Recentdevelopments in thermoelectric 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 Instituteof 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 Kelvin relation 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 ther- malconductivity of ametal, which is dominated by electrons, is in most cases proportional to the electri- calconductivity, 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 electricalconduct- ivity.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 appearance of 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