High thermoelectric cooling performance of n-type Mg3Bi2-based materials

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Science  02 Aug 2019:
Vol. 365, Issue 6452, pp. 495-498
DOI: 10.1126/science.aax7792

Thrifty thermoelectric cooling

Currently available thermoelectric devices for cooling rely on expensive bismuth telluride. Mao et al. systematically developed a far less expensive n-type magnesium-bismuth–based material with good thermoelectric properties. They built a device that could generate a temperature difference of up to 90 kelvin when coupled with a commercially available p-type material. Such materials should provide an excellent basis for cost-effective thermoelectric cooling technology.

Science, this issue p. 495


Thermoelectric materials have a large Peltier effect, making them attractive for solid-state cooling applications. Bismuth telluride (Bi2Te3)–based alloys have remained the state-of-the-art room-temperature materials for many decades. However, cost partially limited wider use of thermoelectric cooling devices because of the large amounts of expensive tellurium required. We report n-type magnesium bismuthide (Mg3Bi2)–based materials with a peak figure of merit (ZT) of ~0.9 at 350 kelvin, which is comparable to the commercial bismuth telluride selenide (Bi2Te3–xSex) but much cheaper. A cooling device made of our material and p-type bismuth antimony telluride (Bi0.5Sb1.5Te3) has produced a large temperature difference of ~91 kelvin at the hot-side temperature of 350 kelvin. n-type Mg3Bi2-based materials are promising for thermoelectric cooling applications.

Thermoelectric modules can directly convert electricity into thermal energy for cooling and heating and can also harvest waste heat for electrical power (1, 2). The global thermoelectric module market was worth ~0.6 billion U.S. dollars in 2018 and it is anticipated to reach ~1.7 billion U.S. dollars by 2027 (3). Most thermoelectric modules have been used for thermal management because the market for power generation is still in its infancy. The cooling capability of a thermoelectric module largely relies on the performance of the materials used. The performance is governed by the dimensionless figure of merit (ZT)=S2ρ1κ1T, where S is the Seebeck coefficient, ρ the electrical resistivity, κ the thermal conductivity, and T the absolute temperature (46). Although advancements have been made in mid- and high-T materials, e.g., lead chalcogenides (7, 8), skutterudites (9, 10), magnesium stannide (Mg2Sn)–based materials (11, 12), tin selenide (SnSe) (13, 14), and half-Heuslers (1517), progress on room-temperature (RT) materials has been sluggish. n-type Bi2Te3–xSex and p-type Bi2–xSbxTe3 have remained the state-of-the-art RT thermoelectric materials for the past several decades. Even though enhancements in the thermoelectric performance of nanostructured n-type Bi2Te3–xSex were reported (18, 19), it is challenging to minimize the electrical contact resistance between the contact material and Bi2Te3–xSex (20) on top of the anisotropy issue of Bi2Te3-xSex (18). Despite the progress made on materials, they have not yet been engineered into viable thermoelectric cooling applications. Additionally, the high cost of tellurium (Te) partially limits the wider applications of thermoelectric modules. Identifying new materials that have high ZT, are low cost, and in which it is easy to minimize the contact resistance is essential for the widespread use of thermoelectric cooling modules.

We report n-type Mg3Bi2-based materials with a high ZT of ~0.9 at 350 K. We constructed a unicouple consisting of n-type Mg3.2Bi1.498Sb0.5Te0.002 and p-type Bi0.5Sb1.5Te3 (Fig. 1A) and measured the cooling performance (Fig. 1B) (21). The Peltier effect (2) allowed us to remove heat from the top, cold-side copper plate and dissipate it into the bottom, hot-side copper blocks by applying an electrical current. This resulted in a T difference between the hot and cold sides (Fig. 1B). This effect increased with increasing current until it eventually saturated at 91 K with the hot-side T maintained at 350 K. We found that the hot-side T-dependent maximum T difference (ΔT) was higher for our unicouple compared with the commercial data (Fig. 1B, inset). Unlike with the nanostructured Bi2Te3–xSex, which has contact problems, we found that Fe and Ni were both good contact materials for Mg3.2Bi2-based materials (fig. S2), and fabrication of the Mg3.2Bi1.498Sb0.5Te0.002 leg with contact materials was easy (21). Our Mg3.2Bi2-based materials should be much cheaper than Bi2Te3–xSex as they minimize the need for expensive Te. The cost of thermoelectric materials makes up nearly one-third of the total cost for thermoelectric modules (22). Replacing Bi2Te3–xSex with the Mg3Bi2-based materials should effectively reduce the cost of thermoelectric modules and potentially expand their usefulness for various cooling applications.

Fig. 1 Thermoelectric cooling measurement.

(A) Experimental setup for the thermoelectric cooling measurement with a unicouple consisting of p-type Bi0.5Sb1.5Te3 and n-type Mg3.2Bi1.498Sb0.5Te0.002. (B) Electrical current–dependent T difference (ΔT) between the hot and cold sides at the hot-side T of 350 K. The inset shows the comparison of hot-side, T-dependent maximum ΔT between our unicouple and commercial data. The commercial data were taken from table S2.

n-type Mg3Sb2-based materials with promising thermoelectric performance were reported recently (2333), mainly targeted for power generation from waste heat. Unlike the semiconducting Mg3Sb2, the isostructural Mg3Bi2 is a semimetal (3436). We found that the stoichiometry of Mg3Bi2 showed p-type conduction (fig. S3B), in agreement with other measurements (34, 35). We attributed the p-type conduction to the presence of a high concentration of Mg vacancies, similar to that in Mg3Sb2 (23, 29). We successfully synthesized n-type Mg3Bi2 samples with excess Mg, i.e., Mg3+δBi2 (δ = 0.05, 0.1, and 0.2). The thermoelectric properties of these samples were very similar to one another (fig. S3). We focused on Mg3.2Bi2, the carrier concentration (n) of which was ~2.1 × 1019 cm−3 at 10 K (Fig. 2A, upper panel). Carrier concentration noticeably increased once T was above 150 K. Below 300 K, the carrier mobility (μ) was more than 200 cm2 V−1 s−1 and reached a high value of ~4198 cm2 V−1 s−1 at 10 K (Fig. 2A, lower panel). The high n and μ in conjunction with the low bipolar conduction T clearly indicated the semimetallic characteristic of Mg3.2Bi2. Electrical resistivity of Mg3.2Bi2 was only ~9 microhm m at 300 K and ~0.58 microhm m at 2 K (Fig. 2B). The S of Mg3.2Bi2 was ~–105 μV K−1 at 300 K and more than –80 μV K−1 over a broad T range between 130 and 350 K (Fig. 2C). The power factor (S2ρ−1) of Mg3.2Bi2 was ~10 μW cm−1 K−2 across a broad T range (Fig. 2D). Doping the samples with a small amount of Te effectively modulated the n of Mg3.2Bi2 (fig. S4A), reducing ρ and slightly enhancing S (Fig. 2, B and C, respectively). This resulted in substantially higher S2ρ−1 on the order of ~20 μW cm−1 K−2 over a broad T range (Fig. 2D). We obtained a peak ZT of ~0.3 at 350 K with Mg3.2Bi1.998Te0.002 and above 0.1 down to 150 K (fig. S5B).

Fig. 2 Electronic thermoelectric properties of Mg3.2Bi2–xTex.

(A) Carrier concentration (upper panel) and mobility (lower panel) of Mg3.2Bi2. (B) Electrical resistivity. (C) Seebeck coefficient. (D) Power factor.

Semimetals usually have a low S because of cancellation between electrons and holes, but the n-type Mg3.2Bi2 studied here has a large S, which is essential for its high thermoelectric performance. To understand the origin of the large S, we calculated the band structure of Mg3Bi2 (fig. S6A). The band overlap energy that we calculated between the conduction band minimum and valence band maximum was ~–0.4 eV; however, the two-band modeling estimated this at ~–0.1 eV (fig. S7). We rigidly shifted band structure with the band overlap energy shifted to –0.1 eV (Fig. 3A). The conduction band minimum located along the L–M line with a valley degeneracy N of 6 (fig. S8A) and the valence band maximum located around the Γ point with an N of 1 (fig. S8B). Different band structures were previously reported for Mg3Bi2 (24, 36, 37) because of differences in the choice of pseudopotential and depending on whether the spin–orbital coupling was considered (36, 37). Owing to the presence of electrons and holes in a semimetal, we expressed S as S=(ρhSe+ρeSh)/(ρe+ρh), where Se and Sh are partial S for electrons and holes, respectively, and ρe and ρh are partial ρ for electrons and holes, respectively. We applied a two-band model to calculate the partial S and μ for Mg3.2Bi2. We found that the partial S for electrons was noticeably larger than that of the holes (Fig. 3B). We attributed the difference in the partial S to the disparity in density-of-states effective mass md*, ~0.530 m0 (where m0 is the free electron mass) for the conduction band, and ~0.276 m0 for the valence band (table S1). Density-of-states effective mass depends on the band effective mass (m*) and the N according to md*=N2/3m* (38). The different N in the conduction and valence bands (fig. S8) accounts for the disparity in md*. We also modeled the partial μ of Mg3.2Bi2 between 100 and 350 K (Fig. 3C). We omitted the values under 100 K because they have relatively large uncertainties. Our modeling showed that the electrons have a higher μ than that of the holes. Carrier mobility is proportional to (m*)3/2(mI*)1 when acoustic phonon scattering is the predominant scattering process and mI* is the inertial effective mass (38). On the basis of the density functional theory results, we extracted from the model m* ~0.161 m0 for electrons and ~0.276 m0 for holes and the mI* was ~0.133 m0 for electrons and ~0.259 m0 for holes (table S1). The differences in the effective masses between the conduction and valence bands explained the disparity in μ between electrons and holes. We can quantify the asymmetrical transport properties between the conduction and valence bands by the electron-to-hole weighted mobility ratio A=(Neme*3/2μe)/(Nhmh*3/2μh) (5, 3941). When the transport properties were highly asymmetrical, i.e., A >> 1 or A << 1, a large S at 300 K could be achieved for semimetals and semiconductors with small Eg (figs. S10 and S11). The calculated electron-to-hole mobility ratio was around 3 and A was above 8 for Mg3.2Bi2 (Fig. 3D). The large A contributed to the high S of n-type Mg3.2Bi2 and also partially explained why p-type Mg3Bi2 has a much lower S and inferior thermoelectric performance (fig. S3). The large S in n-type Mg3.2Bi2 is similar to that in single-crystal bismuth, which has an electron-to-hole mobility ratio of ~9.19 along the trigonal axis (4244), md* ~0.113 m0 for electrons, and md* ~0.093 m0 for holes (44). As a result, A was as large as ~12 along the trigonal axis for bismuth, and thus a high S of ~–100 μV K−1 at 300 K along this direction.

Fig. 3 Band structure and transport properties of Mg3.2Bi2.

(A) Calculated band structure of Mg3Bi2 with the band overlap energy shifted to –0.1 eV. (B) Comparison of partial Seebeck coefficients between electrons and holes. (C) Comparison of mobilities between electrons and holes. (D) Electron-to-hole mobility ratio and electron-to-hole weighted mobility ratio.

The relatively high κ of Mg3.2Bi2 limited the thermoelectric performance (fig. S5A). Partial substitution of Bi with Sb in Mg3.2Bi2 should substantially reduce the lattice thermal conductivity (κlat). We prepared a range of samples with Sb, Mg3.2Bi1.998–xSbxTe0.002 (x = 0, 0.1, 0.3, 0.5, and 0.7). Increased Sb concentration increased ρ of Mg3.2Bi1.998–xSbxTe0.002 (Fig. 4A). We measured ρ ~8.1 μΩ m at 300 K and ~2.2 μΩ m at 2 K for Mg3.2Bi1.998Te0.002. In comparison, we measured ρ ~24.4 μΩ m at 300 K and ~9.9 μΩ m at 2 K for Mg3.2Bi1.298Sb0.7Te0.002. We attributed the increased ρ to the reduced n (fig. S13A) and μ (fig. S13B) after Sb alloying. Similarly, Sb alloying greatly enhanced S (Fig. 4B). Room-temperature S was ~–129 μV K−1 for Mg3.2Bi1.998Te0.002 and ~–229 μV K−1 for Mg3.2Bi1.298Sb0.7Te0.002. We ascribed the enhancement of S mainly to the reduced n (fig. S13A). In addition, the modified band structure after Sb alloying partially influenced the T dependence of S. Because Mg3Bi2 is a semimetal whereas Mg3Sb2 is a semiconductor, we expected a band structure transition from semimetallic to semiconducting in Mg3.2Bi1.998–xSbxTe0.002 solid solutions. To probe the variation in band structure after Sb alloying, we measured the T-dependent ρ of undoped Mg3.2Bi2–xSbx (x = 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, and 0.7). We described this with ρ = ρ300Kexp(Eg/2kBT) (45) (Fig. 4D and fig. S15), and found a clear semimetallic to semiconducting transition with increasing Sb concentration. We determined an Eg of ~–0.013 eV for Mg3.2Bi2 and Mg3.2Bi1.9Sb0.1 showed a nearly zero Eg (~0.005 eV). All of the samples with an Sb concentration of more than 5% (x > 0.1) were semiconducting and Eg increased with greater Sb concentration. The reported Eg of Mg3+δBi0.89Sb1.1Te0.01 was ~0.240 eV (32) and that of Mg3.2Bi1.3Sb0.7 was ~0.147 eV. The lower Eg is reasonable because of the lower Sb concentration. An Eg value of –0.013 eV estimated from the temperature dependence of ρ for Mg3.2Bi2 is smaller than the value that we estimated from the two-band modeling of ~–0.10 eV (Fig. 3A and fig. S7). This suggests that the band overlap energy of Mg3Bi2 should be small but requires high-quality single crystal measurements to completely resolve.

Fig. 4 Thermoelectric properties of Mg3.2Bi1.998–xSbxTe0.002.

(A) Electrical resistivity. (B) Seebeck coefficient. (C) Power factor. (D) Estimated band gap of undoped Mg3.2Bi2–xSbx. (E) Lattice thermal conductivity. (F) ZT. The measurement errors of Mg3.2Bi1.498Sb0.5Te0.002 are shown in fig. S18.

We can also understand the transition after Sb alloying from the variation in T-dependent n (fig. S13A). The n of Mg3.2Bi1.998Te0.002 and Mg3.2Bi1.898Sb0.1Te0.002 increased noticeably with T above 125 K owing to the activation of electron–hole pairs from bipolar conduction. This phenomenon was greatly suppressed in Mg3.2Bi1.698Sb0.3Te0.002 and finally minimized in Mg3.2Bi1.498Sb0.5Te0.002 and Mg3.2Bi1.298Sb0.7Te0.002. In addition, the reduced n in Mg3.2Bi1.998–xSbxTe0.002 with increasing Sb concentration also indicated the downward shift of the Fermi energies due to upward movement of conduction band edges that opened Eg. Despite the semimetal to semiconductor transition after Sb alloying, the S2ρ−1 values among Mg3.2Bi1.998–xSbxTe0.002 samples were comparable (Fig. 4C). We observed a slight enhancement in S2ρ−1 in Mg3.2Bi1.898Sb0.1Te0.002 (Eg ~0.005 eV) and Mg3.2Bi1.698Sb0.3Te0.002 (Eg ~0.063 eV) compared with Mg3.2Bi1.998Te0.002. Power factors at lower T were reduced because of the substantially reduced μ when the Sb concentration was above 25% (x > 0.5) (fig. S13B). We observed a substantial reduction in κ of Mg3.2Bi1.998–xSbxTe0.002 with increasing Sb concentration (fig. S15). We attributed this reduction to the substantially reduced κlat due to alloying scattering (Fig. 4E). The peak κlat around 20 K was as high as ~9.6 W m−1 K−1 for Mg3.2Bi1.998Te0.002 and only ~3.2 W m−1 K−1 for Mg3.2Bi1.298Sb0.7Te0.002. The reduced κlat translated into an enhanced ZT (Fig. 4F). The ZT at 350 K was ~0.3 for Mg3.2Bi1.998Te0.002 and ~0.9 for Mg3.2Bi1.498Sb0.5Te0.002. Although the thermoelectric performance of Mg3.2Bi1.998–xSbxTe0.002 decreased with reduced T, both Mg3.2Bi1.498Sb0.5Te0.002 and Mg3.2Bi1.298Sb0.7Te0.002 maintained a ZT above 0.3 down to 200 K. The average ZT between 200 K and 350 K was ~0.6 for Mg3.2Bi1.298Sb0.7Te0.002, ~0.6 for Mg3.2Bi1.498Sb0.5Te0.002, and ~0.2 for Mg3.2Bi1.998Te0.002. We measured the commercial n-type Bi2Te3–xSex ingot and it showed a ZT of ~0.85 at 350 K, comparable to our Mg3.2Bi1.998–xSbxTe0.002 (fig. S17). However, the commercial Bi2Te3–xSex ingot showed a strong anisotropy in the thermoelectric properties because of its highly preferred orientation. This requires the thermoelectric legs to be cut along the direction with better performance. By contrast, our Mg3.2Bi2-based materials have nearly isotropic thermoelectric properties and the leg fabrication will be easier. In addition, our Mg3.2Bi2-based materials are mechanically robust, whereas the commercial Bi2Te3–xSex ingot can easily delaminate from the cleavage plane. Further enhancements in the thermoelectric properties of Mg3Bi2-based materials are very likely, e.g., improving μ and reducing κlat. Therefore, our n-type Mg3Bi2-based materials are highly attractive for thermoelectric cooling applications.

Supplementary Materials

Materials and Methods

Supplementary Text

Figs. S1 to S18

Tables S1 and S2

References (4648)

References and Notes

  1. See the supplementary materials.
Acknowledgments: We thank Q. Zhu and D. Z. Wang for assistance with the experiments, and C. Chen and Q. Zhang for supplying the commercial n-type Bi2Te3–xSex ingot. Funding: Z.R. acknowledges a Humboldt Research Award from the Alexander von Humboldt Foundation. K. Nielsch at IFW in Dresden, Germany, supported part of the work. Author contributions: J.M. synthesized the samples and designed and performed experiments under Z.R.’s guidance; J.M. performed the data analysis and modeling; J.M. and H.Z. conducted the cooling measurements; L.Z. and G.A.G. helped with the thermoelectric characterization; Z.D. performed the first-principles calculations; J.M. wrote the manuscript. All authors contributed to discussing the results and commenting on the manuscript. The project was directed and supervised by G.C. and Z.R. Competing interests: Z.R. and J.M. have filed a provisional patent application (no. 62/870,884) on the work described here. Data and materials availability: All data are available in the manuscript and supplementary materials.

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