Thermoelectric Materials - UPRMacademic.uprm.edu/pcaceres/Courses/Smart/SMD-8B.pdf · are known as...
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Thermoelectric Materials Thermoelectric devices are based on a phenomenon known as the thermoelectric effect which is the direct conversion of a temperature gradient across two dissimilar materials into electricity. The materials used are known as thermoelectric materials. The thermoelectric effect is reversible i.e. it directly conver;ng electricity into a temperature gradient. The thermoelectric effect is based on a combina;on of two different effects, namely, the Seebeck effect and the Pel4er effect. Water/Beer Cooler
Transcript of Thermoelectric Materials - UPRMacademic.uprm.edu/pcaceres/Courses/Smart/SMD-8B.pdf · are known as...
ThermoelectricMaterialsThermoelectricdevicesarebasedonaphenomenonknownasthethermoelectriceffectwhichisthedirectconversionofatemperaturegradientacrosstwodissimilarmaterialsintoelectricity.Thematerialsusedareknownasthermoelectricmaterials.Thethermoelectriceffectisreversiblei.e.itdirectlyconver;ngelectricityintoatemperaturegradient.
Thethermoelectriceffectisbasedonacombina;onoftwodifferenteffects,namely,theSeebeckeffectandthePel4ereffect.
Water/BeerCooler
Whatisthermoelectricity?Thermoelectricityistheconversionofheatdifferen;alsintoelectricityandviceversa.Thermoelectricenergyconversionisoneofthedirectenergyconversiontechnologiesthatrelyontheelectronicproper;esofthematerial(semiconductor)foritsefficiency.ItisbasedontheSeebeck(PowerGenera;on)andPel;ereffects(HeatPumping).
SeebeckEffectIn1821,ThomasSeebeckaGermanEstonianphysicistfoundthatanelectriccurrentwouldflowcon;nuouslyinaclosedcircuitmadeupoftwodissimilarmetals,ifthe junc;ons of themetals weremaintained at twodifferenttemperatures.If the temperaturegradient is reversed, thedirec;onofthecurrentisreversed.
WhereSistheSeebeckcoefficient.Itisdefinedasthevoltagegeneratedperdegreeoftemperaturedifferencebetweenthetwopoints.
Sisposi;vewhenthedirec;onofthecurrentisthesameasthedirec;onofthevoltage
ThebasisoftheSeebeckeffectiselectronmobilityinconductorsandsemiconductors,whichisafunc;onoftemperature
Whentwodifferentmetalsarejoined,therela;vedifferenceinelectronmobilityineachofthemetalswillmakethattheelectronsfromthemore“mobile”metaljumptothelessmobilemetal.
Apoten4aldifferenceiscreatedbetweenthetwoconductors.Intheabsenceofacircuit,thiscauseschargetoaccumulateinoneconductor,andchargetobedepletedintheotherconductor.
Example:TypeKthermocouple
Measure ?
TheSeebeckEffectTheSeebeckeffectistheconversionofheatdifferencesdirectlyintoelectricity.Whentwodissimilarmaterialswithdifferentcarrierdensi;esareconnectedtoeachotherbyanelectricalconductorandheatisappliedtoonesideoftheconnectors,someoftheheatinputisconvertedtoelectricalcurrent,asthehigherenergymaUerreleasesenergyandcoolstoalowerenergystate.Thenetworkispropor;onaltothetemperaturedifferenceandSeebeckcoefficient.
Thesimplestthermoelectricgeneratorconsistsofathermocouple,comprisingap‐typeandn‐typethermo‐elementconnectedelectricallyinseriesandthermallyinparallel.
Heatispumpedintoonesideofthecoupleandrejectedfromtheoppositeside.Anelectricalcurrentisproduced,propor;onaltothetemperaturegradientbetweenthehotandcoldjunc;ons
Explana1onofSeebeckEffectInathermoelectricmaterialtherearefreecarrierswhichcarrybothchargeandheat.
Ifamaterialisplacedinatemperaturegradient,whereonesideiscoldandtheotherishot,thecarriersatthehotendwillmovefasterthanthoseatthecoldend.Thefasterhotcarrierswilldiffusefurtherthanthecoldcarriersandsotherewillbeanetbuildupofcarriers(higherdensity)atthecoldend.Inthesteadystate,theeffectofthedensitygradientwillexactlycounteracttheeffectofthetemperaturegradientsothereisnonetflowofcarriers.Thebuildupofchargeatthecoldendwillalsoproducearepulsiveelectrosta;cforce(andthereforeelectricpoten;al)topushthechargesbacktothehotend.
Theelectricpoten;alproducedbyatemperaturedifferenceisknownastheSeebeckeffectandthepropor;onalityconstantiscalledtheSeebeckcoefficient(α orS).Ifthefreechargesareposi;ve(thematerialisp‐type),posi;vechargewillbuilduponthecoldwhichwillhaveaposi;vepoten;al.Similarly,nega;vefreecharges(n‐typematerial)willproduceanega;vepoten;alatthecoldend.Ifthehotendsofthen‐typeandp‐typematerialareelectricallyconnected,andaloadconnectedacrossthecoldends,thevoltageproducedbytheSeebeckeffectwillcausecurrenttoflowthroughtheload,genera;ngelectricalpower.
α2σ isthematerialspropertyknownasthethermoelectricpowerfactor.Forefficientopera;on,highpowermustbeproducedwithaminimumofheat(Q). κ= Thermalconduc;vity.Thethermalconduc;vityactsasathermalshortandreducesefficiency.
Pel4erEffectIn1834,aFrenchscien;stJeanPel;erfoundthatathermaldifferencecanbeobtainedatthejunc;onoftwometals,ifanelectriccurrentismadetoflowinthem.
OppositeoftheSeebeckEffect.Theheatcurrent(q)ispropor;onaltothechargecurrent(I)andthepropor;onalityconstantisthePel;erCoefficient(Π).
Whentwomaterialsarejoinedtogether,therewillbeanexcessordeficiencyintheenergyatthejunc;onbecausethetwomaterialshavedifferentPel;ercoefficients.Theexcessenergyisreleasedtothela^ceatthejunc;on,causinghea;ng,andthedeficiencyinenergyissuppliedbythela^ce,crea;ngcooling.
TheSeebeckandthePel;ercoefficientsarerelatedtoeachotherthroughtheKelvinrela;onship–Tistheabsolutetemperature.
Π >0; Posi;vePel;ercoefficient.Highenergyholesmovefromleatoright.Thermalcurrentandelectriccurrentflowinsamedirec;on.
Π <0;Nega;vePel;ercoefficient
Highenergyelectronsmovefromrighttolea.
Thermalcurrentandelectriccurrentflowinoppositedirec;ons.
Ifanelectriccurrentisappliedtothethermocoupleasshown,heatispumpedfromthecoldjunc;ontothehotjunc;on.Thecoldjunc;onwillrapidlydropbelowambienttemperatureprovidedheatisremovedfromthehotside.Thetemperaturegradientwillvaryaccordingtothemagnitudeofcurrentapplied.
Whentwodissimilarmaterialswithdifferentcarrierdensi;esareconnectedtoeachotherbyanelectricalconductor,electricalcurrent(workinput),forcesthemaUertoapproachahigherenergystateandheatisabsorbed(cooling).Theenergyisreleased(hea;ng)asthemaUerapproachesalowerenergystate.Thenetcoolingeffectispropor;onaltotheelectriccurrentandPel;erEffectcoefficient.
ThePel1erEffect
ThompsonEffect
WilliamThompson(1824‐1907)alsoknownasLordKelvin.Heobservedthatwhenanelectriccurrentflowsthroughaconductor,theendsofwhicharemaintainedatdifferenttemperatures(gradienttemperature),heatisevolvedatarateapproximatelypropor;onaltotheproductofthecurrentandthetemperaturegradient.
ThompsonEffect=SeebeckEffect+Pel;erEffect
istheThomsoncoefficientinVolts/Kelvin
Therela;onshipsbetweenthedifferenteffectsarecalledtheKelvinrela;onships.
FirstKelvinrela;onship:
SecondKelvinrela;onship:
CoefficientofPerformance
where
ThermoelectricFigureofMerit(ZT)
Seebeck coefficient Electrical conductivity
Thermal conductivity
Temperature Bi2Te3
Freon
TH = 300 K TC = 250 K
RequirementsforaGoodThermoelectricMaterial
• Generalconsidera;onsfortheselec;onofmaterialsforthermoelectricapplica;onsinvolve:– Highfigureofmerit– largeSeebeckcoefficientα(orS)– highelectricalconduc;vityσ – lowthermalconduc;vityκLaDce+κelectrons – Possibilityofobtainingbothn‐typeandp‐typethermoelements.– Noviablesuperconduc;ngpassivelegsdevelopedyet
• Goodmechanical,metallurgicalandthermalcharacteris;cs– Capableofopera;ngoverawidetemperaturerange.Especiallytrueforhightemperatureapplica;ons.
– Toallowtheiruseinprac;calthermoelectricdevices– Materialscostcanbeanimportantissue!
Thermalconduc;vityconsistsoftwoparts:la^ceconduc;vity(la^cevibra;ons=phonons),κLa,ce,andthermalconduc;vityofcharges(electronsandholes),κelectrons:
Currently,mostoftheresearcheffortsaredevotedtominimizingthela^ceconduc;vityofnewphases.
Minimizingthermalconduc1vity
Somewaystoreducethela^ceconduc;vity:(1)useofheavyelements,e.g.Bi2Te3,Sb2Te3andPbTe;(2)alargenumberNofatomsintheunitcell:thefrac;onofvibra;onalmodes(phonons)thatcarryheatefficientlyto1/N;(3)raUlingoftheatoms,e.g.filledskuUeruditeCeFe4Sb12;disorderinatomicstructure:randomatomicdistribu;onanddeficiencies.
Thelastapproachisnicelyrealizedin"Zn4Sb3",whichcanbecalledan"electron‐crystalandphonon‐glass"accordingtoSlack.Thismaterialhaselectricalconduc;vitytypicalforheavilydopedsemiconductorsandthermalconduc;vitytypicalforamorphoussolids.Infact,itsthermalconduc;vityisthelowestamongstate‐of‐theartthermoelectricmaterials:
Minimizethermalconduc4vityandmaximizeelectricalconduc4vityhasbeenthebiggestdilemmaforthelast40years.!
Bismuthtellurideisthestandardwith ZT=1tomatcharefrigeratoryouneed ZT=4‐5torecoverwasteheatfromcar ZT=2
Cantheconflic4ngrequirementsbemetbynano‐scalematerialdesign?
Reducethela^cethermalconduc;vityby:
• Complexcrystalstructureofhighatomicnumbermaterials.
• RaUlersinthestructure(AtomicDisplacementParameter–ADP).
• NanostructuredThermoelectrics
ComplexCrystalStructures
RaMlers: Theseareweaklyboundatomsthatfillcages. TheyhaveunusuallylargevaluesofAtomicDisplacementParameters Proper1esofmanyclathrate‐likecompoundscanbeunderstoodbytrea1ng“raSler”atomsasEinsteinoscillatorsandframeworkatomsasaDebyesolid. SkuSerudites,LaB6,Tl2SnTe5 ACharacteris1cEinsteintemperature(orfrequency)canbeassignedtoeachraSler
Eu8‐eGa16Ge30PhaseWiththeBa8Ga16Sn30ClathrateStructureType:a=10.62Å
EuNuclearDensityMapatCenterofLargeCage
TunnelingStates!
SrNuclearDensityMapatCenterofLargeCageTunnelingStates?
BaNuclearDensityMapatCenterofLargeCage(6dsiteof
clathratestructure)
X8Ga16Ge30(X=Ba,Sr,Eu)
ADPData(<u2>)From6dSite
AdvantagesofThermoelectrics• Absenceofmovingparts• Highreliability• Quietness• Lackofvibra;ons• Lowmaintenance• Simplestartup• Nopollu;on• Small• Lightweight• Nonoise• Precisetemperaturecontrol:within+/‐0.1C
DisadvantagesofThermoelectrics• Highcost• Lowefficiency• Typicallyabout3to7%
Applica1onsofThermoelectric
• ConsumerApplica;ons
• AutomobileApplica;ons
• IndustrialApplica;ons
• MilitaryandSpaceApplica;ons
ConsumerApplica1ons
BeerCooler
TEFridge
ChocolateCooler
AutomobileApplica1ons
SeatCooler/WarmerCanCooler
IndustrialApplica1ons
ElectronicCooler TEDehumidifier
MilitaryandSpaceApplica;ons
NightVision
BasicPrinciples• MacroscopicThermalTransportTheory–Diffusion
‐‐Fourier’sLaw‐‐DiffusionEqua1on
• MicroscaleThermalTransportTheory–Par1cleTransport
‐‐Kine1cTheoryofGases‐‐ElectronsinMetals‐‐PhononsinInsulators‐‐BoltzmannTransportTheory
BasicPrinciples
Heatisaformofenergy.Thethermalproper;esdescribehowasolidrespondstochangesinitsthermalenergy.
Theheatcapacity(C)ofasolidquan;fiestherela;onshipbetweenthetemperatureofthebody(T)andtheenergy(Q)suppliedtoit.
Themeasuredvalueoftheheatcapacityisfoundtodependonwhetherthemeasurementismadeatconstantvolume(CV)oratconstantpressure(CP).
Thermalconduc1vity
HotTh
ColdTc
L
Q(heatflow)
Fourier’sLawforHeatConduc1on
HeatDiffusionEqua1on
Specificheat
Heatconduc;on=Rateofchangeofenergystorage
1stlaw(energyconserva;on)
• Condi;ons:t>>t≡scaUeringmeanfree;meofenergycarriersL>>l≡scaUeringmeanfreepathofenergycarriers
Breaksdownforapplica;onsinvolvingthermaltransportinsmalllength/;mescales,e.g.nanoelectronics,nanostructures,NEMS,ultrafastlasermaterialsprocessing…
LengthScale
1m
1mm
1mm
1nm
Human
Automobile
BuSerfly
1km
Aircraf
Computer
WavelengthofVisibleLight
MEMS
WidthofDNA
MOSFET,NEMS
BloodCells
MicroprocessorModule
Nanotubes,Nanowires
Par1cletransport100nm
Fourier’slaw
l
D
D
TotalLengthTraveled=L
TotalCollisionVolumeSwept=πD2L
NumberDensityofMolecules=n
Totalnumberofmoleculesencounteredinsweptcollisionvolume=nπD2L
AverageDistancebetweenCollisions,mc=L/(#ofcollisions)
MeanFreePath
σ:collisioncross‐sec;onalarea
NumberDensityofMoleculesfromIdealGasLaw:n=P/kBT
kB:Boltzmannconstant1.38x10‐23J/K
MeanFreePath:
TypicalNumbers:
DiameterofMolecules,D≈2Å=2x10‐10mCollisionCross‐sec;on:σ≈1.3x10‐19m
MeanFreePathatAtmosphericPressure:
At1Torrpressure,mc≈300mm;at1mTorr,mc≈30cm
Wall
Wall
b:boundarysepara;on
Effec;veMeanFreePath:
z
z - z
z + z
u(z-z)
u(z+z)
θ qz
Net Energy Flux / # of Molecules
through Taylor expansion of u
u: energy
Integration over all the solid angles total energy flux
Thermal conductivity:
Specific heat Velocity Mean free path
EFF:WorkFunc;on
Energy
FermiEnergy–highestoccupiedenergystate:
FermiVelocity:
VacuumLevel
BandEdge
FermiTemp:
Metal
Fermi‐Diracequilibriumdistribu;onfortheprobabilityofelectronoccupa;onofenergylevelEattemperatureT
0
1
EFElectronEnergy,E
Occup
a;on
Probability,f
WorkFunc;on,F
IncreasingT
T=0KkTB
VacuumLevel
Density of States -- Number of electron states available between energy E and E+dE
Number density:
Energy density:
in 3D
SpecificHeat
ThermalConduc;vity
ElectronScaSeringMechanisms• DefectScaUering• PhononScaUering• BoundaryScaUering(FilmThickness,GrainBoundary)
e
Temperature,T
DefectScaUering
PhononScaUering
IncreasingDefectConcentra;on
BulkSolids
Meanfree;me:te=le/vF
in3D
MaUhiessenRule:
Electronsdominatekinmetals
Crystallinevs.GlasslikeThermalConduc;vity
P.W.Anderson,B.I.Halperin,C.M.Varma,Phil.Mag.25,1(1972).
InteratomicBonding
1‐DArrayofSpringMassSystem
Equa;onofmo;onwithnearestneighborinterac;on
Solu;on
Freq
uency,ω
Wavevector,K0 π/a
GroupVelocity:
SpeedofSound:
La^ceConstant,a
xn ynyn‐1 xn+1
Freq
uency,ω
Wavevector,K0 π/a
LATA
LO
TO
Op;calVibra;onalModes
TotalEnergyofaQuantumOscillatorinaParabolicPoten;al
n=0,1,2,3,4…;w/2:zeropointenergy
Phonon:Aquantumofvibra;onalenergy,w,whichtravelsthroughthela^ce
PhononsfollowBose‐Einsteinsta1s1cs.
Equilibriumdistribu;on:
In3D,allowablewavevectorK:
p:polariza;on(LA,TA,LO,TO)K:wavevector
DispersionRela;on:
EnergyDensity:
DensityofStates: Numberofvibra;onalstatesbetweenwandw+dw
La^ceSpecificHeat:
in3D
Freq
uency,w
Wavevector,K0 p/a
DebyeApproxima;on:
DebyeDensityofStates:
DebyeTemperature[K]
SpecificHeatin3D:
In3D,whenT<<θD,
ClassicalRegime
Ingeneral,whenT<<qD,
d=1,2,3:dimensionofthesample
Eachatomhasathermalenergyof3KBT
SpecificHeat(J/m
3 ‐K)
Temperature(K)
C∝T3
3ηkBT
Diamond
Kine;cTheory
l
Temperature,T/qD
BoundaryPhononScaUeringDefect
DecreasingBoundarySepara;on
IncreasingDefectConcentra;on
PhononScaUeringMechanisms
• BoundaryScaUering• Defect&Disloca;onScaUering• Phonon‐PhononScaUering
0.01 0.1 1.0
• Phononsdominatekininsulators
