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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.
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FerroelectricThin-FilmWaveguidesinIntegratedOpticsandOptoelectronics
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OtherbooksavailablefromCambridgeInternationalSciencePublishing
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CoherentRadiationProcessesinPlasma
ThermalPlasmaandNewMaterialsTechnology
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Arc-SlagRemeltingofSteelandAlloys
QuantificationandModellingofHeterogeneousSystems
MetallurgyofArcWelding
BibliographyonMechanicalAlloyingandMilling
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FerroelectricThin-FilmWaveguidesinIntegratedOpticsandOptoelectronics
AMProkhorov,YuSKuz'minov,OAKhachaturyan(GeneralPhysicsInstitute,RussianAcademyofSciences,Moscow)
TranslatedfromtheRussianbyMariannaTsaplina
CAMBRIDGEINTERNATIONALSCIENCEPUBLISHING
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PublishedbyCambridgeInternationalSciencePublishing7MeadowWalk,GreatAbington.CambridgeCB16AZ,England
FirstpublishedApril1996
©AMProkhorov,YuSKuz'minovandOAKhachaturyan©1996CambridgeInternationalSciencePublishing
ConditionsofsaleAllrightsreserved.Nopartofthispublicationmaybereproducedortransmittedinanyformorbyanymeans,electronicormechanical,includingphotocopy,recording,oranyinformationstorageandretrievalsystem,withoutpermissioninwritingfromthepublisher
BritishLibraryCataloguinginPublicationDataAcataloguerecordforthisbookisavailablefromtheBritishLibrary
ISBN189832610X
ProductionIrinaStupakPrintedbyStEdmundsburyPress,BuryStEdmunds,Suffolk,England
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ContentsPreface ix
Symbols xi
Introduction xiii
1Epitaxialfilmsofcomplexoxidecompounds
1
1.1Vacuumepitaxy 2
1.2Gas-transportepitaxy 4
1.3Filmsdepositedbyifsputtering 8
1.3.1ThinfilmsofLiNbO3depositedonasapphiresubstrate
9
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
25
1.4.1Out-diffusionkinetics 27
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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
66
1.7Planarion-exchangedKTiOPO4waveguides 69
2Liquid-phaseepitaxyofferrolelectrics
74
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
87
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2.4.1ThephasediagramofLiVO3-LiNbO3 91
2.4.2PhasediagramofLiVO3-Li(Nb,Ta)O3pseudobinarysystem
92
2.4.3Theschemeofthegrowthcell 95
2.5KineticsofepitaxialgrowthofLiNbO3 97
2.5.1Thestationarycrystallizationmodel 97
2.5.2Epitaxyundernon-isothermicconditions 100
2.5.3DeterminationofsupersaturationUanddiffusioncoefficientD
101
2.5.4Epitaxyunderisothermalconditions 106
2.6CrystallizationoffilmsfromLiNb1-yTayO3solidsolutions
109
2.6.1Liquid-phaseepitaxialgrowthofLi(Nb,Ta)O3films
112
2.7ThinfilmsofLiNbO3dopedwithdifferentelements
114
2.8Epitaxialferroelectricfilmswithperovskitestructure
119
2.8.1Liquid-phaseepitaxyofpotassiumniobate 119
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2.8.2Growthofpotassiumlithiumniobatefilmsonpotassiumbismuthniobatesinglecrystals
122
2.9Diffusionliquid-phasemethodofgrowingimmersedwaveguidechannels
123
2.9.1Striplinestructures 124
2.9.2Symmetricwaveguides 124
2.10GrowthofepitaxialfilmsintheKTiOPO4familyofcrystals
127
3Influenceofelectriccurrentuponliquid-phaseepitaxyofferroelectrics
131
3.1.Electricfieldandcrystallization 131
3.1.1Bulkcrystallization 131
3.1.2Thinfilms 134
3.1.3Liquid-phaseelectroepitaxy 136
3.2Physicalbasisofliquid-phaseelectroepitaxy(Thetheoryofthemethod)
138
3.2.1Temperaturedistributioninasystemundertheactionofanelectriccurrent
138
3.2.2Filmgrowthrate 141
3.2.3Chemicalcompositioncontrolofthefilm 142
3.2.4Initialstagesofnucleation 143
3.3Theroleofthermoelectriceffectsinthecourseofliquid-phaseelectroepitaxyofferroelectrics
149
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3.4Electro-LPEgrowthoflithiumniobate-tantalatefilms
151
3.4.1Epitaxialgrowth 152
3.4.2Electrochemicalprocessesintheliquidphase 152
3.4.3Growthkineticsofelectro-LPEgrownlithiumniobate-tantalatefilms
155
3.5OptimizationofconditionsofepitaxialgrowthoflithiumniobatefilmswithallowanceforJouleheat
158
4Structureandcompositionoflightguidingfilms
165
4.1Structureandphysico-chemicalpropertiesoflithiumniobateandtantalatecrystals
165
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
186
4.3.2Diffusion-induceddefectsinfilms 188
4.4Substrate-filminterfaceandtransitionregion 190
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4.5Dislocationstructure 191
4.6Domainstructure 196
4.6.1Epitaxialfilmonadomainboundaryofthesubstrate
197
4.6.2Domainconfigurationsinfilms 198
4.6.3Microdomainsinsubstratesandinepitaxiallayers
199
4.6.4PeriodicallyinverteddomainstructuresinLiTaO3andLiNbO3usingprotonexchange
200
4.6.5Waveguideperiodicallypoledbyapplyinganexternalfield
203
4.6.6DomaininversioninLiNbO3usingdirectelectron-beamwriting
204
4.7Annealing-inducedvariationofthephasecompositionandcrystallinestructureofthelithiumniobatecrystalsurface
206
4.7.1Annealing-inducedvariationofthecrystallinestructureofthelithiumniobatecrystalsurface
206
4.7.2Annealing-inducedvariationofthephasecompositionofthelithiumniobatecrystalsurface
208
5Physicalpropertiesofwaveguidelayers
215
5.1Opticalpropertiesoflithiumniobateandtantalatesinglecrystals
213
5.2Opticalwaveguidemodesinsingle-crystalfilms 215
5.2.1Waveguideandradiationmodes 216
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5.2.2Waveequationandfielddistribution 221
5.2.3OpticalmodesinepitaxialLi(NbTa)O3waveguides
225
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
247
5.3.6Effectofprotonexchangeonthenonlinearopticalproperties
249
5.3.7Sum-frequencygenerationinwaveguides 253
5.4SecondharmonicgenerationintheformofCherenkovradiation
255
5.5Electro-opticeffectsinopticalwaveguides 258
5.6Lightresistanceoflightguides 260
5.7Photorefractivepropertiesoflightguides 264
5.7.1Holographicformationofgratingsinopticalwaveguidelayers
265
5.7.2PhotorefractiveeffectinplanarTi-diffusedguides
269
5.7.3Relaxationofindexchange 274
5.7.4Photorefractiveeffectinannealedproton-exchangedLiNbO3waveguides
275
5.8Energylossinwaveguides. 279
5.8.1LossesinTi-diffusedLiNbO3waveguides 279
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5.8.2Absorptionlossinstripguides 282
5.8.3Lossinepitaxialwaveguides 284
5.9Ferroelectricpropertiesofwaveguides 285
5.9.1Dielectricproperties 285
5.9.2Pyroelectricproperties 287
5.9.2.1Thelow-frequencysinusoidaltemperaturemodulationmethod
287
5.9.2.2Thethermalpulsemethod 287
5.10Temperaturedependenceofthermoelectriccoefficientsoflithiumniobateandlithiumtantalate
289
6Thin-filmstructureinintegratedoptics
293
6.1Principalcharacteristicsofwaveguidingelectro-opticmodulators
293
6.1.1Controlvoltage 293
6.1.2Bandwidth 295
6.1.3Modulationdepthandinsertionlosses 297
6.2Photoinducedpolarizationconversion 298
6.3WaveguidemodulatorsonthebasisofTi:LiNbO3 300
6.3.1Electro-opticmodulatoroncoupledchannelwaveguideswithavariableDb
300
6.3.2Interferometricandperfectinnerreflectionmodulators
304
6.4Practicalexamplesofwaveguideelectro-opticmodulators
308
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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
338
6.7Electro-opticallytunablewavelengthfilter 342
6.8Flip-chipcouplingbetweenfibresandchannelwaveguides
345
6.9KTiOPO4waveguidedevicesandapplications 349
6.9.1PhasematchinginperiodicallysegmentedKTiOPO4waveguides
352
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
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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
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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
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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.
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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
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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
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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
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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-
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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
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variousthin-filmintegro-opticalmodulators,deflectorsandtransducersofradiationarepresented.
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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
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methodsforobtainingfilms(ed.byPoate1978).Comparativeanalysisofthemethodsforobtainingheterostructuresshowstheadvantageofepitaxialmethods.
Thedegreeoffilmperfectionisdetermined,inthefirstplace,bythespecificitiesofeachmethodand,inthesecondplace,byconcretefilmgrowthconditions(thedegreeofvacuum,temperatureregimes,growthrates,impuritycontent).
Therearenowthreebasicwaysofepitaxialgrowthofsingle-crystalfilms:
1.Vacuumepitaxy(involvingmolecularbeam),
2.Gas-transportepitaxy(involvingdecompositionofvolatilecompoundsandtransportchemicalreactions),
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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
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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
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controlled.Lowgrowthtemperaturessuppresstheinfluenceofthediffusionprocesseswhichlevelupthecompositionsofneighbouringlayers.
Duringcrystallizationfromamolecular(atomic)beam,vacuuminthereactorismaintainedatsuchalevelthatthefreepathofthemolecules(atoms)exceeds
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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
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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
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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.
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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
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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
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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
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AB:
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).
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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
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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
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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
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Fig.1.1RelationsbetweenthetransportrateofLiNbO3andtheamontofsulphur(FushimiandSugh1974).
Fig.1.2(right)RockingcurveoftheLiNbO3layerdepositedonaLiTaO3(001)plate(FushimiandSugh1974).
qualityoftheLiNbO3layersandtheirexcellentepitaxyontheLiTaO3substratesoverthewholedepositionareawererevealedbyX-raytopography.Figure1.2showsarockingcurveoftheLiNbO3film
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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
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(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
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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
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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
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Fig.1.3(a)Laserbeaminasingle-crystalLiNbO3filmdepositedbytherfsputteringmethod,and(b)correspondingsample
configuration(Takadaetal.1974).
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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
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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).
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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
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mA.Amagneticfieldparalleltotheprimarybeamwasproducedbypassingacurrentof2Athroughthe100turncoilsmountedonthefilamentandanodehousings.Undertheseconditions,thesubstratetemperatureincreasedduringdepositionto30-50°Cabovetheinitialtemperature.Topermitopticalratemonitoring,thesubstratewastiltedat45°tothetarget,andundertheseconditionsthefilmgrowthratewasapproximately3/4m/h.Films2-4umthickweredeposited.Thelithiumniobatetargetwasmadeofapowderpressedintoa2.5cmdiameterx3mmthickdiscand
Fig.1.6Triodesputteringunit(Forster1971).
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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.
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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
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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,
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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,
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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
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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).
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F.P.Strohkendletal.(1991)reportedonacriterionofplanarwaveguidesforopticalwaveswithpolarizationparalleltothecrystallographicc-axiswithevenlowerimplantationdoses,thatis,withdosesofabout1014cm-2.Prismcoupling,aswellasend-firecouplingofaHeNelaserbeamwithawavelengthof632.8nmwasusedtocharacterizetheTEmodespropagatingalongthea-axisintheionimplantedplanarwaveguides.
KNbO3crystalsampleswerecutperpendiculartotheb-axisandhaddimen-
Fig.1.12IntensityasafunctionofpropagationdistanceforlightscatteredoutoftheTM0modeLiTaO3thinfilmwaveguideonsapphire(Agostinelliand
Braunstein1993).
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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%.
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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
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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
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widthespeciallynearthesurface.Thelateralstragglingoftheincidentionswhichisduetotheinteractionwiththetargetionsleadsalsotonarrowingofthewidthofthestripguides.Theactualwidthofthestripwaveguidesformedbyusingtungstenwires13mmindiameterasanimplantationmaskisreducedto11.4mm.
Fig.1.13ReflectivityasafunctionofeffectiverefractiveindexNeffforwaveguidescreatedwith1and2MeVionsandadoseof5×1013cm-2.
(Strohkendletal.1991).
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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.
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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
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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
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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
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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
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workonbulkmaterialsthatextraordinaryrefractiveindexneincreasesasLi2Oisremovedfromthecrystalbuttheordinaryindexisnotaffected(Carruthersetal.1974).For
inthe0.48<n<0.50range;andfor
wherethemolarfractionv=0.5forastoichiometriccrystal.Thus,theout-diffusionproducesarefractiveindexgradientthathasamaximumpositiveindexchangeatthesurfaceandgraduallyapproachesthebulkindexintheinteriorofthespecimen.Theseout-diffusedlayersserveasexcellentlow-loss
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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,
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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).
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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.
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Theboundaryconditionatthecrystalsurfaceequatesthevaporizationflux,Jv,totheconcentrationgradientatthesurfaceas
Thisassumesimplicitlythatthesolid-vapourinterfaceisstationarywithrespecttothediffusiondistance(i.e.thereisnovapouretchingofthecrystalsurface)andthattheflux,Jv,doesnotchangewithsurfaceconcentration.Fortheout-diffusionproblem,thesurfaceconcentrationchangesbyverysmallamounts,soboththeseassumptionsarevalid,andthesolutiontoequation(1.5)is(CarslawandJaeger,1971)
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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
where
ThevaporizationfluxisrelatedtotheequilibriumvapourpressureofLi2Oover(Li2O)v(Nb2O5)(1-v)bytheLangmuirrelation
orforcomputationalpurposes,
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Fig.1.17Diffusionprofiles-analyticalcurvesforp½ierfc(x/b),erfc(x/b')andexp(x/b'').Atypicalsetofexperimentaldataisfitted
asshownwitha=a'=a"andb=1.36b'=1.97b"(Carruthersetal.1974).
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wheretheLangmuirvapourpressurePLisrelatedtotheequilibriumsaturationvapourpressurePeqby
and
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
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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
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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.
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Fig.1.18Variationofdiffusioncoefficientswithtemperatureas1/Tinlithiumniobatefordiffusionnormalandparalleltothec-axis.Straightlineshavebeenfittedbyleast
squaresregressionanalysis-seeTable1.7(Carruthersetal.1974).
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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
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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),
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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
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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
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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).
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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
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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
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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
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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
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where istheKroneckersymbol.
Differentiatingtheexpression(1.27),multiplyingtheresultby andmakinguseof(1.26),wecometo
InthecaseofthinlayersitturnsouttobesufficientonlytoconsiderthemainstrainsSx,SyandSzalongthex-,y-andz-axes,respectively.Makingallowanceforthisandalsofortheestimate
weobtain
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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+
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sinceithasanadditionaloccupiedelectronshellanditsradiusexceedsthatoftheTi4+ion.Inthequalitativerespect,theactionofthismechanismshouldobviouslybethoughtofasdisputable.
Mechanism3
Thismechanismreflectstherelationbetweenspontaneouspolarizationofadielectricanditsrefractiveindex(theKerreffect).Thisrelationcanbeexpressedintheform(Sugiietal.1978)
whereDPsisvariationofthequantityPsduetoimpuritydiffusion,g13andg33aretensorcomponentsofthequadraticelectro-opticeffect.
Calculationsshow(Sugiietal.1978)that and .
Ontheotherhand,itshouldbetakenintoconsiderationthatpolarizationreversalinthebulkcrystalinducesdeformationsalongthex-,y-andz-axesduetotheelectrostrictioneffect
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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
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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).
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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
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beacomplementaryerrorfunction(erfc)withthesurfaceconcentrationindependentoftime(Shewmon1963).Fordiffusiontimescomparablewiththetimerequiredforallthemetaltoenterthecrystal,theconcentrationprofilewillbeintermediatebetweentheGaussiananderfcprofiles.
ThisbehaviourisillustratedinFig.1.22wheretheNi/Nbcountratiosareplottedasfunctionsofdepthfordiffusionperpendiculartothec-axisintwowaveguides.TheactualNi/Nbconcentrationratioisproportionaltothecountratiowithaproportionalityfactorgreaterthanunity.Thedatawereobtainedbyprobingpointsonaplanenormaltotheplaneoftheevaporatedlayer.Measurements
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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).
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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
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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 ...
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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 ... ...
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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
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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
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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
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andthehighactivationenergyfoundintheTidiffusionintoLiNbO3implythatTidiffusessubstitutionallyintotheLiNbO3crystal.Recently,ithasbeenshownthatTidiffusedintoLiNbO3isall+4valenceandTiionssitnotonvacanciesordefectsbutonwelldefinedsites(Pearsalletal.1976).InLiNbO3,twopossiblesitesremainforsubstitutionalimpurities,aLisiteandaNbsite.ThelatticecontractionwouldoccurifTiionsreplacedeithertheLisiteortheNbsite,sincetheeffectiveionicradiusofTi+4,0.605Å,issmallerthanthoseofLi+1andNb+5of0.68and0.64Å,respectively,whenthecoordinationnumberofallofthemissix.However,thereplacementofNbionsbyTiionsismorefavourablefromthepointofviewofchargecompensation,soitisassumedthatTiisdiffusedassubstitutionalionsfortheNbsiteinLiNbO3.
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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
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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
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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
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crystallinequalityofboththefilmandthesubstratedoesnotdependonthedepositiontechniques(evaporationorsputtering)iflowvoltageandsputteringrateareused.
ThestressesinducedbytheTifilmarethusfoundtobeindependentofthedepositiontechnique.
Forlow-temperaturethermaltreatments(300-500°C)theTifilmwillformanamorphousTioxidelayer.TheoxidationmechanismwasclearlydeterminedasacaptureofOatomsbothfromthesurroundingatmosphereandfromtheLiNbO3substrate.ThislasteffectgivesrisetoanaccumulationofNbattheTi/LiNbO3boundarywhile,duetoitshighionicability,LidoesnotaccumulatebutdiffusesthroughtheTiorTi-oxidefilm.Thechangeoftheoxygenconcentrationintheannealingatmosphere(dryO2ordryAr)willonlyproduceanincreaseordecreaseintheamountoftheOatomscapturedbyTifrom
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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.
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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
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Fig.1.25SchematicofLiNb3O8and(Ti065Nb035)O2growthinLiNbO3aftertheformationoftheTiO2toplayer.
Temperaturesandtimesareonlyindicativefora400ÅthickoriginalTifilm(Armeniseetal.1983).
canbeexpressedasfollows:
whereSisthecomplianceofLiNbO3(Warneretal.1967)andeisthestressalongthex-,y-andx-axes.ThecalculatedstressesforthesamplesaregiveninTable4.3.Thesestresseswerepartiallyrelievedbythegenerationofmisfitdislocationsneartheboundarybetweenthediffusedandsubstrateregions,butthepresenceofcracksindicates
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thatthedensityofthemisfitdislocationswasmuchlowerthantheoneneededforcompleteaccommodationoftheimpurity-inducedstresses.Anisotropyofstresses,(sx)max>(sz)max,resultedinpreferentialgenerationofcracks.
Thesameauthorsalsoconsideredthemechanismcausingrefractive-indexchangesinthediffusedlayer.Thereareatleastthreepossiblemechanismsforrefractive-indexchangesinthediffusedlayer:(i)duetoaphotoelasticeffect
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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.
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Thesecondpossiblemechanismforindexchangesisbydiffusionofimpurityionshavinglargerelectronicpolarizabilitythanthatofthehostionstobesubstituted.Asinmostsolids,therefractiveindexofaferroelectriccrystalshouldoriginatefromelectronicpolarization.Therelationbetweentherefractiveindex,n,andelectronicpolarizability,a,isgivenas
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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
and
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whereQ31=-0.0036m4C-2,andQ33=0.067m4C-2istheelectrostrictivecoefficientforLiNbO3(Iwasakietal.1968).IfDPs<0asrequiredtoincreasetherefractiveindices,itshouldproducestrainsS2>0andS3<0.ThesignsofS2andS3are,however,oppositetothoseoftheobservedstrainseyandez'respectively.Thus,itisunlikelythattherefractiveindexincrementsarecausedbydecreasingthespontaneouspolarization.
Itisconcludedthatthefirstmechanismproposedforrefractive-indexchangesismorelikelythanthesecondandthird.
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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.
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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).
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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
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wavelengthregionmaybesomewhatlimited.
Fig.1.28RelationbetweendiffusiondepthanddiffusiontimeinCu-diffusedLiTaO3.Diffusionwascarriedoutat500°Cinairunderanelectricfieldof10V/mm
(Nodaetal.1974).
Fig.1.29(right)Outputspotswithfaintmline
decoupledwithaGaPprismforTE0andTM0modes.AHe-NelaserbeamisfedintotheCuelectrodiffusedlayerwiththeprism
coupler,andispropagatedalongthex-axisofLiTaO3(Nodaetal.1974).
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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
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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).
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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
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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
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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
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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
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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-
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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
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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
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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
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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,
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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).
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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
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Fig.1.32a)Absorbancebandvst1/2(z-cutproton-exchangedwaveguides).b)Absorbancebandareavsdepth
(z-cutproton-exchangedwaveguides)(Lonietal.1989).
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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
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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
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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.
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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
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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
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migrationofthehydrogen-bondedOHtothesurfaceoftheguidingregionfollowedbyreactionofsurfacehydroxylgroupstogivesurfaceoxidesandwater.Thelatterprocesscaneithertakeplaceviaroute2,orviaroute4followedbyroute5,inthescheme:
Fig.1.34Effectivediffusioncoefficientsat215°Cand235°CversusLi+molefraction(x-cut)(Lonietal1989).
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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
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Fig.1.36Infraredabsorptionspectraofx-cutprotonexchangedwaveguidesfabricatedusingbufferedmelts,at215°C:i)neatbenzoicacid,ii)Li+molefraction=0.28×10-2,iii)Li+molefraction=1.04×10-2(Lonietal.1989).
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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
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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
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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.
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Thevalueswerecalculatedassumingthediffusiondepthdtovaryasfollows(Crank1970):
Fig.1.37Deformationofdiamondappearsinthe planeofLiNbO3
beforeandafterexchange(Minakataetal.1986).
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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
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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
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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
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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
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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.
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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-
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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
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,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)
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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
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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
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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
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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
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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
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temperaturefrom350to400°C.Also,post-annealingaRb-exchangedguideinairfrom300to350°Cfor30minto2hdidnotsignificantlychangedorDn.TheseresultsindicatethattheeffectiveexchangeorthediffusionratefortheRbKsystemisinitiallyhighandthendecreasessignificantlyaftersomepointintheexchangeprocess.ThislargechangeinexchangeordiffusionratecanbeexplainedbyassumingaverylowdiffusionconstantforRbandKinRb-rich
andahighconstantinKTP.Single-crystalRbTiOPO4(RTP)showsamuchlower(~100times)ionicconductivitythanKTPandhenceionicdiffusionisalsoexpectedtobemuchlower.ExchangingKwiththelargerRbioninaKTPsurfacelayerwillalsotendtoblockconductionchannelswhichfurtherlowersionicconductivity.Hence,duringionexchange,asthe
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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.
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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
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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
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indicesusingasimpleWKBmodelthatdoesnotincludetheeffectofthebiaxialnatureofthesubstrateontheTMmodes.However,theTMmodeindicesareaccuratelymodelledusingthissimpleWKBapproachwiththevaluesofDnanddgiven,andthissufficesforpredictingthephase-matchingcharacteristicsforfrequencydoubling.
ItisimportanttocontrolthetemperatureoftheKTPcrystalbeforeandafterdiffusiontopreventcrackingofthesubstrateandunwantedmigrationoftheRbions.ItwasfoundthatimmersingtheKTPcrystalsdirectlyintothemeltfromroomtemperaturecausedthemtocrack,sothesubstrateswerefirstgraduallyheatedinairtonearthetemperatureofthemeltbeforebeingimmersed.ThisphenomenonisaresultoftheparticularthermalandmechanicalpropertiesofKTP.TheKTPcrystalwasheldinapreheatingfurnaceforabout1h,toensurethatthetemperatureofthecrystalhadequilibratedtothefurnacetemperature.Thenthecrystalwasdippedinthemelt.Aftertheprescribeddiffusiontime,theKTPcrystalwasremovedfromthemeltandallowedtocoolrapidlydowntoroomtemperature.BecausethediffusionoftheRbionsissofastforthisRb/Baprocess,unwantedmigrationoftheRbionsfurtherintotheKTPcrystal
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canoccurifthesubstrateisnotcooledrapidly,resultinginchangesintherefractiveindexprofile.ThisisillustratedinFig.1.45,whichshowstherefractiveindexprofileofaplanarKTPwaveguideimmediatelyafterthediffusionprocessandafteranadditional10minofbakinginairat350°C.Itisevidentthattheadditionalheattreatmenthasresultedinasignificantdecreaseinsurfaceindexchangeandanincreaseinthedepthofthewaveguide,andthattherefractiveindexdistributionnolongerhasanerfcprofile.
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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.
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1984;FukudaandHirano1976;FukudaandHirano1980),andliquid-phaseepitaxyfromalimitedvolume(Madoyanetal.1983;Madoyanetal.1985).
Theapplicationofliquid-phaseepitaxymethodsprovidesaclearlypronouncedsubstratefilmboundarywithstep-likerefractiveindicesandarelativelysmoothsurfaceofthestructure.
2.1Theepitaxialgrowthbymelting(EGM)
ToobtainferroelectricsinglecrystalLiNbO3films,Miyazawa(1973)proposedthemethodofepitaxialgrowthbymeltingonLiTaO3substrates.Forsubstrates,LiTaO3singlecrystalswereusedbecausethepointgroupofLiNbO3and
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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.
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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
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Fig.2.1Intensitydistributionprofileof
characteristicsX-rayspectraforNbandTa,perpendiculartothefilmsubstrate
boundary(Miyazawa1973).
Fig.2.2(right)Etchfigureofthefilmsurface,indicating
theferroelectricmodulationpattern(Miyazawa1973).
indicatethattheLiNbO3single-crystalfilmwasepitaxiallygrownonthesubstrate.
Asthetopsurfaceoftheas-grownfilmwasrelativelyrough,itwashandpolishedfirstwithdiamondpasteandthenwith0.05mmA12O3powderinordertodemonstratelightwavepropagationinthe
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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.
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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)
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reportedbyMiyazawainhiswork.
Fig.2.4LiNbO3-LiTaO3phasediagram
(Petersonetal.1970).
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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
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ofabout5dB/cm.Thesamemethodwasalsousedtoobtain(K,Li)LiNbO3films(Adachietal.1979)uptoseveralmicronsthick.Thequalityofthefilmdependsonthechoiceofsubstratesandthewayinwhichtheceramicpowderisdepositedontothesubstratesurface.
2.2Thecapillaryliquidepitaxial(CLE)technique
Thecapillaryliquidepitaxialtechniqueisoneofthenewmethodsforobtaining
Fig.2.5Nb+andTa+intensityaselectronbeamtracksoffilmsurfaceandfilmsubstrate
interface(Ballmanetal.1975).
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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
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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>
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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
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(006)reflectionshowedclearlyseparatedfourpeaksofCuKalandCuKa2radiationfromthefilmandsubstrate(FukudaandHirano1976).
Fig.2.8GeometryforimprovedvariationsoftheCLEtechnique(a)andmultiple-layergrowthtechnique(b)(Fukudaand
Hirano1980).
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Table2.1LiTaO3andLiNbO3thin-filmgrowthconditions(Fukuda,Hirano1976)
Film Substrate Solutiontemperature
(°C)
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
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asthetemperaturebecamelower,manysmallhillocksappearedonthefilmsurfaceandslipboundariesweredetectedneartheedge.Rapidpullingproducedagradualdecreaseinthicknesswithinthecrystal,whileslowerpullingproducedagradualincreaseinthickness.
LiNbO3films,whichweregrownontothe(100)<210>,(131°rotatedYplate)<210>,and(170°rotatedYplate)<210>usingthesamegrowthconditionsasemployedonthe(001)<100>plates,wereofpoorqualityhavingroughsurfacesandmanydefects.Thefilmqualitywasremarkablyimprovedbyadjustingtheinitiatedtemperatureusingdiesofdifferentlengths.Itisassumedthattheappropriategrowthtemperaturewasachievedaftercarvingquicklythesolutionontothesubstrateusingcapillaryactionsothatthefilmdidnotsufferbadeffectsoflargesupercoolingbyloweringthesolutiontemperature.
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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
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Fig.2.10TypicaletchpatternsforaLiNbO3film(a)(-Z)LiNbO3plate(b)(+Z)
LiNbO3plateand(c)(-Z)LiTaO3plate,respectively(FukudaandHirano1980).
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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
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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
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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.
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Ac-cutLiTaO3substrate,positionedslightlyabovethemoltensolutiontobeequilibratedwiththesolutiontemperature,wasdippedinthemoltensolution.Anappropriatedippingtemperaturewas825-850°C.Thesubstratewasthenremovedfromthemoltensolutionandslowlybroughttoroomtemperature.
Fig.2.12Aburiedfilmorlayeredstructurefilmareshown,
whichcanbegrownbycombiningtheCLEtechnique,etchingandpolishing(FukudaandHirano1980).
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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.
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Fig.2.14a)As-grownLiNbO3filmontheLiTaO3substrate.b)cross-sectionalprofilenearthefilmsubstrateedge.Film
thicknesswasabout3.1mm(Kondoetal.1975).
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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
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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
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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.
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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.
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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
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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
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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
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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
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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
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Fig.2.16Partialphasediagram:a)K2WO4-LiNbO3;b)KVO3-LiNbO3;c)NaVO3-LiNbO3
(NeurgaonkarandStaples1981).
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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
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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:
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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
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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
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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-
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Fig.2.18PhasediagramofLiVO3-Li(Nb1-xTax)O3pseudobinarysystem(Kondoetal.1979).
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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
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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
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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
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compoundstoreachastableandstrongsupersaturationwithinawidetemperaturerangeandwithalowtemperaturegradient,whichpermitsrapidgrowthofepitaxial
Fig.2.19Phasediagramillustratingthemethods
ofgrowingsingle-crystalfilmsfromsolutioninmelt(onanexampleoftheLiVO3-LiNbO3
system).
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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
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andKhachaturyan1988).Theliquid-phaseabsorberwasmadeofmicrochannelslabsorkaolincotton.
Thetemperatureregimeoftheprocessisdeterminedbytheslopeoftheliquiduscurve.Forprecipitationofperfectlayersatahigh-temperaturecoefficientofsolubility,thecoolingrateshouldbeverylow.
Fig,2.20Temperatureregimeduringtheepitaxyprocess(left)
andtemperaturedistributionundercapillarytechnology(right)(KhachaturyanandMadoyan1984).
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Animportantadvantageoftheliquid-phasecapillary(LPC)techniqueisaconstantthicknessoftheliquidzoneoverthewholesubstratesurface.Thismakesitpossibletoremovethewedgeshapeandobtainequallythicklayers.Themaximumgapisdeterminedbythefluxviscosityandbythewettingofthesubstratesurface.
TheLPCtechniquepermitseasycontrolofthegrowthrateandthelayercomposition:theprecipitationrateisdeterminedbysupersaturationnearthefront,whichdependsondiffusionandthetemperaturevariationrate.
2.5KineticsofepitaxialgrowthofLiNbO3
Masstransferplaysanimportantroleinthecrystalandfilmgrowth.Havingadirecteffectuponthethicknessandgrowthrate,theseprocessesdeterminethestructuralperfectionandpropertiesofthegrowncrystalsandfilms.Thestudyoftheregularitiesofprocessesintheliquidphaseandattheinterfacesuggestsoptimumversionsofcontrolovergrowthandobtainingepitaxiallayerswithprescribedproperties.
Themajorityofpapersdevotedtokineticsofepitaxialfilmgrowthfromabufferedmeltarebasedonthediffusionapproximationinwhichthefilmgrowthrateislimitedbythediffusionmasstransferofthedissolvedcomponenttothecrystallizationfront.
WehavealsoconsideredthegrowthkineticsofLiNbO3filmsinthediffusionapproximationandestablishedthedomainofitsapplicabilitywithinwhichtheinfluenceofconvectiveprocessesisinessential.Calculationshavebeencarriedoutwithallowanceforspecificitiesofagrowingsystemforthecapillaryversionofepitaxy,whichpermitsahighlyaccuratereproductionofthecalculatedconditionsofepitaxy(MadoyanandKhachaturyan1983).
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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,
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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):
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where ,Disthediffusioncoefficient.
Underquasistationaryconditions(for ),integratingtheexpression(2.2),weobtainthevalueofthemaximumrelativesupersaturationDCm1:
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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
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concentrationbecomesequaltotheequilibriumoneatagiventemperature,andanewconcentrationdistributionoccurs(Fig.2.21c).Precipitationontothesubstratecomesfromthelayer
Afurtherincreaseofdleadstoanincreaseof uptothecriticalvalueatwhichintheregionbetweenthesubstrateandthemiddleofthegapacrystallizationfrontoccursagain.Figure2.21dshowsthethicknessvariationoftheliquid-phaselayerfromwhichincreasedprecipitationcomesontothesubstrate.Thus,intheabsenceofconvectiveflowsandaninducedmixtureofthe
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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
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1980).Theefficiencydeterminedastheexperimental-to-calculatedthicknessratioincreaseswithincreasingcoolingtimeorwithdecreasinggapsize.ToobtainLiNbO3filmswithathicknesscorrespondingtotheequilibriumone,wecanincreasethesoakingtimeataconstanttemperatureafterthecoolingprocessisover.TheconcentrationinthesolutionlevelsupandbecomesequaltoU+Ck,whereUissupersaturationatthecrystallizationfrontandCkisthesaturationconcentrationcorresponding,accordingtotheliquiduscurve,tothefinalepitaxytemperature.Intheformula
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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).
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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.
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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
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insignificantuptothevalued=3ram.Fora=0.4grad/min,thevalued*decreases,whichisevidentlyduetoanincreaseoftemperaturegradientsinthebufferedmeltandtheassociateddensityinhomogeneitiesoftheliquidphaseinthecapillary.Fora=0.6grad/min,thefilmthicknessdoesnotaltersubstantiallyifa>2mm,whichisduetothebeginningofcrystallizationinthebulkmelt.Ford=3mm,thefilmthicknessdecreaseslessthanexpectedwithintheproposedmodel.Thiscanbecausedbyanincompletecoveringofthesurfaceofmaximumsupersaturationbybulknuclei.Inthiscase,theeffectivelayerthickness fromwhichprecipitationcomesontothefilmmustincrease,andthemeanconcentration
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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
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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
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Table2.2ParametersofthegrowthsystemandLiNbO3filmthicknessincapillarygrowthon(0001)and(1120)LiTaO3substrate(Khachaturyanetal.1984)
dmm
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.
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InthecapillarymethodofLPEforferroelectricfilmgrowthwithallowancefortheabove-mentionedrestrictions,crystallizationoutsidethesubstrateisabsentandallthedissolvedsubstanceinthegapprecipitatesontothesubstrateasafilm.Knowingthethicknessofthesolutionlayerandthegrowthtemperaturerange,wecancalculatetheexpectedfilmthicknessusingthestatediagram.
ForacomputercalculationofthefilmthicknessasafunctionofgrowthparametersintheframeworkofthecapillaryLPEmethod,thereexistsanalgorithm,andthefollowingmethodsofcalculationarerealizedasauniversalprogram(onanexampleofepitaxialfilmsoflithiumniobate(Madoyanetal.1982)).
ThecalculationsarebasedontheliquidustemperatureofthephasediagramofthepseudobinarysystemLiVO3-LiNbO3(Madoyanetal.1979).Theanalyticalexpression(2.9)describingthedependenceofthefilmthicknessthegrowthparametersisobtainedonthebasisofcalculatingtheamountoftheprecipitatingcrystallizingsubstanceforagivensystemsupercooling.
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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
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chosenoptimumepitaxyconditions.Thedifferenceof5-10%canbeexplainedbyadditionalprecipitationfromthemeltofthesubstanceremainingonthefilmsurfaceaftertheepitaxyisover.
Thesatisfactoryagreementbetweentheexperimentalandtheoreticaldatasuggestsawiderangeofapplicabilityofprogrammingcalculationoftheepitaxialfilmwidth.
2.5.4Epitaxyunderisothermalconditions
Asdistinguishedfromthenonisothermalcaseforwhichthediffusionprocessesdeterminedbythesystemcoolingratearelimiting,inisothermalepitaxytherateofthediffusionprocessesvarieswithfilmgrowth,andthequestionofarelativecontributionofdiffusionandsurfaceprocessestothegrowthkineticsremainsopen.Inviewofthis,wehaveconsideredthegeneralcasewithallowance
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forthekineticcoefficient.Isothermalepitaxyisinvestigatedunderconditionsofaquasistationaryprocesswhichtakesplaceintheindicatedsystems( ).
Asinthenonisothermalcase,crystallizationproceedsfromalimitedvolumeconsistingoftwoidenticalparallelsubstratesmountedatadistanced(Fig.2.24a).Thequantitativedeterminationofthetimedependenceoffilmthicknessatagiveninitialsupersaturationconsistsofsolvingthedifferentialequationdescribingthediffusionofadissolvedcrystallizingmaterialinsideacapillarywithcorrespondinginitialandboundaryconditions
whereyisadimensionlessdistance(intheunitsd/2)countedfromthegrowthfront.Therangeofyvariationisduetothesymmetryaboutthecapillarycentre.Theinitialandboundaryconditionsoftheproblemhavetheform
1.Fort=0C(y,0)=C0;
2.Inthecapillarycentre ;
3.Atthegrowthfrontsthereholdsthemassconservationconditionofthecrystallizingmaterial:
where
Hereqisthekineticcoefficient.TheboundaryconditionsdisregardUsinceinrealsystems .
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UnderLPEconditions,theinitialsupersaturationDC0=C0-C1issosmallthatthemaximum(final)filmthicknessisnoticeablylessthanthecapillaryhalfwidth.
Solvingequation(2.12)bythemethodofseparationofvariables,weobtainthetimedependenceofthefilmthicknessh:
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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
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Theexpression(2.14)obtainedabove,whichholdsforj>1, ,describesthediffusionregimeinwhichthegrowthrateisdeterminedbythediffusion
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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
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forD=0.5×10cm/s,whichagreesintheorderofmagnitudewithwhatwehaveobtained.Toevaluatetheerroroccurringintheuseofformula(2.18),weshallemploy(2.15),assuming
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Fort/t>p-1,weobtainDh/h0<10-1,whichiswithintheexperimentalerrorforh.Thus,inthegrowthsystemunderconsiderationwedealwiththekineticregimeat sandwiththediffusionregimeat
s.
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
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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).
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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
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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
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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-
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Fig.2.26ProgrammedtemperaturedecreaseinLPEgrownLi(Nb,Ta)O3(I)
andthecorrespondingNbandTadistributionthroughthethicknessofLi(Nb,Ta)O3/LiTaO3hyperstructure(II)
(Khachaturyanetal.1987).
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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.
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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
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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
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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
1 1
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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
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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
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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
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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
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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:
1)
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2)
3)
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
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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
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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).
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Table2.6GrowthconditionsandphysicalcharacteristicsofLiM5+O3films(Neurogaonkaretal.1987)
Flux Substrate/film* Growthtemperature
(°C)
Latticeconstant(Å)
TemperaturecoefficientSAWvelocity(ppm/°C)
a 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
- -
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*)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.
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Thephaseequilibriumwasstudiedbydifferentialthermalanalysis(DTA),
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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
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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
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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
930 0.5 - - surfacedissolution
24Nb2O5
930 0.2 - - surfacedissolution
{0001}A12O3 920 0.5 - - noprecipitation
920 0.5 - - surfaceintensivedissolution
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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-
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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
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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.
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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
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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
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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
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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
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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
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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).
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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.
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Thus,themethodsdiscussedabovemakeitpossibletoobtainlayerswithvariouswaveguideconfigurationsinthefilm.Varyingthegrowthrateandtheannealingtime,wecanobtainsurfaceandimmersedwaveguides,striplinestructuresandlayerswithmetallicbufferedlayersonthesubstrate-filmboundary.
2.10GrowthofepitaxialfilmsintheKTiOPO4familyofcrystals
Asanalternativetodirectlyaddressingtheionicconductivityproblem,andasameanstomoreeffectivelyconfinetheopticalwavetoyieldhigherpowerdensity,filmswithwell-definedstep-likerefractiveindexprofilecanbegrown
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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
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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.
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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)
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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.
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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
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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
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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:
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wherexisthemolefractionofAsinthecrystals.Itwasexperimentallyfoundthatthemaximumlatticemismatchforhighqualityfilmgrowthisabout1%,whichcorrespondstoa35%increaseinarseniccontentintheKTiOASxP1-xO4filmandtoanestimatedrefractiveindexincreaseofDnb~0.0177at1.064mm.Filmcrackingand'scaling'wereobservedforfilmswithlargerlatticemismatch.
SignificantlydifferentgrowthpropertieswereobservedfortungstatefluxandtheK6flux.Atabout850°Candwithcomparablesupercooling(about2°C),thegrowthratewassubstantiallyslowerintheK6fluxthanintungstate.ToachieveacomparablegrowthrateusingtheK6flux,asupercoolingroughlytwicethatusedintungstateisneeded.FilmsgrownfromtheK6fluxtendtohavefilm-substrateinterfacesofpoorerquality.Itislikelythatthisisdue
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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
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satisfied.
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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
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fielduponthecrystallizationprocessdonotprovidefinalunambiguousconclusionsconcerningaunifiedphysicalmechanismoffieldeffect.Inviewofthisweconsiderpossiblemechanismsoftheinfluenceofadirectelectricfielduponcrystallizationprocesses.
3.1.1Bulkcrystallization
In1956,A.F.Ioffegaveatheoreticaldescriptionofmotionofameltedzoneundertheactionofelectriccurrentingermaniumbars(Ioffe1956).This
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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
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applicationofadirectelectriccurrentthroughaninterfaceprovidescontroloverthecrystallizationfrontshapeduringzonecrystalgrowth.Tochoosethecurrentdensitynecessaryforcrystallizationfrontshapecontrol,oneshouldtakeintoaccounttherelationbetweenthePeltierandJouleheatswhicharerespectivelyequalto
PisthePeltiercoefficient,RistheresultantresistanceoftheportionsofliquidandcrystaladjoiningthecrystallizationfrontandJiscurrentdensity.
Theseeffectscanbesummeduporsubtracteddependingonthedirectionofcurrent.
InaregionwherethecurrentdensityissuchthatQJ>Qp,thecrystallizationfrontrises,whilefor itfalls.WhentheJouleandPeltierheatsareequaltoeachother, theappliedcurrentinducesnovariationsofthecrystallizationfrontshape.Thecorrespondingequilibriumdensityofcurrentwillbeequalto
Thedeviationoftheimpurityconcentrationfromtheequilibriumvalue(DC)atthesolid-liquidinterfacecanberepresentedinthegeneralformasan
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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.
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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-
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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.
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Thus,ananalysisofthepapersinvestigatingtheinfluenceofadirectelectriccurrentuponcrystallizationofabulkmaterialrevealedthepossibilityofcontrollingtheimpuritycompositionandstructuralperfectionofgrownsinglecrystals.
3.1.2Thinfilms
Thewideapplicationofthinfilmsinmicro-andoptoelectronicsisexplainedbymanyfactors.Themostimportanthereisobviouslythefactthatitisonlythinfilmsthatpermitobtainingcompactschemesatalowconsumedpowerandahighdensityofschemeelements.Furthermore,themethodsofobtainingthinfilmsprovidehighlypuresubstancesormaterialswithacompositioncontrolledwithprecision.
Researchersengagedingrowingsinglecrystalsandfilmsareinterestedinfindingnewwaysofaffectingagrowingcrystal,whichwouldallowamoreeffectivecontroloverthegrowthrate,surfacemorphology,thedistributionofalloyingimpuritiesinacrystallizationmediumandtheconcentrationofstructuraldefects.
Alargeamountofexperimentalmaterialisavailableontheinfluenceofanelectricfielduponepitaxialgrowthfromthegasphase.Thegeneralchemicofphysicalconsiderationsimplythatsuperpositionofthedifferenceofelectricpotentialsonthesourceandsubstratemaygivethefollowingprincipaleffects:
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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=
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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
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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
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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-
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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
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cellisresponsibleforthesubstancetransportontosubstrateduetoelectromigrationofliquid-phasecomponents.
Assoonastheelectriccurrentisoff,thetransportofsubstanceparticlesstopspracticallyinstantaneously,auniformdistributionofcomponentsisestablishedintheliquidzone,andthermodynamicequilibriumsetsupinthesystem.Thefilmgrownonthesubstrateisnotdissolved,andtheliquid-phasecompositionremainsexactlythesameasbeforethecurrentwasswitchedon.
Ifasourceisabsentinthecrystallizationsystemthensubstanceprecipitationontothesubstrateundertheactionofanelectriccurrent(underanymasstransfermechanism)maybeonlyduetoliquid-phasedepletion,whichleadstoanonequilibriumstateofthecrystallizationsystemaftertheprocessisover.
Applicationofoneortheothermethodshouldbecoordinatedwiththepurposesandtasksofaparticulartechnologicalprocess.
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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;
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c.time-dependentvariationoffilmcomposition(compositiondistributionoverthickness).
3.2.1Temperaturedistributioninasystemundertheactionofanelectriccurrent
Weshallconsiderthesimplestcasewhenthematerialsofthesourceandsubstratearethesame.Intheproblemoftemperaturedistributionsuchaconsiderationisalmostalwaysadmissible.
Inthegeneralcase,thefollowingheatsourcesshouldbetakenintoaccountinthesolutionoftheproblem:
1.Peltierheat-asurfaceheatsource;
2.Jouleheat-abulkheatsource;
3.crystallizationanddissolutionheat-asurfaceheatsource;
*ItisobviousthattheprobleminindicatedgeometryissimilartoZTMG
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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.
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TheDufoureffectinliquidsystemsisinsignificant(DeGrootandMazur1962).Thus,wecanneglectbulkheatsourcesandonlymakeallowanceforsurfacesources,thatis,Peltieranddissolution(orcrystallization)heat.Underthisassumption,theequationforthermalconductivityhastheform
whereKisthethermalconductivityoftheliquid-zonematerial,visthevelocityofzonemotion.
Weassumeherethezonethicknesstoremainunalteredandtheoriginofcoordinatestocoincidewiththeinterface(Petrosyanetal1974).Sinceinarealtechnologicalregimethecurrentdoesnotchangeatallorchangesveryslowly,inthesolutionoftheproblemitcanbethoughtofasconstant.
Thesecondtermintheright-handsideofequation(3.5)describestheinfluence
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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
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wherels,lL,Ll,Larethetemperatureconductivitiesandthicknessesofthesubstrate(source)andliquidzone,respectively,and .Itisreadilyseenthatat ,disregardingthecrystallizationheatandtakingintoaccount ,weobtainfrom(3.7)
Wecanseethatthetemperaturegradientisindependentofthezonethicknessandisdeterminedbythemagnitudeofthedensityofcurrentflowingthroughthesystem.
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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
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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,
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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
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comingtoandfromtheboundary.Attheothermeltboundary(intheabsenceofconvection)oratadistanceofthed-layer(inthepresenceofconvection)theinitialconcentrationremainsunchangedandequalsC0.Thenecessaryconditionisheretheequalitybetweentheparticlefluxescomingthroughtheboundaryofthed-layerandgoingawayintothesolidphase(Birulinetal1984):
wherek0istheequilibriumsegregationcoefficient,visthegrowthrateoftheepitaxiallayer.
DependingontherelationbetweenthevaluesofthebufferedmeltcomponentsmandD,twocomponentconcentrationvaluesnearthesubstratearepossible,namely, and .Intheapproximationthatinthetransition(d)layeroftheliquidphasetheconcentrationvarieslinearly,Birulinatal(1984)derivedtheexpressionforparticleconcentrationofthecomponent
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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
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electromigrationandPeltiereffect.
3.2.4Initialstagesofnucleation
Thepresenceofchargesandelectricfieldsareknowntospeedupnucleationofanewphase(ChernovandTrusov1969;AleksandrovandEntin1971).ChernovandTrusov(1969)estimatedtheprobabilityofnucleationinapoint-chargefieldonthesurfaceofadielectric.Theycalculatedthecontributionoftheelectrostaticfieldtothecriticalnucleationenergyandsolvedthefollowingelectrostaticproblem:apointchargeqislocatedunderthecrystalsurfaceatadepthH.Thedielectricpermittivitiesofthecrystalandmediumareequaltoecrandemcd,respectively.ThesupersaturationofthemediumrelativetothecrystalisDm.Thenucleusofthenewphasehastheshapeofafiatdiscofheighta(aisequaltothelatticeconstant),Fig.3.3(ChernovandTrusov1969).
Theworkofcriticalnucleationisequalto
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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
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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
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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*
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Fig.3.4Schematicofnucleationontheelectrode:1)metallicelectrodes;
2)energysource;A,Bareinitialsubstances;Cisnucleusofthenewphase.
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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.
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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
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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
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Thecoefficientoftheformofthecentreofthenewphaseh**/V**canbeeasilyobtainedfrom(3.27)and(3.28)
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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.
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Thenucleationratewillbedeterminedfromtheformula
whichshowsthatfor thenucleationrateincreases.
3.3Theroleofthermoelectriceffectsinthecourseofliquid-phaseelectroepitaxyofferroelectrics
Theapplicationofadirectelectriccurrentinthecontrolovercrystallization
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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.
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Whenadirectcurrentrunsthroughinterfaces,PeltierheatproportionaltotheproductofcurrentdensitybythePeltiercoefficientisinstantaneouslyreleasedandabsorbed.
Owingtothiseffectthetemperatureattheinterfacefalls,thisfallbeingequalto(Jastrzebskietal1978):
where isthedifferenceofthermoelectromotiveforcesbetweenthesubstrateandsolvent,L1isthesubstratethickness,lsthethermalconductivityofsubstratematerial,T0thetemperatureinthesystempriortoapplicationofcurrent.
Aconsequenceoftemperaturedifferenceinthesystemisconcentrationvariationintheliquidzone
wheremistheslopeoftheliquiduscurve.
Attheinterface,Peltierheatisabsorbedandcrystallizationheatreleased(sincetheyhaveoppositesigns).
Consequently,thisleadsintheendtoadecreaseofabsorbedandreleasedPeltierheat,i.e.toadecreaseofthetemperaturegradient.
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TheresultsofcomparisonoftheoreticalandexperimentaldatasuggestthatthecrystallizationheatcanbeneglectedascomparedtothePeltierheat.Then
wherelListhethermalconductivityofthemelt.
Thus,thetemperaturegradientoccurringattheinterfaceisindependentofthezonethicknessandisdeterminedbythevalueofthecurrentdensity.
Sincethetimewithinwhichthetemperaturegradientissetinthesystem, ,iscomparativelysmall,thecurrentrunsthroughanonuniformlyheatedsystem,thatis,fromtheverystartoftheprocessanadditionalThomsonheatisreleased
wheretTisThomson'scoefficient.
OwingtotheThomsonheat,thesystemcanbeadditionallyheated,thetemperatureincreasebeing
whereMandcarerespectivelymassandthermalcapacityofthesubstrate.
Whenadirectelectriccurrentisapplied,Jouleheatissimultaneouslyreleasedinthesystem:
whereRistotalsystemresistanceandRLisliquidphaseresistance.
Since ,theJouleheatmainlyaffectsthesubstrate.
Beginningfromsomeinstantoftime(tcr),theJouleeffectmaybecomegreaterthanthePeltiereffectsinceaconstanttemperature
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gradientattheinterfaceismaintainedbythePeltierheat,whiletheJouleandThomsonheatsareaccumulatedinthesystem.Consequently,theresultanttemperatureofthesystemstartsexceedingtheequilibriumtemperatureTOandthesystemmayappeartobeundersaturated,whichwillresultindissolutionofthecrystallizedlayer.
Ascanbeseenfromtheaboveformulae,theJouleheatisquadraticandthePeltierheatislinearinJ.ThismeansthatthereexistsacertainoptimumvalueJoptwhentheJouleheatbecomespredominantoverthePeltierheat.TheJouleheatcanthereforebeneglectediftheappliedcurrent
TheThomsoneffectishereduetotemperaturedependenceofcarrierconcentration,andinsuchasystemitcanbeneglected,providedthezonematerialisaliquidmetal.Moreover,thiseffectisalsoquadraticinthecurrent.
GabrielyanandKhachaturyan(1984)investigatedferroelectricfilmgrowthusingliquid-phaseelectroepitaxyandestimatedthecontributionofthermoelectriceffectstothisprocessonanexampleoflithiumniobate.
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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.
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3.4.1Epitaxialgrowth
Theuseofcurrent-inducedliquid-phaseepitaxyforgrowingLiNbO3andLi(Nb,Ta)O3filmsfromalimitedliquid-phasevolumecontainedbetweentwosubstrateslocatedclosetoeachotherwasproposedbyKhachaturyanetal(1986).Figure
Fig.3.8Melttemperaturevariationsduetothermaleffectsasafunctionofcurrentdensityinthecourseof
LEPoflithiumniobate.
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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
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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-
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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
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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.
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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
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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
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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
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fromtheliquidphaseisminimum(0.005÷0.01at%).
Acharacteristicfeatureofelectro-LPEofferroelectricfilmsand,inparticular,oflithiumniobate,isthatsimultaneouslywithlayergrowththefilmismadesingle-domain(polarized).ThemethodofpolarizationofLi(Nb,Ta)O3filmswas
Fig.3.12ThicknessofaLiNbO3filmversusthetimeofapplicationofcurrenttothecrystallizationcell.
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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=
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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
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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
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Fig.3.14TopogramoffilmsofLiNb05Ta05O3solidsolutionsof(1120)and(0001)orientations(a)anddistribution
ofcomponentsalongtheLi(Nb,Ta)O3/LiTaO3heterostructure(b).
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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
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liquid-phaseelectroepitaxyofsemiconductorsandferroelectrics,theroleofoneoranotherfactorandtheirinterrelationsarenotobvious(Milvidskyetal1982).
Themainunitofadeviceforequilibriumandnonequilibriumregimesofelectro-LPEofferroelectricsconsistsofgrowthcellsdepictedinFig.3.16a,b.Conductingelectrodesweremadeofplatinum.Applyingthemethodofequivalenceofthermalandelectricschemes(Stefanakosetal1976)withallowanceforJouleheatingofthegrowthcell,thetemperaturevariationofthecrystallizationfront,T,isdescribedbytheexpression
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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
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willcorrespondtothecriticalcurrentofelectro-LPE.Withaccountof
and ,formula(2.37)acquirestheform
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and
Itisofinteresttoexaminethephysicalnatureofcriticalcurrentunderelectro-LPEasafunctionofsystemtemperature.Thegraphofthedependenceforbothregimesisconstructedanalytically(Fig.3.17).
Aswecanseefromthegraph,thecriticalcurrentofelectro-LPEdependsonsubstratematerial.Thelimitofad.c.JcpitpreventingtheJouleeffectincreaseswithincreasingtemperatureT0.
Sincethecriticalcurrentofelectro-LPEisafunctionofgeometricaldimensionsofthesubstrate,itfollowsthat
wherer0isresistivity,sandlarerespectivelytheareaandthethickness;therefore,increasingthesubstrateareaanddecreasingitsthickness,wecanincreasetheboundaryvalueofJ0.
Anincreaseoftheareaandadecreaseofthethicknessofthesubstrateandthesourceprovideextensionoftherangeofoperatingcurrentdensitiesforelectro-LPEofferroelectrics.
ThethicknessofepitaxiallayersofLiNbO3grownonLiTaO3substratesis
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Fig.3.16Schematicofacellshowingtemperaturedistribution
a)equilibriumregimeofLPE;b)nonequilibriumregimeofLPE.1)platinumelectrode;2)LiTaO3orLiNbO3substrate;3)solutionin
melt[N%LiNbO3-(100-N)%LiVO3];4)LiNbO3source;5)thermalinsulation.
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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
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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
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Fig.3.19ThicknessesofepitaxiallayersofLiNbO3on
LiTaO3substratesasfunctionsofsubstrateandsourcethicknessesinequilibrium(x)and
nonequilibrium()LPEregimes.
forequilibriumandnonequilibriumregimesandfromcomparisonwithexperimentalresults,anoptimumrangeoftheprocessparametersischosenwhichprovidesanepitaxialgrowthofLiNbO3layersofaLiTaO3substrate:
Nonequilibriumregime Equilibriumregime
TosimplifytheanalysisoftemperaturedistributionatthecrystallizationfrontwithallowanceforJouleeffect,weneglectthecontactthermaleffectsassumingthatthephysicalpropertiesofcellelementsareisotropicandthattheisotropyofthepropertiesandthegeometryoftheelementsaretemperatureindependent.Fromthesolutionofthermalconductivityequationincylindricalcoordinatesweobtain,accordingtoBarchukandIvaschenko(1982),theanalyticexpressionforastationarytemperaturedistributionatthecrystallizationfront
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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-
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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
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3
(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.
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Thus,usingthemethodofequivalenceofthermalandelectricschemesforexperimentalcellsinequilibriumandnonequilibriumelectro-LPEregimesofferroelectrics,wehaveintroducedtheconceptofacriticalcurrentofelectro-LPEanddeterminedtheoptimumgrowthparametersforLiNbO3onLiTaO3andLiNbO3substrates,whichpermitplanarstructurestobeproducedunderliquid-phaseelectroepitaxy.
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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
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containingupto58mol.%Nb2O5,butbecauseofthelargedifferenceinliquidandsolidphasecompositionsthisleadstothegrowthofinhomogeneouscrystals.
X-rayandneutrondiffractionanalyseshaverevealedthatlithiumniobatehasthestructurerelatedtoilmenite(Abrahamsetal1966).Boththestructuresare
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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.
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Ionpositionsinthecrystallatticeareofinterestfromthepointofviewof
Fig.4.1CrystallinestructureofLiNbO3;a)seriesofdistortedoctahedralsalongthepolarc-axis;b)reallocation
ofoxygenatomsrelativetolithiumandniobiumatoms(Abrahamsetal1966).
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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
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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)
70.6
59.0
( tocaxis)
Evaporationcoefficient,a 10-4
3
Thermoelectriccoefficientofmelta1(mV.K-1) -0.4
Thermoelectriccoefficientofcrystalas(mV.K-1) 0.76±0.02
Coefficientofcrystallizationemfav(mVs.m-1) 1.25±0.2
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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
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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.
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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.
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Fig.4.3VariationinferroelectricCurietemperaturewithsolidcompositioninLiNbO3-LiTaO3solid-solutionsystem(Petersonetal1970).
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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
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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
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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
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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).
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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
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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.
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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
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Thedistributionofcomponentsoverthethicknessofthelightguidinglayerwasexaminedbymicroroentgendiffractionanalysis(MRDA).Figure4.4presents
Fig.4.4Distributionofcomponentsalongthethicknessof(a)LiNbO3/LiTaO3,
(b)Li(Nb,Ta)O3/LiTaO3and(c)LiNbO3/Al2O3heterostructure.
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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
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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
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Table4.2LatticeparametersandinterplanedistancesofLi(Nb,Ta)O3filmsandLiTaO3substrate(Madoyanetal1985)
No Filmmaterial Latticeparameters(Å)
Orientation Interplanedistances(Å)
a c
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
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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
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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
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HexagonalcellparametersversusLiNb1-yTayO3filmcomposition.
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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-
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Fig.4.7ElectrondiffractionfromtheLiNbO3filmsurfaceonaLiTaO3(1120)substrate,Kikuchilinesareobserved.
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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.
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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
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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
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eziscalculatedfromapairofshiftsDq030andDqhklusingthefollowingexpression
Fig.4.9(a)Relationshipbetweenthe(036)latticeplaneandtheincidentX-raybeam.(b)Inclinationinthe(036)latticeplanesbetweenthesubstrateandtheTi-diffusedlayer.Thedottedlinerepresentsalatticeplane
parallelto(036)s(Sugiietal1978).
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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
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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-
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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
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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.
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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
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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
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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
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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
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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
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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
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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
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importantfactorwhichdeterminesbasicallythemechanismofsinglecrystalnucleationandthekineticsoftheirsubsequentgrowthisthestructureoftherealsurfaceofthesubstrate(Veinsteinetal1979).Oneshouldbearinmindthatthedifferenceinthelatticeperiodsofcontactingmaterialsaffectsthemagnitudeofthesurfaceenergyoftheinterfaceand,accordingly,thecharacterofelementarygrowthprocessesattheearlystageofheteroepitaxyestablishingeithertwo-orthree-dimensionalnucleationmechanism.Thecharacterofelementarygrowthprocessesessentiallydeterminesthestructureperfectionandthemorphologyofthinepitaxiallayersnearheteroboundary.
Figure4.13presentsmodelsofthelayergrowthmechanismfordifferentsupersaturationsintheliquidphaseandthecorrespondingsurfacemicromorphologies
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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
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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
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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
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decreaseinthedensityandsizeofthegrowthpatterns.Thesurfaceroughnessdoesnotexceed0.2µm.Theresultobtainedtestifiesclearlytothefactthatsurfacemorphologyisdeterminedbythestructuredefectsoccurringattheinterfaceduetomismatchoflatticeconstants.Thefilmsurfaceroughnessisconsiderablyinfluencedbythemannerinwhichthesubstratesurfaceisprepared.Mechanicalpolishingleadstotheappearanceofadamagednear-surfacelayer.High-temperatureannealingorchemicaletchinginducetheappearanceonthesamplesurfaceofsomesignsofpolishinghiddenbythenear-surfacelayer.Scratchesonthesubstrateoccuronthesurfaceofthinlayersintheformofshallowgroovesupto3µmwide.Toobtainaperfectsurface,thesubstratewaspreliminarilytreatedinKOHatatemperatureof280-340°Cfor2-3min.
Examinationofsurfacemorphologyhasshownthattoobtainsmoothlayersitisofimportancetocompletelyremovetheresiduesofsolution-meltfromthefilmsurfacewhenthegrowthprocessisover.Arapidcoolingtoroom
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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.
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WhentheTi-diffusedlayerisutilizedasanopticalwaveguide,thedefects
Fig.4.15Diffusion-induceddefectsinTi-diffusedlayersofsamples
ofLiNbO3:TigroupI(g=030)(a)1000°C,10h,(b)1000°C,2.5h,groupI[(Sugiietal1978).
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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.
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Fig.4.16ThesurfaceofaLiNbO3substratewithaTi-diffused'Y'
coupler(a)andthesurfaceofanepitaxialfilmgrownonthissubstrate(b).
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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
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Fig.4.17Boundariesbetweenepitaxialstructures:a)LiNbO3/LiNbO3;
b)Li(Nb,Ta)O3/LiTaO3;c)LiNbO3/LiTaO3(Khachaturyanetal1984).
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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
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occurrenceofdislocationsisthefollowing:
-penetrationofdislocationsfromthesubstratetothefilminwhichtheydegenerate;
-nucleationofdislocationsunderstresscausedbynonuniformimpuritycaptureunderlaminargrowth;
-occurrenceofdefectsduetothenonuniformimpuritydistributioninagrowinglayer.
Onthesubstrate-filmboundary,defectsmayoccurduetomismatchinlatticeconstantsbetweenthefilmandsubstrate.Tominimizethemismatchbetweenthetwolattices,elasticdeformationoffilmsisenergeticallyadvantageous.Ifthemismatchisnotcompensatedcompletelybytheelasticstress,mismatchdislocationsalsooccur(MilvidskyandOsvensky1977).Arelativecontributionofelasticstressesandmismatchdislocationstotheaccommodationofcrystallatticesdependsonthedifferenceinlatticeconstants,filmthickness,geometryofdislocations,characterofbondsontheinterfaceandelasticconstantsoftwointergrowingmaterials.Mismatchdislocationsslidefromthefreesurfaceintotheinterfaceregion.
PlaceswheredislocationsappearonthefilmsurfaceasconicaletchpitswithaclearlypronouncedvortexshowninFig.4.18e,f.Butamixtureofhydrofluoricandnitricacidsdoesnotpermitanexactlocationofdislocationetchpitson
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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
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substrate.Adirectcountofetchingpitshasshownthatthedensityofdislocationsemergingonthesubstratesurfaceisdeterminedbythepositionofthissurfacerelativetothegrowthaxisoftheoriginalcrystal.Thenumberofdislocationsonthey-planeofLiTaO3andz-planeofLiNbO3(thatis,ontheplaneperpendiculartothecrystalgrowthaxis)makesupN~104cm-2,fortheotherplanesitisbyanorderofmagnitudesmaller.
SelectiveetchingoflithiumniobatefilmsinKOHhasshownthatgrowthhillocksonthefilmsurfaceareofdislocationnature.Intheplaceofhillocks
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removedbypolishingtheretypicallyappeardislocationetchingpits(Fig.4.18c).Twomechanismsofthisphenomenonarepossible.
Inmatingtwosingle-typelatticeswithinterplanardistancesa1anda2thereoccurmismatchdislocationswiththelineardensity
where
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
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dislocationscausedbymismatchbetweentheinterplanardistancealongthezaxisandalignedperpendiculartoitishigherbyanorderofmagnitude.Therefore,thesegmentsofmismatchdislocationsoccurringonthegrowthdislocationsthatstretchtothefilmareexpectedtobeperpendiculartothez-axis.
Suchamodelagreeswithsomeoftheexperimentalresults.Inparticular,thesurfacemorphologyonthezplaneisclosetoisotropic,andthedirectionofgrowthhillocksony-andx-orientedfilmsareperpendiculartothez-axis.Introductionoftantalumpentoxidetoalithiumniobatefilm(i.e.matingthelatticeconstantsofthefilmandsubstrate)decreasesthenumberandsizeofthegrowthhillocks.Butthereexistessentialcontradictions.Becauseofsmallthicknessofthepseudomorphouslayers,themismatchdislocationsegmentsmustoccurattheinitialinstantofepitaxy(0.1µm)andmustnothaveanyeffectuponthemorphologyfurtheron.Thefiguresofgrowthincreasewithincreasingfilmthickness,whereastheeffectoflatticemismatchdecreases.
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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
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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
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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
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(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
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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.
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Defectstypicaloflithiumniobateareoxygenvacancieswhichcanbereadilywithdrawnbyhigh-temperatureannealinginoxygenatmosphere.
Lithiumniobatecrystalsarehighlysensitivetoheattreatmentwhichaffects,besidesoxygenvacancies,alsodislocationmigration,impuritydistributionandthecontentofmicrodomains.(Rakovaetal1986;Bocharovaetal1985)pointedouttheappearanceofalienphasesonthesurfaceofLiNbO3underannealingatT=900°C,(OhnishiandYizuka1974)reportedrepolarizationofnear-surfacelayersundermechanicaltreatment.
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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
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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
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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
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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
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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
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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.
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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
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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
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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
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essentialforthedomainstosurvivethe350-
Fig.4.25Measureddepthofinvertedregionswitha20µmperiodagainsttheheattreatment
temperatureforvariousproton-exchange(PE)conditions(Mizuuchietal1991).
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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
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whenanexternalfieldisappliedatroomtemperature.TheexternalfieldfordomaininversionofLiNbO3isclosetothatoftheelectronavalanche,sotheLiNbO3substrateisbrokenwithoutitsspontaneouspolarizationbeinginvertedwiththeapplicationofanexternalfield.
Yamadaetal,(1993)fabricatedtheperiodicdomainstructureforfirst-orderQPM-SHGdevicesinLiNbO3asfollows.Figure4.26showshowexternalfieldisapplied.Theyalsousedaz-cutLiNbO3crystalasthesubstrate.AnAlthinfilm200nmthickwasdepositedonthepositiveandnegativec-faceofthe
Fig.4.26Schematicofapplyingvoltageforperiodically
domaininversion(Yamadaetal1993).
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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
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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
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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)
where
wherexandyaretheperpendiculardistancesofapointchargefromtheconductingplaneasshowninFig.4.27.Thechargeisqandeis
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thedielectricconstantofthemedium.Asexpected,ahighelectricfieldisproducednear
Fig.4.27Normalizedelectricfieldlog(4pea2E(x)/q)contours
duetothepointchargeqneartheconductingsurface(Nuttetal1992).
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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
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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-
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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,
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-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
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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.
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TheelectrondiffractionpatternsofsamplesannealedatT>650°C(Fig.4.28bandc)show,togetherwitharcsfromthetexture,alsoasystemofpointreflexesformedbyamosaicsinglecrystal.Withafurtherincreaseoftemperaturefrom700°Cto900°Cthereflectionsfromthetexturedisappear,andtheelectrondiffractionpatternsonlycontainanetofpointreflexes,whichtestifiestothepresenceofsimilarlyalignedgrains.AnnealingoflithiumniobatesamplesatT=950°Cfor4hsufficesforacompleterestorationofcrystallinityofthenear-surfacelayer.Theelectrondiffractionpatternsofsuchsamplesexhibit
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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
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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.
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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
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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.
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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
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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
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Page211Table4.5Physico-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
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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.
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Fig.4.30(a)Surfacemorphologyofthe(0001)facetoflithium
niobateafterannealingatT=750°Cfor4h.(b)Positionsoflithiumtriniobateisletsonthe(0001)
facetoflithiumniobate,(Bocharova1986).
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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
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facets.Theprismwasarrangedinasmallfurnaceonaspectrometerstage.Therefractiveindicesweretakenateighttemperaturesbetween19and374°Cforeightlinesoftheheliummetalvapourlampat447.1,471.3,492.2,501.6,587.6,667.8,and707.6nm.
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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
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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.
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Ananalysisoftheexperimentaldatahasyieldedtwoequationsforthetemperaturedependencegivingtherefractiveindicesbetween400and4000nm:
whereTisthetemperature,K,listhewavelength,nm.
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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
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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
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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
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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
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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
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havethenfromtheSnelllaw
and
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,
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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
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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
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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
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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-
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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
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for .ThecurvesshowingWversusb/kusingmastheparameterarethemodecharacteristicsofthewaveguide(seeFig.5.15below).
Tosummarize,anyradiusofthequarter-circleshowninFig.5.9representsapossibledirectionforthewavevectorB1describedabove,and istheincidentanglemeasuredbetweenthewavevectorandtheverticalaxis.Thewaveguidemodesoccurintherange
.Withinthisrangeof thereisadiscretesetofthedirectionswhichsatisfiestheequationofthemodes(5.6).Eachdirectioncorrespondstoonewaveguidemodeofthefilm.Thehorizontalcomponentofthewavevector, ,determinesthewave
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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
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Theboundaryconditionsatthefilm-airinterfacesdemandthesamewavemotionparalleltothefilminallthethreemediaconsidered;thiscanbewrittenas
Allthefieldsthusvaryintimeandxaccordingtothefactor.Thiscommonfactorwillbeomittedinallthelater
expressionsforsimplification.Combiningequations(5.11)and(5.12)givesanimportantrelation
Inthefilm, and arethehorizontalandverticalcomponentsofthewavevectorA1orB1discussedbefore.Theyarerespectively
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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
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Fig.5.10a.Thesechoicesgive ,whichsatisfiesequation(5.6).TheboundaryconditionsrequireEyandtobecontinuousatthetwointerfaces.Therefore,
Fig.5.10Theelectricfielddistributionof(a)aTEwaveguidemode;(b)aTEsubstratemode;(c)aTE(even)airmode(Tien1971).
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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.
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Mathematically,thefielddistributionsdescribedaboveareidenticaltothoseoftheproblemofasquarepotentialwellinquantummechanics.Heretheairspaceandthesubstratearethepotentialbarriers.Thewaveenergyisdividedhereintothehorizontalandverticalcomponents,keepingthetotalenergyconstant.Itistheverticalcomponentofthewaveenergythatnegotiates
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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
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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
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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
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Fig.5.11(a)Positionofthec-axiswithrespecttothegeometrical
axesinasolid-solutionLiNbO3-LiTaO3film.(b)CurveAshowsthegradedcompositioninthefilm.(c)CurvesAandBshow,respectively,theindexvariationinasolid-solutionfilmandthatinadiffusedfilm.(d)Photographofthemlinesofasolid-solutionfilm.(e)Photograph
ofthemlinesofauniformwaveguidemadeofaTa205filmonaglasssubstrate(Tienetal1974).
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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
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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
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totheWKBmethod(DickeandWittke1960).Recallthatforauniformwaveguidethemodeequations(Tien1971)are
and
Hereweareconsideringazigzagplanewavepropagatinginthefilmas ,wherebandbarerespectivelytheaandxcomponentsofthewavevector,manddarerespectivelythemodenumberandthefilmthickness, ,wherewistheangularfrequencyandcisthevelocityofthelightwaveinvacuumand,finally, and arerespectivelythephasesadvancedbythezigzagwaveduetothetotalreflectionsofthewaveatthefilm-substrateandfilm-airinterfaces.OnthebasisoftheWKBmethod,foragradedwaveguideofanyindexdistribution
and
Here istheturningpointoftheWKBmethodand,at , and.Consequently,a,canbeconsideredasafunctionofb.For
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Fig.5.13ValuesoftheintegralAversusthemodeindices,b/kforthetwocasesdescribedin
thetext(Tieneta11974).
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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
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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
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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,
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andforthegradeguide,
Thewavefunctionsfortheslabaresinusoidalintherange andexponentiallydecayingoutsidethisrange.Formodessufficientlyfarfromcutoff,mostoftheenergyisconfinedwithin .Thus,neglectingtheevanescenttail,onecandefineaneffectivepenetrationdepthforallTEslabmodesas
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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
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passthroughthepoints , , and ,thenitisfoundthat
Thefactor1.38isofcoursedependentonthechoiceof ,butitcanbeseenthatNsandNgaresimilarforcomparableA,Banda,bparameters.Forexample,ifA=a,then whenB=0.69bforlargeN.
ThewavefunctionsandindexlevelsfortheTE0andTE1modesareshownschematicallyinFig.5.14b.Theintersectionoftheindexlevelwiththecurven(x)definestheturningpoint ,atwhichanequivalentopticalrayoraquantum-mechanicalparticleinasimilarpotentialwellwouldreverseits
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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
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isoneofthefewthatgivesexactanalyticalsolutionstothewaveequation.Thesesolutionsalsoshowanincreaseinthestrengthofthewavefunctionsasxapproachestheturningpoint,withdeeperpenetrationforhigher-ordermodes.Althoughthenumberofmodes,wavefunctionsandpropagationconstantscanbecalculatedwhena"andb"areknown,simpleexpressionsforNandwintermsofa"andb"arenotgiven.However,usefulexpressionscanbeobtainedincertainlimitsasfollows.
Definethefunctions
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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
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byequatingtheright-handsideofequation(5.32)to for ;then
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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
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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.
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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
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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
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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
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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).
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havetheform
here isadegenerategeometricalfunction, istheBesselfunction
Forextraordinarywaves(H-polarization)
Fig.5.17DispersionofordinaryandextraordinaryrefractiveindexincrementforwaveguideswithdiffusiontimetD=12h(dashedlinesindicatecalculatedvalues-seethetext)(Zolotoveta11980).
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Fig,5.18(right)Opticalwaveguidingapparatus(KaminowandCarruthers1973).
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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
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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
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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
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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.
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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
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indicatricesintersect.Varyingthedepth,shapeoftheprofileorincrementoftherefractiveindexofawaveguide,wecanvarythematchinganglesofnonlinearmodeinteraction.Itshouldbenotedthattoperformsuchvariationsoneshouldknowthedependenceofphasecharacteristicsofawaveguideonitsstructureparametersandbeabletocontrolthemduringwaveguidemanufacturing.For
Fig.5.19Indicatricesofordinaryand
extraordinarypolarisationmodesinLiNbO3(Zolotovetal1979).
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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
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waveguidesofLiNbO3awaveguideformsnotonlyduetoTidiffusionintoacrystal,butduetoareversediffusionofLi2Oaswell.Theseprocesseshavedifferentkinetics,andthereforethewaveguideprofileforextraordinarypolarizationiscomplex.
ThemethoddevelopedbyZolotovetal(1977)wasusedtodetermineYw(y)andY2w(y).Thismethodpermitsdeterminationofthecharacteristics(includingmodefieldsanddispersiondependences)ofdiffusedwaveguideswithanyprofileofrefractiveindexdistribution.Themethodisbasedonapproximationoftheunknownwaveguideprofilebythefunctionsthatallowobtainingsolutionsofthewaveequationinananalyticform.InTi-diffusedwaveguidesofLiNbO3(Y-cut),theprofileofthetransversedistributionn0(y)forordinarypolarizationisdefinedbythecombinationofasmoothlysewedparabolaandexponent(5.40).
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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
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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.
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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=-
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0.63,he=8.5mmwerefoundfortheinvestigatedwaveguideonthebasisoftheobtainedspectra .
Themodefieldsoftheinvestigatedwaveguide(Fig.5.21)wereobtainedandtheoverlapintegralsI1m(m=2,3,4)weredeterminedusingtheprofiles.TheintegralI12ismaximumandclosetotheoptimumvalue(Fig.5.20),andtherefore
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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
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inhomogeneities.
Thedependenceofsecondharmonicpowerontheanglebetweenthepump-
Fig.5.24Angulardependenceoftheoutputsecondharmonicpowerinadiffusedwaveguide(Zolotoveta11979).
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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
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ordinarywave.ThisisattributedtoLi2Oout-diffusionduringthefabricationprocess(Nodaetal1975).TheguidecansupportonlydominantTE00andTM00modesat1.064mm,anduptothird-ordermodesat0.532mm.
Figure5.26showsthesecondharmonicpowerversusfundamentalfrequencypowerunderaphasematchedconditiondescribedinthesequel.Experimentalresultscoincidewiththoseshownbythesolidlinewithaslopeof2.The
Fig.5.25Experimentalconfigurationofthesecond
harmonicgenerationusingathree-dimensionalLiNbO3opticalwaveguide(UesugiandKimura1976).
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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
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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
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Fig.5.27Harmonicpowertemperaturedependence.Insettedphotographsshowtypicalnear-fieldpatternsofsecondharmonicwaveguidemodes(Uesugiand
Kimura1976).
Fig.5.28Calculatedphase-matchingtemperaturedifference
betweenTM00andTM20ofathree-dimensionalLiNbO3opticalwaveguide.FundamentalfrequencymodeisassumedtobeTM00.
Theexperimentaltemperaturedifferenceisshownontheordinate.Thewaveguideheightbisestimatedtobeabout5mmfromaninterference
fringemeasurement(UesugiandKimura1976).
onthecompositionofLi2OandNb2O5andonwaveguidedispersion.Itisalsoaffectedbythepyroelectriceffectwhenthecrystaltemperatureisswept.However,thephasematchingtemperaturedifferenceDTbetweenthesecondharmonicdominantTM00modeandthehigherTM20modeareinsensitivetothecompositionand
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pyroelectriceffect.Figure5.28showsthecalculatedtemperaturedifferenceDTasafunctionofthewaveguideheightb.Hereitisassumedthattheindexprofileisastepdistributionoverthecross-section.ThepropagationconstantiscalculatedaccordingtoMarcatili'sapproximation(Marcatili1969).Sellmeier'sequationwasusedtoexpressthetemperatureandwavelengthdependenceofrefractiveindices.Figure5.28servestoexpressseveralaspectratios(a/b).ThesolidlinecorrespondstotherefractiveindexdifferenceDn=0.0025.TheexperimentalresultshowninFig.5.27isequaltoDT=17ºC.
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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-
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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
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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
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wherelisthewavelengthofthefundamentalwaveinvacuum,n(l)istheopticalindexforwavelengthl.TheconditionforQPMis
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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
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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.
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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
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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.
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Fig.5.32VariationofSHGintensitywithincidentpolarizationangleforaZ-cutLiNbO3crystalwiththeXaxisperpendiculartotheplaneofincidence.Crossesareexperimentalpointsandthesolidlineisfromtheoreticalcalculationsfor(a)p-polarizedand(b)s-polarized
outputbeams(Hsuetal1992).
Fig.5.33(right)VariationofSHGintensity
withincidentpolarizationangleforX-cutLiNbO3crystalwiththeZaxisperpendiculartotheplaneof
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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
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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
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etal1992).
byCaoetal.(1991)isduetoneglectofthereflectedsecond-harmonicfieldonboththed33discontinuityatthefilm-substrateinterfaceandangulardependenceofthenonlinearpolarization.TheresultsreportedbyHsu,etal.(1992)indicatethatLiNbO3samplesproton-exchangedfor0.5hat180ºCshowedsomerecoveryofthenonlinearcoefficient,whilstsamplesthatwereproton-exchangedfor1and1.5hdidnotshowanymeasurablerecoveryunderthethermalannealingconditionsused.
Theprotonexchangeprocessfollowedbyannealingmayproducehigherlatticedisorderatthetopsurface,whichcouldexplainwhyitispossibletoseesomewaveguideSHconversioneventhoughthenonlinearcoefficientisdegraded.
IncontrasttoLiNbO3,LiTaO3showedonlypartiallossofopticalnonlinearitymeasuredat532nmuponp-exchangeusingeitherpyrophosphoricacidorbenzoicacid.ThermalannealingproducedonlysmalllossinnonlinearityofLiTaO3p-exchangeinbenzoicacid.Completelossofnonlinearitywasobservedinthecaseofpyrophosphoricacid.TheseresultsalsodifferfromannealingresultsforLiNbO3wheresomerecoveryoftheopticalnonlinear
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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.
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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.
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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.
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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
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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
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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
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thesurfaceandleadstoacharacteristictemperaturedependenceofthedamagethreshold.Zverevetal(1977)hypothesizedtheexistenceinLiNbO3ofanoxygen-depletedabsorptionsurfacelayercontainingtwotypesoftrapslinkedwithoxygenvacanciesandwithreducedNb4+.Anincreaseofabsorption,frompulsetopulse,inthesurfacelayerisduetoaccumulationofelectronsonshallowtrapswhoseabsorptioncross-sectionislargerthanthatofdeeptraps.Anincreaseoflightresistanceofthesurfacewithincreasingspecimentemperatureiscausedbytheemptyingofshallowtrapsforthetimebetweenlaserpulsesduetotheirthermoionization.
InvestigationsofradiationresistanceofLiNbO3filmsandtheirsubstrateshaveshownthatthemechanismsoftheirdamageareabsolutelyidentical.
AQ-switchedgarnet-neodymiumlaser(l=1.06mm,pulseduration10
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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
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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
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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.
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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.
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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
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(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)).
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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
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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,
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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.
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Thehighestdiffractionefficiency(definedaspowercoupledoutinthediffractedbeamdividedbysumofpowerscoupledoutinboththediffracted
Fig.5.43Schematicofapparatususedtowriteanddetectgratingsina
slabwaveguide.Thegratingvectorisparalleltothec-axisoftheLiNbO3slab.Allopticalbeampolarisationsareparallelto
thesurfaceoftheslab.PinandPoutareprismimputandoutputcouplers(Woodetal1975).
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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
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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.
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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
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Fig.5.44clearlydisplaythequadraticbehaviourindicativeofthetwo-photoneffect.Fromthemaximumpowerincidentuponthecouplingprismof2kWandestimatesofthecouplingefficiencyandeffectivewaveguidethickness,onecanestimateamaximumpowerdensityof106W/cm2inthewaveguide.Diffractionefficienciesofseveralpercentwereobservedwithnosignofsaturation.Comparisonoftheseresultswiththedata(vanderLindeetal1974)obtainedusingthesamewavelengthbutinabulkconfigurationshowsafargreatersensitivityforthewaveguidecase.Thediscrepancyislargerthancanbeaccountedforbyexperimentalerrorsorerrorsinestimatingthepowerdensityinthewaveguide.Thediscrepancymaybeduetovariations
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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
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couplingtwobeamsintotheplanarguide,asshowninFig.5.45sothattheyformathickhologrambymeansofthephotorefractiveeffect.Themagnitudeoftheindexchangecanbemeasuredfromthediffractionefficiencyofthehologram(Kogelnik1969)
where istheinteractionlengthandqistheanglebetweenthetwobeams.Thewritingbeamswerecoupledinandoutofthewaveguideusingasingleprism(Saridetal1978),andthediffractionefficiencywasprobedwithaHe-Nebeambyrotatingtheentireprism-waveguideassemblytoobtaincouplingatdifferentwavelength.
Hologramscouldnotberecordedat0.633µm,with300µWofoptical
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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.
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Theinducedhologramwasfoundtorelaxveryrapidlyafterexposure.Forthisreason,longexposureswerealwaysfoundtobelessefficientthanshortexposuresforrecordingholograms.ForshortexposuresthedatainTable5.10gives
Usingthevalueofa=0.08l=0.633and0.515µm(Glassetal,1980)theresultisaphotorefractivesensitivityof
Thisresultisevensmallerthanthatobtainedforthesubstratecrystal,andhencedespitetheexperimentalerrorstheyprovideconclusiveevidencethat
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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
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wavelength,andDn(t)theaverageindexchange
Theprobelightof1.3µmwasinputfromportB.SinceopticalwavesoftwowavelengthsweremixedatoutputportC,theprobelightwaschoppedat270HzbeforeenteringportBandtheprobeoutputwasmeasuredbyalock-inamplifierplacedafteraphotodetector.Theprobelightintensitywaskeptbelow5µWtoensurethatnophotorefractiveeffectwascausedbytheprobe(Fujiwaraetal1989).PortDmonitoredanytemporalvariationofthe1.3µmprobelightduetoinputfibre-waveguidecoupling.
InFig.5.46,thewaveguidewidthis7µmandtheangleqofwaveguidebendingis1.7°.ThelengthLoftheinterferometerarmsis16mm.
Boththeirradiationandprobebeamswerefedthroughopticalfibresbutt-coupledtoinputportsAandBThequantitiesDneandDnocanbedeterminedseparatelybyadjustingtheinputprobepolarizationtotheTMandTEmode,
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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,
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unequalpowerinthetwoarmswouldlimittheextinctionratioofthemodulatortoabout15dB.However,sincetheirradiationintheupperbranchinducesanindexchange,theYbranchbecomesasymmetric,reducingthebranchinglossfrom3dB.Thisopticallyinducedasymmetryexplainstheextinctionratiohigherthan15dB.Further,therelativelyhighextinctionratioindicatesthataspatiallyhomogeneousindexchangewasmeasured;scatteringduetospatialinhomogeneityofindexchangewasnotappreciable.
AphotoinducedindexchangeofDn10-5wasdetectedandafurtherimprovementofthesensitivityshouldbefeasiblewithdesignmodificationssuchasmodulatingtheprobelightbyanexternalfieldapplieduponthelowerarmoftheinterferometer.
Sincetheinterferometeroutputcanbeexpressedbyequation(5.65),theobservedtemporalchangeoftheoutputcanbeconvertedtothetimeevolutionof .ForallwavelengthslirandirradiationintensitiesIir,agoodfittoanexpression
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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
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averagedirradiationintensityIiratthearmwascalculated.ThedependenceofSonIircanbedecomposedtothebehaviourof andtasisseeninequation(5.66).The wasfoundtobeinitiallyproportionaltoIirandthenshowedaslightsaturationathigherIir,whereastheinversetimeconstantofbuildup,1/t,wasnearlyconstantuptoIirof40W/cm2andthenshowedasharpupturnathigherirradiationintensities(Izutzuetal1982).InthefirstregionwhereIirissmall, isproportionaltoIirwhile1/tisconstant,renderingStobenearlyconstant.
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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
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recombiningattheequilibriumsites(SearleandGlass1968).InTi-diffusedLiNbO3therelaxationoftheindexchangewasfoundtobehyperbolic,i.e.Dnl/t(Glassetal1980).AgoodfittotheexperimentalrelaxationcurveisshowninFig.5.49.Thisbehaviour
Fig.5.49Relaxation(at300K)oftheinducedrefractiveindexchangeinplanarLiNbO3waveguides.ThepointsarecalculatedassumingabimoleculardecayDna/t
(Glassetal1980).
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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
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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
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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,
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Fig.5.50Timedependenceofrefractiveindexchange
Dn(t)inAPELiNbO3waveguidesforirradiationintensitiesof65.4and105.3W/cm2atanirradiationwavelengthof488nm.Solidcurvesrepresentfitto
Eq.(5.67)(Fujiwaraetal1992).
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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
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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
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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
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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.
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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
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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).
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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
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axisatanangleof32.75Åfromthecleavededge.Ascribemarkismadeonthewaveguide-containingsurfaceatoneedgeoftheplate;twopairsoftweezersoneithersideofthemarkareusedtomakethebreak.Asisusualoncleavedsurfaces,anumberofterracesappears,asindicatedschematicallyinFig.5.54.TheedgesoftheterracestepsareindicatedbythedottedcurvesinFig.5.54.Thecharacteroftheterracesandthenatureofthecleavedendfacetdependuponwhetherthebreakstartsnearthenegativeorpositiveendofthezaxis.
ThecleavageplaneinLiNbO3wasidentifiedasa{102}plane.However,
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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
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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
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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
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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
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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
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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
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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
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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.
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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
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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
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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
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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).
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Fig.5.59OscillogramofahysteresisloopofaLiNb0.1Ta0.9O3
film.T=750°C,f=60Hz,[email protected]/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
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pyroelectriccurrentJpbutwithaphaseshiftp/2.
Thismethodhasbeenemployedtoinvestigateferroelectriccrystals(CarnandSharp1982).Uniformtemperaturedistributionthroughoutthecrystalthicknesscanbeattainedonlyatverylowmodulationfrequencieswsince .Determinationofthephaseshiftbetweenpyroelectricandnonpyroelectriccurrentsischaracterizedbylowsensitivity.Thephaseshiftj,ascanbereadilyshown(CarnandSharp1982),isequaltoarctan(Jpmax/Jnpmax).Examinationofthinferroelectricfilmsbythismethodhasmadeitpossibletosingleoutthecontributionofpyroelectriccurrentandtomeasurelvaluesuptoabout3%.Thepyroelectriccoefficientisfoundfromtherelationl=Jp.max/(SDTw),wheresisthesamplearea.
5.9.2.2Thethermalpulsemethod
Thedirectionofpyroelectriccurrentinaferroelectricisdeterminedbythe
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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
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measurementscorrespondstothethicknessresolutionof3-5×l0-8m.Analysisoftheeffectofradiationonbothelectrodesmadeitpossibletodirectlydiscoverthehead-ondomainstructureinthesample.Suchastructurecausesoppositepyroelectriccurrentpolarityuponirradiationofeachoftheelectrodes.Currentpolarityisdeterminedonlybythepolarizationdirectionanddoesnotdependontheheatdistributiondirection.
Structureswiththecaxisnormaltothesubstrateplanewereusedinmeasurements;chromiumfilms(10-7minthicknessand(1-3)×10-6m2inarea)manufacturedbythethermalsputteringmethodwereusedaselectrodes.
AtypicaloscillogramofpulsepyroelectricsignalsispresentedinFig.5.61.Analysisofthebehaviourofpulsepyroelectriccurrentresponseofthestructuretothelightpulsebothfromthefilmandsubstratehasshownthatspontaneouspolarizationofthefilmisalignedalongthesubstratepolari-
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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.
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TheexperimentalsetupfordeterminationofSeebeckcoefficientincludedamainfurnace,upperandlowermicroheaters,thermocouplesandaspecimen(RekasandWierzbicka1983).
Fig.5.61Oscillogramofapyroelectricsignaltolightpulse.1)lightpulse,2)pyroelectricresponseofthefilm,
3)responseofthesubstrate.
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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
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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
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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
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mVto367.5mV,whileforlithiumtantalateitchangesfrom28mVto1680mV.Attemperaturesabove1200K,Thomsoncoefficientsforlithiumniobateandtantalatedonotchangeappreciably.
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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
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alowerrefractiveindexwhichplaystheroleofanopticalinsulator.Nootherinsulatinglayersofothermaterials(SiO2,Al2O3)appliedinanumberofintegratedsystemsareneededheresinceseparatinglayersaregrowninaunifiedtechnologicalcycleofobtainingdevicestructures.
WeshallnowcarryoutacomparisonstudyofTi-diffusionandepitaxialtechniquesofintegro-opticdevicesonanexampleofelectro-opticswitchingelementsincrossing-channelwaveguidesorelectro-opticX-switchers(Betts
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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
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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
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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
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wheredistheinterelectrodegap,Gistheoverlapintegraloftheelectrodefieldandthemodefield: dA,whereEisanormalizedfieldofthemode,xisanappliedelectricfield,Visvoltage.
Theconditionfora100%modulationdepthcanbewrittenas
whereDb=(2p/l)dn*,Listheinteractionlengthbetweentheappliedfield
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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
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photogalvaniceffect(Schmidtetal1980;YamadaandMinakata1981).
6.1.2Bandwidth
Thewidthofthemodulatorfrequencybandisdeterminedbyelectrodecapacitanceprovidedthattheelectrodelengthismuchsmallerthanthewavelengthoftheradiofrequencysignal.Itcanbeshownthatthecapacitanceofthesystemofelectrodesperunitlengthisequalto(Alferness1982)
wherers=(d+1)/2G, ,Gistheelectrodewidth,for(LiNbO3)isthedielectricconstantandKisthe
ellipticintegral.
TheratioC/Ldecreasesandthebandwidthincreases(Df=(pRC)-1,Ris
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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
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reductionoftheelectrodewidthis,however,limitedbytwofactors.First,itshouldnotbemademuchlessthanthewaveguidewidthlesttheoverlapoftheelectricandopticalfieldsshouldbesmall.Second,whentheelectrodewidthissmall,theresistanceincreasesandthebandwidthdecreasesaccordingly.
Sincethecontrolvoltageandthebandwidthareinverselyproportionaltothedevicelength,thecontrolvoltage-to-thebandwidthratiocanbethoughofasafigureofmerit:
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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
[email protected],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
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ofthemodulationdepthonthephaseshifthastheform(Barnoski1974):
whileforwaveguidingdevicesemployingphasechangeintheconnectionoftwowaveguidesortwowaveguidemode
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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
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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
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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
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betweentheelectrodes.Whenthepoweroflightwasabout25µW,thedegreeofconversionmadeup95%andthecontrolvoltageincreasedupto7V.Themodulationcurvewasobservedonanoscillographscreentotheinputofwhichasignalwassentfromthephotomultiplierthatregisteredthepoweroflightcomingfromthewaveguide,andasawtoothvoltagewiththeamplitudeof8Vwasappliedtotheelectrodesduring1µs.Thepowerofthe fell( µw)asshowninFig.6.4a,whilethepowerofthe
Fig.6.4Extraordinary(a)andordinary(b)wave
polarizationpowervsvoltage(Kazansky1985).
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-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
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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
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ofpumpinglengths(Papuchonetal1975),whichisdifficultfromapracticalpointofview.Toeliminatethisdefect,suchelectrodesweresuggestedthatcreateincoupledwaveguidesthedifferenceofpropagationconstantsDb=b2-b1whichreversessignanintegralnumberoftimesequaltothenumberofpumpinglengths.Usingthismethodinatwo-sectiondevicegaveanon-offratioof27dBforacontrolvoltageof30V(SchmidtandKogelnik1976).
Thesolutionofthesystemofequations(Kazinsky1985)
forcoupledwaveguideswithavariablesignofDbinthematrixformis(KogelnikandSchmidt1976)
where isthematrixforthemodulatorregionwith
; ;
sin
B1=ksin[x(k2+d2)1/2]/(k2+d2)1/2,wherek=2p/listhecouplingconstant,
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Fig.6.6Modulatoronthebasisofcoupledwaveguides
withavariableDb.1,2)waveguide(Zolotoveta11982).
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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
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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
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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.
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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
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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
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voltageisappliedwithapolaritycorrespondingtoanincreaseoftherefractiveindexinacrystal,intheregionundertheelectrodesthereformsachannelwaveguide(Channin1971).Themodeofthiswaveguidehasasmalltransversedimensioncointhewaveguideplaneand,therefore,alargerdiffractiondivergence~l/w.InthefartherregionthismodemustinterferewiththemodeofaplanarTi-diffusedwaveguide(whichbelongstothecontinuumofradiationmodesofthechannelwaveguide)havingasubstantiallylargertransversedimensionWandasmallerdivergence~l/W(i.e.asmallangulardimensioninthefarregion).Thephasedifferenceofthese
twowaves ,wheredn*isthedifferenceofeffectiverefractiveindices)dependsonthemagnitudeoftheappliedvoltage.Inthecasewhenwavesareinthecounterphase
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( ),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
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andinthecaseofcounterphasesubtraction,accordingly(Fig.6.11)
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Fig.6.10Modulationcharacteristicofaninterference
typemodulator(Kazansky1985).
Fig.6.11Interferencepatternsinthefarregion.Inphasewaveinterference(/+)andcounterphasesubtraction
(/-)(Kazansky1985).
Fromthisweimplytheconditionwheninthecentreoftheinterferencepatternthelightintensitywillbeequaltozero
Toperformanexperimentonasubstrateoflithiumniobate(y-cut),aplanarwaveguidewasmanufacturedbywayoftitaniumdiffusion(theTilayerthickness300Å).Theelectrodestructurewasdepositedphotolithographicallyonthecrystalsurface,asshowninFig.6.9.Thiselectrodestructureconsistedoftwoparallelaluminiumstrips5mmlongand4µmwide.Thedistancebetweentheelectrodeswas6µm.
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He-Nelaserradiationwasintroducedintothewaveguidebymeansofarutileprism.Beamfocusingbyalensewithafocusdistanceof20cmmadeitpossibletoobtainthedimensionoftheGaussianbeamWatthewaveguideinputequalto60µm.Asthepotentialdifferenceontheelectrodeschangesfrom0to5V,thefieldpatterninthefarregionchangesaccordingtothemodelconsideredabove,andthemaximalmodulationdepthobtainedforV=5Vwas95%(Fig.6.10).Figure6.11presentsthemodulationcurveofsuchamodulatorobservedonthescreenofanoscillograph(theappliedvoltagevariedfrom0to20V).Themodulationcurvehasmaximaandminimatypicalofinterferentialphenomena.Itshouldbenotedthatalowvalueofthecontrol
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Fig.6.12Totalinnerreflectionmodulator(Kazansky1985).
voltage,alargemodulationdepthandthepossibilityofrealizingawide(~1GHz)modulationbandmakethistypeofmodulatorsfairlypromisingforpracticaluse.
Tsaietal(1978)andSheem(1978)consideredthemechanismofoperationofthetotalinternalreflectionmodulator,shownschematicallyinFig.6.12.
Whenvoltageofanappropriatepolarityisappliedtotheelectrodes,intheregionbelowtheelectrodestheelectro-opticeffectresultsintheformationofalayerinwhichtheeffectiverefractiveindexofthewaveguidemodeisdecreasedbythevaluedeterminedbytherelation(6.3).MakingallowanceforthisrelationonecancalculatethereflectionfactorofthewaveguideH-modeincidentontheperturbedlayeratanangleq1(BornandWolf1979)
where
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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
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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
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about1GHz(approximately500psswitchingtime)andrequirerelativelylongdevicelengthof3to10mm.Highsinusoidalmodulationrateshavebeenachievedusingatravelingwavegeometry,againwithlongdevicelength(Izutsuetal1977).Auniquelydesignedandfabricatedopticaldirectional
Fig.6.14Schematicdrawingofopticalwaveguidedirectionalcouplerswitchmodulator(Alfernessetal1981).
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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
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waveguide(assumingonecouplinglength)is
wherethepush-pulleffectforelectrodesplacedontopofthewaveguides(Fig.6.14)hasbeeninduced.Visthemaximumadmissiblecontrolvoltage,nistherefractiveindex,lthewavelengthandathegeometricaloverlapbetweentheopticalandappliedelectricfields.Therequiredlengthistherefore
Fromequations(6.22)and(6.24)theRCswitchingtimeis
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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
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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
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Fig.6.16Fabricationstepsforachieving1µmelectrodegap
alignedoverthe1µminterwaveguidegap(Alfernessetal1981).
shortelectricaldrivepulsesfromanelectricalcombgeneratordrivesthemodulator.Thesepulsesareinsynchronismwiththepicosecondopticalpulsesfromasynchronouslypumpedmode-lockeddyelaser.Theopticalpulsesarecoupledintothedevice.Themodulatorresponseismappedoutviasamplingbyusinganelectricalphaseshiftertosweeptheopticalpulsetraintemporallyacrosstheelectricalpulsetrainandmeasuringthemodulatoroutputversustimeshift.
6.4.2Thin-filmelectro-opticlightmodulator
Kaminowetal(1973)demonstratedtheutilityofthinfilmsbybuildingandtestinganefficientwide-bandLiNbO3phasemodulatorwhosecharacteristicscanbesatisfactorilyaccountedforbythebulk
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electro-opticcoefficientofLiNbO3.
Thepowerperunitbandwidth,P/Df,requiredtodriveabulkmodulatorrodoflengthLandsquarecrosssectiond2wasproportional(KaminowandTurner1966)tod2/L.Theminimumvalueofthisfactorisdeterminedbydiffractionofthelaserbeampassingthroughthemodulatorcrystal.Withthebeamfocusedsothatthewaistoccursatthecentreoftherod,theminimumvalueford2/Lis4l/np,wherelistheopticalwavelengthandnistherefractiveindex.Forthisminimumcondition,thepowerdensityattheedgesofthe
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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.
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AsindicatedinFig.6.18,thewidthoftheelectrodes,a,ischosensothat .ThecapacitanceCforacoplanarcondenserwitha=bonauniaxialcrystallikeLiNbO3havingdielectricconstantsea=43andec=28along
Fig.6.17Thin-filmLiNbO3electro-opticphasemodulator(Kaminovetal1973).
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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
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Df=3.2GHz.Transit-timelimitationsareabove3.2GHzforL=6.2mm.
Forthecrystalcaxisorientedalongy,thephasemodulationindexis
wherer33istheelectro-opticcoefficientand istheeffectivemodulatingfield.Thefactoruisanumberlessthanunitythattakesaccountofthefact
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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
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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
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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
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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
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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-
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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
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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
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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,
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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.
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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))
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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
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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.
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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
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showninFig.6.22.Themechanismforinteractionreliesonthefringingelectricfieldsextendingbelowthesurfacebetweeninterdigitalstripelectrodesformedonthecrystalsurface.Thelocalfringingfieldstrengthshouldbereasonablyuniformacrosstheguidedbeamandapproximatelysinusoidalintheplaneoftheguidinglayer,transversetothebeam.Thismaybemostreadilyachievedbyapplyinganisolatinglower-indexlayerabovetheguidinglayer.Thisservestheaddedfunctionofminimizinginteractionoftheopticalbeamevanescenttailwiththelossymetallicsurfaces.Bragg
Fig.6.22Phasegratingformationbythe
electro-opticeffect(Tangonaneta11978).
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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
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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
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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
where
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Table6.1liststherelevantelectro-opticanddielectriccharacteristicsofLiTaO3andLiNbO3at0.53mmand1.06mm.ThesedataareusefulinthedesignofadoubledNd:YAGcommunicationlink.Thechangesine1ande2forLiNbO3ingoingfromtheunclampedtoclampedconditionarequitelarge,
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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
51 78
41 43
45 32
43 28
(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
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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
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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
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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
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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%.
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Theresultsofmeasurementsmadeat1.06mmareplottedinFig.6.25.Themeasureddiffractionefficiencywas98%withanextinctionratioof300:1,or24.7dB.
Fig.6.25Resultsofdiffractionmeasurementsat
1.06mmshowing98%maximumfirstorderdiffractionanda300:1extinctionratio
(Tangonaneta11978).
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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
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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-
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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).
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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
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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
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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
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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.
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Theparameterkeisgivenby
wherekisthecouplingcoefficientwhichappearsinthecoupledwaveequations(Kenanetal1974).Maximumdiffractionoccurswhend=0,whichisusuallyobtainedbyensuringthattheguidedwaveisincidentattheBraggangle.Itisalsousefultonotethatamisalignmentinthedirectionoftheincidentlightcanbecompensatedforbyapplyinganappropriatevoltage.Furthermore,
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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
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Fig.6.28Modulatorefficiency(100%=completeextinction)versusappliedvoltageacrossthe1.59mmelectrodegap.Solidline
correspondstotheory(seethetext)(Goruketal1981).
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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
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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
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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
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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×
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Fig.6.29Designoftheelectro-opticallyinduced
waveguide(Baumerteta11985).
Fig.6.30Near-fieldlightdistribution(l=0.633mm)
(Baumerteta11985).
Fig.6.31Calculatedintensitydistributionforan
appliedvoltageof35V(l=0.633mm)(Baumert
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etal1985).
microscopelenseswereused.Withnoelectricfieldapplied,onlysomelightspotscausedbydiffractionatstress-induceddomainsatthecrystalendfaceswereobserved.Increasingtheappliedvoltageupto30V,anon-offratioof12dBcouldbemeasured,clearlydemonstratingafield-inducedincreaseoftherefractiveindexncbetweenthetwoelectrodes.Baumertetal(1985)measured
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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
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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.
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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
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Fig.6.33Calculatedoutputpolarizationangleq0vs
themodeconvertercouplingstrengthkLforvariousinputpolarizationanglesq1.TheincidentrelativeTE/TMphaseisassumedtobezero(AlfernessandBuhl1981).
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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
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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,
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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
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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.
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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
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Fig.6.35(a)Lightbeaminamediumofvariablerefractiveindexn(x,y).(b)Diagramshowingtheprocessofoptimisingthedeflectionofalightbeam.
(c)Experimentalarrangementusedtodeflectalightbeamthroughrefractions.(d)Experimentalarrangementusedtodeflectalightbeamthroughincompletereflection(DqT)and
refractions(DqR)(Tienetal1974).
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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
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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
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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
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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
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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
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Fig.6.37Schematicdiagramofthepolarization-independentopticalfilter(WMC,polarizationconvertervoltage;VTbirefringencetuningvoltage;Vc,polarizationsplittertuningvoltage)(Waranskyetal1988).
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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
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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
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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.
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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):
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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
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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).
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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
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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
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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.
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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
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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
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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
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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
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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,
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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
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comparedwithothermaterialsinadditiontohavingamuchlargermodulatorfigureofmerit.ItshighopticaldamagethresholdsuggeststhatKTPwaveguidedevicescouldbeusedtocontrolorconverthigh-intensityopticalbeamswithinputwavelengthsextendingfromthevisibletotheIR.KTPwaveguidedevicesshouldbemuchlesssusceptibletopiezoelectricandpyroelectricinstabilitiesbecausetheseeffectshavenotbeenobservedinbulkdeviceapplications,andhencedevicethermalandmechanicalstabilityshouldbemuchbetter.
Severaldemonstrationelectro-opticandnonlinearopticdeviceshavebeenfabricatedbyusingKTPwiththewaveguidefabricationprocessdescribedinchapter2.Themeasured forseveralsingle-channelphasemodulatorsindicatesthatthewaveguidefabricationprocessdoesnotaltertheelectro-opticcoefficient.Usinga6mmwidechannelwaveguideanda0.2mmMgF2bufferlayer,andcouplingtotheelectro-opticcoefficientrc2,BierleinandVanherzeele
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(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
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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
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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
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interactionsarephasematched.Ascanbeseenfromthefigure,blue/greenlightcanbegeneratedatwavelengthsconsiderablyshorterthanthatobtainedbySHGinthebulkcrystal.
Lightfromatitanium-sapphirelaserinthe900-1000mmrangewasusedtosimultaneouslyexcitetheTE0andTM0modesofthewaveguide.Asthewavelengthofthelaserwastuned,SHGinteractionsinvolvingexcitationofhigher-orderTEmodesatthesecondharmonicwereobserved.ThemeasuredwavelengthsatwhichtheseinteractionsoccurredareshowninTable6.5,alongwiththecalculatedvaluesfromFig.6.40.Themeasuredandexpectedwavelengthsforthevariousinteractionsareingoodagreement.ExcitationoftheTE0modeatthesecondharmonicwasexpectedtooccurforafun-
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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
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instructurefromtheprevioussegment,orcouldevenbeasinglesectionwithcontinuouslyvaryingpropertiessuchthat .Toillustratethemethod,thesimplifiedcasewasconsidered,wherethesecond-harmonicgenerationinaperiodicwaveguidestructureconsistedoftwosectionspersegmentasshowninFig.6.41.Forthiscase,afairlysimplequantitativerelationforthegeneratedoutputpowercanbeobtained.Inthestructuresconsidered,thelengthofthesectionsdeviatedstronglyfromtheBraggconditionandtherefractiveindexdifferencesbetweenthesectionsweresmall.Therefore,thereflectioneffectsfromthesubsequentsectionsandthefundamentalbeamdepletioncouldbeignored.Withtheseapproximationsandextendingthisanalysis
Fig.6.41Segmentedwaveguidestructure(Bierlein1990).
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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
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segmentshaveinvertedferroelectricdomains,the-signcorrespondstoapurerefractiveindexgrating.Withthelowindexstepsusableinpractice,itcanbereadilyshownfromequation(6.80)thatthelattersituationleadstomuchlowerconversionefficienciesascomparedtothedomaininvertedcase.
Balancedphasematching(BPM)occurrswhenM=0inequation(6.79)andislimitedtophase-matchedSHGinKTPforawavelengthlongeraboutthat1mm(Bierlein,etal.1990).With theblueregionofthevisible
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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
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optimumfabricationtolerancesforphasefunctionresult.Thispropertyofthesegmentedstructureconstitutesamajoradvantageoveruniformwaveguides,wherethisdegreeoffreedominfabricationisabsent.Intheexperiments,onesegmentwasbulkKTPandtheotherwasanion-exchangedwaveguide.Withthismask24differentwaveguidewidth/segmentperiodcombinationscanbefabricatedonasinglesubstrate.Inatypicalexamplesegmentedy-propagatingwaveguideswerefabricatedonthez-surfaceofaflux-grownKTPsubstrate.UsingatunableTi:A12O3laser,thephase-matchingwavelengthsandconversionefficienciesforthesewaveguidesaregiveninFig.6.42.Overallfundamentalbeamthroughputfromthelasertothewaveguideoutput(includinglenses,couplingandwaveguidelosses)
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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
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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
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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
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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.
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7.YarivA.andYehP.(1984),OpticalWavesinCrystals,NewYork.
8.YarivA.(1985),OpticalElectronics,Holt-SoundersInternationalEditors,NewYork.
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Page371
Index
A
absorptionloss282
activationenergyforvaporization29
actualvaporizationflux30
angularmatching241
annealedproton-exchangedwaveguides56
autodiffusedlayers25
B
bandwidth295
Braggdiffractionmodulator315
Braggreflector247
bufferedmelts59
Bulkcrystallization131
C
capillaryliquidepitaxialtechnique78
channelwidth255
Cherenkovradiation245
cinnamicacid64
coherencelength248
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controlvoltage293
conversionefficiency245
copperdiffusion49
coupledchannelwaveguides302
criticalsupersaturation135
crystallizationfromagasphase6
Curietemperature16
Curie-Weissbehaviour16
Czochralskimethod132
D
degreeoffilmperfection1
dielectricimpermittivitytensor35
dielectricproperties285
diffusiondepth123
diffusionoftransitionmetals37
diffusion-induceddefects188
directelectron-beamwriting203
dislocationstructure191
domainconfiguration198
domaininversion203
domainstructure195
doublewaveguide23
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double-exchange'technique66
Dufoureffect139
E
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
F
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Fabry-Perotloss280
Fabry-Perotresonator260
Fermifunction229
Fermilevel135
ferroelectricfilms210
Fick'ssecondlaw27
filmgrowthrate141
flip-chipcoupling345
G
gas-transportepitaxy1
gas-transportepitaxy6
Gaussiannucleardamage24
Gaussianprofiles39
Glassconstant276
Glassmodel276
Gratingformation267
gratings266
H
holographicwriting267
homoepitaxialLiNbO3films178
hydrogenisotopicexchange58
I
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in-diffusioncoefficient65
indexchange274
insertionlosses293
interferometricMach-Zehndermodulator326
isothermalepitaxy105
J
Jouleeffect133
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Page372
K
Kerreffect48
Kikuchilines207
KLNcrystal121
KNbO3,inducedwaveguidecut-offmodulator331
L
Langmuirrelation28
Langmuirvapourpressure29
lasersputteringmethod17
layercomposition173
layerprecipitationtime124
lightresistance2601
LiNbO3birefringence245
liquid-phaseelectroepitaxy136
liquid-phaseepitaxy74
liquid-phaseepitaxy(LPE)technique83
lithiumniobate165
Lorentz-Lorenzformula36
M
Mach-Zehnderinterferometer271
Marcatili'sapproximation246
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maximalmodulationdepth293
MFESstructurexvi
micro-channelslab125
microdomains199
micromorphologyoffilmsurface186
modenumber231
modulationindex260
monocrystallinity175
N
negativebirefringence215
nucleationrate146
O
one-dimensionalwaveguides22
opticalmodes224
opticalproperties213
opticalswitchingtime309
opticalwaveguideswitchmodulator308
ordinaryrefractiveindex215
out-diffusedlayers26
out-diffusioncoefficient65
out-diffusionindexprofiles26
out-diffusionkinetics27
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out-diffusionsuppression34
P
partitioncoefficient128
PDRwaveguide247
PEwaveguide65
Peltiercoefficient132
perovskite118
phasematching239
photoelasticcoefficient47
photoinducedpolarizationconversion298
photorefractiveeffect269
photorefractiveproperties264
photorefractivesensitivity270
planarion-exchangedKTiOPO4waveguides68
planarwaveguides20
Pockelscoefficient68
potassiumlithiumniobate121
prismcouplingtechnique65
propagationconstant230
propagationloss12
protondiffusion62
proton-lithiumexchange52
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proton-exchangedLiNbO3182
proton-exchangedLiNbO3waveguides51
pseudo-Kosselpattern11
pulsedlaserdeposition17
pumpingpower240
pumpingwavelength240
pyroelectricproperties287
Q
QPM-SHGdevice202
quasi-phasematching200
R
Raoultlaw3
refractiveindexgradient31
rfsputtering8
ridgewaveguidemodulator317
Rutherfordbackscatteringspectroscopy16
S
'sandwichmethod'5
schemeofthegrowthcell95
Schröderequation91
secondharmonicgeneration237
Seebeckcoefficient289
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Sellmeierrelation215
Snelllaw217
spikelikedomains201
stationarycrystallizationmodel97
Stepanovmethod132
striplinestructures123
stripwaveguides21
substratemodes222
sum-frequencygeneration253
supersaturation101
surfaceindex72
symmetricwaveguides124
T
polarizationconversion345