusioncoefficientofLiNbO3intheLi2O-V2O5meltandthecharacteristicsupersaturationUdependingonthematerialandsubstrateorientation.Theexperimentaldeterminationofthesevaluesonthebasisoftheconstructedmodelrequiresrealizationofthegrowthprocessesunderconditionsverycloselyapproachingthestationaryones.LiNbO3andLiTaO3platesofdifferentorientationswereusedassubstrates.Figure2.22presentsthedependenceoftheLiNbO3filmthicknessonthesizeofthegapdbetweenthesubstrates.Intheabsenceofconvectiveflowsthisdependencemustbelinear.Thegraphimpliesthatatacoolingratea=0.2grad/min,thecontributionofconvectivemasstransferis

insignificantuptothevalued=3ram.Fora=0.4grad/min,thevalued*decreases,whichisevidentlyduetoanincreaseoftemperaturegradientsinthebufferedmeltandtheassociateddensityinhomogeneitiesoftheliquidphaseinthecapillary.Fora=0.6grad/min,thefilmthicknessdoesnotaltersubstantiallyifa>2mm,whichisduetothebeginningofcrystallizationinthebulkmelt.Ford=3mm,thefilmthicknessdecreaseslessthanexpectedwithintheproposedmodel.Thiscanbecausedbyanincompletecoveringofthesurfaceofmaximumsupersaturationbybulknuclei.Inthiscase,theeffectivelayerthickness fromwhichprecipitationcomesontothefilmmustincrease,andthemeanconcentration

inthecentreofthecapillaryissomewhathigherthanequilibrium.Thus,theanalysisoftheresultsobtainedshowsthatatthecoolingratea=0.2grad/minandthegapsized<3mmlithiumniobateprecipitatesinaccordancewiththediffusiongrowthmechanismwithoutcrystallizationinthebulk.

Precipitationoftheentireexcessivesubstanceontosubstratesisalongprocess.Butwhensubstratesareheldforalongtimeincontactwiththeliquidphaseatthefinalepitaxytemperature,themassexchangebetweentheliquidphaseandthefilmsurfaceleadstofilmroughnessandthicknessinhomogeneity.Todeterminetheoptimumsoakingtimeq,thefilmthicknesswasinvestigatedasafunctionofthesoakingtimefordifferentcoolingratesofthesystem.Fora=0.2grad/min,precipitationstops10minutesafterthecoolingisover.

Furthersoakingleadstodivergencebetweenthefilmthicknessesontheupperandlowersubstrates,whichmustbeassociatedwiththedownwardgravitationalflowofpermanentlyoccurringanddecayingquasiparticlesand,therefore,withconcentrationnonuniformity.Fora=0.4grad/min,thethicknessreachesitsmaximumvaluewithin20minutesandthendoesnotchange.Within15-20rain,thethicknessreachesitsmaximumvaluealsoatacoolingrateofa=0.6grad/min.Inthiscase,furthersoakingleadstoadecreaseoffilmthickness,whichmustbeassociatedwiththeredistributionofthesubstancebetweenthefilmandsmallcrystalsintheliquidphase.

Underquasistationaryconditionswehaveestimatedthecharacteristicsupersaturationforz-andy-planesofLiTaO3.Weinvestigatedthedependenceofthefilmthicknessonthegapsizeforidenticalsubstrates.Theinitialepitaxytemperaturewas890ºC,thefinal860ºC,thecoolingratea=0.16grad/min.Thecoolingtimewasthreehoursandthesoakingtimeaftertheprocesswasoverwas15-20min.TheresultsobtainedarepresentedinFig.2.22a.ThestraightlineI

correspondstotheonecalculatedfromformula(2.9).Sinceprecipitationisassumedtoproceedbythediffusionmechanism,theexperimentaldependencesarelinear.Thefilmthicknessonthey-planeofLiTaO3issomewhathigherthanthatonthez-plane.Thelithiumniobateconcentrationnearthey-andz-substratesinthismodelexceedsequilibriumby0.24and0.39mol%,respectively.

Characteristicsupersaturationhasastronginfluenceonthethicknessandthegrowthrateofthefilmunderprecipitationinacapillarywhichconsistsofdifferentsubstrates.Theasymmetricprofileoftheconcentrationdistributionleadstothefactthatprecipitationontosubstratesproceedsfromsolutionlayersofdifferentthicknesses.Table2.2presentsthethicknessvaluesunderprecipitationontothey-andz-substratesofLiTaO3.Foraprecipitationrateof0.16grad/min,thethicknessesmaydifferbyafactorof3.Onthebasisoftheresultsobtained,wehaveestimated,usingformula(2.10),thediffusioncoefficientD=(1.5±0.7)×10-5cm2/s.ThecoefficientDdeterminesthediffusionofconcreteatoms(ions,molecules)inthemedium.Butintheframeworkofthemodelconstructed,theestimatedvaluecharacterizesconditionallythediffusionofmolecularlithiumniobateandsimplifiesappreciablythecalculationsoffilmparameters.Thepictureremainsthesameinthecaseofhyperepitaxy.Sincetheintroductionoflithiumtantalateintothebufferedmeltheightenstheliquidustemperatureofthesystem(Kondoetal.1979),theliquid-phasesupersaturation

Table2.2ParametersofthegrowthsystemandLiNbO3filmthicknessincapillarygrowthon(0001)and(1120)LiTaO3substrate(Khachaturyanetal.1984)

hpmm adeg/min

hxmm hzmmmm mm

D×105cm2/s

DD×105cm2/s

1.5 17.19 0.16 22.1±1.5 7.3±0.5 1.13 0.37 0.87 0.1

1.5 17.19 0.2 21.0±1.5 7.5±0.5 1.11 0.39 1.02 0.15

1.5 17.19 0.4 19.5±1.010.2±1.00.98 0.52 1.35 0.3

2 22.92 0.16 29.5±1.512.3±0.31.41 0.59 1.26 0.1

2 22.92 0.2 29.0±2.011.5±0.51.43 0.57 1.65 0.18

2 22.92 0.2 27.0±1.512.5±0.51.37 0.63 2.81 0.35

D0=(1.5±0.7)×10-5cm2/s

hampersdissolvingofthesubstrate,itscompositiondoesnotchangeandalayerofpurelithiumniobateprecipitates.Thesolidsolutionisformedinthenarrowtransitionregionattheexpenseofdiffusionthroughtheinterfaceinthesolidphase.

Figure2.22demonstratesthefilmthicknessasafunctionofcoolingrate.Fora<0.4grad/minthethicknessdoesnotpracticallychange,whilefora=0.5grad/minitfallssharplyowingtothefactthatthecriticalsupersaturationisreachedandcrystallizationproceedsinthebulk.Formula(2.3)implies

Substitutingthevaluedcr=2.5mm,a=0.5grad/min,D=1.5×10-5cm2/s,m=11.6grad/mole,vz=0.39,weobtainDCm0=1.89.Fromthiswecandeterminethecriticalvaluesofthegapsforvariouscoolingrates.

InthecapillarymethodofLPEforferroelectricfilmgrowthwithallowancefortheabove-mentionedrestrictions,crystallizationoutsidethesubstrateisabsentandallthedissolvedsubstanceinthegapprecipitatesontothesubstrateasafilm.Knowingthethicknessofthesolutionlayerandthegrowthtemperaturerange,wecancalculatetheexpectedfilmthicknessusingthestatediagram.

ForacomputercalculationofthefilmthicknessasafunctionofgrowthparametersintheframeworkofthecapillaryLPEmethod,thereexistsanalgorithm,andthefollowingmethodsofcalculationarerealizedasauniversalprogram(onanexampleofepitaxialfilmsoflithiumniobate(Madoyanetal.1982)).

ThecalculationsarebasedontheliquidustemperatureofthephasediagramofthepseudobinarysystemLiVO3-LiNbO3(Madoyanetal.1979).Theanalyticalexpression(2.9)describingthedependenceofthefilmthicknessthegrowthparametersisobtainedonthebasisofcalculatingtheamountoftheprecipitatingcrystallizingsubstanceforagivensystemsupercooling.

Forconvenienceofprogramming,thephasediagramoftheLiVO3-LiNbO3systeminthetemperaturerange800-870ºCwasapproximatedbytheexponentialfunction

whereaandbareconstants;cisthemolarconcentrationofLiNbO3.WehaveusedthestandardapproximationprogramfromthesoftwareofaNairi-2computer.

ThealgorithmsforcalculatingthefilmthicknessasafunctionofgrowthparameterswerepublishedindetailbyMadoyanetal.(1982).

Thus,weobtainthecompletesetofvaluesofLiNbO3filmthicknessasafunctionofvariableparameters.Figure2.23givesthegraphsofthedependenceofthefilmthicknessontheparametersoftheepitaxyprocess.

Fig.2.23LiNbO3filmthicknessversusgrowthconditions:a)startingtemperature,b)overcoolingofthesystem,c)weightofthe

solutionmelt.Pointsareexperimentalvalues.

Thesedependencespermitsaratheraccuratepredictionoffilmthicknessunderconcretegrowthconditions.PointsinFig.2.23indicatethefilmthicknessvaluesobtainedunderexperimentally

chosenoptimumepitaxyconditions.Thedifferenceof5-10%canbeexplainedbyadditionalprecipitationfromthemeltofthesubstanceremainingonthefilmsurfaceaftertheepitaxyisover.

Thesatisfactoryagreementbetweentheexperimentalandtheoreticaldatasuggestsawiderangeofapplicabilityofprogrammingcalculationoftheepitaxialfilmwidth.

2.5.4Epitaxyunderisothermalconditions

Asdistinguishedfromthenonisothermalcaseforwhichthediffusionprocessesdeterminedbythesystemcoolingratearelimiting,inisothermalepitaxytherateofthediffusionprocessesvarieswithfilmgrowth,andthequestionofarelativecontributionofdiffusionandsurfaceprocessestothegrowthkineticsremainsopen.Inviewofthis,wehaveconsideredthegeneralcasewithallowance

forthekineticcoefficient.Isothermalepitaxyisinvestigatedunderconditionsofaquasistationaryprocesswhichtakesplaceintheindicatedsystems( ).

Asinthenonisothermalcase,crystallizationproceedsfromalimitedvolumeconsistingoftwoidenticalparallelsubstratesmountedatadistanced(Fig.2.24a).Thequantitativedeterminationofthetimedependenceoffilmthicknessatagiveninitialsupersaturationconsistsofsolvingthedifferentialequationdescribingthediffusionofadissolvedcrystallizingmaterialinsideacapillarywithcorrespondinginitialandboundaryconditions

whereyisadimensionlessdistance(intheunitsd/2)countedfromthegrowthfront.Therangeofyvariationisduetothesymmetryaboutthecapillarycentre.Theinitialandboundaryconditionsoftheproblemhavetheform

1.Fort=0C(y,0)=C0;

2.Inthecapillarycentre ;

3.Atthegrowthfrontsthereholdsthemassconservationconditionofthecrystallizingmaterial:

Hereqisthekineticcoefficient.TheboundaryconditionsdisregardUsinceinrealsystems .

UnderLPEconditions,theinitialsupersaturationDC0=C0-C1issosmallthatthemaximum(final)filmthicknessisnoticeablylessthanthecapillaryhalfwidth.

Solvingequation(2.12)bythemethodofseparationofvariables,weobtainthetimedependenceofthefilmthicknessh:

wheret=d2/4Disthediffusiontime,v0=v(t=0)

vnaretherootsoftheequationandjv=tanv.

Thefirstsummandin(2.13)isfinalfilmthicknessh0whichisindependentoft.

For and wecanretainonetermintheseries(2.13)

admittingherearelativeerror

Itshouldbenotedthatfort=ttheconcentrationprofilevariationduetodiffusionreachesthepointd/2(Fig.2.24a).For thefilmincreasesinthesamemannerasinaninfinitecapillary,andthedependence isdeterminedbythesolutionofequation(2.12)withtheboundaryconditions

leadingtothefollowingtimedependenceofsupersaturationatthegrowthfront

whereFistheprobabilityintegral.Itshouldbenotedthatforthereholdsakineticgrowthregime,thatis,thefilmgrowthrateisonlydeterminedbythekineticcoefficientandinitialsupersaturation

Theexpression(2.14)obtainedabove,whichholdsforj>1, ,describesthediffusionregimeinwhichthegrowthrateisdeterminedbythediffusion

Fig.2.24Concentrationdistribution(a)andfilmthicknesshasafunctionoftime(b).

coefficientandthecapillarywidthanddependsweaklyonq.

ToestablishthecharacterofLiNbO3crystallizationfromthebufferedLiVO3-LiNbO3melt,thetimedependencesofthefilmthicknessweremeasuredforvariousDC1anddvalues.

TheresultsofthesemeasurementsarepresentedinFig.2.24b.Thefinalthicknessh0isequaltothemaximumfilmthicknessvalueobtainedunderanincreasedsoakingtime.Measurementswerecarriedoutforh>4mmsinceforlowerhtheerroriscomparablewiththefilmthickness.Thelinearcharacterofthedependenceh(t)inlogarithmiccoordinatesisanevidenceofpredominanceofthediffusiongrowthregimeforh>4mm,thatis,practicallythewholeofthefilmisgrowinginthediffusionregime.Theresultsofexperimentssuggestestimatesofthequantitiesentering(2.14)andshowtheerrortowhichthisformulaholds.So,forcurve1(Fig.2.24b)

whichcorrespondstothekineticcoefficient

Thebestcoincidenceof(2.14)withexperimentalresultstakesplace

forD=0.5×10cm/s,whichagreesintheorderofmagnitudewithwhatwehaveobtained.Toevaluatetheerroroccurringintheuseofformula(2.18),weshallemploy(2.15),assuming

Fort/t>p-1,weobtainDh/h0<10-1,whichiswithintheexperimentalerrorforh.Thus,inthegrowthsystemunderconsiderationwedealwiththekineticregimeat sandwiththediffusionregimeat

Theseestimatesconfirmtheconclusionthatthediffusionregimeisprevailingforfilmgrowth.

2.6CrystallizationoffilmsfromLiNbl-yTayO3solidsolutions

Obtainingepitaxialfilmswithagivencompositionisoneoftheimportantproblemsofappliedphysicssinceinsignificantcompositionvariationsmayhaveaconsiderableeffectuponthephysicalpropertiesofgrownstructures.Itisverydifficulttomaintainaconstantcompositionwhenlayersofmulticomponentdielectricmaterialsareprecipitatedfromabufferedmelt,whenintroductionofeachcomponentisspecifiedbyanindividualsegregationcoefficient,dependsonthegrowthconditionsandvarieswithlocalfluctuationsofgrowthparameters(Timofeeva1978).

Toobtainfilmswithaprescribedcomposition,itisnecessarytoestablisharelationshipbetweenthecompositionandacomplexoffactorswhichdeterminetheenteringofcomponentsinthegrowinglayer.InLPE,thesefactorsareindividualcoefficientsofsegregationandthegrowthparameters,namely,thecompositionandthicknessoftheliquidphase,theinitialtemperature,thecoolingrateofthesystem,etc.

LithiumniobateandtantalateformLiNb1-yTayO3solidsolutionsintheentirerangeofthecompositions0<y<1(seeFig.2.4)(MadoyanandKhachaturyan1985).

Aspecificfeatureofcrystallizationoffilmsofsolidsolutionsisthenecessitytotakeintoaccounttheinfluenceoftheamountof

precipitatingcomponentsontheepitaxytemperature,composition,uniformityofcomponentdistributionandfilmthickness(Madoyanetal.1985).

Inprecipitationfromahigh-temperaturemeltofmulticomponentsystems,thecompositionoftheprecipitatinglayerdifferstypicallyfromthecompositionofthedissolvedmaterialsinceenteringofeachcomponentintothelayerisdeterminedbyanindividualsegregationcoefficient.Inepitaxyoflithiumniobate-tantalatefromthesolutionintheLi2O-V2O5melt,thecompositionoftheLiNb1-yTayO3filmisshiftedrelativetothecompositionofthedissolvedmaterialLiNb1-xTaxO3towardsincreasingtantalum,thatis,y>x.AnalysisoffilmcompositionsrevealedashiftofthecompositionoftheLiNb1-yTayO3layerrelativetotheliquidphasetowardsanincreasingmolarfractionoftantalate(y>x).Numericalestimatesgiveavariationoftherelationbetweenniobiumandtantalumbynomorethan3%duringprecipitationofalayerabout10mmthick.Thecorrespondingliquidustemperaturedisplacementdoesnotexceed±5ºwhenthegrowthcelliscooledbyabout40º.Thus,theequilibriumtemperaturevariationsduringgrowthcanbedisregarded,buttheerrorinpredictingthefilmthicknessincreasesupto20%.

Intheliterature,thevariationoftheeffectivecoefficientofsegregationiscustomarilyassociatedwithmasstransferprocessesintheliquidphase,thatis,withdiffusion,convection,electromigration,etc.(Madoyanetal.1985;Milvidsky1986).

Fig.2.25Theeffectivesegregationcoefficientoftantalumversusthegrowthrateofa

Li(Nb,Ta)O3film.

Figure2.25illustratesthedependencesoftheeffectivesegregationcoefficient,definedastherelationk=y/x,onthegrowthratewhenthemolarfractionoftantalumintheliquidphaseisx=0.2and0.4.Thesegregationcoefficientassumesthevaluesfrom1.4to2.35(x=0.4)andfrom1.5to2.75(x=0.2)asthegrowthratevariesfrom0.4to0.1mm/min.Makinguseofthisdependence,wecancontrolthefilmcompositionduringgrowthandobtainLiNb1-yTayO3filmswithyrangingfrom0.2to1.

WhenaLi(Nb,Ta)O3filmgrowsfromasaturatedsolutioninthediffusionepitaxyregime,thegrowthrateisv~ad,whereaisthecoolingratesincethefilmthickness (Avakyanetal.1986).Thus,thechangeinthecoolingrateofthesystemduringgrowthleadstoavariationofthegrowthrateandmodulationincompositionoftheprecipitatinglayerinlinewiththedependencek(v)(Khachaturyanetal.1986).IftheinitialepitaxytemperatureisbelowthephaseequilibriumtemperatureT1,theprecipitationrate,whichismaximumattheinitialmoment,willdecreasetillanequilibriumconcentrationisestablished,andthelayercompositionwillchangeinasimilarway.AtT0>T1,thefilmdoesnotprecipitateandthesubstratesurfaceisslightlydissolvedwhichcausesanuncontrolledvariationoftheliquid-phasecomposition.Consequently,foranefficientcomposition

control,itisnecessarytostarttheprecipitationprocessatatemperatureequilibriumforagivenconcentration.

Independenceofthesegregationcoefficientofmasstransferintheliquidphaseprovidesanefficientlayercompositioncontrolduringgrowth.Figure2.26presentsthegraphsofaprogrammedtemperaturedecrease(1)andthecorrespondingthicknessdistributionofstructurecomponentsobtainedbymicro-X-rayspectralanalysis(2).Foraconstantcoolingrateandequilibriuminitialtemperature(a)thegrowthrateisconstantandthecompositionremainsunchangedthroughouttheentirelayerthickness.Figure2.26(b,c)presentsthegraphsofthecoolingrateatwhichfilmsgrowwithastep-likeandperiodicdistributionofcomponents,whichplaysanimportantappliedrole,forinstance,formaintainingamultiple-modecontrollingintegro-opticwaveguide.

AnimportantfactorofstructuralperfectionofLi(Nb,Ta)O3filmsisalowcontentofvanadiumimpurity.Analysishasshownthattheconcentrationofahomogeneousvanadiumimpuritydoesnotexceed0.1atom%.ApredominantamountofniobiumisexplainedbytheequalityofionicradiiofNb5+andTa5+(0.66Å)asdistinctfromtheionicradiusofV5+(0.4Å).Foranoptimumrangeofgrowthrates,inwhichthecompositionwasmodulatedrelative

toniobiumandtantalum(0.1-0.5mm/min)thevanadiumconcentrationdidnotexceed0.1mol%,andwithafurtherincreaseofthegrowthrateaninhomogeneouscaptureofthebufferedmeltwasobserved.Consequently,variationofgrowthconditionswithinthelimitssufficientforobtainingfilmsofdifferentcompositionwithrespecttoniobiumandtantaluminducesnosubstantialheighteningofthecontentofvanadiumimpurity.

2.6.1Liquid-PhaseepitaxialgrowthofLi(Nb,Ta)O3films

Inthissection,theliquid-phaseepitaxialgrowthofLi(Nb,Ta)O3solid-solutionfilmsonLiTaO3y-platesubstratesisdescribedonthebasisofthephasediagramsobtainedbyKondoetal.(1979).

Theverticaldippingtechniquewasusedfortheexperiment.Athree-zoneresistanceheatingfurnacewasused,toobtainanoptimumverticaltemperaturedistribution.Thetemperaturedifferencebetweenthemeltsurfaceandthebottomofthecruciblewaswithin1°C.Thestartingmaterialwasputinsideaplatinumcrucible.Athermocouple(Pt-Pt/Rh13%)wasattachedexternallytothecrucible.

Thesolutioncompositionwasfixedat50mol%Li2O,5mol%(Nb1-xTax)O5and45mol%V2O5,andthesolutioncompositionparameterxdefinedasTa2O5/(Ta2O5+Nb2O5)inthesolutionwasvariedfrom0.0to1.0.ThiscompositioncorrespondstothepointA,indicatedbythearrowinFig.2.18.

Approximately1mmthicky-platesubstrateswerecutfromaLiTaO3singlecrystal,andtheirsurfacesweremechano-chemicallypolished.

AtypicaltemperatureprogramforLPEgrowthisshowninFig.2.27.ThesolutioninthePt-cruciblewasheatedto1300°Candwasheldatthistem-

Fig.2.26ProgrammedtemperaturedecreaseinLPEgrownLi(Nb,Ta)O3(I)

andthecorrespondingNbandTadistributionthroughthethicknessofLi(Nb,Ta)O3/LiTaO3hyperstructure(II)

(Khachaturyanetal.1987).

Fig.2.27TypicaltemperatureprogrammeforLPEgrowth.Tsshowsthesaturationtemperatureofthesolution

(Kondoetal.1979).

Fig.2.28(right)Epilayerthicknessasafunction

ofgrowthtimeandseveralgrowthtemperatures.Thexofsolutioncompositionwas0.8

(Kondoetal.1979).

peraturefor2-4daystomakeithomogeneous.Thenthetemperaturewasloweredtoagrowthtemperatureatwhichthesolutionwassaturated.Priortodipping,thesubstratewasthermallyequilibratedjustabovethesolutiontobringittothesolutiontemperature.Thenthesubstratewasinsertedintothesolution.Afterfilmgrowth,thesubstratewaswithdrawnatarateof1cm/minfromthesolutionandslowlycooledtoroomtemperature.Thesubstrateswerenotrotatedduringthefilmgrowth.ThefluxadheredtothesamplecouldbeeasilydissolvedbydiluteHClsolution.

Aseriesofgrowthrunswerecarriedout,withgrowthtimeandthegrowthtemperaturesasparameters,todeterminetheireffectsonthegrowthrate.Figure2.28showsarelationshipbetweenfilmthicknessandgrowthtime.Thesolutioncompositionparameterxwasfixedat0.8,andthegrowthtemperatureswere1120,1125and1130°C.Itcanbeseenthatthefilmthicknessincreasesapproximatelylinearlywithtimeuptoabout30miningrowthtime.Thefilmsweregrownat1120°Candthegrowthrateofthesefilmswasestimatedtobe1mm/min.

Thefilmthicknessbelow10mmyieldedsmoothsurface.After12mmgrowth,ripplesappearedonthesurface.At50mmgrowththeripplesdevelopedintoaseriesofsharpridgesknownasfilmfacetingandthefluxwastrappedbetweentheridges.Itcanbesaidthatafilmthicknessoflessthanapproximately10mmisadequateforobtainingasmoothas-grownsurface.

Figure2.29showsthegrowthrateasafunctionofgrowthtemperaturefordifferentsolutioncompositions.Thesolutioncompositionparameterxwas0.5,0.7,0.8,0.9and1.0.Saturationtemperaturesforthesecompositionswereestimatedtobeapproximately1020,1095,1135,1165and1190°C,respectively,aswereindicatedinFig.2.29.Thegrowthtimewasfixedat15minineachcase.Thegrowthratesweredirectlyproportionaltothesupercoolingrangingfrom0toabout30°C,overwhichthegrowthratedepartedfromlinearrelationship.Thiscanbeexplainedintermsofboththecurvatureoftheliquidusslopeinthe

Fig.2.29Growthrateasafunctionofgrowthtemperatureandsolutioncomposition.

Growthtimewasfixedat15min(Kondoetal.1979).

LiVO3-Li(Nb1-xTax)O3systemandthespontaneousnucleationofLi(Nb,Ta)O3whichoccurredpriortoorduringthegrowthatlargesupercooling(Daviesetal.1974).Therefore,themagnitudeofsupercoolingwaschosentobelessthan30°C.

ElectronprobemicroanalysiswasusedtomonitorNb,TaandVconcentrationsinthefilmandthesubstrate.Thesolutioncompositionparameterxofthisfilmwas0.8andthefilmthicknesswasabout30mm.TheTaconcentrationisconstantnotonlyinthesubstratebutalsointhefilmanditvariesdiscontinuouslyattheboundarybetweenthefilmandthesubstrate.TheratioofTaconcentrationinthefilmtothatinthesubstrateisabout0.96.TheNbwasdetectedonlyinthefilmanditsconcentrationisconstantinthefilm.TheconcentrationofVions,whichisafluxelement,islessthan0.2mol%inthefilm.

TherealfilmcompositionwasdefinedasLi(Nb1-yTay)O3,whereyisthemoleratioofTa/(Ta+Nb)inthefilm,andtheresultsaregiveninTable2.3.ItisnotedthatthefilmcontainsahigherTaconcentrationthanthestartingsolution.

2.7ThinfilmsofLinbO3dopedwithdifferentelements

Neurgaonkaretal.(1979)reportedtheLPEgrowthofNa+andCo2++Zr4+dopedLiNbO3filmsfromLi2O-V2O5flux.

Table2.3Thecompositionalrelationshipthesolutionandthegrowthfilm;thesolutioncompositionwasgivenasLi2O:(Nb1-xTax)O5:V2O5=50:5:45inmol%,andthefilmcompositionLi(Nb1-yTay)O3(Kendon,Sugii,Miyasawa,Uehara,1979)

Solutionx Filmy

0.5 0.78

0.7 0.93

0.8 0.96

0.9 0.98

BeforegrowinganyepilayersofLi1-xNaxNbO3andLi1-xCoxNb1-xZrxO3components,thecrystallinesolubilityoftheseionswasfirstestimatedintheLiNbO3phase.Thesubstitutionsweremadeasfollows:

Alltheceramicphaseswerepreparedbysolid-statereactions(1000-1200°C)andwerecheckedbyX-raypowderdiffractiontechniquesinordertoestablishthesolidsolubilityrangeofLiNbO3structure.NaNbO3hasapseudo-monoclinicunitcell(Wood1951)atroomtemperatureandbelongstotheperovskitestructuralfamily.AccordingtoLeComteetal.(1974),amaximumof7mol%Na+canbesubstitutedforLi+intheLiNbO3phase.AlthoughCoZrO3doesnotformacompound,itdissolvestoagreaterextentintheLiNbO3structure.About22mol%CoZrO3canbeaccommodatedintheLiNbO3phasewithoutalteringitscrystalsymmetry.ThesubstitutionofNa+forLi+,andCo2+andZr4+forLiandNb,respectively,intheLiNbO3phaseloweredtheferroelectrictransitiontemperature.

TheLi2O-V2O5fluxwasusedforLPEgrowthwork,andmixturescontaining80mol%LiVO3and20mol%Li1-xNaxNbO3andLi1-xCOxNb1-xZrxO3,where0.04<x<0.15,wereprepared.Here,x=0.15(i.e.NaorCo=Zr)inbothoftheabovecompositionscorrespondstoabout3mol%ofthetotalofthemixtures.SincethephasediagramforthepseudobinaryLiVO3-LiNbO3systemisknown(seeFig.2.17),itwasrelativelyeasytoestablishtheliquidustemperaturefortheNa+andCo2++Zr4+containingphasesbytheDTAtechnique.Themeasurementsshowednosignificantchangesinthemeltingtemperaturesforeitherofthesystems.TheappropriateamountsofLi2CO3,V2O5,Nb2O5andNa2CO3orCoCO3+ZrO2werethoroughlymixed,heatedto600°Candthenmeltedina100ccplatinumcrucible.Averticalplatinum-woundresistancefurnacewas

used,andthegrowthtemperaturewascontrolledwithinanaccuracyof±1°C.Themixturewasheatedto1150-1200°Covernight,afterachievingcompletemelthomogeneity,themoltensolutionwascooledtoabout860°Cattherateof30°C/h.

Any-orz-cutLiNbO3substrate,positionedslightlyabovethemelttoequilibratewiththesolutiontemperature,wasdippedintothemelt.Anappropriatedippingtemperaturewas860-890°Cforboththesystems.Aftertherequiredtimeforgrowthhadelapsed,thesamplewaswithdrawnandcooledveryslowlytoroomtemperature.Thegrowthrateoftheepifilms,whichwasexaminedbychangingthedippingtime,wasestimatedtobeapproximately1.0mm/min.Theresidueofthefluxadheringtothefilmswaswashedawaywitheitherwaterordiluteacids.

ThesurfaceforboththeNa+andCo2++Zr4+-containingfilmswassmoothandclear.Microscopicobservationsathighmagnificationsshowedaslightlyrougheraspectinthecaseofthickerfilms.Co2++Zr4+-dopedfilmswerebluishtintincolour,indicatingtheinclusionoftheseionsinthefilms.Epitaxialfilmsasthickas30-35mmcouldbegrownbythistechnique.

Thecrystallinityandthelatticeconstantawerestudiedforthesubstrateand

Fig.2.30X-raydiffractionpeak(300)takenforthefilm/substrate(Neurgaonkaretal.1979).

thefilmsbytheX-raydiffractiontechnique.They-cutLiNbO3substrateshowedareflectioncorrespondingto(300).Figures2.30(a)-(d)showtherelativeintensityof(300)asafunctionoffilmthickness.ThepeakscorrespondingtoCuKa1andCuKa2representtheLiNbO3substrate,whilethefilmpeakpositionshavebeendenotedby

and .Ascanbeseenfromthisfigure,therelativeintensityofCuKa1andCuKa2graduallydecreasedwithincreasingfilmthicknessandfinallydisappearedcompletelywhenthefilmthicknesswasmorethan10mm.Thepeaksfromthesubstrateandfilmsarewellseparatedandreproducibleundersimilarexperimentalconditions.Thischaracteristicfeatureindicatedthatfilmshaveahighsinglecrystallinitywithgoodepitaxy.

Thelatticeconstantawasestablishedforthesubstrateandfilms.Althoughthelatticeconstantdifferenceforthesubstrateandfilmswaslessthan0.1%,itwaspossibletoidentifythesedifferencesbytheX-raydiffractiontechnique.ThedatashowedthatthefilmsgrownfromtheLi2O-V2O5fluxhavethelatticeconstantasmallerthanthatusuallyobservedinthebulkcrystalsofLiNbO3.Thecrystallinesolid

solubilityofNa+andCo2++Zr4+inthephasehasbeenshowntobeapproximately7and22mol%,respectively.However,itwasfounddifficulttoraisetheirconcentrationinthefilmsusingtheLi2O-V2O5flux.BasedontheseobservationsandtheresultsreportedbyBaudrantetal.(1975)onthesubstitutionofAg+,Cu+,Fe3+,andCr3+intheLiNbO3films,itwouldappearthattheconcentrationoftheseionsisverylow,~1mol%orless.

Table2.4summarizesthecompositionofameltforAgsubstitutedfilms,andtheresultscorrespondingtodifferentgrowthconditionsonthec-axisLiNbO3substrates.Theopticalmeasurementswereperformedbyusinga1.15-mmlaserbeam.IndexvariationsinfilmscontainingCu,CrandFe,weretoosmalltobemeasuredwithaccuracy.InAgsubstitutedfilmsarefractiveindexof2.2361wasfound;withanaccountofthefactthatthesubstrateindexwas2.2300,thisvariation,Dn=6×10-3,allowedthelightpropagation,forinstance,tohave

Table2.4ThecompositionofmeltforAgsubstitutedfilmsandresultscorrespondingtodifferentgrowthconditionsoncaxisLiNbO3substrates(Baudrant,Vial,Daval,1975)

Meltcomposition(molespercent)Nb2O5.9.8,Ag2O:2,Li2CO3:49,V2O5:39.2

Epitaxialgrowth

Temperature(°C)

Time(min)

Thickness(mm)

Growthrate

(m/min)

Observations

952 - 0 0 Tsaturation

950 10 2 0.2 Goodqualityfilmswithflatandsmoothsurfaces

945 10 6.5 0.65

945 30 22 0.7 Goodqualityfilmbuthillysurfaceaspect

942 10 14 1.4 Smallroughparts

935 10 - - Idem,withsmallcrystalsonthesubstrateedges

asinglemodeina5mmthickfilm.

Neurgaonkaretal.(1987)reportedthelimitofstabilityoftheLiM5+O3structurewithrespecttodopantsandtheLPEgrowthofmodifiedLiNbO3andLiTaO3forSAWdeviceapplications.

Toestablishsuchasituation,thestabilitylimitoftheLiNbO3structurewasdeterminedbyintroducingvariousionsfortheLi+,Nb5+orTa5+sites.Thesubstitutionsweremadeasfollows:

Allphasesweresynthesizedbythesolidstatereactiontechnique,andwerecharacterizedbyX-raydiffraction.Table2.5summarizesthesitepreference,solidsolubilityrangeandbehaviourofTcforthevarioussolid-solutionsystems.Basedonthiswork,theresultsmaybegeneralizedasfollows:

(1)ThesizeofsubstitutionalionsshouldbeclosetoLi+orM5+forcompletesolidsolutionintheLiNbO3orLiTaO3phase.

(2)ThesubstitutionsshouldbemadeonboththeLi+andNb5+sitessimultaneouslytoobtainhighersolidsolubilityinLiM5+O3-M2+M4+O3.

(3)Thevalencestatesofsubstitutionalionsshouldbeclosetothehostionstoachieveasubstantialsolubility,e.g.thesolubilityofA13+,Fe3+,ory3+isminimuminLiNbO3andLiTaO3.

TheresultsofthepresentstudyshowthattheunitcellaincreasesandcdecreasesforlargecationsinLiM5+O3.LargerionssuchasNa+wereusedin

Table2.5CrystalchemicaldataonLiM5+O3phase,M=NborTa(Neurgaokaretal.1987)

Dopant Sitepreference Solidsolubility(mol%) Tc(°C)

Latticeconstants(Å)

Lisite M5+site LiNbO3 LiTaO3 a c

Na+ Na+ - 7 9 Decreased Increased Decreased

Ag+ Ag+ - 4 6 Decreased Increased Decreased

Cd2+orCa2++Ti4+

Ca2+ Ti4+ 20 20 Decreased Increased Decreased

Cd2+,Ca2++Zr4+

a)Ca2+ Zr4+ 20 - Decreased Increased Decreased

Mg2++Ti4+ Mg2+ Ti4+ 30 35 Increased Decreased Increased

Co2++Ti4+ Co2+ Ti4+ 30 35 Increased Decreased Increased

Co2++Zr4+ Co2+ Zr4+ 30 35 Decreased Increased Decreased

Fe3+,A13+ Fe3+,Al3+

Al3+,Fe3+1

1 1 - - -

Nd3+,Y3+ Y3+,Nd3+

Nd3+,Y3+

1 1 - - -

In3+ In3+ In3+ 1 1 - - -

a)Structuralchangewasobservedatx=0.21.

thepresentLPEgrowthworktoreducetheSAWvelocitytemperaturecoefficient.

Figure2.31showstheternaryphasediagramfortheLiVO3-NaVO3-LiTaO3system.TheLil-xNaxTaO3phasecrystallizesoveralargecompositionalrangeandisfoundtobeusefulforLPEwork.Asshownin

Fig.2.31,twobinarycompositions,Li0.4Na0.6VO3-LiTaOandLi0.5Na0.5VO3-LiTaO3,werestudiedforLPEgrowth.Usingtheseformulations,about2mol%ofNa+inLiTaO3phasecouldbeincorporated.Theactualsolidsolubilityaccordingtothecrystalchemistryworkisapproximately9mol%and7mol%inLiTaO3andLiNbO3,respectively.AsimilarphasediagramhasalsobeenconstructedfortheLiVO3-NaVO3-LiNbO3systembyNeurgaonkaretal.(1980)anditexhibitsasimilarbehaviour.ThedippingtemperatureoftheLi0.4Na0.6VO3-LiTaO3systemismuchhighercomparedtotheLiNbOsystemasaresultofahighermeltingtemperatureofLiTaO3.

Fig.2.31LiVO3-NaVO3-LiTaO3systeminair,

at1250°C(NeurgaonkarandOliver1987).

Table2.6GrowthconditionsandphysicalcharacteristicsofLiM5+O3films(Neurogaonkaretal.1987)

Flux Substrate/film* Growthtemperature

Latticeconstant(Å)

TemperaturecoefficientSAWvelocity(ppm/°C)

LiVO3 LiNbO3-S 700 5.148 - -

LiNbO3-F 5.142 - 86

Li1-xNaxVO3

LiNbO3-S 720 5.148 - -

Li1-xNaxNbO3-F

5.156 - 56

Li1-xNaxVO3

LiTaO3-Sb) 720 5.15213.785 -

Li1-xNaxNbO3-F

5.156 13.87 -

LiVO3 LiTaO3-S 1050 5.152 - 35

LiTaO3-F 5.146 - -

Li1-xNaxVO3

LiTaO3-S 1050 5.152 - -

Li1-xNaxTaO3-F

5.161 - 28

Li1-xNaxVOa)

LiNbO3-S 1050 - -

Li1-xNaxTaO3-F

*)S=substrate,F=film;a)Polingwasproblem,b)Unsuccessfulgrowth

ThegrowthofNa+-dopedLiTaO3andLiNbO3filmsbytheLPEtechniquewassuccessfulandfilms5to60mmthickweregrown.Table2.6summarizesthegrowthconditionsandlatticeparametersfortheseNa-modifiedLiNbO3andLiTaO3films.TheresultsofX-raydiffractionstudiesshowedthatthelatticeconstantaincreasedfortheNa+-dopedLiNbO3andLiTaO3films,andbasedontheunitcellvalues,approximately1.2mol%and1.8mol%Na+isincorporatedintheLiNbO3andLiTaO3films,respectively.TheadditionofmoreNainthesefilmswasunsuccessfulduetolatticemismatchandresultantcracking.

2.8Epitaxialferroelectricfilmswithperovskitestructure

2.8.1Liquid-phaseepitaxyofpotassiumniobate

Theoreticalandexperimentalinvestigationsontheapplicationofferroelectricthinfilmsintheintegratedoptics(OstrowskyandVanneste1978)andpeculiaritiesofnonlinearopticalpropertiesofpotassiumniobate(Uematsu1974;IngleandMisshra1977)makeitoneofthemostinterestingmaterialsofoptoelectronics.Potassiumniobatecrystalwithmeltingtemperature(T=1039°C)entersthenoncentrosymmetricspacegroupmm2,withtemperaturedecreasethecubicphaseturnsintoatetragonal(T=435°C)thenintoarhombic(T=225°C)and,finally,intoarhombohedralone(T=10°C)(ReismanandHoltzberg1955).

Thepossibilityofobtainingpotassiumniobatefilmsbytheliquidphasewasinvestigatedbytheauthorsusingtheepitaxynon-stationarytechnique.TheyalsodiscussedtheresultsofK2O-V2O5-Nb2O5triplesystemphasediagramstudyandtheconditionsforepitaxialfilmgrowth.

Thephaseequilibriumwasstudiedbydifferentialthermalanalysis(DTA),

byvisuallypolythermalanalysis(VTA)andbyX-phaseanalysis(XPA)(KhachaturyanandMadoyan1984).InvestigatedcompositionswerechosensothatthemoleratioNb/Nb+Vcouldvaryfrom0to1withanintervalof0.1.

Thephasediagramofthethree-componentsystemK2O-V2O5-Nb2O5wasinvestigatedalongthestraightlinefrom46mol%ofNb2O5-54mol%ofK2Oto50mol%ofK2-50mol%ofV2O5.

SuchachoiceofinvestigatedcompositionsisexplainedbyKVO3synthesisundersolidificationofthemeltofstoichiometriccompositionK2O:V2O5=1:1(Holtzbergetal.1956)whilepotassiumniobateprecipitationispossiblewiththemoleratioK2OtoNb2O5=54:46(ReismanandHoltzberg1955).Samplesaccordingtotheindicatedratiowerecarefullymixed,heatedinthefurnaceupto1300°C,keptthereforthreehoursandthencooledtoroomtemperature.

XPAoftransientcompositionsshowedKNbO3toprecipitatewhenthemoleratioofNb/Nb+Vinthechargevariesfrom0.1to1.IftheNbconcentrationisdecreasedfrom0.3to0,otherphasesappear.TheliquidusoftheKVO3-KNbO3pseudo-systemisbuilt(Fig.2.32),varyingfrom30to100mol%.

TheLPEofpotassiumniobatewasrealizedinanindustrialset'Svet-3'byanon-stationarytechniqueinathree-zoneresistancefurnace.

Thetemperatureinthereactorwaschangedatarateof10-300deg/h.

TheK2O-V2O5-Nb2O5fluxwaspreliminarilymeltedforthreehoursat1300°Cinaplatinumcrucibleandthenmountedonaholderintheoperatingzone.Substratesweremountedonaquartzrodplacedalongthecentre.Epitaxywascarriedoutbythecapillarytechniquefromthemeltenclosedbetweentwoparallelsubstrates,duetogoodwetting.Theslotwasadjustedwithin1-5mm.Thesubstrateswerepreparedof

and{0001}platesofleucosapphireandoflithiumniobatewithdimensionsl×10×15mm.

Thesystemwasheatedupto1100°CandafterholdingforalongperiodoftimewascooleddowntotheinitialtemperatureTOofepitaxy(Fig.2.20a);thesubstrateswerethenwettedbythesolutioninmeltandwereslowlycooleddowntoT1=(850-875°C),theliquidzonetemperaturebeing1-3°higherthanthatintheexternalsideoftheplates(Fig.2.20b).Thesystembeingcooledwiththesubstratedippedintothecrucible,thelayerprecipitationwasnotobserved(KhachaturyanandMadoyan1980).

Coolingdowntoroomtemperatureproceededatarateofnotmorethan80deg/h.Thesolidchargebetweentheplateswaseasilyremovedbyboilingthesubstratesindistilledwater.

Theprincipalcharacteristicsofpotassiumniobateliquid-phaseepitaxyarepresentedinTable2.7.

HomogeneouslythickKNbO3filmswereobtainedduringepitaxyof54mol%ofK2O-23mol%ofV2O5-23mol%ofNb2O5fromthebufferedmelt.Theepitaxyinitialtemperatureof920°Ccorrespondstotheliquiduspointofthepresentsystem.TheinitialtemperatureTObeingheightenedto930°C,thesubstratesurfaceisobservedtodissolve.

KNbO3filmsobtainedbyLPEfromaK2O-V2O5-Nb2O5bufferedmeltarecolourlessandtransparent,theirboundarywiththesubstrateissharpandtheirsurfaceroughnessisabout0.1mm(Fig.2.33(a)).Thetransientregionthickness

Table2.7Principalcharacteristicsofpotassiumniobateliquidphaseepitaxy

Substratematerial

Solutionmelt,mol.%

Initialepitaxytemperature°C

Coolingrate,Idgmin-

Layerthicknessmm

Growthratemmmin-1

Remarks

54K2O 950 0.8 to2 - precipitationinseparateareas

46Nb2O5

950 0.8 - - surfacedissolution

54K2O23V2O5

920 0.5 5 - singlecrystalinsmallvolumes

{0001}Al2O3 23Nb2O5

920 0.5 to10 - noprecipitation

920 0.5 6 0.1 singlecrystallayer

925 0.5 - 0.05-0.1 singlecrystallayer

52K2O24V25

24Nb2O5

{0001}A12O3 920 0.5 - - noprecipitation

920 0.5 - - surfaceintensivedissolution

Fig.2.32LiquiduscurveofKVO3-KNbO3pseudobinarysystem(KhachaturyanandMadoyan1984).

isabout0.5mm(Fig.2.33(b)).AnX-rayweakdiffractionwithanangleof20-44.5°wasobservedfromthesamplesurface,whichcorrespondstotheKNbO3facet{200}.

Theeffectofthesystemcoolingrateontheepitaxyprocesswasfound.WithhighratesKNbO3wascrystallizedonlyintheformofplatecrystals.Atacoolingrateof0.2degmin-1thesubstratesurfacewasobservedtodissolve.ThelayerwasprecipitatedatdT/dt~0.5degmin-1.

Inallexperiments,platecrystalswereseparatedinthesolutioninmeltsimultaneouslywiththefilmgrowth.KNbO3filmswereobtainedonleucosapphiresubstratesof orientation.OnAl2O3{0001}substratesthelayerprecipi-

Fig.2.33ChippingoftheKNbO3/AI2O3epitaxialstructure

(a)andthedistributionofAIandNbalongthethicknessoftheKNbO3/AI2O3heterostructure(b)(Khachaturyan

andMadoyan1984).

tationwasnotobserved.WhenanepitaxiallayergrewonLiNbO3substrates,theplatesurfacedissolvedinthebufferedmeltandbecamedulled.

2.8.2Growthofpotassiumlithiuniobatefilmsonpotassiumbismuthniobatesinglecrystals

Potassiumlithiumniobate(hereafterabbreviatedasKLNcrystal)isoneofthemostinterestingmaterialsforvariousapplicationsbecauseofitsexcellentelectro-optic,nonlinearopticandpiezoelectricproperties(ProkhorovandKuz'minov1990).Accordingly,thinfilmsofKLNsinglecrystalshaveprovedtobeexcellentactivemediaforintegratedoptics.ThetypicalcrystallographicpropertiesandrefractiveindicesofKLNatroomtemperatureareshowncomparedwiththoseofpotassiumbismuthniobate(KBN)K1.5Bi1.0Nb5.1O15crystalinTable2.8.Asingle-crystalthinfilmofKLNcanalsobegrownonaKBNsubstratebythesametechniqueasdescribedabove,becausethecrystallinestructuresofKLNandKBNarethesametungsten-bronzetypestructure,andbecausethemeltingpointofKBN

ishigherbyabout250°CthanthatofKLN,asshowninTable2.8.ThelatticemismatchbetweentheKLNfilmandtheKBNsubstrateisabout0.32%and2.3%atroomtemperatureforthea-andc-axesintheKLNcoordinatesystembecausetheKBNcrystalisorthorhombic,asopposedtotheKLNcrystal,whichistetragonal.Thus,itisexpectedthatasingle-crystalthinfilmofKLNgrownonaKBNsubstratewillactasanopticalwaveguide,anditcanbeusedasanopticalwaveguidemodulatorbycoupledwaveinteractionbetweentheguidedandradiationmodes(Adachietal.1979).Intheirpreviouspaper,Adachietal.(1978)describedtheepitaxialgrowthofKLNsingle-crystalfilmsbytherfsputteringtechnique.Intheir1979papertheyreportedtheepitaxialgrowthofKLNsingle-crystalfilmsonKBNsubstratesbytheEGMtechnique.

Single-crystalsofKBNweregrownbytherfheatingCzochralskimethod.

Table2.8CrystallographicpropertiesandrefractiveindicesofKLNandKBNatroomtemperature(Adachi,Shiasaki,Kawabata,1979)

KLN KBN

Symmetry Tetragonal Orthorhombic

Latticeconstant,Å,a~b 12.58 17.85

c 4.01 7.84

Meltingpoint,°C 1050 1312

Refractiveindex,no 2.294 2.237

nc 2.156 2.253

Wavelength,l.,nm 632.8 450

(001)or(100)KBNsubstrateswerecutfromas-growncrystals,andtheirtopsurfaceswerelappedandopticallypolished.Ontheotherhand,reagentgradecarbonatesoflithiumandpotassium,and99.9%pureniobiumpentoxidewereusedasstartingmaterialsforthefabricationofKLNsingle-crystalfilms.Amaterialwithcomposition35mol%K2CO3,7.3mol%Li2CO3and47.7mol%Nb2O5wasmixedwellwithacetoneinaballmill,dried,pressedintoadisc,andcalcinedat800°CforthreehoursThecalcinedmaterialofKLNwasthengroundthoroughly.ThispowderofKLNwasuniformlylaidonthepolishedsurfaceoftheKBNsubstratewithasprayer.Thesubstrate,withthepowderonitstopsurface,washeatedtoabout1120°CinaresistancefurnaceinordertomelttheKLNcrushedpowderalone,andwasthencooledslowlyatarateof10°C/hthroughthemeltingpoint(1050°c)ofKLN.Inthisway,theKLNfilmcrystallizedepitaxiallyontotheKBNsubstrate.

Thetopsurfaceoftheas-grownfilmwasrelativelyrough,andtheKLNfilmobtainedwas~15mmthick.IntheX-raydiffraction

patterns,thepeakscorrespondingtodiffractionsfromtheKLNfilmsandKBNsubstratesareclearlyseparated.Further,thevalueobtainedforthestandarddeviationangleooftheX-rayrockingcurveofKLNfilmisverysmallat0.2.ThelatticeconstantsaandcoftheKLNfilmobtainedbyX-raydiffractionmeasurementare12.53Åand3.98Å,respectively.ThesevaluesagreefairlywellwiththoseoftheKLNsinglecrystal,asshowninTable2.8.TheelectrondiffractionpatternsforKLNfilmsepitaxiallygrownonKBNsubstratesandalsotheKikuchistructureindicatethatthefilmsareofasinglecrystaloffairlygoodquality.Theseresultsshowthatasingle-crystalfilmof(001)KLNisepitaxiallygrownonan(001)KBNsubstrate,andalsothatasingle-crystalfilmof(110)KLNisepitaxiallygrownona(100)KBNsubstratebytheEGMtechnique.

2.9Diffusionliquid-phasemethodofgrowingimmersedwaveguidechannels

ChannelorstriplinewaveguidesonthebasisofLiNbO3arenecessaryelementsforcreationofelectro-opticmodulators,switches,directionalcouplersandotheractivedevicesofintegratedoptics(PhotonicseditedbyBalkanski1975;Tamir

1979;Hunsperger1984;Yariv1983;House1988)suitableforjoiningwithopticalfibres.

Thephysico-chemicalpropertiesofbuffered-meltsystems,hightemperaturesoftheprocesses,alimitedchoiceofmaterialsforsolventandcontainerrestrictstronglythepossibilitiesofLPEinthecreationofvariousdevicestructuresascomparedwithmoretechnologicallyeffectivemethodsofdiffusion,exchangereactions,ionimplantation,etc.Inspiteoftheobviousadvantagesinstructuralperfectionofepitaxiallayers,thismethodonlyservesforobtainingplanarwaveguidelithiumniobatelayersonLiTaO3substrates(FukudaandHirano1980;MadoyanandKhachaturyan1983;BallmanandTien1976).

Tocreateeffectiveintegro-opticdevices,wehaveproposedacombinedmethodofliquid-phaseepitaxyofLiNbO3filmswhichusestheadvantagesofthermaldiffusionandLPEandpermitsobtainingpracticallyanyprescribedwaveguideconfigurationsandrefractiveindexprofiles(KhachaturyanandMadoyan1986).

2.9.1Striplinestructures

Toobtainastriplinestructure,itisnecessarytoprovideavariationofwaveguideparametersalongaLiTaO3substratesurfacebyagivenscheme.

Amaskwithagivenconfigurationisphotographedontoa20×30×2mmsubstratesurface(Fig.2.34),afterwhichametalliclayerisdepositedontothissurfacebysprayinginvacuum(Avakyanetal.1986).Ofparticularinterestarewaveguidelayersobtainedbytitaniumdiffusionintoalithiumtantalatesubstrate,sinceintheselayersmodesofbothpolarizationsarepossible(Zilingetal.1980;Atuginetal.1984;Sugiietal.1980;Shashkin1983).

Films,whichareiondiffusionsources,aretypicallydepositedonto

thesubstratesurfacebythermalevaporationinvacuumorbyion-plasmasprayingoftargets.Accordingtorequirementsonthelightguideparameters,diffusant-filmthicknessisvariedfrom50to80nm.Thediffusiontemperatureis1150°Candthediffusiontime10-16h.

Thedepositedmetaldiffusesintothegrowinglayerthusincreasingitsrefractiveindexalongthephotographedpicture.Theaveragedmetalconcentrationintheline isdeterminedbythesputteredlinethickness

wherehmisthewaveguidelinethickness,Am,rmandMfrfareatomicweightsanddensitiesofthemetalandfilmmaterial,respectively.

Thediffusiondepth(theheightofthewaveguideline)isdeterminedbythediffusioncoefficientofagivenmetalintoasingle-crystalfilmandbytheepitaxytemperature.Therefractiveindexvariationalongthedirection perpendiculartothelayersurfacehastheform(Zilingetal.1980):

HereAe=Dno/c,m=rm×hmisthediffusantspecificmass,q=Dt,where

tisannealingtime,D=D0exp(-U/kT),U=1.5eVistheconstantactivationenergy,D0=4×10-7cm2/s(fortitaniumdiffusion).

Theexpressionspresentedaboveallowustocalculatethenecessaryepitaxytemperatureforobtaininganyarbitraryrefractiveindexprofile.

FortherefractiveindexvariationDnetobeabout0.01whenthechannelheighthreachesapproximately2-4mm,theannealingtimeshouldbeoftheorderof5-10hours,whichexceedsgreatlythecharacteristicepitaxytimes(1-3hours).Consequently,thetimetcanberepresentedast=tpr+tan,wheretpristhelayerprecipitationtimeandtantheadditionalannealingtime.

2.9.2Symmetricwaveguides

Usingthecombineddiffusion-filmmethod,KhachaturyanandMadoyan(1986)obtainedsymmetricwaveguidechannels.Thesequenceofoperationswasthefollowing.Afterremovingtheresist(Fig.2.34),anepitaxialLiNb0.1Ta0.9O3layerwasbuiltupontheTi:LiTaO3substratebythecapillaryLPEmethod.Thefilmcompositionwasdeterminedbytherequiredrefractiveindexdistributionoverthestructurethickness.ThegrowthratevariationinawiderangeprovidedanopticalepitaxyregimeforobtainingperfectLi(Nb,Ta)O3/Ti:LiTaO3.

Thefilm-diffusionwaveguidewastheoreticallyconsideredbySpikhal'sky(1984).Hederivedthedispersionequationforcalculatingthecharacteristicsofmultilayerwaveguidestructures.Healsoestablishedtheparametercharacterizingthedegreeofthelight-fluxmodelocalizationinthevicinityofadefinedinterfacebetweenmediaconstitutingthewaveguide.

Thestudyoftheepitaxialgrowthoflithiumniobate-tantalatefilmswithtitaniumstripsdepositedontoaLiTaO3substratehasshownthat

forveg<0.2mm/minthefilmsurfaceissmoothwithseparatelinescorrespondingtodislocations.Atsuchgrowthratesthelayergrowthislaminar.

Figure2.34showsthesurface ofaLiTaO3substratewithadepositedtitaniumstrips(a)andthemorphologyoftheepitaxialLi(Nb,Ta)O3filmgrownonthissubstrate.TheepitaxialstructuresLiNbO3/Ti:LiNbO3canbereadilygrowninasimilarmanner(KhachaturyanandMadoyan1988(a),(b)).

Distler(1975)reportedthepossibilityofepitaxialgrowthonsubstrateswithpreliminarilydepositedthin(nearly50nm)metalliclayers.ThethicknessofthestripsinvestigatedbyKhachaturyanandMadoyan(1988(a),(b))lieswithintherangeofapproximately100-500nm.Structuralinformationisnottransmittedthroughtitaniumstrips,andinthenormalmechanismthefilmmustsurelybedefectiveonthesestrips.Inlaminargrowththesituationwasdifferent.Thedensityofgrowthstructuresreflectingthedefectivelayerstructureisminimumjustoverthetitaniumstrips.Themetalliclayerobviously'screens'thestructuraldefectsofthesubstratewhichontheremainingsitesgrowintothefilm.Alowdensityofthenucleiguaranteesaninsignificantamountofsmall-angleboundarieswhichaffectneitherthestructuralperfectionofthefilmnortheabsenceofdisorientedsitescausedbynucleationontitaniumstripsthemselves.

Assoonastheepitaxialgrowthprocessisover,theremainingsolventisremovedfromthesurfaceoftheepitaxialfilmusingkaolincottonplugsormicro-channelslabsasliquid-phaseabsorbent(DudkinandKhachaturyan1988).

Fig.2.34Schematicofobtainingadippedwaveguidechannel(a),thesurface

ofaLiTaO3substratewithdepositedtitaniumstrips(b)andthemorphologyofepitaxialLi(Nb,Ta)O3filmgrownonthissubstrate(c).

Amicrochannelslabisasetofregularlypositionedmicroslits-channelswithdiameterfrom7to25mmeachandthelengthchosenwithintherangeof0.3to1.2mm.Thecrosssectionofmicrochannelslabstypicallyvariesfrom30to40mm,whichexceedsthestandarddimensionsoftheworkingfieldofproductsfabricatedusingepitaxialtechnique.Whenmicrochannelslabsareusedforalongtimeattemperaturesexceeding600-1200°C,theslabsarepreliminarilywettedinliquidkaolin('kaolinmilk')andthendried.Themicrochannelslabsprocessedthiswaycanbeusedtoremovetheremainingliquid-phasefluxfromthesamplesurface.Tothisendthemicrochannelslabisbroughtclosetothegapbetweenthesubstratessothatitssurfacetouchessimultaneouslytheentirelayersurface,asshowninFig.2.35.Underequivalentcapillaryforcestheliquidresiduesaredrawnoffalongallthechannels,thatis,uniformlyalongtheentiresurface.

Thus,themethodsdiscussedabovemakeitpossibletoobtainlayerswithvariouswaveguideconfigurationsinthefilm.Varyingthegrowthrateandtheannealingtime,wecanobtainsurfaceandimmersedwaveguides,striplinestructuresandlayerswithmetallicbufferedlayersonthesubstrate-filmboundary.

2.10GrowthofepitaxialfilmsintheKTiOPO4familyofcrystals

Asanalternativetodirectlyaddressingtheionicconductivityproblem,andasameanstomoreeffectivelyconfinetheopticalwavetoyieldhigherpowerdensity,filmswithwell-definedstep-likerefractiveindexprofilecanbegrown

Fig.2.35Schematicoftheuseofmicrochannelslabsto

absorbtheliquid-phasefluxfromthefilmsurface:1)microchannelslab,2)singlechannel,3)substrate,

4)liquidphase5)epitaxialfilm,6,7)contactsofthemeltwithamicrochannelslab.

directlybyliquid-phaseepitaxy.TheKTPcrystalfamilyishighlyversatileandreadilyformssolidsolutionsamongitsmembers(BierleinandGier1976;JarmanandGrubb1988).Themonovalentcations(i.e.K,Rb,CsandT1)arefoundtobemobileduetotheirdirectcovalentlinkagetothebridgingoxygeninthelattice,thepentavalentPandAsions,andthetetravalentTiionsareexpectedtohavenegligiblemobilityevenatelevatedtemperatures.Thus,athinfilmconsistingofsolidsolutionoftheseions(e.g.KTiOAsxP1-xO4orKTixSn1-xOPO4)grownonapureKTPsubstrateisexpectedtohaveawell-definedabruptrefractiveindexprofilealongcdirection.

Effectivewaveguidingisobtainedbysatisfyingtheconditionthatthefilm'srefractiveindicesbehigherthanthatofthesubstrate.Deepchannelwaveguidescanbefabricatedontheseheteroepitaxialfilmsbysubsequention-exchange.Astheevanescentwavebarelypenetratesintothesubstrate,fluctuationinthediffusiveprofileofthesechannelguideswillnotsignificantlyaffecttheirwaveguidingproperties,therebyavoidingtheproblemofionicconductivity.

ThelatticeconstantsforseveralendmembersoftheKTPfamilyare

summarizedinTable2.9.Amongthemanypossiblefilm-substratecombinations,theKTA-KTPsystemwaschosenintheexperimentscarriedoutbyChengetal.(1991).Therearetworeasonsforthis.Asthetitanylgroupisprimarilyresponsiblefortheopticalnonlinearity,replacementoftitaniumwithothertetravalentionsisexpectedtoleadtoasignificantlossinthenonlinearity,whichinturnreducestheusefulnessofthesefilmsinnonlinearfrequencyconversion.Thearsenicforphosphorussubstitutionprovidesthedesiredrefractiveindexincreasewithoutcompromisingonthenonlinearity.TheopticalandthecrystalgrowthpropertiesofKTPandKTAarebettercharacterizedthanthoseofallothermembersoftheKTPfamily(Bierleinetal.1989).Thisallowsforbettercorrelationbetweenexperimentalresultsandtheoreticalpredictions.

Boththetungstatefluxandthepurephosphate-arsenateself-fluxwereusedintheexperimentsbyChengetal.(1991).Theself-fluxusedconsistsofthephosphate-arsenatealongwiththeK6P4O13flux(abbreviatedasK6below)usedforbulkKTPgrowth(Gier1980;Borduietal.1987).Therelativecrystal-fluxcompositionswerechosensuchthatthegrowthtemperatureswere850°C.Althoughsignificantlylowergrowthtemperaturesarepossibleusingthetungstate,theK6fluxbecomesfartooviscousforgrowthbelow750°C.

Table2.9LatticeconstantsforseveralKTPisomorphs(Chengetal1991)

Crystal Latticeconstants Cellvolume(A)

a(Å) bÅ) c(Å)

KTiOPO4 (KTP) 12.822 6.4054 10.589 869.67

RbTiOPO4 (RTP) 12.964 6.4985 10.563 889.89

TlTiOPO4 (TIP) 12.983 6.49 10.578 891.3

KTiOAsO4 (KTA) 13.125 6.5716 10.786 930.31

RbTiOAsO4 (RTA) 13.258 6.6781 10.766 953.2

CsTiOAsO4 (CTA) 13.486 6.8616 10.688 989.02

TlTiOAsO4 (TTA) 13.208 6.6865 10.724 947.09

KGeOPO4 (KGP) 12.602 6.302 10.006 794.65

KSnOPO4 (KSP) 13.146 6.528 10.727 920.56

Variouslyorientedsubstrates,namely{011},{110},{100},{111}and{201}plates,havebeensuccessfullyusedtogiveas-grownfilmswithhighlyspecularsurfaces.KTPandKTiOAsxP1-xO4substrateswereprimarilycutfromflux-growncrystals.

Theuseofhydrothermallygrownmaterialstypicallyleadstoopticaldegradationwiththeformationoffinewhitefilamentsinthesubstrate.Chengetal.(1991)speculatethatthisdegradationisduetotheprecipitationoffinewater-basedinclusionsinthesematerials.

Thesubstratesare~l×lcm2×mmthickplates,cutparalleltothenaturalgrowthfacets.Allplateswerepolishedwithsequentiallyfiner(3-0.25mm)diamondbasedpolishingpowder,andfinishedwitha30schemical-mechanicalpolishincolloidalsilica.Asmall(0.75mm)

hole,drilledatonecornerofthesubstrate,allowsittobetiedontoacrystalrotation-pullingheadwithathinplatinumwire.Thesubstratewasheldverticallytoassistfluxdrainageafterdipping.Aslightetchingofthesubstrateinwarmdilutehydrochloricacidpriortothedippingwasfoundtoimprovetheequalityoftheepitaxialfilm.

Thedippingsetupisidenticaltothebulkgrowthfurnace.Itconsistsofa250mlcrucibleplacedatthebottomofashortzonetop-loadingcruciblefurnacelinedbya4.5-inchquartztube.

Themelt(~200ml)ishomogenizedatabout50°Caboveitsliquidustemperature.AsomewhatlongersoaktimeisoftenneededwhenusingtheK6flux.Thesubstrateisintroducedintothegrowthfurnaceslowly(~5-25mm/min).Themeltisthencooledtoabout1.5-3°Cbelowthesaturationpointandallowedtoequilibratefor30min.Thesubstrateisthendippedintothemeltandspununidirectionallyat10rpm.Thedippingtimeisvarieddependingonthedesiredfilmthickness,thedegreeofsupersaturationused,thechoiceoffluxandthegrowthtemperature.Experimentally,Chengetal.(1991)foundthataslightback-etchingofthesubstratepriortogrowthresultsinsignificantlybetterqualityfilms.Thisisaccomplishedsimplybytakingadvantageofthethermalinertiaofthesystemandsubmergingthesubstratebeforethemeltreachesthegrowthtemperature.

Fig.2.36ProfileofKTiOP0.76AS0.24O4filmonaKTPsubstrate.Thetitaniumprofileisnotshownforclarity.Thespatialresolutionofthescanis~0.5mm(Chengetal.1991).

Uponcompletionofthedipping,theplateiswithdrawnfromthemeltandthefurnaceatapproximately5-25mm/min.Anyresidualfluxpresentiswashedoffwithwarmdilutehydrochloricacid.Thethicknessofthefilmisnearly±5mm.

Usingthedippingprocedureoutlinedabove,Chengetal.(1991)havegrownKTiOAsyP1-yO4filmsbetween4and20mmonsuitablychosensubstratesofKTPorKTiOAsxP1-xO4(wherex<y).Asanindependentconfirmationofthestep-likeofthestep-likerefractiveindexprofileofthesefilms,electronmicroprobetechniquewasusedtomapoutthecompositionofa50mm-thickKTiOP0.76AS0.24O4filmonaKTPsubstrate(Fig.2.36).The'abrupt'increaseinthearseniccontentfromthesubstratetothefilmconvincinglydemonstratesthatphosphorus-arsenicexchangeisnegligibleunderthegrowthconditions(~850°C).Sincetheas-grownfilmhasthesamemorphologyasthatofKTPandthesolidsolutionKTiOAsyP1-yO4istheonlystablephaseinthemelt,Chengetal.(1991)concludethatthefilmisepitaxialandisstructurallyanalogoustoKTP.Therefractiveindexofthefilmcanbeestimatedfromtheknownrefractiveindicesoftheendmembers,andisinexcellentagreementwiththem-lines

spectrometryresults.Chengetal.(1991)havealsogrownthinfilmsofRb0.2Ko.8TiOPO4onKTP.ThesignificantpenetrationoftheRb+intothesubstrateverifiedthattheK+ionsarehighlymobile,andstep-indexfilmscannotbereadilyobtainedfromthecationicsolidsolutions.

Table2.10summarizesthepartitioncoefficientsforarsenicusingthetungstateflux.Thepartitioncoefficient,k,isdefinedas:

where[As]isthemolefractionofAsinthecrystalorthemelt.ThegreaterthanunitypartitioncoefficientsuggeststhatAsisfavouredintheKTiOAsxP1-xO4lattice.Figure2.37plotsthelatticeconstantsoftheKTiOAsxP1-xO4system.Theresultsindicatethat,unliketheRbxK1-xTiOPO4

Table2.10Partitioncoefficient,k,ofarsenicfromatungstenmelt;(As)isdeterminedbyICPanalysisofAsandPinbulkcrystalsgrownatthesametemperature(Chengatal1991)

[As]crystal [AS]melt k

24 20 1.2

39.1 35 1.12

56.1 50 1.12

82.6 75 1.1

87.4 80 1.1

Fig.2.37LatticeconstantsoftheKTiOPxAS1-xO4system.

SolidlinesarepredictionsusingVegard'slaw(Chengetal.1991).

system,thelatticeconstantsa,bandc,increasemonotonicallywitharseniccontent.ThefollowingVegardlawsfittheKTiOAsxP1-xO4resultsverywell:

wherexisthemolefractionofAsinthecrystals.Itwasexperimentallyfoundthatthemaximumlatticemismatchforhighqualityfilmgrowthisabout1%,whichcorrespondstoa35%increaseinarseniccontentintheKTiOASxP1-xO4filmandtoanestimatedrefractiveindexincreaseofDnb~0.0177at1.064mm.Filmcrackingand'scaling'wereobservedforfilmswithlargerlatticemismatch.

SignificantlydifferentgrowthpropertieswereobservedfortungstatefluxandtheK6flux.Atabout850°Candwithcomparablesupercooling(about2°C),thegrowthratewassubstantiallyslowerintheK6fluxthanintungstate.ToachieveacomparablegrowthrateusingtheK6flux,asupercoolingroughlytwicethatusedintungstateisneeded.FilmsgrownfromtheK6fluxtendtohavefilm-substrateinterfacesofpoorerquality.Itislikelythatthisisdue

totheslowdissolutionkineticsoftheK6flux(Chengetal.1991),whichmakestheimplementationofpre-growthetchingdifficult.Thetimelinearityoffilmgrowthforagivensupercoolingwasestablished.

TheKTAprocesseswerereportedtohaveappreciablyhigheropticalnon-linearityandloweropticalscatteringthanKTP(Bierleinetal.1989).Theidealfilm-substratecombinationisthereforeapureKTAfilmonsuitablychosenKTiOAslP1-xO4substrate.Thiscombinationalsoeliminatesanypossiblemicroscopiccompositionalfluctuationinthefilmduetothenon-unitypartitioncoefficientkofarsenic.AlthoughcompositionalvariationsinKTiOAsxP1-xO4substratescaninprincipleoccur,theireffectonthewaveguidingpropertieswillbenegligible.Thefilmwasshowntowaveguideeffectivelyat0.632mm,withnomorethantwoopticalmodes.

Chengetal.(1991)alsoexploredthefilmgrowthofsolidsolutionsinvolvingthetitanylgroup.ThegrowthofKTi1-xSnxOPO4films,thoughpreferredoverKTi1-xGexOPO4,provesdifficultduetotheanomalouslyslowdissolutionofKSP.Incontrast,usingtheprocedureoutlinedabove,Chengetal.(1991)readilygrew10mmKTi0.96Ge0.04OPO4filmson{011}KTPsubstratesusinga20%{Ge}solution.Discouragingly,evenwithalow4.3%Geincorporation,numerouscracksperpendiculartocwereobservedinthicker(30mm)films.Chengetal.(1991)attributethisincreasedfilm-crackingtendencytothefactthat,unliketheKTiOAsxP1-xO4films,theKTi0.96Ge0.04OPO4filmsareundertensilestress.Thisinterpretationisentirelyconsistentwiththeprediction,usingVegard'slawandTable2.9,thatthecracksshouldbenormaltocasobserved.Theseexperimentssuggestthatsolid-solutionfilmsofeitherKTi1-xSnxOPO4orKTi1-xGexOPO4areoflimitedpracticalutility.Thesituationcanhoweverbeimprovedsignificantlybyreversingthefilm-substrateconfiguration,i.e.KTPfilmonKTi1-xGexOPO4substrate-providedthattherefractiveindicesconditionforwaveguidingcanbe

satisfied.

3InfluenceofElectricCurrentuponLiquid-PhaseEpitaxyofFerroelectricsProgressofmicro-andoptoelectronicsdependsmuchonhowsuccessfullytheexistingmethodsforobtainingthin-filmstructuressolvetheproblemofreproducibleformationofperfectmultilayerheteroepitaxialcompositionsbasedonmulticomponentsemiconductorsolidsolutionsofA3B5andferroelectricsmanufacturedfromniobatesandtantalatesofalkalineandalkaliearthmetals.Requirementsonthetechnologyandcrystallographicperfectionofstructuresandonthepropertiesoffilmshaveincreasedsubstantially.Amongtheknownliquid-phasemethodsforobtainingepitaxialstructureswithpredeterminedproperties,liquid-phaseepitaxypossessesthewidestpotentialitiesforfilmcomposition,thicknessandstructurecontrol.Inthischapter,wepresenttheoreticalandexperimentalresultsofstudiesoftheinfluenceofdirectelectriccurrentupontheprocessesofliquid-phaseepitaxy.Wealsopresenttheresultsoforiginalpapersongrowthandinvestigationofthin-filmstructuresofferroelectricsonanexampleoflithiumniobateandsolidsolutionsoflithiumniobate-tantalate.Weaccountforthefactthatanelectricfieldand,inparticular,adirectelectriccurrentflowingthroughacrystalisoneoftheeffectivemeansforchangingcrystallizationconditionsthataffectcrystallographicperfectionandsomephysicalpropertiesofgrownstructures(Khachaturyanetal1987).

3.1.Electricfieldandcrystallization

Anelectricfieldisafairlystrongenergeticfactoraffectingthenucleationandgrowthofanewphaseunderfirst-orderphasetransitions.Butthenumerousreportsontheinfluenceofanelectric

fielduponthecrystallizationprocessdonotprovidefinalunambiguousconclusionsconcerningaunifiedphysicalmechanismoffieldeffect.Inviewofthisweconsiderpossiblemechanismsoftheinfluenceofadirectelectricfielduponcrystallizationprocesses.

3.1.1Bulkcrystallization

In1956,A.F.Ioffegaveatheoreticaldescriptionofmotionofameltedzoneundertheactionofelectriccurrentingermaniumbars(Ioffe1956).This

motionwasexplainedbythepresenceoftemperaturegradientintheliquidzoneduetoPeltierheatrelease(orabsorption)attheliquid-solidinterfaces.In1957,W.Pfann(Pfannetal1957)gaveanexperimentalconfirmationofthetheorysuggestedbyA.F.Ioffe.Awholenumberofnewexperimentalresults(Pfann1970)onthedirectionofmotioninameltedzonedependingonitscompositionrequiredspecificationofthetheory.

TheinfluenceofanelectricfieldontheformationofcrystallizationcentresinsupersaturatedsaltsolutionswasfirstdiscoveredbyShubnikov(1956)whoshowedthatasuperpositionofanexternalelectricfieldcausesasharpincreaseinthenumberofcrystallizationcentres.

Investigationoftheactionofelectriccurrentinacrystal-meltchainingermaniumcrystalgrowthusingCzochralskiandStepanovmethodshasrevealedvariationintheintensityandstriationperiodincrystals(Levinzonetal1969;Dudniketal1973).Germaniumsinglecrystalsweregrowninthe{111}directionanddopedwithantimonytoobtainaresistivityof5-10ohm.cm.

Thedensityofcurrentincreasedfrom0to50A/cm2inthecourseofgrowthofonecrystal.Stepanovgrowningotsexhibitedadecreaseoftheamplitudeandpitchofstriation,whichdoesnotdependonthedirectionofcurrentandisonlyduetoJouleheatrelease(i.e.theJouleheatexceedsthePeltierheat).

ItshouldbenotedthattheparametersofinhomogeneityofcontrolingotsgrowninasimilarmannerbytheCzochralskimethodremainedpracticallyunalteredwhenelectriccurrentwasapplied.

WhengermaniumstripsaregrownbytheStepanovmethod,thetransmittedelectriccurrenthasaneffectnotonlyuponthenatureofstriationinsinglecrystals.Itwasshown(Egorovetal1971)thatan

applicationofadirectelectriccurrentthroughaninterfaceprovidescontroloverthecrystallizationfrontshapeduringzonecrystalgrowth.Tochoosethecurrentdensitynecessaryforcrystallizationfrontshapecontrol,oneshouldtakeintoaccounttherelationbetweenthePeltierandJouleheatswhicharerespectivelyequalto

PisthePeltiercoefficient,RistheresultantresistanceoftheportionsofliquidandcrystaladjoiningthecrystallizationfrontandJiscurrentdensity.

Theseeffectscanbesummeduporsubtracteddependingonthedirectionofcurrent.

InaregionwherethecurrentdensityissuchthatQJ>Qp,thecrystallizationfrontrises,whilefor itfalls.WhentheJouleandPeltierheatsareequaltoeachother, theappliedcurrentinducesnovariationsofthecrystallizationfrontshape.Thecorrespondingequilibriumdensityofcurrentwillbeequalto

Thedeviationoftheimpurityconcentrationfromtheequilibriumvalue(DC)atthesolid-liquidinterfacecanberepresentedinthegeneralformasan

algebraicsumofthedeviationsoftheconcentrationsfromtheirequilibriumvalues,causedbyelectrothermaleffects(DC1standsfortheJouleeffect,Peltiereffectandothers)andelectrictransfer(DC2)

In1963-1964twomodelswereproposed(Tiller1963;Hurleetal1964)attemptingallowanceformigrationofmeltcomponentsundertheactionofanelectriccurrentinstationaryconditions.Althoughtheorderofmagnitudeofdifferentialmobilityofameltedzonecomponentwasdeterminedwithinthesemodels,theywereunabletoexplaintheresultsofsubsequentworksonepitaxialgrowth.

ThePeltiereffectwasappliedtodeterminethecrystallizationrateofInSbinCzochralskitypecrystalgrowth(Singhetal1968;Lichtensteigeretal1971;WargoandWitt1984).Applicationofapulsedcurrenttoacrystal-meltboundaryresultedintheappearanceofstriationinthecrystalstructure,andvariationofthefrequencyandpulseintensitycausedvariationsinthewidthandintensityofthesestriae.ThestriaeresultedfromvariationofimpurityconcentrationduetoachangeofinstantaneousgrowthratecausedbyPeltierheating(orcooling).Theauthorsnoticedthattheimpurityconcentrationinastriaremainsconstantduringallthetimeofapplicationofacurrent,changesinstantaneouslyattheendofapulseandremainsunchangedtillasubsequentpulse.Changingthemagnitudeofelectriccurrentpulseandthuschangingtheimpurityconcentrationinastria,theyestablishedadirectdependenceofimpuritysegregationonthedensityofthecurrentflowingthroughthesystem.TheelectrictransferwhichaccompaniesthePeltiereffectisobservedtorestrictitsactioninmulticomponentsystems.

SimilarresultswereobtainedforGe(Vojdanietal1975).ThetemperaturedistributioninasystemtowhichanelectriccurrentisappliedwasshowntobeafunctionofthePeltiereffect.

Theprocessesproceedingduringthegrowthofpotassium-tungstenbronze(NaxWO3)andlanthanumhexaboride(LaB6)bythemethodcombiningelectrochemicalcrystallizationandCzochralskitechniquewereinvestigatedbyMatteietal(1976),HugginsandElwell1977)andDeMatteiandFeigelson(1978).Ifintheusualcrystalgrowththemotiveforceissupersaturationorthermalgradient,inelectrochemicalcrystallizationthekineticanddiffusionprocessesareactivatedbyanexternalelectricfieldwhosepotentialexceedstheequilibriumpotentialvalue.ElectrochemicalcrystallizationisaFaradayeffect,andtheprecipitationrateattheinterfaceisreadilycontrolledbythestrengthofcurrent.

ProblemsconnectedwiththeinfluenceofelectrictransferandPeltiereffectupontheimpuritydistributioncoefficientwerediscussedonanexampleofgrowthofBi-SbcrystalsdopedwithTe,Se,SnandPb(KrylovandIvanov1980).

Whengrowingchromium-dopedlithiumniobatecrystalsbyCzochralskitechnique,Räber(1976)andFeisstandRäber(1983)examinedtheinfluenceofthestrengthanddirectionoftheelectriccurrentflowingthroughacrystal-

meltsystemuponthevalueofthechromiumdistributioncoefficient.

Applicationof50mApulsesofagainstthebackground5mAcurrentresultedinstriationcausedbyadecreaseofchromiumconcentrationbyaboutafactoroftwo,thecurrentontheseedcrystalhavingpolarity'+'.Thedistributioncoefficient(Kcff)asafunctionofthestrengthanddirectionofcurrentwasestimated.Astheelectriccurrentdensityvariedwithintherange15<j<18mA/cm2,thedistributioncoefficientdecreasedlinearlywithanincreaseofthecurrentdensity.Outsidetheindicatedcurrentdensityrangethecrystalgrowthbecameunstable.Highvaluesofthedensityofcurrentsappliedinducedtheappearanceofgasbubblesinthecrystal.Thecolourofthecrystalchangedwithreversalofpolarity,andthesurfacebecamerough.

Voskresenskayaetal(1985)reportedtheresultsoftheirinvestigationoftheelectricfieldeffectupontheprocessesproceedingatthecrystallizationfrontofbismuthgermanategrownbyCzochralskimethod.Crystalsweregrownfromacruciblewithcathodeandanodepolarizations,thedensityofcurrentswasvariedwithintherangeof(0÷20)mA.Anelectriccurrentwasshowntohaveagreateffectontheimpuritydistributioncoefficientandonthemagnitudeofremanentstressesinthecrystal.Inthecaseofcathodepolarization,thegrowthprocesswasstable,theresistanceoftheelectriccircuitincreasedmonotonicallywithcrystalgrowth.Achangeofpolarizationforananodeoneledtoadecreaseintheelectricresistanceattheboundarybyafactorof25andinducednonstationaryprocessesatthecrystallizationfront,whichareconnectedwithanunstablevalueofresistanceinthecrystal-melt-cruciblechain.Ananalysisofthevalueofremanentstressesindifferentpartsofcrystalsgrownfromacruciblewithcathodepolarizationshowedthatthestressesfalldownto70%ascomparedwithregionsgrowingwithoutanycurrentbeingapplied.

Thus,ananalysisofthepapersinvestigatingtheinfluenceofadirectelectriccurrentuponcrystallizationofabulkmaterialrevealedthepossibilityofcontrollingtheimpuritycompositionandstructuralperfectionofgrownsinglecrystals.

3.1.2Thinfilms

Thewideapplicationofthinfilmsinmicro-andoptoelectronicsisexplainedbymanyfactors.Themostimportanthereisobviouslythefactthatitisonlythinfilmsthatpermitobtainingcompactschemesatalowconsumedpowerandahighdensityofschemeelements.Furthermore,themethodsofobtainingthinfilmsprovidehighlypuresubstancesormaterialswithacompositioncontrolledwithprecision.

Researchersengagedingrowingsinglecrystalsandfilmsareinterestedinfindingnewwaysofaffectingagrowingcrystal,whichwouldallowamoreeffectivecontroloverthegrowthrate,surfacemorphology,thedistributionofalloyingimpuritiesinacrystallizationmediumandtheconcentrationofstructuraldefects.

Alargeamountofexperimentalmaterialisavailableontheinfluenceofanelectricfielduponepitaxialgrowthfromthegasphase.Thegeneralchemicofphysicalconsiderationsimplythatsuperpositionofthedifferenceofelectricpotentialsonthesourceandsubstratemaygivethefollowingprincipaleffects:

1.Changeofconditionsofchemicalequilibriumofheterogeneousreactionsonthesourceandsubstratesurfaces.Indeed,theGibbsexpressionforthefreeenergyofaphysico-chemicalsysteminanelectricfieldcontainsanadditionaltermshowingthattheworkofelectricforcesisproportionaltothestrengthanddependsonthedirectionoftheelectricfieldstrengthvector(Sychev1970):

where istheelectricfieldstrength, theelectricinductionandthedielectricpolarization.

2.Changeofdiffusionactivationenergyanddiffusionrateinthegasphaseonthesourceandsubstratesurfaces.Themaineffectisthatthediffusivemotionofparticlesissuperposedbyadirecteddriftofionsintheelectricfield(Boltaks1972;KolobovandSamokhvalov1975):j=mEC,wherejisachargedparticleflow,mismobilityandCisconcentration.

Electrodiffusionofchargedvacanciescanproceedsimultaneously.ThechangeinthediffusionactivationenergyundertheactionofelectricfieldwasreportedbyGorsky(1969).

3.ChangeinthepositionoftheFermilevelonthesurfaceofasemiconductorcausedbyatransverseelectricfield.Thisresultsindisplacementofequilibriumbetweenachargedandunchargedformsofchemisorptiononthesurface,whichleadstoanadditionaladsorptionordesorptionofmoleculesdependingonthesignofthefield.Thisphenomenonwascalledelectrosorption(Wolkenstein1973).Therelativechangeofadsorbtiveabilityisdescribedbytheformula

whereN0isadsorbtiveabilityintheabsenceofanelectricfield,DN=

N-N0isthechangeofadsorbtiveability,DVs,isthesurfacezonebend, isarelativecontentofadsorbedparticlesonanunchargedsemiconductor(theminusreferstoacceptormolecules,theplustodonormolecules).

Thenear-surfacezonebendDVs,dependsontheelectricchargedensityonthesuperconductorsurfacecausedbothbythepresenceofelectricallychargedadsorbedparticlesandbysuperpositionofanexternalfieldofstrengthE.ForthisreasonDN/N=f(E),theexternalelectricfieldaffectingnotonlytherelationbetweentheevenlyadsorbeddonorandacceptormolecules,butalsothesorptionkinetics(Wolkenstein1973).Ifthecrystallatticeofasemiconductorischaracterizedbyasubstantialcontributionoftheioncomponentofchemicalbond,anelectricfieldcanalsoproduceadefiniteeffectuponthestoichiometryofcrystalcomposition

4.Changeofcriticalsupersaturationnecessaryfortheappearanceandstabilizationofcrystallizationnucleiinthecourseoflaminarcrystalgrowth.AsshownbySirota(1971),inthesimplestcase,whenthephasetransitionheatDH=0,thecriticalsupersaturationscritforcrystallizationnucleationisdescribed,accordingtothegeneralizedThomsontheory,bytheThomsonformula

whereVandrarethevolumeandtheradiusofthecrystallizationnucleus,qistheelectricchargeofthecrystallizationnucleus,gisthesurfacefreeenergyandkistheconstantdependentonthenatureofthesubstance.

AccordingtoChernovandTrusov(1969),thesurfacechargeslowerthenucleationactivationenergybyabout10%.

Itisanexperimentallyestablishedfactthatanelectricfieldhasaneffectuponthegrowthrateandalloydistributionbetweenthegasphaseandthegrowingfilmsofgermanium,silicon(Lyutovichetal1971)andgalliumarsenide(Palienkoetal1971).ItwasnoticedthatthethresholdtemperatureofsiliconepitaxialgrowthlowersunderhydrogenreductionofSiCl4,andtheactivationenergyofprecipitationandthemorphologyofthefilmsurfacealsochange(Chopra1969).

Thestudiesoftheinfluenceofanelectricfieldunderthechemicaltransportofsubstancefromthenearsourceontothesubstrate,i.e.bythesandwichmethod(IkonnikovaandIvleva1974;Korobovetal1977)revealthepossibilityofcontrollingthegalliumarsenidelayergrowthandofsuppressinguncontrolledinhomogeneitiesinthebulkfilm(Korobovetal1977).

Thus,theuseofelectricfieldsofdifferentpolaritiesandstrengthinthecourseofepitaxialgrowthfromthegasphaseisconsideredtobepromisingforanincreaseofintegrationandcontrolledlocalintensificationoftechnologicalprocessesinmicroelectronics.

3.1.3Liquid-phaseelectroepitaxy

Themethodofliquidphaseepitaxyinanelectricfield,calledalsoliquid-phaseelectroepitaxy,wasfirstproposedforobtainingepitaxial

filmsofsemiconductorsonanexampleofthecompoundGaSb(Golubevetal1974a,b).Thismethodisbasedoncrystallizationundertheactionofadirectelectriccurrentrunningthroughasource-bufferedmelt-substratesystem.Asopposedtoelectrocrystallization,wherethecrystallizedsubstanceisaproductoftheelectrodereaction,crystallizationinliquid-phaseelectroepitaxyisasecondaryphenomenon,aresultofthecurrent-inducedvariationinthetemperatureandconcentrationofthesubstance.

Theconcentrationandtemperaturegradientsarisingattheboundaryareaconsequenceofanumberofphysicalphenomenaduetoelectriccurrentindifferentpartsofthegrowthcell,namely,itmaybePeltierheatreleaseorabsorptionatboundaries,electromigrationofcomponentsintheliquidphase,Jouleheatandsomeothereffects.

Twotypesofliquid-phaseelectroepitaxywereinvestigated(Fig.3.1).Thefirsttypeisanequilibriumprocess,wheninthecourseoffilmgrowththeliquidphaseispermanentlyfedbyprecipitatedcomponentsfromthesource(Fig.3.1a),andthesecondtypewhentheliquidphaseisnotfed(Fig.3.1b).

Letusconsidertheessenceofliquid-phaseelectroepitaxy(Gevorkyanetal1977;Khachaturyanetal1977).Priortoepitaxy,thetemperatureofthecrystallizationcellwasT0.Intheinitialstatethesystemconsistsofasourceandasubstratewhichareincontactwiththebufferedmeltandwithcurrent-

Fig.3.1Basictypesofliquidphaseelectroepitaxywithindicationof

temperatureandconcentrationdistributionatthecrystallizationfront:a)withliquidphasefeeding;b)withoutliquidphasefeeding.

conductingelectrodes.AnexternalheatermaintainstheconstanttemperatureT0.Atthistemperature,theliquidphaseissaturatedwiththematerialsofthesourceandthesubstratewhicharedissolvedinthesystem,andtheentiresystemisinthestateofthermodynamicequilibriumyieldingnomaterialtransport.

Ifadirectelectriccurrentofappropriatepolarityrunsthroughthecrystallizationcell,Peltierheatisreleasedatthesource-liquidphaseboundaryandisabsorbedattheliquidphase-substrateboundary.Asaresult,thetemperatureattheboundarieschanges,atemperaturegradientoccursintheliquidphaseleadingtotheappearanceofaconcentrationgradient,thesourceispermanentlydissolvedanditsmaterialistransportedtothesubstrate.Thus,liquid-phaseelectroepitaxyinfactcombineselementsofordinaryliquidphaseepitaxyandelementsofzonemeltingwithatemperaturegradient.Achangeinthecurrentpolarityisresponsiblefordissolutionofthesubstrate,whilethelayerisprecipitatedontothesource.Reversibilityandlowinertiaofheatrelease(Peltierheatreleaseswithinacharacteristictimeofexcessiveenergytransfertoelectronsbyatomsofthemainsubstance)provideaquickandconvenientcontroloverliquid-phaseelectroepitaxy.

Itisalsonoteworthythataflowofcurrentthroughacrystallization

cellisresponsibleforthesubstancetransportontosubstrateduetoelectromigrationofliquid-phasecomponents.

Assoonastheelectriccurrentisoff,thetransportofsubstanceparticlesstopspracticallyinstantaneously,auniformdistributionofcomponentsisestablishedintheliquidzone,andthermodynamicequilibriumsetsupinthesystem.Thefilmgrownonthesubstrateisnotdissolved,andtheliquid-phasecompositionremainsexactlythesameasbeforethecurrentwasswitchedon.

Ifasourceisabsentinthecrystallizationsystemthensubstanceprecipitationontothesubstrateundertheactionofanelectriccurrent(underanymasstransfermechanism)maybeonlyduetoliquid-phasedepletion,whichleadstoanonequilibriumstateofthecrystallizationsystemaftertheprocessisover.

Applicationofoneortheothermethodshouldbecoordinatedwiththepurposesandtasksofaparticulartechnologicalprocess.

Fig.3.2Schematicofgrowthcellforliquidphaseelectroepitaxy,1,5)electrodes,2)substrate,3)liquidphase,4)source.

3.2Physicalbasisofliquid-phaseelectroepitaxy(Thetheoryofthemethod)

WeshallconsidertheproblempresentedinFig.3.2.Thematerialoftheliquidzoneisnotsupposedtoformchemicalcompoundsorsolidsolutionswithmaterialsofthesourceandsubstrate.Thetheoryofzonemeltingwithatemperaturegradient(ZMTG)*(Lozovsky1972)predictstwopossiblezoneregimes:kineticanddiffusion.

Weshallconsideronlythediffusionregimewhichisattainedforafairlysmalltemperaturegradient.Inthiscase,thethermalequilibriuminthesystemwillsetinmuchquickerthanthediffusiononesincetheliquid-phasediffusioncoefficientofatoms,D,ismuchlessthanthethermalconductivityK.ThetimesofestablishingthediffusiontDandthermaltTequilibriaaregivenbytherelations

Since ,from(3.1)and(3.2)itfollowsthat .InasmuchasthestationaryregimeofzonemeltingwithPeltier-inducedmotionwasearlierconsideredbyTiller(1963)andHurleetal(1964),thesolutionoftheformulatedproblemfallsintothreepartsanalysedbyLozovsky(1972)andKhachaturyan(1974):

a.temperaturedistributioninasystemtowhichacurrentisapplied;

b.filmgrowthrateasafunctionofcurrentdensity;

c.time-dependentvariationoffilmcomposition(compositiondistributionoverthickness).

3.2.1Temperaturedistributioninasystemundertheactionofanelectriccurrent

Weshallconsiderthesimplestcasewhenthematerialsofthesourceandsubstratearethesame.Intheproblemoftemperaturedistributionsuchaconsiderationisalmostalwaysadmissible.

Inthegeneralcase,thefollowingheatsourcesshouldbetakenintoaccountinthesolutionoftheproblem:

1.Peltierheat-asurfaceheatsource;

2.Jouleheat-abulkheatsource;

3.crystallizationanddissolutionheat-asurfaceheatsource;

*ItisobviousthattheprobleminindicatedgeometryissimilartoZTMG

4.Thomsoneffect-abulkheatsource;

5.Dufoureffect-abulkheatsource.

Whenanelectriccurrentisappliedtoasource-solution-substratesystem(Fig.3.2),Peltierheatisinstantaneouslyreleasedorabsorbedattheboundaries(pointsz=0andz=L),withasurfacepower

where isthePeltiercoefficientfortheinterfaces,Jisthedensityofcurrentthroughthesystem(mA/cm2),a=(a1-a2isthedifferencebetweenthethermoelectromotiveforcesofthesolventandsource(substrate)material(inV/grad).

Allcalculationsarecarriedoutforthelow-densityregionsofcurrent,andthereforetheJouleheatquadraticinJcanbeneglected.

ThedissolutionandcrystallizationheatshavereversesignsofthePeltierheat.IntheregionswherePeltierheatisreleasedthedissolutionheatisabsorbed,whileintheregionwherePeltierheatisabsorbedthecrystallizationheatisreleased.So,inthegeneralcase,thiscausesadecreaseofabsorbedandreleasedPeltierheat,thatis,adecreaseofthetemperaturegradient.Undercertaingrowthconditionsthecrystallization(dissolution)heatcancompletelycompensatethePeltierheatandsetinisothermalconditionsofcrystalgrowth.Forthesurfacepowerofcrystallizationheatwecanwrite

whereHisspecificheatofcrystallization(dissolution)(kcal/g),disthedensityofsubstanceundercrystallization(dissolution)(g/cm3),visthecrystallization(dissolution)rate(cm/s).

TheThomsoneffectisduetothetemperaturedependenceofcurrentcarrierconcentration,andinoursystemitcanbeneglected(thezonematerialisaliquidmetal).Moreover,itisalsoquadraticinJ.

TheDufoureffectinliquidsystemsisinsignificant(DeGrootandMazur1962).Thus,wecanneglectbulkheatsourcesandonlymakeallowanceforsurfacesources,thatis,Peltieranddissolution(orcrystallization)heat.Underthisassumption,theequationforthermalconductivityhastheform

whereKisthethermalconductivityoftheliquid-zonematerial,visthevelocityofzonemotion.

Weassumeherethezonethicknesstoremainunalteredandtheoriginofcoordinatestocoincidewiththeinterface(Petrosyanetal1974).Sinceinarealtechnologicalregimethecurrentdoesnotchangeatallorchangesveryslowly,inthesolutionoftheproblemitcanbethoughtofasconstant.

Thesecondtermintheright-handsideofequation(3.5)describestheinfluence

oftheinterfacemotionupontemperaturedistribution.Sincethegrowthrateinthesystemisveryslow,itseffectcanbedisregarded.Indeed,forthispurposeitisnecessarythatthefollowingshouldholdtrue

IfliquidBiorGaisusedassolvent,then ,,andfortheliquidzonethicknessL=100mmandthe

crystallizationrate thisinequalityissatisfied.

Giventhis,astationarytemperaturedistributionsetsinwithinthecharacteristictimetTwhichisoftheorderofonemillisecond.Thus,settinginofequilibriumtemperaturedistributionactuallyappearstobehigh-speedandadmitscurrentpulsesthroughthesystemoffrequencyuptotensofHertz.

ThediffusionprocessesinthesystemarecharacterizedbyatimeconstanttD.Assumingthediffusioncoefficienttobeequalto5×10-5cm2/s,wefindthatitisoftheorderofasecondandgreatlyexceedstr.Inallfurthercalculations,thetemperaturedistributioncanthereforeberegardedasstationaryandthetimederivativein(3.5)canbeneglected.Theequationforthermalconductivityhastheform

Thisequationcanbesolvedforeachpartofthesystemseparately.

Kuznetsovetal(1983)solvedtheproblemoftemperaturedistributionforthesystemdepictedinFig.3.2withthefollowingboundaryconditions.Atthesource-liquidzoneandsubstrate-electrodeinterfaces,constanttemperatures,TIIandTI,aremaintained.Attheliquidzone-substrateboundary,thecrystallizationheatreleaseistakenintoaccountalongwithPeltiereffect.Undertheseconditions,thetemperaturedifferenceATattheliquidzoneboundariesisequalto

wherels,lL,Ll,Larethetemperatureconductivitiesandthicknessesofthesubstrate(source)andliquidzone,respectively,and .Itisreadilyseenthatat ,disregardingthecrystallizationheatandtakingintoaccount ,weobtainfrom(3.7)

Wecanseethatthetemperaturegradientisindependentofthezonethicknessandisdeterminedbythemagnitudeofthedensityofcurrentflowingthroughthesystem.

WecanestimatethetemperaturejumpinthezoneandthetemperaturegradientinthesystemGaSb-Bi(Ga).Takingthefollowingvaluesoftheparameters(KhachaturyanaGdSb=150mV/grad,mBl=-20mV/grad.aGa=3mV/grad,L=10-2cm,J=25A/cm2,)lGa27W/mgrad,lBl=14W/mgradandT=723K,wefindthetemperaturedifferenceinthezone

thatis,thetemperaturegradientinthezoneisgradgrad/cm.ItmaybeseenthatthisvaluevarieswithintherangetypicalofZMTG(Lozovsky1972).

ForthesystempresentedinFig.3.2,Gevorkyanetal(1983)foundatemperaturedistributionwithsomewhatdifferentboundaryconditions:attheendsoftheelectrodesaconstanttemperatureismaintainedandattheelectrode-substrate,substrate-liquidzone,liquidzone-sourceandsource-electrodeboundariesthePeltiereffectistakenintoaccount.

3.2.2Filmgrowthrate

Inthesource-solution-substratesystemconsideredabove,alineartemperaturedistributionpracticallysetsinafteradirectelectriccurrentisswitchedon.Atthisstagethesystemisalreadynotinthestateofthermodynamicequilibrium.Ourtaskistodeterminethecomponentconcentrationdistributioninthezoneandthefilmgrowthrateinagiventemperaturefield.

Thecomponentconcentrationdistributionintheliquidzonewithallowancebothfordiffusionandelectromigrationisdeterminedfromthesolutionoftheequation

whereDisthediffusioncoefficient, istheparticledrift

velocityintheelectricfieldE,zcffisaneffectiveparticlecharge,eistheelectroncharge,risresistivityoftheliquidphase.

Inexperimentsonliquid-phaseelectroepitaxy,thecondition istypicallyfulfilled.Forthisreason,thelasttermin(3.10)canbeomitted.Equation(3.10)withoutthelasttermwassolvedbyGevorkyanetal(1983).Solvingequation(3.10),wecometothefinalexpressionforv(t):

whereCsistheconcentrationinthesolidphase.As ,from(3.11)weobtainthestationaryvelocityofgrowth,vst,

Asmightbeexpected,forE=0weobtainfrom(3.12)

From(3.12)wecanseethatvst,dependsnotonlyonthevalue,butalsoonthesignofE,thatis,thetypeofsubstrateandsourceconductivities.

3.2.3Chemicalcompositioncontrolofthefilm

Theliquid-phaseelectroepitaxymethodpermitsobtainingfilmswithcompositioncontrolledthroughoutthethicknessbymeansofcurrentdensityvariation.Birulinetal(1984),ZhovnirandZakhlenuk(1985),ZakhlenukandZhovnir(1985),Jastrebskietal(1978)andBryskiewiecz(1985)showedthepossibilityoffilmcompositioncontrolinliquid-phaseelectroepitaxyforathree-componentsystemwithaccountofPeltierandelectrictransfer.Itisassumedthatduringthewholeprocesstheliquidzoneattheboundarybetweenphasesisinlocaldynamicequilibriumwiththesourceandsubstrateatagiventemperature(thediffusionapproximation),andthefilmcompositionisdeterminedateachinstantoftimebytheliquidphasecompositionattheboundarywiththesubstrate.Ateachtimemoment,thefilmcompositionmustbeinproportionalrelationwithdiffusionfluxesatthesurface,andtheliquidphasecompositionisgivenbytheliquiduscurve.

Assoonasthecurrentthroughthecrystallizationcellisonandthetransitionprocessatthegrowthboundaryisover,acertainvalueoftheconcentrationofoneofthecomponents,Cx,setsin,whichisdeterminedontheonehandbythePeltier-inducedtemperaturevariationatthesolidphase-bufferedmeltboundaryandontheotherhandbyequilibriumoffluxesofparticlesofagivencomponent

comingtoandfromtheboundary.Attheothermeltboundary(intheabsenceofconvection)oratadistanceofthed-layer(inthepresenceofconvection)theinitialconcentrationremainsunchangedandequalsC0.Thenecessaryconditionisheretheequalitybetweentheparticlefluxescomingthroughtheboundaryofthed-layerandgoingawayintothesolidphase(Birulinetal1984):

wherek0istheequilibriumsegregationcoefficient,visthegrowthrateoftheepitaxiallayer.

DependingontherelationbetweenthevaluesofthebufferedmeltcomponentsmandD,twocomponentconcentrationvaluesnearthesubstratearepossible,namely, and .Intheapproximationthatinthetransition(d)layeroftheliquidphasetheconcentrationvarieslinearly,Birulinatal(1984)derivedtheexpressionforparticleconcentrationofthecomponent

intheepitaxiallayerasafunctionofelectriccurrentdensity

wherepisthemeltresistivity, thed-layerthickness,Jthecurrentdensity.

Theanalysisof(3.14)showsthatthedependenceofcrystallizedlayercompositiononthecurrentdensitymayonlybeabsentprovidedthattherelation

remainsunaffectedbycurrentdensityvariation,whichispossibleundertheconditionsthat

1)thetransitionlayerthicknessisverysmall,i.e.

2)thequantity isverylargeandthegrowthratedependslinearlyonthedensityofelectriccurrent;

3)vand dependlinearlyonthecurrentdensity.

Theoretically,whenthedependencev=f(J)isnonlinear,thelayercompositionmustalwaysdependonthecurrentdensity.TheformofthisdependenceisdeterminedforeachparticularcasebythevalueoftherelationbetweenmEandk0v.IfthemEvalueincreasesfasterthank0vwithincreasingcurrent(forexample, ),thecontentofthecomponentwillincrease,whereasifthemEvalueincreasesslowerthan orifthedependencev=f(J)islinear,thecomponentconcentrationwilldecrease.

Onthebasisofgeneralizedequationsofmasstransferandphaseequilibrium,ZhovnirandZakhlenuk(1985)gaveaqualitativeanalysisofsomesituationsoccurringunderliquid-phaseelectroepitaxyinthree-componentsystems,makingallowancefor

electromigrationandPeltiereffect.

3.2.4Initialstagesofnucleation

Thepresenceofchargesandelectricfieldsareknowntospeedupnucleationofanewphase(ChernovandTrusov1969;AleksandrovandEntin1971).ChernovandTrusov(1969)estimatedtheprobabilityofnucleationinapoint-chargefieldonthesurfaceofadielectric.Theycalculatedthecontributionoftheelectrostaticfieldtothecriticalnucleationenergyandsolvedthefollowingelectrostaticproblem:apointchargeqislocatedunderthecrystalsurfaceatadepthH.Thedielectricpermittivitiesofthecrystalandmediumareequaltoecrandemcd,respectively.ThesupersaturationofthemediumrelativetothecrystalisDm.Thenucleusofthenewphasehastheshapeofafiatdiscofheighta(aisequaltothelatticeconstant),Fig.3.3(ChernovandTrusov1969).

Theworkofcriticalnucleationisequalto

Fig.3.3Schematicofnucleationonthecrystal-mediuminterfaceinthepresenceofanelectriccharge.

wheree0isthedielectricpermittivityofthevacuum,thecriticalradiusr.determinedfromtheequation

whereaistheenergyoftheformationofaunitsidesurface,Vcisthevolumeofasingleparticleinthecrystal.

AleksandrovandEntin(1971)considerednucleationasadisplacementofaninfiniteplanecrystal-mediumboundarytowardsthemediumforadistanceequaltothecrystallatticeperioda.Withinsuchanapproach,theworkofcriticalnucleationDG*doesnotdependonthecriticalradiusr*

So,accordingtoChernovandTrusov(1969)andAleksandrovandEntin(1971),thepresenceofachargeonthesubstrateleadstoadecreaseofnucleationenergy,whichinturnspeedsuptheformationofcrystallizationcentres.

DhanasekaranandRamasamy(1986)investigatedtheinfluenceofanelectricfielduponatwo-dimensionalnucleation.Heconsideredcaseswheretheelectricfieldisperpendicularandparalleltothenucleation

andshowedthatsubjecttotherelationbetweenthedielectricpermittivitiesofthenucleusandthemedium,thenucleationcanbeeitheracceleratedordecelerated.

Weshallpresenttheestimatesoftheinfluenceofanelectrostaticfielduponthenucleationrate.Weshallconsiderthecasewhenanewphaseisformedonanelectrode.Inthegeneralcase,betweentheelectrodestherearetwosubstances,AandB,inthesame(say,liquid)phase.Anew(solid)phaseCcannucleateontheelectrodeeitherfromthesubstanceAorfromB(seeFig.3.4).

Tofindouttheeffectoftheelectrostaticfieldonthenucleationrate,oneshouldcalculatethecontributionoftheelectrostaticfielduponthecriticalnucleationenergy.Weshallcarryoutthiscalculationfortwocases:1)whennewnucleiontheelectrodeformametaland2)whentheyformadielectric.

Weproceedtothefirstcase.Supposethenewnucleimakeuphalfofthe

metalsphereontheelectrode.Tocalculatetheelectrostaticcontributiontothenucleationenergy,weshoulddeterminetheenergyvariationofthecondenserfilledwithdielectricA+B(withthedielectricconstante)whenaprotuberance,ahemisphereofradiusaappearsontheelectrode.Sincetheprotrusionandtheelectrodearemetals,theelectrodesurfacesareequipotentials.ThisisschematicallypresentedinFig.3.5.

Thechangeoftheelectrostaticenergyupontheappearanceontheelectrodeofahemisphericalnucleus,when ,isequalto

From(3.15)itisseenthat ,and,therefore,theappearanceofametallicnucleusontheelectrodeisenergeticallyadvantageous,thatis,thepresenceofthefieldE0mustpromotenucleation.

Thenon-electricpartoftheenergychangeuponnucleationintheformofahemisphereisgivenby(Aleksandrov1978)

whereoisthesurfacetensionattheinterface,Dmisthechemicalpotentialvariationunderphasechange,VtheparticlevolumeinthephaseC,lspecificheatofcrystallization,T-T0thesupercooling,T0theequilibriumtemperatureofphasetransition.

Summingup(3.16)and(3.15),weobtainthetotalenergyvariationundernucleation

From(3.17)wecaneasilydeterminethecriticalradiusofthenucleus,a*,andtheheightoftheenergybarrierundernucleation,DG*

Fig.3.4Schematicofnucleationontheelectrode:1)metallicelectrodes;

2)energysource;A,Bareinitialsubstances;Cisnucleusofthenewphase.

Fig.3.5Distributionofelectricpotentialincrystallisation.Horizontallinesareequipotentialsurfaces,verticallinesareelectricfieldstrengths,E0isthefield

strengthinadielectric,distheinter-electrodegap.

From(3.17)and(3.18)itisreadilyseenthata*andDG*decreaserapidlywithincreasingE0.ThisisdemonstratedinFig.3.6.

Thenucleationrateisgivenbytheexpression(Aleksandrov1978)

whereAisapre-exponentialmultiplier.Forthisreason,weassumethepre-exponentialfunctiontobeindependentofE0.Now,substituting(3.19)into(3.20),wecometothefinalexpressionforthenucleationrateasafunctionofthefieldstrength

Thenucleationrateisthusseentoincreasesharplywithincreasingfieldstrength.

Nowweturntothecasewhenthenucleusofthenewphaseisadielectric.Forsimplicityofcalculationsassumethenucleustohavetheshapeofacylindricalprotrusionofareasandheighthontheelectrode.Figure3.7presentstheschemeofnucleationinthesystemA+B.

Weexaminedacaseinwhichtherewasnoexternalfield,i.e.E0=0.SurfacetensionofthesurfaceboundarybetweenthephasesA+BandCiss,attheboundarybetweenthesidesurfaceofthenucleusandthephaseA+Bissh,attheboundarybetweentheelectrodeandthephaseA+Bitisosandatthenucleus-electrodeboundarys0(seeFig.3.7).Thentheenergyvariationuponnucleationhastheform

Itisofinteresttodeterminetheoptimumsizeofthenucleusforagivenvolume,thatis,forV=pr2h=const.Itisequalto .Inviewofthisfactwerewrite(3.22)as

Fig.3.6Energyvariationuponnucleationasafunctionofparametera.

Differentiating(3.23)withrespecttohandequating tozero,weobtaintheequationfromwhichwecanfindtheoptimumvalueoftheheighth*ofthecylindricalnucleus

Thedependence(3.24)hasasimplephysicalmeaning.Asshouldbeexpected,h*increaseswithincreasingss.Forthegivenvolume,thenucleusacquirestheformwhichcorrespondstotheminimumofsurfaceenergy.

Substituting(3.24)into(3.23),weobtainthefollowingexpressionforDG*

From(3.25)wecanseethatDG*asafunctionofVhasamaximum,thatis,theappearanceofsmall-volumenucleileavesthesystemstable,butitbecomesunstableassoonaslarge-volumenucleioccur.Thecriticalnucleationenergycanbereadilyobtainedfrom(3.25)

Thecriticalheighth**andthecriticalvolumeV**havetheform

Thecoefficientoftheformofthecentreofthenewphaseh**/V**canbeeasilyobtainedfrom(3.27)and(3.28)

Fig.3.7Schematicofformationofacylinder-shaped

crystalnucleusonanelectrode.

Theresults(3.26)and(3.29)wereobtainedbyBolkhovityanovandYudaev(1986).

IfanucleusisformedinanexternalfieldE0,thecontributionoftheelectricenergyintothenucleationenergyfor hastheform

whence ,and,therefore,theexternalfieldmustpromotenucleation.Thisfacthasaclearphysicalmeaningsince,asiswellknown,adielectricwithahighdielectricpermittivityvalueisalwaysdrawnintoacondenserconnectedwiththeexternalvoltage.

Withallowanceforthecontributionoftheelectrostaticfield,theenergyvariationis

From(3.31)and(3.23)onecanseethatasubstitutionoffor( )informulae(3.26),(3.27)and(3.28)

givesthedependenceofDGonj.

Thenucleationratewillbedeterminedfromtheformula

whichshowsthatfor thenucleationrateincreases.

3.3Theroleofthermoelectriceffectsinthecourseofliquid-phaseelectroepitaxyofferroelectrics

Theapplicationofadirectelectriccurrentinthecontrolovercrystallization

ofepitaxialstructuresgrownfromaliquidphasearecloselyconnectedwiththermoelectriceffectsobservedduringthisprocess.WeshallagainturntothecrystallizationcellshowedschematicallyinFig.3.2.Thephenomenaoccurringinacrystallizationcellunderliquid-phaseelectroepitaxyarethefollowing(digitsrefertozonesorinterfaceswherecorrespondingphenomenatakeplace):

-(1-5)heattransfer,

-(1-5)Jouleheat,

-(1-5)Thomsonheat,

-(3)diffusion,

-(3)electrictransfer.

Thesewereheatexchangeeffects.Nextcomesurfaceeffects:

-(3-4)heterogeneouscrystallization,

-(4-3),(3-2)crystallization(dissolution)heat,

-(4-3),(3-2),(5-4),(2-1)Peltierheat.

So,inthegeneralcasesystemsofliquid-phaseelectroepitaxyinvolveseveralmechanismsofheatabsorptionmechanisms.Electrictransfer,crystallizationanddissolutionofsolidphasesleadstotheappearanceofconcentrationgradientsofacrystallizingsubstanceintheliquidzoneanddiffusionleadstolevellingupthesegradients.

Thefirstquestiontobeansweredintheanalysisofcrystallizationprocessesishowthemotiveforcesofcrystallizationdependuponcrystallizationconditions.Thesemotiveforcesaredeterminedbythevariationsoftemperatureandconcentrationofacrystallizingsubstanceatthecrystallizationfrontascomparedtoequilibriumvaluesoftheseparameters.

Whenadirectcurrentrunsthroughinterfaces,PeltierheatproportionaltotheproductofcurrentdensitybythePeltiercoefficientisinstantaneouslyreleasedandabsorbed.

Owingtothiseffectthetemperatureattheinterfacefalls,thisfallbeingequalto(Jastrzebskietal1978):

where isthedifferenceofthermoelectromotiveforcesbetweenthesubstrateandsolvent,L1isthesubstratethickness,lsthethermalconductivityofsubstratematerial,T0thetemperatureinthesystempriortoapplicationofcurrent.

Aconsequenceoftemperaturedifferenceinthesystemisconcentrationvariationintheliquidzone

wheremistheslopeoftheliquiduscurve.

Attheinterface,Peltierheatisabsorbedandcrystallizationheatreleased(sincetheyhaveoppositesigns).

Consequently,thisleadsintheendtoadecreaseofabsorbedandreleasedPeltierheat,i.e.toadecreaseofthetemperaturegradient.

TheresultsofcomparisonoftheoreticalandexperimentaldatasuggestthatthecrystallizationheatcanbeneglectedascomparedtothePeltierheat.Then

wherelListhethermalconductivityofthemelt.

Thus,thetemperaturegradientoccurringattheinterfaceisindependentofthezonethicknessandisdeterminedbythevalueofthecurrentdensity.

Sincethetimewithinwhichthetemperaturegradientissetinthesystem, ,iscomparativelysmall,thecurrentrunsthroughanonuniformlyheatedsystem,thatis,fromtheverystartoftheprocessanadditionalThomsonheatisreleased

wheretTisThomson'scoefficient.

OwingtotheThomsonheat,thesystemcanbeadditionallyheated,thetemperatureincreasebeing

whereMandcarerespectivelymassandthermalcapacityofthesubstrate.

Whenadirectelectriccurrentisapplied,Jouleheatissimultaneouslyreleasedinthesystem:

whereRistotalsystemresistanceandRLisliquidphaseresistance.

Since ,theJouleheatmainlyaffectsthesubstrate.

Beginningfromsomeinstantoftime(tcr),theJouleeffectmaybecomegreaterthanthePeltiereffectsinceaconstanttemperature

gradientattheinterfaceismaintainedbythePeltierheat,whiletheJouleandThomsonheatsareaccumulatedinthesystem.Consequently,theresultanttemperatureofthesystemstartsexceedingtheequilibriumtemperatureTOandthesystemmayappeartobeundersaturated,whichwillresultindissolutionofthecrystallizedlayer.

Ascanbeseenfromtheaboveformulae,theJouleheatisquadraticandthePeltierheatislinearinJ.ThismeansthatthereexistsacertainoptimumvalueJoptwhentheJouleheatbecomespredominantoverthePeltierheat.TheJouleheatcanthereforebeneglectediftheappliedcurrent

TheThomsoneffectishereduetotemperaturedependenceofcarrierconcentration,andinsuchasystemitcanbeneglected,providedthezonematerialisaliquidmetal.Moreover,thiseffectisalsoquadraticinthecurrent.

GabrielyanandKhachaturyan(1984)investigatedferroelectricfilmgrowthusingliquid-phaseelectroepitaxyandestimatedthecontributionofthermoelectriceffectstothisprocessonanexampleoflithiumniobate.

Figure3.8presentstemperatureversuscurrentdensityunderliquid-phaseelectroepitaxyofLiNbO3withallowanceforPeltier,JouleandThomsoneffects.ThefigureshowsthatattheinitialinstantsoftimetemperaturevariationsduetoheatexchangeeffectsaresmallerbyseveralordersofmagnitudethantemperaturevariationsduetothesurfacePeltiereffectandcan,therefore,beneglectedatearlystagesofgrowth.Whenthegrowthtimeislong,theresultanttemperatureofthesystemexceedstheequilibriumtemperatureToandthesystemmayappeartobeincompletelysaturated,whichleadstolayerdissolution.

3.4Electro-LPEgrowthoflithiumniobate-tantalatefilms

Thestandardmethodsworkedoutforsemiconductormaterialscannotbeusedforcurrent-inducedliquid-phaseelectroepitaxyofferroelectricsbecauseofthephysico-chemicalspecificitiesofoxidesystems.Weproposetwowaysofcurrent-inducedliquid-phaseelectroepitaxyofferroelectrics:

-current-inducedliquid-phasecapillaryepitaxy

-liquid-phaseelectroepitaxyfromanunlimitedvolumeofthesolutioninmelt.

Filmgrowthinanelectricfieldopensnewhorizonsforgrowthofthin-filmferroelectricswithacurrent-controlledcomposition,thicknessandstructuralperfection.Ofparticularinterestisobtainingasingle-domain(polarized)stateoflayersinthecourseofgrowth.

Inthissectionweconsidertheuseofcurrent-inducedliquid-phaseepitaxialgrowthoffilmsoflithiumniobate-tantalate,electrochemicalprocessesproceedingintheliquidphaseandmodulationinthecompositionofferroelectricfilmsundertheindicatedgrowthconditions.WealsooptimizeconditionsofepitaxialgrowthofLi(Nb,Ta)O3filmswithaccountofJouleheat.

3.4.1Epitaxialgrowth

Theuseofcurrent-inducedliquid-phaseepitaxyforgrowingLiNbO3andLi(Nb,Ta)O3filmsfromalimitedliquid-phasevolumecontainedbetweentwosubstrateslocatedclosetoeachotherwasproposedbyKhachaturyanetal(1986).Figure

Fig.3.8Melttemperaturevariationsduetothermaleffectsasafunctionofcurrentdensityinthecourseof

LEPoflithiumniobate.

3.9presentstheschemeofafilmgrowthdevice.Thecompositionof90%LiVO3+10%Li(Nb,Ta)O3waschosenassolventforliquid-phaseelectroepitaxy.(0001),(1120)platesofLiTaO3servedassubstratesandcrystallineplatesofLi(Nb,Ta)O3servedasasource.Thesubstrateandsourcesizewas20×15×l.5mmandtheliquid-phasethicknesswas1.5÷2mm.Theelectrodesweremanufacturedusingplatinumblackeningandaconductinghigh-temperatureglue.

Apreliminarilypreparedplatinumnielloisdepositedoninoperativesubstrateandsourcesurfaces,thentheplatesareannealedforonehourat400°C.Afterthisashiningmetallizedsurfaceiscoveredwithahigh-temperatureconductingglue.Thesubstrateandsourceplateswithafixedgap(intermediateplane-parallelplatesofagiventhicknessareusedforfixation)aregluedtoaquartzholderwithelectrodes.Thegapbetweenplatesissochosenthatundertheactionofcapillaryforcesthebufferedmeltisuniformlydrawnfromthecrucibleintothespacebetweenthesourceandsubstrate.Foroxidesystems,thegapbetweenthesourceandsubstrateischosenwithintherangeof1-2mm,whichpermitsavoidingconvectivemixing.Thenthesystemismountedinafurnaceoveracruciblefilledwithbufferedmelt.

Thefurnacetemperatureisgraduallyincreasedtillitbecomes50-100°Chigherthantheinitialepitaxytemperature,whichismaintainedfor0.5-1huntilacompletehomogeneityisattained,andthenthetemperatureequaltotheinitialepitaxytemperatureisestablished.Aftersomeholding,theplatesareimmersed1-2mmintothecruciblecontainingthebufferedmelt,asaresultofwhichtheliquidphaseaffectedbycapillaryforcesisdrawnintothegapbetweentheplates.Themomentofcontactbetweentheplatesandthemeltisfixedbyanindicatorlamp.Thentheplateswithliquidphaseareseparatedfromthecrucibleandreturntotheinitialstate.Constant(orpulsed)voltageisappliedtotheplates.Thelayergrowthproceedswhenthepotential

onthesubstrateispositive.Assoonasthecurrentisoff,thelayergrowthceases,andaliquid-phaseabsorberistakentothegapbetweentheplates(DudkinandKhachaturyan1986),afterwhichthesystemisslowlycooleddowntoroomtemperature.

Theessenceofliquid-phaseelectroepitaxyfromanunlimitedbufferedmeltvolume(GabrielyanandKhachaturyan1985)isillustratedinFig.3.9b.Thismethoddiffersfromtheoneindicatedaboveinthattheliquidphaseisnotfedfromthesource,andtheliquid-phasethickness

3.4.2Electrochemicalprocessesintheliquidphase

Inthestudyoftheprocessofliquid-phaseelectroepitaxyanimportantroleisplayedbyacorrectestimateoftherelativecontributionofdifferentstagesofthisprocess.Thedifferenceinthenatureofchargecarriersinoxidecompoundsleadstovariationofthephysicalprocessesproceedinghereascomparedwithliquid-phaseelectroepitaxyofsemiconductorsystems.Asaconsequencethereoccuranumberofspecificeffectstypicalofliquid-phaseelectroepitaxyofcomplexoxideswhicharetobeexaminedonanexampleoflithiumniobate.

Tospecifythecharacterofmasstransferunderliquid-phaseelectroepitaxyofoxidesystems,electrochemicalprocessesattheinterfacebetweencontactingphaseswereinvestigatedandthelayergrowthratewasdeterminedasafunctionofstrengthandtimeofthecurrentappliedtothecrystallizationcell(Khach-

aturyan1988;Gabrielyanetal1989).

Figure3.10showsthetemperaturedependenceofthenumberoflithiumionstransferredinlithiumniobatesinglecrystalofcongruentcomposition.Wecanseethatinthetemperaturerangeof800-900°Csinglecrystalsaremixedconductorswithcomparablecontributionsoftheionandelectroncomponentsofconductivity.AsconcernsmeltsofthesystemLiVO3-LiNbO3,wecanassume,accordingtoPastukhovetal(1984)andShumov(1984),thattheconductionmechanisminthemiscompletelyionandisduetolithiumionmigration( ).Thisimpliesthatinthechain(Fig.3.2)thenatureofthemainchargecarriersdoeschange.AsaconsequenceofionconductivityofthemeltLiVO3-LiNbO3andamixedion-electronconductivityofthecrystalLiNbO3,electrochemicalprocessesproceedinthechainwhenadirectelectriccurrentisappliedtothecrystallizationcell.

Inregion2-3themostprobableistheprocess

withdissolutionofreleasedoxygeninthemeltandaccumulationofLiNb3O8attheboundarywiththeplatinumelectrode.

Throughtheboundary2-3thecurrentcanonlybetransferredbylithiumions,butthroughtheboundary1-2comesonlyhalf( )theamountoflithiumionsrequiredforcurrenttransferinthechain,whiletherestoftheionsareformed,accordingto(3.39),onthesurfaceofalithiumniobatefilm.Finally,attheboundary3-4thereproceedsoxidationofoxygendissolved

Fig.3.9DeviceforLPEfilmgrowth:1)platinumcrucible;2)quartzholder;

3)alayerofcurrent-conductinghigh-temperatureglue;4)substrate;5)Li(Nb,Ta)O3source;6)platinumconductors;7)thermocouple;8)liquidphaseabsorber;9)quartztube;

10)ceramicstand.

Fig.3.10(right)Temperaturedependenceofthenumberoflithiumionstransferredinalithiumniobatesinglecrystalofcongruent

composition.

inthemelt

whichobviouslyleadstoLi2O-enrichmentofthemeltnear(4),bythereaction

Thus,thekineticsofliquid-phaseelectroepitaxywillbedeterminedbytheratioofcrystallizationratesduetoPeltierheatabsorptionandtoelectrochemicalfilm(orsubstrate)dissolutionbythereaction(1)orthelike.

Theroleofdifferenteffectsunderliquid-phaseelectroepitaxyofoxidesystemscanbeconvenientlyillustratedusingafragmentofthesystemstatediagram(Fig.3.11).Supposethatthebufferedmelthasacompositioncorrespondingtopoint1.Peltierheatabsorptioncorrespondstoashiftofafigurativepointofthesystemtowardspoint2.ThesolutionappearstobesupersaturatedwithLiNbO3,andthelatteriscrystallizedonthesubstrate.

Alongapplicationofcurrentmayberesponsibleforheatingoftheentiresystem(GabrielyanandKhachaturyan1984),whichleadstogrowthdecelerationandthentofilmdissolution(thefigurativepointshiftstowardspoint3).Itshouldbenotedthatinthecourseofcrystallizationthemeltcompositionshiftsinthedirection'4'(liquid-phaseelectroepitaxywithoutfeedmaintenance),andinthepresenceofasourceitcanremainunalteredattheexpenseofequivalentfeeding(ZhovnirandZakhlenyuk1985).Accordingtotheanalysiscarriedoutabove,theiontransfer,causingvariationsinthemeltcomposition,inducesdisplacementofpoint1inthedirectionperpendiculartotheplaneofthepicture,thatis,achangeoftheLi2O/Nb2O5ratio.

Theprobablemechanismsconsideredaboveallowustoanalyzethe

dataonlithiumniobatefilmgrowthbytheliquid-phaseelectroepitaxymethod.

WhenaLi(Nb,Ta)O3sourceisabsentfromthecrystallizationcellandcurrentisappliedforatimeexceeding50min,theobserveddecreaseofthegrowthrateorevendissolutionoflithiumniobatefilmiscausedbothbyadecreaseofsupersaturationduetoJouleheatreleaseandbyfilmelectrolysisgoingbyreaction(3.39)(GabrielyanandKhachaturyan1984).Filmdissolutioncanalsobestimulatedbythefactthatasaresultofalimitedamountofoxygendissolvedinthemelt,itsconcentrationfallswhenthecurrentisapplied,thatis,thespeedofthecathodereaction(3.40)necessaryforchargetransferfromthemelttotheelectrodedecreases.Then,tomaintainaconstantcurrentstrengthinthecircuit,thespeedofthereaction(3.39)whichistheonlymolecularoxygensupplierofthemelt,mustobviouslyincrease.Aconsequenceofcathodereactiondecelerationisanincreasedresistanceofthecircuit,whichleadstothenecessityofahighervoltagetobeappliedtothecellinordertomaintainJ=const.

Thus,theanalysisoftheavailableexperimentaldatashowsthatthebuffered-meltsystemLiVO3-LiNbO3isanion-conductingmediumwithaclearlypronouncedelectricproperty.Thedegreeofdissociationdecreaseswithincreasingcontentoflithiumniobateinthebufferedmelt.Themainchargecarriersin

Fig.3.11FragmentofthephasediagramofthepseudobinarysystemLiVO3-LiNbO3.

theliquidphaseattheepitaxytemperaturearelithiumions.Electrochemicalandnear-electrodeprocessesintheliquidphaseleadtotheoccurrenceofLi2Omoleculesand , ionswhosecontributiontoepitaxialprecipitationofLiNbO3layersisinsignificant.

3.4.3Growthkineticsofelectro-LPEgrownlithiumniobate-tantalatefilms

Todeterminethecharacterofmasstransferinelectro-LPEofLi(Nb,Ta)O3,wehaveanalyzedthedependenceoffilmthicknessandgrowthrateonthetimeofapplicationofcurrentinanequilibriumelectro-LPEconsistingofsubstrate-bufferedmelt-source.Fromthethermodynamicpointofview,itwouldbemoreprecisetothinkofthisprocessasaliquid-phaseelectroepitaxywithfeedmaintenanceorwithasource.

Figure3.12presentsthedependenceoffilmthicknessonthetimeofapplicationofcurrenttothecrystallizationcellfordifferentvaluesofcurrentdensity.Therateoflayerformationalterswithintherangeof0.6-0.1mm/minandthefilmsurfaceappearstobemirror-smooth(Khachaturyan1987).MicroX-rayspectralanalysisshowedanevendistributionofthemaincomponentsoftantalumandniobiumovertheheterostructure.Theamountofvanadiumcomingtotheepitaxialfilm

fromtheliquidphaseisminimum(0.005÷0.01at%).

Acharacteristicfeatureofelectro-LPEofferroelectricfilmsand,inparticular,oflithiumniobate,isthatsimultaneouslywithlayergrowththefilmismadesingle-domain(polarized).ThemethodofpolarizationofLi(Nb,Ta)O3filmswas

Fig.3.12ThicknessofaLiNbO3filmversusthetimeofapplicationofcurrenttothecrystallizationcell.

workedout.Forheterostructures,thisprocessischaracterizedbyadifferenceintheCurietemperaturesofthesubstrateandthefilmandbythepresenceoftransitionregionswithasmoothlyvaryingcomposition.10×15and40×60mmcontainerswithplatinumcontactsforsixstructuresweremade.Regimeswereestablishedthatprovideminimumpotentialandtemperaturedifferences,whichisnecessaryfordecreasinginterdiffusionoffilmcomponents,forpalladiumdiffusionintothestructurealongthesidecontactsandforpreventingsamplecrackingundertheactionofcurrent.

Figure3.13presentsthecurvesofthedegreeofpolarizationasafunctionofcurrentdensityforvariousepitaxytimes.Whenthetimeofapplicationofcurrentisincreasedfrom10to35min,single-domainfilmsoflithiumniobateareformedwithinthecurrentdensityrangeof10-15mA/cm2.

TogrowfilmsofsolidsolutionsLi(Nb,Ta)O3,Khachaturyanetal(1987)appliedopposite-polaritypulsestothecrystallizationcell.Thecontrolparameterswerechosenfromthefollowingrelations:currentdensityinpulsesJdirect=3Jrev;therelationbetweenpulsedurationandpausesbetweenthem ,whereJdirectiscurrentdensityinadirectpulse(mA/cm2);Jreviscurrentdensityinareversepulse(mA/cm2);tdirectisdurationofadirectpulse(s);trevisdurationofareversepulse(s);tpauseispauseduration(s);tdifisthecharacteristicdiffusiontime(s).

Thegapbetweenthesourceandthesubstrateisdiminishedto0.5mmforthereasonthatinprecipitationoflayersofsolidsolutionsLi(Nb,Ta)O3.Thisreducesthetimeofdiffusion,fromthesourcetothesubstrate,ofcomponentsdissolvedintheliquidphase,whichimprovescompositioncontrolinsolidsolutions.

Theliquidphasecompositioncorrespondedto90mol.%LiVO3+5mol.%LiNbO3+5mol.%LiTaO3.InitialepitaxytemperatureTcpit=

980°C.Jdirect=10mA/cm2,tdirect=30min,trev=3mA/cm2,trev=6min,tpause=1min.

Whenadirectpulseisapplied,anepitaxiallayerprecipitatesonthesubstratesurface.Then,toneutralizetheelectricallyinducedstateintheliquidphaseandtopreventelectrictransfer,a1minpauseismade,afterwhichareversepulseisappliedtomixionsintheliquidphase.Thenagaina1minpauseandthentheprocessisrepeated.ThelayercompositiondeterminedbymicroX-rayspectralanalysiscorrespondedtoLiNb0.5Ta0.5O3andhadathicknessh=10mm(seeFig.3.14a).

IfweapplyaunipolarpulsedcurrentwithamplitudesJ1andJ2,thecompositionofthegrowingfilmofthesolidsolutionLi(Nb,Ta)O3changesaccordingtoappliedpulses(Fig.3.14b).

ComponentdistributioninafilmwasdeterminedbyamicroX-rayspectralanalysis.ThecharacteristicdistributionspectraofthecomponentsNbandTaoverthestructurethicknessarepresentedinFig.3.15.Asdistinctfromdiffusionwaveguides,epitaxiallayersexhibitasharptransitionfromthesubstratetothefilm.Compositionconstancyofsolidsolutionsoflithiumniobate-tantalateoverfilmthicknessshowsthattheepitaxyprocessisstationary,thatis,theconcentrationprofileintheliquidphaseandtheeffectivecoefficientoftantalumsegregationremainunchanged.Thecalculationofthecompositionscorrespondingtothemicroprobecurveshasshownthatthecontentofniobiumandtantalumina

Fig.3.13DegreeofLiNbO3filmpolarizationasafunction

ofcurrentdensity.Thetimeofapplicationofcurrent:1-10min;2-20min;3-25min;4-35min.

filmofsolidsolutionisconstantandisdeterminedbythelayergrowthrate.Asthecurrentdensityand,therefore,thegrowthratedecrease,theeffectivecoefficientincreasesfrom1.4to2.35(Fig.3.15).Thegrowthrateofthelayer,v,changeswithcurrentdensitybyalinearlawwithintheindicatedrangeofJvalues.

Inprecipitationofmulticomponentsystemsfromasolutioninmeltatahightemperature,thecompositionoftheprecipitatedlayerdifferstypicallyfromthecompositionofthedissolvedmaterialsincethepresenceinthelayerofeachcomponentisspecifiedbyanindividualsegregationcoefficient.InlithiumniobatetantalateepitaxyfromthesolutionintheLi2O-V2O5melt,thecompositionoftheLiNbl-yTayO3shiftsrelativetothecompositionofthedissolvedmaterialLiNbl-xTaxO3towardsanincreaseoftantalum,thatis, .

Thecompositionalshiftisdifferentunderdifferentgrowthconditions.Variationsoftheeffectivesegregationcoefficientarecustomarilyassociatedwithmasstransferintheliquidphase.Alimiteddiffusionofdissolvedcomponentsleadstotheappearanceofconcentrationprofilesintheliquidphaseandmakesitpracticallyimpossibletocontrolefficientlythecompositionofmulticomponent

Fig.3.14TopogramoffilmsofLiNb05Ta05O3solidsolutionsof(1120)and(0001)orientations(a)anddistribution

ofcomponentsalongtheLi(Nb,Ta)O3/LiTaO3heterostructure(b).

Fig.3.15Layergrowthrate(1)andeffectivesegregationcoefficient(2)ofTaversuscurrentdensityinLPEofLi(Nb,Ta)O3.

films.Masstransitioninliquid-phaseelectroepitaxyisduetodiffusionandelectrictransferofcomponentstothecrystallizationfront.Theniobium-to-tantalumratioinafilmisdeterminedbythekineticprocessesofcrystallization.

3.5Optimizationofconditionsofepitaxialgrowthoflithiumniobatefilmswithallowanceforjouleheat

Oneofthebasicnegativeeffectsuponliquid-phaseelectroepitaxyisJouleheat.Topreventthiseffectinliquid-phaseelectroepitaxyofferroelectrics,itisnecessarytospecifyitsroleandcontributiontothecrystallizationprocess(Avakyanetal1988).WecanconditionallydistinguishbetweentwomainsourcesoftemperaturenonuniformityatthecrystallizationfrontassociatedwiththeJouleeffectandleadingbothtopreventingPeltiercoolingandobtainingnon-planarstructures.Thefirstofthesesourcesisduetoconstructiveimperfectionofgrowthdevice,unsatisfactoryqualityofelectriccontactsbetweenconductingelements(Jastrzebskietal1978;Nikishin1984a)andtoinappropriategeometryoftheelements(BarchukandIvaschenko1982).ThesecondsourceisofamorefundamentalnatureandisconnectedwiththefactthatthegrowthdeviceisessentiallyinhomogeneousfromtheviewpointofreleaseanddispersionofJouleheat.Byvirtueofconstructivevarietyofrealgrowthdevicesfor

liquid-phaseelectroepitaxyofsemiconductorsandferroelectrics,theroleofoneoranotherfactorandtheirinterrelationsarenotobvious(Milvidskyetal1982).

Themainunitofadeviceforequilibriumandnonequilibriumregimesofelectro-LPEofferroelectricsconsistsofgrowthcellsdepictedinFig.3.16a,b.Conductingelectrodesweremadeofplatinum.Applyingthemethodofequivalenceofthermalandelectricschemes(Stefanakosetal1976)withallowanceforJouleheatingofthegrowthcell,thetemperaturevariationofthecrystallizationfront,T,isdescribedbytheexpression

where ,isthethermalconductivityoftheithelement, ,isthelineardimensionoftheithelement,R2andR4areresistancesofthesubstrateandsource,respectively.PlkisthedifferenceofPeltiercoefficientsbetweentheelementsiandk,Jisd.c.density,T0isthetemperatureofexternalsurfacesoftheelectrodescorrespondingtothesaturationtemperature,T1isthecrystallizationfronttemperature.

Whenderiving(3.42),thecontactresistanceswereassumedtoplayaninsignificantroleunderJouleheatrelease,whichisconfirmedbyexperimentalmeasurements.Thevaluesofcontactelectrode-substrateandsubstrate-liquidphaseresistanceswererespectivelyequalto5×10-3ohm/cm2and8×10-3ohm/cm2,whichismuchlessthanthesubstrateandsourceresistances,102ohm/cm2,

Withaccountofexperimentalconditions×12=×14=×1,×23=×34=×3,G2=G4G2,R2=R4=R,formula(3.42)acquiresthefollowingsimpleform

From(3.43)wecanwritethecriterionforcoolingthesubstrate-solution-meltboundary

andtherefore

Thequantity

willcorrespondtothecriticalcurrentofelectro-LPE.Withaccountof

and ,formula(2.37)acquirestheform

Itisofinteresttoexaminethephysicalnatureofcriticalcurrentunderelectro-LPEasafunctionofsystemtemperature.Thegraphofthedependenceforbothregimesisconstructedanalytically(Fig.3.17).

Aswecanseefromthegraph,thecriticalcurrentofelectro-LPEdependsonsubstratematerial.Thelimitofad.c.JcpitpreventingtheJouleeffectincreaseswithincreasingtemperatureT0.

Sincethecriticalcurrentofelectro-LPEisafunctionofgeometricaldimensionsofthesubstrate,itfollowsthat

wherer0isresistivity,sandlarerespectivelytheareaandthethickness;therefore,increasingthesubstrateareaanddecreasingitsthickness,wecanincreasetheboundaryvalueofJ0.

Anincreaseoftheareaandadecreaseofthethicknessofthesubstrateandthesourceprovideextensionoftherangeofoperatingcurrentdensitiesforelectro-LPEofferroelectrics.

ThethicknessofepitaxiallayersofLiNbO3grownonLiTaO3substratesis

Fig.3.16Schematicofacellshowingtemperaturedistribution

a)equilibriumregimeofLPE;b)nonequilibriumregimeofLPE.1)platinumelectrode;2)LiTaO3orLiNbO3substrate;3)solutionin

melt[N%LiNbO3-(100-N)%LiVO3];4)LiNbO3source;5)thermalinsulation.

Fig.3.17TemperaturedependenceofthecriticalLPEcurrent(J0).1)nonequilibriumregime,

2)equilibriumregime(dashedlinesareforLiNbO3,solidlinesforLiTaO3

Fig.3.18(right)ThicknessesofepitaxiallayersofLiNbO3onLiTaO3substratesasfunctionsofcurrentdensity

inequilibrium(+)andnonequilibrium()LPEregimes.

plottedagainstthecurrentdensityvariationinequilibriumandnonequilibriumregimesofliquid-phaseelectroepitaxy(Fig.3.18).Thegraphisdividedintothreeregions.Inregion(1),layergrowthproceedsandthefilmthicknessincreaseslinearlywithincreasing

currentdensity.ThisdependencedeviatesfromlinearwhencurrentdensityisclosetoJ0=10mA/cm2inequilibriumregimeandJ0=17mA/cm2innonequilibriumregimeofliquid-phaseelectroepitaxy.Region(II)ischaracterizedbyadecreaseofgrowinglayerthicknessduetotheJouleeffect,whichresultsinasurfacedissolutionofthegrownlayerresponsiblefortheappearanceofetchingpatternsonthesurface.

Accordingtotheexpressions(3.19a,b),theJouleeffectmustexceedthePeltiereffectwithrespecttothechosenparametersforJ0=9mA/cm2inequilibriumregimeandJ0=17mA/cm2innonequilibriumregimeofliquid-phaseelectroepitaxy,andtheformationofLiNbO3layersundersuchcurrentsisexplainedbytheabove-saidapproximations.ForcurrentdensitiesJ0>9mA/cm2inequilibriumregimeandJ0>20mA/cm2innonequilibriumregimetherearenoLiNbO3layersonthesubstrates,thatis,theJouleheatcompletelyoverlapsthePeltiercooling(region(III).

Figure3.19presentsthegraphoftheexperimentaldependenceofepitaxiallayerthicknessonthesubstrateandsourcethicknessbothinequilibriumandnonequilibriumregimes.Asthesubstrateandsourcethicknessesincrease,thecriticalcurrentofelectro-LPEdecreasesand,therefore,theJouleheatincreases,andforthicknessesd>3mminequilibriumregimeandd>4mminnonequilibriumregimethegrowthprocessceases.Consequently,proceedingfromthesolutionofthesystemofequationsofequivalentthermalandelectricschemes

Fig.3.19ThicknessesofepitaxiallayersofLiNbO3on

LiTaO3substratesasfunctionsofsubstrateandsourcethicknessesinequilibrium(x)and

nonequilibrium()LPEregimes.

forequilibriumandnonequilibriumregimesandfromcomparisonwithexperimentalresults,anoptimumrangeoftheprocessparametersischosenwhichprovidesanepitaxialgrowthofLiNbO3layersofaLiTaO3substrate:

Nonequilibriumregime Equilibriumregime

TosimplifytheanalysisoftemperaturedistributionatthecrystallizationfrontwithallowanceforJouleeffect,weneglectthecontactthermaleffectsassumingthatthephysicalpropertiesofcellelementsareisotropicandthattheisotropyofthepropertiesandthegeometryoftheelementsaretemperatureindependent.Fromthesolutionofthermalconductivityequationincylindricalcoordinatesweobtain,accordingtoBarchukandIvaschenko(1982),theanalyticexpressionforastationarytemperaturedistributionatthecrystallizationfront

whereA.andBµarecoefficientsdefinedbytheboundaryconditionsoftheproblem,r1isresistivityofthei-thelement,Ri=j2r/4ki;kiarethecoefficientsoftemperatureconductivityoftheithelement,µaretherootsoftheequationj0(µa)=0,j0(µr)isthezero-orderfirst-classBesselfunction.TheexplicitexpressionsforAµandBµaretoocumbersometoberepresentedhere,andwereferthereaderto(Carslaw1945)wherethealgorithmfortheirdeterminationisgiven.Fromtheexpressionpresentedaboveitisseenthatinthegeneralcasethetemperaturefieldatthesubstrate-liquidphaseinterfaceisnonuniform.BecauseofcomplicacyoftheexplicitanalyticexpressionsforDT(h,r),theanalysisoftemperaturedistributionatthecrystallizationfronthasbeenper-

Fig.3.20Temperaturevariationatthecrystallizationfrontfordifferentcurrentdensities:1)4mA/cm2;

2)17mA/cm2;3)10mA/cm2

Table3.1GrowthcellparametersofLPE-grownlithiumniobate

Cellelement

r,ohm.cm Wcm-1K,grad-1k,cm2/s-1

l,cm a,cm J,mA/cm2

Platinum 1.05×10-4 0.71 1.4×107 10-2 5×10-14÷17

electrode 4×10-4 2×103

Substrate 6×105 3×10-2 10-1 5×10-14÷17

(T=400°C)

2×10-1

Liquidphase

148 1.5×10-2

(T=1200°C)

5×102

(T=890°C)

Source 5×105 4.2×l0- 10-1 5×10-14÷17

(T=400°C)

2×10-1

140 2×10-3

(T=1200°C

formed,inlinewithBarchukandIvashchenko(1982),onthebasisofthenumericalvaluesofgrowthcellparameterslistedinTable3.1.

Figure3.20illustratesthecalculationofAT(h,r)atthecrystallizationfrontinthegrowthcellbothinequilibriumandnonequilibriumregimesofliquid-phaseelectroepitaxyfordifferentcurrentdensities.

ThetemperaturegradientalongtheradialaxisforacurrentdensityofJ=10mA/cm2isaboutsixtimestheoneforJ=4mA/cm2,andforthecurrentdensityJ=17mA/cm2thesamegradientincreasesbyafactorof17.Accordingto(3.49),thegradientbecomesthreetimessmallerasthesubstratediameterdecreasesbyhalf.The'boundary'effectisnotobservedexperimentallyforcurrentdensitiesJ=(4÷6)mA/cm2andforthesubstrateradiusof0.5cm.Theepitaxialstructuresobtainedarecharacterizedbymorphologicaluniformityandplanarity.

Thus,usingthemethodofequivalenceofthermalandelectricschemesforexperimentalcellsinequilibriumandnonequilibriumelectro-LPEregimesofferroelectrics,wehaveintroducedtheconceptofacriticalcurrentofelectro-LPEanddeterminedtheoptimumgrowthparametersforLiNbO3onLiTaO3andLiNbO3substrates,whichpermitplanarstructurestobeproducedunderliquid-phaseelectroepitaxy.

4StructureandCompositionofLightGuidingFilmsForanefficientuseofepitaxialfilmsoflithiumniobatetantalateinoptoelectronics,itisnecessarytoobtainlayershomogeneousinthickness,possessingahighstructuralperfection,alowdefectdensityandalowcontentofuncontrolledimpurities,whichsubstantiallydecreasesattenuationinthecourseofwavepropagationoflightinthefilm.Thishasstimulatedinvestigationsofthecrystallinestructure,composition,orientation,surfacemorphology,substratefilminterface,domainanddislocationstructuresofthefilms.Theinfluenceofgrowthconditionsupontheseparametershasbeenestablished.

4.1Structureandphysico-chemicalpropertiesoflithiumniobateandtantalatecrystals

Lithiumniobate(LiNbO3)isoneofthemostinterestingandwidelyusedferroelectrics.FirstcrystalswereobtainedbyLapitsky(1952)andSue(1937).ThestudyofthestatediagramofthesystemLi2O-Nb2O5hasshownthepossibilityofformationoffourcompounds:Li2O-14N2O5,Li2O-3Nb2O5,LiNbO3andLi3NbO4(RusmanandHolzberg1958).

CrystallizationofLiNbO3ispossibleintheregionof40-60mol.%Nb2O5attemperaturesbetween1160and1253°C.Detailedstudiesofthephasediagraminthisregionhaverevealeddistinctionbetweencongruentandstoichiometriccompositions.TocongruentcompositiontherecorrespondstheratioLi2O/Nb2O5=0.946andthemeltingtemperatureTmelt=1170°C.Upontheliquidphasecompositionvariationwithintherangeof45-58mol.%Li2O,thecrystalcompositionvariesfrom47to50mol.%(Carruthersetal1971).Thus,crystalsofstoichiometriccompositioncanbegrownfromamelt

containingupto58mol.%Nb2O5,butbecauseofthelargedifferenceinliquidandsolidphasecompositionsthisleadstothegrowthofinhomogeneouscrystals.

X-rayandneutrondiffractionanalyseshaverevealedthatlithiumniobatehasthestructurerelatedtoilmenite(Abrahamsetal1966).Boththestructuresare

constructedfollowingthepatternofhigh-densityhexagonalpackagingbutdifferinalternationofoccupiedandunoccupiedoctahedra.InroomtemperatureLiNbO3crystals,octahedralintersticesformedbyoxygenionsinanalmosthigh-densityhexagonalpackagingarefilledwithniobiumions(1/3)andlithiumions(1/3),theremaining1/3beingvacant.Thesuccessionobservedwasasfollows:

Figure4.1showspositionofelementarycellsinlithiumniobate.TheoctahedronwithNbionsformsacommonfacetwiththevacantoctahedronwhichinturnformsafacetoftheoctahedronoccupiedwithlithiumion.Afteradistanceofc/2(cisthelatticeconstant)thepositioningofmetallicionsisrepeated:Nboccupiesthefourthoctahedron,thefifthremainsvacant,Lioccupiesthesixthoctahedron.Thenthecellisrepeated.

ThesymmetryofLiNbO3andLiTaO3crystalsistetragonal(class3m).IntheferroelectricphasethespacegroupisC3v-R3C,inparaphaseD3d-R3C.Therhombohedralcellcontainstwoformulaunitsandthehexagonalcellcontainssix.Thelatticeconstantsintherhombohedralcella=5.4944Å,a=55°52;inthehexagonalcella=5.14829±2×10-5Å,c=13.8631+4×10-4c/a=2.693.Interplanarspacesinthelatticeareequalto1.286Å(x-cut),1.489Å(y-cut)and1.15A(z-cut).Theprincipalcrystallographicdirections(planes)oflithiumniobatearepresentedinthestereographicprojectionofFig.4.2.The[0001]axiscorrespondstothespecialcrystallographicdirection(theopticalaxis)andcoincideswithspontaneouspolarizationdirection.

TheparametersofthecrystallographiccellsandionpositionsintheminLiNbO3aretabulatedinTable4.1.

Ionpositionsinthecrystallatticeareofinterestfromthepointofviewof

Fig.4.1CrystallinestructureofLiNbO3;a)seriesofdistortedoctahedralsalongthepolarc-axis;b)reallocation

ofoxygenatomsrelativetolithiumandniobiumatoms(Abrahamsetal1966).

Table4.1Physico-chemicalconstantsofLiNbO3crystals(Prokhorov,Kuz'minov,1990)

Characteristic Experimentaldata

Densityofsinglecrystals(g.cm-3) 4.612

Mohs'shardness 5

Meltingpoint(°C) 1260

Curiepoint(°C) 1210

Parametersofaunitcell:

Rhombohedral

a(Å) 5.4920

Angle 55°531

Hexagonal

a(Å) 5.14829±0.0002

c(Å) 13.86310±0.00004

Numberofformulaunitsincell

Rhombohedral 2

Hexagonal 6

Thermalexpansioncoefficient

aaxis 16.7±10-6

caxis 2.0±10-6

Dielectricconstant

Refractiveindices(l=0.623µm) no=2.286ne=2.220

Loss-angletangent(v=1kHz) lessthan0.02

Specificresistance(Wcm)

200°C over1014

400°C 5×108

1200°C 140

Watersolubility(mol1-1)

25°C 2.8±10-4

50°C 4.3±10-4

100°C 7.4±10-4

Dissolutionheat(kcalmol-1) 6.2

DiffusionactivationenergyQD(kcalmol-1)

68.21±0.48

68.17±1.24

( tocaxis)

EvaporationactivationenergyQv(kcalmol-1)

( tocaxis)

Evaporationcoefficient,a 10-4

Thermoelectriccoefficientofmelta1(mV.K-1) -0.4

Thermoelectriccoefficientofcrystalas(mV.K-1) 0.76±0.02

Coefficientofcrystallizationemfav(mVs.m-1) 1.25±0.2

theferroelectricpropertiesoflithiumniobate.Asdistinctfromotherferroelectriccrystals,lithiumandniobiumexhibitaconsiderableionshiftfromthesymmetricpositionintheparaphase.Theniobiumionisatadistanceof0.897Åfromthenearestplaneofoxygenatomsandat1.413Åfromthenextplane.TheLiionshiftmakesuprespectively0.714Åand1.597Å.So,appreciableshiftsoflithiumniobateionsarerequiredforreachingaparaelectricstateorpolarizationreversal.AtatemperatureexceedingtheCuriepoint,lithiumandniobiumionsshiftinthesamedirectionsothatNb5+occupiesthecentreoftheoxygenoctahedronandLi+liesintheplaneofoxygenlayers(Fig.4.1(b)).InLiNbO3crystals,theshiftonionsfrompositionstheyoccupyintheparaelectricphaseasthetemperaturelowersthroughtheCuriepointisresponsiblefortheappearanceofspontaneouspolarization.Spontaneouspolarizationmaybealignedeitheralongpositiveoralongnegativedirectionofthethird-orderaxis,boththesestatesbeingenergeticallyequivalent.

ThelargestandmostperfectwereCzochralskigrownlithiumniobatecrystals(Fedulovetal1965;Nassauetal1966).Crystalsobtainedinotherwayshadsmallersizeandsomestructuralimperfections.

Thegrowthconditionsoflithiumniobatecrystalsareconnectedwiththepresenceofcontrolledanduncontrolledimpuritiesinthemelt.Whenstoichiometryisviolated,lithiumandniobiumionsmayenterasimpurities.SolvabilityoftheNb2O5componentintheliquidphaseis45-58mol.%andinthesolidphaseitnarrowsto48-50mol.%.ThisleadstostoichiometryviolationandaffectstheCurietemperature,birefringenceandphasematchingtemperature.ThehighestperfectionofcrystalsisobtainedfortheratioLi/Nb=0.946whichcorrespondstocongruentcomposition.

Theexperimentaldataonthephysico-chemicalpropertiesoflithiumniobate(Kuz'minov1975)arepresentedinTable4.1whichshowsthat

ifimperfectcrystalsaredisregarded,theirdensityrangesbetween4.6and4.7g/cm3.ThemeltingtemperatureofstoichiometricLiNbO3crystalsis1253°C.Thephasetransitiontemperatureis1210±5°C.Atatemperatureof1200°C,lithiumniobatemeltinvacuumandinairisnonvolatile,whichisveryimportantforthetechnologyofthismaterial.ThesurfacetensionofLiNbO3measuredbythemoltendropmethodatthevacuum-meltboundaryatthemeltingtemperaturemakesup50-150dyn/cm.

Refractiveindicesoflithiumniobatearesensitivetostoichiometryviolation,whichleadstoopticalinhomogeneityinbulkcrystal.CrystalsgrownfromameltwithadditionofLi2OandMgOhasalowerrefractiveindex,thedecreaseofnebeingsubstantial,whichleadstoanincreaseofbirefringence.AnexcessNb2O5hasnoeffectuponnoandaverylittleeffectuponne.

AnimportantroleforliquidphaseepitaxyisplayedbythephasediagramofsolidsolutionLiNbO3-LiTaO3andthedependenceoftheCurietemperatureonthecomposition.

Thesolidusandliquidustemperaturesweredeterminedupto1575°Conthermoanalyser.TheresultsofdifferentialthermalanalysisareillustratedinFig.2.4.BothliquidusandsoliduscurvesshowasmoothvariationfromLiNbO3toLiTaO3.Asexpected,thesecurvesdonotmeetateitherendofthispseudobinarysectionsincethestoichiometricandcongruentmeltingcompositiondonotcoincide.

Fig.4.2StereographicprojectionofLiNbO3

Awiderspacingwasfoundbetweenthesolidusandliquiduscurvesbecauseofthelowerhomogeneityofthesamples.

Curietemperaturesweremeasuredonpowderspecimenshydrostaticallypressedatroomtemperatureandsinteredat1100°Cfor12h.ThestraightlineshowninFig.4.3wasfittedtothedatabyleast-squareanalysis.Thestandarddeviationis13°C,andthecorrelationcoefficientof0.9966indicatesthatthestraight-lineapproximationisvalid.

Abrahamsetal(1966)havedeterminedthecrystallinestructureoflithiumniobateoverthetemperaturerangeof24-1200°CbymeansofapolycrystalX-raydiffractionanalysis.Theerrorsinvolvedinhigh-temperatureX-raypowderdiffractionarefrequentlylarge,thusthereisconsiderablescatterinthedatafortheoxygenpositionalparametersasfunctionsoftemperature.

Fig.4.3VariationinferroelectricCurietemperaturewithsolidcompositioninLiNbO3-LiTaO3solid-solutionsystem(Petersonetal1970).

Petersonetal(1970)havethereforedonealinearleast-squaresfittothedatawiththeconstraintthatthehighlyaccuratesingle-crystal(Abrahamsetal1966;1967)parametersshouldbereproducedatroomtemperature.Thepositionalparameterssocalculatedwere(Petersonetal1970)

x=0.005027(T/1000)+0.04908,

y=0.3451-0.0207(T/1000),

z=0.00401(T/1000)+0.06460

andthetemperatureTwasindegreesCentigrade.

LithiumniobatecrystalsgrownbyCzochralskimethodfromacongruentmeltpossessthemosthomogeneouscompositionbutarenonstoichiometricandlithiumdepleted(~1.4mol.%Li2O)(ScottandBurns1972;PetersonandCarnevale1972).Awideenoughhomogeneityregion,fluctuationsofgrowthparametersinthecourseofcrystalgrowthandotherfactorsareresponsiblefortheappearanceofregionswithlocalcompositiondeviationsinlithiumniobatecrystals(Holman1978).Inhomogeneityofcompositionisobservedbothalongtheboulelengthandinradialdirection.Asshownbygravimetricmeasurements(Holman1978),adeviationoflithiumniobatecompositionfromthemeanvalueforspecimenscutoutofonecrystalbouleisinmostcasesequalto0.2andcanevenreach0.66mol.%Li2O.Inhomogeneityofcompositionwasidenticalfordifferentregionsofoneandthesamecrystalcut.Congruentcompositionoflithiumniobatemakesup48.6±0.2mol.%Li2O(Holman1978;Chowetal1974).

Thelargewidthofhomogeneityregionoflithiumniobateisduetothepresenceofintrinsicpointdefectssuchasintersticeatomsandvacanciesincationandanionsublattices(Carruthersetal1971).Thenatureofpointdefectsofthecrystallatticeoflithiumniobate,which

stemfromcrystalcompositiondeviationfromstoichiometry,isnotexactlyknown.Thereexistmodelsofthedefectstructureoflithiumniobate,oneofwhichisconstructedonanidealcationlatticeofniobiumwithlithiumvacancychargecompensationbytheformationofoxygenvacancies(Fayetal1968).Butthedependenceoflatticeconstantsanddensityoflithiumniobateonthecompositioncastdoubtonthemodeloflithiumvacancies.Lerneretal(1968)assumetheexcessniobiuminthelatticeofLiNbO3tooccupythevacantpositionsoflithiumandthustoformantistructureNbL1defects.TheNb+5ionchargeintheplaceofLi+iscompensatedbytheformationoffourVL1vacancies.NassauandLines(1970)proposedamodelofextendedcationpackagingdefectinthedirectionofzaxiswithalternationoflithiumandniobiumatoms.Inextensionofsuchdefectcomplexesthereoccursacomplicatedstructuraldisorder.AmoredetailedreviewandanalysisofthemodelsofdefectstructureoflithiumniobateisgivenbyBallman(1983)andJarzebski(1974).

X-raydiffractionmethodsareinconvenientfortheproofoftheexistenceofniobiumatomsoccupyingthepositionoflithiumatomsinthecrystallatticebecauseoftheirlowconcentration(~1%).PetersonandCarnevale(1972)discoveredtwotypesofsignalsfrom93NbinthespectraofnuclearmagneticresonancefromnonstoichiometricLiNbO3crystals.Theauthorsascribedthe

firstandmostintenselinetotheniobiumthatoccupiescrystallographicallyregularpositioninlithiumniobatelatticeandthesecondtypeofsignaltoexcessniobium,NbL1.Buttheintensityofthesecondlinemadeup6%oftheintensityofthefirstone,thatis,NbL1concentrationexceededtheexpectedone.ThepresenceofanadditionallineintheNMRspectrumtestifiestotheexistenceofthesecondtypeofniobiumatompositioninthelatticeoflithiumniobatebutprovesneitherofthedefectstructuremodelsdescribedabove.Theabsorptionspectraof7LiNMRalsoexhibitedweakadditionallineswhosepresencewasassociated(YatsenkoandSergeev1985)withdynamicdisorderoflithiuminthecrystallinestructureoflithiumniobate.

So,lithiumniobatecrystalsshowappreciablecompositionvariations,aswellasacomplicatedpointdefectspectrum.

Peculiaritiesofconstructingthephasediagramoflithiumniobateandtheobserveddeviationsofcrystalcompositionfromstoichiometrymayleadtoprecipitationoflithiumtriniobateasasecondphaseinthesecrystalsundercertainconditionsofthermaltreatmentorundercoolingofgrowncrystals.Fewdataintheliteraturetestifytothefactthatphaseformationoccursbothinthebulk(ScottandBurns1972)andonthesurface(Armeniseetal1983)oflithiumniobatecrystals.

ThebasicresultsontheformationofLiNb3O8inbulklithiumniobatecrystalswereobtainedbySwaasandetal(1974).TheX-rayphaseanalysisandmeasurementsofopticaltransmissioncoefficientswereusedtoexaminethepropertiesoflithiumniobatecrystalsafteralong-termannealingintheairwithinthetemperaturerangeof600-1000°Cfor100-1000h.Afterthelithiumniobatespecimensofdifferentcompositionwerecooleddowntoroomtemperature,theiropticaltransmissiondecreasedconsiderablyduetotheappearanceofmilk-whiteopalescentregions.Transparencyofthecrystalsdecreasedwith

increasingannealingtimeanddecreasingLi2Ocontentintheoriginalspecimens.So,lithiumniobatecrystalsgrownfromameltwithlessthan48mol.%Li2Oshowedopalescencealreadyaftera10hourannealingat800°C,whereascrystalsgrownfrommeltswithahigherLi2Ocontentrequireda500-hourannealingatthesametemperature.Theauthorsbelievethatachangeinthebulkcrystaltransparencyunderannealingisduetoprecipitationofasecondphase-lithiumtriniobateLiNb3O8whichbordersuponLiNbO3onthesideofniobium-enrichedcompositions.ThisassumptionwasfullyconfirmedinanX-rayphaseanalysisofannealedcrystals.

Uponasecondannealingatatemperatureexceeding1000°Candarapidcoolingtoroomtemperature,inspecimensoflithiumniobatecrystalscontainingthesecondphasethescatteringcentresdisappearedandthecrystalsbecameclearagain.TheX-raydiffractionpatternsofsuchspecimenscontainedreflectionsonlyfromlithiumniobate.Thetemperatureabovethatofbacktransformationdependedonthespecimencomposition,andhadavalueofabout910°Cforcrystalsgrownfromacongruentmelt.Onthebasisofmeasurementsofbacktransformationtemperatureforlithiumniobatespecimensofdifferentcomposition,theauthorstracedoutthelineofLiNb3O8-LiNbO3phaseequilibrium,foundthewidthofthesolidsolutionregionandbuiltthephasediagramfortemperaturesT<100°C(Fig.4.25).

Thus,lithiumniobatecrystalsaremetastableatroomtemperature,unstableunderalong-termthermaltreatmentandwithinacertaintemperaturerangecancontainthesecondphaseLiNb3O8.

TherearecomparativelyfewdataontheconcentrationandlocalizationofLiNb3O8phase.Examinationbyopticalmicroscopyandlightscatteringmethodsshowsthatuponannealinginthetwo-phaseregion,thesubmicroscopicparticles(r<10-5cm)ofthephasearenucleatedheterogeneouslyatblockboundaries,ondislocationsand,alongwithinclusionsofplatinumparticlesandotherimpurities,arelightscatteringcentresinlithiumniobatecrystals.

IncoolingannealedorgrowncrystalsitisalsonecessarytotakeintoaccountthetemperaturefallratesincethisrateisresponsibleforthetimeduringwhichthecrystalwillremainwithinthetemperaturerangetypicalofprecipitationofLiNb3O8.Whenthecoolingrateincreasesto3-5°C/min,thelithiumniobatewaslesspronetocrackingthancrystalscooledataratelowerthanl°C/min.Withoutdenyingthecontributionofothermechanisms,ScottandBurns(1972)supposethattheprecipitatesofthesecondphasecanserveasnucleifortheappearanceanddevelopmentofcracksinlithiumniobatecrystals.Topreventlithiumtriniobatefromprecipitatinginbulkcrystaloflithiumniobate,thecoolingrateshouldbe>20°C/min(Holmanetal1978).

Pioneeringreportsonvariationofthephasecompositionoflithiumniobatecrystalsurfacecausedbytheformationoflithiumtriniobateappearedon1983asaresultofanalysisoftitaniumdiffusionintolithiumniobatecrystalsinthecourseofmanufacturingopticalwaveguides(Armeniseetal1983;DeSarioetal1985).ThecompoundLiNb3O8occurredonthesurfaceoflithiumniobateslabscoveredwithatitaniumlayerinthecourseofannealingwithinthetemperaturerangeof550-900°Cinoxygenatmosphere.Underascanningelectronmicroscopelithiumniobateshowedupasshapelessspotsofmorethan

100µmlocatedinaTiO2layer.Analysisofatomiccompositionhasshownthatthecontentoftitaniumisdecreasedandthatofniobiumincreasedinsuchregionsascomparedtophase-freeregions.AstheannealingtemperatureheightenedtoT>900°C,LiNb3O8wasdisintegratedandspotsdisappearedfromlithiumniobateslabsurface.

InvestigationsofLiNbO3substrates(Armeniseetal1983)haveshownthatLiNb3O8isalsoformedintheabsenceoftitaniumlayer,thatis,phaseformationonthecrystalsurfaceisaspecificbehaviouroflithiumniobateitselfinthecourseofannealingwithintheindicatedtemperaturerange.ThepresenceofLiNb3O8phaseorientationrelativeto(0110)and(0110)LiNbO3substrateswasdiscoveredfromLauediffractionpatternstakeninvariablegeometryandfromthespectraofbackwardRutherfordheliumionscattering.PrecipitationofLiNb3O8phaseoncrystalsurfaceproceedsnotonlyunderannealinginoxygenatmosphere,butalsointheairaswellasinaN2orArflux.AdditionofwatervaporsintotheatmosphereofannealingpreventstheformationofLiNb3O8andinducesdisintegrationofthesecondphaseifithasalreadybeenpresentonthespecimensurface(DeSarioetal1985).DisintegrationofLiNb3O8underannealinginmoistatmospherewashypotheticallyexplainedbytheformationofthehydroxylgroupOH-and(Li1-yHy)NbO3moleculesduetoprotondiffusionintothecrystal.

Phaseformationonthesurfaceoflithiumniobatecrystalswasalsoobservedunderradiationdamagesoflithiumniobate(JetschkeandHehl1985).

AchangeinthephasecompositionofLiNbO3surfaceirradiatedbyN*andP*ionswasdiscoveredbybackwardRutherfordscatteringatatemperatureof279°C.Niobiumconcentrationinthenear-surfacelayerwasfoundtobeincreased.ConnectionbetweenphaseprecipitationandstructuraldamageinthesurfacelayeroflithiumniobatesubstrateswasreportedbyGan'shinetal(1985,1986)whoobservedtheoccurrenceofthecompoundLiNb3O8afterannealingatT=450°Cfor3hofproton-exchangedwaveguidesmanufacturedon(0001),(0110),(2110)and(0114)facetsoflithiumniobate.

Theoperationareaofmanyacousto-andoptoelectronicdevicesisthenear-surfacelayer,aswellasthesurfaceoflithiumniobatesubstrates,andthereforeofparticularimportanceforthecreationofeffectivedevicesiscontroloverthestateoflithiumniobatecrystalsurface,itsstructureandphasecomposition.ThestudyofphaseformationinlithiumniobatecrystalsplaysapracticalrolesinceheattreatmentofLiNbO3isawide-spreadtechnologicaloperationinmanufacturingvariousdevicesonthebasisoflithiumniobatecrystals.

4.2X-raydiffractionanalysisoffilms

InvestigationsoffilmstructurewerecarriedoutusingtheX-raydiffractionmethod.Theanalysisofpatternsthusobtainedallowsustojudgeofpolarization,orientationandlatticeconstants.PolarizationandlatticeconstantswerealsodeterminedbytheelectrondiffractometryandthecompositionbytheX-raydiffractionmethodandlasermicroanalysis.

4.2.1Layercomposition

Thedistributionofcomponentsoverthethicknessofthelightguidinglayerwasexaminedbymicroroentgendiffractionanalysis(MRDA).Figure4.4presents

Fig.4.4Distributionofcomponentsalongthethicknessof(a)LiNbO3/LiTaO3,

(b)Li(Nb,Ta)O3/LiTaO3and(c)LiNbO3/Al2O3heterostructure.

graphsofcomponentdistributioninfilmsonLiTaO3(Fig.4.4(a,b))andA12O3(Fig.4.4(c)).Theconcentrationofthemaincomponentofthesubstrate(TaorA1)attheinterfacedecreasestozerowhileniobiumconcentrationbecomesmaximum(Fig.4.4(a,b,c)).IngrowingfilmsofsolidsolutionLiNb1-yTayO3onaLiTaO3substratetheTaconcentrationattheinterfacedecreasesfrom100%toequaltheTaconcentrationinthefilmFig.4.4(b).Analysisofconcentratedprofileshasshownthatthecompositiondoesnotchangethroughoutthefilmthickness.TherelativecontentofNbandTainafilmofsolidsolutionisdeterminedbytheircontentintheliquidphasewhentheeffectivecoefficientoftantalumconcentrationKcff~1.5.

Asdistinctfromdiffusedwaveguides,epitaxiallayersarecharacterizedbyasharpsubstrate-filminterface.Epitaxialfilmsoflithiumniobate-tantalatearecolourless.

Theresultsobtainedsuggestsomeconclusionsconcerningthegrowthprocess.Sincetantalumconcentrationinagrowinglithiumniobatefilmiszero,thesolution-meltattheinitialepitaxytemperatureisinthemetastableregion,andthesubstratesurfaceisnotadditionallydissolved.ThecompositionconstancyoffilmsofLiNb1-yTayO3solidsolutionsimpliesthattheconcentrationprofileremainsunalteredinthecourseofgrowth,whichcorrespondstothediffusionmodel.

Besidesthedistributionofmacrocomponents,theuncontrolledimpurityofvanadiumatomsinthefilmandthecontentofironions,introducedinconcentrationsof1and2mol.%intothesolution-meltintheformofFeCO3,weredetermined.MRDAdoesnotpermitqualitativeestimationofthecontentoflow-concentrationcomponents.Thepresenceofvanadiumandironimpuritiesinthefilmswasdeterminedbylaseremissionmicroanalysis.

Analysisofthespectraoftheexaminedpatternshasshownthatthefilmscontainvanadiuminconcentrationrangingundergrowth

conditionsbetween0.005and0.1atm.%.ThespectraofLiNbO3filmsandLiTaO3substrateweremeasuredforthesecondtimeusingafour-stepGortmandiaphragmunderthesameconditions.Inthiscase,filmspectrawereinvestigatedbycomparisonwiththespectraofvanadiumandironoxides.Theresultsconfirmedtheabsenceofvanadiumspectrallinesinthelithiumtantalatesubstrate,whereasinthefilmstheywereclearlypronouncedinthesamewavelengthregion.Underoptimumcrystallizationconditions(thegrowthratev<0.2µm/min),aLiNbO3filmonaLiTaO3substrateof(0001)orientationcontains0.005-0.01atm.%ofvanadium.Themaximumconcentration(0.01atm.%)ofhomogeneousvanadiumimpuritywasobtainedataprecipitationrateof0.6-0.8µm/min.Ahomogeneoushighlyconcentratedvanadiumimpuritywasnotobservedwithafurtherincreaseofprecipitationrate.TheupperlimitofhomogeneousvanadiumimpurityconcentrationisobviouslyduetothedifferenceinV5+andNb5+ionradii(Rv=0.4Å,RNb=0.66Å),whichleadstostronglatticedistortionsunderthe substitution.

Asdistinctfromvanadium,theradiiofFe3+ions(0.67Å)areclosetothoseofNb5+andLi5+(0.68Å),whichmakesitpossibletoobtainlithiumniobatecrystalswithironimpurityreaching3weight%(Gabrielyan1978).Investigationofdopedsampleshasshownthatironconcentrationinthesampledepends

Table4.2LatticeparametersandinterplanedistancesofLi(Nb,Ta)O3filmsandLiTaO3substrate(Madoyanetal1985)

No Filmmaterial Latticeparameters(Å)

Orientation Interplanedistances(Å)

LiNbO3 5.137 13.828 (0001) 1.1523

1 ( ) 1.3884

( ) 1.2030

LiNb07Ta03O35.1385 13.808 (0001) 1.1507

2 ( ) 1.3888

( ) 1.2034

LiNb05Ta05O35.1395 13.798 ( ) 1.1498

3 ( ) 1.3891

( ) 1.2036

LiNb02Ta08O35.1408 13.78 ( ) 1.1483

4 ( ) 1.3894

( ) 1.2040

LiTaO3 5.1421 13.772 (0001) 1.1477

5 ( ) 1.3898

( ) 1.2042

onironcontentintheliquidphaseandremainsessentiallyunchangedastherateincreases.Theestimatesoftheeffectiveironsegregationcoefficientobtainedbylaseremissionmicroanalysisliewithinthe

rangeof0.2-0.5.

4.2.2Monocrystallinityandinterplanardistances

X-raysincidentonthecrystallinestructuresurfacediffractinthenear-surfacelayerwhosethicknessisdeterminedbythesamplematerialandlightbeamintensity.X-raysincidentonthesurfaceofepitaxialstructurecanpenetrateintothesampledepthlargerthanthefilmthickness.Inthiscase,X-raysdiffractattwoanglesoneofwhichcorrespondstodiffractiononthefilmandtheotheronthesubstrate.Therelativeintensitiesofthesebeamsdependonfilmthicknessandonthedepthofthelayersonwhichdiffractiontakesplace.Superpositionofbeamsispossibleinthecaseofclosediffractionangles,andthepositionofthediffractionlinescannotthereforebepreciselydetermined.Figure4.5presentsdiffractioncurvesforLiNbO3andLi(Nb,Ta)O3filmsonLiTaO3substratesof(0001)and(1120)orientations.Thedifferenceinthediffractionanglesoflithiumniobateandlithiumtantalateequalto10'forthe(0001)planeand6'forthe(1120)planegivesdifferentpeaksfromtheLiNbO3filmandLiTaO3substrate.ForaLiNbl-yTayO3filmthediffractionmaximumisdisplacedfromthesubstratewithincreasingytowardsthemaximum(Madoyanetal1985;Madoyan1984).Thedifferencebetweenthemaximafromthefilmandsubstratereachesy=0.8.Furtheron,thepresenceofthefilmaffectstheasymmetryofthediffractionpeakprofilebroadened,dependingonthelayerthickness,towardsthefilmorsubstrate(Fig.4.5(c,d)).Theattempttoobtainseparatepeaksfromfilmson(1010)-orientedsubstratesfailed(Dq~3').Forclosevaluesofdiffractionangles,investigationswerecarriedoutonverythickfilms(Fig.4.5(e,f)).Sincethediffractiondepthmakesupabout60µm,forfilmsthickerthan

Fig.4.5X-raydiffractionpatterns:LiNbO3filmsonLiTaO3substratesof(a)(0001)and(b)( )orientations,LiNb0.5Ta05O3onasubstrateof(c)(0001)and(d)( )orientations,LiNb02Ta08O3

onasubstrateof(e)(0001)and(f)( )orientations.

Fig.4.6

HexagonalcellparametersversusLiNb1-yTayO3filmcomposition.

50µmX-raysdonotpracticallyreachthesubstrate,andthediffractionangleisdeterminedbythefilmalone.Thevaluesofthediffractionanglesandlatticeconstantswereestimatedforthick(1010)-orientedLiNbO3andLiNb1-yTayO3films(y<0.8).

Table4.2presentsthevaluesofinterplanardistancesandlatticeconstantsofLi(Nb,Ta)O3filmsandLiTaO3substrate.

ThereiscontroversyintheliteratureastothecharacterofthedependenceofcrystallographicparametersandCuriepointofsolidsolutionsLiNb1-yTayO3ontheamountoftantalum,y.Shapiroetal(1965)andSugiietal(1976)pointtothenonlineardependence,whereasShimuraandFujino(1977)showthatthedivergenceisduetoalackofcorrespondencebetweentheparameteryinthesynthesizedsolidsolutionLiNb1-yTayO3andtheparameterxoftheinitialmaterialLiNb1-xTaxO3.TheconstructeddependenceofthelatticeconstantsaandConthetantalumcontentinthefilmisclosetolinear(Fig.4.6).

AnalysisofX-raydiffractionpatternsallowsustojudgeofstructuralperfectionofepitaxialfilms.Theexistenceofonlyonepeakindicatesthatthefilmissingle-crystal,andasmallhalfwidth(notlargerthanthatofthesubstrates)pointstothelackofblockstructureofthefilmandtoperfectionnotlowerthanthatofbulkcrystals.

Diffractionstudiesoffilmswerealsocarriedoutbytheelectrondiffractometrywhichprovidesahighaccuracyindeterminationoflatticeconstants.Itwasestablishedthatfilmsonsubstratesof(0001),( )and( )orientationsaresingle-crystal,whichfactaccountsforthepoint-likecharacteroftheelec-

Fig.4.7ElectrondiffractionfromtheLiNbO3filmsurfaceonaLiTaO3(1120)substrate,Kikuchilinesareobserved.

trondiffractionpattern(Fig.4.7).Furthermore,highstructuralperfectionofthenear-surfacelayerofthefilmpermitobtainingdiffractionintheformoftheKikuchi-lines.

Fig.4.8Schematicarrangementofatriple-crystalspectrometer(Sugiietal1978).

Sofaraselectrondiffractionpatternonlyprovidesinformationaboutanear-surfacelayer,itpermitsdeterminationoflatticeconstantsofafilmirrespectiveofitsclosenesstothesubstrateparameter.ThisisofparticularimportanceforthediffractionstudyofhomoepitaxiallayersandfilmsofLiNbO3ona( )-alignedLiTaO3substrate.WeshouldnotethatinallthecasestheinterplanardistancesdidnotdifferfromtheresultspresentedinTable4.1.

HomoepitaxialLiNbO3filmsareofinterestinthecasewhentheyaredopedwithtransitionmetalatoms.AdetailedanalysisofFeatomdistributionovercrystallographicpositionswasgivenbyRubinina(1976)whoshowedthatFe2+andFe3+ionssubstitutelithiumorniobiumones.Suchironimpuritymustnotleadtosubstantiallatticedistortions.VariationoflatticeconstantsofLiNbO3uponirondopingwasnotestablishedwithinexperimentalerror.ThediffractionstudiesofLiNbO3filmsonasapphiresubstrateshowedfilmpolycrystallinity.

CreationoflightguidinglayersinLiNbO3usingdiffusionofmetal(inparticulartitanium)ionsnecessitatesdeterminationofstrainsinthesurfacelayerandtheformationofmisfitdislocations.Tosolvetheseproblems,Sugiietal(1978)successfullyappliedX-rays.

4.2.3Measurementofstrainsinthediffusedlayer

TheX-rayrockingcurvemethodwasemployedbySugiietal(1978)forprecisedeterminationofstrainsinthediffusedlayer.Rockingcurvesweretakenusingatriple-crystalspectrometerasshowninFig.4.8.ItconsistsoftwonearlyperfectgermaniumsinglecrystalsC1andC2,andasimplecrystalC3arrangedinthe(+,+,-)position.ForC1andC2thesymmetric(333)reflectionwasused,theBraggangleforCuKa1radiation,q,beingabout45°.TheangularandwavelengthdistributionsoftheX-raybeamdiffractedfromthesecondcrystalC2wereco=2×10-5rad(4''arc)andDl/l0=2×10-5(l0=1.5405Å),respectively.Theyweresmallenoughtoobtainanintrinsicrockingcurveofthesmallsampleforanylatticeplane(hkl).Inaddition,thebeamthusobtainedisalmost

Table4.3StrainsintheTi-diffusedlayerofLiNbO3(Sugii,Fukuma,Iwasaki,1978)

Diffusiontime, t=10h Diffusiontemperature, T=1000°C

T(°C) ey×103 t(h) ey×103 ey×103

1000 -1.3 1.25 -2.19 1.2

1050 -0.71 2.5 -1.66 0.75

1000 -0.39 3.75 -1.28 0.62

- - 10 -0.759 0.52

o-polarized(anelectricfieldvectorEperpendiculartotheplaneofincidence)becausethescatteringangle,2q,isnear90°.AslitwasplacedbetweenC2andC3toobtainabeamofwidth0.5mmandheight2.0mm.Undiffusedsamplesproduced(030)rockingcurveswithwidthathalfmaximumintensity(WHMI)ofabout12''arc,whichisessentiallythetheoreticalWHMIforthe(030)reflectionofaperfectLiNbO3crystalundertheseexperimentalconditions.Ontheotherhand,thediffusedsamplesproduces(030)rockingcurvesaccompaniedbyadiffractionsatellite,displacedinanglewithrespecttothediffractionpeakoftheunperturbedregioninthesubstrate.Precisedeterminationofstrainsinthediffusedlayerispossiblesinceastandardoflatticeconstantisavailableinthesametraceasthediffusedlayer.Thestrainalongtheaaxis,ey(ex),isobtainedfromashiftinangleq030ofthesatelliteas

whereq030istheBraggangleforthe(030)reflection.However,strainalongthecaxis,ez,cannotbedirectlymeasuredonthediffusedlayer,sincethecaxisisparalleltothesurfaceinthey-platecrystal.IfashiftDqhklcanbeobtainedfora(hkl)reflectionwithnon-zerol,thestrain

eziscalculatedfromapairofshiftsDq030andDqhklusingthefollowingexpression

Fig.4.9(a)Relationshipbetweenthe(036)latticeplaneandtheincidentX-raybeam.(b)Inclinationinthe(036)latticeplanesbetweenthesubstrateandtheTi-diffusedlayer.Thedottedlinerepresentsalatticeplane

parallelto(036)s(Sugiietal1978).

Fig,4.10Familyof(036)rockingcurvesforthesamplesofdiffusedLiNbO3:Ti

(Sugiietal1978).

wheredisthe(hkl)latticespacingandqhklistheBraggangleforthe(hkl)reflection.A(036)reflectionwasusedforthispurpose.Thegeometricalrelationshipbetweenthe(036)latticeplaneandthesurfaceisshowninFig.4.9.Theanglebintheinterplanaranglebetweenthe(036)planeandthesurface.Inthe(036)asymmetricreflection,ashift foranincidentbeamwithaglancingangle(q036+b)isgenerallynotequaltoashift foronewithaglancingangle(0036-b),sinceaninclinationofthe(036)latticeplane,Db,isinvolvedinbothshifts(seeFig.4.9(b)).Itisreadilyshownthat( )/2givesDq036tobesubstitutedinequation(4.2),whichisashiftdueonlytothedifferenceinthe(036)latticespacingbetweenthediffusedlayerandthesubstrate.

Thelatticeconstantawasobservedinthediffusedlayersofallthesamplesinvestigatedinthisstudy.Figure4.10showsthreepairsof(036)rockingcurves andDq>036ofthesamples.Theratioofsatellitetosubstratepeakintensityincreaseswithdiffusiontimet,althoughtheabsoluteintensitybecomessmall,duetotheeffectofasymmetricreflection.Thesubstratepeakscouldhardlybedetectedsincetheywereabsorbedbythethickdiffusedlayers.

Usingequations(4.1)and(4.2),Sugiietal(1978)couldcalculate

strainseyandezAlinearrelationshipisfoundbetweenln(ey)and1/T.ThestrainseyandezforLiNbO3:TisamplesaregiveninTable4.3.Thestrainezisaboutoneorderofmagnitudesmallerthanthestraineyineachsample.Thestrainseyareplottedagainstt.Theslopeln(ey)versusIn(t)plotiscalculatedtobe-1/2.Thesetworelationshipsfoundbetweeneyand1/T,andbetweeneyandtaresimilartothosebetweenCsandI/T,andbetweenCsandt,respectively.Therefore,itcanbeconcludedthatthestraineyinthediffusedlayerisproportionaltothesurfaceconcentrationCs.

4.2.4Tidistributionindiffusedlayers

Figure4.11showstheTidistributionsofLiNbO3samples.Here,apositiononthechartwasregardedasthesurfaceatwhichanEPMAresponsedecayedtoavaluehalfwaybetweenthemaximumandbackgroundlevels.Allthediffusedlayershavebell-shapedTidistributionscharacteristicoftheGaussiandistri-

Fig.4.11TidiffusionasdeterminedbyEPMAof

slicesforthesamplesofLiNbO3:Ti(Sugiietal1978).

Table4.4TitaniumatomicfractionsatcrystalsurfaceNs,(Ti),anddiffusioncoefficientsD,diffusiontimet=10h,inLiNbO3:Ti(Sugii,Fukuma,Iwasaki,1978)

T(°C) Ns(Ti)×1021cm-3 D,10-12cm2s-1

1000 1.23 0.506

1050 0.82 1.06

1100 0.57 2.13

bution.TheGaussiandistributionC(y)isexpressedasfollows

whereyisthedepthbelowthesurface,pisthenumberofatomsperunitvolumeinthedepositedfilmofthicknesst,andDisthediffusioncoefficientgivenby

ValuesofEPMAresponseatthesurface,Rs,correspondingtoCs,and

ofthediffusioncoefficientDcouldbedeterminedinsuchawaythatthetheoreticaldistributioncalculatedbyEqs.(4.3)-(4.5)wasfittedtothemeasuredone.Then,theTiatomicfractionatthesurfaceNs(Ti)wasestimatedfromaratioofRstoR0ontheassumptionthattheEPMAresponsewasproportionaltoC(y).ThecalculatedvaluesofNs(Ti)andDaregiveninTable4.4.ItistobenotedthatTihasaremarkablyhighsolubilityinLiNbO3inthetemperaturerangefrom1000to1100°C.ThediffusiondatawerecalculatedasD0=2.19×10-4cm2sec-1andQt=2.18eV.

Fig.4.12Lidepthprofiles(a),Hdepthprofiles(b)andionchanellingresults(c)forX-cutblink,afterprotonexchangeinbenzoicacidat180°C

for1handafterthermalannealinginairat350°Cfor10h(Hsuetal.1992).

4.2.5theStructureofproton-ExchangedLiNbO3

SeveralstudieshavebeenreportedonthestructuralcharacterizationofLiNbO3.Rice(1986)reportedanapproximatephasediagramforthestoichiometricLiNbO3-HNbO3system.Dependinguponcomposition,samplesundergoone,two,orthreephasetransitionswithtemperature.Canalietal(1986)reportedresultsofstructuralanalysisofproton-exchangedlithiumniobateopticalwaveguidesfabricatedinx,y,andz-cutsubstratesimmersedinpurebenzoicacid.Theymeasuredatomiccompositionprofilesandnotedamarkedlatticedistortion.HandLiconcentrationmeasurementsindicatedanexchangeofabout70%oftheLiatoms.Thehydrogendepthprofilemeasurementsshowedasteplikeshapeinagreementwiththerefractiveindexprofilemeasuredoptically.Theyconcludedthatexchangeincludesalargecrystaldistortionstronglycorrelatedtothepresenceofprotons.Leeetal(1986)studiedstructuralphasechangesinproton-exchangedLiNbO3usingtransmissionelectronmicroscopy.Regionsofdiffuseintensitywithinthesinglecrystalelectron

diffractionpatternsofLiNbO3wereobserved.Minakataetal(1986)measuredthelatticeconstantsandelectro-opticconstantsofz-cutproton-exchangedLiNbO3crystalsbymeansofthex-rayrockingcurvemethodandthephasemodulationtechnique.Theyfoundthattthestrainalongthecaxis,Dc/c,wasextremelylarge(+0.45%)whilstthestrainperpendiculartothecaxis,Da/a,wasnegligiblysmallinproton-exchangedLiNbO3singlecrystals.Theelectro-opticcoefficientvalueinthelayerreducedtoone-tenthofthebulkcrystalvalue.Vohraetal(1989)measuredtheconcentrationprofilesofprotonandlithiumprotonexchangedLiNbO3crystalsusingsecondaryionmassspectroscopyandfoundprotonconcentrationprofilesnearlyrectangularinshape.Lonietal(1991)reported,usingsecondaryionmassspectrometry(SIMS)andanopticalmethod,adirectcomparisonof

hydrogendepthdistributionsandrefractiveindexprofilesinannealedproton-exchangedz-cutLiNbO3waveguides.Novaketal(1992)havereportedSIMSdepthprofilemeasurementsofH,Li,Nd,andErinLiNbO3andLiTaO3.Theabovediscussionindicatesthatextensivestudieshavebeencarriedoutonthecharacterizationoftheproton-exchangeprocess.Someresultshavealsobeenreportedonthedegradationoftheelectro-opticcoefficient.Toourknowledge,noresultshavebeenreportedcorrelatingthedegradationofthenonlinearcoefficienttoitsstructuralaspects.Hsuetal(1992)reportedtheresultsofx-rayrockingcurvesstudiesaswellasdepthprofilesofHandLiandionchannelingmeasurementsusingforwardrecoilspectrometry(FRES),theioninducednuclearreactionLi(p,a)He4andRutherfordbackscattering(RBS)techniques,respectively,thatprovidesomestructuralcharacterizationofproton-exchangedandannealedLiNbO3samples.Thesemeasurementsarecorrelatedwithopticalmeasurementsoftherefractiveindexandsecondharmonicgeneration.

Figure4.12ashowstheLiprofilesfrombulkLiNbO3crystal,aproton-exchangedcrystalandanannealedsample.TheseresultsindicateasignificantlossofLifromthesurfaceuponproton-exchangeandrecoveryofitafterthermalannealing(althougharegionofabout0.1µminthicknessstillremainsLideficient).Figure4.12bshowsthehydrogenprofilesofthesamesetofsamples.ThehydrogenpeakatthesurfaceoftheuntreatedLiNbO3crystalcouldbeduetothemoisturepresentatthesurface.Thesimulationresultsindicateasteplikeprofileofhydrogenafterproton-exchangeinagreementwithLonietal(1991).Afterannealing,thehydrogenconcentrationfalls,exceptforasmallpeakinthenear-surfaceregionofthesample.TheRBSchannelingresultspresentedinFig.4.12cshowthattheproton-exchangeinducesdisorderintheNbsublatticeextendingfromthesurfaceofthesampletoadepthofapproximately0.7µm.This

disorderedregioncoincideswiththeLidepletedandhydrogen-occupiedregionsshowninFig.4.12aandb,respectively.Inthermalannealing,mostofthelatticedisorderisrecoveredexceptforanarrowregion,approximately0.1µmthickclosetothesurfaceofthesample.Figures4.12aandbshowthatthisregionisalsoLi-deficientandpresumablyH-rich,respectively.Inthesecond-harmonicreflectancetechnique,thesecond-harmonicsignalisobtainedonlyfromthefrontsurfacesincetheskindepthforthewavelengthemployedisoftheorderof0.1µm.Thisimpliesthatthereflectancetechniquedoesnotprovideafullcharacterizationofthedegradationinwaveguidesthataretypically1µmdeep.Also,sincethereisamarkedrecoveryindeeperregionsofsample,efficientsecond-harmonicgenerationispossibleinLiNbO3,althoughconversionefficienciessmallerthantheoreticalvaluescanbeexpected.

TheRBSchannelingresultsofanx-cutLiNbO3samplethatwasproton-exchangedinbenzoicacidfor30minat180°Candsubsequentlyannealedinairfor2hat350°C,revealeddisorderinthecrystallatticeafterproton-exchangetoadepthofabout0.35µm.However,inthiscase(shortp-exchangetime)thereisalmostcompleterecoveryafterthermalannealing.Indeed,anSHGsignalwasobservedafterthermalannealing,butnotafterprotonexhcange.Also,theprismcouplingmethodindicatedawaveguideinthesampleafterthermalannealing,butnowaveguidewasobservedafterprotonexchange.The

RBSchannelingresultsofanx-cutLiNbO3samplethatwasproton-exchangedfor30rainat230°Cinpyrophosphoricacidandsubsequentlyannealedinairfor1hat350°C,indicateddisorderinthecrystallatticeafterprotonexchangeextendingtoadepthof1.8µm,whichpartiallyrecoversuponthermalannealing.Therefore,protonexchangewithpyrophosphoricacidproducessimilarlatticedisorderasprotonexchangewithbenzoicacid.

ThelargestrefractiveindexofLiNbO3isaresultoftheextremepolarizabilityoftheNb-Obonds.TheprotonexchangeprocessinducesadistortionofthecrystallatticeandhenceadistortionoftheNb-Obonds.Thischangeoftheniobatestructureappearstocausetheindexincrease.Thiseffectappearstobealsothesourceofthedecreaseinthenonlinearopticalcoefficient,apropertythatisalsorelatedtothepolarizabilityoftheNb-Obond.Therefore,itappearsthatitisnotthepresenceoftheprotons,butrathertheireffectontheNb-Olattice,thataffectstheopticalproperties.Afullrecoveryoftheopticalpropertiesoccursnotbyremovingtheprotons,butbyrestoringthecrystallattice.

4.2.6Orientationrelations

X-raydiffractionstudiesalsodeterminedthedirectionofthecrystallographicaxesofsubstrateandfilmsurfaces.Theresultsweremostpreciseonsamplesthediffractionfromwhosesurfacegavetwoclearlyseparatedmaxima.Inthiscase,theabsolutelossoffilmandsubstrateorientationwasmeasuredbytheirorientationlossrelativetothestandard.ItwasestablishedthatcrystallographicdirectionsofthefilmofpurelithiumniobateandsolidsolutionsLiNb1-yTayO3coincidewithidenticaldirectionsofLiTaO3substratesupto20'for(0001)and( )sampleorientationsirrespectiveoforiginalorientationlossinthesubstratesurface.

Ninomuraetal(1978)describedtheprocessofobtainingLiNbO3

filmsonaMgOsubstrate.Sputteringontothe(111)planeofthesubstrateresultedincrystallizationofa(0001)-orientedLiNbO3layer.Suchorientationrelationisexplainedbythefactthatthepositionofoxygenionsintheindicatedplanesisidenticalandtheircoordinatesintheplanedonotdifferbymorethan0.2%oftheoxygensublatticeperiod.

AsdistinctfromMgO,thestructureofLiTaO3isidenticaltothatofLiNbO3,andtheirparametersdifferby4%incand1%ina.

Becauseofsimilarityoflattices,filmorientationispreserved,asexpected,andthesubstrate-to-filmtransitionisduetoformationofthetransitionlayerofLiNb1-zTa2O3ofvariablecomposition,inthecourseofwhichthelatticeconstantchangesfromfilmtosubstrateparameter.Intheabsenceofadditionalsubstratedissolving,thewidthofthetransitionregionappearstobesmall(1µm)andisdeterminedbytheinterdiffusiondepthofsubstrateandfilmatomsafterprecipitation.

Ingrowinghomoepitaxialfilmswithironimpuritynodeviationoflayerorientationfromthatofsubstratewasobserved.

Alithiumniobatefilmgrownona( )sapphiresubstrateexhibitednoX-raydiffractionatananglecorrespondingtothesinglecrystal.ThemostintensescatteringcorrespondedtothezplaneofLiNbO3.Itismostlikelythat

Fig.4.13Mechanismsofepitaxialgrowthoflithiumniobate.

a)model,b)photographsofsurfacemorphologyofLiNbO3

aLiNbO3filmprecipitatesontoan{ }A12O3plateintheformofapolycrystallinelayeroralayerconsistingofregionswithdifferentorientationswithpredominanceofthezdirection.Suchaconclusionisalsoconfirmedbythefactthatnopointelectrondiffractionpatterncorrespondingtoasinglecrystalcouldbeobtained.

4.3Morphologyandperfectionoflayers

Attenuationofalightwaveinawaveguideistheprincipalparameterresponsibleforefficiencyoftheepitaxialstructureinintegratedoptics.Inazigzagpropagationoflight,attenuationisdeterminedbytwofactors-bylightscatteringuponrepeatedreflectionfromsubstrate-filmandair-filminterfacesandbyabsorptioninthebulk.Thescatteringlosstypicallyincreaseswithincreasingorderofthewaveguidemode,whereasthebulklossremainsalmostunchanged.Inthisconnection,perfectionofthefilmsurfaceandofthesubstrate-filminterfaceisofimportance.Thebulklossisduetoabsorptionandscatteringoflightonstructuralinhomogeneitiesofthefilms,whicharedeterminedbythefilmformationmechanisms.

Accordingtomodernconceptsofthenucleationtheory,themost

importantfactorwhichdeterminesbasicallythemechanismofsinglecrystalnucleationandthekineticsoftheirsubsequentgrowthisthestructureoftherealsurfaceofthesubstrate(Veinsteinetal1979).Oneshouldbearinmindthatthedifferenceinthelatticeperiodsofcontactingmaterialsaffectsthemagnitudeofthesurfaceenergyoftheinterfaceand,accordingly,thecharacterofelementarygrowthprocessesattheearlystageofheteroepitaxyestablishingeithertwo-orthree-dimensionalnucleationmechanism.Thecharacterofelementarygrowthprocessesessentiallydeterminesthestructureperfectionandthemorphologyofthinepitaxiallayersnearheteroboundary.

Figure4.13presentsmodelsofthelayergrowthmechanismfordifferentsupersaturationsintheliquidphaseandthecorrespondingsurfacemicromorphologies

ofheteroepitaxialstructuresLiNbO3/LiTaO3(Khachaturyan1987;Khachaturyanetal1987).

Ananalysisofrecentpublicationsonthemechanismoforientedgrowthofvarioussubstancesshowsthattheircommontendencyisrevisionofconventionalandgenerallyacceptedviewpoints.Theseworksrejectthedimensionalgeometricapproachandmakeuseofphaseequilibriumasoneofthecriteriaofthepossibilityofepitaxy(Chernovetal1980;BolkhovityanovandYudayev1986).

4.3.1Micromorphologyoffilmsurfacefordifferentcrystallographicorientationsofthesubstrate

MorphologicalstudiesoflithiumniobateandsolidsolutionsLiNb1-yTayO3haveshownthatsurfacemorphologydependsonthefollowingfactors:materialandpreparationofsubstratesurface,orientation,compositionofprecipitatedlayer,growthrateandtemperatureregimeofepitaxy.

Platesofpreferentiallyzandycutsofsingle-domainsinglecrystalsaretypicallyexploitedtomanufactureintegro-opticelements.Thestateoftheirsurfacelayer,whichisofprincipalimportancefortechnologyoflightguideformation,dependsessentiallyonfinishpolishing.

Thedamagedsurfacelayerisadevelopedsystemofstructuraldefectsandviolationofchemicalcomposition.Directstructuralstudiesofreflectionusingelectrondiffractometryshowthataftermechanicalpolishingthesurfacelayeroflithiumniobateplatesiscompletelydisorderedandamorphous(Sugiietal1980;Rakovaetal1986).Itsstructuralperfectioncanbeimprovedbysubstrateannealinginoxygenatmosphere.Optimumannealingconditionsare1000°Cand1h.Aftersuchheattreatment,electrondiffractionpatternsofsamplesshowKikuchilines,whichisindicativeofhighperfectionofcrystal

surfacestructure.

Figure4.14presentsthephotographsofsurfacemorphologyofLiNbO3filmsonLiTaO3substratesofz,yandxorientations.Perfectlysmooth,mirrorsurfacesaretypicalwhoseroughnessheightonthezplaneisnotlargerthan0.1µm(Fig.4.14(Ia,IIa)).Introductionofironimpurityintosolutionleadstotheformationofroundfiguresofgrowthonthefilmsurface.HeterolayersonLiTaO3substratehavemorphologyanalogoustohomolayersbutthefiguresofgrowthhavepronouncedcontours,theroughnessheightreaches0.5µm(Fig.4.14(IIb,c)).

Thepicturesshowthatthesurfacemorphologyoffilmsisdeterminedfirstofallbythesubstrateorientation.OnthexplaneofepitaxialLiTaO3,thefiguresofgrowthhavetheshapeofatriangleandsometimesofatruncatedpyramid1µmhigh.Longnarrowhillocksdirectedalongthex-axisareobservedony-orientedhomo-andheterolayers(Fig.4.14(lb,IIb,IIIb)).Themorphologyofepitaxiallayersissubstantiallyaffectedbyinterfaceinstability.Athighgrowthrates,thesurfaceonwhichcrystallizationtakesplacebecomesunstableanditsroughnessincreases.Atlowcoolingrates,theeffectofgradientsalongsubstratesincreases,whichleadstotheformationoflayerswithsignificantlydifferentthickness.InvestigationoftheeffectofgrowthrateuponsurfacemorphologyofLiNbO3filmshasshownthatthesmoothestlayerscorrespondtothegrowthrateofnotmorethan0.6µm/min.Anincreaseinthegrowthratehasaspecialeffectuponthemorphologyofz-orientedlayers,atratesnear

Fig.4.14TypicalmorphologyofLiNbO3filmsurfacesofa)(0001);b)( )'c)( )substrateorientations.I)y=0.3,v~0.2µm/min;LiNbO3substrate;II)y=0.8,v~0.6µm/min;LiTaO3substrateIII)y=0.3,v~0.1µm/min;

LiTaO3substrate(Khachaturyanetal1984).

1µm/minthereappearsmosaicstructureofthesurface,andabovethisvaluethefilmiscompletelycoveredwithhillocks.Anincreaseofprecipitationrateonyandxplanesentailsanincreaseinthedensityofthefiguresofgrowthwhichsomewhatincreaseinsizeandhaveatriangularshape(Fig.4.14(IIIb,c)).

Thus,thesurfacemorphologyofLiNbO3filmsisbasicallydeterminedbysubstrateorientationandgrowthconditions.Theappearanceofthree-dimensionalpatternsisduetocrystallographicspecificitiesoflithiumniobatestructure:theyaredeterminedbytheshapeofcross-sectionofelementaryrhombohedronwith(0001),( )and( )planes.

ConnectionbetweenthelatticeparametermismatchandthesurfacemorphologyalsomanifestsitselfinepitaxyofsolidsolutionsLiNb1-yTayO3onaLiTaO3substrate.Figure4.14showsadecreaseinsurfaceroughnesswithincreasingTacontentinthefilmanda

decreaseinthedensityandsizeofthegrowthpatterns.Thesurfaceroughnessdoesnotexceed0.2µm.Theresultobtainedtestifiesclearlytothefactthatsurfacemorphologyisdeterminedbythestructuredefectsoccurringattheinterfaceduetomismatchoflatticeconstants.Thefilmsurfaceroughnessisconsiderablyinfluencedbythemannerinwhichthesubstratesurfaceisprepared.Mechanicalpolishingleadstotheappearanceofadamagednear-surfacelayer.High-temperatureannealingorchemicaletchinginducetheappearanceonthesamplesurfaceofsomesignsofpolishinghiddenbythenear-surfacelayer.Scratchesonthesubstrateoccuronthesurfaceofthinlayersintheformofshallowgroovesupto3µmwide.Toobtainaperfectsurface,thesubstratewaspreliminarilytreatedinKOHatatemperatureof280-340°Cfor2-3min.

Examinationofsurfacemorphologyhasshownthattoobtainsmoothlayersitisofimportancetocompletelyremovetheresiduesofsolution-meltfromthefilmsurfacewhenthegrowthprocessisover.Arapidcoolingtoroom

temperaturetypicallycausesanuncontrolledadditionalcrystallizationfromtheremainingdropsofliquid.

4.3.2Diffusion-induceddefectsinfilms

Thediffusedlayerandsubstratecanbediffractedseparatelybyutilizingthediffractionanglecorrespondingtoeachlatticeconstant.Thusseparatetopographiescanberecordedforthediffusedlayerandsubstrate.Thistechniqueisveryusefulfortheinvestigationofdefectsgeneratedbydiffusion.Sugiietal(1978)tooktopographiesoftheTi-diffusedlayerusingtheLangcameraappliedtothereflectioncasewithCuKa1radiation.

Figure4.15ashowstopographyofthediffusedlayersofthesamplesofgroupI.Theexcessdiffractionconstantobservedinallthesamplesisduetoahighdensityofdefects.Itisfoundthatthehigherthediffusiontemperature,thelessseriousthedegradationincrystallinityinthediffusedlayer.Thiscorrespondstotheresult,obtainedbytherockingcurvemeasurement,thatthemismatchdecreasedwithincreasingdiffusiontemperaturefrom1000to1100°C.

Figure4.15bshowstopographyofthediffusedlayersofsomesamplesofgroupII.Threetypesofdefectsareclearlyobserved:mismatchdislocations,cracksoftypeIrunninginthedirectionperpendiculartothexaxis,andcracksoftypeIIrunninginthedirectionperpendiculartothez-axis.AllofthedefectswereinducedbytheTidiffusion.Mismatchdislocationsshouldbegeneratedsoastorelievestressesinthediffusedlayer.ThedirectionsofthecrackssuggestthatthetypeIcracksmustbegeneratedbyastressalongthea-axisandthetypeIIcracksbyastressalongthec-axis.DensitiesofthemismatchdislocationsandofthetypeIcracksincreasewithdiffusiontimet,however,thedensityoftypeIIcracksisalmostindependentoft.

WhentheTi-diffusedlayerisutilizedasanopticalwaveguide,thedefects

Fig.4.15Diffusion-induceddefectsinTi-diffusedlayersofsamples

ofLiNbO3:TigroupI(g=030)(a)1000°C,10h,(b)1000°C,2.5h,groupI[(Sugiietal1978).

mayincreasethescatteringlossofopticalguidedwavesasobservedintheNb-diffusedLiTaO3waveguides(RamaswamyandStandley1975).

Applyingthecombineddiffusion-filmmethod,onecanobtainchannelsofan'immersed'orsymmetricwaveguide.Figure4.16ashowsaLiTaO3substrateof(1120)orientationwithan'Y'-shapedcouplerpreliminarilydeposedbytitaniumthermodiffusion.Thechannelwidthwasequalto6µmandthegapbetweenthechannelsfordepositingcontrolelectrodesto10µm.Onthissurface,anepitaxialLiNb0.1Ta0.9O3layerwasgrown.Figure4.16bshowsthesurfacemorphologyofepitaxialstructureLiNb0.1Ta0.9O3/Ti:LiTaO3.Thechannelsandthe'Y'-shapedcouplerareclearlyseen.

Varyingthelayercomposition,thesubstratematerial,thethicknessoftitaniumsputteredontosubstrateandthetimeoftheprocessweformdifferentprofilesoftherefractiveindexwithamaximumvalueonthesubstrate-filminterface.Thelighttransmittedthroughthewaveguidehasminimumscatteringlossontheinterface.Therefractiveindexvariationonthewaveguideboundary,whichdeterminesscatteringundercompleteinternalreflection,isbyanorderofmagnitudesmallerthanthatonthefilm-airinterface.

4.4Substrate-filminterfaceandtransitionregion

Thestateandpropertiesoftheinterfacebetweenthewaveguidinglayerandsubstratehaveaneffectuponthepropertiesofthefilmasawholeanduponitsstructure.Theinfluenceofthesubstrateupontheinterfacestructuredependsonthelayergrowthconditionsanddeterminethedensityanddistributionofdefects(inclusions,dislocations,impurityatomsandvacancies)andelasticstressinthetransitionlayer.

Fig.4.16ThesurfaceofaLiNbO3substratewithaTi-diffused'Y'

coupler(a)andthesurfaceofanepitaxialfilmgrownonthissubstrate(b).

Epitaxiallayersarecharacterizedbyaclearlypronouncedsubstrate-filminterface.Thethicknessofthetransitionregionisdeterminedbythegrowthconditionsandmaterials,aswellasbytheinitialepitaxytemperatureatwhichthesubstrateismoistenedbythesolution-melt.Thesubstratesurfacedissolutionincreaseswithincreasinginitialtemperatureforthesamesolutioncomposition.Thisleadstothefactthatunderepitaxy,beforethebeginningofprecipitationattheLiTaO3crystallizationfront,thiscausestheformationofathinliquid-phaselayerenrichedwithTaascomparedtotherestoftheliquidphase,andunderasubsequentcoolingalayerofvariablecompositionisprecipitated.Uponprecipitationofapurelithiumniobatefilm,onthesubstrate-filminterfacethereformsasolidsolutionLiNb1-yTayO3.ThisobviouslyoccursduetosubstratedissolutionsinceintheindicatedpapertheconcentrationofNb2O5inthesolution-meltisby5%smallerthaninstoichiometriccompositions.

Transitionregionswereexaminedonchipsandpolishedcutsofthegrownstructures.Underidealhomoepitaxythefilm-substrateinterfaceisnotpronounced.Figure4.17presentsphotographsofchipsofLiNbO3andLi(Nb,Ta)O3filmsonLiNbO3andLiTaO3showingaclearandstraightinterfaceandaflattransition.IdentityofcrystallinestructuresoffilmandsubstrateandequalNb5+andTa5+radiileadtointerdiffusionofniobiumandtantalumatomsthroughtheinterfaceandtotheformationofthetransitionregionLiNb1-7TazO3wherezvariesfrom0toy.

Theformationofthe'transition'regionisanundesirableprocesswhichmakesepitaxiallayerscloserinthepropertiesandstructuretothediffusionlayers.

Filmswithaconcentrationprofileclosetorectangularcanbeobtainedin

Fig.4.17Boundariesbetweenepitaxialstructures:a)LiNbO3/LiNbO3;

b)Li(Nb,Ta)O3/LiTaO3;c)LiNbO3/LiTaO3(Khachaturyanetal1984).

differentways.Precipitationontoz-LiTaO3throughabufferlayersubstantiallydecreasesinterdiffusion,andthethicknessofthetransitionregionappearstobelowerthanthemicroproberesolution(~0.2µm).Theconcentrationprofiledependsonthegrowthconditions.Theinterdiffusiondepthisdeterminedbytheheattimeanddecreaseswithdecreasingholdtimeafterprecipitation.Forstructuresobtainedatagrowthrateoflessthan0.2µm/minandannealingfor3hthetransitionregionistypicallywide(upto3-5µm)andtheinterfaceisonlypronouncedunderselectiveetchingasshowninFig.4.17a.Precipitationataratev~(0.2-0.3)µm/minandholdingfor1.5hleadstotheformationofstructureswithatransitionregionnotwiderthan0.5µm,whichisobservedatchipswithoutadditionaletchingoftheinterface(Fig.4.17c).

4.5Dislocationstructure

Tocreateeffectivewaveguideswithinsignificantattenuation,filmswithlowdefectdensity,sharpsubstrate-filminterface,mirror-smoothsurfaceoftheepitaxiallayerandhomogeneityoffilmpropertiesthroughoutthethicknessarenecessary.Investigationofstructuralinhomogeneitiesandsurfacemorphologyplaysanimportantroleforgrowingfilmswithprescribedparametersandlowdefectdensity(MadoyanandKhachaturyan1987).

Morphologicalstudieswerecarriedoutusingscanningelectronandlightpolarizingmicroscopes.Structuralinhomogeneitieswererevealedbyselectiveetchinginaboiling1:2mixtureofconcentratedacidsHFandHNO3andinKOH.Etchingtimewasvariedfrom1to40mindependingonthepolarizationvectordirection.

Themosttypicalinhomogeneitiesofepitaxiallayersaredislocations.Analysisofexperimentalpapersonexaminationofthedislocationstructureofferroelectricsshowsthatthemostlikelymechanismofthe

occurrenceofdislocationsisthefollowing:

-penetrationofdislocationsfromthesubstratetothefilminwhichtheydegenerate;

-nucleationofdislocationsunderstresscausedbynonuniformimpuritycaptureunderlaminargrowth;

-occurrenceofdefectsduetothenonuniformimpuritydistributioninagrowinglayer.

Onthesubstrate-filmboundary,defectsmayoccurduetomismatchinlatticeconstantsbetweenthefilmandsubstrate.Tominimizethemismatchbetweenthetwolattices,elasticdeformationoffilmsisenergeticallyadvantageous.Ifthemismatchisnotcompensatedcompletelybytheelasticstress,mismatchdislocationsalsooccur(MilvidskyandOsvensky1977).Arelativecontributionofelasticstressesandmismatchdislocationstotheaccommodationofcrystallatticesdependsonthedifferenceinlatticeconstants,filmthickness,geometryofdislocations,characterofbondsontheinterfaceandelasticconstantsoftwointergrowingmaterials.Mismatchdislocationsslidefromthefreesurfaceintotheinterfaceregion.

PlaceswheredislocationsappearonthefilmsurfaceasconicaletchpitswithaclearlypronouncedvortexshowninFig.4.18e,f.Butamixtureofhydrofluoricandnitricacidsdoesnotpermitanexactlocationofdislocationetchpitson

Fig.4.18Dislocationstructureanddomainconfigurationsinepitaxialfilms,successiveetchingoffilmsurfacewithataperedoutpositive

domain(a,b);domainconfigurationsinsubstrate(c)andinafilmgrownonthissubstrate(d);microdomainson(0001)(e)and( )

(f)surfacesofLiNbO3structureinhomogeneitiesonthesurface( )ofaLiNbO3film(g)andetching-revealeddislocationsandmicrodomainsina(0001)film(h)(Khachaturyanetal1984).

thepositivez-planeand,asanalysisshows,doesnotatallpossesspropertiesofselectiveetchingforthex-plane.ThedislocationstructurewasunambiguouslydeterminedbyetchingintheKOHmeltatatemperatureof400°C.Figure4.18eandfshowszandysurfacesofLiNbO3afteretchinginKOHfor2min.

Sincesubstratedislocationsemergingonthesurfaceunderpseudomorphousfilmgrowthcontinueinthegrownlayer,thestructuralperfectionofthelayerdependsondislocationdensityinthe

substrate.Adirectcountofetchingpitshasshownthatthedensityofdislocationsemergingonthesubstratesurfaceisdeterminedbythepositionofthissurfacerelativetothegrowthaxisoftheoriginalcrystal.Thenumberofdislocationsonthey-planeofLiTaO3andz-planeofLiNbO3(thatis,ontheplaneperpendiculartothecrystalgrowthaxis)makesupN~104cm-2,fortheotherplanesitisbyanorderofmagnitudesmaller.

SelectiveetchingoflithiumniobatefilmsinKOHhasshownthatgrowthhillocksonthefilmsurfaceareofdislocationnature.Intheplaceofhillocks

removedbypolishingtheretypicallyappeardislocationetchingpits(Fig.4.18c).Twomechanismsofthisphenomenonarepossible.

Inmatingtwosingle-typelatticeswithinterplanardistancesa1anda2thereoccurmismatchdislocationswiththelineardensity

Forapseudomorphouslygrownlayerthereexistsacriticalthickness

Onreachingthisthickness,thelayerstopsbeingpseudomorphous,andnetsofmismatchdislocationsappearontheboundary.

Dislocationsofthesubstrate,thatemergeonitssurfaceuponpseudoamorphousfilmgrowth,stretchtothegrownlayeruptothecriticalthickness.Afterthat,dislocationswiththeBurgersvectorparalleltothesubstratebend,becomemismatchdislocationsandthengotothegrownlayer.Inthiscasethereappearonlyseparateregions,insteadofawholenet,ofmismatchdislocations.Asubstitutionofthevaluesofinterplanardistancesoflithiumniobate,dx=1.284Å,dy=1.486Å,dz=1.152Å,andlithiumtantalate,dx=1.286Å,dy=1.487Ådz1.147ÅobtainedbytheX-raydiffractionmethodyieldsthevaluesoflineardislocationdensitiesNy=6.79×104cm-1,Nx=8.48×104cm-1,Nz=34.84×104cm-1andcorrespondinglythevaluesofpseudomorphouslayerthicknesshy.cr=0.074µm,hx.cr=0.059µm,hz.cr=0.014µm.

Thus,duringcrystallizationonthez-planeofLiTaO3themismatchdislocationdensityisminimum,andthesurfacemorphologymustbenearlyisotropic.Fory-andx-orientedlayersthenumberof

dislocationscausedbymismatchbetweentheinterplanardistancealongthezaxisandalignedperpendiculartoitishigherbyanorderofmagnitude.Therefore,thesegmentsofmismatchdislocationsoccurringonthegrowthdislocationsthatstretchtothefilmareexpectedtobeperpendiculartothez-axis.

Suchamodelagreeswithsomeoftheexperimentalresults.Inparticular,thesurfacemorphologyonthezplaneisclosetoisotropic,andthedirectionofgrowthhillocksony-andx-orientedfilmsareperpendiculartothez-axis.Introductionoftantalumpentoxidetoalithiumniobatefilm(i.e.matingthelatticeconstantsofthefilmandsubstrate)decreasesthenumberandsizeofthegrowthhillocks.Butthereexistessentialcontradictions.Becauseofsmallthicknessofthepseudomorphouslayers,themismatchdislocationsegmentsmustoccurattheinitialinstantofepitaxy(0.1µm)andmustnothaveanyeffectuponthemorphologyfurtheron.Thefiguresofgrowthincreasewithincreasingfilmthickness,whereastheeffectoflatticemismatchdecreases.

UnderhomoepitaxyontoaLiNbO3substratethelatticemismatchisabsent,butelongatedhillocksoccuronthefilmsurface.Growthpatternsondislocationsareobviouslyduetoalieninclusions.

Analysisofcrystallizationfromsolutionhasshownthatsheaf-shapedgrowthdislocationsoccuroninclusionsconcentratedforthemostpartalongplaneswhicharetracesofterminationoraccelerationofagrowingfacet.

Inepitaxialgrowth,suchaplaneisthesubstratesurface.Thedifferenceinionradiiofvanadiumandniobiumcausessegregationofsolventintheformofinhomogeneousmicroinclusions.Thedirectionofdislocationsinasheafisconnectedwithfreeenergyanisotropyofunitdislocationlengthwhichisdeterminedbytheelasticmoduliofthecrystal.Forlithiumniobateandtantalate,anisotropyony-andx-orientedplanesissingle-typerelativetothez-axis.Divergenceofthesheavesmustleadtoincreaseinthegrowthpatternsize.Captureofthesolventmayoccurbothunderhomo-andheteroepitaxy.Theshape,sizeandconcentrationofinclusionsaredeterminedbysurfaceprocesses.Introductionoftantalumoxideintheliquidphase,whichstimulatesanincreaseinthegrowthtemperatureandadecreaseinthegrowthratemustresultinadecreaseinthesolventcaptureprobability.Thepresenceofsheavesofdislocationsduetoinclusionsinalithiumniobatefilmisinagreementwiththesurfacemorphology.Thestructureoftheinterfaceisworsenedbyinclusionsleadingtoascatteringofthewaveguidemode.

Thedislocationdensityinthefilmisthusofthesameorderasinthesubstrateorevenhigher.Inadditiontodislocationsgrowthfromthesubstrate,newdislocationsoccurinthefilmduetolatticemismatchandsolventinclusions.Onthelayersurface,dislocationsappearascharacteristicgrowthpatternswhoseshapeisdeterminedbyorientationofthesubstrateandthesizebythethicknessandgrowth

rate.Mismatchdislocationsoccurinpseudomorphouslayersnotthickerthan0.1µm.Theirdensityisminimumonthe(0001)plane.Onthe( )and( )planestheyappearashillocksstretchingperpendiculartothe(0001)axis(Fig.4.18g).Introductionoftantalumpentoxidetothemeltfromwhichalithiumniobatefilmisgrown(i.e.matingthelatticeconstantsofthefilmandsubstrate)decreasesmismatchdislocationdensityandthesizeofthegrowthhillocksintheplacesofdislocationoccurrence.

Duringcrystallizationfromsolution,growthdislocationsintheformofdivergentsheavesoccuroninclusions(Golubevetal1982).Inclusionsarelargelyconcentratedalongtheplaneswhicharetracesofterminationoraccelerationofagrowingfacet(inparticular,thesubstratesurface).Thedifferenceinionradiiofvanadiumandniobium(0.4Åand0.66Å)restrictssolventcapture,andforhighconcentrationsleadstosegregationintheformofinhomogeneousmicroinclusions.Forlowvanadiumconcentrations,strongdeformationsandlocalstressesappearinthelatticethatinitiatetheformationofdislocationsandmicrodomains.Figure4.18h)illustratesetchingofa(0001)filmofLiNbO3withadislocationstretchingthroughtheentirelength.Thefigureshowsthatdislocationsoccuralongwithmicrodomainsalignedperpendiculartothesurface.Dislocationsalignedalongthe( )axisaregeneratedatdifferentdepthsofthefilmandaremostlyconcentratedneartheinterface.

Figure4.19presentsagraphofthedistributionofdislocationdensityover

Fig.4.19Distributionofdislocationdensityalongthethickness

oftheepitaxialstructureLiNbO3/LiTaO3.

thethicknessoftheepitaxialstructure.Dislocationsarebasicallygeneratedinthetransitionregionwhichisthickerbyanorderofmagnitudethanthecalculatedvalueofthepseudomorphouslayer(0.1µm).Therefore,besidesmismatchdislocations,othertypesofdislocationsmustdevelopinthefilm,whichoriginateontheimpuritycentresthatinducelatticedeformationandmicrostrains.Thelatterlead,inturn,totheformationofmicrodomainscoupledwithdislocations.

Structuralinhomogeneitiesoffilmsaffectessentiallytheiropticalproperties.Inparticular,theycausescatteringofchannelledlightonmicroinclusionsanddomainwalls.Thepresenceofdomainswithdifferentpolarizationlowerstheefficiencyofelectro-opticmodulation.

Wepresenttheresultsofmorphologicalstudiesofthefilmsurfaceandsubstrate-filminterfaceoflithiumniobatestructuresgrownbyLPEandliquid-phaseandelectroepitaxy.Figure4.20presentstypicalpicturesofsurfacemorphologyandtransversechipsofthesefilmsgrownbythetwomethodsmentionedabove.

Inthefigureonecanseeimperfectionsclosedonthesubstrate-filmtransitionregionunderliquid-phaseelectroepitaxyoflithiumniobate

(lb,IIb),thicknessandplanarityofepitaxialfilms,aswellasregionsofgrowthdislocationclustersandandoccurrenceofmicrodomains(III).

Figure4.21presentsthedependenceoftheratioofdislocationdensitiesinlithiumniobateunderliquidphaseelectroepitaxyandliquidphaseepitaxy(1)andfilmthickness(2)onthecurrentdensity.Asisseenfromthefigure,anincreaseinthecurrentdensity(J>15mA/cm2)inducesasharpincreaseinthegrowthdislocationdensityascomparedwithliquidphaseepitaxyoflithiumniobate.ThisisapparentlyconnectedwithagrowinginfluenceofJouleeffectuponcrystallizationabovetheindicatedcurrentdensityrange.

4.6Domainstructure

Themosttypicalinhomogeneitiesinferroelectricsaredomainboundaries,growthdislocationsandmicroinclusionsofalienphases.Inplanarintegro-opticwaveguidesonthebasisoflithiumniobate,theseinhomogeneitiesleadtoanadditionalscatteringofchannelledlightandtoloweringofthedeviceefficiency.

Polydomainlithiumniobateandtantalatecrystalsconsistof180°domainswithpolarizationalongthe(0001)axis.Lithiumtantalateusedassubstrateisaperfectstructuralanalogueoflithiumniobate,butthedomainsizeissmallerbytwoordersofmagnitude(10µm).Thedislocationdensitymakesup~104

Fig.4.20Photographsoftransverselayers(I)andmorphology

ofthesurface(II)oflithiumniobatefilmsgrownbyliquidphaseepitaxy(a)andliquidphaseelectroepitaxy

(b)(Khachaturyanetal1987).

Fig.4.21Dislocationdensityratiosinlithiumniobate

filmsgrowthbyliquidphaseepitaxyandliquidphaseelectroepitaxy(1)andthicknessofelectro-LPEfilm

asfunctionsofcurrentdensity(Khachaturyanetal1989).

cm-2,mostofthedislocationsoccurringduringgrowth.Thinrods(upto300µmlong)ofneedle-shapedmicrodomainswereobservedinlithiumniobatealongthe(0001)axiswithpolarizationreversetothatoftheprincipaldomain(Fig.4.22)(ProkhorovandKuz'minov1990).Thepresenceofvacantoxygenoctahedrainthestructurepromotesentrapmentofimpurityandfirstofallmetalions.

Defectstypicaloflithiumniobateareoxygenvacancieswhichcanbereadilywithdrawnbyhigh-temperatureannealinginoxygenatmosphere.

Lithiumniobatecrystalsarehighlysensitivetoheattreatmentwhichaffects,besidesoxygenvacancies,alsodislocationmigration,impuritydistributionandthecontentofmicrodomains.(Rakovaetal1986;Bocharovaetal1985)pointedouttheappearanceofalienphasesonthesurfaceofLiNbO3underannealingatT=900°C,(OhnishiandYizuka1974)reportedrepolarizationofnear-surfacelayersundermechanicaltreatment.

Fig.4.22Needle-shapeddomainstructureofLiNbO3crystal(ProkhorovandKuz'minov1990).

Fig.4.23(right)Growthrateofalithiumniobatefilmversus

coolingtemperature.Thecoolingrates1)0.3deg/min;2)0.16deg/min, )onanegativedomain;)

onapositivedomain.

4.6.1Epitaxialfilmonadomainboundaryofthesubstrate

Nonsymmetricpositionofionsintheferroelectricphaseisresponsibleforthedifferenceinchemicalactivitiesofsurfaceswith

differentpolarizations,whichisobservedinparticularinselectiveetching.

Underepitaxy,whenthegrowthrateisdeterminedbysurfaceprocesses(kineticregime),thesurfaceactivitymusttelluponthekineticsofcrystallizationprocesses.TheCuriepointoflithiumtantalate(660°C)islowerthantheepitaxytemperature,andprecipitationunderheteroepitaxyproceedsonsubstratesintheparaphase.Thesurfacepropertiesareidenticalthroughout,andspontaneouspolarizationhasnodirecteffectupongrowthkinetics.Underepitaxyon(0001),aLiNbO3crystalisintheferroelectricphase(Tc=1210°C),andprecipitationmaytakeplaceontosingle-andpolydomainsubstrates.

Crystallizationfromsolutionassumesthatprecipitatedatomscomefromthedepthofsolutiontothecrystallizationfront,areadsorbedontothegrowingsurfaceandbuiltinthecrystallattice.Forsmallsupersaturations,thegrowthrateislimitedbydiffusionmasstransferandsurfaceprocessesdonotaffecttheprecipitationrate.Filmthicknessesonpositivelyandnegativelychargedsingle-domainsubstratesareequal.Indiffusionregime,theinfluenceofdomainstructureisobservedwhenprecipitationtakesplaceontoapolydomainsubstrate.Ondomainswithdifferentpolarizationsthefilmthicknessisnotatalluniform,butitbecomesuniformfarfromdomainboundaries.Suchapicturecanbeeasilyexplainedifwetakeintoaccountthefactthatfarfromtheboundariesthegrowthrateisonlylimitedbymasstransferandnearthedomainboundariesadifferenceinsurfaceactivitiesleadstoafasterconcentrationloweringon

thenegativedomainand,accordingly,toredistributionofthefluxofprecipitatingatoms.Thus,themasssupplyonthesidesoftheboundaryisdifferent,thegrowthrateonthenegativez-surfaceishigherbyafactorof1.5thanthatonthepositivesurface(Fig.4.23).

Asthesystemcoolingrateincreases,crystallizationislimitedbybuilding-inofatomsintothelattice(kineticregime).Butthereisnoessentialdifferenceinthegrowthratesonpositivelyandnegativelychargedsurfacesofsingle-domainsubstratessincethebreakingeffectofthelessactivepositivesurfaceleadstoanincreaseofsupersaturationandgrowthrate.So,thegrowthratesonsingle-domainsubstratesaredeterminedbythecoolingrateofthesolution-melt(Fig.4.23)(MadoyanandKhachaturyan1987;Madoyanetal1985).

Underepitaxyonapolydomainsubstrate,ahighactivityofthenegativesurfaceleadstotaperingoutofthepositivedomain.Whenthefilmthicknessexceeds30µm,thegrowingfilmsaretypicallysingle-domainandnegativelypolarized.

Figure4.18bdemonstratessuccessiveetchingoffilmsabout25µmthick.Thedashedlineindicatestheregionsofnegativelypolarizedsurface,onwhichpositivedomainsappearafteretching.

4.6.2Domainconfigurationsinfilms

Analysisofdomainstructureofepitaxialfilmshasshownthattheconfigurationandsizeofdomainsdependonsubstratematerialandorientationandonthethicknessoftheprecipitatedlayer.

Ithasbeenestablishedabovethattheboundaryofadomaingrowsthroughthesubstrate-filminterface.Investigationsshowedthatwhenfilmthicknessdoesnotexceed20µm,thedomainconfigurationsofthesubstratearefullyinheritedbythefilmbothunderhomo-andheteroepitaxy.UnderheteroepitaxyonLiTaO3,thesubstrateisin

paraphaseandthelithiumniobatefilmiscrystallizedintheferroelectricphase.ThefinalformationofdomainconfigurationsproceedswhenthesampleiscooledthroughtheCuriepointofthesubstrate(Tc=660°C).Thepolydomainstructuresoffilmandsubstratewerefoundtobeperfectlyidentical.Experiencingnoactionoftheelectricfieldofthesubstrate,aprecipitatedfilmobviouslyacquiresthedomainconfigurationwhichisenergeticallymoreadvantageous.Takingintoaccounttheconnectionbetweenpolarizationdirectionandgrowthkinetics,wemayassumethatthefilmmustbenegativelypolarizedorpolydomainwithpredominanceofnegativedomains.Whenthesampleiscooledbelow660°C,thepolarizationoccurringinthesubstrateleadstofilmrepolarization.Thisprocessispromotedbyalargenumberofintergrainboundariesresultedfromgrowthofnucleiatthecrystallizationfront.Theseintergrainboundariesareplacesofpointdefectanddislocationpile-upalongwhichnewlyformeddomainboundariescanrun.Moreover,thepolarizationeffectofthesubstrateisstrengthenedduetothepresenceinepitaxialstructuresoftransitionregionswithsmoothlyvarying2µm-thickcompositionLiNb1-xTaxO3.Toobtainsingle-domainLiNbO3/LiTaO3films,itsufficestocarryoutcoolinginanelectricfieldthatprovidessubstratepolarization.

Figure4.18canddpresentsthedomainstructureofhomoepitaxialfilmandsubstrateoflithiumniobate.Thefilmnaturallyrepeatsthedomainstructure

ofthesubstrate.Taperingoutofthepositivedomainisobserved,asmentionedabove,forthicknessesof30µm.Onsingle-domainsubstratesthefilmisalsosingle-domainandthepolarizationdirectionofthefilmisidenticaltothatofthesubstrate.

4.6.3Microdomainsinsubstratesandinepitaxiallayers

Atypicalfeatureofthedomainstructureoflithiumniobateisthepresenceofthinneedle-shapedmicrodomainswithapolarizationreversetothatoftheprincipaldomain(Bocharovaetal1985;OhnishiandYizuka1975).Uponselectiveetchingofanegative(0001)plane,needle-shapedmicrodomainsappearastrianglepyramidswithside-faceorientation( ).Theverticesofthesepyramidsareplaceswheremicrodomainsemergeonthefilmsurface(Fig.4.18d).Onthepositivezplane,insuchplacesthereformsmallirregular-shaped(upto1µm)etchingpitscorrespondingtoneedle-shapedmicrodomains.Thesizeofthepitsremainsunchangedastheetchingtimeincreases.Onthe( )planetheyappearasthin300µmstripsrunningalongthez-axis(Fig.4.18f).

Theinfluenceofalienfactorsuponthedomainstructurewasinvestigated.Mechanicalpressingwithadiamondneedle(P=5,10,15g,thediamondneedlepointcurvature~10µm)onthe(0001)planeofLiNbO3leadstotheappearanceofmicrodomainclusterswiththedensityinthecentreupto106cm-2andareasincreasingwithincreasingpressure.

LaserradiationproducesthesameeffectuponLiNbO3crystals.Thedensitiesofmicrodomainsformedundernear-thresholdradiationintensity(l=1.06µm,Jthrcsh=6.5GW/cm2)reached109cm-2inthecentreand105-106cm-2attheclusterboundaries.Thesizeoftheclusterareasdecreasesslightlywithdecreasingintensity,andonthewholetheclusterdiameterisdeterminedbythediameterofthefocalspot.Underselectiveetchingatypicalpatternisobservedinthe

irradiatedarea.

Thisphenomenoncanbeinterpretedindifferentways.LevanyukandOsipov(1975)showedthepossibilityofaphotoinducedreversalofspontaneouspolarizationinferroelectricswithoccurrenceofa'frozen'bulkcharge.Butthismechanismdoesnotaccountfortheindicatedphenomenonsincetheresultantchargeofirradiatedregioniszero.Moreover,thepolarizationreversalregionisstrictlylimitedtotheirradiatedarea,whereasirradiation-inducedmicrodomainsareobservedoutsidetheirradiatedareaaswell.Themechanismofmicrodomainnucleationduetoelasticstrains,whichwasproposedby(Abul-FadlandStefenakos1977)andconfirmedbyexperimentswithmechanicaltreatment,seemstobemostrealistic.Becauseofashortirradiationtimeandalowheattransfercoefficient,irradiationwithahigh-intensitylaserbeaminducedathermalshockwhichisresponsibleforhighlocalstrainsandmicrodomainnucleation.

InepitaxialLiNbO3filmsmicrodomainsareonlyobservedin(0001)-alignedlayers.Themicrodomaindensityvariesfromsampletosample(from10to105cm-2),butasaruleexceedsthemicrodomaindensityonthesubstrate.Thus,microdomainsgrowfromthesubstratetothefilmandemergeinthelayeronlocalinhomogeneitiesandstrains.

4.6.4PeriodicallyinverteddomainstructuresinLiTaO3andLiNbO3usingprotonexchange

SHGbyquasi-phasematching(QPM)ofthefundamentalandharmonicmodescanreleasehighconversionefficiencyandisversatileforgenerationofshorterwavelength,QPMisbasedonthemoodulationofnonlinearpolarizationbyperiodicallydomain-invertedstructure,andthusitispossibletophasematchanarbitarywavelengthbyanappropriatechoiceofperiodofmodulation.Byusingthistechnique,bluelightgenerationinLiNbO3waveguidehasbeenrealized(Liraetal1989;Webjornetal1989).Thisdeviceofferstheadvantageofefficientconversionoflaserradiation,becausethewaveguidealllowslonginteractionlengthwithstrongmodalconfinement.However,asphotorefractivedamageisknowntooccurinLiNbO3itspotentialathigherpowersmaybelimited.

LiTaO3wasreportedtobehighlyresistiveagainstphotorefractivedamageanditalsohastheadvantagesoflargenonlinearsusceptibilities,andshortwavelengthtransparencyfrom280nm.

SeveralmethodshavebeenusedtofabricateperiodicdomaininversioninLiNbO3andLiTaO3.Tiin-diffusion(Miyazawa1979)orLiout-diffusion(Webjornetal1989)neartheCurietemperaturearewell-knowntechniquestoreversethepolarizationinLiNbO3,buttheshapeoftheinverteddomainisnotrectangular.Electronbeambombardment(Keysetal1991;YomadaandKishima1991;Itoetal1991)hasalsobeenemployedtomake'well'-shapedinverteddomains.butitisdifficulttofabricateshortperiodpatterns.PeriodicallypoledstructuresinLiNbO3canberealizedthroughselectiveprotonexchange(PE)followedbyheattreatmentneartheCurietemperature(Mizuuchietal1991).Afewmicrondeepsemicircular-shapeddomainswithafirst-orderperiodhasbeenfabricatedusingprotonexchangeandaquickheattreatmentnearthe

Curietemperature,generating15mWofbluelight(MizuuchiandYamamoto1991).

Makioetal(1992)reportedontheformationoflong(>40µm),'spikelike'inverteddomainstriggeredbyprotonexchangewithone-directionalheating.Thesedomainshavestraightwallsandthesameperiodastheprotonexchangedgrid,whicharefavourableconditionstoachievefirst-orderQPMdevices.

Authorsdescribedtheirfabricationprocessasfollows;a30nmthickTamaskwasdepositedonthec+orc-faceof0.5mmthickLiTaO3orLiNbO3substratesusinganelectronbeamdepositionmethod.Thefirst-orderperiodicpatternwitha3.2µmperiodwasfabricatedontheTamaskbyconventionalphotolithographyandCF4dryetching,formingwindowstoallowprotonexchange.AsmallamountofpyrophosphoricacidwasdroppedontheTamasksideofthesubstrate,whichwasthenplacedonanalreadyheated(230-260°C)hotplateforseveralminutes,namely,one-directionalheatingfromtherearsurfaceofthesubstrate.AfterremovaloftheTamask,somespecimenswerecutintostrips,polished,andetchedwithHFandHNO3toexaminetheprotonexchangeandthedomaininversion.

Theyfoundthatthepolarizationflippedduringtheprotonexchangeprocess,farbelowtheCurietemperature.Figure4.24showsacross-sectionalviewofaLiNbO3sample,protonexchangedat260°Cfor30minandwithoutanypost-PEannealing.Althoughtheproton-exchangedlayerislessthan1µmthick,inverteddomainsstemmedandstretchedfromtheproton-exchangedregiondeep

Fig.4.24Crosssectionalmicrographoftheperiodically

invertedspikelinedomainsfabricatedonLiNbO3(Makioetal,1992).

insidethesubstratefrommorethan40µm.Thedomainslooklikespikes,withthinandsharpends.

Thespikelikedomainscanbeformedonbothc+andc-facesofLiNbO3,unlikeothertypesofdomains.SpikelikedomainscouldbesuccessfullyfabricatedonLiNbO3aswell,inspiteofitshighCurietemperature.

Thesespikelikedomainsseentobesimilartotheso-called'needle-shaped'microdomains(OhnishiandIizuka,1975)whicharecommoninpoledcrystalsasresidualantidomains,usuallybeingisolatedandrandomlydistributed.Theinversionmechanismisnotclear,buttheperiodicstressduetoprotonexchangeislikelytotriggerthegrowthoftheantidomains,whichisacceleratedbythethermalgradientcausedbyone-directionalheating.

Thethermalstabilityofthespikelikedomainswasexaminedduringpost-PEannealing.Heattreatmentwascarriedoutat525°Cforupto2min.Thoughthedataarespreadoutoverawiderange,theyindicatethetendencyforthedomainstobecomeshorterandfinallyvanishastheheattreatmenttimeincreases.Atlowertemperature,though,theysurvivelongertreatmenttime.Fromthepracticalpointofview,itis

essentialforthedomainstosurvivethe350-

Fig.4.25Measureddepthofinvertedregionswitha20µmperiodagainsttheheattreatment

temperatureforvariousproton-exchange(PE)conditions(Mizuuchietal1991).

380°Cheatcycleinordertofabricatewaveguidesonthesubstratebytheannealedprotonexchangemethod.

Thedependenceoftheinverteddepthontheconditionofprotonexchangeandheattreatmenttemperaturewasexaminedforthe-cfacesubstratewithaTamaskof20µmperiod.Onlythe-cfacedoesproduceinversion.Thereasonwhyinversioncannotbeobservedin+cfaceisnotclear,andinvestigationoftheformationprocessofdomaininversionisbeingconductedtoresolvetheinversionmechanism.Figure4.25showstheinversiondepthasafunctionofheattreatmenttemperatureforaheattreatmenttimeof10min.Theinvertedregionbecamedeeperwithincreasingtemperature,butabove610°Caperiodicstructurecannotbeobserved,becauseitisabovetheTcofpureLiNbO3.Thefigurealsoshowsthatthethresholdtemperaturetocausedomaininversionbecomeslowerwithincreasingproton-exchangetimeandsaturatesatalowerlimitof450°C.ThissaturationperhapsindicatestheTcofproton-exchangedLiNbO3.Furthermore,thelargedifferencebetweenthislowerlimitandtheTcofpureLiNbO3showsthelargeextenttowhichtheLiionsareexchangedbyprotonsforthecaseofpyrophosphoricacid.Byknowingthisthresholdtemperaturefordomainreversal,Mizuuchietal(1991)wereabletocarryoutotherprocesses,suchasannealing,atanylowertemperaturewithoutdisturbingthedomain-invertedregions.

4.6.5Waveguideperiodicallypoledbyapplyinganexternalfield

Yamada,etal,(1993)reportedthefabricationofaperiodicallyinverteddomainstructureinaLiNbO3substratebyapplyinganexternalelectricfield,whichyieldsanefficientfirst-orderQPM-SHGdevice.

ItwassaidthatthedomaininversionofLiNbO3isdifficultatroomtemperature.LiNbO3isusuallybrokenwithoutdomaininversion

whenanexternalfieldisappliedatroomtemperature.TheexternalfieldfordomaininversionofLiNbO3isclosetothatoftheelectronavalanche,sotheLiNbO3substrateisbrokenwithoutitsspontaneouspolarizationbeinginvertedwiththeapplicationofanexternalfield.

Yamadaetal,(1993)fabricatedtheperiodicdomainstructureforfirst-orderQPM-SHGdevicesinLiNbO3asfollows.Figure4.26showshowexternalfieldisapplied.Theyalsousedaz-cutLiNbO3crystalasthesubstrate.AnAlthinfilm200nmthickwasdepositedonthepositiveandnegativec-faceofthe

Fig.4.26Schematicofapplyingvoltageforperiodically

domaininversion(Yamadaetal1993).

LiNbO3substrate.TheAlthinfilmonthepositivec-facewasperiodicallypatternedwitha2.8µmperiodbywetetching.Electrodeswerethenfabricatedonbothc-faces.

Next,atroomtemperature,anegativepulsewithawidthof100µsandavoltageof24kV/mm(theelectriccoerciveforceofLiNbO3isabout20kV/mm)wasappliedonaplaneelectrodeonthenegativec-faceandaperiodicelectrodeonthepositivec-facewasgrounded.Afterapplyingthevoltage,theAlelectrodewasremovedinanaqueoussolutionofNaOH.

Thereasontheperiodicelectrodesshouldbefabricatedonthepositivec-faceisthattheinverteddomainnucleiappearonthepositivec-face.Thereasonwhypulsedexternalfieldshouldbeappliedcanbeunderstoodiftheprocessofdomaingrowthisobserved.Whenthereexistsadependenceofthedomaingrowthonthetimetheexternalfieldisapplied,firstthedomainsgrowalongthec-axis,thengrowundertheelectrodes.Iftheexternalfieldisappliedtoolong,thedomainsspreadoutfromundertheelectrodesandcomeintocontactwitheachother.Theexternalfieldmustbeshutoffbeforethedomainsgrowoutformundertheelectrodes.

Usingtheaboveprocedure,az-cutLiNbO3substratewitha2.8µmperiodlaminardomainstructurewasobtained,whichissimilartothatillustratedinFig.4.24.Fromthefigureitisseenthatthedomainsboundariesareparalleltothec-axis.Thisperiodicallyinverteddomainstructureisidealforfirst-orderQPM-SHGdevices.

4.6.6DomaininversioninLiNbO3usingdirectelectron-beamwriting

Directelectron-beamwritingwasachievedusingascanningelectronmicroscope(SEM)convertedforthispurpose(Nuttetal,1992).Beamcurrentsusedwereintherangeof3-7nAandthebeamvoltagerangedbetween20and30kV.Theelectron-beamspotsizewas0.5

µm.Patternswerewrittenwithsaturatedfilamentcurrentatbeamvoltagesof20,25,and30kV.Thebestgratingresolutionwasobtainedat30kV.Althoughsurfacecrackingwasobservedathighvoltages(30kV)andatlowerscanvelocities(235µm/s)withabeamcurrentof7nA,surfacecrackingwasavoidedbyreducingthebeamcurrentwhilstkeepingthebeamvoltagehigh.Samplesusedinthisstudywere500µmthickz-cutLiNbO3.Thedomaininversionprocessiscontrolledbytheelectricfieldcreatedbyelectronbombardment.Hence,a30nmfilmofTametalwassputteredonthec+face,whichactedasagroundelectrode.Sampleswerescannedonthec-facewheretheelectronbeamdepositedavxechargeonthesurface.Thescanvelocitieswerebetween200and800µm/s.Typicalsheetresisitanceofthemetalfilmwas200W/cm2.DomaininversionwasrevealedbyetchingtheLiNbO3sampleinasolutionoftwopartsHNO3andonepartHFat90°Cfor5minsincetheetchrateforthec-faceismuchhigherthanthatofthec+face.

Tounderstandthedomaininversionmechanismunderdirectelectron-beamwriting,metallinesweredepositedonthec+facethatwere200µmwideandspaced280µmapart.Thisgaveaperiodicgroundplane.Singlelinesusingdifferentbeamscanspeeds(500,250,166.7,71.4,and33.3µm/swith30kWbeamvoltageand7nAbeamcurrent)werewrittenperpendiculartothemetallinesonthec-face.Theseresultsshowthatdomaininversioncanbeachieved

betweenmetallineswherethereisnodirectgroundand,secondly,domainspreadingoccursatthemetaledges.Theseresultsimplythatdomaininversionisrelatedtotheelectricfielddensity,whichishigheratthemetaledges.Nosignificantdomainspreadingwasobservedonthec+face.

Thewidthofthedomain-invertedregiononthec+facewasabouttwicethedomainwidthonthec-face.Thisspreadinglimitsthefabricationofhigh-resolutiongratingsonthec+face.

Surprisingly,domaininversionthroughthethicknessofthesamplewasobservedonLiNbO3,whichhadnometalfilmgroundingwhatsoeveronthec+face.However,high-resolutiongratingsonthec+faceshoweddistortion.Thisispossiblyduetocharginganddischargingeffectsobservedduringthewritingprocess.Thisimpliesthatmetalgroundingisneccessaryforhigh-resolutiongratingsalthoughlarge-periodgratingscanstillbewrittenwithoutdirectgrounding.Moresurfacecrackingwasobservedwithsampleswithoutmetalgrounding.

Electronbombardmentwithfocusedbeams(0.5µmindiameter)onthec-faceofLiNbO3withthec+faceasgroundedcanproducehighelectricfieldsnearthesurface.Thedistributionofthenormalcomponentofelectricfield,E(x),duetoapointchargeinauniformdielectricmediumnearaconductingplaneisgivenby(Becker,1982)

wherexandyaretheperpendiculardistancesofapointchargefromtheconductingplaneasshowninFig.4.27.Thechargeisqandeis

thedielectricconstantofthemedium.Asexpected,ahighelectricfieldisproducednear

Fig.4.27Normalizedelectricfieldlog(4pea2E(x)/q)contours

duetothepointchargeqneartheconductingsurface(Nuttetal1992).

thepointcharge.Beamcurrentsusedinthisstudywereoftheorderofafewnanoamperesandthetypicalscanvelocityusedwas300µm/s.Thebeamdiameterwas0.5µm.Thiscorrespondstoadwelltimeofabout1.5msper0.5µmtravel.Hence,thechargedepositedisabout10-10Cin0.5µm.Ifwetakethisasapointchargeq,thenthefieldintensityatadepthof5µmisabout108V/m.Thisisinthevicinityofthebreakdownvoltagefordielectrics.Hence,veryhigh-fieldintensitiesareproducednearthepointcharge.Thefieldintensitynearthepointchargeissimilarinmagnitudetothatofthepolarizationfieldsintheferroelectricmaterial.Thisfieldcanproducereverseddomainsnearthesurface.

Theroleofelectronenergyinthedomain-inversionprocessrequiresfurtherinvestigation.HaycockandTownsend(1986)proposedamechanismfordomaininversioninLiNbO3andLiTaO3whereexcitationofthecrystallatticebyanenergeticbeamofelectronsisrequiredwhileanexternalfieldisapplied.IntheexperimentscarriedoutbyNuttetal(1992),energeticelectronscanprovideexcitationofthecrystallatticeandatthesametimeanelectricfieldiscreatedduetoagroundelectrodeonthec+face.Itisalsopossiblethatlow-energyelectrons(<10keV)maynotproducedomaininversionduetosurfaceconduction,whilehigher-energyelectronspenetratedeeperinthecrystal.

Thedomain-inversionprocessstartswithnucleationofdomains,withtheirpolarizationPorientationantiparalleltotheoriginalpolarizationfieldPsatthesurface.Thereisrapidgrowthofthesenucleiintolongdomainsthroughthethicknessofthecrystal.Finally,thereissidewisegrowthorexpansionofdomains.Theinitialshapeofthedomainmayfollowthefieldprofileduetothepointcharge.Therewillbeacriticalfieldfornucleation.Theinverteddomainsinduceadepolarizingfieldthataidstheexternalfieldinthefurthergrowthofinvertedregionsalongthec+axisofthecrystal.So,theinverteddomainshapewillbe

essentiallyparalleltothecaxisofthecrystalasitgrowsfurther.Thedomainwidthonthec+andc-facesoftheLiNbO3crystalincreasedasthescanspeeddecreased;thissuggeststhatthereisafieldlimit,which,whenexceeded,allowsdomainreversaltooccurspontaneously.Whensmaller-periodmetallines(10µm)wereused,nolateraldomainspreadingwasobservedonthec+faceoftheLiNbO3crystal.The10µmperiodgratingobviouslyactedexactlylikeacontinuousground.Therefore,thesamplethicknessplaysapartinthereversalmechanismbecauseofthedropinfieldintensityacrossthesample.

4.7Annealing-inducedvariationofthephasecompositionandcrystallinestructureofthelithiumniobatecrystalsurface

4.7.1Annealing-inducedvariationofthecrystallinestructureofthelithiumniobatecrystalsurface

Electrondiffractionstudieshaveshownthatthesurfaceofmechanicallypolishedx-,y-andz-cutsoflithiumniobatesubstratesiscoveredwithalayerwithadamagedcrystallinestructure,whichisformedduetobrittlefailureofthematerialinthecourseofmechanicaltreatment.Theelectrondiffractionpatternscontainingonlythediffusionbackgroundwithoutanyreflexessuggestamorphityofthethinnear-surfacelayerofthecrystal(Bocharova1986).

Todeterminethedamagedepthinmechanicallypolishedsamples,thedam-

agedlayerswereetchedonebyoneinamixtureofacidsHF+HNO3atroomtemperaturewithsimultaneouscontrolofthesurfacestructure.Aportionofthesurfacewascoveredwithpiceinwhichpreservedthesurfacefromtheetchingagent,andtheheightofthestepwasindicativeoftheetchedlayerthickness.Thedegreeofstructureperfectionoftheetchedsurfacewascontrolledbyelectrondiffractometryandtheheightofthestepwasdeterminedusinganopticalinterferencemicroscope.Thethicknessoftheamorphouslayervariedwithintherange5nm<d<30nm,wasdependentonthequalityofpolishingandremainedunalteredfromsampletosample.

Betweentheamorphouslayerandtheperfectcrystalthereliesadamagedarea.Thedepthofthedamagedlayerinlithiumniobatecanbeestimatedbyellipsometryandrepeatedtotalinternalreflection.Theellipsometricmeasurementscarriedoutonthey-cutlithiumniobatehaveshownthattheeffectivethicknessofadamagedsurfacelayerdependsstronglyonpolishingqualityandrangesbetween35and160nm(Yakovlev1985).Themethodofrepeatedtotalinternalreflectionwasappliedtorevealanincreaseoflightabsorptionina200nmsurfacelayeroflithiumniobate,whichisexplainedbyahigherdefectdensityinthislayer(Zverevetal1977).

Electrondiffractometricandopticaldatasuggestthatnearthelithiumniobatesurfacethereexistsathinstronglydamagedamorphouslayer(~30nm)andadeeper-lyinglayer(~200nm)ofstrainedmaterial.Therealstructureoflithiumniobatecrystalscontainsdislocations,blockboundaries,microdomainsandothertypesofdefects.Accordingtotheresultsofselectivechemicaletching,thedislocationdensitywas104-105cm-2andthelineardislocationdensitywas~3×104cm-2.

Duringannealingofmechanicallypolishedcrystalsthefollowingtwoprocessesproceed:

-damagedlayerrecrystallization,

-phasecompositionvariation,

thatcanberecordedbyhigh-energyelectrondiffractionbyreflection.Theseprocessesaresimultaneousanddependessentiallyontheannealingtemperature.

Recrystallizationinsolidbodiesconsistsofachangeintheircrystallinestructureandremovalofstructuraldefectscausedbypreliminarymechanicaltreatment.Thestructureofmatterisorderedbythenucleationandgrowthofgrainsaswellasbyenlargementofsomegrainsattheexpenseofothergrains.Thisprocedureresultsinreliefofinternalmicro-andmacrostrains.Theassembled(theassembledrecrystallization)recrystallizationmayequallyoccurinstrainedandunstrainedmaterialsandtypicallyfollowsthedamagedlayerrecrystallization.

Asshownbyelectrondiffractionanalysis,beginningwithT=300°Crecrystallizationofthedamagedlayerinducedbyannealingproceedsataratherhighspeed.Figure4.28a-dpresentsaseriesofelectrondiffractionpatternsoflithiumniobatesamplesalignedparalleltothecrystallographic(0001)planeandannealedatdifferenttemperaturesduringequaltimeintervals(t=4h).Reflectionsfromthesamples,annealedatT=300°C,intheformofarcsandringsarrangedconcentricallyneartheprimarybeam(Fig.4.28a)characterizethechangeinthestructureoftheuppersubstratelayers.Moreover,theelectrondiffractionpatterns

Fig.4.28Electrondiffractionpatternsofthebasefacet(0001)oflithiumniobateversusannealing

temperature(annealingtimet=4h):a)300°C,b)650°C,c)750°C,d)950°C(Bocharova1986).

exhibitweakKikuchilines,farfromtheprimarybeam,formeddeepinsidethecrystal.Thepresenceofarc-andring-shapedreflectionsisindicativeoforderingofthesurface-layerstructureandofformationofsmallcrystallineaggregatesinthislayer.TheestimateofthesizelofthesecrystallitesobtainedfromthehalfwidthofreflexesBgivestherangeof10-50nm.ThecrystallitesformedatT=300°Chavebasicallyrandomposition,butshowatendencyfortextureformation.

Anincreaseofannealingtemperaturefrom300°Cto700°Ccausesadecreaseofazimuthaldisorientationandsegregationofcrystalliteswithpreferentialorientationparalleltoalithiumniobatesubstratesurface.

TheelectrondiffractionpatternsofsamplesannealedatT>650°C(Fig.4.28bandc)show,togetherwitharcsfromthetexture,alsoasystemofpointreflexesformedbyamosaicsinglecrystal.Withafurtherincreaseoftemperaturefrom700°Cto900°Cthereflectionsfromthetexturedisappear,andtheelectrondiffractionpatternsonlycontainanetofpointreflexes,whichtestifiestothepresenceofsimilarlyalignedgrains.AnnealingoflithiumniobatesamplesatT=950°Cfor4hsufficesforacompleterestorationofcrystallinityofthenear-surfacelayer.Theelectrondiffractionpatternsofsuchsamplesexhibit

Kikuchilines(Fig.4.28d).Thevariationofthecrystallinestructureoflithiumniobatefacets( )and( )dependingontheannealingtemperatureproceedsinasimilarmanner.

Thus,recrystallizationofthedamagednear-surfacelayerofcrystalsproceedsgraduallyintheentiretemperaturerangebeginningwith300°C.Thesurfacestructurechangesfromamorphousthroughtexture(T=300-650°C)andmosaic(T=650-900°C)uptosingle-crystal.Thefinalrestorationofasingle-crystalstateofthenear-surfacelayerisachievedatatemperatureT>900°C.

Aspecificfeatureoflithiumniobaterecrystallizationisthatwithinacertaintemperaturerangeitproceedsintheexistenceregionofatwo-phasesystem.

4.7.2Annealing-inducedvariationofthephasecompositionofthelithiumniobatecrystalsurface

Diffractionanalysisofspecimensannealedbetween300and900°Crevealsphasetransformationproceedingonthesurfaceoflithiumniobatecrystalssimultaneouslywithrecrystallization.ThisisalsoconfirmedbytheelectrondiffractionpatternsshowingasimultaneousdiffractionfromLiNbO3andLiNb3O8,bywhichonecantraceoutannealing-inducedvariationofthecrystallinestructureandofthephasecompositionofsubstratesurfacesofdifferentorientations.

VariationsofthephasecompositionandcrystallinestructureofthelithiumniobatesurfaceareobservedalreadyatT=300°C.Thesystemofring-andarc-shapedreflectionsobservedinelectrondiffractionpatterns(Fig.4.28a)isinducedinamonocliniccellwithparametersa=15.26Å,b=5.033Å,c=7.46Å,b=107.33gradcorrespondingtolithiumtriniobatewhichbelongstothespacegroupP21/a(Lundberg1971).DuetoclosenessoftheinterplanardistancesofLiNb3O8andLiNbO3andreflexsmearing,partofreflectionsfromthematrixand

phasearenotseparates,butapermanentstrengtheningofindividualreflexestestifiestothepresenceofatwo-phasesystemonthesamplesurface.

Reflexesfromthemonoclinicphaseoflithiumtriniobateandfromtrigonallithiumniobateareseenmoreclearlyinelectrondiffractionpatternsastheannealingtemperatureincreases.WithinthetemperaturerangeT=300-700°Cthenewlyformedcrystalsofthesecondphasegetlargerandacquireepitaxialorientationrelativetothesubstrate.Pointreflexesappear(Fig.4.28b),andatT=700-900°Ctwophasesareformedconnectedwitheachotherbycertainorientationrelations(Fig.4.28c).Thissuggestssolid-phaseepitaxialgrowthofamonoclinicphaseonthelithiumniobatesurface.

Theoccurrenceofthesecondphaseisvisualizedasatypicalthindullcoatingonthesubstratesurfaceandcanalsobeidentifiedbylightscatteringinplacesofphasenucleation.Thephasechange

proceedsbasicallyinthenear-surfacelayerofalithiumniobatecrystaldamagedinthecourseofmechanicaltreatment.AfterthesurfacelayerhadbeenremovedbyetchinginthemixtureHF+HNO3,theelectrondiffractionpatternsshowedreflectionsonlyfromlithiumniobate,whichisindicativeofspatiallimitationofnucleationandgrowthoftheLiNb3O8phase.Therateoflithiumtriniobatenucleationonthecrystalsurfaceisratherhigh:themonoclinicphaseappearsonelectrondiffractionpatternsaftera10minstayofthesubstrateinthehotregionatT=750°C.

Fig.4.29PhasediagramoftheLi2O-Nb2O5system(Holman1978).

Opticalinhomogeneityofthebulkcrystalbeforeandafterannealinginthetwo-phasetemperatureregionwasdeterminedbycomparingtheRayleighIRandstimulatedBrillouinISBcomponentsofscatteredlight.

UnderannealingatatemperatureT=750°Cfor5-20h,thenumberofscatteringcentresinthebulkcrystalremainsunchanged,whereasalayeroflithiumtriniobatephaseformsonthecrystalsurface.Aconsiderableincreaseinthenumberofscatteringcentresinthebulkcrystalwasonlyobservedafterannealingatthesametemperaturefor40h.

Anincreaseofthenucleationrateonastronglydamagedsurfaceascomparedwiththecrystalbulkisduetotheloweringofthenucleationbarrierandthehigherdiffusionrateofcomponentsintheamorphouslayer.Thisconclusionisconfirmedbythefactthatthelithiumdiffusionactivationenergyinasinglecrystal,equalto68±1.2kcal/molfallsdownto14.28±1.6kcal/mol(Carruthersetal1974;JetschkeandHehl1985).

Electrondiffractionanalysisshowsthatthevariationofthephase

compositionofthelithiumniobatesurfaceduetomonoclinicphasenucleationisareversibleprocess,andatT>900°Cthephasechange

isobserved.TheboundaryoftheexistenceregionoftwophasesforcrystalsofcongruentcompositionliesnearT=900°C,whichagreeswiththephasediagram.Abovethistemperature,onlyLiNbO3ispresentonthesamplesurface,andreflectionsfromLiNb3O8disappearfromelectrondiffractionpatterns(Fig.4.28d).Thephasechange onthesurfaceoftitanium-dopedlithiumniobatecrystalsproceedsinasimilarmanner.

WenotethatatT<900°Cnomonoclinicphasewasobservedonthesubstratesurfaceifannealingwascarriedoutinalithium-enrichedatmosphere,thatis,thepresenceofLivapoursinannealingandtheirabsorptiononthesurfaceinhibitsphasenucleation.Initsnature,theindicatedtransition referstosolid-phaseorder-disordertypetransitionsoccurringinsolidsolutions.ThenucleationofthemonoclinicphaseLiNbO3correspondstodissolvingofexcesssolid-stateniobium.

Lithiumniobatecrystalsofcongruentcompositionaremetastableatroomtemperatureandcontainpointdefects,duetolithiumdeficiency,inaconcentrationexceedingtheequilibriumone.Accordingtothephasediagram(Fig.4.29),atatemperaturebelow900°C,LiNbO3andLiNb3O8canexistsimultaneously.ThenarrowingofthehomogeneityregionwithloweringtemperatureleadstoLiNb3O8phasesegregationaccompanyingannealingofmetastablenonstoichiometriclithiumniobatecrystalswithinthetemperaturerange300-900°C,whichbringsthesystemtoastateenergeticallymoreadvantageousandlowerstheconcentrationofpointdefectsinthecrystals.ThetemperaturerangeT>900°Ccorrespondstotheone-phaselithiumniobatesystemandhasawidehomogeneityregion(upto6mol/%Li2O)withinwhichtheexistenceoflithiumniobatewithwidelydifferentcompositionisenergeticallyadmissible.Atannealingtemperaturesexceeding900°C,thechange isobserved,themonoclinicphasedisappearsandthesamplesurfacebecomessingle-phase.

ThephysicalandchemicalpropertiesoflightguidingferroelectricfilmsaretabulatedinTable4.5.

Temperaturevariationsaffectnotonlythestructureandphasecomposition,butalsothesurfacemorphologywhichisdeterminedbycrystallographicorientationofthesamplesurface.

Theshapesofgrowinglithiumtriniobatecrystalsandthespecificitiesofmicrocrystalpositionsonthesubstratesurfaceinthemonoclinicphasearebestofallpronouncedinthetemperaturerangeof700-900°CthatcorrespondstoanorientedgrowthofLiNb3O8.Thesizesanddensityofislandsofthesecondphasedependontheannealingtimeandonthedegreeofdamageofthenear-surfacesamplestructure.ThethicknessoftheLiNb3O8layerwasestimatedbytheheightofthegrowthpatternsonelectron-microscopicpicturesand

ellipsometrically.AfterannealingatT=750°Cfor4h,thegrowthpatternsofLiNb3O8rangedontheaveragewithin150-500nm,andtheellipsometricallymeasuredthicknessoftheislandlayerofthephasemadeup15-40nm.TheislanddensityNofthephasevariedfromsampletosamplewithinarangeof107to1010cm-2,thedistributionofislandsoverthesurfaceofoneandthesameislandbeingnonuniform.Phasesegregationareconcentrated,inparticular,inthevicinityofscratchesresultingfromsamplepolishing.Theislanddensityinsuchplacesmakesup1010-1011cm-2.

Accordingtoelectrondiffractiondata,lithiumtriniobateisorientedrelativetothe(0001)substrateasfollows:( )

TheshapesofgrowingLiNb3O8crystalsonthebasefacetoflithiumniobatearebasicallyrepresentedbypinacoidal and{h00}typeplaneselongatedalongthe[010]direction(Fig.4.30a).Itshouldbenotedthatthepinacoid( )paralleltothesubstratesurfaceisnotalwayspresentinthehabitusofmicrocrystalsofthenewphase,andisoccasionallytaperedoutwithitsotherfacetspositionedatanangletothesurface.InFig.4.30aphaseislandswithsuchfacetsareshownbythearrows2;thearrow1indicatesaLiNb3O8microcrystalwhosehabituscontainsthe( )facet.Thisisindicativeofthedifferenceingrowthconditionsofislandsononeandthesamesubstrate,which

Table4.5Physico-chemicalparametersofcrystalsandfilmsofoxideFerroelectrics(Ivleva,Kuzminov,1985)

Crystal Solvent Meltingpoint

Latticeparameters Refractiveindex

Electro-opticcoefficient

Films-substrate T,°C a,Å c,Åno ne r33 r13l=0.63µm 10-12 m/V

1LiNbO3 1253 5.14813.8622.289 2.201 30.8 8.6

2LiNbO3-LiNbO3 LiVO3 5.142

3LiTaO3 1650 5.15213.7852.177 2.183 35.8 7.9

4LiNbO3-LiTaO3 LiVO3 13.851

5LiNbO3-LiTaO3 LiVO3 13.85 2.288(4)2.191(4)

6LiNbO3-LiTaO3 2.200 2.184 12 2.3

7LiNbO3-LiTaO3 2.29 2.20 28.5

8LiNbO3:Li+-LiTaO3 Li2WO4 5.143

9LiNbO3:Nb5+-LiTaO3 K2WO4 5.153

10Li1-xNaxNbO3-LiNbO3 LiVO3 5.154

11Li1-xCOxNb1-xZrxO3--LiVO3 LiNbO3 5.144

12LiNbO3:Ag+-LiNbO3 LiVO3 2.2361

13LiTaxNb1-xO3-LiTaO3 LiVO3 13.80

14KNbO3 1039

15Sapphyre(Al2O3) 2030 4.75812.9911.766 1.758

16KNbO3-Al2O3 KVO3

17LiNbO3:Cr3+(Fe3+,Cu2+)-LiNbO3 LiVO3

18K289Li1.55Nb5.11O15 1050 12.584.01 2.294(8)2.156(8)

19K1.5Bi10Nb5.1O15 1312 17.857.84 2.237 2.253

K1.5Bi10Nb5.1O1520K239Li155Nb5.11O15--K1.5Bi1.0Nb5.1O15

12.533.98

Comments:1.Prokhorov,Kuz'minov,1990;2.Baudrantetal,1975;3.Kuz'minov,1975;4.Miyasawa,1973;5.Miyasawaetal,1975;6.Fukunishietal,1974;7.Tienetal,1974;8.Baudrantetal,1975,Ballmanetal,1975;9.Baudrantetal,1975,Ballmanetal,1975;10.Neurgaonkar1981;11.Neurgaonkaretal,1979;12.Baudrantetal,1975;13.Kosminaetal,1983,Tienetal,1974;14.Prokorov,Kuz'minov,1990;15.Schaskolskaya1982;16.Khachaturyanetal,1984;17.Baudrantetal,1975;18,19,20.Adachietal,1979.

isevidentlyduetoinhomogeneityoflithiumniobatecompositionandinhomogeneityofstrainsinthesurfacelayerofthecrystal.

Accordingtothesymmetryofthebasefacetoflithiumniobate,LiNb3Omicro-crystalsoccupythreeequivalentpositionsonthesubstrate,makinganangleof120°(Fig.4.30b),whichformdendrite-typeadhesions(joints)showninFig.4.30a.

Fig.4.30(a)Surfacemorphologyofthe(0001)facetoflithium

niobateafterannealingatT=750°Cfor4h.(b)Positionsoflithiumtriniobateisletsonthe(0001)

facetoflithiumniobate,(Bocharova1986).

5PhysicalPropertiesofWaveguideLayersPracticaluseofvarioustypesofthin-filmferroelectricstructuresneedsadetailedstudyofthephysico-chemicalpropertiesofthesubstancesinvolved,aswellastechnologicalperfectionofobtainingthesesubstances.Thiswillpermitcreationofmaterialswiththerequiredphysicalpropertiesoptimumforaparticularapplication.

Inthischapterwedescribetheinvestigationsofwaveguiding,nonlinearopticandferroelectricpropertiesofepitaxialfilmsoflithiumniobateandlithiumtantalateandtheirsolidsolutions.Thedielectricandpyroelectricproperties,andthetemperaturedependenceofthermoelectriccoefficientsarepresented.Wealsoconsidertheopticalpropertiesofthethin-filmstructures:surfaceresistanceandtheeffectoflaserradiation,therefractiveindicesandthemodestructureoffilms,lightextinctionuponwaveguidepropagation.

5.1Opticalpropertiesoflithiumniobateandtantalatesinglecrystals

Lithiummeta-niobatesinglecrystalsareuniaxialnegative(no-ne),transparentfromabout0.4to5mm(Fig.5.1)(Boydetal1964).Thenatureoftheirtransmissionspectradependsontheconditionsofheattreatmentandpolarizationofcrystals.Crystalspreparedwithnodirectcurrentmaintainedthroughthemduringthegrowthareclearandcolourless.

ThedispersiondependencesofnoandneoverawidefrequencyrangeforlithiumniobatecrystalsgrownfromcongruentmeltcompositionsarecollectedinTable5.1.

Thetemperaturedependenceofrefractiveindiceswasmeasuredusingalithiumniobateprismwiththeopticalaxisparalleltothetwomajor

facets.Theprismwasarrangedinasmallfurnaceonaspectrometerstage.Therefractiveindicesweretakenateighttemperaturesbetween19and374°Cforeightlinesoftheheliummetalvapourlampat447.1,471.3,492.2,501.6,587.6,667.8,and707.6nm.

Table 5.1 Refractive indices of lithium niobate crystals (Weiss andGaylord1985)

l,nm Laser Stoichiometric(T=25°C)

Congruentlymelting(T=24.5°C)

no ne no ne

441.6 He-Cd2.3906 2.2841 2.3875 2.2887

457.9 Ar2.3756 2.2715 2.3725 2.2760

465.8 Ar2.3697 2.2664 2.3653 2.2699

472.7 Ar2.3646 2.2620 3.3597 2.2652

476.5 Ar2.3618 2.2596 2.3568 2.2627

488.0 Ar2.3533 2.2523 2.3480 2.2561

496.5 Ar2.3470 2.2468 2.3434 2.2514

501.7 Ar2.3535 2.2439 2.3401 2.2486

514.5 Ar2.3370 2.2387 2.3326 2.2422

530.0 Nd2.3290 2.2323 2.3247 2.2355

632.8 He-Ne2.2910 2.2005 2.2866 2.2028

693.4 Ruby2.2770 2.1886 2.2726 2.1909

840.0 GaAs2.2554 2.1703 2.2507 2.1719

1060.0Nd2.2372 2.1550 2.2323 2.1561

1150.0He-Ne2.2320 2.1506 2.2225 2.1519

Fig.5.1Thedispersionspectrumoflithiumniobate.

Ananalysisoftheexperimentaldatahasyieldedtwoequationsforthetemperaturedependencegivingtherefractiveindicesbetween400and4000nm:

whereTisthetemperature,K,listhewavelength,nm.

Table5.2Refractiveindices,noandne,formixedLiNb1-yTayO3crystalsat (accordingtoShimura1977)

lÅ y=0.81 y=0.92 y=0.97 y=1.00

no ne no ne no ne no ne

58932.2057 2.1986 2.1984 2.1946 2.1902 2.1933 2.1862 2.1910

63282.1954 2.1888 2.1888 2.1853 2.1800 2.1829 2.1766 2.1815

80002.1702 2.1638 2.1643 2.1604 2.1561 2.1589 2.1531 2.1579

85002.1666 2.1606 2.1598 2.1559 2.1516 2.1545 2.1484 2.1529

90002.1615 2.1553 2.1557 2.1519 2.1478 2.1507 2.1446 2.1491

106002.1517 2.1457 2.1460 2.1422 2.1385 2.1413 2.1351 2.1396

Thestandarddeviationof112experimentallydeterminedvaluesoftherefractiveindicesfromthosecalculatedaccordingtoformulae(5.1)and(5.2)is2.2×10-4.

Thevalueofthenegativebirefringencedecreaseswitharisingtemperatureanddropsofftozeroat882°Cforl=632.8nmandat

888°Cforl=1152.3nm.

Thechangein(no-ne)withtemperature,aspredictedbyequations(5.1)and(5.2)differsby±0.0010fromtheexperimentaldataforabout600°C.Abovethistemperaturehigher-ordertermscomeintoplay.Inthelithiumniobatecrystal,itistheextraordinaryrefractiveindex,ne,thatdependssignificantlyonthemeltcompositionratio,whiletheordinaryrefractiveindex,no,remainsvirtuallyataconstantlevel(Fig.5.2)(Bergmanetal1968).Thecompositionofthemeltand,hence,thecompositionofcrystalsgrowntherefrommayvarythroughoutthegrowthprocess.Anisomorphicdopantofniobiumistantalum.Thestartingmaterialmaycontainacertainamountoftantalumoxide.Sometimes,toreducetheCurietemperatureandnaturalbirefringence,mixedLiNb1-yTayO3crystalsaregrown.Suchcrystalshavedifferentrefractiveindicesandtheirdispersions.Table5.2isacompilationofthedispersionsoftherefractiveindices,noandne,forvariouscontentsoftantaluminmixedlithiumniobatetantalatecrystals.ForpracticalapplicationsrefractiveindicesforvariouswavelengthsarecalculatedaccordingtotheSellmeierrelation(DiDomenicoandWemple1969):

where istheaverageoscillatorpositionandS0istheaverageoscillatorstrength.The andS0-valuesforvarioustantalumcontentsarelistedinTable5.3.TherefractiveindicesnoandneandthebirefringencecalculatedusingtherelationaregiveninFigs.5.3and5.4,respectively.

5.2Opticalwaveguidemodesinsingle-crystalfilms

Theopticalpropertiesofplanarwaveguidescanbearbitrarilydividedinto

Fig.5.2Refractiveindicesno(uppercurve)

andne(lowercurve)oflithiumniobateversusmolarratioLi2O/Nb2O5inthe

melt(Bergmaneta11968).

Fig.5.3(right)Refractiveindicesno(fullcircles)andne(opencircles)versusTacontentinmixedLiNb1-yTayO3crystalsfor

variouslightwavelengths(Shimura1977).

Table5.3Sellmeierconstants andS0forcalculationofrefractiveindicesofLiNb1-yTayO3crystals(accordingtoShimura1977)

y ,mm>

no ne nb ne

1.00 1.2195 1.2123 0.1687 0.1696

0.97 1.2121 1.2121 0.1695 0.1698

0.92 1.2036 1.2121 0.1709 0.1699

0.81 1.1905 1.2121 0.1724 0.1703

twogroups,thefirstresponsibleforwaveguidepropagationandthesecondforlightcontrolefficiency.Thefirstgroupincludesrefractiveindices,theirprofiles,themodecompositionandopticallosses.Thesecondinvolveselectro-,acousto-andnonlinearopticalfilmparameterswhosevaluesdependonthewayinwhichthewaveguidewasmanufactured.

5.2.1Waveguideandradiationmodes

Tien(1971)gaveavisualinterpretationoftheoccurrenceofmodesincoplanarwaveguides,whichwerepresentbelow.

Thefilmconsideredherehasathicknessoftheorderof1mmorless;itissothinthatithastobesupportedbyasubstrate.Wethusconsiderthreemedia:afilm,anairspaceabove,andasubstratebelow.AsshowninFig.5.5,thethicknessofthefilmisintheX-Yplane.Forathinfilmtosupportpropagatingmodesandtoactasadielectricwaveguideforthelightwaves,therefractiveindexofthefilmn1mustbelargerthanthatofthesubstratenoandnaturallythanthatoftheairspaceaboven2.Mathematically,theprobleminvolvesasolutionoftheMaxwellequationsthatmatchestheboundaryconditionsatthefilm-substrateandfilm-airinterfaces.Thesolutionsindicate

Fig.5.4Birefringence(ne-no)inmixedLiNb1-yTayO3

crystalsversus forvariousTacontentsinthecrystal(Shimura1977).

Fig.5.5(Right)Thelightwavepropagatesinthefilmto

thex-axis.Thesurfaceofthefilmisinthexy-planeanditsthicknessinthezdirection(Tien1971).

threepossiblemodesofpropagation.Thelightwavecanbeboundandguidedbythefilmasthewaveguidemodes.Itcanberadiatefromthefilmintoboththeairandsubstratespacesastheairmodes,oritcanradiateintothesubstrateonlyasthesubstratemodes.TheairandsubstratemodesaretheradiationmodesdiscussedbyMarcuse(1969,1970).ThemodesdescribedabovecanbeexplainedsimplyandelegantlybytheSnelllawofrefractionandtherelatedtotalinternalreflectionphenomenoninoptics.

Let(Fig.5.6a)n0,n1,andn2berefractiveindicesand , ,and betheanglesmeasuredbetweenthelightpathsandthenormalsoftheinterfacesinthesubstrate,film,andair,respectively.Here We

havethenfromtheSnelllaw

Letusincrease graduallyfrom0.When issmall,alightwave,forexample,startsfromtheairspaceabovethefilm,canberefractedintothefilm,andisthenrefractedagainintothesubstrate(Fig.5.6a).Inthiscase,thewavespropagatefreelyinallthethreemedia-air,film,andsubstrate-andtheyaretheradiationfieldsthatfillallthethreespaces(airmodes).Next,as isincreasedtoavaluelargerthanthecriticalangle ofthefilm-airinterfaceasshowninFig.5.6b,theimpossibleconditionincurredinequation(5.4), ,indicatesthatthelightwaveistotallyreflectedatthefilm-airboundary.Nowthewavecannolongerpropagatefreelyintheairspace.Wethusdescribeasolutionthatthelightenergyinthefilmradiatesintothesubstrateonly(substratemodes).Finally,whenq1islargerthanthecriticalangle ofthefilm-substrateinterface,thelightwave,asshowninFig.5.6c,

Fig.5.6(a)When ,thelightwaveshown

representstheairmode.Thelightwaveoriginatedinthefilmisrefractedintoboththesubstrateand

airspace(b).As increasessothat ,thelightwaveshownnowrepresentsthesubstratemode.Itisrefractedintothesubstratebutistotallyreflectedatthefilm-airinterface(c).When increasesfurthersothat ,thelightwaveshownistotally

reflectedatboththefilm-airandfilm-substrateinterfaces.Itisconfinedinthefilmasistobeexpectedinthewave

guidemode(Tien1971).

Fig.5.7(right)(a)Lightwaveinthewaveguidemodecanbeconsideredasaplanewavewhich

propagatesalongazigzagpathinthefilm.ThewavecanberepresentedbytwowavevectorsA1andB1.(b)ThewavevectorsA1andB1canbedecomposed

intoverticalandhorizontalcomponents.Thehorizontalcomponents determinethewave

velocityparalleltothefilm.Theverticalcomponents determinethefielddistributionacrossthethicknessof

thefilm(Tien1971).

istotallyreflectedatboththeupperandlowersurfacesofthefilm.Theenergyflowisthenconfinedwithinthefilm;thatistobeexpectedinthewaveguidemodes.

Itisinterestingtonotethatinthewaveguidemodesthelightwaveinthefilmfollowsazigzagpath(Fig.5.6c).Thelightenergyistrappedinthefilmasthewaveistotallyreflectedbackandforthbetweenthetwofilmsurfaces.ThiszigzagwavemotioncanberepresentedbytwowavevectorsA1andB1,asshowninFig.5.7a.Thenthewavevectorsaredividedintotheverticalandhorizontalcomponents,asinFig.5.7(b).ThehorizontalcomponentsofwavevectorsA1andB1areequal,indicatingthatthewavespropagatewithaconstantspeedinadirectionparalleltothefilm.TheverticalcomponentofthewavevectorAtrepresentsanupwardtravelingwave;thatofthewavevectorB1,adownwardtravellingwave.Whentheupward-anddownwardtravelingwavesaresuperposed,theyformastandingwavefieldpatternacrossthethicknessofthefilm.Bychanging ,wechangethedirectionofthewavevectorsA1andB1andthustheirhorizontalandverticalcomponents.Consequently,wechangethewavevelocityparalleltothefilmaswellasthestandingwavefieldpatternacrossthefilm.

Sincewediscusshereaplanargeometry,thewavesdescribedaboveareplanewaves.TheyareTEwavesiftheycontainthefieldcomponentsEy,Hz,andHx;theyareTMwavesiftheycontainthefieldcomponentsHyEzandEz.Herexisthedirectionofthewavepropagationparalleltothefilm.ThewavevectorsA1andB1discussedabovehavethusamagnitudekn1,where ,wandcare,respectively,theangularfrequencyofthelightwaveandthespeedof

Fig.5.8(a)Alightwaveinthewaveguidemodeisaninfinitelywidesheet

ofplanewavewhichfoldsbackandforthinazigzagmannerbetweenthetopandthebottomsurfaceofthefilm.(b)Alightwavepropagatinginsidethefilmistotallyreflectedatthetwofilmsurfaces.Thefigure

showsthatinorderthatthewaveanditsreflectionscouldaddinphase,thetotalphasechangeforthelightwavetotravelacrossthethicknessofthefilm,upanddowninoneroundtrip,must

beequalto2mp.Thefigurealsoshowsthatthelightwavesuffersaphasechangeof and attheupperandlowerfilm

surfaces,respectively.Thesephasechangesdeterminethefielddistributionacrossthethicknessofthefilm,whichisshownattherightofthefigure

forthem=3waveguidemode(Tien1971).

Fig.5.9(right)Anyradiusofthequarter-circleattheright

sideofthefigurerepresentsapossibledirectionforthewavevectorB1.Intheblackregionofthecircle,thewavevectorrepresentsthesubstrateorairmode.Inthewhite

regionofthecircle,thewavevectorrepresentsthewaveguidemode,butonlyadiscretesetofthedirectionsinthisregionsatisfiestheequationofthewaveguidemodes.

Eachdirectionofthisdiscretesetrepresentsonewaveguidemodeandeachwaveguidemodehasitsownfielddistributionasshownintheleftsideofthefigure

(Tien1971).

lightinvacuum.Inthepictureofwaveoptics,thewavevectorsA1andB1arethenormalsofthewavefronts,whenaninfinitelywidesheetofplanewavefoldsbackandforthinazigzagmannerbetweenthetwofilmsurfaces(Fig.5.8a).Nowconsideranobserverwhomoveswiththewaveinthedirectionparalleltothefilm.Hedoesnotseethehorizontalcomponentsofthewavevectors.Whatheobservesisaplanewavethatfoldsupwardanddownward,onedirectlyontopoftheotherasshowninFig.5.8b.Thecondition,then,forallthosemultiplereflectedwavestoaddinphase,asseenbythisobserver,isthatthetotalphasechangeexperiencedbytheplanewaveforittotraveloneroundtrip,upanddownacrossthefilm,shouldbeequalto2mp,wheremisaninteger.Otherwise,ifafterthefirstreflectionsfromtheupperandlowerfilmsurfaces,thephaseofthereflectedwavediffersfromtheoriginalwavebyasmallphased,thephasedifferencesafterthesecond,third,...,reflectionswouldbe2d,3d,...,andthenthewavesofprogressivelylargerphasedifferenceswouldaddfinallytozero.AsshowninFig.5.8b,theverticalcomponentsofthewavevectorsA1andB1haveamagnitude ThephasechangefortheplanewavetocrossthethicknessWofthefilmtwice(upanddown)isthen .Inaddition,thewavesuffersaphasechangeof duetothetotalreflectionattheupperfilmboundaryand,similarly,aphasechangeof atthelowerfilmboundary.Herethephase and represent,infact,theGoos-

Haenchenshifts(Lotsche1968).Consequently,inorderthewavesinthefilmcouldinterfereconstructively,thecondition

musthold,whichistheconditionforthewaveguidemodes.Herem=0,1,2,3,...,istheorderofthemode.AccordingtoBornandWolf(1970)onthetheoryoftotalreflection,

fortheTEwaves,and

fortheTMwaves.

Itisclearthatinspiteofthezigzagwavemotiondescribedabove,thewaveinthewaveguidemodeappearstopropagateinthehorizontaldirectiononly;theverticalpartofthewavemotionsimplyformsastandingwavebetweenthetwofilmsurfaces.Toavoidconfusion,itisdesirabletousebandvexclusivelyforthephaseconstantandthewavevelocityparalleltothefilm.Thus,

Anotherquantitywhichwillalsobeusedfrequentlyistheratiob/k.Asshowninequation(5.9),itistheratioofthespeedoflightinvacuumtothespeedofwavepropagationinthewaveguide.

Aftersubstitutingequations(5.7)and(5.8)intoequation(5.6),Tien(1971)foundthatboth(5.6)and(5.9)aretranscendentalequations.Fortunately,thetranscendentalfunctionsinvolve only.Foragivenn0,n1,n2,andmonecanreadilycomputebothb/kandWforacommon ,andthentabulateb/kandWbyassigningdifferentvalues

for .ThecurvesshowingWversusb/kusingmastheparameterarethemodecharacteristicsofthewaveguide(seeFig.5.15below).

Tosummarize,anyradiusofthequarter-circleshowninFig.5.9representsapossibledirectionforthewavevectorB1describedabove,and istheincidentanglemeasuredbetweenthewavevectorandtheverticalaxis.Thewaveguidemodesoccurintherange

.Withinthisrangeof thereisadiscretesetofthedirectionswhichsatisfiestheequationofthemodes(5.6).Eachdirectioncorrespondstoonewaveguidemodeofthefilm.Thehorizontalcomponentofthewavevector, ,determinesthewave

motionparalleltothefilm,whileitsverticalcomponent, ,determinesthestandingwavefieldpatternacrossthefilm.AsshownintheleftsideofFig.5.9,whenm=0thestandingwavepatternhasaformsimilartoahalf-sinewave.Whenm=1,ithasaformsimilartoafullsinewave,andsoon.Theairandsubstratemodesoccurintherange ;theyoccupytheblackregionofthequartercircle.As isvariedcontinuouslyfrom0to fortheairmodesand

to forthesubstratemodes,thecorresponding andsweepthroughtheentirespaceofthesubstrateandtheairspace.Itisthuspossibletoexpressanyradiationfieldbysuperposingwavesoftheairandsubstratemodes.WhathasbeendiscussedhereisthereforesimplyanexpansionofthesolutionoftheMaxwellequationintoplanewavesofallpossibledirections.

5.2.2Waveequationandfielddistribution

Havingbeendescribedpurelyonanintuitivebasis,themodesoflightwavepropagationcannowbederivedmathematically.Forsimplicity,assumethelightwaveinthefilmtobeinfinitelywideintheYdirectionsothat (Fig.5.5).LetXbethedirectionofthewavepropagationparalleltothefilm.TheMaxwellequationsinEyforTEwaves(orHyforTMwaves)canbereducedtothewaveequationbelow

wherenJistherefractiveindexofthemediumj.Thesubscriptsj=0,1,and2denotethesubstrate,thefilm,andtheairspace,respectively.Atimedependenceexp(-iwt)isusedinequation(5.10),where .Thesolutionofthewaveequationisintheformofexp

,whichmaybesubstitutedintoequation(5.10)toobtain

Theboundaryconditionsatthefilm-airinterfacesdemandthesamewavemotionparalleltothefilminallthethreemediaconsidered;thiscanbewrittenas

Allthefieldsthusvaryintimeandxaccordingtothefactor.Thiscommonfactorwillbeomittedinallthelater

expressionsforsimplification.Combiningequations(5.11)and(5.12)givesanimportantrelation

Inthefilm, and arethehorizontalandverticalcomponentsofthewavevectorA1orB1discussedbefore.Theyarerespectively

and .Inthewaveguidemodes,onecanfindfromequation(5.13)andfromthecondition that , isreal,and and areimaginary.ThefielddistributioninFig.5.10aisthusastandingwaveinthefilmandexponentialinthesubstrateandintheairspace.Next,forthesubstratemodes,thereholdsequation(5.13)andfromthecondition that and arereal,butisimaginary.Thefieldsinthiscasearestandingwavesinthefilmandinthesubstrate,butexponentialintheairspace(Fig.5.10b).Finally,fortheairmodes, ,and , ,and arereal.Thefieldsinallthethreemediaarenowstandingwaves(Fig.5.10c).Itisconvenienttodenote by whenitisrealandby whenitisimaginary.For thewaveguideisasymmetric.Theupperandtheupperandlowerfilmsurfacesarechosentobe and .Thethicknessofthefilmisthen .

Thefielddistributionsarederivedbychoosingz=0atthepositionwhereEyismaximumforanywaveguidesubstrate,orevenairmode,andEy=0foranyoddairmode.Itisimportanttonotethatthesepositionsofz=0aredifferentfordifferentmodesinanasymmetricwaveguide.Thesechoicesarenecessarytosimplifymathematicssothatthefielddistributionsofvariousmodescouldbeeasilywecanvisualized.Toavoidconfusion,EyofaTEwaveonlyisconsideredbelow.

Forthewaveguidemodes,asmentionedearlier,thewavesuffersaphasechangeof attheupperfilmsurface,andaphasechangeof

atthelowerfilmsurfacebecauseoftheinertialtotalreflections.Thefieldsatthetwofilmsurfacesmustthereforebe and

,respectively,whereAisaconstant.Letthefieldatz=0beamaximumvalue,A.Thenonecanchoose sothatthefieldattheupperfilmsurface, ,canbeA .Similarlyonecanchoose sothatthefieldatthelowerfilmsurface, ,canbeA ifm=evenand-A ifm=oddsshownin

Fig.5.10a.Thesechoicesgive ,whichsatisfiesequation(5.6).TheboundaryconditionsrequireEyandtobecontinuousatthetwointerfaces.Therefore,

Fig.5.10Theelectricfielddistributionof(a)aTEwaveguidemode;(b)aTEsubstratemode;(c)aTE(even)airmode(Tien1971).

intheairspaceand

inthesubstrate.

Forthesubstratemodes,oneagainassumesamaximumfieldAatz=0andchooses (Fig.5.10b).Thefieldat isstillAandthatintheairspaceisstillA .ThefieldatthelowerfieldsurfaceisthenA andthatinthesubstrateis

Fortheairmodes,theevenandoddmodesmustbetreatedseparately.Foranasymmetricwaveguide,thez=0planecanbechosenanywherebetween and .However,onceitischosen,thesamez=0planeshouldbeusedforalltheairmodes.Fortheevenmodes,thefieldisamaximumatz=0andthefieldsatthetwofilmsurfacesareA andAcos ,respectively(Fig.5.10c).Theboundaryconditionsrequirethefieldsinthesubstrateandintheairspaceintheform

wherej=0and2.Fortheoddmodesthefieldiszeroatz=0andisAand-A atthefilmsurfaces.Thefilmsinthesubstrate

andairspacearethen

wheretheplussignisforj=2andtheminussignisforj=0.TheresultsdiscussedabovearesummarizedinTable5.4.

Mathematically,thefielddistributionsdescribedaboveareidenticaltothoseoftheproblemofasquarepotentialwellinquantummechanics.Heretheairspaceandthesubstratearethepotentialbarriers.Thewaveenergyisdividedhereintothehorizontalandverticalcomponents,keepingthetotalenergyconstant.Itistheverticalcomponentofthewaveenergythatnegotiates

Table5.4Electricfielddistributionin(a)awaveguidemode,(b)asubstratemode,and(c)theevenandoddairmodes(Tien1972)

Waveguidemode

Medium Ey(TEwave)

Film =b =b1 A

Substrate =b = A

Air-space =b = A

Substratemode

Medium = Ey(TEwave)

Film =b =b1

Substrate =b =b0

Air-space =b = A

Evenandoddairmodes

aInderivingtheseexpressions,wehavechosenz=0atthepositionwhereEyiseitherzeroormaximum.Thesepositionsofz=0arethereforedifferentfordifferentmodes.

thepotentialbarriersmentionedabove.Thewavevectorrepresentsthe

momentumanditssquare,thewaveenergy.Withintheinterval and,becauseofthelargehorizontalcomponentofthewavevectorb,

theverticalcomponentoftheenergyissmallenoughsothatthewave,ortheparticle,istrappedinthepotentialwell.Themodespectrumortheenergylevelisthusdiscrete(waveguidemodes).Asthehorizontalcomponentofthemomentumisreducedtoavalue ,theverticalcomponentofthewaveenergyislargeenoughtoovercomethelowerpotentialbarrier.Thewavefunctionspillsovertheentiresubstratespaceandoneentersintotheregionofthesubstratemodes.Themodespectrumortheenergylevelisnowcontinuous.Astheverticalcomponentofthewaveenergyisincreasedfurtherbyreducingbbelow thewavecanspillovertheupperandthelowerbarriers.Themodespectrumremainscontinuousanditbelongstotheairmodes.

5.2.3OpticalmodesinepitaxialLi(NbTa)O3waveguides

Solid-solutiongrowthof single-crystalfilmsonLiTaO3substrateshasbeendiscussedabove.ThesefilmsaregrownbyEGM(epitaxial

growthbymelting)method.However,thespecialprocessusedbyTienetal(1974)permittedobtainingverythinfilmswithagradedcomposition.Thecompositionofeachfilmismaximumattheair-filminterface,anditdecreasesgraduallytozerotowardsthesubstrate,asillustratesbycurveAinFig.5.11b.Becauseofthisgradedcomposition,anyeffectduetomismatchinlatticeconstantbetweenthefilmandthesubstrateisminimized,andconsequentlyfilmsasgrownareuniformandsmooth.InFig.5.11a,thezaxisisnormaltothesurfaceofthefilm,andz=0andz=daretheair-filmandfilm-substrateinterfaces,respectively.Alltheopticalmeasurementswereperformedbyusinga0.6328-mmhelium-neonlaser,andthexaxiswaschosenasthedirectionoflightwavepropagation.Becauseofthedifferencesintherefractiveindicesandthegradedcompositionofthefilm,therefractiveindexvariesinsidethefilmasshownbycurveAinFig.5.11c.Thesolid-solutionfilmhas andathicknessof3.87mm.Thefilmsformedexcellentopticalwaveguides;allthewaveguidemodesobservedarewellseparated,andtheycanbeindividuallyexcitedbyaprismcoupler.Moreover,severalfilmshadoneTEandoneTMwaveguidemodeonly.Tienetal(1974)reportedsomeinterestingobservationsofthewaveguidemodesanddiscussedasimplemethodofcalculationforthegradedwaveguides.Thissimplemethodcanbeusedforcalculationoftheeffectiveindicesofthewaveguidemodesaswellasfortheevaluationoftheindexdistributioninthefilm.Theprismcoupler(Tien1971;Tienetal1972)isanimportanttoolforthestudyofthefilmproperties.

Tostudythewaveguidemodes,afilmwithnineTEmodeswaschosen.ThefilmwasgrownparalleltooneofthecleavageplanesofLiTaO3.Thecaxisthusformsanangleof33°fromthesurfaceofthefilm(Fig.5.11(a)).Letabeaprojectionofthecaxisonthefilmandletbbenormaltoa.TheTEwaveisanordinarywavewhenthelightpropagatesalonga,and

Fig.5.11(a)Positionofthec-axiswithrespecttothegeometrical

axesinasolid-solutionLiNbO3-LiTaO3film.(b)CurveAshowsthegradedcompositioninthefilm.(c)CurvesAandBshow,respectively,theindexvariationinasolid-solutionfilmandthatinadiffusedfilm.(d)Photographofthemlinesofasolid-solutionfilm.(e)Photograph

ofthemlinesofauniformwaveguidemadeofaTa205filmonaglasssubstrate(Tienetal1974).

Fig.5.12(a)Modeindicescalculatedonthebasisofanexponentialdistributionofrefractiveindex.

(b)Modeindicesmeasuredfromoneofthesolid-solutionfilms.(c)Modeindicescalculatedonthebasisofanindexdistributionintheformofa

Fermifunction(Tien1974).

itisanextraordinarywavewhenthelightpropagatesalongb.Themlines(Tien1971;Tienetal1969)observedforthecaseoftheordinarywaveareshowninFig.5.11(d).TheTMwaveisalwaysanextraordinarywave.Consequently,asthedirectionofthelightpropagationvariesfromatob,theeffectiveindices(Tienetal1972)b/koftheTEmodesvarycontinuously,whereasthoseoftheTMmodesdonotvary.Toavoidconfusion,onecanuse'uniformwaveguides'forthosehavingaconstantrefractiveindexnFthroughoutthefilmand'gradedwaveguides'forthoseinwhichnFvariesinz.Forcomparison,themlinesobservedinauniformwaveguidemadeofaTa2O5filmonglassareshowninFig.5.11e.Thedifferencebetweenthemodepatternsofauniformandagradedwaveguideisthatthemodespacingincreaseswiththemodenumbermintheformer,whereastheoppositeistrueinthelatter.

Modesinthegradedwaveguideshavebeencalculatedbymanyauthors(Tayloretal1972).Inparticular,aneleganttheoryhasbeen

developedbyConwell(1973).Sheusedanindexdistributionforthefilminthefollowingform:

where istherefractiveindexofthesubstrate.SuchadistributionisillustratedbycurveBinFig.5.11c.ThistheorywasusedtocalculatetheeffectiveindicesofthemodesforthecaseofaTEwavepropagatingalonga.Forhavingninemodes,theargument(Conwell1973)oftheBesselfunctionX=29,d=2.23mm, ,and

werechosen.TheresultsofthecalculationsareplottedinFig.5.12aandtheyshouldbecomparedwiththemeasuredvaluesofFig.5.12b.Obviously,theexponentialdistributiongivenbyequation(5.14)doesnotapplytothesolid-solutionfilms,sincethemodespacingshowninFig.5.12adecreasesmuchmorerapidlywiththemodenumbermthanthoseobservedinFig.5.12b.

Searchforatheorywhichappliestoanydistributionofthefilmhasled

totheWKBmethod(DickeandWittke1960).Recallthatforauniformwaveguidethemodeequations(Tien1971)are

Hereweareconsideringazigzagplanewavepropagatinginthefilmas ,wherebandbarerespectivelytheaandxcomponentsofthewavevector,manddarerespectivelythemodenumberandthefilmthickness, ,wherewistheangularfrequencyandcisthevelocityofthelightwaveinvacuumand,finally, and arerespectivelythephasesadvancedbythezigzagwaveduetothetotalreflectionsofthewaveatthefilm-substrateandfilm-airinterfaces.OnthebasisoftheWKBmethod,foragradedwaveguideofanyindexdistribution

Here istheturningpointoftheWKBmethodand,at , and.Consequently,a,canbeconsideredasafunctionofb.For

Fig.5.13ValuesoftheintegralAversusthemodeindices,b/kforthetwocasesdescribedin

thetext(Tieneta11974).

Table5.5Modeindices,b/k's(Tienetal1974)

Case1:9modes

m Conwell'stheory Tien'smethod

0 2.2400 2.2399

1 2.2196 2.2192

2 2.2059 2.2057

3 2.1961 2.1959

4 2.1889 2.1888

5 2.1838 2.1835

6 2.1802 2.1800

7 2.1781 2.1778

8 2.1771 2.1771

Case2:2modes

m Conwell'stheory Tien'smethod

0 2.1897 2.1898

1 2.1789 2.1790

allthefilms, issmallandtheindexofthefilmissubstantiallylargerthanthatoftheair;onecantake .AccordingtothestandardlinearapproximationoftheWKBmethod(DickeandWittke1960)attheturningpoint, isobviouslyp/4.Lettheintegralin(5.17)beA.Withagivenindexdistribution ,Tienetal(1974)couldcomputeb(z)from(5.18)and from(5.19),andthenevaluatetheintegralAforanyvalueofb.Infact,wecanplotAversusb/k,andthevaluesofb/kcorrespondingtoA=(m+0.75)pform=0,1,2,...,aretheeffectiveindicesofthewaveguidemodes.Tosubstantiatethis

method,thedistributiongivenbyequation(5.14)wasusedandthecalculationswereperformedfortwocases.Onecasehasninemodesand ,ns=2.177,andd=2.23mm;theothercasehastwomodesonlyandDn=0.043,ns=2.177,andd=0.931mm.TheA-versus-b/kcurvesforthesetwocasesareshowninFig.5.13.TheresultsobtainedbythismethodarethencomparedinTable5.5withthosecalculatedfromtheexacttheoryofConwell(1973).Theagreementbetweenthetwomethodsiswithin .

Itisalsopossibletouseequations(5.17)-(5.19)toevaluatetheindexdistributionofthefilmfromthemeasuredb/k'softhewaveguidemodes.Asnoticedearlier,themodeindexb/kistherefractiveindexofthefilmattheturningpoint.Thelocationsoftheturningpointsforthewaveguidemodescanbesolvedintermsofthemeasuredb/k'sbyforming,basedon(5.17),asetofsimultaneousequations,oneequationforeachmode.Extensivecalculations

ofthisnaturehaveshownthattheindexdistributionofthesolid-solutionfilmscanbecloselyrepresentedbyaFermifunction

SuchadistributionisshownbycurveAinFig.5.11b.Thereisaregionnearz=0,inwhichtherefractiveindexisrelativelyconstant,indicatingthebeginningoftheformationofahomogeneousepitaxiallayer.Thishomogeneousregionisfollowedbyabroadtransitionregionwheretherefractiveindexvariesmorerapidly.Theparametersdandadetermine,respectively,thethicknessofthefilmandthesharpnessofthetransitionregion.Currently,theseparametersarecorrelatedwiththegrowthprocess.Fortheparticularfilmdescribedabove,Dn=0.0710,a=0.286mm,andd=3.87mm.Basedontheseconstants,thecalculatedmodeindicesareshowninFig.5.12c,whichagreeswiththemeasurementshowninFig.5.12bwithintheexperimentalerroroftheorderof .

5.2.4Characteristicsofout-diffusedwaveguides

Theasymmetricplanarslabwaveguide,producedbydepositingauniformguidinglayeronasubstrate,andtheplanargradedindexguidearesimilarintheirwaveguidingpropertiesbutdiffersomewhatindetail.Carruthersetal(1974)comparedtwocharacteristicsoftheslabandgradedguides,namely,thenumberofthemodesNsupportedbytheguideandtheeffectivepenetrationdepthwlforenergyinthei-thmode.

TherefractiveindexprofilesfortheslabandgradedguidesareillustratedschematicallyinFig.5.14.Forbothguides,n=1forx<0,and for .Fortheslab,

andforthegradeguide,

Thewavefunctionsfortheslabaresinusoidalintherange andexponentiallydecayingoutsidethisrange.Formodessufficientlyfarfromcutoff,mostoftheenergyisconfinedwithin .Thus,neglectingtheevanescenttail,onecandefineaneffectivepenetrationdepthforallTEslabmodesas

Fig.5.14Refractiveindexprofilesfor(a)anasymmetricplanar

slabwaveguideand(b)aplanargradedindexwaveguide.TE0andTE1wavefunctionsareindicatedschematicallyalongwithturningpointsx1(Carrutherseta11974).

Thevariousmodeshavepropagationconstantsbithatareplottedasindexlevels inFig.5.14(a),with andltheopticalwavelength.ThenumberofTEmodesthatcanbesupportedistheintegerlessthan

withasimilarexpressionforTMmodes(NelsonandKenna1967).Theanalogywiththequantummechanicalproblemofaparticleinaboxhavingturningpointsatx=0andx=Bisapparent.Intheopticalproblem,theturningpointsrepresentreflectingsurfacesforraystrappedintheguide.

Thegradedindexproblem,likemostquantummechanicalpotential-wellproblems,cannotbesolvedanalyticallywithoutapproximationexceptinspecialcases.Marcuse(1978)givesWKBsolutionstoathree-segmentpiecewiselinearapproximationtoanarbitraryindexprofile.Ifequation(5.22)isapproximatedbylinearsegmentsthat

passthroughthepoints , , and ,thenitisfoundthat

Thefactor1.38isofcoursedependentonthechoiceof ,butitcanbeseenthatNsandNgaresimilarforcomparableA,Banda,bparameters.Forexample,ifA=a,then whenB=0.69bforlargeN.

ThewavefunctionsandindexlevelsfortheTE0andTE1modesareshownschematicallyinFig.5.14b.Theintersectionoftheindexlevelwiththecurven(x)definestheturningpoint ,atwhichanequivalentopticalrayoraquantum-mechanicalparticleinasimilarpotentialwellwouldreverseits

direction.Mostoftheenergyinamodefarfromcut-offisconfinedtotheregion ,sothepenetrationdepthcanbedefinedas

where increaseswithincreasingmodenumberi.Thewavefunctionsareoscillatoryintherange ,andincreaseinamplitudenear ;theydecayexponentiallyoutsidethisrange(Marcuse1978;Smithgalletal1977;Conwell1973).

Toobtainanestimatefor ,thequantityn(x)maybeapproximatedcrudelybyastraightlinetangentton(x)atx=0asshowninFig.5.14b.Itcanbeseenthatthevalueof obtainedfromsuchanapproximationwillbesmallerthanthetruevalueandwillgivealowerboundon .Forthisapproximation,Marcuse(1978)found

with86%oftheTE0modeenergywithin .Combiningequations(5.25)and(5.27)yields

Solutionsforthewavefunctionsofthe erfc(x/b')profile(seeFig.l.9),whichshouldbesimilartothosefor ierfc(x/b),havebeencomputednumericallyandcomparedgraphicallywiththosefortheslabguide(Smithgalletal1977).Theseresultsshowclearlythatthemodeenergyisburiedmoredeeplyforhigherordermodes.Herea'=a,b''=0.73bforcoincidenceatDn=a,a/2,and0.

Theexponentialfunction

alsogivesareasonablygoodfittothedata,asshowninFig.l.9.ForcoincidenceatDn=a,a/2,and0,Carruthersetal(1973)requirea''=a,b"=0.506b.AsshownbyConwell(1973),theexponentialprofile

isoneofthefewthatgivesexactanalyticalsolutionstothewaveequation.Thesesolutionsalsoshowanincreaseinthestrengthofthewavefunctionsasxapproachestheturningpoint,withdeeperpenetrationforhigher-ordermodes.Althoughthenumberofmodes,wavefunctionsandpropagationconstantscanbecalculatedwhena"andb"areknown,simpleexpressionsforNandwintermsofa"andb"arenotgiven.However,usefulexpressionscanbeobtainedincertainlimitsasfollows.

Definethefunctions

then,for

where and ,arerelatedsothattheBesselfunction

Nearcut-off, ,andinthislimitthezero'sinequation(5.33)aregivenapproximatelyby

Themaximum isgivenbyequation(5.30);andthenumberofmodesisthelargestintegeri+1obtainedfromequation(5.34)atcut-off

whichmaybecomparedwithequation(5.25)forb=1.97b".Becauseofitsextensivetail,theexponentialprofileoverestimatesbothNand.

Theturningpoint maybeobtainedbyequatingtheright-handsideofequation(5.32)to ;then

Intheotherlimit,farfromcut-off,miand ,arelarge;fori=0,equation(5.33)issatisfiedfor

Equation(5.37)maybeinsertedintoequation(5.32)toobtainthedispersioncurvefarfromcut-off.Theturningpointmaybeestimated

byequatingtheright-handsideofequation(5.32)to for ;then

Fig.5.15Normalisedguideindex

versusnormalisedfrequency (Carruthersetal1974).

whichisnearlyidenticalwithequation(5.27)forb"=0.506b.

UniversaldispersioncurvessuitableforbothTEandTMmodesoftheexponentialprofileinequation(5.29)calculatedfromcomputersolutionsofequations(5.32)and(5.33)for areplottedinFig.5.15.TheexponentialTE0modeshowsmuchlessdispersionthantheTE0modeforaslabhavingthesamecut-off,thatis,A=a",B=4b"/3.

ItisclearfromtheprecedingdiscussionthatNandwforthegradedguidecanbeadjustedjustasfortheslabguideprovidedaandbcanbecontrolledindependently.Toassuresinglemodeoperation,itisnecessarytorestrictNtotherange: .SuchguideshavebeenmadeinLiNbO3for mmbyrestrictingttoafewminutes.Anexampleofasinglemodeguideisasampleforwhicht=5minandT=1100°C,yieldinga=1.65x10-4andb=20mm.Fromequations(5.25)and(5.27),respectively,itiscalculatedthat and .Ontheotherhand,usingConwell'sexponentialapproximation(Conwell

1973),itisfoundthatNe=1.95and mm.

From(5.27)and(5.38),thepenetrationdepthw0islimitedbytherangeofsurfacegradient a/bavailablebyvaryingT.ForLiNbO3,

mm-1ispracticallytemperatureindependentbecause,so mmfortheavailablerangeT<Tc.Therefore,itmaybe

preferabletoout-diffuseatlowertemperatureswheretherequireddiffusiontimesarelongertomaintainbettercontrolovertheprocess,i.e.theheatingandcoolingtransientswillhaveasmallereffectontheprofile.ForLiTaO3,ontheotherhand, a/bcoverstherange

,so coverstherange6-16mmasTvariesfrom1400°Cto930°C.Therefore,smallerpenetrationdepthsareachievedathighertemperatures;however,theshorttimesrequiredmakecontroloftheprocessdifficult.Anevengreaterchangeofpenetrationdepth,w0withTwouldbefoundinmaterialsforwhichQvandQDdiffermorewidely.

Thus,verylow-lossout-diffusedlayerscanbefabricatedwithcharacteristicssimilartothoseofasinglemodeslabguidethickness

,where mmforLiNbO3and forLiTaO3.Theseratherlargeeffectivewidthsmaylimittheoperationofdevicesbasedoninteractionswithsurfacefieldsofshortwavelength.Ontheotherhand,thelargewidthmayproveadvantageousinapplicationswheretheplanarguideisconvertedtoaridgeorstripguidebyetching.Inthesecases,fieldscanbeappliedalongedgesoftheridge;andcouplingcantakeplaceattherelativelylargefacets.

5.2.5Propertiesofdiffusedwaveguides

Toestablishtheparametersoftherefractiveindexprofileindiffusedwaveguides,thefollowingmethodsareused:

1)interferentionalmicroscopy,2)directmeasurementofTiconcentrationdistributioninthewaveguidecross-section(X-raymicroanalysis,Augerspectroscopy),definitionofthefunctionn(y)fromtheobservedspectrumoftheeffective values(Naitohetal1977;Zolotovetal1976).

Inviewofthefactthatinterferentionalmicroscopyisonlysuitableforastudyofthickenough(>10mm)diffusedlayersandthesecondgroupofmethodsrequiressophisticateddevicesandasubsequentcalibration,Zolotovetal(1980)usedidentificationofdiffusedwaveguideprofilesfromthespec-tramofeffective values.Theparametersofn(y)distributionoveradiffusedwaveguidewereidentifiedfromthespectrumof valuesusingthecombinationoftheparabolicandexponentialfunctions(Zolotovetal1976)forwhichthereexistsananalyticalsolutionofdifferentialequationsofthetype

thatdescribetheelectricfielddistributioninweak diffused

waveguides.

ThedependenceofthewaveguideparametersonthetimeofdiffusionwasdeterminedusingmeasurementsforE-andH-waves(ifthecrystalorientationisfixed,theordinaryrefractiveindexn0(y)correspondstoE-waveswhiletheextraordinaryrefractiveindexne(y)correspondstoH-waves).InthewaveguidesinvestigatedbySugiietal(1978),two-threeE-modesandfive-sixH-modescouldbeexcitedatawavelengthof0.63pro,whileatawavelengthof0.44mmfour-fiveE-modesandsix-nineH-modeswereobserved.Thespectrumofvalueschangedwithdiffusiontime.Theanalysisofthespectra

obtainedhasshownthatthewaveguideprofilesforordinaryandextraordinarypolarizationsareapproximatedfairlywellbythecombinationoftheparabolicandexponentialfunctions

Hereaandbareparabolaparameters,histheexponentparameter,cisthedistancefromtheparabolavertextoitsconjugatepointwiththeexponent.

Thedistributionsof obtainedforawaveguidewithdifferentdiffusiontimesarerepresentedinFig.5.16andTable5.6givesthenumericalvaluesoftheirparameters.ThedistributionsoftherefractiveindicesofTi-diffusedLiNbO3waveguidesforwaveswithdifferentpolarizationsdifferpracticallyonlyintheincrementoftherefractiveindexonthewaveguidesurface,Dn,andintheexponentialfunctionparameterh.ThedifferenceAncanbeexplainedbydifferentproportionalitycoefficientsbetweenthetitaniumconcentrationCT1,andtheincrementsoftheordinaryandextraordinaryrefractiveindices.Theassumptionofdirectproportionalitybetween and isconfirmedbythelackofdependenceoftheratio onthediffusiontime(seeTable5.6).

Thedifferenceintheexponentparameterhinthedistributionsofn0(y)andne(y)isduetothefactthattheincrementoftheextraordinaryrefractiveindexiscaused,besidestitaniumdiffusion,alsobythereversediffusionofLi2Owhichincreasessubstantiallythewaveguidelength.

Themodefieldsintheabove-mentionedwaveguidesareobtainedfromthesolutionofthewaveequation(5.39)forordinarywaves(E-polarization)and

Table5.6Numericalvaluesofdiffusedwaveguideparameters( )(Zolotoval.1980)

,h E-waves H-waves

b/a c/a h,m b/a c/a h,mm

5 0.0161 2.99 -0.6 0.89 0.88 0.0374 2.99 -0.6 0.98 3.32 2.32

10 0.0127 4.27 -0.6 0.89 1.23 0.0296 4.00 -0.6 0.97 4.10 2.33

12 0.0115 4.56 -0.56 0.9 1.09 0.0259 4.56 -0.56 0.97 4.73 2.25

15 0.0112 5.20 -0.45 0.85 1.63 0.0231 4.95 -0.45 0.97 4.83 2.26

19 0.0088 6.27 -0.45 0.85 1.86 0.0192 6.17 -0.45 0.95 4.60 2.18

Fig.5.16Distributionofordinary(a)andextraordinary(b)refractiveindicesforTi-diffusedwaveguides(dashedlinesindicatecalculatedvalues).1)diffusiontime h;

2)10h;3)15h(Zolotovetal1980).

havetheform

here isadegenerategeometricalfunction, istheBesselfunction

Forextraordinarywaves(H-polarization)

Fig.5.17DispersionofordinaryandextraordinaryrefractiveindexincrementforwaveguideswithdiffusiontimetD=12h(dashedlinesindicatecalculatedvalues-seethetext)(Zolotoveta11980).

Fig,5.18(right)Opticalwaveguidingapparatus(KaminowandCarruthers1973).

TheconstantsC1,C2andC3aredeterminedfromtheconditionofequalitytozeroofthewavefunctionattheboundarywithairandcontinuityofthefuctionatthesewingpoint

Animportantcharacteristicofopticalwaveguidesisthedispersionoftherefractiveindexincrement.Thedataonthewaveguidedispersionarenecessaryforcreationofsomeintegro-opticaldevices,inparticular,nonlineartransducers.Zolotovetal(1980)investigatedthedispersionofwaveguidecharacteristicsinawidewavelengthrange:0.44,0.53,0.63,0.89,1.06,1.15mm.Itisanexperimentallyestablishedfactthataslvariestheshapeoftheprofilesofno(y)andne(y)remainsunaltered,anditisonlytherefractiveindexincrementsDnoandDnethatexhibitdispersion(Fig.5.17).

Guidingcanbedemonstrated(Tien1971;TienandUlrich1970)withtheprismcouplerarrangementshowninFig.5.18,wherecrystalsareorientedwitha,b,andcalongz,x,andy,respectively,andanincidentbeamispolarizedasanextraordinary(TE)wave.Abrightstreakappearsalongthesurfacewhenqisadjustednearanangleq0slightlylessthanthecriticalangle.Thereisnoobservabledecayinthestrengthofthescatteredlightoveracentimetrelengthofthestreak,whichsuggeststhatthelossis<1dB/cm.Themodesradiatesfromtheendoftheguide,producingafar-fieldpatternnarrowintheydirectionbutelongatedinthexdirection.Measurementofbeamangleaprovidesanestimatefortheextenthofthefieldinthexdirectionintheguide: .ForsampleI-3, (KaminowandCarruthers1973),whichindicatesthat,beingcoupled,theopticalenergyforthe

modesisconfinedtotheneighbourhoodofmaximumDnenears=0,wheresisthedepth.

Anoutputprismcouplerproducesawell-definedspotatq'=q0whenq=q0.Afaint'm-line'passesthroughthespot,indicatingonlyminorscatteringintodegeneratemodespropagatinginotherdirectionsintheplane.Waveguiding,asdemonstratedbythecoupled-outspot,existsoverarangeofanglesDq0.CalculationsshowthatDq0foreachsamplecorrespondstoarangeofwaveguidepropagationconstantsDbgivenapproximatelyby2pA/l.Thus,thewaveguidesupportsalargenumberofunresolvedmodes.Toproduceguidesthatsupportonlyafewlow-ordermodes,theproductA1/2BmustbereducedbyadjustmentoftandT.

5.3Secondharmonicgenerationinwaveguides

Integratedopticsisawidefieldforheighteningtheefficiencyofnonlinear

interactions.Theuseofopticalwaveguidespermitsobtaininghighintensitiesoflight,inafilmwiththicknessoftheorderofthelightwavelength,fromcomparativelylow-powersources,e.g.gaslasers.Asdistinctfromthecasewhennarrowingthelightbeamtosmalldimensionscausesitslargediffractiondivergence,asmallcross-sectionofthebeam(andthereforeitshighdensity)inawaveguideremainsunchangedthroughout.Anotheradvantageofthin-filmwaveguidesisthepossibilitytoattainphasematchingofinteractingwavesduetomodedispersion.Thisallowstheuseofisotropicmediapossessinghighnonlinearcoefficients.Anisotropicwaveguidesdonotrequiretemperaturetuningforattaininga90-degreematchingthatcanbereachedthroughthechoiceoftherefractiveindexprofile.

Butinspiteoftheobviousadvantagesofopticalwaveguidesfornonlinearconversion,thesuccessinthisfieldremainsrathermoderate.Inparticular,theefficiencyofsecondharmonicgenerationreachedexperimentallyinvariousmaterialswastwoorthreeordersofmagnitudelowerthanthetheoreticallypredictedone(Itoetal1974;VanderZieletal1975),whichisobviouslyexplainedbyalowqualityoftheguides.Toobtainaneffectivenonlinearconversion,thefilmnonuniformitythroughthethicknessmustnotexceed0.01mmper1min.Non-observanceofthisconditionleadstophasemismatchand,therefore,toaloweringofthesecondharmonicpower(Boyd1972).

Planarwaveguidesonthebasisoflithiumniobatearenowpromisingforthestudyandpracticaluseofnonlinearsecond-ordereffects.Thisisconnectedwithalargevalueofthenonlinearsusceptibilitytensorofthecrystalaswellaswiththepossibilityofangularandtemperaturetuningofmatchedinteraction.

Weshallmentionsomemosttypicalpapersoutofacomparativelysmallnumberofpublicationsconcerningnonlinearprocessesinplanar

waveguides.

Fejeretal(1986)obtainedsecondharmonicgeneration(SHG)inalaseronagarnetwithneodymiuminaTi:MgO:LiNbO3waveguide,inwhichatemperature-inducedphasematchinggeneratedradiationatawavelengthof532nmwithanefficiencyof1.5×10-2.SHradiationof22mWwasobtainedinanon-stopregime;inapulsedoperationtheconversionefficiencywasoftheorderof25%.Phasematchingwasreachedbothforthecase (thezerothmodeoffundamentalradiationisconvertedintothezerothmodeofsecondharmonic)andfor .

ThecorrespondingmatchingtemperaturesareequaltoT=102ºCand21.7ºC.

SHGinTi:LiNbO3waveguideswasobtainedbyArvidssonandLaurell(1986)andRegeneretal(1981)whoreached,usinganadditionalresonatorforproducingthefundamentalfrequency,asubstantialincreaseofthefieldstrengthinthewaveguide,whichresultsinasharpheighteningoftheefficiencyofnonlinearopticconversion.InasimilarwayRegeneretal(1981)reachedanefficiencyoftheconversionintoasecondharmonicoftheorderof10-2forameaninputradiationpowerof1.5mW.

Othernonlinearprocessessuchasdifferencefrequencygeneration(Uesugi1980;Suche1984),parametricamplificationandgeneration(Sucheetal1985)werealsoattainedinplanarwaveguides.

5.3.1Phasematchinginanopticalwaveguide

Asiswellknown,aneffectivesecondharmonicgenerationrequiresphasematchingofinteractingwaves.Inanisotropiccrystals,dispersionatfrequenciesoffirstandsecondharmonicsiscompensatedbyexploitingdifferentpolarizationsofinteractingwaves.Thephasematchingdirectionwillcoincidewiththedirectionofintersectionofindicatricesoftheirrefractiveindicesn(j0,w)=n(j0,2w),whichinthethree-dimensionalcaseisdeterminedbybirefringenceanddispersionofthecrystal.Ifthematchingdirectiondoesnotcoincidewiththeopticalaxis,theinteractionlengthwillbelimitedtothedivergenceofwavesofthefirstandsecondharmonicsduetobirefringence.Therefore,toobtainaneffectivenonlinearinteractionitispreferabletousea90-degreematchingwhichgivesnobirefringenceandinthethree-dimensionalcaseisreachedbytemperaturetuning.

Inopticalwaveguides,therefractiveindiceshaveincrementsDnoandDnerelativetothesubstrate.Iftheseincrementsexceeddispersionoftherefractiveindices,nw-n2watthefrequenciesoffirstandsecondharmonics,thenthenw-n2wcanbecompensatedbymodedispersion.Isotropicmediacanwellbeusedinthiscase,too.Inthecaseof'weak'waveguidesinwhichtheincrementoftherefractiveindexofthewaveguidinglayerismuchlessthantherefractiveindexofthesubstrate ,phasematchingisonlyduetobirefringence.Theuseofmodedispersionwidenssignificantlytheregionofphasematching.ThiscanbereadilyseenfromFig.5.19whichshowspossiblepositionsofmodeindicatricesatfrequenciesofthefirstandsecondharmonicsinananisotropicwaveguideinanegativecrystal.Theregionswhichcancontainindicatricesofordinarilyandextraordinarilypolarizedmodesaredashed,andtheoverlapoftheseregionsdeterminestherangeofpossiblematching.Foreachpairofmodes,phasematchingoccursatacertainangleatwhichmode

indicatricesintersect.Varyingthedepth,shapeoftheprofileorincrementoftherefractiveindexofawaveguide,wecanvarythematchinganglesofnonlinearmodeinteraction.Itshouldbenotedthattoperformsuchvariationsoneshouldknowthedependenceofphasecharacteristicsofawaveguideonitsstructureparametersandbeabletocontrolthemduringwaveguidemanufacturing.For

Fig.5.19Indicatricesofordinaryand

extraordinarypolarisationmodesinLiNbO3(Zolotovetal1979).

Ti-diffusedwaveguidesinLiNbO3,theanglesofpossiblemodematchingliewithintherange ,thatis,a90-degreematchingcanbeattainedwithouttemperaturetuning.

5.3.2Overlapoffieldsofinteractingmodes

Phasematchinginanopticalwaveguideisnotasufficientconditionforobtaininganeffectivenonlinearconversion.Thedecisiveroleisplayedbythedegreeofoverlappingofopticalfieldsofinteractingmodeswhichischaracterizedbytheoverlapintegral

whereYw(y)andY2w(y)isthetransversedistributionofmodefieldsatafrequencyofthefirstandsecondharmonics.Theoverlapintegralentersintheexpressionfortheefficiencyofsecondharmonicgeneration(derivedforthecaseofphasematchingintheplainwaveapproximation(ZernikaandMidwinter1973;Conwell1973):

wheredisanonlinearcoefficient,Ppumthepumpingpower,P2wthesecondharmonicpower,Ltheinteractionlength,lthepumpingwavelength,ntherefractiveindexofthesubstance,Wthebeamwidthinthewaveguideplane.

Asisseenfromtheexpression(5.41),theoverlapintegraldependsonthefielddistributionofmodeofbothharmonics,whichareverydifficulttofindfordiffusedwaveguidessincetheirprofilesarenotknowninadvance,buteveniftheywereknown,itisnotalwaysthatthereexistsananalyticsolutionofthewaveequationforthem.IfLiNbO3isused,thesituationbecomesevenmorecomplicatedbecauseananisotropiccrystalandwaveguideshavedifferentprofilesforordinaryandextraordinarypolarizations.Moreover,inTi-diffused

waveguidesofLiNbO3awaveguideformsnotonlyduetoTidiffusionintoacrystal,butduetoareversediffusionofLi2Oaswell.Theseprocesseshavedifferentkinetics,andthereforethewaveguideprofileforextraordinarypolarizationiscomplex.

ThemethoddevelopedbyZolotovetal(1977)wasusedtodetermineYw(y)andY2w(y).Thismethodpermitsdeterminationofthecharacteristics(includingmodefieldsanddispersiondependences)ofdiffusedwaveguideswithanyprofileofrefractiveindexdistribution.Themethodisbasedonapproximationoftheunknownwaveguideprofilebythefunctionsthatallowobtainingsolutionsofthewaveequationinananalyticform.InTi-diffusedwaveguidesofLiNbO3(Y-cut),theprofileofthetransversedistributionn0(y)forordinarypolarizationisdefinedbythecombinationofasmoothlysewedparabolaandexponent(5.40).

Fig.5.20Overlapintegralsfordifferentinteractionsversusdimensionlessthicknessaofawaveguide(dashedlinecorrespondstothicknessofsampleunder

investigation)(Zolotovetal1979).

TheoverlapintegralsI1m(m-1,2,3,4)fortheinteractiono+o=ewerecalculatedusingtheobtainedmodefielddistributionsinaTi-diffusedLiNbO3waveguide.ThedependencesofI1monthevalueofdimensionlessthickness fortypicalparametersoftheTi-diffusedwaveguide(seeTable5.6)areshowninFig.5.20.Thecalculationsdidnotmakeallowanceforinsignificantvariationsofthestructureparameterratiosc/a,h/awithvaryingasincetheydidnotpracticallyaffectthecharacterofthedependencesoftheoverlapintegralsI1m(a).TheoverlapintegralsInmofmodesinthickerwaveguides(a>6),wheren>1,isnotconsideredsinceinthesewaveguidesphasematchingisattainedforhighermodesonly(m>3),andthereforetheoverlapintegralsaresmall.

AnanalysisshowsthatforoptimizationofsecondharmonicgenerationinT-diffusedwaveguides,fromtheviewpointoftheoverlapintegralofinteractingmodesoneshouldchoosenotverythick

waveguideswiththeuseoflowermodeinteraction.

5.3.3Angularmatching

Secondharmonicgeneratedusingawaveguideobtainedby

thermodiffusionofTiintotheY-cutofLiNbO3.Thewaveguidemodespectrum wasmeasuredonagoniometerbyradiationoutputthroughaphotoresistivegrating(l=0.3462mm)depositedonthesurface(Zolotovetal1976).TheresultsareshowninFig.5.21.ModesH1-H4,E1andE2wereexcitedinawaveguideatawavelengthl=0.53mmandmodesE1andH1atawavelengthD=1.06mm.Figure5.22presentsindicatricesofrefractiveindicesofwaveguidemodesatthefrequenciesoffirstandsecondharmonics.Phasematchingconditionsareonlymetforthefollowingo+o=etypeinteractions:

TheindicatrixofthemodeH1doesnotintersecttheindicatricesofofmodesoffirstharmonic,andthereforethephasematchingforH1isunattainable.

Fig.5.21Distributionofrefractiveindicesandopticalfieldsforordinaryandextraordinarywavesofdiffused

waveguides:a)l=1.06mm,b)l,=0.53mm(Zolotovetal1979).

Fig.5.22Indicatricesofeffectiverefractiveindicesofdiffusedwaveguidemodes(Zolotovet

al1979).

Theprofilesofrefractiveindexdistributionforordinaryandextraordinarypolarizations,whichwererespectivelycharacterizedbytheparameters ,Dno=0.0035,ao=4mm,(c/a)o=0.7,ho=1.5mm, ,Dne=0.015,ae=14mm,(c/a)e=0.97,(b/a)e=-

0.63,he=8.5mmwerefoundfortheinvestigatedwaveguideonthebasisoftheobtainedspectra .

Themodefieldsoftheinvestigatedwaveguide(Fig.5.21)wereobtainedandtheoverlapintegralsI1m(m=2,3,4)weredeterminedusingtheprofiles.TheintegralI12ismaximumandclosetotheoptimumvalue(Fig.5.20),andtherefore

Fig.5.23Theoretical(dashedline)andexperimental(solidline)dependencesofeffectiveSHGonthepumpingpower(experimental)pointscorrespondtoCWlaserpumping

(D),apulsedlaserpumpinginfreegenerationregime(o)apulsedQ-switching,()(Zolotov,etal,1979).

theconversion wasused.PumpingwasrealizedbyYAG:Nd3+-lasersoperatinginpulsedandnon-stopregimes.Alightbeamwasfedinto(andout)withthehelpofrutileprismsinthedirectionofmatching,thebeamwidthbeing .

TheefficiencyofsecondharmonicgenerationasafunctionofpumpingpowerisgiveninFig.5.23.Themaximumconversionefficiencywasobtainedthroughpumpingof andmadeup16%.

Thedependenceoftheefficiencyofnonlinearconversiononthepumpingpower(seeFig.5.23)wasnoticeablyoverestimatedincalculationsascomparedwithexperimentalvalueswhichweresaturatedalreadyfor .Suchadifferenceisexplainedbynonuniformityofthewaveguideoverthickness andbytherefractiveindexinhomogeneities,inducedbysecondharmonicradiation,whichwereobservedatapumpingpowerof .So,afurtherincreaseinthenonlinearconversionefficiencywasduetotheimprovementofthewaveguidesurfacequalityaswellastotheheighteningofthethresholdoftheoccurrenceofoptical

inhomogeneities.

Thedependenceofsecondharmonicpowerontheanglebetweenthepump-

Fig.5.24Angulardependenceoftheoutputsecondharmonicpowerinadiffusedwaveguide(Zolotoveta11979).

ingwavepropagationdirectionandtheopticalaxisofthecrystal(Fig.5.24).Thefigureshowsthatthiscurveisnonsymmetricrelativetothecentralmaximum(theinteraction )sinceitsleftsideisoverlappedbythemaximacorrespondingtotheinteractions and

.Therelativeheightofthemaximaisinsatisfactoryagreementwiththevaluesoftheoverlapintegrals.Thewidthofthecentralmaximumwasfourtimesthetheoreticalvalue,whichisexplainedbyinhomogeneityofthewaveguide.

5.3.4Temperaturematching

Figure5.25showstheexperimentalsetupusedbyUesugiandKimura(1976).Thefundamental-frequencylaserbeamatawavelengthof1.064mm,generatedbyacwNd:YAGlaser,wasfedintoasingle-modefibrewitha×20microscopeobjective.Thecoredimensionofthefibrewasequalto5.5mmandtheindexdifferenceDnbetweenthecoreandcladwas0.25%.Thefibrewasthenbutt-joinedtoaLiNbO3waveguidewithamanipulator.Single-modelaunchingwithacouplinglossaslowas1.4dBwaspreparedwiththebutt-joinedprocedure.TheLiNbO3opticalwaveguidewasmountedonacopperblockwhosetemperaturewascontrolledwithathermoelectricelement.Theopticalwaveguideandthecopperblockwerekeptinadry-nitrogengasambienttopreventwater-vapourcondensation.Thewaveguidetemperaturewasmeasuredatthecrystalsurfacebyacopper-constantanthermocouple(Uesugietal1976).

Thethree-dimensionalLiNbO3opticalwaveguidewasfabricatedbyTi-in-diffusionintoac-plateofLiNbO3crystalat1050ºCfor20h.TheindexdifferenceAnwas0.002-0.003andthecoredimensionwasabout5mm.Thewaveguidelengthwas1cm.Therefractive-indexdistributionwasassumedtobeGaussian.Itwasestimated,fromlighttransmissionexperiments,thattheextraordinaryrefractive-indexdifferencebetweenthecoreandsubstrateislargerthanthatofan

ordinarywave.ThisisattributedtoLi2Oout-diffusionduringthefabricationprocess(Nodaetal1975).TheguidecansupportonlydominantTE00andTM00modesat1.064mm,anduptothird-ordermodesat0.532mm.

Figure5.26showsthesecondharmonicpowerversusfundamentalfrequencypowerunderaphasematchedconditiondescribedinthesequel.Experimentalresultscoincidewiththoseshownbythesolidlinewithaslopeof2.The

Fig.5.25Experimentalconfigurationofthesecond

harmonicgenerationusingathree-dimensionalLiNbO3opticalwaveguide(UesugiandKimura1976).

Fig.5.26Dependenceofsecondharmonicpoweron

fundamentalfrequencypowerunderphase-matchingcondition(Uesugiand

Kimura1976).

fundamental-wavepolarizationcorrespondstotheTE(ordinary)wave,andthegeneratedsecond-harmonicwaveisfoundtobelinearlypolarizedwithTM(extraordinary)polarization,whichisinducedbythesecond-ordernonlineartensorelementd31.Opticaldamagewasnotobservedintheexperimentuptoabout3mWfundamentalinput.

ThephasematchingconditionissatisfiedbyusingthetemperaturedependenceofLiNbO3birefringence.Figure5.27showsthetemperaturedependenceoftheharmonicpower.Inthismeasurement,thecrystalwascooledatfirstto-29ºCandthetemperaturewasraisedatarateofabout1ºC/min.Photographsshowingtypicalnear-fieldpatternsofthesecondharmonicwaveguidemodesaredepictedinFig.5.27.Thepeaksat-2and15ºCcorrespondtothesecondharmonicTM00andTM20modes,respectively.Thepeakat10ºCisestimated,fromthenear-fieldpattern,tobeCherenkovradiation.TheCherenkovradiationisgeneratedwhenthenonlinearpolarizationpropagationconstantislargerthanthatoftheharmonicwaveinthebulkcrystal(Tienetal1973).For2mWfundamentalfrequencyinputpowerintheTE00mode,theconversionefficiencyat-2ºCwas1.5×10-4.A

conversionefficiencyashighas0.1isexpectedforan1.4Winput.Theconversionefficiency,calculatedonthebulk-crystaldata,is3.1×10-4fora2mWfundamentalplane-waveinput,whichisconfinedina5×5-mmcross-sectionforthelengthofacm.Thedifferencebetweentheexperimentalandcalculatedvaluesmaybeduetofractionalspatialoverlapofthenonlinearpolarizationandtheharmonicwaveguidemode,waveguideloss,andinsufficientcoherentinteractionlengthbetweenthefundamentalandharmonicwaves.Thegeneratedsecondharmoniclightwaseasilyobservedonascreenandatthewaveguideendsurfacewithanakedeye.

Theconversionefficiencyofsecondharmonicpowerintheopticalwaveguideisproportionaltothesquareoftheoverlapintegralbetweenthefielddistributionofthefundamentalandsecondharmonicwaves.TheoverlapintegralisthelargestwhenthefundamentalandsecondharmonicwavesarebothinthedominantTE00andTM00modes,respectively.TheharmonicTM10modewashardlyobserved.TheTM20modewasweakerthanthedominantmode.ThephasematchingtemperatureoftheLiNbO3opticalwaveguidedepends

Fig.5.27Harmonicpowertemperaturedependence.Insettedphotographsshowtypicalnear-fieldpatternsofsecondharmonicwaveguidemodes(Uesugiand

Kimura1976).

Fig.5.28Calculatedphase-matchingtemperaturedifference

betweenTM00andTM20ofathree-dimensionalLiNbO3opticalwaveguide.FundamentalfrequencymodeisassumedtobeTM00.

Theexperimentaltemperaturedifferenceisshownontheordinate.Thewaveguideheightbisestimatedtobeabout5mmfromaninterference

fringemeasurement(UesugiandKimura1976).

onthecompositionofLi2OandNb2O5andonwaveguidedispersion.Itisalsoaffectedbythepyroelectriceffectwhenthecrystaltemperatureisswept.However,thephasematchingtemperaturedifferenceDTbetweenthesecondharmonicdominantTM00modeandthehigherTM20modeareinsensitivetothecompositionand

pyroelectriceffect.Figure5.28showsthecalculatedtemperaturedifferenceDTasafunctionofthewaveguideheightb.Hereitisassumedthattheindexprofileisastepdistributionoverthecross-section.ThepropagationconstantiscalculatedaccordingtoMarcatili'sapproximation(Marcatili1969).Sellmeier'sequationwasusedtoexpressthetemperatureandwavelengthdependenceofrefractiveindices.Figure5.28servestoexpressseveralaspectratios(a/b).ThesolidlinecorrespondstotherefractiveindexdifferenceDn=0.0025.TheexperimentalresultshowninFig.5.27isequaltoDT=17ºC.

LiNbO3hasapyroelectriccoefficientaslargeas4×10-9C/cm2Cat25ºC.Whenthecrystaltemperatureisraisedby1ºCandthespontaneouspolarizationremainsuncompensated.theelectricfieldalongthec-axisbecomes1.67kV/cm.Thiselectricfieldinducesbirefringence,whichcorrespondstoatemperaturechangeof0.4ºC.Inthisexperiment,theobservedphasematchingtemperaturesarehigherthanrealphasematchingtemperatures,duetothepyroelectriceffect.Itwasobservedthatwhenthecrystaltemperatureissweptfromhightolow,thephasematchingtemperatureislowerthanthatintheoppositesituation.Thehysteresisseemstoresultfromthepyroelectricsurfacechargecompensation.Thepyroelectriceffectcouldbeavoidedifab-platecrystalwithshort-circuitedelectrodesonc-surfaceswereused.

5.3.5Second-harmonicgenerationinawaveguidewithperiodicallydomain-invertedregions

Second-harmonicgeneration(SHG)thatusesaquasi-phasematching(QPM)inLiNbO3opticalwaveguidewithperiodicallydomain-invertedregions(PDRwaveguide)isapromisingapproach(Limetal1989(a)).Suchwaveguidespossessahighpowerdensityandalargenonlinearcoefficient.However,sincetheQPMconditionisverydifficult,thehigh-conversionexperimentsweremadearrangingsuitableperiodsofdomain-invertedregionspreciselyorusingatunablelaserforthefundamentalwave(Limetal1989(b)).

Shinizakietal(1991)describedaself-quasi-phase-matchedSHGthatusesaPDRwaveguide.ThefundamentalwavesatisfyingtheQPMconditionwasgeneratedbyanLD(laserdiode)whichwaslasedbyafeedbackwavesfromthePDRwaveguide.Astheopticalrefractiveindexofthedomain-invertedregionsisslightlyhigherthantheundopedregion,theperiodicaldomain-invertedregionsactasadistributedBraggreflector(DBR).Astheperiodofthedomain-

invertedregionswasdesignedtosatisfytheQPMconditionsandthehigh-reflectanceconditionsofthequasi-phasematchedfundamentalwave,theLDwaslasedatthewavelengthsatisfyingtheQPMcondition.

Intheexperimentalarrangements,showninFig.5.29,thePDRwaveguideandtheLDwithantireflectioncoatingfacetsareopticallyconnectedbysingle-modefibre(SMF).Periodicaldomain-invertedregionswereformedbyTi-diffusion.TheTilayerevaporatedonac-cutLiNbO3substratewaspatternedbythelift-offtechnique.TheTilayerwas5nmthickandtheTilineswere4mmwide.Heattreatmentconsistedofa2hrampupfromroomtemperatureto1050ºCand1hsoakat1050ºC;afterthisthefurnacewasturnedoff.Thedomain-invertedperiodwasL=13mm.Theopticalwaveguidewasfabricatedtooverlapperpendicularlyontheperiodicaldomain-invertedgrating.Thewaveguide(6mmwide,2mmlong)wasfabricatedbyproton-exchangedprocess(seeChapter1).TheLDwaslasedbyfeedbackwavesfromthePDRwaveguide.Theperiodofdomain-invertedregions,actingasDBR,is13mm.Iftheeffectiveguideindexfortheradiatedwaveat1.327mmisequalto2.195,thehighreflectanceconditionissatisfied.WhenrgwLDlasedat1.327mminwavelength,thesecond-harmonic(SH)wavewasobserved.TheSHspectrumwhichwasmeasuredisshowninFig.5.30.ThewavelengthoftheSHwaveis662.4nm,whichcorrespondstothehalfwavelengthofthefundamentalwave.The

Fig.5.29Experimentalarrangementoftheself-QPMSHG.TheSHGdeviceiscomposedofPDRwaveguideonthe+cfacetofthelithiumniobatewafer.LDswithanantireflectioncoatingfacetareopticallyconnectedtotheSHGwaveguidebysingle-mode

fibre(Shinozakietal1991).

Fig.5.30SHGspectrumfromthePDRwaveguide.The

fundamentalwavewasgeneratedbytheInP/InGaAsPLDwithAR-coatedfacets

(Shinozakietal1991).

normalizedSHconversionefficiencywas4.1%/Wcm2.

TheQPMconditionsaresatisfiedifthehalf-periodofdomain-invertedregions,L/2,isequaltooddtimesofthecoherencelength.Thecoherencelength isgivenby

wherelisthewavelengthofthefundamentalwaveinvacuum,n(l)istheopticalindexforwavelengthl.TheconditionforQPMis

Fig.5.31Lengthofdomaininvertedregions(Lc)infirstorderofQPMandthehalfperiodsof43rdorderofDBR(Lw)versusthefundamentalwavelength.These

linesintersectat1.327mminfundamentalwavelength,6.5mminLcorLw(Shinozakieta11991).

wheremispositiveinteger,andk1andk2arethewavevectorsforthefundamentalandSHwaves,respectively.Thentheperiodofthedomain-invertedregions,L,isgivenby iftheLsatisfiestheQPMconditiongivenasequation(5.46).Theperiodicaldomain-invertedregionsactasDBR.IftheperiodLisdesignedtosatisfythehighreflectanceofthefundamentalwave,theQPMconditionissatisfied.Thatis,iftheLDwithanantireflection-coatedfacetislasedbythefeedbackwavesfromtheperiodicaldomain-invertedregions,theradiatedwavesatisfiestheQPMcondition.Theself-QPMconditionsareasfollows

wherepispositiveinteger.Figure5.31showstherelationshipsgivenbyequation(5.47),thelengthofthedomain-invertedregions, ,inthefirstorderofQPM(m=0)andthehalf-periodof43rdorderofDBR(p=43),Lw[=pl/4n(l)],againstthefundamentalwavelength.Thedispersionfunctionoftheproton-exchangedLiNbO3materialisgivenbyn(l)=n'(l)+0.05(DeMichelietal1983),wheren'(l)isanopticalindexdispersionofcongruentLiNbO3.Thesetwolinesintersectat1.327mminfundamentalwavelength,6.5mminLcor

Lw,asshowninFig.5.31.Intheexperiment,thewavelengthofthefundamentalwavewas1.327mm,thehalfperiodofDBR,L/2,was6.5mm.TheallowanceoftheDBRperiodDLisequalto0.039mm.Itisverydifficulttodesignandfabricateadomain-invertedregiontoachieveahighSHconversionefficiency.

5.3.6Effectofprotonexchangeonthenonlinearopticalproperties

Protonexchangeusingbenzoicacidhasbeenshowntobeaccompaniedbyasubstantialreductionintheelectro-opticcoefficient(Becker1983;Yan1983);somedecreaseinthenonlinearopticalcoefficient(d)hasalsobeenobserved(Suharaetal.1989;Caoetal.1991).Limitedrecoveryofanelectro-opticalcoefficientandanonlinearopticalcoefficientoccursunderthermalannealing(Caoetal,1991;Suchoskietal,1988).Laurelletal(1992)havereporteda30-foldreductionintheopticalnonlinearityforLiNbO3,theyfoundthattheopticalnonlinearitycannotbeeffectivelyrestoredbythermalannealing.

Bortzetal(1992)havemeasuredthed33nonlinearcoefficientinproton-exchangedLiNbO3usingangle-dependingreflectedSHGandobservedareductionto<1%ofthebulkLiNbO3value.

Recently,animprovedprotonexchangesourceusingpyrophosphoricacidhasbeenimplementedbecauseofitshigherboilingtemperature(300ºC)andlowvapourpressure.Low-loss(0.5dB/cm)waveguideshavebeenpreparedinLiNbO3andLiTaO3usingpyrophosphoricacidandefficientblue-lightgenerationhasbeenachieved(Mizuuchieta1.1991)However,theeffectoftheprotonexchangeprocessusingpyrophosphoricacidonthenonlinearopticalcoefficientisnotknown.Hsuetal.,(1992)reportedtheeffectoftheprotonexchangeprocesscarriedoutusingbenzoicacidandpyrophosphoricacidonnonlinearopticalpropertiesofLiNbO3andLiTaO3andrecoveryofthenonlinearcoefficientunderthermalannealing.Thenonlinearopticalcoefficientwasevaluatedusingareflectiontechnique.

X-cutandZ-cutLiNbO3andLiTaO3crystalswereusedinthisstudy.Waveguideswerepreparedbyprotonexchangeinbenzoicacidandinpyrophosphoricacid(H4P2O7)withaheatingrateof10ºC/minandcoolingrateof20ºC/min.

Iftheincidentbeammakesanangleqi,withthesurfacenormal,hasapolarizationanglejwithrespecttothenormaltotheplaneofincidence,andhasanintensityI,thenthenonlinearpolarizationforZ-cutLiNbO3withtheY-axisperpendiculartotheplaneofincidencecanbewrittenas(Dicketal.1985)

wheredijarenonlinearcoefficientsandfiarelinearFresnelcoefficients.Themeasuredintensityofthes-andp-polarizedSHGin

reflection(neglectingbirefringence)ispropotionaltononlinearpolarization.

Figures5.32and5.33showresultsofsuchmeasurementsat1064nmandtheoreticalcalculations.Theratioofd33/d31andd22/d31wasobtainedas6.2and-0.30byfittingthetheoreticalresultswithexperimentaldata.Thesevaluesareslightlydifferentfromthepublishedvalues(7.0and-0.53fromNishiharaetal1989),butthereappearstobequiteavariationintheliteraturedata(Yariv1984).

Resultsofd-coefficientmeasurementsatfundanmentalwavelengthsof532nmforproton-exchangedLiTaO3usingbenzoicacidandpyrophosphoricacidarepresentedinTable5.7.Theincidentbeampowersusedwerebelowthresholdforphotorefractiveeffectstobeobservedasnochangeinsignalwasobservedevenfor1hexposuretotheincidentbeam.Theshapeofthepatternisrelatedtothestructuralsymmetryofthecrystalandofthesurface.Thelargescatterintheexperimentaldataattheincidentp-polarizedlightonX-cutcrystaloccursbecauseofpossiblesmallmisalignmentsofthecrystal.

Fig.5.32VariationofSHGintensitywithincidentpolarizationangleforaZ-cutLiNbO3crystalwiththeXaxisperpendiculartotheplaneofincidence.Crossesareexperimentalpointsandthesolidlineisfromtheoreticalcalculationsfor(a)p-polarizedand(b)s-polarized

outputbeams(Hsuetal1992).

Fig.5.33(right)VariationofSHGintensity

withincidentpolarizationangleforX-cutLiNbO3crystalwiththeZaxisperpendiculartotheplaneof

incidence.Crossesareexperimentalpointsandthesolidlineisfrom

theoreticalcalculationsfor(a)p-polarizedand(b)s-polarizedoutputbeams(Hsuet

a11992).

Insitumeasurementofrecoveryofd33wasmadeunderthermalannealing.ThesaamplewaslocatedinaheatingfurnaceandtheSHsignalwascontinuouslymonitoredwhilstthesamplewasmaintainedatatemperatureof310ºC.Figure5.34showstherecoveryoftheSHsignalasafunctionoftime.Norecoveryisseenfortheinitial30minduringwhichthefurnacewasheatedupfromroomtemperaturetothefinalannealingtemperature(310ºC).Thereisquickrecoveryofd33,whichbeginsatapproximately1.25hintotheannealingprocess,whichsaturatestoavalueofapproximately50%oftheblankLiNbO3value.

Becker(1983)hasshownthataprotonexchangeprocessusingbenzoicacidgivesrisetoaconsiderablereduction,byafactorof2.7,intheelectro-opticcoefficient.Ifthenonlinearresponseispurelyaresultofelectronicpolarizations,theelectro-opticanddcoefficientsareproportional(Yariv1984),andanydecreaseintheelectro-opticcoefficientisnecessarilyaccompaniedbyacorrespondingdecreaseind.However,theelectro-opticcoefficientforLiNbO3isknowntohavecontributionsformionicpolarizations.SuchpolarizationshavenoeffectupontheSHGprocess.Hence,itispossiblefortheelectro-opticandSHGprocessestobeaffecteddifferentlybyprotonexchange.Suharaetal.(1989)reporteda50%reductioninthedcoefficientat1064cmforprotonexchangeinbenzoicacid.Similarly,Caoetal.(1991)havereporteda40%reduction,howeverannealingrestoredthedcoefficientto90%ofthebulkvalue.Intheexperimentsat532nm,Laurelletal.(1992)findthattheopticalnonlinearitycannotbeeffectivelyrestoredbythermalannealing.Bortzetal.(1992)suggestthatthedifferencebetweentheirresultsandthosereported

Table5.7Measuredvaluesofdcoefficientforx-cutp-exchangedLiNbO3andLiTaO3relativetotheblankcrystal.Measurementerroris±10%.Annealingtemperature350ºC

Annealingtime

Protonexchangetime(h)

LiNbO3,%recoveryofd33comparedtoblank

LiNbO3

LiTaO3,%recoveryofd33comparedtoblankLiTaO3

0h 1h 3h 7h 17h 0 1h

0.5 0% 52% 51% 59% 54%

1 Norecoveryobserved

1.5 Norecoveryobserved 69%* 56%*

0.5 Norecoveryobserved

1 Norecoveryobserved 39%** 0%**

*protonexchangedat200ºC

**at230ºC

Fig.5.34VariationofSHsignalwithannealingtime

foranx-cutLiNbO3samplethatwasproton-exchangedinbenzoicacidfor0.5hat180ºC.Annealingtemperaturewas310ºC(Hsu

etal1992).

byCaoetal.(1991)isduetoneglectofthereflectedsecond-harmonicfieldonboththed33discontinuityatthefilm-substrateinterfaceandangulardependenceofthenonlinearpolarization.TheresultsreportedbyHsu,etal.(1992)indicatethatLiNbO3samplesproton-exchangedfor0.5hat180ºCshowedsomerecoveryofthenonlinearcoefficient,whilstsamplesthatwereproton-exchangedfor1and1.5hdidnotshowanymeasurablerecoveryunderthethermalannealingconditionsused.

Theprotonexchangeprocessfollowedbyannealingmayproducehigherlatticedisorderatthetopsurface,whichcouldexplainwhyitispossibletoseesomewaveguideSHconversioneventhoughthenonlinearcoefficientisdegraded.

IncontrasttoLiNbO3,LiTaO3showedonlypartiallossofopticalnonlinearitymeasuredat532nmuponp-exchangeusingeitherpyrophosphoricacidorbenzoicacid.ThermalannealingproducedonlysmalllossinnonlinearityofLiTaO3p-exchangeinbenzoicacid.Completelossofnonlinearitywasobservedinthecaseofpyrophosphoricacid.TheseresultsalsodifferfromannealingresultsforLiNbO3wheresomerecoveryoftheopticalnonlinear

coefficientwasobserved.TheLiTaO3indexincreasesafterannealingwhiletheLiNbO3indexdecreases.Increaseintheindexmaycausesomedistortioninthestructure,whichcanaffecttheSHsignal.Tounderstandthedegradationmechanism,structuralcharacterizationofproton-exchangedandannealedLiNbO3andLiTaO3isongoing.

5.3.7Sum-frequencygenerationinwaveguides

Therehasbeenrecentincreasedinterestincompactshort-wavelengthlightsourceswiththeobjectiveofrealizingoutputpowersinthemWrangebasedondiodelasers.OneofthemostpromisingtechniquestodothisistousenonlinearfrequencyupconversioninQPMwaveguides(Limetal.1989;vanderPoeletal.1990;Mizuuchi,etal.1991).Byfarthemostwidelyusednonlinearprocessissecond-harmonicgeneration(SHG)sinceonlyonelightsourceisrequired.AnalternativetoSHGissum-frequencygeneration(SFG),especiallywhenfinetuningofthegeneratedwavelengthisrequiredorfundamentallightsourceforSHGisdifficulttofind.SFGcanalsobecombinedwithSHGinsuchawaythattwoIRlightsourcesgeneratethreevisiblewavelengthssimultaneously(Yamamotoetal.1991).WaveguideSFGhasbeenreportedusingbirefringencephase-matching(Useugietal.1978).Cherenkovradiation(SanfordandRobinson1989;Laurelletal.1990).Amajordrawbackwithalltheseexperimentshasbeenthelow-outputpowderobtained.

Laurell,etal.,(1992)reportedefficientSFGinsegmentedKTPwaveguides(Bierleinetal.1990)usingQPM(vanderPoeletal.1990).

Twoconditionshavetobefulfilledtoobtainquasi-phased-matchedSFG,energyconservation

andmomentumconservation,

wherel1andl2arethefundamentalwavelengths,l3theSFwavelength,N(l)istheeffectivemodeindexatthecorrespondingwavelengths,andmandLaretheorderandtheperiodoftheQPMstructure,respectively.

A4.5mm-longflux-grownz-cutKTPsamplewasmaskedwithatitaniumfilmwithrectangularopeningsforionexchangetoformthewaveguideinthex-direction.Thesamplewasthenendpolishedandimmersedfor45minina98mol%RbNO3:2mol%Ba(NO3)2moltensaltbathat330ºCforsimultaneousionexchangeanddomainreversal.Thewaveguidesinvestigatedonthesamplewere4mmwideandhasperiodsof3,4,5and6mm.Fortheseperiods,theratiobetweentheexchangedandunexchangedregionswas2/1,3/1,4/1and5/1respectively.Theseperiodswerechosentogiveup

Fig.5.35Tuningcurveforthesumfrequencygenerationvsfundamentalwavelengthsinwaveguideswith

(a)3mm,(b)4mm,(c)5mmand(d)6mmperiods(Laurelletal1992).

convertedlightfromnearUVtoblue-greenbyfirstorder(m=1)QPM.

Toanalyzethenonlinearpropertiesofthewaveguide,twoindependentlytunableTi-sapphirelaserswereused.ThelasersystemconsistedofanArionlaserwhichpumpedtwocwTi:sapphirelaserstogeneratetunableradiationbetween730and1070nm.Theradiationfromlaserswascombinedusingabirefringentbeamsplitterandusedasthefundamentalwavelengthsforthesum-frequencygenerationexperiment.ThewaveguidesonthesamplewerefirstinvestigatedinSHGexperiementswherethelaserwavelengthwastunedoverthephase-matchingpeakandtheSHintensityrecorded.ThewavelengthofthefundamentalandtheSHwavewasmeasuredwithawavemeterandamonochromator,respectively,andthepowersweremeasuredwithcalibrateddetectors.FromthewidthandshapeoftheSHcurveswereofhighhomogeneity,sothefullwaveguidelengthwasutilized

forconversion.BoththemodeatthefundamentalandattheSHwavelengthswereapproximatelycircularinalwaveguides.Atdegeneracy,thesecond-harmonicwavelengthwas394,425,454,and480nmforthe3,4,5and6mmperiodwaveguides,respectively.Agoodagreementwasobtainedbetweenthemeasuredandthecalculatedphase-matchingwavelengths.

TheSHGmeasurementswerefollowedbySFGexperiments.Here,bothlaserswerefirsttunedtoSHGandthenthewavelengthofthelaserstunedinoppositedirections,maintainingthephasemathcing.Thetuningrangewaslimitedbythewavelengthregionthelaserscouldcover.Figure5.35showsthetuningcurveforthefourperiods.Theaccuracy(0.1nm)ofthemonochromatorwasfoundtobeinsufficienttouseintheplotofthetuningcurve,andtheSFGwavelengthwasthereforecalculatedfromthefundamentalwavelengths,Eq.(5.48).ThelargesttunabilityoftheSFwavelengthwas3nmobserved

forthe5mm-periodwaveguide.Thiswaveguidealsogavethehighestoutputpowerintheblue,2.7mWofthe454nmradiation,generatedwith149mWat942nmand106mWat875nmcoupledthroughthewaveguide.Thefundamentalpowersmeasuredattheoutputofthelaserswereapproximatelythreetimeshigher.Normalizedattheoutputofthewaveguide,thiscorrespondstoaconversionefficiencyof84%W-1cm-2or17%/W.ThehighestefficiencyforSFGwas112%W-1cm-2,obtainedwiththe4mm-periodwaveguide,butlowertotal-fundamentalpowersinthiscaseresultedinlowerSGFoutput.

5.4SecondharmonicgenerationintheformofCherenkovradiation

Enhancedfluxdensityoflightandlargeinteractionlengthexplainanincreasinginterestinnonlinearopticaleffectsinopticalwaveguidestructuresforrealizingefficientfunctionaldevices(StegemanandStolen1989).Amongtheseeffects,thesecond-ordernonlineareffectpermitsobservingfrequencyconversionsuchasSHGandsum-ordifference-frequencygeneration.Inparticular,SHGinopticalconfinementstructuressuchasopticalfibreschannelwaveguideswillfindmanyapplicationsthatrequireaminiaturizedvisiblelightsourcewithlightcoherence.Anefficientguided-waveSHGdevicestructurewhichcanextractbluelighthasbeendemonstrated.ItemploysaCherenkovradiationschemetoachievephasematchingata0.84mmwavelengthfromaGaAslaserdiode(TaniuchiandYamamoto1987,SanfordandConnors1989),andbluepowerontheorderof1mWfrom50to100mWinputhasbeendemonstratedwitha6mmdevicelength(TaniuchiandYamamoto1987).Inthisscheme,thephasematchingconditionbetweenthefundamental(pumping)guidedmodeandthesecondharmonicradiationmodecanbeautomaticallysatisfiedbyadjustingthewaveguideparameters(Tienetal1970).However,thesecondharmonicpowergenerateddependsontheparametersinacriticalfashion,andthereforeitisofgreatimportance

todetermineoptimumparametersfortheguidestructure,crystallineorientation,refractiveindex,etc.(SanfordandConnors1989;HayataandKoshiba1989;Hayataetal1990).

AnotherpossibilityforperformanceofCherenkovtypeSHGdevicesbymeansoftailoringthetransverse(ydirection)nonlinearsusceptibilityprofileintheguidingregionisexamined.Moreradiationefficiencyisexpectedasaresultoftheincreasingoverlapbetweenthenonlinearpolarizationwave(dividingsource)andthegeneratedSHwave(drivenfield)inanalogywiththebeamsteeringtechniqueinaphased-arrayantenna.Linearanddomain-inverted(poled)channelsembeddedinanonlinearsubstrateareconsidered,andtheSHGefficiencyforeachcaseiscomparedwiththatforaconventionalnonlinearchannelwithoutdomaininversion(SanfordandConnors1989).NumericalresultsobtainedbyawaveopticstreatmentshowthataremarkableenhancementoftheSHGisrealizable,particularlywithadomain-invertedchannel.

TheschematicillustrationsareshowninFig.5.36,wherenisthebuilt-inrefractiveindexdependentonthewavelengthanddisthethicknessofthechannel.InFig.5.36bthevalueofthechannelwidth(W)isimplicitlyincludedthroughanapplicationofaneffectiverefractiveindexapproximation

Table5.8ParametersofLiNbO3waveguidesn1=n'1(air)

l,mm n2x n2y n2z n3x n3y n37

0.84LDpumping 2.373 2.293 2.373 2.25 2.17 2.25

1.06YAGpumping 2.352 2.276 2.352 2.232 2.156 2.232

l,mm n'2x n'2y n'27 n'3x n'3y n'32

0.84 2.601 2.491 2.601 2.411 2.301 2.411

1.06 2.514 2.425 2.514 2.324 2.235 2.324

(HayataandKoshiba1989;HayataandSugawara1990).HayataandYanagawa1990)thusconsidertheslabwaveguideasshowninFig.5.36binwhatfollows.

Here,caremustbetakentoemploythisreducedgeometry.AlgebraicmanipulationofMaxwell'sequationswithnonlinearpolarizationyieldsthefollowingequationforthey-polarized(TM)mode(HayataandKoshiba1989):

whereh'xistheslowlyvaryingenvelopeofthelateralcomponentoftheSHmagneticfield,e=[ex,ey,ez]Tisthepumpingelectricfield(Tstandsfortransposition), ,bisthepropagationconstant,k0isthefree-spacewavenumber, , ,Z0=337W,[e']isthelinearrelativepermittivitytensorwhosediagonalelementsaree'x,e'y,ande'z[d']isthesecondordernonlinearopticaltensor,andtheprimeandthehatdenoterespectivelythequantityforthesecondharmonicwaveandaunitvector.Inthederivationofequation(5.50),theslowlyvaryingenvelopeapproximationhasbeenemployedandpump

depletionhasbeenneglected,thatis, .

ConsidertheZ-cutLiNbO3(caxis/yaxis)asasubstratematerial.WaveguideparametersusedintheanalysisareasinTable5.8;theexplicitvalueof[d']hasbeenobtainedfromtheTableshownbyYarifA.Yehp(1984).TheTM0modeisconsideredasapumpingconditionontoz=0.

Asanonlinearsusceptibilityprofileinthefilm(|y|<d/2;thefilmcentreisaty=0),Hayataetal(1990)consideredthreecases:(A)linearfilm,i.e.alltheelementsin[d']vanishanywhereinthefilm;(B)nonlinearfilmwiththesamesignofnonlinearsusceptibilityinthesubstrate;and(C)domaininvertedfilmwithoppositesignofnonlinearsusceptibilityinthesubstrate,thatis,[d']film=-[d']substrate.Occurrenceofthecasesconsideredabovedependsontheactualfabricationprocess.Forinstance,case(A)maybeobservedin

Fig.5.36Schematicsofproblem(a)3Dview;(b)sideview(Hayataetal1990).

Fig.5.37TotalSHpowerversusguidethickness(w=2.0mm).Solid,dottedanddashedlinesindicatedomain-inverted[case(C)],linear[case(A)],andnonlinearchannelwithoutdomaininversion[case(B)],respectively.(a)l0=0.84mm,

(b)l0=1.06mm(Hayataetal1990).

asituationinwhichdegradation(damage)oftheidealcrystallinestructureinthechannelcannotbeignored.Ontheotherhand,case(C)canberealizedbyadequatelypolingacertainkindofferroelectriccrystalsuchasZ-cutLiNbO3(Limetal1989;ThaniyavarnandMiyazawa1979).

Figure5.37showsacomparisonbetweenthesecases,wheretheSHGefficiencyisdefinedbyP'/P2withP'asthesecondharmonicpowerandPasthepumpingpower.Theseresultsareobtainedfromastationaryanalysis inequation(5.50)],withwhichtheoptimumgeometryoftheguideispredictable.Thevalidityofthisapproachhasalreadybeenensuredintheliterature(Nodaetal1975;Tienetal1973)throughacarefulcomparisonwiththeresultsobtainedbya

moreinvolvednonstationaryanalysisandwithexperimentalresults.Thesharpminimaoccurringinthefiguresareduetointerferenceeffectsacrossthefilmforgrazinganglesofthesecondharmonicwave(Tienetal1973).Itisevidentfromtheseresultsthattheutmostsecondharmonicpowerisobtainableincase(C).Inthevicinityoftheoptimumgeometry,d=0.35mmforl0=0.84mmandd=0.53mmforl0=1.06mm,theefficiencyofcase(C)isanorderofmagnitudegreaterthanthatofcase(B)(i.e.theorderof10mWfroma50-100mWinputwithl0=0.84mmanda5-10mmdevicelength).ThissignificantenhancementoftheSHGcanmathematicallybeattributedtotheincreasingoverlapquantifiedbytheintegraloftheproductbetweenthenonlinearpolarizationtermandthedesiredsecondharmonicmodepropagatingalongtheCherenkovangle.Inordertoprovidephysicalinsightintotheresults,Fig.5.38givesschematicillustrationsfortherelationshipbetweenthenonlinearpolarizationwave(source)andthe

secondharmonicwave(radiation).Itshouldbenotedthat1)aconsiderablepartofthenonlinearpolarizationwavepenetratesthesubstrateasaresultoftheextendedevanescenttailofthepumpfieldand2)thewavefrontofthesecondharmonicwavetiltswiththeCherenkovangleagainstthatofthenonlinearpolarization(z-direction).AsisseenfromFig.5.38,secondharmonicwavesgeneratedatdifferentlocations(oneinfilmtheotherinsubstrate)alongthey-directionaddpartiallyoutofphaseandcanceleachotherintheconventionalgeometry(Fig.5.38a),whereastheyaddinphasebymakingthefilmdomaininverted(Fig.5.38b).Thelinearfilm(case(A))isintermediatebetweenthetwoextremecases.Itisinterestingtonotethatonecanfindananalogousmechanismtobeamprofilinginaphased-arrayantennasysteminwhichtherelativephasedifferencebetweenadjacentdipoleelementsistailoredsothatinterferenceisinphaseforthedesireddirection.Thisfactindicatesthattheuseofhomogeneouslydomain-invertedchannelisveryeffectiveinenhancingCherenkov-typeSHGefficiencyinLiNbO3opticalwaveguides.

5.5Electro-opticeffectsinopticalwaveguides

Electro-opticcoefficientsinwaveguidesofsolidsolutionsoflithiumniobatetantalateweremeasuredbytheinterferentionalmethod.TheschemeofmeasurementsispresentedinFig.5.39.

Acoherentlightbeamisseparatedbyaseparationprismintotwoindependentlightbeamseachofwhichisfedintoalightguidebytheprism

Fig.5.38SchematicillustrationsforexplainingtheenhancedSHG,NLPandSHareabbreviationsfornonlinearpolarizationandsecondharmonic,respectively.(a)Conventionalgeometry(caseB),

(b)domain-invertedfilm(casec)(Hayataeta11990).

Fig.5.39Schematicillustrationofadeviceformeasuringelectro-opticcoefficients:

1)radiationsource;2)l/4-plate;3)focusinglens;4,6)input-outputprismsforopticalradiation;5)investigatedsample;7)objective;8)screen;

9)microscope;10)controlelectrodes;11)mounting.

method.Oneofthebeamsisledintheinterelectrodegapofthesystemofcoplanarelectricguides(10),thesecondbeampropagatesoutsidetheelectrodesysteminthedirectionparalleltothefirstone.Theoutputofopticalradiationfromthespecimenisrealizedusingthesecondprism(6).Thecollectinglens(7)providesconvergenceofbothlightbeamsintheplane(8)inwhichinterferenceisobserved.

Whencontrolvoltageisappliedtotheelectrodes,therefractiveindexofthemodechangesbyaquantityDnproportionaltotheelectro-opticcoefficientsofthelightguidematerialandtotheappliedvoltage.Thisleadstoachangeoftheopticalpathlengthofthelightbeampropagatinginafilmneartheelectrodes.ThischangeisequaltoDL=Dnl,wherelisthelengthofthecontrolelectrodes,whichinturninducesadisplacementoftheinterferencepatternbyMfringes(DL=Ml).

Inthecaseoflinearelectro-opticeffect,thechangeoftherefractiveindexofagivenmode,Dn,isgivenbytheexpression

wherenistherefractiveindexofthefilmforagivenlightmode,rijistheelectro-opticcoefficient,Ezisthelongitudinalcomponentoftheelectrodefieldinthefilm.

Inthecase ,del>2s,wheredelistheinterelectrodedistance,histhefilmthickness,sishalfwidthofthelightbeam,thequantityEzisdeterminedbytheexpressionEz=2U/pdel(Uisthevoltageappliedtotheelectrodes).SincethequantityAncanalsobeexpressedas

,thevalueoftheelectro-opticcoefficientisdeterminedbytheexpression

Whenlightpropagatesinthex-directionalongtheY-cutofLiNb1-yTayO3,wehaverij=r33.

Thevoltageappliedtothestructureofelectricguidesischangedinthecourseofmeasurements,andthedisplacementMiscontrolledvisually.IftoameasuredMtherecorrespondstheappliedvoltageU,thenknowingthelightwavelengthl,theelectrodelength ,theinterelectrodegapdelandtheeffectiverefractiveindexofthemode,onecancalculatetheelectro-opticcoefficientusingtheexpression(5.52).

Investigationshaveshownthatinepitaxialstructuresthathavenotbeenmadesingle-domaintheelectro-opticcoefficientsaresmall,butthesensitivityofthedevicewasnothighenoughtomeasurethesecoefficients.Afterfilmsarepolarized(andthusbecomesingle-domain),theirelectro-opticcoefficientsincreasesignificantly.Measurementsofthecoefficientr33foranumberofsingle-domainspecimenshaveshownthatitsvaluevarieswithintherange(15-24)×10-12m/V,whichisclosetothevalueofthiscoefficientforlithiumtantalate.

Thedependenceofinducedbirefringenceontheelectricfield(3×102-5×105V/m)islinearandisindicativeofahighpolarizationofheteroepitaxialfilms.

Theelectro-opticconstantsofproton-exchangedLiNbO3opticalwaveguidesweremeasuredbyMinakataetal(1986)bymeansofphasemodulationtechnique(Yariv1985)633nmlaserlightwasfedintothewaveguidefromtheendfacet,andthepropagationmodewasthefundamentalTM-likemode.Therelevantelectro-opticconstantwasr33.Themodulationcharacteristicsweremeasuredbyapplyinga50MHzsinusoidalsignalviaelectrodes.ThemodulationspectraweredetectedbyusingthescanningFabry-Perotresonator.Figure5.40showstheexperimentalresults.Thepowerratio(orpeakvalueratio)ofthefirstsidebandfrequencytothecarrierfrequencywasgivenbytheBesselfunctionasaparameterofamodulationindexuasfollows:

wherel=633nmand anddarecoplanarelectrodelengthandthegap,respectively.G,determiningthemodulationefficiency,isgivenbythefollowingequation(Minakata1978):

whereE(yz),Ez(yz)areanopticalelectricfieldandanappliedelectricfieldofthezcomponent,atpointP(yz)inthecrystal;x,y,zarethecoordinates.Aguidedwavepropagatesalongthex-axis.They-andz-axesareparallelandperpendiculartothesubstratesurface,respectively.E0=V/dandEGistheaverageappliedelectricfieldviaelectrodes,whichiscalculatedbythesuccessiveoverrelaxationmethod(Minakataetal1978).ThecalculatedGvaluewas0.32forthetestsamples.InFig.5.40,opencirclesareexperimentaldata,thethreesolidlines,asaparameterofr33,aretheoreticalcurves.When

r33=3.3×10-12(m/V),thetheoreticalvaluesareingoodagreementwiththeexperimentalones.Thusitisclearthatthevalueofr33reducedtoone-tenthincomparisonwiththevirgincrystal.

Figure5.41showstherelationshipbetweentheLi%,thestrainDc/c,themeasuredr33,andtheDnequotedfromDeMichelietal(1983).ItisclearthatstrainDc/candDnearereduced,andr33isincreasedwithanincreaseinLi%.

5.6Lightresistanceoflightguides

Theopticalqualityoflightguidesisbasicallycharacterizedbytheopticallossfactorandbyradiationresistance.Theradiationresistancemustbetakenintoaccountinworkwithlasersofpowerhigherthan1mW.Atthisandhigherpower,itsdensityinthelightguidecanreachthevalueof105-106

Fig.5.40Measuredmodulationspectraandphasemodulation

characteristics;opencirclesareexperimentaldata,threesolidlines,asparameterr33,aretheoreticalcurves

(Minakataetal1986).

Fig.5.41RelationbetweenLi%,strainDc/c,

measuredr33,andDnequotedfromDeMichellietal1983(Minakataetal1986).

Wcm-2atwhichnonlinearandthermaleffectsaffecttherefractiveindicesofthematerial.

Asisknown,thedamageofthesurfaceofoxygen-containingcrystals(LiNbO3,LiTaO3,BaTiO3,etc.)possessessomespecificfeatures:thedamageisduetoaccumulationwhichlowersthelightresistanceof

thesurfaceandleadstoacharacteristictemperaturedependenceofthedamagethreshold.Zverevetal(1977)hypothesizedtheexistenceinLiNbO3ofanoxygen-depletedabsorptionsurfacelayercontainingtwotypesoftrapslinkedwithoxygenvacanciesandwithreducedNb4+.Anincreaseofabsorption,frompulsetopulse,inthesurfacelayerisduetoaccumulationofelectronsonshallowtrapswhoseabsorptioncross-sectionislargerthanthatofdeeptraps.Anincreaseoflightresistanceofthesurfacewithincreasingspecimentemperatureiscausedbytheemptyingofshallowtrapsforthetimebetweenlaserpulsesduetotheirthermoionization.

InvestigationsofradiationresistanceofLiNbO3filmsandtheirsubstrateshaveshownthatthemechanismsoftheirdamageareabsolutelyidentical.

AQ-switchedgarnet-neodymiumlaser(l=1.06mm,pulseduration10

Table5.9DamagethresholdvaluesforsurfacesofepitaxialLiNbO3filmsondifferentsurfaces

No.Material Breakdownthreshold(GW/cm2)

Accumulationthreshold(GW/cm2)

Maximumnumberofflares

1 LiNbO3 3.2 0.45 10-15

2 LiTaO3 12 4.1 8-12

3 LiNbO3/LiNbO3 6.5 0.25 50

4 LiNbO3/LiTaO3 6.1 1 30-40

5 LiNbO3(Fe)/LiTaO3 4.5 0.3 50

ns)wasusedasaradiationsource.Theradiationwasfocusedbyashort-focuslens(f=11mm)ontofilmspecimensunderinvestigation.Theneckdiameterwas15mm.Thelaseroperatedinasingle-pulseregime,pulserecurrenceratebeingequalto2Hz(Khachaturyan1980).

Table5.9presentsaveragedvaluesofthedamagethreshold,aswellasthedamagethresholdvaluesdeterminedbytheaccumulationeffectbothinfilmsthemselvesandintheirsubstrates.

Itwasestablishedthatthethresholdintensityofthedamageofalithiumniobatefilmincreasedseveraltimesascomparedwithabulkcrystal.BreakdownthresholdsofahomoepitaxialLiNbO3filmandofaheterolayeronLiTaO3donotdiffermuch,andanintroductionofironimpurity(upto0.5at.%)lowersthethresholdby .

Analysisoftheresultsobtainsshowsthatthethebreakdownthresholdoflithiumniobatefilmsisdeterminedbyperfectionofthespecimenstructureandsurface.Zverevetal(1977)reportedthepresencein

lithiumniobatecrystalsofasurfaceabsorptionlayerofabout2mmthick,buttheydidnotdescribethemethodsofsamplesurfacepreparation.Asisknown,mechanicalpolishingofthesurfaceleavesadamagedlayerofabout1mm.Mirror-smoothsurfacesofepitaxialfilmsrequirenoadditionaltreatment.Theincreaseinthedamagethresholdofthefilmisevidentlyduetothelackofadamagedsurfacelayeronit.

Investigationoftheeffectoflaserradiation(l=1.06mm)uponlithiumniobatefilmshasshownthatat'under-threshold'radiationintensityahighlydense( attheclustercentreand105-106Wcm-2ontheperiphery)clusterofmicrodomainsoccursataplaceofirradiation.Whentheirradiatedpositivez-planeundergoesselectiveetching,becauseoftheirhighdensitytheetchingholesmergetoformatypicaltracery.Clusterareasdecreasewithdecreasinglightintensity.Thesevariationsintheclusterareasarehoweverinsignificant,andthediameteroftheclusterismainlydeterminedbythediameterofthefocalspot.

Thisphenomenoncanbeinterpretedasfollows(LevanyukandOsipov1975;HolmanandGressman1982).LevanyukandOsipov(1975)haveshownthe

possibilityofaphotoinducedchangeofspontaneouspolarizationinferroelectrics.Whenaregionofacrystalisexposedtolight,polarizationreversalinthisregionleadstotheappearanceofadepolarizingfieldwhich,actingonfreecarriersthatinteractunderimpurityionization,causestheoccurrenceoffreechargeattheboundariesofthisregion.Assoonasthelightisoff,thephotoexcitedstatesofimpuritiesrelax.Thespacechargemayremainforalongtimesinceitsonlyclean-outchannelinalow-conductivitycrystalisatemperature-inducedejectionofcarrierstrappedondonorsintotheconductionband,whichishardlyprobableatalowtemperature.Thus,whenaspecimenisexposedtolight,spontaneouspolarizationisreversedandthechargedistributionoverthebulkis'frozen'afterthelightisoff.Thismechanismdoesnotobviouslycorrespondtotheobservedphenomenonsincetheoccurrenceofmicrodomainsimpliesadecreaseofthetotalpolarizationintheexposedregion,andthe'frozen'volumechargeisclosetozero.Moreover,thepolarizationreversalregionmustbestrictlylimitedbytheexposedregion,whereastheradiation-inducedmicrodomainsarealsoobservedoutsidetheexposedregion.

Themechanismofoccurrenceofmicrodomainsduetoelasticstrainisobviouslyclosertotherealprocess.Asmentionedabove,localstraininaspecimenleadstotheappearanceofatenseregionofmicrodomainclusters.Whenahighlyintenselaserbeamisused,athermalshockisobserved.Becauseofashortradiationtreatmenttimeandasmallheattransfercoefficient,thisthermalshockcausesahighlocaltensionand,asaconsequence,theappearanceofmicrodomains.Thegeometryoftheobservedpatternisdeterminedbythecrystalsymmetry.Theclusterareaisdeterminedbythediameterofthelightspot.Thislimitationisnotstrict,andathighradiationintensitiesthetensionnearthespotmayprovesufficientfortheoccurrenceofmicrodomains.

Wehavecarriedoutcomparativestudiesofopticaldamageofsingle-modelightguidesformedusingautodiffusion,metaldiffusion,ion-exchangedoping(Goncharenko1967)andliquid-phaseepitaxy.Theoutputpowerwasmeasuredasafunctionofexposuretimeandoftheinputlightintensity.Thelatterwasvariedwithintherangeof0.5÷7mW,andtheobservationtimereached200h.Allthespecimensexhibitedloweringoftheoutputsignalwithsaturation.ThedependenceofoutputlightintensityontheinputintensityisdepictedinFig.5.42whichshowsthatTi:LiNbO3lightguidespossessthelowestopticalstrengthandepitaxialonesthehighest.

Experimentsonlightresistancesuggestthattheopticalstrengthoflightguidesisfirstofalldeterminedbytheconcentrationoftrapstheroleofwhichcanbeplayedbyoxygenvacanciesinthecrystallattice(particularlyforlightguidesformedinavacuum).Importantisalsotheimpurityionizationenergyvariationsinacrystal,trapdepthandequilibriumconcentrationshiftinoxidizedandreducedformsofactiveimpurities.JudgingbytheresultsreportedbyHolmanandGressman(1982),thelowlightresistanceofTi:LiNbO3isexplainedbytheappearanceinthelightguidestructureofaspecialtypeoftrapsforphotoinducedelectron-holepairsoccurringduetoanuncompensatedchargeexchangeunderthe substitutioninthecrystallatticesitesinthecourseofdiffusion.

Fig.5.42DependenceofthepowerlossT,atthesaturationlevel,ontheinputpowerPininlightguides:1)LiNbO3:Ti;2)LiNbO3:Tl;3)out-diffused;

4)epitaxial.

5.7Photorefractivepropertiesoflightguides

Theinterferometricmethodisusedtoexaminephotorefractivepropertiesofepitaxialstructures,namely,refractiveindexchangesundertheactionofphotoactiveradiation.

Thismethodisrealizedinthesameschemeasthestudyofelectro-opticpropertiesoffilms(seeFig.5.39).Thepartofthewaveguidebetweenelectrodesisexposedtolaserradiationperpendiculartotheplaneofthewaveguidelayer.Argon(l=488,514nm;P=6W)andkrypton(l=647nm;P=8W)laserswereusedforphotorefractiverecording.

ThevaluesofinducedrefractiveindexchangeDne(t)weredeterminedfromthenumberofdisplacedfringesMintheinterferencepatterngivenbytheformulae

Theestimatesofthemaximumlight-inducedrefractiveindexchangeshowthatwithintheexperimentalerror theDnevalueispracticallyindependentofthewavelengthofrecordinglightand

(Dne)maxmakesup .Thelimitingvalue(Dne)maxdoesnotpracticallydependontheLi(Nb,Ta)O3filmcompositioneither.

Thechange(Dne)maxisaresultofelectro-opticeffectinthebulkcrystal.Fromitsvalueonecanestimatethestationaryvalueoftheinternalelectricfield:

Usingthevaluesne=2.187,r33=2×10-11m/Vand(Dne)st=2×10-3atthewavelengthl=632.8nm,weobtainthelowerestimateoftheexternalelectricfieldinthefilm,Est~191kV/cmwhichagreeswiththevaluesobtainedforbulkmaterials(188kV/cmforLiNbO3and250kV/cmforLiTaO3(Schwarz1986)).

TheobtainedEstvalueisindicativeofahighelectricresistanceoftheinvestigatedepitaxialstructuresandisnotlimitingsincethevalue(Dne)maxthatcanbereachedinexperimentsisrestrictedbyelectricbreakdownsalongthefilmsurface(whichleadstoaspontaneousloweringofDne).

Assumingthelightabsorptioncoefficientalayerintheepitaxiallayertobeclosetotheabsorptioncoefficientinthesubstrate(a<5cm-1forl=488nmanda<1cm-1forl=647nm),onecanestimatethephotorefractivesensitivitySph:

whereWistheabsorbedenergy,Iistheincidentlightintensity,tistheexposuretime.

Substitutingtypicalexperimentalvalues forl=488nm,W/cm-2andt=15min,weobtain

Theobtainedvalue(l=0.488m)isanoverestimation.Sinceforlithiumniobatetheboundaryoffundamentalabsorptionliesatl<0.4mmandforlithiumtantalateforl<0.3mm(ed.byShaskol'sky1982),onemayassumethataLi(Nb,Ta)O3filmhas,infact,alaycr(l)>lsubstr(l)for>0.3mm.

TheSvaluesobtainedforLi(Nb,Ta)O3filmsareincloseagreementwiththevaluesofphotorefractivesensitivityoflithiumniobate,S=2×10-8,andlithiumtantalate,S=6×10-11cm2/J(Kuz'minov1982),andindicatethatthewaveguidestructuresobtainedpossesshigheropticalresistancethanlithiumniobatestructures.

5.7.1Holographicformationofgratingsinopticalwaveguidelayers

Theformationofthickphase(Bragg)gratingsinopticalwaveguidesbyelectro-optic(Hammeretal1973)oracousto-optic(Kuhnetal

1970)effectsiswellknown.Suchgratingsmayfindapplicationinintegratedopticsdevicessuchasswitches(Kenanetal1974;TaylorandYariv1974),modulators(TaylorandYariv1974),mirrors,beamsplitters,etc.Gratingsthatareformedphotorefractively,thatis,throughchangesintheindexofrefractionoccurringwhenamaterialisilluminatedwithlightcapableofalteringthedistributionormagnitudeofthepolarizabilitiesofitsconstituents,appeartoofferthefollowingadvantages:(i)thegratingspacingcanbesmallenoughsothatarbitrarilylargediffractionanglescanbeachieved;(ii)therefractiveindexchangesproducedcanbequitelarge,consequentlyefficientdiffractiongratingsarepossible;and(iii)noexternalstructuresareneededandnooperatingpowerisrequired.

Woodetal(1975)haveproducedsuchgratingsbyintersectingguidedcoherentbeamsof0.488-mmwavelengthinwaveguidesformedonthesurfaceofLiNbO3crystalsbyeffusionoflithiumandinawaveguideformedonthesurfaceofaLiTaO3crystalbyin-diffusionofavapour-depositedlayerofNb,

bywhichmeansavarying-compositionlayerofLiTa1-xNbxO3wasformed.Formingthegratingthiswayismuchsuperiortousingexternalbeamsintersectingatthewaveguidelayer.Theprincipaladvantagesofusingintersectingguidesbeamsarethattheavailablewritingpowerdensitiesarehigh,thepropergratingorientationisachievedautomatically,andthegratingislocatedintheregionofmaximumenergydensityoftheguidedwave.

AschematictopviewoftheexperimentalarrangementusedtowriteanddetectthegratingsisshowninFig.5.43.TheLiNbO3orLiTaO3slabandtherutileprismcouplersarerotatableasaunitabouttheaxisAAwhichliesintheslab.Thisdegreeoffreedomisrequiredfortheadjustmentofthecouplingangle.Thegratingiswrittenbythephotorefractiveeffectutilizingthe0.488µmlineonanargon-ionlaser.Thepowerdensityinthewaveguideisestimatedtobeabout1W/cm2.Writingtimesforthegratingswereinthe1-10minrange,dependingupontheironcontentofthesample.

Afterthegratingwaswritten,mirrorsM1andM2wereusedtoindependentlyadjustthedirectionandpositionofthe0.633µmbeamtomaximizetheamountof0.633µmlightdiffractedbythegrating.Sincetheacceptanceangleofthegratingis mrad,thisadjustmentiscritical.

ThegratingsineffusedwaveguidesweredoneusingY-cutcrystalsofundopedLiNbO3heatedinoxygentoformLi-deficientsurfacelayerswithhigherextraordinaryrefractiveindicesthanthebulk.SuchlayerscanbeproducedtosupportanywherefromonetoseveralhundredTEmodes;TMmodesarenotguided.Whileitwasnotdifficulttoformgratingsinsuchlayers,andwhileadiffractionbeamcouldbeobserved,itsintensitywasverylow.Thisappearedtoresultfromthelowmaximumdiffractionefficiency(generallyunder1%)obtainableinundopedorverylightlydopedLiNbO3.

Thehighestdiffractionefficiency(definedaspowercoupledoutinthediffractedbeamdividedbysumofpowerscoupledoutinboththediffracted

Fig.5.43Schematicofapparatususedtowriteanddetectgratingsina

slabwaveguide.Thegratingvectorisparalleltothec-axisoftheLiNbO3slab.Allopticalbeampolarisationsareparallelto

thesurfaceoftheslab.PinandPoutareprismimputandoutputcouplers(Woodetal1975).

andundiffractedbeams)inaneffusedguidewasobtainedinamultimodeguideinheavilyiron-doped(1000ppminmelt)LiNbO3.Aninterferencephotographshowedthatthisguidehadanoverallextraordinaryindexchangeofabout0.004andadiffusionlengthofabout140µm;itshouldsupportaround60TEmodesatthe0.488µmhologramwritingwavelength(KaminowandCarruthers1973).Adiffractionefficiencyof52%at0.488µmwasattained.

GratingformationwasalsostudiedinashallowguideproducedbyheatingaLiNbO3platefor14minat1118°C.Suchaguideshouldsupportonlyabout5TEmodesat0.633µm;individualmodescouldnotberesolvedexperimentally.Thisplatewasfromaboulegrownfromameltdopedwithjust50ppmiron,andthemaximumdiffractionefficiencyobtainableinthebulksample(withoutthewaveguide)foragratingwrittenwith0.488-µmlightandreadat0.633µmwas2.4%.Themaximumdiffractionefficiencywasobtainedwiththeread-beampolarizationparalleltothecaxis,thesameorientationasintheguideTEmodes.Themaximumdiffractionefficiencyat0.633µmforagratingwrittenwith0.488-µmlightinthewaveguidewas3.1%greaterthanthatobtainableinthebulkcrystal.Neitherthedifferenceingratingthickness(extentinthedirectionoftheincidentbeam)northedifferenceintheanglebetweenthewritingbeamsissufficienttoaccountfortheobserveddifference.Possiblythehigherpowerdensityintheguidedbeamledtoahighermaximumrefractiveindexchange.

Shallowwaveguidelayerswithlargeindexchanges,supportingonlyafewmodes,maybeproducedbydiffusingNbintoLiTaO3(seechapter1).

TEmodespropagatingalongtheaaxiswereusedtowrite(at0.488µm)andread(at0.633µmandat0.488µmbyblockingonewritebeam)agratinginthewaveguide.Anefficientgratingwithaperiod

of1.4µmformedreadilydespitethepresumablyunpoledstateofthesample.Themaximumdiffractionefficienciesobtainedwere28%at0.633µmand65%at0.488µm.Forcomparison,nodiffractionefficiencyabove1.2%couldbeobtainedateitherwavelengthforgratingsformedthroughoutthebulkLiTaO3crystal,eitherwithorwithouttheinfusedNblayeratthesurface.

Analternativelinearphotorefractivetechniqueistheuseofshort-wave-lengthlighttoformthehologramsandlong-wavelengthlight,forwhichthephotorefractivesensitivityisnegligible,astheoperatingwavelength.Thistechniqueissatisfactoryonlyforsimpleplane-gratinghologramssincecomplexthickhologramssufferlargelossesinfidelityandefficiencyifthereadandwritewavelengthsdiffer.

Aholographicwritingtechniquewhichhastheusefuladvantagesofavoidingdestructivereadout,producingstableholograms,andretainingthelowopticallossofout-diffusedwaveguidesinundopedcrystalsisbasedupontheuseofmultiphotonabsorption(vanderLindeetal1974)forinitiatingthephotorefractiveprocess.Veberetal(1977)havedemonstratedthathologramsmayberecordedbyatwo-photonabsorptionprocessinout-diffusedLiNbO3waveguidesbyintersectingtwoguidedwaves,andthattherequiredenergyandintensityarereadilyachievedinthewaveguideusingcommerciallyavailablelasers.

TheabsorptionofabeamoflightofintensityI(W/cm2)inatwo-photonprocessisdescribedby

wherea2isthesecond-orderabsorptioncoefficientandxisdepthinthecrystalmeasuredfromthesurfaceuponwhichthebeamisincident.Theindexchangeassociatedwiththephotorefractiveeffectisproportionaltothenumberofelectronsexcitedintotheconductionband.Forthetwo-photonprocess,thisnumberwillbeproportionalto(1/2)N,whereNisthenumberofphotonsabsorbedpercm3.Theindexchangeisthen

whereSisaproportionalityconstantcharacteristicofthematerialandthegeometry.Foranopticallythinsample,Dnisnotafunctionofxand

wheretisthetimeduringwhichthesampleisirradiatedandhnisthephotonenergy.IftheirradiationoccursintheformofMequalrectangularpulsesofdurationDt,then

whereallconstantshavebeenabsorbedintok.Thetwo-photonprocessisthenindicatedbyaquadraticdependenceofDn/MuponI.

ThisquadraticdependencewasobservedusingaNd:YAGlaserwithanintercavitydoublerwhichproduced140nspulsesof0.53µradiation.Afterreflectionfromawedgebeamsplitterthelaseroutputwasprismcoupledintoanout-diffusedwaveguideinthesurfaceofanundopedLiNbO3slab.ThevalueoftheinducedAnwasmonitoredbymeasuringthediffractionefficiencyoftheholographicgratingformedinthebeamoverlapregion.Thedatashowninthelog-logplotin

Fig.5.44clearlydisplaythequadraticbehaviourindicativeofthetwo-photoneffect.Fromthemaximumpowerincidentuponthecouplingprismof2kWandestimatesofthecouplingefficiencyandeffectivewaveguidethickness,onecanestimateamaximumpowerdensityof106W/cm2inthewaveguide.Diffractionefficienciesofseveralpercentwereobservedwithnosignofsaturation.Comparisonoftheseresultswiththedata(vanderLindeetal1974)obtainedusingthesamewavelengthbutinabulkconfigurationshowsafargreatersensitivityforthewaveguidecase.Thediscrepancyislargerthancanbeaccountedforbyexperimentalerrorsorerrorsinestimatingthepowerdensityinthewaveguide.Thediscrepancymaybeduetovariations

Table5.10DiffractionefficiencyhandphotorefractivesensitivityaSofplanarTi-diffusedwaveguidesat0.458µm(Glass,Kaminow,Ballman,Olson,1980)

Inputpower(µW)

Exposuretime(s)

EnergydensityEinguide(J/cm2)

h h/E(cm2/J)

(cm2/J)

17 120 20 0.011 0.0052 1.3×10-7

120 20 24 0.1 0.013 3.0×10-7

250 10 25 0.1 0.016 3.0×10-7

Fig.5.44Log-logplotofDn/pulseversuspowerdensityforagratingwritteninanout-diffusedLiNbO3waveguidewithpulsed0.53µradiation.Thesolidlinehasaslopeof2.Thegratingspacingis0.55µ

(Vebereta11977).

inducedbytheout-diffusionprocessortoothercompositionaldifferencesinthesamplesusedforthetwosetsofmeasurements.

5.7.2PhotorefractiveeffectinplanarTi-diffusedguides

Theformationofelementaryhologramshasbeendescribedaboveforout-diffusedLiNbO3waveguides(Glassetal1980).AsimilarmethodisemployedusingaTi-diffusedplanarguide.Thetechniqueinvolved

couplingtwobeamsintotheplanarguide,asshowninFig.5.45sothattheyformathickhologrambymeansofthephotorefractiveeffect.Themagnitudeoftheindexchangecanbemeasuredfromthediffractionefficiencyofthehologram(Kogelnik1969)

where istheinteractionlengthandqistheanglebetweenthetwobeams.Thewritingbeamswerecoupledinandoutofthewaveguideusingasingleprism(Saridetal1978),andthediffractionefficiencywasprobedwithaHe-Nebeambyrotatingtheentireprism-waveguideassemblytoobtaincouplingatdifferentwavelength.

Hologramscouldnotberecordedat0.633µm,with300µWofoptical

Fig.5.45Experimentalarrangementformeasuring

photorefractivesensitivityofplanarTi-diffusedLiNbO3waveguides.Thepolaraxisisinthe

planeofthewaveguideparalleltotheprismapex(Glassetal,1980).

power.Theresultswerethesamewithinexperimentalerrorsat0.515µm.Boththeexposureandthediffractionefficiencycouldbemeasuredwithanaccuracyofbetterthan5%,thusthemajorerrorliesintheestimateoftheenergydensityintheguide.InTable5.10theenergydensityinthewaveguidewasestimatedasfollows.Thewidthofthetwobeamswas0.3mm,andtheeffectivedepthoftheguidewastakentobe3µm.(Twomodescouldbelaunchedintheguide.)At0.458µmthetotalinsertionlossoftheentireprism-waveguideassemblywas15dB(at0.633µm,loss=10dB).Thislossisconsiderablygreaterthanthatreportedforoptimizedprisms(Saridetal1978)presumablybecausenospecialprecautionsweretakentooptimizethetaperbetweentheprismsandguidesforanywavelength.Glassetal(1980)assumedthat10dBofthelossoccurredattheinputcouplergivinganenergydensityintheguideofabout104timestheincidentpower.Anerrorinestimatingthecouplingefficiencyof±5dBleadstoanerrorintheestimatedpowerdensityintheguideofafactorof3.

Theinducedhologramwasfoundtorelaxveryrapidlyafterexposure.Forthisreason,longexposureswerealwaysfoundtobelessefficientthanshortexposuresforrecordingholograms.ForshortexposuresthedatainTable5.10gives

Usingthevalueofa=0.08l=0.633and0.515µm(Glassetal,1980)theresultisaphotorefractivesensitivityof

Thisresultisevensmallerthanthatobtainedforthesubstratecrystal,andhencedespitetheexperimentalerrorstheyprovideconclusiveevidencethat

TiimpuritiesdonotcontributesignificantlytothephotorefractiveeffectinLiNbO3waveguidesdirectly.Theresultsofequation(5.63)and(5.64)areconsistentwiththeinterpretationthatthephotorefractiveeffectinTi-diffusedwaveguidesisduetoresidualFe2+impuritiespresentintheLiNbO3substratematerialbeforediffusion.

Fujiwaraetal(1989)reportedonanewnovelmethodofquantifyingthephotorefractivesensitivityofTi-indiffusedLiNbO3waveguides.TheproposedmethodissimilartotheonebyBeckerandWilliamson(1985)inusingawaveguideMach-Zehnderinterferometer.Byseparatingtheirradiationlight(includingtheindexchange)andprobelight,theintensityandthewavelengthoftheirradiationlightcouldbereadilyvariedemployingthesamewaveguidepattern.Frommeasurementsofthephotorefractivesensitivityatvariousirradiationwavelengths,Fujiwaraetal(1989)estimatedthelevelofcrosstalkdegradationasafunctionofirradiationintensityandwavelength.

ThewaveguidepatternwasdesignedandfabricatedbyFujiwaraetal(1989)asshowninFig.5.46.ItisbasicallyaMach-Zehnder(MZ)interferometerforthe1.3µmwavelengthinwhichtheirradiationbeamofwavelengthlirisfedintotheupperarm.LightinputfromportAbroughtaboutaphotoinducedindexchangeandconsequentlyanasymmetryoftheopticalpathbetweenthetwointerferometerarms.Thephaseretardationoftheupperarmrelativetothatofthelowerarm,

causedtheprobeoutputtobemodulatedas

where isthelengthoftheinterferometerarms,lp,theprobe

wavelength,andDn(t)theaverageindexchange

Theprobelightof1.3µmwasinputfromportB.SinceopticalwavesoftwowavelengthsweremixedatoutputportC,theprobelightwaschoppedat270HzbeforeenteringportBandtheprobeoutputwasmeasuredbyalock-inamplifierplacedafteraphotodetector.Theprobelightintensitywaskeptbelow5µWtoensurethatnophotorefractiveeffectwascausedbytheprobe(Fujiwaraetal1989).PortDmonitoredanytemporalvariationofthe1.3µmprobelightduetoinputfibre-waveguidecoupling.

InFig.5.46,thewaveguidewidthis7µmandtheangleqofwaveguidebendingis1.7°.ThelengthLoftheinterferometerarmsis16mm.

Boththeirradiationandprobebeamswerefedthroughopticalfibresbutt-coupledtoinputportsAandBThequantitiesDneandDnocanbedeterminedseparatelybyadjustingtheinputprobepolarizationtotheTMandTEmode,

Fig.5.46ConfigurationoftheTi-diffusedwaveguidepattern

fabricatedinanLiNbO3substrateforthemeasurementofaphotoinducedindexchange(Fujiwaraetal1989).

Fig.5.47Typicaltimedependenceoftheprobeoutputofthe

Mach-Zehnderinterferometeraftertheonsetofirradiationofwavelength0.633µm(Fujiwaraetal1989).

respectively.Theirradiationbeampolarizationwasadjustedtobe45°fromtheopticalaxisofthesubstrate.Thewaveguides,designedtobesinglemodeatl=1.3µm,naturallysupportafewmodesforl=0.63-1.06µm.

Atypicalrelationbetweenprobeoutputversusirradiationtimetforlu=0.633µmisshowninFig.5.47.SincetheMZinterferometerwasinitiallysymmetrical,theoutputIpisatamaximumintheunirradiatedstate.Inthefigure,theintensityratioofthefirstmaximumandthefirstminimumcorrespondstoanextinctionratioof18dB,whichwasatypicallevelforallirradiationwavelengths.Inthe'symmetric'Ybranchinwhichtheirradiationwasfedintotheupperarm,a3dBlossofthe1.3µmprobelightwasexpected.Hence,

unequalpowerinthetwoarmswouldlimittheextinctionratioofthemodulatortoabout15dB.However,sincetheirradiationintheupperbranchinducesanindexchange,theYbranchbecomesasymmetric,reducingthebranchinglossfrom3dB.Thisopticallyinducedasymmetryexplainstheextinctionratiohigherthan15dB.Further,therelativelyhighextinctionratioindicatesthataspatiallyhomogeneousindexchangewasmeasured;scatteringduetospatialinhomogeneityofindexchangewasnotappreciable.

AphotoinducedindexchangeofDn10-5wasdetectedandafurtherimprovementofthesensitivityshouldbefeasiblewithdesignmodificationssuchasmodulatingtheprobelightbyanexternalfieldapplieduponthelowerarmoftheinterferometer.

Sincetheinterferometeroutputcanbeexpressedbyequation(5.65),theobservedtemporalchangeoftheoutputcanbeconvertedtothetimeevolutionof .ForallwavelengthslirandirradiationintensitiesIir,agoodfittoanexpression

Fig.5.48PhotorefractivesensitivitySplottedasafunctionofirradiationintensityIirforeachwavelength

(Fujiwaraetal1989).

couldbeobtained,wherethebarovern(t)denotesspatialaveragingalongthepath .Thephotorefractivesensitivitywasdefinedas

Attheinitialstage,

wheretistheirradiationtimeand isthesaturatedindexchange.InobtainingIir,thewaveguidewasassumedtobeuniformlyilluminatedinsidethecrosssectionof5×10-7cm2forallirradiationwavelengths.IndeterminingthedependenceofSontheirradiationintensity,thesubstratewasannealedat180°Cfor30minaftereachmeasurementtoerasetheinducedindexchange.Theannealingtemperaturewasfoundtocompletelyreverttheinterferometertoasymmetricone.

TheopticalintensitydependenceofSforeachwavelengthisshowninFig.5.48.TheirradiationintensitywasmeasuredatthearmoftheMZinterferometerbycutbackofthewaveguide,andthespatially

averagedirradiationintensityIiratthearmwascalculated.ThedependenceofSonIircanbedecomposedtothebehaviourof andtasisseeninequation(5.66).The wasfoundtobeinitiallyproportionaltoIirandthenshowedaslightsaturationathigherIir,whereastheinversetimeconstantofbuildup,1/t,wasnearlyconstantuptoIirof40W/cm2andthenshowedasharpupturnathigherirradiationintensities(Izutzuetal1982).InthefirstregionwhereIirissmall, isproportionaltoIirwhile1/tisconstant,renderingStobenearlyconstant.

Inthesecondregion,the vsIirrelationdeviatesfromlinearity,while1/tisstillconstant,andthereforetheratio graduallydecreaseswithincreasingIir.Inthethirdregionatstillhigherirradiationintensitylevels,thesharpincreaseof1/twithIirpredominatesthebehaviourofS .Acombinedeffectofthesecondandthethirdregionsresultsinadipinthethreecurves.Themechanismforthesharpincreaseof1/tisyettobeclarified.

Intheintensity-independentregion,SdecreaseswithincreasingwavelengthforbothTMandTEmodes.TheSfortheTMmode,STM,isaboutthreetimesgreaterthanthatfortheTEmodeforalllirandIirTheratioofthephotoinducedphasechangesfortheTMandTEmodesis ,whereGTMandGTEare,respectively,theoverlapintegralsbetweentheinternallyinducedelectricfieldandtheTMandTEopticalfields(Glass1978).At1.3µm, isabout3.2(Holmesetal1983).Althoughtheoverlapintegralscouldnotatthatstagebereliablyestimated,takingtheratio accountsfortheexperimentallyobservedratioSTM/STEof3.2-3.4.

5.7.3Relaxationofindexchange

Norelaxationoftheinducedindexchangewasobservedinbulksingle-crystalTi:LiNbO3overaperiodofdays;theindexchangepersistsforalongtimeduetothehighresistivityofcrystalsandthepresenceofdeeptrappingsites.Inwaveguides,ontheotherhand,theinducedindexchangerelaxesoveraperiodofhours.Therelaxationratedecreaseswithincreasingtime,asshowninFig.5.49.Therelaxationdoesnotfollowanexponentiallaworthesumoftwoexponentials.

ThisbehaviourhadbeenobservedpreviouslyinthedecayofX-rayinducedcentresinMgO.Inthatcasethedecaywasshowntobehyperbolicnotexponential.Thisbehaviouroccursifthermallyactivatedcarriershaveahighprobabilityofbeingretrappedinsteadof

recombiningattheequilibriumsites(SearleandGlass1968).InTi-diffusedLiNbO3therelaxationoftheindexchangewasfoundtobehyperbolic,i.e.Dnl/t(Glassetal1980).AgoodfittotheexperimentalrelaxationcurveisshowninFig.5.49.Thisbehaviour

Fig.5.49Relaxation(at300K)oftheinducedrefractiveindexchangeinplanarLiNbO3waveguides.ThepointsarecalculatedassumingabimoleculardecayDna/t

(Glassetal1980).

impliesthatthetrappedcarriersareinshallowtraps(thenatureofwhichisnotknown)andthatprobabilityofrecombinationatasimilartrappingsiteislargecomparedwithrecombinationatFe3+(excitedFe2+)centres.Inanycasethedatadosuggestamuchlowerdensityofdeeptrappingsitesinthewaveguidesthaninbulkcrystals.SinceitisknownthatFe3+ionsareindeeddeeptrapsinbulkLiNbO3crystals,therelaxationbehavioursuggestsalowdensityofFe3+ionsintheTi-diffusedlayers,thatis,allunexpectedFeionsareinthereducedstate.ThiswouldalsoaccountforabimolecularrelaxationifthedensityofshallowtrapsismuchgreaterthanthedensityofFe3+ions.

ItisprobablethatTi4+ionssubstituteforNb5+ionsintheLiNbO3crystalinwhichcasetheTi-ionsitecarriesaneffectivenegativecharge.CompensationmaybeaccomplishedbyreducingimpuritiessuchasFe3+tothebivalentstate,i.e.theTiin-diffusiontendstostabilizethereducedstatesoftheimpurities.TheFe2+-Ti4+complexisneutralifitcompensatesforaLi+-Nb5+pair.Thereducedstateofseveralions(Fe2+,Mn2+,Cu1+)isknowntoenhancethephotorefractiveeffectinLiNbO3(Petersonetal1971;StaeblerandPhillips1972).

ReductionofallmultivalentimpuritiesinthecrystalisalsolikelytoresultinincreasedphotoconductivitysinceithasbeenestablishedthatthefreecarriermobilityinFe-dopedLiNbO3singlecrystalsisgreatlyincreasedinreducedcrystalsduetothereductionoftheFe3+trapdensity(StaeblerandPhillips1974).ThisfactmayexplainthehighphotoconductivityobservedinTi-diffusedLiNbO3filmscomparedwithbulkcrystals.Itshouldbepointedoutthatindevicesrequiringanappliedfield,photoconductivityleadstospacechargefieldsandindexchangesinthesamewayasthezerofieldphotorefractiveeffect.

5.7.4Photorefractiveeffectinannealedproton-exchangedLiNbO3waveguides

Fujiwara,etal.(1992)presentedacomparativestudyofthephotorefractiveeffectinPEandAPELiNbO3waveguidesatanirradiationwavelength(lir)of488nm.Fromaquantitativemeasurementofthetemporalbehaviourofthephotoinducedindexchangeduetoirradiationatseveralintensities,theintensitydependenceofthesaturatedindexchangeaswellasthebuild-uptimeconstantinPEandAPELiNbO3waveguidesaredetermined,andthephotorefratorysensitivityinbothwaveguidesisevaluated.Theresultsindicateanincreaseinthesaturatedindexchangeofthephotorefractiveeffectduetoannealing,ahigherphotorefractivesensitivityofAPEwaveguidesthanthatofPEwaveguidesandalargercontributionofthedarkconductivitytothephotorefractiveeffectintheintensityrangeusedintheexperiments.

SevenmicrometerwidePEandAPEwaveguides,sinlgemodeatthewavelengthof1.3µm,wereusedinthemodifiedMach-Zehnderinterferometerconfiguration.ThewaveguidepatternwasdelineatedonanaluminiummaskevaporatedonthecfaceandLiNbO3substratebyetching.Proton-exchangewascarriedoutinbenzoicacidat220°Cfor88minforPEand20minforAPELiNbO3waveguides.AfterremovingtheAlmask,theAPEwaveguideswereformedbyannealingat350°Cfor6h.

Bymeasuringtheoutputintensityoftheprobelightduringirradiationexposure,theauthorsobtainedthetimedependenceofthephotoinducedindex

changeDn(t).Figure5.50showsthetypicalresultsforDn(t)forirradiationintensities(Iir)of65.4and105.3W/cm2forAPELiNbO3waveguides.Theabovevaluesoftheintensityrepresentspatialaveragesacrossthewaveguidecross-section,assuminguniformilluminationandareestimatedbytakingintoaccountthelossesatthearmintheinterferometer.Theauthorshaveusedthevaluesof7.0×10-8cm2forPEand2.7×10-7cm2andAPEwaveguidecross-sectionsinobtainingtheirradiationintensityforalltheexperimentaldata.ThebuildupoftheindexchangeshowninFig.5.50isexponentialandiswrittenas

whereDnsisthesaturatedindexchange,andtisthebuild-uptimeconstant(Fujiwara,etal.1989).ThesolidlinesrepresentthefitofthedatapointstoEq.(5.67).

BasedontheGlassmodel,Dnsisproportionaltothesaturatedspace-chargefield(Eswhichisexpressedas wherekistheGlassconstant,aistheabsorptioncoefficient,andsdandspharethedarkandphotoconoductivityrespectively.Assumingthatthephotoconductivityisproportionaltoboththeabsorptionandtheirradiationintensity, ,theauthorsobtained

whereneistheextraordinaryindex,r33istheelectro-opticcoefficient

andaisaconstantexpressedas ,whereeistheelectroncharge,

Fig.5.50Timedependenceofrefractiveindexchange

Dn(t)inAPELiNbO3waveguidesforirradiationintensitiesof65.4and105.3W/cm2atanirradiationwavelengthof488nm.Solidcurvesrepresentfitto

Eq.(5.67)(Fujiwaraetal1992).

hnthephotonenergy,µtheelectronmobility,t0thecarrierlifetimeandfthequantumefficiency.AccordingtoEq.(5.68),inthelowerintensityregionwherethedarkconductivityispredominant,thesaturatedindexchangecanbeexpressedapproximatelyas ;therefore,parameterArepresentstheresponseofthesaturaedindexchangeinthelowerintensityregiondominatedbythedarkconductivity.Inthehigh-intensityregion,wheretheresponseisgovernedbythephotoconductivity, approachesA/B,whichisindependentofboththeirradiationintensityandopticalabsorption(Fujiawaetal1989)anddependsupontheratio(r33k/a)only.

Ontheotherhand,thebuild-uptimeconstanttcanbeexpressedas,whereeristhedielectricconstant.Theintensity

dependenceof1/tisgivenby

where .Therefore,theintensitydependenceof1/t,givenbyEq.(5.69),yieldsthevaluesofbothdark-conductive(1/td)andthephotoconductive(aa/ere0)terms.

Moreover,ifwewriteEq.(5.69)as

Fujiwaraetal.(1992)havefittedthemeasureddependenceofDns,onIirtoEq.(5.68)usingAandBasadjustiveparametersandtheresultsareshowninFig.5.51.ThevalueofAisgiveninTable5.11forbothPEandAPELiNbO3waveguides.Inbothcases,thesaturatedindexchangeDns,varieslinearlywithintensityinthecornerintensityregion,andtendstodeviateslightlyfromthelinearbehaviourinthehigherintensityregion.Thisalmostlinearbehaviourindicesthatthedark-conductivitycomponentisdominantincreatingthespace-chargefieldandthecontributionofthephotoconductivityisnegligible.Inotherwords,productBIirisstilllessthanunitywithintheintensity

rangeusedintheexperiments.DnsofAPELiNbO3waveguidesisabouteighttimesthatofPEwaveguidesatirradiationintensityofupto100W/cm2ThealmostlinearbehaviourofDns(Iir)doesnotpermitanaccuratedeterminationofBbytheabovefittingprocedure.

Figure5.51alsoshowsthefitoftheintensitydependenceof1/ttoEq.(5.69).Fromtheintercept,thedarkconductivityofthePEandAPEwaveguidesisobtained,whichislistedinTable5.11.Theratiooftheslopeandtheinterceptofthe1/t(Iir)straightlinesyieldsB.ThevaluesofBarelistedinTable5.11.

FromEqs.(5.68)and(5.70),thephotorefractivesensitivityS(definedby )(Fujiwaraetal1989)isexpressedas

Figure5.52presentsaplotofthedependenceofirradiationintensityofDns/tforPEandAPEwaveguides,andinthelastcolumnofTable5.11thereis

Fig.5.51IntensitydependenceofDnsand1/t

forPEandAPELiNbO3waveguidesatanirradiationwavelengthof488nm.Solid

andbrokenlinesrepresentthebestfitofthedatatoEqs.(5.68)and(5.69),

respectively.

Fig.5.52(right)IntensitydependenceofDnsand

1/tforPEandAPELiNbO3waveguidesatanirradiationwavelengthof488nmshowinga

linearbehaviour.Theslopeofthelinesgivesthephotorefractivesensitivityforthe

correspondingwaveguide(Fujiwaraetal1992).

Table5.11ThevaluesofparametersdescribingthephotorefractiveeffectinPEandAPELiNbO3waveguidesatanirradiationlengthof

488nm(Fuyiwaraetal1992)

A×10-7(cm2/W)

sd×10-4(ohmcm)-1

B×10-3(cm2/W)

Dns×10-4

S×10-9(cm2J)

PE 0.88±0.04 1.5±0.1 0.37±0.08 2.6±0.7 0.54±0.01

APE 6.6±0.4 0.56±0.17

6.1±3.2 1.6±0.9 1.8±0.06

alistofvaluesofthephotorefractorysensitivityforPEandAPEwaveguides,obtainedfromtheslopoftwostraightlines.

Theeffectofannealingonthephotorefractivepropertiesofproton-exchangedLiNbO3waveguideswillnowbediscussed.Firstofall,theparametersAincreasesbyalmostanorderofmagnitudeasaresultofannealing.Thisiscausedbyalmostafactorof3increaseinther33coefficient(Becker1983)andadecreaseinthedarkconductivitybyalmostthesamefactor.Whilethereducedelectro-opticcoefficientinPEwaveguidesisattributedtothenear-cubicsymmetryoftheproton-richLiNbO3,thehigherdarkconductivityofPELiNbO3waveguidesmaybeaconsequenceofthepresenceofshallowdonorlevels(traps),probablyresultingfromtheincorporationofprotonsatinterstitialsites.

5.8Energylossinwaveguides

5.8.1LossesinTi-diffusedLiNbO3waveguides

Animportantconsiderationintheperformanceofanyopticalwaveguidedeviceisitsinsertionloss,L=-10logT,whereTisthepowertransmissioncoefficient.Aconvenientmethodforobtainingthewaveguidepowerattenuationcoefficienta(indB/cm)istomeasureLasafunctionofguidelength .Foratitanium-diffusedLiNbO3stripguide,however,theproblemistochange withoutchangingthecouplingintoandoutoftheguidethroughtheendfacetsofthecrystal.Polishingtheendswithoutroundingrequiresgreatcare;butcleavinghasthepotentialforprovidingreproducibleandrectangularendswithlittledifficulty(HsuandMilton1976).However,thecleavingmethodrequiresaspecialcrystalorientationand,inaddition,reflectionsfromtheparallelendfacetsleadtostanding-wavebehaviourthatmustbetakenintoaccount.KaminowandStulz(1978)describedlossmeasurementsinacleavedcrystalcontaininga4-µm-widesingle-modeTi-diffusedwaveguide.Inordertoillustratetheisolationfrommetalelectrodesprovidedbyadielectricbufferlayer,theauthorsalsomeasuredaguideovercoatedwithametallayerseparatedfromguidebyAl2O3orSiO2.

TheexperimentalsetupisillustratedinFig.5.53.ThepowerincidentontheinputmicroscopeobjectivefromthepolarizedHe-Nelaser,Pin,ismaintainedatlessthan2.5µWtoavoidopticaldamageinthecrystalandnonlinearityintheunbiasedphotodiodeusedtomeasurePinandPout.Theoutputobjective(×20,0.57N.A.)hasasufficientlylargeaperturetocollectallthelightfromtheguide.Anirisisprovidedtoisolatethewaveguidemodefromextraneousscatteredlight.Thepolarizationoftheoutputspotisobservedtobethesameasthatoftheinput.Aheater,shownschematicallyinFig.5.53,tunestheFabry-Perotformedbythecleavedendfacetsthroughmaximaand

minimabythermallyvaryingtherefractiveindexn.With ,theFresnelreflectioncoefficientR=0.14,whichiscalculatedbytheformulaR=[(n-1)/(n+1)]2.

IfT=Pout/Pin,theinsertionlossListhesumofthreecontributions:ThetwolensesintroducelossL1whichismeasuredintheabsenceofthecrystalas1.2dB.ThemismatchbetweenthecircularGaussianinputwavefunctionandthestrip-guidewavefunctionintroduceslossL2.ThecrystalintroduceslossL3duetothewaveloss, ,andtheeffectsoftheFresnelmirrors.

BurnsandHocker(1977)haveshownthatbychoosingtheGaussianinputspotradiuswtobethegeometricmeanoftheequivalentspotsizesw1andw2measuredalongtheprincipalaxesofthewaveguidemode,themismatchlossL2maybeassmallas0.8dB.Fortheguideunderinvestigation,the

Fig.5.53Intersectionlossmeasurementapparatus(KaminowandStulz1978).

value .Thecondition wasachievedbytestingvariousmicroscopeobjectivesinordertofindonethatgaveminimumL.ForanobjectivewithnominalnumericalapertureNandpupildiameterDfocusingalaserbeamofGaussiandiameterd,KaminowandStulz(1978)estimatedwusingparaxialGaussianbeamopticsas

Forthepresentmeasurementsatl=0.63µmwithd=1mm,itwasfoundthata×10lenswithnominalN=0.25andD=8mmgavetheminimumloss.Thespotdiameter2wcalculatedfromequation(5.72)was12pro,whichmaybereasonableforanominal4µm-widestripguide,allowingforlateraldiffusionandsmallguide-substrateindexdifference.

Thetransmissionthroughthecrystalwas

iftheendfacetsdonotprovidecoherentreflections,butwithFabry-Perotbehaviourthetransmissionrangesbetween

Inequations(5.73)and(5.74)thetransmissionthroughthewaveguidewas

whereaismeasuredindB/cm.ItshouldbenotedthatbyconvertingTtoL,equations(5.73)and(5.74)give

for ,sothatL0isalsotheaverageFabry-Perotloss.

TheorientationofthecleavedcrystalisindicatedinFig.5.54.The250µmthickplateisnormaltothecrystalxaxisandcontainstheopticz

axisatanangleof32.75Åfromthecleavededge.Ascribemarkismadeonthewaveguide-containingsurfaceatoneedgeoftheplate;twopairsoftweezersoneithersideofthemarkareusedtomakethebreak.Asisusualoncleavedsurfaces,anumberofterracesappears,asindicatedschematicallyinFig.5.54.TheedgesoftheterracestepsareindicatedbythedottedcurvesinFig.5.54.Thecharacteroftheterracesandthenatureofthecleavedendfacetdependuponwhetherthebreakstartsnearthenegativeorpositiveendofthezaxis.

ThecleavageplaneinLiNbO3wasidentifiedasa{102}plane.However,

Fig.5.54Cleavedcrystalorientationshowinga4µmwideguideandevaporatedelectrodespaces9µmapart.Thedottedcurvesonthecleaved

facerepresentterracesteps;thefirstfewofthesestepsstartnearthescribemarkonthesurfaceoftheplate(Kaminowand

Stulz1978).

thereissomeambiguityinassociatingthegeneric{102}planewitheitheroftheactual(102)or(012)planesinthecrystallattice.Nevertheless,examinationofacrystallatticemodel(Megaw1973)revealsthelikelyplaneastheonewhichcontainsthelayerofvacantoctahedralsitessurroundedbyalayerofLiononesideofthecleavageandalayerofNbontheother(indicatingpossiblechargeneutrality).Theatomicspacingsacrosstheproposedcleavageplanearerelativelylarge,indicatingweakbonding.

Lightpolarizednormaltothecrystalplate,paralleltothexaxis,isanordinarywave.Theguideisorientedperpendiculartotheendfacetswithin1/4°.InsertionlossLcanbeobserved(withanoscilloscopeconnectedtothephotodiode)topassthroughFabry-Perotmaximaandminima,asinequation(5.74),asthetemperaturevariesoverafewdegreesofCentigrade.Ontheotherhand,lightpolarizedintheplaneofthecrystalplateisanextraordinarywave.Inorderthatthe

Poyntingvectorbeparalleltotheguideaxis,theincidentbeammustenteratabout4.5°fromthenormal(BurnsandWarner1974).Thewave-normalvectoristheguideisthenabout2°fromtheguideaxisandthewavefrontsarenolongerparalleltothecleavedfacets.Thenthelossbehaviourcorrespondstoequation(5.73)andnomaximaorminimaareobserved.

Waveguideswerefabricatedbydiffusing4µmwide180ÅthickTistripesinflowingO2usingstandardacousticgradeLiNbO3substrates.Tiwasevaporatedfromatungstencoil.ThelossmeasurementsonsuchaguideareplottedinFig.5.55.Agoodfittothedatafortheordinary-wavemaximaandminimawasobtainedfora0=1.0dB/cm,L1=-1.2dB,L2=0.8dB,andR=0.14.Theestimatedaccuracyofthelossmeasurementswas±0.2dB.Notefromequation(5.74)thatameasurementofLmaxandLminatone issufficienttoobtaina0forgivenL1,L2,andR.However,measurementsatseveralvaluesof giveaddedprecision.Theextraordinary-wavedataisfittedbyalinewiththeslopeae=1.5dB/cm,forthesameL1,L2,andR.

Metalelectrodes(consistingof300ÅofTiplus700ÅofAg)20lainwideandspaced9µmapart,wereevaporatedalongsideasimilar4µmwideguide

Fig.5.55InsertionlossLversuswaveguidelength for

a4-µmwideTi:LiNbO3guide.Solidlinesgivemaximum,minimumandaverageloss(Lmax,

Lmin,andL0)ofFabry-Perotresonatorcalculatedfora0=1.0dB/cmandthedashed

linegivesthelossforae=2.5dB/cm.Soliddotsaremeasuredfortheordinarywaveandcirclesaremeasuredfortheextraordinary

wave(KaminowandStulz1978).

asinFig.5.54.Theattenuationcoefficientsmeasuredinthiscasewerea0=3.0dB/cmandae=2.5dB/cmindicatingthatsomeoftheopticalfieldsisincontactwiththeelectrodes.Theelectrodeswerethenstrippedoffandthemeasuredattenuationcoefficients,a0andae,werewithinexperimentalerrorofthoseobtainedinFig.5.55.

Inapracticaldevice,Rcanbereducedtozerobyantireflectioncoating,andL1andL2couldalsobemadesmallbycouplingdirectlyfromasingle-modefibrewithsuitablecircular-to-ellipticalmodetransformerortaper.Thenonlythewaveguideinsertionlossalwillremain.TheattenuationcoefficientinbulkLiNbO3isverysmall:lessthan0.1dB/cmatl=1.15µm.However,thesourceoftheexcessattenuationinthesestripwaveguidesisnotunderstoodatpresent.The

attenuationmightbeduetoabsorptionbyimpuritiesintheLiNbO3substrateorbythediffusedTi,oritmightbeduetoscatteringfromgeometricalimperfectionsintheguideoronthecrystalsurface.Thus,Ti-diffusedLiNbO3waveguideswithlosssubstantiallylessthan1dB/cmarearealpossibility.

5.8.2Absorptionlossinstripguides

TomeasuretheabsorptionlossinTi-diffusedLiNbO3(Kaminowetal1980)theguideswerepreparedbydepositing300ÅofTiontotheLiNbO3substratefollowedbyheatingfor6hat980°Cinoxygenandcoolingtoroomtemperatureforseveralhours.ThefirstarrangementwastousetheelectrodegeometryshowninFig.5.56,whichhasbeenusedforelectro-opticmodulation.Coplanarelectrodesspaced9µmapartweredepositedalongtheentirelengthofthecrystaloneachsideofthe5-µmwidewaveguide.Withabout100µWoflightmodulatedat150Hzcoupledintotheendofthewaveguide,thepyroelectricsignalduetoabsorptionoflightintheguidecouldbeeasilymeasuredwithalock-inamplifier.Thepyroelectricresponsewasverysensitivetothecouplingefficiencyintothewaveguideandcouldbeusedasamoreconvenientmeansofcouplingalignmentthanthefar-fieldpatternof

Fig.5.56ExperimentalarrangementforpyroelectricmeasurementofabsorptionlossinLiNbO3stripguides.Thepolarc-axisisintheplaneofthewaveguideat32.75°

fromthecleavedends(Glassetal1980).

thetransmittedlight.Thismethodofalignmentwouldalsolenditselftoservocontrolofthecoupling.

Thecoplanarelectrodegeometrywasnotsatisfactoryforabsolutemeasurementoftheabsorptionlossbecauseofthegeometricalcorrectionfactorforthefielddistributionbetweentheelectrodesandbecausethermaldiffusionfromthewaveguideintothesubstratewasveryrapid.Thecorrespondingattenuationofthepyroelectricsignalisalsodifficulttocalculatebecauseofthegeometry.Theattempttouseshortopticalpulsesfailedbecausetwo-photonabsorptionintheguideswasdominantatthehighintensitiesrequiredtoobtainameasurablesignal(Glass1978).

ThepreferredgeometryforabsolutemeasurementsofabsorptionlossinthewaveguidewastoevaporateelectrodesonthetwosidesofthesubstratecrystalalongtheentirelengthasshownshadedinFig.5.56.Thenthepyroelectricresponseoftheentirewaveguideandsubstratewasmeasuredwiththelock-inamplifier.Equation(5.76)canbeusedforthisgeometry,andthethermalrelaxationtimetothesurroundingsisnowlong(1s)andcanbeneglected.TodeterminethelossintheTi-diffusedwaveguide,theincidentlightisfirstinjectedintothesubstrate,andthevalueofthepowerabsorbedinacrystalofgood

quality ,wheredistheopticalpathlengththroughthecrystal.Hence,thevaluesofafortheundopedsubstratearemeasured.Thenbycouplingthelightintothewaveguide(withordinarywavepolarization)thechangeinpyroelectricresponsegivesthechangeofabsorptionlossintheTi-diffusedregiondirectly.Intheseexperimentsthesignal-to-noiseratioallowedachangeof5%inthelosstobedetected.TheexperimentaldataaresummarizedinTable5.11.

Thevaluesofalistedforthewaveguideat0.514and0.488inTable5.11representalowerlimitsincethefollowingfactorscanacttodecreasethedifferencebetweenthepyroelectricsignalsforlightcoupledintowaveguideandsubstratemodes.First,theintensityoflightcoupledintothewaveguidemodemaynotbethesameasthatcoupledintothesubstratemodeeventhoughcouplingwasoptimized(insertionlossminimized)usingthefar-fieldpatternofthetransmittedlight.Withasimilarexperimentalarrangementthisfactorhasbeenmeasuredtobe0.8dB(KaminowandStulz1978).Second,theintensityofthelightintheguidemaybedecreasedbyscatteringfromtheguideintothesubstrate.Thiscanbecorrectedbymeasuringboththeinsertionlossandelectricalresponsefortwoormoredifferentwaveguidelengths.(Thetotalinsertionlossofthe1.8-cmcrystalwas5.5dBat0.633µm,increasing

to9dBat0.488µm).Anotherfactorthatcanaffecttheaccuracyofmeasurementofwaveguidelossinthisexperimentisabsorptionofscatteredlightbythemetalelectrodes,whichinturnheatsupthecrystal.Thisdoesnotseemtohavebeensignificantintheseexperimentssincethiswouldgiveanincreasedpyroelectricresponseat0.633forlightcoupledintothewaveguidewherescatteringisgreaterthaninthesubstrates.

At0.633µm,noincreaseoflossinthewaveguideregioncouldbedetected.Thepyroelectricsignalwasthesamewhetherthelightwascoupledintothewaveguideorthesubstrate.Thusatthiswavelengththeabsorptionlossis0.3dB/cmintheguideandislimitedbythelossinthesubstrate.NoadditionalabsorptionduetoTicouldbedetectedat0.633µm.Atshorterwavelengthsincreasedlossinthewaveguidewasmeasurable.At0.515µmand0.458µmpyroelectricsignalsincreasedby50and60%,respectively,whenthebeamwascoupledintotheguidepresumablyduetotheshiftoftheabsorptionedgetothevisible.

5.8.3Lossinepitaxialwaveguides

Thelosswascalculatedfromthemeasureddistributionofscatteredlightfromthewaveguidemode.Thescatteredlightdistributionwasanalysedusingamicroscopemountedonamicromanipulator,aphotodetectorandaselectivemicrovoltmeter.ThevoltmeterreadingUwasproportionaltotheintensityofscatteredlight.HavingmeasuredthescatteredlightintensityattwopointsspacedbyadistanceL,onecancalculatetheattenuationcoefficientbytheformula

LightlossmeasurementsforseveralexaminedsampleshaveshownthatTM-modeattenuationisasarulehigherthanthatofTEmodes.ThisisevidentlyduetothefactthatTMmodesaremorecriticalto

interfacenonuniformitythanTEmodes.Itshouldbenotedthatsomeofthesamplesusedintheexperimentexhibitedadecreaseoflossto0.7dB/cmforTEmodes.

Inepitaxiallayersofsolidsolutionsoflithiumniobate-tantalatetheattenuationisequaltoldB/cmforl=0.63µmand0.8dB/cmforl=1.15µm.Thephotorefractivefilmsensitivitystudiedbycomparisonwasnohigherthanthatofthesubstrate.

Thelowestattenuationisobservedin(0001)-orientedlayers.InaLiNbO3filmonaLiTaO3substratelossesdonotexceed2dB/cmforlowermodes.ItisestablishedthatlightpropagationoccursinLiNb1-yTayO3filmsfory=0÷1fororientation(0001);y=0.3÷0.99for( )andy=0.4÷0.99for( );thelightattenuationinthewaveguidedecreaseswithincreasingtantalumcontentinthefilms(Fig.5.57).Attenuationinbestsamplesdoesnotexceed1dB/cmfory>0.2,0.6and0.9fororientations(0001),( )and( ),respectively,andincreasessharplywithincreasingorderofthemode.

Absorptioninlithiumniobate-tantalatefilmsisinsignificantanddoesnotexceed0.3-0.5dB/cm,whichshowsahighstructuralperfectionofthelayer.

Fig.5.57Waveguidepropertiesandinsertionloss

versusfilmcomposition:-effectivewaveguides;

-rapidlyattenuatingwaveguides;-nowaveguiding.

Increaseinlightattenuationwithincreasingorderofmodesisaconsequenceoflightscatteringonsubstrate-filmandfilm-airinterfaces.Thepresenceofirregularitiesoninterfacescausesenergytransferfromonewaveguidemodetoothers.Inhomogeneityoftheinterfaceisanimportantfactordeterminingefficiencyofthepracticaluseofstructures.Periodicirregularitiescanbeused(asacouplingelement)forlightoutputfromadielectricwaveguide.Butrandominhomogeneitiesthatoccurinwaveguidemanufacturingweakenapropagatingwave.Thelossfactorvariesinproportionwithroot-mean-squareroughnessofthewalls.Roughnessontheinnerfilmboundariesisapparentlyofairregularnature.Theindicatedweakattenuationoflow-ordermodesshowsthatwaveguidesobtainedthroughliquidphaseepitaxyoflithiumniobatemeetthestrictrequirementsimposedonwallsmoothnessinintegratedopticsschemes.

5.9Ferroelectricpropertiesofwaveguides

5.9.1Dielectricproperties

Thecapacity(c)andconductivity(s)ofcapacitorsformedbythe

planarstructureofplatinumelectrodesonthefilmsurfaceweremeasuredtodeterminethetemperaturedependenceofdielectricpermittivity(e)offilms.Measurementswerecarriedoutinthetemperaturerangebetween20and970°Cinthe'weak'fieldregime(Emcas<104V/m)bythebridgemethod.Figure5.58representstypicaltemperaturedependencesofcandsfora6µmLiNb0.1Ta0.9O3filmonaLiTaO3substrateoforientation( ).

Typicalofthestructuresinvestigatedisthepresenceoftwopeaksofc(T)ands(T),thefirstlyinginthevicinityof580°Cforc(T)andat575°Cfors(T),thesecond,amoresmearedone,at770°Cforc(T)andat750°Cfors(T).Thepeaksofc(T)ands(T)near580°Careduetophasetransitioninthesubstrate,whichisclearfromasmallersmearingandarathersmalldisplacementofthemaximumofc(T)relativetos(T).ThisfactisalsoconfirmedbywellknowndataindicatingthatforasinglecrystalLiTaO3thephasetransitiontemperaturelieswithintherangeof550÷680°C(ed.byShaskol'skaya1982).SincephasetransitioninLiNbO3crystalsoccursat1140÷1180°C,itisnaturaltoexpectthephasetransitioninLiNb01Ta0.9O3tooccurwithintherangeof550÷1190°C,thatis,smearedmaximainc(T)ands(T)at770(750)°C

Fig.5.58Temperaturedependenceofdielectricpropertiesof

LiNb01Ta09O3/LiTaO3:a)capacity(1)andconductivity(2);b)dielectricpermittivityofsubstrate(1)andfilm

(2),calculatedvalues.

maybeduetophasetransitioninthefilm.

Assumingthedielectricpermittivitiesofthefilme1andsubstratee2tohaveonlyonemaximum(each)thatcorrespondstotheirphasetransition,onecansolvetheproblemofestimatinge1(T)ande2(T)bymeasuringthecapacityCstofthestructure.ThefollowingfactsandassumptionsareusedtodetermineCst

1.Itcanbeeasilyshownthat

whereCstisthecapacityofthestructure, thestructureperiod(300µm),atheelectrodewidth(100µm),dthefilmdepth(6÷20µm).

2.IntherangeT>750°C, and,asfollowsfrom(5.78),e1(T)canberestoredwithasatisfactoryaccuracy.

3.Knowingthebehaviourofe1(T)forT>750°Cande(20°C)=46(WangHongandWangMing1986)onecaninterpolatee(T)totheregionT<700°Cand,usingthisinterpolation,restoree2(T)inthistemperaturerange.Fortherelationsbetweenfilmthicknessandlattice

period,e2alwaysrestrictsthestructurecapacityfromabove.TheresultsofthecalculationsforthedielectricpermittivityofthefilmandsubstrateispresentedinFig.5.58b.

ThebehaviourofthestructureinstrongelectricfieldswasinvestigatedforT>750°C,wheretheinfluenceofthesubstrateissmall,sinceatthesetemperaturesitisintheparaelectricphase.AtypicaloscillogramofthedependenceofspontaneouspolarizationPsonthestrengthoftheelectricfieldEispresentedinFig.5.59.

Analysisofdielectrichysteresisloopsshowsthatat750-800°CthestrengthofthecoercivefieldforLiNb0.1Ta0.9O3filmsonLiTaO3( )makesup(2-3)×105V/mandPs=0.46C/m2.Theobservedeffluentonhysteresisloopsisobviouslyduetochargeescapefromsmalltrapsduetoredistributionoftheappliedelectricfieldcausedbyadecreaseofferroelectricimpedanceatthemomentofrepolarization(LinesandGlass1977).

Fig.5.59OscillogramofahysteresisloopofaLiNb0.1Ta0.9O3

film.T=750°C,f=60Hz,Ps@0.46C/m2,Ec2.3105V/m.

5.9.2Pyroelectricproperties

Thepyroelectricpropertiesoffilmsweremeasuredbythethermalpulseandlow-frequencysinusoidaltemperaturemodulationmethods(Antsygin1987).

5.9.2.1Thelow-frequencysinusoidaltemperaturemodulationmethod

TheabsolutevalueofthepyroelectriccoefficientgwasfoundusingasetupshownschematicallyinFig.5.60(Antsyginetal1986).ThebasicelementofthisdevicesetupisathermoelectricdeviceenablingthesampletemperaturetochangeaccordingtoastrictlysinusoidallawwithamplitudeDT.Thetemperaturemodulationfrequencywischosentobesuchthatitcouldprovideauniformtemperaturedistributionthroughouttheentiresamplethicknessd,thatis, ,where isthethermalrelaxationtimeofthesample.ThenatureofpyroelectriccurrentissuchthatmagnitudeofpyroelectriccurrentJpisproportionaltodT/dt.Thisisjustwhatdiffersthepyroelectriceffectfromallotherphysicalphenomenathatarecharacterizedbyvariationofcurrentthroughaspecimenwithvaryingtemperatureandpermitsdistinguishingthecontributionofpyroelectriccurrentintothetotaltemperature-inducedcurrent.Temperaturevariationinasamplebysinusoidallawisresponsibleforthesamelawforvariationof

pyroelectriccurrentJpbutwithaphaseshiftp/2.

Thismethodhasbeenemployedtoinvestigateferroelectriccrystals(CarnandSharp1982).Uniformtemperaturedistributionthroughoutthecrystalthicknesscanbeattainedonlyatverylowmodulationfrequencieswsince .Determinationofthephaseshiftbetweenpyroelectricandnonpyroelectriccurrentsischaracterizedbylowsensitivity.Thephaseshiftj,ascanbereadilyshown(CarnandSharp1982),isequaltoarctan(Jpmax/Jnpmax).Examinationofthinferroelectricfilmsbythismethodhasmadeitpossibletosingleoutthecontributionofpyroelectriccurrentandtomeasurelvaluesuptoabout3%.Thepyroelectriccoefficientisfoundfromtherelationl=Jp.max/(SDTw),wheresisthesamplearea.

5.9.2.2Thethermalpulsemethod

Thedirectionofpyroelectriccurrentinaferroelectricisdeterminedbythe

Fig.5.60Schematicofadeviceformeasuringpyroelectriccoefficient.

1)thermalbath;2)sample;3)temperaturegauges;4)meansampletemperaturegauges;5)heatconductingbufferlayer;6)thermocouple;7)electrometer;8,9)amplifiers;

10)two-coordinatex,yrecorder;11,12)unitsforthermocouplecontrol;13)printer;14)crate'Camak';15)computer;16)display;

17)monitor.

spontaneouspolarizationvectorPs,whichfactcanbeusedininvestigationofpolarizationdistributionthroughoutthesamplethickness.

Themethodconsistsinprobingasamplebyshortradiationpulsesthatheatthethinabsorbingelectrode.Movingfromtheheatedelectrodeinthesampletowardstheoppositeelectrode,thethermalfluxinducestheoccurrenceofpyroelectricsignal.Theinitialpolarityofthiscurrentisdeterminedbythepolarizationdirectioninthevicinityoftheabsorbingelectrode.Ifinabulkferroelectricthepolarizationdirectionreverses(head-ondomainstructure),thisisexpressed,beginningfromsomeinstantoftime,asasharpdecreaseinthemagnitudeofofpyroelectriccurrentevenreachingpolarizationreversal.Thethermalpulsemethodshowsahigherresolutioninfilmstudiesthanincrystalstudies(Chynoweth1956).Thispromotedinvestigationofpyroelectricprocessesdirectlyneartheelectrodesurface.Thetimeresolutionofabout10-9sattainedinthe

measurementscorrespondstothethicknessresolutionof3-5×l0-8m.Analysisoftheeffectofradiationonbothelectrodesmadeitpossibletodirectlydiscoverthehead-ondomainstructureinthesample.Suchastructurecausesoppositepyroelectriccurrentpolarityuponirradiationofeachoftheelectrodes.Currentpolarityisdeterminedonlybythepolarizationdirectionanddoesnotdependontheheatdistributiondirection.

Structureswiththecaxisnormaltothesubstrateplanewereusedinmeasurements;chromiumfilms(10-7minthicknessand(1-3)×10-6m2inarea)manufacturedbythethermalsputteringmethodwereusedaselectrodes.

AtypicaloscillogramofpulsepyroelectricsignalsispresentedinFig.5.61.Analysisofthebehaviourofpulsepyroelectriccurrentresponseofthestructuretothelightpulsebothfromthefilmandsubstratehasshownthatspontaneouspolarizationofthefilmisalignedalongthesubstratepolari-

zationdirection,andthepyroelectriccoefficientoffilmsestimatedbytheinitialslopeofthecurrentresponseis grad.Thisvalueagreeswellwith gradobtainedforsolidsolutionsofthesamecomposition(WangHongandWangMing1986),whichisindicativeofhighqualityoftheepitaxialstructure.

Theobserveddecreaseofpyroelectricresponsewith s,aswellasthenonlineardependenceofpyroelectricstressonloadimpedanceatsubsonictemperaturemodulationfrequenciesindicatetheexistenceofanonferroelectriclayerinthestructure.Theabsenceofcurrentresponsedelayrelativetothelightpulse(under10-8s)uponlightabsorptionbyelectrodesbothonthesideofthefilmandsubstrateimpliesthatthislayerislocatedonthefilm-substrateinterface.

5.10Temperaturedependenceofthermoelectriccoefficientsoflithiumniobateandlithiumtantalate

Thermoelectriceffectsinlithiumniobateandlithiumtantalateferroelectricsaffectgreatlythefilmcrystallizationconditions.

Khachaturyanetal(1988)investigatedthermoelectricSeebeck,ThomsonandPeltiereffectsforLiNbO3andLiTaO3singlecrystalsandtheirtemperaturedependenceintherangeof300-1400K.

Themainresultsofthethermodynamictheoryofthermoelectricphenomenacomedowntoestablishingrelationshipbetweenvariousthermoelectriceffects(SamoylovichandKorenblit1953),namely:

wheretisThomson'scoefficient,IIisPeltier'scoefficient,aisSeebeck'scoefficientandTistemperature.

So,havingmeasuredtheSeebeckcoefficientforaparticularmaterialonecanreadilyobtainthevaluesofPeltierandThomsoncoefficients.

TheexperimentalsetupfordeterminationofSeebeckcoefficientincludedamainfurnace,upperandlowermicroheaters,thermocouplesandaspecimen(RekasandWierzbicka1983).

Fig.5.61Oscillogramofapyroelectricsignaltolightpulse.1)lightpulse,2)pyroelectricresponseofthefilm,

3)responseofthesubstrate.

Fig.5.62TemperaturedependenceofSeebeckcoefficientsofLiNbO3andLiTaO3.

Table5.12Thermoelectriccoefficientsoflithiumniobateandtantalate

LiNbO3 LiTaO3

T,K amV/deg IImV tmV/deg amV/deg IImV tmV/deg

700 0.3 210 -5.2 0.04 28 1.2

750 0.05 37.5 -5.1 0.13 97.5 5.52

800 -0.65 -520 -5.0 0.91 728 6.9

850 -0.65 -552.5 -5.0 1.12 952 7

900 -0.2 -180 5 1.5 1350 7.1

950 0 0 5.1 1.69 1605.5 7.2

1000 0.2 200 5.1 1.66 1660 1.1

1050 0.35 367.5 5.2 1.6 1680 -1.6

1100 0.2 220 -2.5 1.44 1584 -1.5

1150 0.1 115 -2.4 1 1150 -9

1200 0.1 120 -0.37 0.8 960 -9.1

1250 0.1 125 -0.36 0.53 662.5 -9.1

SamplesofLiNbO3andLiTaO3crystals(10×10×10mm)werepositionedbetweentwoplatinumelectrodes.Thecrystalsurfacescontactingtheelectrodeswascoveredwithplatinumniello.Twoinnermicroheatersweremountedonrodsandenabledtemperaturegradientstooccurthroughoutthespecimenthickness.Temperaturewascontrolledbythreeplatinum-rhodiumthermocouples,measurementswerecarriedoutbythecompensationmethodinairataconstantnormalpressure,thetemperaturegradientwas10deg/cm.Thethermo-electromotiveforceofcrystalswasmeasuredwithinexperimentalerror

of1-3%.Figure5.62presentsthetemperaturedependenceoftheSeebeckcoefficient(a)forLiNbO3andLiTaO3singlecrystals.Withintheexperimentalerror,nodependenceofaoncrystallographicorientationofthecrystalwasobserved.Thedislocationdensityof(2-4)×104cm-2remainedunalteredinallthespecimens.

AsisseeninFig.5.62,the300-1400KtemperaturevariationoftheSeebeckcoefficientforLiNbO3canbedividedintothreetemperatureranges.Intherangeof300-750KtheSeebeckcoefficientstartsincreasingandthenfallssharply,whichsuggestsanintricatenatureofconductionofLiNbO3singlecrystalsintheindicatedtemperaturerange.AtlowtemperaturesthereprevailstheimpurityconductionofLiNbO3(Kuz'minov1987;Kuz'minov1975).Inthetemperaturerangeof750-950K,achangessign,whichisindicativeofthecontributionoftheelectroncomponenttotheintrinsicconduction.AsubsequentsignchangeintheSeebeckcoefficientinthetemperaturerangeof950-1400KagreeswiththefactthatthemaincarriersareLi+ions(D'yakovetal1985).

ThevaluesofthecoefficientaforLiTaO3arepositiveintheentiretemperaturerangeunderexamination.Atthephasetransitiontemperature(T=933K)amaximumisobserved,whichsuggeststheinfluenceofthephasetransitionuponthecharacterofconduction.ItisobviousthatthemaincarriersinLiTaO3singlecrystalsareLi+ions.ComparingthevaluesofSeebeckcoefficientsforlithiumniobateandtantalatesinglecrystalswithintheinvestigatedtemperaturerangeonecanassumethatthehighertheavalue,thehighertheconductionofthematerial.For

ThecalculatedvaluesofPeltierandThomsoncoefficientsintheindicatedtemperaturerangearetabulatedinTable5.12whichshowsthatforlithiumniobatethePeltiercoefficientchangesfrom-662.5

mVto367.5mV,whileforlithiumtantalateitchangesfrom28mVto1680mV.Attemperaturesabove1200K,Thomsoncoefficientsforlithiumniobateandtantalatedonotchangeappreciably.

6Thin-FilmStructuresinIntegratedOpticsIntegratedopticsismainlydevelopedinthedirectionofintegrationofwaveguideandoptoelectroniccomponentsonasinglesubstratetotheeffectofcreationofmultifunctionaldevices.

Opticalfilmwaveguidesarethebasiccomponentsofintegro-opticalmodulators,switchers,filters,nonlinearopticalfrequencyconverters,commutators,andlightbeamdeflectorsforcorrelationandspectralanalysisoflightsignalsduringtheirprocessing.Hybridbistableopticaldevicesonthebasisofchannelwaveguidesoperatingatsmalllevelsofopticalpowerareusedassensorsoflightintensityinautomaticsystemsandopticalmultivibrators.

Forintegralnonlinearopticaldevices,channelwaveguidesareofgreatinterestandhaveadvantagesoverplanarones.Propagationofalightbeamalongachannelincreasestheluminousenergyconcentrationand,accordingly,theefficiencyofnonlinearconversion.Thephasematchingconditionscanbemaintainedbyvaryingthegeometricalsizeofwaveguides.

Inthischapter,wearemainlyconcernedwithdevicesbasedonwaveguidelithiumniobateandtantalatestructuresandinvolvingelectro-opticeffect.

Asdistinctfromthediffusionmethod,liquid-phaseepitaxyforobtaininglightguidestructuresinlithiumniobate-tantalatesystemsisveryflexibleandsuggestsnewpossibilitiesforcreatingintegro-opticschemeswithintegrationofelementsbothinhorizontalandverticalplanes.Inaverticallyintegratedstructure,waveguidelayersareseparatedbylayersofasolidsolutionoflithiumniobate-tantalatewith

alowerrefractiveindexwhichplaystheroleofanopticalinsulator.Nootherinsulatinglayersofothermaterials(SiO2,Al2O3)appliedinanumberofintegratedsystemsareneededheresinceseparatinglayersaregrowninaunifiedtechnologicalcycleofobtainingdevicestructures.

WeshallnowcarryoutacomparisonstudyofTi-diffusionandepitaxialtechniquesofintegro-opticdevicesonanexampleofelectro-opticswitchingelementsincrossing-channelwaveguidesorelectro-opticX-switchers(Betts

etal1986).Single-modeswitchersareoftheutmostpracticalinterest.Inthiscase,forasufficientlysmallwidthofwaveguides,theoperationofsuchaswitcherisbasedoninterferenceofevenandoddmodesintheintersectionregionandonelectriccontroloftheirphaserelations(Neyer1984).Switchersofthistypehavearathersimpledesignandarefairlystableascomparedtoothertypesofswitchers(Bettsetal1986).Thecontrolstructureconsistsoftwometallicelectrodeswithagapof1÷3µmpositionedonthelightguidestructureandorientedalongthelongdiagonalofarhombforanefficienteven-modecontrol.Toreducethetotallossesthistypeofdevice,thereisabufferlayerbetweenmetallicstripsandthelightguidelayer.

Thetechnologicalprocessofmanufacturingsuchlightguidesusingthediffusionmethodincludesthefollowingoperations:

-depositionofacontrolledwidthoftitanium,

-photolithographyforobtainingapictureofchannellightguides,

-titaniumdiffusionforobtainingthelightguidestructure,

-depositionofaSiO2orAl2O3insulatinglayer,

-surfacemetallizationfortheformationofacontrolledstructure,

-placinginsidethedevice.

Itshouldbenotedthatthediffusionprocessallowstheformationofonlynonsymmetriclightguidestructures,whichsuggestsdifficultiesinafurthermatchingofsuchastructurewithfibrespossessingaxialsymmetry.Thecalculationsshow(Lazarev1986)thatevenuponaprecisiondiffusionofTiwiththepurposeofobtaininganoptimalprofileofachannellightguideformatchingwithaxial-symmetricfibresthereoccurmorethan10%oflossesduetomatching.Fibresarenowtypicallyface-adjustedtointegro-opticaldevices,whichrequires

polishingofdevicefaces.ThepositionofTi-diffusivelightguidesdirectlyinthenear-surfaceregionimposesstrictrequirementsupontheprocessingofplatefacestoremoveoravoidpossiblechippingsintheregionofthelightguidingstructure.

Whenadeviceismadeusingepitaxialtechnique,thenaftertitaniumisdeposedandphotolithographyisperformed,theimmersedlightguidingstructuresareformedbythediffusion-filmmethod.Thisyieldssymmetriclightguidingstructuresallowingadecreaseoflossesinthecourseoffibreadjustment.Italsolowerstherequirementsonthesizeofchippingsduringfacepolishing,andaninsulatinglayerneednotbespeciallydepositedsinceitisformedinthetechnologicalprocessofobtainingimmersedlightguidingstructures.

6.1Principalcharacteristicsofwaveguidingelectro-opticmodulators

Modulatorsarecharacterizedbyacontrolvoltage,bythebandwidth,bythemaximalmodulationdepthandbyinsertionlosses(Tamir1979;MustelandParygin1970).WeshallconsiderthesecharacteristicsfollowingAlferness(1982).

6.1.1Controlvoltage

Animportantcharacteristicofmodulatoriscontrolvoltage(aminimalvoltageforwhichthemodulationdepthismaximal).Inspiteofthefactthatthe

Fig.6.1Integro-opticphasemodulator.a)generalview;b)sideview(Alferness1982).

magnitudeofcontrolvoltagedependsonaspecificmodulatorscheme,thebasicconclusionsontheeffectoftheexternalfieldcanbemadeonthebasisofasimplephasemodulator(Fig.6.1).Ifelectrodesareplacedonbothsidesofawaveguide,thehorizontalcomponentoftheelectricfield isused,whileifanelectrodeliesonthewaveguidesurface,theverticalcomponentoftheelectricfield isused.Inthelattercase,todecreaselightlossundertheelectrodes,especiallyforpolarizationoftheperpendicularplaneofthecrystal(TM-modes),abufferlayerofSiO2orAl2O3shouldnecessarilybedepositeduponthewaveguidesurface(Ucharaetal1975).Inbothcases,crystalorientationissochosenthattheelectro-opticcoefficientr33hasthehighestvalue.Whenlightpropagatesbetweentheelectrodes,thecoefficientr33isusedforTE-modesonthey-cut,whereaswhenlightpropagatesundertheelectrodes,r33isusedforTM-modesonthez-cut.

Therefractiveindexvariationundertheactionofthefieldduetoelectro-opticeffectisgivenbytheexpression

wheredistheinterelectrodegap,Gistheoverlapintegraloftheelectrodefieldandthemodefield: dA,whereEisanormalizedfieldofthemode,xisanappliedelectricfield,Visvoltage.

Theconditionfora100%modulationdepthcanbewrittenas

whereDb=(2p/l)dn*,Listheinteractionlengthbetweentheappliedfield

andthelight,p=1anddependsonthetypeofmodulator.So,

ThetransmissionbandwidthcanbeshowntobeinverselyproportionaltoL(Alferness1982).So,tobroadenthebanditisnecessarytodecreasethequantityV×Lbyminimizingthegeometricparameterd/G.Tothisendoneshouldknowhowtheoverlapintegraldependsontheinterelectrodegap,onthemagnitudeofthemodefield,ontheelectricfieldcomponent( or )andonthepositionofthewaveguiderelativetotheelectrodes.Thedependenceoftheoverlapintegralontheseparameters(forhalf-infiniteelectrodes)wasconsideredbyMarcuse(1982).Themodefielddistributioninwidth(withdimension )isassumedtobedescribedbytheGaussianfunctionandindepth(withdimension )bytheHermitian-Gaussianfunction.Forawaveguidelyingbetweentheelectrodesinagapdequaltoorslightlygreaterthanthemodedimension,symmetricpositionrelativetotheseelectrodesisoptimal.Iftheverticalcomponentoftheelectrodefieldisused,thenoptimalisthecaseofcoincidentinneredgeoftheelectrodewiththemodefieldedge(withdimension (Fig.6.1)).Figure6.2illustratesthedependenceoftheproductofthefield-inducedchangeoftheeffectiverefractiveindexbythemodewidth ,onthenormalizedgapsize forthecasewhenboththeverticalandhorizontalfieldcomponentsareused(Marcuse1982).Thesedependencesshowthatanincreaseofdn*requiresadecreaseofthewaveguidemodeandofagapbetweentheelectrodes, .Forthecaseoftheuseofthis requirementislesscriticalthaninthecaseof (Alferness1982).

Aphotorefractiveeffectmayresultinasignificantincreaseofthecontrolvoltage(ataconstantvoltage)duetocompensationoftheappliedfieldbyphotoelectrons.Therearetworeasonsforthis:first,thephotoconductivityintheexternalfieldand,second,the

photogalvaniceffect(Schmidtetal1980;YamadaandMinakata1981).

6.1.2Bandwidth

Thewidthofthemodulatorfrequencybandisdeterminedbyelectrodecapacitanceprovidedthattheelectrodelengthismuchsmallerthanthewavelengthoftheradiofrequencysignal.Itcanbeshownthatthecapacitanceofthesystemofelectrodesperunitlengthisequalto(Alferness1982)

wherers=(d+1)/2G, ,Gistheelectrodewidth,for(LiNbO3)isthedielectricconstantandKisthe

ellipticintegral.

TheratioC/Ldecreasesandthebandwidthincreases(Df=(pRC)-1,Ris

Fig.6.2Theproductofthefield-inducedeffectiverefractiveindexbythewidthofthemode andtheoverlapintegralFasfunctionsofnormalisedvalueofthegapforfields

(a)and (b)(Alferness1982).

Fig.6.3CapacityofanelectrodesystemperunitlengthC/Land

productofthebandwidthbytheelectrodelengthDfRC.Lversusthevalueoftheinterelectrodegap-electrodewidthsratiod/G(Alferness1982).

theloadresistance)withincreasingratiod/G(Fig.6.3).Sincetheproductofthecriticalfrequency,whichisdeterminedbythesignalpassagetime,bytheelectrodelength cm(cishespeedoflight),itisinexpedienttoused/G>0.8.

Itisknownfromtheforegoingthattolowerthecontrolvoltage,thegapbetweentheelectrodesshouldbesmall.Thus,toobtainawideband,itisnecessarytoreducetheelectrodewidth(since ).A

reductionoftheelectrodewidthis,however,limitedbytwofactors.First,itshouldnotbemademuchlessthanthewaveguidewidthlesttheoverlapoftheelectricandopticalfieldsshouldbesmall.Second,whentheelectrodewidthissmall,theresistanceincreasesandthebandwidthdecreasesaccordingly.

Sincethecontrolvoltageandthebandwidthareinverselyproportionaltothedevicelength,thecontrolvoltage-to-thebandwidthratiocanbethoughofasafigureofmerit:

TheratioV/Dfdecreaseswithdecreasinggap(downto )becauseC/Lincreasesslower(Fig.6.3)thandecreasesthecontrolvoltage(Fig.6.2).Butastheinequality decreases,anincreaseofC/Lwillnotbecompensatedbytheloweringofthecontrolvoltage.So,V/Dfhasaminimumford/w<0.5and .InsofarasC/Ldependslogarithmicallyond/G,theelectrodecanbewidenedwithoutanoticeableincreaseofV/Df.

Thesmallestattainablegapisrestrictedbythesmallestattainablemodedimension(Alferness1982): andfrom therefollows

Forn@2.2,Dn=0.01,l=0.63µm:dmin=1µm.Thus,

(since ford/G=0.5),wheretheoverlapintegralG=0.3or0.2formodulatorsthatemploy or ,respectively.Assumingp=1,R=50Ohmandneglectingtheelectroderesistance,onecanobtaintheminimalvalueV/Df:0.5V/GHzand1.5V/GHzforl=0.63µmand1.32µm,respectively(Alferness1982).

6.1.3Modulationdepthandinsertionlosses

SupposethatwithoutanappliedvoltagetheintensityoflightcomingoutofthemodulatorisequaltoI0.Thenthemodulationdepthisdeterminedas(Barnoski1974):

whereIistheintensityoflightatacorrespondingvoltage.Whenacontrol(halfwave)voltageisapplied,themodulationdepthiscalledamaximalmodulationdepth.Theactionofthemajorityofmodulatorsisbasedonthephasechange( )whichistransformedintothechangeofintensity.Forinterferentionalmodulators,thedependence

ofthemodulationdepthonthephaseshifthastheform(Barnoski1974):

whileforwaveguidingdevicesemployingphasechangeintheconnectionoftwowaveguidesortwowaveguidemode

whereListheinteractionlengthandkisthecouplingconstant.

Thetheoreticallyadmissiblemodulationdepthis100%,whileinexperimentitisnormallyalittleless(about96%)duetolightscatteringonwaveguidedefectsandontheelectrodestructure,andalsoduetoconversionoflightpolarization.Thefirstreasonresultsfromthetechnologicaldifficultiesofmanufacturingawaveguidemodulator(micronsize,highclassofsurfacepolishing,etc.).Thesecondisduetothephotorefractiveeffectandtheassociatedlightpolarizationconversion.Thedependenceofthemodulationdepthofawaveguidemodulatoronthepolarizationoflightis,inturn,aconsequenceoftwofacts.First,theelectro-opticcoefficientsarenotthesameforTE-andTM-waves:inthecaseofz(y)-cutoflithiumniobate,whenthefieldisdirectedalongthezaxisforaTE(TM)-waveDb~r13V,andforaTM(TE)-waveDb~r33Vandr33/r13=3;second,theincrementoftherefractiveindex,Dn,isnotthesameforTE-andTM-waves(Dne>Dno),andthereforethemagnitudeofthemodefieldandthecouplingcoefficientdepend,inthecaseofmatchedwaveguides,onthepolarizationoflight(Leonberger1983).

Adecreaseinthemodulationdepthduetoconversionofpolarizationoflightonthepassivepartofthemodulator(unaffectedbytheelectricfield)canbestoppedbyplacingatthemodulatorexitananalyserallowingonlyonepolarizationoflight(eitheraTM-oraTE-wave).Butthiswillstimulatetheinsertionloss.

Theinsertionlossisdeterminedasfollows(Barnoski1974):

whereIinistheintensityoflightenteringthemodulator.Insertionlossesalsoincludetheinputandoutputlossesandthosedueto

propagationalongthemodulatingstructure.

Itshouldbeemphasizedthattheinsertionlosseswillalsobeincreasedbyaphotoinducedradiationoutputfromthewaveguides.

6.2Photoinducedpolarizationconversion

Ifvoltageisappliedtoelectrodesplacedonbothsidesofawaveguide(forthey-cutoflithiumniobate),thenalongwiththephasemodulationtheamplitudemodulationofradiationmayoccur.RadiationintensityvariationmustbearesultofphasemismatchbetweenTE-andTM-wavesand,therefore,ofachangeinthedegreeofpolarizationconversion.Theestimationbyformula(6.1)yieldsacontrolvoltageofabout7VforL=10mm,d=10µm,l=0.63µmandG=0.3.SuchamplitudemodulationwasexperimentallydiscoveredbyZolotovetal(1983).

Thewaveguidesweremanufacturedbytitaniumthermodiffusionintolithiumniobatecrystals(they-cut)fromstrips,15µmwideand300Åthick,depositedalongthexaxis.Thediffusionwascarriedoutfor6hinairatatemperature

of960°C.Thentheelectrodestructure(twoparallelaluminiumstrips15µmwideand14mmlongwerephotolithographicallydepositedonbothsidesofthewaveguideonthecrystalsurface.Thedistancebetweentheelectrodeswas10µm(Fig.6.1).

Atthewavelengthoflaserradiation,0.63pro,an wasexcitedwhosepolarizationcorrespondedtothatofanordinarywave.Withanincreaseofthepoweroflightintroducedtothewaveguide,thepowerwasloweredandan appearedwhichcorrespondedtoanextraordinarywave.ThedegreeofpolarizationconversiondependedonthepoweroflightintroducedtothewaveguideP,andforP@25µWtheconversionwaspracticallycomplete( ).

Thenthepotentialdifferencewasappliedtotheelectrodes,andthepowerofthe wasmeasuredasafunctionofvoltageV.Thevoltageatwhichtheconversionstopped(thecontrolvoltage)andthe onlywasobservedattheoutputincreasedwithincreasingpoweroflightfedintothewaveguide.Thisisevidentlyassociatedwithanincreaseinthemodulationdepthoftherefractiveindexintheholographicgratingand,therefore,withanincreaseofthecouplingconstantbetweenthe and .Whenthelightpowerwasabout5µW,thedegreeofconversion(Pe/Po~60%)wasabout60%andthecontrolvoltagewasequalto~2.5V.Butaftersometime(~30s)thepolarizationreturnedtoitsinitialstatewhichwaslikelyduetothenewlyinducedholographicgratingrestoringphasematchingbetweenthe and modesandduetoacompensationoftheappliedfieldbyphotoelectrons.Ifthepotentialdifferenceofoppositepolaritywasappliedtotheelectrodes,thenwithanincreaseofthevoltagethepowerofthe firstgrew(themaximumwasobservedforV@-3V)andthenstartedfalling.Thisislikelytosuggestthatwhenradiationpolarizationconversionisincomplete,theholographicgratingdoesnotyieldaperfectmatchingbetweenmodesoftheordinaryandextraordinarypolarizationintheabsenceofvoltage

betweentheelectrodes.Whenthepoweroflightwasabout25µW,thedegreeofconversionmadeup95%andthecontrolvoltageincreasedupto7V.Themodulationcurvewasobservedonanoscillographscreentotheinputofwhichasignalwassentfromthephotomultiplierthatregisteredthepoweroflightcomingfromthewaveguide,andasawtoothvoltagewiththeamplitudeof8Vwasappliedtotheelectrodesduring1µs.Thepowerofthe fell( µw)asshowninFig.6.4a,whilethepowerofthe

Fig.6.4Extraordinary(a)andordinary(b)wave

polarizationpowervsvoltage(Kazansky1985).

-modegrewasshowninFig.6.4b.Whileattheinitialinstantoftimethepowerofthe felltotheminimumatavoltageof7V,afterafewsecondsthemodulationcurvebecamemoregentle(thecontrolvoltageincreased)anditsmaximumwasdisplacedtowardsthehighervoltage.Suchabehaviourofthedependenceofthepoweronthevoltagecanbeexplainedbytheinfluenceofthefieldofspacechangesinducedbytheeffectoftheconstantcomponentofthesawtoothvoltageuponthepolarizationconversionmechanism.Itshouldbenotedthatthemodulationbandwasdeterminednotbytheslowphotorefractionprocesscausedbythechangedriftbutratherby

theelectrodecapacitancewhichinthegivencasemadeup7picofarads,whichcorrespondstothebandwidthof900MHz

calculatedforalodeof50Ohm.

Thepoweroflightcomingfromthewaveguideafterananalysertransmittingradiationpolarizedatanangleof45°tothedirectionofpolarizationofthe and wasmeasuredasafunctionofthevoltage.Herechangedthecharacterofpolarizationoflightundertheactionofvoltagewhichaffectedthephasedifferencebetweenthe

andthe transformedfromthe bymeansofthephotorefractiveeffect(Fig.6.5).

Fig.6.5Thepoweroflightpolarisedatananglep/4tothewaveguideplaneversusvoltage(Kazansky1985).

Itisnoteworthythatontheonehandthediscoveredamplitude

radiationmodulationisundesirablefortheoperationofaphasemodulator,butontheotherhand,theelectro-opticcontroloveraphotoinducedradiationpolarizationconversionconfirmsthemechanismofthisneweffectbasedonphasematchingoftheordinaryandextraordinarypolarizationmodesusingabulkphasegrating;theelectro-opticcontrolcanalsobeusedforlightmodulation.

Thephasemodulatorbelongstosometypesofamplitudeintegro-opticmodulatorsusingcoupledwaveguides(Papuchonetal1975;KogelnikandSchmidt1976)andinterferentionalmodulators(Papuchon1977).

6.3WaveguidemodulatorsonthebasisofTi:LiNbO3

6.3.1Electro-opticmodulatoroncoupledchannelwaveguideswithavariableDb

Themainshortcomingofthemodulatoroncoupledwaveguidesisalowcontrastof90%(Bozhevil'nyetal1981).Toreachahighcontrast,thecouplinglengthbetweenthewaveguidesshouldbeequaltoanintegral(odd)number

ofpumpinglengths(Papuchonetal1975),whichisdifficultfromapracticalpointofview.Toeliminatethisdefect,suchelectrodesweresuggestedthatcreateincoupledwaveguidesthedifferenceofpropagationconstantsDb=b2-b1whichreversessignanintegralnumberoftimesequaltothenumberofpumpinglengths.Usingthismethodinatwo-sectiondevicegaveanon-offratioof27dBforacontrolvoltageof30V(SchmidtandKogelnik1976).

Thesolutionofthesystemofequations(Kazinsky1985)

forcoupledwaveguideswithavariablesignofDbinthematrixformis(KogelnikandSchmidt1976)

where isthematrixforthemodulatorregionwith

B1=ksin[x(k2+d2)1/2]/(k2+d2)1/2,wherek=2p/listhecouplingconstant,

Fig.6.6Modulatoronthebasisofcoupledwaveguides

withavariableDb.1,2)waveguide(Zolotoveta11982).

Fig.6.7Statediagramofamodulatoronthe

basisofcoupledwaveguides(KogelnikandSchmidt1976).

x=L/2,listhepumpinglength,R0andS0arethewaveamplitudesatthewaveguideinput.IfS0=0,thentheconditionforthecrosstalk,thatis,forlightpumpingfromwaveguide1towaveguide2(Fig.6.6)canbeobtainedprovidedthatA2=0:

Forthestraightforwardstate(B2=0)onecanaccordinglywrite

Figure6.7showsastatediagramforasystemofcoupledchannelwaveguideswithavariablesignofDb.Inthisdiagram,thepointslyingonthecurvecorrespondtothestateinwhichthelightiscompletelypumpedoverfromwaveguideItowaveguide2(Fig.6.6),whilethepoints onthecurvecorrespondtothestatewhenthepumpingisstopped.

Theelectro-opticmodulatoronthebasisofcoupledchannelwaveguideswasmanufacturedonaz-cutlithiumniobateplate(Fig.6.6)(Zolotovetal1982).Thesystemofwaveguideswascreated

bywayofsputtering300Å.oftitaniumontotheplatesurfacewithasubsequentetchingoftitaniumthroughaphotoresistivemaskandbydiffusioninairatatemperatureof960°during6h.Thebandwidthofthetitaniummadeup3.5µm,whichprovidedobtainingsingle-modewaveguidesattheradiationwavelengthof0.63.Thedistancebetweenwaveguideswas4.5µm.Todecreasepropagationlossesundertheelectrodes,thewaveguidesurfacewassputteredwithaSiO2film2000Åthick.Theelectrodestructureonthewaveguides(Fig.6.6)wasfabricatedbyetchingthe2000ÅthickAllayersputteredontothecrystalsurfacethroughaphotoresistivemask.Thelength,widthandthedistancebetweentheelectrodeswererespectively8mm,20µmand4.5µm.

Toestablishthepumpinglength,theHe-Nelaserradiationwas,usinga

Fig.6.8Modulationcharacteristicofmodulatoron

thebasisofcoupledwaveguides(Kazansky1985).

×20microlens,introducedinturnineachofthefivesystemsofcoupledwaveguides,andtheintensityoflightatthewaveguideoutputwasregisteredbyaphotomultiplier.Themaximumintensityoflightinthecaseofthe modewasobservedatacouplinglengthof7mm.Lightpumpingbetweenthewaveguideswasalsoobservedasamodetrackunderamicroscope.Thepumpinglengththusdeterminedwas3.5mm.Theexperimentonlightmodulationwascarriedoutoncoupledwaveguideswithacouplinglengthof7.5µm.Forzerovoltage,theradiationaftertwopumpingswaspropagatedinwaveguide1(Fig.6.6).Whenacorrespondingvoltagewasappliedtotheelectrodes,thephasemismatchontheregion0<x<L/2ofcoupledwaveguideswasresponsibleforadivisionofthelightintensityintotwoequalpartsbetweenthewaveguides.IntheregionL/2<x<Lofcoupledwaveguidestheelectro-opticallyinducedphasedifferencehasareversesignascomparedtothephasedifferenceontheregion0<x<L/2.Thisaffectsthevariationintheenergypumpdirectionanddecreasesthelightintensityinwaveguide1.

Toobtainthemodulationcharacteristicofelectrodes,asawtoothvoltagewithanamplitudeof20Vwasappliedtotheelectrodes.Theoutputradiationwasappliedtoaphotomultiplierwhosesignalwasobservedontheoscillographscreen(Fig.6.8).Themaximalmodulationdepthwas14dBandwasreachedatavoltageof~9V.

Thetotallightlosseswere8dB.Thecapacitanceoftheelectrodesystemmadeup4.4picofarad.

Whenaconstantcontrolvoltageisapplied,thelightpoweratthemodulatoroutputwasfirstdecreased,butafter10sitincreaseduptotheinitialvalue;therelaxationtimewasindependentofthelightintensity.SucharelaxationislikelytobeduetotheconductivityofthebufferlayerofSiO2resultedfromanincompleteoxidationofSiO2(Tangonanetal1978).

Thebasisoftheeffectiverefractiveindexmethodmodefielddistributionallowedcalculationofthemodefielddistributioninawaveguideandpumpinglengthsweredetermined.Forthe thepumpinglengthwas3.6µmandforthe itwas60mm.

Thelargepumpinglengthofthemode ascomparedtothepumpinglengthofthe isexplainedbythefactthattheincrementoftherefractiveindexDnand,therefore,modelocalizationwithanextraordinarypolarizationof largerthatthemodeswithanordinarypolarizationof (Alfernessetal1979).Thus,theexperimentalvalueofthepumpinglengthinthecaseof isincloseagreementwiththetheoreticalvalue,while

Fig.6.9Interferometertypemodulatorwith

aninducedchannelwaveguide(Zolotovetal1982).

inthecaseof thetheoreticalcalculationisindicativeofthepracticallackofcouplingbetweenthewaveguides,whichwasobservedinexperiment.

TheoverlapintegralofthemodefieldwiththefieldofelectrodeswasevaluatedfromthestatediagramsofthesystemofcoupledchannelwaveguideswithDbelectrodes(Fig.6.7)

Whenthelightintensityincreasesupto5µW,thepoweroflightatthemodulatoroutputwasdecreased,andnophotoinducedpolarizationconversionwasobserved,whichislikelyduetolargelossesoflightofextraordinarypolarization(oftheTM-mode)undertheelectrodes(6dB/cm)becauseofimperfectionofthebufferlayerofSiO2.Adecreaseoflightintensityisevidentlyconnectedwiththephotoinducedvariationoftherefractiveindexofthewaveguides,whichleadstophasemismatchbetweenmodesofcoupledwaveguides.

6.3.2Interferometricandperfectinnerreflectionmodulators

Zolotovetal(1982)consideredthemechanismoftheactionofatechnologicallysimpleinterferometertypemodulator(Fig.6.9).When

voltageisappliedwithapolaritycorrespondingtoanincreaseoftherefractiveindexinacrystal,intheregionundertheelectrodesthereformsachannelwaveguide(Channin1971).Themodeofthiswaveguidehasasmalltransversedimensioncointhewaveguideplaneand,therefore,alargerdiffractiondivergence~l/w.InthefartherregionthismodemustinterferewiththemodeofaplanarTi-diffusedwaveguide(whichbelongstothecontinuumofradiationmodesofthechannelwaveguide)havingasubstantiallylargertransversedimensionWandasmallerdivergence~l/W(i.e.asmallangulardimensioninthefarregion).Thephasedifferenceofthese

twowaves ,wheredn*isthedifferenceofeffectiverefractiveindices)dependsonthemagnitudeoftheappliedvoltage.Inthecasewhenwavesareinthecounterphase

( ),inthecentreoftheinterferencepatternaminimummustbeobserved,whereasattheboundariesofthispicturenocompletemutualwaveextinctionwilloccursincetheirangulardimensionsdifferstronglyfromoneanother.Bytheestimates(6.1)thecontrolvmakesup(forl=0.63µm,d=6µm,L=5mm):

Toobtainthemaximalmodulationdepth,weshallfindtherelationbetweenthewidthoftheGaussianbeamWincidentonthemodulatorandthewidthcoofthemodefieldoftheinducedchannelwaveguide.Thenormalizedfieldoftheincidentbeamhastheform

Accordingly,thenormalizedfieldofthemodeofthechannelwaveguideweapproximatebytheGaussianfunction

whereh=2/[w/W)+(W/w)]istheefficiencyoflightinputintothechannelwaveguide.

ForthelightpropagatingoutsidethechannelwaveguideErad=Einc-Echan.Theintensityoflightinthefarregion isrelatedtothe

fieldinthenearregionas

where ,(herey1isthecoordinateinthedirectionperpendiculartothelightpropagationdirectionatadistancexfromthemodulator.Thentheinterferencepatterninthefarregioninthecaseofinphasewaveinterferencehastheform

andinthecaseofcounterphasesubtraction,accordingly(Fig.6.11)

Fig.6.10Modulationcharacteristicofaninterference

typemodulator(Kazansky1985).

Fig.6.11Interferencepatternsinthefarregion.Inphasewaveinterference(/+)andcounterphasesubtraction

(/-)(Kazansky1985).

Fromthisweimplytheconditionwheninthecentreoftheinterferencepatternthelightintensitywillbeequaltozero

Toperformanexperimentonasubstrateoflithiumniobate(y-cut),aplanarwaveguidewasmanufacturedbywayoftitaniumdiffusion(theTilayerthickness300Å).Theelectrodestructurewasdepositedphotolithographicallyonthecrystalsurface,asshowninFig.6.9.Thiselectrodestructureconsistedoftwoparallelaluminiumstrips5mmlongand4µmwide.Thedistancebetweentheelectrodeswas6µm.

He-Nelaserradiationwasintroducedintothewaveguidebymeansofarutileprism.Beamfocusingbyalensewithafocusdistanceof20cmmadeitpossibletoobtainthedimensionoftheGaussianbeamWatthewaveguideinputequalto60µm.Asthepotentialdifferenceontheelectrodeschangesfrom0to5V,thefieldpatterninthefarregionchangesaccordingtothemodelconsideredabove,andthemaximalmodulationdepthobtainedforV=5Vwas95%(Fig.6.10).Figure6.11presentsthemodulationcurveofsuchamodulatorobservedonthescreenofanoscillograph(theappliedvoltagevariedfrom0to20V).Themodulationcurvehasmaximaandminimatypicalofinterferentialphenomena.Itshouldbenotedthatalowvalueofthecontrol

Fig.6.12Totalinnerreflectionmodulator(Kazansky1985).

voltage,alargemodulationdepthandthepossibilityofrealizingawide(~1GHz)modulationbandmakethistypeofmodulatorsfairlypromisingforpracticaluse.

Tsaietal(1978)andSheem(1978)consideredthemechanismofoperationofthetotalinternalreflectionmodulator,shownschematicallyinFig.6.12.

Whenvoltageofanappropriatepolarityisappliedtotheelectrodes,intheregionbelowtheelectrodestheelectro-opticeffectresultsintheformationofalayerinwhichtheeffectiverefractiveindexofthewaveguidemodeisdecreasedbythevaluedeterminedbytherelation(6.3).MakingallowanceforthisrelationonecancalculatethereflectionfactorofthewaveguideH-modeincidentontheperturbedlayeratanangleq1(BornandWolf1979)

Undertheconditionn'*<n*sinq1thereoccursatotalinternallightreflection.So,varyingthevoltageappliedtotheelectrodesonecanchangethedn*valueand,therefore,thelightreflectioncoefficient.

Radiationwithawavelengthof0.63µmwasintroducedintothewaveguideusingarutileprismandwasdirectedtotheelectrodesatanangleof89.5°.Thedependenceofthepowerofthereflectedlight,Prefonthevoltageappliedtotheelectrodeswithintherangefrom0to20VisillustratedinFig.6.13.Forthepotentialdifferenceof15Vthereflectioncoefficientwas95%±3%.Thisvalueagreescloselywiththe94%calculatedbyformulae(6.3)and(6.21).Thecapacitanceoftheelectrodestructuremadeup2pF,whichadmits

Fig.6.13Modulationcharacteristicoftheinnerreflection

modulator(Kazansky1985).

inprinciplethebandwidthof>1GHzfortheloadresistanceof50Ohm.

Whenlightofpower1mWwasintroducedintothemodulators,inthewaveguidesthereoccurredastronglightscatteringinthem-line(Tangonanetal1977)causedbyinducedopticalinhomogeneities,whichissimilartothescatteringwithoutpolarizationreversalinbulkcrystals(MagnussesandGaylord1974;Voronovetal1980).Suchascatteringwasresponsibleforadecreaseofthemodulationdepth(to~50%).Butnophotoinducedradiationpolarizationconversionwasobserved,whichisalsoassociatedwithaphotorefractivebeamscatteringinaplanarwaveguideand,therefore,withadecreaseofoflightintensityinthiswaveguide.

6.4Practioalexamplesofwaveguideelectro-opticmodulators

6.4.1Opticalwaveguideswitchmodulator

Fastwaveguideopticalswitchmodulatorsareimportantcomponentsforfuturewidebandlightwavecommunicationsystems.High-speedswitchingmaybeespeciallyusefulfortimedivisionmultiplexing.Severalhigh-speedswitches(CrossandSchmidt1979;Mikamietal1978)andmodulators(NeyerandSohler1979;AuracherandKiel1980;Leonberg1980)usingTi-diffusedlithiumniobatewaveguides.Mostofthesedeviceshavedemonstratedmodulationbandwidthof

about1GHz(approximately500psswitchingtime)andrequirerelativelylongdevicelengthof3to10mm.Highsinusoidalmodulationrateshavebeenachievedusingatravelingwavegeometry,againwithlongdevicelength(Izutsuetal1977).Auniquelydesignedandfabricatedopticaldirectional

Fig.6.14Schematicdrawingofopticalwaveguidedirectionalcouplerswitchmodulator(Alfernessetal1981).

couplerswitchwithademonstratedswitchingtimeof110pswasdescribedbyAlfernessetal(1981).High-speedswitchingwasachievedbyusingveryshort(750µm)electrodeswithasmall(1µm)interelectrodegap(Fig.6.14).Thesmallcapacitanceresultingfromtheshortdevicelengthyieldshigh-speedswitching.Atthesametime,thesmallinterelectrodegapallowsalowswitchingvoltageinspiteoftheshortdevicelength.

AschematicofthewaveguidedirectionalcouplerswitchisshowninFig.6.14.Thedirectionalcouplerwasdesignedsothat ,wherekisthecouplingcoefficientandnistheoddintegersothatintheabsenceofanappliedfieldmostofthelightincidentinonewaveguidecrossesovertotheother.Formodulatorapplications,thisconditionneednotbestrictlysatisfied.Applicationofanappropriatevoltagesufficientlymismatchesthetwowaveguidessothatthelightstaysintheincidentwaveguide.

Theopticalswitchingtimecanbeminimizedbyfixingthecontrolvoltage(power)atsomeacceptablelowlevel.ForthelumpedelectrodesconsideredheretheswitchingtimeisgivenbytheRCtimeconstant,whereCiselectrodecapacitanceandR=50isaparallelresistancetomatchtoanexternaldrivingcircuit.Theelectrodecapacitanceisgivenapproximatelyby(KaminowandStulz1975)

whereLandWaretheelectrodelengthandwidth,respectively,anddistheinterelectrodegap.NotethatthecapacitanceincreaseslinearlywithLbutitincreasesonlylogarithmicallywithdecreasinggap.

Clearlyforhigh-speedswitching,shortdevicelengthisdesirable.However,thedevicelengthmustbesufficientlylargetoyieldanacceptablylowswitchingvoltage.Therequiredelectro-opticallyinducedphasemismatchtoswitchthelightbacktotheincident

waveguide(assumingonecouplinglength)is

wherethepush-pulleffectforelectrodesplacedontopofthewaveguides(Fig.6.14)hasbeeninduced.Visthemaximumadmissiblecontrolvoltage,nistherefractiveindex,lthewavelengthandathegeometricaloverlapbetweentheopticalandappliedelectricfields.Therequiredlengthistherefore

Fromequations(6.22)and(6.24)theRCswitchingtimeis

Fig.6.15Calculatedrequiredelectrodelengthandresultingmodulationbandwidthversusinterelectrodegap.AdrivevoltageV=5V,electrodewidthW=30µm,

opticalwavelengthl=0.6328µm,andoverlapparametera=0.5areassumed(Alfernessetal1981).

Theresultsofequations(6.24)and(6.25)areshowninFig.6.15,wheretherequiredLandtheresultingmodulationbandwidthDf=1/ptareplottedversustheinterelectrodegap.ItisassumedthatV=5V,r=r33(lithiumniobate)=30×10-12m/V,l=0.6328µm,W=30µm,anda=0.5andthatineachcaseLcorrespondstoonecouplinglength.Clearlyforfixedswitchingvoltagethemodulationbandwidthismaximizedbyusingasmallinterelectrodegapd.Asmalldisdesirablebecausealthoughitresultsinalargercapacitance/length,theresultinglargerelectricfield(forafixedappliedvoltage)allowsashorterdevicelength.Becausetheelectrodecapacitancedependslinearlyuponlengthandonlylogarithmicallyupond,thesmallgapmakespossibleanetenhancementoftheswitchingspeed.Ofcourse,theresultingshortlengthisalsodesirableforincreasedpackingdensityindcswitchingnetworksandresultsinloweropticalandelectricalloss.

Specialfabricationcareisrequiredtoachievethedesiredone-micronelectrodegapalignedoverthewaveguides.Thislimitationwas

overcomeusingthenoveltwo-stepalignmentprocedureoutlinedinFig.6.16.First,theelectronbeamwrittenelectrodemaskwith1µmgapwasintentionallymisalignedlaterallybyabout1µm.Thepatternwasexposed,developedandchrome/aluminiumelectrodespatternedbyliftoff.Theresultisthatwhileoneelectrodeisproperlyalignedoveronewaveguide,becauseoflinebroadening,theotherisnot.Thesameelectrodepatternisthenalignedoverthewaveguidesasecondtime,howeverwithanintentional1µmshiftintheoppositedirection.Afterasecondevaporationandliftoff,thedesired1µminterelectrodegapalignedovertheinterwaveguidegapisachieved.Inaddition,toprovidethedesired1µmgap,thedoublemetalthicknessobtainedbythistechniqueisbeneficialtoreducetheelectroderesistance.

Thedevicewasevaluatedatl=0.6µmusingtheTMpolarizationwhichseesther33coefficient.Usingdcconditionswithasix-voltbias,anadditional6-Vmodulationresultsinanabout-7dBmodulationinthelightoutputfromthecrossoverwaveguide.Theswitchingspeedofthisdevicewhendrivenbyashortelectricaldrivepulsewasmeasuredwithanovelopticalsamplingtechniquereportedindetailelsewhere(Alfernessetal1980).Asequenceof

Fig.6.16Fabricationstepsforachieving1µmelectrodegap

alignedoverthe1µminterwaveguidegap(Alfernessetal1981).

shortelectricaldrivepulsesfromanelectricalcombgeneratordrivesthemodulator.Thesepulsesareinsynchronismwiththepicosecondopticalpulsesfromasynchronouslypumpedmode-lockeddyelaser.Theopticalpulsesarecoupledintothedevice.Themodulatorresponseismappedoutviasamplingbyusinganelectricalphaseshiftertosweeptheopticalpulsetraintemporallyacrosstheelectricalpulsetrainandmeasuringthemodulatoroutputversustimeshift.

6.4.2Thin-filmelectro-opticlightmodulator

Kaminowetal(1973)demonstratedtheutilityofthinfilmsbybuildingandtestinganefficientwide-bandLiNbO3phasemodulatorwhosecharacteristicscanbesatisfactorilyaccountedforbythebulk

electro-opticcoefficientofLiNbO3.

Thepowerperunitbandwidth,P/Df,requiredtodriveabulkmodulatorrodoflengthLandsquarecrosssectiond2wasproportional(KaminowandTurner1966)tod2/L.Theminimumvalueofthisfactorisdeterminedbydiffractionofthelaserbeampassingthroughthemodulatorcrystal.Withthebeamfocusedsothatthewaistoccursatthecentreoftherod,theminimumvalueford2/Lis4l/np,wherelistheopticalwavelengthandnistherefractiveindex.Forthisminimumcondition,thepowerdensityattheedgesofthe

apertureislessthan1/e2timesthepowerdensityatthecentreoftheaperture.Inordertoalleviatethealignmentproblem,modulatorsareusuallydesignedwithasafetyfactorS(KaminowandTurner1966)suchthat

withS>3.

Inaplanarwaveguide,thereisnobeamspreadingnormaltotheplane,butdiffractionintheplanestilllimitselectrodespacingaccordingto(6.26).However,sincealignmentissimplerandreflectionsfromcrystalsurfacesarenotaproblem,onemayemploytheminimumvalue intheplanarstructure.

Kaminowetal(1973)haveusedthesimplemodulatorstructureillustratedinFig.6.17:aLiNbO3planarwaveguidewithaluminiumelectrodesevaporatedonthesurface,andinputandoutputrutileprismcouplers.Theout-diffusedcrystalhasdimensionsof15×2×5mmalongthea,b,andccrystalaxes,respectively.Theextraordinaryindexprofileisgivenby

wherexisthedepthbelowthesurface,A=4×10-3,andB=530µm.Theguide,whichcansupportabout198modes,isexcitedinTEmodesviatheinputcouplerbya0.633µmlaserpolarizedalongthecrystalcaxis.

Theelectrodeswereformedphotolithographicallywithdimensionschosensothat

wherebistheelectrodespacingand .Theextraordinaryindex,ne,measuredonasampleatl=0.633µm,is2.214.

AsindicatedinFig.6.18,thewidthoftheelectrodes,a,ischosensothat .ThecapacitanceCforacoplanarcondenserwitha=bonauniaxialcrystallikeLiNbO3havingdielectricconstantsea=43andec=28along

Fig.6.17Thin-filmLiNbO3electro-opticphasemodulator(Kaminovetal1973).

Fig.6.18CoplanarelectrodeonLiNbO3guiding

layer(Kaminovetal1973).

theaandcaxes,respectively,isgivenapproximatelyby(ProkhorovandKuz'minov1990)

Themodulatingfieldcomponentsjustbelowthesurfaceofthecrystalare

whereVisthevoltagebetweenelectrodes.TheEycomponentdecreaseswithdepthatleastasfastas(Engan1969)exp(x/x0),where

Formosteffectiveuseofthemodulatingfield,thepenetrationdepthoftheopticalbeamshouldbecomparablewithx0.TheelectrodedimensionswereL=6.2mm,a=44µm,andb=57µm,yieldingS=1.22,x0=45µm,andC=2.0pF.Themeasuredcapacitanceat50MHzwasabout3pF.

IfaloadresistanceRisplacedinparallelwithCandthecombinationisdrivenbyamatchedvoltagegeneratorwithimpedanceR,thebasebandwidthisgivenby(KaminowandTurner1966)

ForR=50WandthecalculatedC=2pF,themaximumbandwidthis

Df=3.2GHz.Transit-timelimitationsareabove3.2GHzforL=6.2mm.

Forthecrystalcaxisorientedalongy,thephasemodulationindexis

wherer33istheelectro-opticcoefficientand istheeffectivemodulatingfield.Thefactoruisanumberlessthanunitythattakesaccountofthefact

Fig.6.19Apparatusforheterodynemeasurementofthephase

modulationindex(Kaminovetal1973).

thatEyvariesacrossthebeam.Withr33=31×l0-12m/V,thecalculationyieldsh/V=0.18u/V.

Themodulationindexcanbemeasuredbyusingtheheterodynesystem(Kaminow1965)illustratedinFig.6.19.ThestabilizedHe-Nelaseroscillateinonlyonelongitudinalmodebecauseoftheirrestrictedlength.Thelocal-oscillatorlasercanbesweptovera500-MHzrangewithoutappreciablevariationinamplitudebyvaryingthemirrorspacing.Thespectrumofthemodulatedcarrierlasermixeswiththelocaloscillatorinaphotodiode;thephotocurrentispassedthrougha70-MHz-i.f.amplifierandisdetectedanddisplayedonanoscilloscope.TheratioofsidebandtocarrieramplitudesisJ1(h)/J0(h),whereJnisthenthorderBesselfunction.Theamplituderatioismeasuredwiththeaidofcalibratedopticalattenuatorsplacedinfrontofthelocaloscillator,andhiscalculatedfromtheresult.Theuseofinputandoutputprisms,ratherthanfocusingthebeamintoandoutoftheedgesofthelayer,ensuresthatonlyguidedlightisdetected.

Intheexperiment,aGeneralRadiooscillatorfeedsaminiature50Wcoaxialcableleadingtoapanelconnectoradjacenttothemodulatorcrystal.Thingoldwiresfromtheconnectorconnectthevoltagetotheelectrodesonthecrystal.Thecapacitanceoftheconnector,leads,andelectrodesmeasuredattheconnectorisabout4pF.Inordertoobtain

acorrectreadingofVathighfrequency,itisnecessarytoplacethevoltmeterprobeindirectcontactwiththeelectrodes.

Themeasurementsyieldh/V=0.13V-1,constanttowithin10%overtheavailablemeasuringrangeoftheapparatus,50-500MHz.Voltagewasalsovariedfrom0.7to7Vwithoutalteringh/V.Themeasuredandcalculatedvaluesofh/Vagreeiftheeffectivefieldfactoruissetequalto0.7,whichisreasonablyclosetounity.Thus,Kaminowetal(1973)confirmthatthebeampassescleanlybetweentheelectrodesinthex=0planeanddoesnotpenetratemuchdeeperthanx0,justifytheassumptionthattheelectro-opticcoefficientsintheguidinglayerandbulkcrystalarepracticallythesame,anddemonstrateexperimentallyabasebandwidthatleastasgreatas500MHz.

Theobservedvalueofumayseemsurprisinglyclosetounityinviewofthefactthatthepenetrationofthemodulatingfieldisapproximatelyx0=45µmwhilethethicknessoftheguidinglayerisapproximately

B=530µm.Thelikelyexplanationisthat,byadjustingtheinputangletotheprismcouplerformaximummodulation,onlytheshallowlow-ordermodesareselectivelyexcited.Theexperimentalerrorinthemeasurementofh/Visprobablylessthan15%.Thepeakvoltagerequiredtoobtainh=1radis7.7V.ThecorrespondingpowerP=V2/2Rconsumedinthe550Wloadis590mW,and,forDf=3.2GHz,P/Df=0.19mW/MHz.IfoneusesthecapacitancemeasuredattheconnectorratherthanthecalculatedC,DfwillbehalvedandP/Dfdoubled.

InordertoimproveP/Df,theopticalbeamandmodulatingfieldsmustbeconfinedtosmallercrosssectionsovertheirinteractionlength.Opticalconfinementinthey=0planecanbeimprovedbyreducingtheout-diffusiontimeand/ortemperatureinordertoreducethelayerthickness(KaminowandCarruthers1973).Otherschemesarebeingconsideredthatwillguidetheopticalbeaminthex=0planeinordertoeliminatediffractioneffects;thenb2/Lmaybereducedindefinitely.Inordertousethemodulatingfieldmosteffectively,themodulatingfielddistributionshouldbetailoredtojustoverlaptheopticalbeam;forthecloselyconfinedopticalbeam,thiscanbeachievedbyreducingtheelectrodespacing.

6.4.3Braggdiffractionmodulator

Intheirwork,HammerandPhillips(1974)reportedtheproductionoflow-lossLiNbxTa1-xO3opticalwaveguidesandtheiruseasthebasisofelectro-opticmodulatorswithover80%modulationatvoltagesbelow5V.

AsimpletechniqueofdiffusingmetallicniobiumintotheLiTaO3substratesproducesahigh-indexsurfacelayerofLiNbxTa1-xO3whichactsasanopticalwaveguide.Theeffectivethicknessandindexcanbecontrolledtoreadilyproducesingle-modewaveguides.Lossesofabout1dB/cmat6328Ahavebeenmeasuredonasingle-mode

guideofthistype.

Usingaperiodicelectrodestructure,Braggdiffractionmodulation(Hammeretal1973)isobtainedwhichswitchesover80%oftheguidedlightatvoltagesof3.5,4.5,and6.5Vforlaserlinesat4976,5592,and6323A,respectively.Theseresultsholdforbothoperationatdcandwithpulserisetimesoflessthan3nsec.Frequencyresponseinthemicrowaverangewithpowerrequirementsbelow0.2mW/MHzisexpected.

Thelowpowerandvoltagerequirementsoftheseopticalwaveguidemodulatorsarecompatiblewithintegratedcircuittechnology.This,plustheexcellentandcontrollablewaveguideproperties,makesthesedevicesextremelyattractiveforuseinavarietyofopticalcommunicationandintegratedopticapplications.

LaserlightiscoupledintothefilmwithSrTiO3prismcouplers.Theeffectiveindexfortheguidedlightmaybecalculatedfromthecouplingangle(Tienetal1969).ThevaluesfoundfallintherangeexpectedforopticalwaveguideswithindicesbetweenthoseofLiNbO3andthoseofLiTaO3.

Forexample,inasingle-modex-zplanesampletheeffectiveindexfortheTE0modepropagatingat51°tothezaxisismeasuredtobe2.188atl=6328Å.Thisfallsintherangebetween2.179and2.237whicharetheindicesinthisdirectionforpureLiTaO3andLiNbO3,respectively.Propagationat51°ischosentooptimizetheelectro-opticcoefficientandretainrelatively

strongguidingasdescribedbelow.Foraguideofthistypetohaveonlyonemodethethicknessatwhichthegradedindexdifferencebetweenfilmandsubstratefallsto10%ofitsmaximumvalueis0.7-1.6mm(Marcuse1973).

Thelossisdeterminedbymeasuringtheintensityoflightscatteredoutofthewaveguideasafunctionofdistanceusingafibreopticprobe.At6328ÅthelossinthesolitaryTE0modeislessthan1dB/cm.Atthe5592-and4845-ÅHe-Nelaserlinesthelossesare4.3and6.7dB/cm.ThisrepresentsamorerapidincreaseinlossthanthedependenceexpectedforRayleighscattering(l0isthefree-space

wavelength).Itispossiblethatimpurityionabsorption,particularlyFe2+,isresponsible.

HammerandPhillips(1974)notedthatforthex-zsubstratesandtransverseelectricfieldsusedinthemodulator,propagationofaTEmodeinthecdirectiongivesrisetothelargestindexdifferencebetweenlithiumniobateandlithiumtantalate(Dn0=0.113)butanelectro-opticcoefficientisequaltozero.PropagationalongthexdirectionreversesthesituationwithDne=0.021andr33=3×10-12m/V.PropagationintheplaneatanarbitraryanglefwithrespecttothezaxisgivesanindexdifferentialDn'suchthat andaneffectiveelectro-opticcoefficientr'whichisalinearcombinationofr13,r33,andr51.maybechosentomaximizer'.TheresultingvaluesforLiNbO3canbeshowntobef=±51°,r'=±34.4×10-12m/V,andDn'=0.058.Thus,theoperatinganglecanbechosentomaximizetheelectro-opticcoefficientwithoutminimizingtheindexdifferentialrequiredforwaveguiding.

ThewaveguidemodulatorisproducedbyapplyingavoltagetoaninterdigitalelectrodepatterndepositedonthewaveguidesurfaceasshowninFig.6.20a.

Applicationofavoltagetotheelectrodesresultsinanelectro-

opticallyinducedBraggdiffractiongrating.LightenteringthegratingatanangleqBisdiffractedthroughanangle2qBinthewaveguideplanewheresinqB=l0/4Sng.ngistheeffectiverefractiveindexfortheguidedmodebeingconsidered.ThefractionoftheenteringlightdiffractedisI/I0=sin2(Df/2)andtofirstorderinr' ,whereEistheaverageinplanefieldcomponentcausedbythevoltageV0.Thus,I/I0hastheformsin2(BV0).

ThepercentagediffractionasafunctionofvoltageforthreelaserwavelengthsisshowninFig.6.20b.Thesquares,crosses,andcirclesarethedatapointsfor4976,5592and6328Ålaserlines,respectively.Thesolidcurvesareplotsofsin2(BV0)normalizedtothedataI/I0=75%.Thefunctionalagreementisgood.Novariationwasobservedinthesepercentagesfromdcuptopulseswithrisetimesbelow3nsec.Theobservedvariationofvoltagewithwavelength,however,isgreaterthanthefirst-ordertheorypredictsifdispersionintheelectro-opticcoefficientsisignored.ThisdispersionforLiNbxTa1-xO3isunderstudy.Themeasuredcapacitanceofthissampleis20pFwhichgivesindicatedcapacitivepowerrequirementsbelow0.2mW/MHz.Thetotallossintroducedbytheelectrodesisunderstudybutappearstobelessthan1dB.

TheLiNbxTa1-xO3opticalwaveguidesdescribedinthisreportarerelativelysimpletomake,haveexcellentandcontrollablewaveguideproperties,andcanbeorientedtomakeoptimaluseofthestrongelectro-opticeffectofbothLiNbO3andLiTaO3.Thehighefficiencyandlowvoltageandpowerrequirementsofthegratingmodulatorformedonthistypeofguiderepresentatleast

Fig.6.20(a)SchematicofgratingmodulatorinLiTaxNb1-xO3waveguide.Guidedlightisdiffractedthroughanangle2qBwhena

voltageisappliedtotheinterdigitalelectrodes.Sis7.6mmandLis0.3cm.(b)Thecurveshowsthepercentageoflightdiffractedasafunctionofvoltage.Opensquares4976

Å(He-Selaser),crosses5598Å(He-Selaser),andsolidcircles6328Å(He-Nelaser).Thesolid

curvesareplotsofsin2(BV0)normalisedtothedataat75%(HammerandPhillips,1974).

anorder-of-magnitudeimprovementinperformanceoverbulkdevicesandearlierwaveguidegratingmodulators.Similarimprovementsmaybeexpectedforotherformsofelectro-opticandpossiblyacousto-opticwaveguidemodulatorsandswitchesiftheLiNbxTa1-xO3guideisemployed.

6.4.4Ridgewaveguidemodulator

Kaminowetal(1974)reportedanexperimentalLiNbO3ridgewaveguidemodulatorrequiringamodulatingpowerofonly0.02

mW/MHz/rad.

ALiNbO3crystalhavingdimensions25mm×6mm×3mmalongthecrystallographicX,Y,andZaxes,respectively,wasout-diffusedtoproduceaplanarguidewithextraordinaryindexprofilebasedontheintegralerrorfunctioncomplement

where .Inordertoapproachsingle-modeoperation;theresultantcoefficientswerea=2×10-4,b=33mm.Iftheprofile(equation(6.34))isapproximatedbyanexponentialfunction

thencalculations(Conwell1973)indicatethattheplanarguidewillsupportjusttwomodes.FortheTE0andTE1modes,respectively,

wherebandkarethepropagationconstantsintheguideandinfreespace,respectively.

Aridgewasproducedbyion-beametchingthe6×25mmsurfaceofthecrystaleverywhereexceptforanarrowcentralstripalongthe25mmdimension.Aquartzfibreofsquarecrosssectionadheredtothecrystalsurfacewithphotoresistorservingasthemask.Aniongunfiredargonionsat30°fromthenormalontothecrystalsurface.With100mAionbeamcurrent,theetchingrateforthisconfigurationwasapproximately1mm/hforboththeLiNbO3crystalandquartzfibre.Afterionetchingandwiththefibremaskstillinplace,thesamplewascoatedwithCr(250Å)andAl(3000Å)electrodesbyevaporation.Inordertoensurecoatingthesidewallsoftheridge,thesamplewastiltedfirsttoonesideandthentheotherduringevaporation.Afterexaminationofthecompletedridge,thebestregionwasselectedandtheremainderofthecrystalwasgroundoffandtheendspolished.

Ascanningelectronmicrographofthesampleshowsthatthewallsoftheridgearesmoothandrectangular.Althoughthecross-sectiondimensionsmayvaryby±1mmalongthelengthoftheridge,theaverageheighthis7.5mmandaveragewidthwis19mm.ThelengthLoftheridgeis11.5mm.

Aheterodynemeasuringsetwasusedtodeterminethephasemodulator.A0.633-mmlaserbeamwasinjectedintotheendoftheridgewitha×20microscopeobjective;a×40objectivewasusedtoimagetheoutputendontoascreenandlatertocollimatethebeaminthemeasuringset.Thebeamappearstobesingle-mode,slightlyellipticalincrosssection,andisalmostcompletelyconfinedwithintheridgeitself,ratherthanpenetratingintotheplanarwaveguideregionbelowtheridge.

Ifoneassumestheexponentialindexprofile(6.35)fortheoriginalplanarguideandthenremoves7.5mmtoformtheridge,theplanarguideoutsidetheridgewillhaveanexponentialprofilewithcoefficientsap=aexp(-2h/b)=1.3×10-4andbp=b.ThenusingthecurvesofFig.5.15(Carruthersetal1974)oneobtainsforTE0andTE1modes,respectively,

Thentheeffectiveindexapproximationcanbeused(Ramaswamy1974)todeterminetheconfinementwithintheplane.Theeffectiveindexchangeforthesymmetricalguidewithintheplaneis(fromequations(6.36)and(6.37))

Fig.6.21SchematicdiagramoftheLiNbO3ridgewaveguide

modulator(Kaminovetal1979).

forTE0andTE1modes,respectively.Ineithercase,computationshowsthatonlythefundamentalmodeisguidedintheplane.TheplanarTE1modeisprobablynotstronglyexcitednorisittightlyconfinedintheridgeguide.Otherapproachestotheanalysisofridgeguide(orequivalentlyribguide)modesgivesimilarresults.

TheridgewaveguidemodulatorisshownschematicallyinFig.6.21.Theelectrodesareattachedbythinwirestoaminiaturecoaxialconnector.Avoltmeterand50Wloadareplacedinparallelwiththecrystalattheconnectorandthemodulationindexhismeasuredatfrequenciesbetween50and200MHz.TheseriesinductanceoftheleadsandstraycapacitanceoftheconnectorinterferewiththemeasurementofpeakmodulatingvoltageVathighfrequency.However,theseunwantedimpedancescanbeeliminatedorreducedinapracticaldevice.

Thecapacitancemeasuredattheconnectoris19pF,whilethecapacitanceCofthemodulatorcrystalalone,obtainedbysubtractingthecapacitancemeasuredwhentheleadsaredisconnectedatthecrystal,is10pF.Thecalculatedcapacitanceoftheridgecapacitorinparallelwiththeassociatedplanarcapacitorisonly5pF,sothata

furtherreductionofCandanincreasedbandwidthmustbepossible.

Themeasuredvalueofh/Vis0.85V-1.Thevaluecalculatedassumingthebeamtobecompletelyconfinedwithinaridgeofwidthw=19mmis0.98V-1.Thisexcellentagreementisfurtherevidencethatthebeamiswellguidedwithintheridge.Foraplanarmodulator,h/Vwas0.13V-1.ThatdevicewasdiffractionlimitedsothatthesafetyfactorSwasunity.Fortheridgeguide,ifw=dinequation(6.26),thenS=0.28.SincemodulatingpowerPperunitbandwidthperunitmodulationindexisproportionaltoS2,theridgeguidemodulatorrepresentsapotentialthirteenfoldimprovementinefficiencyoverthediffraction-limitedplanarmodulatorandanadditionalorder-of-magnitudeimprovementoverbulkmodulatorsforwhichthesafetyfactorisusuallygreaterthan3.

ThemodulatorbandwidthisDf=(pRC)-1and,withR=50WandmeasuredC=10pF,Df=640MHz.Thenusingthemeasuredh/VandP=V2/2R,Kaminowetal(1974)obtainedP/Df=20mW/MHzforh=1rad.

Theopticalattenuationduetoabsorptionbythemetalwallsontheridgeguidemaybeestimatedfromcalculationsforaplanarsymmetricalmetal-cladguideoperatingintheTM2mode(Kaminowetal1974).Thecalculatedlosseswere4and3dB/cmforCrandAlelectrodes,respectively.Agelectrodeswouldintroducealossofonly0.2dB/cm.Themajorsourceoftransmissionlossinthedeviseatpresent,however,isimperfectinputcouplingintothedominantmetal-cladridgeguidemode.Theridgewaveguidephasemodulatoriswellsuitedtoincorporationinabalancedbridgearrangementinanintegratedopticalcircuitforuseasswitchoramplitudemodulator.

6.4.5Ti-diffuseddiffractionmodulator

Tangonanetal(1978)describedthedesignandfabricationofthin-filmBraggdiffractionmodulatorsinTi-diffusedLiTaO3waveguides.Themodulatorperformancewasadequatefornear-termsystemsapplicationswithademonstrateddiffractionefficiencyof98%atthevisibleandnearIRwavelengths,ahighextinctionratio(<250:1),andadesignbandwidthof GHz.LiTaO3wasswitchedasthewaveguidematerialbecauseofthemuchhigherimagethresholdofwaveguidesformedbyTi-diffusedinLiTaO3thaninLiNbO3(Tangonanetal1977).

Beamdiffraction,asamechanismforintensitymodulationbyelectro-opticmeansinthethinfilms,isachievedbyproducinganelectricallycontrolledphasegratinginthepathofthepropagatingbeam.Thediffractionprocessresultsfromaperiodicperturbationoftherefractiveindextransversetothebeampropagationdirection.Ausefulmethodforelectro-opticallygeneratingthedesiredphasegratingis

showninFig.6.22.Themechanismforinteractionreliesonthefringingelectricfieldsextendingbelowthesurfacebetweeninterdigitalstripelectrodesformedonthecrystalsurface.Thelocalfringingfieldstrengthshouldbereasonablyuniformacrosstheguidedbeamandapproximatelysinusoidalintheplaneoftheguidinglayer,transversetothebeam.Thismaybemostreadilyachievedbyapplyinganisolatinglower-indexlayerabovetheguidinglayer.Thisservestheaddedfunctionofminimizinginteractionoftheopticalbeamevanescenttailwiththelossymetallicsurfaces.Bragg

Fig.6.22Phasegratingformationbythe

electro-opticeffect(Tangonaneta11978).

diffractioninvolvesintroducingtheinputbeamataspecificangleqB,theBraggangle,withrespecttotheelectrodearray(HammerandPhillips1974;Nodaetal1974).DiffractionoccursreflectivelyinasingleoutputattwicetheinputanglewhentheBraggconditionissatisfied.

Thephasechangef,inradians,inducedbytheelectricalsignalfieldoverapathlengthLis

whereDnistherefractive-indexincrementcausedbytheelectro-opticeffect,l0andisthefree-spacewavelength.ThestrongestinteractioninLiTaO3andLiNbO3occurswhentheappliedelectricfieldandopticalelectricpolarizationarebothparallel(ornearlyparallel(HammerandPhillips1974))tothecrystallinecaxis(theopticaxis).Forthiscondition,therefractive-indexincrementis

wheren3istheextraordinaryrefractiveindex,r33istheappropriateelectro-opticcoefficient,andE3istheappliedelectricfield(Chen1970).Thus,thecrystalmustbecutwithitscaxisintheplaneofthewaveguideessentiallytransversetothebeampropagationdirection,andthepropagatingopticalmodemusthaveTEpolarization.Thispolarizationhastheleastlosscharacteristicsinproximitytothemetalelectrodesurfaces.Hence,thisminimizestheinsertionlossofthemodulatorcausedbyabsorption.

Combiningequations(6.39)and(6.40)yields

Assumethatthecaxis-orientedelectricfieldintheregionoftheguidedlayerisapproximatelysinusoidalinthetransversedirection(areasonableassumptionforaregionaboutadistancesbelowthe

surface).ForBraggdiffraction,thezero-andthefirst-orderpowersareproportional,respectively,tocos2(f/2)andsin2(f/2).Formodulation,correspondingto100%depletionofthezero-orderbeamintheidealizedcase,themaximumrequiredvalueoffisp.

Todesignasuitablediffractionmodulator,onehastodeterminetheallowabledimensionsoftheelectrodearray,basedonbandwidthrequirementsanddriverpowerlimitations.Thiscanbedoneinafairlystraightforwardmanner,andboththepowerandthecapacitancecanbeeasilyexpressedintermsoftheratiooftheelectrodespacingtoelectrodelength,s/L.

Withoptimizedvideopeaking,thepowerrequiredtodriveacapacitanceCoverabandwidthBwithpeakdrivervoltageVmis

where istheshuntresistanceneededtodissipatethepowerandprovideanRC-limitedbandwidthB.ThecapacitanceofaninterdigatedelectrodearrayhavingNfingerpairsonanx-ory-cutuniaxialcrystalsuchasLiTaO3is(JoshiandWhite1969)

whereKisacorrectionfactor(BarrosandWilson1972)determinedfromtheratioofelectrodewidthtospacingw/s.ForLiTaO3intheclampedcondition(whichisexpectedtoobtainovermostoftheoperatingband),thecapacitanceis

Thenumberofelectrodepairsisreadilydeterminedfromthetotalwidthoftheelectrodearray.Foraninputlaserbeamhavinga1/e2diameterDequaltoabout1mm,itturnedouttobesufficienttoassumeanelectrodearraywidthof1.5D,whichyields

whereSistheperiodicity(expressedincentimeters).

TheappliedelectricfieldE3intheactiveregionofthebeamisestimatedtobeapproximately(JoshiandWhite1969;BarrosandWilson1972)

whenthedistancebelowthesurfaceiscomparabletos.Thisistheassumeddesignconditionthatleadstoareasonablyuniformfieldstrengthacrosstheopticalbeam.ItisconvenienttoexpressVmintermsofthecommonlyusedelectro-opticparameterE3L,thefield-lengthproduct

Table6.1liststherelevantelectro-opticanddielectriccharacteristicsofLiTaO3andLiNbO3at0.53mmand1.06mm.ThesedataareusefulinthedesignofadoubledNd:YAGcommunicationlink.Thechangesine1ande2forLiNbO3ingoingfromtheunclampedtoclampedconditionarequitelarge,

Table6.1Propertiesofelectro-opticmaterials(Tangonaneta11978)

Quantity LiTaO3 LiNbO3

0.53mm 1.06mm 0.53mm 1.06mm

n3 2.21 2.14 2.23 2.16

~31 ~29 32.2 ~32

30.3 ~29 30.8 ~30

33.5 ~28.4 35.7 ~32

32.7 ~28.4 34.1 30

(T)=unclamped

(S)=clamped

Table6.2Resultsofdesigncalculations(Tangonan,Persechini,Lotspeich,Barnoski,1978)

Parameter 0.53mm,3Wdrive 1.06mm,24Wdrive

B=0.7GHz B=1.4GHz

K=1,s=w

E3×L,V 1606 3732

L,mm 2.5 5

s,mm 4.6 6.9

S,mm 18.4 27.5

N 81 54

C,pF 77 104

Rs,W 6 2.2

Q 11 20

afactwhichadverselyaffectsthefrequencyresponsecharacteristics.Similarly,thechangeinr33issubstantiallygreaterthanthatofLiTaO3,thusproducingastrongereffectontheelectro-opticfrequencyresponse.

Forw/s=1,amaximuminteractionlengthof2.5mmwaschosen0.53mmtokeepwithinreasonablelimitsofopticalloss.Itwasfoundthatthewaveguidelossat5145ÅforTi-diffusedLiTaO3guideswas3-5dB/cm.Forthe1.06-mmcase,whereopticallossesaresubstantiallylower( dB/cm),alengthof5mmwasarbitrarilychosenasareasonableupperlimit.

Table6.2givestheresultsderivedfromtheprecedingequationsforthetwowavelengthsofinterest.TheTableincludesaparameterQdefinedby

Fig.6.23SerieselectrodemodificationforBraggdiffractiongrating(Tangonanetal1978).

Fig.6.24(right)Splitelectrodepatternofmodulator

(Tangonaneta11978).

whichdescribesthesamenatureofthediffraction.BraggdiffractionoccursmostefficientlywhenQ>10.

ExaminationofthevaluesofshuntresistanceRsforthetwocasesshownclearlyindicatestheneedforimpedancematchingfroma50Wdriversource.Somedevelopmentsinthedesignofwidebandrfimpedancetransformershaveledtoverywidebanddevicescapableofoperatingfrombelow1MHztowellabove500MHzwithinsertionlossesof0.5dBandless,providedtheimpedanceratiosdonotexceedabout3or4to1.Forlargerstep-downratios,theinsertionlossesaresubstantiallyhigher.Asanalternative,adifferentelectrodedesignmaybeusedtoprovidematchingtoa50Wdriver.Forthecaseof0.53mmdesign,themodificationfollowsaschemeproposedbyNodaetal(1974)inwhichtheelectrodearrayisdividedintoseveralsections,say3,eachoflengthL/3,arrangedinseriesbothelectricallyandoptically.Thisdevicereducesthecapacitancebyafactorof9,whichincreasesshuntresistanceinthesameproportion.This

modificationisshowninFig.6.23.Forthecaseofthe0.53mmmodulatordesign,thisclearlyyieldsashuntresistanceof0.54Wandacapacitanceof8.6pF.Thepenaltypaidbythisapproachisthatthedrivervoltageisincreasedbyafactorof3.

Opticalwaveguideswereformediny-cutLiTaO3wafersbyTiin-diffusionfollowingtheprocessingtechniquedescribedinchapter1.InterdigitalelectrodesemployingthedesignparametersinTable6.2for0.53mmoperationwerefabricatedonthewaferswiththefielddirectionsalignedwiththecaxis.Diffractionefficiency,measurementsweremadeat6328Å(He-Ne),5145Å(Ar),andat10.640Å(Nd:YAG).Diffractionmeasurementsindicatethatthesearethemostefficientelectro-opticBraggmodulatorstodate:98%efficiencywithextinctionratiosashighas300:1.

Forthemodulatorstructuresfabricated,theelectrodepatternswereformedbyphotoetching1500ÅAlfilmsthathadbeenevaporateddirectlyonthe

waveguidesampleoronabufferfilmofSiO2(1500Å).Thisthicknessofthebufferlayerhasbeenfoundtobeeffectiveinprovidingthenecessaryisolationtopreventdirectinteractionsoftheopticalfieldwiththemetalgrating.Figure6.24isaphotographofaportionofasplitelectrodedesignusedtoreducetheeffectivecapacitancebyafactorof9.Thewidth-to-spacingratioachievedwascloseto0.5forallthesamplesstudied.

Thediffractionefficiencyofmodulatorswithandwithoutelectrodebufferlayerswasstudiedtodeterminethedegreeofenergytransferfromthem=0undiffractedbeamtothedifferentgratingorders.Electricalleakagecanhinderdeviceevaluation,andsevereleakagecurrentswereobservedinseveralsamples.TheleakagecurrentsoriginatefromincompleteoxidationoftheSiO2.Theappliedvoltagewassimplyturnedonandkepton.Itisclearfromthetracethattheeffectivefieldoverthewaveguidestructuregoestozeroinashorttime.TheseresultswereobtainedformodulatorswithasputteredSiO2bufferlayer.ThesesamesampleswerestrippedoftheAlelectrodepatternandplacedinanoveninanoxygenatmosphereat500°Cforafewhours.Thesampleswerethenreprocessedandnewmodulatorpatternsfabricatedonthem.Thesesampleswerefoundtoexhibitgooddcproperties:noleakagewasobserved,andmodulationtestscouldbecarriedout.

Diffractionefficiencymeasurementsweremadeat5145Å.Thismodulatorhadnobufferlayeronitandwasusedtodeterminetheeffectsofthemetalgrating.ThemetalgratinginducedadeflectedspotattwiceqBofintensityequalto15-25%oftheundeflected(m=0)spot.Themeasuredvoltageformaximumdiffractionwas17.5V,whichisquiteclosetothecalculatedvalueof17.0Vfor5145Åoperation.ThecalculatedvaluefordoublesNd:YAGoperation(0.53mm)is17.7V.Thediffractionefficiencymeasuredinthisexperimentwas95.3%.

Theresultsofmeasurementsmadeat1.06mmareplottedinFig.6.25.Themeasureddiffractionefficiencywas98%withanextinctionratioof300:1,or24.7dB.

Fig.6.25Resultsofdiffractionmeasurementsat

1.06mmshowing98%maximumfirstorderdiffractionanda300:1extinctionratio

(Tangonaneta11978).

Table6.3Characteristicsofelectro-opticinterferencetypemodulator

Controlvoltage 2V

Operatingfrequencybands 50Hz-500MHz

Operatingwavelength 0.85mm

Opticalinsertionloss,notmorethan 12dB

Controlinputcapacity 10pF

6.4.6InterferometricMach-Zehndermodulator

Anopticalinterferometer-typemodulatorwasrealizedinpracticeusingtheepitaxialthin-filmtechnique.

ThemodulatorwasmanufacturedbytheMach-ZehnderinterferometerschemeonanY-LiTaO3substrate.Single-modechannellightguideswiththedistributionprofileDnclosetoacylindricalonewereformedbythefilmdiffusionmethod.Thesizeofthemodespotatawavelengthof0.85mmmadeup~9mm.Analuminiumelectrodestructurewithdimensionsl(length)20mm,d(width)5mmwasformedonthefilmsurface.

TheLi(Nb,Ta)O3filmthicknesswash=13mm,L=20mm,theinterelectrongapwidthd=3mm,l=0.85mm,n=2.18,r=20×10-12m/V.UndersuchconditionstheoverlapintegralG=0.8.ThecalculationsshowthatthevalueofthecontrolvoltagewillbeequaltoV=1V,whileexperimentalvalueswere2V.Theexperimentalmodulationdepthm(equation(6.8))wasequalto82%whenweworkedwithlinearlypolarizedradiationattheinput.

A100%modulationdepthwhichistheoreticallyadmittedistypicallysomewhatlessinexperimentduetolightscatteringonwaveguidedefectsandontheelectrodestructure.Inourexperimentsmwasequal

to82%whenweworkedwithlinearlypolarizedradiationattheinput.

Theinsertionlossesincludeinputandoutputradiationlossestopropagationaboutthemodulatingstructure.Themeasuredvalueofawas12dB.Forlinearlypolarizedradiationthisvaluefallsdownto9dB.Thelossesoflightscatteredfromchannellightguidesonthestructurewere6dB,andthelosseson'Y'brancheswereequalto2dB.

Themodulatorsweremanufacturedintegro-opticallyonalithiumtantalatesubstratesmeasuring20×30×2mm3onwhichtwoMach-Zehnderinterferometerswereplaced.Themodulatorsaredistinguishedinthattheirlightguidestructureisformedinanepitaxialfilmofasolidsolutionoflithiumniobate-tantalateandrepresentschannellightguidesobtainedbythecombinedfilmdiffusionmethod.Suchlightguides,ascomparedwithlithiumniobate,arehighlyresistanttoopticaldamages.Thecontrolstructureofthemodulatoriswellprotectedfromtheinfluenceoftheatmosphere.

Themodulatorsaremountedintoametallicframemeasuring75×15×35mm3.Thecontrolvoltageisappliedthroughjoints.Thereexiststwoversionsofadjustmentwithexternalopticalchains.

Themodulatorcanbefabricatedintwomodifications.First,asemicon-

Fig.6.26Thinfilmintegro-opticmodulator(generalview).

ductorlasermatedwithamodulatormayserveasalightsource.Thelightistransmittedthroughasingle-modefibreadjustedimmediatelytothemodulatorend.Inthesecondversionthelightisputinandoutofthemodulatorthroughasingle-modefibrejoinedtothesubstrateends.

TheprincipalparametersofthemodulatorarepresentedinTable6.3.

Figure6.26givesapictureofthemodulator(Dubrovennazetal1988).

Significantinterestliesinproducingopticalwaveguidedevicesinmaterialwithahigherelectro-opticcoefficientwhichcouldbeusedformakingcompactlow-voltageelectro-opticmodulatorsandswitches(EknoyanandSwenson1991).AsuitablechoiceforthisisSr0.6Ba0.4Nb2O6(SBN:60),becauseitsr33electro-opticcoefficient(420×10-12m/V)ismorethananorderofmagnitudelargerthanthatforLiNbO3andLiTaO3(ProkhorovandKuz'minov1990(a)).OtherrelevantparametersofSBN:60areitsrelevantdielectricconstantvaluese11=470ande12=880,andrefractiveindiceswhichat0.83mmwavelength(ProkhorovandKuz'minov1990(b))arene=2.2435andn0=2.2375.Theinterestinthismaterialisparticularlyattractiveduetomajoradvancesinitsgrowthtechniques,whichnowmakesitpossibletoproducecrystalsinlargesizes(2-3cmindiameter)ofexcellentquality(Neurgaonkar1989).

OpticalwaveguideshavebeenproducedinSBN:60byZndiffusionfromvapourphase.Usingelectronmicroprobewavelength-dispersivespectroscopy,theZndistributionwasdeterminedandavalueof7.3mmforthediffusiondepthwasobtained.Thebestwaveguideswererealizedbydiffusionat1000°Cfor30minfollowedbyannealingat600°Cfor~100h.

TheopticalwaveguideswereproducedbyZndiffusionfromthevapourphaseinto1mmthickZ-cutSBNsubstrates,inaprocesssimilartoonedescribedearlierwithLiTaO3crystals.TungstenbronzeSBN:60istetragonalatroomtemperatureandexhibitstheCuriepointTcat78°C.ThecrystalsweregrownbytheCzochralskitechniqueandthesurfaceswerepreparedaccordingtocurrentneeds.WaveguidingwasobservedforbothTEandTMpolarizationsbyend-firecouplingat0.83mmwavelength.Electro-opticmodulationatawavelengthof0.83mmonaMach-Zehnderinterferometerwasdemonstratedforthefirsttimeinthismaterial.Withelectricfieldappliedtobotharmsoftheinterferometer,avoltage-lengthproductof0.48Vcmwasobtained.LowervaluesofVpcanbeexpectedbyfurtheroptimizingthepolingprocedureorusingmaterialofhigherelectro-opticcoefficientlikeSBN:75.Electro-optic

Fig.6.27(a)Geometryusedforwritingaholographicgrating

intoaTi-diffusedLiNbO3waveguidewith0.5145mmlight;(b)beamsplittingofaguidedwave(l=0.6328mm)bya

holographicgrating;(c)modulationofaguidedbeambytheapplicationofanelectricfieldacrossaholographicgrating

(1.59mmgapelectrodes)(Goruketal1981).

modulatorsandswitchesinSBNareattractiveastheymightpavethewaytocompactlow-voltagedevices.

6.4.7Electro-opticphotorefractivemodulator

Goruketal(1981)describedanovelmodulatorbasedonacombinationofthephotorefractiveandelectro-opticeffects.Itisessentiallyanintegratedopticsversionoftheelectro-opticswitchfirstdemonstratedinbulkLiNbO3byKenanetal(1974).LightincidentontoaphotorefractivegratingatandneartheappropriateBraggangleisfirstsplitintotwobeamswhoserelativeintensityvarieswiththeexposuretimeusedinwritingthegrating.Theelectro-opticeffectisthenusedtomodulatetemporallythesebeamsviaaninputelectricalsignal.Theresultingmodulatorisausefullowcostlaboratorytoolwhichdoesnotrequireelaboratefabrication.Furthermore,byusingstandardholographictechniques,variousopticalelementssuchaslensesandcouplersmaybewrittenintothewaveguideandswitched

onandoffbythismethod.

ThephotorefractivemethodofwritinggratinghologramsinplanaropticalwaveguideshasbeenreportedbyChenetal(1968)andWoodetal(1981).Goruketal(1981)madeuseofthelargephotorefractiveeffectknowntooccurinLiNbO3whenlightinthebluegreenregionofthespectrumisincident.Twoguidedwaves(writingbeamsatl=0.5145mmfromanAr+laser)withwavevectorsb1andb2interferetoproduceagratingwithperiodicity .ForthecaseillustratedinFig.6.27a,bg=2b0sinq0,where ,q0istheanglebetweenb(orb2)andthexaxis,andbgliesalongthezaxis.Theeffectivewaveguiderefractiveindexisgivenby

andthemodulationdepthDndependsonthenumerousfactorssuchasthewritingbeamintensitiesandduration,waveguide,andmodeparameters.

ConsidernowasetofelectrodesdepositedontothewaveguidesurfaceasindicatedinFig.6.27c.WhenavoltageVisappliedtotheelectrodeswhichareseparatedbyadistanced,aneffectiveindex(Marcuse1975)changeDN,

issuperimposedontothephotorefractivegratingviatheelectro-opticeffect.(Thereisanadditionaleffectduetothematerialpiezoelectricity,butthisisbelievedtobeasecondarymechanismhere.)Theparameterr33istheappropriateelectro-opticcoefficientforthegeometryshowninFig.6.27(c).Hence,thetotalrefractiveindex

AsimilarphenomenonhasbeenanalysedpreviouslyviaacoupledmodeapproachbyKenanetal(1974).(Intheircaseasurfacecorrugationinsteadofaholographicgratingwasusedtoobtaintheinitialdivisionoftheincidentguidedwaveintotwobeams.)TheyshowedthatthediffractedlightintensityIdisgivenintermsoftheincidentguidedwavelightintensityIiby

HereLgisthelengthofthegratingwithperiodicityL,anddisthephasemismatchtermduetoboththeelectro-opticeffectand(or)misalignmentDqoftheincidentbeamfromtheBraggangleqB,i.e.

Theparameterkeisgivenby

wherekisthecouplingcoefficientwhichappearsinthecoupledwaveequations(Kenanetal1974).Maximumdiffractionoccurswhend=0,whichisusuallyobtainedbyensuringthattheguidedwaveisincidentattheBraggangle.Itisalsousefultonotethatamisalignmentinthedirectionoftheincidentlightcanbecompensatedforbyapplyinganappropriatevoltage.Furthermore,

thevoltageDVwhichmustbeappliedtogofromthemthtothem+lminimumisgivenapproximately(keL<p/2)by

Thewaveguidesstudiedwerey-cutandx-propagatingTiin-diffusedLiNbO3waveguidescharacterizedapproximatelybyexponentialrefractive-indexprofiles(equation(6.35)).GratingswerewrittenintothewaveguideasindicatedinFig.6.27bycouplingtwocwlaserbeamsfromanargon-ionlaser(l=0.5145mm)intoTE0waveguidemodesviafutileprisms.Twoseparategratingswerestudied;theanglesbetweenthewritingbeamswhichweresymmetricaboutthexaxiswere3°(1.59mmspacingbetweenelectrodes)and4°(0.3mmspacing).Typicallytheincidentpowersineachbeamwere1mW,andthegratingwerewrittenin1sexposures.Theseparameterswereadjustedtoproduceapproximatelya50:50splittingratiowhenHe-NeguidedwavelightwasincidentattheappropriateBraggangle.Thefirstsetofelectrodesconsistedoftwostripsseparatedby1.6mmpaintedonwithsilverpaint.Thesecondhadasetofevaporated1500Åthickaluminiumelectrodeswitha0.3mmspacing.

Themodulatorcharacteristicswerestudiedwith0.1mWofHeNelaserlight.LightwascoupledintoandoutoftheTE0modeviarutileprisms.Thegratingswerestudiedwithinafewmonthsoftheirfabrication,anditwasverifiedsixmonthslaterthatthegratingswerestillpresent.Modulationwasobtainedbyapplyingavoltagevaryingwithtimeacrosstheelectrodes,andthedeflectedandundeflectedbeamintensitiesweremeasuredwithacalibratedphotodiode.

SomeofthepertinentoperatingcharacteristicsofthemodulatorareshowninFigs.6.27cand6.28.Whentheincidentanddeflectedbeamswerekeptawayfromtheelectrodeedges,thequalityofbothbeamswasgood,asindicated

Fig.6.28Modulatorefficiency(100%=completeextinction)versusappliedvoltageacrossthe1.59mmelectrodegap.Solidline

correspondstotheory(seethetext)(Goruketal1981).

inFig.6.27c.ForlightincidentattheBraggangle,theoutputsignalistheharmonicofthefundamental.AwayfromtheBraggangle,theoutputcanbechosentobeeitherinphaseoroutofphasewiththemodulationsignal.

Detailedmeasurementsofthemodulatorresponsefunction(modulatorefficiencyarereproducedinFig.6.28.(100%efficiencycorrespondsinthiscasetoacompleteextinctionofthediffractedbeam.)AsisevidentfromFig.6.28,theagreementbetweenexperimentandtheoryisexcellent.Thebestextinctionratioobtainedwas20dB,andtheappliedvoltagecorrespondedtoanappliedelectricfieldof0.22×106V/m.

Thebeamqualitydisplayedanomalousbehaviourwhenevertheincidentand(or)deflectedbeamswerepropagatedneartheelectrodeedges.Goruketal(1981)hypothesizedthatthefieldsattheelectrodeedgesaresufficientlyhightocausethewaveguidetoapproachthecutoffcondition,andhencethebeamqualityismuchmoresusceptibletolaserdamage.

Basedontheseobservations,itwasimportanttokeeptheguidedwavebeamsawayfromtheelectrodestomaintainreasonablebeamquality.

6.4.8KNbO3inducedwaveguidecut-offmodulator

Potassiumniobate(KNbO3,pointgroupsymmetrymm2atroomtemperature)isaveryinterestingelectro-opticalmaterialforbothbulkandwaveguideapplications,becauseofitslargeelectro-opticandnonlinearopticcoefficients,goodphotorefractiveproperties,andhighdamagethreshold(60MW/cm2pulsedatl=0.86mm)(ProkhorovandKuz'minov1990).ThesepropertiesmakeKNbO3attractiveforthin-filmwaveguides,suchaselectro-opticmodulators,whichwouldbenefitfromhighfiguresofmeritnr33=680pm/Vandnr42=4350pm/V(n3=2.1683isaprincipalrefractiveindex,n4=2.254isan

averagerefractiveindexinthebcplane,andr42=380pro/V)comparedtonr33=341pm/VforLiNbO3,oranefficientfrequencydoublerforAlxGa1-xAssemiconductorlasers,allowingcollinearphase-matchedtypeIinteractionaroundroomtemperaturewithinthiswavelengthrange.Tuckeretal(1974)observedopticalwaveguidinginnaturallyformedplanarsheetdomainsinKNbO3.Moreusefulwaveguideswouldrequeststructureswithcontrollableparametersinpreferredorientationsofsingledomaincrystals.Baumertetal(1985)reportedonthefirstwaveguidesinKNbO3inducedbytheelectro-opticeffect.KNbO3needslow-temperatureprocessing(Curietemperaturearound+220°C)andcarefulhandling,otherwiseferroelectricdomainsmayappear.Uptonow,ithasnotyetbeenpossibletoprepareopticalwaveguidesbyin-diffusionofTiionsfromthecrystalsurface.

Inordertousetheelectro-opticalcoefficientr33inKNbO3,acrystalplatewascutnormaltothebaxis,andtwoelectrodeswithawidthof(s-h)=100mm,separatedbyagapofwidth2h=10mm,weredepositedonthepolishedbface(seeFig.6.30).Theedgesoftheelectrodeswereparalleltotheaaxis.Thehorizontal(paralleltothecaxis)componentEx(x,y)oftheappliedelectricfieldyieldsanincreaseoftherefractiveindexncofthecrystalinthegapregiongivenby

withA=3.262×10-4mm/Vforl=0.63mm.TherefractiveindexchangeDnb,duetotheverticalelectricfieldEy(x,y),hasbeenneglectedbecauseofthesmallelectro-opticcoefficientr23=1.3pm/V(ProkhorovandKuz'minov1990).Therefore,withthistypeofwaveguideonlyTEmodespropagatingalongtheaaxisareguided.InordertoevaluatetheworkingvoltageandthelightfielddistributionofthepropagatingmodesBaumertetal(1985)havecalculatedtherefractiveindexdistributionnc+Dnc(x,y)asafunctionoftheappliedvoltage.TheelectricfieldcomponentsEx(x,y)andEy(X,y)insidethecrystal,belowtheelectrodegap,wereobtainedbysolvingtheLaplacepotentialequationusingtheconformalmappingtechnique(VandenbulckeandLagasse1976;Wei1977)andaregivenby

wherez=x+iy,k=h/s,K(k)isthecompleteellipticintegralofthefirstkind,and

Uisappliedvoltage, and arethefreedielectricconstants(at25°C)ofKNbO3alongthec-andb-axes,respectively.

ApreferentiallysingledomainKNbO3crystalwasgrownbyatopseededhigh-temperaturemeltpullingtechnique(FluckigerandArend1978).Chipswithasizeof4×3.4×0.7mmwerecutfromthecrystalandorientedbyx-rayandpreferentialetchingmethods(Wiesendanger1973).AftersurfacepolishingtheremainingdomainswereremovedinastrongpolarizingdcfieldneartheCurietemperature.Oppositeendsofthesinglecrystalswerepolishedinordertoallowforend-fire

couplingoflaserlight.Thisprocess,however,hascausedstress-inducedmicrodomainsalongtheedgesofthefacetthatcouldnotentirelyberemovedbypoling.Forelectrodepreparation,athinchrome/goldfilmwasdepositedbyelectronbeamevaporationontheb-cutsurface.Apositiveelectricfieldwasappliedandthesurfacewasbakedverycarefullytopreventcreationofnewdomains(heating/coolingcyclewithdT/dt<2°C/min).Theelectrodestructurewaspatternedandthemetalfilmetched.Theelectrodeshadalengthof3mm(Fig.6.29).Thesamplesweremountedonaceramicsubstrateandcontactedusingcopperwireandsilverpaste.

LightofaTE-polarizedHe-Nelaserbeamwascoupledintotheelectro-opticallyinducedwaveguide.Fortheend-firein-andout-coupling,two20×

Fig.6.29Designoftheelectro-opticallyinduced

waveguide(Baumerteta11985).

Fig.6.30Near-fieldlightdistribution(l=0.633mm)

(Baumerteta11985).

Fig.6.31Calculatedintensitydistributionforan

appliedvoltageof35V(l=0.633mm)(Baumert

etal1985).

microscopelenseswereused.Withnoelectricfieldapplied,onlysomelightspotscausedbydiffractionatstress-induceddomainsatthecrystalendfaceswereobserved.Increasingtheappliedvoltageupto30V,anon-offratioof12dBcouldbemeasured,clearlydemonstratingafield-inducedincreaseoftherefractiveindexncbetweenthetwoelectrodes.Baumertetal(1985)measured

thewavelengthdependenceofthenear-fieldlightdistribution.Thefollowinglaserlightsourceswereused:InGaAsP/InPdiode(1.3mm),Nd:YAG(1.064mmand0.532mm),argonpumpeddye(0.86mm),andHe-Ne(0.633mm).Figure6.30showsthenear-fieldlightdistributionsat0.633mmforanappliedvoltageof0and35V.Foravoltageof35Vtheintensitydistributionofthefundamentalmodeoftheelectroopticinducedwaveguidewascalculated(Fig.6.31).Goodagreementbetweencalculated(Fig.6.31,10mm)andmeasured(Fig.6.30,3.8±0.5mm)widthoftheintensityprofileswasfounddespitethemicrodomainsattheedges.

6.5Waveguideelectroopticpolarizationtransformer

Polarizationtransformationisanessentialfunctionforopticalsignalprocessing.Itisespeciallyimportantforsingle-modefibresystemsbecause,althoughshortlengthsofspeciallyfabricatedpolarizationpreservingbirefringentfibreshavebeenreported(Ramaswamyetal1978a;Stolenetal1978),typicalsingle-modefibresdonotmaintainlinearpolarization(Ramaswamyetal1978b;Kapronetal1972).Formanycommunicationapplication,thepolarizationindependentswitch(Alferness(1979)andon/offmodulator(Burns1978)canbeeffectivelyusedinspiteofanincidentsignalofunknownandtemporallychangingpolarization.However,forinterferometricsignalprocessingapplicationssuchas,forexample,heterodynedetectionorfibresensors,areceivedsignaloffixedpolarizationidenticaltothatofsomereferencesignalisrequired.Inthesecases,activepolarizationstabilization(Ulrich1979)maybenecessary.Polarizationtransformationsuitableforsuchstabilizationhasbeenachievedbybulkmechanicalelementswhichsqueeze(Johnson1979)ortwist(UlrichandJohnson1979)thefibretoinducelinearbirefringenceoropticalactivity,respectively.Thesedevicesarebulkyandmayresultinfibrefatigue.However,becauseitreliessolelyuponchangingthe

birefringence,twoelectroopticalcrystalswithproperrelativeorientationarerequired.Furthermore,becauseitisabulkdevice,alargecontrolvoltage(~425V)isrequired.ThewaveguideelectroopticpolarizationtransformerdescribedbyAlfernessandBuhl(1981)iscompact,nonmechanical,capableoffastresponse,hashighfidelityandneedsonlylowcontrolvoltage.

Thepolarizationstateofanopticalwavecanbedefinedbytwoparameters,qandf.IntermsoftheseparameterstherelativeTEandTMfieldcomponentsofanopticalguidedwaveare

Thus,qdefinesthemagnitudeoftherelativeTEandTMamplitudesandqtherelativephasebetweenthesecomponents.Forq=0,thelightislinearlypolarizedatanangleq;q=0representspureTEpolarizationandq=½ppureTM.Rightcircularpolarizationisgiven,forexample,byq=0.25pandf=0.5p.

Fig.6.32Schematicdrawingofpolarizationtransformer

(AlfernessandBuhl1981).

Thedemonstratedpolarizationtransformer,whichunderelectroopticalcontrolprovidesanydesired transformation,isshownschematicallyinFig.6.32.Itiscomprisedofasingle-modewaveguidewiththreeelectroderegions.Theoutertwoelectrodepairs(Fig.6.32)providetheE/Ochangeofthebirefringence.ForthecrystalorientationshowntheelectricallyinducedphaseshiftbetweentheTEandTMmodesis

whereVistheappliedvoltage,d1theinterelectrodegap,Ltheelectrodelength,ltheopticalwavelength,no,etheordinaryandextraordinaryrefractiveindicesandrthee/ocoefficients.Thecentreelectrodeprovides modeconversionbyutilizinganoffdiagonalelementofthee/otensortocoupletheotherwiseorthogonalTEandTMmodes(Alferness1980).Theeffectofthemodeconverterupontheamplitudecomponentsinequation(6.60)isgivenbythematrix

Fig.6.33Calculatedoutputpolarizationangleq0vs

themodeconvertercouplingstrengthkLforvariousinputpolarizationanglesq1.TheincidentrelativeTE/TMphaseisassumedtobezero(AlfernessandBuhl1981).

wherethecouplingcoefficientis

whered2istheinterfingerseparationandatheoverlapparameter(Alferness1980).Periodicelectrodesarerequiredbecauseofthematerialbirefringenceoflithiumniobate.

AlfernessandBuhl(1981)outlinedsomekeyfeaturesofthedeviceoperationbeforepresentingexperimentalresults.First,themodeconverterwasessentialbecausetherelativeTE/TMamplitudescannotbealteredbysimplechangingthebirefringence.However,themodeconverteralonewas,infact,alsoinsufficienttoproducegeneralTE/TMamplitudechanges,thatisthearbitrarychange .ThisfactisdemonstratedinFig.6.33,wherethecalculatedoutputpolarizationangleq0isplottedversustheelectricallyinducedmodeconvertercouplingstrength(proportionaltoV2)forseveralinputpolarizationanglesq1.Theresultswerecalculatedusingthetransformationmatrixofequation(6.62)withtheassumptionthattherelativeTE/TMphaseuponincidencetothemodeconverter iszero.Ofcourse,foreitherpureTEorTMinput(qi=0or½p,respectively)withpropervoltage,anarbitraryangleq0canbeachieved.However,astheangleqiincreasesfrom0ordecreasesfromp,theresultsofFig.6.33showthattherangeofachievableq0becomesgreatlylimited.Indeed,for ,regardlessofthevoltage(V2)appliedtothemodeconverter,theangleq0remainsequalto¼p.

Thekeytoovercomingthislimitationistheuseofthee/ophaseshifterbeforethemodeconvertertoadjusttherelativeTE/TMphaseofthesignalincidentuponthemodeconverterto±p.Inthesecases,apropervalueofthemodeconvertervoltagecanbeshowntoexist,sothatany changeispossible.Indeed,onlyforthesespecialrelative

phasevaluescansucharbitrarytransfomationsbeachieved.Fortunately,forthesecasesthemodeconverteractsasalinearrotatorwithrespecttothepolarizationangle.For p,forexample,

wherekaV2isthesubjectoftheequation(6.62).Thus,controloverqisachievedbythecombinationofthefirstphaseshifterandthemodeconverter.

Thedesiredoverallrelativephasetransformationisthenachievedwiththefinalphaseshifter.ItshouldbenotedthatiftherelativeTE/TMinputphasetothemodeconverteris-0.5p,thentheoutputphasefromthemodeconverterisalso-0.5p.Furthermore,thebirefringentsubstratesthereisarelativephaseshift ,whereLTisthetotalcrystallength,andNTEandNTMaretheeffectiveindicesoftheTEandTMmodes,respectively.Thus,

Fig.6.34Measuredresultsofthedeviceasalinearpolarizationrotator,therequiredmodeconvertervoltagetoachieveanoutputTEfieldvsinputpolarizationangle

V1=-4.1VandV3=0(AlfernessandBuhl1981).

toachievethedesiredvalueoff0thevoltageofthesecondphaseshiftermustbeadjustedtoobtainaphaseshiftDf2,sothat,

whereDf2isthechangeinducedbythefirstphaseshifter.ThevalueofDf2doesnotaffectq0.

Thedevicewastestedinseveralmodesofoperation.First,thenecessityofthefirstphaseshifterwasverified;forV1=0arbitrary

transformationscouldnotbeachievedregardlessofthemodeconvertervoltage.Next,thedevicewasoperatedasalinearrotatorwiththegoaloftransforminganarbitraryinputlinearpolarizationtoanoutputwave,thatis,pureTE.TofindthepropervalueofV1toachievea½pTE/TMphaseshiftatthemodeconverter,theangleqiwassetto¼pandV1adjustedtomaximizetheoutputTEcomponent.Oncedetermined,thisvalueofV1wasfixed.TherequiredmodeconvertervoltagetoachieveapureTEoutputpolarizationversustheinputpolarizationanglewasthenmeasured.Theresultsareshownin

Fig.6.34.Aspredicted(equation(6.63)),alinearrotationisobservedand,indeed,anyvalueofq1canbetransformed.Therotationrateis15°/V.Theorthogonalpolarizationcomponent(TM)wastypicallygreaterthan23dBdownfromthedesiredone.Withcareinvoltageadjustmentvaluesof-27dBcouldbeachieved.

Becausethelargebirefringenceoflithiumniobatenecessitatesperiodicelectrodesforthemodeconverter,thedemonstrateddeviceiseffectiveonlyoveralimitedspectralbandwidthof~10Å(AlfernessandBuhl1980).However,thedevicecanbebroadbandedeitherbyshorteningthemodeconverterelectrodelengthorbylinearlyvaryingtheelectrodeperiod.Effectivespectralbandwidthsofseveralhundredangströmsshouldbereadilyachievable.Alternately,thedevicecanbefabricatedusingalessbirefringentsubstratelikelithiumtantalateoranonbirefringentone.Althoughthreecontrolvoltagesarerequiredforthemostgeneralpolarizationtransformation,formanyapplicationsonlyoutputlightthatispureTEorTMisrequired.Inthiscase,onlythefirstphaseshifterandthemodeconverterarerequired.

6.6Lightbeamscanninganddeflectioninelectro-opticwaveguides

Tienetal(1974)reportedamethodoflightbeamscanninganddeflectioninwhichtheangleofdeflectionvarieswiththeappliedfield.Inoneoftheexperimentstheauthorswereabletoscanalightbeamcontinuouslyupto4°intheplaneofthefilm.Theexperimentswerecarriedoutinanelectro-opticwaveguideofasingle-crystalLiNbO3filmgrownepitaxiallyinLiTaO3.

Thetheoryandexperimentforthelightbeamdeflectionandtheconditionsthatoptimizethedeflectionefficiencyarediscussedbelow.

Ageneralequationofalightpathinamediumofvariableindexofrefractionisconsidered.Theequation(BornandWolf1959;Tienetal1965)is

Heredsisanelementofthelightpathandristhepositionvectorofds.Letthefilmlieintheyxplane.Therefractiveindexofthefilmvariesinxandyasitisexcitedbytheelectro-opticeffect.Theoriginofthecoordinatesarechosentolieonthexaxis(Fig.6.35(a)),andthelightpathisconsideredwhichdeviatedfromthexdirectionbyanangleqnotmorethan10°.Thentan andqissmall.Thus,

wherexandyaretheunitvectorsalongthexandydirections,respectively.Equation(6.66)nowbecomes

Fig.6.35(a)Lightbeaminamediumofvariablerefractiveindexn(x,y).(b)Diagramshowingtheprocessofoptimisingthedeflectionofalightbeam.

(c)Experimentalarrangementusedtodeflectalightbeamthroughrefractions.(d)Experimentalarrangementusedtodeflectalightbeamthroughincompletereflection(DqT)and

refractions(DqR)(Tienetal1974).

Aftersimplification,wehave

Sincedy/dx(=tan )issmall,equation(6.68)becomes

Here,inthefirstintegral,dxisreplacedby(dx/dy)dywhichis(1/tanq)dy.Equation(6.69)isageneralequationfordeflectingalightbeamandDqisthedeflectionangleoccurringafterthelightbeamhastracedapathfrom(x1,y1)to(x2,y2).Theanglesq1andq2aretheentranceandexitanglesofthelightbeamat(x1,y1)and(x2,y2),respectively.Thequantitiesn,tanq, ,and areevaluatedalongthelightpath.Equation(6.69)hasseveralintersectingfeatures:First,thefirstintegralinvolves( )whereasthesecondintegralinvolves( ).Next,thefirstintegralcontainsafactorof(1/tanq)andthesecondintegralcontainsafactoroftanq.Sincetanqissmall,thefirstintegralin(6.69)isusuallymuchlargerthanthesecondone.Todemonstratetheprocessleadingtotheoptimizationof ,letusconsiderinFig.6.35balightbeamwhichisdeflectedbypassingthrougharectangularregionofrefractiveindex(n+Dn)surroundedbyauniformmediumoftherefractiveindexn.Tobespecific,thecasewheredx,dy,tanq,DnandDqareallpositive.ForoptimizingDqintheportionofthelightpathwheretherefractiveindexisincreasing,theconditionsare , ispositive,andtanqshouldbesmall.Byplacing ,theentireamountofDnhastobecontributedby

alone.Consequently, canhavethelargestpossiblevalueforagivenDnandsoisthefirstintegralin(6.69).Moreover,because

,thesecondintegralin(6.69)iszero.Otherwise,thisintegralwouldbenegativeandwouldreducethevalueofDq.Usingasimilar

argument,Tienetal(1974)foundthatfortheportionofthelightpathwheretherefractiveindexisdecreasing,theconditionsare and

isnegative.AsillustratedinFig.6.35b,alltheaboveconditionsaresatisfied,ifalightbeamwhichentersintotheregionof(n+Dn)throughthebottomleavesitattherightwithouttouchingthetopsideoftherectangle.Thesamelightpath(Fig.6.35b)optimizedanegativeDq,ifDnisnegative.

Toproduceaproperdistributionofelectricfieldonthefilm,Tienetal(1974)usedthecircuitshowninFig.6.35d.Itconsistsoftwomainelectrodes,AandB,andfourparallelfingerseach5mmwide.Thespacingsbetweenthefingersare20mmandthetotalspacingbetweenAandBis120mm.TheelectrodesandthefingersareL=2.7mmlongalong .Byapplying

Fig.6.36ThedotsarethemeasurementofDqvstheintensity

oftheappliedfieldusingtheexperimentalarrangementshowninFig.6.35(c).Solidlineindicatedtheresult

calculatedfromequation(6.71)usingr33=28.5×10-12m/V(Tienetal1974).

propervoltagestotheelectrodesandthefingers,avarietyofelectricfielddistributionscanbeproducedbetweenAandB.ThecircuitisfabricatedonaglasssubstratebytheusualphotolithographictechniqueandisthenattachedontopoftheepitaxialLiNbO3film.AcoatofEUKITTisappliedbetweenthefilmandthecircuitinordertoavoidelectricbreakdowninair.Thefilmhasthecaxisparalleltoandtherefractiveindicesofthefilmaren0=2.290andne=2.220.Intheexperiments,al=0.6328mmHe-Nelaserbeamwascoupledintothefilmbyarutileprismcoupler.Thelightbeaminthefilmwas60mmwideandpropagatednearlyparallelto intheTE(m=0)waveguidemode(Tien1971).Tosimplifythecomputation,themodeindexwastakentobeequaltoneofthefilm.

ThefirstexperimentisillustratedinFig.6.35c.ByapplyingavoltageacrossAandB,auniformelectricfieldEyisexcitedbetweentheelectrodes.TheelectricfielddistributionisillustratedinthisFig.bydashedlines.Duetotheelectro-opticcoefficientr33ofLiNbO3,therefractiveindex(extraordinary)ofthefilminthespacebetweenAandBisincreasedbyanamountDnsuchas

ThiswasareproductionofthesituationshowninFig.6.35b-aregionof(Dn+ne)surroundedbyamediumofne.Here,DnispositiveornegativedependinguponthesignofEy.WhenEyvariesfrom7.0to-6.7V/mm,thelightbeamscansfirstover rad(whenDnisnegative)andthenover rad(whenDnispositive),asshowninfigures6.35cand6.36.Tocalculatethesedeflections,itcanbeshownfromequations(6.68)and(6.69)that

whereq1andq2areexpressedinradians.FromtheexperimentalvaluesofDqandusing(6.70)and(6.71)Tienetal(1974)obtainedr33=28.5x10-12m/Vfortheirfilm,whichwassubstantiallylargerthanthatreportedbyFukunishietal(1974)fortheirLiNbO3films.Infact,thevalueofr33obtainedbyTienetal(1974)wasonlyabout10%lessthanthatofbulkLiNbO3.Usingtheexperimentalvaluer33ofthefilm,themeasuredvaluesofDqarecomparedinFig.6.36withthosecomputedfromequations(6.70)and(6.71);theagreementisexcellent.

Tienetal(1974)discussedaphenomenonofrefraction.Thelightwavewasrefractedasitenteredintotheregionof(ne+Dn)andwasrefractedagainasitlefttheregion.Foroptimizing theauthorsarrangedthelightpathsothatthesetworefractionsadded.Itisevidentfrom(6.71)thatthismodeofoperationappliesonlyfor

.Otherwise,thelightbeamwouldbetotallyreflected.

ThesecondexperimentisillustratedinFig.6.35d.ConsideragainthegapbetweentheelectrodesAandB.Byapplyingpropervoltagestothefingersandtheelectrodesanindexdistributionwasexcited,suchthatDn(=Dn)-wasnegativeinthetoppartofthegapandDn(=Dn)+waspositiveinthelowerpart.Theoverallvariationoftherefractiveindexinthegapwas .Alightbeamwithanentranceangleq1facesanegativegradientoftherefractiveindexwhichcausesthelightpathtobend.IfthenegativeDnislargeenough,thelightbeamtracesacirculararcinsidethegapandfinallyemergesattherightwithanexitangleq2=q1.Thisiswhatonewouldexpectforatotalintegralreflection.However,whenAnislessnegative,thearctracedbythelightbeambecomeslarger.Soon,onefindsthatthegapisnotlongenoughforthelightbeamtocompletethisarc.This

Fig.6.37Schematicdiagramofthepolarization-independentopticalfilter(WMC,polarizationconvertervoltage;VTbirefringencetuningvoltage;Vc,polarizationsplittertuningvoltage)(Waranskyetal1988).

incompletetotalreflectionmakesq2againvarywithDnwhichofcoursedependsontheintensityoftheappliedelectricfield.Itcanbeshownfurtherthat,forvaluesof(2Dn/n)muchlessthan ,thelightbeaminsidethegapisdeflectedthroughtheincompletetotalreflection(illustratedinFig.6.35(d)by ).Inthismodeofoperationthedeflectionislinearwith fromq2=0toq2=-q1andthenstaysatq2=-q1forafurtherincreaseof .Ontheotherhand,intherangebetween and0(orpositive),thelightbeamisdeflectedbyrefractionsasdiscussedearlierinthefirstexperiment(illustratedinFig.6.35dby ).Theseparatinglinebetweenthesetwomodesofoperation, ,issimplytheconditionofthecriticalangle.

6.7Electro-opticallytunablewavelengthfilter

Wavelengthdivisionmultiplexing(WDM)isaveryattractiveschemetoincreasetheinformationbandwidthoffibreopticcommunicationsystemsandnetworks.WavelengthdemultiplexingandchannelselectioninsuchWDMsystemsrequiretunablenarrow-bandopticalfiltersthatarecompatiblewithsingle-modefibres.Furthermore,applicationswithfibresthatdonotpreservepolarizationrequireopticalfiltersthatoperateindependentlyoftheinputpolarization.Variousschemesoftunableopticalfiltershavebeendemonstratedwithsingle-modewaveguides,suchaswavelengthselectiveintegratedopticaldirectionalcouplers(AlfernessandSchmidt1978)andinterferometers(RottmanandVoges1987)orfibreopticBraggreflectors(Whalenetal1986)andFabry-Perotresonators(StoneandStulz1987).Waranskyetal(1988)proposedanddemonstratedthefirstpolarization-independentelectro-opticallytunablewavelengthfilterwithsingle-modewaveguides.TheLiNbO3wavelengthfilterhasabandwidthofonly12Åandatuningrangeofatleast110Å.Ithadtwooutputportsservingasabandpassandanotchfilter,anditcanbeusedforwavelengthdemultiplexingaswellasfor

multiplexing.

Thepolarization-independentfilteremploystwoidenticalwavelength-de-pendent polarizationconvertersandtwoidenticalTE/TMpolarizationsplittersintheinputandoutputofthepolarizationconverters.Theinputpolarizationsplitterdemultiplexesthequasi-TEandquasi-TMpolarizedcomponentsofinputlightandrouteseachcomponentseparatelythroughoneofthetwoparallelpolarizationconverters,wherethetwopolarizationcomponentsexperiencethesamewavelength-dependent polarizationconversionbeforetheyarerecombinedattheoutputpolarizationsplitter.Figure6.37showsaschematicdiagramofthefiltreimplementedwithsingle-modestripwaveguidesonx-cuty-propagatingLiNbO3.Thetwoelectro-optic polarizationconvertersarewavelengthtunableandconsistofacascadeofshortsectionsofpolarizationconverterelectrodesalternatingwithshortsectionsofbirefringencetuningelectrodes(AlfernessandBuhl1985).ThetwopolarizationsplittersareidenticalwaveguidedirectionalcouplerswithDb-reversaltuningelectrodesandaredesignedtocoupleTM-polarizedlightcompletelyintothecrossoverwaveguidewhileleavingTE-polarizedlightintheinput(straight-through)waveguide(AlfernessandBuhl1984).

Thefilteroperatesasfollows.Arbitrarilypolarizedlightentersthefilter

intheinputwaveguide(No.1inFig.6.37)ofthefirstpolarizationsplitter,whereallTM-polarizedlightiscompletelycoupledintothecrossoverwaveguide(No.2inFig.6.37),whileallTE-polarizedlightstaysinthestraight-throughwaveguide(No.1).Thetwoseparatedpolarizationcomponentspassthroughidenticalnarrow-bandpolarizationconverters.Iftheirwavelengthisatthecentrewavelengthofthepolarizationconverters,thentheTE-polarizedlightofwaveguideNo.1iscompletelyconvertedintoTM-polarizedlight,andlikewise,theTM-polarizedlightinwaveguideNo.2iscompletelyconvertedintoTE-polarizedlight.TheoutputpolarizationsplittercouplesthenowTM-polarizedlightofwaveguideNo.1completelyintothecrossoverwaveguide(No.2)whileleavingthenowTE-polarizedlightinwaveguideNo.2.ThusthetwopolarizationcomponentsarerecombinedandexitthefilterinwaveguideNo.2(thecrossoverwaveguide).

Onthecontrary,ofthewavelengthoftheinputlightisoutsidethebandwidthofthepolarizationconverters,thenthetwopolarizationcomponentspassthepolarizationconverterswithoutchangeinpolarization,andtheoutputpolarizationsplittercouplestheTM-polarizedcomponentofwaveguideNo.2completelybackintoinputwaveguide(No.1),whereitisrecombinedwiththeTE-polarizedinputlight.Inthiscase,bothpolarizationcomponentsexitthefilterinwaveguideNo.1(theinputwaveguide).

ThuslightatawavelengthwithinthebandwidthofthepolarizationconvertersexitsthefilterinwaveguideNo.2,whereaslightatotherwavelengthsexitsthefilterinwaveguideNo.1.ThedevicethereforeactsasabandpassfilterwhentheoutputistakenfromwaveguideNo.2andasanotchfilterwhentheoutputistakenfromwaveguideNo.1.Notethatbothoutputportscanbeusedsimultaneously,thusallowingapplicationsasawavelengthtapinabus-typenetworkorasawavelengthmultiplexer.

Thedetailsoftheelectro-optic polarizationconvertersandtheTE/TMpolarizationsplittersusedinthefilterweredescribedbyHeismannandAlferness(1988),Habara(1987),HeismannandBuhl(1987).InthewaveguideorientationofFig.6.37,theTE-andTM-polarizedmodeshavedifferentpropagationconstantsbecauseofthelargebirefringenceofLiNbO3,thusrequiringperiodiccouplingforefficient polarizationconversion.Periodiccouplingofthetwomodesisachievedelectro-opticallybyinducingaperiodicgratingofindexperturbationsinthewaveguideviaaspatiallyalternatingelectricfieldExandther51electro-opticcoefficient( m/V).Mostefficient polarizationconversionisobtainedatafree-spacewavelength ,whereListhespatialperiodoftheappliedelectricfieldEx,andDnphisthedifferenceoftheeffectiveindicesofthetwopolarizationmodes( ).Theopticalbandwidthoftheefficient conversionisdeterminedbytheoverallinteractionlengthL(HeismannandAlferness1988):

where isthegroupindexdifferenceofthetwomodesatl0.

Tuningofthecentrewavelengthl0isaccomplishedelectro-opticallybychangingthebirefringenceDnphinthewaveguideviaaspatiallyuniformelectricfieldEz,andther33andr13electro-opticcoefficients( m/Vand m/V).Herethefieldsforpolarizationconversion,Ex,andforbirefringencetuning,Ez,areappliedalternatelyoveralargenumberofshortsections.Inthisdevice,45sectionsofuniformbirefringencetuningelectrodesareperiodicallyinterleavedbetween46sectionsofperiodicpolarizationconverterelectrodes,whereallbirefringencetuningelectrodesaredrivenbyacommonvoltageVTandallpolarizationconverterelectrodesbyacommonvoltageVMC.Thetuningrateofthecentrewavelengthl0isgivenby(HeismannandAlferness1988)

where istheshiftofthecentrewavelength,GisthenormalizedoverlapintegraloftheappliedelectricfieldEzwiththeopticalfields,Gisthegapofthebirefringencetuningelectrodes,and and arethelengthsofasinglepolarizationconverterandbirefringencetuningsection,respectively.

Operationofsuchtunable polarizationconverterasawavelengthfilterrequireslinearTE-(orTM-)polarizedinputlightandalinearTM-pass(TE-pass)polarizationfilterintheoutputbeam.Notethatthewavelengthdependenceofelectro-opticconversionisindependentofthedirection,i.e. conversionhasthesamecentrewavelength,bandwidth,andtuningrateasconversion.This symmetryofthewavelengthresponseisessentialfortheoperationofthepolarizationindependentfilter.HereidenticalwavelengthresponsesforTE-andTM-polarizedinputlight

areobtainedbyusingidenticalpolarizationconvertersinthetwobranchesofthefilter.Inthepresentdevice,thetwopolarizationconverterssharethesameinterdigitalfingerelectrodes,asshowninFig.6.37,toobtainthesamecentrewavelengthsforTE-andTM-polarizedinputlight.Thebirefringencetuningelectrodesofbothconvertersaredesignedtohaveexactlythesamelengthstoobtainidenticaltuningrates.Thetuningelectrodesarearrangedinsuchawaythatnocrossconnectionsareneededwithintheelectrodestructure.However,thiselectrodelayoutrequirestwotuningvoltages,VTand2VT.toobtainaneffectivetuningvoltageofVTforbothpolarizationconverters.

Thepolarizationsplittersareconventionalwaveguidedirectionalcouplersdesignedtohavecouplingcoefficientsof forTM-polarizedlightand forTE-polarizedlight,whereLcisthecouplinglength.Polarizationsplittingwithlowcrosstalkisachievedbydetuningthecouplersviatwo-sectionDb-reversalelectrodesutilizingther33(forTE)andr13(forTM)electro-opticcoefficientssothatTM-polarizedlightiscompletelycoupledintothecrossoverwaveguide,whileTE-polarizedlightstaysintheinputwaveguide(Habara1987).

Fig.6.38Normalizedfiltertransmissionoftheuntuned(VT=0V,solidandthindashedlines)andtunedbandpassfilter(VT=+100and-100V,bolddashedlines)measuredforTE-andTM-polarizedinputlight(Waranskyetal1988).

Thefiltreisrealizedinx-cutandy-cutpropagatingLiNbO3usingstandardfabricationtechniques.The polarizationconvertersaredesignedforoperationaround mm.ThebasicperiodoftheinterdigitalfingerelectrodesisL=21mm( ),andthetotalinteractionlengthis19mm.Thepolarizationsplitter/directionalcouplershaveacentre-to-centrewaveguideseparationof17.5mmandatotalcouplinglengthof8mm.Polarizationsplittingwithcrosstalkoflessthan-18dBisachievedbyapplyingvoltagesof-37and+40VtothetwosectionsoftheDb-reversalelectrodes.Theoveralllengthofthefiltreis52mm.

PolarizedlightfromatunablecolorcentrelaserisusedtotestthefilterresponseseparatelyforTE-andTM-polarizedinputlight.Fig.6.38showsthetransmissionofthebandpassfiltre(outputportNo.2)versuswavelengthforTEaswellasforTMinputlight.Forbothinputpolarizationsthecentrewavelengthoftheuntunedfiltre(VT=0)is1.5254mmandtheopticalbandwidthis12Å,asexpectedforthe19mmlongpolarizationconverters( ).Thevoltageforcomplete conversionisVMC=+37grV.AlsoshowninFig.6.38isthefiltretransmissionwhentuningvoltagesofVr=-100and+100

Vareappliedtothebirefringencetuningelectrodes.Herethecentrewavelengthisshiftedby55Åtoshorterandlongerwavelength,respectively,whereidenticalresultsareobtainedforbothinputpolarizations.Thusthefiltrecanbetunedoverarangeofatleast110Å.

6.8Flip-chipcouplingbetweenfibresandchannelwaveguides

Efficientcouplingbetweensingle-modefibresandTi-diffusedLiNbO3channelwaveguidesisessentialfortheinclusionofLiNbO3waveguidedevicesinsingle-modefibresystems.Suchcouplingisdifficulttoachievebecauseofcriticalpositioningandpreparationtolerances.Micromanipulatorscanbeusedforthefibre/channelalignmentforend-firecoupling(Nodaetal1978;KeilandAuracher1979;FukumaandNoda1980).Hsuetal(1978)demonstratedfibre/channelend-firecouplingusingtheflip-chipapproachwhereV-groovesarepreferentiallyetchedinaSiwafer.TheLiNbO3end-faceswerecleaved.Infibre/fibrecoupling,improvedaltitudinalalignmenthasbeendemonstratedwithtaperedfibrespositionedingroovesatrightanglestotheinputandoutput

Fig.6.39SchematicofSiV-groove/flip-chip

couplingstructure(Bulmeretal1980).

fibregrooves(SheemandGiallorenzi1978).Bulmeretal(1980)usedtaperedfibresintransversegroovesinSiV-groove/flip-chipcouplingmethodandhaveconsistentlymeasuredcouplingefficienciesof>70%,correspondingtoan~3dBtotalthroughputloss(Bulmeretal1980)forTE-andTM-modepolarizations.ThecouplingstructureisindicatedschematicallyinFig.6.39.Itiscompactandcanbemaderigid.

Thereareseveralverystringentrequirementsforefficientcoupling:(i)accuratehorizontal,vertical,andangularpositioning;(ii)planar,defect-freewaveguideandsurfaces,normaltothepropagationdirection;and(iii)forcompletecoupling,matchingofthewaveguidefielddistributions.Bulmeretal(1980)aimedtoachievetranslationalalignmentof<1mmandangularalignmentof<10.OnlyLiNbO3waveguideorientationswereusedinordertoavoidanisotropicleaky-mode(Sheemetal1978)anddoublerefractioneffects(KaminowandStulz1978)whichoccurwhenwavesarepropagatingalonganonaxialdirection,andsoachievepolarization-independentpropagationlossesandcouplingefficiencies.AsLiNbO3hasonlyonecleavageplane,alonganonaxialdirection,itisnecessarytopreparethecubicandfacesoftheLiNbO3substratesbypolishing.TheLiNbO3substrateedgesshouldhaveminimalrounding.

Accuratepositioninginthehorizontalplaneisachievedbyaligningmatchingregistrationlines(groovesandchannels)whichareregisteredalongthecouplingfibreV-groovesintheSiwaferandalongthechannelwaveguidesintheLiNbO3.Theregistrationlinesareseveralmicronswideandareregisteredwithanaccuracybetterthan0.5mm.Accurateverticalpositioningisprovidedbytaperedalignmentfibres,withdiameterstaperedby0.5-1mm/mm,placedunderthecouplingfibresindeepV-grooves,atrightanglestothecouplingfibregrooves.Thehightoftheinputoroutputfibreiscontinuouslyadjustedbypushingorpullingthetaperedfibreinitstransversegroovesothatthecouplingismaximized.Withoutsuchfinealtitudinalalignment,ahighcouplingefficiencycouldbeachievedonlywithcouplinggroovespreciselytothedepthappropriateforafibreofknowno.d.(opticaldamage)andperfectconcentricity.

Bulmeretal(1980)usedhigh-resistivity<100>Siwafers,withan1mmthickmaskinglayerofSiO2,andalignedthephotolithographicgroovemask

tothewaferaxestobetterthan1°.Themaskhastworegistrationgroovesalongeithersideofeachcouplinggroove.Inthealignmentoftheflipped-overLiNbO3ontopoftheSiwafer,acorrespondingTi-diffusedlineintheLiNbO3,toeithersideofeachchannelwaveguideorwaveguidedevice,isarrangedtoliebetweenthesetworegistrationgrooves.InthecentralregionwhereLiNbO3substrateistobelaid,onlyhalfwaythroughtheSiO2masklayerwasetchedsothattheregistrationlinesarenotoveretchedduringtheSiV-grooveetchingprocess.ThecouplingandalignmentcouplinggrooveswerethenetchedintheSiusinganethyl-enediamine-pyrocatechol-watermixture(FinneandKlein1967).IftheregistrationgroovesareetchedintheSi,theydeteriorategreatlyowingtoundercuttingandthefinitepreferentialetchratio,whichmakesexactalignmentverydifficult.ThecompletepatternontheSiwaferconsistedofsixcouplinggrooveswithdeepertransversealignmentgroovestoeithersideofsubstrateregion.Couplinginturntoeachofsixdifferentchannelwaveguidesisthereforepossiblewithasingleunit.

TheLiNbO3endsurfaceswerepreparedbyanopticalcontactpolishingmethod.TheTi-diffusedLiNbO3substratewasopticallycontactedtoadummyLiNbO3substrate,theinputandoutputedgeswerepolished,andthesubstrateswerethenseparatedbymildthermalshock.Toallowopticalcontact,TiwasdiffusedovertheentireLiNbO3substrateexceptclosetothechannelwaveguidepattern.Asthereisnogapbetweenthesubstrates,chip-freeedgeswithnoroundingareobtained.Veryflatfibreends,withlittleornolip,normaltothefibreaxis,wereobtainedusingtheconventionalcleavingtechnique.Ifthewaveguidefielddistributionsareperfectlymatched,100%couplingispossible(neglectingreflectionlosseswhichcanbeminimizedwithantireflectioncoatings).However,perfectmatchingisnotpossiblebecausethechannelwaveguidefielddistributionhasanon-unityaspectratio,isasymmetricperpendicular

tothesurface,andisnotexactlyGaussianeitherparallelorperpendiculartothesurface,whereasthefibrefieldisessentiallyGaussian(BurnsandHocker1977).ThechannelwaveguidefieldcanbeoptimizedsomewhatbyanappropriatechoiceofTidiffusionconditions(Fukudaetal1979).

Bulmeretal(1980)defined3and4mmwidestraightchannelwaveguidesand3mmwidechannelwaveguideMach-Zehnderinterferometersin170-220Å.Tionz-cut,x-propagatingLiNbO3substrates.ThediffusionwasperformedinO2for6hat1000°C,andinsomecasesinthepresenceofLiNbO3powdertoreduceLi2Oout-diffusion.Thechannelswereperpendicular,to1°,totheedgeswhichwerethenpolished.An4000ÅSiO2layerwassputteredoneachsubstrateandthenoxidizedfor9hat600°C.ItwasneededtoisolatetheopticalwaveguidesfromtheA1electrodeslaterdepositedalongtheinterferometer.Toobtainpolarization-independentbehaviour,authorsusedhorizontalandverticalfieldelectrodes.Theauthorsusedsingle-modefused-silicafibrewithNA0.1andcoreandcladdingdiametersof4.5and88mm,respectively.Theouterplasticjacketwasremovedinthecouplingregionandalongsectionsoftheinputandoutputfibreswherecladdingmodeswerestripped.Thefibrebeatlengthwas~20m.Measurementsweremadeat633nm,separatelyforeachopticalpolarization.Thepolarizationwasrotatedwithahalf-waveplateattheinputtothe0.5mlonginputfibreanditwascheckedatthefibre

output.Thepolarizationwasmaintainedto~99%.

Bulmeretal(1980)entirelyneglectedanymodepropagationlossesincalculationsofflip-chipcouplingefficiencies.Usingtheflip-chiparrangementdescribedabove,theauthorsobtained76and72%couplingbetweenthesameinputfibresandthe3and4mmchannels,respectively,foreachopticalpolarization.Thus,theflip-chipcouplingefficiencieswereashighasthosemeasuredwiththemicropositioner.Thecouplingcouldbesmoothlyvariedbetweenmaximumandnearzerobymovingthetaperedalignmentfibre.Ifthecouplingfibregrooveswereetchedtoodeeply(byseveralmm),therewassomefrictionbetweenthetwofibres,resultinginappreciablehorizontalmotionofthecouplingfibre,whichaidscouplingiftheLiNbO3-Siwafertransversealignmentisimperfect.

With3and4mmwidechannelsoneachsubstratecementedtoaSiwafer,andwithfibre/channelseparationof<10mm,Bulmeretal(1980)havemeasuredTE-andTM-modecouplingefficienciesof70-88%,correctedforreflectionlosses.ProvidedthattheinitialSi/LiNbO3alignmentisaccurateto1mm,themeasurementswererepeatablewithin10%andthesamecouplingefficiencieswereobtainedforcouplingwithoneinputfibreorwithinputandoutputfibres.ThevaluesforsubstratesweredeterminedallowingforsmallFabry-Perotresonances(BornandWolf1970)usingtheexpression

HerePmax(mm)isthemaximum(minimum)outputpower,Pinistheinputpower,kisthefibre/channelcouplingefficiency,and arethereflectivitiesateitherendoftheFabry-Perotcavity;representsthefractionofpowerreflectedateitherendofthecavitywhichremainsguidedinthechannelwaveguide( indicatescompletelossonreflectionbecauseofnonperpendicularchannelend

facets).Inthecasesunderconsideration, .Equation(6.74)wasderivedintheassumptionofzeromodeattenuationinthecavityandwithdisregardofanyeffectofthe7.5cmlasercoherencelength.Foroneofthesamples,fromcomparisonsoftheoutputswithindexmatchingoilandairbetweenthefibreandLiNbO3,theLiNbO3itselfappearedtobeactingasaresonantcavity.ThiswasverifiedbyheatingandcoolingtheLiNbO3tovarytheopticalpathlengthandobservingtheresultantoscillatoryvariationinoutputofupto7%duetothermalexpansionandrefractiveindexchange.

Inordertoestimatethemaximumcouplingefficiencyforperfectalignmentlimitedonlybythemodefieldmismatch(BurnsandHocker1977),modedistributionsweremeasuredbyscanningwitha100mmdiam.pinholeinthehorizontal(x)andvertical(y)directionsacrossthemagnifiednear-fieldimagesofthechannelwaveguideandfibreoutputs.Alltheprofileswereextremelysmooth,andshowednoindicationofimperfectionsinthechannelandsurfaces.Fromthe1/epointsoftheseintensityprofiles,theGaussianmodefieldhalfwidthwasdetermined(seeTable6.4).Forthechannel,thesewerewx,

Table6.4Measuredchannelmodefieldhalf-widthswx,wyandcorrespondingtheoreticalmaximumcouplingefficiencieskmand fromnumericaloverlapofbeamprofiles(Bulmer,Sheem,Moeller1980)

Mode wx(mm) wy(mm) km(%) k'm(%)

2.9 2.2 88 92

3.6 3 91 93

2.9 2 86 89

3.2 2.3 89 92

wyoftherectangularGaussian(BurnsandHocker1977)(where,e.g.,whichapproximatesthewaveguidemodeelectricfield

(wxisparallelandwyperpendiculartothesurface).Forthefibre,assumingacircularGaussianfield,themoderadiuswasa=3.0mm.Thenforaperfectalignment,azeroseparationandnoreflectionlosses,thepowercouplingcoefficientwasestimatedas

wherethefactor0.93isacorrectionforthedeviationoftherealmodefieldsfromtheirGaussianapproximations.Table6.4presentsthekmvaluescorrespondingtothemeasuredmodewidths.Theyareafewpercenthigherthantheexperimentalcouplingefficiencies.Themaximumcouplingefficiencieswerealsoestimatedbyanumericaloverlapofthenormalizedmodeprofilesandareshownas inTable6.4.Thevaluesare2-4%higherthanthecorrespondingkmvalues.Sincetheoryintends itcanbeconcludedthatthecorrectionfactor0.93isslightlyconservativeforthiscase.

6.9KTiOPO4waveguidedevicesandapplications

KTPhasseveralpotentialadvantagesforopticalwaveguidedevice

comparedwithothermaterialsinadditiontohavingamuchlargermodulatorfigureofmerit.ItshighopticaldamagethresholdsuggeststhatKTPwaveguidedevicescouldbeusedtocontrolorconverthigh-intensityopticalbeamswithinputwavelengthsextendingfromthevisibletotheIR.KTPwaveguidedevicesshouldbemuchlesssusceptibletopiezoelectricandpyroelectricinstabilitiesbecausetheseeffectshavenotbeenobservedinbulkdeviceapplications,andhencedevicethermalandmechanicalstabilityshouldbemuchbetter.

Severaldemonstrationelectro-opticandnonlinearopticdeviceshavebeenfabricatedbyusingKTPwiththewaveguidefabricationprocessdescribedinchapter2.Themeasured forseveralsingle-channelphasemodulatorsindicatesthatthewaveguidefabricationprocessdoesnotaltertheelectro-opticcoefficient.Usinga6mmwidechannelwaveguideanda0.2mmMgF2bufferlayer,andcouplingtotheelectro-opticcoefficientrc2,BierleinandVanherzeele

(1989)observeda of6Vcmat6328Å,whichisclosetothetheoreticallypredictedvalueforKTP'sbulkelectro-opticanddielectricconstants(Bierleinetal1989).Thesedevicesaredcstableforbothhydrothermallyandflux-grownsubstrates.The waslowerthan6Vcmatlowfrequenciesandincreasedto6Vcmathighfrequency.Theoccurrenceofionic-conductioneffectssuggeststhatthedcconductivityoftheRb-richopticalwaveguideislowerthanthatofbulkKTP.LimiteddataonthedielectricpropertiesofbulkRbTiOPO4indicatesuchalowerconductivity,aresultthatisnottotallyunexpectedbecauseRbhasalargerionicradiuscomparedwithK,givingalowerionhoppingrate.

AMach-Zehndermodulatorwasalsofabricatedona1mmthick,z-cutKTPsubstratebyusing6mmwideRb-exchangedwaveguidesandtraveling-waveelectrodesthatshowabandwidthofnearly16GHz(Laubacheretal1988).Thismodulatorwasfabricatedwitha0.4mmSiO2bufferlayer,a1cmelectricfieldinteractionlength,anda25mmelectrodegapandhada of10Vata1.3mminputwavelengthand5Vat0.633mm.Thismodulatordidnotshowanyinstabilitiesduetoopticaldamageorphotorefraction,whicharecommonlyobservedinothermaterials,evenwithinputsofasgreatas1mW.

Thenonlinear-opticalpropertiesofKTPwaveguideshavealsobeenevaluatedbymeasuringtheSHGoutput,usingadiode-pumpedNd:YAGinputat1.064and1.31mm.Usinga6mmwideRb-exchangedchannelwaveguide,Bierlein(1989)measuredconversionefficienciestothegreeninthe4%W-1cm-2range.Thisconversionefficiencyisclosetothebestvaluesmeasured(4.8%)forTi:LiNbO3waveguides.At1.31mminputconversionefficienciesofapproximately1%W-1cm-2wereobtained.

ForfrequencydoublingexperimentsconductedbyRisk(1991)awaveguidewasfabricatedonthec-sideofaKTPsubstratewitha

depthofd~2mmandfoundtobesinglemodeattheinfraredwavelengthusedforSHG.InbulkKTP,typeIInonlinearprocessesareused,sincethesehavehigheffectivenonlinearcoefficients.Theseprocesses,suchasfrequencydoublingof994nmlight(Risketal1989),orsum-frequencymixingof809and1064nmlight(Baumert1988),requirebothx-andz-polarizedfieldsattheIRwavelengthsforpropagationalongthey-axis.ThegeneratedSHfieldispolarizedalongx.ThephasematchingconditionforSHGisthus1/2

.Inthewaveguide,theanalogousinteractioncorrespondsto ,wherem,n,andparemodenumbers.Themostdesirableinteractionisform=n=p=0,whichinvolvesonlythelowest-ordermodes.Interactionsinvolvinglowest-ordermodesatthefundamental(m=n=0)andhigher-ordermodesatthesecond-harmonic( )permitgenerationofblue/greenwavelengthsshorterthanthoseobtainedusingthebulkmaterial.

Figure6.40showscalculatedvaluesfortherefractiveindicesinvolvedinthebulkinteractionandforeffectivemodeindicesintheguided-waveinteraction.ThebulkrefractiveindexvaluesarecalculatedfromSellmeierequations.TheeffectivemodeindiceshavebeencalculatedbytheWKBmethodusingtheparametersofthewaveguidemeasuredbyprismcouplingat633nm.Thedashedcurvesrepresent1/2[ ],correspondingtofundamental

Fig.6.40Phase-matchingcharacteristicsforfrequency

doublinginaplanarKTPwaveguide.Lowerhorizontalscalereferstofundamentalwavelengths;upper

horizontalscalereferstocorrespondingsecond-harmonicwavelengths(Risk1991).

Table6.5Wavelengthsofphase-matchedinteractions(Risk1991)

Interaction Calculatedwavelength Measuredwavelength

1130nm N/A

966nm 969nm

913nm 923nm

905nm 906nm

wavelengthsonthelowerhorizontalscaleandnx(2w),correspondingtosecond-harmonicwavelengthsontheupperhorizontalscale.Attheintersectionofthesetwocurves,thebulkphase-matchingconditiongivenaboveissatisfied;thiscorrespondstoSHGwithafundamentalwavelengthof994nm(Risketal1989).ThesolidcurvesinFig.6.40showthedispersionoftheeffectiveindicesforwaveguidemodes.Theintersectionsofthecurverepresentingtheaverageofthe andmodeindiceswiththecurvesrepresentingthemodeindicesforthe

modesdefinewavelengthsforwhichguided-modeSHG

interactionsarephasematched.Ascanbeseenfromthefigure,blue/greenlightcanbegeneratedatwavelengthsconsiderablyshorterthanthatobtainedbySHGinthebulkcrystal.

Lightfromatitanium-sapphirelaserinthe900-1000mmrangewasusedtosimultaneouslyexcitetheTE0andTM0modesofthewaveguide.Asthewavelengthofthelaserwastuned,SHGinteractionsinvolvingexcitationofhigher-orderTEmodesatthesecondharmonicwereobserved.ThemeasuredwavelengthsatwhichtheseinteractionsoccurredareshowninTable6.5,alongwiththecalculatedvaluesfromFig.6.40.Themeasuredandexpectedwavelengthsforthevariousinteractionsareingoodagreement.ExcitationoftheTE0modeatthesecondharmonicwasexpectedtooccurforafun-

damentalwavelengthof1130nm,butcouldnotbeobservedsincethiswavelengthwasoutsidethetuningrangeofthetitanium:sapphirelaser.Forwavelengthsshorterthan905nm,excitationofradiationmodesatthesecondharmonic(Cherenkovdoubling)wasobserved.

6.9.1PhasematchinginperiodicallysegmentedKTiOPO4waveguides

Bierleinetal(1990)describedanewtechniqueusedforachievingphasematchinginKTiOPO4(KTP)waveguidesbutequallyapplicableforbothbulkandotherwaveguidesystems.Thisschemecannotonlygivephase-matchedsecond-harmonicconversionefficienciesbutcansignificantlyextendprocessinglatitudewhichisparticularlyimportantforpracticalnonlinearopticalchannelwaveguidedevices.

Intheconventionalphasematchinginvolvingthenonlinearinteractionofthreebeamsinacrystalwherethefrequenciesofthethreebeamsarerelatedas ,eitherthedirectionofpropagationorthetemperatureistunedsothatthepropagationconstants ofthesebeamsobeytherelation ,or

.Herethe arethebeampropagationconstants,n'stherefractiveindices,andl'sthecorrespondingwavelengths.Thecrystalorwaveguideisdividedintosegments,eachsegmentconsistingofsectionsoflength andpropagationconstantmismatch suchthatforeachsegment ,wherethesumisoverallsections.Thelengthofeachsectionislessthanitscorrespondingcoherencelength,thatis .Whentheseconditionsaremet,eventhoughthebeamsarenotphasematchedisthesectionsindividually,theyarephasematchedattheendofeachsegmentandthegeneratedoutputpowerwillincreaseasthesquareofthenumberofsegments.

Eachsegmentcouldinprincipleconsistofmanysections,mightdiffer

instructurefromtheprevioussegment,orcouldevenbeasinglesectionwithcontinuouslyvaryingpropertiessuchthat .Toillustratethemethod,thesimplifiedcasewasconsidered,wherethesecond-harmonicgenerationinaperiodicwaveguidestructureconsistedoftwosectionspersegmentasshowninFig.6.41.Forthiscase,afairlysimplequantitativerelationforthegeneratedoutputpowercanbeobtained.Inthestructuresconsidered,thelengthofthesectionsdeviatedstronglyfromtheBraggconditionandtherefractiveindexdifferencesbetweenthesectionsweresmall.Therefore,thereflectioneffectsfromthesubsequentsectionsandthefundamentalbeamdepletioncouldbeignored.Withtheseapproximationsandextendingthisanalysis

Fig.6.41Segmentedwaveguidestructure(Bierlein1990).

toincludeferroelectricdomainreversals,thesecond-harmonicpowergeneratedfromthesegmentedstructure,P,normalizedtothepowergeneratedinaperfectlyphase-matcheduniformwaveguideofequallength,P0,isgivenby

whereGdescribestheeffectsoftheperiodicgratingandItheinternalSHGwithinasingleperiod.TheeffectsofoverlapbetweenfundamentalandharmonicguidedmodeswereassumedtobeidenticalforbothPandP0.

Thegratingfunction,G,inequation(6.76)isgivenby

whereNisthetotalnumberofperiodsinthewaveguideand

isthephasematchingbetweenthefundamentalandsecond-harmonicwaveguidemodesinasingleperiod.The and arethelengthsandcorrespondingpropagationconstantmismatchesofthetwosegments.ThefunctionGwillpeakifthesecondharmonicwavesfromsubsequentperiodsaddinphase,thatis,at ,whereM=0,±1,±2,etc.andthephase-matchingconditionbecomes

Theinternalfunction,I,inequation(6.76)describeshow,withinasingleperiod,thesecond-harmonicfieldsofneighbouringsegmentsinterfere.Atphasematching,Iisgivenby

where arethecoherencelengthsofthetwosections.The+signinequation(6.80)correspondstothecasewhereadjacent

segmentshaveinvertedferroelectricdomains,the-signcorrespondstoapurerefractiveindexgrating.Withthelowindexstepsusableinpractice,itcanbereadilyshownfromequation(6.80)thatthelattersituationleadstomuchlowerconversionefficienciesascomparedtothedomaininvertedcase.

Balancedphasematching(BPM)occurrswhenM=0inequation(6.79)andislimitedtophase-matchedSHGinKTPforawavelengthlongeraboutthat1mm(Bierlein,etal.1990).With theblueregionofthevisible

Fig.6.42Second-harmonicgenerationin5mmRb/Baflux

KTPsegmentedwaveguides.(a)Absoluteconversionefficiencyat850.5nmfora4mmperiod,4mmwaveguide.(b)Wavelengthscanfora5mmperiod,4mmwaveguide.Pwistheguidedfundamentalpower(Poeletal1990).

Fig.6.43Phase-matchingwavelengthvssegment

periodof4mm-widewaveguides.Solidlinesand()arefor interactions,dashedlines

and(x)arefor interactions.Misdefinedinequation(6.79)(Poeleta11990).

spectrumbecomesavailableforphase-matchedsecond-harmonicgeneration.Thewaveguidedepthcanbechosentominimizetheeffectsofdepthvariationsontherefractiveindexmismatchsuchthat

optimumfabricationtolerancesforphasefunctionresult.Thispropertyofthesegmentedstructureconstitutesamajoradvantageoveruniformwaveguides,wherethisdegreeoffreedominfabricationisabsent.Intheexperiments,onesegmentwasbulkKTPandtheotherwasanion-exchangedwaveguide.Withthismask24differentwaveguidewidth/segmentperiodcombinationscanbefabricatedonasinglesubstrate.Inatypicalexamplesegmentedy-propagatingwaveguideswerefabricatedonthez-surfaceofaflux-grownKTPsubstrate.UsingatunableTi:A12O3laser,thephase-matchingwavelengthsandconversionefficienciesforthesewaveguidesaregiveninFig.6.42.Overallfundamentalbeamthroughputfromthelasertothewaveguideoutput(includinglenses,couplingandwaveguidelosses)

Fig.6.44Phase-matchedwavelengthbandwidthsfor

segmentedKTPwaveguides.(a)M=0,typeII,5mmperiod,5mmwidth.(b)M=1,typeI ,4mmperiod,5mmwidth.(c)M=2,typeI ,4mm

period,4mmwidth(Poeleta11990).

isabout40%.Twowaveguidemodesareobservedtogivephase-matchedSHG.Fromthenear-andfar-fielddistributions,thesemodescorrespondtocouplingsbetweenthelowestorderguidedfundamentalmodeand,respectively,thelowestandfirst-orderguidedharmonicmodes,asindicatedinFig.6.42.

AtypicalefficiencyplotisalsoshowninFig.6.42which,atlowfundamentalpowers,indicatesanefficiencyof80±5%/Wcm2.Dependingonwaveguideprocessingconditions,significantlylowerphase-matchedtypeIefficienciescanalsooccurwithbothhydrothermalandflux-grownsubstrates.Forexample,loweringtheexchangetemperatureby20°Cdecreasestheconversionefficiencybynearlythreeordersofmagnitude.

Forawaveguidewidthof4mm,theSHGphase-matchingwavelengthsweremeasuredforfourdifferentsegmentperiodspresentonthesameKTPsubstrate.InFig.6.43,themeasurementsarecomparedwiththeoreticalpredictionsforvariousphase-matchingM

valuesandnonlinearinteractions.TheinteractionsincludetypeIcouplingthroughthed33nonlinearopticalcoefficient( )andthroughthed32coefficient( ).EfficientSHGphase-matchedoutputisobservedfromdeeppurpleat0.38mmtoblue-greenat0.48mm.ForKTP,thiswavelengthrangeisnormallynotaddressablebyconventionalphase-matchingtechniques.Forperiodsof3,4,5and6mm,theobservedphase-matchingwavelengthsforthesevariouscombinationsareingoodagreementwiththosepredictedfromequation(6.79)usingbulkKTPrefractiveindices(BierleinandVanherzule1989).Thedifferencesbetweenthecalculatedandexperimentalwavelengthsarequitesmallconsideringthatinthecalculationbulkrefractiveindicesratherthaneffectivewaveguideindiceswereusedinequation(6.79).

Thewavelengthbandwidths,asmeasuredin5mmsegmentedwaveguides,aresummarizedinFig.6.44andcomparedtoatypicalresultusingBPM.From

aTaylor'sexpansionofequation(6.77),usingequation(6.79)andtheSellmeierequationsforbulkKTP(Bierleinetal1989),wavelengthbandwidthsfullwidthathalfmaximumof0.67nmcmfortypeIIat1.06mmand0.06nmcmfortypeI, at0.80mmarepredicted.Thecloseagreementbetweenthepredictedandmeasuredbandwidthsindicatesthatnearlyperfectphasematchingoccursoverthefull5-mmsamplelength.Thisalsoaccountsforthehighabsoluteconversionefficiencyobserved(3%at100mWfundamentalpowerforM=1).Themeasuredtemperaturebandwidthisabout3°C.AlsoshowninFig.6.44isthetypeI phase-matchedpeak.ThispeakcorrespondstophasematchingforM=2,withanexpectedwavelengthbandwidthof0.05nmcm.

Preliminaryresultsfromlow-temperatureelectrostatictuningandfromsurfaceSHGexperimentsindicatethattheoriginoftheselargetypeIconversionefficienciesisferroelectricdomainreversalinducedbythewaveguideprocessingwhenBaispresentintheexchangebath.AssumingthatthedepthoftheferroelectricdomaincorrelateswiththeBaionconcentrationinthewaveguideand,sincetheeffectiveSHGmodeoverlapisexpectedtovarystronglywithdomaindepth(ArvidssonandJaskorzynskii1989),thismechanismwouldalsoexplainthelargechangesinconversionefficiencythatoccurwithchangesinion-exchangetemperature.Ion-exchangeexperimentswithdifferentsubstratematerials,differentsurfacepolarities,andavarietyofmoltensaltcompositionsareinprogresstoclarifythemechanismfordomainreversalinthesematerialsandtogainimprovedunderstandingofandcontroloverthefabricationprocess.

ConclusionsInasinglebook,evenofthisvolume,itisdifficulttoembraceallaspectsofferroelectricthin-filmwaveguides,fromalargenumberof

methodsoffabricationtoevenalargernumberofpossibleapplicationsindevicesforlaserradiationcontrol.Asindicatedbythecontents,thebookexaminesmainlytheeffectofthephysico-chemicalfactorsontheopticalandwavepropertiesofthinfilmswhichareofprimaryimportanceforpracticalapplication.Wehavealsopresentedseveralmethodsofexaminingthethinfilmsandtheoreticalconclusionsregardingthevariationoftherefractiveindicesandthelawsoflightpropagationinthefilm.Onlyinthefinalchapterwehaveexamined,asexamples,severaldevicesforelectro-opticallightmodulation.,deviationsandtransformationstothesecondharmonics.Inthisperiodcharacterizedbytheappearanceofalargenumberofpublicationsinmanyscientificjournalstheauthorssometimesomitinitialstudiesinwhichthefundamentalresultsfortheexaminedproblemwereobtained.Wehavethereforetriedtostresstheroleofinitialpublicationsinwhichthephenomenonunderexaminationisoftenstudiedinconsiderabledetail.Wehopethebookwillbeusefulforexpertsworkingintheareaofproducingandapplyingthinlightguidefilmsforlaserradiationcontrol.

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FurtherReading

1.HausH.A.(1988),WavesandFieldsinOptoelectronics,EnglewoodCliffs,Prentice-Hall,NewJersey.

2.HunspergerR.G.(1984),IntegratedOpticsTheoryandTechnology,SpringerVerlag,Berlin,Heidelberg,NewYork.

3.ProkhorovA.M.andKuz'minovYu.S.(1990),PhysicsandChemistryofCrystallineLithiumNiobate,AdamHilger,Bristol,NewYork.

4.ProkhorovA.M.andKuz'minovYu.S.(1990),FerroelectricCrystalsforLaserRadiationControl,AdamHilger,Bristol,NewYork.'

5.PropertiesofLithiumNiobate(1990),EMIS,England.

6.SmolenskyG.A.(ed)(1985),PhysicsofFerroelectricPhenomena,Nauka,Leningrad.

7.YarivA.andYehP.(1984),OpticalWavesinCrystals,NewYork.

8.YarivA.(1985),OpticalElectronics,Holt-SoundersInternationalEditors,NewYork.

absorptionloss282

activationenergyforvaporization29

actualvaporizationflux30

angularmatching241

annealedproton-exchangedwaveguides56

autodiffusedlayers25

bandwidth295

Braggdiffractionmodulator315

Braggreflector247

bufferedmelts59

Bulkcrystallization131

capillaryliquidepitaxialtechnique78

channelwidth255

Cherenkovradiation245

cinnamicacid64

coherencelength248

controlvoltage293

conversionefficiency245

copperdiffusion49

coupledchannelwaveguides302

criticalsupersaturation135

crystallizationfromagasphase6

Curietemperature16

Curie-Weissbehaviour16

Czochralskimethod132

degreeoffilmperfection1

dielectricimpermittivitytensor35

dielectricproperties285

diffusiondepth123

diffusionoftransitionmetals37

diffusion-induceddefects188

directelectron-beamwriting203

dislocationstructure191

domainconfiguration198

domaininversion203

domainstructure195

doublewaveguide23

double-exchange'technique66

Dufoureffect139

effectivesegregationcoefficient110

electro-opticcoefficient259

electro-opticeffects258

electro-opticmodulators293

electro-opticphotorefractivemodulator328

electro-opticX-switchers292

electro-opticallytunablewavelengthfilter342

electrodiffusion49

electronpolarizability36

electrostrictioneffect36

energylossinwaveguides279

epitaxialferroelectricfilms118

epitaxialgrowth151

epitaxialgrowthofLiNbO397

equilibriumsegregationcoefficient142

evaporationcoefficient33

exchangetime66

extraordinaryrefractiveindex215

Fabry-Perotloss280

Fabry-Perotresonator260

Fermifunction229

Fermilevel135

ferroelectricfilms210

Fick'ssecondlaw27

filmgrowthrate141

flip-chipcoupling345

gas-transportepitaxy1

gas-transportepitaxy6

Gaussiannucleardamage24

Gaussianprofiles39

Glassconstant276

Glassmodel276

Gratingformation267

gratings266

holographicwriting267

homoepitaxialLiNbO3films178

hydrogenisotopicexchange58

in-diffusioncoefficient65

indexchange274

insertionlosses293

interferometricMach-Zehndermodulator326

isothermalepitaxy105

Jouleeffect133

Kerreffect48

Kikuchilines207

KLNcrystal121

KNbO3,inducedwaveguidecut-offmodulator331

Langmuirrelation28

Langmuirvapourpressure29

lasersputteringmethod17

layercomposition173

layerprecipitationtime124

lightresistance2601

LiNbO3birefringence245

liquid-phaseelectroepitaxy136

liquid-phaseepitaxy74

liquid-phaseepitaxy(LPE)technique83

lithiumniobate165

Lorentz-Lorenzformula36

Mach-Zehnderinterferometer271

Marcatili'sapproximation246

maximalmodulationdepth293

MFESstructurexvi

micro-channelslab125

microdomains199

micromorphologyoffilmsurface186

modenumber231

modulationindex260

monocrystallinity175

negativebirefringence215

nucleationrate146

one-dimensionalwaveguides22

opticalmodes224

opticalproperties213

opticalswitchingtime309

opticalwaveguideswitchmodulator308

ordinaryrefractiveindex215

out-diffusedlayers26

out-diffusioncoefficient65

out-diffusionindexprofiles26

out-diffusionkinetics27

out-diffusionsuppression34

partitioncoefficient128

PDRwaveguide247

PEwaveguide65

Peltiercoefficient132

perovskite118

phasematching239

photoelasticcoefficient47

photoinducedpolarizationconversion298

photorefractiveeffect269

photorefractiveproperties264

photorefractivesensitivity270

planarion-exchangedKTiOPO4waveguides68

planarwaveguides20

Pockelscoefficient68

potassiumlithiumniobate121

prismcouplingtechnique65

propagationconstant230

propagationloss12

protondiffusion62

proton-lithiumexchange52

proton-exchangedLiNbO3182

proton-exchangedLiNbO3waveguides51

pseudo-Kosselpattern11

pulsedlaserdeposition17

pumpingpower240

pumpingwavelength240

pyroelectricproperties287

QPM-SHGdevice202

quasi-phasematching200

Raoultlaw3

refractiveindexgradient31

rfsputtering8

ridgewaveguidemodulator317

Rutherfordbackscatteringspectroscopy16

'sandwichmethod'5

schemeofthegrowthcell95

Schröderequation91

secondharmonicgeneration237

Seebeckcoefficient289

Sellmeierrelation215

Snelllaw217

spikelikedomains201

stationarycrystallizationmodel97

Stepanovmethod132

striplinestructures123

stripwaveguides21

substratemodes222

sum-frequencygeneration253

supersaturation101

surfaceindex72

symmetricwaveguides124

polarizationconversion345

ferroelectric thin-film waveguides in integrated optics and optoelectronics

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