Recent Developments in Thermoelectric Materials

Recentdevelopments in thermoelec tric materials

G.Chen, M.S.Dresselhaus, G.Dresselhaus, J.-P. Fleurial and T.Caillat

F Fermi–Dirac integral de ned byequation (8) Efficient solidstate energy conversion based on f distribution function theP eltier effect for coolingand the Seebeck effect ò Planck’s coe Ycient divided by2 p, J s for powergeneration calls for materials with high I current, A electrical conductivity s,highSeebeck coefficient k thermal conductivity, Wm – 1 K – 1 S,andlow thermal conductivity k.Identifying k Boltzmann’s constant, JK – 1 materials with ahighthermoelectric figure of merit B 2 L functions dened byequation (4) Z(=S s/k)hasproven to bean extremely m* eVectivemass, kg challengingtask. After 30 yearsof slowprogress, Q thermoelectric materials researchexperienced a heat current, W – 1 resurgence,inspired by the developments of new S Seebeck coeYcient, V K conceptsand theories to engineerelectron and T temperature, K phonontransport in bothnanostructures and bulk V voltage, V materials. Thisreview provides a critical summary v velocity,m s – 1 of somerecent developments of newconcepts and Z gure of merit, K – 1 newmaterials. Innanostructures,quantum and ZT non-dimensional gure of merit classicalsize effects provide opportunities to tailor theelectron and phonon transport through Q azimuthal angle structural engineering.Quantum wells, h polar angle superlattices,quantum wires, andquantum dots L mean free path, m havebeen employed to changethe band structure, m chemical potential, J energylevels, and density of statesof electrons, k T j chemical potential divided by B andhave led to improvedenergy conversion P Peltier coeYcient, V capabilityof chargedcarriers comparedto thoseof s electricalconductivity, Sm their bulkcounterparts. Interface reflection andthe t relaxationtime, s scatteringof phononsin thesenanostructures v angularfrequency, Hz rad havebeen utilised to reducethe heat conduction loss.Increases in thethermoelectric figure of merit basedon sizeeffects for either electronsor Introduction phononshave been demonstrated. In bulk materials, newsynthetic routes have led to Solid state cooling and power generation based on engineeredcomplex crystal structures with the thermoelectric e Vects havebeen known since the desiredphonon– glass electron– crystal behaviour. Seebeck eVect (for power generation) and the Peltier Recentstudies on new materials haveshown that eVect (for cooling and heat pumping)werediscovered dimensionlessfigure ofmerit ( ZÖ temperature) in the 1800s. 1 The Seebeck e Vect is associated with valuesclose to 1·5 couldbe obtained at elevated the generation of avoltagealong a conductor when temperatures. Theseresults have led to intensified it is subjected to atemperature di Verence. Charged scientific efforts to identify, design,engineer and carriers (electrons or holes) di Vuse from the hot side characterisenovel materials with ahighpotential to the cold side, creatingan internal electric eld that for achieving ZT muchgreater than1 nearroom V Y temperature. IMR/397 opposes further di usion. The Seebeck coe cient is dened asthe voltagegenerated per degree of temper- ©DrChen is in theMechanical Engineering Department, ature diVerence between two points Massachusetts Instituteof T echnology, Cambridge,MA V 02139,USA ([email protected]). Dr M. S.Dresselhaus is S= 1 2 ...... (1) in theDepartment of Physics, Departmentof Electrical DT1 2 Engineering andComputer Science, Massachusetts Instituteof T echnology, Cambridge,MA 02139,USA. DrG. The Peltier e Vect reects the factthat when carriers Dresselhaus is in theFrancis BitterMagnet Laboratory, owthrough aconductor, they also carryheat. The Massachusetts Instituteof T echnology, Cambridge,MA heat current Q isproportional to the chargecurrent I 02139,USA. DrFleurial andDr Caillat are in theJet Propulsion Laboratory,California Institute of T echnology, Q=PI ...... (2) 4800Oak GroveDrive, MS277–207, Pasadena, CA91109, USA. and the proportionality constant P is calledthe Peltier coeYcient. When two materialsare joined ©2003IoM Communications Ltdand ASM International. Published byManey for the Institute of Materials, Minerals together and acurrent is passed through the interface, andMining andASM International. there willbe anexcess or deciency in the energyat the junction because the two materialshave di Verent Peltier coeYcients. The excess energyis released to the lattice atthe junction, causingheating, and the List ofsymbols deciency in energyis supplied bythe lattice, creating C phonon volumetric specic heat per unit cooling. The Seebeck and the Peltier coe Ycients are frequency interval,J m – 3 K – 1 Hz – 1 related through the Kelvinrelation P=ST, where T E electron energy,J is the absolute temperature. 1 Atypicalthermoelectric e electron unit charge,C cooler is shown in Fig.1 a.P-type and n-type semi-

DOI 10.1179/095066003225010182 InternationalMaterials Reviews2003 Vol. 48 No. 145 46 Chen et al. Recentdevelopments in thermoelectric materials

the units of inverse Kelvin and it often appears asa product with anabsolute temperature T , such as the averagedevice temperature. Thus, the dimensionless numerical gure of merit Z T is often cited rather than Z by itself. The central issue in thermoelectrics materials research isto increase Z T. The best Z T materialsare found in heavilydoped semiconductors. Insulators havepoor electricalconductivity. Metals haverela- tivelylow Seebeck coe Ycients. In addition, the thermalconductivity of ametal, which is dominated by electrons, is in most cases proportional to the electricalconductivity, asdictated bythe Wiedmann–Franz law.It is thus hard to realisehigh Z T in metals. In semiconductors, the thermal conductivity has contri-

butions from both electrons ke and phonons kp , with the majorityusually coming from phonons. The phonon thermal conductivity canbe reduced without causingtoo much reduction in the electricalconductivity.A proven approach to reduce the phonon thermal conductivity is through alloying. 2 The mass diVerence scattering in analloy reduces the lattice thermal conductivity signicantly without much degradation to the electricalconductivity. The com- mercialstate of the art thermoelectric cooling mater-

ialsare based on alloysof Bi 2 Te3 with Sb2 Te3 (such as Bi0 ·5 Sb1 ·5 Te3 ,p-type) and Bi 2 Te3 with Bi2 Se3 (such as Bi2 Te2 ·7 Se0 ·3 ,n-type), eachhaving a Z T at room a cooler; b powergenerator; c actual device temperature approximatelyequal to 1.Refrigerators 1Illustration of thermoelectric devices based on such materialstypically have a coe Ycient of performance (COP)of about 1, 1 compared to compressor based refrigerators with aCOPbetween conductor elements areinterconnected on the cold 2and 4operating over acomparable working temper- and the hot sides, such that acurrent ows through ature range.Their lowCOP has limited thermo- allthe elements in series, whilethe energythey carry electric coolers to niche market sectors, such as (byelectrons and holes) leavesthe cold side in parallel. temperature stabilisation of semiconductor lasers and Thermoelectric power generators work in reverse to picnic coolers. The market for thermoelectric coolers, thermoelectric coolers, asshown in Fig.1 b. Because however, is rapidlyincreasing, partlydue to the the hot side has ahigher temperature, electrons and explosivegrowth of optical telecommunication. State holes aredriven to the cold side through di Vusion of the art power generation materialsare PbT eand and owthrough anexternalload to do useful work. Si0 ·8 Ge0 ·2 ,which havebeen used in deep space radio- Practicaldevices aremade of manypairs of p–n legs isotope thermoelectric power generators that operate (Fig. 1c),usuallyarranged such that current ows in at ~900°Cwith amaximum e Yciencyof about 7%. series through allthe legsand energy ows inparallel From equation (3),one caninfer that the best from the cold side to the hot side. thermoelectric devices should havea thermal conduct- In addition to the temperatures of the hot and cold ivityclose to zero. One possibility is using vacuum sides, which areimportant to allthermal engines, the between the cold and the hot side. Electrons canbe eYciencyof actualthermoelectric devices is deter- emitted through athermionic emission process from mined bythe thermoelectric gure of merit ametal surface and owthrough avacuum. This is S2 s the principle behind thermionic power generators, Z = ...... (3) which weredeveloped in the 1950s. 3 In a vacuum k based thermionic power generator, the emitter isheld where s is the electricalconductivity and k is the ata high temperature. Electrons with energyhigher thermal conductivity. The appearanceof S in Z is than the work function canescape from the emitter self-explanatory. The reason that the electricalcon- surface and reach the collector. Conceivably,rather ductivity s enters Z is due to Joule heating. When athan for power generation, vacuum thermionic emis- current passes through the thermoelectric elements, sion canalso be used for cooling, ifa current drives Joule heat isgenerated which canbe conducted back electrons from the emitter to the collector, asin a to the cold junction. The thermal conductivity k vacuum tube. The major problem, however, is that appears in the denominator of Z because, in thermo- most metals havea largework function value,which electric coolers or power generators, the thermoelec- makes room temperature refrigeration based on tric elements also actas the thermal insulation vacuum thermionic emission impractical. 4 between the hot and the cold sides. Ahigh thermal The progress since the 1960sin improving Z T had conductivity causes too much heat leakagebetween been veryslow before the 1990s.The valueof maxi- the hot and the cold sides. The gure of merit Z has mum Z T had essentiallyremained around 1and

InternationalMaterials Reviews2003 Vol. 48 No. 1 Chen et al. Recentdevelopments in thermoelectric materials 47

published three volume series. 1 3 Afewother reviews and introductory reports havealso been published, emphasising bulk thermoelectric materials. 1 4 – 1 7 Proceedings of International Conferences on ‘Thermoelectrics’, 1 8 which areheld annually,and sev- eralvolumes 1 9 of the MRSproceedings on this topic givebroad coverageof progress made in recent years. This reviewis directed more towards low-dimensional materials,although bulk materialsare also covered to provide readers with aquick overviewof current thermoelectric materialsresearch. The selection of the coveragewas in uenced bythe research focus of the present authors and reects their assessment of the eld. The abovementioned references should be consulted for more comprehensive coverage.

Directionsin search ofhigh ZT 2Non-dimensional figure of merit ZT as function of temperature for state of the art materials materials Expressions for thermoelectric properties areoften derived from the Boltzmann equation under the relax- research funding in this areadwindled. The landscape ation time approximation 2 0 in thermoelectrics research changed quite signicantly L(2 ) L(1 )L(1 ) L(1 ) in the 1990sdue to severalnew conceptual devel- s=L(0 ), k = , S= (4) opments and renewed interested from several e e2 T e2 TL(0 ) eTL(0 ) USresearch funding agencies.New developments where occurred both in bulk materialsand in low-dimensional materials.The best thermoelectric materials d 3 k ç f L(a) =e2 F D t[E(k)][v(k)]2 [E(k) m]a weresuccinctly summarised as‘ phonon–glass elec- P 4p3 A ç E B tron–crystal’ (or PGECin short),which means that ...... (5) the materialsshould havea lowlattice thermal con- f ductivity asin aglass,and ahigh electricalconduct- In the aboveexpressions, F D is the Fermi–Dirac ivityas in crystals. 5 In bulk materials,the major new distribution, t is the electron (hole) relaxationtime, concept that wasdeveloped is the use of ‘phonon k is the electron wavevector, ke is the electronic rattlers’to reduce the lattice thermal conductivity. contribution to thermal conductivity, v isthe electron These phonon rattlers arenormally interstitial atoms group velocity,and e is the unit charge.If the relax- inserted into empty spaces inthe host materials.Their ation time is assumed to be aconstant and athree- vibration is not in harmony with the atoms in the dimensional (3D)parabolic electronic energyband is host material,thus scattering the phonons in the assumed, Z T canbe expressed as 1 ,2 1 originallattice. In this connection, severalclasses of [(5F /3F ) j*]2 (3F /2) materialshave been discovered and /or re-investigated Z T = 3 /2 1 /2 1 /2 (6) 3 D + 2 with regardto their potential for high Z T, such as 1/B3 D 7F5 /2 /2 (25F 3 /2 /6F1 /2 ) skutterudites and clathrates. In low-dimensional where materials,such asthin lms, superlattices, and quan- (m*)3 /2 2k T 3 /2 k2 Tm tum wires,several approaches havebeen proposed. B B B . . . . . (7) 3 D = 2 2 For transport alongthe lm plane (wireaxis) direc- 3p ò ekp tion, quantum size e Vects areconsidered to increase A B and m* (m m m )1 /3 is the eVectivedensity of states the electronic power factor S2 s and boundary scat- = x y z mass of electrons in the band, k is the phonon tering to reduce k.6 ,7 For transport in the direction p contribution to the thermal conductivity, k is perpendicular to the lm plane, severalpossibilities B weresuggested. One wasto use the band-edge dis- Boltzmann’s constant, m is the electron mobility, j* is the chemical potential normalised by k T, and F is continuity asa lter for cold electrons. 8 This was B i later developed into athermionic emission cooling the Fermi–Dirac integral de ned as approach.9 ,1 0 Another approach wasbased on ? xi dx phonon reection atinterfaces to reduce the lattice F (j*)= ...... (8) i exp(x j*)+1 thermal conductivity. 1 1 ,1 2 Figure2 shows a‘snapshot’ P0 of the reported Z T values. The Z T valuesof low- In equations (6)and (7),the subscript 3Dis used to dimensional structures aresubject to higher uncer- indicate that those expressions arederived considering taintyand should be taken cautiously, primarilydue the density of states of 3Dbulk crystals.In low- to the diYculties involvedin characterising the Z T dimensional structures, these expressions must be of low-dimensional materials. reformulated. 2 1 In equation (6),the reduced chemical In this paper, it is intended to provide aconcise potential j*is afree variablethat canbe controlled criticalreview of some recent developments in ther- bydoping. The optimum valuefor the chemical moelectrics research. Anextensive review of most of potential is chosen to maximise Z T.Therefore, ther- the topics discussed here is contained in arecently moelectric materialsdevelopment involvescareful

InternationalMaterials Reviews2003 Vol. 48 No. 1 48 Chen et al. Recentdevelopments in thermoelectric materials control and optimisation of doping. The only other weightmaterial. Its success relies on its multiple variablethat a Vects the Z T valuein equation (6)is carrier pockets that givea reasonably high density of the B factor, which depends on the electron e Vectivestates and, more importantly, on the alloyingmethod mass, the carrier mobility, and the phonon thermal that signicant lowers its thermal conductivity com- conductivity. The largerthe B factor, the largeris Z T.pared to that of bulk Si or Ge. High temperature

Thus, thermoelectric materialsresearch is often operation alsohelps to increase the Z T of Si1 – x Gex . guided by nding materialsthat havea large B factor, While the general Z T formulation for bulk mater- which include alargeelectron (hole) e Vective mass ialshas playedand willcontinue to playan instrumen- and ahigh mobility, and alowlattice thermal con- talrole in developing strategies in the search for ductivity. Such materialsare succinctly called highly eYcient thermoelectric materials,it should be phonon–glass electron– crystal materials by Slack. 5 It kept in mind that these expressions arederived by should be pointed out that the requirements of ahigh using aset of approximations. Those related to the mobility (which needs alowmobility e Vectivemass) present discussion aregiven below. and ahigh density of states (which demands alarge 1.Bulk density of states for electrons and holes. density of states e Vectivemass) arenot necessarilyExpressions such as( 6)and (7)arederived by mutually exclusive.In anisotropic media, either in assuming 3Dparabolic bands. Quantum structures bulk form or in superlattices, it is possible to havea to be discussed later havea drasticallydi Verent small eVectivemass in the current owdirection to density of states and expressions (6)and (7)will givea high mobility and largee Vectivemasses inthe changecorrespondingly. directions perpendicular to the current owto givea 2.Local equilibrium approximation. Expressions high density of states. for the transport coe Ycients, equations (4)and (5), It should be mentioned that the derivation of arederived byassuming that electrons deviateonly equation (6)is based on the constant relaxationtime slightlyfrom their equilibrium distributions. This is approximation. Amore realistic form of the relaxation validonly when the characteristic length alongthe time has anenergy dependence t!Ec,which depends transport direction is much longer than the electron on the scattering mechanisms. For example, c=1/2 mean free path. This assumption willnot be validfor for optical phonons, and c= 1for acoustic transport atthe interfaces and for carrier transport phonons.1 It canbe shown that Z T also depends on in the direction perpendicular to verythin lms. In c.Thus, one strategythat is sometimes used to addition, the electrons and phonons aretypically improve Z T is to control the scattering mechanism. assumed to be in thermal equilibrium. This assump- The thermal conductivity of phonons is also often tion is not necessarilytrue, asin the wellknown hot modelled from the Boltzmann equation under the electron eVect in semiconductor electronics. relaxationtime approximation, i.e. 3.Isotropic relaxationtime for both electrons and phonons. Manylow-dimensional structures, such as d 3 k ç f superlattices, arehighly anisotropic. Expressions such k = æ [v (k)]2 p t ò v p 8p3 p x T p asequation (9)for the thermal conductivity areno p ç P longer correct. 1 Much of the development in low-dimensional struc- = C(v)v (v)L (v) dv ...... (9) 3 p p tures canbe attributed to relaxingone or severalof P these approximations. This allowsfor more independ- for anisotropic bulk material,where fp is the phonon ent control of S, s, or k,aswill be seen in the distribution function, C isthe specic heat of phonons followingdiscussion. atfrequency v, vp is the phonon group velocity, tp is the phonon relaxationtime, L is the free path of p Low-dimensionalthermoelectric phonons at v and the summation isover the di Verent phonon polarisations. To reduce the thermal conduct- materials ivity,materials with asmallphonon group velocityLow-dimensional materials,such asquantum wells, and ashort relaxationtime aredesired. Roughly superlattices, quantum wires,and quantum dots o Ver speaking, the phonon group velocityis proportional newways to manipulate the electron and phonon to (K /m)1 /2 , where K is the spring constant between properties of agivenmaterial. In the regimewhere the atoms and m is the mass of the atom. Thus, quantum e Vects aredominant, the energyspectra of materialswith high atomic mass areoften used for electrons and phonons canbe controlled through thermoelectric materials.The phonon relaxationtime alteringthe size of the structures, leadingto newways canbe reduced byscattering, such asthrough to increase Z T.In this regime,the low-dimensional alloying2 and byadding phonon rattlers. 1 5 structures canbe considered to be newmaterials, Successful bulk thermoelectric materialsthat were despite the factthat they aremade of the same atomic developed in the past weredirected bythe principles structures astheir parent materials.Each set of size derived from the abovegeneral discussion for bulk parameters provides a‘new’material that canbe materials.For example,Bi 2 Te3 wastested because of examined, to acertain extent, both theoretically and its high atomic weight. 2 2 Other important character- experimentally,in terms of its thermoelectric prop- istics of Bi2 Te3 that werediscovered later, such asits erties. Thus, searching for high Z T systems in low- multiple carrier pockets, high mobility, and lowther- dimensional structures canbe regarded asthe equival- malconductivity, allcontributed to its high Z T valueent of synthesising manydi Verent bulk materialsand because allthese factors work favourablyto increase measuring their thermoelectric properties. Because the B factor. In contrast, SiGe is not ahigh atomic the constituent parent materialsof low-dimensional

InternationalMaterials Reviews2003 Vol. 48 No. 1 Chen et al. Recentdevelopments in thermoelectric materials 49 structures aretypically simple materialswith well known properties, the low-dimensional structures are amenable to acertain degree of analysis,prediction and optimisation. In contrast, theoretical predictions for bulk materialsproperties areoften di Ycult2 3 and the investigation of eachnew material presents a diVerent set of experimental and theoretical challenges. When quantum size e Vects arenot dominant, it isstill possible to utilise classicalsize e Vects to alter the transport processes, asfor examplethe exploi- tation of boundaries to scatter phonons more e Vec- tivelythan electrons. Investigations over the past decade on low-dimensional structures haveexploited both quantum and classicalsize e Vects for electrons and phonons. The focus of discussion here is along three directions. One is for electron transport parallel 3Calculated dependence of non-dimensional to the plane of thin lms or alongthe axisof figure of merit ZT (within quantum well or nanowires. Another is for the electron transport per- within quantum wire) on well or wire width for Bi2 Te3-like material at optimum doping pendicular to the lm plane. The third emphasises concentration for transport in highest mobility phonon transport. Although no devices based on low- direction: also shown is ZT for bulk (3D) Bi 2 Te3 dimensional structures areclose to commercialisation, calculated using corresponding 3D model 6,25 research on low-dimensional thermoelectricity has been stimulating to recent developments in thermoelectrics research, and newresearch groups worldwide 4,and that the model calculations werein good arenow starting to bring newideas to the eld based agreement with the experimental observations. Soon on nanostructures. thereafter, it wasshown that anenhanced thermoelectric gure of merit could also be observed for p-type 3 0 ,3 1 Electron bandgap engineered materials: PbTequantum wells, which is, of course, an transport parallel tofilm planeor nanowire important consideration for thermoelectric devices, axis which depend on havingboth n-type and p-type legs. These modelling calculations and experimental The development of band gapengineering inquantum dataare based on the consideration of transport structures for thermoelectric applications started with inside the quantum wellsonly, and thus the reported the modelling of singlequantum wells 6 and soon Z T valuesare referred to as( Z T ) .Theoretical moved on to the consideration of superlattices. 2 1 It 2 D modelling pointed out that when the barrier regions V wassoon recognised that quantum wireswould o er of the superlattices arealso considered, the overall more quantum connement and therefore would have gain in Z T of the whole structure is considerably advantagesover quantum wellsfor thermoelectric 3 2 ,3 3 2 4 ,2 5 reduced because the barriers do not contribute applications, asshown in Fig.3. In due course, to the electricaltransport, but do contribute to the researchers also beganto consider the benets of reverse heat conduction. In the limit that the barrier quantum dot systems for thermoelectric applications. is thin, it wasalso suggested that tunnelling between V The keyidea is to use quantum size e ects to increase quantum wellsreduces the Z T enhancement inside the electron density of states atthe Fermi leveland anindividual quantum well.How to address this in this wayto optimise the power factor. Further issue is veryimportant for the utilisation of quantum benets to thermoelectric performance canbe realised size eVects on the electron transport alongthe lm byexploiting boundary scattering to reduce the ther- plane. One possible approach, suggested bythe malconductivity preferentially, without much loss to Dresselhaus group, is to use both the quantum wells the electricalconductivity. and barriers for thermoelectric transport alongthe Quantum wellsand superlattices lm plane.3 4 For example,by proper choice of the The most elementary generic calculations, 6 ,2 4 ,2 5 and widths of the quantum wellsand barriers for alsomore sophisticated calculations on specic mater- GaAs/AlAssuperlattices, the carriers in the C-point ials,2 6 both predict enhanced thermoelectric perform- and L-point valleyscontribute to transport in the ancewithin the quantum wellsof multiwell GaAsregions, whilethe X-point valleyscan contrib- superlattices relativeto bulk materialsof the same ute to transport in the AlAsregions. 3 5 Furthermore, stoichiometry. To show proof of principle experimen- for agivensuperlattice system, such asSi /Ge superlat- tally,special superlattices weredesigned bythe tices and their alloys, 3 6 model calculations canbe Dresselhaus group and fabricated bythe Harman used to optimise the superlattice geometry to achieve group atMIT Lincoln labfor PbTebased superlat- the maximum Z T of the whole superlattice structure. tices2 7 and bythe Wanggroup atUCLA to make Although there arelimited experimental datasuggest- Si/Ge superlattices. 2 8 ,2 9 The rst proof of principles ingthis possibility, more experimental e Vorts are experiment to conrm the enhancement of Z T within needed to demonstrate the e Vectiveness of this carrier aquantum wellwas reported for n-type PbTequan- pocket engineering approach. 2 7 tum wellswithin PbTe /Eux Pb1 – x Tesuperlattices. The theoretical work has inspired experimental The results showed that the power factor within the studies of thermoelectric e Vects in superlattices. The PbTequantum wellcould be increased bya factor of past fewyears have seen steady improvements in the

InternationalMaterials Reviews2003 Vol. 48 No. 1 50 Chen et al. Recentdevelopments in thermoelectric materials

5Cross-sectional view of Bi nanowires in 4Thermoelectric non-dimensional figure of merit cylindrical channels of 65 nm average diameter versus carrier concentration for high quality within anodic alumina template, shown as bulk PbTe material in comparison to much transmission electron microscope (TEM) image: higher ZT for PbSeTe/ PbTequantum dot template has been mostly filled with Bi, and superlattice structureat 300 K 7 (courtesy T. TEM image was taken after top and bottom Harman) sidesof sample had been ion milled with 6kV Ar ions44,48 thermoelectric performance of specic superlattices. nels from 7to 100nm in diameter and 50 mm in For example,experimental thermoelectric datafrom length with packing densities of 10 1 0 channels cm – 2 Harman’s group demonstrated that for PbTe /Te (Refs.44, 45 ).These pores within the channels can superlattices, obtained bythe addition of afewnano- then be lled with promising thermoelectric materials, metres of Teabove the PbTelayer before the barrier such asBi or Bi Sb alloys.Because of the low layeris added, the Z T increased from 0·37to 0·52at 1 – x x eVectivemasses and largeanisotropy of the constant room temperature and this increase in Z T was associ- energysurfaces of these materials,quantum conne- ated with the formation of aquantum dot structure ment eVects at77 K arepredicted for wirediameters atthe interface. 3 1 The Harman group further disco- aslarge as 50nm, 4 6 asdiscussed further below. These vered experimentallythat quantum dot superlattices eVects havebeen veried experimentallyby transport Z T based on PbTe /PbSeTe havean even higher . For measurements. 4 4 ,4 7 example,PbSeTe /PbTequantum dot superlattices Figure5 shows anexampleof ananodised alumina show alargeenhancement in the Seebeck coe Ycient template which is lled with Biusing the pressure relativeto bulk PbTesamples with the same carrier injection method. 4 8 One important advantageof these concentration. 7 Atthis stage,detailed mechanisms for Binanowires is their crystalproperties which canbe the reported Seebeck coe Ycient enhancements in seen in the X-rayand electron di Vraction patterns these quantum dot superlattices arenot clear.Among shown in Fig.6 for anarray of Binanowires 52nm the speculations areboth quantum connement e Vects in averagediameter, indicating that eachwire has a and amore favourablescattering mechanism associ- similarcrystal orientation alongthe nanowire axis. ated with quantum dots. Furthermore, anestimation This is veried in Fig.6 bycomparison of the X-ray of Z T for such quantum dot superlattices, based on diVraction pattern with the corresponding electron the phonon thermal conductivity of equivalent alloys diVraction pattern for atypicalnanowire, showing a that areconsidered bythe authors asconservative, unidirectional orientation of the nanowires alongthe yieldsa room temperature valueof 0·9,which ismore wireaxes. In principle, the crystallineorientation can than afactor of 2greaterthan has been achieved be controlled, but thus farthe preferred growth see V with the best bulk PbTematerial ( Fig. 4). E orts direction for agivengrowth method has dominated arepresently underwayby several groups worldwide the nanowire crystallineorientation. Asa result of to obtain reliablemeasurements of the in-plane ther- 3 7 – 4 1 the high crystallinityof these nanowires, high carrier malconductivity of smallsuperlattice samples. mobility and long mean free paths areachievable, The growth bymolecular beam expitaxyof PbTe which is of direct benet for thermoelectric based superlattices and quantum dot superlattices applications. canbe relativelyfast, making it feasibleto growvery In addition to pressure injection, physicalvapour thick superlattices (50–100 mmtotal thickness) for deposition4 9 has alsobeen used to llthe templates simple devicetesting. 4 2 and to make Binanowires with singlecrystal prop- Quantum wires erties, havingthe same crystalstructure and lattice General theoretical considerations suggest that, constants asbulk Bi.Electrodeposition is veryattract- because of their increased quantum connement ivefor llingthe pores of analumina template, eVects, 1Dquantum wirescould havean even larger because of the easein makinggood electricalcontacts. enhancement in Z T 2 4 ,4 3 than 2Dquantum wells( see The exibilityof the electrodeposition approach has

Fig.3 ).To fabricatecontrolled arraysof quantum allowednanowire arraysof Bi,CoSb 3 , and Bi2 Te3 to wires,anodic alumina(Al 2 O3 )templates havebeen be produced. The nanowire arraysthus farproduced developed and these templates canbe made to haveby electrodeposition arepolycrystalline and arethere- regulartriangular arrays of porous nanoscale chan- fore expected to havelower carrier mobilities than

InternationalMaterials Reviews2003 Vol. 48 No. 1 Chen et al. Recentdevelopments in thermoelectric materials 51

6X-ray diffraction pattern for anodic alumina / Bi nanowire composites (average wire diameter of Bi nanowires isabout 52 nm) and selected area electron diffraction pattern (inset) taken from same sample: these two experimental resultsindicate that Bi nanowires are highly crystalline and possessstrongly preferred growth orientation 44,45 the arraysprepared by llingfrom the vapour phase or bypressure injection. Bismuth has ahighlyanisotropic band structure with some verysmall e Vectivemass tensor com- – 2 ponents (~10 free electron masses), and high a subband structure at77 K ofBi quantumwires oriented mobility carriers makingit averyattractive thermo- along [011Â 2]growth direction, showing energies ofhighest electric material,except that in bulk form, Biis a subbands forT-point hole carrier pocket, L-point electron semimetal with equal concentrations of electrons and pockets (A,BandC) as well as L-point holes, which are holes, thus leadingto anearlycomplete cancellation indicated in Brillouin zone shown on right (zeroenergy refersto conduction bandedge in bulk Bi): aswire diameter between the positive and negativecontributions to decreases, conduction subbands moveup in energy,while the Seebeck coe Ycient. However, for Bias a quantum valencesubbands movedown; at dc =49·0 nm, lowest wellor aquantum wire,the band edgefor the lowest conduction subband edgeformed by L(B,C) electrons subband in the conduction band rises abovethat for crosses highest T-point valencesubband edge,and semimetal–semiconductor transition occurs ( D0 is band the highest subband in the valenceband ( see Fig. 7) 45 overlap and EgL is L-point bandgap); b Fermisurfaces of thereby leadingto asemimetal–semiconductor trans- Bi, shown in relationto Brillouin zone corresponding to ition. This is predicted to occur atawirediameter of fifth-bandhole pocket aboutT-point andthree sixth-band 49nm for Binanowires oriented alongthe favoured L-point electron pockets labelled A,B,andC: mirrorplane growth direction. Bismuth nanowires areof interest symmetryof bulk bismuth structure results in crystallographic equivalence ofL-point carrier pockets B for thermoelectric applications when in the semicond- andC; however,L-point carrier pocket Ais notequivalent ucting regime, under heavydoping conditions. crystallographically tocarrier pockets BorC Temperature dependent resistance measurements 7Diameter dependence of band edges for Bi (see Fig. 8a)in conjunction with model calculations nanowires: 3D Brillouin zone in b shows (see Fig. 8b)show that these bismuth nanowires are important band edges participating in semi- converted from asemimetal into asemiconductor due metal–semiconductor transition to quantum size e Vects.5 0 This is seen bythe monotonic temperature dependence of the resistance in the the resistance of both nanowire arraysand of single semiconducting phase for wirediameters below 48nm nanowires. These di Yculties arisefrom problems with and the non-monotonic behaviour with temperature makinggood ohmic contacts to allthe nanowires of for wireswith diameters largerthan 70nm, above ananowire arrayand with the oxidation of the which the wiresare in the semimetallic regimes, in individual nanowires, when they areremoved from agreement with theoretical predictions (Fig.8 b). The their templates. non-monotonic dependency of resistance on the The Bi1 – x Sbx alloysystem is interesting asa nanowire diameter is due to the extrinsic carriers method for obtaining alow-dimensional p-type semi- contributed byuncontrollable impurities, which conductor with verylow e Vectivemasses and high becomes more important asband gapincreases. So mobility carriers, which is important because thermo- far,there exists no conclusive experimental datashow- electric devices require both n-type and p-type legs. ingan enhanced power factor in Binanowire arrays, Since Sb is isoelectronic with Biand has the same due to diYculties in measuring the absolute valueof A15crystal structure asBi, bulk Bi 1 – x Sbx alloys InternationalMaterials Reviews2003 Vol. 48 No. 1 52 Chen et al. Recentdevelopments in thermoelectric materials

SM=regions wherealloy is semimetal; SC =region where alloy is semiconductor 9Schematic diagram for energy bands near Fermi level for Bi1 – x Sbx bulk alloys asfunction of x at low T (à 77 K):51 when highest valence band is at L-point, direct gap semiconductor results;for x values where highest valence statesare at T or H,indirect semiconductor isobtained

a experimentaltemperature dependence of normalised resistance forBi nanowire arraysof various wire diameters preparedby vapour deposition method,in comparison with corresponding datafor bulk Bi: measurementof resistance 10 Phase diagram of electronic band structureof was madewhile Bi nanowires werein theiralumina Bi Sb nanowires:52 bold arrow in centre templatesusing two-probemeasurement technique; 49 1 – x x b calculated temperaturedependence of resistance forBi indicates condition where 10 hole pockets nanowires of36 and 70 nm, using semiclassical transport (about T-point, 3L-points and 6H-points in model45 Brillouin zone) coalesce in energy 8Temperature dependence of resistance measurements for Bi nanowires concentration, the wiresare predicted to be semimetallic,a direct gapsemiconductor, or anindirect gap provide ahigh mobility material,but with electronic semiconductor. The calculations of Fig.10 show how properties that canbe variedconsiderably asthe Sb variationof the nanowire diameter canbe used to concentration is varied( see Fig.9 ).Of particular changethe electronic structure quite dramatically interest for thermoelectric applications is the lowwith no basic changeoccurring in the crystalstruc- Sb concentration range( below x =0·07 )where the tures. Of particular interest in this diagramfor the bulk materialis semimetallic, the regions for Bi 1 – x Sbx nanowires is the point at x =0·13, and a 0·07leads to anenhanced Seebeck coe Ycient and anincreased another important degree of freedom in the control Z T.5 2 ,5 3 The feasibilityof observing interesting trans- of the electronic structure, showing regions where, port properties in Bi 1 – x Sbx nanowires has been depending on the nanowire diameter and Sb alloy demonstrated byshowing that the high degree of

InternationalMaterials Reviews2003 Vol. 48 No. 1 Chen et al. Recentdevelopments in thermoelectric materials 53 crystallinityof the Binanowires is preserved upon Sb Bowers predicted that solid state thermionic coolers alloyingas is the high carrier mobility. havea largercooling power than that of thermoelec- Thus far,progress in the fabrication and measure- tric devices. Mahanand co-workers 5 7 ,5 8 followed up ment of the thermoelectric performance of test with athermionic cooling and power generation samples is most advancedfor 2Dsystems where model for multiple layerstructures. In this case,the superior performance has alreadybeen demonstrated. advantageof the non-uniform heat generation inside 9 The excellent Z T3 D for these superlattices is attributed adouble heterojunction structure due to the ballistic to the presence of quantum dot structures atthe electron transport is lost. Their initialcalculation 5 7 ,5 8 nanoscale,7 whose behaviour is not yetunderstood in suggests that multilayerthermionic coolers canhave detail, nor has the structure yetbeen optimised for a high eYciency.Yet in another paper, Viningand thermoelectric performance. The 1Dquantum wiresMahan 5 9 compared the equivalent B factor that deter- havein contrast been modelled in detail, though mines the Z T for thermionic multiple layerstructures materialsproblems involvingsurface oxidation and and similarthermoelectric multiple layerstructures with the formation of good individual contacts to the and found that the B factor of thermionic structures is nanowires haveslowed the experimental evaluationnot largerthan that for thermoelectric structures. and optimisation of the thermoelectric performance Their conclusion is that the thermal conductivity of the quantum wires.It is thus expected that further reduction 1 1 ,1 2 willbe the major benet of multiple emphasis willbe givento materialsscience issues, layerstructures, which is consistent with the studies before the construction of reliablequantum wirecarried out bythe Ehrenreich group. 5 5 In addition to thermoelectric devices willbe seriously undertaken. anall solid state cooling strategy,vacuum thermionic refrigeration based on resonant tunnelling through triangularwells and smallspatial gaps in the vacuum Electron transport perpendicularto film plane has been proposed recently. 6 0 ,6 1 Theoretical calcu- Most of the eVort so farhas been focused on thin lations predict operation atroom temperature and lms and superlattices. There aretwo lines of consid- below, with acooling power density of 100W cm – 2 . eration for electron transport perpendicular to the No net cooling based on such vacuum thermionic thin lm plane: (i)control of the density of electron coolers has been reported experimentally. states using quantum size e Vects, and (ii)energy Theoretically,the modelling of electron transport ltering through thermionic transport. Twotheo- perpendicular to the connement direction is con- reticalpapers considered quantum size e Vects siderably more di Ycult compared to that alongthe on thermoelectric properties for electron transport lmplane, because the lm thickness maybe compar- perpendicular to the superlattice plane. 5 4 ,5 5 A slight ableto severalcharacteristic lengths of the charge increase in Z T for Si/SiGe superlattices made of carriers, including the wavelengthand the mean free extremelythin layers( ~5 A)is predicted. 5 4 Radtke path. Thus far,quantum based models, which consider 5 5 et al. studied Hgx Cd1 – x Tesuperlattices, and their the electrons astotally coherent, and thermionic calculation shows that a20%increase in power factor emission models, which consider the electrons as is possible in narrow-wellnarrow-barrier superlattice totallyincoherent, havebeen constructed. But there systems, but suggested that the gainin Z T will most is no theory so farfor the overlapping region. In likelycome from athermal conductivity reduction addition, there arealso thermoelectric e Vects inside rather than from apower factor increase. So far,there the lm, which maybe coupled with thermionic e Vects seems to be no experimental e Vort aimed atpursuing atthe interface to yielda total Z T of the structure. apower factor increase due to quantum size e Vects There havebeen afewstudies that treat both e Vects for transport perpendicular to superlattice planes. and phonon size e Vects byZeng and Chen. 6 2 – 6 4 Their In the limit that the quantum size e Vect is not modelling suggests that when the lm is verythin, important, for this case,there is still apossibility for energyconversion is dominated bythe thermionic increasing Z T.It wasproposed that the energybar- emission and when the lm is thick, thermoelectric riers atthe junctions of di Verent materialsbe used astransport governs the energyconversion e Yciency. In anenergy lter to increase the thermoelectric energy the intermediate lm thickness range,both e Vects conversion e Yciency.8 Electron transport over such contribute to the nal Z T.Their work alsosuggests barriers is described bythermionic emission theory. that the thermal conductivity reduction willcontrib- In atheoretical paper, Mahan 5 6 considered the cool- ute more to the Z T enhancement compared to the ingpower of vacuum based thermionic coolers, which thermionic emission, Z T which is consistent with arebased on the same principle asvacuum based previous studies that inferred the importance of the thermionic power generators. His calculation showed thermal conductivity reduction based on experimental that vacuum based thermionic coolers willnot be results. 5 5 ,5 9 ableto run atroom temperature because of the large Experimentally,Shakouri and co-workers have work function of known materialsand because of fabricated thin lm thermoelectric coolers based on space chargee Vects. Shakouri and Bowers 9 suggested singleheterojunction structures 6 5 and superlattice that this could be circumvented using double hetero- structures 6 6 –7 0 based on InP and Si /Ge superlattices. junction structures. The barrier height between two The maximum temperature rise measured on asingle materialscan be precisely tailored in theory aswell element deviceis 12K ata 200 °Csubstrate temper- asin practice for certain materialssystems. Another ature from Si /Ge superlattices. 7 0 Mahan1 0 pursued advantageof this approach is that Joule heating is metal–semiconductor superlattice structures for cool- mostly rejected atthe hot side due to the ballistic ing.No cooling e Vect has yetbeen reported from transport. Basedon asimplied model, Shakouri and such structures. It should be emphasised that testing

InternationalMaterials Reviews2003 Vol. 48 No. 1 54 Chen et al. Recentdevelopments in thermoelectric materials asingledevice is verydi Ycult and involvesmany removal of the substrate. 3 7 – 3 9 ,8 3 Veryfew studies have forms of losses that maydegrade the deviceperform- reported thermal conductivity in both the in-plane ance. Thus, these devices mayhave better performance and cross-plane directions. 3 8 ,4 0 Allthese experiments ifsuccessfully developed asarrays, rather than as conrmed that the thermal conductivities of the super- individual devices. So far,there areno systematic lattices in both directions aresigni cantly lower than experimental investigations on whether the observed the predictions based on the Fourier lawand the cooling is due to thermionic or thermoelectric mech- properties of their bulk parent materials.In the cross- anisms, or both. Fieldemission coolers based on plane direction, the thermal conductivity valuescan GaAsare also being investigated, but no cooling denitely be reduced below that of their correspond- eVect has been observed so far. 7 1 ing alloys.1 2 ,8 1 In the in-plane direction, the reduction is generallyabove or comparable to that of their Engineeringphonon transport equivalent alloys, 4 0 although afewexperimental data Phonon transport in low-dimensional structures is indicate that k valueslower than those of the corres- also aVected bysize e Vects and canbe utilised to ponding alloysare possible. 1 1 increase Z T. Size eVects in the thermal conductivity Afewgroups havedeveloped theoretical expla- area wellknown phenomenon that is important atnations for the thermal conductivity of superlattices, lowtemperatures for bulk materials. 7 2 Severalstudies for both in-plane and cross-plane directions. Two of the thermal conductivity of thin lms werecarried schools of thought areapparent from the literature. out inthe 1970sand 1980s,mostly for polycrystalline One starts from the phonon spectrum calculation and metallicor semiconductor thin lms. The rst experi- attributes the thermal conductivity reduction to ment on superlattices wasperformed byYao 3 7 for the changes in the group velocity,density of states, and thermal conductivity alongthe lm plane. He scattering mechanics. 8 8 – 9 3 The other approach starts observed that the thermal conductivity of the super- from the simple picture of interface reection and lattices investigated washigher than that for their treats phonon transport in terms of particles. 9 4 –9 7 The compositionally equivalent alloys.One caneasily former assumes that phonons aretotally coherent infer that the reported valuesare also signicantly and the latter treats phonons in eachlayer as totally lower than the valuescalculated from bulk properties incoherent. The coherent phonon picture is accurate according to the Fourier theory. The rst experiment ifthe interfaces and internal scattering do not destroy in the cross-plane direction wasreported byChen the coherence of the phonons. Compared to the et al.3 8 Theymeasured the thermal conductivity of acoherent picture, the particle approach does not treat semiconductor laserstructure, which contained short the followingmechanisms correctly: (i)phonon inter- period superlattices, in both directions and observed ference, which givesminigaps in the superlattice afactor of 10reduction of k in the cross-plane phonon spectrum, (ii)phonon tunnelling, which direction compared to predictions bythe Fourier occurs for verythin layersabove the criticalangle for theory. The reduction in the in-plane direction is total internal reection of phonons, and (iii)long smaller but also signicant. In areviewpaper, Tien wavelengthphonons, which do not ‘see’the existence and Chen7 3 suggested that the newspectrum in of the interfaces. These three factors, however, do not superlattices canpotentially leadto super thermal seem to be dominant in the observed thermal conduct- insulators. The studies byYao 3 7 and Chen and ivitybehaviour of superlattices. This is because heat co-workers3 8 ,3 9 weremainly geared towards thermal conduction involvesthe contribution from allallow- management applications for semiconductor lasers. 7 4 ablephonons coveringthe entire phonon frequency Venkatasubramanian proposed to use the potentially range.Minigaps created byinterference e Vects cover lowcross-plane thermal conductivity of superlattices only asmallfraction of the total thermal energy. for thermoelectric devices. 1 1 ,7 5 The ideais to use the Tunnelling is important only when eachlayer is only phonon reection atinterfaces to reduce the thermal 1–3monolayers thick due to the smallphonon wave- conductivity, whilemaintaining the electron trans- length. In addition, the di Vuse interface scattering mission atthe interfaces bycombining materialswith occurring atmost interfaces, which seems to be avery smallor, ideally,zero band-edge o Vset. Such struc- important factor, destroys the phonon coherence. tures arecalled electron-transmitting phonon-block- Comparison of lattice dynamics, 9 2 acoustic wave 9 8 9 4 ,9 6 ,9 7 ingstructures. This strategyon the Bi 2 Te3 /Sb2 Te3 propagation, and Boltzmann equation simu- system seems to haveled to asignicant increase of lations with experimental data,by Chen and Z T 1 1 ,7 6 asindicated in Fig.2. As a word of caution, co-workers, leads to the conclusion that the major because the characterisation of Z T is extremely reason for the observed thermal conductivity diYcult in this direction, the valuesshould be sup- reduction in the cross-plane direction is the phonon ported bymore research, preferably bydi Verent reection, particularlythe total internal reection. 1 2 groups. Although phonon connement due to the spectral Extensiveexperimental dataon the thermal con- mismatch canpotentially contribute signicantly to ductivity of various superlatttices, including Bi 2 Te3 / the thermal conductivity reduction, it is likelythat 7 5,77 ,78 37–39,79,80 40 ,81 – 8 3 Sb2Te3, GaAs/AlAs, Si/Ge, InAs/ manyphonons leakout due to inelastic scattering. 8 4 8 5 8 6 AlSb, InP/InGaAs, CoSb3 /IrSb3 , and PbTeFor both the in-plane and the cross-plane directions, based superlattice 4 1 havebeen reported in recent diVuse interface scattering of phonons seems to play years.Most of these measurements arein the cross- acrucialrole. Asan example,in Fig.11 a the simulated plane direction, 7 5 ,8 1 – 8 6 using the 3v method8 7 or the thermal conductivity reduction in Si /Ge superlattices optical pump-and-probe method. 8 0 Measurements in both the in-plane and the cross-plane directions alongthe lm plane direction relied heavilyon the based on lattice dynamics modelling of the phonon

InternationalMaterials Reviews2003 Vol. 48 No. 1 Chen et al. Recentdevelopments in thermoelectric materials 55

a lattice dynamics simulation ofthermal conductivity normalised tobulk values; 92 b temperaturedependence of thermal conductivity ofSi /Ge (20/20 A)superlattice along (subscript x)and perpendicular (subscript z)to film plane; 40 c thickness dependenceof thermal conductivity ofGaAs /AlAs superlattices along film plane (GaAs andAlAs layers areof equal layer thickness); 94 d period thickness dependenceof thermal conductivity ofSi /Gesuperlattices in cross-plane direction 97 (also plotted in b–d arefittings based on solutions ofBoltzmann equations with p representingfraction ofspecularly scattered phonons atinterface,and values calculated based on Fourier law andmeasured bulk thermalconductivities ofSi andGe) 11 Results indicating crucial role of diffuse interface scattering of phonons spectrum in superlattices 9 2 is shown in comparison is contrary to most experimental observations on to experimental results (Fig.11 b–11d)4 0 on a Si/Ge GaAs/AlAssuperlattices and Si /Ge superlattices, superlattice. The simulation based on the phonon asshown in Fig.11 c and 11d,9 4 ,9 7 except in the very group velocityreduction leads to only asmall thin layerregion where experimental dataon reduction in k in the in-plane direction, whilethe Bi 2 Te3 /Sb2 Te3 superlattices indeed show arecovery cross-plane direction shows arelativelylarge drop trend with decreasing period thickness. 1 1 Acoustic (Fig. 11a).The lattice dynamics models implyperfect wavesimulation suggests that the recoveryin the interfaces and thus no di Vuse interface scattering. thermal conductivity atthe verythin period limit is Experimentally,the thermal conductivity reductions due to the tunnelling of phonons from one layerinto in both directions aremuch larger,as shown in another for incidence abovethe criticalangle. 9 8 In Fig. 11b.In addition, the lattice dynamics simulation reality,however, there also exists the possibility that leads to athermal conductivity that rst decreases such arecoveryis due to interface mixingthat creates with increasing superlattice period thickness and then alloysrather than superlattices. In the thicker period approaches aconstant that issignicantly lower than regime, the Boltzmann equation based modelling that that of its corresponding bulk values.Such behaviour treats phonons asparticles experiencing partially

InternationalMaterials Reviews2003 Vol. 48 No. 1 56 Chen et al. Recentdevelopments in thermoelectric materials specular and partiallydi Vuse scattering atthe He proposed that the correct starting point should interfaces, canlead to areasonable tto the experi- be from the followingexpression for the thermal mental data,as shown in Fig.11 b–11d.The parameter conductivity p in Fig. 11b–11d represents the fraction of specularly v p p scattered phonons atthe interface and (1 p) that of 1 max 2 k = sin2 Q dQ C(v)n(v, h, Q) the diVuse scattering that maybe caused byinterface p 4p 0 0 0 mixingand roughness, or anharmonic forces atthe P GP CP interface. The agreement between modelling and Ö 2 experimental results suggests that the phonon coher- L(v, h, Q) cos h sin h dh dv . . . (10) ence length in superlattices is short and the loss of DH coherence is probably due to di Vuse interface where h and Q arethe polar and azimuthal angles scattering. formed with the heat uxdirection. The task of Toexhibit signicant size e Vects, the phonon mean reducing the thermal conductivity is to reduce the free path in the bulk materialshould be largerthan valueof the aboveintegral. Low-dimensional struc- the lm thickness or other characteristic lengths of tures o Ver severalnew ways to reduce the thermal the structure. The estimation of the phonon mean conductivity integralin equation (10).First, the group free path, however, must be done carefully.Often, velocitycan be altered in nanostructures. The forma- one tends to estimate the phonon mean free path L tion of standing wavesin nanostructures means that from the simple kinetic formula k =CvL/3,using the the group velocitybecomes smaller, thus reducing the specic heat and speed of sound in bulk materials. thermal conductivity. In superlattices, the bulk acous- The mean free paths of phonons that actuallycarry tic phonons canbe changed into optical phonons, the heat could be much longer, because: (i)optical thereby drasticallyreducing their group velocity. phonons contribute to the specic heat but not much Second, itis possible to induce anisotropic scattering to thermal conductivity due to their smallgroup in low-dimensional structures. For example,interface velocity,and (ii)the acoustic phonon group velocityre ection and transmission arehighly angle depen- canbe much smaller than the speed of sound due to dent. Totalinternal reection means that phonons dispersion e Vects. For example,a carefulestimation abovethe criticalangle will be reected backwards. of the phonon mean free path in silicon leads to Asanother example,the optical phonons in two 2500–3000 A,9 7 ,9 9 compared to the kinetic theory materialshave totally di Verent frequencies. It is likely value of ~400 A.Becauseof this, some apparently that the scattering of optical phonons atthe interface lowthermal conductivity materials,such aswill be highlydirectional, i.e. the optical phonons will

Bi2 Te3 /Sb2 Te3 and CoSb3 /IrSb3 superlattices, can be preferentially scattered backwards. In the context actuallybe engineered to havelower valuesby explor- of the phonon dispersion curve, this is calledphonon ing size eVects. Another important point isthat typi- connement. The e Vects of total internal reection callythe thermal conductivity reduction in the cross- and the phonon connement on the thermal conduct- plane direction is largerthan in the in-plane direction ivitycan also be interpreted asreducing the angle because interfaces impede the phonon transport more and frequency integration limits of equation (10), in the cross-plane direction than alongthe lm plane, thus decreasing the thermal conductivity. Third, the asis suggested byFig. 11 b.For polycrystalline mater- specic heat of nanostructures canbe changed by ialsthis maynot necessarilybe true, because the changing:( i)the density of states and (ii)the degrees columnar grainstructures canactually cause amore of freedom of the atomic vibrations. Theoretical stud- signicant reduction in the in-plane direction, asis ies on superlattices, however, suggest that these observed in diamond thin lms. 1 0 0 Other factors such changes arenot strong, except atlow temper- asthe dislocation orientation (occurring in threading atures.1 0 3 – 1 0 5 Basedon these arguments, Chen 1 2 sug- dislocations) mayalso create more scattering in the gested that low-dimensional structures mayhave a in-plane direction, although there havebeen neither smaller minimum thermal conductivity. Figure12 detailed theoretical nor experimental studies. shows the experimental thermal conductivity of a Existingexperimental datahave clearly shown that Si/Ge superlattice compared to predictions based on the thermal conductivity of superlattices canbe made the minimum theoretical thermal conductivity of bulk smaller than that of their corresponding alloys. Si and Ge. The gure suggests the possibility of Remember that alloyinghas been used in thermoelec- reachingvalues lower than that theoretically attain- tric materialsresearch asan e Vectiveway to reduce ablein bulk materials. the lattice thermal conductivity. This raises the ques- Thus, it seems that the followingstrategies maybe tion of whatis the minimum thermal conductivity of pursued to engineer the phonon transport in order superlattices. Slack 1 0 1 proposed that the minimum to reduce the lattice thermal conductivity. thermal conductivity one canreach for amaterialis 1.For transport alongthe interfaces, i.e. alongthe when the phonon mean free path in equation (9)is lmplane and wireaxis, the thermal conductivity can replaced bythe wavelength.Later, Cahill et al.1 0 2 be reduced bycreating di Vuse interface scattering and further limited it to halfthe wavelength.The more reducing the interface separation distance. In addition fundamental question is whether low-dimensional to the naturallyexisting interface roughness due to structures aresubject to the same limit or not. Chen 1 2 the mixingof atoms atthe interfaces, other possibil- argued that the same minimum maynot be applicable ities arearti cially corrugated interfaces, such asthin to low-dimensional materialswhich arehighly aniso- lms grown on step-covered substrates, and quantum tropic, because anistropy causes directional depen- dot interfaces. In controlling the interface structures dence of the relaxationtime and of the group velocity.for phonon thermal conductivity reduction, the

InternationalMaterials Reviews2003 Vol. 48 No. 1 Chen et al. Recentdevelopments in thermoelectric materials 57

than periodic superlattices, or composite superlattices with diVerent periodicities, mayprovide methods to localisesome, ifnot all,of these long wavelength phonons. 4.Defects, particularlydislocations, canprovide another vehicleto reduce the lattice thermal conduct- ivityin low-dimensional systems. Clearly,whether all or some of these strategies willwork for the improve- ment of the energyconversion e Yciencywill depend on their impacts on the electron /hole energyconversion capabilities. More studies of these e Vects should be done. The phonon size e Vects in quantum wiresand quantum dots areconceivably more signicant than in thin lms and superlattices due to their increased 12 Comparison of measured thermal conductivity surface/interface area.Up to now, studies of the of highly dislocated Si / Ge superlattice with thermal conductivity of quantum wireshave been predictions of minimum thermal conductivity scarce. There area fewexperimental and theoretical theory for bulk Si and Ge and their multilayer composite, latter iscalculated based on Fourier studies on the thermal conductivity of quantum dot 1 0 7 ,1 0 8 theory:12 solid and dashed lines are from arraysand nanostructured porous media. minimum thermal conductivity theories by Theoretically,one canexpect alargerthermal con- Slack101 and Cahill et al.102 respectively ductivity reduction in quantum wirescompared to thin lms.1 0 9 ,1 1 0 The measurements of the thermal interface eVects on the electron transport must also conductivity in quantum wireshave been challenging. be considered. It may,however, be possible to capital-Recent measurements on the thermal conductivity of ise on the diVerent wavelengthsof electrons and individual carbon nanotubes 1 1 1 provide apossible phonons, such that phonons arescattered more approach for related measurements on thermoelectric diVusely atthe interface than electrons, because the nanowires of interest. Nanowires for thermoelectrics, dominant phonon wavelengthis typicallyshorter however, havevery low k compared to carbon nano- than the electron wavelength. tubes, and this largedi Verence inbehaviour willcreate 2.For transport perpendicular to the interfaces, newchallenges for measurements on nanowires of increasing the phonon reectivity is the keystrategy interest to thermoelectricity. for reducing the thermal conductivity. This could be realised byincreasing the mismatch between the Bulkmaterials properties of the two constituents, such asthe density, group velocity,speci c heat, and the phonon spectrum The search for ‘phonon–glass electron– crystal’ bulk between adjacent layers.The e Vects of interface rough- materialshas now moved beyond the traditional Bi Te based binarysystem. Severalclasses of bulk ness canbe positive or negative,depending on 2 3 whether the di Vuse phonon scattering actually materialshave been discovered or re-investigated as decreases or increases the phonon reectivity at the interesting for potential thermoelectric applications. interfaces. Experiments and modelling so farseem to Representative among them areskutterudites, clath- indicate that di Vuse scattering is more e Vective when rates, b-Zn4 Sb3 ,half-Heusler intermetallic com- the mismatch in the materialproperties is not large. pounds, and complex chalcogenides. The phonon Phonon connement occurs due to the mismatch rattler concept developed bySlack has proven to be between the bulk phonon dispersion relations, and a very eVectivein reducing the thermal conductivity of large diVerence in the dispersion favours more phonon materialswith open cages,such asskutterudites and connement. How much phonon connement canbe clathrates. The highest Z T in lled skutterudites achieved,however, is anopen question. Needless to reached 1·4at ~600°C,asshown in Fig.2. In this say,however, in pursuing the phonon thermal con- section, severalpromising bulk thermoelectric mater- ductivity reduction, the e Vects of interfaces on the ialswill be briey reviewed. electron transport must be considered. Paststudies on electron transport, particularlyin the development Skutterudites of vertical-cavitysurface-emitting lasers (VCSELs), Existenceand composition indeed suggest the possibility of much stronger In the early1990s, a systematic search for advanced reduction in the thermal conductivity than in the thermoelectric materialsresulted in the ‘rediscovery’ electricalconductivity. For example,digitally or con- of afamilyof attractivesemiconducting materials tinuously graded interfaces areoften used to reduce with the skutterudite crystalstructure. 1 1 2 For state of the electricalresistivity of Braggre ectors used for the art thermoelectric materials,such asPbTe and 1 0 6 VCSELs, whileit is likelythat such graded Bi 2 Te3 alloys,the number of isostructural compounds interfaces cancreate more phonon back reection is limited and the possibilities to optimise their bulk and thus alargerthermal conductivity reduction. 3 8 properties for maximum performance atdi Verent 3.Some long wavelengthphonons maynot ‘see’ temperatures of operation arealso very limited. This the interfaces in structures, such assuperlattices. The isnot the casefor the skutterudite familyof materials, localisation of these phonons canfurther decrease the where 11binarycompounds and manysolid solutions lattice thermal conductivity. Using aperiodic rather and related phases areknown to exist. 1 1 3 These

InternationalMaterials Reviews2003 Vol. 48 No. 1 58 Chen et al. Recentdevelopments in thermoelectric materials materialscover alargerange of decomposition temperatures and band gaps,which o Ver the possibility to adjust the composition and doping levelfor a specic temperature rangeof application. Anexcellent in-depth reviewof skutterudites asnovel thermoelectric materialswas recently written byUher. 1 1 4 The unit cellof the skutterudite structure (cubic, Im space group 3,prototype CoAs 3 )contains square 4 – radicals[As 4 ] .This anion, which is located in the centre of the smaller cube, is surrounded by8 trivalent transition metal Co 3 + cations. The unit cellconsists of 8of these smaller cubes, or octants, two of them 4 – empty, and sixof them containing the anions [As 4 ] in the centre. This arrangement is necessary to main- 3 + 4 – tain the stoichiometric ratio Co : [As4 ] =4 : 3. Takinginto account one-half of the full 32atom unit celland its empty octant, one canrepresent the h h skutterudite formula as T4 Pn1 2 , where is the empty octant, Tisthe transition metal and Pnisthe 13 Schematic of filled skutterudite 34 atom unit pnicogen atom. If considering asimple bonding cell of novel thermoelectric materials –each scheme,1 1 5 eachtransition metal contributes 9elec- cell contains 8transition metal atoms: Fe, Ru, trons and eachpnicogen contributes 3electrons to Os,Co, Rh, Ir, Ni, Pd or Pt; 24 pnicogen atoms: P,As,Sb (substitution by S,Se or Tepossible); the covalent bonding, for avalenceelectron count 2rare earth atoms filling vacant octantsin h (VEC)total of 72for each T4 Pn1 2 unit. The VEC skutterudite structure:La, Ce, Pr, Nd, Sm, Eu, is auseful number in determining the skutterudite Gd, Th and U compositions that aresemiconducting. The valence electron count of 72corresponds to adiamagnetic It should be noted, however, that even ifa simple semiconductor for the skutterudite materials.Uher 1 1 4 VECscheme maybe used to explainthe various gavea detailed discussion on the bonding scheme that favours the semiconducting behaviour. There are atomic composition permutations in skutterudites, the actualpicture is certainlyquite abit more compli- eleven h T Pn binaryskutterudites reported in the 4 1 2 cated, especiallywhen tryingto explainthe transport literature. The nine semiconducting compositions are properties of the more complex skutterudites, in view formed with allnine possible combinations of T = of some doping and compositional limitations. Much Co,Rh, Ir and Pn =P,As,Sb. Twoadditional eVort has been devoted in recent yearsto understand- skutterudite phosphides werereported, NiP 3 and PdP .However,in these two compounds, the total ingthe valenceof transition metals and some rare 3 earth llingatoms in ternary and lled skutterudites VECis 73,resulting in metallicbehaviour. 1 1 6 but results aresomewhat inconclusive atthis point. 1 1 4 The existence of manyternary skutterudites has been determined. Nine ternary compounds havebeen Transport properties reported in the literature, and atleast 17more have The transport properties of both n-type and p-type been discovered. 1 1 7 Ternaryskutterudite compos- conductive binaryskutterudite compounds, mostly itions arederived from binarycompounds bykeeping antimonides and arsenides, havebeen thoroughly h atotal VECof 72.Using Co4 Sb1 2 (CoSb3 )asan characterised in the past fewyears ( see e.g. Refs. example,substituting trivalent Co(Co 3 + )bydivalent 124–126 ).Associated with alowhole e Vectivemass, Fe (Fe2 + )and tetravalent Pd (Pd 4 + ),results in veryhigh hole mobilities, lowelectrical resistivities h Fe2 Pb2 Sb1 2 (Fe0 ·5 Pb0 ·5 Sb3 ).If instead, Sb is and moderate Seebeck coe Ycients areobtained in h replaced bySn and Te,then Co4 Sn6 Te6 p-type skutterudites (Fig.14 ).Most of the samples (CoSn1 ·5 Te1 ·5 )is obtained. If substitutions occur on shown in this gure werenot nominally doped. They both the transition metal and pnicogen sites, then weregrown using agradient freeze technique from h 1 2 7 Fe4 Sb8 Te4 (FeSb2 Te)is obtained. non-stoichiometric, Sb rich melts. One should note Alled skutterudite structure is simply derived that the room temperature mobility valuesof p-type from the skutterudite structure byinserting one atom skutterudites arevery high (Fig.14 a),about 10to in eachempty octant, asillustrated in Fig.13. A large100 times higher than those for p-type Si and GaAs number of these compounds havebeen known for atsimilar carrier concentrations. RhSb 3 exhibits the some time (see e.g.Refs. 116, 118 –121),where the greatest hole mobility, 8000cm 2 V – 1 s – 1 for acarrier llingatom is typicallya rare earth lanthanoid, concentration of 2·5 Ö 101 8 cm – 3 ,which is about 70 though other compositions with actinoids Th and times higher than p-type GaAsand still 5times higher U,1 2 1 ,1 2 2 aswellas alkalineearths Ca,Sr and Ba 1 2 1 ,1 2 3 than n-type GaAs.For acomparable doping level, havealso been reported. For atypical lled skutterud- the carrier mobilities of n-type samples areabout an ite composition, such asLaFe 4 P1 2 ,the rare earth order of magnitude lower than the valuesachieved element contributes 3electrons, but due to the on p-type samples. However, the much largerelectron divalentFe ( Fe 2 + ),the total VECis only 71.This eVectivemasses and Seebeck coe Ycients make n-type decit results in metallicbehaviour for most simple skutterudites promising candidates aswell.

lled ternary compounds. Only CeFe 4 P1 2 , UFe4 P1 2 Unfortunately, the room temperature thermal con- – 1 – 1 and CeFe4 As1 2 havebeen reported assemiconductors. ductivity of binaryskutterudites (10–25 W m K ) InternationalMaterials Reviews2003 Vol. 48 No. 1 Chen et al. Recentdevelopments in thermoelectric materials 59

order of magnitude lower in some ternary unlled or lled compositions. Also, asshown in the table, high

doping levelsin n-type CoSb 3 result in a70% reduction in lattice thermal conductivity, ane Vect comparable to that obtained byforming solid solutions. Asa result, Z T valuesas high as0· 85 are obtained in the 850–900 K temperature rangein 1 2 8 heavilydoped n-type CoSb 3 , asshown inFig.2. These experimental results thus demonstrate that the skutterudite familyof compounds and alloyso Ver extremelyattractive possibilities for the search for high Z T materials.Skutterudites haveexcellent electricaltransport properties and the thermal conduct- ivitiescan be reduced bya factor of 20,down to nearlyglassy characteristics. Since the work of Chasmarand Stratton, 1 2 9 it has been obvious that high Z T valuesrequire materialswith ahigh mobility, high eVectivemass and lowlattice thermal conductivity,where ideallyone canseparately optimise the power factor and minimise the thermal conductivity, or assummarised bySlack, 5 fabricatea PGEC.While the conceptual approach to high Z T has been known for over 40years, much e Vort has been devoted into nding out ifskutterudites could truly be such PGEC materials,that is conserving the excellent electrical properties of the binarycompounds whilereducing the thermal conductivity to valuessubstantially lower

than that of state of the art of Bi 2 Te3 alloys. However, anumber of experimental and theoretical results published in recent yearson both ternary unlled and lled skutterudite compounds indicate that their electronic band structure and transport properties arevastly di Verent from the pure binary compounds.1 3 0 ,1 3 1 For example,the study of such

ternary compounds asFeSb 2 Te, Fe0 ·5 Ni0 ·5 Sb3 and Ru0 ·5 Pd0 ·5 Sb3 derived from high carrier mobility CoSb3 and RhSb3 shows that they areheavily doped semiconductors with carrier concentration values rangingfrom 1 Ö 102 0 to 1Ö 102 1 cm – 3 . Comparing

these compounds to CoSb 3 atsuch high carrier concentrations, they arecharacterised bysigni cantly lower carrier mobility, and lattice thermal conduct- 14 a Hall mobility variation asfunction of carrier ivityvalues as much as50 to 75%lower. Such low concentration and b Seebeck coefficient as lattice thermal conductivity valuesare somewhat function of temperature for binary skutterudite compounds: samples were not nominally doped127 Table 1Room temperature conductivity type, carrier concentration N,and lattice thermal conductivity kp of various is too high to result in high Z T values.Substantial skutterudite compounds and alloys, reductions in the lattice thermal conductivity must including filled compositions be obtained to achievevalues comparable to those Compound Conductivity N, cm – 3 k , W m – 1 K – 1 of state of the art thermoelectric materials p – – 19 (1–4 W m 1 K 1 ).Severalapproaches to the CoP3 p 3Ö 10 23·7 Ö 18 reduction of the lattice thermal conductivity in skut- CoAs3 p 4 10 14·0 18 CoSb3 p 9Ö 10 10·3 terudites havebeen pursued: heavydoping, and for- 21 CoSb3 n 1Ö 10 3·4 mation of solid solutions and alloys,as well as the 18 CoP1·5 As1·5 p 5Ö 10 3·8 study of novel ternary and lled skutterudite com- 19 Co0·88 Ir0·12 Sb3 p 1Ö 10 2·9 pounds. Allthose approaches haveresulted in skut- 20 FeSb2 Te p 5Ö 10 2·3 terudite compositions with substantially lower 18 OsSb2 Te p 4Ö 10 2·1 19 thermal conductivity values.The room temperature RuGe0·2 Sb2 Te0·8 p 9Ö 10 1·4 20 lattice thermal conductivity and carrier concentration Ru0·5 Pd0·5 Sb3 p 1Ö 10 1·5 19 valuesof selected skutterudite compounds and alloys IrSn1·5 Se1·5 p 3Ö 10 2·7 20 arereported in Table1 for comparison. It is interes- CeRu4 P12 p 1Ö 10 8·0 Ö 21 ting to note that, compared to binarycompounds, CeFe4 Sb12 p 3 10 1·6 Nd Ru Co Sb p 2Ö 1020 1·8 the lattice thermal conductivity valuescan be one 0·7 2 2 12

InternationalMaterials Reviews2003 Vol. 48 No. 1 60 Chen et al. Recentdevelopments in thermoelectric materials surprising considering that the atomic mass and volume diVerences introduced bythe substituting anion/cation arefairly small: Fe and Ni for Co,Ru and Pd for Rh,Te for Sb. Apossible explanation givenfor the unusually high phonon scattering rate is that transition metal elements havemixed valence states and electrons aretransferred between the diVerent ions, thus scattering the phonons in this process.1 3 2 ,1 3 3 This would be consistent with low carrier mobilities aswell as with the experimental diYculties encountered in controlling their electrical properties since changes in carrier concentration are not easyto achievebecause dopants canbe compen- sated bysmall uctuations in the overallvalence of the transition metals. Interestingly enough, the search for high Z T values in skutterudites has been most successful so farin compounds that do not share the exceptional carrier mobilities of the pure binarycompounds, but rather havea combination of high degeneracy,unusually 15 Room temperature lattice thermal con- largeSeebeck coe Ycient valuesand lowlattice ther- ductivity asfunction of filling atom rattling malconductivities: lled and partially lled skutterud- amplitude for various fully filled and fully dense ites. Amaximum Z T valueof 1·4has been achieved filled skutterudite compounds: carrier con- to date atatemperature of 875K in Ce Fe Co Sb centrations are also reported to account for f 4 – x x 1 2 additional charge carrier scattering of phonons and Laf Fe4 – x Cox Sb1 2 , where f<1 and 01·5 defect scattering. havenot yetbeen synthesised, but it is clearthat If comparing fully lled compositions and taking atequivalent concentrations, Ni substitution res- into account chargecarrier concentration levels,how- ults in less Ce llingthan Cosubstitution. However, ever,it canbe shown that the lattice thermal conduct- because Ni donates two electrons instead of only one ivitydoes indeed decrease signicantly with increasing for Cowhen replacingFe, the decrease in carrier rattling amplitude of the llingatom, asshown in concentration and the corresponding changein prop- Fig.15. The rattling amplitude is dened asthe erties with increasing x is much stronger for diVerence between the void ller covalent radius and Cef Fe4 – x Nix Sb1 2 .One cansee from these results that the radius of the cage. 1 3 6 The rattling amplitude semiconducting compositions canbe obtained for Co increases arethe largestwhen goingfrom the phos- rich compositions. However, they typicallyshow phides to the antimonides which havelarger unit cells mixed conduction e Vects atroom temperature. 1 1 7 and cagesizes, and verylittle when goingfrom Fe Recent theoretical studies on n-type lled skutteru- based to Rubased compositions. dites1 3 7 and newexperimental materialspreparation The most recent research e Vorts on skutterudites approaches through high pressure, high temperature havefocused on improving Z T over awidetemper- synthesis or the use of thin interdi Vusing layers 1 3 8 ,1 3 9 ature rangeby attempting to conserve the excellent mayeventually allow for the characterisation of semiconducting behaviour of the unlled binaryskut- ‘optimised’skutterudite compositions with perhaps terudites when introducing a‘compensating’atom for high Z T valuesat room temperature. In the mean- the addition of the ‘lling’atom into the structure, time, skutterudites arenow being activelypursued and goingback to aVECof 72.However, preparing for introduction into advancedthermoelectric power lightlydoped extrinsic p-type and n-type compos- generation devices and systems with the potential

InternationalMaterials Reviews2003 Vol. 48 No. 1 Chen et al. Recentdevelopments in thermoelectric materials 61

frequency phonons bythe Sr atoms that areloosely bonded inside the structure and arefree to rattle around their atomic positions. Agood indicator of the possible motion of the guest atoms is the atomic displacement parameter (ADP)that is ameasure of the mean-square displacement amplitude of anatom around its equilibrium site. Unusually largeADP valueshave been measured for guest atoms, such as Csand Sr in Ge based clathrates. 1 4 3 Sales et al. have recently proposed amodel to estimate the lattice thermal conductivity based on ADPvalues. 1 4 5 At room temperature, the thermal conductivity of

Sr8 Ga1 6 Ge3 0 is close to that of amorphous Ge. Low thermal conductivity valueshave also been observed in other Gebased clathrates. Silicon based clathrates tend to havehigher thermal conductivity values.A good thermoelectric materialmust combine alow lattice thermal conductivity with good electronic properties. The electronic properties of severalSi, Ge, solid lines representexpected transition forNi andCo fromp-type to n-type (when VEC reaches 72),taking into and Sn based clathrates havebeen measured. Metallic account both f and x variations: when Feis totallyreplaced to semiconducting behaviour canbe achievedby byCo, only verysmall amountof Ce remains in sample varyingthe doping and /or composition. Both n- and (f=0·07); chain dottedline was calculated based on p-type materialscan be obtained bythe same process. CeFe Sb –Ce Co Sb rangeof ‘ solid solution’ 4 12 0·065 4 12 Good Seebeck coe Ycient valuesup to 300 mV K – 1 compositions (Ce f Fe4 – x Nix Sb12 compositions with x>1·5 havenot yet been synthesised, butit is clear thatat havebeen achieved.To date, the best dimensionless equivalentconcentrations, Ni substitution results in less gure of merit Z T obtained for n-type clathrate Cefilling thanCo substitution) compounds is about 0·34with aprojected value >1 16 Ce filling fraction f for Cef Fe4 – x Mx Sb12 samples above700 K. The abilityof engineering clathrate asfunction of x,Fe substitution by M,with compounds with glass-likethermal conductivity com- M=Co, Ni, and Ru bined with their relativelygood electronic properties has ranked clathrates among PGECmaterials, for 15%conversion e Yciencyin the 25–700 °C tem- although full decoupling between their electronic and perature range. 1 4 0 thermal properties remains to be demonstrated in these materials.Nevertheless, the encouraging results obtained to date combined with the numerous options Othernovel bulk materials for optimisation warrantfurther investigations of Clathrates these interesting materials. Among other materialsof interest aspotential new thermoelectric materialsare clathrates. Aclathrate b-Zn4 Sb3 materialcan be dened asone with alattice that Another materialre-investigated recently for thermo- contains voids that canbe lled with guest atoms or electric power generation is b-Zn4 Sb3 with ahexag- molecules. Silicon, Ge, and Sn based clathrates lled onal rhombohedric crystalstructure, and space group with alkalineatoms havebeen reported 1 4 1 ,1 4 2 and R3C,asshown in Fig.17. Caillat et al.1 4 6 have haverecently been investigated for their thermoelec- measured the thermal conductivity of polycrystalline 1 4 3 tric properties. Theycan be divided into two major b-Zn4 Sb3 samples. The lattice thermal conductivity groups: type Iand type II. Both types havea cubic is nearlytemperature independent between 300and unit cell,but di Veraccording to the number and size 650K, with aroom temperature lattice thermal con- of the voids present in the structure. Ternarycom- ductivity of 0·65W m – 1 K – 1 at300K, nearly2 times pounds havealso been reported. There arenumerous lower than that of Bi 2 Te3 alloys.This remarkablylow possible compositional, structural, and llingvari- valueand unusual temperature dependence (a1 /T ations in those materials,resulting in vastlydi Verent temperature dependence is usuallyobserved )canbe electronic properties rangingfrom semimetallic to attributed to the relativelycomplex crystalstructure, semiconducting. Recently,Nolas et al.1 4 4 have meas- aswell as the presence of vacanciesin the lattice. The ured the thermal conductivity of semiconducting electronic transport properties aretypical of asemimetal with lowelectrical resistivity that increases with Sr8 Ga1 6 Ge3 0 polycrystalline samples and observed a temperature dependence typicalof amorphous mater- increasing temperature. The Seebeck coe Ycient also ial.These results havetriggered extensivetheoretical increases with increasing temperature and peaks at and experimental research e Vorts to synthesise several 675K with avalueof about 200 mV K – 1 . This rela- of these materialsand further understand their pecul- tivelyhigh Seebeck valuefor ametal is the result of iartransport properties. Acomprehensive reviewof afairlylarge e Vectivemass. 1 4 6 The best Z T obtained these materialshas recently appeared in the to date on polycrystalline samples is about 1·4 at 1 4 3 1 4 6 literature. 675K (Fig.2 ). Above 765 K, b-Zn4 Sb3 transforms 2 The lowtemperature T temperature dependence into c-Zn4 Sb3 that has poorer thermoelectric prop- 1 4 4 1 4 7 observed byNolas et al. for Sr8 Ga1 6 Ge3 0 polycrys- erties. Bandstructure calculations predict ametallic tallinesamples wasattributed to the scattering of lowbehaviour with improved thermoelectric performance

InternationalMaterials Reviews2003 Vol. 48 No. 1 62 Chen et al. Recentdevelopments in thermoelectric materials

coeYcient values.Large power factors on the order of 25–30 mW cm – 1 K – 2 havesince been experimen- tallyobtained for severalof these materials,e.g. ZrNiSn and HfNiSn. The impact on the electronic properties of compositional variationsand /or atomic substitutions on the various sublattices has been investigated, showing that both doping leveland conductivity type canbe altered. While the power factors arepromising, the thermal conductivity of ternary compounds, such asZrNiSn and HfNiSn, is rather high. The total thermal conductivity (which is essentiallythe lattice thermal conductivity for these materials)ranges from 5·9to 17Wm – 1 K – 1 for ZrNiSn.1 5 1 The spread in the valueswas primarily due to the diVerence of structural qualityintroduced, for example,by annealing the samples. Attempts to reduce the lattice thermal conductivity of these mater- ialsusing mass-defect scattering on the various sublattices weremade. Although lattice thermal conductivity valuesof 5–6 Wm – 1 K – 1 wereobtained for alloys,these valuesare still too high compared to those obtained for state of the art thermoelectric alloys,such asBi Te alloys. EVorts should therefore 17 Schematic representation of Zn 4 Sb3 crystal 2 3 structureillustrating various Sb and Zn focus on further reducing the lattice thermal conduct- atomic sites ivityof these materialsthat otherwise possess impress- iveelectronic properties that canbe tuned through for lower doping levels.Little success has however doping and alloying.Possible schemes for reducing been obtained experimentallyto optimise the doping the thermal conductivity mayhowever be somewhat limited apartfrom the introduction of point defect levelof this compound. b-Zn4 Sb3 forms afull range of solid solutions with the isostructural compound scattering, since these materialsare not ‘cage-like’ Cd Sb .Lowtemperature thermal conductivity materials,such asskutterudites or clathrates. Most 4 3 transport property measurements on half-Heusler measurements on Zn 4 – x Cdx Sb3 mixed crystals showed anearlytemperature independent variation alloysto date havebeen limited to lowtemperatures of the thermal conductivity, which is lower than for but these materialsmay actually be quite interesting attemperatures up to 800–900 K, considering that b-Zn4 Sb3 (Ref.148 )mostly due to point defect scattering. Zn Cd Sb mixed crystalsappear to be less they typicallybehave as semimetals attemperatures 4 – x x 3 below 300K and semiconductors abovethat temper- stable than b-Zn4 Sb3 itself and a Z T maximum of 1·4atabout 400K wasobtained for these mixed ature. Transport property measurements above300 K V would therefore be of interest to fullyassess the crystals. E orts to incorporate b-Zn4 Sb3 into advanced,high e Yciencythermoelectric unicouples potential of these materialsfor thermoelectric arein progress. 1 4 9 Further optimisation of the prop- applications. erties of these compounds is limited because of the Complex chalcogenides diYculties to dope them and the restricted compos- While severalmaterials with Z T >1havebeen ident- itional variationspossible. ied aboveroom temperature, there is agreatneed Half-Heusler intermetallic compounds for newthermoelectric materialswith Z T >1 for Half-Heusler intermetallic compounds with the gen- cooling applications. Atand below room temperature, eralformula MNiSn (M =Zr,Hf, Ti)havealso only two materialshave been known for manyyears attracted considerable interest aspotential newther- to havedecent thermoelectric properties: Bi–Sb and 1 5 0 moelectric materials. These materialspossess the Bi2 Te3 alloys.Past studies suggest newlow temper- MgAgAsstructure and areclosely related to the full ature semiconducting thermoelectric materialsare likelyto be found in narrow band gapmaterials. 1 4 Heusler compounds MNi 2 Sn which aremetals. Replacingone Ni atom byan ordered lattice of Anextensive e Vort atMichigan State University vacanciesleads to agapformation in the density of has focused on anumber of newchalcogenides com- states and to asemiconducting character with band posed mostly of heavyelements. Asaresult, anumber gapvalues on the order of 0·1 to 0·2eV.As a result of potential newmaterials for lowtemperature ther- of the largeelectron e Vectivemass inthese materials, moelectric applications havebeen identied. Acom- high Seebeck coe Ycients aretypically obtained at prehensive reviewof these materialshas recently appeared in the literature. 1 5 3 Anumber of complex 300K and higher. E Vectivemasses of 2–3 m0 were estimated byUher et al.1 5 1 for ZrNiSn, and Seebeck phases havebeen prepared preferably bya uxtech- coeYcients ashigh as 300 mV K – 1 weremeasured nique and severalnew compounds havebeen ident- at300K for this material.It wasoriginally suggested ied. Among the materialsinvestigated arethe 1 5 2 by Cook et al. that these materialsmight be good sulphides KBi 6 ·3 3 S1 0 and K2 Bi8 S1 3 ,the selenides b- thermoelectric materials,considering their combi- K Bi Se and K Bi Se , A Pb Bi Se 2 8 1 3 2 ·5 8 ·5 1 4 1 + x 4 – 2 x 7 + x 1 5 nation of lowelectrical resistivity with largeSeebeck (A =K,Rb)compounds, and the tellurides A /Bi/Te InternationalMaterials Reviews2003 Vol. 48 No. 1 Chen et al. Recentdevelopments in thermoelectric materials 63 and A/Pb/Bi/Te.A common feature for most of these Thermoelectric materialsrequire high doping with materialsis their lowthermal conductivity, compar- carrier concentrations of ~101 9 cm – 3 . Careful ableor even lower than that of Bi 2 Te3 alloys.Many optimisation of the doping concentration is necessary. of these compounds show veryanisotropic transport Thus anexperimental thermoelectric research pro- properties. Perhaps the most promising compound grammemust be prepared in the synthesis and identied to date is CsBi 4 Te6 .This compound has a optimisation, aswell as fast characterisation turn- layeredanisotropic structure with Csions between around capability.

[Bi4 Te6 ]layers.The ADPsof the Csions are1· 6 Most thin lms in electronic devices areon the times greaterthan those of the Biand Teatoms. order of submicrometres in the lm thickness.

Crystalsof CsBi 4 Te6 growwith aneedlelike morph- Thermoelectric thin lms should typicallybe thicker, ologyand arestable in airand water.The crystalsboth for characterisation purposes and for device areamenable to doping and SbI 3 , BiI3 , and In2 Te3 applications. For thermoelectric devices in the cross- havebeen successfully used to optimise the carrier plane direction, lms thicker than afewmicrometres concentration of this material.The power factor can or even much thicker aredesirable in terms of sustain- be maximisedthrough doping and amaximum power inga reasonable temperature di Verential. For thermo- factor valueof about 50 mW cm – 1 K – 2 wasobtained electric devices intended for use for in-plane transport at185K for the p-type material. 1 5 3 The total thermal applications, the reverse heat owfrom the supporting conductivity alongthe growth axisis about substrate must be minimised. This means either the 1·5 W m – 1 K – 1 at300 K and is essentiallyconstant removalof the substrate or depositing verythick down to 100K. This atypicaltemperature dependence lms. Thus, both in-plane and cross-plane devices suggests againthat the rattling Csions signicantly demand relativelythick lms, whilequantum or contribute to phonon scattering in this compound. classicalsize e Vects typicallyrequire individual layers The best Z T to date obtained alongthe needle of the order of severaltens of angstroms. Such con- direction is 0·82 for the p-type material( Fig.2 ), icting requirements impose asevere limit for the slightlybetter than p-type Bi 2 Te3 atthis temperature. practicalscale up of materialssynthesis methods, The In2 Te3 ‘doped’n-type materialhas poorer ther- although in research, manythin lm deposition moelectric properties. Nevertheless, p-type CsBi 4 Te6 methods, such asmolecular beam epitaxy,metallo- is the rst compound identied in the lowtemperature organicchemical vapour deposition, pulsed laser rangeto match or evenoutperform Bi 2 Te3 alloys.deposition, and sputtering, areall being explored. Whether or not this compound canbe further Thermoelectric materialsemploy relativelylarge optimised through doping and /or alloyingwill need numbers of alloycompositions. For example, to be determined inthe future aswellas its mechanical Si0 ·8 Ge0 ·2 is typicallyused in bulk thermoelectric stabilityunder thermal stresses to warrantits practicalgenerators. For comparison, electronic devices based use in devices. on SiGe alloys,such asheterojunction bipolar transis-

Pentatelluride materialssuch asHfTe 5 and ZrTe5 tors, use 1–5%Ge concentration. Alargerconcen- and their alloyshave been considered promising new tration of Ge is required for thermoelectrics thermoelectric materialsat lowtemperatures because applications to create more thermal conductivity of their relativelylarge Seebeck coe Ycient valuesat reduction. Evenin superlattices, arelativelylarge lowtemperatures which, combined with relativelylow equivalent Ge concentration is needed for su Ycient electricalresistivity values,result in largepower factor thermal conductivity reduction. For superlattices values.1 5 4 Their electronic properties canbe tuned made of materialswith alargemismatch in their through alloyingand doping, but the challengefor lattice constants, bu Ver layersare needed. Togrow these materialsis to reduce their lattice thermal 20 /20 A Si/Ge superlattices, for example,graded conductivity. Another challengelies in the veryaniso- buVer layersof SiGe alloysfrom 1to 5 mm with tropic nature of these materialsthat requires the continuously varyingGe concentrations havebeen growth and characterisation of singlecrystals for used. These bu Ver layerscomplicate the characteris- transport properties. Single crystalwhiskers wereation and usuallydegrade the deviceperformance. obtained bya vapour transport technique, but The characterisation of thermoelectric properties measurements on these smallcrystals o Ver greatof potentially interesting thermoelectric materials, challenges.Further investigations willbe required to particularlysamples consisting of low-dimensional determine whether or not the transport properties of structures, imposes aneven greater challenge. Even these materialscan be further optimised and ifthermal for bulk materials,thermal conductivity measure- conductivity valuesclose to those for state of the art ments arenever easyand areprone to largeuncer- thermoelectric materialscan be obtained without tainty. For low-dimensional structures, thermal signicantly degrading their electronic properties. conductivity measurements aremuch trickier. The most widelyused method for cross-plane thermal Specialchallenges in materials conductivity measurements is the 3 v method that relies on the deposition of smallheaters that alsoact synthesis andcharacterisation astemperature sensors. 8 7 The principle of the 3 v Compared to semiconductor materialsfor electronic method is simple, but when applied to specic low- and optoelectronic devices, thermoelectric materialsdimensional structures, it canbe quite involved,due impose diVerent sets of materialsrequirements, which to the followingfactors. in turn create newchallenges in their materialssyn- 1.Thermoelectric lms areconducting, thus an thesis and characterisation. Some of these special insulator is needed for electricalisolation between the challengeswill be briey discussed here. sensor and the sample. The insulator has unknown

InternationalMaterials Reviews2003 Vol. 48 No. 1 64 Chen et al. Recentdevelopments in thermoelectric materials thermal conductivity. Often, adi Verential method electric transport in both low-dimensional and bulk is used.1 5 5 materials.However, there is much left to be done, in 2.Superlattices aregrown on substrates and newmaterials syntheses, characterisation, physical buVers, whose properties arenot exactlyknown. understanding, and devicefabrication. It is hoped Although the principle of the 3 v method allowsthe that this reviewwill arouse broader interest in thermo- measurements to be made on the thermal conductivity electrics research from the materialsresearch com- of the substrate, the determination of ahigh thermal munity. Meanwhile,the authors would like to conductivity substrate is actuallysubject to quite emphasise that thermoelectric materialsresearch is a largeuncertainties. The bu Ver layerstypically have multidisciplinary endeavour and requires close collab- unknown and anisotropic thermal conductivities that oration between researchers in di Verent elds to cannot be easilydetermined. address issues in materials,theory, characterisation, 3.Superlattices also haveanisotropic properties, and eventually,devices. and thus caremust be taken to ascertain which direction is being measured. Through carefulmodel- Acknowledgements ling,both the in-plane and cross-plane direction thermalconductivity canbe determined. 4 0 Severalother Twoof the authors (GCand MSD) gratefully factors, such asthe thermal property contrast between acknowledge their collaborators in thermoelectric the lm and the substrate and the lm heat capacity research, including Professors R.Gronsky, J.-P. Issi, eVects, arediscussed in detail byBorca-Tasciuc T.D.Sands, K.L.Wang,Dr J.Heremans, and et al.1 5 5 In addition to the 3 v method, other methods T.Harman, and contributions from allstudents in that havebeen used often arethe accalorimetry their respective research groups. The authors are method for determining the thermal conductivity gratefulfor support for this work byDoD MURI: alongthe lm plane direction, 1 5 6 and the pump-and- N00014–97– 1– 0516 (GC and MSD), USNavy probe method for determining the cross-plane thermal Contract N00167–98 –K–0024 ( MSD), DARPA conductivity. 8 0 Contract N66001–00 –1–8603 ( MSD), DARPA The determination of the Seebeck e Vect is usuallynot HERETICProject (J-PFand GC),JPL:004736– 001 considered to be abigchallenge for bulk materials, (J-PFand GC),and NSF Grant DMR01– 16042 but it canbe quite tricky for superlattices that are (MSD). grown on substrates and bu Vers because the substrate maymake alargecontribution to the overallmeas- References ured properties. Although corrections canbe made 1. h. j. goldsmid :‘Thermoelectricrefrigeration’ ; 1964,New based on simple circuit theory, there is no strong York,Plenum Press. evidence that such corrections arereliable. 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The Z T valuesin the cross-plane 14. g. d. mahan: SolidSt atePhys ., 1998, 51, 81–157. 1 1 direction for Bi 2 Te3 /Sb2 Te3 superlattices have been 15. g. s. nolas,d. t.morelli and t. m. tritt: Ann.R ev. Mater. measured using the transient Harman method. 1 Sci., 1999, 29, 89–116. It should be emphasised that allthe measurements 16. f.j. disalvo : Science, 1999, 285,(5428),703–706. 17. g. s. nolas and g. a. slack: Am. Sci., 2001, 89,(2),136–141. should be done in the same direction and preferably 18.Proc. Int. Conf. on ‘ Thermoelectrics’: e.g.ICT’ 97 ( IEEE Cat. alsoon the same sample. For low-dimensional struc- no.97TH8291 ),ICT’98 ( IEEE Cat.no. 98TH8365 ),ICT’99 tures, this has proven to be averydi Ycult goal to (IEEE Cat.no. 99TH8407 ),ICT’00 ( BabrowPress, Wales, achieve.For these reasons, the Z T valuesof low- UK,ISBN0951928627 ),ICT’01 (IEEE Cat.no. 01TH8589 ). dimensional structures plotted Fig.2 should be 19.MRS Proceedingson Thermoelectrics: 478 (1997), 545 (1998), 626 (2000);Warrendale,PA, MaterialsResearch Society. further conrmed. 20. n. w.aschroft and n. d. mermin:‘Solidstate physics’ ; 1976, ForthWorth, Saunders College Publishing. 21. m. s. dresselhaus,y .-m. lin,s. b.cronin, o. rabin, m. r. Concludingremarks black,g. dresselhaus, and t. koga: Semicond.Semimet. , 2001, 71, 1–121. In summary, the recent resurgence in thermoelectric 22. j. goldsmid:inProc. 17th Int. Conf. on ‘ Thermoelectrics’, materialsresearch has led to quite alargeincrease in ICT’98, 1998, 25– 28 (IEEE Cat.no. 98TH8365 ). 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