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Band Degeneracy, Low Thermal Conductivity, and High Thermoelectric Figure of Merit in SnTe-CaTe Alloys Rabih Al Rahal Al Orabi, Nicholas Mecholsky, Junphil Hwang, Woochul Kim, Jong-Soo Rhyee, Daehyun Wee, and Marco Fornari Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.5b04365 • Publication Date (Web): 18 Dec 2015 Downloaded from http://pubs.acs.org on December 28, 2015

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Chemistry of Materials

Band Degeneracy, Low Thermal Conductivity, and High Thermoelectric Figure of Merit in SnTe-CaTe Alloys Rabih Al Rahal Al Orabi,∗,†,‡ Nicholas Mecholsky,¶ Junphil Hwang,§ Woochul Kim,§ Jong-Soo Rhyee,k Daehyun Wee,† and Marco Fornari∗,‡ Department of Environmental Science and Engineering, Ewha Womans University, Seoul, 120-750, Korea, Department of Physics and Science of Advanced Materials Program, Central Michigan University, Mt. Pleasant, MI 48859, USA , Department of Physics and Vitreous State Laboratory, The Catholic University of America, Washington, DC 20064, School of Mechanical Engineering, Yonsei University, Seoul, 120-749, Korea, and Department of Applied Physics, College of Applied Science, Kyung Hee University, Yongin-si, Giheung-gi, Gyeonggi-do 446-701, Korea E-mail: [email protected]; [email protected]

Abstract Pure lead-free SnTe has limited thermoelectric potentials because of the low Seebeck coefficients and the relatively large thermal conductivity. In this study, we provide ex∗

To whom correspondence should be addressed Department of Environmental Science and Engineering, Ewha Womans University, Seoul, 120-750, Korea ‡ Department of Physics and Science of Advanced Materials Program, Central Michigan University, Mt. Pleasant, MI 48859, USA ¶ Department of Physics and Vitreous State Laboratory, The Catholic University of America, Washington, DC 20064 § School of Mechanical Engineering, Yonsei University, Seoul, 120-749, Korea k Department of Applied Physics, College of Applied Science, Kyung Hee University, Yongin-si, Giheunggi, Gyeonggi-do 446-701, Korea †

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perimental evidence and theoretical understanding that alloying SnTe with Ca greatly improves the transport properties leading to ZT of 1.35 at 873 K, the highest ZT value so far reported for singly doped SnTe materials. The introduction of Ca (0-9%) in SnTe induces multiple effects: (1) Ca replaces Sn and reduces the hole concentration due to Sn vacancies, (2) the energy gap increases limiting the bipolar transport, (3) several bands with larger effective masses become active in transport, and (4) the lattice thermal conductivity is reduced by about 70% due to the contribution of concomitant scattering terms associated with the alloy disorder and the presence of nanoscale precipitates. An efficiency of ∼10% (for ∆T = 400 K) was predicted for high temperature thermoelectric power generation using SnTe-based p- and n-type materials.

Introduction Thermoelectric converters are solid-state devices with no moving parts. They are silent, reliable, and scalable, and provide an optimal technology for distributed energy recovery systems and cooling. Traditional thermoelectric modules include p-type and n-type legs connected electrically in series and thermally in parallel. Ideally, in each leg, the only carriers available are holes or electrons for both electrical and thermal transport: 1–4 the requirement of low thermal conductivity (k) and large power factor (S 2 σ where S is the Seebeck coefficient and σ the electrical conductivity) stems from this consideration. The conversion efficiency of the thermoelectric device is often expressed in terms of ZT =S 2 σT /k, where T is the operating temperature. Although many factors such as mechanical properties, thermal stability, and dopability complicate the design of thermoelectric modules, ZT is indicative of the performance of active materials components. In order to optimize the power factor, thermoelectric materials should be heavily doped semiconductors. 1 Doping introduces extrinsic carriers and increases the electrical conductivity, such an increase affects the thermal conductivity. The Wiedemann-Franz relationship defines the Lorenz number as the proportionality factor between the electronic thermal conductivity, ke , and σ. The lattice 2


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contribution to the thermal conductivity, kL , is associated with anharmonicities in the lattice vibrations. Two main approaches have been used to enhance the thermoelectric performance: increasing the power factor by tuning the electronic band structure and the doping level, and minimizing the lattice thermal conductivity by alloying and nanostructuring. 1,5 Lead chalcogenides PbQ (Q = S, Se, Te), which have a simple rock-salt structure, are considered to be some of the best thermoelectric materials for mid temperature. PbTe-based compositions, especially, have been extensively studied. 6–11 Heremans et al. 12 reported an enhanced Seebeck coefficient in PbTe doped with Tl. An improved maximum ZT value of 1.5 was observed at 800 K. Thermoelectric performances were further enhanced through a combination of band structure engineering and nanostructuring leading to ZT values of 1.5 at 765 K for PbTe-6%CaTe-1%N2 Te, 13 and ZT =2 at 823 K for Pb0.98 Na0.02 Te-6%MgTe. 14 The highest figure of merit value, reaching ∼ 2.2, was reported for the nanostructured p-type Pb1−x Nax Te-SrTe at T= 923 K. 6 PbTe serves as a model for PbQ-based materials (Q = S, Se and Te) and also for isostructural SnTe compositions that exhibit similar electronic bands and do not raise environmental concerns associated with Pb toxicity. SnTe was suggested as a promising thermoelectric material 15,16 but it has a ZT ∼ 0.4 at 900 K. 17 The low value of ZT was attributed to: (a) a high carrier concentration (1020 - 1021 cm−3 ) caused by intrinsic Sn vacancies which favors a low Seebeck coefficient and a high electronic thermal conductivity, (b) a very low energy band gap (∼ 0.18) at room temperature 18,19 leading to bipolar transport, and (c) a large separation in energy between valence bands with heavy and light effective masses 15 which hinders the contribution of the heavier holes to the Seebeck coefficients. Very recently, however, Zhang et al. 20 reported ZT ∼ 1.1 at 873 K for SnTe doped with In, and Tan et al. 21 reported ZT ∼1.3 at 923 K for Cd-doped SnTe with endotaxial CdS nanoscale precipitates. In this last case, the isovalent alloying (Cd, Hg, Mg and Mn) enhanced the Seebeck coefficient of SnTe based materials by increasing the energy band gap and decreasing the energy separation between heavy and light valence bands. 22–25 CaTe alloying has been well investigated in p-type PbTe for its role in the significant

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reduction of the lattice thermal conductivity compared to those of pristine PbTe. 13 However, to the best of our knowledge, thermoelectric properties were not investigated for Ca doped SnTe. The similarities in band and crystal structures between PbTe and SnTe hint that Ca alloying can cause a reduction of the lattice thermal conductivity and lead to an effective multi-valley band structure (band convergence). In this study, for the first time, we present the effect of Ca alloying on the band structure and high temperature thermoelectric properties of SnTe, using both experimental and computational studies. We show that isovalent Ca alloying significantly modifies electronic band structure of SnTe by enlarging the band gap, decreases energy difference between the light hole and heavy hole valence bands, leading to an enhanced Seebeck coefficient. We also show that the substitution of Sn with Ca atoms in SnTe induces nanoscale precipitates in the matrix, which effectively scatter phonons on multiple length scales leading to very low lattice thermal conductivities. This yields a high figure of merit ZT of ∼1.35 at T = 873K for a Ca concentration of 9%, to our knowledge the largest ZT observed in singly doped SnTe materials.

Experimental procedures Samples preparation Recently, Tan et al. 21 have shown that Sn self-compensation is an effective path for enhancing the thermoelectric performance of SnTe by decreasing the hole carrier density. High quality ingots with nominal compositions of Sn1.03−x Cax Te (x = 0, 0.03, 0.05, 0.07 and 0.09) were synthesized by mixing appropriate ratios of high purity elemental precursors from Sn shot (99.999+ %), Ca shot (99.5+ %) and Te shot (99.999+ %) in silica tubes. The tubes were then evacuated to a residual pressure of ∼ 10−4 Torr, flame sealed and slowly heated to 1023 K, soaked at this temperature for 3 h, then heated up to 1273 K in 3 h, soaked for 10 h to ensure the homogeneity of composition and subsequently quenched in ice water. 4


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The obtained samples of Sn1.03−x Cax Te (x = 0, 0.03, 0.05, 0.07 and 0.09) were ground into fine powders and then densified by sintering (at ∼ 10−2 mbar) via hot uniaxial pressing (HUP). The pressing conditions were as follows: the pressure was applied from the beginning of the temperature ramp to the end of the high-temperature dwell. A typical quantity of 10 g of powder was introduced into 12 mm diameter graphite dies previously coated with boron nitride. The applied load was 50 MPa at 800 K for 2 h for all experiments. The densities for all pellets were calculated to be 95% of the theoretical values after measuring volume and weight.

Powder X-ray diffraction and scanning electron microscopy Samples were characterized by powder X-ray diffraction (PXRD) with Cu Kα (λ = 1.5406 ˚ A) radiation at room temperature using a Bruker D8 diffractometer. Lattice constants and volumes were calculated by Rietveld refinement using the Fullprof software. Scanning electron microscopy images were obtained using a JSM-6701F microscope.

Electrical transport measurements The HUPed pellets were cut into ∼ 3.5 mm x 3.5 mm x 10 mm bars for simultaneous measurement of the electrical conductivity and the Seebeck coefficient. Measurements were performed under He atmosphere from room temperature to 873 K using a Ulvac Riko ZEM-3 instrument. The room temperature Hall coefficients were measured using a PPMS system. Four-contact Hall-bar geometry was used for the measurement. The effective carrier concentration (Np ) was estimated using the relationship Np = 1/eRH , where e is the electronic charge and RH is the Hall coefficient. The Hall mobility (µH ) was calculated using the relationship µH = σRH with σ being the electrical conductivity.

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Thermal transport measurements The HUPed pellets were cut and polished into a squared-shaped of ∼ 10 mm x 10 mm x 1 mm and cylinder-shaped of ∼ 12 mm in diameter and 1 mm thick for thermal diffusivity measurements. The thermal diffusivity coefficient (D) was measured with a laser flash diffusivity method using apparatus (Netzsch LFA 457). The heat capacity (Cp ) was obtained by Cp = Cp,300 +Cp1 ×((T /300)α −1)/((T /300)α +Cp1 /Cp,300 ). 26 The total thermal conductivity, k, was calculated using the formula k = DCp d where d represents the density of the sample.

Computational procedures First principles calculations Our calculations are based on Density Functional Theory (DFT). We used the full-potential linearized augmented plane wave (FLAPW) approach, as implemented in the WIEN2K code. 27 The muffin-tin radii (RM T ) were chosen small enough to avoid overlapping during the band structure calculation. A plane-wave cutoff corresponding to RM T Kmax = 7 was used in all calculations. The radial wave functions inside the non-overlapping muffin-tin spheres were expanded up to lmax =12. The charge density was Fourier expanded up to Gmax = 14 ˚ A−1 . Total energy convergence was achieved with respect to the Brillouin zone (BZ) integration mesh with 500 k-points. Structure relaxations were performed using the PBE functional for the 64-atoms cubic supercells for Sn32 Te32 , Sn31 CaTe32 (∼ 3 mol % Ca-doped) and Sn29 Ca3 Te32 (∼ 9 mol % Cadoped) with Ca atoms substituted for Sn atoms in SnTe. The Ca sublattice was simple cubic for Sn32 Te32 , body-centered cubic for Sn31 CaTe32 , and face-centered cubic for Sn29 Ca3 Te32 . During the geometry optimization, both the atomic positions and lattice constant were fully relaxed until force acting on all atoms becomes less than 0.02 eV/˚ A. For the electronic band structures we used the modified Becke-Johnson (mBJ) functional

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which leads to excellent agreement with the experimental values for the energy separation between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). 28 We represented the band structures along the high symmetry lines of the cubic Brillouin zone (supercell) for direct analysis of the effects of Sn-Ca substitutions. We used 20000 k-points in the BZ to compute the band structures and the density of states (PDOS).

Evaluation of the effective masses Effective masses at special points within the Brillouin zone were computed by finding the ellipsoidal fit of the band structure around that point. In a generic case, for a given band, the band structure around the special point was fit to a 4th order polynomial surface. The inverse effective mass surface 29 was then computed in every direction from that point by evaluating half of the second directional derivative. This angular surface was then fit to a general ellipsoidal inverse effective mass surface with Euler angles and masses as the fitting parameters. In all cases, the fits were excellent and relative error of the fitted surface was on the order of 10−8 or smaller. Correspondingly, the relative error of the calculated band energies from the ellipsoidal approximation and the band energies from DFT for points near the special point was typically less than 1%.

Theoretical consideration on devices’ performance The device figure of merit (ZT )d for a single pair of p- and n-type legs was calculated by assuming reported data for n-type (Sn1−x Pbx )Cd0.03 Te (see Ref. 56) and our experimental results for p-type Sn0.94 Ca0.09 Te. Hot and cold side temperatures are assumed to be 700 K and 300 K, respectively. The integrated value is obtained using

ZTd =

Z

Th Tc

(Sp − Sn )2 T 2

[(Kp ρp )1/2 + (Kn ρn )1/2 ] ∆T

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dT,

(1)


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where (Sp and Sn ), (ρp and ρn ) and (kp and kn ) represent the Seebeck coefficients, electrical resistivities, and total thermal conductivities of the p- and n-type materials. The conversion efficiency (η) of the aforesaid pair of materials was theoretically calculated from the equation,

ηT E

p ( 1 + ZTavg − 1) Th − Tc = p , ( 1 + ZTavg + TThc ) T h

(2)

where (ZT )avg is an average figure of merit for a pair of thermoelectric materials, Th and Tc are the hot and cold side temperatures, and

Th −Tc Th

refers to the Carnot efficiency.

Results and discussion Structure and morphology All our powder X-ray diffraction patterns for the Sn1.03−x Cax Te (x = 0.00, 0.03, 0.05, 0.07 and 0.09) samples (Figure 1) index on the pure SnTe F m¯3m space group; no secondary Ca or CaTe phase was observed within the detectabilty limits of X-ray diffraction. The lattice parameter increases linearly with the increase of Ca content, consistently with the larger ionic radius of Ca2+ (99 pm) compared to that of Sn2+ (93 pm). Vegard’s law (Figure 1b) describes well the variation of lattice parameter in the concentration range we examined. Ca solubility in SnTe (estimated with PXRD) compares with the values reported for Mg and Mn (∼ 12 mol %) and is substantially larger than that of Cd and Hg (∼ 3 mol %). 21–24 Morphological features at the nanoscale were observed with high resolution SEM as we discuss later in this article.

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The room temperature carrier concentration (Np ) and mobilities (µH ) of our samples are shown in Figures 2b and c. The room temperature Hall coefficients, RH , of all Sn1.03−x Cax Te ( 0 ≤ x ≤ 0.09) samples are positive, which indicates, as expected, p-type carriers. Notice that the carrier concentration (Np ) at 300 K decreases gradually with increasing the Ca concentration up to 5% and then remains constant up to 9% concentration. Anomalous changes in the carrier concentration with the increase of Ca concentration are difficult to explain but we can conjecture that the presence of substitutional defects influences the formation energy of the vacancies. Anomalous changes in the carrier concentration in SnTe alloyed with In, Mg, Cd and Hg have been observed recently. 21–23 The room temperature hole mobility (µH ) first increases with increasing Ca concentration up to 5% and then slightly deteriorates. As expected, the room temperature electrical conductivity decreases gradually with decreasing carrier concentration.

Figure 2: (a) Temperature dependence of electrical conductivity of Sn1.03−x Cax Te samples. (b) Carrier concentration (Np ) and (c) carrier mobility (µ) at room temperature with respect to Ca alloying concentration (x). The Seebeck coefficients, as shown in Figure 3, are consistent with hole conductivity and increases almost linearly with temperature. Remarkable enhancement in S has been achieved by Ca doped in SnTe, both at high and low temperatures: the improvement is of the order of 30-40 µV /K across all temperature range. 10


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To assess the effectiveness of Ca alloying, we compare the room temperature S vs Np plot for Sn1.03−x Cax Te samples with the theoretical curve (Pisarenko plot) obtained within a simple valence band model by Zhang et al. 20 . This model used a light-hole band effective mass of 0.168me , a heavy-hole band effective mass of 1.92me , and an energy gap between the two valence band maxima of 0.35 eV. Experimental data from the literature are included for comparison. 17,20–23,30,31 The data points for Cu, Sb and Bi doped and un-doped SnTe samples fall exactly on the Pisarenko curve, while the In, Cd/Hg/Mg alloyed SnTe samples show much higher Seebeck coefficient than the theoretical curve due to the formation of resonance levels, 20 and/or an optimized multivally band structure near the Fermi level. 21–23 Our Ca-doped SnTe samples also display larger Seebeck coefficients than indicated by the Pisarenko plot calculation. Using our experimental data, we estimated the effective mass of all Sn1.03−x Cax Te samples. Using the room temperature value of the Seebeck coefficients, the chemical potential (µ) is calculated within a single parabolic band model 32,33 using eq 4 with (λ = 0) (acousticphonon scattering), where Fj (µ) are the Fermi integrals given in eq 5. The hole effective mass is then determined from eq 6 using the measured carrier concentration (Np ). kB S= e

(2 + λ)F1+λ (µ) −µ (1 + λ)Fλ (µ)

Fj (µ) =

Z

h2 m = 2kB T ∗

∞ 0

ζ j dζ 1 + e(ζ−µ)

Np 4πF1/2 (µ)

2/3

(4)

(5)

(6)

The results are in Table 1 and exhibit trend similar to the one predicted by first principles calculations. It must be noted that experimental results are fitted using a simplistic model which does not include the full details of the band structure discussed in the next section. The presence of Ca modifies the electronic structure by “activating” hole pockets below the 11



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HOMO. The effective mass associated with these hole pockets is larger and the thermopower increases. The detrimental effect of Ca doping on the electrical conductivity does not cancel out the improvement in S. To quantify these considerations we determined the experimental power factor (Figure 4). The Ca-doped samples have much higher values than the Sn1.03 Te samples. This is due to the significant enhancement in the Seebeck coefficient at both low and high temperatures. For instance, the power factor increases from 2 µW cm−1 K −2 to 11 µW cm−1 K −2 at room temperature and from 16 W cm−1 K −2 to 26 W cm−1 K −2 at high temperature. The highest power factor obtained is 26 W cm−1 K −2 at 873 K for in Sn0.94 Ca0.05 Te.

Figure 3: (a) Temperature dependence of Seebeck coefficient (S) of Sn1.03−x Cax Te (x = 0, 0.03, 0.05, 0.07 and 0.09) samples. (b) Room temperature S vs Np plot. Data are from this work for Sn1.03−x Cax Te samples and from previously reported experiments for pure SnTe, 30 Cd-, 21 Mg-, 22 In-, 20 Cu-, 31 Bi-, 17 Hg-, 23 Sb-. 17 The theoretical Pisarenko curve is also plotted. 20

Table 1: Carrier concentration (Np ) and effective mass (m∗ , in term of the electron mass me ) for Sn1.03−x Cax Te (x = 0, 0.03, 0.05, 0.07 and 0.09) samples at 300 K. Compositions Sn1.03−x Te Sn1 Ca0.03 Te Sn0.98 Ca0.05 Te Sn0.96 Ca0.07 Te Sn0.94 Ca0.09 Te

Np (1019 cm−3 ) 7.7 5.9 3.9 4.4 4.1

12

m∗ (me ) 0.133 0.28 0.3 0.21 0.35


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Figure 4: Temperature dependent power factor (S 2 σ) of Sn1.03−x Cax Te (x = 0, 0.03, 0.05, 0.07 and 0.09) samples.

Theoretical electronic structure As mentioned in the introduction, the band structure of pure SnTe exhibits features that do not favor large thermoelectric performances. The first limit relies on the energy separation between occupied and unoccupied states (0.12 eV in SnTe) that is below the optimal value predicted by Goldsmid-Sharp formula Eg = 2eSmax Tmax of 0.35 eV at high temperature (corresponding of 6kB T , where kB is Boltzmann constant, and T is the operating temperature). 34 The second limit is due to the relative low effective masses associated with the valence bands active in transport. Ca alloying resolves both of these limitations by increasing the overall ionic character with the effect of inducing a shift of the LUMO with respect to the HOMO and increasing the effective masses of the valence bands near the Fermi level. The density of states (PDOS) of Sn32 Te32 , Sn31 CaTe32 and Sn29 Ca3 Te32 are shown in Figure 5. The HOMO-LUMO gap increases from 0.12 eV to ∼ 0.3 eV (Figure 6) when increasing the Ca concentration from 0% to 9% (the value computed for SnTe matches recent 13



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experimental data 22 and greatly improves the DFT result obtained with PBE functionals 21,22 because the mBJ functional leads to excellent agreement with the experimental values for the HOMO/LUMO energy gap). 28 Ca alloying in SnTe does not create resonant states, which are characterized by humps in proximity of the Fermi level. 20 In all our calculations we considered stoichiometric materials with the Fermi energy level within the forbidden energy gap and, for this reason, any enhancement of the Seebeck coefficient will not be related to the presence resonant states. 35 Ca derived states do not seem to contribute substantially to the energy region near the HOMO and the LUMO. However, with increasing concentration, a feature in the DOS at about -0.75 eV develops. This hints to modifications in the valence bands.

Figure 5: Density of states calculation of undoped SnTe (Sn32 Te32 ) (a), ∼3% Ca doped SnTe (Sn31 CaTe32 ) (b) and ∼9% Ca doped SnTe (Sn29 Ca3 Te32 ) (c) cubic supercell computed from DFT. Energies are refereed to the top of the valence band (HOMO).

As shown in Figure 6a, the HOMO-LUMO gap is direct (the bottom of conduction band, LUMO, and top of valence band, HOMO, corresponding to the light hole band are at the Γ point) for all concentrations. However, just below the HOMO, several other bands may contribute to the transport properties. We are particularly interested in the valence band maximum located at Γ and at ε along R → X direction in the Brillouin zone (corresponding to the heavy hole band). Two effects occur when Ca is introduced in SnTe: the degeneracy at the HOMO is removed with the appearance of a split-off band near E = −0.2 eV and the valence band local maximum at ε approaches the Fermi level from below and decreases the energy seperation between the light and heavy holes in the valence band (∆ε ) from ∼ 14


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and applied the Wiedemann-Franz law. The calculated Lorenz numbers for all samples are in the range of 2.3 × 10−8 to 1.6 × 10−8 W ΩK −2 (from room temperature to high temperature) and are lower than the metallic limit of 2.45 × 10−18 (Supporting Information, Figure SI 3). The lattice thermal conductivity decreases with increasing Ca concentration, presumably because of increased alloy scattering and the possible contribution of interfacial scattering of phonons at the grain boundaries. The minimum lattice thermal conductivity values are ∼ 0.5 W/mK for Sn0.96 Ca0.07 Te at 420 K and ∼ 0.6 Sn0.94 Ca0.09 Te at 700 K. The reduction of klat of ∼75 % after Ca doping SnTe is very large and leads to values of klat that are lower than the reported results for In-/Cd-/Mn- and Mg- doped SnTe. 20–23

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klat,d

tan−1 χ = klat,p , χ

ΘD V klat,p Λ χ= hυ 2

1/2

(8)

where klat,p is the lattice thermal conductivity of the undoped sample (Sn1.03 Te), χ is the disorder scaling parameter, V is the average atomic volume, ΘD is the Debye temperature (∼ 140 K for SnTe 40 ), υ is the average sound velocity (∼ 1800 m/s for SnTe 41 ), h is Planck’s constant. Λ is the scattering parameter that combines several effects such as strain contrast, mass, and bonding force. Λ can be computed as

" 2 2 # 1+r adisorder − apure Mdisorder − Mpure 2 x(1 − x) (9) (G + 6.4γ) + Λ= 9 1−r xapure Mpure where G is a ratio between the relative change of bonding length and the bulk modulus which can be taken as a constant value of 3, 42,43 γ is the Gr¨ uneisen parameter (2.1 for SnTe 44 ), r is the Poisson ratio (0.244 for SnTe 45 ), adisorder and apure represent the lattice constants of disordered and pure alloys respectively, Mdisorder and Mpure denote the the atomic mass of disordered and pure alloys, respectively, and x is the doping fraction. The calculated lattice thermal conductivities are shown in Figure 8c and are larger than the experimental values. Two reasons can justify these findings: alloying scattering must be combined with the effect on the phonon mean free path due to nanoscale precipitation 13,25,46–49 or the error in assuming the parameters for Sn1.03 Te can not be ignored. To disentangle these effects we performed SEM/EDS analysis on two compositions with 0% and 9% Ca concentrations. Figure 9a shows the SEM image for Sn1.03 Te, indicating a uniform sample with no Sn precipitates in the matrix, consistent with the PXRD results shown in Figure 1 and Figure SI 6a, and with the previous studies reported on the literature. 21,22 For the 9% composition, however, the situation is substantially different and, at nanoscale, precipitates were found within SnTe the matrix (highlighted by the red circles, revealing the consistent nature of the composition, Figure 9b). These dishomogeneities were not detected

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tering distance within the model proposed by Cahill et al. 50 : we obtained a value of ∼0.2 W/mK. For all samples, the klat values are higher than the kmin , indicating that further reduction may be possible, which might be achieved, for example, by reducing the grain size in order to enhance the boundry scattering of heat-carrying phonons.

Figure of merit By combining the electronic transport and thermal conductivity data, we determined the dependence of ZT (Figure 11a). The figure of merit for our Sn1.03−x Cax Te samples reach ZT ∼ 1.35 at 873 K for Sn0.94 Ca0.09 Te. This value is ∼125 % improved with respect to Sn1.03 Te and, to the best of our knowledge, is the highest ZT value reported for singly doped SnTe materials (Figure 11b). Sn0.94 Ca0.09 Te competes with other p-type lead-free thermoelectric materials, 20,21,24,25,51–55 as shown in Figure 11c for optimal performances with minimal toxicity. The ZTave for Sn0.94 Ca0.09 Te between 300-900 K and 500-900 K improves over several other singly doped SnTe materials (Figure 11d). 20–22,24 Specifically, the ZTave value between 300 and 900 K are 0.45, 0.55, 0.6, 0.72, and 0.77 for singly Cd, In, Mg, Mn and Ca-doped SnTe, respectively, while those between 500 and 900 K are 0.61, 0.72, 0.71, 0.87, and 0.93, respectively. Note that a significant enhancement of ZTave is desirable for overall thermoelectric conversion efficiency rather than just increasing the maximum value of ZT . 3,4 The overall device efficiency (ZTd ) for a pair of legs of p-type (Sn0.94 Ca0.09 Te) and n-type (previously reported (Sn1−x Pbx )0.97 Cd0.03 Te) 56 was estimated as a function of temperature (Figure 11e) using eq 1. Theoretically estimated thermoelectric figure of merit, (ZTavg ), was estimated to be ∼0.65 considering ∆T = 400 K. The estimated (ZTavg ) was used for theoretical calculation of the thermoelectric conversation efficiency (Figure 11f) in eq 2. A maximum efficiency (ηmax ) of ∼10% was achieved for the temperature difference of 400 K.

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Conclusions In conclusion, we have synthesized high quality samples of Sn1.03−x Cax Te (x = 0, 0.03, 0.05, 0.07 and 0.09) by simple vacuum sealed tube melting reactions. CaTe solubility is relatively high in SnTe (9%). The substitution of Sn with Ca atoms in SnTe leads to a series of profound effects on the electronic and thermal transport: (a) it modifies significantly the band structure by increasing the band gap and decreasing the energy separation between the two valence bands (Γ and ε), which results in an enhancement of the Seebeck coefficient (Figure 6); (b) it induces nanoscale precipitates in the matrix, which effectively scatter phonons on multiple length scales leading to very low lattice thermal conductivities (Figure 8b); in addition (c) Ca alloying controls the vacancy formation energies. These multiple beneficial consequences of Ca alloying in SnTe yield a high thermoelectric figure of merit of ∼1.35 at 873 K, which is among the highest reported for p-type SnTe (Figure 11c) and exhibits one of the highest average ZT values of ∼0.65 (from 300 K to 700 K), which is important in determining device efficiency (Figure 11e). A thermoelectric conversion efficiency (ηmax ) of ∼10% was estimated by considering a virtual thermoelectric module consisting of present p-type Sn0.94 Ca0.09 Te and n-type previously reported (Sn1−x Pbx )0.97 Cd0.03 Te (x= 0.73), by maintaining the temperature difference of 400 K (Figure 11f). The high performance could make Ca-doped SnTe a serious candidate for consideration in medium temperature thermoelectric power generation when lead-free materials are desired.

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Acknowledgement We thank Profs. R´egis Gautier and Bruno Fontaine for useful discussions. R. A. R. A. O. and D. W. thank Solvay Special Chemicals for financial support. This work was partially supported by Mid-career Researcher Program (No. 2011-0028729) and Nano.Material Technology Development Program (No. 2011-0030147) through the National Research Foundation of Korea (NRF) grant funded by the Ministry of Education, Science and Technology (MEST). Computations were performed at Institut des Sciences Chimiques de Rennes and at the High Performance Computing Center at Michigan State University. M. F. acknowledges collaboration with the AFLOW Consortium (http://www.aflowlib.org) under the sponsorship of DOD-ONR (N000141310635).

Supporting Information Available Thermal diffusivity, electrical conductivity, and calculated Lorenz number as a function of x for Sn1.03−x Cax Te (x = 0, 0.03, 0.05, 0.07 and 0.09); thermoelectric properties of Sn0.94 Ca0.09 Te sample of initial and reproduced measurment; total electronic band structure on function of BZ of Sn32 Te32 , Sn31 CaTe32 , and Sn29 Ca3 Te32 cubic supercells; Powder XRD patterns for Sn1.03 Te and Sn0.94 Ca0.09 Te samples; density of Sn1.03−x Cax Te (x = 0, 0.03, 0.05, 0.07 and 0.09) samples. This material is available free of charge via the Internet at http://pubs.acs.org/.

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