Approaching topological insulating states leads to high thermoelectric

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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 J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.8b09029 • Publication Date (Web): 13 Sep 2018 Downloaded from http://pubs.acs.org on September 13, 2018

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Journal of the American Chemical Society

Approaching

topological

insulating

states

leads

to

high

thermoelectric performance in n-type PbTe Yu Xiao,1 Dongyang Wang,1 Bingchao Qin,1 Jinfeng Wang,2 Guangtao Wang,2 and Li-Dong Zhao1,*

1

School of Materials Science and Engineering, Beihang University, Beijing 100191,

China 2

College of Physics and Materials Science, Henan Normal University, Xinxiang,

453007, China

1

ACS Paragon Plus Environment

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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 cm2V-1S-1 in Pb0.89Sn0.11Te0.89Se0.11 at room temperature, thus in a high power factor. Meanwhile, we found that the lattice thermal conductivity κl can be reduced from ~ 0.77 Wm-1K-1 in PbTe to ~ 0.45 Wm-1K-1 in (Pb0.91Sn0.09)(Te0.91Se0.09) through producing point defects via Sn and Se co-alloying. Coupling reducing lattice thermal conductivity with integration of optimizing effective mass and carrier mobility by a means of electronic band inversion, we obtained a maximum ZT value ~ 1.4 at 773K in n-type (Pb0.93Sn0.07)(Te0.93Se0.07). Keywords: thermoelectric; n-type PbTe; ZT; electronic band inversion

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INTRODUCTION Thermoelectric technology can directly convert heat into electric power without pollutant emission based on 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 interrelationships among these parameters make it challengeable 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, which can enhance Seebeck coefficient through enlarging effective mass m*, however, a high effective mass m* is detrimental to carrier mobility µ. Nanostructuring is an effective method to achieve low lattice thermal conductivity κl and enhance ZT values through scattering phonons,12-13 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 high-performance thermoelectrics. p-type PbTe is the best intermediate temperature thermoelectric material, which has 3



been well developed in last decades. To match its high performance p-type counterpart, n-type PbTe is urgent to be developed. In n-type PbTe, preserving superior carrier mobility is a critical factor to obtain high thermoelectric performance because of its much less complex band structures than p-type PbTe. In order to maintain high carrier mobility in n-type PbTe, it is essential to obtain both lower effective mass and avoid carriers scattering. Recently, topological insulating states achieved in PbTe and PbSe motivate us to enhance the thermoelectric performance of n-type PbTe through Sn and Se co-alloying.14-16 Pb1-xSnxTe could be topological crystalline insulator (TCI) through 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 ~ 0.23 in Pb0.77Sn0.23Se19, the band gap reaches closely to zero, indicating that Se alloying could promote the band inversion of PbTe. During the process of band inversion, approaching topological insulating states, the electronic band structures will become sharper that 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 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 n-type PbTe. A peak ZT of ~ 1.4 at 773K is achieved in n-type (Pb0.93Sn0.07)(Te0.93Se0.07), which is 40% higher than that of Sn/Se-free. 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 defects scattering).

EXPERIMENTAL SECTION Raw materials, Pb, Te, Sb, Sn and Se are loaded into silica tubes under an 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 and maintained at this temperature for 10 h and finally furnace cooling to room temperature. The obtained 4


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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 get densified disk-shaped samples. The phase identification was evaluated by X-ray diffraction (XRD) using powder. Scanning electron microscopy (SEM) with 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 infrared diffuse reflection method with a Fourier transform infrared spectrometer (IRAffinity-1S). Elastic

properties

were

measured

using

ultrasonic

instrument

(Ultrasonic

Pulser/Receiver Model 5058 PR, Olympus, USA). The electrical conductivity and Seebeck coefficient were measures using Cryoall CTA instrument. Thermal diffusivity (D) was acquired with Netzsch LFA457. 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 Supporting Information (SI).

RESULTS AND DISCUSSION Electrical Transport Properties. The n-type PbTe matrix with optimized carrier density

23

was selected to introduce Sn and Se co-alloying. The powder X-ray

diffraction (PXRD) patterns in Figure S1(a) exhibit single phase in cubic rock salt structure without extra peaks. With increasing co-alloying content x, the main peaks gradually shift to high angle that indicates lattice shrink. The calculated lattice parameter in Figure S1(b) shows almost linear decrease with increasing content Sn and Se up to 0.11, which is consistent with Vegard’s law suggesting a complete solid 5



solution formed in the Sn and Se co-alloyed PbTe. The electrical conductivity in all the samples rapidly goes down with increasing temperature in Figure 1(a), presenting a degenerated semiconductor transport behavior. After Sn and Se co-alloying, the room-temperature electrical conductivity firstly 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) sample, and then decreases with increasing co-alloying content, ~ 1610 S/cm in (Pb0.89Sn0.11)(Te0.89Se0.11). From Figure 1(b), all the samples show negative Seebeck coefficient and the absolute value of Seebeck coefficient shows mild variation, denoting an unobvious change of carrier density after Sn and Se co-alloying in PbTe matrix. Combining the slightly decreased electrical conductivity and undistorted Seebeck coefficient, the power factor maintains a relatively high range and the maximum power factor increases from ~ 19.6 µWcm-1K-2 in PbTe to ~ 22.8 µWcm-1K-2 in (Pb0.99Sn0.01)(Te0.99Se0.01), as shown in Figure 1(c). The room-temperature Hall measurement in Figure 1(d) unveils 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 cm2V-1S-1 in PbTe to ~ 251 cm2V-1S-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 are higher than nanostructured n-type PbTe systems,24-26 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 well elucidated by the Pisarenko relationship in the inset of Figure 1(e). Indeed, Figure 1(e) shows that the effective mass in (Pb1-xSnx)(Te1-xSex) sample undergoes a decreasing tendency with increasing Sn and Se co-alloying content, which is related to the electronic band 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 1(f) clearly shows that the carrier mobility values in this work are much higher than 6


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other n-type PbTe samples with nanostructures, namely, ~ 176 cm2V-1S-1 in n-type PbTe-I-In,25 ~ 190 cm2V-1S-1 in n-type PbTe-I with Pb vacancies,27 ~ 93 cm2V-1S-1 in n-type PbTe-La-Ag2Te,24 and ~ 100 cm2V-1S-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 of its much less complex band structures than p-type PbTe.28-30

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), and (f) carrier mobility 7



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-Sb26.

To investigate the band structure modification in (Pb1-xSnx)(Te1-xSex), we conducted optical band gap measurements. Figure 2(a) shows the optical band gap 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) sample. 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 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 to zero when Sn content x achieves to ~ 0.23 in Pb1-xSnxSe19 and ~ 0.40 in Pb1-xSnxTe,17, 32-34 after that, with further increase of Sn alloying content, the band gap opens again, which is schematically shown in Figure 2(b). Since the band inversion caused by Sn alloying will start early in PbSe (Sn = 0.23) than that in PbTe (Sn = 0.40), thus, we believe that the Se alloying will promote the band inversion of PbTe. Density functional theory (DFT) calculations are conducted to further investigate the band structures evolution in (Pb1-xSnx)(Te1-xSex). From pristine Pb27Te27 sample in Figure 2(c) to low Sn and Se co-alloyed Pb26SnTe26Se (∼ 3.7 %) sample in Figure 2(d), no obvious changes in band structures are observed. While in the highly co-alloyed Pb7SnTe7Se (∼ 12.5 %) sample in Figure 2(e) and Pb2Sn2Te2Se2 (∼ 50 %) sample in Figure 2(f), the band gap largely decreases from ~ 0.1 eV in PbTe to nearly zero, and the low conduction and valence band is obviously overlapped forming Dirac cones. The decreasing tendency of 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 lowering the symmetry with respect to PbTe and thus the conduction band minimum (CBM) and valence band maximum 8


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(VBM) folded 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 electronic band structure of PbTe after Sn and Se alloying, therefore, as we discussed in Figures 1 (e) and (f), the effective mass and carrier mobility were calculated based on the single Kane band (SKB) model 29, 35 instead of single parabolic band (SPB) model,35-36 and the calculation details can be found in Supporting Information (SI). As well known, the conduction band shape becomes sharper that will cause low effective carrier mass and high carrier mobility as following relationships:23, 30

 ∂ 2E ( k )  * 2 mb = h    ∂k 2    eτ µ ∝ *0 m

-1

(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 well elucidate the origins of higher carrier mobility, which attributes larger power factors in (Pb1-xSnx)(Te1-xSex).

9



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.

Thermal Conductivity and Microstructures Observation. The total thermal conductivity in Figure 3(a) shows a significant decrease from 3.89 Wm-1K-1 in PbTe to 2.36 Wm-1K-1 in (Pb0.89Sn0.11)(Te0.89Se0.11) at room temperature. The reduction of total thermal conductivity arises from dramatically reduced lattice thermal 10


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conductivity after Sn and Se co-alloying in Figure 3(a). The minimum lattice thermal conductivity is suppressed from ~ 0.77 Wm-1K-1 in PbTe to ~ 0.45 Wm-1K-1 in (Pb0.91Sn0.09)(Te0.91Se0.09) sample. The reduction in lattice thermal conductivity can be well estimated using Callaway model,27, 37 as shown in Figure 3(b). Massive point defects in solid solution can play an essential role to intensify phonon scattering due to size and mass fluctuation in crystal lattice. Owning to significant size difference and mass discrepancy between Te2- (~ 2.21 Å, ~ 127.6 g/mol) and Se2- (~ 1.98 Å, ~ 78.96 g/mol), Pb2+ (~ 1.2 Å, ~ 207.2 g/mol) and Sn2+ (~ 1.12 Å, ~ 118.7 g/mol), it is obvious that Sn substituting in Pb sites contributes more to the reduction of lattice thermal conductivity due to large mass difference.

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

Experimental lattice thermal conductivity values are well consistent with Callaway model, which indicate 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

scanning

electron

microscopy (SEM) and transmission electron microscopy (TEM) analyses are performed on the (Pb0.93Sn0.07)(Te0.93Se0.07). Figure 4(a) shows SEM image of the polished surface. Generally, the surface is relatively flat only with several voids, 11



which indicates the sample is well densified through spark plasma sintering (SPS) process. The corresponding energy dispersive X-ray energy dispersive spectroscopy (EDS) maps illustrate that all elements (Te, Pb, Sn and Se) are distributed homogeneously throughout the sample in Figure 4(b). Figure 4(c) and 4(d) are typical low and high magnification TEM images, respectively. Both the inset diffraction pattern of Figure 4(c) and the high magnification TEM image of Figure 4(d) along [110] direction match with the crystal structure of PbTe, and no splitting additional spots are observed, indicating that the Sn and Se completely forms solid solution in the PbTe matrix.

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

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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 5(a) shows a dramatic enhancement after Sn and Se co-alloying, ~ 20% increase in (Pb0.93Sn0.07)(Te0.93Se0.07) compared with pristine PbTe sample, which mainly comes from the enhanced parameter µ/κl in the insert of Figure 5(a). With the integration of maintained carrier mobility and reduced lattice thermal conductivity, we obtained 40% increase of 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 5(b). The ZT value obtained in this work is comparable to 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 methods

6, 40, 41, 42, 43

to enhance 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 high power factor in n-type PbTe. Present result provides a promising approach to maintain high carrier mobility through reducing effective mass and avoiding nanostructures in the process of band inversion.

Figure 5. Thermoelectric performance in (Pb1-xSnx)(Te1-xSex): (a) quality factor as a function of 13



Sn and Se co-alloying content x, and (d) temperature dependence of ZT values.

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 moving closer, resulting in lower effective mass and larger carrier mobility, which are favorable to superior power factor in PbTe after Sn and Se co-alloying. Meanwhile, through 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 through utilizing electronic bands inversion.

ASSOCIATED CONTENT Supporting Information Experimental details; Single Kane band (SKB) 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); This material is available free of charge via the Internet at http://pub.acs.org.

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AUTHOR INFORMATION Corresponding Author *

[email protected]

ORCID Li-Dong Zhao: 0000-0003-1247-4345 Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS This contribution was supported by National Natural Science Foundation of China under grant Nos. 51632005, 51571007 and 51772012, the Beijing Municipal Science & Technology Commission under Grant No. Z171100002017002, and the Academic Excellence Foundation of BUAA for PhD Students. This work is also 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.

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Approaching topological insulating states leads to high thermoelectric

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