Shen Han, Chenguang Fu and Tiejun Zhu
State Key Laboratory of Silicon Materials, and School of Materials Science and Engineering, Zhejiang University, Hangzhou 310027, People’s Republic of China
E-mail:zhutj@zju.edu.cn
Studies of thermoelectric properties of half-Heusler (HH) compounds have been carried out since the end of the 20th century, focusing on compositions with 18 valence electrons represented by three typical systems, i.e. MNiSn (M = Ti, Zr, Hf), MCoSb and XFeSb (X = V, Nb, Ta). In recent years, the 18-electron NbCoSn, ReNiSb (Re is a rare earth element), and nominal 19-electron XCoSb compounds have also attracted increasing attention. A summary of the peak zT values obtained for different HH compounds is shown in figure4, and a detailed comiplation of representative data are given in table3. These advances make HH compounds promising thermoelectric candidates for power generation applications with advantages of mechanical robustness, thermal stability, and relatively low-cost constituents.
The intermetallic MNiSn, found to exhibit semiconducting behavior around 1988 [231], was the first HH system to seriously arouse the interest of the thermoelectric community before the end of the 20th century [232]. With the efforts in the past two decades, MNiSn-based HH compounds have now been developed into the best n-type HH thermoelectric materials with peak zT above unity [164,188,192,193,233]. MCoSb has attracted research attention since 2000 and rapidly developed as a representative p-type thermoelectric system with a zT of about unity [168,214]. It is worth noting that n-type MCoSb has recently been found to show a similar high zT value as its p-type counterpart [169–171], making it the first HH system with both good n-type and p-type thermoelectric performance. The studies on the thermoelectric properties of XFeSb started as early as those on MNiSn and MCoSb [172], but it did not attract much attention at that time, owing to the poor thermoelectric properties. Since 2014, with guidance of the band engineering concept and the selection of rational dopants, the heavy-band XFeSb-based HH system has been developed as
high-performance p-type thermoelectric materials with a peak zT value of about 1.5 through rational compositional design and optimal doping [173–177,179]. Very recently, prototype eight-pair HH thermoelectric modules using n-type MNiSn and p-type XFeSb were assembled [234,235]; they show a maximum conversion efficiency of 10.5% and power density of 3.1 W cm−2for a temperature difference of 680 K, demonstrating the encouraging prospect of HH compounds for power generation.
The nominal 19-electron HH system was usually thought to show metallic behavior and thus, it was unexpected that NbCoSb exhibited a respectable zT value of 0.4 in 2015 [180]. Subsequently, with the knowledge of defect chemistry [236], XCoSb was identified to be a defective HH compound with a
considerable fraction of cation vacancies (up to∼20%). Through tuning the content of cation vacancies that lead to suppressed lattice thermal conductivity and optimized electrical properties, a peak zT∼ 0.9 was achieved in Nb1−xCoSb [181], demonstrating that the nominal 19-electron HH system provides a new class of material for the exploration of high-performance thermoelectrics and the understanding of the
relationship between vacancies and transport properties.
In addition, some other HH compounds have also attracted some attention, including ZrCoBi, which was reported to show a peak zT of∼1.4 for p-type and ∼1.0 for n-type [185,186]. The thermoelectric properties of ReNiSb, a family of HH compounds with rare-earth elements, were also studied [191]. Further performance improvement is expected if the optimization strategies, generally used for MNiSn, MCoSb, and XFeSb, are successfully applied to ReNiSb. Similarly, NbCoSn, another 18-electron system with the predicted high PF for both p-type and n-type [237], has also been investigated. A peak zT of∼0.6 was reported when it was doped as n-type [187,189], whereas optimal p-type doping for NbCoSn is still not successful.
Different from many other good thermoelectric materials, HH compounds are characterized by their high PF (S2σ), which directly contributes to their high zT value. The high crystal symmetry, from their cubic structure, leads to multiple carrier pockets and high band degeneracy NVnear the band edge, such as the NV
of 8 for p-type NbFeSb and ZrCoSb [238,173]. Thus, a large density of states (DOS) effective mass is obtained, resulting in a large Seebeck coefficient even at a high carrier concentration. In addition, the low deformation potential guarantees weak carrier scattering by phonons and thus the relatively high carrier mobility in the heavy-band HH system [175,188]. Another distinct feature of the heavy-band HH system is the high optimal carrier concentration nopt, defined as the carrier concentration where the peak zT occurs. In a single-band system, the noptis approximately proportional to (m∗dT)3/2under the classical statistics approximation [239], where m∗d is the DOS effective mass. For the HH system, noptincreases from
Figure 4. Summary of the peak zT values for typical HH thermoelectric materials [163–230].
∼4 × 1020cm−3for n-type ZrNiSn,∼2.6 × 1021cm−3for p-type NbFeSb, to∼4 × 1021cm−3for n-type TiPtSb, whilst the m∗d increases from 2.8 me, 6.4 me, to 14.5 me, respectively [174,184,188]. In comparison, the noptof PbTe is about 3× 1019cm−3[240], one or two orders of magnitude lower than that of the HH system. High noptindicates that a high level of chemical doping is required for optimizing the electrical performance, which could also bring additional point-defect scattering of phonons. Thus, the selection of a rational doping element is important for the simultaneous optimization of PF and strong suppression of lattice thermal conductivity in the heavy-band HH system [175,179].
Knowledge of the intrinsic electronic structure of thermoelectric materials is of vital importance for the selection of optimization strategies. The bandgap Egis considered to be the foremost parameter for a semiconductor. The calculated Egfor MNiSn, MCoSb, and XFeSb by density functional theory (DFT) is 0.4–0.5 eV, 0.95–1.13 eV, and 0.34–0.86 eV, respectively [163,172,173,237,238,241–243]. Experimentally, polycrystalline MNiSn samples, synthesized using high-temperature techniques and probably having excess Ni-induced in-gap states, show Egvalues of 0.1–0.36 eV by different experimental methods. Recently, using high-quality ZrNiSn single crystals, a combined study involving resistivity and optical measurements together with angle-resolved photoemission spectroscopy (ARPES) gave experimental Egvalues of 0.5–0.66 eV [244]. These results demonstrate the effect of defects on the electronic structure and thermoelectric properties of HH compounds. Experimental studies on the interplay between defects and electronic structure for the other HH compounds are required.
Most HH compounds with high thermoelectric performance are generally heavily doped
narrow-bandgap semiconductors. The dominant scattering mechanism is acoustic phonon scattering (APS) and the electrical transport properties can be explained using the SPB model. Under the assumption of SPB and APS, the weighted mobility µWperforms as a good descriptor characterizing the electrical performance for thermoelectric materials [245]. The µWvalues of MNiSn and XFeSb are above 300 cm2V−1s−1at room temperature and above 60 cm2V−1s−1at temperatures higher than 900 K. In contrast, the MCoSb system shows values of 100–250 cm2V−1s−1at room temperature and less than 60 cm2V−1s−1at high-temperature, corresponding to the lower zT compared with that of MNiSn and XFeSb. It is worth noting that ZrCoBi and NbCoSn also have a µWabove 300 cm2V−1s−1at room temperature, implying their potential as good TEs.
High lattice thermal conductivity, κL, is the main disadvantage of HH compounds that prevents high thermoelectric figures of merit. By introducing multiple phonon scattering mechanisms through alloying, nanostructuring, the formation of nanocomposites, and phase separation, the κL, at the temperature where the peak zT occurs, can be largely suppressed to values of 2–3 W m−1K−1, which, however, is still higher than its minimum value (∼1 W m−1K−1above 300 K) estimated using the Cahill model [246]. In comparison,
the nominal 19-electron HH compounds, such as unalloyed XCoSb and TiPtSb, show significantly lower κL
below 2 W m−1K−1in the high-temperature region [182–184], which can be ascribed to strong point defect scattering resulting from the existence of substantial intrinsic cation vacancies. However, the net lower carrier mobility, compared to the routine 18-electron HH systems, limits their thermoelectric performance.
This highlights the dilemma in developing high-performance HH thermoelectric materials, specifically, how to maximally suppress lattice thermal conductivity while maintaining high carrier mobility [124].
In summary, the past two decades have witnessed significant development of HH thermoelectric materials with the establishment of several low-cost, high-performance material systems. Targeting the future optimization of thermoelectric performance and practical application of HH compounds, several future directions are suggested:
(a) The interplay of point defects, electronic structures and transport properties is an appealing theme, including intrinsic defects in the 18-electron HH system and short-range order in the defective 19-electron HH system.
(b) Further reduction in thermal conductivity, especially near room-temperature, is highly desirable, with the aim of improving the average zT.
(c) The development of devices using the current best HH thermoelectric compounds is progressing but the related interfacial issues need to be solved. In addition, active Peltier coolers, which requires materials with high PF and high κ also brings new potential applications for HH compounds [247].
(d) HH is a large compound family with many members; the exploration of new thermoelectric candidates in the HH system is always attractive. To aid exploration and development, guidance from accurate, rapid electronic and phonon calculations is important.
Acknowledgments
Tiejun Zhu and Chenguang Fu acknowledge the support from the National Key Research and Development Program of China (2019YFA0704902) and the National Science Fund for Distinguished Young Scholars (No.
51725102).
Table3.HalfHeuslerthermoelectricproperties. MaterialT(K)µw (cm2V−1s−1)κL(Wm−1K−1)S(µVK−1)σ (Ω−1cm−1)zTEg(eV)µ0 (cm2V−1s−1)ms∗(me)εrorε(ε0)κ (Wm−1K−1)References MNiSn(M=Ti,Zr,Hf)system ZrNiSn309172.7—−224.7298.10.070.1–0.36 (Exp.) 0.5(DFT) 0.66 (ARPES)
37.12.820.6–26(Cal.)6.06[163,188,237, 241,244,248–250] 87489.6—−222.6754.40.60————5.22 ZrNiSn0.99Sb0.01309301.47.35−129.21604.60.10—48.12.8—7.44 874122.94.48−205.71259.10.77————5.45 Hf0.5Zr0.5Ni0.8Pd0.2Sn0.99Sb0.01300300.5—−104.02115.50.15————4.52[192] 80071.3—−153.21182.70.69————3.07 Hf0.75Zr0.25NiSn0.975Sb0.025312316.5—−73.13663.50.09————7.04[193] 97792.6—−158.31950.20.81————5.83 Hf0.6Zr0.4NiSn0.98Sb0.02291301.1—−92.12377.30.12—45.02.8—5.00[233] 103075.4—−170.61485.41.01————4.28 Ti0.5Zr0.25Hf0.25NiSn0.998Sb0.002373202.62.88−215.8515.20.26————3.34[164] 82492.10.76−206.5854.61.21————2.47 MCoSb(M=Ti,Zr,Hf)system ZrCoSb3340.8—−121.45.41.06(DFT)—17.9–19(Cal.)16.36[165,238,249–251] 9912.4—−149.156.70.02————6.56 ZrCoSn0.1Sb0.9328241.4—161.2956.00.08—10.59.2—9.87 95659.2—257.1382.30.45————5.40 Zr0.5Hf0.5CoSb0.8Sn0.2322151.3—109.71100.00.11—10.95–9—4.04[166] 96535.6—173.8613.10.49————3.61 Zr0.5Hf0.5CoSb0.8Sn0.2301214.12.85146.3887.60.17————3.40[167] 97453.42.19216.7565.80.80————3.24 Ti0.25Hf0.75CoSb0.85Sn0.15391192.42.98196.1659.20.29—4.9——3.43[168] 98171.21.99266.3429.51.15————2.68 Zr0.5Hf0.5Co0.9Ni0.1Sb300107.75.07−112.7677.60.05—6.36—5.44[169] 107458.82.37−226.9641.21.02————3.44 (Zr0.4Hf0.6)0.88Nb0.12CoSb300184.43.86−98.91391.40.08—9.26.5—4.68[170] (Continued.)
Table3.(Continued.) MaterialT(K)µw (cm2V−1s−1)κL(Wm−1K−1)S(µVK−1)σ (Ω−1cm−1)zTEg(eV)µ0 (cm2V−1s−1)ms∗(me)εrorε(ε0)κ (Wm−1K−1)References 117440.12.04−212.7588.90.99————3.15 (Hf0.3Zr0.7)0.88Nb0.12CoSb301129.24.15−114.8794.50.07—6.96.5—4.60[171] 112339.32.22−228.2451.00.85————3.04 XFeSb(X=V,Nb,Ta)system NbFeSb300——−2.77.20.54(DFT)——23(Cal.)—[172,173,242,249, 250] V0.95Ti0.05FeSb300——57.62125.6—————— (V0.6Nb0.4)0.8Ti0.2FeSb300267.23.09143.51142.70.19—7.610—3.70[173] 90064.62.37214.1626.70.80————3.24 Nb0.8Ti0.2FeSb300431.64.5471.64833.50.09—24.980(Exp.)7.47[174,252] 110071.12.68204.01048.41.09————4.55 Nb0.88Hf0.12FeSb301723.54.8293.75893.60.19—32.56.9—8.31[175] 120079.92.62246.1823.51.45————4.21 Nb0.95Ti0.05FeSb3041150.4—175.63427.80.25—35.87.5—13.09[176] 975144.4—306.3542.60.74————6.57 (Nb0.6Ta0.4)0.8Ti0.2FeSb300508.31.7674.75416.40.18—25.06.9—5.07[177] 120063.91.43218.2910.11.60————3.19 NbFe0.94Ir0.06Sb300164.46.21−76.81700.20.04—81.01.620(Exp.)6.89[178] 110124.03.46−205.9346.30.50————4.11 Ta0.74V0.1Ti0.16FeSb304460.82.33116.02832.20.29————3.93[179] 96993.81.56227.7868.81.52————2.91 19-electronHHmaterials NbCoSb303170.73.98−59.22393.70.04—3.7——5.56[180] 97438.83.04−139.81013.80.40————4.80 Nb0.8CoSb29968.74.17−174.2203.30.041.0(DFT)0.5(GSF)2.9——4.26[181,236] 112321.11.92−225.7249.40.62————2.36 Nb0.83CoSb299155.64.83−87.41372.90.06—7.07.7—5.64 112336.81.93−204.0558.80.90————2.93 Nb0.8Co0.92Ni0.08Sb299118.03.85−106.3801.00.07————4.31[182] 112332.51.69−213.0445.10.90————2.49 V0.855Ti0.1CoSb300148.22.20−57.92093.70.06—3.310—3.56[183] 97250.01.73−147.51188.40.67————3.74 (Continued.)
Table3.(Continued.) MaterialT(K)µw (cm2V−1s−1)κL(Wm−1K−1)S(µVK−1)σ (Ω−1cm−1)zTEg(eV)µ0 (cm2V−1s−1)ms∗(me)εrorε(ε0)κ (Wm−1K−1)References Ti0.82PtSb301131.82.53−78.11339.00.080.33(GSF)2.014.5—3.34[184] 107232.21.55−164.0728.50.74————2.86 OtherHHmaterials ZrCoBi0.65Sb0.15Sn0.20303293.12.18129.91501.00.26——12—2.98[185] 97383.21.59232.2735.81.42———2.73 ZrCo0.9Ni0.1Bi0.85Sb0.15302147.43.25−111.4951.00.09——6.8—3.78[186] 97261.71.86−212.0687.91.04———2.92 NbCoSn301—7.94−65.4——1(DFT)——22.6(Cal.)7.95[187,249,250] 97233.44.36−284.9160.20.26————4.63 NbCoSn0.9Sb0.1302301.17.64−85.62758.30.07—18.96—9.31 97360.93.53−179.8989.80.61————5.15 NbCo0.95Pt0.05Sn319226.44.65−123.21358.70.13—14.36.5—5.45[189] 77092.13.26−198.7845.60.59————4.34 ErPdSb333119.1—241.2189.70.070.28(AF)———5.55[190] 69845.8—141.6710.80.16————6.37 ErPdBi332126.9—82.81398.90.060.05(AF)———5.30 49575.3—71.01806.90.08————6.50 ScNiSb34154.3—221.4113.00.020.38(AF)0.21(GSF)30.61.52—9.74[191] 80726.0—122.5634.10.10————7.55 DyNiSb32930.2—46.9612.10.010.13(AF)0.09(GSF)53.50.56—3.67 71735.6—72.51452.60.11————4.90 ErNiSb34328.7—80.6342.50.010.17(AF)0.13(GSF)10.910.9—4.13 68847.3—106.71115.60.17————5.31 TmNiSb31896.7—205.1218.70.070.21(AF)0.15(GSF)17.117.1—3.82 69855.3—130.0989.00.26————4.53 LuNiSb32359.9—113.3416.20.030.19(AF)0.12(GSF)29.129.1—5.06 69956.6—113.61247.80.18————5.88 Notes: AF—Arrheniusformula. APERS—angle-resolvedphotoemissionspectroscopy. Cal.—calculation. DFT—densityfunctionaltheory. Exp.—experiment. GSF—Goldsmid–Sharpformula.