Approaching Topological Insulating States Leads to High

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Cite This: J. Am. Chem. Soc. 2018, 140, 13097−13102

Approaching Topological Insulating States Leads to High Thermoelectric Performance in n‑Type PbTe Yu Xiao,† Dongyang Wang,† Bingchao Qin,† Jinfeng Wang,‡ Guangtao Wang,‡ and Li-Dong Zhao*,† †

School of Materials Science and Engineering, Beihang University, Beijing 100191, China College of Physics and Materials Science, Henan Normal University, Xinxiang 453007, China

‡

J. Am. Chem. Soc. 2018.140:13097-13102. Downloaded from pubs.acs.org by MIAMI UNIV on 10/29/18. For personal use only.

S Supporting Information *

ABSTRACT: Realizing high thermoelectric performance requires high electrical transport properties and low thermal conductivity, which are essentially determined by balancing the interdependent controversy of carrier mobility, effective mass, and lattice thermal conductivity. Here, we observed an electronic band inversion (approaching topological insulating states) in Sn and Se co-alloyed PbTe, resulting in optimizing effective mass and carrier mobility. The Sn alloying in PbTe(Se) can narrow its band gap due to band inversion and induce a sharper conduction band (equals to lower carrier mass), which further facilitates high carrier mobility, ∼251 cm2 V−1 s−1 in Pb0.89Sn0.11Te0.89Se0.11 at room temperature, thus leading to a high power factor. Meanwhile, we found that the lattice thermal conductivity κl can be reduced from ∼0.77 Wm−1 K−1 in PbTe to ∼0.45 Wm−1 K−1 in (Pb0.91Sn0.09)(Te0.91Se0.09) by producing point defects via Sn and Se co-alloying. Coupling reducing lattice thermal conductivity with integration of optimizing effective mass and carrier mobility by means of electronic band inversion, we obtained a maximum ZT value ∼1.4 at 773 K in n-type (Pb0.93Sn0.07)(Te0.93Se0.07).

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INTRODUCTION Thermoelectric technology can directly convert heat into electric power without pollutant emission based on the Seebeck effect. As a kind of eco-friendly energy, it offers an alternative solution to relieve the emerging severe energy crisis. However, compared to the traditional heat engine, the relatively low conversion efficiency of thermoelectric technology limits its large-scale practical application. The conversion efficiency is characterized by the dimensionless figure of merit in thermoelectric materials, ZT = S2σT/(κl + κe), where σ, S, T, κl, and κe denote the electrical conductivity, Seebeck coefficient, working temperature in Kelvin, lattice thermal conductivity, and electronic thermal conductivity, respectively.1−3 Apparently, an excellent thermoelectric material should simultaneously possess high electrical transport properties (PF = S2σ) and low thermal conductivity (κtot = κl + κe).4,5 However, the complex inter-relationships among these parameters make it challenging to maximize the ZT value and conversion efficiency. To simplify these coupled parameters, quality factor B is used to evaluate thermoelectric performance, which is defined as B = T5/2m*μ/κl.6 In the expression of B, m* denotes effective mass and μ is carrier mobility, and the product (m*μ) is called weighted carrier mobility. Typically, band structure engineering including band convergence7−9 and resonate states10,11 can enhance Seebeck coefficient by enlarging the effective mass m*; however, a high effective mass m* is detrimental to carrier mobility μ. Nanostructuring is an © 2018 American Chemical Society

effective method to achieve low lattice thermal conductivity κl and enhance ZT values through scattering phonons12,13 but leads to strong carrier scattering and largely reduces μ. Therefore, the approach of maintaining high carrier mobility μ and simultaneously keeping large effective mass m* and lowering thermal conductivity κl is critical to achieve highperformance thermoelectrics. The p-type PbTe is the best intermediate temperature thermoelectric material, which has been well developed in past decades. To match its high-performance p-type counterpart, ntype PbTe is urgentto be developed. In n-type PbTe, preserving superior carrier mobility is a critical factor for obtaining high thermoelectric performance because its band structures are much less complex than those of p-type PbTe. In order to maintain high carrier mobility in n-type PbTe, it is essential to both obtain lower effective mass and avoid carrier scattering. Recently, topological insulating states achieved in PbTe and PbSe motivated us to enhance the thermoelectric performance of n-type PbTe through Sn and Se coalloying.14−16 Pb1−xSnxTe could be a topological crystalline insulator (TCI) by elaborately tailoring the Pb/Sn ratio due to electronic band inversion. When Sn content increases to 0.40 in Pb0.6Sn0.4Te17,18 and Sn content to ∼0.23 in Pb0.77Sn0.23Se,19 the band gap reaches close to zero, indicating that Se alloying could promote the band inversion of PbTe. During the process Received: August 22, 2018 Published: September 13, 2018 13097

DOI: 10.1021/jacs.8b09029 J. Am. Chem. Soc. 2018, 140, 13097−13102

Article

Journal of the American Chemical Society of band inversion, approaching topological insulating states, the electronic band structures will become sharper, which can cause a smaller carrier effective mass and a higher carrier mobility.19−22 Moreover, nanostructures are expected to be avoided due to complete solubility of Sn and Se in the PbTe matrix, which also could maintain high carrier mobility. In this work, we found that the electronic band inversion (approaching topological insulating states) leads to high-performance ntype PbTe. A peak ZT of ∼1.4 at 773 K is achieved in n-type (Pb0.93Sn0.07)(Te0.93Se0.07), which is 40% higher than that in sample without Sn/Se. The high performance achieved in this work is attributed to smaller effective mass and higher carrier mobility (electronic band inversion) and lower lattice thermal conductivity (point defect scattering).

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EXPERIMENTAL SECTION

Raw materials, Pb, Te, Sb, Sn, and Se were loaded into silica tubes under a N2-filled glovebox with nominal compositions, flame-sealed at a residual pressure below ∼10−4 Torr, slowly heated to 1323 K with 50 K/h, maintained at this temperature for 10 h, and finally cooled in a furnace to room temperature. The obtained ingots are ground into powders and sintered by spark plasma sintering (SPS-211Lx) at 873 K for 15 min under an axial compressive stress of 50 MPa to obtain densified disk-shaped samples. The phase identification was evaluated by X-ray diffraction (XRD) using powder. Scanning electron microscopy (SEM), X-ray energy-dispersive spectroscopy (EDS) studies, and transmission electron microscopy (TEM) were performed to observe microstructures. Hall coefficient (RH) was measured by the Van der Pauw method using a Hall measurement system (Lake Shore 8400 series, model 8404, USA). The optical band gap was measured using an infrared diffuse reflection method with a Fourier transform infrared spectrometer (IRAffinity-1S). Elastic properties were measured using an ultrasonic instrument (ultrasonic pulser/receiver, model 5058 PR, Olympus, USA). The electrical conductivity and Seebeck coefficient were measureed using Cryoall CTA instrument. Thermal diffusivity (D) was acquired with a Netzsch LFA457 instrument. The density (ρ) was determined using the dimensions and mass of the sample, and the specific heat capacity (Cp) was estimated with the Dulong-Petit law. The combined uncertainty for all measurements involved in the calculation of ZT was less than 20%. Density functional theory (DFT) calculations were conducted using the Perdew−Burke−Ernzerhof functional of the generalized gradient approximation as implemented in the Vienna ab initio simulation package. More experimental details can be found in the Supporting Information.

Figure 1. Electrical transport properties in (Pb1−xSnx)(Te1−xSex): (a) electrical conductivity, (b) Seebeck coefficient, (c) power factor, and (d) room temperature carrier density and comparison of carrier mobility between this work and n-type PbTe-MnTe.23 (e) Room temperature carrier effective mass as a function of Sn and Se alloying content x. The inset shows Pisarenko relationships with different effective mass m* = 0.25, 0.35, and 0.45 (me). (f) Carrier mobility as a function of carrier density and the comparison of carrier mobility with other n-type PbTe-based samples with nanostructures: PbTe−In−I,25 PbTe−Pb vacancies,30,31 PbTe−Ag2Te,24 and PbTe−Pb−Sb.26

with increasing co-alloying content, ∼1610 S/cm in (Pb0.89Sn0.11)(Te0.89Se0.11). From Figure 1b, all the samples show a negative Seebeck coefficient, and the absolute value of the Seebeck coefficient shows mild variation, denoting an unobvious change of carrier density after Sn and Se co-alloying in the PbTe matrix. When the slightly decreased electrical conductivity and undistorted Seebeck coefficient are combined, the power factor maintains a relatively high range, and the maximum power factor increases from ∼19.6 μW cm−1 K−2 in PbTe to ∼22.8 μW cm−1 K−2 in (Pb0.99Sn0.01)(Te0.99Se0.01), as shown in Figure 1c. The room temperature Hall measurement in Figure 1d reveals that the carrier density in co-alloyed samples changes slightly, varying from ∼4.77 × 1019 cm−3 in PbTe to 4.01 × 1019 cm−3 in (Pb0.89Sn0.11)(Te0.89Se0.11), and the carrier mobility experiences a decrease from ∼364 cm2 V−1 s−1 in PbTe to ∼251 cm2 V−1 s−1 in (Pb0.89Sn0.11)(Te0.89Se0.11). When the carrier density is fixed, it should be noted that the present carrier mobility in (Pb1−xSnx)(Te1−xSex) samples is higher than that in nanostructured n-type PbTe systems24−26 and even higher than that of n-type PbTe−MnTe without nanostructures.23 This superior carrier mobility is considered to arise from lower carrier effective mass, which is elucidated by the Pisarenko relationship in the inset of Figure 1e. Indeed, Figure 1e shows that the effective mass in the (Pb1−xSnx)(Te1−xSex) sample undergoes a decreasing tendency with increasing Sn and Se coalloying content, which is related to the electronic band

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RESULTS AND DISCUSSION Electrical Transport Properties. The n-type PbTe matrix with optimized carrier density23 was selected to introduce Sn and Se co-alloying. The powder X-ray diffraction (PXRD) patterns in Figure S1a exhibit a single phase in the cubic rock salt structure without extra peaks. With increased co-alloying content x, the main peaks gradually shift to a high angle that indicates lattice shrinkage. The calculated lattice parameter in Figure S1b shows an almost linear decrease with increasing content Sn and Se up to 0.11, which is consistent with Vegard’s law, suggesting a complete solid solution formed in the Sn and Se co-alloyed PbTe. The electrical conductivity in all the samples rapidly decreases with increasing temperature, as shown in Figure 1a, representing a degenerated semiconductor transport behavior. After Sn and Se co-alloying, the room-temperature electrical conductivity first undergoes a slight increase in samples of x = 0.01 and 0.03, from ∼2540 S/cm in PbTe to ∼2840 S/cm in (Pb0.97Sn0.03)(Te0.97Se0.03), and then decreases 13098

DOI: 10.1021/jacs.8b09029 J. Am. Chem. Soc. 2018, 140, 13097−13102

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increase of Sn alloying content, the band gap opens again, which is schematically shown in Figure 2b. Because the band inversion caused by Sn alloying will start early in PbSe (Sn = 0.23) compared to that in PbTe (Sn = 0.40), we believe that the Se alloying will promote the band inversion of PbTe. DFT calculations are conducted to further investigate the band structures evolution in (Pb1−xSnx)(Te1−xSex). From the pristine Pb27Te27 sample in Figure 2c to the low Sn and Se coalloyed Pb26SnTe26Se (∼3.7%) sample in Figure 2d, no obvious changes in band structures are observed. In the highly co-alloyed Pb7SnTe7Se (∼12.5%) sample in Figure 2e and the Pb2Sn2Te2Se2 (∼50%) sample in Figure 2f, the band gap largely decreases from ∼0.1 eV in PbTe to nearly zero, and the low conduction and valence bands are obviously overlapped, forming Dirac cones. The decreasing tendency of a band gap with increasing Sn and Se co-alloying content is consistent with our optical band gap measurements. It is worthy to point out that the Sn and Se atoms in supercell Pb7SnTe7Se lower the symmetry with respect to PbTe, and thus the conduction band minimum (CBM) and valence band maximum (VBM) fold from L to around Γ. Moreover, the band shape also shows a dramatic modification, from a flat band shape to a very sharp band shape. Considering the distinct modification in the electronic band structure of PbTe after Sn and Se alloying, therefore, as we discussed in Figure 1e,f, the effective mass and carrier mobility are calculated based on the single Kane band (SKB) model29,35 instead of single parabolic band (SPB) model,35,36 and the calculation details can be found in the Supporting Information. As is well-known, the conduction band shape becomes sharper, which will cause a low effective carrier mass and high carrier mobility as in the following relationships:23,30

inversion (will be discussed later). Furthermore, the carrier scattering on nanostructures is avoided in Sn and Se co-alloyed samples, which is confirmed by microstructure observation. Figure 1f clearly shows that the carrier mobility values in this work are much higher than those of other n-type PbTe samples with nanostructures, namely, ∼176 cm2 V−1 s−1 in n-type PbTe−I−In,25 ∼190 cm2 V−1 s−1 in n-type PbTe−I with Pb vacancies,27 ∼93 cm2 V−1 s−1 in n-type PbTe−La−Ag2Te,24 and ∼100 cm2 V−1 s−1 in n-type PbTe−Pb−Sb.26 In n-type PbTe, preserving superior carrier mobility is a critical factor to obtain a high thermoelectric performance because its band structures are much less complex than those of p-type PbTe.28−30 To investigate the band structure modification in (Pb1−xSnx)(Te1−xSex), we conducted optical band gap measurements. Figure 2a shows that the optical band gap

ij ∂ 2E(k) yz zz mb* = ℏ2jjj j ∂k 2 zz k {

−1

μ∝

eτ0 m*

(1)

(2)

where mb* denotes the single band effective mass, m* is the DOS (density of state) effective mass, defined as m* = (NV)2/3mb*. The μ denotes the carrier mobility, which is reciprocal to m*. Hence, a sharper band shape will lead to a lower mb* and then a lower m*, thus a higher μ to maintain a high electrical transport properties. The DFT calculations elucidate the origins of higher carrier mobility, which contributes to larger power factors in (Pb1−xSnx)(Te1−xSex). Thermal Conductivity and Microstructure Observation. The total thermal conductivity in Figure 3a shows a significant decrease from 3.89 Wm−1 K−1 in PbTe to 2.36 Wm−1 K−1 in (Pb0.89Sn0.11)(Te0.89Se0.11) at room temperature. The reduction of total thermal conductivity arises from dramatically reduced lattice thermal conductivity after Sn and Se co-alloying in Figure 3a. The minimum lattice thermal conductivity is suppressed from ∼0.77 Wm−1 K−1 in PbTe to ∼0.45 Wm−1 K−1 in (Pb0.91Sn0.09)(Te0.91Se0.09). The reduction in lattice thermal conductivity can be well estimated using the Callaway model,27,37 as shown in Figure 3b. Massive point defects in solid solution can play an essential role to intensify phonon scattering due to size and mass fluctuations in the crystal lattice. Owing to the significant size difference and mass discrepancy between Te2− (∼2.21 Å, ∼127.6 g/mol) and Se2− (∼1.98 Å, ∼78.96 g/mol), and Pb2+ (∼1.2 Å, ∼207.2 g/mol)

Figure 2. Band structures in (Pb1−xSnx)(Te1−xSex) samples: (a) optical band gap, (b) schematic picture of energy band evolution, and DFT-calculated band structures in (c) pristine PbTe, (d) Pb26SnTe26Se, (e) Pb7SnTe7Se, and (f) Pb2Sn2Te2Se2.

gradually decreases with increasing Sn and Se co-alloying content, from 0.27 eV in PbTe to 0.21 eV in (Pb0.89Sn0.11)(Te0.89Se0.11). The significant reduction of band gap for PbTe in this work arises from band inversion caused by Sn alloying. It is well-known that heavily Sn alloyed PbTe(Se) can change to be a topological insulator, and when Sn is alloyed into the PbTe(Se) lattice, the higher Sn 5s states push the valence band into higher energy level, leading to a decrease of band gap at L point.16,21 Accordingly, the band gap of Pb1−xSnxTe(Se) initially decreases with increasing Sn content and then approaches zero when Sn content x is ∼0.23 in Pb1−xSnxSe19 and ∼0.40 in Pb1−xSnxTe.17,32−34 After that, with further 13099

DOI: 10.1021/jacs.8b09029 J. Am. Chem. Soc. 2018, 140, 13097−13102

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TEM images, respectively. Both the inset diffraction pattern of Figure 4c and the high-magnification TEM image of Figure 4d along the [110] direction match with the crystal structure of PbTe, and no splitting of additional spots is observed, indicating that the Sn and Se completely form a solid solution in the PbTe matrix. Quality Factor and Figure of Merit ZT. The obtained high thermoelectric performance can be well described by the general accepted quality factor, B = T5/2m*μ/κl, which can satisfactorily evaluate the thermoelectric performance for a given material regarding the complex interdependent thermoelectric parameters (carrier mobility μ, effective mass m, and lattice thermal conductivity κl).38,39 The quality factor B in Figure 5a shows a dramatic enhancement after Sn and Se co-

Figure 3. Thermal conductivity in (Pb1−xSnx)(Te1−xSex): (a) the total thermal conductivity and lattice thermal conductivity and (b) comparison of room temperature lattice thermal conductivity between experimental results and Callaway model estimations.

and Sn2+ (∼1.12 Å, ∼118.7 g/mol), it is obvious that Sn substitution at Pb sites contributes more to the reduction of the lattice thermal conductivity due to large mass difference. Experimental lattice thermal conductivity values are very consistent with those in the Callaway model, which indicates that nanostructures are excluded in the PbTe with Sn and Se co-alloying. To confirm elemental composition distributions as well as microstructural information in (Pb1−xSnx)(Te1−xSex), both SEM and TEM analyses were performed on (Pb0.93Sn0.07)(Te0.93Se0.07). Figure 4a shows the SEM image of the polished surface. Generally, the surface is relatively flat, only with several voids, which indicates the sample is well densified through a SPS process. The corresponding EDS maps illustrate that all elements (Te, Pb, Sn, and Se) are distributed homogeneously throughout the sample in Figure 4b. Figure 4c,d shows typical low- and high-magnification

Figure 5. Thermoelectric performance in (Pb1−xSnx)(Te1−xSex): (a) quality factor as a function of Sn and Se co-alloying content x and (d) temperature dependence of ZT values.

alloying, ∼20% increase in (Pb0.93Sn0.07)(Te0.93Se0.07) compared to that with a pristine PbTe sample, which mainly comes from the enhanced parameter μ/κl in the inset of Figure 5a.

Figure 4. Microstructure observation in (Pb0.93Sn0.07)(Te0.93Se0.07) sample: (a) SEM image, (b) EDS elemental maps indicate that Te, Pb, Sn, and Se distribute homogeneously in the sample, (c) typical TEM image along the [110] direction, as indicated by the inset selected area diffraction pattern, and (d) high-resolution TEM image of the selected area in (c). 13100

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supported by The High Performance Computing Center of Henan Normal University. The authors are grateful to Professor Mercouri G. Kanatzidis, Professor Gangjian Tan. and Dr. Songting Cai for helpful discussions.

With the integration of maintained carrier mobility and reduced lattice thermal conductivity, we obtained a 40% increase of the final maximum ZT value, from ∼1.0 in PbTe to ∼1.4 in (Pb0.93Sn0.07)(Te0.93Se0.07) at 773 K, as shown in Figure 5b. The ZT value obtained in this work is comparable to that in other reported n-type PbTe systems, such as ∼1.4 in PbS-alloyed PbTe,6 ∼1.38 in GeTe-alloyed PbTe,40 ∼1.2 in MgTe-alloyed PbTe,41 ∼1.3 in Ag2Te-alloyed PbTe,42 and ∼1.5 in AgPbmSbTem+2.43 Noticeably, these methods6,40−43 to enhance the thermoelectric performance of n-type PbTe mainly focus on nanostructures to lower lattice thermal conductivity, which also causes strong carrier scattering. Here, it is significant to maintain high carrier mobility to obtain a high power factor in n-type PbTe. The present result provides a promising approach to maintain high carrier mobility by reducing effective mass and avoiding nanostructures in the process of band inversion.

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CONCLUDING REMARKS In summary, we reported that the thermoelectric performance of n-type PbTe can be enhanced by means of utilizing electronic band inversion through Sn and Se co-alloying. It is demonstrated that electronic bands will be sharper and move closer, resulting in lower effective mass and larger carrier mobility, which are favorable for superior power factor in PbTe after Sn and Se co-alloying. Meanwhile, by introducing point defects instead of nanostructures, the lattice thermal conductivity was reduced but could maintain high carrier mobility. After optimizing complex thermoelectric parameters, we acquired a significant improvement in the maximum ZT, increasing from ∼1.0 in PbTe to ∼1.4 in (Pb0.93Sn0.07)(Te0.93Se0.07) at 773 K. Our results open prospects for enhancing thermoelectric performance by utilizing electronic band inversion.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/jacs.8b09029. Experimental details; single Kane band model calculation; XRD patterns of (Pb1−xSnx)(Te1−xSex) (x = 0− 0.11) (Figure S1); temperature dependence of thermal transport properties in (Pb1−xSnx)(Te1−xSex) (Figure S2) (PDF)

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*[email protected] ORCID

Li-Dong Zhao: 0000-0003-1247-4345 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This contribution was supported by National Natural Science Foundation of China under Grant Nos. 51632005, 51571007, and 51772012, and National Key Research and Development Program of China under Grant No. 2018YFB0703600, the Beijing Municipal Science & Technology Commission under Grant No. Z171100002017002, and the Academic Excellence Foundation of BUAA for Ph.D. Students. This work is also 13101

DOI: 10.1021/jacs.8b09029 J. Am. Chem. Soc. 2018, 140, 13097−13102

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DOI: 10.1021/jacs.8b09029 J. Am. Chem. Soc. 2018, 140, 13097−13102