Band inversion induced multiple electronic valleys for high thermoelectric performance of SnTe with strong lattice softening

Journal Pre-proof Band Inversion Induced Multiple Electronic Valleys for High Thermoelectric Performance of SnTe with Strong Lattice Softening Guizhen Xie, Zhi Li, Tingting Luo, Hui Bai, Jinchang Sun, Yu Xiao, Li-Dong Zhao, Jinsong Wu, Gangjian Tan, Xinfeng Tang PII:

S2211-2855(19)31109-7

DOI:

https://doi.org/10.1016/j.nanoen.2019.104395

Reference:

NANOEN 104395

To appear in:

Nano Energy

Received Date: 3 October 2019 Revised Date:

29 November 2019

Accepted Date: 9 December 2019

Please cite this article as: G. Xie, Z. Li, T. Luo, H. Bai, J. Sun, Y. Xiao, L.-D. Zhao, J. Wu, G. Tan, X. Tang, Band Inversion Induced Multiple Electronic Valleys for High Thermoelectric Performance of SnTe with Strong Lattice Softening, Nano Energy, https://doi.org/10.1016/j.nanoen.2019.104395. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.

Band Inversion Induced Multiple Electronic Valleys for High Thermoelectric Performance of SnTe with Strong Lattice Softening Guizhen Xie,1 Zhi Li,1 Tingting Luo,1 Hui Bai,1 Jinchang Sun,1 Yu Xiao,2 Li-Dong Zhao,2 Jinsong Wu,1, Gangjian Tan 1,* and Xinfeng Tang1,* 1. State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Wuhan University of Technology, Wuhan 430070, China 2. School of Materials Science and Engineering, Beihang University, Beijing 100191, China

Corresponding Authors: [email protected] (G. T.), [email protected] (X. T.)

1

Abstract Band engineering has been under development as an efficient method to improve thermoelectric performance. However, except conventional methods like engineering the resonant states or band convergence, there is still no other effective way to engineer the electronic structure. Here, in this study we demonstrate a new mechanism achieved by alloying GeTe and PbTe into SnTe where multiple electronic valleys are introduced due to band inversion effect. The modification of band structure in SnTe leads to considerable enhancement of Seebeck coefficient. In the meanwhile, GeTe/PbTe coalloying leads to significant lattice softening by intense internal stains, arisen from the high density dislocations at the grain boundaries. The lattice softening leads to a low lattice thermal conductivity. In combination with Cd doping for band gap enlargement, a high thermoelectric figure of merit ZT >1.4 is achieved at ~873 K in the sample Sn0.48Cd0.02Ge0.25Pb0.25Te, which is doubled compared to that of pristine SnTe. It is the first example that multiple electronic valleys are introduced into SnTe system via band inversion. This new approach for band structure engineering should be equally applicable to other thermoelectric materials. Keywords: Thermoelectric; Lattice dislocations; Band engineering; Multiple bands

2

1. Introduction Thermoelectric energy conversion technology has potential applications in all-solid-state waste-heat power generation, air conditioning, and spot cooling of electronic devices.[1] Yet its hitherto low conversion efficiency is restricted by the material’s thermoelectric dimensionless figure of merit: ZT=S2σT/κ=S2σT/(κele+κlat), where S is the Seebeck coefficient, σ is the electrical conductivity, T is absolute temperature in Kelvin, and κ is the total thermal conductivity that consists of contributions from electrons (κele) and lattices (κlat). As those transport parameters in solids are strongly interrelated, it is challenging to independently optimize ZT.[2] Recently it has been demonstrated that by converging at least two electronic bands that have comparable energy within a few kBT (kB is Boltzmann constant), it is able to partly decouple the thermoelectric coefficients, leading to improved power factors (PF=S2σ) and enhanced ZTs by the well accepted “band convergence” effect.[3, 4] This effect has been successfully examined in many advanced thermoelectric materials, such as PbTe,[3, 5, 6] PbSe,[7-10] SnTe,[11-16] GeTe,[17, 18] Mg2Si1-xSnx,[4, 19] CoSb3 (Ref. [20]), SnSe[21-23] and so on. A common feature of these materials is that there is a second electronic band in the vicinity of the primary one and by proper doping of guest elements the energy separation of the two bands can be effectively diminished, see the schematic diagram shown in Figure 1(a). Please bear in mind that the degree of band convergence described here is to a large extent determined by the solubility of dopants.[5] This solubility issue becomes particularly important in materials (for example SnTe and PbSe)[8, 12] where the two electronic bands are separated by a large energy gap. Unfortunately, most active dopants for band convergence have very low solubility limit in their host material; for instance, only ~4 mol% Mg is soluble in PbTe.[6] This makes the greatest potential of band convergence not fully fulfilled in those compounds. Here we report a brand new and feasible “band inversion” approach to create multiple electronic valleys in a material that originally has only one single band, leading to substantially boosted thermoelectric performance. Band inversion is usually 3

assumed to arise from the band splitting at the Γ point of the Brillouin zone caused by either spin-orbit coupling (SOC) or lattice strains.[24-26] In the case of band inversion, the exchange of the conduction and valence bands after band crossing leads to two-fold electronic valleys which are beneficial to achieve high Seebeck coefficient, see Figure 1(b). In this study, we successfully utilized “band inversion” principle to introduce multiple electronic valleys in SnTe. We find that, while GeTe or PbTe alloying alone doubles the number of valence bands of SnTe, GeTe/PbTe coalloying in SnTe gives rise to at least three valence bands that are almost converged in energy, resulting in considerably enhanced Seebeck coefficient. To the best of our knowledge, this is the first time that more than two converged electronic bands are reported in SnTe. In addition, it is shown that GeTe/PbTe coalloying significantly softens the lattice of SnTe, leading to much decreased lattice thermal conductivity. As a consequence, a high ZT exceeding 1.4 at 873 K is achieved in the single phase sample Sn0.48Cd0.02Ge0.25Pb0.25Te, which is twice that of pristine SnTe and is also much larger than those of samples with band convergence or resonant states. This research paves a new avenue towards high performance thermoelectric materials with multiple electronic bands. This “band inversion” induced band structure reconstruction approach is also applicable to many other technologically important thermoelectric materials composed of heavy elements, such as Bi1-xSbx, Bi2Te3, half-Heusler alloys, etc.

2. Experimental procedures 2.1 Synthesis Sn1-2xGexPbxTe (x=0-0.25) and Sn0.5-yCdyGe0.25Pb0.25Te (y=0.01, 0.02 and 0.03) samples were prepared by mixing stoichiometric amount of high purity elements (4N or higher) in silica tubes under vacuum (< 10-4 Torr) in sealing line. The element mixtures were then melted inside computer-controlled box furnace (KSL-1200X, Kejing Inc., China) at 1323 K for 8 h and subsequently quenched in supersaturated 4

salt water. The obtained ingots were ground into fine powders, which later were loaded into 15 mm diameter graphite dies and densified in vacuum by spark plasma sintering (SPS, Ed-PAS-III, Japan) at 823 K for 5 min under a uniaxial pressure of 40 MPa.

2.2 Characterization Powder X-ray diffraction (XRD) analysis (PANalytical-Empyrean; Cu, Kα) was used to identify phase compositions. Electron probe micro-analysis (EPMA, JEOL JXA-8230) was utilized to detect the homogeneity of samples. High resolution transmission electron microscopy (HRTEM) measurements were carried out utilizing Talos F200S equipment (Talos F200S, FEI) equipped with energy dispersive spectroscopy (EDS) capabilities. The Seebeck coefficients (S) and electrical conductivity (σ) were simultaneously recorded under low-pressure helium atmosphere from 300 K to 873 K with CTA-3 (Cryoall, Beijing) apparatus. The total hermal conductivity (κ) was calculated according to the formula of κ = λ•ρ•Cp, where λ is the thermal diffusion coefficient (Figure S1) measured from 300 K to 873 K by laser flash diffusivity methods (LFA-457, Netzsch), the density (ρ) is gauged by the Archimedes method, and Cp is heat

capacity

estimated

from

the

relation

Cp/kB

per

atom

=

3.07

+

(4.7×10-4×(T-300)).[3, 5, 6] The lattice thermal conductivity (κlat) was obtained by subtracting κele from κ , κlat = κ - κele, where κele was calculated using Wiedemann-Franz law: κele =LσT (L is Lorentz number estimated by the empirical formula L = 1.5 + exp( −

S 116

) , S in µV/K and L in 10-8 WΩK-2, Figure S2).[27] Errors

in calculating ZT from thermal diffusivity (5%), mass density (3%), heat capacity (5%), electrical conductivity (10%) and Seebeck coefficient (3%) are estimated to be ~15%. The Hall coefficients (RH) were measured by physical property measurement system (PPMS-9, Quantum Design). The charge carrier concentration (p) and mobility (µH) are calculated by: p = 1/(e•RH) and µH = σ/ne, respectively. Raman 5

measurements (HORIBA, LabRAM HR Evolution) were performed with 633 nm excitation laser in the frequency range from 250 – 50 cm-1 with 0.8 cm-1 resolution.

2.3 Computational details The first-principles calculations are carried out with the Vienna ab initio simulation package (VASP) which implements the projector augmented-wave (PAW) method.[28] Generalized gradient approximation of Perdew-Burke-Ernzerhof (GGA-PBE)[29] is taken as electron exchange-correlation function. The plane-wave cutoff energy is set as 400 eV, at which Ge 3d electrons, Pb 5d electrons, Sn 4d electrons and Te 5s electrons are considered as valent electrons. The crystal structure of SnTe primitive cell is optimized with a k-mesh of 9×9×9. The energy convergence criterion for self-consistency is 10-8 eV, and all the atoms are fully relaxed to their equilibrium position until the Hellmann-Feynman forces between them are less than 0.005 eV/Å. To simulate the doping situation in the experiment, we build a 2×2×2 supercell of Sn8Te8 and replace two Sn atoms with two Ge or two Pb atoms or four Sn atoms with two Ge and two Pb atoms to create Sn6Ge2Te8, Sn6Pb2Te8 and Sn4Ge2Pb2Te8 compounds, respectively. It is necessary to declare that in Sn4Ge2Pb2Te8 compound, there are two types of configuration: two Ge or Pb atoms occupy the (i) nearest-neighboring sites (config. A) or (ii) the second nearest-neighboring sites (config. B), See Figure S3. The formation energy of config. A is slightly lower than that of config. B, but very similar band structures are obtained under the two different configurations. A high symmetric path in first Brillouin zone proposed by Wahyu Set yawan and Stefano Curtarolo[30] is adopted when we perform band structure calculation. The spin-orbital coupling (SOC) is taken into consideration throughout the calculation.

3. Results and discussion 3.1 Phase compositions and microstructures Figures 2(a) and (b) shows the powder XRD patterns of Sn1-2xGexPbxTe 6

(x=0-0.25) samples before and after SPS, which show no significant difference. All diffraction peaks can be well indexed to the rocksalt SnTe phase. The lattice parameters shown in Figure 2(c) decrease linearly with increasing x by following a Vegard’s law. It suggests a solid solution behavior between SnTe and GeTe/PbTe, the crystal structure of which is schematically displayed in Figure 2(d). Indeed, the BSE image of x=0.25 sample shows no apparent phase separation at least at the micron scale, and all constitute elements distribute evenly in the matrix as revealed by the EDS mappings, Figures 2(e) and (f). Note that the color contrast seen in Figure 2(c) is mainly caused by the slight surface irregularity of the sample during polishing. It does not reflect any composition inhomogeneity. We further carried out transmission electron microscopy (TEM) study to investigate the homogeneity of x=0.25 sample at nanoscale. Figure 3(a) shows a typical TEM image at low magnification where dense dislocation arrays as illustrated by the arrowheads are clearly present. While the lattice distortions within the dislocation cores can be seen in Figure 3(g) which is an inverse fast Fourier transform (iFFT) image obtained from the area outlined by the red square in Figure 3(e). Similar phenomenon is observed previously in Bi2Te3 alloys,[31] Mg2Si-based compounds[32] and lead chalcogenides[33, 34]. These dislocations, which likely reflect the intense internal lattice strains inside the materials caused by high alloying fraction, are supposed to effectively scatter mid-frequency heat-carrying phonons through the dislocation cores and strain fields.[35, 36] The enlarged TEM image of the area highlighted by the yellow frame in (a) suggests that those dislocations appear both at the grain boundaries and inside the grains, as shown in Figure 3(b). The scanning transmission electron microscopy (STEM) collected by the high angle angular dark field (HAADF) detector of yellow area in (a) shows little Z-contrast, except the difference in the sample thickness (thickness variation possibly induced during TEM sample preparation, in Figure 3(c)). In combination with the EDS mappings shown in Figures 3(d1–d4), we can conclude that the sample composition is highly homogeneous and there is no impurity or secondary phase. This again confirms the solid solution feature of Sn1-2xGexPbxTe alloys. Figure 3(e) shows a HRTEM image of 7

the blue area highlighted in (b) where there is an interface within the crystal oriented along the [001] zone axis. The crystal orientation is identified by the corresponding selected-area electron diffraction (SAED) patterns where only one set of diffraction spots is revealed as shown in Figure 3(f). The interface is formed by the dislocations arrays as shown in Figure 3(g). Thus, the scattering of charge carriers at these coherent interfaces should be negligibly small.[5, 37, 38]

3.2 Band inversion induced multiple electronic valleys in SnTe The temperature dependent electrical conductivity and Seebeck coefficient for Sn1-2xGexPbxTe (x=0-0.25) are shown in Figures 4(a) and (b), respectively. σ decreases while S increases gradually with increasing temperature up to 873 K, indicative of degenerate semiconductors. Regardless of temperature, there is a clear decline trend of σ with increasing x, while S has an opposite tendency. For example, at 300 K, the values of σ are ~7500 S/cm and ~2560 S/cm for x=0 and 0.25 samples, respectively; on the other hand, S increases from ~9 µV/K for pristine SnTe to ~48 µV/K for the x=0.25 sample, which is more than five times enhancement. To shed light on the influence of GeTe/PbTe coalloying on the electrical properties of SnTe, we carried out Hall measurements and plot the room temperature Seebeck coefficients as a function of charge carrier concentration (p), Figure 4(c). The solid curve in Figure 4(c) is the theoretical Pisarenko plot for p-type SnTe based on a two-valence-band-model,[39] the reliability of which has been well validated by numerous experimental data of doped SnTe from earlier reports.[8, 11, 13] We note that while the S values of low alloying content samples (x=0 and 0.05) are in good agreement with the theoretical prediction, the rest of samples have significantly higher Seebeck coefficients than predicted by the curve. Figure 4(d) compares the Seebeck coefficients of several SnTe-based thermoelectric materials[12, 39-41] with the same p=~4×1020 cm-3 around room temperature. Among them, pristine SnTe[41] displays the lowest S of ~25 µV/K. Mg/Mn doping boosts the Seebeck coefficient of SnTe to ~38/~37 µV/K because of the well-accepted band convergence effect.[12, 40] Indium dopant introduces resonant 8

states[39] inside the valence band of SnTe, leading to a sharp increase of density of states near the Fermi level. Therefore, In-doped SnTe possesses the highest Seebeck coefficient of 61 µV/K. The Seebeck coefficient of our GeTe and PbTe coalloyed SnTe is ~48 µV/K, which is much larger than that of Mg/Mn doped SnTe, though lower than that of In-doped one. These results suggest that GeTe/PbTe alloying has a significant impact on the electronic band structure of SnTe. We then conduct first-principles calculations to investigate the band structures evolution in Sn1-2xGexPbxTe alloys, Figure 5. It is demonstrated that pristine SnTe is a very narrow gap semiconductor dominated by one single valance band locating at Γ point in the Brillouin zone, which is consistent with earlier studies,[11, 12, 15, 42] Figure 5(a). Alloying with GeTe or PbTe clearly closes the band gap of SnTe, resulting in the semimetal behavior in the band structures, Figures 5(b) and (c). More importantly, we note that the number of valence band maxima (VBM) becomes two (instead of one) in Sn0.75Ge0.25Te and Sn0.75Pb0.25Te, one along the Γ-L and the other along the Γ-X directions. Such a VBM splitting phenomenon in mixed alloys is attributed to the well-known “band inversion” effect,[26, 43-45] namely, the valence and the conduction bands are inverted (in PbTe or GeTe) from those of SnTe, see the schematic picture shown in Figure 1(b). As shown in Figure 5(d), GeTe and PbTe coalloying makes the electronic band structure of SnTe even more complex than the single component alloying. There are at least three VBMs very close to each other. We denote them as VBM1, VBM2 and VBM3 respectively in the order of energy, see inset of Figure 5(d). The energy gap between VBM1 and VBM2 is only ~0.03 eV, much smaller than the value of ~0.15 eV reported in the case of PbTe at room temperature[46, 47]. In addition, the energy gap between VBM1 and VBM3 is also very small at ~0.04 eV. Such small energy gaps are easily crossed by the Fermi level as the hole doping approaches ~4×1020 cm-3, Figure 4(c). Therefore, it is not surprising that GeTe and PbTe coalloyed SnTe has higher Seebeck coefficients than Mg/Mn doped one because of the band inversion induced multiple electronic valleys. 9

3.3 Significant lattice softening in GeTe and PbTe coalloyed SnTe GeTe and PbTe coalloying not only considerably modifies the electronic band structure of SnTe but also causes strong internal strains, leading to significant lattice softening and much declined lattice thermal conductivity. Figure 6(a) shows the total and lattice thermal conductivities of Sn1-2xGexPbxTe (x=0-0.25), both of which decrease with increasing temperature and doping concentration. There are generally two phonon engineering mechanisms in crystalline materials: (i) lattice softening as a result of decrease in the phonon speed (υp), and (ii) phonon scattering because of changes in the direction of the phonon velocity vector without a necessary change in υp.[48] While the latter has been widely studied in many advanced thermoelectric materials[37, 49, 50], the former is relatively underexplored but actually seems more efficient in decreasing κlat of solids especially above Debye temperature (θD), as recently demonstrated in IV-VI compounds[48, 51]. This is true because of the approximate cubic dependence of κlat on υp (details can be found in our recent study, ref.[48]) at sufficiently high temperatures (T > θD) where phonon–phonon scattering becomes predominated. We measured the room temperature sound velocities (υs) of four selected Sn1-2xGexPbxTe samples with x=0, 0.10, 0.20 and 0.25, which are 1946, 1828, 1670 and 1500 m/s, respectively. There is an apparent decline trend of υs with increasing coalloying content of GeTe and PbTe in SnTe, indicating significant lattice softening. If we use υs as an estimate of υp, the temperature dependent κlat values of Sn0.8Ge0.1Pb0.1Te, Sn0.6Ge0.2Pb0.2Te and Sn0.5Ge0.25Pb0.25Te can be simulated by normalizing to the SnTe control sample and considering the cubic dependence of υs on κlat as stated above. The simulated dotted curves are in excellent agreement with the experiment solid lines for all the three samples, Figure 6(b). This means that lattice softening is almost completely responsible for the reduction of κlat in GeTe and PbTe coalloyed SnTe. In fact, this lattice softening effect in coalloyed SnTe arises from a significant increase in internal strain. Figure 6(c) shows the evaluation of internal strain of the 10

pellet samples by Williamson-Hall analysis of XRD peak broadening[52]. β is the integral breadth of the diffraction peak at angle θ after correcting for the instrument broadening. The slope of βcos(θ) versus sin(θ) is a direct measure of magnitude of internal strain present in the samples. It is clearly seen from the slopes that higher GeTe and PbTe coalloying fraction considerably leads to larger internal strains in SnTe. The strong internal strains of Sn1-2xGexPbxTe alloys are actually reflected in their microstructures with a high density of dislocations, see the related discussions in Figure 3. To better understand the phonon scattering mechanism Sn1-2xGexPbxTe, we analyzed their Raman spectra, Figure 6(d). Two Raman sensitive phonon vibration modes are observed in the wavenumber range from 50 to 250 cm-1, which is in line with an earlier study[53]. The first mode appears around 124 cm-1 which is ascribed to the Raman peak of longitudinal optical phonons near the Γ point; the second one locating at ~147 cm-1 is assigned to the transverse optical phonons near the X point.[54] When SnTe is coalloyed with GeTe and PbTe, the most notable change of the Raman spectra is the shift of peaks toward the low-frequency side (red shift effect). Under the classical vibrational model[55], the vibrational frequency of a phonon f relates to force constant of a bond (K) and reduced mass of the compound (M) through the expression: f ~ (K/M)1/2. When SnTe is equally replaced by GeTe and PbTe, the resultant Sn1-2xGexPbxTe alloys have negligibly small mass changes as compared to SnTe itself. For example, the mole mass of Sn0.5Ge0.25Pb0.25Te is 256.9 g/mol, which is only ~4% larger than that of SnTe (246.3 g/mol). We speculate that the red shift of Raman sensitive phonon vibration modes is primarily contributed by the weakened chemical bonding in SnTe by the simultaneous introduction of GeTe and PbTe. This kind of lattice softening effect can significantly reduce the phonon group velocity, resulting in low lattice thermal conductivity.[48] Due to Seebeck coefficient enhancement by multiple electronic valleys and thermal conductivity reduction by lattice softening, GeTe and PbTe coalloying considerably boosts the thermoelectric performance of SnTe, Figure 7. The highest ZT approaches 1.2 in the sample Sn0.5Ge0.25Pb0.25Te at 875 K, which is almost doubled in 11

comparison with that of pristine SnTe. However, we should note that severe bipolar conduction might be at play in our Sn1-2xGexPbxTe samples because of their “semimetal-like” electronic band structures (Figure 5), which would unavoidably deteriorate their thermoelectric properties, especially at elevated temperatures. We expect that even higher ZT values are attainable in Sn1-2xGexPbxTe alloys if their band gap can be effectively engineered. In view of this, below we proceed to dope Sn1-2xGexPbxTe with Cd for the purpose of band gap enlargement.

3.4 Band gap enlargement of Sn1-2xGexPbxTe by Cd doping Up to 3 mol% Cd was doped into Sn0.5Ge0.25Pb0.25Te without introducing any noticeable impurity phase in powder XRD, Figure 8(a). Infrared absorption spectra for Sn0.5-yCdyGe0.25Pb0.25Te show that the absorption edge shifts towards higher energy with y increasing from 0 to 0.03, Figure 8(b), indicating an increase of optical band gap and the successful substitution of Sn by Cd. In general, the hole density (p) estimated from Hall measurement decreases with increasing doping concentration of Cd till y=0.02. Figure 8(c). We speculate that the decline of p in Sn1-2xGexPbxTe upon Cd doping is attributed to the suppression of Sn vacancies by enlarged band gap. It is also worth noting that y=0.02 and 0.03 samples have quite close values of p, indicating that impurity phase might emerge at doping levels of y > 0.02, though it cannot be detected by XRD because of the low volume fraction. In the meantime, the Hall mobilities (µH) roughly increase with increasing y (Figure 8(d)) because of the decreased population of charge carriers which scatter against each other. The temperature dependent electrical conductivity and Seebeck coefficient for Sn0.5-yCdyGe0.25Pb0.25Te (y=0-0.03) are shown in Figure 9(a). With increasing doping fraction of Cd, there is a slight decrease of σ, from 2560 S/cm for y=0 to 1950 S/cm for y=0.03 at 300 K, probably due to the decline of p (Figure 8(c)). On the other hand, S is enhanced by Cd doping in Sn0.5Ge0.25Pb0.25Te with the highest value approaching 230 µV/K for y=0.02 sample at 873 K. The saturation of Seebeck coefficient in y=0.03 sample is attributed to the presence of impurity phase. We plot the room temperature Seebeck coefficient of Sn0.5-yCdyGe0.25Pb0.25Te as a function of hole 12

concentration and compare the data with the theoretical Pisarenko plot[39] of pristine SnTe, Figure 9(b). It is shown that all samples display much higher values of S than suggested by the theoretical curve. For instance, when p is in the range of 4-5×1019 cm-3, the expected S of SnTe should be around 10 µV/K at 300 K; while in reality, our y=0.02 and 0.03 samples have S values above 50 µV/K, five to six times larger than the prediction. This unambiguously suggests that the multiple electronic valleys in Sn1-2xGexPbxTe are well preserved after the incorporation of Cd, contributing to enhanced Seebeck coefficients, although we have difficulties (ultra large supercell and many possible lattice configurations) in precisely calculating the electronic band structure of Cd-doped Sn1-2xGexPbxTe. Figure

9(c)

shows

the

total

and

lattice

thermal

conductivities

of

Sn0.5-yCdyGe0.25Pb0.25Te (y=0-0.03) as a function of temperature. κ is suppressed by doping Sn0.5Ge0.25Pb0.25Te with Cd, largely due to the decreased electrical conductivity. There is also a slight decrease of κlat with increasing y, because Cd dopant introduces more point defects that scatter heat-carrying phonons. Generally speaking, for high-quality compounds dominated by the anharmonic phonon-phonon (Umklapp) scattering process, κlat can be estimated by the following equation[56, 57]:

mυs 3 1 κ lat = C 2 3 2 Ω γ T

(1)

where C is a fixed constant, m and Ω are the average atomic mass of constituent atoms and the average atomic volume of each atom, respectively, and γ is the Grüneisen parameter. In Figure 9(d), we plot the lattice thermal conductivity of Sn0.5-yCdyGe0.25Pb0.25Te (y=0 and 0.01) as a function of 1000/T. It is shown that for both two samples κlat vs. 1000/T well follows a linear relationship before onset of bipolar diffusion, demonstrating that κlat is dominated by Umklapp scattering. We also note that Cd doping delays bipolar diffusion and decreases the value of bipolar thermal conductivity (κbip). This is reasonable because κbip is sensitive to the band gap (Eg) through the relation[58, 59]: 13

κ bip = ΛT n exp(−

Eg 2kBT

)

(2)

In Eq. (2), Λ and n are two adjustable parameters and kB is the Boltzmann constant. Obviously, the enlarged Eg by doping Cd in Sn0.5Ge0.25Pb0.25Te helps reduce κbip. The ZT values of Sn0.5-yCdyGe0.25Pb0.25Te (y=0-0.03) as a function of temperature are displayed in Figure 10(a). Cd doping significantly enhances the thermoelectric performance of Sn0.5Ge0.25Pb0.25Te, especially at elevated temperatures where bipolar diffusion becomes highly relevant. The highest ZT of ~1.42 at ~873 K is achieved in the sample with y=0.02, which is ~18% improvement over the y=0 sample because of the suppression of bipolar diffusion. This value is also significantly higher than those of pristine SnTe (~0.7 at 873 K), Sn1-xInxTe with resonant states (~0.8 at 867 K)[11], and Sn1-xMgxTe with conventional band convergence (~1.1 at 859 K)[40], Figure 10(b). Table 1 summarizes the recent advances of SnTe-based thermoelectric materials, particularly those with band convergence or resonant states. It is very straightforward that the ZT value over 1.4 achieved in this study is among the best results reported so far. We anticipate that even higher performance can be obtained in the future by optimizing GeTe/PbTe ratio.

4. Concluding remarks In summary, we propose the reconstruction of electronic band structures by virtue of band inversion to achieve high thermoelectric performance in bulk materials. This is demonstrated in SnTe alloyed with GeTe and PbTe, where multiple electronic valleys and high Seebeck coefficients are verified both theoretically and experimentally. Moreover, GeTe/PbTe alloying causes significant softening of SnTe lattices and reduces the sound velocity, giving rise to much declined lattice thermal conductivity. In addition to the suppressed bipolar diffusion by band gap enlargement through Cd doping, a high ZT > 1.4 at ~873 K is attained in the sample Sn0.48Cd0.02Ge0.25Pb0.25Te, outperforming many other SnTe-based thermoelectric materials even when resonant states or band convergence is introduced. This study highlights the potential of engineering the band structures of solids in a more feasible 14

manner.

Acknowledgements We would like to acknowledge the financial support from the Natural Science Foundation of China (Grant No. 11804261) and “the Fundamental Research Funds for the Central Universities (WUT: 2019IVA068 and 2019IVB049)”. L. Z. acknowledges the financial support from the Natural Science Foundation of China (Grant No. 51772012) and Beijing Natural Science Foundation (JQ18004).

Appendix A. Supporting information Supporting Information Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.nanoen.XXXX.XX.XXX.) Author Information *Corresponding Author: [email protected] (G.T.); [email protected] (X.T.)

15

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19

Table 1. Recent advances of SnTe-based thermoelectric materials.

reference

dopant

11

In&Cd

band structure modification

microstructure engineering

peak ZT

synergy of resonant states

point defect + CdS nanostructuring

1.4@923 K

& band convergence 12

Mn

band convergence

point defect + MnTe nanostructuring

1.3@900 K

13

Mn&Cu

band convergence

interstitial defects

1.6@900 K

14

Ag&In

n/a

1@856 K

synergy of resonant states & band convergence 15

Cd

band convergence

point defect + CdS nanostructuring

1.3@873 K

39

In

resonant states

point defect + grain size refinement

1.1@873 K

40

Mg

band convergence

n/a

1.2@860 K

41

In

resonant states

lattice vacancies

1.1@923 K

This study

Ge&Pb

band inversion induced multiple electronic valleys

n/a

1.4@873 K

20

Figure Captions Figure 1. Schematic diagram of (a) band convergence and (b) band inversion. Figure 2. Powder XRD patterns of Sn1-2xGexPbxTe (a) before and (b) after SPS. (c) Room temperature lattice constants as a function of x. (d) Schematic crystal structure of Sn1-2xGexPbxTe. (e) Back-scattered electron image of x=0.25 sample and (f) its EDS mappings. Figure 3. (a) Low magnification TEM image of Sn0.5Ge0.25Pb0.25Te. (b) A zoom-in view and (c) the corresponding HAADF-STEM image as well as EDS mappings (d1: Te; d2: Sn; d3: Ge; d4: Pb) of the yellow area highlighted in (a). (e) HRTEM image of the blue area highlighted in (b). (f) Electron diffraction patterns of the yellow area highlighted in (a) along [001] zone axis. (g) iFFT image of the red area highlighted in (e). Figure 4. (a) Electrical conductivity and (b) Seebeck coefficient of Sn1-2xGexPbxTe as a function of temperature. (c) Carrier concentration dependent Seebeck coefficients for Sn1-2xGexPbxTe at room temperature. The solid curve is theoretical Pisarenko plot for SnTe.[39] (d) Comparison of Seebeck coefficients of several doped SnTe[12, 39-41] at the same hole density of 4×1020 cm-3 at 300 K. Figure 5. Theoretical electronic band structure calculations for (a) SnTe, (b) Sn0.75Ge0.25Te, (c) Sn0.75Pb0.25Te and (d) Sn0.5Ge0.25Pb0.25Te. Inset of (d) is a zoom-in view of the blue area to get more details in the vicinity of the valence band maxima. Figure 6. (a) Temperature dependent total and lattice thermal conductivities of Sn1-2xGexPbxTe. (b) Comparison of lattice thermal conductivities between experimental results (solid curves) and fitted values (dotted curves) for x=0.1, 0.2 and 0.25 samples. (c) Williamson-Hall analysis of XRD peak broadening. (d) Raman spectra for x=0, 0.1 and 0.2 samples. Figure 7. ZT values as a function of temperature for Sn1-2xGexPbxTe. Figure 8. (a) Powder XRD patterns, room temperature (b) infrared absorption spectra, (c) carrier concentration and (d) mobilities of SPSed Sn0.5-yCdyGe0.25Pb0.25Te pellets. Figure 9. (a) Electrical conductivity and Seebeck coefficients as a function of temperature for Sn0.5-yCdyGe0.25Pb0.25Te. (b) Room temperature Seebeck coefficient versus carrier concentration for y=0-0.03 samples. The solid curve is theoretical Pisarenko plot for SnTe. The arrow indicates a remarkable enhancement of Seebeck coefficient. (c) Temperature dependent total and lattice thermal conductivities for Sn0.5-yCdyGe0.25Pb0.25Te. (d) Lattice thermal conductivity as a function of 1000/T for y=0 and y=0.1 samples with similar carrier concentration. The solid lines show linear relationship between κlat and 1/T. Figure 10. (a) ZT values as a function of temperature for Sn0.5-yCdyGe0.25Pb0.25Te. (b) Comparison of ZT values among several best performing SnTe-based compounds in the literatures[11, 40].

21

Figure 1

22

Figure 2

23

Figure 3

24

Figure 4

25

Figure 5

26

Figure 6

27

Figure 7

28

Figure 8

29

Figure 9

30

Figure 10

31

Guizhen Xie received his Bachelor of Engineering on Materials Physics from Wuhan University of Technology (WUT) in 2018. He then conducted one-year research assistant program on thermoelectric materials under the supervision of Prof. Gangjian Tan at WUT and now is working as a research assistant at Institute of physics, Chinese Academy of Science. His research interests include designing high performance thermoelectric materials and exploring effective methods to improve electrochemical properties on Na-ion batteries.

Zhi Li is a phD candidate studying thermoelectric materials under the joint supervision of Prof. Xinfeng Tang at WUT and Prof. Mercouri G. Kanatzidis at Northwestern University, Evanston. He received his bachelor degree in materials science and engineering from WUT in 2016. His research involves ab initio design and analysis of advanced thermoelectric materials.

Tingting Luo is now a PhD candidate working on thermoelectric materials synthesis and characterization supervised by Prof. Xinfeng Tang at Wuhan University 32

of Technology. She received her Master degree from WUT in 2012. Her research interests include high entropy alloys and their potential as high performance thermoelectric materials.

Hui Bai is currently a PHD student working on thermoelectric materials under the supervision of prof. Xinfeng Tang and electron microscopy co-supervised by prof. Jinsong Wu at WUT. He received his B.E degree of materials science from WUT in 2017. His research interests focus on the study of thermoelectric materials in electron microscopy.

Jinchang Sun is currently a PhD student working on thermoelectric materials under the supervision of Prof. Xinfeng Tang at WUT. He received his B.E. degree of materials science from WUT in 2018. His research interests focus on design and optimization of advanced thermoelectric materials.

Yu Xiao is currently a postdoctoral fellow at School of Materials Science and Engineering in Beihang University. He obtained his bachelor degree from the Harbin University of Science and Technology in 2013 and PhD degree in materials science 33

from Beihang University in 2019. His research interests mainly focus on nanostructure design and performance optimization in thermoelectric materials.

Dr. Li-Dong Zhao is a full professor of the School of Materials Science and Engineering at Beihang University, China. He received and his Ph.D. degree from the University of Science and Technology Beijing, China in 2009. He was a postdoctoral research associate at the Université Paris-Sud and Northwestern University from 2009 to 2014. His research interests include electrical and thermal transport behaviors in the

compounds

with

layered

structures.

Group

website:

http://shi.buaa.edu.cn/zhaolidong/zh_CN/index.htm

Jinsong Wu earned his Ph.D. degree from the Department of Materials Science and Engineering at Dalian University of Technology in 1998. He is currently a professor and executive director of Nanostructure Research Centre at Wuhan University of Technology. Wu’s research interests include transmission electron microscopy, electron tomography, in-situ transmission electron microscopy and nanomaterials for energy storage.

34

Dr. Gangjian Tan is a full professor of materials science at Wuhan University of Technology, China. He received his Ph.D. degree from WUT in 2013. Following that, he worked as a postdoctoral research fellow at Northwestern University, Evanston till 2018. He is interested in the understanding of electron, phonon and ionic transport behaviors in solids for energy conversion and storage.

Prof. Xinfeng Tang received his Ph.D. from Tohoku University in 2000. He joined in Wuhan University of Technology as a full professor in April of 2001. He has been a Chair Professor of materials science since 2011. He is a Fellow of the American Physical Society and Royal Society of Chemistry. His current research focuses on advanced thermoelectric materials and related applications.

35

Reconstruction of electronic band structure has been demonstrated in SnTe through band inversion Multiple electronic valleys in SnTe contributes to high Seebeck coefficient Strong lattice dislocations induced by GeTe and PbTe coalloying in SnTe lead to much suppressed thermal conductivity A high ZT>1.4 was realized at 873 K in SnTe-based thermoelectric materials

Declaration of interests

□√ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: