ELECTRONICANDTHERMALTRANSPORTINCOPPER-BASEDCHALCOPYRITESEMICONDUCTORSFORTHERMOELECTRICAPPLICATIONSByWinstonD.CarrADISSERTATIONSubmittedtoMichiganStateUniversityinpartialentoftherequirementsforthedegreeofPhysics|DoctorofPhilosophy2016ABSTRACTELECTRONICANDTHERMALTRANSPORTINCOPPER-BASEDCHALCOPYRITESEMICONDUCTORSFORTHERMOELECTRICAPPLICATIONSByWinstonD.CarrThethermoelectricwasdiscoveredin1821whenThomasSeebeckobservedthatacircuitmadeoftwodissimilarmetals,withjunctionsattwottemperatures,acompassneedle.However,intheensuingnearlytwo-hundredyearsthermoelectricdeviceshavefailedtouseinanybutnicheapplications.Thisslowprogress,whencomparedtothatofphoto-voltaicdeviceswhichhavegreatlyimprovedinroughlyhalfthetime,isdueinlargeparttothecontraindicatedparameterswhichgoverntheofathermoelectricmaterial.Optimizingoneparameterforthermoelectricperformanceoftencomesatthecostofhinderinganother,somultipleapproachesmustbeusedtoimprovethethermoelectricperformanceofamaterial.Therefore,materialoptimizationrequiresaunderstandingoftheunderlyingtransportphysicsandmaterialssciencegoverningamaterial.Whenevaluatingtheviabilityofamaterialforthermoelectricusethedimensionlessofmerit,ZT,isthestandardmetric.ThisdimensionlessisacombinationoftheSeebeckcotandtheelectricalandthermalconductivitiesofthematerial,aswellastheoperatingtemperature,andisdirectlyrelatedtotheofathermoelectricgenerator.Inthepast25yearstheofthermoelectricityhasprovidedmanymaterialswithaZTinexcessofunity,andrecentlymaterialshavebeenreportedwithvaluesgreaterthantwo.However,elementtoxicity,lowelementalabundance,andcomplexsynthesistechniqueshavepreventedmanyofthesematerialsfromreachingcommercialviability.ThisworkpresentsasystematicstudyofthechalcopyritefamilyofsemiconductorswithchemicalstructureI-III-VI2wherethegroupIelementiscopper.Thisfamilycontainsmanypossibilitiesfornon-toxic,earthabundantmaterialswhichcanbesimply,andinsomecasesrapidly,synthesized.Abetterunderstandingofthephysicsgoverningthetransportmecha-nismsinthesematerialscouldleadtotheiradoptioninfuturethermoelectricapplications,helpingimprovetheenergyyofdevicesofallsizes.Iwouldliketodedicatethisworktomymathteachers,Mrs.BrendaCharlesandMr.TerryJohnson,forstartingandencouragingmypassionformathandphysics,tomyparents,BridgetandBob,forsupportingmealongtheway,andespeciallytoGingerforhelpingmekeepitalltogether.Icouldnothavedonethiswithoutyouall.InthewordsofMr.Johnson:\Perseverance,keepyournosetothegrindstone".ivACKNOWLEDGMENTSIwouldliketothankmyadvisor,Dr.DonaldT.Morelli,forgivingmetheoppor-tunitytoworkinhisresearchgroup,forallowingmetotraveltoconferencesandpresentmywork,forencouragingmetoexploreanyideasIhad,andforputtingupwithendlessquestionsonanytopic.Iwouldalsoliketothankallofmygroupmemberswhohelpedmethroughouttheyearswithsynthesis,measurements,conversations,andthoughts:Dr.VijayPonnabalam,Dr.SteveBoona,Dr.XuLu,Dr.GloriaLehr,Mr.JaredWilliams,andMr.SpencerWaldrop.Iwasalsoassistedbytwotalentedundergradresearchers,Mr.SpencerMathers,andMr.AdamMarsh,forwhichIamthankful.Outsideofourgroup,IwouldliketogreatlythankDr.TravisThompson,Dr.MichaelBennett,andMr.ChristopherWillisallforhoursofhelpfuldiscussionandinsight.And,Ihavetothankmyfaithfulwritingcompanion,Daisy,forstayingwithmeandmoralsupportthroughallthehotdayswhileIwaswritingthisthesis.Herdedicationwasaninspirationtome.Iamgratefultomyguidancecommitteemembers,Dr.Sakamoto,Dr.PhilDuxbury,Dr.StuartTessmer,andDr.TimHogan.YouwereallveryhelpfulanytimeIhadquestions,especiallyDr.DuxburywhoIpesteredweeklyduringourstatisticalmechanicscourse.IwanttothankDr.SiHuiaswellasDr.CtiradUherforprovidinglasermeasure-mentsformewhenthesystematMSUwasdown.FinallyIwouldlikeacknowledgethatthisresearchwasfundedbytheDepartmentofEn-ergyofSciencethroughtheRevolutionaryMaterialsforSolidStateEnergyConversionEnergyFrontierResearchCenter,Award#DE-SC0001054.vTABLEOFCONTENTSLISTOFTABLES....................................viiiLISTOFFIGURES...................................ixChapter1Introduction................................11.1TheHistoryandImportanceofThermoelectricity...............11.2MotivationforThermoelectricPowerGeneration................7Chapter2ThePhysicsofThermoelectricMaterialsandDevices......112.1ThermoelectricDevice........................122.2ElectricalConductivity..............................162.3TheSeebeckCocient.............................252.3.1Bandtheoryoftransport.........................302.4ThermalConductivity..............................322.5MotivationforChalcopyriteCompounds....................39Chapter3ExperimentalProcedures........................433.1MaterialsSynthesis................................433.1.1FurnaceHeatingProcedure.......................443.1.2SinteringProcedures...........................453.2CharacterizationTechniques...........................463.2.1X-raytion.............................463.2.2tialScanningCalorimetry....................473.2.3HallMeasurements............................483.2.4LowTemperatureTransportProperties.................503.2.4.1ElectricalResistivity......................513.2.4.2SeebeckCotandThermalConductivity........513.2.5HighTemperatureTransportProperties................533.2.5.1ElectricalResistivityandSeebeckCot........533.2.5.2ThermalConductivityandThermaly.......54Chapter4Tellurides..................................554.1FamilyOverview.................................554.2CuAlTe2......................................564.3CuInTe2......................................604.3.1ElectronicDoping.............................604.4CuGaTe2.....................................654.4.1TransportProperties...........................664.4.2ElectronicDoping.............................694.4.2.1N-typeDopants:Zinc,Germanium,Tin,andIodine....69vi4.5SolidSolutions..................................754.5.1CuIn1{xGaxTe2..............................754.5.2Cu(In1{xGax)0.99Zn0.01Te2.......................804.5.3CuInTe2(1{x)S2x.............................844.6Conclusions....................................87Chapter5Selenides..................................885.1FamilyOverview.................................885.2CuInSe2......................................895.2.1ElectronicDoping.............................905.3CuGaSe2......................................925.3.1ElectronicDoping.............................935.4SolidSolutions..................................975.4.1CuIn0.99Zn0.01Te2(1{x)Se2x-Hotpressed................975.4.2CuInTe2(1{x)Se2x-SparkPlasmaSintered...............1035.4.3CuIn1{yZnyTe1Se1............................1075.4.4CuGaTe2(1{x)Se2x............................1125.4.5CuGa1{yZnyTeSe.............................1175.5Conclusions....................................120Chapter6...................................1236.1FamilyOverview.................................1236.2CuFeS2......................................1246.2.1ElectronicDoping.............................1286.2.2CuFeS2RapidSPSSynthesis......................1326.3CuInS2.......................................1406.4CuGaS2......................................1416.5SolidSolutions..................................1426.5.1CuFeS2(1{x)Se2x.............................1426.5.2CuFeS2(1{x)Te2x.............................1496.5.3CuFe1{xGaxS2..............................1506.6Conclusions....................................151Chapter7RelatedMaterials............................1527.1Bornite:Cu5FeS4.................................1527.2DefectChalcopyrite:Zn0.5GaTe2andZn0.5InTe2...............1587.2.1SolidSolution:CuGaTe2-Zn0.5GaTe2.................1627.3CoppertCuGaTe2............................166Chapter8ConclusionsandFutureWork.....................172REFERENCES.....................................178viiLISTOFTABLESTable6.1DensityofsamplesofCuFeS2synthesizedbydirectSPSreaction.ThetheoreticaldensityofCuFeS2is4.1823gcm3usingthelatticeparametersobtainedfromXRD.....................134viiiLISTOFFIGURESFigure1.1Ontheleft,atemperaturetialgeneratesavoltagepotential(theSeebeckect)whileontherightanappliedvoltagedrivesacurrentwhichwilleitherliberateorgenerateheatatthejunction(thePeltier...........................2Figure1.2LawrenceLivermoreNationalLabestimated2013energyuseintheU.S.Theleftsiderepresentsthesourcesofenergy,andtherightsidetheenduses................................7Figure1.3TheE1thermoelectricgeneratorfromAlphabetEnergy.Ontheleftisalargedieselgenerator,withtheexhaustconnectedtotheE1TEGontheright.[1]..............................9Figure2.1Schematicofathermoelectricunicouple.Ageneratorismadefromagroupofthesestackedelectricallyinseriesandthermallyinparallel.12Figure2.2ofathermoelectricgeneratorasafunctionofZTandhotsidetemperature.Thecoldsideissetat300K.AsZTtendstoytheapproachestheCarnotlimit...........15Figure2.3Carrierconcentration(n)incm3asafunctionofreducedFermienergy(EfkbT)calculatedfromequation(2.21).=0refersthetheconductionbandedge.Theemass(m)istakentobethefreeelectronmasshere..........................18Figure2.4Carrierconcentrationasafunctionofinversetemperatureforadopedsemiconductor,showingthefreezeoutregionatlowtemperature,thesaturationregion,andthehightemperatureregionwhenintrinsiccarriersdominate........................21Figure2.5ElectricalconductivityofCuInTe2andCuIn0.99Zn0.01Te2versustem-perature.Asshown,thedopedsamplehasmetallicbehavior,withtheelectricalconductivitydroppingwithincreasingtemperature.Athighenoughtemperatures,bothsamplesbecomeintrinsic.......24Figure2.6DiagramoftheSeebeckinann-typematerial.Thehotelectronswfromtheleftsideandaccumulateontherightside,inducinganelectricandaresultantpotential...........25ixFigure2.7Seebeckcot(S)inµVK1asafunctionofreducedFermien-ergy(EfkbT)calculatedfromequations(2.43)and(2.44),assuming=-1/2..................................28Figure2.8S2ne*106inµWVscm3K2asafunctionofreducedFermien-ergy(EfkbT)calculatedfromequation(2.45),usinganemassof1meandatemperatureof800K................29Figure2.9SchematicdiagrammingUmklappScattering.Phononsq1andq2combinetoformphononq3whichliesoutsidethe1stBrillouinzoneandissubsequentlyfoldedbackintothe1stBZ............38Figure2.10CrystalstructuresofSi,ZnSe,Zn2Se2,andCuGaSe2fromlefttoright.AthightemperaturestheorderinginCuGaSe2breaksdown,andthecrystalcanbereducedbacktoacubicstructurewithCuandGaatomsoccupyingsitesinterchangeably,aswillbeshowninlaterchapters..................................40Figure2.11ElectronicbandstructuresofCuGaTe2(ontheleft)andofCuGaS2(ontheright)showingtherelativelyvalencebands,whichindicateahighemass.[2,3].......................41Figure3.1Stepsinmaterialsynthesis.Fromlefttoright,elementsweighedoutinampoule,ampoulebeingsealed,andtheresultingingotafterthefurnaceprocedure.............................44Figure3.2ExperimentalsetupforHallmeasurements.Theappliedmagneticisintothepage...........................48Figure3.3ExampleoftypicalHalldata,showingtheHallresistanceversusrelationship.Theslopeisequalto1/net,wheretisthesamplethick-ness,eistheelementarycharge,andnisthecarrierconcentration..49Figure3.4Experimentalsetupforlowtemperaturetransportmeasurements.Themeasurementisperformedunderaliquidnitrogenw,withthesamplesurroundedbyvacuum....................50Figure4.1X-raytionpatternofCuAlTe2withPDFoverlay.They-scaleisintensity,inarbitraryunits.PDF#01-075-0102[4]........56Figure4.2ElectricalresistivityofCuAlTe2asafunctionoftemperature.....57Figure4.3SeebeckcoetofCuAlTe2asafunctionoftemperature.....58xFigure4.4ThermalconductivityofCuAlTe2asafunctionoftemperature....59Figure4.5X-raydpatternofCuInTe2withPDFoverlay.They-scaleisintensity,inarbitraryunits.ThepatternisPDF#01-082-0450.[5]60Figure4.6ElectricalresistivityoftheseriesCuIn1{yZnyTe2asafunctionoftemperature.OpensymbolsrepresentCuIn1{yZnyTe2.Filledsym-bolsaredatafromLiuetal.forCuInTe2annealedfor1,72,and168hours.Forcomparison,oursampleswereannealedfor24hours.[6].61Figure4.7SeebeckcotoftheseriesCuIn1{yZnyTe2asafunctionoftem-perature.OpensymbolsrepresentCuIn1{yZnyTe2.FilledsymbolsaredatafromLiuetal.forCuInTe2annealedfor1,72,and168hours.Forcomparison,oursampleswereannealedfor24hours.[6].62Figure4.8PowerfactoroftheseriesCuIn1{yZnyTe2asafunctionoftemper-ature.OpensymbolsrepresentCuIn1{yZnyTe2.FilledsymbolsaredatafromLiuetal.forCuInTe2annealedfor1,72,and168hours.Forcomparison,oursampleswereannealedfor24hours.[6].....63Figure4.9ThermalconductivityoftheseriesCuIn1{yZnyTe2asafunctionoftemperature.OpensymbolsrepresentCuIn1{yZnyTe2.Filledsym-bolsaredatafromLiuetal.forCuInTe2annealedfor1,72,and168hours.Forcomparison,oursampleswereannealedfor24hours.[6].64Figure4.10ZToftheseriesCuIn1{yZnyTe2asafunctionoftemperature.OpensymbolsrepresentCuIn1{yZnyTe2.FilledsymbolsaredatafromLiuetal.forCuInTe2annealedfor1,72,and168hours.Forcomparison,oursampleswereannealedfor24hours.[6]..............64Figure4.11XRDpatternofCuGaTe2,withaPDFoverlay.ThepatternisPDF#01-079-2331.[7]............................65Figure4.12ElectricalresistivityofCuGaTe2asafunctionoftemperature.Squaresrepresentourdata,whilethediamondsarefromPlirdpringetal.[8],andthetrianglesarefromLietal.[9].................66Figure4.13SeebeckcotofCuGaTe2asafunctionoftemperature.Squaresrepresentourdata,whilethediamondsarefromPlirdpringetal.[8],andthetrianglesarefromLietal..[9].................66Figure4.14PowerfactorofCuGaTe2asafunctionoftemperature.Squaresrep-resentourdata,whilethediamondsarefromPlirdpringetal.[8],andthetrianglesarefromLietal.[9]..................67xiFigure4.15ThermalconductivityofCuGaTe2asafunctionoftemperature.Squaresrepresentourdata,whilethediamondsarefromPlirdpringetal.[8],andthetrianglesarefromLietal.[9]..................68Figure4.16ZTofCuGaTe2asafunctionoftemperature.Squaresrepresentourdata,whilethediamondsarefromPlirdpringetal.[8],andthetrianglesarefromLietal.[9].......................68Figure4.17ThermalconductivityoftheseriesCuGaTe2(1{x)I2xasafunctionoftemperature................................70Figure4.18PowerfactoroftheseriesCuGaTe2(1{x)I2xasafunctionoftemper-ature....................................71Figure4.19ZToftheseriesCuGaTe2(1{x)I2xasafunctionoftemperature...71Figure4.20Electricalresistivityofn-typedopedsamplesofCuGaTe2asafunc-tionoftemperature............................72Figure4.21Seebeckcotofn-typedopedsamplesofCuGaTe2asafunctionoftemperature..............................72Figure4.22Powerfactorofn-typedopedsamplesofCuGaTe2asafunctionoftemperature................................73Figure4.23Thermalconductivityofn-typedopedsamplesofCuGaTe2asafunc-tionoftemperature............................74Figure4.24XRDpatternsoftheseriesCuIn1{xGaxTe2.Frombottomtotop,samplesarex=[0,0.25,0.35,0.5,0.65,0.75,1].They-axisisshowsintensityinarbitraryunits.TotopPDFisCuGaTe2(#01-079-2331)andthebottomisCuInTe2(#01-082-0450).[5,7]...........75Figure4.25CalculatedlatticeparametersoftheseriesCuIn1{xGaxTe2asafunc-tionofgalliumconcentration(x),usingthe204and424peaks....76Figure4.26ElectricalresistivityoftheseriesCuIn1{xGaxTe2asafunctionoftemperature................................77Figure4.27SeebeckcontoftheseriesCuIn1{xGaxTe2asafunctionoftem-perature..................................78Figure4.28PowerfactoroftheseriesCuIn1{xGaxTe2asafunctionoftemperature.79xiiFigure4.29ThermalconductivityoftheseriesCuIn1{xGaxTe2asafunctionoftemperature................................79Figure4.30ZToftheseriesCuIn1{xGaxTe2asafunctionoftemperature....80Figure4.31ElectricalresistivityoftheseriesCu(In1{xGax)0.99Zn0.01Te2asafunctionoftemperature.........................81Figure4.32SeebeckcotoftheseriesCu(In1{xGax)0.99Zn0.01Te2asafunc-tionoftemperature............................81Figure4.33PowerfactoroftheseriesCu(In1{xGax)0.99Zn0.01Te2asafunctionoftemperature..............................82Figure4.34ThermalconductivityoftheseriesCu(In1{xGax)0.99Zn0.01Te2asafunctionoftemperature.........................83Figure4.35ZToftheseriesCu(In1{xGax)0.99Zn0.01Te2asafunctionoftemper-ature....................................83Figure4.36XRDpatternofCuInTe2(1{x)S2xwithPDF.ThetoppatternisCuInTe2,followedbyx=0.005,0.01,and0.015,atwhichpointsecondarypeakscorrespondingtoCuInS2wereobserved.PatternsarePDF#01-082-0450and#01-075-0106forCuInTe2andCuInS2respectively.[5,10]............................84Figure4.37ElectricalresistivityoftheseriesCuInTe2(1{x)S2xasafunctionoftemperature................................85Figure4.38SeebeckcotoftheseriesCuInTe2(1{x)S2xasafunctionoftemperature................................85Figure4.39ThermalconductivityoftheseriesCuInTe2(1{x)S2xasafunctionoftemperature................................86Figure4.40ZToftheseriesCuInTe2(1{x)S2xasafunctionoftemperature....86Figure5.1XRDpatternofCuInSe2withPDF.They-scaleisintensity,inarbi-traryunits.ThepatternisPDF#01-075-2916.[11].........89Figure5.2ElectricalresistivityoftheseriesCuIn1{yZnySe2versustemperature.ThedataforCuInSe2showsalargeamountofduetothelargesampleresistanceandtheyinmakinggoodelectricalcontacttothesample...........................90xiiiFigure5.3SeebeckcotoftheseriesCuIn1{yZnySe2asafunctionoftem-perature..................................91Figure5.4PowerfactoroftheseriesCuIn1{yZnySe2asafunctionoftemperature.91Figure5.5X-raypatternforCuGaSe2withPDFoverlay.They-scaleisintensity,inarbitraryunits.ThepatternisPDF#01-075-2916.[12]92Figure5.6ElectricalresistivityoftheseriesCuGa1{xZnxSe2asafunctionoftemperature................................94Figure5.7SeebeckcotoftheseriesCuGa1{xZnxSe2asafunctionoftem-perature..................................94Figure5.8PowerfactoroftheseriesCuGa1{xZnxSe2asafunctionoftemperature.95Figure5.9ThermalconductivityoftheseriesCuGa1{xZnxSe2asafunctionoftemperature................................96Figure5.10ZToftheseriesCuGa1{xZnxSe2asafunctionoftemperature....96Figure5.11XRDpatternsofthesolidsolutionCuIn0.99Zn0.01Te2(1{x)Se2xwithPDFs.ThetoppatternisforCuIn0.99Zn0.01Te2,witheachpatternshowingsubstitutionsin25%increments.They-scaleisintensity,inarbitraryunits.ThepatternsarePDF#01-082-0450and#01-075-2916forTeandSerespectively.[13,11]................97Figure5.12LatticeparametersofthesolidsolutionCuIn0.99Zn0.01Te2(1{x)Se2xwithliteraturevaluesshowninopensymbols.Thedashedlinesaretoguidetheeyes.[4,14,13,6,15,8]..................98Figure5.13ThermalconductivityandelectricalresistivityofCuIn0.99Zn0.01Te2(1{x)Se2xat300K.Bothshowastrongdependenceonseleniumconcentration.99Figure5.14ElectricalresistivityoftheseriesCuIn0.99Zn0.01Te2(1{x)Se2xasafunctionoftemperature,showingthestrongdependenceonseleniumconcentration...............................100Figure5.15ThermalconductivityoftheseriesCuIn0.99Zn0.01Te2(1{x)Se2xasafunctionoftemperature,showingthestrongdependenceonseleniumconcentration..............................101Figure5.16SeebeckcotoftheseriesCuIn0.99Zn0.01Te2(1{x)Se2xasafunc-tionoftemperature............................101xivFigure5.17PowerfactoroftheseriesCuIn0.99Zn0.01Te2(1{x)Se2xasafunctionoftemperature..............................102Figure5.18ZToftheseriesCuIn0.99Zn0.01Te2(1{x)Se2xasafunctionoftemper-ature....................................102Figure5.19XRDpatternsforthesolidsolutionCuInTe2(1{x)Se2xviaSPSwithPDFs.ThebottompatternisforCuInTe2,witheachsubse-quentpatternshowingsubstitutionsin25%increments.They-scaleisintensity,inarbitraryunits.PDFsare#01-082-0450and#01-075-2916forTeandSerespectively.[13,11]................103Figure5.20SeebeckcontoftheseriesCuInTe2(1{x)Se2xasafunctionoftemperature................................104Figure5.21ElectricalresistivityoftheseriesCuInTe2(1{x)Se2xasafunctionoftemperature................................105Figure5.22PowerfactoroftheseriesCuInTe2(1{x)Se2xasafunctionoftemper-ature....................................105Figure5.23ThermalconductivityoftheseriesCuInTe2(1{x)Se2xasafunctionoftemperature................................106Figure5.24ZToftheseriesCuInTe2(1{x)Se2xasafunctionoftemperature...106Figure5.25SeebeckcotoftheseriesCuIn1{yZnyTe1Se1asafunctionoftemperature................................108Figure5.26ElectricalresistivityoftheseriesCuIn1{yZnyTe1Se1asafunctionoftemperature................................109Figure5.27PowerfactoroftheseriesCuIn1{yZnyTe1Se1asafunctionoftem-perature..................................110Figure5.28ThermalconductivityoftheseriesCuIn1{yZnyTe1Se1asafunctionoftemperature..............................110Figure5.29ZToftheseriesCuIn1{yZnyTe1Se1asafunctionoftemperature..111Figure5.30XRDpatternsoftheseriesCuGaTe2(1{x)Se2xwithPDFs.ThetoppatternisforCuGaTe2,witheachpatternshowingseleniumsubsti-tutionsin25%increments,withCuGaSe2shownatthebottom.They-scaleisintensityinarbitraryunits.ThePDFsare#01-079-2331and#01-075-2916forTeandSerespectively.[7,12].........112xvFigure5.31LatticeparametersoftheseriesCuGaTe2(1{x)Se2x.Opensymbolsrepresentliteraturedata,whilethesymbolsaredatafromthestudyhere.[4,14,13,15,8,16]....................113Figure5.32ThermalconductivityandelectricalresistivityoftheseriesCuGaTe2(1{x)Se2xatroomtemperature.Thermalconductivityshowsthetypicalparabolicrelationship,whiletheelectricalresistivityshowsanexponentialde-pendenceonseleniumconcentration...................114Figure5.33ElectricalresistivityoftheseriesCuGaTe2(1{x)Se2xasafunctionoftemperature................................114Figure5.34SeebeckcocientoftheseriesCuGaTe2(1{x)Se2xasafunctionoftemperature................................115Figure5.35PowerfactoroftheseriesCuGaTe2(1{x)Se2xasafunctionoftem-perature..................................115Figure5.36ThermalconductivityoftheseriesCuGaTe2(1{x)Se2xasafunctionoftemperature..............................116Figure5.37ZToftheseriesCuGaTe2(1{x)Se2xasafunctionoftemperature...117Figure5.38ElectricalresistivityoftheseriesCuGa1{yZnyTeSeasafunctionoftemperature................................118Figure5.39SeebeckcotoftheseriesCuGa1{yZnyTeSeasafunctionoftemperature................................119Figure5.40PowerfactoroftheseriesCuGa1{yZnyTeSeasafunctionoftemper-ature....................................119Figure5.41ZTversustemperaturefortheseriesCuGa1{yZnyTeSe........120Figure5.42Hightemperaturethermalconductivityoftellurium-seleniumsolidsolutionsasafunctionofseleniumconcentration.CompositionsareCuGaTe2(1{x)Se2x,CuInTe2(1{x)Se2x(SPS)andCuIn0.99Zn0.01Te2(1{x)Se2x(HP).Measurementswereperformedat860K.............121Figure5.43Hightemperatureelectricalresistivityoftellurium-seleniumsolidsolutionsasafunctionofseleniumconcentration.CompositionsareCuGaTe2(1{x)Se2x,CuInTe2(1{x)Se2x(SPS)andCuIn0.99Zn0.01Te2(1{x)Se2x(HP).Measurementswereperformedat860K.............122xviFigure6.1XRDpatternofCuFeS2.ThepatternshownbelowisPDF#01-083-0983.[17].................................124Figure6.2SeebeckcotofCuFeS2asafunctionoftemperatureascom-paredtoliteraturereports.DataisfromTsujiietal.andLietal..[18,19,20]................................125Figure6.3ElectricalresistivityofCuFeS2asafunctionoftemperatureascom-paredtoliteraturereports.DataisfromTsujiietal.andLietal..[18,19,20]................................126Figure6.4PowerfactorofCuFeS2asafunctionoftemperatureascomparedtoliteraturereports.DataisfromTsujiietal.andLietal..[18,19,20]127Figure6.5ThermalconductivityofCuFeS2asafunctionoftemperatureascom-paredtoliteraturereports.DataisfromTsujiietal.andLietal..[18,19,20]................................127Figure6.6ZTofCuFeS2asafunctionoftemperatureascomparedtoliteraturereports.DataisfromTsujiietal.andLietal..[18,19,20].....128Figure6.7ElectricalresistivityoftheseriesCu1{yZnyFeS2asafunctionoftem-peratureascomparedtoliteraturereports.Opensymbolsrepresentdataobtainedhere,whilethesymbolsrepresentdatafromTsujiietal.andLietal..[18,19,20].....................129Figure6.8SeebeckcotoftheseriesCu1{yZnyFeS2asafunctionoftem-peratureascomparedtoliteraturereports.Opensymbolsrepresentdataobtainedhere,whilethesymbolsrepresentdataisfromTsujiietal.andLietal..[18,19,20].................130Figure6.9PowerfactoroftheseriesCu1{yZnyFeS2asafunctionoftemperatureascomparedtoliteraturereports.DataisfromTsujiietal.andLietal..[18,19,20]............................130Figure6.10ThermalconductivityoftheseriesCu1{yZnyFeS2asafunctionoftemperatureascomparedtoliteraturereports.DataisfromTsujiietal.andLietal..[18,19,20].....................131Figure6.11ZToftheseriesCu1{yZnyFeS2asafunctionoftemperatureascom-paredtoliteraturereports.DataisfromTsujiietal.andLietal.[18,19,20]................................132xviiFigure6.12Thetoppatternisfortwopowdersmixedbyhand,themiddlepatternisthepowderafter5minutesofvibratorymilling,andthebottompatternistakenafterthepowderhasbeenbytheSPS.ThepatternsshownbelowarePDF#01-083-0983,PDF#01-079-2321,andPDF#03-065-6841forCuFeS2,CuS,andFeSrespectively.[17,21,22]..................................133Figure6.13ElectricalresistivityofseveralsamplesofCuFeS2asafunctionoftemperature.SamplesweresynthesizedbydirectreactionduringSPS.ThesquaresrepresentsCuFeS2madebytraditionalmeltingandhotpressing..............................134Figure6.14SeebeckcotofseveralsamplesofCuFeS2asafunctionoftem-perature.SamplesweresynthesizedbydirectreactionduringSPS.ThesquaresrepresentsCuFeS2madebytraditionalmeltingandhot-pressing..................................135Figure6.15PowerfactorofseveralsamplesofCuFeS2asafunctionoftempera-ture.SamplesweresynthesizedbydirectreactionduringSPS.ThesquaresrepresentsCuFeS2madebytraditionalmeltingandhotpressing.136Figure6.16ThermalconductivityofseveralsamplesofCuFeS2asafunctionoftemperature.SamplesweresynthesizedbydirectreactionduringSPS.ThesquaresrepresentsCuFeS2madebytraditionalmeltingandhotpressing..............................137Figure6.17ZTofseveralsamplesofCuFeS2asafunctionoftemperature.Sam-plesweresynthesizedbydirectreactionduringSPS.ThesquaresrepresentsCuFeS2madebytraditionalmeltingandhotpressing...138Figure6.18ElectricalresistivityofseveralsamplesofCuFeS2synthesizedbydi-rectreactionduringSPScomparedtoliteraturevaluesforCuFeS2{.TheXsymbolrepresentsthedatafromsamplesmadeinthisstudy,theothersymbolsarefromLietal.[23]................139Figure6.19SeebeckcotofseveralsamplesofCuFeS2synthesizedbydirectreactionduringSPScomparedtoliteraturevaluesforCuFeS2{.TheXsymbolrepresentsthedatafromsamplesmadeinthisstudy,theothersymbolsarefromLietal.[23]..................139Figure6.20XRDpatternofCuInS2.ThepatternshownbelowisPDF#01-075-6866.[24].................................140Figure6.21ElectricalresistivityofCuInS2asafunctionoftemperature.....141xviiiFigure6.22ThermalconductivityofCuInS2asafunctionoftemperature....141Figure6.23ElectricalresistivityofseveralsamplesofCuGaS2fromworkbyJulienetal.Thesamplesweresimplydescribedbytheirapparentcolors.[25]................................142Figure6.24XRDpatternsoftheseriesCuFeS2(1{x)Se2x.ThetoppatternispureCuFeS2,witheachpatternbeneathitincreasingxby0.05,theatthebottombeingpatternCuFeS1.4Se0.6.Notetheadditionalpeaksinthebottompattern,indicatingthepresenceofasecondaryphase.PDFsforpatternsare#01-075-6866and#01-081-1959forCuFeS2andCuFeSe2respectively.[26,27]...................143Figure6.25LatticeparametersoftheseriesCuFeS2(1{x)Se2xasafunctionofx.Increasingseleniumleadstoalargerlattice,howeveratx=0.3thegrowthstops,asasolubilitylimitisreached..............144Figure6.26SpheatoftheseriesCuFeS2(1{x)Se2xasafunctionoftemper-ature.Thepeaksindicatedecompositionintoamixtureofbinaryphases,followedbythesublimationofsulfur..............145Figure6.27TemperatureofthepeakintheDSCcurvefortheseriesCuFeS2(1{x)Se2x.Thepeaksindicatedecompositionintoamixtureofbinaryphases,followedbythesublimationofsulfur..................145Figure6.28ElectricalresitivityoftheseriesCuFeS2(1{x)Se2xasafunctionoftemperature................................146Figure6.29SeebeckcotoftheseriesCuFeS2(1{x)Se2xasafunctionoftemperature................................147Figure6.30PowerfactoroftheseriesCuFeS2(1{x)Se2xasafunctionoftemperature.148Figure6.31ThermalconductivityoftheseriesCuFeS2(1{x)Se2xasafunctionoftemperature................................148Figure6.32ZToftheseriesCuFeS2(1{x)Se2xasafunctionoftemperature....149Figure6.33XRDPatternsofCuFeS2(1{x)Te2x.ThetoppatternisforpureCuFeS2,followedbyx=0.05,0.10,0.2,and0.3.Thepatternsbe-lowarefromPDF#01-075-6866and#01-070-3094forCuFeS2andCuFeTe2respectively.[26,28]......................150xixFigure7.1XRDpatternofnominallypurebornite(Cu5FeS4)andfourdopedcompositions.ThetoppatternispureCu5FeS4,followedbythe1%and5%p-typedopedsamples,andallythe1%and5%n-typedopedsamples.Theextrapeaksobservedinthe1%n-typesampleareduetoasecondaryphaseofFeS.They-scaleisintensity,inarbitraryunits.Source:PDF#98-000-0123.[29]...........153Figure7.2Electricalresistivityofsamplesofnominallypurebornite(Cu5FeS4)andfourdopedcompositionsasafunctionoftemperature.Literaturedataisshownwithcoloredsymbolsforcomparison.[30,31].....154Figure7.3Seebeckcotofsamplesofnominallypurebornite(Cu5FeS4)andfourdopedcompositionsasafunctionoftemperature.Literaturedataisshownwithcoloredsymbolsforcomparison.[30,31].....154Figure7.4Powerfactorofsamplesofnominallypurebornite(Cu5FeS4)andfourdopedcompositionsasafunctionoftemperature.Literaturedataisshownwithcoloredsymbolsforcomparison.[30,31].........156Figure7.5Thermalconductivityofsamplesofnominallypurebornite(Cu5FeS4)andfourdopedcompositionsasafunctionoftemperature.Literaturedataisshownwithcoloredsymbolsforcomparison.[30,31].....157Figure7.6ZTofsamplesofnominallypurebornite(Cu5FeS4)andfourdopedcompositionsasafunctionoftemperature.Literaturedataisshownwithcoloredsymbolsforcomparison.[30,31].............158Figure7.7XRDpatternsofthedefectchalcopyritecompounds:Zn0.5GaTe2,Zn0.475GaTe2,andZn0.5InTe2fromtoptobottomrespectively.They-scaleisintensity,inarbitraryunits.Source:PDF#01-089-4209and#01-074-0218forZn0.5GaTe2andZn0.5InTe2respectively.[4].159Figure7.8Electricalresistivityofdefectchalcopyritecompounds,withCuGaTe2asareference,asafunctionoftemperature...............160Figure7.9Powerfactorofdefectchalcopyritecompounds,withCuGaTe2asareference,asafunctionoftemperature.................160Figure7.10Thermalconductivityofdefectchalcopyritecompoundsasafunctionoftemperature..............................161Figure7.11ZTofdefectchalcopyritecompoundsasafunctionoftemperature..162xxFigure7.12XRDpatternsofthepartialsolidsolutionofCuGaTe2andZn0.5GaTe2.ThetoppatternisCuGaTe2,followedbyCu0.995Zn0.0025GaTe2,Cu0.990Zn0.0050GaTe2,Cu0.900Zn0.0500GaTe2,andatthebottomCu0.800Zn0.1000GaTe2.ThePDFoverlayisforCuGaTe2.They-scaleisintensity,inarbitraryunits.Source:PDF#01-079-2331.[7]163Figure7.13ElectricalresistivityofthepartialsolidsolutionCuGaTe2-Zn0.5GaTe2asafunctionoftemperature.......................163Figure7.14SeebeckcotofthepartialsolidsolutionCuGaTe2-Zn0.5GaTe2asafunctionoftemperature.......................164Figure7.15PowerfactorofthepartialsolidsolutionCuGaTe2-Zn0.5GaTe2asafunctionoftemperature........................165Figure7.16ThermalconductivityofthepartialsolidsolutionCuGaTe2-Zn0.5GaTe2asafunctionoftemperature.......................165Figure7.17ZTofthepartialsolidsolutionCuGaTe2-Zn0.5GaTe2asafunctionoftemperature..............................166Figure7.18XRDpatternofcoppertCuGaTe2.ThetoppatternisCuGaTe2,followedbythe5%,10%,and15%coppersamplesrespec-tively.They-scaleisintensity,inarbitraryunits.Source:PDF#01-079-2331.[7]............................167Figure7.19Carrierconcentrationandmobilityat300KfortheseriesCu1{xGaTe2asafunctionofvacancyconcentration(x)...............167Figure7.20ElectricalresistivityoftheseriesCu1{xGaTe2asafunctionoftem-perature..................................168Figure7.21SeebeckcotoftheseriesCu1{xGaTe2asafunctionoftem-perature..................................169Figure7.22PowerfactoroftheseriesCu1{xGaTe2asafunctionoftemperature.169Figure7.23ThermalconductivityoftheseriesCu1{xGaTe2asafunctionoftem-perature..................................170Figure7.24ZToftheseriesCu1{xGaTe2asafunctionoftemperature......171Figure8.1ComparisonoftheelectricalresistivityofthebasecompoundsCuInTe2,CuGaTe2,CuInSe2,CuGaSe2,andCuFeS2.CuInS2isnotshownhere,butthevaluesareontheorderof108cm..........173xxiFigure8.2Comparisonofthethermalconductivityofthebasechalcopyritecom-pounds...................................175xxiiChapter1Introduction1.1TheHistoryandImportanceofThermoelectricityTheofthermoelectricitybeganin1821whenThomasJohannSeebeckdiscoveredthatifhemadealoopoutoftwotmetals,andheldonejunctionatahighertemperaturethantheotherhecouldacompassneedle.[32]Itwaslaterdeterminedthatthiswasduetoathermallydrivencurrentwingthroughtheloop.Thiscanbeseenmoreeasilybysimplyformingonejunctionbetweentwomaterials,heatingorcoolingthejunction,andmeasuringtheresultingvoltageacrossthetwoleads.Thevoltagegeneratedbythisisgivenas:V=(SASBT(1.1)whereisthegeneratedvoltagealongamaterials,isthetemperaturealongthesamematerial,andSAandSBaretheSeebeckcots(alsocalledthethermopowers)ofthetwomaterials.Sincethejunctionismadeoftwomaterials,theresultisasumofthevoltagesofthetwolegs,however,byusingasuperconductor,whichhasaSeebeckcotofzero,onematerialcanbemeasuredindependently.Alternatively,1onecanuseamaterialforwhichtheSeebeckcotisverywellknowninoneleg,andusethatdatatodeterminethevaluefortheothermaterial.TheSeebeckcothasunitsofvoltsperKelvin,inmagnitudeistypicallyintherangeof10sto100sofµVK1,andcanbebothpositiveornegative.Thesignconventionisnedsuchthatp-typematerialshaveapositiveSeebeckcot,andn-typematerialshaveanegativecot.Thisiscommonlyusedtodayinthermocouplestomeasuretemperature.Figure1.1:Ontheleft,atemperaturetialgeneratesavoltagepotential(theSeebeckwhileontherightanappliedvoltagedrivesacurrentwhichwilleitherliberateorgenerateheatatthejunction(thePeltierFollowingSeebeck'sdiscovery,in1834JeanCharlesAthanasePeltierdiscoveredwhatisnowcalledthePeltierHefoundthatifonemadeajunctionoftwotmetalsandpassedacurrentthroughit,thejunctionwouldeitherheatuporcooldowndependingonthedirectionofthecurrent.Thepowerofthisheatingorcoolingcanbeexpressedas:_Q=AB)I(1.2)where_Qistherateatwhichheatisbeinggeneratedorremoved,Iisthecurrentpassingthroughthematerial,andA=BisthePeltiercotofeachmaterial.2Finally,in1851LordKelvin(thenWilliamThomson)predicted,andthenobserved,whatisnowcalledtheThomsonHisworkshowedthatifonepassedacurrentthroughahomogeneousmaterial,whichwasalsounderatemperaturegradientparallelthecurrentw,heatcouldbemovedfromoneendtotheother.Thiscanbeexpressedmathematicallyas:_Q=KJrT(1.3)where_Qisagaintheheatw,Jisthecurrentdensitythroughthesample,rTisthetemperaturegradient,andKistheThomsoncot.HealsoderivedarelationbetweentheSeebeck,Peltier,andThomsoncots:K=ddTS(1.4)and=TS(1.5)Equations(1.3)-(1.5)alldescribeinteractionsbetweenelectricchargeandheat,andcombinedcanbeusedtoexplainandunderstandthermoelectricmaterials.TheSeebeckdescribesamethodformeasuringtemperature,aswedowiththermocouplestoday,orforgeneratingpowerfromaheatsourceasisdonewiththermoelectricgenerators.ThePeltierdescribesasolidstatemethodforheatingorcoolingdevices,andtheThomsonshowsaconnectionbetweenthetwophenomena.Whilethethreethermoelectricwerediscoveredanddescribedinthemid1800s,progressintheofthermoelectriccoolers3andgeneratorswasquiteslow,andlargeprogressinthewasnotmadeuntilthe1940sand1950s.In1909and1911atheoryandformulaforthemaximumforpowergeneration(whichwillbediscussedinthefollowingchapter),aswellasmaximumcoolingpowerforrefrigeration,wasdevelopedbyAltenkirch,givingtheguidetooptimizingthermoelectricmaterials.[35,36]Thatworkshowedtheimportanceofthedimensionlessureofmerit,ZT,whichdeterminesthencyofathermoelectricgeneratororrefrigerator:=ThTcThp1+ZT1p1+ZT+Tc=Th(1.6)ZT=S2˙T(1.7)Laterworkinthe1930sbyOnsagerwouldshowadeeperconnectionbetweenallthreeef-fects,earninghimtheNobelPrizeinchemistryin1968fortheOnsagerreciprocalrelations.[37,38,39]In1957SemiconductorThermoelementsandThermoelectricCoolingbyA.F.(translatedtoEnglishbyA.Gelbtuch)waspublished,addinggreatlytothetheoreticalframeworkforthermoelectricdevices.Hewasoneofthescientiststoputforwardtheideaofusingsemiconductors,andnotmetals,tomaketthermoelectricdevices.TheworkbyGoldsmid,especiallytheinitialreportsonthepropertiesofBi2Te3,con-tributedheavilytotheandthiscompoundremainedoneofthebestlowtemperaturethermoelectricmaterialsforthenext50years.[40,41]WorkbyTelkessurveyedavarietyofalloysatuseatthetime,aswellastheperformanceofbothtraditionalandsolarbasedgeneratorsinthelate1940sand50s.[42,43,44]Herworksuggestedsomeidealparame-4tersofmaterialscomprisingathermoelectricgenerator,withadesiredthermalconductivityof1Wm1K1andanelectricalresistivityofcm.However,shestatedthatatthetime,nosuchmaterialswereavailable.ThereportbyGoldsmidonBi2Te3whichshowedaroomtemperaturethermalconductivityof2.1Wm1K1andanelectricalresistivityof2.5cmforBi2Te3cameoutthesameyear.[40]Alsointhelate1950s,workonloweringthermalconductivitybyalloying,ortheformationofsolidsolutions,wasshowntobeasuccessfultechniqueforimprovingthermoelectricperfor-mance.Workonsilicon-germaniumalloys,PbTe{PbSesolidsolutions,Bi2Te3{Bi2Se3solidsolutions,andothercompoundsshowedthatalloyingcandrasticallylowerthermalconduc-tivity,andinsomecasesleavetheelectronicpropertiesrelativelyunchanged.[45,46,47,48]Forexample,comparingpuregermaniumtoanalloyofcompositionSi0.4Ge0.6,workatRCAlabsshowedthethermalconductivitycouldbereducedbyafactorofthreeatroomtemperature,whiletheSeebeckcotremainednearlyconstant.[46]Fromthe1950supintothe1990s,progressmadeintheeldofthermoelectricswasslow.PbTeandBi2Te3basedmaterialsremainedthecentralfocus,andwhilemodestZTimprovementswerebeingmade,ZTvaluesstillremainedatorbelowunity.However,inthe1990sanewclassofcage-likematerialsbegantobestudiedforthermoelectricuses.SkutteruditeshavechemicalcompositionTPn3,whereTisatransitionmetal(Fe,Ru,Os,Co,Rh,Ir)andPnisapnictogen(P,As,Sb),e.g.CoSb3.Earlyworkinthe1980sandearly1990sfocusedonthesuperconductingpropertiesofskutteruditecompoundswithcompositionLaT4P12.[49,50]However,forthermoelectricsoneoftheimportantaspectsoftheskutteruditestructurewastheabilitytothe\cage"formedbythepnictogenatomswithrareearthelements,creatingsocalledskutteruditeswithcompositionoftheformRT4Pn12whereRrepresentsarareearth.Clathratecompounds,withchemical5compositionAxByC46y,possesssimilarstructures,withcagelikevoidsthatcanbetomanipulatethetransportproperties.[51]In1995,workbyMorelliandMeisnershowedthatCeFe4Sb12showedpromisingthermo-electricproperties,withmetallic-likeelectricalresistivityontheorderofafewcm,andaSeebeckcotthatroselinearlyinTtoaroomtemperaturevaluenear70µVK1,quitelargeforametallicmaterial.However,moreimportantlytheirworkshowedthatthethermalconductivityoftheskutteruditewasonetotwoordersofmagnitudelowerthanthatoftheCoSb3andIrSb3.[52]Furtherreportsonthehightemperaturepropertiesin1996showedthattheironatomscouldbepartiallyreplacedwithcobalttooptimizetheelectricalproperties,andapeakZTof1.4at625Cwasreported.[53]Theoftheseinitialreportscouldbeclearlyseenatthe1996InternationalConferenceonThermoelectricsbythesheernumberofskutteruditepresentations.[54,55,56,57,58]Alsointhe1990s,studiesontheofquantumtonthermoelectrics,focusedonquantumwellsuperlattices,aswellassimplernedstructuressuchasananowires,showedpromise.[59,60,61,62]However,whiletheinitialstudiesledtomorecomputationalstudies,therewaslimitedexperimentalsuccesswiththeconcept.ReportsofZTvaluesinexcessof2.0werepublished,buthavenotbeenreproduced,andremainhighlydisputed.[63]61.2MotivationforThermoelectricPowerGenerationFigure1.2:LawrenceLivermoreNationalLabestimated2013energyuseintheU.S.Theleftsiderepresentsthesourcesofenergy,andtherightsidetheenduses.AsshowninFigure1.2,theUnitedStatesproducesjustshyof100Quadsofenergyperyear,whereonequadisequalto11015BTUs.Roughly80%ofthatenergycomesfromnonrenewablefossilfuels,andwhilealternativeenergyisgaining,nonrenewableenergyislikelytoremainacrucialpartoftheenergymarketforsometime.Withanincreasingglobalpopulation,aswellasincreasingenergydemandsindevelopingcountries,theneedtoincreaseenergyisparamount.Further,fromtheLawrenceLivermoreNationalLabstudy,summarizedinFigure1.2,onecanseethatroughly60%oftheenergyproducedintheUnitedStatesislostasrejectedenergy,withthemajoritybeinglostintheformofwasteheatrejectedduringelectricitygenerationandintransportation.7Thesecondlawofthermodynamicsinformsusthatentropyinaclosedsystemwillalwaysincreaseorremainconstant,andthataperfectengineisnotpossible,solosseswillalwaysbeapartofourpowergenerationtechnology.Oneoptionforimprovingthenistoawaytousethewasteheatinasecondstageofpowergeneration.ThishasbeenheavilystudiedandappliedinpowergenerationplantsintheformofCombinedCycleGasTurbines(CCGT),wheretheexhaustgasfromaturbinegenerator(burningcoalornaturalgasforexample)ispassedthroughaheatexchangertoboilwater,whichisthenpipedintoasteamturbineforthesecondstageofgeneration.[64,65]Whilethistechnologyworkswellforlargepowerplants,itdoesnotscaledowntothelevelofanautomobileorahome,andrequiresathresholdtemperatureofexhaustgastowork.Thermoelectricgenerators,ontheotherhand,canworkwithvirtuallyanytemperaturegradient.Athermoelectricgeneratorisascalablesolidstateenergyconversiondevice,whichcanbeoptimizedforttemperaturesandsizestoconvertheatdirectlyintoelectricity.Thatscalability,aswellasthelowmaintenancerequiredduetonomovingparts,hasledtomanynicheapplications.Theradioisotopethermoelectricgenerator(RTG)wasusedbyNASAin1961inaUSNavysatelliteandproduced2.5Wofpowerusingplutonium-238astheheatsource.[66]RTGshavelongstablelifetimes,theVoyager1and2probeshavecontinuedtorunonRTGsfornearly40yearswithzeromaintenance.ThecurrentMarsRover(Curiosity)ispoweredbyaRTGproducing125Wofpoweratitslaunch,withanexpectedpoweroutputof100Wafter14years,stillusingPu-238asaheatsource.[67]8Figure1.3:TheE1thermoelectricgeneratorfromAlphabetEnergy.Ontheleftisalargedieselgenerator,withtheexhaustconnectedtotheE1TEGontheright.[1]ShownaboveinFigure1.3istheE1thermoelectricgeneratorproducedbyAlphabetEnergy.Theirgeneratorsarebuiltinshippingcontainersforeasytransportation.Theyaredesignedtobeplacedontheexhaustoflargestationarydieselgeneratorsusedinre-motelocations,suchasminingoperations,andusetheexhaustgastoproduceadditionalelectricity.AnothernicheapplicationforTEGsisinindustrialmanufacturing.RGSDevelopmentBV,aDutchcompanyspecializinginsilicontapecastingtechnology,hasdevelopedther-moelectricgeneratorsaimedfordeploymentinsteelcastinglines.Theirgeneratorscaptureheatcomingfromthesteelcastingsastheycool,andgenerateadditionalpowerforthefactory.[68]ThisshowstheuniqueapplicationspossibleforTEGsascomparedtotraditionsteamturbines,wherehigherheatoutputswouldberequired.AsFigure1.2shows,electricitygenerationhasapproximately25QuadsofrejectedenergyintheUnitedStates.If10%ofthatheatcouldbecapturedandconvertedtoelectricity,thatwouldaddback2.5Quadsofenergy,morethanwasgeneratedbysolar,wind,and9geothermalcombinedin2013.Placingthermoelectricgeneratorsonpowerplantsalsoavoidssomeoftheissuesofsteadysupplythatarefoundwithmanyrenewableresourceslikesolar.TEGswouldproducepowerallhoursofthedayregardlessoftheweather,andcouldbeplacedatlocationswhereconnectingtothegridiseasy.Fortheseapplicationstobecomearealityonalargescale,newmaterialswithtailoredthermoelectricpropertiesandthatcanbeproducedinexpensivelywillberequired.Physicsplaystheroleofprovidingafundamentalunderstandingofthepropertiessothatthesenewmaterialscanbedesignedwiththedesiredproperties\builtin"totheirstructure.10Chapter2ThePhysicsofThermoelectricMaterialsandDevicesThermoelectricmaterialsaresubjecttothelawsofsolidstatephysics,andtheirbehaviorcanlargelybeunderstoodintermsofthreeprimarymaterialpropertiesgoverningtheirperformance:theSeebeckcot(S),theelectricalconductivity(˙),andthethermalconductivity().Whiletheunderlyingtheoryisfairlydeveloped,andcomputationalpowerandtechniqueshaveadvancedgreatlyoverthelastseveraldecades,thecomplexityofmanymaterialsstillmakestheoreticalpredictionsofpropertiesInparticular,thefactthatthermoelectricdevicesaremadefrompolycrystallinesamples,wheregrainsizeanddefectsarehardtopredicta-priori,alongwiththeoftenlargetemperaturegradientsalongthesamplemakesafullpredictionofZThighlyThischapterwillpresenttheunderlyingtransporttheory,inantogiveabetterunderstandingoftheimportantconceptsandparametersinvolvedinevaluatingthermoelectricmaterials,aswellastohelpbetterunderstandtheresultspresentedinfurtherchapters.112.1ThermoelectricDeviceFigure2.1:Schematicofathermoelectricunicouple.Ageneratorismadefromagroupofthesestackedelectricallyinseriesandthermallyinparallel.AsshowninFigure2.1athermoelectricgeneratorconsistsoftwolegs,onep-andonen-type,whichareconnectedthermallyinparallelandelectricallyinseries.Thehighertemperatureonthehotsidecauseschargecarrierstowdownthelegstowardsthecoldside,atwhichpointtheytravelalongelectricalconductorstodriveaload.If,insteadofdrivingaload,powerissuppliedtothegeneratorandcurrentforcedthroughtheunicouple,thedevicewouldactasaPeltiercoolerandchargeswouldliberateheatfromonesidewhilecarryingittotheother.WhilethebasicunicoupleshowninFigure2.1isadequatetogeneratepower,theresultingvoltagewouldbeverylow,typicallyontheorderof100sofmicrovolts.Connectingmanyunicouplesinseries,typicallyarrangedinagrid,allowsthedevicetobetothesizeoftheheatsourceandtodeliverthedesiredpower.12Thekeyconcernwithathermoelectricgeneratoristhe.Theisastheratiooftheoutputpowersuppliedtotheloadtothepowerinputatthehotside.Theoutputpowerissimply:Pout=I2RL(2.1)whereIisthecurrentandRListheloadresistance.ThecurrentcanbefoundsimplyusingOhm'slawandaccountingfortheresistanceofbothlegs,aswellastheloadandusingtheSeebeckcttocalculatethevoltage:I=VR=(SpSnTRp+Rn+RL(2.2)whereSpandSnaretheSeebeckcoientsoftheindividuallegs(nandpreferringtothecarriertypes)andsimilarly,RnandRparetheresistancesofthelegs.Theinputpowerismadeupofthreeterms:theheatinputfromanoutsidesource(apositiveinput),theheatcarriedawaybyconduction(negativebecauseitisaloss),andtheheatcarriedawaybyjouleheating(anotherloss).Radiativelosseswillbeneglectedhere.PSeebeck=(SpSn)ThI(2.3)PConduction=(Kn+KpT(2.4)PJoule=12I2(Rp+Rn)(2.5)Here,Thisthehotsidetemperature,Tisthetemperaturegradient,Kisthethermalconductanceoftheleg(porn)andRisagaintheresistanceofthelegortheloaditself(p,13n,orL).Combiningallthetermsgivestheas:=I2RL(SpSn)ThI(Kn+KpT12I2(Rp+Rn)(2.6)Next,newvariablesandsimplifying:Snp=(SpSn)(2.7)Knp=(Kn+Kp)(2.8)r=RLRn+Rp(2.9)=TThr1+r(Rp+Rn)KpnS2pn(1+r)2Th12TTh(2.10)Then,theofmerit,Z,as:Z=S2pnKpnRpn=S2pn(2.11)wecanwritetheasafunctionofZ,temperature,andr:=TThr1+r(1+r)2ThZT2Th(2.12)Finally,byoptimizingequation(2.12)withrespecttor,andsimplifyingfurthertheisgivenas:14=ThTcThp1+ZT1p1+ZT+Tc=Th(2.13)=carnotp1+ZT1p1+ZT+Tc=Th(2.14)whereTc,Th,andTrepresentthecoldside,hotside,andaveragetemperatureofthedevice.[69]ZhasunitsofK1,soitiscommontomultiplybyTtogetthedimensionlessofmerit,ZT,whichistypicallyexpressedforeachindividuallegofthegenerator:ZT=S2˙T(2.15)Itisalsocommontoisolatethenumerator,S2˙,whichiscalledthepowerfactor.Figure2.2:ofathermoelectricgeneratorasafunctionofZTandhotsidetem-perature.Thecoldsideissetat300K.AsZTtendstoitytheapproachestheCarnotlimit.AsshowninFigure2.2,asZTapproachesythesimplytendstowardstheCarnotlimit.Historically,ZTvaluesgreaterthanunityweretoachieve,givingamaximumofnear15%.ValuesofZThaveexceededtwoinsomerecentcases,15openingupthepossibilityofnearing25%.2.2ElectricalConductivityTheelectricalconductivityofamaterialisaproductofthenumberofavailablechargecarriers,themobilityofthosechargecarriers,andthechargetheycarry:˙=(2.16)wherenisthecarrierconcentration,typicallygiveninunitsofcm3,eisthefundamentalelectriccharge,andisthemobilityofthecarriers,typicallygiveninunitsofcm2V1s1.ThecarrierconcentrationcanbecalculatedusingFermi-Diracstatisticsandthedensityofstatesforthematerial.Here,wewillconsideronlyelectrons,howevertheequationsforholesareverysimilar.Withthatinformationonecanwritethat:n=Z10fn(E)D(E)dE(2.17)wheretheFermi-Diracdistributionanddensityofstatesforfreeelectronsinthreedi-mensionsare:[70]fn(E)=11+eEEFkbT(2.18)D(E)=p2m3=2h3ˇ2p2E(2.19)16wheremistheemassfortheconductionband,andtheenergyisrelativetotheconductionbandedge,Ec.Combiningequations(2.17),(2.18),and(2.19)yieldsthefollowingequations:n=m3=2h3ˇ2Z10p2E1+eEEFkbTdE(2.20)n=Nc2pˇF1=2EFkbT=Nc2pˇF1=2()(2.21)Nc=22ˇmkbTh23=2(2.22)wherekbistheBoltzmannconstant,histhePlanckconstant,Ncistheedensityofstatesatthebandedge,andF1=2()istheFermi-Diracintegral,andEfkbT.Theresultforholesissimilar.Theemasswillrefertoeithertheconductionorvalenceband,dependingonwhetheritpertainstoholesorelectrons.ShowninFigure2.3isthecarrierconcentration(incm3)asafunctionofthereducedFermienergy,,assuminganemassequaltothefreeelectronmass.17Figure2.3:Carrierconcentration(n)incm3asafunctionofreducedFermienergy(EfkbT)calculatedfromequation(2.21).=0refersthetheconductionbandedge.Theemass(m)istakentobethefreeelectronmasshere.Atthispoint,furtherassumptionsaboutthematerialmustbemadetoelucidateinfor-mationfromthecarrierconcentrationequation.IftheassumptionismadethattheFermienergyisseveralfactorsofkbTintothegapfromthebandedge(thatisthesemicon-ductoris"non-degenerate"),thentheFermidistributioncanbeandthecarrierconcentrationcanberewrittenas:nˇm3=2h3ˇ2e(EcEf)kbTZ1Ece(EEc)kbTp2EdE(2.23)Thelawofmassactionstatesthattheproductoftheelectronandholecarrierconcen-trationsareandequaltotheintrinsicconcentrationsquared(np=ni2).[70,71,72]MultiplyingtheequationsfornandpandassumingthatonlyenergieswithinafewkbTofthebandedgecontributetotheintegralabove(duetotheexponentialfactorinthe18integrand)onecangetanexpressionfortheintrinsiccarrierconcentration:ni(T)=pNcNveEg=2kbT(2.24)ni/m3=2T3=2eEg2kbT(2.25)And,forintrinsicsemiconductorstheFermienergycanbeexpressedas:[70]Ef;int=Ev+12Eg+34kbTlnmvmc(2.26)Equation(2.24)showsthatforanintrinsicsemiconductorthecarrierconcentrationisgovernedprimarilybythebandgapofthematerialandthetemperature.Thisisbecauseintrinsicsemiconductorsonlyhavecarriersifanelectronisexcitedacrossthegap,movingintotheconductionbandandleavingbehindaholeinthevalenceband.Equation(2.26)showsthatforanintrinsicsemiconductorwithmv=mctheFermilevelliesinthemiddleofthegap.IfthemassesarenotequaltheFermilevelispulledtowardsthelighterband,howeverformostmaterialstheratioofmasseswillbenearunity,andassuchtheFermilevelwillonlybeafewkbTfromcenter.Evenincaseswithlargemassthechangeistypicallysmall,forexample,InPhasaband-gapof1.35eV,anevalencebandmassof0.64m0andconductionbandmassof0.077m0at300K.[72]Evenwiththelargemassat300KtheFermienergyhasmoveduptowardstheconductionbandbyonly41meV.Oneofthemostusefulfeaturesofsemiconductorsistheabilitytodopethembyinten-tionallysubstitutingimpurityatomsintothecrystalstructure.Byreplacingoneatomina19compoundwithanotherelementwhichhasavalencehigherorlowerthenumberofcarrierscanbeadjusted,e.g.replacingsilicon(fourvalenceelectrons)withphosphorusevalenceelectrons)willaddelectronstothesystem,whilereplacingsiliconwithboron(threevalenceelectrons)willremoveelectrons(i.eaddholes).Atomswhichaddelectrons(n-typedopants)areknownasdonors(becausetheydonateelectrons)whileatomsthatremoveelectrons(p-typedopants)arecalledacceptors(becausetheywillacceptanotherelectron).Becausechargeneutralitymustbemaintainedinthecrystal,forthecaseofn-typedopingthenumberofelectronsintheconductionbandwillnowequalthenumberofholesinthevalenceband(n=pinanintrinsicsemiconductor)plusthenumberofionizeddonoratoms.Atlowtemperatures,thedonorimpurityatomsarenotfullyexcited,andthematerialissaidtobe\frozenout",withanelectroncarrierconcentrationgivenas:nˇrNDNc2eEd=2kbTifND˛12NceEd=kbT˛NA(2.27)whereNcisgivenbyequation(2.22)andEdisasEcED,theenergybetweentheconductionbandandtheenergylevelofthedonoratom.However,onceallofthedonorandacceptoratomsareexcited,thecarrierconcentrationinann-typematerialis:[72]n=12(NDNA)+q(NDNA)2+4n2i(2.28)ˇNDifND˛NAandjNDNAj˛Ni(2.29)20Athighenoughtemperaturesthethermalexcitationscauseintrinsiccarrierstoagainbe-comethedominantcarrier.Thetemperatureatwhichthistransitionoccursdependsonthematerialandthedopinglevel.Thereforeinadopedsemiconductorthecarrierconcentrationinitiallyincreaseswithtemperatureasthedopantatomsbecomeionizedandactive,thenasaturationwillbereachedonceallofthedopantsareactivatedandthecarrierconcentrationbecomestemperatureindependent,andathighenoughtemperaturestheintrinsiccarriersbecomeexcitedacrossthegapandthecarrierconcentrationagainincreaseswithtemperature.Figure2.4:Carrierconcentrationasafunctionofinversetemperatureforadopedsemicon-ductor,showingthefreezeoutregionatlowtemperature,thesaturationregion,andthehightemperatureregionwhenintrinsiccarriersdominate.Itshouldbenotedthatfora\pure"intrinsicsemiconductortheequationsaboveyieldaroomtemperaturecarrierconcentrationontheorderof1010cm3.Whilethepreviousequationsdescribethenatureofthecarrierconcentration,themobilityisalsoneededtocalculatetheelectricalconductivity,asshowninequation(2.16).The21mobilitycanbewrittenintermsofthectivemassandtheaveragescatteringtimeofthecarrier:=e˝m(2.30)wheremisagaintheeemass,and˝istheaveragescatteringtime.Matthiessen'srulestatesthatscatteringrates(orthemobility)fortprocessescanbeadded:1˝=1˝impurities+1˝lattice+1˝defects+:::(2.31)1=1impurities+1lattice+1defects+:::(2.32)Fortheworkhere,typicallythetwodominantscatteringmechanismswereionizedim-purityscattering(electronsorholesscatteringfromtheionizedatomsusedtodopethematerial)andlatticescattering(chargecarriersbeingscatteredbyphonons).Ifthemobilityisduetoionizedimpurityscattering,thenthemoreenergythechargecarrierhas(e.g.thefastertheelectronismoving)thelesslikelyitisthatitwillbescatteredbyionizedatoms.And,asmoreimpuritiesareadded(NI)thescatteringwillbemoreprevalentandmobilitywilldecrease.Calculationsandexperimentsshowthatthemobilityfromionizedimpuritiesis:[72,73]i/m1=2NI1T3=2(2.33)Latticescatteringisdueprimarilytoacousticphononsinteractingwithandscatteringchargecarriers.Asthetemperatureofthematerialincreasestherewillbemoreandmore22excitedphonons,andassuchthemobilitywouldbeexpectedtodecrease.Thisisinfactwhatisseenexperimentally,andthemobility,whengovernedbyphononscattering,canbeexpressedas:[74]l/m5=2T3=2(2.34)Equations(2.33)and(2.34)combinedshowthatatsometemperaturethemobilitywillhaveamaximumafterwhichitwilldecreasewithincreasingtemperature,howeveritwilldecreaseasapowerlawwhilethecarrierconcentrationisconstant(inthesaturationregion)orincreasingexponentially(intheintrinsicregion).Thiswouldindicatetheelectricalcon-ductivitymayhaveahumpinthesaturationregionasthemobilityisrising,followedbyadipasmobilitydecreaseswhilestillinthesaturationregion,andwillthenincreaseexponen-tiallyastheintrinsiccarrierconcentrationrisesfasterthanthemobilityfalls.However,thisdependsonwherethemobilitypeaksandwherethesaturationregionisforamaterial.Athightemperatures,asasemiconductorenterstheintrinsicregionthecarrierconcentra-tionwillbelargeenoughsuchthatelectron-electronscatteringbecomesanotherimportantscatteringmechanism.Thusthemobilitywilldecreaseenoughtobalancetheintrinsiccarrierexcitationandtheelectricalconductivitywilldecreasewithtemperature,showingmetallicbehavior.Forheavilydoped,alsocalleddegenerate,semiconductorstheelectricalconductivitydisplaysttrends.Typically,asemiconductorisasdegeneratewhentheFermileveliswithin1-2kbTofthebandedge(forn-type,theFermilevelisjustbelowtheconductionband,forp-typejustabovethevalenceband).[72,71]Whenthisoccurs,theelectricalconductivityresemblesthatofametalmorethanasemiconductor,asisshown23belowinFigure2.5.Withthehighcarrierconcentrationelectron-electronscatteringisveryimportant,andtheelectricalconductivitydecreaseswithtemperature.Figure2.5:ElectricalconductivityofCuInTe2andCuIn0.99Zn0.01Te2versustemperature.Asshown,thedopedsamplehasmetallicbehavior,withtheelectricalconductivitydroppingwithincreasingtemperature.Athighenoughtemperatures,bothsamplesbecomeintrinsic.ShownaboveinFigure2.5isthemeasuredelectricalconductivityforCuInTe2andCuIn0.99Zn0.01Te2.Forthenominallyundopedsampletheconductivityinitiallyrises,ascarriersbecomeexcited,theninasaturationregion,andthenagainincreasesasintrinsiccarriersbecomeexcitedathightemperature.Then,near750Ktheelectricalcon-ductivitypeaksandbeginstofallasthecarrierconcentrationforbothsamplesbecomesintrinsicandcarrier-phononscatteringincreasesandlowersthemobility.Ontheotherhand,thesamplewhichisdopedwithzincshowsasteadydeclineasafunctionoftempera-tureuntilnear750K,whereagain,thesampleenterstheintrinsicregionandcarrier-phononscattingbeginstodrasticallylowerthemobility.Thisalsoshowsthatevenforheavilydopedsemiconductorswithalargesaturationregion,eventuallytheintrinsicregionwillbereached,andtheelectricalconductivitywillbecomparabletothatofanundopedsample.242.3TheSeebeckCotTheSeebeckcot(alsocalledthethermopower)ofamaterialisanotherkeyther-moelectrictransportproperty.Asstatedintheintroduction,theSeebeckcotcanbewrittensimplyastheratioofthevoltagealongasampleandthetemperaturegradientwhichproducedit:S=VT=(VHotVCold)(THotTCold)(2.35)Figure2.6:DiagramoftheSeebeckctinann-typematerial.Thehotelectronswfromtheleftsideandaccumulateontherightside,inducinganelectricandaresultantpotentialFirst,tounderstandthenegativesigninequation(2.35),consideranelectricallyisolatedbarwithoneendheldatTHotwhiletheothersideisheldatalowertemperature,TCold.Theendwhichishotterwillhavemoreenergeticcarriers,andthosecarrierswillddowntothecoldendcreatingachargeimbalanceacrossthebar.Thisbuildupofchargeonthecoldsidewillinduceanelectricandasaresultthecoldsidewilleitherhavealowerpotentialthanthehotsideifthechargecarriersareelectrons,orwillhaveahigherpotentialthanthecoldsideifthecarriersareholes.Thenetresultisthatequation(2.35)willyield25anegativeSeebeckcotforann-typematerial,andapositiveSeebeckequationforap-typematerial.TheSeebeckcotcanbederivedusingBoltzmanntransporttheoryandconsideringonlysmallperturbations.Consideringaparabolicbandalsotheprocess,astheemasscanbegivenasinglevalue,ratherthanworkingwithatensorversion.UsingtheBoltzmanntransportequation,onecanshowthattheelectriccurrentinamaterialwithatemperaturegradientisgivenby:[71]Je=e3ˇ2mZ10k3@f0@k˝(k)EEfTrT+r(Efe˚)dk(2.36)wheref0istheequilibriumFermidistribution,˝istherelaxationtime,and(Efe˚)isthecombinedchemicalandelectrostaticpotentialenergy.Byassumingaparabolicbandstructure(e.g.E=h2k22m)tochangeintegrationvariables,andsettingthecurrentequaltozero(steadystateopencircuitconditions)equation(2.36)canbere-writtenas:0=Z10E3=2@f0@E˝(E)EEfTrT+r(Efe˚)dE(2.37)=rTTZ10E5=2˝(E)@f0@EdEEfrTTZ10E3=2˝(E)@f0@EdE(2.38)+r(Efe˚)Z10E3=2˝(E)@f0@EdE(2.39)Then,theSeebeckcotastheratiooftheelectric(fromthepotential)tothetemperaturegradient,andswitchingtheintegrationvariabletoscaledenergy(=26E/kbT,=Ef=kbT):[71]S=r(˚Efe)rT(2.40)=kbe24R105=2˝()@f0@R103=2˝()@f0@35(2.41)Byassumingasimpleenergydependentrelaxationtime,˝(E)/E,equation(2.41)canbewritteninaformclosetothatoftheFermi-Diracintegralsfoundinthecarrierconcentration:S=kbe24R105=2+@f0@R103=2+@f0@35(2.42)AnditcanbeshownthatinfacthisreducestoarelationinvolvingtheFermi-Diracintegrals(seereference[71],appendix5):S=kbe"(52+)F3=2+()(32+)F1=2+()#(2.43)whereis3/2ifionizedimpurityscatteringisthedominantmechanism,and-1/2whenacousticphononscatteringisthedominantmechanism.IftheclassicalBoltzmannstatisticswereused,ratherthanFermi-Dirac,theresultingequationwouldinsteadbesimplylinearin:Sclassical=kbe((5=2+))(2.44)27Figure2.7showsequations(2.43)and(2.44)plottedasafunctionofthereducedFermienergy,assuming=-1/2,showingthatwhilethecarrierconcentrationincreaseswith(Figure2.3),theSeebeckcotdecreases,oneofthecontraindicatedparametersfoundinthermoelectrics.Figure2.7:Seebeckcot(S)inµVK1asafunctionofreducedFermienergy(EfkbT)calculatedfromequations(2.43)and(2.44),assuming=-1/2.Bycombiningequations(2.21)and(2.43)onecancalculateatheoreticalvalueforS2nasafunctionofthereducedFermienergy.Again,assumingscatteringisdominatedbythelattice(typicallytrueathightemperatures)sothat=-1/2:S2n=2pˇkb2e2NcF1=2()2F1()F0()2(2.45)=4pˇkb2e22ˇmkbTh23=2F1=2()2F1()F0()2(2.46)28Figure2.8:S2ne*106inµWVscm3K2asafunctionofreducedFermienergy(EfkbT)calculatedfromequation(2.45),usinganemassof1meandatemperatureof800K.AsFigure2.8shows,forthemaximumvalueofS2netheFermilevelshouldbeslightlyabove(orbelowforp-type)thebandedgewithavalueofnearunity.IntheS2nhasbeenmultipliedbyeaswell,sothattheplotreallyshowsthepowerfactordividedbythemobility.AlargeremasswillincreasetheproductS2n,however,themobilityvariesinverselyasthemass,andincreasingtheemasswilllower.Thisisanotherexampleofacontraindicatedparameters,whereoptimizingonepropertyresultsinhinderinganother.Forahighlydegeneratesemiconductor,ifoneassumesaparabolicbanditcanalsobeshownthattheSeebeckcotcomesoutas:[75]S=8ˇ2k2b3eh2mTˇ3n2=3(2.47)ThisrelationshipisoftencalledthePisarenkorelationship,andjustaswasshowninFig-29ure2.8itshowsagainthatincreasingtheFermienergy,andthereforethecarrierconcentra-tion,isdetrimentaltotheSeebeckcot.Italsorevealsthattheemassplaysarole,andalargeemassincreasesS.However,againtheelectricalconductivitydependsinverselyontheemassshowingthecontraindicatedparameters.2.3.1BandtheoryoftransportTheprevioustheoryontheSeebeckcotdealtprimarilywiththe\free-electron"modeloftransport.However,modernsemiconductortheoryisbasedheavilyonthebandtheory,whichalsohelpfulinsightintothenatureofelectronictransport.Thebasisofthebandtheoryofelectronlevelsisthatduetotheperiodicpotentialfoundincrystals,theeigen-statesforasingleelectronHamiltoniancanbeexpressedas:(Bloch'sTheorem)[70] nk(r)=eikrunk(r)(2.48)whereunk(r)isperiodicintheBravaislatticevectorR.Thisinturnmeansthattheeigen-statescanbeexpressedas: nk(r+R)=eikR nk(r)(2.49)ByrestrictingktotheBrillouinzone,allowedduetotheperiodicityink,onecanexpressthesolutionstotheHamiltonianintermsofafamilyofenergieswhichdependonn,thebandnumber,andk,thewavevector,whichyieldstheband-structureofthematerial.Thisinturnleadstoanexpressionforthedensityofavailableenergylevels:30Dn(E)=ZSn(E)dS4ˇ31jrEn(k)j(2.50)wheretheintegraliscarriedoutoverthesurfaceofconstantenergy,Sn(k).Inequation(2.17)itwasshownhowtheelectricalresistivitydependeddirectlyonthedensityofstates,alongwiththeFermi-distribution.However,equation(2.41)didnotshowanyexplicitdependenceintheSeebeckcotonthedensityofstates.TheMottequationexpressestheSeebeckcotas:[76]S=ˇ23kbekbTd(ln(˙(E))dEE=Ef(2.51)which,with˙=andn/D(E),showstheconnectionbetweenSandthedensityofstates,D(E).Thisdependencecanalsobeseeninequation(2.47)intheemassterm.Theemass(m)isinbandtheoryas:1m=1h2@2E@k2(2.52)m=h21@2E@k2(2.53)whichmeansthatforalargeSeebeckcot,amaterialshouldpossessalargeivemass,andthereforasecondderivate,orinotherwordsaband.Aenergybandwouldinturnmeanalargederivativeinthedensityofstates.SofromthisanalysiswethatforalargeSeebeckcot,alargevaluefor@D(E)@Eisdesired.Thisisagainanexampleofcontraindicatedparameters,asexpressingase˝=mintheequationforelectricalconductivityshowsthatasmalleemassisdesirableforincreasingelectricalconductivity.31Therearetwomainpossibilitiesforalargeeoccurinamaterial.First,theelectronicbandstructurecouldsimplycontainverybands,suchasthosefoundwhenf-shellelectronsareinvolved.Thesecondpossibilityisthatofoverlappingbands,whichcouldbeacombinationoflightorheavybands,howeverwhenoverlappingthedensityofstateswouldbeincreasedregardless.ThiscaseisfoundinPbTe,whereathightemperaturesitissuspectedthatasecond\heavyhole"valencebandmovesuptoalignwiththe\lighthole"valenceband,givinganincreaseinthedensityofstates,andapossibleexplanationforthelargeSeebeckcot(250µVK1)whilealsopossessingaverylowelectricalresistivity(4cm).[77]Thus,bandtheoryshowsthatsharplyincreasingdensityofstatesisdesirableforalargeSeebeckcot,andtomaintainalowelectricalresistivityitismoredesirabletohavealargeamountofbandoverlap,ordegeneracy,ratherthansimplyoneverybandattheFermilevel.Thisdesireforahighdegeneracycanbeachievedbycrystalstructureswithhighsymmetry,howeveraswillbeshowninthefollowingsection,thishighsymmetrycanbeundesirableforachievingalowthermalconductivity.2.4ThermalConductivityThethermalconductivityisamaterialpropertywhichquaneshowwellittransportsheat.Insemiconductors,therearetwoprimarymethodsoftransportingheat:viathechargecarriers(electronsorholes),andviathemovementoftheactualatomsorlattice,intheformofquantizedvibrationscalledphonons.Thus,thethermalconductivitycanbesplitintotwoparts,efortheelectroniccomponentandLforthelatticeportion.Theelectronicportionofthethermalconductivityisdirectlyrelatedtotheelectrical32conductivitythroughtheWiedemann-Franzlaw,whichstatesthat:[78]e˙=LT(2.54)whereListheLorenznumber,whichcanvary,butwillbetakeninthisworktobeequaltothefreeelectronvalue:L0=ˇ23kbe2(2.55)L0=2:44108WK2(2.56)Again,fromtheequationforZT,theelectronicthermalconductivityandtheelectricalconductivityarecontraindicatedparameters,asincreasingtheelectricalconductivityinanattempttoincreaseZTwillalsoincreasethermalconductivity,therebyhavingnoofpossiblyevenloweringZT.Forthematerialsstudiedinthiswork,typicallytheelectronicportionofthethermalconductivityislessthan10%ofthetotalthermalconductivityatroomtemperature.Thethermalconductivityshowninplotswillalwaysbethetotal(electronicandlattice)unlessotherwisestated.Thelatticeportionofthethermalconductivitydependsonseveralpropertiesofama-terial,andcanbederivedfromtheBoltzmanntransportequationsimilarlytotheSeebeckcot,butnowappliedtophonons.Startingwiththeequationforphononheatwthroughamaterial:h=XN(kh!(k)v(k)(2.57)whereN(k)isthenumberofphononswithmomentumk,h!(k)istheenergyofthe33phonon,andvisthegroupvelocity.Thethermalconductivityisthentheheatwdividedbythetemperaturegradient:=hT=1TXN(kh!(k)v(k)(2.58)Usingtherelaxationtimeapproximation,@N@T=N0N˝,andassumingthedeviationinthephononpopulationfromequilibriumissmallsuchthat@N@Tˇ@N0@TtheBoltzmanntransportequationyields:[79]=13Z!max0h!v2˝@N0@Tf(!)d!(2.59)wheref(!)isthephonondensityofstatesand˝istherelaxationtime.TheDebyemodelfurtherassumesalineardispersioncurve(!(k)=vk)andallowsmoreofequation(2.59).Thelatticethermalconductivitycanthenbewritten(withx=h!=kbT)as:[79]=kb2ˇ2vkbh3T3ZD=T0˝(x)x4ex(ex1)2dx(2.60)=13v2ZD=T0˝(x)C(x)dx(2.61)=13vZD=T0l(x)C(x)dx(2.62)where˝(x)istherelaxationtime,l(x)isthemeanfreepath(l=v˝),DistheDebye34temperatureofthematerial,andC(x)istheditialheatcapacity:C(x)=3kb2ˇ2v3kbh3T3x4ex(ex1)2(2.63)C=ZD=T0C(x)dx=3kb2ˇ2v3kbh3T3ZD=T0x4ex(ex1)2dx(2.64)Equation(2.62)issimilartothesimpleequationoftengivenforthermalconductivity:=13cvl,butnowinanintegralformtoaccountforchangesinspecheatandmeanfreepathwithtemperatureandphononfrequency.[70]Fromhere,theexplanationofthethermalconductivitytemperaturedependencecanbelookedatfromtwopieces,intermsofthespheat,andsecondintermsoftherelaxationtime,˝.Forthespheat,atlowtemperaturesD/Tislargeandtheupperlimitontheinte-gralinequation(2.64)canbetakentoytoyieldthetypicalresultofaT3dependence.Athightemperatures,D/TissmallandtheintegrandcanbeTaylorexpandedtoyieldthecommonresultofaconstantheatcapacityathightemperatures,theDulong-Petitlaw.C/TD3T˝D(2.65)C=ConstantT˛D(2.66)Therelaxationtimeismorecomplicatedthanthespheat,anddependsnotonlyoncompositionandcrystalstructure,butalsoonthesamplesize,shape,andpurity.Themaincontributionstobeconsideredhereare:boundaryscattering,impurityscattering,andUmklappscattering.35Boundaryscatteringsimplydependsonthesizeofthesampleitself,andtypicallyisonlyimportantatlowtemperaturesbecauseatlowtemperaturethemajorityofphononsarelongwavelengthphonons.[70,79,80]Reducingthegrainsize(bymillingandsinteringwithvarioustechniquesforexample)hasasimilarandcanbethoughtofasreducingthemeanfreepathdownfromthecrystallitesize(atverylowtemperatures)tothatoftheaveragegrainsize.Impurityscatteringcancomefromseveraltypesofimpurities.PredictionsbyPomer-anchuk,andlaterworkbySlackstudyingSi,Ge,andKClatlowtemperaturesshowedthatisotopes,duetotheirtmass,playedaveryimportantroleinscatteringphonons,andlimitedthethermalconductivity.[81,82]Workwithneutronirradiationondiamondsshowedthatvacanciesinthelatticecouldalsoplayaveryimportantroleinreducingthermalconductivityandshiftingthepeakintowardshighertemperatures.[83]Relatedtothat,massmis-matchscatteringiscausedwhenanatomicsiteisoccupiedbyatelementwithadimass.EarlyworkbyRayleighonsoundwavescatteringbyanobstructionfoundthecrosssectionforscatteringwasinverselyproportionaltothewavelengthofsoundtothefourthpower.[84]Extendingthetheorytophononsinalatticeleadstothefollowingscatteringrate:1˝(!)=cpa3!44ˇv3MM2(2.67)wherecpistheratioofdefectstolatticesitespervolumeanda3isthevolumeperatom.MuchlaterKlemens,usingperturbationtheory,gotthesameresult,andshowedthatthethermalresistanceduetoamasswas:[85]36Wm=12ˇ2TVB0:897hv2MM2(2.68)whereVisunitcellvolumeandBisaconstantwhichhegivesas1/12.Thekeyfeatureisthatthethermalresistanceisquadraticinthemassofthetwoelements.Solidsolutionformationhasbeenusedheavilyinthermoelectrics,mostnotablyinSi-GeandPbTe-PbSe,thoughitisacommonpracticenowinthestudyofanythermoelectricmaterial.Scatteringcanalsooccurduetodislocationsandothercrystaldefectswhichwillnotbediscussedhereindetail,butdetailscanbefoundinworkbySlack.[86]Finally,Umklappscatteringisathree(ormore)phononprocessbywhichtwophononswithmomentum!q1and!q2combinetoformaresultingphononwithmomentum!q3whosevectorisoutsideofthe1stBrillouinzone,asdiagrammedinFigure2.9.Whenthishappens,bysubtractingalatticeconstantvectorfromtheresultingvectortobringitbackintothe1stBrillouinzonetheresultingvectorpointsawayfromtheinitialtwo.37Figure2.9:SchematicdiagrammingUmklappScattering.Phononsq1andq2combinetoformphononq3whichliesoutsidethe1stBrillouinzoneandissubsequentlyfoldedbackintothe1stBZ.ForlowtemperaturesSlackstatesthatthescatteringduetoUmklappgivesatemperaturedependenceof:[86]U/TeD=2Tfor10T<D(2.69)Athightemperatureshowever,thetemperaturedependenceislessclear.Thephononpopulationbeginstogrowexponentially,andthiscausesanincreaseinphonon-phononUmklappscatteringprocesses,whichcausesastrongdecreaseinthethermalconductivity.AthightemperaturetheoverallthermalconductivityistypicallyproportionaltoT1,duetoacombinationofallthescatteringmechanisms.[86,87,79]AnexcellentoverviewofthevariousscatteringmethodsisgivenbyGlassbrennerandSlackintheirstudyofsiliconandgermanium.[88]38AusefulguidefortheselectionofamaterialbasedonthethermalconductivitycomesfromworkbySlack,whichgivestheexpressionforthelatticethermalconductivityabovetheDebyetemperatureas:[89,90,91]=AM3d2Tn2=3(2.70)whereAisaconstant,Mistheaverageatomicmass,3isthevolumeperatom,istheGruneisenparameter,andnisthenumberofatomsperunitcell.Thisgivesaguideforselectingamaterialwithlowthermalconductivity.Itshowsthatforlowintrinsicthermalconductivity,amaterialshouldhavealargeGruneisenparameter,manyatomsperunitcell,andalowDebyetemperature.Whiletheequationappearstobelinearintheaverageatomicmass,itshouldbenotedthattheDebyetemperaturevariesinverselywiththeatomicmass,andthereforeaheaviermassisactuallydesiredforlowthermalconductivity.2.5MotivationforChalcopyriteCompoundsCombiningequations(2.16),(2.47),and(2.70)cangivesomeguidancetoselectingamaterialwithapotentialhighZT.Thethreecombinedshow:ZT/m22M3D(2.71)whichmeansforahighZTamaterialneedsasmallDebyetemperature(andthereforalargeaverageatomicmass)andalowvolumeperatom.ItshouldalsopossessalargeGruneisenparameter,whichisrelatedtotheanharmonicityofthelatticeandtothether-malexpansion.Themorechallengingcombinationcomesintheelectricalpropertieswhich39requirealargeemassbutalsoalargemobilitywhicharetypicallyinverselyrelated.WorkinthisstudywascarriedoutonthecopperbasedcompoundsoftheI-III-VI2chalcopyritefamily.Thecopperbasedcompoundswerestudiedinparticulartoavoidtheissuesofhighcostinvolvedintheotheroptions(silverandgold).Thechalcopyritefamilyofsemiconductorscomeintwovariants,II-IV-V2andI-III-VI2.ThesecompoundscanbethoughtofasanaturalextensionoftheIII-VandII-VIsemiconductors,whichareinturncanbethoughtofasderivedfromtheclassicelementarysemiconductors,siliconandgermanium.Figure2.10:CrystalstructuresofSi,ZnSe,Zn2Se2,andCuGaSe2fromlefttoright.AthightemperaturestheorderinginCuGaSe2breaksdown,andthecrystalcanbereducedbacktoacubicstructurewithCuandGaatomsoccupyingsitesinterchangeably,aswillbeshowninlaterchapters.Startingfromsilicon(orgermanium),whichformsinthediamondstructure,andre-placingonehalfoftheatomicsiteswithanelementtotheleftontheperiodictable,andonehalfwithanelementtorightonthetableleadstothefamilyknownasIII-Vsemicon-ductors,forexampleGaAs.MovinganotherrowleftandrightgivestheII-VIcompounds,suchasZnSe,asisshowninFigure2.10.BydoublingtheunitcellofaII-VI(orIII-V)unitcelltoform,e.g.Zn2Se2,thesamemethodologycanbeperformedonthecation,togiveaternarycompound.Forexample,startingfromII2-VI2andsplittingthegroupII40elementproducestheI-III-VI2family.ThesamethoughtexperimentcanbedoneonIII-VcompoundstoarriveattheII-IV-V2chalcopyritecompounds.Eachtimethisdoublingandreplacingtechniqueisused,anaverageoffourvalenceelectronsperatomismaintained,andinmostcasesthecompoundremainsinadiamond-likeform.[14]RecentlythisconcepthasbeencarriedonestepfurtherfromtheI-III-VI2tostudythekersteritestructure,whichhastheformI2-II-IV-VI4,e.g.Cu2ZnSnS4(alsoknownasCZTS).Thisprocessleadstoaninterestingfamilyofmaterialsformultiplereasons.First,itgivesseveraloptionsforn-andp-typedopantatoms(I-III-VI2couldbedopedwithagroupII,IV,V,orVIImaterialforinstance).Second,thelargerstructurehastwiceasmanyatomsperunitcellasthecubicII-VIcompounds,givingalowerthermalconductivity.Threeatomicsitesprovidesseveraloptionsforsolidsolutionstolowerthermalconductivityfurther.Thereportedbandgapsrangefrom0.5eVupto3.49eVforthefamily,awideabilitytotunetheelectronicpropertiesandstudytheunderlyingphysics.[92]Figure2.11:ElectronicbandstructuresofCuGaTe2(ontheleft)andofCuGaS2(ontheright)showingtherelativelyvalencebands,whichindicateahighemass.[2,3]41ShowninFigure2.11,thebandstructuresforCuGaS2andCuGaTe2(aswellasmanyotherchalcopyritecompounds)displayrelativelyvalencebandswithseveraloverlapping,ordegeneratebands.Theatbandsindicatealargeemass,whichisbfortheSeebeckcot,asistheoverlappingbandsnearthevalenceedge.Allofthesefactorsleadtoacomplexandwidelyvariedfamilyofsemiconductors,whichshowpromiseforuseinthermoelectrics,solarcells,andmanyothersemiconductorapplications.Interestingly,whilechalcopyritecompoundshaveundergonetdevelopmentasphoto-voltaicmaterials,withsomeproductsalreadyonthemarket,therehasbeenmuchlessresearchandworkdoneontheirthermoelectricproperties,andthisprovidesthemotivationforthepresentstudy.42Chapter3ExperimentalProcedures3.1MaterialsSynthesisSamplesynthesisbeganbyweighingoutstoichiometricamountsofeachelementandplacingthemintoaquartzampoule.TheelementswerepurchasedeitherfromAlfa-AeasarorSigma-Aldritch,dependingonavailabilityandpurity.Typicalelementswereaminimumpuritylevelof99.99%.Theampouleswerethenplacedintoasealingstationandevacuatedtoapressurelessthan1105torr,andweresealedwithanoxygen-methanetorch.43Figure3.1:Stepsinmaterialsynthesis.Fromlefttoright,elementsweighedoutinampoule,ampoulebeingsealed,andtheresultingingotafterthefurnaceprocedure.3.1.1FurnaceHeatingProcedureThetelluriumbasedsampleswereheatedat1.0Cmin1toanultimatetemperatureof900C,atwhichpointtheywereheldfor24hourstoallowfullmixing.After24hoursthesampleswerewaterquenched,andplacedbackintothefurnaceat600Ctoannealfor24hours.Theselenidesamplesweremadeinthesamemanner,excepttheinitialheatingratewasloweredto0.4Cmin1toaccountforthevolatilityofseleniumandconcernsoverthevaporpressurecausingtheampouletorupture.FortheheatingprocedureeitheraThermolyneF21100tubefurnaceoraThermoFisherBF51800boxfurnacewasused.Thesampleswerealsoheatedat0.4Cmin1to900C,howeveraftersoakingfor24hourstheywerecooledat1.0Cmin1to300Candannealedatthattemperaturefor24hoursbeforequenching.Quenchingesamplesfromhightemperatureoftenledtocrackedampoulessoachangewasmadetoslowcoolingto300C.Theannealingstepwas44requiredonallsamplestoincorporateanymaterialdepositedontheampoulewallduringquenching.Whileinprinciplethethermoelectriccharacterizationcouldbeperformeddirectlyontheingots,thiswasnotdonebecausemanyoftheingotsobtainedwereporousandbrittle.Toovercomethisissue,anadditionalpowderprocessingandconsolidationprocedurewascarriedoutinordertoprovidedense,crackfree,smallgrainsizesamplessuitableforcuttingandmeasuring.Tocarryoutthisstep,theresultingingotwasthenremovedfromtheampouleandgroundusingamortarandpestletoobtainapowder.Thepurityofthepowderwascheckedwithx-rayThepowderwasthenplacedintoastainlesssteelballmilljar,sealedunderanargonatmosphereandwrappedwithPandmilledforsixtyminutesintwothirtyminuteincrements.ASPEXMixerMill8000DoraMixerMill8000Mwasusedforthemillingprocess.ThepowderwasagaincheckedwithXRD,andthenplacedintoagraphitedietobesintered.Sinteringwasperformedeitherviahotpressing,orbysparkplasmasintering.3.1.2SinteringProceduresInitialsamplesinthestudyweresinteredbyhotpressing.Thesamplepowderwasplacedina10mmdiametergraphitedie,withstainlesssteelplungersplacedinbothendsandgraphitefoilspacersbetweenthepowderandplungers.Thediewasthenplacedintoauniaxialpressandsurroundedbyaheater.Thesamplepowderwasheatedto475Cunder90MPaofpressureandheldfor15minutesbeforebeingallowedtocool.Thisprocedurewasperformedentirelyinanargongloveboxtopreventanyoxidation.Finalsamplessynthesizedwiththehotpresshaddensitiesgreaterthan90%theoreticaldensity.45LaterinthestudysamplesweresinteredusingthenewlyacquiredDr.Sinterspark-plasma-sinter211LX(SPS).Inthatprocess,thesamplepowderwasagainloadedintoa10mmdiametergraphitedie,withgraphitefoilspacersplacedbetweenthepowderandgraphiteplungers.Thiswasthenplacedintoauniaxialpress,whereitwasplacedunder40MPaofpressure,andheatedat100Cmin1tothedesiredtemperature,heldfor10minutes,andthenallowedtocool.TheprimaryintheSPSversusthehotpressisthatheatingintheSPSwasperformedbypassingacurrentthroughthedieitself.TheramsontheSPSwerewatercooled,andtypicallythesamplewouldreachroomtemperatureinunder15minutes,muchfasterthanthehotpresswhichhadnoactivecooling.Finalsamplesweresandedtoremovethegraphitefoilanddicedonadiamondsaw.SPSsamplestypicallyhadhigherdensitythansamplesinthehotpress,withvaluestypicallygreaterthan95%theoreticaldensity.3.2CharacterizationTechniques3.2.1X-rayX-ray(XRD)wasperformedonaRigakuIusingCu-Kradiationasasourcewith=1.54A.Whencalculatinglatticeparameters,toadjustforanycausedbyvarianceintheheightofthepowderontheXRDslide,thesamplewasscannedtwice,oncealone,andoncewiththeadditionofhighpuritysilicon.Usingtheknownsiliconpeaksonecanshifttheoverallpatterntoaccountforinthescanningplaneofthesample.Afterthis,peakswereusingtheJade9softwarepackage,andcomparedtopreviouslyreportedpatternsinthePDFdatabase.Usingthepeaks,d-spacingvalueswerethentoextractthelatticeparameters(aandc)usingthefollowingequation,where46h,k,andlarethemillerindicesofcrystallographiclatticeplane:1d2hkl=h2+k2a2+l2c2(3.1)Itshouldbenotedthatmanypatternsexhibitdoubletpeaks.Forthechalcopyritecompoundsstudiedinthiswork,manyhaveana:cratioofverynear1:2,whichleadstodegeneracyinpeaks.Forexample,the106andthe302peakshavetheexactsamed-spacingwhenc=2a,howeverifc=1.98athepeakswillsplitandappearasadoublet.ShayandWernickfoundadirectcorrelationbetweenthedevianceinthec:arationandthevalueofthecrystalsplittingcorrectiontotheband-gap.Thecauseofthedevianceinc:afrom2:1islikelyduetochangesinbondstrengths.3.2.2tialScanningCalorimetrytialscanningcalorimetry(DSC)wasperformedusingNetzschDSC200F3Maia.Adailybackgroundmeasurementwasperformedbeforescanningasapphirestandardandthesampleitself.Sampleswereapproximately50mginmass,andwerepolishedtohaveasurfaceonthebottom.Thesampleswereplacedintoaluminumcrucibleswithpiercedlids(necessaryforthereleaseofvaporsthatoccurduringsublimation)forthemeasurement,whichwascarriedoutoverarangeof50to600C.Theratiomethodwasperformedtocalculatethespheatofthesamples,usingtheNetzschProteusAnalysissoftware.473.2.3HallMeasurementsFigure3.2:ExperimentalsetupforHallmeasurements.Theappliedmagneticisintothepage.Hallmeasurementswereperformedatroomtemperaturewithamagneticrangingfrom-0.3to+0.3TeslausingaPower&Buckleymodel3474precisionelectromagnet,poweredbyaLakeShoremodel668electromagnetpowersupply.Typicalsampledimensionswere4mmx7mmx0.5mm.SamplecurrentwassuppliedbyaLakeShore370ACResistanceBridge.MagneticmeasurementsweremadewithaLakeShore421Gaussmeter.VSamplewasmeasuredwithaKeithleyprecisionmultimeter,andwasusedtocalculateelectricalresistivity,whileVHallwasusedtocalculatethecarrierconcentrationaccordingtothestandardsinglecarrierHallmodel:48RHall=Bnet(3.2)whereBistheappliedmagneticnisthecarrierconcentration,eistheelementarycharge,andtisthethicknessofthesample.Ratherthanasinglepoint,aseriesofsixpointsweremadepertemperature,andalinewastoaplotofRHallversusB,wheretheslopeisequalto1=net.Thecombinedmeasurementsyieldedthemobility(=˙/ne).Figure3.3:ExampleoftypicalHalldata,showingtheHallresistanceversusrelationship.Theslopeisequalto1/net,wheretisthesamplethickness,eistheelementarycharge,andnisthecarrierconcentration.493.2.4LowTemperatureTransportPropertiesFigure3.4:Experimentalsetupforlowtemperaturetransportmeasurements.Themeasure-mentisperformedunderaliquidnitrogenw,withthesamplesurroundedbyvacuum.LowtemperaturepropertiesweremeasuredinaJaniscryostatunderawofliquidnitrogenfrom80Kto350K,in10Kincrements.ThecryostatchamberwasevacuatedusingaEdwardsT-Station75turbopumpingstationtoapressurelessthan1105torr.ThetemperatureofthebasewascontrolledbyaLakeShore311temperaturecontroller,whilethethermocouplesmeasuredthetemperaturegradientalongthesample.ThesampleandSeebeckvoltagesaremeasuredbyaKeithley2000multimeter,theheatervoltagebyaKeithley2001,andthethermocouplemeasurementsbyKeithley2182Ananovoltmeters.TheheaterandsamplecurrentsweresuppliedbyKeithley2400-LVsourcemeters.Thesamplewasdicedintoarectangularprism,withtypicaldimensionsof3mmx4mmx8mm.Copperstripswereattachedacrossthesample,asshowninFigure3.4,withEpo-Tek50H2OEsilverepoxy.Thesamplewasthenattachedtoacopperbase,andaresistorwrappedincopperattachedtothetop,againwithsilverepoxy,toensuregoodelectricalandthermalcontact.Thecopperbasewasthenattachedtothecryostat,andwiresweresolderedontothecoppercontacts.Thethermocouplesweremadeofcopperandconstantan,andthecurrentleadsweremadeofphosphorbronzewire.3.2.4.1ElectricalResistivityElectricalresistivitywasmeasuredbypassingacurrentthroughthesampleandmeasuringthevoltagedrop,usingthetwocopperwiresofthethermocouples.Themeasurementwasperformedtwice,withbothapositiveandanegativecurrent.Usingsampledimensionstheelectricalresistivityofthesamplewascalculatedasfollows:ˆ=VSampleISamplewdp(3.3)whereVSampleandISamplerepresentthemeasuredvoltageandcurrent,w,d,andparethewidth,depth,andprobespacingofthesample.Themeasurementuncertaintyisestimatedbasedonequipmentas3%.3.2.4.2SeebeckCotandThermalConductivityAftertheelectricalresistivitymeasurementwasperformed,currentwassupplied(IHeater)totheresistorontopofthesampletocreateatemperaturegradient.Thecurrenttotheheaterwasleftonfortenminutestoensureasteadystatehadbeenreached,andacurrentvaluewassettoobtainatemperatureof1-1.5K.Afterthattimehadpassed,themeasurementswereperformed,withbeingmeasuredwiththethermocouplesandmeasuredfromthecopperleadsofboththermocouples.51TheSeebeckcotisasfollows:S=VT(3.4)ThemeasurementincludestheSeebeckcotofthecopperleads,whicharesub-tractedtoyieldtheSeebeckcotofthesampleitself.TheuncertaintyintheSeebeckcotmeasurementisestimatedat5%.Simultaneously,thethermalconduc-tivitymeasurementwasperformed.Thecurrentsuppliedtotheheater(IHeater)andthevoltageacrosstheheater(VHeater)weremeasuredatthesametimeasthetemperatureThethermalconductivitywascalculatedfromthosevaluesaswellasfromthedimensionsasfollows:=IHeaterVHeaterTpwd=PowerTpwd(3.5)whereagainp,w,anddarethesampledimensions.Whilethemeasurementwasper-formedunderavacuumtopreventmeasurementuncertaintyduetoconductionandconvec-tion,radiationlossescouldnotbepreventedandmustbecorrectedformanually.Inourmeasurements,aradiationcorrectionisappliedasfollows:actual=wdp"KmeasuredKradT3003#(3.6)whereKmeasuredrepresentsthemeasuredthermalconductance,andKradis0.0015WK1,avalueobtainedexperimentallybycalibrationperformedinourlabpreviously.Theerrorinthermalconductivitymeasurementisestimatedat10%inthecryostatsetup.Thethermalconductivityiscomposedoftwocomponents,theelectronicandthelattice52portions,andthroughtheuseoftheWiedemann-FranzLawtheelectronicportioncanbeestimatedas:electronic=L˙T(3.7)whereListheLorenznumber(takeninthisworktobethefreeelectronvalue,2:44108WK2),˙istheelectricalconductivity,andTisthetemperature.Thelatticeportionofthethermalconductivitywastakentobethemeasuredvalueminustheelectronicportion.Inallofthesamplesreportedinthisworkthethermalconductivitywascomposedprimarilyofthelatticecomponent.3.2.5HighTemperatureTransportProperties3.2.5.1ElectricalResistivityandSeebeckCotHightemperatureelectricalresistivityandSeebeckcotmeasurementswereperformedonanUlvac-RikoZEM3system.ThesamesamplefromthecryostatwassandeddowntoremovecontactsandthenmountedintheZEM3system.Thesamplewasclampedbetweentwoelectrodesandspringloadedthermocouplesformedpressurecontactstothesideofthesample.Measurementswereperformedexactlyastheyareatlowtemperature.Propertiesweremeasuredfrom300Kupto873K.Anat300KinmeasuredpropertieswillbeseenindatawhenswitchingfromthecryostattotheZEMsystemforsomesamples.CalibrationoftheSeebeckcotandelectricalresistivitymeasurementwasperformedusingBi2Te3standardfromNIST.Theuncertaintyinelectricalmeasurementsathightemperatureisestimatedat5%.533.2.5.2ThermalConductivityandThermalyAthighertemperaturesradiativelossesmakemeasuringthermalconductivityusingthetypical4-probetechnique,aswasdoneatlowtemperature,impossible.Instead,thetypicalmethodinvolvesmeasuringthermaly()vialasermethodandthencombiningthiswiththespheatandsampledensity.InourcalculationsroomtemperaturedensitywillbeusedincombinationwiththeDulong-Petitvalueforspheattocalculatethermalconductivitybythefollowingequation:=ˆCp(3.8)whereisthermaly,ˆisthesampledensity,andCpisthespheat.Laser-measurementswereperformedinDr.TimHogan'slabatMichiganStateUniversityonaNetzschLFA457MicroFlashsystem,usingapyroceramstandardforcomparison.SampledensitywasmeasuredusingtheArchimedesmethodinethanol,andagain,theDulong-Petitvaluewasusedforspheatcapacity.Theuncertaintyinmeasurementisestimatedat10%.54Chapter4Tellurides4.1FamilyOverviewTherearefourtelluriumcontainingmembersofthecopperbasedchalcopyritefamily:CuAlTe2,CuGaTe2,CuInTe2,andCuTlTe2.CuAlTe2hasbeenstudiedinthinandisreportedaschalcopyritestructurewithabandgapof2.06eV,howeververyfewstudiesonthebulkcompoundhavebeendone,likelyduetotheyinsynthesizinghighpuritysamples.[93]CuTlTe2wasnotstudiedhere,duetothetoxicityofthalliumanditslowmeltingpoint;howeverstudiesonthetransportpropertieshavebeenreportedpreviously.[94]CuFeTe2formsalayeredstructurewithironandcopperatomsbeinginterchangeable,ratherthanthechalcopyritestructureoftheothercompounds,andsowasalsonotstudiedhere.[95,96]CuInTe2hasareportedbandgapat300Cof0.97eVto1.07eV,whileCuGaTe2hasre-portedvaluesof1.2eVto1.23eV.[97,98,99,6,92,8]Bothcompoundshavebeenpreviouslyreportedastthermoelectricmaterials,withareportedpeakZTof1.4forCuGaTe2and1.18forCuInTe2.[6,8]Inthischapterresultswillbeshownforbothcompounds,aswellasforsolidsolutionsofthetwo.554.2CuAlTe2Figure4.1:X-raypatternofCuAlTe2withPDFoverlay.They-scaleisintensity,inarbitraryunits.PDF#01-075-0102[4]LiteraturedataonCuAlTe2primarilyconsistsofthinstudies,typicallysynthesizedbydepositingalternatinglayersofcopper,aluminum,andtelluriumbyvapordepositionfollowedbysubsequentannealing.Bulksamplesaretomakeduetotheyofaluminumforoxygenandvolatilityoftellurium.Twomethodswereusedinthisstudyinattemptstosynthesizepurebulksamples.Fortheattempt,copper(AlfaAesar,99.999%)andaluminumshot(AlfaAesar,99.9995%)wereweighedoutina1:2molarratioandreactedbyarcmeltingtoformCuAl2.Thearcmeltingwasperformedwithawatercooledhearthunderanargonatmosphere,andthematerialwasmeltedseveraltimesfor10-15secondspermeltuntiltheingotlookedhomogenous.56Theresultingingotwasthengroundusingamortarandpestle,checkedwithXRD,andthenplacedintoastainlesssteelballmilljar.Tothatwasaddedcopperpowder(AlfaAesar,10µ99.999%)andtelluriumchunks(AlfaAesar99.999%)tobringthemolarratioofCu:Al:Teto1:1:2.Thejarwasandsealedinanargonatmosphere,andballmilledfor60minutes.TheresultingpowderwascheckedagainwithXRD,thenwascoldpressedandsealedinaquartzampoule,whichwassubsequentlyevacuatedandsealed.Afterthat,thesamplewasplacedinaboxfurnaceandheldat450Cfor18daysuntilbeingquenchedintowater,andsparkplasmasinteredat650Cfor10minutes.Theresultingsamplewasdenseandx-rayshowedprimarilyCuAlTe2withsomesecondarypeaksobserved.Afterthis,asecondattemptwasmadeusingthesameinitialsteps,butratherthanannealing,thepowderwasplaceddirectlyintoagraphitedieandsparkplasmasinteredat400Cfor20minutes.AsshowninFigure4.1thesampleagainwasprimarilysinglephase,withsomeminorimpurities.Figure4.2:ElectricalresistivityofCuAlTe2asafunctionoftemperature.57Figure4.3:SeebeckcotofCuAlTe2asafunctionoftemperature.AsshowninFigure4.2theelectricalresistivityofCuAlTe2wasfoundtobefairlyhigh,andrelativelytemperatureindependent.Contrarytothehighelectricalresistivity,Figure4.3showsthattheSeebeckcotwasverylow.Combined,theresultingpowerfactorisminuscule,showingoverallpoorthermoelectricproperties.ThescatteringinthedatafortheSeebeckcotisduetothesmallsignal.58Figure4.4:ThermalconductivityofCuAlTe2asafunctionoftemperature.ThethermalconductivitywascomparabletothatofCuGaTe2,withvaluesnear20Wm1K1at80K,droppingtoroughly5.5Wm1K1at350K.ThejumpindatainFigure4.4at230Kisduetoameasurementissueanddoesnotindicateanactualtrend.Itissuspectedthattheup-tickisduetomoistureevaporatingundervacuumasthesampleheatsup.OverallthepropertiesofCuAlTe2werefoundtobeveryillsuitedforthermoelectrics.594.3CuInTe2Figure4.5:X-raypatternofCuInTe2withPDFoverlay.They-scaleisintensity,inarbitraryunits.ThepatternisPDF#01-082-0450.[5]Thereportedlatticeparametersrangefrom6.16Ato6.1904Aforaandfrom12.32Ato12.3976Aforc.[6,4,14]Thevaluescalculatedfromthesamplesmadeinthisstudywere6.19Aand12.33Aforaandcrespectively.TheXRDpatternshowninFigure4.5matcheswelltothatofCuInTe2,indicatingthesamplewashighpurity.4.3.1ElectronicDopingZincwaschosenasap-typedopant,actingasanacceptorbyreplacingthenominallytri-valentindiumwithdi-valentzinc.Electronicmeasurementsshowedthatzincdidinfactactasanacceptor,reducingtheelectricalresistivitybytwoordersofmagnitudeatlowtemper-60atures,asshowninFigure4.6.Hallmeasurementsshowedanincreaseinroomtemperaturecarrierconcentrationfrom5:61017cm-3to3:41019cm-3,againindicatingzincwasanep-typedopant.WhencomparingworkbyLiuetal.tothisexperiment,they=0.005sampleagreedwiththeliteraturevalueatroomtemperature,howevertheliteraturedatawasindependentoftemperatureabove600K,whileallofthesamplessynthesizedhereshowedariseinresistivityabove700K.[6]TheSeebeckcotshowedthesameresults;atroomtemperaturethedatafromLiuetal.forthe72-and168-hourannealedsamplesmatchedcloselytothatofthe0.5%and1%dopedsamplesmadehere,butabove700K.Figure4.6:ElectricalresistivityoftheseriesCuIn1{yZnyTe2asafunctionoftemperature.OpensymbolsrepresentCuIn1{yZnyTe2.FilledsymbolsaredatafromLiuetal.forCuInTe2annealedfor1,72,and168hours.Forcomparison,oursampleswereannealedfor24hours.[6]61Figure4.7:SeebeckcontoftheseriesCuIn1{yZnyTe2asafunctionoftemperature.OpensymbolsrepresentCuIn1{yZnyTe2.FilledsymbolsaredatafromLiuetal.forCuInTe2annealedfor1,72,and168hours.Forcomparison,oursampleswereannealedfor24hours.[6]InFigure4.8itwasobservedthatdopinggreatlyincreasedthepowerfactorfrom80Kupto700K,atwhichpointtheundopedsamplematchedthatofthezincdopedsamplesasintrinsiccarriersoverrodeextrinsiccarriers.ItwasalsoobservedinFigure4.6thattheelectricalresistivitiesconvergedatthispointaswell.62Figure4.8:PowerfactoroftheseriesCuIn1{yZnyTe2asafunctionoftemperature.OpensymbolsrepresentCuIn1{yZnyTe2.FilledsymbolsaredatafromLiuetal.forCuInTe2annealedfor1,72,and168hours.Forcomparison,oursampleswereannealedfor24hours.[6]ComparingpowerfactorsinFigure4.8wethatoursampleshaveapeakinpowerfactoraround550K,whiletheliteraturedatashowsapowerfactorpeakingaround700Kandremainingconstantabovethattemperature.Fromthepowerfactordataitwasshownthatreplacing1%oftheindiumwithzincyieldedthebestelectronicproperties,howeverthereasonfortherenceinourdatafromthatoftheliteratureisunclear,butcouldbeduetoinsampledensity.Thethermalconductivityforthesampleswereallsimilar,includingtheliteraturevaluesasshowninFigure4.9.TheliteraturedatashowedaslightlyhigherpeakZT,asshowninFigure4.10.63Figure4.9:ThermalconductivityoftheseriesCuIn1{yZnyTe2asafunctionoftemperature.OpensymbolsrepresentCuIn1{yZnyTe2.FilledsymbolsaredatafromLiuetal.forCuInTe2annealedfor1,72,and168hours.Forcomparison,oursampleswereannealedfor24hours.[6]Figure4.10:ZToftheseriesCuIn1{yZnyTe2asafunctionoftemperature.OpensymbolsrepresentCuIn1{yZnyTe2.FilledsymbolsaredatafromLiuetal.forCuInTe2annealedfor1,72,and168hours.Forcomparison,oursampleswereannealedfor24hours.[6]644.4CuGaTe2Figure4.11:XRDpatternofCuGaTe2,withaPDFoverlay.ThepatternisPDF#01-079-2331.[7]ThelatticeparametersofCuGaTe2wereslightlysmallerthanthoseofCuInTe2,asexpectedfromthesmallerionicradiusofgallium.Literaturereportsvaryfrom5.99Ato6.025Aand11.92Ato11.948Aforaandcrespectively.[8,4,14,5,15,100]ThevaluescalculatedfromourXRDpatternsare6.02Aand11.85A,andourXRDpatternmatcheswellwiththatofPDF#01-079-2331.[7]CuGaTe2alsohasalargerbandgapthanCuInTe2,whichistypicalofdiamond-likesemiconductorswhenmakinganisoelectronicsubstitutionwithanelementaboveitintheperiodtable.[14]654.4.1TransportPropertiesFigure4.12:ElectricalresistivityofCuGaTe2asafunctionoftemperature.Squaresrepresentourdata,whilethediamondsarefromPlirdpringetal.[8],andthetrianglesarefromLietal.[9].Figure4.13:SeebeckcotofCuGaTe2asafunctionoftemperature.Squaresrepresentourdata,whilethediamondsarefromPlirdpringetal.[8],andthetrianglesarefromLietal..[9]AsshownintheFigure4.12andFigure4.13,thesamplessynthesizedhereshowcloseagreementwiththeliteraturedatafromPlirdpringetal.(2012),butthedatafromLietal.66(2012)showedalowerresistanceandamuchlowerSeebeckcot.Thatdisagreementwaslikelyduetoerencesintheamountofdefectsinthesamples,aswellasindensity.Forthesamplesynthesizedhere,theelectricalresistivitydecreasedoverthewholetemperaturerange,typicalofasemiconductor,whiletheSeebeckcotinitiallyincreaseslinearlyinTuntilreachingamaximumof400µVK1at350K,afterwhichtheSeebeckcotdecreased,likelyduetothermalexcitationofminoritycarriers.Thevalueispositiveoverthewholerangeindicatingholesarethemajoritycarriersinagreementwithpreviousstudies.[8,101,9]Figure4.14:PowerfactorofCuGaTe2asafunctionoftemperature.Squaresrepresentourdata,whilethediamondsarefromPlirdpringetal.[8],andthetrianglesarefromLietal.[9].Thepowerfactorofthesampleincreasedupuntil766K,abovewhichthevaluedroppedslightly,reachingapeakvalueof11.7µWcm1K2,slightlyhigherthanvaluespresentintheliterature.67Figure4.15:ThermalconductivityofCuGaTe2asafunctionoftemperature.Squaresrep-resentourdata,whilethediamondsarefromPlirdpringetal.[8],andthetrianglesarefromLietal.[9].ThethermalconductivitydataforallofthesamplesshowedatypicalT1behavior,droppingfromavalueof6-8Wm1K1at300Kdowntoavaluelessthan1Wm1K1at870K.Previousstudiesagreedwellwiththevaluesobtainedinthisstudy.ThesampledisplayedapeakZTof1.04at870K,inlinewithvaluesobtainedbyPlirdpringetal.[8]Figure4.16:ZTofCuGaTe2asafunctionoftemperature.Squaresrepresentourdata,whilethediamondsarefromPlirdpringetal.[8],andthetrianglesarefromLietal.[9].684.4.2ElectronicDopingComputationalstudiesbyGudellietal.in2013indicatedthatCuGaTe2couldreachaZTgreaterthan2.0withaholeconcentrationof61019cm3,howeverHallmeasurementsshowedthesynthesizedsampletohaveaconcentrationof1:41018cm3atroomtem-perature.Substituting1%zincforgallium,aswasdoneforCuInTe2,increasedtheroomtemperaturecarrierconcentrationupto6:21019cm3,howevertheZTfortheundopedsamplewas1.04,whilethedopedsamplereachedapeakZTat870Kof1.16,anincrease,butstilllessthanthepredictedvalue.[102]In2014,calculationsbyYangetal.usingdensityfunctionaltheoryshowedthatn-typeCuGaTe2couldbeevenmorepromisingthanthep-typecompound,withapredictedZTof2.1at950K.[103]Severaldtelementswereusedinattemptstocreateann-typesampleofCuGaTe2,howevernonewesuccessful.Theirpropertiesarereportedinthefollowingsection.4.4.2.1N-typeDopants:Zinc,Germanium,Tin,andIodineAzincatomsubstitutingforcoppershouldactasdonor,withzincbeingnominallydivalentandcoppermonovalent,howeversampleswithboth2%and5%zincsubstitutedforcopperstillshowedpositiveSeebeckcocientvaluesoveralltemperaturerangesmeasured.Nootherdivalentcationswereattempted.Onthegalliumsite,samplesweremadewith2%and5%germaniumandtinsubstitution,againnoneofwhichshowedn-typecharacter.Germaniumwassubstitutedupto10%,atwhichpointXRDshowedmultiplephases(amixtureofCuGaTe2,GaTe,Cu2GaTe2andrawgallium)indicatingthesolubilitylimithadbeenpassed,butallsamplesuptothenstillexhibitedpositiveSeebeckcotvalues.Finallyonthetelluriumsite,samplesweremadewithiodinesubstitutionbyusingbinary69CuIasaprecursor.Figure4.17:ThermalconductivityoftheseriesCuGaTe2(1{x)I2xasafunctionoftempera-ture.Theiodinecontainingsamplesshowedasurprisingdropintotalthermalconductivity,asseeninFigure4.17.Laterworkonplacingvacanciesinthelatticebycoppershowedsimilarresults,indicatingthattheiodinemayhavesublimatedout,leavingvacancies.Theyalsoshowedadecreaseinpowerfactorwithincreasingiodineconcentration.Samplesshowedpoorhightemperaturestability,andoftenweredeformedafterhightemperaturemeasurements,likelyduetoiodinesublimatingout,makingthedopantpoorlysuitedforthermoelectricuse.Overall,theiodinedopedsamplesshowedsimilarZTvaluestotheundopedsamples,butfromstabilityissueduetoiodinesublimation.70Figure4.18:PowerfactoroftheseriesCuGaTe2(1{x)I2xasafunctionoftemperature.Figure4.19:ZToftheseriesCuGaTe2(1{x)I2xasafunctionoftemperature.Figure4.20showsthat2%germaniumsubstitutioncausedaslightincreaseintheroomtemperatureelectricalresistivity,and5%showedanincreasebyafactoroften,aswouldbeexpectedwhenattemptingtodopeanalreadyp-typesemiconductortoben-type.Substitut-ing2%germaniumalsocausedalargedropinSeebeckcocient,whichcouldbeindicativeofminoritycarrierscompetingwiththemajorityholes.Thesamplewith5%germanium71showedahigherSeebeckcot,albeitavaluestillhalfthatofthepureCuGaTe2.Figure4.20:Electricalresistivityofn-typedopedsamplesofCuGaTe2asafunctionoftemperature.Figure4.21:Seebeckcotofn-typedopedsamplesofCuGaTe2asafunctionoftem-perature.72Figure4.22:Powerfactorofn-typedopedsamplesofCuGaTe2asafunctionoftemperature.Tinsubstitutionshowedatwithboth2%and5%tindopedsamplesdisplayinganelectricalresistivitythatwasafactoroftwolowerthanthepureCuGaTe2.TheSeebeckcotagreedwiththisresult,withalargedropaswouldbeexpectedfromamoremetallicsample.Thesetwofactorsindicatedthatthegermaniumisnotactingasann-typedopant,andratherappearedtobeactingasap-typedopant.Theexplanationforthisisunclear,butitislikelythatthegermaniumwaseithernotresidingonthegalliumatomicsite,orwascausingothersiteanti-sitedefectstheBothtinandgermaniumweredetrimentaltothepowerfactorofthesample,withroomtemperaturepowerfactorsforallfoursamplesafactorofroughly20lessthanthepureCuGaTe2.73Figure4.23:Thermalconductivityofn-typedopedsamplesofCuGaTe2asafunctionoftemperature.Thethermalconductivityforboththetinandgermaniumdopedsampleshowedadrop,asexpected,withthe5%dopedsamplesdisplayingalowervaluethanthe2%.Overall,theZTwasstronglyreduced,asexpectedfromthedrasticdropinpowerfactor.744.5SolidSolutions4.5.1CuIn1{xGaxTe2Figure4.24:XRDpatternsoftheseriesCuIn1{xGaxTe2.Frombottomtotop,samplesarex=[0,0.25,0.35,0.5,0.65,0.75,1].They-axisisshowsintensityinarbitraryunits.TotopPDFisCuGaTe2(#01-079-2331)andthebottomisCuInTe2(#01-082-0450).[5,7]WithbothCuInTe2andCuGaTe2displayingaZToverunity,thenextapproachwastoformasolidsolutionofthetwocompounds.Itwashypothesizedthatgiventheirclosebandgaps(1.07eVvs1.2eVrespectively)andbecausebothindiumandgalliumnominallyhavethesamevalence,substitutingoneelementfortheotherwouldhavelittleontheelectricaltransportproperties.However,theinmassofindiumandgalliumreducethe75thermalconductivityduetoalloyscattering,asdescribedinChapter2.PreviousworkbyLietal.hadshownthatsampleswith36%and64%indiumsubstitutedforgalliumdiddisplaylowerthermalconductivitythantheendmembers,andtheyalsoreportedariseinelectricalresistivityandasubstantialincreaseintheSeebeckcotatroomtemperature.[9]Toandexpandupontheirresults,afullsolidsolutionofCuIn1{xGaxTe2wasformedforvaluesofx=[0,0.25,0.35,0.5,0.65,0.75,1].Figure4.25:CalculatedlatticeparametersoftheseriesCuIn1{xGaxTe2asafunctionofgalliumconcentration(x),usingthe204and424peaks.AsseeninFigure4.24,theXRDpatternsexhibitedasystematicshiftinpeakstowardshigherwithincreasinggalliumconcentration,indicatingashrinkinglatticeparameteraswasexpectedfromthesmallersizeofgallium.ThisalsoagreeswiththeworkdonebyLeonetal.[5]Thatworkalsoshowedthatontopofatypicallinearshiftinbothaandc,asgalliumisreplacedwithindiumthecopper-telluriumbondlengthremainsnearlywhilethebondbetweenthegroupIIIatomandtelluriumgrows,leadingtoadistortionof76thelatticewithincreasingindiumconcentration,andsubsequentlyachangeintheratioofthectoalatticeparameter.[5]Thechalcopyritecompoundsnominallyhavearatioofc:aequalto2.0,butdefectsandsubstitutionsshiftthisslightlyaboveorbelow,whichleadstoasplittingofpeaksasobservedintheXRDpatternsinFigure4.24.ShowinFigure4.25arethevaluesfortheaandclatticeparametersinangstroms,showingtheoveralllineartrendasafunctionofcomposition.Figure4.26:ElectricalresistivityoftheseriesCuIn1{xGaxTe2asafunctionoftemperature.77Figure4.27:SeebeckcotoftheseriesCuIn1{xGaxTe2asafunctionoftemperature.WiththeexceptionofCuIn0.5Ga0.5Te2,whichhadthehighestroomtemperatureelec-tricalresistivity,alloftheothersamplesdisplayedatrendofdecreasingelectricalresistivitywithincreasinggalliumconcentrationasshowninFigure4.26.ThesamplesalsoshowedadecreaseinSeebeckcotwithincreasinggalliumconcentration.AsseeninFigure4.28thiscombinationleadstoapeakpowerfactorinCuGaTe2ofnearly12µWcm1K2at766K,withvaluesdecreasingwithincreasingindiumcontentdowntoCuInTe2'svalueofslightlyover8µWcm1K2.78Figure4.28:PowerfactoroftheseriesCuIn1{xGaxTe2asafunctionoftemperature.Thethermalconductivitymeasurementsshowedthatthetwoendmembersofthecom-poundhavethehighestvalues,asexpected,witharoughlyparabolictrendforthemixtures.Theismorepronouncedatlowertemperatures,at300KthethermalconductivityofCuGaTe2isovertwicethatofCuIn0.5Ga0.5Te2,whileathightemperaturestheyarealllessthan1Wm1K1.Figure4.29:ThermalconductivityoftheseriesCuIn1{xGaxTe2asafunctionoftempera-ture.79CombiningthepowerfactordataandthethermalconductivitydatatocalculateZT,Figure4.30showsthatthereisageneraltrendofincreasingZTwithincreasinggalliumconcentration,withtheexceptionofCuIn0.25Ga0.75Te2whichisslightlyhigherthanthepuregalliumsample.Thus,asmallamountofindiumcanlowerthethermalconductivityenoughtosetthereductioninthepowerfactor,givinganincreaseinZT.Figure4.30:ZToftheseriesCuIn1{xGaxTe2asafunctionoftemperature.4.5.2Cu(In1{xGax)0.99Zn0.01Te2Followingthepreviouswork,andwiththeincreasedZTofbothCuInTe2andCuGaTe2bythesubstitutionof1%zinc,theprevioussolidsolutionwasrepeated,butwith1%ofthegroupIIIatomsreplacedbyzinc.Unlikeintheundopedseries,whereallofthesamplesshowedaSeebeckcotpeakingaround300Kandthendroppingthesampleswithzincstartatavaluenear50µVK1at80Kandriselinearlyintemperatureacrossthewholerange,neverturningover,asshowninFigure4.31.Theelectricalresistivityofthezincdopedsamplesincreasedwithtemperature,whiletheundopedsamplesdecreasedinresistivityasthetemperatureincreased.80Figure4.31:ElectricalresistivityoftheseriesCu(In1{xGax)0.99Zn0.01Te2asafunctionoftemperature.Figure4.32:SeebeckcotoftheseriesCu(In1{xGax)0.99Zn0.01Te2asafunctionoftemperature.81Figure4.33:PowerfactoroftheseriesCu(In1{xGax)0.99Zn0.01Te2asafunctionoftemper-ature.However,asweseeinFigure4.33,evenwiththedecreaseinSeebeckcoientthezincsubstitutionleadstoabroadpeakinthepowerfactorfrom500-700K,ratherthanthesharppeakseeninFigure4.28fortheundopedsamples.Thethermalconductivityshowsthesametrendastheundopedsamples,andthevaluesarenearlyidenticaltotheundopedasseeninFigure4.34.ThisleadstoZTvaluesthatareaboveorequaltotheundopedsamplesforeachmemberintheseries,asshowninrefCuInTe2-CuGaTe2-ZN-ZT.AswellasanincreasedpeakZT,thebroadpeakedpowerfactorleadstoanincreasedaverageZT.And,againitwasfoundthatthesamplewith25%indiumand75%galliumhadthehighestZT.82Figure4.34:ThermalconductivityoftheseriesCu(In1{xGax)0.99Zn0.01Te2asafunctionoftemperature.Figure4.35:ZToftheseriesCu(In1{xGax)0.99Zn0.01Te2asafunctionoftemperature.834.5.3CuInTe2(1{x)S2xFigure4.36:XRDpatternofCuInTe2(1{x)S2xwithPDF.ThetoppatternisCuInTe2,followedbyx=0.005,0.01,and0.015,atwhichpointsecondarypeakscorrespondingtoCuInS2wereobserved.PatternsarePDF#01-082-0450and#01-075-0106forCuInTe2andCuInS2respectively.[5,10]AfullsolidsolutionofCuInTe2andCuInS2wasunabletobeformedduetothelargeinionicradiioftheelements,sosmallerconcentrationsofsulfurweresubstitutedtoascertainthesolubilitylimit.At15%sulfursubstitutionsecondarypeakswereobservedintheXRDpatterns,asshowninFigure4.36,correspondingtoCuInS2indicatingasolubilitylimithadbeenreached.Sampleswith5%and10%sulfurweresynthesizedandmeasured.Thesamplesshowedaslightdecreaseinlatticeparametersasexpectedfromthesmalleratomicradiusofsulfur.84Figure4.37:ElectricalresistivityoftheseriesCuInTe2(1{x)S2xasafunctionoftemperature.Figure4.38:SeebeckcotoftheseriesCuInTe2(1{x)S2xasafunctionoftemperature.Thesubstitutionofsulfurleadtoanincreaseinelectricalresistivity,butonlyaslightincreaseintheSeebeckcotathightemperature,leadingtoanoveralldecreaseinpowerfactor.Thethermalconductivitydecreasedwithsulfurcontentasexpected,andthereductionwasstrongforasmallevena5%substitution,showingthestrongofthelargemassHowever,asshowninFigure4.40evenwiththelargedecrease85inthermalconductivitythedecreaseinpowerfactorwasmoredetrimental.CuInTe1.9S0.1showedalmostidenticalZTvaluesasthepurecompound,whileCuInTe1.8S0.2decreasedbyroughlyafactorof2athightemperatures.Figure4.39:ThermalconductivityoftheseriesCuInTe2(1{x)S2xasafunctionoftempera-ture.Figure4.40:ZToftheseriesCuInTe2(1{x)S2xasafunctionoftemperature.864.6ConclusionsInthischaptercompoundsofCuGaTe2,CuInTe2,CuAlTe2andafullsolidsolutionoftheindium/galliumcompoundsweresynthesized.CuInTe2hasbothahigherelectricalresistivityandSeebeckcotthanCuGaTe2,butalowerpowerfactor.Thistrendisconsistentacrossthesolidsolution,allowingforoptimizationbysubstitution.ThethermalconductivityofCuGaTe2ishigherthanthatofCuInTe2,andthesolidsolutionfollowedthetypicalparabolicformofamixture.Allofthesamplesinthesolidsolutionwerefoundtohaveathermalconductivitylessthan1Wm1K1above700KduetothestrongofUmklappscatteringathightemperatures.Finally,zincwasfoundtobeanep-typedopantforbothcompounds,increasingtheroomtemperaturecarrierconcentrationsfrom5:61017cm3to3:41019cm3forCuInTe2andfrom1:41018cm3to6:241019cm3forCuInTe2withasubstitutionof1%zincforthegroupIIIelement.Severalattemptsweremadetosynthesizeann-typesampleofCuGaTe2,butnoneweresuccessful.Withanoptimizedindium/galliumratioaswellaszincdoping,ZTvaluescloseto1.6wereachieved,thehighestreportedforchalcopyritecompounds.87Chapter5Selenides5.1FamilyOverviewTheselenidefamilyofcopperbasedchalcopyritecompoundscontainsCuAlSe2,CuGaSe2,andCuInSe2.CuAlSe2wasnotstudiedhereduetoboththeyinsynthesizingitandduetothelarge(2.71eV)bandgap.[104]CuFeSe2,anaturallyoccurringmineralknownaseskebornite,existshoweveritdoesnotforminthechalcopyritestructure,andsowasalsonotstudiedhere.[105,106]Synthesisofthesecompoundswascarriedsimilartothetelluriumcompounds,withtheexceptionthattheheatingrateinthefurnacewasloweredfrom1.0Cmin1to0.4Cmin1toaccountforthevolatilityofselenium.Allthesamplesinthefamilywereagainfoundtobep-type,butwithnoticeablyhigherelectricalresistivitythanthetelluriumbasedsamples.885.2CuInSe2Figure5.1:XRDpatternofCuInSe2withPDF.They-scaleisintensity,inarbitraryunits.ThepatternisPDF#01-075-2916.[11]AsFigure5.1shows,thesamplesynthesizedwasfoundtobesinglephase.Theobtainedlatticeparametersshowedgoodagreementwithliteraturevalues,withvaluesofarangingfrom5.77Ato5.78A,cfrom11.54Ato11.63A,andthevaluesobtainedhereof5.79Aand11.51Aforaandcrespectively.[14,4,11]CuInSe2hasareportedbandgapof0.98to1.04eV[107,108,109],comparabletothatofCuInTe2.Nevertheless,thesampleswerefoundtobehighlyresistivecomparedtothetelluridecounterpart.Undopedsampleshadaroomtemperatureelectricalresistivityof1104cm,versus1:4102cmforCuInTe2,andinfactcouldnotbemeasuredathighertemperaturesintheZEM3duetotheirhighresistance.895.2.1ElectronicDopingFigure5.2:ElectricalresistivityoftheseriesCuIn1{yZnySe2versustemperature.ThedataforCuInSe2showsalargeamountofduetothelargesampleresistanceandtheyinmakinggoodelectricalcontacttothesample.AswithCuInTe2,initialdopingtooptimizeelectronicpropertieswascarriedoutusingzincasap-typedopant,insubstitutionforindium.Samplesweremadewith1%,2%,and5%zincanddidindeedexhibitacleardopingwithgreatlydecreasedvaluesofelectricalresistivity,asshowninFigure5.2.90Figure5.3:SeebeckcotoftheseriesCuIn1{yZnySe2asafunctionoftemperature.Figure5.4:PowerfactoroftheseriesCuIn1{yZnySe2asafunctionoftemperature.Whilethesampleswith2%and5%zinchadlowerelectricalresistivitythanthe1%,theyalsoshowedmuchlowerSeebeckcotvaluesandasaresultamuchlowerpowerfactor.TheSeebeckcoientdataforundopedCuInSe2isnotshown;duetothelargeresistivityofthesampletheSeebeckcotvaluesweretoaccuratelymeasureonourequipment.ThethermalconductivitywascomparabletothatofCuInTe2,withroom91temperaturevaluesofapproximately3-4Wm1K1forsampleregardlessofthedopinglevel.Overall,theZTforCuInSe2,evenforthebestzincdopedsample,waslessthan0.002at300K.5.3CuGaSe2Figure5.5:X-rayionpatternforCuGaSe2withPDFoverlay.They-scaleisintensity,inarbitraryunits.ThepatternisPDF#01-075-2916.[12]UnlikethecaseofCuInTe2andCuInSe2,thebandgapofCuGaSe2islargerthanthatofCuGaTe2,asistheusualtrendindiamondlikesemiconductorswhenreplacinganelementwithanotherfromarowabove.[14]ThereportedbandgapofCuGaSe2rangesfromto1.6eVto1.7eV,whichislargerthantypicalforconventionalthermoelectricmaterials.[109,110,111]Samplesweresynthesizeddespitethatinordertobetterunderstandthe92underlyingphysicsofthechalcopyritecompounds.AswasthecaseforCuInSe2,CuGaSe2exhibitedhighelectricalresistivity,notunexpectedduetothelargebandgap,withelectricalresistivityvaluesstartingat1104cmat80Kanddroppingto2:5103cmat300K.PreviousstudiesontheholemobilityofCuGaSe2alsoshowedthevaluestobequitelow,intherangeof10-20cm2V1s1atroomtemperatureascomparedtovaluesnear100forCuGaTe2.[112]TheSeebeckcotwastomeasure,andfrompositivetonegative,notreachingavaluelargerthan10µVK1inmagnitudeuntil300K.Together,thisyieldedapowerfactorthatpeakedat820Kwithavalueof0.8µWcm1K2,morethananorderofmagnitudelessthanthatofCuGaTe2.5.3.1ElectronicDopingFurthersamplesweremadeusingzincasadopantatomwiththecompositionCuGa1{xZnxSe2andx=0.01,0.02,0.03,and0.05.AsseeninFigure5.6thezincdopedsamplesdisplayedmuchlowerelectricalresistivity,withroomtemperaturevaluesintherangeof10sofcm,anorderofmagnitudelessthantheundopedCuGaSe2.AsFigure5.6shows,athightem-peraturethesamplesallhadsimilarvalues,ontheorderof100sofcm.TheSeebeckcotforallofthedopedsampleswaslowerthanthanoftheundopedsample,asshowninFigure5.7.Whilethethermopoweroftheundopedcompositionwaslessthan50µVK1until320K,thevalueroserapidlyafterthistolevelatavaluenear500µVK1at600K.However,thedopedsamplesmaintainedlowvaluesoveramuchgreaterrange,with1%and2%Znsamplesshowingnearlyidenticalvaluesuntil750K.93Figure5.6:ElectricalresistivityoftheseriesCuGa1{xZnxSe2asafunctionoftemperature.Figure5.7:SeebeckcotoftheseriesCuGa1{xZnxSe2asafunctionoftemperature.AsseeninFigure5.8thepowerfactorbelow600Kincreaseswithincreasingzinccon-centration,withCuGa0.95Zn0.05Se2showingthehighestvaluebelow600K.However,abovethispointthepowerfactoroftheundopedsamplebegantorapidlyrisejustastheSeebeckcotdid.Forthezincdopedsamples,thepowerfactorwaslessconsistent.The3%zincsamplehadthehighestelectricalresistivityat860K,evenhigherthantheundoped94sample,andassuchshowedthelowestpowerfactor.However,the1%and2%zincdopedsamplesshowedsimilarvaluestotheundopedsampleat800K,with5%zincexhibitingaslightlylowervalue,andthe3%samplethehighestvalueofall.Figure5.8:PowerfactoroftheseriesCuGa1{xZnxSe2asafunctionoftemperature.Thethermalconductivityforallsampleswasverysimilar,asexpected.At80Kthevaluesvariedfrom5-8Wm1K1,likelyduetosmallindefects,butathightemperaturesthevalueswereallwithinasmallmarginofeachother,asshowninFigure5.995Figure5.9:ThermalconductivityoftheseriesCuGa1{xZnxSe2asafunctionoftemperature.Figure5.10:ZToftheseriesCuGa1{xZnxSe2asafunctionoftemperature.UltimatelytheZTvaluesforpure,andzincdoped,CuGaSe2werequitelow.TheheaviestdopedsampleshowedthehighestZTvalueat0.14,roughlyanorderofmagnitudelowerthanthatofthetelluriumbasedsample,primarilyduetothelargevaluesofelectricalresistivity.965.4SolidSolutionsFullsolidsolutionsofbothCuGaTe2(1{x)Se2xandCuInTe2(1{x)Se2xwereabletobeformed,andtheirpropertiesweremeasured.Thegallium-basedsolidsolutionwasusingSPS,whiletheindium-basedserieswasmadetwice;onceusingthehotpresstodensifythesamples,andthenagainusingtheSPSforcomparison.5.4.1CuIn0.99Zn0.01Te2(1{x)Se2x-HotpressedInitialsamplesofCuInSe2werefoundtohavehighelectricalresistance,sothesolidsolutionwasmadewitha1%substitutionofzincontheindiumsiteacrossthewholerange,aswasdoneinthesolidsolutionofCuIn1{xGaxTe2.Figure5.11:XRDpatternsofthesolidsolutionCuIn0.99Zn0.01Te2(1{x)Se2xwithPDFs.ThetoppatternisforCuIn0.99Zn0.01Te2,witheachpatternshowingsubstitutionsin25%increments.They-scaleisintensity,inarbitraryunits.ThepatternsarePDF#01-082-0450and#01-075-2916forTeandSerespectively.[13,11]97Figure5.12:LatticeparametersofthesolidsolutionCuIn0.99Zn0.01Te2(1{x)Se2xwithlitera-turevaluesshowninopensymbols.Thedashedlinesaretoguidetheeyes.[4,14,13,6,15,8]AsshowninFigure5.11andFigure5.12therewasasystematicshiftofthepeaksto-wardslargertwo-thetaasseleniumwassubstitutedfortellurium,indicatingadecreaseinlatticeparametersasexpectedfromthesmallerionicradiusofselenium.ViewingthelatticeparametersasafunctionofseleniumconcentrationinFigure5.12therewasaclearlineartrendinagreementwithVegard'slaw.[113]98Figure5.13:ThermalconductivityandelectricalresistivityofCuIn0.99Zn0.01Te2(1{x)Se2xat300K.Bothshowastrongdependenceonseleniumconcentration.Asseleniumwassubstitutedfortelluriumaparabolictrendwasobservedinthethermalconductivitywithrespecttocompositionaswasexpected.[57]ThisgaveaminimuminthethermalconductivityatthecompositionCuInTeSeasshowninFigure5.13.Similarlytheelectricalresistivityincreaseswithseleniumconcentrationuntilthehalfwaypoint,andthendecreasesagain.99Figure5.14:ElectricalresistivityoftheseriesCuIn0.99Zn0.01Te2(1{x)Se2xasafunctionoftemperature,showingthestrongdependenceonseleniumconcentration.However,unlikethethermalconductivitywhichdecreasedbyafactorofroughlythreeatroomtemperature,theelectricalresistivityincreasedbynearlythreeordersofmagnitude.Thisindicatesthatthedefectsinthelatticedisrupttheholetransportmuchmorethanthephonontransport.Bothtrendsarepresent,butlessdramatic,athightemperaturesasshowninFigure5.14andFigure5.15.100Figure5.15:ThermalconductivityoftheseriesCuIn0.99Zn0.01Te2(1{x)Se2xasafunctionoftemperature,showingthestrongdependenceonseleniumconcentrationThetrendintheSeebeckcotwaslessclear,asshowninFigure5.16,withx=0.25sample(CuIn0.99Te1.5Se0.5)displayingamuchlowerSeebeckcotthantheothersamplesacrossthewholetemperaturerange,andthex=0.50(CuIn0.99Te1Se1)samplerisingquitesteeplytosurpassalltheothersamplesfrom400Kto800K.Figure5.16:SeebeckcotoftheseriesCuIn0.99Zn0.01Te2(1{x)Se2xasafunctionoftemperature.101Overall,thepowerfactordecreaseddramaticallywithanyamountofseleniumsubstitu-tion.Thepuretelluriumsamplereachedavaluenear12µWcm1K2,butitdroppedbyafactorof3with25%seleniumsubstitution,andalloftheothersamplespeakedatavaluelessthan1µWcm1K2,asseeninFigure5.17.UltimatelyadecreaseinZTwasfoundforallsampleswiththesubstitutionofseleniumascomparedtoCuIn0.99Zn0.01Te2.Figure5.17:PowerfactoroftheseriesCuIn0.99Zn0.01Te2(1{x)Se2xasafunctionoftemper-ature.Figure5.18:ZToftheseriesCuIn0.99Zn0.01Te2(1{x)Se2xasafunctionoftemperature.1025.4.2CuInTe2(1{x)Se2x-SparkPlasmaSinteredFollowingthesolidsolutionofCuIn0.99Zn0.01Te2(1{x)Se2x,theserieswasmadeagainwith-outtheadditionofzinc,andusingtheSPS.Thiswasdonetoaddressconcernsofvariabilityinthedensityofthehotpressedsamples.Thesamplesmadewiththehotpresshaddensitiesof93%-99%,whilethesamplessynthesizedwiththeSPSwereallgreaterthan98%theoreticaldensity.Figure5.19:XRDpatternsforthesolidsolutionCuInTe2(1{x)Se2xviaSPSwithPDFs.ThebottompatternisforCuInTe2,witheachsubsequentpatternshowingsubstitu-tionsin25%increments.They-scaleisintensity,inarbitraryunits.PDFsare#01-082-0450and#01-075-2916forTeandSerespectively.[13,11]103Figure5.20:SeebeckcoientoftheseriesCuInTe2(1{x)Se2xasafunctionoftemperature.AsshowninFigure5.20,thex=0(CuInTe2)andx=0.25(CuInTe1.5Se0.5)samplehadSeebeckcotscomparabletothatofthezinc-dopedandhotpressedsamplesinFigure5.16.Bothplotsshowedvaluesstartingaround100µVK1andthenrisingtoleveloutaround300-400µVK1.Thehotpressedx=0andx=0.25showedaslightup-tickabove600KwhiletheSPSsamplesdidnot.Also,showninFigure5.20,therewasaverysharppeakforx=0.25,0.50,and0.75near600K.ThedropinSeebeckcotforsampleswithx>0.25wasmuchmorepronouncedintheSPSsamplesthaninthehotpressedsamples.104Figure5.21:ElectricalresistivityoftheseriesCuInTe2(1{x)Se2xasafunctionoftempera-ture.Figure5.22:PowerfactoroftheseriesCuInTe2(1{x)Se2xasafunctionoftemperature.Theelectricalresistivityvariedoveramuchsmallerrange,asshowninFigure5.21,whencomparedtothehotpressedversion,butagainathightemperaturesshowedatrendofhigherelectricalresistivitycorrespondingtohigherseleniumconcentration.Likewise,thepowerfactordecreasedwitheachincreaseinseleniumconcentration,justaswasfoundinthehotpressedversion.105Figure5.23:ThermalconductivityoftheseriesCuInTe2(1{x)Se2xasafunctionoftemper-ature.Asexpected,thex=0.25,0.5,and0.75samplesdisplayagreatreductioninthermalconductivityascomparedtotheendmembersoftheseries.However,whencombinedwiththedecreaseinpowerfactor,andwiththereductioninthermalconductivitybecominglessdramaticathightemperatures,theoverallZToftheseriesagaindecreaseswithincreaseseleniumconcentration,asshowninFigure5.24.Figure5.24:ZToftheseriesCuInTe2(1{x)Se2xasafunctionoftemperature.106SomewereobservedfortheSPSversushotpressedsamples.ThesamplesmadewiththeSPSshowedhigherthermalconductivity,withvaluesat300KfortheTe1Se1sampleof2Wm1K1fortheSPSsampleversus1.2Wm1K1forthehotpressedsample.Therewasalsoalargeceinelectricalresistivity,withtheSPSsamplesshowingavalueroughlyoneorderofmagnitudelowerthanthesamplesfromthehotpress.Themostlikelycauseforthesesisvarianceinthesampledensities.Sampleswiththehotpressweretypically95%theoreticaldensity,whilethesamplesmadewiththeSPSweretypically98%orhigher.Thislowerdensitymeantmoredefectstoscatterelectronsandphonons,resultinginalowerthermalconductivityandahigherelectricalresistivityforthehotpressedsamplesascomparedtothosemadewithSPS.CuInTe2showedanincreaseinZTfrom0.75tonear1.4bydensifyingwithSPS,amassiveincrease.Themainfactorwasaslightdecreaseinelectricalresistivity,anda50%reductioninthermalconductivityat860K,form0.73Wm1K1forthehotpressedsampleto0.52Wm1K1forthesamplebySPS.5.4.3CuIn1{yZnyTe1Se1FollowingtheworkonthesolidsolutionofCuInTe2withCuInSe2,aseriesofsamplesweremadewiththecompositionCuIn1{yZnyTe1Se1withy=0,0.01,0.03,0.05inhopesofmaintainingthelowthermalconductivityfromthesolidsolution,whilemitigatingsomeoftheriseinelectricalresistivity.Thesampleswereat450Cfor15minutesusingtheSPS.107Figure5.25:SeebeckcoetoftheseriesCuIn1{yZnyTe1Se1asafunctionoftemperature.Regardlessofdopinglevel,theSeebeckcotofthesamplesshowedalineartrenduntilapproximately500K,atwhichpointtheyalldisplayedasharpupwardtrendwithapeakat600Kfollowedbyadownwarddip,asseeninFigure5.25.ThispeakisalsoseenintheelectricalresistivityasshowninFigure5.26.Itissuspectedthanthisisindicativeofanorder-disorderphasetransition.Athightemperatureschalcopyritecompoundshavebeenshowntotransformintothesimplerzinc-blendestructure,inthiscaseindicatingthatthecopperandindiumarenolongerorderedwithtwoeachbondedtothegroupVIatom,butareratherrandomlydistributedonthecationsite.[114,109]Typically,thistransitionisseenathighertemperatures,e.g.inexcessof900K.[115,116,117]Itislikelythattransitiontemperaturewasdecreasedduetothestrainpresentinthesystemfromthedisordercausedbythesolidsolution.108Figure5.26:ElectricalresistivityoftheseriesCuIn1{yZnyTe1Se1asafunctionoftempera-ture.TheelectricalresistivitydatainFigure5.26showszincwaseasap-typedopant,witheachincreaseinzincconcentrationfurtherloweringtheresistivity.Again,asseenintheSeebeckcot,aclearchangeinbehaviorisobservedatroughly600K.PureCuInTeSeshowsadropinresistivityof85cm,decreasingbyalmosthalf,whileCuIn0.95Zn0.05TeSeshowsadropofonly10cm,adecreaseofapproximately14%.EvenwiththedropinelectricalresistivityandthesharppeakinSeebeckcot,thepowerfactorforthesamplesstillremainedroughlyafactorof10lowerthanthatofCuInTe2.Thedopedsamplesshowedanincreasedpowerfactorascomparedtotheundopedsamplebeforethephasetransitionandalsoshowedapronouncedpeakat600K,whiletheundopedsampleshowedasmoothincreaseupto800K,reachingahighervalue.109Figure5.27:PowerfactoroftheseriesCuIn1{yZnyTe1Se1asafunctionoftemperature.Figure5.28:ThermalconductivityoftheseriesCuIn1{yZnyTe1Se1asafunctionoftemper-ature.Thethermalconductivityvalues,asseeinFigure5.28,werelowerthanthatoftheendcompoundsofthesolution,withroomtemperaturevaluesof2Wm1K1,andvaluesat860Koflessthan0.5Wm1K1.Thelowtemperaturedatafory=0.03isnotshownherebecausetherewasapoorvacuumduringmeasurement,whichgaveerroneousdatafor110thermalconductivity.WiththeexceptionofCuIn0.97Zn0.03TeSe,allthesamplesreachedaZTofapproximately0.3at860K,includingthesamplewithnozincaddition.Figure5.29:ZToftheseriesCuIn1{yZnyTe1Se1asafunctionoftemperature.OveralltheZTfortheseriesCuIn1{yZnyTe1Se1showedlittletonodependenceonzincconcentration.Thesamplewith3%zincshowedasmallervalues,butthe1%and5%dopedsampleswerewellwithinmeasurementerroroftheundopedCuInTeSe.Whilethezincdidincreasethepowerfactorofthesamplesatlowtemperature,athightemperaturethesamplesalldisplayedintrinsiccarrierconcentrations,andthezincwaseatincreasethepeakZT.1115.4.4CuGaTe2(1{x)Se2xFigure5.30:XRDpatternsoftheseriesCuGaTe2(1{x)Se2xwithPDFs.ThetoppatternisforCuGaTe2,witheachpatternshowingseleniumsubstitutionsin25%increments,withCuGaSe2shownatthebottom.They-scaleisintensityinarbitraryunits.ThePDFsare#01-079-2331and#01-075-2916forTeandSerespectively.[7,12]112Figure5.31:LatticeparametersoftheseriesCuGaTe2(1{x)Se2x.Opensymbolsrepresentliteraturedata,whilethesymbolsaredatafromthestudyhere.[4,14,13,15,8,16]Figure5.30displaystheXRDpatternsforthisseriesofsamples,togetherwiththereferencepeaksfromthePDFdatabase.ThelatticeparametersextractedfromthesepatternsareshowninFigure5.31.Again,aswiththeindiumbasedsolidsolution,thelatticeparametersdecreasedlinearlywithincreasingseleniumconcentration,however,latticeparameterswereunabletobecalculatedfromthepatternofCuGaTeSe.AsthesamplecompositionmovedfromthepureendcompoundstowardsCuGaTeSeincreasedpeakbroadeningwasobservedlikelyduetolatticestrainfromthesizeofseleniumandtellurium.Thisbroad-eningcausedseveralofthedoubletpeakstooverlapinCuGaTeSeasshowninFigure5.30,preventingaclearofpeakpositions.Electronically,whilebothCuInTe2andCuInSe2hadbandgapsofaround1eV,CuGaTe2andCuGaSe2havereportedbandgapsof1.2eVand1.7eVrespectively.[8,111]Thislarge113wasevidentintheroomtemperatureelectricalresistivity,whichshowedanexpo-nentialdependenceonseleniumconcentrationasshowninFigure5.32.Thistrendcontinuedoverthewholetemperaturerange,asshowninFigure5.33,withCuGaSe2displayingare-sistivityroughly100xgreaterthanthatofCuGaTe2.Figure5.32:ThermalconductivityandelectricalresistivityoftheseriesCuGaTe2(1{x)Se2xatroomtemperature.Thermalconductivityshowsthetypicalparabolicrelationship,whiletheelectricalresistivityshowsanexponentialdependenceonseleniumconcentration.Figure5.33:ElectricalresistivityoftheseriesCuGaTe2(1{x)Se2xasafunctionoftempera-ture.114Figure5.34:SeebeckcotoftheseriesCuGaTe2(1{x)Se2xasafunctionoftemperature.TheSeebeckcotofCuGaTe2andCuGaTe1.5Se0.5werenearlyidentical,whilethatofCuGaTeSeandCuGaTe0.5Se1.5showedasharppeakat600K,justaswasseenintheindiumsolidsolution,againlikelyduetoaorder-disorderphasetransition.TheSeebeckcotofthepureselenidesampledisplayedabroadpeakat650Kreachingavalueof500µVK1,almostdoublethatofCuGaTe2.Figure5.35:PowerfactoroftheseriesCuGaTe2(1{x)Se2xasafunctionoftemperature.115Thepowerfactorwasfoundtodecreasewithincreasingseleniumconcentration,primar-ilyduetothelargeincreaseinelectricalresistivity.ByCuGaTeSethepowerfactorhaddroppedbyalmostafactorof10,overwhelmingthereductioninthermalconductivity.AsFigure5.32shows,thethermalconductivityfollowedtheexpectedparabolictrendinse-leniumconcentration,whiletheelectricalresistivityincreasedexponentially,leadingtoanoveralldecreaseinZT,asshowninFigure5.37.Figure5.36:ThermalconductivityoftheseriesCuGaTe2(1{x)Se2xasafunctionoftemper-ature.116Figure5.37:ZToftheseriesCuGaTe2(1{x)Se2xasafunctionoftemperature.5.4.5CuGa1{yZnyTeSeAftertheformationofthesolidsolutionCuGaTe2(1{x)Se2xsamplesofthemidpointcom-pound,CuGaTeSe,weresynthesizedwithvariouslevelsofdoping.Again,zincwasusedtosubstituteforgalliumasap-typedopant.CompositionsofCuGa1{yZnyTeSeweremadewithy=0.01,0.02,0.03,and0.05.Theelectricalresistivityofthesamplesdecreasedwithincreasingzincsubstitution,butthereductionwasminimalasshowninFigure5.38.117Figure5.38:ElectricalresistivityoftheseriesCuGa1{yZnyTeSeasafunctionoftemperature.TheSeebeckcotagainshowedapeakat600K,afterwhichitdipsdownwithallsamplesendinginthe200-250µVK1range,asshowninFigure5.39.Thecalculatedpowerfactorshowedthatthesamplewith1%zinchadthebestelectronicproperties,butdidnotimproveonthatoftheundopedCuGaTeSeat860K.Ajumpintheresistivity,andapeakintheSeebeckcotwasonceagainobservednear600Kforallofthesamples.Aswiththecasedescribedinsection5.4.3,itwashypothesizedthatthisisduetoanorder-disordertransition.118Figure5.39:SeebeckcotoftheseriesCuGa1{yZnyTeSeasafunctionoftemperature.Figure5.40:PowerfactoroftheseriesCuGa1{yZnyTeSeasafunctionoftemperature.Thethermalconductivityforallofthesamplesshowedsimilarvalues,reachingamini-mumvalueoflessthan1.0Wm1K1,indicatingthatthedopantatomshadlittleonthethermalconductivityasexpected.TheZTcalculationsshowedthatthepureandthe2%dopedsamplehadsimilarvalues,withthe2%showingahigheraverageZTfrom300Kto900Kthanthepurecompound.Thepeakvalueof0.20isstillmuchlowerthanthat119ofpureCuGaTe2,whichreachedavalueinexcessofunity.Figure5.41:ZTversustemperaturefortheseriesCuGa1{yZnyTeSe.5.5ConclusionsInthischapterfullsolidsolutionsofbothCuInTe2(1{x)Se2xandCuGaTe2(1{x)Se2xweresynthesizedandmeasured.Theindiumsolutionwasmadeusingboththespark-plasma-sinteringtechnique,aswellaswiththehotpress.ForpureCuInTe2itwasfoundthattheSPSleadtodensersamples,andthatinturnleadtobetterthermoelectricpropertiesandaZT.AsshowninFigure5.42allthreeseriesdisplayedaparabolicrelationbetweenseleniumconcentrationandthermalconductivity,withaminimumthermalconductivityobservedataratioofTe:Seof1:1.TheindiumbasedsamplesshowedalowerthermalconductivitywhenwiththeSPSthanwiththehotpress.120Figure5.42:Hightemperaturethermalconductivityoftellurium-seleniumsolidso-lutionsasafunctionofseleniumconcentration.CompositionsareCuGaTe2(1{x)Se2x,CuInTe2(1{x)Se2x(SPS)andCuIn0.99Zn0.01Te2(1{x)Se2x(HP).Measurementswereper-formedat860K.TheelectricalresistivitiesinFigure5.43exhibitedtwottrends.CuGaTe2(1{x)Se2xdisplayedanexponentialdependenceonseleniumconcentration,suggestingthatthein-creasingbandgap(1.2eVto1.7eV)istheprimarycauseoftheincrease.However,thiswasalsoseenintheSPSseriesofcompositionCuInTe2(1{x)Se2x,wherethebandgapisnegligible(bothendcompoundshavetheoreticalvaluesnear1eV).[107,108,109,97,98,99]Theindiumbasedseriesviahotpressshowedalesscleartrend,showingthelowerdensityhadontransportproperties.121Figure5.43:Hightemperatureelectricalresistivityoftellurium-seleniumsolidsolutionsasafunctionofseleniumconcentration.CompositionsareCuGaTe2(1{x)Se2x,CuInTe2(1{x)Se2x(SPS)andCuIn0.99Zn0.01Te2(1{x)Se2x(HP).Measurementswereperformedat860K.Ultimatelyneithersolidsolutionanincreaseinthethermoelectricofmerit.Theriseinelectricalresistivitywithseleniumsubstitutionwasmorethanbythereductioninthethermalconductivitythatwasobtainedfromthesubstitution.However,bothseriesofcompoundsgreattunabilityinelectricalresistivity.RoomtemperaturevaluesincreasedexponentiallywithseleniumconcentrationfromaroomtemperaturevalueofcmforCuGaTe2touptocmforCuGaSe2.CuInTe2(1{x)Se2xalsoshowedalargerangeinresistivity,withvaluesslightlyhigherthanthanofthegalliumbasedsample.122Chapter66.1FamilyOverviewInthefamilyoftherearethreecompoundsofinterest:CuInS2,CuGaS2,andCuFeS2.CuFeS2isdistinctforbeingtheonlyn-typematerialfoundinthisstudyaswellasforbeingthenaturallyoccurringmineralforwhichchalcopyritecompoundsarenamed.Again,thealuminumcontainingcompoundCuAlS2wasnotstudiedduetothesynthesisre-quired.Inparticular,thereactionbetweenaluminumandsulfurtoformAl2S3isextremelyexothermic.AttemptstosynthesizethecompoundfrompowderedCuandAl2S3commer-ciallyavailablewereunsuccessful,duetotherapiddecompositionofAl2S3intoAl2O3andH2Soncontactwithair.Quenchingandannealingofsamples,aswasdonewithseleniumandtelluriumbasedcompounds,leadtofrequentcrackingofampoulesduringsynthesis.Samplesweresuccess-fullysynthesizedbyslowheatingto900C,holdingfor24hours,slowcoolingto300C,holdingforanadditional24hours,andquenchingintowater.1236.2CuFeS2CuFeS2istheearth-abundantmineralknownaschalcopyrite,afterwhichthestructureisnamed.Thestructurewasoriginallyreportedin1917byBurdickandEllisasbeingtetragonalwithana:cratioof1:0.985,butwaslaterupdatedbyPaulingandBrockway,andfurtherbyHallandStewart,wheretheyobtainedlatticeparametervaluesofa=5.289Aandc=10.423A,givingana:cratioof1:1.97.[118,119,26]CurrentliteraturevaluesforlatticeparametersagreewiththoseobtainedbyHall,andsamplessynthesizedinthisworkhadaandcvaluesof5.286Aand10.431Arespectively.Figure6.1:XRDpatternofCuFeS2.ThepatternshownbelowisPDF#01-083-0983.[17]ThereportedbandgapofCuFeS2rangesfrom0.3to0.6eV,withrecentstudiestypicallycitingvaluesnear0.5eV.[120,121,23]Thatvalueismuchsmallerthanthe1.5eVor2.5eVfoundintheindiumandgalliumcontainingcompounds,howeverbandstructurecalculations124showtheconductionbandisalmostentirelyduetod-levelsofironwhichlieinanarrowbandrightabovetheFermilevel,breakingupwhatwouldotherwisebealargerbandgapbetweenthecopperandsulfurlevels.[121]CuFeS2wasfoundtobelessstablethanthepreviouslystudiedcompounds,showingamasslossaround700KforsamplesviaSPS,attributedtosulfursublimation.[18,19]Duetothisstabilityissue,propertiesofCuFeS2weremeasuredonlyupto450C,or723K.Figure6.2:SeebeckcotofCuFeS2asafunctionoftemperatureascomparedtoliteraturereports.DataisfromTsujiietal.andLietal..[18,19,20]125Figure6.3:ElectricalresistivityofCuFeS2asafunctionoftemperatureascomparedtoliteraturereports.DataisfromTsujiietal.andLietal..[18,19,20]AsshowninFigure6.2,CuFeS2exhibitedanegativeSeebeckcot,indicatingn-typecarriers.Thesamplessynthesizedhereagreedwellwithotherreportedmeasurements,withtheelectricalresistivitylyingdirectlybetweentworeportedvalues.[19,20]BoththeSeebeckcotfromthesamplesinthisstudy,andthesamplemeasuredbyTsujiietal.displayedabroadtemperaturedependence,withmagnitudesof300-500µVK1acrossthewholetemperaturerange.[18,19]Thisleadstoamaximumpowerfactorof3µWcm1K2from400Kto650Kforthesamplesynthesizedinthisstudy.126Figure6.4:PowerfactorofCuFeS2asafunctionoftemperatureascomparedtoliteraturereports.DataisfromTsujiietal.andLietal..[18,19,20]Figure6.5:ThermalconductivityofCuFeS2asafunctionoftemperatureascomparedtoliteraturereports.DataisfromTsujiietal.andLietal..[18,19,20]Thethermalconductivityshowstypicalbehavior,withtheexpected1/Ttemperaturedependence.At723Kaminimumvalueof1.5Wm1K1wasmeasured,incloseagreementwiththatofpreviousresultsasshowninFigure6.5.ThethermalconductivityofthesamplemadebyTsujiietal.showedastrongpeakinthermalconductivityatlowtemperature,127alongwithwithhigherelectricalresistivityasseeninreferenceFigure6.3,indicatingthesamplelikelyhadaloweramountofdefectsincomparisontothesamplesynthesizedhere.ThepeakZTvalueobtainedinthisstudyforpureCuFeS2was0.12,whilethatintheliteraturereachesapeakof0.21,primarilyduetoahigherelectricalresistivityfoundinsamplesstudiedhere.[20]Figure6.6:ZTofCuFeS2asafunctionoftemperatureascomparedtoliteraturereports.DataisfromTsujiietal.andLietal..[18,19,20]6.2.1ElectronicDopingAswithothersamples,zincwasusedasadopantelementforCuFeS2.However,sinceCuFeS2wasfoundtoben-type,zincwassubstitutedonthecoppersite,ratherthanforthegroupthreeelement.Thisreplacedamonovalentatomwithadivalentone,thelatteractingasann-typedonor.Samplesweresynthesizedwith1%and2%zincsubstitutingforcopper.Hallmeasurementsshowedanincreaseincarrierconcentrationfrom61018cm3at300Kfortheundopedsample,uptoavalueof11020cm3forboththe1%and2%zincdopedsamples.128Theectivemass(calculatedbycarrierconcentrationandSeebeckdatatoequa-tions(2.21)and(2.43))forthesamplesincreasedfrom3.1meforthepuresampleupto3.3meand4.1meforthe1%and2%zinccontainingsamples.Thevalueswerelargerthantypicalforann-typesemiconductor,butagreedwithpreviousstudiesbyTsujiietal.[19]BandstructurecalculationsshowCuFeS2hasabroadconductionband,inagreementwiththehighvaluesofemassobtainedbyHallmeasurementshere.[121]Figure6.7:ElectricalresistivityoftheseriesCu1{yZnyFeS2asafunctionoftemperatureascomparedtoliteraturereports.Opensymbolsrepresentdataobtainedhere,whilethesymbolsrepresentdatafromTsujiietal.andLietal..[18,19,20]AsisseenwhencomparingFigure6.3andFigure6.7,zincwasaneedopantatom,loweringtheelectricalresistivitygreatlywhencomparedtothenominallyundopedsamplesinagreementwiththeHallmeasurements.Atlowtemperaturesthedinelectricalresistivitybetweenthedopedandundopedsamplewasroughlytwoordersofmagnitude,whileatroomtemperaturethewasoneorderofmagnitude.Betweenthe1%and2%zincdopedsamplestherewaslittleinelectricalresistivityvalues,withbothsamplesexhibitingvaluesontheorderofcmingoodagreementwithresultsintheliterature,asshowninFigure6.7.129Figure6.8:SeebeckcotoftheseriesCu1{yZnyFeS2asafunctionoftemperatureascomparedtoliteraturereports.Opensymbolsrepresentdataobtainedhere,whilethesymbolsrepresentdataisfromTsujiietal.andLietal..[18,19,20]TheSeebeckcotshowedtypicaldegeneratesemiconductorcharacter,increasinginmagnitudelinearlywithtemperatureupto400K,atwhichpointtheSeebeckcotforallthesamplesstarttolevelout,likelyduetoanexcitationofminoritycarriers.Again,theliteraturedatamatchedcloselytothatobtainedinthisstudy.Figure6.9:PowerfactoroftheseriesCu1{yZnyFeS2asafunctionoftemperatureascom-paredtoliteraturereports.DataisfromTsujiietal.andLietal..[18,19,20]Theresultingpowerfactordatashowedthatthe1%and2%zincsamplesarenearlyindis-130tinguishableatlowtemperatures,butfrom300Kto600KthepowerfactorofCu0.99Zn0.01FeS2washigher.AsshowninFigure6.9Cu0.98Zn0.02FeS2matchedthe3%and5%dopedsam-plesshownintheworkbyLietal.,whilethehighervalueofCu0.99Zn0.01FeS2agreedwiththedatafromtheworkofTsujiietal.[19,20].Figure6.10:ThermalconductivityoftheseriesCu1{yZnyFeS2asafunctionoftemperatureascomparedtoliteraturereports.DataisfromTsujiietal.andLietal..[18,19,20]PreviousstudiesonCu(1{x)Fe(1+x)S2showedalargereductioninthermalconductivity,whichwasattributedtostrainfromchangesintheiron-sulfurandcopper-sulfurbondlengths.Heresimilarwereobservedwiththesubstitutionofzincforcopper,thoughtoasmallerextent.Thereductionat80Kist,fromnear7Wm1K1forpureCuFeS2downtoaround4.5Wm1K1forthezincdopedsamples,howeverat725Kallthesamplesshowedvaluesnear1.5Wm1K1.Again,goodagreementwasfoundbetweenthevaluesobtainedinthisstudyandthoseavailableinliterature.[20,19]131Figure6.11:ZToftheseriesCu1{yZnyFeS2asafunctionoftemperatureascomparedtoliteraturereports.DataisfromTsujiietal.andLietal.[18,19,20]ThepeakZTforthesamplesinthisstudymatchedverycloselytothatofLietal.asshowninFigure6.11,reachingamodestvalueof0.3ataround700Kforboththe1%and2%zincdopedsamples.[20]WhilethisvaluewaslowerthanthatobtainedfromCuInTe2orCuGaTe2,itdidalowcost,earth-abundantoption.6.2.2CuFeS2RapidSPSSynthesisThesynthesisofCuFeS2requiredalongslowheatingprocesstoavoidtherapidvaporizationofsulfurandsubsequentampouleexplosion.Lietal.showedin2013thatCuFeS2couldbesynthesizedbymechanicalalloyingandspark-plasma-sintering.[23]Thatstudyfoundthatplanetarymillingrawcopper,iron,andsulfurpowdersfor13hoursat450rpm,followedbysinteringat650CviaSPS,singlephasematerialcouldbeobtained.Asanalternativeapproachastudywasdoneonthedirectreactionofbinarypowdersbyspark-plasma-sintering.Rawbinarypowders(CuS99.8%200meshandFeS99.9%100mesh)wereweighedoutina1:1stoichiometricratioandplacedintoazirconiavibratory132milljar.Thepowderwasmilledforeminutestoensurehomogeneousmixing,afterwhichthepowderwasviasparkplasmasinteringateither450C,500C,or550Cwithaholdingtimeofeither5,10,or20minutes.Theresultsshowedthatsamplesat450Cweremultiphase,evenwithaholdtimeoftwentyminutes,whilethosesamplessynthesizedat500Coraboveweresinglephaseinaslittleaseminutes.Asshownbelow,theballmillingmixedthebinarypowdersbutdidnotresultinanyinitialmechanicalalloying.However,afterSPS,samplesmadeat500Cwerefoundtobesinglephase.Figure6.12:Thetoppatternisfortwopowdersmixedbyhand,themiddlepatternisthepowderafter5minutesofvibratorymilling,andthebottompatternistakenafterthepowderhasbeendbytheSPS.ThepatternsshownbelowarePDF#01-083-0983,PDF#01-079-2321,andPDF#03-065-6841forCuFeS2,CuS,andFeSrespectively.[17,21,22]133Table6.1:DensityofsamplesofCuFeS2synthesizedbydirectSPSreaction.ThetheoreticaldensityofCuFeS2is4.1823gcm3usingthelatticeparametersobtainedfromXRD.|450C500C550C5minFailed4.1594gcm34.1566gcm310minFailed4.2150gcm34.2002gcm320minFailed4.1950gcm34.2190gcm3AsshowninTable6.1above,thesamplesheldforeminutesshowedamarkeddecreaseindensityascomparedtothoseheldfortenortwentyminutes.Forcomparison,thedensityofCuFeS2madewiththeconventionalfurnaceheatingandhotpressinghadameasureddensityof4.005gcm3.Thesamplesheldat550Cdisplayedamuchmorebrittlecharacter,oftenchippingandcrackingwhilecutting.Thereisnohightemperaturethermalconductivityforthesamplessynthesizedat550Cduetothediscscrackingduringthecuttingandsandingprocess.Figure6.13:ElectricalresistivityofseveralsamplesofCuFeS2asafunctionoftemperature.SamplesweresynthesizedbydirectreactionduringSPS.ThesquaresrepresentsCuFeS2madebytraditionalmeltingandhotpressing.134Figure6.14:SeebeckcotofseveralsamplesofCuFeS2asafunctionoftemperature.SamplesweresynthesizedbydirectreactionduringSPS.ThesquaresrepresentsCuFeS2madebytraditionalmeltingandhotpressing.Figure6.13showsthattheSPSsynthesizedsamplesweremuchmoreelectricallyconduc-tive,withthedatafortheSPSsamplesconsistentlyanorderofmagnitudeormorebelowthehotpressedsample.Inlinewiththis,Figure6.14showedalargedecreaseinthemagnitudeoftheSeebeckcotascomparedthehotpressedsample.135Figure6.15:PowerfactorofseveralsamplesofCuFeS2asafunctionoftemperature.SamplesweresynthesizedbydirectreactionduringSPS.ThesquaresrepresentsCuFeS2madebytraditionalmeltingandhotpressing.AsFigure6.15shows,thecompoundsdirectlyreactedintheSPSdisplayedamuchimprovedpowerfactor,thoughstilllessthanthezincdopedsamplesofCuFeS2displayedpreviouslyinFigure6.9.Thesamplessynthesizedat550Cshowlargervaluesthanthesamplessinteredat500C,howeverasmentionedabove,theyweremechanicallylessrobust,andpronetochipping.136Figure6.16:ThermalconductivityofseveralsamplesofCuFeS2asafunctionoftemperature.SamplesweresynthesizedbydirectreactionduringSPS.ThesquaresrepresentsCuFeS2madebytraditionalmeltingandhotpressing.ThethermalconductivityalsoshowsalargereductionwithSPSsynthesis.Thiscouldbeduetothesmallparticlesize(100and200mesh,or150and75micron)startingpowdersleadingtoasmallergrainsizeaftersintering,whichinturnleadtoincreasedphononscattering.137Figure6.17:ZTofseveralsamplesofCuFeS2asafunctionoftemperature.SamplesweresynthesizedbydirectreactionduringSPS.ThesquaresrepresentsCuFeS2madebytradi-tionalmeltingandhotpressing.InattemptingtounderstandtheintheSPSdirectreactionsamplesascom-paredtotheconventionallymadesamplesoneconcernwassulfursublimationduringsynthe-sis.Thisseemstobealikelyoccurrence,andcomparisontoworkbyLietal.appearedtothehypothesis.TheirworkstudiedsynthesisofCuFeS2bymechanicalalloyingviaplanetarymilling,andalsostudiedintentionallysulfurtchalcopyrite,CuFeS2{x.[23]Theyshowedthatthesinteringtemperaturewascrucialforcontrollingsulfurloss,andre-portedpropertiesonintentionallysulfurtsamples.138Figure6.18:ElectricalresistivityofseveralsamplesofCuFeS2synthesizedbydirectreactionduringSPScomparedtoliteraturevaluesforCuFeS2{.TheXsymbolrepresentsthedatafromsamplesmadeinthisstudy,theothersymbolsarefromLietal.[23]Figure6.19:SeebeckcotofseveralsamplesofCuFeS2synthesizedbydirectreactionduringSPScomparedtoliteraturevaluesforCuFeS2{.TheXsymbolrepresentsthedatafromsamplesmadeinthisstudy,theothersymbolsarefromLietal.[23]Comparingtheelectricalproperties,thesamplessynthesizedhereappeartoberoughlyCuFeS1.75,asisseenbycomparingFigure6.18andFigure6.19.Thissulfurlossissomewhatunsurprising,asoneofthebinarypowders,CuS,isreportedtodecomposeat507C.[122]139ThisindicatesthatthemajorityoftheCuSisreactingwithFeS,butintheprocesssomeofthesulfurissublimatingtooquicklytoreact.6.3CuInS2CuInS2hasareportedbandgapof1.47eVto1.55eVandcanreportedlybedopedeithern-orp-type,howeverthesamplessynthesizedinthisstudywererepeatedlyfoundtobep-typeandhighlyresistive.[123,124]ThesampleshownbelowwassynthesizedinthesamemannerasCuFeS2,withperformedbyhotpressing.Figure6.20showsacleansinglephaseXRDpattern,indicatingthesamplepuritywashigh.Shownbelowistheelectricalresistivityandthermalconductivity.Nohightemperaturepropertiesweremeasured,asthesamplewastooresistivetobemeasuredintheZEM3.Figure6.20:XRDpatternofCuInS2.ThepatternshownbelowisPDF#01-075-6866.[24]140Figure6.21:ElectricalresistivityofCuInS2asafunctionoftemperatureFigure6.22:ThermalconductivityofCuInS2asafunctionoftemperature6.4CuGaS2CuGaS2isawidegapsemiconductor,withareportedbandgapof2.4to2.5eV.[125,110,25]StudiesbyTelletal.foundthatsamplesthatwereannealedunderhighsulfurpressuredisplayedaroomtemperatureelectricalresistivityof1103cm,whilesamplesannealed141underalowpressureofsulfurhadaroomtemperatureelectricalresistivitygreaterthan1108cm.[125,110]AsseeninFigure6.23,datafromworkbyJulianetal.showssimilarresults,withelectricalresistivitiesinexcessof1107cm.[25]Duetothehighelectricalresistivityandlargebandgap,nosamplesofCuGaS2weresynthesizedinthisstudy.Figure6.23:ElectricalresistivityofseveralsamplesofCuGaS2fromworkbyJulienetal.Thesamplesweresimplydescribedbytheirapparentcolors.[25]6.5SolidSolutions6.5.1CuFeS2(1{x)Se2xAlthoughCuFeSe2doesnotforminthechalcopyritestructure,andassuchafullsolidsolutionwasunabletobeformed,thesolubilitylimitofseleniumforsulfurwasnonethelessstudied.[105,106,126]Samplesweremadewith5%incrementsofseleniumsubstitutionupto30%,abovewhichpointsecondaryphaseswerediscoveredbyXRDandDSC.142Figure6.24:XRDpatternsoftheseriesCuFeS2(1{x)Se2x.ThetoppatternispureCuFeS2,witheachpatternbeneathitincreasingxby0.05,theatthebottombeinglpatternCuFeS1.4Se0.6.Notetheadditionalpeaksinthebottompattern,indicatingthepresenceofasecondaryphase.PDFsforpatternsare#01-075-6866and#01-081-1959forCuFeS2andCuFeSe2respectively.[26,27]143Figure6.25:LatticeparametersoftheseriesCuFeS2(1{x)Se2xasafunctionofx.Increasingseleniumleadstoalargerlattice,howeveratx=0.3thegrowthstops,asasolubilitylimitisreached.AsshowninFigure6.25,seleniumsubstitutioncausedashiftintheXRDpeakstowardslower2,indicatinganincreaseintheunitcellsizeasexpectedfromthelargerionicradiusofselenium.AsshowninFigure6.25boththeaandclatticeparametersincreaselinearlyinseleniumconcentrationuptox=0.25(CuFeS1.5Se0.5),butabovethisthex=0.3sampleshowsnearlyidenticalparametersasthatofx=0.25,indicatingtheseleniumisnolongergoingintothestructuresubstitutionallyforsulfur.144Figure6.26:SpheatoftheseriesCuFeS2(1{x)Se2xasafunctionoftemperature.Thepeaksindicatedecompositionintoamixtureofbinaryphases,followedbythesublimationofsulfur.Figure6.27:TemperatureofthepeakintheDSCcurvefortheseriesCuFeS2(1{x)Se2x.Thepeaksindicatedecompositionintoamixtureofbinaryphases,followedbythesublimationofsulfur.AsthespcheatdatashowsinFigure6.26,alargepeakisobservedforallthe145samplesathightemperature.WorkbyTsujiietal.usingthermogravimetricandtialthermalanalysis(TG-DTA)foundthatat820KCuFeS2decomposedintoamixtureofFeS2,CuS,andFeS,andshortlyabovethattemperaturesulfursublimated.[19]ThisalignsverywellwiththeobserveddatafromourDSCmeasurements,whereapeakinspheatisobservedat840K.Aswesee,withincreasingseleniumconcentration,thepeakshiftstolowertemperatures.Itissurmisedthatlatticestrainfromthelargeratomicradiusofseleniumpushesthetransitiontolowertemperatures.Alineartrendwasfoundbetweentheseleniumconcentrationandthetemperatureatwhichthespcheatcurvepeaked,asshowninFigure6.27.Forthex=0.30sample,(CuFeS1.4Se0.6)asecondpeakwasobservedintheDSC.This,alongwiththeextrapeaksinXRDthematerialwastwophaseandthatasolubilitylimithadbeenreachedbetween25%and30%.Figure6.28:ElectricalresitivityoftheseriesCuFeS2(1{x)Se2xasafunctionoftemperature.146Figure6.29:SeebeckcotoftheseriesCuFeS2(1{x)Se2xasafunctionoftemperature.Figure6.28showsthatincreasingseleniumsubstitutionleadtoadecreaseinelectricalresistivity.Asthesubstitutionisisoelectronic,itissuspectedthatadecreaseinthebandgapiscausingthisratherthandoping.TheSeebeckcotshowedaslightdecreaseinmagnitudewithincreasingseleniumconcentrationasshowninFigure6.30,inlinewiththedecreasedelectricalresistivity,butallsamplesstilldisplayednegativevaluesindicatingn-typecarriers.147Figure6.30:PowerfactoroftheseriesCuFeS2(1{x)Se2xasafunctionoftemperature.TheincreaseintheelectricalconductivitycombinedwiththeminimaldropinSeebeckcotmagnitudeleadtoariseinpowerfactor,withCuFeS1.6Se0.4showingthehighestvalue.ThebroadpeakinSeebeckcotismirroredinthepowerfactor,withvaluesabove350Knearlytemperatureindependent.ThevaluesarecomparabletothatobtainedfromthesamplessynthesizedbydirectSPSreactionofpowders.Figure6.31:ThermalconductivityoftheseriesCuFeS2(1{x)Se2xasafunctionoftempera-ture.148Theisoelectronicsubstitutionofseleniumforsulfurcausedalargedropinthermalconductivityatlowtemperatures,asshowninFigure6.31,andwiththeexceptionofCuFeS1.7Se0.3alltheseleniumcontainingsamplesexhibitlowerthermalconductivitythanthepureCuFeS2sample.Ultimately,valuesnear1.3-1.5Wm1K1areobtainedforallthesamplesare700K.Figure6.32:ZToftheseriesCuFeS2(1{x)Se2xasafunctionoftemperature.OveralltheZTisincreasedforthreesamples:CuFeS1.9Se0.1,CuFeS1.6Se0.4,andCuFeS1.5Se0.5,whilefortheothersamplestheresultingZTisthesameasthatoftheunmoCuFeS2.Atradeisalsofoundwithseleniumconcentration,asincreasingtheseleniumcontentlowersthemaximumoperatingtemperatures,asshownbyDSCmeasurements.6.5.2CuFeS2(1{x)Te2xAsstatedintheintroduction,CuFeTe2doesnotforminthechalcopyritestructure,butratherformsalayeredstructurewithspacegroupP4/nmm.[127,128]Itisreportedaszerogapsemiconductor,withareportedroomtemperaturecarrierconcentrationontheorderof14911020cm3to11021cm3.[129,130]SamplesofCuFeTe2werenotsynthesizedinthisstudy,duetotheirdtstructure,andthezerogapnaturemakingCuFeTe2illsuitedforthermoelectrics.However,sampleswithlowamountsoftelluriumweresynthesizedtoestablishthesolubilitylimitoftelluriuminCuFeS2.AsFigure6.33shows,evenwithonly5%ofsulfurreplacedwithtelluriumextrapeakswereobserved.Figure6.33:XRDPatternsofCuFeS2(1{x)Te2x.ThetoppatternisforpureCuFeS2,followedbyx=0.05,0.10,0.2,and0.3.ThepatternsbelowarefromPDF#01-075-6866and#01-070-3094forCuFeS2andCuFeTe2respectively.[26,28]6.5.3CuFe1{xGaxS2AnattemptwasmadetoformasolidsolutionofCuFeS2withCuGaS2.Whilethetwocompoundsareelectronicallyveryt(reportedbandgapof0.5eVversus2.4eV)[125,110,25,120,121,23]thelatticeparametersareverysimilar.However,allattemptstomakeasolidsolutionyieldedamulti-phasematerial,typicallyconsistingofamixtureof150CuFeS2,CuGaS2,andGaS.Thesampleswerealsoverypronetocrackingtheampoulesuponquenching.6.6ConclusionsThecompoundswerefoundtobeoveralllesspromisingthanthetelluridecompoundsforthermoelectricapplications.CuInS2andCuGaS2displayedlargeelectricalresistivities,aswasexpectedfromtheirlargerbandgaps(roughly1.5eVand2.5eVrespectively).However,theearth-abundantmineralforCuFeS2showedintriguingproperties.Itdisplayedn-typeconduction,standingoutfromalloftheothermaterialsstudiedinthisfamily,aswellasasmallerbandgap(0.3eV-0.5eV)whencomparedtoothercompoundsstudiedinthiswork.However,theperformanceislimitedsomewhatbysulfursublimation,limitingtheoperatingtemperaturetolessthan450C.CuFeS2alsoshowedpoorsolubilitylimitswithisoelectronicelements.Attemptstosub-stitutegalliumforironortelluriumforsulfurwasunsuccessfulonalllevels,andonlyyieldedmultiphasematerial.Thesolubilitylimitforseleniumonthesulfursitewasfoundtobebetween25%and30%,however,substitutingseleniumpushedthesublimationpointtolowertemperatures,loweringthepossibleoperatingtemperaturefurther.ZincwasfoundtobeanctivedopantforCuFeS2,givinganincreaseinZTtoapeakvalueof0.3at725K.ItwasalsofoundthatsulfurtCuFeS2couldberapidlysynthesizedbydirectlyspark-plasma-sinteringmixturesofCuSandFeS,withpeakZTvaluesagainnear0.3.OverallCuFeS2doespromiseasareasonablygoodthermoelectricwithn-typeprop-ertiesthatcouldbepairedwithoneofthemanyotherp-typechalcopyritecompounds.151Chapter7RelatedMaterialsAspartofourstudyofchalcopyritecompoundssomesimilarandrelatedphaseshavebeeninvestigatedaswell.Theseincludeanaturallyoccurringmineralcalledbornite(Cu5FeS4),aswellasseveraldefect-chalcopyritephases.7.1Bornite:Cu5FeS4Borniteisanaturallyoccurringmineral,asisCuFeS2,howeverthestructureofborniteismuchmorecomplex.Ithasreportedstructuralphasetransitionsatboth200Candat265C.[131,132,133]Thehightemperaturephaseisacubicstructure(spacegroupFm3m)withareportedlatticeconstantaof5.49A,consistingofanFCCsulfurlattice,withcopper,iron,andvacanciesontheeighttetrahedralinterstitialsites.Atintermediatetemperaturesthecompoundformsasuperstructure(stillFm3m)withalatticeparameteraof10.95A,whichonecanpictureasadoubleofthecellinallthreecrystallographicdirections,withlongrangeorder.Below200Cthecompoundformsamorecomplexsuperstructurewhichisorthorhombic(spacegroupPbca)witha=b=10.95Aandc=21.862A.[30]152Figure7.1:XRDpatternofnominallypurebornite(Cu5FeS4)andfourdopedcompositions.ThetoppatternispureCu5FeS4,followedbythe1%and5%p-typedopedsamples,andthe1%and5%n-typedopedsamples.Theextrapeaksobservedinthe1%n-typesampleareduetoasecondaryphaseofFeS.They-scaleisintensity,inarbitraryunits.Source:PDF#98-000-0123.[29]Inthiswork,samplesofpurebornite,alongwithfourzincdopedsamplesweresynthe-sized.Bornitehasbeenshowntoexhibitbothn-andp-typeconduction,andsodopingwasattemptedwithzinconboththecopper(nominallymonovalent)andtheiron(nominallytrivalent)sitesinanattempttodopeitbothp-andn-type.AsshownFigure7.1the1%n-typedopedsample(Cu4.95Zn0.05FeS4)showedextrapeaks,whichwereidenasFeS,howevertheothersamplesallappearedtobesinglephase,matchingwelltothedatabasepattern.[29]153Figure7.2:Electricalresistivityofsamplesofnominallypurebornite(Cu5FeS4)andfourdopedcompositionsasafunctionoftemperature.Literaturedataisshownwithcoloredsymbolsforcomparison.[30,31]Figure7.3:Seebeckcotofsamplesofnominallypurebornite(Cu5FeS4)andfourdopedcompositionsasafunctionoftemperature.Literaturedataisshownwithcoloredsymbolsforcomparison.[30,31]AsseeninFigure7.2bornitedisplayedaverylargeelectricalresistivityat80K,withthepuresample,aswellasthedopedsamples,showinganelectricalresistivitynear1109cm.Thevaluedroppeddramaticallywithtemperature,possiblyindicatinganarrow154bandgap,withallsamplesmeasuredhere,aswellasliteraturevalues,droppingto10-15cmat800K.[30,31]TheSeebeckcotatlowtemperaturesdisplayedn-typeconductionforallsamples.ThedatafromtheZEMshowedalargermagnitudethanthecryostatdataat300K,givinganinthedata,forallsamplesexceptCu4.95Zn0.05FeS4.Again,withtheexceptionofCu4.95Zn0.05FeS4whichshowedimpuritiesinXRD,theSeebeckcotforthesamplesshowachangeintrendnear420K(150C)withalargeupwardswing.Overtherangefrom420Kto520KCtheSeebeckcotofCu5FeS4increasesfrom-378µVK1to+195µVK1,achangeofnearly600µVK1.Thisswingcorrespondstotheinitialphasetransition,whichwasreportedtooccurat470K.Above520K,theSeebeckcotdis-playsasmalldownwardtrend,withthesamplesremainingpositivefortheremainderofthemeasurement.Whiletheelectricalresistivityisverysimilarforallesamples,regardlessofthezincdopinglevel,theSeebeckcotdidshowaatlowtemperature.Theirwasnocleartrendwithzincconcentration,indicatingzincwaseasadopant.Withthehighamountofvacanciesinthecompound,itistoknowwherethezincwillsitinthelattice.155Figure7.4:Powerfactorofsamplesofnominallypurebornite(Cu5FeS4)andfourdopedcompositionsasafunctionoftemperature.Literaturedataisshownwithcoloredsymbolsforcomparison.[30,31]ThestrongdecreaseinelectricalresistivityalongwiththerelativelySeebeckcoef-tabove500Kleadstoasharpincreaseinthepowerfactor.Allofthesamplespeaknear700K,withpeakvaluesrangingof2-3µWcm1K2.ThesamplessynthesizedherematchwellwiththedatapublishedbyQiuetal.,whilethatfromGuelouetal.ThesamplesinthestudybyGuelouweresynthesizedbymechanicalalloying;therawelemen-talpowderswereballmilledfor20hoursbeforehotpressing.[31]ThosesynthesizedinthereportbyQiuweresynthesizedinthesamefurnacetechniqueasthosesamplesmeasuredinthisstudy.[30]ThehigherpowerfactorseeninthestudybyGuelouascomparedtothatobtainedinworkhereandthedatareportedbyQiu,couldbeduetothehighsensitivitytodefectsorstoichiometry.Thetsynthesistechniques(mechanicalalloyingbyGuelouversustraditionalmeltandquenchtechniqueusedinthisworkandbyQiu)couldalsoplayanimportantroleincontrollingtheelectronicpropertiesofthematerial.156Figure7.5:Thermalconductivityofsamplesofnominallypurebornite(Cu5FeS4)andfourdopedcompositionsasafunctionoftemperature.Literaturedataisshownwithcoloredsymbolsforcomparison.[30,31]Thethermalconductivityforallsamplesshowedverylowvalues,lessthan1.0Wm1K1.AsshowninFigure7.5thethermalconductivityinitiallyshowedarisewithtemperature,withapeaknear300K,afterwhichthevaluesdroptoaminimumat500K,thesametemper-atureatwhichtheSeebeckcoientchangedsign,correspondingtothephasetransition.Thethermalconductivityshowsariseabovethistemperature,howeverthevalueforthesamplesremainedbelow1Wm1K1.Thermalconductivityisnotshownforthepurebornite,orforCu4.95Zn0.05FeS4orCu4.75Zn0.25FeS4becausethelaserdiscsbroke.Bornitewasfoundtobebrittle,andthediscswerepronetocracking.157Figure7.6:ZTofsamplesofnominallypurebornite(Cu5FeS4)andfourdopedcompo-sitionsasafunctionoftemperature.Literaturedataisshownwithcoloredsymbolsforcomparison.[30,31]TheresultingZTisshowninFigure7.6.WorkbyGuelouetal.showedapeakZTofnear0.55at540K,whilethedatafromQiuetal.,aswellatdataforsamplesinthisstudyshowedapeakintheZTat700K,withapeakvalueofjustover0.40forCu4.95Zn0.05Fe0.95S4.ZTisnotshownfortheothersamplesathightemperaturebecausethelaserdiscsbroke,andnothermalconductivitydatawasavailable.Bornitehasalsobeenreportedtobeacopperionicconductor,whichwouldbedetrimentaltoitsuseasathermoelectric.However,furtherstudiesintodopingcouldalleviatethisissue,ashasbeenshownwithtetrahedrite.[134,135]7.2DefectChalcopyrite:Zn0.5GaTe2andZn0.5InTe2Thedefectchalcopyritestructurecanbethoughtofasreplacinghalfofthemonovalentatomswithadivalentatomwhileleavingtheotherhalfemptyasvacancies,maintainingtheaveragevalencecountof4peratom.Inthisworkdivalentzincwassubstitutedforhalfof158themonovalentcopper.ThecompoundsZn0.50GaTe2,Zn0.475GaTe2,andZn0.50InTe2weresynthesizedandthelowtemperaturepropertiesweremeasured.Figure7.7:XRDpatternsofthedefectchalcopyritecompounds:Zn0.5GaTe2,Zn0.475GaTe2,andZn0.5InTe2fromtoptobottomrespectively.They-scaleisintensity,inarbitraryunits.Source:PDF#01-089-4209and#01-074-0218forZn0.5GaTe2andZn0.5InTe2respectively.[4]FirstprinciplecalculationsperformedonZn0.5GaS2,Zn0.5GaSe2,andZn0.5GaTe2pre-dictedthebandgapofZn0.5GaTe2tobe0.53eV,veryclosetothatofCuFeS2.[136]ThereportedlatticeparametersforZn0.5GaTe2area=5.26Aandc=10.39A,givingac:aratioof1.98:1.TheXRDpatternsshowninFigure7.7matchtothepublishedpatternsbyHahnetal.forbothZn0.5GaTe2andZn0.5InTe2.159Figure7.8:Electricalresistivityofdefectchalcopyritecompounds,withCuGaTe2asaref-erence,asafunctionoftemperature.Figure7.9:Powerfactorofdefectchalcopyritecompounds,withCuGaTe2asareference,asafunctionoftemperature.AsshowninFigure7.8,theelectricalresistivityofthedefectsampleswasmuchhigherthanthatofthenominallyundopedCuGaTe2.Zn0.50GaTe2displayedanelectricalresistiv-itynear1107cmfrom80-350K,whiletheindiumcontainingsample,andthevacancyheavysample(Zn0.475GaTe2)bothdisplayedanelectricalresistivityseveralordersofmag-160nitudehigher.TheSeebeckcotdataisnotshownhere,asthehighresistivitymadethevaluetomeasure.NonethelessthepowerfactorisshowninFigure7.9,anditcanbeseenthatthedefectstructurehasanepowerfactorofzerowhencomparedtoCuGaTe2.Figure7.10:Thermalconductivityofdefectchalcopyritecompoundsasafunctionoftem-perature.Thethermalconductivityshowedremarkablylowvalues,asshowninFigure7.10.Allofthedefectsamplesshowvaluesmuchlowerthanthenormalchalcopyritestructurecom-pound.TheroomtemperaturethermalconductivityofCuInTe2isnear4.5Wm1K1,whileZn0.50InTe2isnearlyhalfofthat,witharoomtemperaturevalueof2.5Wm1K1.Thegalliumcontainingcompoundshowedanevenlargerdeduction;theroomtemper-aturethermalconductivityofCuGaTe2was7.0Wm1K1,whilethatofZn0.50GaTe2isonly0.45Wm1K1,andthatofZn0.475GaTe2is1.75Wm1K1.Thisdrasticreductioninthermalconductivity,especiallywhencomparingtheindiumcontainingsampletothegalliumcontainingsample,isnotfullyunderstoodatthetime.Previousworkscomparingthedefectzinc-blendecompoundsIn2Te3andGa2Te3found161thethermalconductivityofIn2Te3toberoughlythreetimesaslargeasthatofGa2Te3atroomtemperature.WorkbyKurosakifoundthatGa2Te3naturallyformedsuperlatticestructureswithorderedlayersofvacanciesthroughoutthestructure,andattributedtheinthermalconductivityvaluestothat.[137]Whetherasimilarmechanismisre-sponsibleinZn0.50GaTe2isunknownatthistime,futureworkonthismaterialwouldbeenlightening.Whilethethermalconductivitydropwasdramatic,thepowerfactornegatedallthebandtheresultingZTwaselyzeroforthefulldefectcompounds,asshowninFigure7.11.Figure7.11:ZTofdefectchalcopyritecompoundsasafunctionoftemperature.7.2.1SolidSolution:CuGaTe2-Zn0.5GaTe2InattempttogainsomeofthethermalconductivitybofZn0.5GaTe2whilemaintainingtheelectricalpropertiesofCuGaTe2asolidsolutionwasformedstartingfromCuGaTe2andsubstitutingsmallamountsofZn0.5GaTe2.AsshowninFigure7.12therewasnovisiblechangeinXRDpatternuptoCu0.8Zn0.1GaTe2.162Figure7.12:XRDpatternsofthepartialsolidsolutionofCuGaTe2andZn0.5GaTe2.ThetoppatternisCuGaTe2,followedbyCu0.995Zn0.0025GaTe2,Cu0.990Zn0.0050GaTe2,Cu0.900Zn0.0500GaTe2,andatthebottomCu0.800Zn0.1000GaTe2.ThePDFoverlayisforCuGaTe2.They-scaleisintensity,inarbitraryunits.Source:PDF#01-079-2331.[7]Figure7.13:ElectricalresistivityofthepartialsolidsolutionCuGaTe2-Zn0.5GaTe2asafunctionoftemperature.163Figure7.14:SeebeckcoentofthepartialsolidsolutionCuGaTe2-Zn0.5GaTe2asafunctionoftemperature.Theelectricalresistivityshowedaslightdecreasewithsmallamountsofvacancies,butforlargeramountstheresistivityincreasedtovaluesgreaterthanthepurecompound.Thiswasmostevidentatlowtemperatures,athightemperaturesallsamplesshowedsimilarvaluesforelectricalresistivity,asshowninFigure7.13.TheSeebeckcotshowedsimilarresults,withmoreelectricallyconductivesamplesdisplayinglowerthermopowervaluesasistypical.AsshowninFigure7.14theSeebeckcoentofallsamplesrangedfrom200-250µVK1.164Figure7.15:PowerfactorofthepartialsolidsolutionCuGaTe2-Zn0.5GaTe2asafunctionoftemperature.CombiningtheelectricalresistivityandSeebeckcot,thepowerfactorshowedanincreasewith0.005and0.025zincconcentrations,andadecreaseforhigheramounts.Thevalueat870Kwassimilar,butthesampleswithsmallamountsofzincshowedahigherpeakandaveragevalue,asshowninFigure7.15.Figure7.16:ThermalconductivityofthepartialsolidsolutionCuGaTe2-Zn0.5GaTe2asafunctionoftemperature.165Thegoalinmindwiththesolidsolutionwastolowerthethermalconductivity,andasshowninFigure7.16thewassomewhatsuccessful.Thesubstitutionofzincandvacanciesonthecoppersitedecreasedthethermalconductivitywitheachincrease,howeveraswithothersolidsolutionsstudiedhere,athightemperaturesthedecreasewassmall.Figure7.17:ZTofthepartialsolidsolutionCuGaTe2-Zn0.5GaTe2asafunctionoftem-peratureThepeakZTwasslightlyenhancedforCu0.99Zn0.005GaTe2andCu0.95Zn0.025GaTe2,andtheaverageZTwasincreasedforCu0.99Zn0.005GaTe2.7.3CoppertCuGaTe2StudyingCu0.90ZnxGaTe2totheoptimumzincconcentration,itwasfoundthatsampleswithnozincatall,andasimple10%copperhadthebestproperties.ThatresultledtoaseriesofsampleswithcompositionCu1{xGaTe2andx=0,0.05,0.10,and0.15.Figure7.18showednodiscerniblechangeintheXRDpatternsupto15%copper.166Figure7.18:XRDpatternofcopperdtCuGaTe2.ThetoppatternisCuGaTe2,followedbythe5%,10%,and15%coppersamplesrespectively.They-scaleisintensity,inarbitraryunits.Source:PDF#01-079-2331.[7]Figure7.19:Carrierconcentrationandmobilityat300KfortheseriesCu1{xGaTe2asafunctionofvacancyconcentration(x).AsshowninFigure7.19,Hallmeasurementsrevealedthattheremovalofsmallamounts167ofcoppercausedadropincarrierconcentration,andanincreaseinthemobility.Above10%copperalargeincreaseinthecarrierconcentrationandadecreaseinthemobilitywasobserved.Itissuspectedthatthelargevacancyconcentrationcausesincreasedscatter-ing,loweringthemobility,andtheremovalofcopperactedasap-typedopant.However,theinitialdropincarrierconcentrationforlowamountsofvacanciesisnotfullyunderstood.Theelectricalresistivity,showninFigure7.20,alsoshowedinterestingtrends.Cu0.90GaTe2inparticulardisplayedaninitialincreaseinelectricalresistivity,followedbyapeakandthenfollowedatrendsimilartotheothersamples.HightemperatureHallmeasurementswouldaddmuchneededinformationandpossiblyexplainthemechanismcausingthisbehavior.Figure7.20:ElectricalresistivityoftheseriesCu1{xGaTe2asafunctionoftemperature.168Figure7.21:SeebeckcotoftheseriesCu1{xGaTe2asafunctionoftemperature.The5%coppertsampledisplayedanincreaseinSeebeckcotascomparedtothepurecompounduntil650K,atwhichpointthetwosampleswerenearlyindistinguish-able.However,the10%and15%showedadropofabout50µVK1acrossmostofthetemperaturerange,asshowninFigure7.21Figure7.22:PowerfactoroftheseriesCu1{xGaTe2asafunctionoftemperature.Thepowerfactorforallfoursamplesissimilarintrend,withasteepincreasenear400K,169andoutat650K.AllthreecoppertsamplesshowedvalueshigherthanthepureCuGaTe2,withthe5%samplebeingthehighestbyasmallmargin.Figure7.23:ThermalconductivityoftheseriesCu1{xGaTe2asafunctionoftemperature.Figure7.23showsthatthecoppercausedadecreaseinthermalconductivity,aswasexpectedfromtheadditionofvacancies.The5%coppertsampleshowedonlyaminimaldecrease,butthe10%and15%samplehadroomtemperaturevaluesroughlyhalfthatofthepureCuGaTe2,whichcombinedwiththeincreasedpeakpowerfactor,leadtoanincreaseinZT.TheZTwashigherforallofthecoppertsamples,withCu0.90GaTe2andCu0.85GaTe2matchingcloselyoverthewholerange.Apeakvalueof1.22wasreachedforCu0.90GaTe2,ascomparedtoCuGaTe2whichhadapeakvalueof0.97at870K.170Figure7.24:ZToftheseriesCu1{xGaTe2asafunctionoftemperature.171Chapter8ConclusionsandFutureWorkThegoalofthisworkwastounderstandtheunderlyingphysicsofthechalcopyritefamilyofsemiconductorsandtostudyhowtotunetheelectronicandthermaltransportproperties.Thechalcopyritefamilycontainsalargenumberofcompoundswithawiderangeofelectronicandthermalproperties.Thebandgapofcopperbasedchalcopyritecompoundsrangesfrom0.53eVforCuFeS2upto3.49eVforCuAlS2whichawiderangeforthermoelectricorphoto-voltaicapplications,aswellasanabilitytounderstandtheconnectionbetweenthebandstructureandthephysicsofthetransportproperties.Thiswiderangeofbandgapvaluesisinthegreatrangeofelectricalresistivitiesreportedinthiswork,showninFigure8.1.[92,23]FurthermoreasshowninFigure8.2,thecomplexcrystalstructureofthechalcopyritecompoundsleadtothermalconductivityvaluesatorbelow1Wm1K1athightemperaturesforallofthecompoundsstudiedhere,andthedefectchalcopyritecompoundsshowedthatvacancysubstitutioncouldreducethosevalueevenfurther.Theelectronicpropertiescoveredawiderange,andwhilethecompoundswerenotintrinsicallyveryconductive,p-typedopingwaseinincreasingthecarrierconcentrationandreducingtheelectricalresistivitywithmostofthecompoundsinthisstudy.Itshouldalsobenotedthatfora\pure"intrinsicsemiconductortheequationsdiscussed172inChapter2givearoomtemperaturecarrierconcentrationontheorderof1010-1013cm3.However,thenominallyundopedsamplessynthesizedinthisstudyallshowedmuchhigherroomtemperaturecarrierconcentrations,typicallyontheorderof10171018cm3.Thisindicatesahighlevelofintrinsicdefectsinthesamplesthatresultfromthesynthesistechniques.Themostlylikelysourceofdefectsischalcogensulfur,selenium,andtelluriumallboilat900Cintheampoule,whichmakessomelossofchalcogenatomsunavoidable.Duetothis,itislikelythatthesamplessynthesizedinthisstudycouldbeexpressedasI-III-VI2whereisasmallnumber.Figure8.1:ComparisonoftheelectricalresistivityofthebasecompoundsCuInTe2,CuGaTe2,CuInSe2,CuGaSe2,andCuFeS2.CuInS2isnotshownhere,butthevaluesareontheorderof108cm.Basedonourunderstandingoftheunderlyingfundamentaltransportpropertiesthreecompoundsstoodoutinthisworkaspromisingforthermoelectricapplications:CuGaTe2,CuInTe2,andCuFeS2.CuGaTe2andCuInTe2bothpossesaZTinexcessofunity,andtheformationoffullsolid-solutionallowedfurtheroptimizationoftheelectronicandthermal173properties.Further,densifyingthesampleswithSPSratherthantraditionalhotpressingyieldedsampleswithhigherdensity,andinthecaseofCuInTe2anincreaseinZTtonear1.4,nearthatofbulkoptimizedPbTe-PbSealloys,andgreaterthanaveragevaluesreportedforskutteruditeorTAGS(Te-Ag-Ge-Sballoys),placingthiscompoundamongthebestperformingp-typematerialsinthe400-800Ktemperaturerange.[138,139,140]Theselenidesamplesshowedpoorelectronicpropertiesascomparedtothetelluriumbasedcompounds.CuGaSe2hadthelargestbandgapofanymaterialstudiedhereat1.68eV,whichismuchlargerthantypicallyselectedasidealforthermoelectricmaterials.[92,141]PolycrystallinesamplesofCuGaSe2alsosufromlowholemobility(calculatedfromHallmeasurements),intherangeof10-20cm2V1s1whichismuchlowerthanthatofCuGaTe2whichwasfoundinthisstudytohavearoomtemperaturemobilitynear100cm2V1s1.[112]Thispartlyexplainsthemorethantwoorderofmagnitudeinelectricalconductivitybetweenthetwogalliumcontainingsamples,asshowninFigure8.1below.174Figure8.2:Comparisonofthethermalconductivityofthebasechalcopyritecompounds.CuInSe2hasareportedbandgapof1.04eV,veryclosetothatofCuInTe2.[142]However,despitethatsimilaritythetwomaterialsshowedverydistinctelectronicproperties.CuInTe2wasfoundtohaveaveryhighholemobilityinthisstudy,withameasuredvalueof250cm2V1s1at300Kandnumerousstudiesshowingvaluesnearorabove100cm2V1s1,whilestudiesonCuInSe2reportvaluesintherangeof20-25cm2V1s1.[6,143,144,145]Thislargedecreaseinholemobilityagainleadstoalargeincreaseinelectricalresistivity.Thisenceinmobilitybetweentheselenideandtelluridecompoundsisunexplainedatthistime.Somehavesuggestedthatitcouldbeduetotheamountoftetragonaldistor-tioninthecompound,i.e.howfarthec:aratiovariesfrom2.0.However,nocorrelationwasfoundinthisstudyorinareviewofliteraturevalues,betweenlatticeconstantsandmobilityvalues.Anotherpossibilityisthelowmobilityisduetotheelectro-negativitydif-ferences.ForCuInTe2andCuGaTe2theaverageelectro-negativityis0.26and0.25respectively.OntheotherhandforCuInSe2andCuGaSe2theare0.71175and0.70respectively.DatacompiledbySlack,aswellasworkbyPauling,showedthattheweightedmobilityas(m=m0)3=2)decreasedrapidlywithincreasingaverageelectro-negativity147]HightemperatureHallmeasurementscouldyieldusefulinformationonthenatureofthelowmobilityandclarifytheunderlyingphysics.CuFeS2showedpromiseasalow-costmaterialmadefromearthabundantmaterials.Intheworkpresentedhere,CuFeS2wastheonlyn-typematerialdiscovered.Itisalsothenaturallyoccurringmineralforwhichthefamilyisnamed;infactchalcopyritemineralsarethemostabundantsourceofcopperontheEarth.WhiletheundopedcompoundonlydisplayedaZTof0.1,dopingwithzincincreasedthatvalueto0.3;otherreportsshowedvaryingtheratioofCu:Fewasalsoeindopingthecompound,andproducedverysimilarvalues.However,thecompoundislimitedincomparisontothetelluriumbasedmaterialsinthatitisonlystableinairtoaround450Cbeforesulfursublimationoccurs.CuFeS2alsoappearedtobelimitedelectronicallybyalowcarriermobility.However,giventheverylowcostoftheelementsinthecompound,futurestudiestoimprovetheperformancewouldbeveryvaluable.Furtherworkontransitionmetaldopingcouldalsoshowinterestingphysics.ThebandgapofCuFeS2ismuchsmallerthanthatofCuGaS2,eventhoughtheirlatticeparametersarenearlyidenticalandironandgalliumhavethesamevalenceandverysimilarelectro-negativityvalues.BandstructurecalculationsshowedthatthevalencebandinCuFeS2aroseprimarilyfromtheirondlevels,soothertransitionmetalsmayshowinterestingpropertiesaswell.[121]Thepossibilityofcreatingann-typematerialotherthanCuFeS2isalsoveryintriguing.Whileattemptsinthisworkwereallunsuccessful,manypossibleelementsfordopingstillremain.Futurebandstructurecalculationswouldassistgreatlyinunderstandingthephysicsofdopantatomsandpossiblypredictelementswhichwouldbemore176easn-typedopants.Futurestudiesonthedefectchalcopyritecompoundscouldbeveryenlightening.Theextremelylowthermalconductivity,especiallythatfoundinZn0.5GaTe2,showsthestrongimpactvacanciescanhaveonthephysicsofphononscattering.Theelectronicpropertiesofdefectchalcopyritecompoundsareratherunexplored,andfutureworkonunderstandingthephysicsoftheelectronictransportwouldbeinsightful.Thereportedbandgapsofthedefectcompoundsarelargerthanthosefoundinchalcopyritecompounds,andthetwomaterialsstudiedherewerefoundtobehighlyresistive.[148]Iftheelectronicpropertiescouldbecontrolledwhilemaintainingthelowthermalconductivityfromthedefectstructure,thedefectcompoundswouldbeverypromisingthermoelectricmaterials.Overall,thechalcopyritefamilyofcompoundsawiderangeofinterestingphysicsintermsofelectronicandthermaltransport.Abetterunderstandingofthetransportmecha-nismsandtheirinteractionswiththedefectsandchangesinthestructureandstoichiometrycouldleadtowideuseofchalcopyritematerialsinthermoelectrics.Alreadytheyarebe-ingusedsuccessfullyinsolarapplications,andtheirfutureinthermoelectricslookstobepromisingwiththehighZTvaluesobtainedinthiswork,andinotherstudies.177REFERENCES178REFERENCES[1]AlphabetEnergyInc.AlphabetEnergyE1.https://www.alphabetenergy.com/product/e1/,2016.[2]DaifengZou,ShuhongXie,YunyaLiu,JianguoLin,andJiangyuLi.First-principlesstudyofthermoelectricandlatticevibrationalpropertiesofchalcopyriteCuGaTe2.J.AlloysCompd.,570:150{155,sep2013.[3]IreneAguilera,JulienVidal,PerlaWon,LuciaReining,andSilvanaBotti.First-principlesstudyofthebandstructureandopticalabsorptionofCuGaS2.Phys.Rev.B,84(8):085145,aug2011.[4]HarryHahn,GnterFrank,WilhelmKlingler,AnneDorotheeStrger,andGeorgStrger.UntersuchungenberternreChalkogenide.VI.berTernreChalkogenidedesAlumini-ums,GalliumsundIndiumsmitZink,CadmiumundQuecksilber.ZeitschriftfrAnorg.undAllg.Chemie,279(5-6):241{270,jul1955.[5]MLeon,J.M.Merino,J.L.MartinDeVidales,andM.Leon.ComparativestudyofthecrystalstructureofsynthesizedCuGa1yInyTe2compounds.J.Vac.Sci.Technol.AVacuum,Surfaces,Film.,11(5):2430,sep1993.[6]RuihengLiu,LiliXi,HuiliLiu,XunShi,WenqingZhang,andLidongChen.TernarycompoundCuInTe2:apromisingthermoelectricmaterialwithdiamond-likestructure.Chem.Commun.,48(32):3818,apr2012.[7]M.Leon,J.M.Merino,andJ.L.MartinDeVidales.CrystalstructureofsynthesizedCuGaTe2determinedbyX-raypowderactionusingtheRietveldmethod.J.Mater.Sci.,27(16):4495{4500,jan1992.[8]TheerayuthPlirdpring,KenKurosaki,AtsukoKosuga,TristanDay,SamadFirdosy,VilupanurRavi,GSnyder,AdulHarnwunggmoung,TohruSugahara,YujiOhishi,HiroakiMuta,andShinsukeYamanaka.ChalcopyriteCuGaTe2:AHigh-BulkThermoelectricMaterial.Adv.Mater.,24(27):3622{3626,jul2012.[9]YapengLi,QingsenMeng,YuanDeng,HongZhou,YulanGao,YiyunLi,JiangfengYang,andJiaolinCui.HighthermoelectricperformanceofsolidsolutionsCuGa1xInxTe2(x=01.0).Appl.Phys.Lett.,100(23):231903,2012.179[10]HarryHahn,GnterFrank,WilhelmKlingler,Anne-DorotheeMeyer,andGeorgStrger.UntersuchungenberternreChalkogenide.V.bereinigeternreChalkogenidemitChalkopyritstruktur.ZeitschriftfrAnorg.undAllg.Chemie,271(3-4):153{170,feb1953.[11]J.M.Merino,M.DiMichiel,andM.on.StructuralanalysisofCuInSe2andCuIn3Se5atttemperatureswithsynchrotronradiation.J.Phys.Chem.Solids,64(9-10):1649{1652,sep2003.[12]B.Grzeta-Plenkovic,S.Popovic,B.Celustka,andB.Santic.CrystaldataforAgGaxIn1xSe2andCuGaxIn1xSe2.J.Appl.Crystallogr.,13(3):311{315,jun1980.[13]MLeon,J.M.Merino,andJ.L.MartinDeVidales.CrystalstructureofsynthesizedCuGa0.5In0.5Te2determinedbyx-raypowderractionusingtheRietveldmethod.J.Mater.Sci.,28:2466{2470,sep1993.[14]N.A.Goryunova.TheChemistryofDiamond-likeSemiconductors.MITPress,Cam-bridgeMA,1965.[15]JCWoolley.SomeCross-SubstitutionalAlloysofCdTe.J.Electrochem.Soc.,113(9):2{4,1966.[16]CarlosRinconandF.J.Ramirez.LatticevibrationsofCuInSe2andCuGaSe2byRamanmicrospectrometry.J.Appl.Phys.,72(9):4321,1992.[17]TKratzandHFuess.SimultaneStrukturbestimmungvonKupferkiesundBornitaneinemKristall.ZeitschriftfurKrist.,186:167{169,1989.[18]NaohitoTsujiiandTakaoMori.HighThermoelectricPowerFactorinaCarrier-DopedMagneticSemiconductorCuFeS2.Appl.Phys.Express,6(4):043001,apr2013.[19]NaohitoTsujii,TakaoMori,andYukihiroIsoda.PhaseStabilityandThermoelectricPropertiesofCuFeS2-BasedMagneticSemiconductor.J.Electron.Mater.,43(6):2371{2375,jun2014.[20]YulongLi,TiansongZhang,YutingQin,TristanDay,G.Snyder,XunShi,andLidongChen.Thermoelectrictransportpropertiesofdiamond-likeCu1-xFe1+xS2tetrahedralcompounds.J.Appl.Phys.,116(20),2014.[21]HJGotsis,aCBarnes,andPStrange.ExperimentalandtheoreticalinvestigationofthecrystalstructureofCuS.J.Phys.Condens.Matter,4(50):10461{10468,1992.180[22]E.J.Fasiska.SomedefectstructuresofironPhys.StatusSolidi,10(1):169{173,1972.[23]JianhuiLi,QingTan,andJing-FengLi.SynthesisandpropertyevaluationofCuFeS2xasearth-abundantandenvironmentally-friendlythermoelectricmaterials.J.AlloysCompd.,551:143{149,feb2013.[24]G.Brandt,A.auber,andJ.Schneider.ESRandx-rayanalysisoftheternarysemiconductorsCuAlS2,CuInS2andAgGaS2.SolidStateCommun.,12(6):481{483,mar1973.[25]CJulienandSBarnier.PropertiesofseveralvarietiesofCuGaS2microcrystals.Mater.Sci.Eng.B,86:152{156,2001.[26]S.R.HallandJ.M.Stewart.Thecrystalstructuretofchalcopyrite,CuFeS2.ActaCrystallogr.Sect.BStruct.Crystallogr.Cryst.Chem.,29(3):579{585,mar1973.[27]J.M.Delgado,G.DiazdeDelgado,M.Quintero,andJ.C.Woolley.Thecrystalstruc-tureofcopperironselenide,CuFeSe2.Mater.Res.Bull.,27(3):367{373,mar1992.[28]AAVaipolin,VDProchukhan,YuVRud,andEVSkoriukin.NoTitle.Izv.Akad.NaukSSSRNeorg.Mater.,20:578,1984.[29]K.KotoandNobuoMorimoto.Superstructureinvestigationofbornite,Cu5FeS4,bythemopartialPattersonfunction.ActaCrystallogr.Sect.BStruct.Crystallogr.Cryst.Chem.,31(9):2268{2273,sep1975.[30]PengfeiQiu,TiansongZhang,YutingQiu,XunShi,andLidongChen.Subornitethermoelectricmaterial:anaturalmineralwithultralowthermalconductivity.EnergyEnviron.Sci.,00:1{7,oct2014.[31]GabinGuelou,AnthonyVPowell,andPazVaqueiro.Ballmillingasanerouteforthepreparationofdopedbornite:synthesis,stabilityandthermoelectricproperties.J.Mater.Chem.C,2015.[32]T.JSeebeck.UeberdiemagnetischePolarisationderMetalleundErzedurchTempeAnn.Phys.,82(2):133{160,1826.[33]J.C.Peltier.Nouvellesexperiencessurlacaloricitedescourantselectriques.Ann.Chim.Phys.,56(371):371,1834.181[34]W.Thomson.AccountofResearchesinThermo-Electricity.Proc.R.Soc.London,7(0):49{58,jan1854.[35]E.Altenkirch.NoTitle.Phys.Zeitschrift,12:920,1911.[36]E.Altenkirch.UberdenderThermosaule.Phys.Zeitschrift,10:560{580,1909.[37]LarsOnsager.Reciprocalrelationsinirreversibleprocesses.I.Phys.Rev.,37:405{426,1931.[38]LarsOnsager.Reciprocalrelationsinirreversibleprocesses.II.Phys.Rev.,38(4):2265{2279,1931.[39]TheNobelPrizeinChemistry1968,2014.[40]HJGoldsmidandRWDouglas.theUseofSemiconductorsinThermoelectricRe-frigeration.Br.J.Appl.Phys.,5(NOV):386{390,1954.[41]HJGoldsmid.TheElectricalConductivityandThermoelectricPowerofBismuthTelluride.Proc.Phys.Soc.London,71(460):633{646,1958.[42]MariaTelkes.Theofthermoelectricgenerators.I.J.Appl.Phys.,18(12):1116{1127,1947.[43]MariaTelkes.PowerOutputofThermoelectricGenerators.J.Appl.Phys.,25(8):1058,1954.[44]MariaTelkes.Solarthermoelectricgenerators.J.Appl.Phys.,25(6):765{777,1954.[45]A.F.e.HEATTRANSFERINSEMICONDUCTORS.Can.J.Phys.,34(12A):1342{1355,dec1956.[46]M.C.SteeleandF.D.Rosi.Thermalconductivityandthermoelectricpowerofgermanium-siliconalloys.J.Appl.Phys.,29(11):1517{1520,1958.[47]R.Bowers,J.E.Bauerle,andA.J.Cornish.InAs1-xPxasathermoelectricmaterial.J.Appl.Phys.,30(7):1050{1054,1959.[48]DonaldD.GlowerandDuaneC.Wallace.ThermalStudiesofCaxBa1-xTiO3.J.Phys.Soc.Japan,18(5):679{684,may1963.182[49]L.E.DeLongandG.P.Meisner.ThepressuredependenceofthesuperconductingtransitiontemperatureofLaT4P12(T=Fe,Ru,Os).SolidStateCommun.,53(2):119{123,jan1985.[50]D.Jung,M.Whangbo,andS.Alvarez.ImportanceoftheX4RingOrbitalsfortheSemiconducting,Metallic,orSuperconductingPropertiesofSkutteruditesMX3andRM4X12.Inorg.Chem.,29:2252{2255,1990.[51]BoBrummerstedtIversen,AndersE.C.Palmqvist,DavidECox,GeorgeSNolas,GalenDStucky,NickPBlake,andHoriaMetiu.WhyareClathratesGoodCandidatesforThermoelectricMaterials?J.SolidStateChem.,149(2):455{458,feb2000.[52]DonaldT.MorelliandGregoryP.Meisner.LowtemperaturepropertiesoftheskutteruditeCeFe4Sb12.J.Appl.Phys.,77(8):3777,1995.[53]Jean-PierreFleurial,AlexBorshchevsky,andThierryCaillat.HighFigureofMeritinCe-FilledSkutterudites.15thInt.Conf.Thermoelectr.,3:91{95,1996.[54]H.Nakagawa,H.Tanaka,A.Kasama,K.Miyamura,H.Masumoto,andK.Matsubara.ThermoelectricpropertiesofCoSb3preparedbycoppermoldquenchingtechnique.FifteenthInt.Conf.Thermoelectr.Proc.ICT'96,pages117{121,1996.[55]ABorshchevsky,TCaillat,andJ.-P.Fleurial.Solidsolutionformation:improvingthethermoelectricpropertiesofskutterudites.InFifteenthInt.Conf.Thermoelectr.Proc.ICT'96,pages112{116.IEEE,1996.[56]K.Matsubara,TSakakibara,YNotohara,HAnno,HShimizu,andTKoyanagi.ElectronictransportpropertiesoftheSkutteruditeCoSb/sub3/andmixedalloys.InFifteenthInt.Conf.Thermoelectr.Proc.ICT'96,number1,pages96{99.IEEE,1996.[57]B.Abeles.Latticethermalconductivityofdisorderedsemiconductoralloysathightemperatures.Phys.Rev.,131(5):1906{1911,sep1963.[58]T.Koyanagi,TTsubouchi,MOhtani,KKishimoto,HAnno,andK.Matsubara.ThermoelectricpropertiesofCo(M/subx/Sb/sub1-x/)/sub3/(M=Ge,Sn,Pb)com-pounds.InFifteenthInt.Conf.Thermoelectr.Proc.ICT'96,pages107{111.IEEE,1996.[59]L.D.HicksandM.S.Dresselhaus.ofquantum-wellstructuresonthethermo-magneticofmerit.Phys.Rev.B,47(19):727{731,1993.183[60]L.D.HicksandM.S.Dresselhaus.Thermoelectricofmeritofaone-dimensionalconductor.Phys.Rev.B,47(24):16631{16634,1993.[61]L.D.Hicks,T.C.Harman,X.Sun,andM.S.Dresselhaus.Experimentalstudyoftheofquantum-wellstructuresonthethermoelectricofmerit.Phys.Rev.B,53(16):R10493{R10496,1996.[62]M.S.Dresselhaus,G.Dresselhaus,X.Sun,Z.Zhang,S.B.Cronin,andT.Koga.Low-dimensionalthermoelectricmaterials.Phys.SolidState,41(5):679{682,may1999.[63]RVenkatasubramanian,ESiivola,TColpitts,andBO'Quinn.thermoelec-tricdeviceswithhighroom-temperatureofmerit.Nature,413(6856):597{602,2001.[64]E.Godoy,N.J.Scenna,andS.J.Benz.Familiesofoptimalthermodynamicsolutionsforcombinedcyclegasturbine(CCGT)powerplants.Appl.Therm.Eng.,30(6-7):569{576,may2010.[65]ManuelValdesandJoseL.Rapun.Optimizationofheatrecoverysteamgeneratorsforcombinedcyclegasturbinepowerplants.Appl.Therm.Eng.,21(11):1149{1159,aug2001.[66]LloydI.ShureandHarveyJ.Schwartz.NasaTmX-52158N66-14775.Technicalreport,LewisResearchCenter,Cleveland,OH,1965.[67]NASA.SpaceRadioisotopePowerSystems:Multi-MissionRadioisotopeThermoelec-tricGenerator,2008.[68]RGSB.V.Development.ApplicationAreas.http://www.rgsdevelopment.nl/page24.html,2016.[69]A.F.SemiconductorThermoelementsandThermoelectricCooling.InfosearchLimited,London,1957.[70]NeilW.AshcroftandN.DavidMermin.SolidStatePhysics.ThomsonPress,1976.[71]V.Fistul.HeavilyDopedSemiconductors.PlenumPress,NewYork,1969.[72]S.M.Sze.PhysicsofSemiconductorDevices.Wiley-Interscience,secondedition,1981.184[73]J.BardeenandW.Shockley.Deformationpotentialsandmobilitiesinnon-polarcrys-tals.Phys.Rev.,80(1):72{80,1950.[74]E.ConwellandV.F.Weisskopf.TheoryofImpurityScatteringinSemiconductors.Phys.Rev.,77(3):388{390,feb1950.[75]EricS.Toberer,AndrewF.May,andG.Snyder.ZintlChemistryforDesigningHighThermoelectricMaterials.Chem.Mater.,22(3):624{634,feb2010.[76]JosephP.Heremans,VladimirJovovic,EricS.Toberer,AliSaramat,KenKurosaki,AnekCharoenphakdee,ShinsukeYamanaka,andGreySnyder.EnhancementofThermoelectricinPbTebyDistortionoftheElectronicDensityofStates.Science(80-.).,321(5888):554{557,jul2008.[77]KanishkaBiswas,JiaqingHe,QichunZhang,GuoyuWang,CtiradUher,VinayakPDravid,andMercouriGKanatzidis.Strainedendotaxialnanostructureswithhighthermoelectricofmerit.Nat.Chem.,3(2):160{6,feb2011.[78]R.FranzandG.Wiedemann.Ueberdiearme-LeiahigkeitderMetalle.Ann.derPhys.undChemie,165(8):497{531,1853.[79]R.Berman.ThermalConductioninSolids.OxfordUniversityPress,Oxford,1edition,1976.[80]H.B.G.Casimir.Noteontheconductionofheatincrystals.Physica,5(6):495{500,1938.[81]I.Pomeranchuk.NoTitle.J.Phys.U.S.S.R.,6:237,1942.[82]GlenA.Slack.ofIsotopesonLow-TemperatureThermalConductivity.Phys.Rev.,105(3):829{831,feb1957.[83]DonaldT.Morelli,ThomasA.Perry,andJohnW.Farmer.Phononscatteringinlightlyneutron-irradiateddiamond.Phys.Rev.B,47(1):131{139,1993.[84]JohnWilliamStruttandBaronRayleigh.TheTheoryofSound.MacmillanAndCo,NewYork,2edition,1896.[85]PGKlemens.TheScatteringofLow-FrequencyLatticeWavesbyStaticImperfections.Proc.Phys.Soc.Sect.A,68(12):1113{1128,1955.185[86]GlenA.Slack.ThermalConductivityofPotassiumChlorideCrystalsContainingCalcium.Phys.Rev.,105(3):832{842,feb1957.[87]E.V.MielczarekandH.P.R.Frederikse.ThermalConductivityofIndiumAntimonideatLowTemperatures.Phys.Rev.,14(4):888,1959.[88]C.J.GlassbrennerandGlenA.Slack.ThermalConductivityofSiliconandGermaniumfrom3KtotheMeltingPoint.Phys.Rev.,134(4A):A1058{A1069,may1964.[89]G.A.Slack.Nonmetalliccrystalswithhighthermalconductivity.J.Phys.Chem.Solids,34(2):321{335,jan1973.[90]SlShindeandJGoela.Highthermalconductivitymaterials.SpringerUS,2006.[91]GlenA.Slack.TheThermalConductivityofNonmetallicCrystals.InSolidStatePhys.-Adv.Res.Appl.,volume34,pages1{71.AcademicPress,1979.[92]J.JaandAlexZunger.Theoryoftheband-gapanomalyinABCf2gchalcopyritesemiconductors.Phys.Rev.B,29(4):1882{1906,feb1984.[93]T.Bekkay,M.Boustani,K.ElAssali,A.Khiara,J.C.Bernede,andJ.Pouzet.Struc-turalandopticalpropertiesofCuAlTe2thinpreparedbyRF.sputtering.Int.J.Electron.,92(8):445{449,aug2005.[94]NAMohsen,SNElsayed,andAHAEl-Ela.Electricalconductivity,thermoelectricpowerandthermalconductivityofCuTlTe2inthesolidandliquidstates.ActaPhys.Hungarica,67(1-2):223{228,1990.[95]LVKradinova,AMPolubotko,VVPopov,VDProchukhan,YuVRud,andVESkoriukin.Novelzero-gapcompounds,magnetics:CuFeS2andCuFeTe2.Semicond.Sci.Technol.,8(8):1616{1619,aug1993.[96]V.V.Popov,P.P.Konstantinov,andYu.V.Rud'.Kineticphenomenainzero-gapsemiconductorsCuFeS2andCuFeTe2:ofpressureandheattreatment.J.Exp.Theor.Phys.,113(4):683{691,nov2011.[97]IGAustin,CHLGoodman,andAEPengelly.NewSemiconductorswiththeChalcopyriteStructure.J.Electrochem.Soc.,103(11):609,1956.186[98]GMarin,CarlosRincon,S.M.Wasim,Ch.Power,andG.SanchezPerez.TemperaturedependenceofthefundamentalabsorptionedgeinCuInTe2.J.Appl.Crystallogr.,81(11):7580{7583,1997.[99]I.V.Bodnar,A.Th.Doering,W.Schmitz,K.Bente,V.F.Gremenok,I.A.Victorov,andV.Riede.GrowthandCharacterisationof(CuInTe2)1-x(2ZnTe)xSolidSolutionSingleCrystals.Cryst.Res.Technol.,35(10):1135{1140,oct2000.[100]MLeon,J.M.Merino,andJ.L.MartinDeVidales.CrystalstructureofsynthesizedCuGaTe2determinedbyX-raypowderusingtheRietveldmethod.J.Mater.Sci.,27:4495{4500,1992.[101]V.P.Zhuze,W.M.Sergeeva,andE.L.Shtrum.NoTitle.J.Tech.Phys.,28:2093,1958.[102]VijayKumarGudelli,V.Kanchana,G.Vaitheeswaran,A.Svane,andN.E.Chris-tensen.ThermoelectricpropertiesofchalcopyritetypeCuGaTe2andchalcostibiteCuSbS2.J.Appl.Phys.,114(22):223707,2013.[103]JuemingYang,YuliYan,YuanXuWang,andGuiYang.ImprovedthermoelectricperformanceofCuGaTe2withconvergenceofbandvalleys:astudy.RSCAdv.,4(54):28714,2014.[104]J.andAlexZunger.Electronicstructureoftheternarychalcopyritesemiconduc-torsCuAlSf2g,CuGaSf2g,CuInSf2g,CuAlSef2g,CuGaSef2g,andCuInSef2g.Phys.Rev.B,28(10):5822{5847,1983.[105]J.Lamazares,F.Gonzalez-Jimenez,EJaimes,L.D'Onofrio,RIraldi,G.Sanchez-Porras,M.Quintero,J.Gonzalez,J.C.Woolley,andG.Lamarche.Magnetic,trans-port,X-rayandossbauermeasurementsonCuFeSe2.J.Magn.Magn.Mater.,104-107:997{998,feb1992.[106]D.Berthebaud,O.I.Lebedev,andA.Maignan.Thermoelectricpropertiesofn-typecobaltdopedchalcopyriteCu1xCoxFeS2andp-typeeskeborniteCuFeSe2.J.Mater.,1(1):68{74,mar2015.[107]B.Tell,J.L.Shay,andH.M.Kasper.Room-temperatureelectricalpropertiesoftenI-III-VI2semiconductors.J.Appl.Phys.,43(1972):2469{2470,1972.[108]J.RodrLQuiroga,ACamacho,andRBaquero.ElectronicbandstructureofCuInSe2:Bulkand(112)surface.Phys.Rev.B,59(3):1555{1558,jan1999.187[109]J.L.Shay,J.H.Wernick,andB.R.Pamplin.TernaryChalcopyriteSemiconductors:Growth,ElecronicProperties,andApplications.PergamonPressInc.,1975.[110]B.TellandP.Bridenbaugh.AspectsofthebandstructureofCuGaSf2gandCu-GaSef2g.Phys.Rev.B,12(8):3330{3335,oct1975.[111]Yu-JunZhaoandAlexZunger.ElectronicstructureandferromagnetismofMn-substitutedCuAlS2,CuGaS2,CuInS2,CuGaSe2,andCuGaTe2.Phys.Rev.B,69(10):104422,mar2004.[112]SusanneSiebentrittandSchuler.Defectsandtransportinthewidegapchal-copyriteCuGaSe2.J.Phys.Chem.Solids,64(9-10):1621{1626,2003.[113]L.Vegard.DieKonstitutionderMischkristalleunddiederAtome.ZeitschriftfrPhys.,5(1):17{26,jan1921.[114]S.R.Hall.CrystalStructuresoftheChalcopyriteSeries.Can.Mineral.,13:168{172,1975.[115]P.GrimaGallardo.Order-DisorderPhaseTransitionsinAlloySystems.PhysStatSol,134:119{125,1992.[116]Su-HuaiHuaiWei,L.G.Ferreira,andAlexZunger.First-principlescalculationoftheorder-disordertransitioninchalcopyritesemiconductors.Phys.Rev.B,45(5):2533{2536,feb1992.[117]AlexZunger.Order-disordertransformationinternarytetrahedralsemiconductors.Appl.Phys.Lett.,50(3):164{166,jan1987.[118]CharlesL.BurdickandJamesH.Ellis.THECRYSTALSTRUCTUREOFCHAL-COPYRITEDETERMINEDBYX-RAYS.J.Am.Chem.Soc.,39(12):2518{2525,dec1917.[119]LinusPaulingandL.O.Brockway.TheCrystalStructureofChalcopyriteCuFeS2.ZeitschriftfurKrist.-Cryst.Mater.,82(1-6),jan1932.[120]TeruoTeranishi,KatsuakiSato,andKen'ichiKondo.OpticalPropertiesofaMagneticSemiconductor:ChalcopyriteCuFeS2.:I.AbsorptionSpectraofCuFeS2andFe-DopedCuAlS2andCuGaS2.J.Phys.Soc.Japan,36(6):1618{1624,jun1974.188[121]ToshikiHamajima,TakeshiKambara,andKenIchiroGondaira.Self-consistentelec-tronicstructuresofmagneticsemiconductorsbyadiscretevariationalXacalcuation.ChalcopyriteCuFeS2.Phys.Rev.B,24(6):3349{3353,1981.[122]R.BlachnikandA.Muller.TheformationofCu$2$Sfromtheelements:I.Copperusedinformofpowders.Thermochim.Acta,361:31{52,2000.[123]S.MishraandB.Ganguli.ofNasubstitutiononelectronicandopticalpropertiesofCuInS2chalcopyritesemiconductor.J.SolidStateChem.,232:131{137,dec2015.[124]B.Tell,J.L.Shay,andH.M.Kasper.ElectricalProperties,OpticalProperties,andBandStructureofCuGaS2andCuInS2.Phys.Rev.B,4(8):2463{2471,1971.[125]B.Tell,J.L.Shay,andH.M.Kasper.Room-temperatureelectricalpropertiesoftenI-III-VI2semiconductors.J.Appl.Phys.,43(5):2469{2470,1972.[126]WinstonD.CarrandDonaldT.Morelli.TheThermoelectricPropertiesandSolubilityLimitofCuFeS2(1x)Se2x.J.Electron.Mater.,2,sep2015.[127]A.-MLamarche,J.CWoolley,GLamarche,I.PSwainson,andT.MHolden.Structureandmagneticpropertiesoftheternarycompoundcopperirontelluride.J.Magn.Magn.Mater.,186(1-2):121{128,1998.[128]T.Nomiyama,H.Kuriyaki,andK.Hirakawa.Photo-rechargeablebatteryusingnewlayercompoundCuFeTe2.Synth.Met.,71(1-3):2237{2238,1995.[129]LVKradinova,AMPolubotko,VVPopov,VDProchukhan,YuVRud,andVESkoriukin.Novelzero-gapcompounds,magnetics:CuFeS2andCuFeTe2.Semicond.Sci.Technol.,8(8):1616{1619,aug1993.[130]AAVaipolin,SAKijaev,LVKradinova,AMPolubotko,VVPopov,VDProchukhan,YuVRud,andVESkoriukin.InvestigationofthegaplessstateinCuFeTe2.J.Phys.Condens.Matter,4(40):8035{8038,oct1992.[131]AlfredJ.Frueh.AnextensionofthePatterson'tofacilitatethesolutionoforderdisorderproblems.ActaCrystallogr.,6(6):454{456,jun1953.[132]BenjaminA.Grguric,AndrewPutnis,andRichardJ.Harrison.Aninvestigationofthephasetransitionsinbornite(Cu5FeS4)usingneutronandtialscanningcalorimetry.Am.Mineral.,83(1978):1231{1239,1998.189[133]RichardARobie,RoberyR.Seal,andBruceS.Hemingway.Heatcapacityandentropyofbornite(Cu5FeS4)between6and760KandthethermodynamicpropertiesofphasesinthesystemCu-Fe-S.Can.Mineral.,32:945{956,1994.[134]JSHEMILT,BSTEELE,andJWESTON.Thermodynamicsandmobilityofcopperinbornite(Cu5FeS4).SolidStateIonics,2(2):73{85,apr1981.[135]EmilMakovickyandBrianJ.Skinner.STUDIESOFTHESULFOSALTSOFCOPPERVII.GRYSTALSTRUCTURESOFTHEEXSOLUTIONPRODUCTSCu12.3Sb4S13ANDCu13.8Sb4S13OFUNSUBSTITUTEDsYNTHETtcTETRA-HEDRI.Can.Mineral.,17:619{634,1979.[136]JiangXiao-Shu,YanYing-Ce,YuanShi-Min,MiShu,NiuZhen-Guo,andLiangJiu-Qing.Trendsintheband-gappressurecotsandbulkmoduliintstruc-turesofZnGa2S4,ZnGa2Se4andZnGa2Te4.ChinesePhys.B,19(10):107104,2010.[137]KenKurosaki,HideakiMatsumoto,AnekCharoenphakdee,ShinsukeYamanaka,Man-abuIshimaru,andYoshihikoHirotsu.Unexpectedlylowthermalconductivityinnat-uralnanostructuredbulkGa2Te3.Appl.Phys.Lett.,93(1):3{5,2008.[138]YanzhongPei,XiaoyaShi,AaronLaLonde,HengWang,LidongChen,andGSnyder.Convergenceofelectronicbandsforhighperformancebulkthermoelectrics.Nature,473(7345):66{9,may2011.[139]GSnyderandEricSToberer.Complexthermoelectricmaterials.Nat.Mater.,7(2):105{14,feb2008.[140]Jin-chengZheng.Recentadvancesonthermoelectricmaterials.Front.Phys.China,3(3):269{279,jul2008.[141]J.Shay,B.Tell,H.Kasper,andL.Schiavone.p-dHybridizationoftheValenceBandsofI-III-VIf2gCompounds.Phys.Rev.B,5(12):5003{5005,jun1972.[142]J.Shay,B.Tell,H.Kasper,andL.Schiavone.ElectronicStructureofAgInSef2gandCuInSef2g.Phys.Rev.B,7(10):4485{4490,1973.[143]YuboLuo,JunyouYang,QinghuiJiang,WeixinLi,YeXiao,LiangweiFu,DanZhang,ZhiweiZhou,andYudongCheng.LargeenhancementofthermoelectricperformanceofCuInTe2viaasynergisticstrategyofpointdefectsandmicrostructureengineering.NanoEnergy,2015.190[144]BarryP.Rand,JanGenoe,PaulHeremans,andJefPoortmans.SolarCellsUti-lizingSmallMolecularWeightOrganicSemiconductors.Prog.PhotovoltRes.Appl.,15(February2013):659{676,2007.[145]YiTang,R.Braunstein,andBolkoVonRoedern.DeterminationofdriftmobilityandlifetimefordominantchargecarriersinpolycrystallineCuInSe2byphotomixing.Appl.Phys.Lett.,63(17):2393{2395,1993.[146]GlenSlack.CRC-95-Chapter34.pdf.InCRCHandb.Thermoelectr.,pages407{440.CRCPress,1995.[147]LinusPauling.TheNatureoftheChemicalBond.J.Chem.Educ.,69(7):656,jul1992.[148]XiaoshuJiangandWalterR.L.Lambrecht.ElectronicbandstructureoforderedvacancydefectchalcopyritecompoundswithformulaI-III2-VI4.Phys.Rev.B,69(3):035201,jan2004.191