Indium substitution effect on thermoelectric and optical properties of Sn1−xInxSe compounds

Accepted Manuscript Indium substitution effect on thermoelectric and optical properties of Sn1−xInxSe compounds Jin Hee Kim, Suekyung Oh, Yun Min Kim, Hyeon Seob So, Hosun Lee, Jong-Soo Rhyee, Su-Dong Park, Sung-Jin Kim PII:

S0925-8388(16)31327-5

DOI:

10.1016/j.jallcom.2016.04.308

Reference:

JALCOM 37527

To appear in:

Journal of Alloys and Compounds

Received Date: 6 January 2016 Revised Date:

27 April 2016

Accepted Date: 28 April 2016

Please cite this article as: J.H. Kim, S. Oh, Y.M. Kim, H.S. So, H. Lee, J.-S. Rhyee, S.-D. Park, S.-J. Kim, Indium substitution effect on thermoelectric and optical properties of Sn1−xInxSe compounds, Journal of Alloys and Compounds (2016), doi: 10.1016/j.jallcom.2016.04.308. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. 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.

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Indium substitution effect on thermoelectric and optical properties of Sn1−x InxSe compounds

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Jin Hee Kima , Suekyung Oha , Yun Min Kima , Hyeon Seob Soa , Hosun Leea , Jong-Soo Rhyeea,∗ , Su-Dong Parkb , and Sung-Jin Kimc a

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Department of Applied Physics and Institute of Natural Sciences, Kyung Hee University, Yongin 17104, Korea b Advanced Electrical Materials Group, Korea Electrotechnology Research Institute, Changwon 51543, Korea c Department of Chemistry and Nano Science, Ewha Womans University, Seoul, 03760, Korea

Abstract

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Recent investigations of the high thermoelectric figure-of-merit ZT of 2.6 for SnSe crystalline compound demonstrated the state-of-the-art highest thermoelectric performance in spite of the high ZT value in a narrow temperature range and along a specified crystallographic direction. We investigated the thermoelectric properties of polycrystalline Sn1−x Inx Se (x = 0.0, 0.01, 0.05, and 0.1) compounds and the optical properties of single crystalline compounds. Sn1−x Inx Se exhibits increased electrical resistivity, an increase in the Seebeck coefficient and band gap energies, and a significant decrease in the Hall mobility with an increase in the In-doping concentration, whereas the Hall carrier density does not changed significantly. These abnormal results and the decrease in the lattice volume with an increase in the In-doping concentration strongly imply the existence of band renormalization by In 4dand Se 4p-orbital hybridization. We argue that the significant flat bands by band renormalization induce significantly decreased Hall mobility and increases in the electrical resistivity and Seebeck coefficient, resulting in the deterioration of the thermoelectric properties. Keywords: Thermoelectric, SnSe, Hybridization, Band renormalization

Preprint submitted to Journal of Alloys and Compounds

April 27, 2016

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1. Introduction

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Thermoelectricity can convert waste heat into electricity and can transport heat by applying electric bias, which can be applied to waste heat power generation and environmentally friendly solid-state cooling technologies. Thermoelectricity has been intensively investigated in order to obtain high thermoelectric energy conversion efficiency. The thermoelectric efficiency depends on the dimensionless figure-of-merit ZT , which is defined by the relationship of ZT = S 2 σT /κ, where S, σ, T , and κ are the Seebeck coefficient, electrical conductivity, absolute temperature, and thermal conductivity, respectively. State-of-the-art high ZT materials have been competitively reported recently. Examples include grain-boundary-controlled Bi0.5 Sb1.5 Te3 (ZT = 1.86 at 320 K)(1) and PbTe-based compounds for thermoelectric cooling near room temperature and for energy harvesting in the mid-temperature range, respectively. By doping and structural modifications, the ZT values of PbTe-based compounds have been increased steadily, such as Tl-doped PbTe (1.5 at 773 K)(2), PbTe1−x Sex (x = 0.015, 1.8 at 850 K)(3), nanoand micro-sized texture-controlled Na-doped PbTe (2.0 at 773 K)(4), and SrTe/Na-doped PbTe (2.2 at 915 K)(5) as p-type materials for power generation. Recently, as a Pb-free thermoelectric material, SnSe was reported to have an extremely high ZT value of 2.6 at 923 K along the c-axis crystallographic orientation due to its extremely low thermal conductivity(6). However, a high ZT is observed only in a narrow temperature range in single-crystalline compound along the c-axis direction. Therefore, the temperature range with a high ZT value should be widened, especially in a polycrystalline compound, for practical applications. As part of this effort, many Sn-based chalcogenide compounds have been investigated, with some showing promising thermoelectric properties. Examples include p-type Cd-/In-co-doped SnTe (1.4 at 923 K)(7) and n-type Idoped SnSe (1.0 at 773 K)(8). Sintered polycrystalline SnSe shows a very low carrier concentration (1.1∼3.6)×1017 cm−3 compared to its optimized carrier concentration at room temperature(9; 10). In an effort to increase the carrier concentration, several doping studies of SnSe have been conducted. While Te-doping in SnSe1−x Tex (x = 0.0625) decreases the electrical conductivity by decreasing the carrier concentration(11), Ag-doping in SnSe increases the electrical conductivity, resulting in an enhancement of ZT for Ag 1 % and 3 % doped compounds(12). 2

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In this paper, we investigate the In-doping effect on the polycrystalline compound Sn1−x Inx Se, as indium can cause hole doping. Contrary to our expectations, In doping decreases the carrier concentration and increases the energy band gap of SnSe. We argue that the unconventional behaviors of electrical transport and the optical properties are related to the existence of band renormalization by orbital hybridization. 2. Experimental Details

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The polycrystalline compounds of Sn1−x Inx Se (x = 0.0, 0.01, 0.05, and 0.1) were prepared by direct melting and hot press sintering with pure elements of Sn (99.999 %), In (99.999 %), and Se (99.999 %). These elements were mixed in an evacuated quartz ampoule under a high vacuum (≤ 10−5 torr). The ampoules were slowly heated to 1,223 K then held at this temperature for 48 hours, after which they were slowly cooled to room temperature. The ingots were pulverized and sintered by an evacuated (≤ 10−3 torr) hot press method at a temperature of approximately 850 K under a uniaxial pressure of 70 MPa for 1 hour. The densities of the obtained pellets ranged from 5.87 g/cm3 to 5.93 g/cm3 , i.e., close to 95 % of the theoretical density. We also grew single crystals of Sn1−x Inx Se in order to measure their optical properties. The single crystals were grown by the Bridgman method at 1,223 K at a growth rate of 2 mm/h. Phase identification of the samples was conducted by powder X-ray diffraction (XRD) with Cu-Kα radiation. Using high-resolution transmission-electron microscopy (HR-TEM, JEOL 2100F) and energy-dispersive X-ray spectroscopy (EDS), we confirmed a small amount of In segregation near the grain boundaries of the Sn1−x Inx Se (x = 0.1) compound. The Seebeck coefficient and electrical resistivity were measured using the four-probe method in a thermoelectric measurement system (ZEM-3, ULVAC, Japan) from room temperature to 823 K. The thermal conductivity was determined from the relationship κ = ρs Cp λ, where ρs , Cp , and λ are the density, specific heat, and thermal diffusivity, respectively. The thermal diffusivities were measured by the laser flash method (LFA457, NETZSCH, Germany) in the same temperature range. The specific heat was measured by a physical property measurement system (PPMS, Quantum Design, USA) with the high temperature value estimated by the fitting of the Dulong-Petit law. All thermoelectric properties were measured parallel to the hot press direction. The Hall resistivity ρxy was measured by the five-contact 3

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method using a physical property measurement system (PPMS Dynacool 14 T, Quantum Design, USA). The Hall coefficient RH and Hall carrier density nH were calculated by the relationship RH = ρxy /H and nH = −1/(RH e), where H, RH , and e are the applied magnetic field, the Hall coefficient, and the elementary charge, respectively. Using the single crystals of Sn1−x Inx Se (x = 0.01, 0.05, and 0.1), we measured the ellipsometric angles (Φ, ∆) in the spectral range between 0.7 eV and 6 eV at room temperature with three angles of incidence (65◦ , 70◦ , and 75◦ ) by means of spectroscopic ellipsometry (V-VASE, Woollam Inc.).

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3. Results and Discussion

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Figure 1 presents the powder X-ray diffraction (XRD) patterns of Sn1−x Inx Se (x = 0.0, 0.01, 0.05, and 0.1). The XRD patterns show the SnSe single phase with an orthorhombic Pnma structure (JCPDS 32-1382) without any detectable impurity phases. The lattice parameters are tabulated in Table 1. The lattice parameters and lattice volume are slightly increased with In substitution when x = 0.01 and are systematically decreased with an increase in the In concentration. The lattice parameters of stoichiometric SnSe are similar to previously reported values(11). Because the covalent radius of In (142 pm) is slightly larger than that of Sn (139 pm), In substitution can increase the lattice parameters when x = 0.01. The decrease in the lattice parameters indicates that the strong covalent bonding of indium shrinks the lattice parameters. The crystal structure of SnSe is the NaCl type of structure with strong covalent bonding between Sn-Se along the bc-plane. The corrugated Sn-Se layers in the shape of a square sawtooth are stacked along the a-direction as a type of van der Waals interaction(13). From the calculation of the phonon dispersion and Gr¨ uneisen parameter, several authors have argued that a small Gr¨ uneisen parameter gives rise to low lattice thermal conductivity(6). A change in the small lattice parameter implies In substitution at the Sn-Se covalent bonding site. The temperature-dependent electrical resistivities ρ(T ) of the polycrystalline Sn1−x Inx Se compounds are presented in Fig. 2(a). The resistivity of the pristine compound SnSe is 3.7 Ωcm at 300 K, which differs from those of other previously reported polycrystalline samples, at approximately 1.1 Ωcm(9) and 0.6 Ωcm(12) at room temperature. The thermoelectric properties of the SnSe compounds depend on the synthesis method. This may be caused by the texture and Se off-stoichiometry during the sintering process 4

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due to the high Se vapor pressure at a high temperature. The resistivities of the In-doped Sn1−x Inx Se compounds increase with an increase the In doping concentration, except when x = 0.1. Here, ρ(T ) shows semiconducting behavior with the activation energy gap Ea , ρ = ρ0 exp(Ea /2kB T ). From the Arrhenius plot of the ρ(T ) shown in the inset of Fig. 2(a), the activation energy gaps Ea of Sn1−x Inx Se (x = 0.0, 0.01, 0.05, and 0.1) were obtained, as presented in Table 2. The activation energy when x = 0.0 is similar to that of single-crystal SnSe (0.06∼0.07 eV) near room temperature(14; 15). The activation energy gaps of Sn1−x Inx Se (x = 0.0, 0.01, and 0.05) increase with an increase the In-doping concentration, except for the case of x = 0.1. The relatively low activation energy when x = 0.1 implies that the x = 0.1 compound exceeds the solubility limit of In-doping of Sn1−x Inx Se due to the excess amount of indium as an impurity. We confirmed the excess amount of In as an impurity in the Sn0.9 In0.1 Se compound from the high-resolution transmission electron microscopy (HRTEM) and energy dispersive X-ray spectroscopy (EDS) measurements with x = 0.1, as shown in Fig. 3(a). In the HR-TEM image of the Sn0.9 In0.1 Se particle, there are dark and bright regions which show excess indium at levels as high as 1.63 % and 0.35 %, respectively, compared to the stoichiometric ratio of Sn0.9 In0.1 Se. This finding demonstrates the inhomogeneity of indium due to the solubility limit. We also measured the energy band gap Eg by linear extrapolation of the absorption coefficient (LEA) using spectroscopic ellipsometry, as shown in Fig. 3(c), of single crystals of Sn1−x Inx Se (x = 0.01, 0.05, and 0.1) using the relationship (αE)1/2 = C(E − Eg ), where α and C are the absorption coefficient and a constant, respectively(16). The indirect band gap of the SnSe crystal was measured and found to be 0.82 eV(14), specifically calculated as 0.829 eV and therefore similar to that of the present SnSe crystal, as shown in Table 2(17). The obtained optical band gap energies when x = 0.01 and 0.05 are increased as compared to that of the pristine SnSe compound. The decreased band gap of 0.71 eV in x = 0.1 can be considered as a cause of the excess indium. Although the activation gap Ea is obtained from the electrical resistivity of the polycrystalline compounds and the optical band gap Eg is measured considering the absorption coefficient of the single-crystalline samples, the significant difference in the energy gap between the activation energy and the optical band gap indicates the impurity level between the conduction and the valence bands in the polycrystalline compounds. 5

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The increase in the electrical resistivity for In substitution is related to the increase in the optical band gap. We estimated the Hall carrier density nH from the measurement of the Hall resistivity ρxy , as shown in Table 2 and in Fig. 3(b) (left axis, black closed square). The Hall carrier density when x = 0.01 is increased as compared to that when x = 0.0, contrary to the increase in the electrical resistivity and the optical band gap. The Hall carrier density with respect to the In concentration does not appear to be related to the behavior of the electrical resistivity and the band gap. For the In-doped SnTe, the hole carrier concentrations of the polycrystalline Sn1−x Inx Te (x = 0.0, 0.0025, 0.005) compounds are increased below x = 0.01, which shows that In doping can increase the carrier concentration as an acceptor. The decreased carrier concentration of Sn1−x Inx Te (x ≥ 0.008) is affected by the extra indium as a donor(18). In this sense, the abnormal increase of the carrier density of the Sn1−x Inx Se (x = 0.1) compound may come from the excess indium acting as a donor. The Hall mobility µH is obtained from the relationship 1/ρ = nH eµH , as presented in Table 2 and Fig. 3(b) (right axis, red open circle). The Hall mobility of the In-doped Sn1−x Inx Se (x = 0.01) shows a drastic decrease by nearly 360 times as compared to that of the pristine SnSe compound. Hence, the increase in the resistivities in Sn1−x Inx Se (x = 0.01, 0.05, and 0.1) mainly stem from the greatly decreased Hall mobility caused by In doping. When we summarize the behavior of the (optical and activation) energy band gap, the Hall carrier density, and the mobility levels of those compounds apart from the case with x = 0.1 (out of the solubility limit), the band gaps show an increase and the Hall mobilities show significant decreases with an increase in the In concentration, whereas the Hall carrier density does not show the significant variation with In substitution. The first possibility is the carrier scattering by In-doping. However, it is unlikely because, in usual cases, the Hall carrier density is increased when the Hall mobility is decreased which is contrary to this case. The more promising candidate scenario is the heavy hole band formation with preservation of the band degeneracies of SnSe via In substitution. The possible scenario of the increase in the band gap with the formation of a heavy hole band is band renormalization originating from the orbital hybridization between the In 4d- and Se 4porbitals.(19) The decreased lattice volume with the incorporation of indium with a larger ionic size than Sn supports the idea of orbital hybridization and band renormalization. The temperature-dependent Seebeck coefficients of Sn1−x Inx Se (x = 0.0, 6

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0.01, 0.05, and 0.1) are shown in Fig. 2(b). The Seebeck coefficient of the pristine polycrystalline SnSe is 547 µV/K at room temperature, which is greater than those in previous reports (448∼510 µV/K)(9; 12). The Seebeck coefficients of the In-doped Sn1−x Inx Se compounds increase with an increase in In concentration, except when x = 0.1 near room temperature. This is caused by the increased electrical resistivity. The maximum Seebeck coefficient is 997 µV/K when x = 0.05 at 300 K. The dramatically decreased Seebeck coefficient when x = 0.1 is affected by the excess In. From the measured Seebeck coefficient (S) and Hall carrier concentration (nH ), the effective mass of the carrier m∗ (in Table 2) was determined by the following equation(20):  π 2/3 2 8π 2 kB ∗ (1) m T 3eh2 3n The effective mass of the carrier when x = 0.01 nearly doubles compared to its parent compound. When we draw a Pisarenko plot of the Seebeck coefficient versus the carrier density (not shown here), the data do not fit the parabolic band model. The significant deviation of the Pisarenko plot also supports energy band renormalization. In our previous study of Ce1−x Cux Se2 compounds, we found band renormalization due to the strong enhancement of Cu 3d- and Se 4p-orbital hybridization by Cu doping from the calculation of the local spin density approximation with the Coulomb potential (LSDA+U)(21). We argued that band renormalization enhances the Seebeck coefficient due to the presence of localized flat bands. These localized flat bands give rise to very low Hall mobility. From the Mott’s formula, the Seebeck coefficient is proportional to the summation of energy derivative for energy-dependent carrier density and mobility as follows:(2)   2 π 2 kB T d ln n(E) d ln µ(E) S= + (2) 3q dE dE E=EF

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S=

Sn1−x Inx Se also shows an enhanced Seebeck coefficient and significantly decreased Hall mobility by In substitution. The abnormal increase of Seebeck coefficient for x = 0.01 compound can be understood by the high energydependent carrier density contribution due to the high density of states near the Fermi level. We believe that the significant decrease of mobility by Indoping is not solely depend on the scattering of carriers because energy band gap also increased by In-doping while carrier concentration is not changed 7

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significantly. Therefore, this behavior may be related to band renormalization by dp-orbital hybridization. With regard to band renormalization, the effective mass calculation from the parabolic band assumption is not valid. It should be investigated as further research in terms of the theoretical band structure calculation. A more reasonable effective mass can be estimated by the calculation of the theoretical band structure. Figure 2(c) shows the power factor S 2 σ of polycrystalline Sn1−x Inx Se (x = 0.0, 0.01, 0.05, and 0.1). The maximum power factor is observed to be 0.27 mW m−1 K−2 for the pristine compound at 815 K, which is slightly higher than in a previous report, which found a value of 0.2 mW m−1 K−2 near 800 K(9). In spite of the increase in the Seebeck coefficients, the power factors of the In-doped Sn1−x Inx Se (x = 0.01, 0.05, and 0.1) compounds are decreased as compared to those of the pristine SnSe compound due to the increased electrical resistivity, which is mainly affected by the decreased Hall mobility. For the compounds of Ce1−x Cux Se2 , the band gap energy was decreased by Cu doping, resulting in an enhancement of the power factor. In contrast, in this case, the band gap is increased with an increase in the indium concentration. The temperature-dependent thermal conductivities of the polycrystalline Sn1−x Inx Se (x = 0.0, 0.01, 0.05, and 0.1) compounds are presented in Fig. 4(a). The thermal conductivity of SnSe is 0.76 W m−1 K−1 at 300 K, which is lower than those previously reported for polycrystalline SnSe compounds, at 0.9∼1.0 W m−1 K−1 (9; 12). The thermal conductivity when x = 0.01 shows the lowest value of 0.61 W m−1 K−1 at 300 K compared to the other compounds. To evaluate the contribution of the phonon to the thermal conductivity, the electronic thermal conductivity κel can be obtained by the Wiedemann-Franz law κel = L0 σT , where L0 , σ, and T are the Lorenz number, the electrical conductivity, and the absolute temperature, respectively. In spite of the lowest electrical resistivity of 0.04 mΩcm (x = 0.0 at 815 K) and the small Lorenz number L0 of 1.5×10−8 V2 /K2 (6; 9), the electronic thermal conductivity κel is less than 0.03 W m−1 K−1 . This indicates that the electrical contribution of the thermal conductivities of Sn1−x Inx Se (x = 0.0, 0.01, 0.05, and 0.1) can be neglected. The lower thermal conductivity values of Sn1−x Inx Se (x = 0.01, 0.05, and 0.1) as compared to that of SnSe (x = 0.0) are due to phonon scattering by In. The temperature-dependent ZT values of the polycrystalline Sn1−x Inx Se (x = 0.0, 0.01, 0.05, and 0.1) compounds are shown in Fig. 4(b). The maximum ZT value of when x = 0.0 is 0.62 at 823 K, which is similar to the previous SnSe(9) and the ZT value 8

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along the a-axis of single-crystalline SnSe(6). The ZT values of In-doped Sn1−x Inx Se (x = 0.01, 0.05, and 0.1) decrease with an increase the In doping concentration due to the increased electrical resistivity.

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4. Conclusions

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The thermoelectric properties of polycrystalline Sn1−x Inx Se (x = 0.0, 0.01, 0.05, and 0.1) compounds were investigated with optical reflectivity measurements using single-crystalline compounds. The increased resistivity with In substitution is mainly caused by the significantly decreased Hall mobility. The activation gap and the optical band gap energies of Sn1−x Inx Se (x = 0.0, 0.01, and 0.05) increase with an increase in the In concentration. It is very unusual for the Hall carrier concentration of the compounds to not change significantly when the band gaps increase with an increase in the In concentration. The increase in the electrical resistivity stems from the significant decrease in the Hall mobility via the In substitution process. The decrease in the lattice volume, the significant decrease of the Hall mobility, and violation of the Pisarenko plot while the band gap energies increase with an increase in the In concentration all strongly support band renormalization by dp-orbital hybridization. The flat bands caused by band renormalization can give rise to a significant decrease in the Hall mobility via the formation of localized heavy hole bands. Due to the significant decrease in the Hall mobility and the increase in the electrical resistivity, the power factor is significantly decreased by In doping. The thermal conductivity of the Indoped Sn1−x Inx Se compounds (x = 0.01, 0.05, and 0.1) shows lower values than that of pristine SnSe due to the phonon scattering caused by In doping.

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5. Acknowledgments

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This research was supported by Nano-Material Technology Development Program (2011-0030147) through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology and Energy Efficiency & Resources program of the Korea Institute of Energy Technology Evaluation and Planning(KETEP) grant funded by the Korea government Ministry of Knowledge Economy (No. 20112010100100), and LG Electronics.

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Electronic mail: [email protected]

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x 0.00 0.01 0.05 0.10

a (˚ A) 11.498(7) 11.502(9) 11.499(3) 11.497(7)

b (˚ A) 8.300(8) 8.305(6) 8.303(2) 8.297(8)

c (˚ A) 8.881(0) 8.888(6) 8.880(4) 8.880(6)

V (˚ A3 ) 847.677(3) 849.203(4) 847.909(4) 847.259(1)

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Table 1: Lattice parameters and lattice volume of the Sn1−x Inx Se (x = 0.0, 0.01, 0.05, and 0.1) compounds.

Eg (eV) nH (×1017 cm−3 ) 0.82 2.3 0.86 2.9 1.16 1.5 0.71 4.0

m∗ (me ) µH (cm2 V−1 s−1 ) 0.01 7.2 0.21 0.019 0.14 0.030 0.003 0.044

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Ea (eV) 0.08 0.29 0.31 0.19

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x 0.00 0.01 0.05 0.10

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Table 2: The activation energy Ea (polycrystals), indirect band gap Eg (single crystals), Hall carrier concentration nH , effective mass of the carrier m∗ , and Hall mobility µH of the Sn1−x Inx Se (x = 0.0, 0.01, 0.05, and 0.1) compounds at 300 K.

Figure 1: The powder x-ray diffraction patterns of Sn1−x Inx Se (x = 0.0, 0.01, 0.05, and 0.1).

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Figure 2: Temperature-dependent electrical resistivity ρ(T ) (a), Seebeck coefficient S(T ) (b), and power factor S 2 σ (c) of Sn1−x Inx Se (x = 0.0, 0.01, 0.05, and 0.1). The inset of Fig. 2 (a) shows the linear fit of lnρ versus 1/T.

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Figure 3: HR-TEM and EDS images of the Sn1−x Inx Se (x = 0.1) crystal (a), the Hall carrier concentration nH (left axis, black closed square) and the Hall mobility µH (right axis, red open circle) (b), as well as nd the linear extrapolation of the optical absorption coefficient (αE)1/2 (c) of the Sn1−x Inx Se crystals (x = 0.0, 0.01, 0.05, and 0.1).

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Figure 4: Temperature-dependent total thermal conductivity κ(T ) (a) and dimensionless figure-of-merit ZT (b) of Sn1−x Inx Se (x = 15 0.0, 0.01, 0.05, and 0.1) compounds.

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We investigated thermoelectric properties of polycrystalline Sn1-xInxSe series compounds.

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The electrical resistivity, band gaps are increased with increasing the In concentration.

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The decrease of μH while nH is not sensitive with In supports the flat band formation.

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The band renormalization can cause the increase of the band gap and decrease μH.

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