SINGLECRYSTALGROWTHANDCHARACTERIZATIONOFZINTLPHASE THERMOELECTRICCOMPOUNDS By DavidM.Smiadak ADISSERTATION Submittedto MichiganStateUniversity inpartialoftherequirements forthedegreeof MaterialsScienceandEngineeringŒDoctorofPhilosophy 2020 ABSTRACT SINGLECRYSTALGROWTHANDCHARACTERIZATIONOFZINTLPHASE THERMOELECTRICCOMPOUNDS By DavidM.Smiadak Zintlphaseshavebeenthefocusofrecentthermoelectricresearchduetotheircomplexcrystal structures,whichincludecovalentlybondedanionicsub-structuresinalatticeofelectropositive cations.Thecovalentbondsleadtohighmobility,whilestrictelectron-countingrulescontributeto theformationofcomplexstructures,whichinturnleadtolowthermalconductivity.Inthismanner, thesecompoundscantheidealphonon-glassandelectron-crystalmodelforthermoelectric materials.AlthoughZintlphasesareapromisingclassofthermoelectricmaterialsthathavebeen studiedintensivelysince2005,therearestillseveralimportantfundamentalquestionsthatremain unanswered.Theseincludequestionsrelatedtoanisotropictransportandhowitrelatestothecrystal structure,andtheroleplayedbyintrinsicdefectsindeterminingcarrierconcentration.Additionally, theofZintlcompoundsiseverexpanding;throughtheuseofexploratorysinglecrystalgrowths andthecarefulselectionofstartingcomposition,novelcompoundsandstructuretypescanbe discoveredthatmaybepromisingthermoelectriccandidates. ZintlswiththeCa 5 M 2 Sb 6 (M=Al,Ga,In)structuretype,characterizedbyone-dimensional, ladder-likepolyanions,werepreviouslypredictedtohavehighlyanisotropicelectricalconductivity. Toinvestigatethisanisotropicbehavior,singlecrystalsofCa 5 M 2 Sb 6 (M=Al,Ga,In)weregrownin thecurrentworkviathemethod.Thesecrystalsgrewpreferentiallyalongthepolyanionic "ladders"ofthestructure,butonlymeasuredafewmillimeterslongbytensofmicronsthick. Characterizingthetransportpropertiesofthesecrystalsbothparallelandperpendiculartothe growthdirectiondemandedanovelcharacterizationtechnique,asplacingcontactsbyhandwas infeasibleintheperpendiculardirection.Micro-fabricationtechniqueswillbeutilizedwhereby micro-ribbonsareextractedfromcrystalsbothperpendicularandparalleltothepreferredgrowth directionusingafocusedionbeammillingtechnique.Photolithographywasthenutilizedtocreate acircuitofsensorsfortransportmeasurements.Theresistivity,carrierconcentration,andmobility ofamicro-ribbonofCa 5 In 2 Sb 6 perpendiculartothepreferredgrowthdirectionwassuccessfully characterizedusingthisapproach.Resistivitymeasuredintheparalleldirectionusingafour-probe resistivitysetupwasfoundtobenearly20timeshigherthantheperpendiculardirection, theoreticalpredictions. Experimentalinvestigationofintrinsicdefectsinsinglecrystalsisalsoexploredinthepromising Mg 3 Sb 2 system,accomplishedusingsinglecrystalX-raydiffraction.Thedefectchemistryof thissystemforbothMg-andSb-richsinglecrystalsynthesisisinvestigated,wherevacanciesand interstitialsitesareandincollaborationwithresearchersattheMaxPlanck InstituteforChemicalPhysicsofSolidsinDresden,Germany. Lastly,thediscoveryofanewquaternaryZintlphase,Ca 9 Zn 3 : 1 In 0 : 9 Sb 9 isreported,which wasdiscoveredasaby-productduringtheattemptedgrowthofZn-dopedCa 5 In 2 Sb 6 .Thenew Ca 9 Zn 3 : 1 In 0 : 9 Sb 9 structurewassolvedwiththehelpofcollaboratorsattheUniversityofDelaware. MeasurementsoftheelectricalresistivityoftheCa 9 Zn 3 : 1 In 0 : 9 Sb 9 crystalsperformedatMichigan StateUniversityshowedresultssimilartothatofalready-optimizedCa 9 Zn 4 : 5 Sb 9 compounds, pointingtopromisingthermoelectricperformance. IdedicatethisworktomywifeSaeeda, mydaughterandallmyfriendsandfamily. Withoutyou,noneofthiswouldbepossible. Iloveyouwithallmyheart. iv ACKNOWLEDGMENTS Iwouldliketoacknowledgemyadvisor,Dr.AlexZevalkink.Thankyouverymuchforyour guidance,assistance,knowledge,andgoodhumor.SecondlyIwouldliketothankmydoctoral committeeDr.CarlBoehlert,Dr.TimHogan,andDr.JasonD.Nicholasfortheiradviceand probingquestionsthathelpedshapethisworkforthebetter.Iwouldalsoliketothankmyfriendand colleagueMarioCalderónforhishelpinthelaboratoryandonthesoccerpitch.Specialthanksto MackMarshallandMeganRylkofortheirassistancewithsinglecrystalgrowthsynthesis.Alsoto Dr.W.AdamPhelan,ResearchScientistandAssociateDirectorofthePARADIMCrystalGrowth FacilityatJohnsHopkinsUniversityforhisadviseandassistance. Singlecrystalgrowthprojectswouldnotbepossiblewithoutpropercharacterizationandfor thatIwouldliketoexpressmygratitudetoDr.RichardJ.Staples,ManageroftheCenterfor CrystallographicResearchinMichiganStateUniversity'sDepartmentofChemistryandChemical Biology,forhisassistancewithsinglecrystalX-raydiffractionacrossallofourcompositionsand projects.IwouldalsoliketothankDr.SvilenBobevandhispost-docDr.SviatoslavBaranetsatthe UniversityofDelawarefortheirassistanceinresolvingtheCa 9 Zn 3 InSb 9 singlecrystalstructure, theirexpertisewasinvaluable. IwouldliketothankDr.DonMorelliandhisgroupforprovidingassistancewithelectronic transportcharacterization.Thisworkwouldnothavebeenasuccessifitwerenotfortheassistance ofDr.VijayPonnambalamandCoreyCooling. IwouldalsoliketothankmycolleaguesatboththeIFWandMaxPlanckInstituteinDresden, Germany.IhadthepleasureofworkingattheIFWDresdenasaGuestScientistforthreemonths, acrosstworesearchtrips,andhadawonderfullearningexperience.IwouldliketothankAlmut PöhlforherinvaluableworkFIBcuttingourcrystalsamples,CindyKupkaforprovidingassistance andtrainingintheMicrostructuringLab,andtoLauritzUleSchnatmann,ConstantinWolf,Sepideh Izadi,andVidaBaratiforprovidingday-to-dayassistance.IwouldliketothankDr.GuodongLifor hishelpfuladviceonphotoresistsandsamplerecoverytechniques.IamgratefultoDr.HeikoReith v forallowingmeintohislaboratoryandusinghisequipmenttocompletemyproject.Specialthanks toDr.NicolásPerezRodriguez,whowasmymaincontactattheinstituteandhelpedinanumberof waysoutsideofhisresponsibilitiesofprovidinglowtemperaturecharacterizationassistance.Lastly, IwouldliketothankDr.habil.GabiSchierning,HeadofDepartmentThermoelectricMaterials andDevicesformakingeverythingpossibleandprovidingassistanceinachievingourprojectgoals. ThisprojectwasasuccessduetothewonderfulteamattheIFWandIamverygratefulformy experiencethere.IwouldalsoliketoacknowledgethesupportprovidedbytheNational ScienceFoundation,IFWDresden,andMichiganStateUniversity. Mysuccesswouldalsonotbepossiblewithouttheloveandsupportofmywife,Saeedaand myyoungdaughterWehavefacedanumberofchallengesbutwehavedoneittogether.I amastrongerandbetterpersonbecauseoftheirIwouldliketothankmyclosefriends DavidandLaurenLuc,BenjaminandStaceyCrowgey,SamandSimoneKauffold,Brettand RachelJustice,andSteveandLilaHugheyallfortheircontinuedloveandsupportovertheyears, you'vemadethisexperiencesomuchbetterwithyourfriendship.Iwouldalsoliketothankmy family,especiallymyfatherMattSmiadak,whoasofthiswritingiscontinuingtoworkandprovide essentialstothecommunityduringthepandemicandtomymotherPamelaSmiadakwhocontinues toshowerloveonusandourdaughter.TheyhavebeenpillarsofsupportformesinceIwasborn andIcannotthankthemenough.Iwouldliketothankmybrother-in-lawSammyUsmanJr.and hisgirlfriendTiffanySavoie,mysister-in-lawCarmelScott-EmuakporandherhusbandOnomeall fortheirlovingsupportaswell. IwouldalsoliketothankJohnBrandenburgandJohnPloughfrommyEastLansingHigh Schooldaysforinstillingaloveofmathandscience.AndspecialthankstoDr.MehmetSözenfor providingmewithanindependentstudyduringmyundergraduateatGrandValleyStateUniversity andconferenceopportunitiesevenafterIhadgraduated.Reachingouttome,wasmotivationto takealeapbackintoresearchandgraduateschool. Lastly,thankyoualsotoallofthefrontlineworkerandessentialemployeesthatarecurrently riskingtheirlives,manyoutofnecessity,toprovideforothersduringthistime.Ihopethat vi welearnfromthisexperienceandcreateamorefairandequitablesocietyasaresult. vii TABLEOFCONTENTS LISTOFTABLES ....................................... xi LISTOFFIGURES ....................................... xiii CHAPTER1INTRODUCTION:THERMOELECTRICS .................. 1 1.1Thermoelectrics....................................1 1.2ThermoelectricEffects................................3 1.3ElectronicTransport..................................6 1.4ThermalTransport...................................7 1.4.1ElectronicThermalConductivity.......................7 1.4.2LatticeThermalConductivity.........................8 1.5Optimizationof zT ..................................9 CHAPTER2ZINTLTHERMOELECTRICS ........................ 13 2.1ZintlPhaseOverview.................................13 2.1.1Zintl-KlemmConcept.............................14 2.1.2ThermoelectricPerformanceofZintlPhases.................16 2.1.3A 5 M 2 Pn 6 ZintlPhases............................16 2.1.4AM 2 X 2 ZintlPhases.............................17 2.1.5A 9 M 4 Pn 9 ZintlPhases............................18 2.2SummaryofResearchDirection...........................19 2.2.1AnisotropicTransport.............................19 2.2.2CharacterizationofDefects..........................23 2.2.3UnexploredPhaseSpace...........................24 CHAPTER3CRYSTALGROWTHFROMMOLTENMETALFLUX ........... 26 3.1Introduction......................................26 3.1.1Ca 5 Al 2 Sb 6 ..................................26 3.1.2Ca 5 Ga 2 Sb 6 ..................................27 3.1.3Ca 5 In 2 Sb 6 ...................................27 3.1.4Ca 5 Al 2 Bi 6 ..................................28 3.2Background-SingleCrystalGrowth.........................28 3.2.1FluxGrowth..................................30 3.2.2FluxGrowthofZintlPhases.........................32 3.2.3Energy-dispersiveX-raySpectroscopy....................36 3.2.4SingleCrystalX-rayDiffraction.......................37 3.3ExperimentalMethods................................38 3.3.1FluxGrowth..................................38 3.3.2VaporTransport................................39 3.3.3MaterialCharacterizationTechniques....................39 3.4Results&Discussion.................................41 viii 3.4.1PhaseDiagramDeterminationandCrystalGrowthOptimization......41 3.4.2CrystalStructureandComposition......................52 3.4.3CrystalMorphology..............................59 3.5ConcludingRemarks.................................62 CHAPTER4 ELECTRONICCHARACTERIZATIONOFCa 5 In 2 Sb 6 SINGLECRYSTALS 63 4.1Introduction......................................63 4.2Background......................................64 4.2.1PhotolithographyforMaterialCharacterization...............64 4.2.2FocusedIonBeamMilling..........................65 4.2.3SelectionandTreatmentofPhotoresists...................65 4.2.4SpinCoating.................................69 4.2.5SoftandHardBakes.............................70 4.2.6Exposure...................................71 4.2.7FloodExposure................................71 4.2.8Developer...................................71 4.2.9SputterDepositionandLift-off........................72 4.3ExperimentalMethods................................72 4.3.1FocusedIonBeamMilling..........................72 4.3.2SubstratePreparation.............................73 4.3.3CircuitDesign.................................73 4.3.4PhotoresistApplication............................74 4.3.5SoftandHardBakes.............................74 4.3.6LaserLithography..............................74 4.3.7FloodExposure................................75 4.3.8PhotoresistDevelopmentandEvaluation...................75 4.3.9SputterDeposition..............................76 4.3.10Lift-off....................................77 4.3.11TransportCharacterization..........................77 4.4Results&Discussion.................................78 4.4.1RibbonProcessing..............................78 4.4.2CircuitDesign.................................79 4.4.3PhotoresistOptimizationandSelection....................81 4.4.4DevelopmentOptimization..........................84 4.4.5LineWidthRepeatability...........................87 4.4.6SputterDepositionEvaluation........................90 4.4.7Lift-off....................................90 4.4.8FinalOptimizedProcess...........................93 4.4.9TransportCharacterization..........................94 4.5ConcludingRemarks.................................99 CHAPTER5CRYSTALGROWTHANDCHARACTERIZATIONOFMg 3 Sb 2 ..... 101 5.1Introduction......................................101 5.2ExperimentalMethods................................103 5.2.1Synthesis...................................103 ix 5.2.2StructuralCharacterizationandMetallography................103 5.2.3TransportCharacterization..........................104 5.3Results&Discussion.................................104 5.3.1CrystalGrowthandMorphology.......................104 5.3.2StructureDescription.............................105 5.3.3ElectronicTransportProperties........................108 5.4ConcludingRemarks.................................111 CHAPTER6 STRUCTUREANDELECTRONICPROPERTIESOFNEWZINTL PHASECa 9 Zn 3 : 1 In 0 : 9 Sb 9 ........................... 112 6.1Introduction......................................112 6.2ExperimentalMethods................................113 6.2.1Synthesis...................................113 6.2.2StructuralandThermalCharacterization...................114 6.2.3ResistivityMeasurements...........................115 6.3Results&Discussion.................................116 6.3.1CrystalMorphologyandComposition....................116 6.3.2ThermalAnalysis...............................117 6.3.3StructureDescription.............................118 6.3.4ComparisonwiththeCa 9 Zn 4 : 5 Sb 9 StructureType..............119 6.3.5ElectronicTransportProperties........................121 6.4ConcludingRemarks.................................122 CHAPTER7CONCLUSIONS&FUTUREWORK .................... 123 7.1Conclusions......................................123 7.2FutureWork......................................125 7.2.1PhotolithographytoUnderstandAnistropicTransport............125 7.2.2FluxGrowthsforPhaseDiagramandNewCompoundExploration.....127 APPENDIX ........................................... 131 BIBLIOGRAPHY ........................................ 155 x LISTOFTABLES Table3.1: Viscositydataforselectedelementsalongwithdensityinformationfor singlecrystaltargetcompounds...........................34 Table3.2: CrystaldatacollectedfromsinglecrystalX-raydiffractionfortheCa 5 Ga 2 x In x Sb 6 compositions.Programsused:APEX2,SAINT,SHELXS97,SHELXL97,and OLEX2.Unitcelldimensionsareingoodagreementwithpublisheddata.....54 Table4.1: Optimizedtemperatureanddurationofsoftbakeforselectedphotoresists.AZ 926024 m misatwostepapplicationstartingwithAZ926010 m mlayer.AZ 5214Ewasoptimizedasapositivephotoresistandintheimagereversalstate...83 Table4.2:Developmenttimesforselectphotoresists......................84 Table4.3:Lift-offtemperaturesandtimesforselectphotoresists...............90 Table4.4: Anisotropicthermoelectricpropertiesat220and300Kforselectedone- dimensional(1D)compounds,vanderWaals(vdW)compounds,andcovalently bondedtwo-dimensional(Cov.-2D)compounds..................99 Table5.1: AtomicpositionsandoccupancydataforMg 3 Sb 2 singlecrystalsgrownfrom bothMg-andSb-riches.............................106 Table5.2: CrystallographicdataforMg 3 Sb 2 singlecrystalsgrownfrombothMg-and Sb-riches....................................107 Table7.1:Listofelementcombinationsforpotentialquaternarycompoundsintheform A 9 (T 1 x M x ) 4 Pn 9 .ReferencesareincludedforknownA 9 T 4 + x Pn 9 ternaries andknownquaternarycompoundstakingtheformA 9 (T 1 x M x ) 4 Pn 9 .......129 TableA1: Quantitativeresults:Ca 5 Ga 2 Sb 6 singlecrystalsfromaGa 73 Sb 42 Areas AŒFfromFigureA1.................................134 TableA2: Quantitativeresults:Ca 5 In 2 Sb 6 singlecrystalsfromanIn 73 Sb 42 Areas AŒFfromFigureA4.................................137 TableA3: Quantitativeresults:Ca 5 Ga 2 x In x Sb 6 singlecrystalsfromaGa 37 : 5 In 37 : 5 Sb 42 AreasAŒEfromFigureA7(left)........................141 TableA4: Quantitativeresults:Ca 5 Ga 2 x In x Sb 6 singlecrystalsfromaGa 37 : 5 In 37 : 5 Sb 42 AreasFŒJfromFigureA7(right)........................142 xi TableA5: Quantitativeresults:Ca 5 Al 2 Sb 6 withAl 73 Sb 42 AreasA-DfromFigureA10. 145 TableA6:Quantitativeresults:Ca 5 Al 2 Sb 6 withSb 20 AreasA-EfromFigureA13...148 TableA7: Quantitativeresults:Ca 5 Al 2 Bi 6 singlecrystalsfromaSn 15 AreasAŒG fromFigureA15-A16................................151 TableA8: Quantitativeresults:Ca 5 Al 2 Bi 6 singlecrystalsandcomponentsfroma Bi 20 AreasAŒGfromFigureA18.......................154 xii LISTOFFIGURES Figure1.1: Thermoelectricmodule(left)withdetailofsinglejunction(right).Charge carriersdiffusetothecoldside( T cold )foragiventemperaturegradient......2 Figure1.2: ThermocouplecircuitillustratingtheSeebeckeffectwhereavoltagediffer- ence, D V ,appearsacrosstheterminalatT 1 andT 2 (left).circuit illustratingthePeltiereffectwherebyanappliedvoltageproducesacurrent, I , creatingacoolingeffectatT c ,whileexpellingheatatT h (right).........4 Figure1.3: LayeredthermoelectricsBi 2 Te 3 (left),GeAs(center),andSnSe(right)with lowin-planeandhighout-of-planeresistivitywithmoreanisotropicbehavior observedforSeebeckcoef.........................10 Figure2.1: TheNaSiunitcellwithionicallybondedNacationsandcovalentlybonded anionicSitetrahedra([Si 4 ] 4 )(left).NaTlunitcellwithdiamondnetworkof Tlatoms(right)...................................15 Figure2.2: TheofCa 5 In 2 x Zn x Sb 6 samples,comparedagainstNa-doped Ca 5 Al 2 Sb 6 [ 1 ](left).TheforselectZintlphasecompounds withrespecttotemperatureafterdopingoptimization(right)...........17 Figure2.3: TheMg 3 Sb 2 structure(left),Ca 9 Zn 4 + x Sb 9 structure(center),andtheCa 5 Al 2 Sb 6 structures(right)..................................18 Figure2.4: TheorthorhombicunitcellofZintlphasesCa 5 M 2 Sb 6 (M=Al,Ga,In)(left) withisolatedone-dimensionalpolyanionicchainsconnectedbySb-Sbbonds (right)........................................20 Figure2.5: PreviouslyreportedbandstructuresofCa 5 M 2 Sb 6 (M=Al,Ga,In)com- pounds,illustratingahighdegreeofanisotropyinthevalenceband.The bandmass( m X U )paralleltotheanionicstructuresislighterthantheother perpendiculardirections( m X S and m X G )[2]..................21 Figure2.6: densityfunctionaltheory(DFT)calculationsforelectricalconductivity(left), Seebeckcoefcient(center)andpowerfactor(right)indifferentcrystallo- graphicdirectionsalongwiththepolycrystallineaverage[3]...........22 Figure2.7: Young'smodulustensorwithrespecttocrystallographicorientationforanisotropic Bi 2 Te 3 (top)andapproximatelyisotropicCa 5 In 2 Sb 6 (bottom)[ 4 ].Fermisur- faceofCa 5 In 2 Sb 6 ,apseudoone-dimensionalelectricalconductor[3](right)..23 xiii Figure2.8: (a)CrystalstructureofMg 3 Sb 2 withproposedinterstitialsites.(b)Defect formationenergyforSb-excessMg 3 Sb 2 withFermilevelat900K.(c)Defect formationenergyforMg-richMg 3 Sb 2 withundopedFermilevelat900K[5]..25 Figure3.1: ComparisonofthechainpackingbetweentheCa 5 Ga 2 As 6 (left)andCa 5 Al 2 Bi 6 (right)structure-types.TheCa 5 M 2 Sb 6 (M=Al,Ga,In)compoundsbelongto theCa 5 Ga 2 As 6 structure-typewiththedifferencebeinghowthepolyanionic chainsarepackedintotheunitcell.........................28 Figure3.2: Schematicdiagramofagrowthampule(left),containingquartzwool forcushioningduringtransportandcentrifuging,growthcruciblecontaining thecompoundandwhilethecatchcrucibleisempty.Thetwocrucibles areseparatedbyaaluminasievetocatchcrystalsanddrainliquidFlux growthcanbeusedoffstoichiometrytogrowincongruentmeltingcompounds (right)........................................32 Figure3.3: CharacteristicX-rayproductionfromincidentelectronsforenergy-dispersive X-rayspectroscopy(EDS)analysis(left).Electrontransitionsofmajorlines, characteristicoftheemittingatom(right).....................37 Figure3.4: Horizontaltubefurnacewithtwoampulespositionedoppositeeachother(left). Illustratedtemperatureandvapormotion(topright)withdeposited elementsvisibleonampulessurfaceafterprocessing(bottomright).....40 Figure3.5: (1)Oxford600lowtemperaturedevice,(2)X-rayemitter,(3)Charge-Integrating PixelArrayDetector(CPAD),(4)Cameraforviewingcrystal,(5)three-axis goniometer,and(6)samplemountedonnylonloop................41 Figure3.6: Differentialscanningcalorimetry(DSC)andthermogravimetricanalysis (TGA)dataforCa 5 Ga 2 Sb 6 fromroomtemperatureto1000 ° Cshowsin- congruentmeltingbeginningabove760°C.....................43 Figure3.7: TheCa-Ga-Sbternaryphasediagramwithknownbinaries(black),desired Ca 5 Ga 2 Sb 6 (blue),andotherternaryphases(purple).Unsuccessful(red squares)andsuccessful(greensquare)growthswereusedtodetermine theblacktielines.(upperright)Aplausiblepseudo-binaryphasediagramwas developedbasedonthesuccessfulgrowth.(lowerright)opticalimageof growncrystals....................................46 Figure3.8: TheCa-In-Sbternaryphasediagramwithknownbinaries(black),desired Ca 5 In 2 Sb 6 (blue),andotherternaryphases(purple).Unsuccessful(red squares)andsuccessful(greensquare)growthswereusedtodetermine theblacktielines.Aplausiblepseudo-binaryphasediagramforthesuccessful growth(upperright)andSEMimageofgrowncrystals(lowerright).....46 xiv Figure3.9: TheCa-Al-Sbternaryphasediagramwithknownbinaries(black),desired ternaryphaseCa 5 Al 2 Sb 6 (blue),andundesirableternaryphases(purple).Un- successful(redsquares)andsuccessful(greensquare)growthsdeveloped blacktielinesbetweencompounds.Aplausiblepseudo-binaryphasediagram forthesuccessfulSb 20 (upperright)andSEMimageofgrowncrystals (lowerright).....................................47 Figure3.10: TheCa-Al-Biternaryphasediagramwithknownbinaries(black),desired ternaryphaseCa 5 Al 2 Bi 6 (blue).Successful(greensquare)growthde- velopedblacktielinebetweencompounds.Aplausiblepseudo-binaryphase diagramforthesuccessfulBi 20 (upperright)andSEMimageofgrown crystals(lowerright)................................47 Figure3.11: LargeCa 5 Ga 2 x In x Sb 6 singlecrystalwithwellfacets(left).Similarly largecrystalbutconstructedofalargenumberofsmallerCa 5 Ga 2 x In x Sb 6 singlecrystalsgrowninparallel(right).......................48 Figure3.12: Aluminumvapordamagetothequartzampule,concentratedatthegapbe- tweenthecruciblesandsievepriorto(left).Carbon-coatedquartz ampulesformedaprotectivebarrier(right).....................50 Figure3.13: Alloyedreferencestructure(left).Linearrelationshipbetweenunitcellpa- rameterdimensionsbetweenalloyphaseCa 5 Ga 1 : 12 In 0 : 88 Sb 6 andunalloyed ternaryphasesCa 5 Ga 2 Sb 6 andCa 5 In 2 Sb 6 (right).................52 Figure3.14: (a)TheCa 5 Ga 1 : 12 In 0 : 88 Sb 6 crystalstructurewithselectatomlabels.Polyhe- drabondlengthcomparisonbetween(b)Ca 5 Ga 1 : 12 In 0 : 88 Sb 6 (c)Ca 5 Ga 2 Sb 6 , and(d)Ca 5 In 2 Sb 6 .................................53 Figure3.15: EDSanalysisof(a)Ca 5 Ga 2 Sb 6 crystalandelements,(b)Ca 5 In 2 Sb 6 crystals,(c-d)Ca 5 Ga 2 x In x Sb 6 singlecrystals,and(e-f)Ca 5 Al 2 Bi 6 single crystals.......................................57 Figure3.16: EDSanalysisofCa 5 Al 2 Sb 6 crystalsgrownfroma(a)Al 73 Sb 42 (b)Sb 20 (c)Sn 15 back-scatteredelectronimagetohighlightand(d) Sn 15 standardSEM..............................58 Figure3.17: SinglecrystalsmountedatsinglecrystalX-raydiffraction(SC-XRD)for(a) Ca 5 Ga 2 Sb 6 fromaGa 73 Sb 42 and(b)Ca 5 In 2 Sb 6 fromaIn 73 Sb 42 ..60 Figure3.18: Singlecrystalsof(a)Ca 5 Ga 2 Sb 6 fromGa 73 Sb 42 withrectangularcross sections,(b-c)Ca 5 In 2 Sb 6 fromsameGa 73 Sb 42 and(d)Ca 5 Al 2 Sb 6 from Sb 20 .....................................61 xv Figure4.1: (a)FalsecolorimageoftheNbPmicro-ribbon(green)withsputteredheater line(upperleft)andapairofthermometers.(b)usedtomea- suretheelectricalconductanceG=J/E.(c)usedtomeasure thermoelectricconductanceGT=J/ j Ñ T j withtheredandgreenendsofthe colorgradientrepresentinghotandcoldsidesofthecircuit[6]..........64 Figure4.2: Thephotoresistprocesssequenceforpositive,imagereversal,andnegative resists.Whilechemicallydifferentthroughthedevelopment,deposition,and lift-offphasestheyarestructurallyequivalentforlowresolutionstructures, combinedhereforsimplicity.Resistarebasedofflargedoseexposures.66 Figure4.3: Selectedphotoresistsandtheirtypes:positivephotoresist(left),imagereversal (center),andbi-layer(right).Thegoldlayerrepresentsthesputterdeposition priortothelift-offprocess.............................67 Figure4.4:Floodexposureapparatus( l = 375nm)......................76 Figure4.5: Sputterdepositiondevice(left).Insidethechamber,withlabeledAuandCr targetsangledoverthestage.Notetheshuttersovereach,usedtokeepeach componentisolatedfromeachother(right)....................77 Figure4.6:Summaryofprocessedmicro-ribbonsthroughstagesofdevelopment.......78 Figure4.7: Successfullyfocusedionbeam(FIB)milledmicro-ribbonreadyforextrac- tion(left).SuccessfullyFIBmilledmicro-ribbonsreadyforextractionboth perpendicularandparalleltogrowthdirection(right)...............79 Figure4.8: PrototypeHallcircuit(left),andviewofsensorsoverthemicro- ribbonatcenter(right)...............................81 Figure4.9: Fullcharacterizationcircuitdesign(left),andviewofsensorsover themicro-ribbonatcenter(right)..........................82 Figure4.10: Optimizedspincoatingforselectphotoresistsgroupedbycolor.Ti PrimeisappliedpriortoAZ5214E(purple).liftoffresist(LOR)3Bis appliedpriortoma-P1205(blue).AZ926010 m mcanbeusedsingularly orprecedingtheAZ926024 m mthatisasecondapplicationofthe photoresist(black).................................82 Figure4.11: pathsacrossthephotoresistsurfacefortheLOR3Bandma-P1205 photoresists(left),andTiPrime+AZ5214Ephotoresist(right).Padnumbers correspondtoHallcircuitlabelsinFigure4.8...................86 xvi Figure4.12: pathsillustratedacrossaLASI7designedHallcircuit(left).Each contactpadis0.4mmsquare.dataonAZ9260,24 m mtarget photoresistthicknessshowsthicknessvariability(right)........87 Figure4.13: analysisoftheAZ9260photoresistafterdevelopmentwithfullyde- veloped10 m m(left),under-developed10 m m(center),andunder-developed 24 m mtargetthickness(right).Thethicknessoftheresistwaslessthanthe targetthicknessinallthreecasestudies.PadnumberscorrespondtoHall circuitlabelsinFigure4.8.............................88 Figure4.14: Examplepowerstudyforlaserpowers2-100%with2%increments(left). Linewidthstudiesforpoweroptimizationwithnoribbonfortargetthickness of2,3,and4 m mlinethicknesses.SlideswerecoatedinTiPrimeandimage reversedAZ5214Eresist.Powerpercentageisforthelaser,1x1pass, on,uni-directionalandinvertedwithabufferforimagereversal(right)......89 Figure4.15: ATiPrime+AZ5214Eimagereversalphotoresistcircuitwithcorrect undercutafterthedevelopmentstage(left)comparedtoapoorlyundercut LOR3B+ma-P1205photoresistcircuitthatfailedtolift-offcorrectly(right)..89 Figure4.16: Successfullift-offofTiPrimeandAZ5214Ephotoresist.paths acrossthesputteredcircuitpadsafterlift-off,measuringthethicknessofthe sputteredchromiumandgoldstack(left).Opticalimageofthepadsleading totheHallcircuitatcenter(right).PadnumberscorrespondtoHallcircuit labelsinFigure4.8.................................91 Figure4.17: Poorlift-offofanAZ9260photoresistcircuitwithsidewalldepositionadher- ingtosubstratesurface(left)comparedtoanoptimizedcircuitdesignusing TiPrime+AZ5214Eimagereversalphotoresistaftersuccessfullift-off(right).92 Figure4.18: SuccessfullyprintedfullcharacterizationcircuitoveraCa 5 In 2 Sb 6 micro- ribboncutperpendiculartothec-direction.Sensorsarelabeledandenumer- ated,withthetwocharacterizationlistedatright..........94 Figure4.19: Ca 5 In 2 Sb 6 micro-ribboncutparalleltothec-direction(left).Micro-circuit bondedsuccessfullytosurroundingphysicalpropertiesmeasurementsystem (PPMS)puck(right)................................95 Figure4.20: FourproberesistivityprobesattachedtosinglecrystalCa 5 In 2 Sb 6 parallelto thec-direction(left)withtheresultingresistivityvaluesfordifferentinput currents(right)...................................96 xvii Figure4.21: Resistivity,resistivityratio,carrierconcentration,andmobilityofCa 5 In 2 Sb 6 singlecrystalribboncutperpendiculartothec-directioncomparedtomea- suredpolycrystallinesamples.Increasedresistivityinthea-bplaneisconsis- tentwithDFTpredictionsofanisotropicbehaviorinsinglecrystals........97 Figure5.1: ScanningelectronmicroscopyimagesofMg 3 Sb 2 singlecrystalplatelets, notethehexagonalgrowthbehavior.Crystalsurfacesawayfromthegrowth perimeterwereandsmooth...........................105 Figure5.2: CrystalstructureofMg 3 Sb 2 fromMg-richgrowthconditionswithMginter- stitialatomsandtraceSb(I)vacancies(left).CrystalstructurefromSb-rich growthconditionswithpartialMg(I)occupancy(right)..............106 Figure5.3: ResistivityvaluesforselectMg 3 Sb 2 singlecrystalsfromSb-andMg-rich growthconditions,comparedtopublishedvalues[7]...............109 Figure5.4: InverseHallcoefofseveralMg 3 Sb 2 samples,measuredacrossthree batches.......................................110 Figure6.1:RepresentativeSEMimagesofCa 9 Zn 3 : 1 In 0 : 9 Sb 9 singlecrystals.........116 Figure6.2: EDSanalysisareaofsinglecrystalCa 9 Zn 3 : 1 In 0 : 9 Sb 9 (left).EDSspectrawith uniqueandisolatedZnandInpeaksneartheprominentCaandSbemissions (right)........................................117 Figure6.3: CombinedTG/DSCanalysisonthesinglecrystalsofCa 9 Zn 3 : 1 In 0 : 9 Sb 9 . Weight%andheatwareshowninblueandred,respectively. Theheatingsequencestartsat373K;thecoolingsequencecompletesat773K..117 Figure6.4: (a)AveragecrystalstructureofCa 9 Zn 3 : 1 In 0 : 9 Sb 9 .(b)Localcoordination environmentforCa1.(c)LocalcoordinationenvironmentforCa2.(d)Poly- hedroncoordinationwithmixedZn1/In1site.(e)Coordinationforpartially occupiedZn2site..................................118 Figure6.5: ComparisonofCa 9 Zn 4 : 5 Sb 9 ,orthorhombicspacegroup Pbam ,andCa 9 Zn 3 : 1 In 0 : 9 Sb 9 , hexagonalspacegroup P ¯ 62 m ............................120 Figure6.6: FourproberesistivityprobesattachedtosinglecrystalCa 9 Zn 3 : 1 In 0 : 9 Sb 9 , Sample1(left).Resultingresistivityvalueswereconsistentfortwodifferent crystals,showinglow,linearlyincreasingresistivity(right)............121 Figure7.1: ProposedsolubilitystudybetweenthetwostablecompoundsCa 5 Al 2 Sb 6 and Ca 5 Al 2 Bi 6 .Dashedlinerepresentspossiblegrowthmeltcompositions withrespecttoextractiontemperature.......................128 xviii FigureA1: Ca 5 Ga 2 Sb 6 crystalsfromaGa 73 Sb 42 withsuperimposedEDSareas highlighted.CorrespondingEDSdataisshowninFigureA3andTableA1....132 FigureA2: SimulatedEDSpatternsforpotentialcrystalcandidatesgrownfromaCa-Ga- Sb.......................................132 FigureA3:EDSspectraforCa 5 Ga 2 Sb 6 withGa 73 Sb 42 AreasAŒFfromFigureA1..133 FigureA4: Ca 5 In 2 Sb 6 crystalsfromanIn 73 Sb 42 withsuperimposedEDSareas highlighted.CorrespondingEDSdataisshowninFigureA6andTableA2....135 FigureA5: SimulatedEDSpatternsforpotentialcrystalcandidatesgrownfromCa-In-Sb 135 FigureA6:EDSspectraofCa 5 In 2 Sb 6 singlecrystalsfromanIn 73 Sb 42 AreasAŒF fromFigureA4...................................136 FigureA7: Ca 5 Ga 2 x In x Sb 6 crystalsfromaGa 37 : 5 In 37 : 5 Sb 42 withsuperimposed EDSareashighlighted.CorrespondingEDSdataisshowninFiguresA8-A9 andTablesA3-A4..................................138 FigureA8: EDSspectraofCa 5 Ga 2 x In x Sb 6 singlecrystalsfromaGa 37 : 5 In 37 : 5 Sb 42 AreasAŒEfromFigureA7(left)..........................139 FigureA9: EDSspectraofCa 5 Ga 2 x In x Sb 6 singlecrystalsfromaGa 37 : 5 In 37 : 5 Sb 42 AreasFŒJfromFigureA7(right)..........................140 FigureA10: Ca 5 Al 2 Sb 6 crystalsfromaAl 73 Sb 42 withsuperimposedEDSareas highlighted.CorrespondingEDSdataisshowninFigureA12andTableA5...143 FigureA11:SimulatedEDSpatternsforknownCa-Al-Sbternaryphases...........143 FigureA12: EDSspectraofCa 5 Al 2 Sb 6 singlecrystalsfromaAl 73 Sb 42 AreasA-D fromFigureA10..................................144 FigureA13: Ca 5 Al 2 Sb 6 crystalsfromaSb 20 withsuperimposedEDSareashigh- lighted.CorrespondingEDSdataisshowninFigureA14andTableA6.....146 FigureA14: EDSspectraofCa 5 Al 2 Sb 6 singlecrystalsfromaSb 20 AreasAŒGfrom FigureA13.....................................147 FigureA15: Ca 5 Al 2 Sb 6 crystalsfromaSn 15 imagedusingbackscatteredelectrons (left)tohighlightcoatingthecrystal.SuperimposedEDSareahighlighted (right)withcorrespondingEDSdatashowninFigureA17andTableA7.....149 xix FigureA16: Ca 5 Al 2 Sb 6 crystalsfromaSn 15 withsuperimposedEDSareashigh- lighted.CorrespondingEDSdataisshowninFigureA17andTableA7.....149 FigureA17: EDSspectraofCa 5 Al 2 Sb 6 singlecrystalsfromaSn 15 AreasAŒGfrom FigureA15-A16..................................150 FigureA18: Ca 5 Al 2 Bi 6 crystalsfromaBi 20 withsuperimposedEDSareashighlighted. CorrespondingEDSdataisshowninFigureA19andTableA8..........152 FigureA19: EDSspectraofCa 5 Al 2 Bi 6 singlecrystalsandcomponentsfromaBi 20 AreasAŒGfromFigureA18.........................153 xx CHAPTER1 INTRODUCTION:THERMOELECTRICS 1.1 Thermoelectrics AstheenergyneedsoftheUnitedStatesandtheworldcontinuetoincrease,thermoelectrics havecomeintofocusasapossibleenvironmentallyfriendlyalternative.Theestimatedenergy consumptionoftheUnitedStatesfor2017was97.7Quads( 1 : 03 10 20 J)with66.7%ofthis consumptionlostasrejectedenergy[ 8 ].Thermoelectricsofferasolutionforwasteheatrecovery andhavefar-rangingapplicationsinindustryandspaceexploration.Applicationsincludebutare notlimitedtothermalcyclesforDNAsynthesizers,carseatcooler/heaters,laserdiodecoolers,low- wattagepowergenerators,andmilitaryapplicationssuchasheat-seekingmissilesandnight-vision systems[ 9 ].Additionally,thermoelectricscanprovideacleanenergyalternative,replacingmore environmentallycostlysourcessuchasfossilfuels.Thermoelectricsareappealingfortheirsmall size,robustnessindifenvironments(solid-statedevices),andrapidresponsetimes[10,11]. AthermoelectricgeneratoriscapableofconvertingheattoelectricityasshowninFigure 1.1.Thisdeviceconsistsofthermoelectricjunctionsthatareelectricallyinseriesandthermally inparallel.Eachjunctionconsistsofa p -and n -typematerialconnectedbyshuntsmadeofan electricalconductorsuchascopper.Ina p -typematerial,holesdiffusetothecoldsidewhilein an n -typematerial,electronsdiffusetothecoldside.Thiscarriermotiongeneratesavoltagethat drivesacurrentthrougheachjunction,producingelectricity[ 12 ].Themaximumthermoelectric efyofadevicecanbeexpressedas h max = T hot T cold T hot p 1 + ZT 1 p 1 + ZT + T cold T hot ; (1.1) where T hot isthehotsidetemperature, T cold isthecoldsidetemperature,and ZT isthethermo- electricdevicet.ThetermontherightsideofthisexpressionistheCarnot 1 Figure1.1:Thermoelectricmodule(left)withdetailofsinglejunction(right).Chargecarriers diffusetothecoldside( T cold )foragiventemperaturegradient. efy( h Carnot =( T hot T cold ) = T hot ),whichisthetheoreticalmaximumefyofaheat engineequivalentto zT = ¥ .Thelargestchallengefacingtheexpansionofmodernthermoelectric utilizationisperformance;mostcommonlyrepresentedbythedimensionless zT , foracompound, zT = a 2 s T k e + k l ; (1.2) where a istheSeebeckcoef s istheelectricalconductivity, T istheoperatingtemperature, k e isthethermalconductivitycontributionfromelectronsandholestransportingheat,and k l isthe thermalconductivitycontributionfromphononstravelingthroughthelattice.FromEquation1.2, itcanbeobservedthatanoptimalthermoelectricmaterialwouldsimultaneouslypossessalarge Seebeckcoefhighelectricalconductivity,highoperatingtemperature,andminimalthermal conductivity. Whileeverymaterialpossessesthermoelectriceffectsinsomecapacity,manyarenotwellsuited toserveasathermoelectricduetotheirprohibitivelylow zT .Formetals, a isusuallyprohibitively 2 small,withthermalconductivitiesaretoolarge.Insulators,ontheotherhand,sufferfromresistivity ( r = 1 = s ) valuesthataretootoovercome.Thisnarrowstheofthermoelectric candidatestosemiconductor-likematerials. Thehighestthermoelectricperformancetypicallycomesfromheavilydopedsemiconductors withpeakperformanceacrossavarietyoftemperatureranges[ 13 ].Nearroomtemperature applications(300-500K)utilizepromisingBi 2 Te 3 -based[ 14 Œ 16 ]andMgAgSballoys[ 17 , 18 ]. Medium-temperaturerange(500-900K)thermoelectricsarenumerous,includingPb(Te,Se,S)[ 19 Œ 22 ],PbTe-AgSbTe 2 [ 23 ],GeTe-AgSbTe 2 [ 24 ],AgSbTe 2 [ 25 ],andSnSe[ 26 ].Morerecentadditions tothistemperaturerangeincludetetrahedrites[ 27 ],Zn 4 Sb 3 [ 28 , 29 ],In 4 Se 3 [ 30 ],Cu 2 (S,Se,Te) [ 31 , 32 ],andanumberofZintlphasesdiscussedingreaterdetailinsubsequentsections[ 29 , 33 Œ 37 ]. Hightemperatureapplications( > 900 K)includehalf-Heuslers[ 38 Œ 40 ],SiGe[ 41 Œ 43 ],andZintl phases[44,45]amongothers. 1.2 ThermoelectricEffects Thethermoelectriceffectsofamaterialcaneithercreateanelectricalpotentialfromatemper- aturedifferenceorproduceatemperaturedifferencegivenanelectricalpotential.Theseeffects manifestinthreedifferentways:theSeebeck,Peltier,andThomsoneffects. TheSeebeckeffectwasdiscoveredbyThomasSeebeckin1821[ 46 ]whentwoelectrically conductingmaterials(AandB)wereconnectedacrossatemperaturegradient.Amagneticneedle waswhenplacedneartheapparatus,theresultofanelectricalcurrentwingintheclosed loopratherthanamagneticpolarization.Themagnitudeofthisvoltagedifference, D V ,wasfound tobeproportionaltothetemperaturedifference, D T , a AB = D V D T ; (1.3) wheretheproportionalitycoef a AB ,istheSeebeckcoefforthematerialcouple.A positiveSeebeckrepresentsaelectromotiveforcedrivinganelectricalcurrentthroughmaterialA fromthehottocoldjunction.Thisloopcanbeseparated,asshowninFigure1.2(left),andtheopen 3 circuitvoltage, D V ,canbeexpressedas D V = Z T 2 T 1 a AB dT ; (1.4) where a AB = a B a A = D V B D T D V A D T : (1.5) Inthismanner, a AB canbedecoupledintoindividualmaterialSeebeckcoefTheSeebeck coefiscommonlyreportedin µ V = K andisevaluatedatopencircuitconditions.Avoltage differenceisrequired,necessitatingacouplingoftwounlikematerials. Intrinsically,theSeebeckcoefdescribestheresponseofelectronstoatemperaturegradient. Materialsthatare n -typecreateanegativeSeebeckcoefinopencircuitconditionswherethe electricpointsinthedirectionofthecoldsidewhenexposedtoatemperaturegradient.A p -typematerial,incontrast,possessesapositiveSeebeckcoefwiththeoppositeeffect. Apracticalwaytotakeadvantageofthiseffectisintheconstructionofthermocouples.Inthe traditionalmetal/metal-alloythermocouple,twodifferentelectricalconductorsareweldedtogether toformanelectricaljunctionwherethetwoconductorsareelectricallyinseriesbutthermallyin parallelasshowninFigure1.2(left). Figure1.2:ThermocouplecircuitillustratingtheSeebeckeffectwhereavoltagedifference, D V , appearsacrosstheterminalatT 1 andT 2 (left).circuitillustratingthePeltiereffect wherebyanappliedvoltageproducesacurrent, I ,creatingacoolingeffectatT c ,whileexpelling heatatT h (right). 4 ThePeltiereffectdescribesthereversecaseoftheSeebeckeffectandwasdiscoveredby JeanCharlesAthanasePeltierin1834[ 47 ].Itisthefundamentaleffectgoverningthermoelectric refrigeration.Peltierdiscoveredthatwhenacurrentwaspassedthroughtwodissimilarbutphysically connectedmaterials,aheatingorcoolingeffectoccursattheirmatingsurfaceasshowninFigure 1.2(right).Thecoolingeffect, Q c ,canbeexpressedas Q c = P AB I ; (1.6) where P AB isthedifferentialPeltiercoefbetweenmaterialAandB,and I istheapplied electricalcurrent.Alternatively,theappliedcurrentwcanbereversedproducingaheatingeffect at T cold .ThePeltiercoefisalsorelatedtotheSeebeckcoef a AB = P AB T : (1.7) ThethirdthermoelectriceffectistheThomsoneffect,discoveredbyWilliamThomson,later knownasLordKelvin,in1857[ 48 ].TheThomsoncoef K ,describedtheheatingorcooling ofaconductorinatemperaturegradientgivenanexternallyappliedcurrentandisrelatedtothe Seebeckcoef a AB = Z K AB T dT (1.8) wherethedifferencebetweentheThomsoncoefcientsofthetwomaterialsistherateofheating perunitlengththatistheresultoftheappliedcurrent[49]. Forthermoelectricpowergeneration,theSeebeckeffectiscriticallyimportantasdescribedin Equation1.3,whichdescribeshowwellamaterialtransformsthermalenergytoelectricalpowerdue totheelectricalbiasgeneratedinamaterialunderatemperaturegradient.TheSeebeckcoef isaquadraticterminthe zT equation,illustratingitslargeonthermoelectricperformance. 5 1.3 ElectronicTransport Electricalconductivity, s ,isthereciprocalofresistivity, r ,andisameasureofhowwella materialconductselectricity.Forsemiconductorsitcanbeexpressedas, s = ne m d ; (1.9) where n isthecarrierconcentration, e istheelectroncharge,and m d isthedriftvelocity.Thisdrift velocityistheaveragevelocityoftheelectronsdividedbytheappliedinthedirectionoftravel, whichrelatestotheeffectivemassoftheelectronitself.Driftvelocitycanbeexpressedas, m d = e t m e ; (1.10) where t isthemeanfreetimebetweencollisions( i.e. ,meanscatteringtime,relaxationtime) and m e istheeffectivemassoftheelectron.Themeanfreetimemultipliedbythemeanspeed oftheelectrons, v ,yieldsthemeanfreepath, l .Themeanfreetimeisofcriticalimportance inthermoelectricsasitrelatesdirectlytotheprocessesthatscatterelectrons.Thesescattering mechanismsincludethermallatticevibrations( i.e. ,phonons), t T ,andimpurities, t I ,amongothers. Theoverallfrequencyofscatteringcanbeexpressedas, 1 t = 1 t T + 1 t I + :::: (1.11) Itisdesiredthatelectronsbehighlymobileinthestructure,withlongtimesbetweencollisions generatingahigh t whichinturnincreaseselectricalconductivity. Insemiconductors, m e isconsideredtoincorporatetheeffectoftheperiodicpotentialofthe atomsandthebandcurvatureanddopingofthematerial.Theeffectivemassdetermines boththeelectronicstructureandtransportwhenparabolicbandmodelingisutilized[50]. 6 1.4 ThermalTransport Thermalconductivity, k ,inanisotropicmaterialrelatestotheheatexpressedasFourier's law[51], q = k O T ; (1.12) where q istheheatvector, k isthethermalconductivityand O T isthetemperaturegradient.For thermoelectricmaterialsthathavemultiplecarriers,thetotalthermalconductivityconsistsprimarily ofanelectronicandlatticecomponent, k = k e + k l ; (1.13) where k e isthethermalconductivitycontributionfromelectronsandholestransportingheatand k l isthecontributionfromphononstravelingthroughthelattice. 1.4.1 ElectronicThermalConductivity Thefreeelectronsandholesthatcontributeto s alsocarryheatwith k e relatingto s accordingto theWeidemann-FranzLaw[52], k e = L s T = ne m LT ; (1.14) where L istheLorenznumber,as L = p 2 k 2 B = 3 e 2 = 2 : 44 10 8 W W K 2 forafreeelectron gaswithparabolicdispersionneartheFermienergylevel.Thisvalueappliestomostmetalsand degeneratesemiconductors.Fornon-degeneratesemiconductors, L = 1 : 5 10 8 W W K 2 .The k e componentofthermalconductivitythusscaleslinearlywith s and T .Whileallheatconduction shouldbeminimizedforhigh zT ,inpractice, k e israrelytargetedbecauseoftheneedforhigh s . 7 1.4.2 LatticeThermalConductivity Thelatticecomponentofthermalconductivitydescribesthecontributionofphononstraveling throughthelattice,anditisoftenthefocusinthermoelectricapplicationsasitisindependentof electricalconductivity.Thislatticecontributionistheproductofheatcapacity, C V ,phononvelocity, v ,andthephononmeanfreepath, l [53], k l = 1 3 C V vl = 1 3 C V v 2 t ph (1.15) where t ph representsthemeanfreetimebetweenphononinteractions.Thephononvelocityisoften approximatedbythelowfrequencyspeedofsound, v sound µ q E d ,where E istheelasticmodulus and d isthedensity.Strategiesforselectingmaterialswithlowlatticethermalconductivitiesinclude identifyingmaterialswithlowphononvelocities,whichariseindensematerialswithsoftbondor throughthereductionof t byintroducingpointdefectsornanostructuringtoscatterphonons[ 54 ]. Thesescatteringmechanisms, i ,obeyMatthiessen'srule, 1 l = å 1 l i : (1.16) Thedominantscatteringmechanisminpurematerialstransitionsfromboundaryscattering effectstophonon-phononUmklappscatteringwithincreasingtemperature.Umklappscatteringis duetoanharmonicwaveinteractionsfromwhichthermalresistanceisproduced.Thiscontribution wasdescribedbyDebye[ 55 ],wherebythermalmotionwasastheaccumulationofall possiblevibrationsinalattice.FromtheDebyemodelithasbeenexperimentallyproventhatwhen T > q D ,where q D istheDebyetemperature,latticethermalconductivityproportionalto T 1 is indicativeofUmklappscattering[56]. Forthermoelectricapplications,materialsthathaveinherentlylowlatticethermalconductivity arepreferredwhere t ph isreducedbydecreasingphononvelocityand/ormeanfreepath.This meanscomplexcrystalstructuresthatcanbefurtherdopedand/orfurthercomplicatedwithpoint defects.Differencesinbondcharacterandstrengtharealsopathwaystoreducing k L . 8 1.5 Optimizationof zT Thermoelectricmaterialsareoptimizedbymaximizing zT ,whichexpressestheefyof the p -and n -typecouplematerials.FromEquation1.2,itisobservedthat zT ismaximizedthrough increasingthepowerfactor( a 2 s )andoperatingtemperaturewhileminimizing k [ 57 Œ 59 ].The powerfactorisadescriptivemetricofcarrierconcentrationeffectsasboththeSeebeckcoef andelectricalconductivityarestronglydependentonit.Unfortunately a and s haveopposing dependenceon n .Fordegeneratesemiconductorswithasinglecarrier,theSeebeckcoefcan beexpressedas, a = 8 p 2 k 2 b 3 eh 2 m DOS T p 3 n 2 = 3 (1.17) where k b istheBoltzmannconstant, h isthePlanckconstant, m DOS isthedensity-of-stateseffective massofthecarrier[ 59 ].Thisexpressionisvalidforlargecarrierconcentrationsand/orlow temperature.Fromthisexpressionitisobservedthat a isinverselyproportionalto n .Conductivity ontheotherhand,isproportional, s = ne m d : (1.18) Large a isproducedwhenasingletypeofcarrierisdominant,eitherelectrons(dominantin n -type)orholes(dominantin p -type).Whenatemperaturegradientisappliedtoamaterial,these chargecarriersmovetothecoldsideandinthecaseofmixedcarriers,theyeffectivelycancelout portionsoftheinducedSeebeckvoltagethroughrecombination,reducingefciency.Therefore low n andinsulatingmaterialbehaviorisdesiredforhigh a .Alternatively,high s isachievedin materialspossessinghigh n ,oftenthecaseinmetals.Foragiventhermoelectricmaterial,its zT valueismaximizedthroughcarrierconcentrationoptimization.Usuallyacompromiseofthese requirementsleavesamaterialoptimizedasaheavilydopedsemiconductorwith n intherange of10 19 Œ10 21 cm 3 .Bothintrinsicandextrinsicdefectscontrolthetunabilityof n withmany 9 Figure1.3:LayeredthermoelectricsBi 2 Te 3 (left),GeAs(center),andSnSe(right)withlow in-planeandhighout-of-planeresistivitywithmoreanisotropicbehaviorobservedforSeebeck coef thermoelectricmaterialshavingdefectconcentrationsthataretoolarge,orpreventdoping n- or p- type. Assumingthat n canbeoptimizedindependentlybydoping,thematerialqualityfactor, B , isdesignedtoremovethe n -dependencefromthe zT equation.Itisparticularlyusefulinthe explorationofnewthermoelectriccandidatematerials,whichmaynotyethaveoptimized n .The materialqualityfactorundertheassumptionofacousticphononscatteringisgivenby[60], B = 2 k 2 B ¯ h 3 p C l N V m I X 2 k l T ; (1.19) where ¯ h isthereducedPlanckconstant( h = 2 p ), C l istheaveragelongitudinalelasticmodulus, N V isthevalleydegeneracy, m I istheinertialeffectivemass,and X isthedeformationpotential. InEquation1.19,itisobservedthat k l isgenerallyindependentoftheelectronicbandstructure, emphasizingthataselectedmaterialmustpossessaninherentlysmall k l .Valleydegeneracyrefers tothenumberofvalleys/bandsthatcontributetothecarriertransport.Foraconstant a ,agreater banddegeneracy, N v ,willresultinalargercarrierconcentration.Additionally, N v increasesboth 10 electricalconductivityand zT [ 61 ].Highbandcurvaturedecreasesineffectivemass,which increaseconductivity,whileshallowbandsincreasesineffectivemassandSeebeck. Amongthematerialpropertiesin B ,the m I , X ,and k ,aredependentoncrystallographic direction(x,y,z).Theanisotropyof k l isafunctionoftheanisotropyofthespeedofsound(and thereforetheelasticmoduli)andphononscatteringmechanisms.Theanisotropyofthelatterisnot yetwellunderstood.Theaveragedinertialeffectivemass, m I ( i.e. ,conductivityeffectivemassor thesusceptibilityeffectivemass),isatensorpropertywhichdescribesparticlemotionina directioninresponsetoaforce.Itcanbeexpressedanisotropicallyas, m I = 3 1 m x + 1 m y + 1 m z 1 : (1.20) Estimatesof m x , m y ,and m z ,canbeobtainedfromthecurvatureofthebandstructuresobtained fromDFTcalculations.Thisisdifferentfrom m DOS inEquation1.17whichisascalarproportional tothedensity-of-statesneartheFermilevelwhichneedstobemaximizedtoincrease a .While m DOS and m I areequivalentforasingleisotropicband,theydivergeforanisotropiccases.Because m DOS isbyisotropic, m I ; avg canbehighlyanisotropic,itispossibletoachievehigh s inthe m I directionwhilesimultaneouslymaintainingahigh m DOS toachievehigh a .Finally,the factorscontrollingthedeformationpotential, X ,whichdeterminestheelectron-phononscattering rate, t T ,arenotwellunderstoodatthispoint.Thus,itsisdiftopinpointitsanisotropy. Inagivenmaterial, k l , m I ,and X usuallyhavedifferentdegreesofanisotropy.Thismeansthata potentialwaytocircumventtheinherentcontradictionsintheoptimizationof B (andthus zT )isthe useofanisotropicsinglecrystals.Fromthisframework,anidealanisotropicthermoelectriccandidate materialcanbetheorized.Thematerialwouldpossessacomplexstructurewithintrinsicallylow, butisotropiclatticethermalconductivityandwouldpossessacrystallographicdirectionwithhigh mobilitythatminimizes m I and X .Alongthehighmobilitydirection,suchamaterialwouldbean idealphonon-glass,electron-crystal[58]. Becauseanisotropicpropertiesaredifculttostudy,thereareonlyahandfulofanisotropic thermoelectricmaterialsthathavebeenprovenexperimentallytopossessapreferredcrystallographic 11 orientationforthermoelectricapplications.Becauseelectricalconductivityismoredependenton crystallographicorientationthan a ,materialswithhighlyanisotropiccrystalstructuresallowfor thermoelectricoptimizationalongthehighmobility(low m I and X )crystallographicaxis.Usually s canvarysiwhile a remainsrelativelyconstant,asisthecasewithlayeredBi 2 Te 3 [ 62 , 63 ],GeAs[ 64 ],CsBi 4 Te 6 [ 65 , 66 ],andSnSe[ 26 , 67 ]thermoelectriccompounds,illustrated inFigure1.3.Recently, zT > 2 wasachievedbyexploitingthehigh s directionofSnSesingle crystals[ 67 , 68 ].Throughpropermaterialinvestigationandcarrierconcentrationoptimization,new thermoelectriccandidatematerialscanbediscoveredandsubsequentlyoptimizedwithanisotropy playinganimportantroleinresolvingseeminglycontradictorymaterialpropertydemands. 12 CHAPTER2 ZINTLTHERMOELECTRICS 2.1 ZintlPhaseOverview Zintlphaseshavebeenthefocusofrecentthermoelectricresearch,duetotheircomplexbonding, whichincludescovalentlybondedanionicsub-structuresinalatticeofelectropositivecations. ThesestructuresadheretoavalenceelectroncountingsystemknownastheZintl-Klemmconcept. Thisresearchspaceispromisingforthermoelectricsasthepolyanionsinthesephasesmaycreate veryanisotropicnetworks,whichinsomecasesactasconductivepathways.Thesepolyanions canbefoundtocrystallizeinadiversesetofcomplexstructuresfromisolatedzero-dimensional moietiestothree-dimensionalnetworks.Duetotherequirementofbeingvalenceprecise,Zintl phaseshaverelationshipsbetweentheirphysicalandelectronicstructures,leadingtoa semiconductor-likeenergygap.Unlikemetals,Zintlphasesshowincreasingelectronicconductivity withincreasingtemperature[ 69 ].Further,aamountoftheZintlphasespaceisstill unexplored[70]. Broadlyspeaking,Zintlphasesincludeanalkalimetal(group1),alkalineearth(group2), orrareearthmetalreactedwithanypost-transitionmetalormetalloid(group13-16).Theterm Zintlphasecameintousein1941[ 71 ],originatingfromtheworkofEduardZintl[ 72 Œ 76 ]who focusedonintermetalliccompoundsthatpossessedsalt-likestructures[ 76 ].Salt-likecompounds arecharacterizedbybothcationandanionsachievingafulloctetofelectrons,butmakeforpoor thermoelectricmaterialsduetotheirinsulatingbehavior( i.e., largebandgaps).Alternatively, numerousotherclassesofintermetallicsdonotpossessabandgap,andexhibitmetallicbehavior thatmakethempoorthermoelectricmaterials.Zintlphaseshavebeenfoundtobeacompromise betweenthesetwoextremesasusefulsemiconductorsinmanycases[77]. Fromasynthesisstandpoint,Zintlphasesarecharacteristicallybrittle,possesshighmelting temperatures,andaretypicallylinecompounds,possessingverynarrowhomogeneitywidth[ 78 , 79 ]. 13 Zintlmaterialsalsoofferinexpensiveandnon-toxicalternativestocurrentthermoelectricmaterials [80,81]suchasPbTe,whichisbothtoxicandexpensive[9]. 2.1.1 Zintl-KlemmConcept TheZintl-Klemmconcept(ZKC)isaformalismdevelopedbyEdwardZintlandexpandedby WilhelmKlemminwhichacombinationofvalenceelectroncountingrulesandstructure-based chemicalconsiderationsareusedtoexplainbondingbehavior[ 69 , 82 ].Here,electopositivemetals ( A )suchasalkali,alklineearthandrareearthmetalsarecombinedwithmaingroupelements( X ) inthegeneralform A a X x ,wherethe X atomsform X n y polyanionstructuresandarebondedwith covalent X X bonds.Thesestructurescanberationalizedbyaccountingforallofthevalence electrons,includingthosedonatedbythe A atoms[ 83 ].The A X interactionsareassumedtobe almostentirelyionic.Inthismanner,theZKCobeysthe( 8 N )rulepioneeredbyLewis[ 84 ], whichdescribestheinclinationofmaingroupelementstopossessafulloctetshellwithincompound formation[ 85 ].Here N isthenumberofvalenceelectronsofthe X atoms.Thisoctetrulewasa milestoneintheofchemistry,helpingtoexplainchemicalbondingandstabilitiesacrossan immensestretchofcompounds,givingrisetowhatwouldlaterbetermedLewisnotation. Klemm'sworkappliedLewis's( 8 N )frameworktoZintlphases.Here,the VEC isused todeterminethenumberoftotalelectronsavailabletoeachanion,includingthosedonatedby cations.AdvancesinDFTcalculationshaveexplainedtheroleofthecationsforcompounds [ 86 ],withZintlphasesprovidingarichfortheoreticalelectronlocalizationfunction(ELF) calculationsintothiscombinedionicandcovalentbonding. Oneofthesimplestexamplesoftheseanionic-substructuresisexhibitedintheZintlphase NaSi(Na + Si )showninFigure2.1(left)whereNaatomsactastheionicallybondedcationwhile covalentlybondedSianionsform[Si 4 ] 4 tetrahedrasubstructures.EachNaatomdonatesone valenceelectrontoaSiatom,satisfyingchargebalancingaccordingtoZKCrules.Thenumber ofbonds, N ,isequalto8-( VEC /anion).Thus,forNaSi,eachSihasvevalenceelectrons,so VEC = 5and N = 8 5 = 3,whichisthenumberofcovalentSi-Sibonds. 14 Figure2.1:TheNaSiunitcellwithionicallybondedNacationsandcovalentlybondedanionicSi tetrahedra([Si 4 ] 4 )(left).NaTlunitcellwithdiamondnetworkofTlatoms(right). TheZKCalsoappliestotheNaTlbinaryshowninFigure2.1(right)thatisnotresolvedbythe traditional(8- N )formulationortheHume-Rotheryrules[ 87 , 88 ]thatformulatedelectronnumber relationsbasedoncrystaltypes.HereZKCyieldsa VEC = 4 ,and N = 8 4 = 4 .This explainswhyeachTlformsfourTl-Tlcovalentbonds. TheZKCexplainsthattheTlatomsformadiamondnetworkwherebyeachNaatomdonatesits valenceelectrontoaTlatom,resolvingtheobservedarrangementofNaandTl,andsatisfyingthe spatialrequirementsoftheNaatomswithintheTlframework.ThisisduetotheTl anionshaving thesamenumberofvalenceelectronsasgroup14elements,creatinganetworkoffour-bonded Tlatoms[ 89 , 90 ].ThisNaTl-typestructureisrare[ 91 , 92 ],withonlysixotherknownbinaries: LiZn[ 93 ],LiCd[ 94 ],LiAl[ 95 ],LiGa[ 96 ],LiIn,andNaIn.Mostotheralloysordertomaximize neighborsoftheoppositeelementwhilethesebinariesforminterpenetratingdiamondsubstructures [ 97 ].Thisstructure-typealsoextendstoselectternarysystems[ 98 , 99 ].NaTldoesnotpossess abandgapandbehavesmetallically,makingitapoorchoiceforthermoelectrics[ 100 ],butother Zintlphaseshaveshownpromiseinboththeirsemiconductorbehavioranduniquecomplexityof formation. 15 2.1.2 ThermoelectricPerformanceofZintlPhases ThecovalentregionsofsomeZintlphasesarethoughttoprovideelectroncrystalpropertiesand crystallographicdirectionsofhighmobility.Theionicregionscontributetotheformationof complexstructureswhichinturnleadtophonon-glasspropertiesthatcancreatedisorderandbe dopedtooptimizecarrierconcentration.Inthismannerthesecompoundscantheidealphonon- glassandelectron-crystalmodel.TheclassicalviewofZintlphasesdescribevalenceprecise semiconductors,however,degeneratebehaviorisaproductofvacanciesandinterstitialswhichcan beexplainedthroughelectroncountingschemes.Forthisreason,metallicbehavingcompounds arealsoreferredtoasZintlphases.Generallyspeaking,thermoelectricperformanceisfoundin heavily-dopedsemi-conductorswithcarrierconcentrationsintherangeof 10 19 to 10 21 carriers/cm 3 , numbersthatcanbeachievedforZintlphases[ 59 ].GoodZintlthermoelectricsincludeZn 4 Sb 3 [ 29 ],Mg 3 Sb 2 [ 33 ]Ca x Yb 1 x Zn 2 Sb 2 [ 34 ],Ca 9 Zn 4 + x Sb 9 [ 35 ],Yb 14 Mn 1 x Zn x Sb 11 [ 36 , 44 , 45 ], andYbCd 2 x Zn x Sb 2 [37]with zT valuesgreaterthanunity. ThepotentialanisotropicpropertiesoftheCa 5 M 2 Sb 6 (M=Al,Ga,In)systemareofparticular interestdespitetheirmodestdoped zT valuesbelowunity.Thiscompoundfamilycanbe p -type optimizedthroughdopingasisshowninthecaseofCa 5 In 2 Sb 6 inFigure2.2(left).Doped meritvaluesfortheCa 5 M 2 Sb 6 (M=Al,Ga,In)compoundsarecomparedtoothermaterialsystems ofinterestinFigure2.2(right).Here,both p -and n -typeMg 3 Sb 2 arelistedwiththesuperior n -type performanceof zT = 1 : 51 [ 33 ].TheCa 9 Zn 4 + x Sb 9 compoundspossesssomeofthehighest p -type performancevaluesforthermoelectricsaswell[35]. 2.1.3 A 5 M 2 Pn 6 ZintlPhases TheA 5 M 2 Pn 6 -type(A=Ca,Sr,Ba;M=Al,Ga,In;Pn=As,Sb)Zintlfamilyofcompounds crystallizeinthestructureshowninFigure2.3(right),consistingofMSb 4 polyanionictetrahedra sub-structuresthatareconnectedbycovalentSb-Sbbonds.TheMSb 4 tetrahedraformone- dimensionalchainsthataresurroundedbyionicallybondedCa 2 + cations[ 80 ].Transportproperties ofcompoundsinthisfamilyhaveyieldedsemiconductingbehavior[60,101Œ107]. 16 Figure2.2:TheofCa 5 In 2 x Zn x Sb 6 samples,comparedagainstNa-doped Ca 5 Al 2 Sb 6 [ 1 ](left).TheforselectZintlphasecompoundswithrespecttotempera- tureafterdopingoptimization(right). TheCa 5 M 2 Sb 6 (M=Al,Ga,In)[ 108 , 109 ]compoundsexhibitsemiconductingbehaviorand havebeeninvestigatedextensivelyaspotentialthermoelectricmaterials.Whiledoped zT values haveremainedunderunity,Ca 5 In 2 Sb 5 experiencesnearlyave-foldincreaseinperformance duetoZndopingontheInsite[ 1 ]whileCa 5 Ga 2 Sb 5 experiencesanearlynine-foldincrease [ 110 ].Ca 5 Al 2 Sb 6 wasoptimallydopedwithNaontheCasite,producingasix-foldincreasein performance[ 111 ].ThepotentialanisotropicpropertiesofCa 5 M 2 Sb 6 systemareofparticular interest. 2.1.4 AM 2 X 2 ZintlPhases TheAM 2 X 2 familyofcompounds[ 112 , 113 ]offersastaggeringnumberofcompositionsthat crystallizeintheCaAl 2 Si 2 structure-type[ 114 Œ 122 ].Thisstructuretakestheformofatrigonal bi-layerwithtwo-dimensionalslabsof[Al 2 Si 2 ] 2 comprisedofAlSi 4 tetrahedra,whichareedge sharingwiththreeadditionaltetrahedra.Theseslabsalternatewithtrigonallyarrangedcationsin thea-bplaneasshowninFigure2.3(left). Thermoelectricinterestinthiscompoundfamilybeganin2005withthecharacterizationof Ca x Yb 1 x Zn 2 Sb 2 ( 0 x 1 )solidsolutionswithapeak zT ˇ 0 : 55 [ 34 ].Othersolidsolution 17 Figure2.3:TheMg 3 Sb 2 structure(left),Ca 9 Zn 4 + x Sb 9 structure(center),andtheCa 5 Al 2 Sb 6 structures(right). studiesfollowed[ 37 , 123 Œ 126 ]producingapeak zT ˇ 1 : 3 at873K[ 126 ].High zT hasalsobeen characterizedwithEuZn 2 Sb 2 (0.9at700K)[ 127 ],and n -typeMg 3 Sb 2 (1.51at716K)[ 33 ]where MgoccupiesboththeCaandAlsites. Thermoelectricperformanceofthismaterialfamilyisgenerallystrongduetolighteffective masswhichtranslatestohighelectronicmobility[ 111 ].Alsothelargesubstitutioncapacityofthis familymakesitanappealingareatodiscoverandcharacterizenovelthermoelectriccompounds. 2.1.5 A 9 M 4 Pn 9 ZintlPhases ThisfamilyofZintlphases,oftenreferredtoasthe9-4-9systemhasbeenknownsincethe late1970s[ 128 ]andhassteadilyexpandedtoincludeavarietyofelements[ 129 Œ 131 ].More recentdevelopmentsdiscoveredpartiallyoccupiedZninterstitialssitesintheYb 9 Zn 4 + x Sb 9 and Ca 9 Zn 4 + x Sb 9 compositions[ 132 ],laterexpandingtootherM-siteelementsacrossdifferent9-4-9 compounds[ 130 , 131 , 133 Œ 137 ].Theseoccupiedinterstitialsitesresultincompoundsthatare notvalence-precisebutallowcarrierconcentrationstobeoptimized.Thermoelectrictuningofthe Ca 9 Zn 4 + x Sb 9 systemhasresultedin zT > 1 [ 138 , 139 ]withapeak zT = 1 : 1 at875K[ 35 ].These interstitiallystabilizedcompoundsmakeupasizeablegroupA 9 M 4 + x Pn 9 (A=Yb,Eu,Ca,Sr;M= Mn,Zn,Cd;Pn=As,Sb,Bi),andinmostcases,sharealikestructuretype( Pbam ).Exceptionsdo exist,however,asisthecasewithCa 9 Zn 4 + x As 9 andCa 9 Mn 4 + x Sb 9 ( Pnma )[131]. 18 Thesepartiallyoccupiedsitesdecreaselatticethermalconductivitybyaddingcomplexity throughadditionaldisorder.CationsubstitutionhasalsobeenexploredinthecaseofEuin Ca 9 Zn 4 + x Sb 9 wheretheEuatomspreferentiallyreplacedCasitesfarawayfromtheZn-Sb structures.Thissubstitutionreduceslatticethermalconductivitybyintroducingpointdefectsfor thecompositionCa 6 : 75 Eu 2 : 25 Zn 4 : 7 Sb 9 ,highlightingthetunabilityofthismaterialsystemandZintl phasesasawhole. 2.2 SummaryofResearchDirection WhileZintlphasesareapromisingclassofthermoelectricmaterialsthathavebeenstudied intensivelysince2005,therearestillseveralimportantfundamentalquestionsthatremainunan- swered.Theseincludequestionsrelatedtoanisotropictransportandhowitrelatestothecrystal structure,andtheroleplayedbyintrinsicdefectsindeterminingcarrierconcentration.Additionally, theofZintlcompoundsiseverexpandingandthroughtheuseofexploratorysinglecrystal growthsandthecarefulselectionofstartingcompounds,novelcompoundsandstructuretypescan bediscoveredthatmaybepromisingthermoelectriccandidates. 2.2.1 AnisotropicTransport Anisotropicmaterialshavethepotentialtopossessexploitablehighconductivityinstronglybonded directions,yieldingapreferredcrystallographicorientationforthermoelectricapplications[ 16 , 26 , 64 , 65 , 67 ].Ingeneral,electricalconductivityhasbeenfoundtovarymoresthanthe Seebeckcoefcient,whichremainsrelativelyconstantasafunctionofdirection.Thisisbecause electricalconductivityisrelatedtoinertialeffectivemass,whichisatensorproperty,whilethe SeebeckcoefisdeterminedprimarilybytheDOSeffectivemass,whichisascalar. ManyZintlstructuretypesarehighlyanisotropic,oftencontainingfeaturessuchascovalent chains,layers,oreventunnels.Thissuggests,accordingtoDFTstudies[ 140 Œ 142 ],thattheir electronicandthermalpropertiesmightbehighlyanisotropicaswell.Unfortunately,allofthe previousstudiesofthermoelectrictransportpropertiesinZintlphasesdiscussedaboveinvolved 19 Figure2.4:TheorthorhombicunitcellofZintlphasesCa 5 M 2 Sb 6 (M=Al,Ga,In)(left)with isolatedone-dimensionalpolyanionicchainsconnectedbySb-Sbbonds(right). polycrystallinesamples,meaningthatthereportedtransportpropertieswereaveragedoverall crystallographicdirections. TheCa 5 M 2 Sb 6 (M=Al,Ga,Sb)Zintlsystemisanexampleofastructurepredictedtoexhibit extremeanisotropyintheinertialeffectivemass.TheCa 5 M 2 Sb 6 structure,showninFigure2.4, possessescomplexbondingthatadherestotheoctetruleundertheassumptionthateachbond iseitherpurelyionicorcovalent.ValencebalanceisachievedbetweenveCa 2 + atomsand theanionic(M 2 Sb 6 ) 10 sub-structure.Theanionicsub-structuresconsistofparalleltetrahedral chainsformedfrompolarcovalentM-Sbbonds,whichareconnectedtoneighboringchainsby covalentSb-Sbbonds.ThebridgingatomsaregivenavalenceofSb 1 ,withtwoSb 1 shared betweentwotetrahedra,andtwoSb 2 thatareonlybondedtoasingleMatom.Accordingto DFTcalculationsCa 5 M 2 Sb 6 Zintlphasesexhibitparticularlyanisotropicbehaviorduetothese one-dimensionalpolyanionicchains[ 2 ].Thesecalculationshaveshownahighdegreeofinertial bandmassanisotropy,whichisevidentintheelectronicbandstructuresshowninFigure2.5.The bandstructuresofallthreecompounds(M=Al,Ga,In)reveallightereffectivemass inthec-direction( m c < m a ; m b ). 20 Figure2.5:PreviouslyreportedbandstructuresofCa 5 M 2 Sb 6 (M=Al,Ga,In)compounds, illustratingahighdegreeofanisotropyinthevalenceband.Thebandmass( m X U )paralleltothe anionicstructuresislighterthantheotherperpendiculardirections( m X S and m X G )[2]. ByusingthebandstructurefromDFTandtheBoltzmanntransportmodel,Thunisetal.[ 3 ], showedthattheanisotropyintheCa 5 M 2 Sb 6 (M=Al,Ga,In)systemleadstoenhancedthermo- electricpropertiesinthec-direction,paralleltothetetrahedralchains.Highlyanisotropicelectrical conductivityispredictedasshowninFigure2.6(left),withahigherconductivity inthec-directionthanthea-andb-direction.Thedashedcurvesshowtheaverageofthethree directions,whichisequivalenttotheconductivityofpolycrystallinesamples( n = 7 10 19 cm 3 ). Incontrast,thepredictedSeebeckcoefremainrelativelyisotropic,asshowninFigure 2.6(center).Overall,thepreferentialc-directionresultsinasuperiorpowerfactor( a 2 s ),shownin Figure2.6(right). ThecalculationsshowninFigure2.6makeseveralassumptionsaboutthesinglecrystalprop- ertiesthatrequiremoredetailedinvestigations:First,themeanfreetimeofelectronsbetween collisions( t )wassetempiricallysothe"average"conductivityvaluewouldagreewiththeexper- imentalpolycrystallineconductivityreportedinref.[ 2 ].Since t forelectronsisachallenging portiontocalculatedfromprinciples(itremainsunclearif t isanisotropic),experimental characterizationisneeded.Oneapproachtoexperimentallyestimate t istousemeasuredmobility coupledwiththeeffectivemasspredictedfromDFTtoextractabetterestimatefor t forelectrons. Anothergapinliteratureonthissystemislackofphononcalculations.Thereforedetailedcalcula- tionsoftheanisotropyofthelatticethermalconductivityinthisfamilyofZintlcompoundsdoesnot yetexist.However,whileDFTcanbeusedtoreadilypredictphononvelocities,accuratepredictions 21 Figure2.6:DFTcalculationsforelectricalconductivity(left),Seebeckcoef(center)and powerfactor(right)indifferentcrystallographicdirectionsalongwiththepolycrystallineaverage [3]. ofscatteringrates(phonon t )incomplexmaterialsremainchallenging,andshouldbeinvestigated experimentally. NearlyallpaststudiesofZintlphaseshavefocusedonpolycrystallinesamplesforcharacteri- zation,overlookinghowthecrystallographicdependenceof s , a ,and k L affectsthermoelectric properties.WhilelayeredstructuressuchasBi 2 Te 3 ,andGeAshavebeenstudiedextensively,these arelayeredvanderWaalsgapmaterialswithweakout-of-planebonding,instarkcontrasttothe ionicandcovalentbondsfoundintheCa 5 M 2 Sb 6 (M=Al,Ga,In)system.Thedifferencebetween thesepotentiallyanisotropiccompoundsandthatofthevanderWallgapmaterialsisimportant. WhilethevanderWaalgapmaterialshavearelativelyanisotropicelastictensorduetotheweak inter-layerbonding,theCa 5 M 2 Sb 6 compoundspossessrelativelyisotropicbehavior.Figure2.7 comparestheYoung'smodulustensoralongdifferentcrystallographicplanesforBi 2 Te 3 (top)and Ca 5 In 2 Sb 6 (bottom).Additionally,theFermisurfaceofCa 5 In 2 Sb 6 isillustratedinFigure2.7(right) whereitbehavesasapseudoone-dimensionalelectricalconductor.Theisotropicelasticbehavior ofCa 5 M 2 Sb 6 compoundstranslatesintoamostlyisotropicspeedofsoundwhichisafactorin k l inEquation1.15bythephononvelocity.Fromthis,itissurmisedthatnominallylow k l foundintheCa 5 M 2 Sb 6 compositionscanberetained. Inordertoinvestigatethisanisotropicbehavior,singlecrystalsmustbegrown.Single crystalYb 5 Ga 2 Sb 6 hasbeengrownfromaGa[ 106 ],offeringapotentialsynthesisrouteforthe Ca 5 M 2 Sb 6 (M=Al,Ga,Sb)systemgivenitssimilarstructure,butcharacterizationofthecrystals 22 Figure2.7:Young'smodulustensorwithrespecttocrystallographicorientationforanisotropic Bi 2 Te 3 (top)andapproximatelyisotropicCa 5 In 2 Sb 6 (bottom)[4].FermisurfaceofCa 5 In 2 Sb 6 , apseudoone-dimensionalelectricalconductor[3](right). indifferentcrystallographicdirectionswasnotaccomplished,asthegrowncrystalsweresmall andmeasurementsperpendiculartothegrowthdirectioncannotbeaccomplishedbyhand. Inthiswork,Ca 5 M 2 Pn 6 (M=Al,Ga,In;Pn=Sb,Bi)Zintlphasecrystalgrowthfroma isdetailed(Chapter3),andelectronicconductivitymeasurementsofselectedcrystalsintwo crystallographicdirectionsarediscussed(Chapter4). 2.2.2 CharacterizationofDefects Intrinsicpointdefectsplayanimportantroleinthermoelectricoptimizationofmaterials,because theyimpactchargecarrierconcentration.Intrinsicdefectsarepresentatalltemperaturesabove absolutezero,sincetheirformationincreasescoentropy,leadingtoadecreasein freeenergy[ 143 ].Pointdefectscanbebothandharmfulinthermoelectrics.Onone hand,theymayscattershort-wavelengthphononsbyaddingcomplexitytoastructure.However, sometypesofdefectspintheFermilevel,limitingthecarrierconcentrationsthatcanbeobtained bydoping.Thepresenceofdefecttypesinamaterialisgovernedbythecorrespondingdefect formationenergywithextrinsicdefectsincorporateddeliberatelyasdopants.Thisdefectenergy canbebygrowthconditions,allowingfordefectengineeringofthermoelectriccandidate 23 materials.Identifyingandunderstandingtheconditionsthatfosterusefuldefectscanleadtoabetter understandingofamaterialandfurtheroptimization. WhileZintlcompoundsaregenerallyconsideredtobelinecompounds,therealityisthat eachcompositionhasacertainlinewidthduetothepresenceofintrinsicpointdefects.Intrinsic defectconcentrationsaredeterminedbytheirformationenergies,whichchangebasedongrowth conditions( e.g. ,whichphasethecompoundisinequilibriumwithduringgrowth).DFThasbeen usedextensivelytopredictdefectconcentrationsinZintlphases[ 140 Œ 142 ],butfewsystemshave beencharacterizedexperimentally.Suchcalculationsofdefectshavebeenappliedtocompounds suchasMg 3 Sb 2 wherechangingthegrowthenvironmenthasbeenpredictedtothedefect chemistrytochangethedominantchargecarriertype.Thiscompound,grownunderstoichiometric mixturesispersistently p -type,whereholesarethedominantcarrierduetoMgvacancies.However, withchangestothegrowthenvironment,electronscanbecomethedominantcarrierasisevidenced bytherecentsuccessof n -typeMg 3 Sb 2 ( zT = 1 : 51 at716K)[ 33 ]growninMg-richconditions. DefectformationenergiesarecomparedforbothSb-andMg-richgrowthconditionsinFigure2.8. Experimentalinvestigationofintrinsicdefectsismosteasilyaccomplishedusingsinglecrystal X-raydiffraction,eitherwithalaboratoryorsynchrotronsource.Bothrequirehighqualitysingle crystalsproducedfromdifferentgrowthconditions.Thedefectchemistryofthissystemisfurther investigatedinChapter5forbothSb-andMg-richsinglecrystalsynthesiswherevacanciesand interstitialsitesareandincollaborationwithresearchersattheMaxPlanck InstituteforthePhysicsofComplexSystemsinDresden,Germany. 2.2.3 UnexploredPhaseSpace TheZintlphasespaceisimmense,withnewphasesstillbeingdiscovered[ 44 , 127 , 134 , 144 ].These newphasesaretypicallydiscoveredusingexploratorygrowths,whereelementsaremelted togetherintoamoltenmixturebeforesolidifyingintosinglecrystals.Smallsinglecrystalscanthen bepickedoutandcharacterizedstructurallyusingSC-XRD. Whileagreatdealofefforthasbeenfocusedonthediscoveryandcharacterizationofnew 24 Figure2.8:(a)CrystalstructureofMg 3 Sb 2 withproposedinterstitialsites.(b)Defectformation energyforSb-excessMg 3 Sb 2 withFermilevelat900K.(c)DefectformationenergyforMg-rich Mg 3 Sb 2 withundopedFermilevelat900K[5]. ternaryZintlphases,thevastquaternaryphasespaceisrelativelyunexploredduetoitsinherent complexity.However,withincreasedcomplexitycomestheopportunitytofurthersuppress k l and additionalroutestotuningproperties. TheCa-In-Zn-Sbcompositionspaceisapromisingareatosearchforthermoelectricmaterials. ThisspaceincludesthepromisingthermoelectriccandidatesZn 4 Sb 3 [ 29 ],CaZn 2 Sb 2 [ 145 ],and Ca 9 Zn 4 : 5 Sb 9 [35].InChapter6,thediscoveryofanewquaternaryZintlphaseCa 9 Zn 3 : 1 In 0 : 9 Sb 9 , whichwasdiscoveredasaby-productduringtheattemptedgrowthofZn-dopedCa 5 In 2 Sb 6 is detailed.ThenewCa 9 Zn 3 : 1 In 0 : 9 Sb 9 structurewassolvedwithassistancefromcollaboratorsatthe UniversityofDelaware.MeasurementsoftheelectricalresistivityoftheCa 9 Zn 3 : 1 In 0 : 9 Sb 9 crystals wereperformedatMichiganStateUniversityandshowedresultssimilartothatofCa 9 Zn 4 : 5 Sb 9 compounds[35]. 25 CHAPTER3 CRYSTALGROWTHFROMMOLTENMETALFLUX 3.1 Introduction Ca 5 M 2 Sb 6 (M=Al,Ga,In)Zintlphaseshavebeenreportedtobepromisingthermoelectric materialswithzTvaluesrangingfrom0.35Œ0.7whenoptimallydopedwitheitherNa[ 111 ],Zn [ 1 , 110 , 146 ]orMn[ 147 ].However,allofthesestudiesfocusedonpolycrystallinesamples.Calcu- lationsoftransportbehaviorinCa 5 Al 2 Sb 6 havepredictedenhancedthermoelectricperformance inthepoly-anionicchaindirectionwithamaximum zT = 1 : 37 at800K[ 142 ]forcrystalswithan optimalcarrierconcentrationof ˘ 6 10 19 cm 3 [ 141 ].Toexperimentallycharacterizeanisotropic propertiesofCa 5 M 2 Pn 6 (M=Al,Ga,In;Pn=Sb,Bi)Zintlphases,itisnecessarytogrowhigh quality,macroscopicsinglecrystals.Typically,largesinglecrystalsofsemiconductingmaterialsare grownusingtheCzochralskiorzonetechniques.InthecaseoftheCa 5 M 2 Pn 6 (M=Al, Ga,In;Pn=Sb,Bi)compounds,thesemethodsareimpracticalasthemeltingbehaviorofthese compoundsisincongruent,themeltishighlyreactivewithcontainers,andtheelementspossess highvaporpressures.Forthesereasons,macroscopic(>1mm)singlecrystalsofthisstructure-type havenotbeenpreviouslyreported.InthisworksinglecrystalgrowthofCa 5 M 2 Pn 6 (M=Al,Ga,In; Pn=Sb,Bi)Zintlphasesfromamoltenmetalisreported,alongwithsinglecrystalstructural characterization. 3.1.1 Ca 5 Al 2 Sb 6 TheCa 5 Al 2 Sb 6 composition[ 108 ]possessesanundopedpeak zT ˇ 0 : 10 at725Kbutisapromising thermoelectriccandidateduetoitsinherentlylowlatticethermalconductivity( k min = 0 : 53 W/mK) andabilitytobeoptimallydoped.OptimizationstocarrierconcentrationcanbeachievedwithNa 1 + dopingontheCa 2 + siteforCa 4 : 75 Na 0 : 25 Al 2 Sb 6 whichproducesamaximum zT > 0 : 6 at1000K [ 111 ].FollowupstudieshavealsoinvestigatedZn 2 + [ 146 ]andMn 2 + [ 147 ] p -typedopingonthe 26 Al 3 + sitewithmaximum zT ˇ 0 : 4inbothcases. The n -typecompoundhasnotbeenproducedastheadditionofelectronsthroughdopingwill preferentiallytheSb-Sbantibondingstates.Thisdestabilizingforcecouldleadtotheformation ofCa 3 AlSb 3 [2]. 3.1.2 Ca 5 Ga 2 Sb 6 FromliteratureitisknownthatCa 5 Ga 2 Sb 6 behavesasanintrinsicsemiconductorpossessinga smallerbandgap( E g =0.43eV)thaneithertheAl( E g =0.65eV)orIn( E g =0.64eV)analogwith thisdifferenceexplainedinpartduetorelativeelectronegativities[ 2 ].Italsohasthehighestbipolar contributiontothermalconductivityduetoitssmallerbandgap.Roomtemperaturemeasurements wherethiseffectisminimalplaceitsthermalconductivitybetweenthatoftheAlandInanalogs[ 2 ]. Ca 5 Ga 2 Sb 6 possessesreducedphononvelocitiesandimprovedcarriermobilitywhencomparedto itsCa 5 Al 2 Sb 6 counterpartand p -typedopingofZn 2 + ontheGa 3 + sitehasshowntobeeffectivein modestlyincreasingperformancewith zT ˇ 0 : 35 at750KforCa 5 Ga 1 : 9 Zn 0 : 1 Sb 6 [ 110 ].Thispeak zT value,however,issmallerthanitscounterpartsduetothesmallerbandgap. 3.1.3 Ca 5 In 2 Sb 6 Likeitscounterparts,Ca 5 In 2 Sb 6 behavesasanintrinsicsemiconductorwithlow p -typecarrier concentration.Thiscarrierconcentrationcanbeoptimizedwith p -typedopingoftheIn 3 + sitewith Zn 2 + .WhiletheundopedCa 5 In 2 Sb 6 compositionhasapeak zT ˇ 0 : 15 ,dopedCa 5 In 1 : 9 Zn 0 : 1 Sb 6 hasapeak zT ˇ 0 : 7 at1000K[ 1 ].Ca 5 In 2 Sb 6 alsopossessabandgapgreaterthantheGa composition,allowingformoreeffectivedopingthanthatdeterminedbyZn-dopingofCa 5 Ga 2 Sb 6 [ 140 ].Ca 5 In 2 Sb 6 possessesthegreatestdensityoftheCa 5 M 2 Sb 6 (M=Al,Ga,In)compounds withlatticestiffnessdecreasingwithheavierMatoms.Thistranslatestoalowerbondstrengthand asoftercrystalstructure,leadingtolowerthermalconductivity. 27 Figure3.1:ComparisonofthechainpackingbetweentheCa 5 Ga 2 As 6 (left)andCa 5 Al 2 Bi 6 (right)structure-types.TheCa 5 M 2 Sb 6 (M=Al,Ga,In)compoundsbelongtotheCa 5 Ga 2 As 6 structure-typewiththedifferencebeinghowthepolyanionicchainsarepackedintotheunitcell. 3.1.4 Ca 5 Al 2 Bi 6 TheCa 5 M 2 Sb 6 (M=Al,Ga,In)compoundsallsharealikestructure-type,whileCa 5 Al 2 Bi 6 [ 148 ]takesonadifferentstructure-type.TheCa 5 Al 2 Bi 6 structure-typecompoundshaveamixof metallicandsemiconductingbehavior.BothCa 5 Al 2 Bi 6 andYb 5 M 2 Sb 6 (M=Al[ 104 , 105 ],Ga [ 106 ],In[ 107 ])systemspossesseithernobandgap,yieldingpoorthermoelectricperformancewith zT < 0 : 15 [ 149 ].TheSr 5 In 2 Bi 6 [ 102 ]compositionexhibitssemiconductorbehavior( E g =1.5eV) accordingtoinitialbandstructurecalculations,providingsomehopeforadditionalstudiesintothe compoundasapotentialthermoelectric.Thesetwostructure-typesarecomparedinFigure3.1with withthedifferencebeinghowthepolyanionicchainsarepackedintotheunitcell. 3.2 Background-SingleCrystalGrowth Singlecrystalscanbeproducedbyavarietyofmethodsthatutilizeeitheragas,liquidorsolid statematerialtoatomicallyarrangeaquantityofcompoundintoasinglecrystal.Growthfrom vaporcanbeaccomplishedbyepitaxialprocesses,sublimation-condensationandsputteringamong others[ 143 ].Vaportransportmethodsareoccasionallyusedinthisworktoremoveundesirable 28 fromsinglecrystalsamples.Thismethodwasnotusedtogrowsinglecrystalsduetocomplexities arisingfromtheselectionofapropertransportingagentandunfavorablepartialpressuresofthe crystallineelements. Solid-stategrowthmethodsareprimarilydrivenbyatomicdiffusion.Strainannealing,sintering, heattreatment,depolymorphicphasechanges,precipitationfromsolidsolution,and quenchingaresomeexamplesofsolidgrowthmethods[ 143 ].Thesetechniquesaremoreassociated withgraingrowththansinglecrystalproductionastheiratomicdiffusionmechanismsareextremely slowmakingsinglecrystalproduction,eveninalaboratoryenvironment,prohibitivelytimecon- suming.ManyoftheCa 5 M 2 Pn 6 (M=Al,Ga,In;Pn=Sb,Bi)compoundsdiscussedinthiswork wereoriginallydiscoveredusingsolidstategrowth,inwhichthereactantsweresimplyannealed toallowgrainsofthetargetphasetoform.Bycrushingandseparatingtheresultingsmallgrains (perhaps10-50microns),sufcientlylargecrystalsforstructuredeterminationusingSC-XRDcould beobtained[ 108 , 109 , 148 , 150 , 151 ].Thesecrystalswouldnotbelargeenoughfortransport measurements,however.Inthiswork,sinteringwasusedasanintermediateprocessingstepto condensepolycrystallinesamplesbutstoppedshortofproducingsinglecrystals. Theliquid-to-solidcrystallizationprocessismostoftenusedtoobtainlargebulksinglecrystals. Majormethodsincludethezone,Bridgman,Czochralski,micro-pullingdown,Verneuil, andgrowth[ 152 ],thelatterofwhichisleveragedinthiswork.Theatomiclevelprocessesin allofthesemethodscanbebrokenintothreeparts,beginningfromadisorderedliquidphase: i. Supersaturation isachievedinthesystemallowingcrystalgrowthtopropagateaslongassu- persaturation/supercoolingoftheliquidmeltismaintained.Supersaturationisthedrivingforce fornucleationandcanbeexpressedasthedifferenceinchemicalpotentialofanatom/molecule inthesolution, m s ,andinthesinglecrystal, m c , D m = m s m c : (3.1) When D m > 0 thenthesolutionisassupersaturatedwhileanegativevalueimplies 29 decompositionofthesolid[ 153 ].Inturn,thisquantitycanberelatedthermodynamicallytothe temperature, D m = kT ln S r ; (3.2) where k istheBoltzmannconstant, T isthetemperature,and S r isthesupersaturationratio. Supersaturationisthedrivingforcebehindcrystalgrowthandrelatestothedecreaseinfree energymakingcrystalgrowthfavorable[ 154 ].Temperatureistheexperimentalknobusedto controlthedegreeofsupersaturation. ii. Nucleation canbeexpressedgenerallyasanatomiclevelprocesswherebyatomsormolecules arrangethemselvesinorderedclusters.Theworkrequiredtoformtheseclustersisthedifference inGibb'sfreeenergyoftheinitialandarrangements.Forsinglecrystalgrowth,nucleation ofasinglecrystalliteisdesired,butinpractice,manycrystallitesmightcompete. iii. Crystalgrowth istheprocessbywhichatomsormoleculesareincorporatedintothesurfaceof acrystal.Thisarrangementisgovernedbysurfaceenergytheorywheretheshapeofthesurface isdrivenbyminimizingthesurfaceenergy.Thisenergydeterminesthemostappropriate placementsforanatomtoincorporateitselfbyminimizingthenumberofhighenergydangling bonds[ 143 ].Surfaceenergyisafunctionofcrystallographicorientation,andlargedifferences insurfaceenergycanleadtohighlyanisotropiccrystalmorphology. 3.2.1 FluxGrowth Thetechniqueisthegeneralprocessbywhichcrystallizationoccursfromahightemperature moltensolution,knownasaThismethodhashadsuccessforafarrangingnumberofmaterials includingmetals,semiconductors,andoxides[ 143 ].Heretheelementsofthedesiredcrystalare dissolvedinathatactsasasolvent.Duetothepresenceofthecrystalscanprecipitatewell belowtheirmeltingtemperature.Thischaracteristiciscriticalintheprocessingofincongruently meltingcompoundsandforcompoundsthathaveultra-highmeltingtemperatures.Additionally, 30 phasetransitionsincongruentlymeltingcompoundscanbeavoidedifthevolumechangeassociated withthetransitionleadstodamageofthesinglecrystal.Themethodalsohastheof reducingthermalstrainduetorelativelycoolergrowthtemperaturesandamoregradualtemperature gradientduringcoolingwhencomparedtothezonetechnique. Onedrawbackoftraditionalgrowthisuncontrolledmulti-nucleation.Nucleationcanoccur anywhereinthecrucible,buttypicallyinitiatesagainstthecruciblewalls.Extremelyslowcooling ratesareusedtotrytoencouragefewernucleationsites.Interferencebetweencompetingfacets canleadtointergrowthofcrystallites.Becauseinterferencelimitsthemaximumsizeofindividual crystals,thetypicalcrystalsizeissmallerthanthatofothermelttechniques.The selectionofanappropriatecanalsobechallenging,particularlyinternaryandquaternary compoundswithunknownphasediagrams,andtheremovalofpostcrystalgrowthisoften problematic.TheselectionofanappropriateiselaboratedonbelowinSection3.2.2.1.Despite thesedrawbacks,traditionalgrowthsarestillwidelyutilizedbecausetheydonotrequire expensivespecializedequipment,andthegrowthconditionsarerelativelyrepeatable.Smallscale growthscanalsobecompletedquicklyforexploratorystudies,makingitacost-andtime-effective solutionforcompoundswithunknownmeltingbehavior.ThezoneandCzochralskimethods typicallyrequireaten-foldincreaseintheamountofstartingcompound. ThegrowthsetupisillustratedinFigure3.2wherethedesiredphase,whichinthiscase isportionsofapre-synthesizedpolycrystallinepelletisloadedintothegrowthcruciblealong withelementsusedastheHeretwocruciblesareloadedwithopenendsfacingeachother, separatedbyasieve[ 155 ].Thegrowthisthenheateduntiltheentiremixtureisliquidandslow cooledpastthepointwherecrystallizationofthedesiredphaseoccurs,stillsurroundedbythe liquidThegrowthisthenremovedatthiselevatedtemperature,upsidedownand centrifuged,toseparatethegrowncrystalsfromtheThesecruciblesarecontainedinasealed quartzampule.Quartzmakesanappropriatethin-walledcontainerformanycrystalgrowthsdue toitsexcellentthermalshockresistance,lowcoefofthermalexpansion,andgoodchemical resistance.Thesealingofaquartzampulealsoensurescontroloverthegrowthatmosphere,pressure 31 Figure3.2:Schematicdiagramofagrowthampule(left),containingquartzwoolfor cushioningduringtransportandcentrifuging,growthcruciblecontainingthecompoundand whilethecatchcrucibleisempty.Thetwocruciblesareseparatedbyaaluminasievetocatch crystalsanddrainliquidFluxgrowthcanbeusedoffstoichiometrytogrowincongruent meltingcompounds(right). andvaporizationandprovidesaprotectiveenvironmentforvolatilematerialcontainingsamples [ 156 ].AdditionallyquartziscompatiblewithstandardAl 2 O 3 cruciblesuptotemperaturesinexcess ofourexpectedexperimentalrange[157]. 3.2.2 FluxGrowthofZintlPhases ManyZintlphasesareincongruentlymeltingcompoundsand/orhighlyreactiveasamelt.Ifan incogruently-meltingcompoundiscooledfromtheliquidphaseofthetargetstoichiometry,the resultwillneverbeaphasepuresample.Thereisalwaysaneighboringhigh-meltingtemperature compoundthatwillcrystallizeThegrowthmethodisappropriateforincongruentlymelting compounds,asillustratedinFigure3.2(right),becausethemeltcanhaveanoffstoichiometry composition.IfABisthetargetphase,thenoneusesanA-richWhenthemeltiscooledinto L+ABregion,theABcompoundwillbegintosolidify.Theremainingliquidcanberemovedby centrifugationaslongasthetemperatureisaboveT 1 .Thisiscriticalinsystemswherethemelting 32 behaviorofasystemisunknown,asisthecaseoftheCa 5 M 2 Pn 6 (M=Al,Ga,In;Pn=Sb,Bi) phasecompounds.Subsequenttestingrevealedincongruentmeltingbehaviorthatmakescrystal growthbyothermethodsdif FluxgrowthsareverywidespreadforZintlcompounds[33,132,158],includingseveral5-2-6 familycompounds[ 144 ].SinglecrystalsofZintlphaseYb 5 Ga 2 Sb 6 havebeensuccessfullygrown fromawithitsresistivitysuccessfullycharacterizedinthepreferredgrowthdirection[ 106 ]. ThiscompoundtakesonthesamestructureastheCa 5 Al 2 Bi 6 structureandactsasaproofofconcept forourCa 5 M 2 Pn 6 (M=Al,Ga,In;Pn=Sb,Bi)growths. Thismethodalsoprovidesxibilitywithanumberofexperimentalparametersthatcanbe adjustedincludingcruciblesize,temperature,heatingrate,holdingtimes,coolingrate,extraction temperature,andcompositionamongothers.Theseparameterscanbeoptimizedandtrackedto producelargercrystalsinrepeatablegrowthconditions[159]. 3.2.2.1 MetallicFluxSelection TheselectionofanappropriateforgrowthofZintlphasescanalsobechallenging,inparticular internaryandquaternarycompoundswithunknownphasediagrams.Appropriatecandidatesare selectedbasedofanumberoffactors,includinglowmeltingtemperature,adiscrepancy betweenitsmeltingtemperatureandboilingpoint,likelihoodtoseparatefromgrowncrystalsby eitherphysicalorchemicalmeans,and,mostimportantly,aninabilitytoformstablebinaryor ternarycompoundswithanyofthereactants[ 160 ].SelectedelementsarelistedinTable3.1 alongwiththeirmeltingtemperatures( T m ),viscosityattheirmeltingtemperature( h ( T m ) ),and solidandliquid(at T m )densities.Alowviscositymakesthecentrifugingprocessmoreeffective, whilesimilardensitytothetargetphasepreventslargecompositiongradientsinthemelt.Chemical etchingcanremoveexcessbuttheetchingprocesscanalsopotentiallyattackthegrowncrystals. Aluminum Aluminumisacommon[ 161 Œ 165 ]duetoitslowvaporpressure(2327 ° C,1atm.),andlow viscosityasshowninTable3.1.Ifcentrifugingisnotcompletelysuccessful,aluminumcan 33 Table3.1:Viscositydataforselectedelementsalongwithdensityinformationforsingle crystaltargetcompounds. Density(g/cm 3 ) T m (°C) h ( T m ) (mPas)SolidLiquid( T m ) Al6601.302.702.38 Bi2721.809.7810.05 Ga302.045.916.10 In1571.897.317.02 Pb3282.6511.3410.66 Sb6311.226.706.53 Sn2321.857.276.99 Zn4203.857.146.57 Ca 5 Al 2 Sb 6 ŒŒ4.26Œ Ca 5 Al 2 Bi 6 ŒŒ6.25Œ Ca 5 Ga 2 Sb 6 ŒŒ4.70Œ Ca 5 In 2 Sb 6 ŒŒ5.00Œ alsoberemovedchemicallybyNaOH[ 166 ]orHCl[ 165 ]solutions.Aluminumvapor,however, reactswithquartzampules,compromisingtheinternalinertvacuumatmospheresealedinside, 4Al + 3SiO 2 ! 2 a -Al 2 O 3 + 3Si[167,168]. Inordertodiminishtheseverityofthisreaction,growthscanbeperformedmorequicklyor quartztubescanbecarboncoated.AnotherdrawbackofusinganAlisthatitpossessesa highermeltingtemperaturethanmostoftheeslistedinTable3.1.Thisisnotanissueprovided thattheremovalandcentrifugetemperaturearehigher.FortheprospectiveCa 5 Al 2 Sb 6 growth,this wasnotanissueduetothehighextractiontemperature. Bismuth Bismuthisacommon[ 169 Œ 172 ]thathasalsoproveneffectiveasa[ 173 , 174 ], possessingalowmeltingtemperatureandvaporpressure(1627 ° C,1atm.).Inthiswork,Biwasused asaforthegrowthsofCa 5 Al 2 Bi 6 andsinglecrystalsolubilitystudyfortheCa 5 Al 2 Pn 6 (Pn=Sb,Bi)system.Bismuthcanalsoberemovedwithdilutehydrochloricacid. Gallium Galliumisapopular[ 175 Œ 177 ]duetoitsextremelylowmeltingtemperatureandvapor pressure(2427 ° C,1atm.).Adrawbackofthiselementisthatittendstowettothesurfacesof growncrystalsevenafterthoroughcentrifuging[ 166 ],possessingahigherviscositywhencompared 34 toAl,In,andSbasshowninTable3.1.ExcessGacanberemovedbysoakingcrystalsina5MI 2 dimethylformamide(DMF)solutionwhereitisabletoformsolubleGaI 3 [178]. Indium Indiumisanotherpopular[ 179 Œ 181 ]lowmeltingpointthathasapropensitynottowetto crystalsurfaces[ 166 ].Italsohasalowvaporpressure(2167 ° C,1atm.)andviscosityasshownin Table3.1.ExcessIncanalsoberemovedwithdilutedHClsolutionsifcentrifugingproves insuf[181].ThismakesforanidealcandidatefortheCa 5 In 2 Sb 6 singlecrystalgrowth. Lead Leadisanothercommonchoice[ 182 Œ 185 ]withlowmeltingtemperatureandvaporpressure (1737 ° C,1atm.).PbdoesnotformbinaryphaseswithSb[ 186 ],Ga[ 187 ],orAl[ 188 , 189 ],and binaryphasesareonlyformedwithInattemperaturesmuchlowerthantheextractiontemperature forthiswork[ 190 ].ThischoicesuffersfromwettingissuessimilartothatofGa,andSn, makingitdiftoseparatefromgrowncrystals[ 166 ].Secondly,itishighlytoxic,complicating synthesis.Lastly,Pbisextremelydenseandthehomogeneityofthemeltcompositionmaysuffer. Tin Tinisapromisingduetoitslowmeltingtemperature,lowvaporpressure(2727 ° C,1atm.), anditsgeneralaversiontoformingbinarycompounds[ 191 , 192 ],makingitacommonchoicefor crystalgrowth[ 182 , 193 Œ 195 ].Snunfortunatelywetstogrowncrystalsmorereadilythanmost es.Inordertoremovefromcrystalsurfaces,aHgbathcanbeusedthatcanbedistilled awaythroughevaporation.Anon-toxicalternativeissoakinginGa,butaprocesstoremovetheGa isthenneeded[ 196 ].ThisisappealinginthegrowthofCa 5 Al 2 Sb 6 astheAl-Snsystemisa simpleeutecticthatformsnobinaries[197]. Antimony Whileantimonyhasahighermeltingtemperaturethanmostoftheeslistedhere,itpossess asufcientlylowvaporpressure(1617 ° C,1atm.),andverylowviscositylistedinTable3.1.While examplesofitbeingusedasaexist[ 198 ],itisnotcommonlyusedasitformsstablephases withrare-earthelementsthatarepreferentiallygrowninplaceofthedesiredphase[ 166 ].Thiswork 35 utilizesatleastanSbpartialforalloftheCa 5 M 2 Pn 6 (M=Al,Ga,In;Pn=Sb,Bi)compounds. 3.2.2.2 CrucibleSelection Alumina(Al 2 O 3 )crucibleswereusedforallgrowthtrialsasitisacosteffectiveoptionthatis stableuptohightemperaturesandchemicallyresistanttocommonlowmeltingtemperature elementssuchasAl,Bi,Cu,Ga,Ge,In,Pb,Sb,andSn.Highpurityaluminacruciblesarealso widelyavailableinmanygeometriesandevencruciblesetsforgrowththatinclude compatiblesieves[ 199 ].Cleaningthesecruciblesisdifcultifnotimpossibleduetothemolten elementspenetratingintothegrainboundariesofthecrucible,makingthemasingleuseitem[ 154 ]. 3.2.3 Energy-dispersiveX-raySpectroscopy Energy-dispersiveX-rayspectroscopy(EDS)wasusedtoperformelementalanalysisofsingle crystals.Thisprocessusesacceleratedelectronsgeneratedfromanelectronguntoirradiatea samplewiththekineticenergyoftheseelectrons.Thiselectronkineticenergyisdissipatedwithin thesampleandgeneratescharacteristicX-raysoftheatomstruckbytheelectronbygenerating anelectronholethatisthenbyanelectronfromanoutershellasshowninFigure3.3(left). Thisprocess,aformofthephotoelectriceffect,emitsX-raysthatarecollectedandusedtoidentify elementswithinacompound,basedonthecharacteristicemissionoftheelements.Electron transitionsofmajorlines,areillustratedinFigure3.3(right)whicharecharacteristicoftheemitting atom.Thisanalysisdetectselementsthatarepresentintheoutermost10nmofthesamplemaking itheavilybyanyelementsthatmayremain. AnenergysweepontheorderofkeVisperformedandaspectrumiscollectedwiththearea underneaththecurverelatingtotheamountofeachelementpresent.ofeachelement istypicallycalculatedwiththeexpression, I ij = KT ( KE ) L ij s ij Z n i ( z ) e z = l ( KE ) cos q dz ; (3.3) 36 Figure3.3:CharacteristicX-rayproductionfromincidentelectronsforEDSanalysis(left). Electrontransitionsofmajorlines,characteristicoftheemittingatom(right). where I ij istheareaofpeak j fromelement i , K istheinstrumentconstant, T ( E K ) thetransmission functionoftheanalyzer, L ij ( g ) theangularasymmetryfactorfororbital j ofelement i , s ij the photoionizationcross-sectionofpeak j fromelement i , n i ( z ) theconcentrationofelement i ata distance z belowthesurface, l ( E K ) theinelasticmeanfreepathlength,and q isthetake-offangleof thephotoelectrons.X-rayareaoftheirradiatedsampleandthesolidangleofthephotoelectrons acceptedbytheapparatusarecontainedwiththeinstrumentconstant K [ 200 ].Thisexpression assumesanamorphoussamplestructurewhilesinglecrystalscangeneratepeakintensitiesthat deviatefromexpectedvaluesduetotheirorderedstructureandorientationtothebeamanddetector. 3.2.4 SingleCrystalX-rayDiffraction SC-XRDisanon-destructiveanalyticaltechniquethatprovidesinformationonthestructureof thecrystallatticeincludingunitcelldimensions,atomicpositions,site-ordering,bond-lengthsand bond-angles[ 201 ].AdiffractionpatterniscollectedasthecrystalisrotatedthroughtheX-ray beam.Thespotsgeneratedinadiffractionpatternaretermedastheyareoffof orderedparallelplanesintheatomicstructure,satisfyingBragg'slaw.Fromthisdiffractionpattern theunitcellcanbedetermined( a,b,c and a , b ,and g ).TheCa 5 M 2 Pn 6 (M=Al,Ga,In;Pn=Sb, 37 Bi)systemofinterestinthisworkformstheorthorhombiccrystalstructurewhere a 6 = b 6 = c and a = b = g = 90° .Thefacesofthisunitcellaretypicallythemostapparentsetsofplanesandact assourcesofdiffractionthataredesignatedbylatticeindices,alsoknownasMillerindices[202]. TheX-raysourceiscreatedbybombardingametaltarget,inourcaseMo,withelectrons producedbyaheatedandsubsequentlyacceleratedbyanelectricThesehigh-energy electronsstrikeanddisplaceanelectronfromaloworbital,liketheprocessdescribedforEDS butinthetargetratherthanthesample.Anelectronfromahigherorbitaldropsintothevacancy, emittingtheexcessenergyofthistransitionasanX-rayphotonasillustratedinFigure3.3(left). Thetargetmaterialproducesnarrowcharacteristiclinesofwavelengths[ 203 ].Inorderto produceamonochromaticoutputfromaMosource,asecondaryZrisusedtoremove K b radiation.Braggfromthesamplearemeasuredonascintillationcounterthatcontainsa phosphorescentmaterialthatproducesaoflightwhenanX-rayisabsorbed[204]. Thistechniquerequiressmall( ˇ 0.1mminlongestdiagonaldirection),butexcellentquality singlecrystals.Thecrystalsmustnotpossessntimperfections(cracks,twinning,multi- crystals).Sampleswithtwinscanbeanalyzed,howeveranyfurtherdisordermakes thismethodprohibitivelydifAsageneralrule,thelongestdiagonalthroughthesinglecrystal mustnotexceedthebeamsize. Oncedatacollectioniscompletetherawintensitiesareprocessed.Scalingiscompletedwhereby ofthesameindexthatweremeasuredinmultipleframesaregivenidenticalintensities. Nextiscompletedwhereusabledatafrompartialisrecoveredand spuriousdataremovedthroughtheprocessofdatareduction[205]. 3.3 ExperimentalMethods 3.3.1 FluxGrowth FluxgrowthexperimentswerecarriedoutinaThermoFisher1100 ° Cboxfurnacewith temperaturemaintainedthroughaUP150programmablecontrollerandmonitoredwithtypeK thermocouples.Al 2 O 3 cruciblesetswereloadedintosealedquartzampulesatavacuum 38 oflessthan4 10 6 torr. HighpurityelementswereusedinthesynthesisofthevariousCa 5 M 2 Pn 6 (M=Al,Ga,In;Pn= Sb,Bi)compounds,including:Al(AlfaAesar:shot,approx.4-8mm,99.999%),Bi(Sigma-Aldrich: granular,99.99+%),Ca(Sigma-Aldrich:dendriticpieces,99.9%),Ga(Sigma-Aldrich:solid, 99.99%),In(AlfaAesar:shot,5mm&down,99.9995%),Pb(AlfaAesar:shot,3mm,99.999%), Sb(AlfaAesar:shot,6mm&down,99.999%),andSn(AlfaAesar:shot,3mm,99.9999%).The overallmeltcompositionsforthevariousgrowthsareshowninFigures3.7-3.10.TheCa 5 M 2 Sb 6 (M=Al,Ga,In)singlecrystalswereallsuccessfullygrownfromatemperatureofroom temperatureto900 ° Cin12hours,followedbyasoakfor2hoursthenslowcoolingto730 ° Cata rateof3 ° C/hr.TheCa 5 Al 2 Bi 6 singlecrystalsonlydifferedintheirextractiontemperature,which was470°C. 3.3.2 VaporTransport Vaportransportwasusedinsomecasestoremoveexcessfromsinglecrystalsgrowths.Samples weresealedinsideaquartzampuleandplacedhorizontallyinaMTICorporationGSL-1100Xtube furnace.Theendwiththesamplewasplacedinthefurnace,whiletheotherendoftheampulewas atroomtemperature,externaltothefurnace.Figure3.4showsapairofsamplesbeingprocessed with T hot = 500°C. 3.3.3 MaterialCharacterizationTechniques 3.3.3.1 Microscopy OpticalmicroscopeimagesweretakenwithaKeyenceVHX-600upto1000x Scanningelectronmicroscope(SEM)wasperformedonaZeissEvoLS25,andaTescanMira 3XMH. 39 Figure3.4:Horizontaltubefurnacewithtwoampulespositionedoppositeeachother(left). Illustratedtemperatureandvapormotion(topright)withdepositedelementsvisible onampulessurfaceafterprocessing(bottomright). 3.3.3.2 Energy-dispersiveX-raySpectroscopy EDSwasperformedusinganEDAXApolloXmodulewithanactiveareaof10mm 2 .Imageswere collectedandprocessedwiththeTextureandElementalAnalyticalMicroscopy(TEAM)software suitetodeterminetheapproximatechemicalcompositionofcrystalandcomponents.Single crystalswereplacedonconductingcarbontapetoeliminateanypotentialchargebuildup.All samplesevaluatedweresemiconductingormetallicincharacter. 3.3.3.3 SingleCrystalX-rayDiffraction SinglecrystalX-raydiffractionwasperformedusingaBruker-AXSApexIICCDinstrumentshown inFigure3.5at173K,withdataacquiredusingagraphite-monochromatedMoK a radiationsource( l = 0 : 71073 Å)producinga0.5mmbeamdiameter.Datawasintegratedwith SAINT[ 206 ].Singlecrystalswerecutdowntoanappropriatesizewithasurgicalscalpeland mountedtoagoniometerhead.Sampleswerethenheldinacoldnitrogenstreamtoreducethermal motionoftheatomsandimprovescrystalscatteringpower,leadingtoabetterqualitystructure. Structuresweresolvedusingdirectmethodsandon F 2 usingSHELX[ 207 ]subroutines withintheOlex2-1.2crystallographicsuite[ 208 ].weremergedusingSHELXLwith respecttothecrystalclassforthecalculationofApreliminaryrotationimagewas 40 Figure3.5:(1)Oxford600lowtemperaturedevice,(2)X-rayemitter,(3)Charge-Integrating PixelArrayDetector(CPAD),(4)Cameraforviewingcrystal,(5)three-axisgoniometer,and(6) samplemountedonnylonloop. collectedtoperformaninitialqualitycheckanddeterminationofunitcelldimensions. 3.3.3.4 DifferentialScanningCalorimetryandThermogravimetricAnalysis Differentialscanningcalorimetry(DSC)isathermalanalysistechniquewherethedifferencein theamountofheatrequiredtoincreasethetemperatureofthesampleandreferenceisrecorded asafunctionoftemperature[ 209 ].WhileDSCisathermalanalysistechniquefocusedonheat, thermogravimetricanalysis(TGA)isfocusedonthemassofasubstanceinresponsetoheat.TGAis usefulforidentifyingphasetransitions,absorption,adsorptionanddesorption[ 210 ].Simultaneous DSC/TGAexperimentswereconductedonaTAInstrumentsSDTQ600systemandcarriedout atthePlatformfortheAcceleratedRealization,Analysis,andDiscoveryofInterfaceMaterials (PARADIM)atJohnsHopkinsUniversity. 3.4 Results&Discussion 3.4.1 PhaseDiagramDeterminationandCrystalGrowthOptimization Inthisstudy,singlecrystalsweregrowninfourdifferentternarysystems(Ca 5 M 2 Sb 6 withM=Al, Ga,In,andCa 5 Al 2 Bi 6 ).Ineachcase,littleinitialknowledgeoftheternaryphasediagramsexists. Startingwithonlythebinaryphasediagrams,itwasnecessarytocarryoutexploratorysynthesisto 41 identifyselectedtielines,eutecticpoints,andliquidussurfacesintheregionsofthephasediagram usedforgrowthusingpowderandsinglecrystalX-raydiffraction. 3.4.1.1 Ca 5 Ga 2 Sb 6 SinglecrystalgrowthbeganwiththeCa 5 Ga 2 Sb 6 compositioninpartduetoitschemicalsimilarity withYb 5 Ga 2 Sb 6 ,whichhaspreviouslybeenreportedtogrowfromaGaTheCa-Ga-Sb ternaryphasediagram,showninFigure3.7,isconstructedfromtheknownbinaryphasediagrams [ 211 Œ 213 ]andincludesthetwoternaryphasesthatarecurrentlyknowntoexist:fellowZintlphase Ca 11 GaSb 9 [ 214 ],andtargetphaseCa 5 Ga 2 Sb 6 [ 109 ].Nothingwasknownaboutthe oftheternarycompositionsinthisphasespace.Ouraimwastodeterminetheapproximate meltingtemperatureandwhetherornotCa 5 Ga 2 Sb 6 meltscongruently. BothDSCandTGAanalysiswereperformedusingapolycrystallineCa 5 Ga 2 Sb 6 sample (synthesisdescribedinref.[ 2 ])fromroomtemperatureto1000 ° C.FromthedatainFigure 3.6,heatwintothesampleattemperaturesapproaching760 ° Cisobserved,which subsequentX-raydiffraction(XRD)analysiswouldasincongruentmelting.Rietveld analysiswasperformedtodeterminethat,uponmeltingandthecompoundhad partlydecomposedintoCa 11 Sb 10 ,Sb,andGa.Fromthepresenceofdecompositionproducts,it canbeconcludedthatthiscompoundisincongruentlymelting,makinggrowthanappropriate growthmethod.Further,theCa-richmeltwasfoundtoreactseverelywiththeAl 2 O 3 crucible, presumablyformingcalciumoxidewiththealuminacrucible, Al 2 O 3 + 3Ca ! 3CaO + 2Al .This suggeststhatcrystalgrowthofthiscompoundinAl 2 O 3 crucibles(oneofthemostcost-effective options)requiresatodilutethereactiveCa. TheCa-Ga-Sbternaryphasediagramcontainsseveralhighmelting-temperaturebinaryCa-Sb andCa-Gaphases.Forthisreason,initialfocusisonesrichinGaand/orSb,movingthetotal meltcompositionontheternaryphasediagramfurtherawayfromCaandtheundesiredternary Ca 11 GaSb 9 .TheonlybinarybetweenGaandSbisGaSb( T m =712 ° C),whichcanbeavoided entirelyiftheextractiontemperatureissufcientlyhigh.TheCa 5 Ga 2 Sb 6 meltingtemperatureis 42 Figure3.6:DSCandTGAdataforCa 5 Ga 2 Sb 6 fromroomtemperatureto1000 ° Cshows incongruentmeltingbeginningabove760°C. approximatedfromtheDSC/TGAresultsas T m ˇ 780° C,whichledtotheselectionofanextraction windowofapproximately720-750degrees. Severalgrowthsusingofdifferentcompositionswereattempted,includingGa,Ga+Sb, andSb.elementsweretypicallytargetinga9:1ratiooftopolycrystalline Ca 5 Ga 2 Sb 6 precursorasaprecautionagainstreactivity.Theoverallcompositionsofthemelt foreachgrowthareshownasthesquaresymbolsinFigure3.7,withgreenandredsquaresrepre- sentingsuccessfulandunsuccessfulcrystalgrowths,respectively. ASb 20 wasattemptedbutfailedtoproducesinglecrystalsofthedesiredphase,producing polycrystallineCa 5 Ga 2 Sb 6 ,Sb,andverysmallamountsofGaSbandCaSb 2 .FromtheseXRD resultsatielineconnectingCa 5 Ga 2 Sb 6 andSbonthephasediagramcanbeinferred,withCa-rich portionsofthemeltformingCaSb 2 andmoreGa-richportionsformingGaSb.AGa 34 Sb 34 producedpolycrystallineCa 5 Ga 2 Sb 6 ,SbandGaSb,whilepureGaesproducedpolycrystalline Ca 5 Ga 2 Sb 6 ,CaGa 4 ,andelementalGa.Fromthesephasetrianglesanumberofusefultielinesfor thisphasediagramaredetermined. 43 NonseswerealsoattemptedwithaBi 20 decomposingtoCa 11 Sb 10 ,Ca 2 Sb,Ga, andBi.Snes(Sn 81 ,Sn 115 ,Sn 130 ,Sn 288 )werealsoattemptedbutdidnotproducecrystals. AsmalleramountofSn(Sn 15 20 )wasshowntoproducecrystalsintheCa 5 Al 2 Sb 6 trialsbut severewettingissuesmadethisanimpracticalchoiceevenifloweramountsofSnwerefoundtobe successful. Ultimately,itwasdeterminedthatCa 5 Ga 2 Sb 6 crystalscouldbegrownoptimallyinaGa 73 Sb 42 Successfulcrystalgrowthyieldscrystalslargeenoughtoremaininthegrowthcrucible sideofthesieveaftercentrifuging.AnopticalimageofthesecrystalsisshowninFigure3.7. Ahightemperaturesoakof900 ° CfortwohourswasselectedtoensurethatelementalCawas completelydissolveinthemeltandthattheelementsweremixedhomogeneously.Anappropriately slowcoolingrateof3 ° C/hrwasselectedandremainedunchangedwhilethecomposition wasadjusted.Crystalgrowthsizecouldpotentiallybeimprovedbyaslowercoolingrate.These parametersinbothtemperatureandcomposition(M 73 Sb 42 )translateddirectlytothe Ca 5 In 2 Sb 6 andCa 5 Al 2 Sb 6 compositions. 3.4.1.2 Ca 5 In 2 Sb 6 TheternaryCa-In-SbphasediagraminFigure3.8isconstructedfromtheknownbinaryphase diagrams[ 212 , 215 , 216 ]alongwiththetwoternaryphasesknowntoexist:fellowZintlphase Ca 11 InSb 9 [ 214 , 217 ]anddesiredphaseCa 5 In 2 Sb 6 [ 109 ].ItisverysimilartothatoftheCa- Ga-Sbphasediagram,anditisalsopresumedthatCa 5 In 2 Sb 6 alsomeltsincongruently.Similar totheGa-analogue,In-andSb-richeswerefavoredastobetteravoidgrowingtheCa-rich Ca 11 InSb 9 .ThissystemfromonlypossessingasinglelowermeltingpointIn-Sbbinary, InSb( T m = 527° C).Thiscouldpotentiallyallowforalowerextractiontemperatureifneeded.A pureSb(Sb 20 )wasattemptedbutdidnotproducecrystalsmainlyduetotheexistenceof Ca 8 In 3 ,withthepolycrystallineCa 5 In 2 Sb 6 decomposingtoCa 8 In 3 ,CaSb 2 andelementalSb.As evidencedbythephasediagraminFigure3.8thisnarrowlymissesthetargetphase.Auseful phasetrianglecanbededucedfromthishowever,concludingthatamixedSb-Inthatismore 44 In-richwouldhavebetterresults,byshiftingtheoverallmeltcompositionintothethree-phase regionboundbyCa 5 In 2 Sb 6 ,Sb,andInSb. SinglecrystalsofCa 5 In 2 Sb 6 weresuccessfullygrownfromanIn 73 Sb 42 withapproximately 0.25gramsofpolycrystallineCa 5 In 2 Sb 6 used.Thisamountwasenoughtogeneratehundredto thousandsofcrystalspergrowth,largelydependentonthesuccessofthespontaneousnucleation. AnSEMimageofthegrownCa 5 In 2 Sb 6 singlecrystalsareshowninFigure3.8.Thesurfacesof thesecrystalsappearedcleanerthantheirCa 5 Ga 2 Sb 6 counterparts,largelyduetothepoorwetting propertiesofGa,whichresultedinitadheringtocrystalsurfacesmorereadilythaneitherInorSb. 45 Figure3.7:TheCa-Ga-Sbternaryphasediagramwithknownbinaries(black),desiredCa 5 Ga 2 Sb 6 (blue),andotherternaryphases(purple).Unsuccessful(redsquares)andsuccessful(greensquare) growthswereusedtodeterminetheblacktielines.(upperright)Aplausiblepseudo-binary phasediagramwasdevelopedbasedonthesuccessfulgrowth.(lowerright)opticalimageof growncrystals. Figure3.8:TheCa-In-Sbternaryphasediagramwithknownbinaries(black),desiredCa 5 In 2 Sb 6 (blue),andotherternaryphases(purple).Unsuccessful(redsquares)andsuccessful(green square)growthswereusedtodeterminetheblacktielines.Aplausiblepseudo-binaryphase diagramforthesuccessfulgrowth(upperright)andSEMimageofgrowncrystals(lower right). 46 Figure3.9:TheCa-Al-Sbternaryphasediagramwithknownbinaries(black),desiredternary phaseCa 5 Al 2 Sb 6 (blue),andundesirableternaryphases(purple).Unsuccessful(redsquares)and successful(greensquare)growthsdevelopedblacktielinesbetweencompounds.Aplausible pseudo-binaryphasediagramforthesuccessfulSb 20 (upperright)andSEMimageofgrown crystals(lowerright). Figure3.10:TheCa-Al-Biternaryphasediagramwithknownbinaries(black),desiredternary phaseCa 5 Al 2 Bi 6 (blue).Successful(greensquare)growthdevelopedblacktielinebetween compounds.Aplausiblepseudo-binaryphasediagramforthesuccessfulBi 20 (upperright) andSEMimageofgrowncrystals(lowerright). 47 Figure3.11:LargeCa 5 Ga 2 x In x Sb 6 singlecrystalwithwellfacets(left).Similarlylarge crystalbutconstructedofalargenumberofsmallerCa 5 Ga 2 x In x Sb 6 singlecrystalsgrownin parallel(right). 3.4.1.3 Ca 5 Ga 2 x In x Sb 6 TheelementsGaandInareisoelectronic,soitisexpectedthatCa 5 Ga 2 Sb 6 andCa 5 In 2 Sb 6 would exhibiteitherpartialorcompletesolubility.Further,theelectronandphononscatteringmechanisms inalloysaredominatedbypointdefectscattering,meaningthattheanisotropyofelectronicand thermalconductivityinalloyedcrystalsmightbedifferentthaninthepurecompounds.Forthese reasons,growthofalloyedCa 5 Ga 2 x In x Sb 6 crystalswerepursued. WereportthesinglecrystalalloyCa 5 Ga 2 x In x Sb 6 ,successfullygrownfromavepart mixtureofCa 5 Ga 2 Sb 6 (polycrystalline)+Ca 5 In 2 Sb 6 (polycrystalline)+Ga 37 : 5 +In 37 : 5 +Sb 42 elements.ThesametemperatureandtimeparametersdescribedforCa 5 Ga 2 Sb 6 wereused forthealloyedsamples.Asdiscussedbelow,theEDSandSC-XRDanalysisthatthe crystalscontainmixedoccupancyofGaandInonthemetalsite.Fromthiscrystalgrowth,two largecrystallinemassesweregrownalongwithathickarrayofsmallercrystals,showninFigure 3.11.ThecrystalshowninFigure3.11(left)measures7.34mminlengthand0.57mminwidth withfacetsthatrunthelengthofthecrystal,implyingthecrystallinemassisalmost entirelyasinglecrystal.Incontrast,thecrystallinemassshownin3.11(right)hasnolargewell facetsandappearstoabuildupofsmallercrystalsthatallgrewparalleltooneanotherin thegrowthenvironment.Thismassmeasures8.39mminlengthand1.40mminwidth. 48 3.4.1.4 Ca 5 Al 2 Sb 6 TheCa-Al-SbternaryphasediagraminFigure3.9isconstructedfromtheknownbinaryphase diagrams[ 212 , 218 Œ 220 ].IncontrasttotheGaandInphasediagrams,theCa-Al-Sbphasediagram hasfourternaryphasesknowntoexist:ZintlphasesCa 3 AlSb 3 [ 148 ],Ca 14 AlSb 11 [ 150 ],Ca 11 AlSb 9 [214],anddesiredphaseCa 5 Al 2 Sb 6 [108]. TheZintlphaseCa 3 AlSb 3 isanotherthermoelectriccandidatecompoundformingtheCa 3 InP 3 structure-type,andcomposedofchainsofcorner-sharingAlSb 4 tetrahedra.Thiscomposition hasbeensuccessfullydopedwithNa + 1 ontheCa + 2 siteforpolycrystallinesamples,producinga maximumof zT = 0 : 8 at777 ° CforCa 3 x Na x AlSb 3 (x=0.03,0.06)[ 221 ].This compoundwillbedifculttodiscernfromourintendedCa 5 Al 2 Sb 6 singlecrystalsynthesisas EDSwillmostlikelynotbesensitiveenoughtoidentifytheexcessCaofCa 3 AlSb 3 .Fortunately, SC-XRDcanbeusedinsteadtoreadilydistinguishbetweenthetwostructures.TheZintlphase Ca 14 AlSb 11 hasalsobeenstudiedforpotentialthermoelectricapplications[ 222 ]asitoffersunusual Sb-SbbondingmanifestinginlinearSb 7 3 chainsandisolatedAlSb 4 tetrahedra[ 223 , 224 ].This compositionwillbeeasilydistinguishablefromourintendedCa 5 Al 2 Sb 6 atEDSduetoitsrelative AlyandatSC-XRDduetoitslargerunitcell. TheCa 14 AlSb 11 compositionhasbeenstudiedforpotentialthermoelectricapplication[ 222 ]as itoffersunusualSb-SbbondingmanifestinginlinearSb 7 3 chainsandisolatedAlSb 4 tetrahedra [ 223 ].[ 224 ].ThiscompositionwillbeeasilydistinguishablefromourintendedCa 5 Al 2 Sb 6 atEDS duetoitsrelativeAlyandatSC-XRDduetothelargerunitcell(Ca 5 Al 2 Sb 6 /Ca 14 AlSb 11 : a =14.07/16.68, b =12.09/16.68, c =4.46/22.42). Inadditiontothechallengeofavoidingformationofthecompetingternaryphasesdescribed above,growthofCa 5 Al 2 Sb 6 crystalsisfurthercomplicatedbythefactthataluminumvaporattacks thequartzampules,asshowninFigure3.12(left).Inrarecases,thisreactioncausedtheampules toshatterduringcentrifuging.Thisproblemwaseliminatedbycarboncoatingtheinteriorofthe quartztubesbyburningoffacetoneandrotatingthequartztubeunderamethane-richwith resultsshowninFigure3.12(right). 49 Figure3.12:Aluminumvapordamagetothequartzampule,concentratedatthegapbetweenthe cruciblesandsievepriorto(left).Carbon-coatedquartzampulesformedaprotectivebarrier (right). FluxgrowthsweresuccessfulinproducingCa 5 Al 2 Sb 6 singlecrystalsusingthreedifferent compositions:Al 73 Sb 42 ,Sb 20 andSn 15 ,showninFigure3.16.TheAlandSbutilizedwasthe sameasthoseusedintheothersuccessfulCa 5 M 2 Sb 6 (M=Ga,In)singlecrystalgrowths.These Sbesweresuccessfulmainlybecauseoverallmeltcompositionfellinsideofthethreephase trianglecontainingSb,Ca 5 Al 2 Sb 6 ,andCaSb 2 .ThiswasincontrasttotheCa 5 In 2 Sb 6 system, whichcontainsadifferentthree-phaseregionincludingCa 8 In 3 . TheamountwasreducedintheSb 20 (comparedtoAl 73 Sb 42 )trialbutnoCareaction withthecontainerwasobserved.TheSb 20 producedcrystalsinlargenumberswithlittle adheredtothecrystalsurfaces,withresultscomparabletotheAl 73 Sb 42 WhileSbhas notshowntowettocrystalsurfacesthereappearstobeabaselevelofthatremainsafter centrifugingduetotheliquidgettingcaughtbetweenthehundredstothousandsofthegrown crystalsperrun.Smallerquantitiesofstartingmaterialmayreducethisissuebutmayriskadditional reactionofCawiththecrucible. SinglecrystalgrowthofCa 5 Al 2 Sb 6 wasalsoattemptedfromaSn 20 andSn 15 witha representativecrystalshowninFigure3.16(c-d).Theyieldsforthesegrowthswereextremelylow andthecrystalswereheavilycoatedintosuchanextentthatSC-XRDwasnotpossiblewithout 50 asecondaryprocesstoremovetheSnAPbwasalsoattempted(Pb 94 )butdidnotproduce crystals.SimilartotheCa 5 In 2 Sb 6 attempt,asmalleramountofPbmayimproveintermixing, buttoxicityandwettingconcernsmakethisanunfavorablechoicewhenotheroptionshaveshown success. 3.4.1.5 Ca 5 Al 2 Bi 6 TheCa-Al-BiternaryphasediagraminFigure3.10isconstructedfromtheknownbinaryphase diagrams.IncontrasttotheSb-containingphasediagrams,thereisnobinarycompoundalongthe Bi-Aledge.ThegrowthattemptoftheCa 5 Al 2 Bi 6 replicatedthesuccessfulCa 5 Al 2 Sb 6 +Sb 20 growthusingaBi 20 andanextractiontemperatureof730 ° C.Thistemperaturewas toohigh,withtheentiremeltdrainedintothecatchcrucible,indicatingthatnothinghadyet Successfulcrystalgrowthoccurredwithanextractiontemperatureof470 ° Cwith elementalcompositionbyEDSandstructuralbySC-XRD.Crystalsare showninFigure3.10(right)and3.15(e-f).Thetemperaturestillsoakedat900 ° Cfortwo hoursbeforecoolingatarateof10 ° C/hruntil620 ° Cwhereitwasthencooledby3 ° C/hrtothe 470 ° Cextractiontemperature.Thisslowerratewastoaccountforthelikelycrystalformation duringthistime.Growthscouldbefurtheroptimizedtopotentiallyhavealowersoaktemperature therebyreducingexperimenttime. 3.4.1.6 Crystalgrowthsummary SinglecrystalsofCa 5 M 2 Sb 6 (M=Al,Ga,In)weresuccessfullygrownusingaM 73 Sb 42 and atemperatureprofroomtemperatureto900 ° Cin12hours,atwohoursoakat900 ° Candthen slowcooledto730 ° Cat3 ° C/hr.Ca 5 Al 2 Sb 6 wasalsosuccessfullygrowninaSb 20 andSn 15 usingthesametemperatureSinglecrystalCa 5 Al 2 Bi 6 wasgrownfromaBi 20 with aslowcoolat3°C/hrfrom620°Ctothe470°Cextractiontemperature. 51 Figure3.13:Alloyedreferencestructure(left).Linearrelationshipbetweenunitcellparameter dimensionsbetweenalloyphaseCa 5 Ga 1 : 12 In 0 : 88 Sb 6 andunalloyedternaryphasesCa 5 Ga 2 Sb 6 and Ca 5 In 2 Sb 6 (right). 3.4.2 CrystalStructureandComposition SC-XRDwasperformedtothecrystalstructureandcompositionofthesinglecrystals andtoidentifytheorientationoftheneedle-likecrystalswithrespecttotheorthorhombicunit cell.CrystallographicdataissummarizedinTable3.2.Allcompositionsweretobe orthorhombicandinthe Pbam spacegroup.Thelatticeparametersandatomicpositionsareallin excellentagreementwithpublishedvalueswithallunitcelldimensionsshowingadiscrepancyof lessthan0.50%.Singlecrystalresultswereencouragingwhenitcametothealloyedcomposition, thatbothGaandInwereincorporatedintothesamelatticeasopposedtosimply producingamixtureofCa 5 Ga 2 Sb 6 andCa 5 In 2 Sb 6 crystalswhichthestartingspark plasmasintering(SPS)pelletcompositions.UsingSC-XRDtheMsiteoccupancywasusing amixtureofGaandIn,resultinginaresolvedcompositionofCa 5 Ga 1 : 12 In 0 : 88 Sb 6 .Thealloyed compositionmaintainsthe Pbam spacegroupwithintheorthorhombiccrystalstructurewiththeIn andGaatomsbothpartiallyoccupyingthecenteroftheanionicpolyhedralstructuresasillustrated inFigure3.13(left). ThelatticeparametersofanalloyedcompositioncanbepredictedaccordingtoVegard'sLaw 52 Figure3.14:(a)TheCa 5 Ga 1 : 12 In 0 : 88 Sb 6 crystalstructurewithselectatomlabels.Polyhedrabond lengthcomparisonbetween(b)Ca 5 Ga 1 : 12 In 0 : 88 Sb 6 (c)Ca 5 Ga 2 Sb 6 ,and(d)Ca 5 In 2 Sb 6 . [ 225 , 226 ],whichisanempiricalrulestatingthatalinearrelationshipexistsbetweenthecrystal latticeparametersofanalloyandtheconcentrationsoftheconstituentelementsataconstant temperature.Foranalloyedcomposition, a A ( 1 x ) B x = a A ( 1 x ) + a B x ; (3.4) where a A ( 1 x ) B x isthelatticeparameterforthealloyedcomposition, a A and a B arethelattice parameterforthetwounmixedcompositions,and x isthemolarfractionof B inthesolidsolution. Thelatticeparametersofthealloyedcompositionarecomparedtothelatticeparametersofthe Ca 5 Ga 2 Sb 6 andCa 5 In 2 Sb 6 inFigure3.13(right),wherethelinearrelationshipcanbeobserved. ThetetrahedrabondlengthsofthealloyedstructurealsofallinbetweenthatofCa 5 Ga 2 Sb 6 and Ca 5 In 2 Sb 6 asdetailedinFigure3.14.TheincreaseinlatticeparameterwithincreasingIncontentis duetoInbeingalargeratomthanGawiththecrystalstructureexpandingtoaccommodate.This mayalsobethereasonfortheslightpreferenceofGatooccupythissiteinthecompound. 53 Table3.2:CrystaldatacollectedfromsinglecrystalX-raydiffractionfortheCa 5 Ga 2 x In x Sb 6 compositions.Programsused:APEX2, SAINT,SHELXS97,SHELXL97,andOLEX2.Unitcelldimensionsareingoodagreementwithpublisheddata. Crystaldata EmpiricalformulaCa 5 Al 2 Sb 6 Ca 5 Al 2 Bi 6 Ca 5 Ga 2 Sb 6 Ca 5 Ga 1 : 12 In 0 : 88 Sb 6 Ca 5 In 2 Sb 6 Formulaweight984.861,508.241,070.341,109.801,160.54 Crystalsystemorthorhombicorthorhombicorthorhombicorthorhombicorthorhombic SpacegroupPbamPbamPbamPbamPbam Unitcelldimensions a(Å) 12.0486(4)[-0.34%]7.5569(4)[-0.33%]12.0647(5)[-0.34%]12.0789(4)12.0934(12)[-0.33%] b(Å) 14.0356(4)[-0.24%]23.2361(13)[-0.42%]13.9859(5)[-0.25%]14.0924(4)14.2222(15)[-0.24%] c(Å) 4.45290(10)[-0.16%]4.5175(3)[-0.25%]4.4382(2)[-0.28%]4.49710(10)4.5585(5)[-0.30%] a (°)9090909090 b (°)9090909090 g (°)9090909090 Volume (Å 3 ) 753.03(4)793.24(8)748.88(5)765.50(4)784.04(14) Z22222 Density,calc.(g/cm 3 )4.3446.3154.7474.8154.916 Absorptioncoef12.38468.00215.85615.29014.650 F(000)86412489369681008 Crystalsize(mm)0 : 110 0 : 047 0 : 0340 : 141 0 : 087 0 : 0340 : 041 0 : 027 0 : 0260 : 167 0 : 059 0 : 0320 : 308 0 : 065 0 : 043 q range2.228°to26.391°3.506°to65.166°2.229°to24.986°2.89°to30.39°2.211°to28.772° Indexranges 14 h 15 11 h 10 14 h 14 16 h 17 16 h 16 17 k 17 35 k 35 16 k 16 20 k 20 19 k 18 5 l 5 6 l 6 5 l 5 6 l 5 6 l 5 collected10,27114,61614,91313,1787,752 Independent8831,604564892957 Largestdiff.peakandhole2.973/-1.2702.92/-5.742.78/-2.024.975/-2.1646.68/-2.54 54 EDSwasusedtoquicklyevaluatetheapproximatechemicalcompositionofmanyindividual crystals,aswellastoidentifyimpurityphasespresenteitheronthesurface,orasinclusions.This analysistechniquesuffersfrompotentialpeakoverlapwhichmakesresolvingexactquantitiesof individualelementsdifForthisreason,tielinesfortheternaryphasespacewereconstructed frompowderandsinglecrystalX-raydiffractionresultsonly.Toshedlightonpotentialpitfalls, EDSpatternsweresimulatedusingaMonteCarlomodelinNISTDTSAII[ 227 , 228 ]forthe Ca 5 M 2 Sb 6 (M=Al,Ga,In)compositionsandcanbefoundintheAppendix.Forthissystem,the CaandSbpeakswerefoundtooverlapinthe3-5keVenergyrangebuthaveenoughseparationto thepresenceoftheelementsinapproximatequantities.Gapossessesanisolatedenergy peakatapproximately1.09keVwhichrepresentsLorbitaltransitionswithcontributionsfrom the a , b ,and g transitions,highlightinghowthispeakisinmagnitudewithincreasing Gacontent.ThepresenceorabsenceofGaintheEDSscanisreadilyapparentgivingfurther experimentaloftheconsistencyofthesecrystalgrowths.TheCa/Sbratiosdeviate fromtheexpected5:6ratio,whichwascommontoeverycrystalcompositiontested. However,thisisalmostcertainlyduetotheoverlapoftheEDSpeaks,asopposedtotruedeviation instoichiometry.TheexcellentagreementoftheSC-XRDresultswithpriorworkthis assumption.OntheCa 5 Ga 2 Sb 6 crystals,homogeneoussphericaldropletsonthesurfacewere aspureGafromtheGaRegionsdevoidofanycrystallinefacetswereacombination ofexcessGaandSbelements.Sbtendednottowetdirectlytothesurfaceofthecrystalbut wouldaccumulatebetweencrystalsinthecentrifugingprocess. MonteCarlosimulationswerealsorunfortheCa-In-SbknownternaryphasesCa 5 In 2 Sb 6 and Ca 11 InSb 9 .TheInL a 1 + 2 peakatapproximately3.29keVwasandseparatefrom theCaandSbpeaks.Additionally,therelativelyCa 11 InSb 9 compositioncouldbe separatedfromthemoreIn-richCa 5 In 2 Sb 6 .Furtherdetailsofthisanalysiscanbefound intheAppendix. ThealloyedcompositionCa 5 Ga 2 x In x Sb 6 underwentextensiveEDSanalysistobetterevaluate theconsistencyoftheGa:Inratioacrossmanyindividualcrystals.DuetotheuniqueGapeak 55 atapproximately1.09keVandtheuniqueInpeakatapproximately3.29keVthistechniquecan reliablydetectthepresence/absenceoftheminorityelement.Resultswereveryconsistentwithall measuredcrystalscontainingbothGaandIn.Gawasslightlypreferred,consistentwiththeresults ofSC-XRD. Ca 5 Al 2 Sb 6 singlecrystalsfromanAl 73 Sb 42 areshowninFigure3.16(a),fromaSb 15 inFigure3.16(b),andSn 15 inFigure3.16(c-d).Forthesecrystals,SC-XRDwasinvaluableto thecompositionandstructuretype,duetotheexistenceofseveralnearbyternaryphases withsimilarstoichiometry.Inparticular,theMonteCarlomodelinNISTDTSAII[ 227 , 228 ] showedthatthattheCa 5 Al 2 Sb 6 andCa 3 AlSb 3 patternsarenearlyindistinguishableduetotheir similarstoichiometry.However,bycomparison,theCa 14 AlSb 11 andCa 11 AlSb 9 ternariesare distinguishableduetoasmallerAlK a 1+2/AlK b 1peakcenteredat1.48keV. TheEDSanalysisconductedinFigure3.16displaysheterogeneityinthecompositions,more totheAlcontent.ThisvariationwasnotdetectedinsubsequentSC-XRDbutcouldbe contributedtosomecrystalspossessingaAl-richsurface.Insomecasesthiscouldbecontributed toAl-richesbutthisvariationwasalsodetectedinnonAlessuchasSb 20 inFigure 3.16(b).ThisvariationwaslimitedtotheCa 5 Al 2 Sb 6 compositionwhileCa 5 Al 2 Bi 6 produced moreconsistentAlamounts.ThishighlightshowEDSanalysiscannotbeusedexclusivelyinthe ofcompoundcompositions. Finally,EDSanalysisfortheCa 5 Al 2 Bi 6 compositionisshowninFigure3.15(e-f).Inthiscase, therearenocompetingternaryphasesintheCa-Al-Bisystem,soEDScouldreadilydifferentiate thetargetphase.AdditionallyBiproducesuniqueenergypeaksdistancedfromanypotentialAl andCapeaks.Thesepeaksareatapproximately10.85keVrepresentingL a 1 + 2 emissions,and approximately13.01keVrepresenting L b 1 + 2 emissions,makingresultseveneasiertoresolve.A detailedsummaryofEDSacrossallcompositionsandesisconductedintheAppendix. 56 Figure3.15:EDSanalysisof(a)Ca 5 Ga 2 Sb 6 crystalandxelements,(b)Ca 5 In 2 Sb 6 crystals, (c-d)Ca 5 Ga 2 x In x Sb 6 singlecrystals,and(e-f)Ca 5 Al 2 Bi 6 singlecrystals. 57 Figure3.16:EDSanalysisofCa 5 Al 2 Sb 6 crystalsgrownfroma(a)Al 73 Sb 42 (b)Sb 20 (c)Sn 15 back-scatteredelectronimagetohighlightand(d)Sn 15 standardSEM. 58 3.4.3 CrystalMorphology Crystalshapeisbyboththeintrinsicpropertiesofthecrystallographicstructureand extrinsicfactorssuchasthegrowthenvironment.Inthisstudy,singlecrystalsweregrownfroma thatactedasasolvent,thegrowthenvironment.Thecrystalmorphologyisby thesurfaceenergiesassociatedwiththeexposedsurfaces.Thissurfaceenergyattemptstominimize itselfwiththefastestgrowthoccurringonsurfacesthatexposethelowestenergy.Thegrowncrystal shapeisdeterminedbytheminimizationoftotalsurfacefreeenergyofthecrystal.Thissurface energyisdependentonseveralfactorsincludingchemicalcomposition,atomicscaleroughness, surfacereconstructionandcrystallographicorientation[143].TheCa 5 M 2 Pn 6 (M=Al,Ga,In;Pn =Sb,Bi)crystalshaveapreferredgrowthdirection,[001],makingthe(001)surfacethehighest surfaceenergyplane. SubsequentsurfaceenergystudieshavebegunontheCa 5 M 2 Sb 6 (M=Al,Ga,In)crystal systemtoexplainhowtheintrinsicpropertiesofthecrystalandextrinsicpropertiesof thedrivecrystalgrowth.Hereabriefoverviewisprovided,limitingthescopetogeometric considerationsbyutilizingtheBravais-Friedel-Donnay-Harker(BFDH)law[229]. Whileanumberofcrystalsadheredtogetherwithamorphousmanycrystals wereisolated,allowingforadetailedmorphologystudytotakeplacewherethedimensionsofthe crystalsweremeasured.Crystalseparationwasfurtherimprovedwiththeuseofvaportransport methodspreviouslydescribed.SomecrystalstestedatSC-XRDwerelargeenoughtosuccessfully identifyplanes,asshowninFigure3.17,basedoffunitcellThisanalysissubstitutes formorereliableEBSDmethodswhichareexceedinglydiftoperformonsmall,brittle,single crystalsduetotherequirementofahighlypolishedsurface. CrystalsgrowninaM 73 Sb 42 tookonrectangulargeometriesthathadapreferredgrowth directionasshowninFigure3.17(a)fortheCa 5 Ga 2 Sb 6 compositionandFigure3.17(b)forthe Ca 5 In 2 Sb 6 composition.Whilethemajorityofcrystalsappearedtohavechamferedlongedges asshowninFigure3.18(c-d).Preliminarymeasurementsoftheseangledfacetsleadustobelieve thesearethe{110}familyofplanes.Interestinglyenough,growthswereprimarilyamixtureof 59 Figure3.17:SinglecrystalsmountedatSC-XRDfor(a)Ca 5 Ga 2 Sb 6 fromaGa 73 Sb 42 and (b)Ca 5 In 2 Sb 6 fromaIn 73 Sb 42 thesetwogeometrieswithFigure3.18(b-c)comingfromthesameCa 5 In 2 Sb 6 growth,eventhough theyexhibitdifferentmorphologies.Thisislikelyduetoacompositiongradientwithinthe Figure3.18(d)illustratesasinglecrystalofCa 5 Al 2 Sb 6 grownfromaSb 20 thatexhibitsmore prominent{110}growthplanes. TheseplanesareingoodagreementwithpreliminaryBFDHcalculations.TheBFDHlawreveals acorrelationbetweenthemorphologicalimportanceofacrystalfaceanditsinterplanardistance d hkl ,where d hkl isthedistancethatseparatesphysicallyidenticalsurfaces.Themorphological importanceofacrystalfaceisunderstoodasitsrelativesizeinagivencrystalhabit[ 230 ]such asthosedisplayedinFigure3.17.UsingtheMercurysoftwarepackage[ 231 ],relativeBFDH areasarecalculatedfortheCa 5 M 2 Sb 6 (M=Al,Ga,In)which(110),(1 ¯ 1 0),( ¯ 1 ¯ 1 0),( ¯ 1 10)the mostfavorableforgrowthfollowedby(001)/(00 ¯ 1 ),andlastly(0 ¯ 2 0)/(020).Thesearethefacesthat shouldappearinthecrystalmorphologywhichisinagreementwithobservedgeometriesfrom SEMimages.FortheCa 5 In 2 Sb 6 compositionaportionofthesinglecrystalsgrowntookondistinct rightanglessuchasthecrystalobservedinFigure3.15(b)withthelongaxisbelongingtothe<001> directionfamilyandtheothergrowthaxes<100>and<010>. TheBFDHisapracticalgeometricmethodthatisbasedofftheintrinsicpropertiesofacrystal butdoesnottakeintoaccountgrowthenvironmentandhasnoenergyconsiderations[ 230 ].Forthis 60 Figure3.18:Singlecrystalsof(a)Ca 5 Ga 2 Sb 6 fromGa 73 Sb 42 withrectangularcrosssections, (b-c)Ca 5 In 2 Sb 6 fromsameGa 73 Sb 42 and(d)Ca 5 Al 2 Sb 6 fromSb 20 reasonthepredictedplanesandtheirrelativeprominenceremainsunchangedamongtheCa 5 M 2 Sb 6 (M=Al,Ga,In)crystals.Thismethodologyalsointroducesconfusionbetweenthelatticeandthe structure,leadingtoanunnecessarymultiplicationofMillerindiceswhichmaybethecasefor the(020)planes[ 232 ].TheorderingoftheplanesfromtheBFDHdoesnotmatchtheorderof prominenceinourgrowthswithour(010)/(020)planeshavingthemostsurfacearea. SinglecrystalsfromaAl 73 Sb 42 areshowninFigure3.16(a),fromaSb 20 inFigure 3.16(b),andSn 15 inFigure3.16(c-d).ThecrystalgeometryappearedtochangefortheSn 15 displayingmorecompetingfacetsalongthecrystallengthbutsomeribbon-likegeometries werestillpresent. TheCa 5 Al 2 Bi 6 compositionpossessesadifferentstructure-typeandproducesauniquelist 61 ofBFDHareas.Here(00 ¯ 1 )/(001)arethemostfavorableforgrowth,followedby(0 ¯ 1 0)/(010) then( ¯ 1 00)/(100).Thisdeviatesfromthecrystalstructureobservedmoresubstantiallyasthese crystalshadapreferredgrowthdirectionalong[001]butweregenerallythickerwithanumberof competingfacetsalongthelengthoftheneverappearingrectangularastheirorthorhombic crystalsystemmightsuggest.Thisshowshowthegrowthenvironmentcan crystalgrowthandwhyamoredetailedsurfaceenergystudywouldberequiredtounderstandthese interactions. 3.5 ConcludingRemarks InthisworksinglecrystalCa 5 M 2 Pn 6 (M=Al,Ga,In;Pn=Sb,Bi)compoundshavebeengrown fromamoltenmetalTheCa 5 M 2 Sb 6 compoundswereallsuccessfullygrownfromaM 73 Sb 42 withCa 5 Al 2 Sb 6 alsobeingsuccessfullygrownfromanSb 20 andSn 15 Ca 5 Al 2 Bi 6 was grownfromaBi 20 asimpleroptionthanthemixedThesinglecrystalalloy Ca 5 Ga 2 x In x Sb 6 wassuccessfullygrownfromavepartmixtureofCa 5 Ga 2 Sb 6 (polycrystalline) +Ca 5 In 2 Sb 6 (polycrystalline)+Ga 37 : 5 +In 37 : 5 +Sb 42 elements.Inaddition,severaltielines havebeenaddedtotheCa 5 M 2 Pn 6 (M=Al,Ga,In;Pn=Sb,Bi)ternaryphasediagramswhere noneexistedbefore,providingguidancetofuturecrystalgrowthandsynthesisstudies.Single crystalsinexcessof7mmweregrownbuttheaveragecrystalsizewassmaller.These singlecrystals,however,aresuflargeforcharacterizationusingamodernphotolithography processwherenormalapplicationofcontactsbyhandareimpractical. TheCa 5 M 2 Pn 6 (M=Al,Ga,In;Pn=Sb,Bi)crystalshaveapreferredgrowthdirection,[001], withthe(001)surfacethehighestsurfaceenergyplane.Othermorphologicalhabitsobservedwere dependentonthegrowthenvironmentandcompositiongradientswithinthemelt,withdifferent crystalshapesproducedfromthesamecrystalgrowthexperiment. 62 CHAPTER4 ELECTRONICCHARACTERIZATIONOFCa 5 In 2 Sb 6 SINGLECRYSTALS 4.1 Introduction SinglecrystalsofCa 5 M 2 Sb 6 (M=Al,Ga,In)weregrownviathemethod.Thesecrystals possessedapreferredgrowthdirectionalongthecovalentchainsofthestructurebutonlymeasured afewmillimetersandtensofmicronsintheperpendiculardirection.Ourdesiretocharacterize thetransportpropertiesofthesecrystalsbothparallelandperpendiculartothegrowthdirection demandedanovelcharacterizationtechnique,asplacingcontactsbyhandisinfeasibleintheper- pendiculardirection.Micro-fabricationtechniqueswereutilizedwithmicro-ribbonsofCa 5 Ga 2 Sb 6 andCa 5 In 2 Sb 6 extractedbothperpendicularandparalleltothepreferredgrowthusingafocused ionbeammillingtechnique.Photolithographywasthenutilizedtocreateacircuitofsensorsforlow temperaturecharacterizationofHalleffect,andsimultaneousmeasurementofsamplethermalcon- ductivity,Seebeckcoefcient,andelectricalresistivity.Here,atemporarycoatofphotoresistwas applied,transferringadesignedmicro-circuitontothesubstratesurroundingandcoveringportions ofthemicro-ribbon.Themicro-circuitfabricationwasaccomplishedusingalaserphotolithography process.Aftertheexposureandsubsequentdevelopment,alayerofchromiumandgoldwasapplied andselectivelyremovedtoformthecharacterizationcircuit.Thismethodshowsgreatpotentialin eliminatingtheneedforlargesinglecrystalsamplestoperformcharacterization,allowingsamples tobeevaluatedfortheirthermoelectricpotentialbeforemoreresourcesareinvestedinscalingup crystalgrowth.Theresistivity,carrierconcentration,andmobilityofamicro-ribbonofCa 5 In 2 Sb 6 , perpendiculartothepreferredgrowthdirection,wassuccessfullycharacterizedusingthisapproach. Resistivitywasmeasuredintheparalleldirectionusingafour-proberesistivitysetupandwas accomplishedbymanuallycontactingthesamplewithsilverpaste.Inthismanner,theanisotropy ofresistivityinCa 5 In 2 Sb 6 wasdeterminedandcomparedtootherclassesofmaterials. 63 Figure4.1:(a)FalsecolorimageoftheNbPmicro-ribbon(green)withsputteredheaterline(upper left)andapairofthermometers.(b)usedtomeasuretheelectricalconductanceG= J/E.(c)usedtomeasurethermoelectricconductanceGT=J/ j Ñ T j withtheredand greenendsofthecolorgradientrepresentinghotandcoldsidesofthecircuit[6]. 4.2 Background 4.2.1 PhotolithographyforMaterialCharacterization Photolithographyiswidelyusedintheproductionofcommercialgradeintegratedcircuits(ICs)but hasonlyrecentlybeguntomakeanimpactasapathwaytocharacterizingmaterialpropertiesin research.Theofthismethodisthatsamplescanbepreciselycutindifferentcrystallographic directionstoisolatetheirproperties.Additionally,micro-ribbonsofmaterialareused,extracted fromlargercrystalssoonlysmallsamplesarerequired.Theapplicationofsensorsoverthetop ofthesemicro-ribbonshasbeensuccessfullyperformedbyGoothetal.[ 6 ].Twothermocouples andaresistiveheaterlinewereusedtomeasureconductanceandareshowninFigure4.1.Each micro-ribbonmeasuredapproximately50 m m 2.5 m m 0.5 m minsize[ 6 ].Inprinciple,allof thethermoelectrictransportproperties(Seebeckcoefcient,electricalandthermalconductivity) canbemeasuredonsamplesassmallas25 m m. Inthisstudy,focusedionbeammilling,photolithography,andthesubsequentelectricaltransport characterizationwerecarriedoutattheLeibnizInstituteforSolidStateandMaterialsResearch (IFW)inDresden,Germanywhichwasaccomplishedovertworesearchstaysattheinstitute. 64 4.2.2 FocusedIonBeamMilling Removingmaterialbyionmilling( i.e. ,sourcesputtering)isthemostwidelyusedapplicationfora focusedionbeam(FIB)system.Thismethodiscapableofextractingmicro-ribbonsofmaterialfrom largersinglecrystalswithmicrometerscaledlengthsandnanometerscaledfeaturesandthicknesses. Theprocessislimitedbyremovalrate,resolution,andcrystalquality[ 233 ].Removalratesneedto becarefullyadjustedbasedoneachcrystalcomposition,withheavierelementsslowingtherateof milling.Semiconductor-typematerialsarefavorableforthismethodasmoreinsulatingceramics canaccumulatechargeandtheionbeamifgivenaninsufcientpathtoground,which islimitedduringthecuttingandextractionofmaterial[ 234 ].Forconductingmaterials,milled materialisremovedfromthebulkbyacombinationofsystemvacuumandredepositionelsewhere inthechamber[235]. 4.2.3 SelectionandTreatmentofPhotoresists Inthisstudy,aphotolithographyprocesswasoptimized,beginningwiththeselectionofphotore- sists.Aphotoresistisaphotoactivepolymersuspendedinasolvent.Thispolymericstructure protectsasubstratefromchemicalorphysicalattackduringthephotolithographyprocess.While photoresistscanworkforavarietyofprocesses,mostresinsareoptimizedtoapplications. Aphotoresistchemicallychangeswhenexposedtowavelengthswhichcreatesadifference inthedissolutionrateofthephotoresistwhenexposedtoadevelopersolution.Thisdiscrepancyin dissolutionrateallowsforthecreationofmicro-structureswhereacircuitofconductingmaterial canselectivelybeplaced. Photoresistscanbecharacterizedaseitherpositiveornegative.Positiveresistsaresoluble inthedeveloperafterexposurewhilenegativeresistsbycomparisonarecross-linkedwithinthe exposedareasandremain,whilenon-exposedareasareremovedinthedevelopmentprocess[ 236 ]. Thiscross-linkingprocessisnotadrivingforceinpositiveresists.Somepositivephotoresistsare alsocapableofimagereversalwherebythetoneofthephotoresistisreversedsimilartonegative photoresists.Imagereversalcanbeappliedusingahardbakeandexposureafterthemain 65 Figure4.2:Thephotoresistprocesssequenceforpositive,imagereversal,andnegativeresists.While chemicallydifferentthroughthedevelopment,deposition,andlift-offphasestheyarestructurally equivalentforlowresolutionstructures,combinedhereforsimplicity.Resistarebasedoff largedoseexposures. exposure.Theprimaryofnegativephotoresistsisthattheyaregenerallycheaperwhile positivephotoresistsofferbetterresolution.ThesephotoresisttypesarecomparedinFigure4.2 wheretheprocesswsfromtoptobottom. Propertiesofagivenphotoresistarelargelydrivenbythephotoactivepolymerchainlength. Increasingtheaveragechainlengthincreasesthesofteningtemperatureandasaconsequence,the stabilityagainstthermalroundingwhichcanimpedesubsequentlift-offoperations.Decreasingthe averagechainlengthimprovesadhesiontothesubstratesoacompromisemustbestruck. Positivephotoresistshavebeenusedexclusivelyinthisstudyandbelongtoeitherthediazonaph- thoquinone(DNQ)/Novolakorpolymethylglutarimide(PMGI)groups.Thesetypesofphotoresists areappliedasaliquidtothesubstrateandspincoatedtouniformthickness.DNQisaninhibitor whichreducesthedevelopmentrate( i.e. ,alkalinesolubility)intheunexposedstaterelativetopure phenolicresin,inthiscaseNovolak,apolymerizedphenolicmadeofformaldehydeandphenol 66 Figure4.3:Selectedphotoresistsandtheirtypes:positivephotoresist(left),imagereversal(center), andbi-layer(right).Thegoldlayerrepresentsthesputterdepositionpriortothelift-offprocess. [ 237 ].ExposurewavelengthsforDNQtypicallyrangebetween320-440nm.Themechanism behindtheDNQ-Novolakinteractionhasbeenanareaofextensivestudy[ 238 Œ 244 ].Whileefforts continuetounderstandthefundamentalmechanismbehindtheunexposedDNQinhibitingthe dissolutionofNovolakitislargelyassumedtobechangesinthehydrogenbonding[245]. ThePMGIpositivephotoresistbi-layerdescribesaPMGIbottomplanarizationlayerandatop imaginglayerphotoresistsuchasaDNQ-Novolakblend.Theapplicationandsoftbakeofthe PMGIlayerpriortotheapplicationoftheimagingresistpreventsintermixingofthetwolayers. DuringexposurethePMGIlayerproducesanundercutrelativetotheimagingresistabove. PMGIresistsalsofrompossessinganarrowrangeofsensitivityanddonotrequireasolvent fordevelopment[ 246 ].ThisnarrowrangeallowsforthepotentialdevelopmentofthePMGI whiletheimagingresistmaintainsitsstructure.Thisphotoresiststackwaspatentedfortheusein themanufacturingofmetal-semiconductorfecttransistors(MESFETS),modulation-doped fecttransistors(MODFETS),metal-oxide-semiconductorfecttransistor(MOSFETS), andotherstructureswithgatemetalusage[ 246 ].Anumberofphotoresistswereattemptedinthis studytothemostaccurateandrepeatableprocess.Theseincludedpositive,positivebi-layer andpositiveimagereversalphotoresists. 4.2.3.1 Positivephotoresists TheAZ9260positivephotoresist,manufacturedbyMicrochemicals[ 247 ],wasdesignedforthick resiststructurepatterningupto24 m m.Thisphotoresistwasappealingforitsthickness,ensuring thatanymicro-ribbonprocessedwouldbecompletelysubmergedintheresistwherethicknesses 67 ofonly0.2-0.5 m mareanticipated.Thethickphotoresistcanalsominimizetextureeffectsthat couldnegativelyimpactspincoatingconsistency.Likemanythickphotoresists,AZ9260offers excellentadhesioncharacteristicssonoadhesionpromoterisrequired[ 248 ].Thisphotoresistis illustratedinFigure4.3(left).ThesidewallsoftheAZ9260willbehigher,duetoits higherviscositythantheAZ5214Epositivephotoresistbutareshownasequivalentforsimplicity. 4.2.3.2 Imagereversalphotoresist TheAZ5214Ephotoresist,manufacturedbyMicrochemicals[ 249 ],canbeutilizedineitherthe positiveorimagereversalThisphotoresistwasdesignedandhasproveneffective forlift-offapplications[ 250 ].Theimagereversalstateiscapableofproducinganegativesidewall whichisidealforourlift-offapplication.Itisnotedthatthethicknessislessthan thatoftheAZ9260andoptimizationisrequiredforgeneratingarepeatableandeffectivenegative sidewall.ThisphotoresistintheimagereversalisillustratedinFigure4.3(center). Theundercut,whensufoptimizedcanprovideadditionalclearanceforourlift-offprocess. 4.2.3.3 Positivebi-layerphotoresist Apositivephotoresistbi-layerisalsoaviableoptionandhasproveneffectiveforlift-offapplications [ 251 ]withribboncharacterizationbeingsuccessfullycompletedusingaLOR3Bandma-P1205 photoresiststackbyGoothetal.[6]. LOR3BisbasedoffthePMGIplatformandmanufacturedbyKayakuAdvancedMaterials,Inc. [ 252 ].Itisusedinconjunctionwithpositiveresistsandactsasanunderlayerinthebi-layerlift-off process.Thema-P1205positivephotoresist,alsomanufacturedbyKayakuAdvancedMaterials, Inc.[ 253 ],isusedinconjunctionwithLOR3B.ThisphotoresiststackisillustratedinFigure 4.3(right)wheretheLOR3Bprovidesanundercut,allowingforeasierseparationduringthelift-off process. 68 4.2.4 SpinCoating Spincoatingisatechniquewhereaphotoresistisdispensedontoasubstratewhichisthenspun atarateofseveralthousandRPM.Thecentrifugalforcegeneratedbythisrotationproduces anevenlydispensedphotoresistlayeracrossthesubstratesurface,whileexcessphotoresistis spunofftheperimeter[ 254 ].Theresistisfurthersettledinthisprocessasaportionofthe solventwithinthephotoresistevaporates.Thishighlyreproducibletechniquealsofroma simpleapplicationandshortcycletimes[ 255 ].Additionally,processrepeatabilityisnotseverely temperaturedependent.Whilehighertemperaturesleadtoincreasedsolventevaporationtheyalso increaseresistviscosity,withthesephenomenacounteractingeachotheritprovidestheuserafew °Crangeinwhichtoapplyandspincoatthephotoresistforconsistentresults[256]. Thespincoatingoperationrequiresatleasta100orbettercleanroomenvironmentwithexcellent airThisislargelyduetothephotoresistbeingtackyforaperiodoftime, makingitsusceptibletoairborneparticulateduringandafterthespinningoperation.Laboratory humidityshouldalsobetightlycontrolled( < 30% 2%)assolventevaporationduringthespinning operationwillcoolthesubstrate,creatingpotentialwatervaporcondensation[255]. Adisadvantageofthismethodisthatairturbulenceovertheedgesofthesubstratecanresult inaccelerateddryingwhichcanlimitthespin-offofexcessphotoresistfromthecenterdueto accumulationalongtheperimeter.Thisedgebeadissueisexasperatedwiththeuseofmoreviscous resists,andsubstrategeometrieswithsharpedgessuchasrectanglesorsquares.Fornon-circular substratestheedgescanbebrokenoffentirelybutriskscontaminationfromthebreakingprocess [257]. Anothercharacteristicofthistechniquetoconsideristhatanysubstratetexturereducesthe homogeneityoftheresistcoating,sothemicro-ribbonusedinthisprocessmustbethinenoughnot toproduceatextureeffectinthephotoresistandmustbesubmergeduniformlyinthe resist. Resistdiscontinuitiescanalsoresultifcontaminationorairbubblesarepresentintheresist, emphasizingtheneedforcleanroomconditionsandcarefulapplication.ForDNQ-basedpositive 69 andimagereversalphotoresists,nitrogenbubblescanoccurduetothegradualthermaldecompo- sitionofthephotoactivecompound.Ultrasonicbathscanbeemployedtooutgasthesenitrogen bubblesifnecessary[ 237 ].Discontinuitiescanbereducedoreliminatedwithhighspincoating accelerations(1,000sofRPM/s)leadinguptotheprimaryspinspeed.Multistagespincoating canbeusedtocompensatefortexturedsubstratesaswell,whereaslowerrotationalspeed isheldforseveralsecondsbeforeacceleratingtotheprimaryspincoatingspeed[255]. Spinspeedcorrelatesdirectlytotheresistthickness.Forliquidphotoresiststheresist thicknesscanbeapproximatedbytheinversesquarerootofthespinspeed[ 255 ].Thereforeone canadjustresistthicknessbysimplyadjustingthespinspeed,providedthatthephotoresistisspun untildry.Thisdryingeffectisalsodependentontheresidualsolventcontentofthephotoresist, withtheremainingsolventbeingremovedduringthesoftbakeimmediatelytofollow. 4.2.5 SoftandHardBakes Ingeneralasoftbake( i.e. ,pre-bake)isanybakingprocessstepthatheatsthesampleprior toexposure.Thephotoresistsinthisstudyrequiredasoftbaketoreducetheresidualsolvent concentrationstillpresentinthephotoresistafterspincoating.Thesoftbakealsoannealsstressin theapplied[ 255 ].ThisprocessofresidualsolventreductionisforDNQ-basedresists toavoidthebubblingofnitrogen,whichisaby-productoftheexposureprocess.Anoptimized softbake,bothintemperatureanddurationensuresamoreuniformsurfacequalityandimproved repeatability.Whilesolventsassistinthethinningofaphotoresisttheyabsorbradiationapplied intheexposureprocessandalsonegativelyaffectadhesion.Over-bakingasubstrateincreasingly polymerizesthephotoresistandreducesitsphoto-sensitivitywhileunder-bakingaffectsadhesion andexposure.Resistabsorptionratesrelativetosoftbaketimeandtemperaturecanbedone experimentallyorcomputationaltoassistintheoptimizationofsoftbakeparameters[258]. Ahardbakeormore,apost-exposurebake,isabakingstepwhichimmediately followstheexposureforimagereversalandnegativephotoresists.Forimagereversalphotoresistsa post-exposurebakeisusedtoinvertareasoftheresistthatwereexposedduringthephotolithography 70 process,renderingtheminsolubleinthedeveloper.Typicalpost-exposurebakehotplateparameters are100-130°Cforafewminutes. 4.2.6 Exposure Theexposureinaphotolithographyprocessistypicallycarriedoutinoneofthreemethods:using maskaligners,astepper,orlaserdirectwriting.Laserdirectwriting,wasusedinthisstudyandis achievedwithafocusedrasteringlaser.Thereisnophysicalphotomask,ratherthecircuitdesignis programmedintothelaserandselectivelyexposedintothephotoresist.Theabsenceofaphotomask isaadvantageofthistechnique,allowingforquickofthedesignbutsuffers fromlongercycletimes.Generallyspeaking,thephotoreactionforpositiveandimagereversal resistsisaone-photonprocesswiththerequiredexposuredoseafunctionofbothintensityand time[ 259 ].Alaserapplicationappliesahighintensityofphotonsbutislimitedtoapixel-by-pixel approach,incontrasttotheblanketoflightemployedinthemaskalignerandsteppermethods previouslymentioned. 4.2.7 FloodExposure Aexposure,alsoreferredtoasanopenframeexposure,exposestheentiresubstratetoblanket radiation.Herenomaskispresent,withtheexposurefollowingboththemainexposureand hardbake.Forimagereversalphotoresistsaexposureisutilizedtocompletelyconvertthe photoinitiator.Fornegativephotoresists,aexposurecompletesthecross-linkingprocessthat wasinitiatedinthemainexposure. 4.2.8 Developer Thedevelopersusedinthisstudyincludemetalion-free(MIF)organictetramethylammonium hydroxidewhichispreferredtodilutedsodiumhydroxideassodiumcontaminationofacircuitcan degradeitsproperties[ 260 Œ 262 ].Careneedstobetakentoisolatethedevelopersfromopenairas muchaspossiblebecauseCO 2 exposurereducestheactivityofthedeveloper. 71 4.2.9 SputterDepositionandLift-off Afterdevelopmentsampleshavetheirmetalconductivelayerssputteredontothesurface,adhering tothesubstrateandphotoresist.Thelift-offprocessremovestheremainingphotoresist,taking thesputteredmetalswithit.Whileallorganicsolventscanactasasuitablelift-offmedium,low boilingtemperaturesolventsarenotrecommendedasthisevaporationcancausere-depositionof removedmetal.Inorderforrepeatablelift-offtobeachieved,thesputteredlayerscanonlybeafew hundrednanometersthick.Itisonlydesirableforthelift-offmediumtoattackthephotoresistbut animportantconsiderationinthisstudyisthatthemicro-ribbonwillbepartiallyexposedandcan bepotentiallyetchedorevendamagedifitmustremainsubmergedintheremoverforextended periodsoftime. 4.3 ExperimentalMethods TheFIBmillingandphotolithographyprocessesrequiredanumberofexperimentalmethods thatcollectivelyproduceadesiredcircuitdesign.Eachprocesswasoptimizedforselectphotoresists usingblanksubstrates,withthebestresultsdeterminingwhichphotoresistwouldbeusedforthe processingofthesinglecrystalmicro-ribbons.TheFIBmillingwasaccomplishedbytechniciansat theLeibnizInstituteforSolidStateandMaterialsResearch(IFW)inDresden,Germany. 4.3.1 FocusedIonBeamMilling AFEIHeliosNanoLab600iSEMinstrumentintegratedwithaFIBwasusedtocutsmalloriented micro-ribbonsfromgrownsinglecrystals.Thesesystemsarecapableof insitu specimen tionthroughionmillingordepositionwithprecisionmaterialremovaloccurringwithnano-scale resolution[ 263 ].WhileseveraltypesofFIBsystemsexist,thesystemhereindiscussedandutilized isaGaliquidmetalionsource,whichisthemostcommonsourcetype.TheGasourceisvery stablewithbothalowvaporpressureandmeltingpointwhilebeingrelativelyheavywhichoffers favorablesputteringrates[ 234 , 264 ].Crystalcompositionwasalsopriortocuttinga 72 regionbyEDSusinganEDAXSDDApolloXdetectorat30.00kV,0.00tilt,andatakeoffangle of36.49°. ThenominalprocessingtimeforFIBmillingofaCa 5 M 2 Sb 6 (M=Ga,In)micro-ribbonfroma largersinglecrystalwas16hourswiththemicro-ribbonextractiontakinganadditional1to1.5 hours.Millingvoltageandcurrentwereabovenormalat30kVand65nArespectivelyasdeepcuts throughregionsweresometimesrequired.Sampleswerethinnedbeginningat30kV/21nA withcurrentdecreasingto80pA.Thecuttingoftheedgeswhichsupportthemicro-ribbonbeganat 0.79nAanddecreasedto80pA. 4.3.2 SubstratePreparation Opticalqualityborosilicateglasswafersmeasuring 10 10 mmwithathicknessof300 m mwere usedasthecircuitsubstrate.Optimizationexperimentswereconductedoncoverslipsproducedby Menzel,measuring18x18mm. Substratecleaningisacriticalaspectofthephotolithographyprocess.Allsubstrateswere cleanedsequentiallywithanacetone(C 3 H 6 O)bath,isopropanol(C 3 H 8 O)bath,andadeionized waterrinse.Substrateswerethendriedwithanitrogenpistolanddehydrationbakeonahotplateat 120 ° Cfor10minutestoremoveanytracemoisture.Forsubstrateswithamicro-ribbonpresent,the nitrogenblow-offstepwasbypassedduetoconcernsthatthemicro-ribbonpositionwouldshift orbelostcompletely.Itwasimportantthatallmoisturewasremovedfromthesurfaceasmany photoresistsarehydrophobic,leadingtoapplicationandadhesionissuesifnotproperlybaked. 4.3.3 CircuitDesign Themicro-structureappliedacrossthesinglecrystalmicro-ribbonswasdetailedinadigitalpho- tomask.ThismaskwasdesignedinLASI7(LAyoutSystemforIndividuals),alayoutanddesign programforintegratedcircuits[ 265 ].Herecomplexmicro-structuredesignsaremadefromsimpler hierarchicalobjectsthatareassembledandappliedinsubsequentdesignlayerstoproduceatop 73 layerstructurethatcanbeexposedatalaserlithographer.Thisconstructionsubstitutesforthemore traditionalphysicalmasksthatareplacedabovethephotoresistduringexposure. Themainsensorcomponentsweredrawnandthenconnectedtoasurroundingpadframe.These padsaretheinterfacebetweenthecircuitandwiredconnectionsoftheexternalcharacterization equipment.Whilecommonlymadefromaluminumorcopperinindustrialapplications[ 266 ],our lowtemperatureapplicationutilizedgoldbecauseitisanoblemetalthatresistsoxidationinthe absenceofindustrystandardpassivationtechniques. 4.3.4 PhotoresistApplication Allphotoresistswereappliedusingamanualstaticspincoatingprocessusingspincoatersmanu- facturedbyPolos,wherebyresistwasappliedtothesubstrateusingapipettepriortoinitiatingthe spinSpecialcarewasmadetonottransferbubblestotheappliedphotoresistasthesecan leadtoinhomogeneitiesorvoidsinthespunresist.Bakingonahotplateimmediatelyafterspin coatingwasimplementedtominimizethechancesofintroducingparticulatecontamination,which canresultinopaquespotsorpinholesafterexposureanddevelopment. 4.3.5 SoftandHardBakes Softandhardbakeswereaccomplishedusinghotplates,manufacturedbyPräzitherm.Hotplates wereselectedoverovensduetotheirfasterappliedtemperaturegradientwhichleadstomore precise,repeatableresults.Aftereitherasoftorhardbakewascompletedthesubstratewascooled atambientfortwominutespriortothenextprocessingstep. 4.3.6 LaserLithography Theexposureprocesswasperformedusinga m -PG101micropatterngenerator,manufactured byHeidelbergInstruments.Thesystemwasequippedwithalaserdiodewhichemits375nm wavelengthradiation,allowingittoexposebothstandardandUVresists.Substratescouldbe aslargeas 100 100 mmwithexposedstructuresdownto0.6 m m.Lasersettingsweresetto 74 40addressgrid,0.9 m mminimumstructure,andawritespeedof5mm 2 /minute.Bothmanual andpneumaticfocusingmethodswereusedtofocusonthemicro-ribbonsandsubstrate.Micro- structureswererotatedandalignedwiththeobservedmicro-ribbonbymarkingtheoppositecorners oftheribbon.Thesecornerscorrespondtogeometriccoordinatesinthedesignedmask.The coordinaterepresentsthephotomaskoriginwhiletheotherrequiredaprecisemeasurementofthe lengthandwidthofthemicro-ribbonusingeitheraLeicaDM2700MorOlympusBX53Moptical microscope. Allsampleswereprocesseduni-directionallywherebythelaserwasonlyemittedduringforward movement.Thisledtobetterstabilitybutincreasedprocessingtimecomparedtoastandardbi- directionalexposure.Batchexposureswereprocessed,incrementinglaserpowerforoptimization inenergyseries.Gridsoffeatureswerecreatedinthismannerandcomparedtooneanotherfor optimizationpurposes.Sampleswerealsoruninstandard 1 1 ,and 1 2 energymodeswiththe numberreferringtothenumberofexposuresconductedwhilethesecondisareductionin exposurespeed.A 1 2 energymodeexecutesoneexposurewithdoublewriteenergy,accomplished byreducingthestagespeedbyafactoroftwo.Reductionsinspeedledtolongerprocessingtimes butinsomeinstancesimprovedmarkingquality. 4.3.7 FloodExposure Thisphotolithographystudyutilizedahardbake,twominutecooldown,andexposureforthe AZ5214Eimagereversalphotoresist.Floodexposureunder375nmlightoccurredfor30seconds. TheexposureapparatusisshowninFigure4.4. 4.3.8 PhotoresistDevelopmentandEvaluation Thephotoresistsutilizedinthisstudyweredevelopedbysubmergingthesubstrateinaglasspetri dishwiththerecommendeddeveloper.Substrateswerethenrinsedindeionizedwater anddriedwithnitrogenblow-offs.PhotoresistthicknesswasevaluatedwithaBrukerDektakXT 75 Figure4.4:Floodexposureapparatus( l = 375nm). stylusafterdevelopment.Hereastylusisdraggedacrossthesurfaceofeitherthedeveloped photoresistorsputteredcircuitelements,producingfeedbackonthetopologyofthestructure. 4.3.9 SputterDeposition SputterdepositionwasconductedinaCompactResearchCoater(CRC-622-2G2-RF-DC)manufac- turedbyTorrInternational.ThismanualplanarmagnetronsystemutilizesDCcurrenttosputter materialfromtwoinchdiametertargets,showninFigure4.5.Thechamberwasevacuatedwitha turbomolecularvacuumpumpwithmatchingdualstagerotaryvanepump,pullingavacuumof 1 2 10 5 Torrwithwingargonusedtosputter.Duetothetargetsbeingangledrelativetothe substrate,theplatformwasrotatedtoproduceamoreuniformcoatingduringthesputteroperation. Anadhesionlayerofchromiumwassputteredontopofthedevelopedphotoresist,substrate,and micro-ribbon,followedbyathickerconductivelayerofgold.Theparametersforsputteringwere independentofthephotoresistsused.TheCrtargetwasenergizedfor5minutespriortoexposing thesubstratetothesputtering,thisisdonetoremoveanyoxidelayerformedonthesurface.Once sufclean,theCrtargetissputteredontothesubstratesurfaceforfourminutes( ˇ 50nm thickness)asitrotatesontheplaten.Thisdepositionisthenstoppedandthesubstrateissputtered withAutoathicknessof120-200nm. 76 Figure4.5:Sputterdepositiondevice(left).Insidethechamber,withlabeledAuandCrtargets angledoverthestage.Notetheshuttersovereach,usedtokeepeachcomponentisolatedfromeach other(right). 4.3.10 Lift-off EachremoverwaspouredintoaquartzPetridishwithalidandheatedonahotplateinsideafume hoodtoreduceprocessingtime.Aplasticpipettewasusedtoremoveracrossthesurfaceof thesubstrateandtopickattheedgesinordertoexpeditelift-off.Decreasingprocessingtimeis importantwhenasinglecrystalmicro-ribbonispresentbecausesomeportionsofthemicro-ribbon areindirectcontactwiththeremoverwhichcanundesirablyetchthesample. 4.3.11 TransportCharacterization TheglasssubstratesinwhichcircuitsweresuccessfullyprintedonweremountedtoPPMSpucks withGEvarnishandbondedtoexternalcontactpadswitheither25 m mAuor33 m mAlwire usingaTPTHB16semi-automaticbonder.Electricaltransportcharacterizationwascarriedout onaDynacoolcryostatwith14TmagnetmanufacturedbyQuantumDesign.Resistancewas characterizedusingasourcemeterKeithley2400andananovoltmeterKeithley2182A. 77 4.4 Results&Discussion Figure4.6:Summaryofprocessedmicro-ribbonsthroughstagesofdevelopment. AsummaryoftheprocessingresultsisshowninFigure4.6.Thisprocesswwasbrokeninto threeregions:FIBprocessing,photolithography,andelectronictransportcharacterization.FIB processingwascompletedbytechniciansattheIFWDresden,whilethephotolithographyand electronictransportcharacterizationwasconductedduringresearchvisitswithagroupofsupporting scientistsattheIFWDresden.ThemajorityofprocesslossesoccurredinthetimeconsumingFIB millingprocess,withonlyeightsamplebeingviablegoingintophotolithography.Oftheseeight, threemadeittotheelectronictransportcharacterizationwithapartialdatasetcompletedona Ca 5 In 2 Sb 6 ribboncutperpendiculartothec-direction. 4.4.1 RibbonProcessing SinglecrystalsofCa 5 Ga 2 Sb 6 andCa 5 In 2 Sb 6 werecutintomicro-ribbonsmeasuring18-80 3-7 0.2-0.5 m musingFIBmillingasillustratedinFigure4.7.TheGacontainingCa 5 Ga 2 Sb 6 crystalsproveddifculttocut.WhentheionbeamstruckanylatentGaonthesurfaceora Ga-richinclusioninthecrystaltheGawouldimmediatelyliquifyandburst,ruiningthepartiallycut 78 Figure4.7:SuccessfullyFIBmilledmicro-ribbonreadyforextraction(left).SuccessfullyFIB milledmicro-ribbonsreadyforextractionbothperpendicularandparalleltogrowthdirection(right). micro-ribbon.TheseCa 5 Ga 2 Sb 6 crystalshadbeengrowninaGa-andSb-richwithexcessGa collectingonthesurfaceofcrystalsduetoitsunfavorablewettingbehavior.Oncemounted,several cutswereattemptedfromeachsampleasshowninFigure4.7(right).Someofthesemicro-ribbons wouldspringloosepriortotransfer.WhiletheFIBsystemwascapableoftilting,allcutsweremade perpendiculartothebeam,utilizingsamplerotationinstead. TheCa 5 In 2 Sb 6 samplesweregrowninanIn-andSb-richandappearedtohavecleaner surfacesasIndoesnotwettothesurfaceofthegrowncrystalsasreadilyasGa.Thesecrystals howeverdidsufferfrominhomogeneousregionsasexcessInandSbformedtheInSbbinarywhen trappedbetweengrowncrystals.Distinctphasecontrastwasobservedinsomeinstanceswiththe millingoperationwellunderway,resultinginthatregionofthesinglecrystalbeingabandoned.Other micro-ribbonsbentasaresultofthemillingprocess.Successfullycutsamplesweretransferred toaglasssubstrateusingamicromanipulatortobeginthephotolithographyprocess.Duetoair sensitivityconcerns,bothsinglecrystalsandcutmicro-ribbonswerestoredundervacuumina desiccatorbeforeandafterFIBmillingtheeightsuccessfullyextractedmicro-ribbons. 4.4.2 CircuitDesign Thegoalofthiscircuitdesignistofullycharacterizemicro-ribbonsofourcompoundsbothparallel andperpendiculartothec-axis.Thisisaccomplishedbydevelopinganumberofsensorsthatwill 79 measureHall,Seebeck,resistivity,andthermalconductivity. InordertooptimizeindividualphotoresistcombinationsaprototypeHallcircuitwasgenerated showninFigure4.8.Thisdesignwaslimitedtosixsensorscomparedtothefullcharacterization circuitwhichwouldhave16,showninFigure4.9.ThisreducedHallcircuitcutdownoncycletime atthelaserandallowedforthecreationof 2 2 gridsofthiscircuitatdifferentpowerlevelsona singlesubstrate.measurementsweretakenoverthelargercircuitcontactpadstodetermine photoresistdepthanduniformity.Thesecontactpadsarewherethecircuitisexternallybondedto characterizationequipment.Duetothesemi-manualnatureofplacingthesecontacts,largerpads aremadetomaketheprocesseasier.Theselargerareasarealsousefulformeasurements asthefeaturesinproximitytothemicro-ribbonarebelowthetolerancesinwhichthe canreliablydetect.Resistivitymeasurementswereconductedusingafourprobemethodwhere acurrentispassedthroughtwooutercontactswhilethevoltageismeasuredbetweentwoinner contacts.Halleffectismeasuredusingafourprobeinthepresenceofamagnetic TheHallsensorsusedtomeasurevoltagearepositionedoppositeeachotheratthemicro-ribbon center.AprototypeHallcircuitisshowninFigure4.8. TheSeebeckcoefismeasuredbyrunningacurrentthroughasensorincloseproximity totheendoftheribbon,referredtohereafterasaheater,withapairofthermometersmeasuring thedifferenceininducedvoltageacrossthemicro-ribbon.Thermalconductivityisdeterminedby measuringthethermalconductanceofthemicro-ribbonbytakingintoaccountthevoltagedrop betweensensorsandthetemperaturedifferencebetweenthethermocouples. Auniquedigitalmaskwascreatedforeachmicro-ribbonbasedoffitsdimensions.Thiswas especiallycriticalbecauseitwastomaximizetheallowedspacebetweensensorsandalso todeterminethecorrectspacingbetweentheHallcontactswhichwererequiredtocontactopposite edgesofasamplebutnotcontacteachother.Allofthesesensorsareintegratedintoasingledesign asshowninFigure4.9. BothcircuitdesignsinFigure4.8and4.9aremadewithsensorsthathaveawidthof4 m m. Throughoptimizationsitwasdeterminedthat3 m mandinsomeinstances2 m marealsopossible 80 Figure4.8:PrototypeHallcircuit(left),andviewofsensorsoverthemicro-ribbonat center(right). but4 m mwasusedbecauseitprovidesmoretoleranceintheprocess.Thesewidercontactsproved usefulinalleviatingsomecontactissuesasthesputterdepositionwasnotthickenoughinsome instancestoconsistentlycoatsubstrateandmicro-ribboninterface. 4.4.3 PhotoresistOptimizationandSelection AnumberofphotoresistswereutilizedwiththeirspincoatingcomparedinFigure4.10.Ti PrimeandAZ5214E(purple),LOR3Bandma-P1205(blue),andAZ926010 m mandAZ9260 24 m m(black)constitutethedifferentphotoresiststacks.Theseoptimizedparameterswerewithin therecommendedmanufacturer'srangeforbothspeedanddurationbutwereadjustedslightlyto ourspincoaterandlaboratoryconditions. ThelowviscosityTiPrimeadhesionlayerisspunathighspeedandsoftbakedtothesubstrate priortotheapplicationoftheAZ5214Ephotoresistforboththestandardpositiveandimage reversalLOR3Bisspincoatedandsoftbakedpriortotheapplicationofma-P 1205andusedasapositivephotoresistbi-layerwheretheLOR3Bisundercutinthedevelopment procestoimprovethesubsequentlift-off.TheAZ926010 m mcanbeusedonitsownorasthe 81 Figure4.9:Fullcharacterizationcircuitdesign(left),andviewofsensorsoverthe micro-ribbonatcenter(right). Figure4.10:Optimizedspincoatingforselectphotoresistsgroupedbycolor.TiPrimeis appliedpriortoAZ5214E(purple).LOR3Bisappliedpriortoma-P1205(blue).AZ926010 m m canbeusedsingularlyorprecedingtheAZ926024 m mthatisasecondapplicationofthe photoresist(black). 82 Table4.1:Optimizedtemperatureanddurationofsoftbakeforselectedphotoresists.AZ9260 24 m misatwostepapplicationstartingwithAZ926010 m mlayer.AZ5214Ewasoptimizedas apositivephotoresistandintheimagereversalstate. Temperature(°C)Time(s) TiPrime120120 AZ5214E11050 AZ5214E(IR)90240 LOR3B180250 ma-P120510030 AZ9260(10 m m)11080 AZ9260(24 m m)110160 baselayerfortheAZ926024 m mthicknesswherebythephotoresistisappliedasecondtimeafter theapplicationisspincoatedandsoftbaked.TheAZ9260photoresistwashighlyviscousand whencoupledwiththesmall,difsquaregeometryproducedanoticeableedgebeadalongthe substrateperimeterwhichworsenedatthecorners.Thisnon-uniformapplicationofphotoresistwas laterbydataoncethephotoresisthadbeendeveloped. SoftbaketemperaturesanddurationsarelistedinTable4.1.WhiletheTiPrimeparameters remainedthesameforbothoftheAZ5214Ephotoresist,thephotoresistitself requireddifferentoptimizationsdependingonitsstate.Thisphotoresistwaslessviscousthanthe AZ9260photoresistandhadalessenededgebeadatthesubstrateperimeteronce thesoftbakewascomplete.TheLOR3Bphotoresistrequiredthelongestandhottestsoftbake andwascoupledwithma-P1205toproduceabi-layerundercutpost-development.Both ofthesephotoresistsshowedasmall,non-detrimentaledgebead,similartothatoftheAZ5214 E.Whilethelaboratoryenvironmentwashumiditycontrolled,nttemperatureincreases wereexperiencedinthelaboratoryduetohotsummerweatherresultinginsometimessporadicand unreliableresults.Specialcarewasusedtoprocessthesesamplesquicklyandpreferablyduringthe coolermorninghours. 83 Table4.2:Developmenttimesforselectphotoresists. PhotoresistDeveloperTime(s) LOR3B+ma-P1205ma-D33120 AZ9260 10 m mAZ400K1:4420-660 24 m mAZ400K1:4660-1200 TiPrime+AZ5214E StandardAZMIF72650 ImageReversalAZMIF72640 4.4.4 DevelopmentOptimization Thelaserlithographyprocessrequiredextensiveoptimization,asdifferentpowersettingswould producedifferentlinethicknessesinthephotoresistdespiteimplementingacommondigitalmask. Challengesalsoaroseinthedevelopmentstageasonehadtobecautiousnottoover-developthe patterninthephotoresist.Theseprocessesdirectlyimpactedtheeffectivenessofthesubsequent lift-offwhichwasalsofoundtobeheavilycircuitgeometrydependent.Someofthelift-offissues wereresolvedwithcircuitdesignoptimization,wherebysensorswereseparatedasmuchaspossible andtheanglesinwhichtheyexitedthemicro-ribbonstagingareawerestaggered. Priortothecriticaltaskoflinethicknessoptimization,appropriatedevelopertimesneeded tobeestablished.Developmentfollowedthelaserlithographyprocess,immediatelyafterinthe caseofthepositivephotoresists,andafterahardbake,cooldown,andexposureforimage reversalphotoresists.Thedevelopmentprocesssubmergedthesubstrateinthemanufacturer's recommendeddeveloperforaamountoftimebeforeitwasrinsedcleanwith deionizedwateranddriedwithnitrogenblow-offs.Initialtimesweredictatedbymanufacturer recommendationbutdeviatedinthecaseoftheAZ9260.Finaldevelopmentdurations arelistedinTable4.2foreachphotoresist.Sampleswereobservedunderanopticalmicroscopeto evaluatethedeveloperprogress,re-submergingsubstratesininstancesofunder-development.When over-developed,thesubstratewassimplyscrappedinoptimizationtrialsbutcouldberecoveredby submergingthesubstrateinanappropriateremovertobegintheprocessagainifamicro-ribbon neededtoberecovered. 84 Thema-D331alkalineaqueousbaseddevelopersolutionwasusedtodeveloptheLOR3Band ma-P1205photoresists.Thisbi-layerdevelopedthecircuitarearepeatablyinonly20seconds,but morevariabilitywasobservedintheundercutlayerofLOR3B,whichiscriticalforthesubsequent lift-offprocess.TheseconsistentcircuitdevelopmentresultsareshowninFigure4.11(left)forthe sixsensorHallcircuitdesign,shownpreviouslyinFigure4.8withnominalpadwidthsof0.4mm. Hereaneedlewasdraggedacrossthesurfaceofthephotoresistandglasssubstrate.The exposedcircuitdesignwasdeveloped,withthephotoresistbeingremovedcompletelyasindicated bythebottomsthattherecorded.Thetargetdepthofthistrough,whichisameasurement ofphotoresistthickness,wasexpectedtobeinthe0.8to1.0 m rangeasdictatedbythespincoating ThesemeasurementsfailtocapturetheamountofundercutthatthebaselayerofLOR 3Bexperiences,sowhiletheseresultsareencouraging,moreoptimizationwasrequiredoncethe effectivenessofthelift-offcouldbeevaluated. TheTiPrimeandAZ5214Ephotoresistperformedrepeatablyforboththestandardandimage reversalusingAZMIF726asadevelopersolution.resultsforthestandard applicationareshowninFigure4.11(right)witharepeatabledepthofapproximately1.4 m m.As wasthecasewiththebi-layerphotoresistadditionaltestswithlift-offarenecessaryastheundercut geometryofthedevelopedphotoresistsidewallcannotbedirectlyevaluated. TheAZ400Kdevelopersolutionwasusedina1:4ratiowithdistilledwaterforthe developmentoftheAZ9260photoresist.AsshowninTable4.2,thedevelopmenttimesforthe AZ9260photoresistwereextremelylongandvariablewithseveraloptimizationstudiesfailingto producesatisfactoryresults,wherebyaportionofthecircuitremainedunder-developedwhilethe intricatesensorsnearthemicro-ribbonwereseverelyover-developed.resistthickness variationwasobservedfortheAZ9260photoresistasshowninFigure4.12(right).Herethe wasrunacrosstwocontactpadsasshowninFigure4.12(left)withthecontoursnormalizedtothe glasssubstrate.Despiteaphotoresisttargetdepthof24 m mbasedoffthespincoatingspeed,the remainingphotoresistvariedwidelybetweenapproximately6and23 m m.Thiswaslargelydue tothehighviscosityofthisphotoresistcoupledwiththeverysmallsubstratesize.Thissizeis 85 Figure4.11:pathsacrossthephotoresistsurfacefortheLOR3Bandma-P1205 photoresists(left),andTiPrime+AZ5214Ephotoresist(right).Padnumberscorrespondto HallcircuitlabelsinFigure4.8. constrainedbythemountingrequirementsforastandardPPMSsamplepuckusedforelectronic characterization.Theedgebeadforthisphotoresistislarger,makingthephotoresistthickness widelyvariableacrossthecenterofthesubstrateduetopoorremoval.Additionallyanytiltinthe spincoaterstationcanbeasourceofphotoresistthicknessvariability.Whilelargedifferencesin theheightoftheremainingphotoresistcanpotentialcauseslightsputteringdifferencesthevariable topologyisdetrimentaltothelift-offprocess,causingsomeareastoprogressmorequickly,with otherareasbeingunabletolift-off,asshowninFigure4.17(left). Anotherissuehighlightedbymeasurementsistheunder-developmentofsomeofthe largecontactpadswhilethemoreintricatefeaturesincloseproximitytothemicro-ribbonwould over-developandlosedimensionalcontrol.AproperlydevelopedAZ9260photoresistwitha targetdepthof10 m misshowninFigure4.13(left).Despitenotachievedthetargetdepth,the developmentwassuccessfulwitheachpadshowingasurfaceagainsttheglasssubstrate.An under-developedcaseisshowninFigure4.13(center)withdevelopmentissuesbeingexacerbated whenasecondphotoresistlayerisappliedforanintendedtargetdepthof24 m mshowninFigure 86 Figure4.12:pathsillustratedacrossaLASI7designedHallcircuit(left).Eachcontact padis0.4mmsquare.dataonAZ9260,24 m mtargetphotoresistthicknessshows thicknessvariability(right). 4.13(right).Herephotoresistisstillpresentontheglasssurface,creatingtextureinwhatshould beasurface.Thisresistcouldpotentiallybeimprovedgivenbetterspincoatingoptimization viafasteraccelerationsorbyincreasingthelaserexposurepower,buttheover-developmentof featuresatthecircuitcenterismorediftosimultaneouslyresolve.Therepeatableresultsfrom theAZ5214EandLOR-3B+ma-P1205arepreferred. 4.4.5 LineWidthRepeatability Withaconsistentdevelopmentprocessinplace,poweroptimizationstudiesbeganwherebylaser powerintheexposureprocesswasadjustedincrementally.Thesestudieswereconductedwiththe selectedphotoresistsinordertodetermineaccuracyandrepeatabilitytocircuitfeature dimensions.ApoweroptimizationstudywasconductedfortheAZ5214Eimagereversalphotore- sistshowninFigure4.14(left)withmeasureddimensionsforeachpoweraveragedandcompared inFigure4.14(right).Heretheheaterelementfromthecircuitdesignwasisolatedandrepeated withatargetthicknessof2,3,and4 m m.Thisheaterpathwayhasanumberofbendswhichwere 87 Figure4.13:analysisoftheAZ9260photoresistafterdevelopmentwithfullydeveloped 10 m m(left),under-developed10 m m(center),andunder-developed24 m mtargetthickness (right).Thethicknessoftheresistwaslessthanthetargetthicknessinallthreecasestudies.Pad numberscorrespondtoHallcircuitlabelsinFigure4.8. individuallymeasuredandthenaveragedtoprovideabettersenseofrepeatabilityforeachpower level. Inthecaseofimagereversalphotoresiststhelaserexposesthenegativespaceofthecircuit design,thisaccountsforwhythereiscoatingremovedfromthesquaresurroundingthedesignsin Figure4.14(left).Increasingthisbufferimprovestheoddsofaproperlift-offbutincreasescycle time.Positiveandpositivebi-layerphotoresistsonlyhavethelaserrasteracrossthecircuitdesign itselfwhichreducestheexposedarea.Thesepowerstudies,whichfocusedontheadjustmentofthe laserlithographyparameterswereevaluatedafterthelift-offstage. ThecircuitisconstructedfromaprimarylayerofAu.UnlikeindustrialICswhichareconstructed withCu,thereisnoencapsulationorsimilarmethodusedtopassivatethestructures.Forthisreason, noblemetalssuchasAuorPtarepreferredtopreventdegradationofthesputteredstructures. Electricalconductivityisalsoimprovedwithlessheatinginthecurrentlineswhichwas atthelowtemperaturesinwhichcharacterizationwascompleted. Aproperundercutwasfoundtobecriticaltothesuccessofthelift-off.Figure4.15(left)shows acorrectlydevelopedundercutpriortosputterdeposition.Theedgesofthecircuitappearsomewhat brighterandoutoffocusduetothephotoresistbeingviewedtop-down,withtheundercutobserved throughaportionofthephotoresist.Incontrast,designsthatlackedaproperundercuthavesidewalls 88 Figure4.14:Examplepowerstudyforlaserpowers2-100%with2%increments(left).Line widthstudiesforpoweroptimizationwithnoribbonfortargetthicknessof2,3,and4 m m linethicknesses.SlideswerecoatedinTiPrimeandimagereversedAZ5214Eresist.Power percentageisforthelaser,1x1pass,on,uni-directionalandinvertedwithabufferforimage reversal(right). Figure4.15:ATiPrime+AZ5214Eimagereversalphotoresistcircuitwithcorrectundercutafter thedevelopmentstage(left)comparedtoapoorlyundercutLOR3B+ma-P1205photoresistcircuit thatfailedtolift-offcorrectly(right). 89 thatappearedsharpandvertical.Thisledtolift-offissuesasdepictedinFigure4.15(right).Herean insufcientundercutwasproducedbytheLOR3Bandma-P1205bi-layerphotoresist.Thiscircuit designwasforasmallersamplewhichexacerbatedlift-offissuesbycreatingnarrowcoatingsthat requiredremoval. 4.4.6 SputterDepositionEvaluation Witharepeatabledevelopmentandlaserexposureprocessinplace,thesubsequentsputterdeposition canbeevaluatedasshowninFigure4.16.Afterthelift-offprocessthewasrunacross thedepositedcontactpads.Thesputterdepositionthicknesstargetforthiscircuitwas250 m m withanadhesionlayerofCraccountingforapproximately50 m m.Allmeasurementsofthese thicknesseswereextremelyaccurateandconsistent,thatthesputterdepositionwas reliable.ThespikesinthicknessontheedgesofthepadsshowninFigure4.16(left)werelargely duetotheneedleitself,draggingandcatchingonportionsoftheappliedcoatingduringthe measurement.Thisalsoaccountsforsomeofthetextureobservedonthetopofeachpadaswell. Someofthesecleanlift-offedgesareshowninFigure4.16(right). 4.4.7 Lift-off Table4.3:Lift-offtemperaturesandtimesforselectphotoresists. PhotoresistsRemoverTemperature(°C)Time(minutes) LOR3B+ma-P1205NMP6020+ AZ9260 10 m mAZ1008060-120 24 m mAZ1008060-150 TiPrime+AZ5214E Standard11658040-95 ImageReversal11658010 Lift-offtimesfortheselectedphotoresistsarelistedinTable4.3.Substratesweresubmergedin removerandplacedonhotplatestoacceleratetheprocess.Thesubstrateconsistsofaphotoresist layerunderneaththesputterdepositionlayersinpositionswherethecoatingwasundesirableand 90 Figure4.16:Successfullift-offofTiPrimeandAZ5214Ephotoresist.pathsacrossthe sputteredcircuitpadsafterlift-off,measuringthethicknessofthesputteredchromiumandgold stack(left).OpticalimageofthepadsleadingtotheHallcircuitatcenter(right).Padnumbers correspondtoHallcircuitlabelsinFigure4.8. requiresremoval.Otherareasthatmustberetainedaresimplythecoatingdirectlysputteredonto theglasssubstrateandmicro-ribbon.Removersareunabletoremoveanyofthesputterdeposition coatingbutareabletobreakdowntheremainingphotoresist.Thisprocesswasacceleratedbyusing tweezerstoscratchportionsoftheslidethatrequiredremoval,actingaspointsofinitiationforthe remover.Apipettewasalsousedtoremoveracrossthesurfaceremovingdebrisintheprocess. ToremoveunwantedphotoresistfromtheLOR3Bandma-P1205substratesanN-Methyl-2- pyrrolidone(NMP)bath,manufacturedbyMicroChemicals[ 267 ]wasused.Thisprocesstooka minimumof20minutesandinsomeinstancesdidnotproduceaneffectivelift-offevenwhenleft overnight.Thisprocesswasimprovedwithoptimizedcircuitdesignwhichmaximizedinter-sensors distancesandremovedunfavorablegeometrythatpreventedportionsofthemetalfromliftingoff. Variabilitystillexisted,however,duetoaninsufcientundercutproducedbyLOR3B.TheLOR3B seemedtohaveahighersensitivitytochangesinambienttemperatureduringprocessingwhichmay havecontributedtosomeofthisvariability.Longcycletimesaredetrimentaltoourprocessbecause portionsofthemicro-ribbonareexposedtotheremover,etchingordestroyingthemicro-ribbon. 91 Figure4.17:Poorlift-offofanAZ9260photoresistcircuitwithsidewalldepositionadheringto substratesurface(left)comparedtoanoptimizedcircuitdesignusingTiPrime+AZ5214Eimage reversalphotoresistaftersuccessfullift-off(right). TheAZ100removermanufacturedbyMicroChemicals[ 268 ]wasusedforbothtargetthick- nessesoftheAZ9260photoresist.Duetolargevariabilityinthephotoresistthicknessandno undercuttoassistindetachingmetalfromthephotoresistsidewalls,lift-offwaspoorasillustrated inFigure4.17(left).Insteadofrinsingawaywiththedissolvedphotoresist,goldadheredtothe substratesurfacewhereitwasunabletoberemovedeveninadditionalrinses.Incontrast,an optimizeddesignforalongermicro-ribbonisshowninFigure4.17(right)usingTiPrimeandAZ 5214Eimagereversalphotoresist.Thelaserisabletoproperlyexposethenegativespaceofthe designandgenerateasufundercutofthephotoresisttoallowforarepeatablelift-off. Micropositremover1165manufacturedbyDowElectronicMaterials[ 269 ]wasusedfor strippingtheTiPrimeandAZ5214Ephotoresist.AsnotedinTable4.3whenAZ5214Ewasused asastandardpositivephotoresistthetimewaslongertolift-offthefeaturesofthestructure. ThisissuedidnotoccurwhileusingAZ5214Eimagereversalwhereprocessingtimeswerekept to10minutesinallexperiments,makingittheshortestandmostrepeatablelift-offprocess.All subsequentoptimizationsweredoneusingthisimagereversalphotoresist. 92 4.4.8 FinalOptimizedProcess Positive,positivebi-layer,andimagereversalphotoresistswereinvestigatedandoptimizedto determinethemostappropriatechoiceforourmicro-ribbonlift-offapplication.OfthesetheAZ 5214EimagereversalphotoresistwithaTiPrimeadhesionlayerwasfoundtobethemosteffective andrepeatablethroughthelift-offportionofthephotolithographyprocess. TiPrimewasappliedtothesubstrateandspincoatedat6,000RPMfor30secondsfollowed byasoftbakeonahotplateat120 ° Cfor120seconds.NexttheAZ5214Ephotoresistwasapplied andspincoatedat3,500RPMfor30seconds.TheprocessshowedgoodresultsforthepositiveAZ 5214Ephotoresistbutimprovedlift-offpropertiesintheimagereversalThisimage reversalrequiredanadjustedsoftbakeof90°Cfor240seconds. Oncethephotoresistapplicationwascomplete,laserlithographywasperformed.Micro-ribbons weresuccessfullyprocessedwithalaserpowerof5mW,35%power(13%applied), 1 1 , uni-directional,andinvertedwitha1mmbuffer.Followingthelaser,ahardbakewasperformedon ahotplateat120 ° Cfor120seconds,followedbya120secondcool-down,anda30second exposure( l = 375 nm).TheimagereversalphotoresistwasthendevelopedinAZMIF726.As showninTable4.2,thedevelopmenttimewaslessthanaminute. Afterdevelopment,aCr(50 m m)andAulayer(200 m m)weresputteredontothesubstrate.The Aulayerwasincreasedfrom150 m mduetotheoff-centeredsputteringtargetsandthepotential forthemicro-ribbontoproduceashadoweffect.Thesputterdepositionstagewasalsorotatedto improvetheuniformityofthisconductionlayer. Lift-offprovidedthemostvariabilitybetweenthedifferentphotoresistsandthicknesseswith resultssummarizedinTable4.3.HereAZ5214Eintheimagereversalwasthemost repeatable,liftingoffsuccessfullyforavarietyofcircuitdesignsin10minutes. TheprocesswithaCa 5 In 2 Sb 6 micro-ribboncutperpendiculartothec-directionisshown inFigure4.18.Duetothehighlevelofoptimization,thecircuitdesignwasabletoaccommodate twothermometers,aheater,Hallprobesandcurrentlines.Thisallowsthemicro-ribbonstobe fullycharacterizedusingthetwolistedinFigure4.18(right).WhilethePPMSpuck 93 Figure4.18:SuccessfullyprintedfullcharacterizationcircuitoveraCa 5 In 2 Sb 6 micro-ribboncut perpendiculartothec-direction.Sensorsarelabeledandenumerated,withthetwocharacterization listedatright. waslimitedtothreechannels,thecircuitcouldbebondedonceandtheprobesswappedusingan externalswitchboxtoswitchbetweenevenatlowtemperatures.1is capableofmeasuringSeebeck,electricalresistivity,andthermalconductivity.2is capableofmeasuringelectricalresistivity,carrierconcentration,andmobility.AsecondCa 5 In 2 Sb 6 micro-ribbon,cutparalleltothec-directionwassuccessfullyprocessedandisshowninFigure4.19 alongwiththesuccessfulbondingtoaPPMSpuck. 4.4.9 TransportCharacterization AsillustratedaboveinFigure4.6,outof19FIB-processedribbons,onlyasingleribbon,cut perpendiculartothegrowthdirection,wassuccessfullycharacterized.Further,althoughthegoalof thephotolithographyapproachwastoapplyacircuitthatwouldallowforcompletecharacterization ofthethermoelectrictransportproperties(Seebeckcoefthermalconductivity,andelectrical conductivity),ultimatelyonlyapartialcharacterizationofresistivityandcarrierconcentrationwas collectedpriortothemirco-ribbonbreakingapart. 94 Figure4.19:Ca 5 In 2 Sb 6 micro-ribboncutparalleltothec-direction(left).Micro-circuitbonded successfullytosurroundingPPMSpuck(right). ResistivityandHallcarrierconcentrationwascollectedonthesuccessfulCa 5 In 2 Sb 6 micro- ribbon,cutperpendiculartothec-direction,inalimitedtemperaturerangefrom220Œ300K.Further datacollectionwasnotpossible,asthesamplewasdestroyedduringtesting,mostlikelydueto excessiveappliedcurrent.Severalofthecontactswerenotsufcientlyconnected,butenoughprobes werefoundtobecontactedtorunafour-probecharacterizationonasamplecutperpendiculartothe c-direction.Lowresistancecontactsallowedforathree-terminalmeasurementacrossan11 m m segmentofthesample.Measurementswereunabletoberepeatedasthecontactshadbeendestroyed. Othersamplesproducedpartialdatasetsbeforetheytooweredestroyedduetoeitherexcessapplied currentorthermalload.Additionally,noreliabledatawasproducedfromthecrystalcutparallel tothec-directionduetoanattemptedcontactrepairthatdestroyedthesample.Fortunately,the c-directionisthepreferredgrowthdirectionofthecrystal,sosufcientlylargecrystals( ˘ 5mm) couldbecharacterizedusingafour-proberesistivitymeasurementbymanuallyplacingcontacts,as showninFigure4.20. Herefour-terminalresistancemeasurementswerecollectedwherebytwoleadspassacurrent throughthesamplewhiletwootherleadsmeasurethepotentialdropacrossthesample.Ohm'sLaw, R = V = I ,isusedtocalculatethesampleresistancewhere R istheresistanceofthematerialthrough whichthecurrent, I ispassedthroughwhichexhibitsavoltage V .Theresistivity, r ,isindependent 95 Figure4.20:FourproberesistivityprobesattachedtosinglecrystalCa 5 In 2 Sb 6 paralleltothe c-direction(left)withtheresultingresistivityvaluesfordifferentinputcurrents(right). ofsampledimensionsandrelatesto R , r = RA p ; (4.1) where p istheprobedistancewherethevoltageismeasured,and A isthecross-sectionalareathatis perpendiculartothedirectionofthecurrent. Electricalresistivityismeasuredinthesamplebymeasuringthevoltagedifferencebetween thetwoattachedthermocouples,generatedbythecurrentsuppliedat I sample,in andexpelled through I sample,out .ThecurrentisthenrunintheoppositedirectiontoeliminatethePeltiereffect contribution.ElectricalresistivityisinEquation4.1fortheprobesetup.Inthismannerthe dataistestedforrepeatability,appropriatecontactqualityandsampleuniformity.Themeasurements werecarriedoutfrom70KŒ320Kusingliquidnitrogentocooltochamber. ResistivityvaluesfortheCa 5 In 2 Sb 6 micro-ribboncutperpendiculartothec-directionare comparedwiththemeasurementstakenparalleltothec-directiononmacroscopiccrystalsinFigure 4.21(upperleft).Theresistivityperpendiculartothec-directionwasfoundtobeafactorof13- 18timeshigherthantheparalleldirectionasdepictedinFigure4.21(upperright).Thecarrier concentrationwasmeasuredonlyonthemicro-ribbon,andwasfoundtoincreasewithincreasing temperature,whichindicatesthatthecrystalisanintrinsicsemiconductor,asshowninFigure 4.21(lowerleft).Themagnitudeofthecarrierconcentrationsfromthemicro-ribbonissimilarto 96 Figure4.21:Resistivity,resistivityratio,carrierconcentration,andmobilityofCa 5 In 2 Sb 6 single crystalribboncutperpendiculartothec-directioncomparedtomeasuredpolycrystallinesamples. Increasedresistivityinthea-bplaneisconsistentwithDFTpredictionsofanisotropicbehaviorin singlecrystals. thatofthepreviouslyreportedpolycrystallineCa 5 In 2 Sb 6 [ 2 ],whichisbecauseitimplies similarpointdefectdensitiesandthusanarrowhomogeneityrange( e.g. ,Ca 5 In 2 Sb 6 isatrueline compound). Weareabletocalculatemobilityinbothsinglecrystalsamplesfrom s = ne m byassuming identicalcarrierconcentrationsinbothofthecharacterizedcrystals.Notethatcarrierconcentration 97 isnotafunctionofcrystallographicdirection.Becausethecarrierconcentrationwasonlymeasured from220-300K,datawasextrapolatedtolowtemperaturesusinganexponentialMobilityinthe perpendicularandparalleldirectionsarecomparedwiththemobilityofapolycrystallinesample inFigure4.21(lowerright).Thepolycrystallinedatacomesfromthehightemperaturetransport characterizationcarriedoutbyZevalkinketal.fortheCa 5 M 2 Sb 6 (M=Al,Ga,In)family[ 2 ].Due tothesmallsampledimensionsofthesinglecrystalmicro-ribbon,high-temperaturemeasurements arenotgenerallyfeasible(duetoinstrumentgeometrylimitations),thereforesinglecrystaldata canonlybecomparedtopolycrystallinepublishedvaluesnearroomtemperature.Thecomparison ofsinglecrystalandpolycrystallinemobility4.21(right)showsthatthec-directionmobilityis higher,whilethedirectionperpendiculartocislower.Thisagreeswiththecalculated DFTresultsthatpredictedimportantanisotropybehavior,withincreasedresistivityinthea-bplane, andlowerresistivityinthec-directionparalleltothecovalent"ladder"polyanions. SinglecrystalCa 5 In 2 Sb 6 couldpotentiallyexperienceathermoelectricperformance increaseifthec-directionisexploited.Itisimportanttonote,however,thatthesinglecrystalsin thisstudyareextremelyresistivecomparedtotheCa 5 In 2 Sb 6 sampleswiththehighestreported zT values.Thus,evenifallofthethermoelectrictransportpropertiesweremeasuredinthec-direction, ahigh zT isnotexpected.Theelectricalresistivitycanbeexpectedtodecreasewithincreasing dopinglevels,whichcanhaveanimportantimpactontheAdditionally,the Ca 5 In 2 Sb 6 micro-ribbonswereevaluatedforpotentialmagnetoresistancebetween0and14Tat 220and300K.Dataupto5Tdidnotexceedthelevelofanticipatedbackgroundnoise,yieldingno magnetoresistancebehaviorofnote. TheresistivityanisotropyofCa 5 In 2 Sb 6 iscomparedtoothersinglecrystalmeasurementsfrom highlyanisotropicmaterialsinTable4.4at220and300K.MostofthecompoundsinTable4.4are layeredcompounds,inwhichcase"parallel"referstoin-planeand"perpendicular"isout-of-plane. InthecaseofCa 5 In 2 Sb 6 andCsBi 4 Te 6 ,whichbothcontainone-dimensionalcovalentchains, thedataisparallelandperpendiculartothechaindirection.Itisobservedthattheresistivityof Ca 5 In 2 Sb 6 ismoreanisotropicthanthatofthetetradymitecompounds(Bi 2 Te 3 andSb 2 Te 3 ). 98 Table4.4:Anisotropicthermoelectricpropertiesat220and300Kforselectedone-dimensional (1D)compounds,vanderWaals(vdW)compounds,andcovalentlybondedtwo-dimensional (Cov.-2D)compounds. 220K300K Compound,direction r ( W cm) r ? = r k r ( W cm) r ? = r k Ref. 1D Ca 5 In 2 Sb 6 ? 3.39E+0018.61.56E+0013.1Thiswork k 1.82E-011.19E-01 CsBi 4 Te 6 ? 4.00E-02126.93.96E-0286.7[66] k 3.15E-044.57E-04 vdW Bi 2 Te 3 ? ŒŒ4.84E-056.13[270] k Œ7.90E-06 PbBi 4 Te 7 (Cd) ? 1.30E-035.71.28E-034.3[271] k 2.26E-042.98E-04 PbSb 2 Te 4 (SbI 3 ) ? 3.49E-0312.04.31E-0310.1[271] k 2.91E-044.25E-04 Sb 2 Te 3 ? ŒŒ4.27E-041.8[272] k Œ2.41E-04 Cov.-2D Mg 3 Sb 2 ? 1.39E+023.952.59E+000.49[7] k 3.52E+015.32E+00 SnSe ? ŒŒ5.00E-015[67] k Œ1.00E-01 ThedifferencebetweentheZintlphasesCa 5 In 2 Sb 6 andMg 3 Sb 2 listedinTable4.4,andthe otherlayeredmaterialsisthat k L isnotexpectedtobehighlyanisotropicintheZintlphases.A thermoelectricperformanceincreaseforCa 5 In 2 Sb 6 isexpected,whileMg 3 Sb 2 behaves relativelyisotropicallyasevidencedbyits r ? = r k < 1 at300K.Thisanalysisprovidesexperimental oftheorizedanisotropythatcanbeexploitedtodramaticallyincrease zT valuesin singlecrystalCa 5 M 2 Sb 6 (M=Al,Ga,In). 4.5 ConcludingRemarks Resistivityandcarrierconcentrationvalueswerecollectedonasinglecrystalmicro-ribboncut perpendiculartothec-direction.Thiscoupledwithresistivityvaluescollectedonasinglecrystal paralleltothec-directionyieldedhighlyanisotropicelectronictransportproperties.Thisisthe experimentalofthisbehaviorin5-2-6Zintls,showingnearlya20xincrease inresistivitymeasurementsintheperpendiculardirection.Itisanticipatedthatlatticethermal conductivitywillremainisotropic,allowingforathermoelectricperformanceboost 99 paralleltothec-direction. Whilelackingacompletecharacterizationacrossthelowtemperatureregimethisstudyproved thathighqualitymicro-ribbonscouldbeproducedfromlargersinglecrystalsusingaFIBmilling technique.Arepeatablephotolithographyprocesshasbeenestablishedthatistransferabletoother micro-ribboncompoundsandprojectsbeyondjustthermoelectricmaterials.Thephotolithography optimizationisrobustenoughtoallowforanumberofsensorstobeplacedacrosssamples. 100 CHAPTER5 CRYSTALGROWTHANDCHARACTERIZATIONOFMg 3 Sb 2 TheZintlphaseMg 3 Sb 2 hasproventobeapromisingnewthermoelectriclargelyduetoitsexcellent n -typeperformance.Electronictransportpropertiesandtheabilitytodope n -or p -typehavebeen showntodependstronglyontheMg:Sbratiopresentduringsynthesis.WhileMgvacanciesare suspectedtoberesponsibleforthisbehavior,thepresenceofvacancieshasnotbeenby directexperiments.Inthepresentstudy,highqualitysinglecrystalshavebeensuccessfullygrown fromMg-andSb-riches. ofSC-XRDrevealeddifferencesintheoccupancyoftheoctahedrally- coordinatedMg(I)site.Further,therevealpreviouslyunknowninterstitialsites.Despite differencesinMgoccupancy,theMg-andSb-richcrystalsarefoundtoexhibitintrinsicsemicon- ductingbehavior,suggestingthatthepresenceofgrainboundariesmightplayaroleinthehighly p -typetransportreportedinpreviouslystudies. 5.1 Introduction Thermoelectricmaterialsofferthereversibleconversionofheatandelectricity.Themaximum powerandefciencyofathermoelectricmaterialisgovernedbyits zT = a 2 s T = k , where a istheSeebeckcoef s istheelectricalconductivity, T istheabsolutetemperature, and k isthethermalconductivity[ 59 ].Extensiveeffortshavebeenmadetodiscovermaterialsthat maximize zT ,withhighperformancedevicesconsistingofmaterialswith zT exceedingunity[9]. Mg 3 Sb 2 isanexcellent n -typethermoelectricwithahigh zT ˇ 1 : 5 [ 33 ].Comparedwith state-of-the-artthermoelectricmaterialssuchasPbTeandBi 2 Te 3 ,itislighter,lesstoxicandmore earthabundant.Mg 3 Sb 2 crystallizesinthetrigonal,layeredCaAl 2 Si 2 structure,whereMgatoms occupyboththeoctahedrally-coordinated(Mg(I))andtetrahedrally-coordinated(Mg(II))cation sites[ 273 ].Ithasalonghistory,beginningwithitsdiscoveryinthe1930s[ 73 , 274 ].Initialstudies ofthethermoelectrictransportinMg 3 Sb 2 characterizeditsundopedcharacter[ 275 ]andavariety 101 ofdopingoptionsonboththeMg(Zn[ 276 , 277 ],Cd/Ag[ 278 ])andSb(Bi[ 279 Œ 283 ],Pb[ 284 ])site, yielding p -typebehavior. Thesestudiesfoundpersistent,butlimited p -typethermoelectricperformancebelowunity.A highwasonlyrecentlyrealizedexperimentallybyTamakietal.[ 33 ]usingMg- richgrowthconditionscombinedwithTedopingontheSbsite(Mg 3 : 2 Sb 1 : 5 Bi 0 : 49 Te 0 : 01 ).These resultswereundersimilarconditionsinsubsequentstudies[ 5 , 285 , 286 ].Thesuperior performanceof n -typeMg 3 Sb 2 isduetoacombinationofhigherbanddegeneracyandsmaller effectivemass[ 287 , 288 ].Thisresultsinalargethermoelectricqualityfactor, b ,whichisametric ofintrinsicmaterialpropertiescorrelatingtohighperformancethermoelectrics[ 285 ].Consequently the n -typecompositionachievesahighperformanceof zT ˇ 1 : 5 at716K[ 33 ]comparedtothe p -typeperformancebelowunity. Intrinsicdefectsareunderstoodtoplayacriticalroleindeterminingthedominantcarrier typeinMg 3 Sb 2 .DFTcalculationsofdefectenergiesshowthatMgvacanciesareresponsiblefor thepersistent p -typebehaviorinSb-richgrowths[ 5 , 33 , 289 ].Mg-richsynthesisconditionsare predictedbyDFTtoincreasetheformationenergyofMgvacanciesanddecreasetheformation energyofMginterstitials.Thisisthoughttoleadstoanoveralldecreaseinacceptortypedefects [5,33]. Althoughelectronictransportpropertiesanddefectcalculationsbothstronglysupportthetheory thatMg-vacanciesplayarolein n -and p -typedoping,thepresenceofMgvacancieshavenot previouslybeendirectlyobservedinstructuralcharacterizationofMg 3 Sb 2 samples.Inthecurrent study,singlecrystalsofMg 3 Sb 2 weregrownfromMg-andSb-richenvironmentsusinga method.ThesecrystalshavebeencharacterizedandcomparedusingSC-XRDandelectronic transportmeasurements.Thisapproachallowsfordirectassessmentoftherelationshipbetween growthconditionsandintrinsicdefectconcentrations. 102 5.2 ExperimentalMethods 5.2.1 Synthesis ElementalMg(granules,99.8%),andSb(shot,99.999%)wereweighed,mixed,andloadedinto2 mlcapacityaluminacruciblesetswith13mmOD 25mmheight[ 155 ].Mg 3 Sb 2 single crystalsweregrownusingamethodwitheitherexcessMg(Mg 3 Sb 2 +Mg 6 : 90 )orSb (Mg 3 Sb 2 +Sb 3 : 56 ).Aluminacruciblesweresealedinquartzampules,14/16mmID/OD.Mg-rich growthsweredoublesealedusingalargerquartzampule,17/19mmID/ODtosafeguardagainst potentialrupturesduetoMgvaporizationlossesreactingwiththequartz.ForMg-richgrowths,a largeexcessofMgwasneededassomeoftheelementalMgwasremovedfromthesystemdue toformationofMgOwiththeAl 2 O 3 crucibles,whichproducedanoticeablegraydiscoloration. Reactivitywiththequartzampuleswasmorestill,appearingblackasthevaporized MgreactedwiththeSi(2Mg+Si ! Mg 2 Si)orO(2Mg+SiO 2 ! 2MgO+Si)inthequartz. Tantalumtubeshavebeenreportedasanalternativetoaluminacrucibles.However,Tareactswith Sb[ 290 ],formingalayerofTaSb 2 ontheinnersurfacethatactsasnucleationsiteforMg 3 Sb 2 crystalsasdescribedinXinetal.[7]. TheSb-richgrowthswereheatedto800 ° Candthencooledto675 ° Catarateof3 ° C/hrwhere theywereextractedfromthefurnace,andcentrifuged.TheMg-richcompositionwasheated to800 ° Candcooledto650 ° Catarateof3 ° C/hrwhereitwasextractedfromthefurnace, andcentrifuged.Allgrowthswerecentrifugedfortwominutesat2500RPMsseparatingthegrown crystalsfromtheremainingNowasremovedfortheMg-richgrowthsasMgreactionand vaporizationlosseswere 5.2.2 StructuralCharacterizationandMetallography Singlecrystalsurfaceswereobservedusingpolarizedlightmicroscopy.Sampleswerealsoobserved usingaZeissEvoLS25SEMwithanattachedEDAXApolloXEDS.Datawerecollectedand processedwiththeTEAMsoftwaresuitetodetermineapproximatechemicalcompositions.Electron 103 backscatterdiffractionwascarriedoutonaTescanMira3XMHSEMequippedwithanEDAX-TSL EBSDsystem.MicroscopyrevealedhomogeneousmainphasewithonlyislandsofelementalSb metal.Thus,itmaybeconcludedthatthemeasuredphysicalpropertiesaretheproperties ofthemainMg 3 Sb 2 phase.CrystalstructureandcompositionwereevaluatedwithSC-XRDatthe MaxPlanckInstituteforChemicalPhysicsofSolidsinDresden,Germany. 5.2.3 TransportCharacterization ResistivityandHallcoefweremeasuredonseveralcrystalsinthein-planedirectionona PhysicalPropertyMeasurementSystem(PPMS)manufacturedbyQuantumDesign.Resistivity wasmeasuredfrom210to360Kwithastandardfour-pointcontactingmethodusingAgpaint.Hall voltagewasmeasuredfrom100to350Kasafunctionofmagnetic 5.3 Results&Discussion 5.3.1 CrystalGrowthandMorphology ThemorphologyofthegrownMg 3 Sb 2 crystalscanbedescribedaslarge,platelets,measuring greaterthan5mmacross,withsizeconstrainedmainlybythecruciblediameter.Growthoccurred preferentiallyalongthea-bplane,byEBSD,instackedlayersparalleltothecrucible bottom.NoMgdrainedfromtheMg-richgrowthsastheexcessMgeitherreactedwith thecontainerorvaporized.Sb-richgrowthsfromSbbeingagood[ 198 ]thatdoes notreadilywettothesurfacesofcrystals,drainingtheliquidawayfromthecrystalsinthe centrifugeprocess.WhileSbhasahighermeltingtemperaturethanmostcommones[ 166 ] itpossessasufcientlylowvaporpressure(1617 ° C,1atm.)andverylowviscosity(1.22mPas) [291]. ThesurfacemorphologyofMg 3 Sb 2 crystalswasobservedusingSEM,showninFigure5.1. Herethehexagonalgrowthbehaviorisobservedinplaneasstep-likegrowthterminations.While thetransportpropertiesareisotropic,thestructurehasaclearpreferredgrowthdirectionthatis 104 Figure5.1:ScanningelectronmicroscopyimagesofMg 3 Sb 2 singlecrystalplatelets,notethe hexagonalgrowthbehavior.Crystalsurfacesawayfromthegrowthperimeterwereand smooth. in-plane,suggestingthatdanglingin-planebondsaremoreenergeticallycostlythanout-of-plane bonds.ThisgrowthbehaviorisconsistentwiththatdescribedinXinetal.[ 7 ]forMg 3 Sb 2 single crystals.TheorientationofthecrystalswasfurtherusingEBSDanalysis. 5.3.2 StructureDescription TheatomicpositionsandoccupanciesobtainedfromsinglecrystalareshowninFigure 5.2withcrystaldatalistedinTable5.2.ThemoststrikingdifferencebetweentheMg-andSb-rich crystalsisintheoccupancyoftheoctahedrallycoordinatedMg(I)site.InSb-richgrowths,itwas observedthattheMg(I)sitewaspartiallyoccupiedat87%,whileinMg-richgrowthsthissitewas 105 Figure5.2:CrystalstructureofMg 3 Sb 2 fromMg-richgrowthconditionswithMginterstitial atomsandtraceSb(I)vacancies(left).CrystalstructurefromSb-richgrowthconditionswith partialMg(I)occupancy(right). Table5.1:AtomicpositionsandoccupancydataforMg 3 Sb 2 singlecrystalsgrownfrombothMg- andSb-riches. AtomSitex/ay/bz/cB(is/eq)occ. Mg-rich Mg11a0003.6(5)*1 Mg22d2/31/30.634(2)2.9(3)*1 Mg32d2/31/30.038(10)2.5310.035(10) Sb12d2/31/30.2281(4)2.60(6)*0.965(10) Sb-rich Mg11a0001.74(8)*0.87(1) Mg22d2/31/30.6350(4)1.59(5)*1 Sb12d2/31/30.22836(6)1.430(10)1.00(1) Sb22c000.684(4)1.4(5)*0.014 fullyoccupied.ThisislargelyconsistentwithDFTdefectcalculations[ 5 , 33 , 289 ]whichhave predictedlowformationenergiesforMgvacancieswhenMg 3 Sb 2 isinequilibriumwithSb.Past studieshavealsoconsistentlyindicatedthatvacanciesontheoctahedrally-coordinatedMg(I)site arelowerinenergythanvacanciesonthetetrahedralMg(II)site. Inadditiontovacancies,DFTstudieshaveconsideredanumberofpossibleanti-sitedefectsand avarietyofinterstitialdefects.Theyconsistentlypredictthatthe(0,0,0.5)positionisthemost stablesiteforaMginterstitial,witha2+oxidationstate.Indeed,the(0,0,0.5)siteisthelargest voidintheMg 3 Sb 2 structure,soitseemslikethemostnaturalplaceforanextraatom.Incontrast, 106 Table5.2:CrystallographicdataforMg 3 Sb 2 singlecrystalsgrownfrombothMg-andSb-rich es. SpacegroupP-3m1P-3m1 a(Å)4.561(3)4.5672(6) c7.250(6)7.227(1) Cellvolume(Å 3 )130.6(3)130.54(6) F(000)(electrons)138.0138.1 Numberofatomsincell5.04.9 Calculateddensity(g/cm 3 )4.023(9)4.034(2) Absorptioncoef(1/cm)106.28107.85 RadiationandwavelengthMoK0.70930MoK0.70930 ModeofF(hkl)F(hkl) Numberofatomsites44 Two-thetaandsinT/l(max)66.400.77285.840.960 Numberofmeasured8592733 Numberofcondit.8592733 Numberofunique221405 usedin152385 R(sig),R(eq)0.0510,0.06780.0270,0.0550 R(F),Rw0.0756,0.07570.0312,0.0341 Goodnessof2.1301.040 Scalefactor0.32(1)[8.688284]0.269(3)[13.77765] Numberoffreeparameters1013 inthecurrentstudy,thereisnoevidenceofinterstitialelectrondensityatthepredictedlocationof (0,0,0.5). IntheMg-richcrystals,interstitialelectrondensityisobservedat(2/3,1/3,0.038)asshownin Figure5.2(left).InMg-richgrowthconditions,theinterstitialsaremorelikelytobeMgthanSb.In eithercase,theseinterstitialsitesareonlyphysicallyreasonableifdefectcomplexesforminthis structure,suchasaFrenkelpair.ArecentDFTinvestigation[ 289 ]showedthataMgvacancynext toaMg-interstitial(Frenkelpair)returnstotheoriginalstructureuponrelaxation,whichiscontrary toourexperimentalresults. TheofSb-richcrystalsyieldedinterstitialpositionsat(0,0,0.684),showninFigure 5.2(right),thathavenotbeenconsideredinpreviousdefectcalculations.Theinterstitialelectron densitycannotbeunambiguouslyassignedtoMgorSb.However,inSb-richgrowthconditions, Mginterstitialsareunlikely.ItisproposedherethatSb5+tobeamorelikelypossibility.Formation 107 ofMg(I)vacanciesasacceptortypedefectsduringgrowthinwillpushtheFermilevel deepintothevalenceband.Inresponse,thismightstabilizehighoxidationstateinterstitialion suchasaSb5+.ConsideringthevacanciesandpresumedSbinterstitials,theoverallcomposition oftheSb-richcrystalswouldbeMg 2 : 87 Sb 2 .TheresultingMgyof0.13Mgperunitcell translatestoaconcentrationof 1 : 0 10 21 Mg/cm 3 or 2 : 0 10 21 holes/cm 3 .Thisshouldresultin adegenerate p -typesemiconductor.However,asdiscussedbelow,thisisnotconsistentwiththe observedelectronictransportbehavior. 5.3.3 ElectronicTransportProperties Thein-planeresistivityofMg-andSb-richMg 3 Sb 2 crystalsareshowninFigure5.3.Themagnitude andtemperature-dependenceoftheresistivitysuggestintrinsicsemiconductingbehaviorunderboth growthconditions.TheintrinsicbehaviorisconsistentwithreportsfromsinglecrystalsgrowninSb byXinetal.[ 7 ],whichareshownasthedashedcurves.Notethatthein-planeandout-of-plane resistivityreportedbyXinetal.showsonlyaverysmalldegreeofanisotropyandthatelectronic transportisnearlyisotropic,despitethehighly-anisotropiccrystalmorphology. TheelectricalresistivityoftheSb-richsampleswastotheequationdescribingintrinsic behavioroftheintrinsicsemiconductor, r = aT 3 = 2 e E g = 2 k B T ; (5.1) where a isaconstant, T istemperature, E g isthebandgap,and k B istheBoltzmannconstant.This expressionresultedinbandgapsof0.59eVand0.66eV,consistentwithpreviousreports.The resistivityofthecrystallitefromtheMg-richbatchdoesnotshowthetypicalexponentialbehavior ofanintrinsicsemiconductor.Itseemsthatthedopinglevel,whichcausedthelevelingoffofthe Hallcoefbelow300K,asshowninFigure5.4,isalsoresponsibleforthelevelingoffofthe resistivitywithdecreasingtemperature. HallmeasurementswereperformedonseveralMg-andSb-richcrystals.Themagnitudeand temperature-dependenceofthechargecarrierconcentration( n H = 1 = R H e )asmeasuredbythe 108 Figure5.3:ResistivityvaluesforselectMg 3 Sb 2 singlecrystalsfromSb-andMg-richgrowth conditions,comparedtopublishedvalues[7]. Halleffectsuggestsintrinsicsemiconductingbehaviorforbothsetsofcrystals.Themostnotable exceptionisthe p -typetemperature-independentbehaviorofsomecrystallitesfromtheMg-rich samples,withaverylowchargecarrierconcentrationcorrespondingtotheconcentrationofMg defectsontheorderof10ppm,whichiswellbelowthedetectionlevelofSC-XRD.Onepiece fromtheMg-richbatchshowed n -typechargecarriersandfollowstheexponentialtemperature behaviorofanintrinsicsemiconductorbutonlyattemperaturesabove300K.Below300K,the chargecarrierconcentrationdoesnotdropfurther,pointingto n -typedefectswithaconcentration ofapproximately 10 14 cm 3 .TheMg-richsamplebatchrevealsthedifofcrystalgrowth froma ThecrystallitesfromtheSb-richsamplesconsistentlyshowintrinsiccarrierconcentrations. Thisissurprising,giventhelargepredictedMywhichshouldleadtohighp-typecarrier concentrations.Inlightoftheintrinsicsemiconductingbehaviorofallsamples,itisplausiblethat theMgmaybecompensatedbyadditionalSb 5 + interstitialsinthevicinityoftheMg vacanciestoachieveachargebalancedmaterial. 109 Figure5.4:InverseHallcoefofseveralMg 3 Sb 2 samples,measuredacrossthreebatches. ThesignoftheHalleffectforintrinsicsemiconductorsisdeterminedbythemobilityofthe holesandelectrons,typicallyresultingin n -typebehaviorduetoelectronshavinglargermobility, expressedas, R H = p m 2 h n m 2 e e ( p m h + n m e ) 2 p = n = n i ! m h m e en i ( m h + m e ) ; (5.2) where p , n and n i arethehole,electronandintrinsicchargecarrierconcentrations.Themobility m h ; e = e t h ; e = m h ; e ofthecorrespondingchargecarriersisproportionaltothetransportscattering time t h ; e andinverselyproportionaltotheinertialorconductivityeffectivemassineachband m h ; e . Thechargecarrierconcentrationofanintrinsicsemiconductorisgivenby[292], n i = 1 4 2 k B T p ¯ h 2 3 = 2 ( m c m v ) 3 = 4 e E g = 2 k B T ; (5.3) where k B istheBoltzmannconstant, T isthetemperature,and m e isthemassofafreeelectron.In thiscase,theeffectivemassesoftheelectronsandholesintheconductionandvalencebands, m c and m v ,areslightlydifferentduetothegeometricalaveragingofthebandanisotropyandmultiplicity. Weestimatetheexpectedtemperaturedependenceofthechargecarrierconcentrationbyas- sumingabandgapof E g = 0 : 6 eV.TheDOSeffectivemassesareprovidedbyZhangetal.and 110 accountfortheholesatthe G pointto0.58 m e ,andfortheelectronsatthe K pointto0.45 m e [ 285 ].Forthisestimation,electronsintheminimumoftheMLbandarenotconsidered,withan effectivemassof1.05 m e andlyingonly0.02eVabovetheminimumoftheconductionbandat the K point.Theelectronsaroundthe K pointandaroundtheminimumoftheMLconduction bandhavesinglevalleyeffectivemassesof0.28 m e and0.32 m e butaregreatlyincreasedbythe bandmultiplicitiesoftwoandsix,respectively.Themultiplicityoftheholepocketatthe G pointis one.Thedeterminingfactorforthesign,andpartiallyalsoforthesizeoftheHalleffect(measured chargecarrierconcentration),areholeandelectronmobilities.Zhangetal.estimatedthesetobe16 cm 2 /Vsand84cm 2 /Vsforholesandelectrons,respectively[ 285 ].Thetemperaturedependence oftheenergygapandmobilitieswerenotincludedintheestimate.Theestimateispresentedas theblacklineinFigure5.4,andisplotas 1 = R H e = n i ( m h + m e ) = ( m h m e ) : Thisestimatecorrectly describestheorderofmagnitudeandthetemperaturebehaviorofmostofthedata. 5.4 ConcludingRemarks SinglecrystalsofMg 3 Sb 2 weresuccessfullygrownfrombothMg-andSb-richenvironments withSC-XRDrevealingpreviouslyunreportedinterstitialpositionsforbothconditions. Mg-richgrowthshadfullyoccupiedMg(I)sitesandinterstitialelectrondensityat(2/3,1/3,0.038) wheretheyaresuspectedtoformadefectcomplex.Sb-richgrowthsrevealedpartialoccupancy oftheMg(I)site,consistentwithDFTresultsduetothelowformationenergyanticipatedforMg vacancies.Whileanumberofanti-siteandinterstitialdefectshavebeenconsideredwithDFT, interstitialposition(0,0,0.684)isreportedfromthisanalysiswhereitisproposedthatSb5+isa likelyoccupant.Allmeasuredcrystalsexhibitedintrinsicsemiconductingbehavior,despiteMg vacancies. 111 CHAPTER6 STRUCTUREANDELECTRONICPROPERTIESOFNEWZINTLPHASE Ca 9 Zn 3 : 1 In 0 : 9 Sb 9 6.1 Introduction ManynewcompounddiscoveriesareoccurringintheZintlphasespace[ 44 , 127 , 134 , 144 ], oftenasanunintendedconsequenceofattemptstodopeoralloyknownphases,whichresultsinthe discoveryofnovelcompounds.Thisisoftentheresultofgrowths,inwhichcandidateelements areheatedtoformahomogeneousmeltandslowcooledtoproducecrystals.Unlikeexploratory powdersynthesis,growthshaveachanceofyieldingsingle-phasesinglecrystalsofanew compoundorstructure,iftheoverallmeltcompositionhappenstointersectthecorrectsolid+liquid regionofthephasediagram. Previously,Ca 5 In 2 Sb 6 singlecrystalshavebeensuccessfullygrownfromasofmolten InandSb.EarlierstudiesofpolycrystallinesampleshaveshownthatCa 5 In 2 Sb 6 isanintrinsic semiconductorwithhighresistivity,andthereforelowzT.However,ithasalsobeenshownthat Ca 5 In 2 Sb 6 canbedopedwithZn 2 + ontheIn 3 + site,yieldingamaximum zT = 0 : 7 at950Kfor Ca 5 In 1 : 9 Zn 0 : 1 Sb 6 [ 1 ].Inthisportionofthestudy,Ca-In-Zn-Sbelementsaremixedinagrowth. ThisquaternaryphasespacealsoincludesthepromisingthermoelectriccandidatesZn 4 Sb 3 [ 29 ], CaZn 2 Sb 2 [ 145 ],Ca 14 Zn 1 + x Sb 11 [ 293 ],andCa 9 Zn 4 : 5 Sb 9 [ 35 ].TheZintlphaseCa 9 Zn 4 : 5 Sb 9 ,in particular,hasgoodthermoelectricpropertiesduetothetunabilityoftheZninterstitialsite. Frompreviouswork,itisknownthatCa 5 In 2 Sb 6 singlecrystalscanbeoptimallygrownina In 73 Sb 42 EffortstoZn-dopethiscompoundbeganwiththeadditionofsmallamountsof ZntothesameinhopesofproducingCa 5 In 2 x Zn x Sb 6 singlecrystals.Dopedsinglecrystal growthiscomplicatedbyalargenumberofpotentialbinaryphasesformingbetweenZnandany oftheelementsintheoriginalCa-In-Sbternarysystem.Theseincludingthecongruentlymelting CaZn 2 ( T m =704 ° C),CaZn 5 ( T m =695 ° C),andCaZn 11 ( T m =724 ° C)[ 294 ].Fortunately,noknown 112 Zn-Inbinariesexist[ 295 ]andpotentialZn-Sbbinariesarenotasconcerning,dueto temperatureswellbelowthegrowthextractiontemperaturesof730 ° C[ 296 ].Informationon theternaryphasediagramislimitedfortheCa-In-Sbsystemandevenmoresoforthequaternary systemwiththeadditionofZn. UnlikeInandSb,Znisnotapreferredchoiceforgrowthduetoitshighervaporpressure (907 ° C,1atm.).Thereareinstances,however,ofcrystalgrowthusingZnasa[ 297 , 298 ], motivatedbyitslowmeltingtemperature.Znalsohashighviscosity,implyingthatZninexcessmay behardtoseparatefromgrowncrystalsduringcentrifuging.Thehighervaporpressuredoesallow forasecondarysinteringprocesstoremoveexcessZnthroughevaporationifnecessary[ 196 ].This studytreatsZnasadopantandwillbeaddedtogrowthsinsmallquantitiesandattemperatures wherethevaporpressureisnotyetaconcern. 6.2 ExperimentalMethods 6.2.1 Synthesis Highpurityelementswereusedinthesynthesisincluding:Ca(Sigma-Aldrich:dendriticpieces, 99.9%),In(AlfaAesar:Indiumshot,5mm&down,99.9995%),Sb(AlfaAesar:Antimonyshot, 6mm&down,99.999%),andZn(AlfaAesar:Zincshot,1-5mm,99.999%).Elementsweremixed instainlesssteelballmilljarsunderanargonatmospherewithtwostainlesssteelballs(dia.=12.7 mm)usingaSPEXMixerMill8000D.Themillwasrunfor60minutesforeach5gramsample processed.Thisprocesspromotesthorough,homogeneousmixingoftheconstitutivepowders,shot, andpellets. ADr.Sintersparkplasmasinter211LXsystemwasusedtoprocesspowdersamplesusing graingraphite(POCOEDM-3)diesetswithgraphitefoilspacerspunchedfromsheets (AlfaAesar,0.13mmthickness,99.8%metalsbasis).Thesefoilsseparatethesamplefromthe graphitepunchesandpromoteamoreuniformcontactandconductingsurface.Uniaxialpressure wasappliedtoapairofwater-cooledsteelplatensthattransferredthisforcethroughtwoconductive graphitepedestals.BothpressureandDCcurrentwereappliedtosamplessimultaneously.Samples 113 wereheatedto550 ° Cin5minutesandheldattemperaturefor10minutestoconsolidatethepowder intothedesiredphase.Temperaturesweremeasuredusingatype-Kthermocouplethatwasplaced intoaclearanceholeonthesideofthegraphitedie.Allsampleswereprocessedundervacuum ( ˇ 1 10 2 torr).Samplesroutinelyachieveddensityyieldsgreaterthan99%theoreticalfor Ca 5 In 2 Sb 6 . 6.2.1.1 FluxGrowth FluxgrowthexperimentswerecarriedoutinaThermoFisher1100 ° Cboxfurnace.Al 2 O 3 cruciblesetswereloadedandsealedinquartzampulesatavacuumoflessthan 1 10 4 torr.Fluxgrowthswereamixtureofelements:Ca1.4wt.%,Zn1.7wt.%,In56.5wt.%,andSb 40.4wt.%( ˇ Ca 5 In 2 Sb 6 +In 68 : 4 +Sb 41 : 5 +Zn 3 : 7 )withbothInandSbcontributingasthemajor elements.Fluxgrowthswereheatedfromroomtemperatureto900 ° Cin12hours,heldat 900 ° Cfortwohoursbeforeslowcoolingto730 ° Catarateof3 ° C/hr,atwhichpointgrowthswere extractedandcentrifugedat2500RPMfortwominutes. 6.2.2 StructuralandThermalCharacterization SEMwasperformedonaTescanMira3XMHwhileEDSwasperformedusinganEDAXApolloX modulewithanactiveareaof10mm 2 .ImageswerecollectedandprocessedwiththeTextureand ElementalAnalyticalMicroscopy(TEAM)softwaresuitetodeterminetheapproximatechemical compositionofcrystalandcomponents.Singlecrystalswereplacedonconductingcarbontape toeliminateanypotentialchargebuildup.Allsamplesevaluatedweresemiconductingormetallic incharacter. InitialSC-XRDwasperformedatMichiganStateUniversitywhilethedatausedinthe structureanalyseswerecollectedatUniversityofDelaware.DatawascollectedusingaBruker APEXIICCD-baseddiffractometer,usingmonochromatedMoK a radiation( l = 0 : 71073 Å). Theoperatingtemperaturewas200(2)K,maintainedbyacoldnitrogenstream.Crystalswere selectedunderamicroscopeandcuttosuitablesizes(ca.0.1mminalldimensions).Manycrystals 114 weretriedandevaluatedbyrapidscans,beforethebestwerechosenforfulldatacollection.Data wereacquiredinbatchrunsatvaried w and q andwereintegratedusingtheSAINTsoftware [ 299 ],multi-scanabsorptioncorrectionwasperformedusingSADABS[2].Crystalstructureswere solvedwiththeShelXTprogramusingtheintrinsicphasingsolutionmethodandwereusing full-matrixleastsquaresminimizationonF2withtheaidofShelXL[ 300 , 301 ].Atomiccoordinates werestandardizedusingSTRUCTURETIDY[302]. Simultaneousthermogravimetry/differentialscanningcalorimetrymeasurements(TG/DSC) wereconductedatUniversityofDelawareonaTAInstrumentsSDTQ600analyzer.Thesamples wereloadedincappedaluminapans.Afterequilibrationat323K,thetemperaturewasincreasedto 1073Katarateof20 ° /min.Topreventoxidation,themeasurementsweredoneunderaconstant wofhigh-purityargon. 6.2.3 ResistivityMeasurements Electricalresistivitywasmeasuredonacustom-buildcryostatsystem,withsimilarapparatus describedinpreviouspublications[ 303 ].Afour-terminalresistancemeasurementwasconducted wherebytwoleadspassacurrentthroughthesamplewhiletwootherleadsmeasurethepotential dropacrossthesample.Ohm'sLaw, R = V = I ,wasusedtocalculatethesampleresistancewhere R istheresistanceofthematerialthroughwhichthecurrent, I ,ispassedthroughwhichexhibitsa voltage V .Theresistivity, r ,isindependentofsampledimensionsandrelatesto R , r = RA p ,where p istheprobedistancewherethevoltageismeasured,and A isthecross-sectionalareathatis perpendiculartothedirectionofthecurrent. SinglecrystalsamplesweremountedoninsulatingchipsusingGEvarnish.Electricalcontacts wereattachedbyhandwithPelcoColloidalsilverliquidfromTedPellausinggaugeinsulated singlestrandcopperwire,dia.0.07mm.Astandardfourproberesistivitymeasurementwas completedwithanappliedcurrentof0.75mAoveratemperaturerangeof320Œ80K. 115 6.3 Results&Discussion 6.3.1 CrystalMorphologyandComposition Figure6.1:RepresentativeSEMimagesofCa 9 Zn 3 : 1 In 0 : 9 Sb 9 singlecrystals. Fluxgrowthsyieldedcrystalsthatappearedaslongmetallicribbonswithsmoothve surfaces.Thesamegrowthconditionswererepeatednumeroustimes,producinglargecrystals greaterthan4mmineachrun.RepresentativecrystalsareshowninFigure6.1.EDSwasused tocheckthecompositionofthecrystals,withresultsshowninFigure6.2.Despitetheveryhigh In:Znratiousedinthex,EDSclearlyshowedthatthecrystalscontainedmoreZnthanIn.Since thesolubilityofZninCa 5 In 2 x Zn x Sb 6 isexpectedbe x < 0 : 2 frompriorliterature,thehighZn:In ratio( ˇ 3:1 )ofthesecrystalswastheindicationthattheymaynothaveformedtheintended Ca 5 In 2 Sb 6 structuretype.Themorphologyofthecrystalswasalsosubtlydifferentfromwhat hadbeenobservedintheCa 5 In 2 Sb 6 crystalswithntlylongercrystalsrelativetotheother growthdirectionsandadifferentlayeringsurfacetexture. 116 Figure6.2:EDSanalysisareaofsinglecrystalCa 9 Zn 3 : 1 In 0 : 9 Sb 9 (left).EDSspectrawithunique andisolatedZnandInpeaksneartheprominentCaandSbemissions(right). 6.3.2 ThermalAnalysis Figure6.3:CombinedTG/DSCanalysisonthesinglecrystalsofCa 9 Zn 3 : 1 In 0 : 9 Sb 9 .Weight% andheatwareshowninblueandred,respectively.Theheatingsequencestartsat 373K;thecoolingsequencecompletesat773K. DSC/TGAwasperformedattheUniversityofDelawaretoassessthestabilityofthecrystals. Afterequilibrationat323K,thetemperaturewasincreasedto1073Katarateof20 ° /min.To preventoxidation,themeasurementsweredoneunderaconstantwofhigh-purityargon.DSC datadonotindicateanyintrinsicthermaleventsuptoca.950K.Asthetemperatureapproaches 1000K,thesamplebegantodisplaypoorthermalstability,asdemonstratedbythemass 117 lossshowninFigure6.3.Intheabsence,ofcompetingcrystalgrowthphasesitmaybeadvantageous tofurtherdecreasetheextractiontemperatureofthegrowthtrials. 6.3.3 StructureDescription SC-XRDwasusedtoinvestigatethecrystalstructure.Fromtheinitialanalysis,itwasimmediately clearthatthecrystalstructurewasnotthesameasthatofCa 5 In 2 Sb 6 ,sincethepatternscouldnot besolvedusingthesameorthorhombicspacegroup.Initialanalysisalsoruledoutanyotherknown ternaryphaseintheCa-In-Zn-Sbphasespace,suchastheCa 9 Zn 4 : 5 Sb 9 structure.Themostlikely crystalsystemaccordingtotheinitialwashexagonal.However,allattemptstothe atomicpositionsusingahexagonallatticeyieldedwhatseemedtobeunphysicalstructureswith interatomicdistancesthatweretooshort.Forthisreason,crystalsweresenttotheUniversityof DelawareforadditionalSC-XRDmeasurementsandstructuralanalysis. Figure6.4:(a)AveragecrystalstructureofCa 9 Zn 3 : 1 In 0 : 9 Sb 9 .(b)Localcoordinationenvironment forCa1.(c)LocalcoordinationenvironmentforCa2.(d)Polyhedroncoordinationwithmixed Zn1/In1site.(e)CoordinationforpartiallyoccupiedZn2site. TheaveragestructuresolutionofthecrystalsispresentedinFigure6.4(a)alongwith detailsofthelocalcoordinationenvironmentin6.4(b-e).Theoverallcompositionwasas Ca 9 Zn 3 : 1 In 0 : 9 Sb 9 .ThisisconsistentwiththeEDSresults,whichshowamoreZn-richstructure 118 comparedtoIn.Whiletheactualstructureisheavilydisordered,theaveragedunitcellhasbeen assignedtothehexagonal P ¯ 62 m spacegroup.Severalsuperstructureswithlargerunitcellswere considered,butinallcases,acantamountofdisorderremainedthatcouldnotbereadily resolved.Inthiswork,attentionisfocusedonthe P ¯ 62 m interpretationthatwasabletoresolveatomic positionsaccuratelybutadditionalwererequiredtodeterminethepartialoccupancyof theZn2interstitialsite. BothCaatoms,showninFigure6.4(b-c),arecoordinatedbysixSbatoms.TheZn1andIn1 atomsoccupytwosymmetry-equivalentsitesbondedtofoursurroundingSbatoms(showninFigure 6.4(d)),formingatetrahedralstructuresomewhatsimilartowhatwasobservedintheCa 5 M 2 Sb 6 (M =Al,Ga,In)system.TheseZn1/In1sitesareonlypartiallyoccupiedwithacombinedoccupancy of50%.Further,sincetheneighboringZn1/In1sitesareonly1.618(7)Åapart,theycannotbe simultaneouslyoccupied.TheZn2atoms,showninFigure6.4(e),aresituatedin-planewitha triangleofSbatomsthatformchainsparalleltothec-axis.Atomiccoordinatesandoccupations revealsthepartialoccupationofboththeZn1/In1(35.2%Znand14.8%In)andZn2(34.1%)sites. 6.3.4 ComparisonwiththeCa 9 Zn 4 : 5 Sb 9 StructureType TheMSb 4 tetrahedrasub-structureisacommonmotifinpnictide-basedZintlphases,another examplebeingtheCa 5 M 2 Sb 6 (M=Al,Ga,In)systemdiscussedinpreviouschapters,which hasanionicbuildingblocksofM 2 Sb 6 .TheanionicribbonsfoundinCa 9 Zn 4 : 5 Sb 9 aresimilarly constructedfromcorner-sharingtetrahedra.Whilethenovelstructurereportedheresharessimi- laritiestotheinterstitial-richCa 9 Zn 4 : 5 Sb 9 ( x 0 : 8 )[ 35 , 132 ],illustratedinFigure6.5(left),itis morecomplex.OtherinterstitiallymocompoundsincludeEu 9 Zn 4 : 5 Sb 9 [ 131 ] andYb 9 Zn 4 : 5 Sb 9 [ 132 ],whichbothbelongtothe Pbam spacegroup,andCa 9 Mn 4 : 5 Sb 9 ,belonging tothe Pnma spacegroup[ 131 ],illustratinghowadditionalinterstitialdisorder,evenwithmajority vacantinterstitialsitescanaltertheresultingstructure. Theadditionofafourthelementtothese9-4-9typecompoundsisnotwithoutprecedent, ashasbeenrecentlyshowninthesynthesisofAE 9 Mn 4 x Al x Sb 9 (AE=Ca,Yb,Eu)withAl 119 Figure6.5:ComparisonofCa 9 Zn 4 : 5 Sb 9 ,orthorhombicspacegroup Pbam ,andCa 9 Zn 3 : 1 In 0 : 9 Sb 9 , hexagonalspacegroup P ¯ 62 m . substitution[ 304 ],whichareisostructuralwithCa 9 Mn 4 Bi 9 [ 128 ],crystallizingintheorthorhombic spacegroup Pbam .Substitutionhasalsobeenperformedonthecationsiteinthecompositions Ca 9 x RE x Mn 4 Sb 9 (RE=La-Nd,Sm; x ˇ 1 )whichsuccessfullyelectron-dopedthestructurewith RE 3 + ontheCa 2 + site[305]. UnliketheCa 5 M 2 Sb 6 (M=Al,Ga,In)system,theinitiallyproposedCa 9 Zn 4 Sb 9 structureis withrespecttotheZKCcountingscheme, Ca 9 Zn 4 Sb 9 =( Ca 2 + ) 9 ( Zn 2 + ) 4 ( Sb 3 ) 9 ( h + ) ; (6.1) where h + representsanelectron-hole.Thisywasresolvedwiththediscoveryofa partlyoccupiedinterstitialZnsite,leadingtotheformationofCa 9 Zn 4 : 5 Sb 9 compounds, Ca 9 Zn 4 : 5 Sb 9 =( Ca 2 + ) 9 ( Zn 2 + ) 4 : 5 ( Sb 3 ) 9 : (6.2) TheadditionofZninterstitialsresultsinavalence-precisecompound.Valenceprecisionisresolved 120 inanothermannerfortheCa 9 Zn 3 : 1 In 0 : 9 Sb 9 compoundwhichcanbeapproximatedas, Ca 9 Zn 3 InSb 9 =( Ca 2 + ) 9 ( Zn 2 + ) 3 ( In 3 + )( Sb 3 ) 9 : (6.3) Itisproposedthatthisislikelythelong-rangeordersolubilitylimitfortheinclusionofIninto thestructurewhichissupportedbytheIn-richsinglecrystalgrowthconditions. 6.3.5 ElectronicTransportProperties ResistivitymeasurementsonsinglecrystalsofCa 9 Zn 3 : 1 In 0 : 9 Sb 9 asshowninFigure6.6fortwo differentsinglecrystalsamples.Resultswereveryconsistentbetweenthetwomeasuredsingle crystals.Sample1hadaprobeseparationofapproximately1.50mm,asamplewidthof0.46mm, andthicknessof0.30mm.Sample2hadaprobeseparationofapproximately1.75mm,asample widthof1.14mm,andwasextremelythinwithathicknessofonly0.07mm. Figure6.6:FourproberesistivityprobesattachedtosinglecrystalCa 9 Zn 3 : 1 In 0 : 9 Sb 9 ,Sample1 (left).Resultingresistivityvalueswereconsistentfortwodifferentcrystals,showinglow,linearly increasingresistivity(right). Bothsinglecrystalsamplesexhibitedlinearmetallic-likeresistivitybehavioroverthemeasured temperaturerangeof80-320K.Theresistivityatroomtemperatureof ˘ 1m W cmiscomparableto theresistivityofmanyoptimizedthermoelectricmaterials,includingCa 9 Zn 4 : 5 Sb 9 [ 5 ].Assuming thatthecurrentcrystalsare p -type(whichisthemostlikelycaseforZintlcompounds)theirlow 121 resistivitysuggeststhattheirstoichiometrydeviatessomewhatfromthevalence-precisecomposition ofCa 9 Zn 3 In 0 : 9 Sb 9 .AslightdeviationtowardsaZn-richcomposition(assuggestedbyEDSandSC- XRDwouldleadtoafreeholeconcentration,andtheobservedmetal-like resistivity. 6.4 ConcludingRemarks WereportthediscoveryofnovelquaternaryZintlphase,synthesizedfromanIn-andSb-rich EDSandSC-XRDrevealedacompositionofCa 9 Zn 3 : 1 In 0 : 9 Sb 9 takingonahexagonalstructure typewithextensivedisorderdueinparttothepartialoccupationofboththeZn1/In1(35.2%Znand 14.8%In)andZn2(34.1%)sites.Thiscompositionisverynearlyvalenceprecise,implyingthatthis maybenearthesolubilitylimitofIninthestructure.Temperature-dependentelectricalresistivity measurementsshowlowresistivityandmetallicbehavioroverthetemperaturerangeof80-320K. 122 CHAPTER7 CONCLUSIONS&FUTUREWORK 7.1 Conclusions ThisworkhasfocusedonsinglecrystalgrowthandcharacterizationofselectZintlphase thermoelectrics.SinglecrystalsofCa 5 M 2 Sb 6 (M=Al,Ga,In;Pn=Sb,Bi)weregrownfroma moltenmetalTheCa 5 M 2 Sb 6 compositionswereallsuccessfullygrownfromaM 73 Sb 42 with Ca 5 Al 2 Sb 6 alsogrownfromaSb 20 andSn 15 es.Ca 5 Al 2 Bi 6 wasgrownfromaBi 20 elementswerepreferredastheydonotintroduceanadditionalelementthatcouldform undesirablephaseswithorinadvertentlydope.Fromthesegrowthsseveralusefultielines havebeenaddedtothecorrespondingternaryphasediagramswherenoneexistedbefore.This providesguidancetofuturecrystalgrowthandsynthesisstudies. Inadditiontotheabovelistedcompositionsthesinglecrystalalloyofcomposition Ca 5 Ga 2 x In x Sb 6 hasbeenreported,synthesizedfrompolycrystallineCa 5 Ga 2 Sb 6 andCa 5 In 2 Sb 6 withamixedofGa 37 : 5 In 37 : 5 Sb 42 .TheresolvedcompositionwasCa 5 Ga 1 : 12 In 0 : 88 Sb 6 withsubsequentquickscansonothersinglecrystalsshowingaslightpreferenceforGaontheM site.TheseresultswerefurtherwithEDSresultson30individualcrystals,allreporting moreGathanIn.Thealloyedcompositionmaintainsthe Pbam spacegroupwithintheorthorhombic crystalstructurewiththeInandGaatomsbothpartiallyoccupyingthecenteroftheanionicpolyhe- dralstructures.ThelatticedimensionsobeyedVegard'sLaw.Theincreaseinlatticeparameterwith increasingIncontentisduetoInbeingalargeratomthanGawiththecrystalstructureexpanding toaccommodate.ThiswaslikelythereasonforthepreferenceofGatooccupythissite. Inadditiontothestructuralcharacterizationdescribedabove,electroniccharacterizationwas alsoconducted.TheCa 5 In 2 Sb 6 compositionwascharacterizedbothperpendicularandparallelto thec-axistoinvestigateanisotropy.Fromthedetailedstructuralcharacterizationitisknownthat thepreferredgrowthdirectionofthecrystalsisalongthec-axis.Crystalgrowthperpendicularto 123 thec-axiswasmodest,measuringlessthanamillimeter.Duetosuchdiminutivedimensions,the perpendicularmeasurementrequiredFIBcuttingandanoptimizedphotolithographyprocessto sputtersensorsoverthetopofthesampleforcharacterization.Thephotolithographyprocessproved repeatable,allowingforthepotentialofacompletethermoelectricperformancecharacterization (i.e.,resistivity/conductivity,Seebeckcoefandthermalconductivity)tobeperformed.This photoresiststackandprocessingparameterscanbetransferredtoothersystemsaswelltochar- acterizegeneralmicro-ribbonsamples.Resistivityvaluescollectedonasinglecrystalparallelto thec-directionwereaccomplishedwithmanuallyplacedprobesonacustombuiltcryostatsystem. Theseresultscombinedtoprovideproofofhighlyanisotropicelectronictransportpropertieswith anearly20-foldincreaseinresistivityintheperpendiculardirection.Theseresultsareinagree- mentwithDFTcalculationsthatpredictedenhancedthermoelectricperformanceinthec-direction. Itispredictedthatlatticethermalconductivitywillremainisotropic,allowingfora thermoelectricperformanceboostforcrystalsorientedparalleltothec-direction. Asidefromquantifyinganisotropy,singlecrystalscanalsobeusedtostudythedefectchemistry ofsystems.Inthiswork,singlecrystalsofMg 3 Sb 2 weregrownfrombothaMg-andSb-rich andthedefectchemistrywasexploredthroughSC-XRD.Thiscompoundhasbeenproventobea promising n -typethermoelectricwhensynthesizedinaMg-richenvironment.WhileMgvacancies aresuspectedtoberesponsibleforthis,notexperimentalobservationshavebeeninvestigated. Inthiswork,Sb-richgrowthsrevealedpartialoccupancyoftheMg(I)site,consistentwithDFT calculationswithMgvacanciesexhibitingalowformationenergytopreferentiallyform.While anumberofanti-siteandinterstitialdefectshavebeenconsideredwithDFT,interstitialposition (0,0,0.684)isreportedwhereSb5+asalikelyoccupant.Allmeasuredcrystalsexhibitedintrinsic semiconductingbehavior,despiteMgvacancies. Thisworkhasshownhowsinglecrystalscansuccessfullycharacterizecompoundanisotropy andalsodescribethedefectchemistryofacompound.Athirduseofsinglecrystalsistheusein exploratorygrowths.Inthiswork,singlecrystalworkcontinuedwiththediscoveryofZintlphase Ca 9 Zn 3 : 1 In 0 : 9 Sb 9 fromanIn-andSb-richStructuralcharacterizationwascompleted 124 withEDSandSC-XRDwhereitwasdiscoveredthattheaveragestructuretookonthehexagonal structuretypewithextensivedisorderdueinparttothepartialoccupationofboththeZn1/In1and Zn2sites.Lowtemperatureelectricalresistivitymeasurementsshowlowresistivityandmetallic behavior. Thisworkdemonstratesthexibleutilizationofsinglecrystalgrowthandhowitcanbelever- agedtoproduceresultsthatarenotpossibleinthesynthesisandcharacterizationofpolycrystalline samples.Theprocesseshereindescribedcanprovideguidanceforfuturecharacterizationand exploratoryefforts. 7.2 FutureWork TheprimarygoalsofthisthesisweretousesinglecrystalgrowthofZintlphasestoexplore anisotropictransportproperties,intrinsicpointdefects,andtodiscovernewphases.Whilesome excitingprogresswasmade,thisworkalsoopenedadditionalquestions.Workinthisstudyhas providedawiderangeofpotentialfutureworkprojectsrangingfromphotolithographyofdifferent thermoelectricmicro-ribbonstoexploratorygrowthsofnovelcompounds.Detailedbeloware projectsthatcanbuildoffofthesesuccesses. 7.2.1 PhotolithographytoUnderstandAnistropicTransport Atthispoint,countlessquestionsremainregardinghowbondingdeterminesanisotropicelectronic andthermaltransportinZintlphases.Inthepresentstudy,anisotropyofelectricalconductivityin oneun-dopedZintlcompoundhasbeenFutureworkistoincludea)characterizethe remainingtransportpropertiesincludingthethermalconductivityandSeebeckcoefandb) characterizethesamepropertiesinsampleswithdifferentalloyingtovarythescatteringmechanism, andc)differentdopinglevels,includingsampleswithoptimizedcarrierconcentrationto thehighzT.Oncethepropertiesofthissinglecompoundarethoroughlyunderstood,workwill progresstootherZintlstructuretypes. Toachieveinwideningthescopeofthisresearch,itisnecessarytofurtherthepho- 125 tolithographyprocessdescribedinChapter4.Thephotolithographyprocessallowsforsmallsingle crystalmicro-ribbonstobecharacterized,bypassingtheneedforlargersinglecrystalswhichcanbe impracticaltogrowinsomeinstances.Inthiswork,amicro-ribbonofCa 5 In 2 Sb 6 wascharacterized intheperpendiculartoc-directionforresistivityandcarrierconcentration.Thefullsuiteofsensors werenotleveragedduetothesamplebeingdestroyedintheprocessoftesting,however,itwas shownasaproofofconceptthatsensorscouldbeplacedonmicro-ribbonsrepeatablyusingthe optimizedphotolithographyprocessoutlined.Thisfullsuiteofcircuitsensorsbuildsontheprevious workofGoothetal.[ 6 ]whichusedtwothermometersandaresistiveheaterline.Thisworkutilized similarsensorsalongwiththeadditionoftwoisolatedcurrentlinesandHallsensorsacrossthe middleofthemicro-ribbon,allowingforthecharacterizationoftheHalleffect,Seebeckcoef electricalandthermalconductivity. Inordertoimprovethroughputoffutureprojects,appropriatecompositionsmustbeselected. ThechallengeistogoodcandidatematerialsthatcanbeprocessedusingFIBcutting. Sampleswithheavierelementsrequiredreducedcuttingspeedsandlowmeltingtemperature elementswereshowntoviolentlyvaporizewhenexposedtothebeam.Forthisreasonlowmelting temperatureelementssuchasGaareproblematic.ThisissuewasmadeworseduetoGabeingused asaelementinthegrowthofsinglecrystalCa 5 Ga 2 Sb 6 whilealsopossessingpoorwetting propertiesthatallowedittoclingtocrystalsurfacesmorereadily.Thisknowledgecanhelp outpoorsinglecrystalcandidatesforthisprocessinadvance,savingvaluabletimeandlabor. Oncemicro-ribbonshavebeenextractedfromFIBcutting,arepeatablephotolithographyprocess hasbeendevelopedthatcanbereadilyappliedtoanycompoundcuttotheappropriatedimensions andsurfacequality.Thisallowsforthecharacterizationofanymaterialalongagrowth direction,notlimitedtoZintlphasesoreventhermoelectrics,potentiallyusefulforsuchasthe developmentandcharacterizationofscintillationmaterialswheresinglecrystalsareoftendirectly usedinapplications[204]. 126 7.2.2 FluxGrowthsforPhaseDiagramandNewCompoundExploration Fluxgrowthsarecapableofproducinghighqualitysinglecrystalsthatprovidesaneffectivepathway tocrystallizingincongruentlymeltingcompounds.Thismethodisausefultoolinthealloyingof compoundsaswasthecasewiththesynthesisofsinglecrystalCa 5 Ga 2 x In x Sb 6 ,andofdiscovering newones,aswasthecasewithCa 9 Zn 3 : 1 In 0 : 9 Sb 9 .Growthscanalsoassistinthedescribingthe ternaryphasespacewherenophasediagramexists.Fromknowledgegainedinthecrystalgrowth process,intelligentchoicescanbemadeinmaterialsystemsforvariouspurposes. 7.2.2.1 SolubilityStudy InthisworksinglecrystalsofCa 5 Al 2 Sb 6 andCa 5 Al 2 Bi 6 havebeengrown.Futureworkwiththese compositionscanincludeasolubilitystudythatwilltestthesolubilitylimitsofSbandBiineach structuretype.ItisimportanttorememberthatCa 5 Al 2 Bi 6 isadifferentstructuretypecomparedto theCa 5 M 2 Sb 6 (M=Al,Ga,In)classofcompoundswiththedifferencebeinghowthepolyanionic chainsarepackedintothestructure. SinglecrystalsofCa 5 Al 2 Sb 6 weregrownusingaSb 20 withanextractiontemperatureof 730 ° CwhileCa 5 Al 2 Bi 6 singlecrystalsweregrownfromaBi 20 withanextractiontemperature of470 ° C.Theandextractiontemperaturescouldbevariedlinearlybetweenthetwoasshown inFigure7.1simplybymixingelementstogether.AdditionallyCa 5 Al 2 Bi 6 singlecrystalgrowth couldbeattemptedwithanSbatlowertemperatures,avoidingtheformationofCa 5 Al 2 Sb 6 . 7.2.2.2 ExploratoryGrowths DuringtheattemptedsynthesisofZn-dopedCa 5 In 2 Sb 6 ,anewZintlphase,Ca 9 Zn 3 : 1 In 0 : 9 Sb 9 ,was discovered.Thisphasewasgrownrepeatablyandwillencourageotherexploratorygrowthsofthe samestructuretype.Thiscompoundhasauniquevalence-precisionthatcanbegeneralizedas A 9 T 3 MPn 9 =( A 2 + ) 9 ( T 2 + ) 3 ( M 3 + )( Pn 3 ) 9 ; (7.1) 127 Figure7.1:ProposedsolubilitystudybetweenthetwostablecompoundsCa 5 Al 2 Sb 6 and Ca 5 Al 2 Bi 6 .Dashedlinerepresentspossiblegrowthmeltcompositionswithrespectto extractiontemperature. whereAcouldpotentiallybeCa,Sr,Yb,orEuandT=Zn,Cd,orMn,withMpotentiallyoccupied byAlorGa,whilePncanbeoccupiedbyeitherSborBi.Thisstructurewouldaccommodate theseatomsatthesesites,butfurthergrowthsareneededtotheirexistence.Thisyieldsthe potentialfor72possiblecombinationsoftheA/T/M/PnelementswhicharelistedinTable7.1.From these,24totalternaryphasesintheformA 9 T 4 + x Pn 9 aretheorized,with16ofthesealreadydiscov- eredandstructurallycharacterized.ThreequaternarycompoundsintheformA 9 (T 1 x M x ) 4 Pn 9 havebeendiscovered[ 304 ]withthisworkproducingthefourthofpotentially72compositions. InadditiontothesecompoundsarseniccanalsooccupythePnsiteasisevidencedbytherecent synthesisofCa 9 Zn 4 : 5 As 9 [ 131 ],implyingthistablecouldbeexpandedfurther.Table7.1can actasachecklistforpotentiallynewZintlphasecompoundswithasharedvalencecountingand stoichiometry. Whilesomegrowthsleadtothediscoveryofnovelcompounds,otherscanprovideamore efpathwaytothesynthesisofknowncompounds.Fromoursuccessofsinglecrystalgrowth 128 Table7.1:Listofelementcombinationsforpotentialquaternarycompoundsintheform A 9 (T 1 x M x ) 4 Pn 9 .ReferencesareincludedforknownA 9 T 4 + x Pn 9 ternariesandknownquater- narycompoundstakingtheformA 9 (T 1 x M x ) 4 Pn 9 . ATMPnA 9 T 4 + x Pn 9 A 9 (T 1 x M x ) 4 Pn 9 ATMPnA 9 T 4 + x Pn 9 A 9 (T 1 x M x ) 4 Pn 9 CaZnAlSbYbZnAlSb CaZnGaSb[132]YbZnGaSb[134] CaZnInSbThisworkYbZnInSb CaZnAlBiYbZnAlBi CaZnGaBi[133]YbZnGaBi[133] CaZnInBiYbZnInBi CaCdAlSbYbCdAlSb CaCdGaSbYbCdGaSb CaCdInSbYbCdInSb CaCdAlBiYbCdAlBi CaCdGaBi[133]YbCdGaBi[133] CaCdInBiYbCdInBi CaMnAlSb[304]YbMnAlSb[304] CaMnGaSb[131]YbMnGaSb[134] CaMnInSbYbMnInSb CaMnAlBiYbMnAlBi CaMnGaBi[134]YbMnGaBi[134] CaMnInBiYbMnInBi SrZnAlSbEuZnAlSb SrZnGaSbEuZnGaSb SrZnInSbEuZnInSb SrZnAlBiEuZnAlBi SrZnGaBi[133]EuZnGaBi[133] SrZnInBiEuZnInBi SrCdAlSbEuCdAlSb SrCdGaSb[133]EuCdGaSb[131] SrCdInSbEuCdInSb SrCdAlBiEuCdAlBi SrCdGaBi[133]EuCdGaBi[133] SrCdInBiEuCdInBi SrMnAlSbEuMnAlSb[304] SrMnGaSbEuMnGaSb SrMnInSbEuMnInSb SrMnAlBiEuMnAlBi SrMnGaBiEuMnGaBi SrMnInBiEuMnInBi ofCa 5 M 2 Sb 6 (M=Al,Ga,In)withaM 73 Sb 42 itwastheorizedthatthepotentiallyanalogous Sr 5 Ga 2 Sb 6 phasewhich,ifitexists,couldbesynthesized.BothSr 5 Al 2 Sb 6 andSr 5 In 2 Sb 6 have beendiscoveredandcharacterized,leadingfurthertothepossibilityofaGaanalog.Thisworkwas unabletoproducethetheorizedcompoundbutdidsuccessfullysynthesizesinglecrystalSr 7 Ga 8 Sb 8 fromaGa 73 Sb 42 Thecrystalstookonarectangularappearancebuttheyieldwasexceptionally low.Thiswouldprovideastartingpointataminimumforfuturegrowthsoftheseratherunique 7-8-8compounds.Thiscrystalstructurewasreportedin2010byBobevetal.[ 306 ],sowhile compoundshavebeendiscoveredrecently,characterizationisnon-existentbeyondastructural description.Suchgrowths,coupledwithelectricalresistivitycharacterization,canbeusedaspartof 129 ascreeningprocessforpromisingthermoelectricsandtobetterternaryphasespaces. 130 APPENDIX 131 EDS:Ca 5 Ga 2 Sb 6 withGa 73 Sb 42 FigureA1:Ca 5 Ga 2 Sb 6 crystalsfromaGa 73 Sb 42 withsuperimposedEDSareashighlighted. CorrespondingEDSdataisshowninFigureA3andTableA1. FigureA2:SimulatedEDSpatternsforpotentialcrystalcandidatesgrownfromaCa-Ga-Sb 132 FigureA3:EDSspectraforCa 5 Ga 2 Sb 6 withGa 73 Sb 42 AreasAŒFfromFigureA1. 133 TableA1:Quantitativeresults:Ca 5 Ga 2 Sb 6 singlecrystalsfromaGa 73 Sb 42 AreasAŒF fromFigureA1. AreaElementWeight%Atomic%NetInt.NetInt.Error A CaK24.9546.963615.820 GaK14.1215.28410.610.03 SbL60.9337.764003.510 Ca 5 Ga 1 : 63 Sb 4 : 02 B CaK24.9546.963615.820 GaK14.1215.28410.610.03 SbL60.9337.764003.510 Ca 5 Ga 1 : 67 Sb 4 : 03 C CaK25.0547.036123.360 GaK14.4615.61697.470.02 SbL60.4837.366689.310 Ca 5 Ga 1 : 66 Sb 3 : 97 D CaK24.8746.696349.280 GaK14.9016.08751.120.02 SbL60.2337.226959.810 Ca 5 Ga 1 : 72 Sb 3 : 99 E CaK2.194.82535.890.03 GaK44.5856.542271.390.01 SbL53.2338.646010.0880 Ga+Sb F CaK0.931.63215.310.05 GaK95.9296.564694.270 SbL3.151.81345.010.06 Ga 134 EDS:Ca 5 In 2 Sb 6 withIn 73 Sb 42 FigureA4:Ca 5 In 2 Sb 6 crystalsfromanIn 73 Sb 42 withsuperimposedEDSareashighlighted. CorrespondingEDSdataisshowninFigureA6andTableA2. FigureA5:SimulatedEDSpatternsforpotentialcrystalcandidatesgrownfromCa-In-Sb 135 FigureA6:EDSspectraofCa 5 In 2 Sb 6 singlecrystalsfromanIn 73 Sb 42 AreasAŒFfrom FigureA4. 136 TableA2:Quantitativeresults:Ca 5 In 2 Sb 6 singlecrystalsfromanIn 73 Sb 42 AreasAŒFfrom FigureA4. AreaElementWeight%Atomic%NetInt.NetInt.Error A CaK23.0947.345353.232.45 InL18.1412.992280.571.95 SbL58.7739.675903.281.17 Ca 5 In 1 : 37 Sb 4 : 19 B CaK22.6746.746707.082.43 InL18.513.322967.941.84 SbL58.8339.947538.551.13 Ca 5 In 1 : 42 Sb 4 : 27 C CaK22.8747.036965.832.42 InL18.5313.33058.691.88 SbL58.639.677728.671.14 Ca 5 In 1 : 41 Sb 4 : 22 D CaK22.7446.856706.12.43 InL18.413.232940.681.83 SbL58.8639.927519.041.13 Ca 5 In 1 : 41 Sb 4 : 26 E CaK22.8346.986297.542.43 InL18.3113.152736.971.86 SbL58.8639.877032.141.14 Ca 5 In 1 : 40 Sb 4 : 24 F CaK22.7746.896387.852.45 InL18.3113.162784.231.95 SbL58.9239.947159.381.14 Ca 5 In 1 : 40 Sb 4 : 26 137 EDS:Ca 5 Ga 2 x In x Sb 6 withGa 37 : 5 In 37 : 5 Sb 42 FigureA7:Ca 5 Ga 2 x In x Sb 6 crystalsfromaGa 37 : 5 In 37 : 5 Sb 42 withsuperimposedEDSareas highlighted.CorrespondingEDSdataisshowninFiguresA8-A9andTablesA3-A4. 138 FigureA8:EDSspectraofCa 5 Ga 2 x In x Sb 6 singlecrystalsfromaGa 37 : 5 In 37 : 5 Sb 42 Areas AŒEfromFigureA7(left). 139 FigureA9:EDSspectraofCa 5 Ga 2 x In x Sb 6 singlecrystalsfromaGa 37 : 5 In 37 : 5 Sb 42 Areas FŒJfromFigureA7(right). 140 TableA3:Quantitativeresults:Ca 5 Ga 2 x In x Sb 6 singlecrystalsfromaGa 37 : 5 In 37 : 5 Sb 42 AreasAŒEfromFigureA7(left). AreaElementWeight%Atomic%NetInt.NetInt.Error A CaK24.1947.388624.550.00 GaK7.118.00499.680.03 InL8.385.731721.060.02 SbL60.3138.899636.870.00 Ca 5 Ga 0 : 84 In 0 : 60 Sb 4 : 10 B CaK24.1247.057110.610.00 GaK8.149.12473.110.03 InL8.615.861461.710.02 SbL59.1337.977817.090.00 Ca 5 Ga 0 : 97 In 0 : 62 Sb 4 : 04 C CaK24.1647.267979.590.00 GaK7.408.32481.460.03 InL8.525.821622.570.02 SbL59.9338.598874.530.00 Ca 5 Ga 0 : 88 In 0 : 62 Sb 4 : 08 D CaK24.1847.297880.120.00 GaK7.458.38478.950.03 InL8.435.751581.900.02 SbL59.9438.588756.670.00 Ca 5 Ga 0 : 89 In 0 : 61 Sb 4 : 08 E CaK24.0847.127511.730.00 GaK7.568.50462.680.03 InL8.796.011581.050.02 SbL59.5738.368336.430.00 Ca 5 Ga 0 : 90 In 0 : 64 Sb 4 : 07 141 TableA4:Quantitativeresults:Ca 5 Ga 2 x In x Sb 6 singlecrystalsfromaGa 37 : 5 In 37 : 5 Sb 42 AreasFŒJfromFigureA7(right). AreaElementWeight%Atomic%NetInt.NetInt.Error F CaK24.1647.307459.850.00 GaK7.228.14438.340.03 InL8.615.881531.970.02 SbL60.0238.688312.450.00 Ca 5 Ga 0 : 86 In 0 : 62 Sb 4 : 09 G CaK24.0747.248392.590.00 GaK6.917.80475.400.03 InL9.076.221823.960.02 SbL59.9538.749364.620.00 Ca 5 Ga 0 : 83 In 0 : 66 Sb 4 : 10 H CaK23.8646.928246.970.00 GaK7.158.08485.620.03 InL8.675.951727.760.02 SbL60.3239.059353.860.00 Ca 5 Ga 0 : 86 In 0 : 63 Sb 4 : 16 I CaK24.0147.057210.640.00 GaK7.528.47444.550.03 InL8.645.911496.170.02 SbL59.8338.588055.290.00 Ca 5 Ga 0 : 90 In 0 : 63 Sb 4 : 10 J CaK24.2147.457905.850.00 GaK6.957.83446.900.04 InL8.215.611545.850.02 SbL60.6339.118875.990.00 Ca 5 Ga 0 : 82 In 0 : 59 Sb 4 : 12 142 EDS:Ca 5 Al 2 Sb 6 withAl 73 Sb 42 FigureA10:Ca 5 Al 2 Sb 6 crystalsfromaAl 73 Sb 42 withsuperimposedEDSareashighlighted. CorrespondingEDSdataisshowninFigureA12andTableA5. FigureA11:SimulatedEDSpatternsforknownCa-Al-Sbternaryphases. 143 FigureA12:EDSspectraofCa 5 Al 2 Sb 6 singlecrystalsfromaAl 73 Sb 42 AreasA-Dfrom FigureA10. 144 TableA5:Quantitativeresults:Ca 5 Al 2 Sb 6 withAl 73 Sb 42 AreasA-DfromFigureA10. AreaElementWeight%Atomic%NetInt.NetInt.Error A CaK25.9642.777188.522.38 AlK8.9521.921577.168.3 SbL65.0935.317912.221.39 Ca 5 Al 2 : 56 Sb 4 : 13 B CaK23.4742.866427.132.43 AlK5.2814.32870.548.76 SbL71.2542.838544.41.34 Ca 5 Al 1 : 67 Sb 5 : 00 C CaK21.6739.533063.652.64 AlK6.3717.25542.919.03 SbL71.9643.224454.941.43 Ca 5 Al 2 : 18 Sb 5 : 47 D CaK25.744.574972.622.42 AlK6.4816.71775.68.73 SbL67.8238.725754.271.43 Ca 5 Al 1 : 87 Sb 4 : 34 145 EDS:Ca 5 Al 2 Sb 6 withSb 20 FigureA13:Ca 5 Al 2 Sb 6 crystalsfromaSb 20 withsuperimposedEDSareashighlighted. CorrespondingEDSdataisshowninFigureA14andTableA6. 146 FigureA14:EDSspectraofCa 5 Al 2 Sb 6 singlecrystalsfromaSb 20 AreasAŒGfromFigure A13. 147 TableA6:Quantitativeresults:Ca 5 Al 2 Sb 6 withSb 20 AreasA-EfromFigureA13. AreaElementWeight%Atomic%NetInt.NetInt.Error A CaK24.3742.376899.492.41 AlK7.1418.441248.888.48 SbL68.4939.28500.781.36 Ca 5 Al 2 : 18 Sb 4 : 63 B CaK26.2345.336369.672.38 AlK6.3616.32955.58.63 SbL67.4238.367179.571.42 Ca 5 Al 1 : 80 Sb 4 : 23 C CaK26.4246.775256.12.4 AlK5.0513.28613.519 SbL68.5439.955976.131.42 Ca 5 Al 1 : 42 Sb 4 : 27 D CaK26.2843.787720.932.36 AlK8.1920.281521.458.34 SbL65.5335.948449.111.39 Ca 5 Al 2 : 32 Sb 4 : 10 E CaK25.444.332227.82.63 AlK6.3616.47343.49.58 SbL68.2439.22623.691.6 Ca 5 Al 1 : 86 Sb 4 : 42 148 EDS:Ca 5 Al 2 Sb 6 withSn 15 FigureA15:Ca 5 Al 2 Sb 6 crystalsfromaSn 15 imagedusingbackscatteredelectrons(left)to highlightcoatingthecrystal.SuperimposedEDSareahighlighted(right)withcorresponding EDSdatashowninFigureA17andTableA7. FigureA16:Ca 5 Al 2 Sb 6 crystalsfromaSn 15 withsuperimposedEDSareashighlighted. CorrespondingEDSdataisshowninFigureA17andTableA7. 149 FigureA17:EDSspectraofCa 5 Al 2 Sb 6 singlecrystalsfromaSn 15 AreasAŒGfromFigure A15-A16. 150 TableA7:Quantitativeresults:Ca 5 Al 2 Bi 6 singlecrystalsfromaSn 15 AreasAŒGfrom FigureA15-A16. ScanElementWeight%Atomic%NetInt.Error%KratioZAF A CaK29.3245.899275.992.290.30941.16270.89121.0224 AlK9.7822.742032.107.980.03921.18240.33831.0058 SbL60.9131.388469.041.400.55950.89351.03330.9988 Ca 5 Al 2 : 48 Sb 3 : 42 B CaK30.7651.458740.152.310.31571.17450.88811.018 AlK5.3913.39989.818.580.02071.1940.33071.0049 SbL63.8535.168001.901.380.57250.90251.02890.9989 Ca 5 Al 1 : 30 Sb 3 : 42 C CaK30.0448.838560.232.260.32121.1680.89511.0227 AlK7.3117.641331.148.320.02891.18760.33081.006 SbL62.6533.527837.031.450.58240.89761.03690.9988 Ca 5 Al 1 : 81 Sb 3 : 43 D CaK26.5347.148835.262.270.31451.16540.89391.0226 AlK8.5720.321657.548.230.03411.1850.3341.0059 SbL61.9132.548135.81.440.57360.89551.03590.9988 Ca 5 Al 2 : 16 Sb 3 : 45 E CaK29.1545.89048.392.280.30951.16290.8931.0225 AlK9.6622.551958.298.010.03871.18260.33711.0059 SbL61.1931.658346.541.420.56540.89361.03520.9988 Ca 5 Al 2 : 46 Sb 3 : 46 F CaK29.6145.868905.332.30.30961.16310.8931.0226 AlK9.5922.411911.888.180.03841.18280.33681.0059 SbL61.2531.728220.311.430.56610.89371.03530.9988 Ca 5 Al 2 : 44 Sb 3 : 46 G CaK29.5646.509232.372.140.28011.1220.90721.0226 AlK9.3621.881992.177.790.0351.14150.35711.0059 SbL61.0731.628391.941.60.50430.86211.05360.9988 Ca 5 Al 2 : 35 Sb 3 : 40 151 EDS:Ca 5 Al 2 Bi 6 withBi 20 FigureA18:Ca 5 Al 2 Bi 6 crystalsfromaBi 20 withsuperimposedEDSareashighlighted. CorrespondingEDSdataisshowninFigureA19andTableA8. 152 FigureA19:EDSspectraofCa 5 Al 2 Bi 6 singlecrystalsandcomponentsfromaBi 20 Areas AŒGfromFigureA18. 153 TableA8:Quantitativeresults:Ca 5 Al 2 Bi 6 singlecrystalsandcomponentsfromaBi 20 AreasAŒGfromFigureA18. AreaElementWeight%Atomic%NetInt.NetInt.Error A CaK23.7749.601122.086.09 AlK7.3722.84428.858.47 BiL68.8627.56386.528.75 Ca 5 Al 2 : 30 Bi 2 : 78 B CaK22.1146.211065.636.25 AlK8.3525.92497.58.11 BiL69.5427.87402.198.64 Ca 5 Al 2 : 80 Bi 3 : 02 C CaK22.7847.91135.176.14 AlK7.724.06472.678.3 BiL69.5228.04415.378.46 Ca 5 Al 2 : 51 Bi 2 : 93 D CK15.1251.22242.517.38 OK13.7334.93189.3711.44 BiL71.1413.85512.938.05 Bi E CaK22.0148.711011.036.26 AlK6.3520.88358.548.63 BiL71.6430.41400.388.95 Ca 5 Al 2 : 14 Bi 3 : 12 F CaK17.9944.381268.16.24 AlK5.2819.34474.398.32 BiL76.7336.284012.311.89 Ca 5 Al 2 : 18 Bi 4 : 09 G CaK17.3542.621243.276.27 AlK5.8121.18529.718.38 BiL76.8436.194063.221.77 Ca 5 Al 2 : 48 Bi 4 : 25 154 BIBLIOGRAPHY 155 BIBLIOGRAPHY [1] A.Zevalkink,J.Swallow,andG.J.Snyder.ThermoelectricpropertiesofZn-dopedCa 5 In 2 Sb 6 . DaltonTransactions ,42(26):9713Œ9719,2013. 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