- Email: [email protected]
Thermoelectric transport properties of Pb doped SnSe alloys (PbxSn1-xSe): DFT-BTE simulations
Journal of Solid State Chemistry 270 (2019) 413–418
Contents lists available at ScienceDirect
Journal of Solid State Chemistry journal homepage: www.elsevier.com/locate/jssc
Thermoelectric transport properties of Pb doped SnSe alloys (PbxSn1-xSe): DFT-BTE simulations
MARK
⁎
Hyo Seok Kima, Garam Choia, Min Young Haa, Dong Hyun Kima, Sang Hyun Parkb, In Chunga, , ⁎ Won Bo Leea, a b
School of Chemical and Biological Engineering, Institute of Chemical Processes, Seoul National University, Seoul 08826, Republic of Korea Korea Institute of Energy Research, Daejeon 34129, Republic of Korea
A R T I C L E I N F O
A BS T RAC T
Keywords: Thermoelectric Doping Density functional theory Tin selenide
Thermoelectric transport properties of Pb doped SnSe alloys, PbxSn1-xSe, were systematically investigated by DFT-BTE simulations. The figure of merit is mainly enhanced by reducing lattice thermal conductivity which is estimated about 43% decrease with Pb addition. Electrical conductivity and Seebeck coefficient evaluated by using the Boltzmann transport equation with a constant relaxation time approximation. These electronic transport properties hardly changed with Pb addition, and did not make any significant change in electron transport. However, the considerable change in phonon transport and lattice thermal conductivity are shown. This investigation elucidates the electrons and phonons transport phenomena in alloys, leading the design of new high-performance thermoelectric materials.
1. Introduction The growth of world energy demands has triggered the exploration of alternative energy resources. Thermoelectric materials have been a major focus because of their potential in wearable devices [1], waste heat recovery [2], and other various applications [3,4]. To be commercially viable, raising the efficiency has been one of the most important challenges in this area. The efficiency, called the figure of merit (ZT), is determined by ZT = S2σT/(κe+ κL): S is the Seebeck coefficient, σ is electrical conductivity, κe is electrical thermal conductivity, κL is the lattice thermal conductivity, and T is temperature. A number of IV–VI compounds have been reported to be highperformance thermoelectric materials. PbTe [5–7], PbSe [8,9], SnTe [10–12], and their alloys have been main subjects of research. Their narrow band gap energy, large effective mass, and highly resonant levels enable these IV–VI compounds to have high-performances [13]. SnSe, another IV–VI compound, has recently been extensively studied because of the high thermoelectric efficiency of its bulk crystal form and economic competitiveness. SnSe has a Pnma structure (#62) at ~800 K, and its experimentally determined lattice constants are a = 11.49, b = 4.15, and c = 4.45 Å [14]. At around 800 K, a phase transition from the Pmma to Cmcm (#63) structure occurs; the Sn2+ state is preferred, and the d-orbitals are involved in long-range interactions. In the Pnma case, each Sn2+ atom is surrounded by seven Se atoms in a perturbed arrangement with a corresponding resonant structure [15]. ⁎
Recently, a value of ZT = 2.6 along the b-axis was measured by Zhao et al. [15], which was a great advance in thermoelectric research. Since then, SnSe has drawn the attention of many researchers and meaningful advances are being made. Its intrinsic high-performance is verified not only experimental approaches, but also theoretical and computational approaches. Zhao et. al. firstly investigated the highperformance thermoelectric properties of SnSe using band-structure analysis [16]. They presented all valence band maxima of SnSe and their effective mass, and indicated that multiple valleys enable a high Seebeck coefficient. Hong et. al. indicated that a weak hybridization exists between Sn 5 s-states and Se-4p states from projected density of states(pDOS) analysis, and a high Seebeck coefficient of SnSe can attribute to the hybridization [17]. In addition, Li et. al. reported the hybridization also cause a phonon anharmonicity, thereby an ultra-low lattice thermal conductivity of SnSe is achieved [18]. Based on these findings, there have been several attempts to improve the performance of SnSe through doping [13,19–21], increasing the band degeneracy [22,23], and decreasing the lattice thermal conductivity [10,24,25]. The attempts to optimize the performance through doping are especially noteworthy. It was revealed that heavily hole-doped SnSe showed an improved ZT at lower temperatures. One of the novel strategies to tune the optimum performance temperature of SnSe was proposed by Lee et al. [26]. They verified that ZT can be enhanced to ~1.2 at 773 K with hole-doped polycrystalline PbxSn1−xSe by changing the phase transition temperature. However,
Corresponding authors. E-mail addresses: [email protected] (I. Chung), [email protected] (W.B. Lee).
https://doi.org/10.1016/j.jssc.2018.12.003 Received 27 August 2018; Received in revised form 7 November 2018; Accepted 1 December 2018 Available online 04 December 2018 0022-4596/ © 2018 Elsevier Inc. All rights reserved.
Journal of Solid State Chemistry 270 (2019) 413–418
H.S. Kim et al.
calculated using PHONO3PY [32] and PHONOPY [33]. Harmonic and anharmonic interatomic force constants (IFCs) were calculated using VASP [28,29] and the PBEsol [34] exchange–correlation functional. The atomic displacement was set to 0.03 Å, and the k-meshes for the force calculations were set to 2 × 2 × 2. To calculate the lattice thermal conductivity, the q-meshes were set to 7 × 7 × 7. The lattice thermal conductivity was computed from a solution of the linearized phonon Boltzmann transport equation (LBTE) [32]. The equation can be written in a closed form,
there have still been leaving questions how electrons and phonons behave in an alloy in which these factors are intricately intertwined. Especially, there is little First-principles research on verifying the effect of Pb alloying on reducing lattice thermal conductivity, which is critical to define high figure of merit. Here, we investigated the thermoelectric properties of PbxSn1−xSe alloys based on first-principles calculations. First, the electronic band structures are calculated, and the differences between a pure SnSe and a Pb-doped SnSe are discussed. The transport properties are then provided by solving the Boltzmann transport equation (BTE). Finally, the ZT values are evaluated, and the influence of Pb doping on the thermoelectric transport properties is discussed.
κ=
All the density functional theory (DFT) calculations described in this work were performed by using the projector augmented wave (PAW) formalism, as implemented in the Vienna Ab–initio Simulation Package (VASP) [28,29]. The exchange–correlation functional, given by the generalized gradient approximation (GGA) suggested by Perdew, Burke, and Ernzerhof (PBE) [30], was selected. The potentials used for Sn, Se, and Pb include the 4d105s25p2, 4s24p4, and 5d105s25p2 valence electrons, respectively. The energy convergence threshold was set to 1 × 10−8 eV. The final total energies were calculated using 7 × 13 × 13 meshes and the tetrahedral k-point integration method. The cutoff energy was set to 500 eV for all calculations. Three kinds of PbxSn1−xSe alloy were studied: pure SnSe, Pb0.0625Sn0.9375Se, and Pb0.125Sn0.875Se. The crystal structures are shown in Fig. 1. Supercells consisting of 1 × 2 × 2 primitive cells containing 32 atoms were used. Pb atom dopants were introduced by replacing the atomic positions of Sn with Pb without relaxing the supercell. The thermoelectric properties were calculated using the semi-classical Boltzmann transport theory within the constant relaxation time and rigid band approximations, which was implemented with BoltzTraP code [31]. Within the rigid band approximation, the electronic band structure is assumed to be maintained with any change of carrier doping or temperature. The final integral forms of the electrical and thermal conductivity are
v (T ; μ ) = −
1 qT Ω
3.1. Crystal structures From the lattice relaxation calculations, the lattice constants are a = 11.77, b = 4.21, and c = 4.57 Å which agree with the previous calculations [35,36]. The experimental values are a = 11.58, b = 4.20, and c = 4.50 Å [26]. Typically, it is known that the GGA exchange– correlation functional overestimates the lattice constant [34], and this trend was also confirmed in this work. 3.2. Electronic structures We present electronic band structures in Fig. 2 to elucidate the change of the electronic transport properties with Pb addition. The first and second conduction band minima (CBM1 and CBM2) are shown in the Γ-Y and U-Z directions, respectively. The first and second valence band maxima (VBM1 and VBM2) are shown in the Γ-Z and Γ-Y directions, respectively. The positions of CBM1 and VBM1 are consistent with the previous result [37]. The band gaps of PbxSn1−xSe were 0.6022, 0.6183, and 0.6355 eV for x = 0, x = 0.0625, and x = 0.125, respectively. Such a change in band gap energy was not detected experimentally [26]. It was demonstrated by a density of states analysis that the p-states of Se are dominant in the valence band region, and the additional p-states of the Pb dopant only exist in the same states as those of the Se p-states. Thus, Pb cannot effectively increase the valence band energy [26]. In SnSe, it is important to consider the multi-valence band effect to understand its electronic structure. However, one of our previous results states that the change of the second valence band energy with Pb addition is too minor to affect the electrical transport properties of SnSe [26]. Thus we don’t discuss the multi-valence band effect in this paper. The projected density of states for x = 0.0625 are presented in Fig. 3. For SnSe, it is known that the highest pick in valence band from fermi level to − 4.0 eV is mainly occupied with the hybridization of Sn 5 s orbital and Se 4p orbitals. This bonding pick is unstable and it can contribute to the high Seebeck coefficient [17]. In Fig. 3, the doped sand p-states of Pb showed dos similar to the s, p states of Sn in most energy domains. However, near the Fermi level, both s- and p-states of Pb are significantly different from s- and p-states of Sn in the valence band. The s- and p-states of Sn were hybridized with Se p-states to form peaks, but Pb did not. Nevertheless, the overall shape of the valence band does not change. Because the Se 4p orbital is mainly contribute to the valence band, the contribution of doped Pb is limited. PbxSn1-xSe have a two-phase region at around x = 0.12 [14]. The spin-orbital interaction (SOI) was also considered. Pb 6p orbital is generally changed by SOI. However, any significant changes cannot be found in the result.
∫ σ (ε)(ε−μ) ∂f (ε∂, εμ, T ) dε
S = E (∇T )−1 = (σ −1) ν, κ 0 (T ; μ ) = −
1 q 2T Ω
∫ σ (ε)(ε − μ)2 ∂f (ε∂, εμ, T ) dε
where Ω is the volume of the cell. The σ(ɛ) is the transport distribution, which is expressed by
σ (ε ) =
1 N
∑ σ (k ) k
λ
3. Results and discussion
∫ σ (ε) ∂f (ε∂, εμ, T ) dε
1 Ω
∑ Cλ vλ ⊗ vλ τλSMRT
where V0 is the volume of a unit cell, and vλ and τλSMRT are the group velocity and single mode relaxation time (SMRT) of phonon mode λ , respectively.
2. Calculation details
σ (T ; μ ) = −
1 NV0
δ (ε − ε k ) dε
where N is the number of k-points and σ (k) is the conductivity tensor, which can be obtained by q2 τ υ2(k). The Phonon dispersion and lattice thermal conductivity was
Fig. 1. Crystalline structures of the SnSe compounds (Pb: black, Sn: gray, Se: green) generated with VESTA [27]: (a) pure SnSe, (b) Pb0.0625Sn0.9375Se, and (c) Pb0.125Sn0.875Se.
414
Journal of Solid State Chemistry 270 (2019) 413–418
H.S. Kim et al.
Fig. 2. Band structures of SnSe primitive cell (a), 1 × 2 × 2 supercell of SnSe (32 atoms) (b), Pb0.0625Sn0.9375Se(c), Pb0.125Sn0.875Se(d).
However, at 600 K, shown in Fig. 3(d), Seebeck coefficient of Pb-doped SnSe was less than that of prisitine SnSe under nH ≈ 1 × 1018. This suggests that the carrier concentration can change the Seebeck coefficient of PbxSn1-xSe in the high temperature region, although the effect is limited. In Fig. 4(e) and (f), the effect of Pb doping on the power factor of PbxSn1−xSe is marginal, since the electrical conductivity slightly decreases while the Seebeck coefficient slightly increases. These factors offset each other, and the power factor was almost constant at 600 K, which matches well with the experimental results [26]. At 300 K, the dependence on Pb doping is more obvious; the power factor slightly increases as the Pb concentration increases, though the change is not linearly proportional to the Pb concentration. The power factor is maximized at nH ≈ 1 × 1020, which is consistent with the previous paper [37].
Fig. 3. The projected density of states per atom of PbxSn1−xSe for x = 0.0625.
3.3. Electrical transport properties 3.4. Phonon transport properties The electronic transport properties were calculated from the band structures, both at 300 and 600 K. It is known that SnSe starts to change its phase to CmCm (#63) from 650 K, and complete the transition ~800 K, and doped Pb atoms change its transition temperature region [26]. Thus, it is difficult theoretically as well as experimentally to distinguish the electrical transport properties of Pb doping from the characteristic that is caused by the phase change at high temperature. Here, we focus on the transport properties in Pnma (#62) at high temperature. Electrical conductivity could be calculated per unit of relaxation time, given by the ratio σ/τ. In Fig. 4(a) and (b), the electrical conductivity slightly decreased as the Pb concentration increased. This trend agrees with the experimental data [26]. These results can be attributed to decreased hole mobility. However, the reduction of electrical conductivity in this result is limited, because we don’t consider the relaxation time, which is main contribution on mobility. In Fig. 4(c) and (d), the Seebeck coefficients slightly increase for the Pb-doped SnSe. This trend is more obvious at 300 K than at 600 K. At 300 K, the trend is observed regardless of carrier concentration.
To understand thermal transport, the phonon properties are calculated. The relaxed lattice constants obtained for SnSe using PBEsol are a = 11.43, b = 4.15, and c = 4.36 Å, which are close to the experimental data [26]. The experimental values are a = 11.58, b = 4.20, and c = 4.50 Å. In Fig. 5(a) and (b), the phonon dispersions of PbxSn1−xSe are shown. The calculated phonon dispersion of SnSe in Fig. 5(a) shows a good agreement with the previous ab initio calculations [37]. Fig. 5(b) shows the phonon dispersions for x = 0.0625. The eight atoms in the SnSe unit cell give 24 phonon branches in Fig. 5(a), while the 1 × 2 × 2 supercell in Fig. 5(b) gives 4 times more. The small group velocities of the optical phonons along the Γ–X direction indicate the weak interactions between the layers [37], and the softened acoustic modes along the Γ–X direction suggest weak interatomic bonding along the a-axis and a strong anharmonicity [15]. Both the small group velocities of the optical phonons and softened acoustic modes are observed in Fig. 5(a) and (b). Although numerous bands appear to be present in Fig. 5(b), the group velocities of the optical and acoustic phonons hardly change along the Γ–X direction. 415
Journal of Solid State Chemistry 270 (2019) 413–418
H.S. Kim et al.
Fig. 4. Calculated transport properties of PbxSn1−xSe (x = 0.0–0.125). (a, b) σ/τ, (c, d) S, and (e, f) σS2/τ against carrier concentration for undoped and p-doped SnSe at (a, c, f) 300 K and (b, d, e) 600 K.
be defined. The carrier concentration was set to 1.0 × 1020 to maximize the power factor, and the electronic relaxation time was set to a constant value of 1.0 × 10−15. It is difficult to determine the exact electronic relaxation time, so a constant value is usually used to estimate properties in the relaxation time approximation approach [17]. The seebeck coefficient increased when Pb is added in Fig. 6(a). It can be attributed to decreased chemical potential when Pb added, shown in Fig. 6(d). The chemical potential shifted down ~ 0.02 eV. It means that carrier drift velocity increases, because the drift velocity is the integral of chemical potential, as mentioned above. However, this result is not consistent with experiment, because chemical potential is constant, regardless of Pb content. Therefore, the enhancement of Seebeck coefficient upon Pb addition is hard to be realized. The power factor and ZT values are shown in Figs. 6c and 7. The power factor and ZT values found here are lower than the experimental values due to the lower calculated Seebeck coefficients [14,26]. In Fig. 6(c), the power factor slightly increases with the amount of Pb added. However, in Fig. 6(d), ZT is considerably improved with Pb addition, which indicates that the major factor in improving ZT is the reduction in the lattice thermal conductivity that occurs with Pb addition. These findings are consistent with the experimental results [26].
Instead, the acoustic phonons along the Γ–Y and Γ–Z directions are slowed down. That is, the Pb substitution mainly influences the b- and c-axis directions rather than the a-axis direction. In Fig. 5(c), the lattice thermal conductivities of SnSe were 0.61, 1.67, and 1.16 W m−1 K−1 at 300 K along the a-, b-, and c-axis, respectively. These results are lower than those of a previous calculation performed using the local density approximation (LDA), which found corresponding values of 0.69, 1.87, and 1.41 W m−1 K−1 at room temperature [37]. It should be noted that the different lattice constants obtained affect the calculated lattice thermal conductivities [38]. The relaxed lattice constants using PBEsol are different from those using LDA, so the lattice thermal conductivity can be different. In Fig. 5(d), the lattice thermal conductivities for x = 0.0 and x = 0.0625 were presented. For x = 0.0625, the lattice thermal conductivity decreased to 0.65 W m−1 K−1 at 300 K. The calculated lattice thermal conductivities agree with the experimental data on polycrystalline PbxSn1−xSe [14,26]. Each lattice thermal conductivity value of PbxSn1−xSe shown in Fig. 5(d) is the average of the value of a-, b-, and c- axis. Generally, lattice thermal conductivity decreases alloying by point defect [13]. Wei et al. employed the Debye approximation model to explain the reduction of lattice thermal conductivity by point defect [14]. They also revealed that the doping-induced mass fluctuation plays a key role in phonon scattering in PbxSn1-xSe. In Fig. 5(d), the reduction ratio by Pb doping is considerably similar with the result of Wei et al. Thus, our results from DFT+BTE simulations confirms that the reduction of lattice thermal conductivity is mainly due to the point defect in PbxSn1−xSe. Fig. 6 shows the changes in the thermoelectric properties with temperature. To compute the properties, some parameters needed to
4. Conclusions In summary, we analyzed the effect of Pb doping in PbxSn1−xSe, presented the thermoelectric properties of PbxSn1−xSe based on the DFT +BTE simulation, and compared the results to data obtained from experiments and other calculations. It was verified that band gap energy and total density of states does not change with Pb addition, but the 416
Journal of Solid State Chemistry 270 (2019) 413–418
H.S. Kim et al.
Fig. 5. Calculated phonon dispersions along the high-symmetry paths for PbxSn1−xSe for (a) x = 0.0 and (b) x = 0.0625, with (c) lattice thermal conductivities of SnSe (d) the lattice thermal conductivities of PbxSn1−xSe. Each calculated lattice thermal conductivity value is the average of the a-, b-, c- axis.
Fig. 6. Variations in the calculated thermoelectric properties with temperature. Seebeck coefficient (a), electrical conductivity (b), power factor (c), and Chemical potential (d).
417
Journal of Solid State Chemistry 270 (2019) 413–418
H.S. Kim et al.
[13] G. Tan, L.D. Zhao, M.G. Kanatzidis, Rationally designing high-performance bulk thermoelectric materials, Chem. Rev. 116 (2016) 12123–12149. http://dx.doi.org/ 10.1021/acs.chemrev.6b00255. [14] T.R. Wei, G. Tan, C.F. Wu, C. Chang, L.D. Zhao, J.F. Li, G.J. Snyder, M.G. Kanatzidis, Thermoelectric transport properties of polycrystalline SnSe alloyed with PbSe, Appl. Phys. Lett. 110 (2017) 053901. http://dx.doi.org/10.1063/1.4975603. [15] L.-D. Zhao, C. Chang, G. Tan, M.G. Kanatzidis, SnSe: a remarkable new thermoelectric material, Energy Environ. Sci. 9 (2016) 3044–3060. http://dx.doi.org/10.1039/ C6EE01755J. [16] L.-D. Zhao, S.-H. Lo, Y. Zhang, H. Sun, G. Tan, C. Uher, C. Wolverton, V.P. Dravid, M.G. Kanatzidis, Ultralow thermal conductivity and high thermoelectric figure of merit in SnSe crystals, Nature 508 (2014) 373–377. http://dx.doi.org/10.1038/nature13184. [17] A.J. Hong, L. Li, H.X. Zhu, Z.B. Yan, J.-M. Liu, Z.F. Ren, Optimizing the thermoelectric performance of low-temperature SnSe compounds by electronic structure design, J. Mater. Chem. A 3 (2015) 13365–13370. http://dx.doi.org/10.1039/C5TA01703C. [18] C.W. Li, J. Hong, A.F. May, D. Bansal, S. Chi, T. Hong, G. Ehlers, O. Delaire, Orbitally driven giant phonon anharmonicity in SnSe, Nat. Phys. 11 (2015) 1–8. http://dx.doi.org/ 10.1038/nphys3492. [19] L.-D. Zhao, G. Tan, S. Hao, J. He, Y. Pei, H. Chi, H. Wang, S. Gong, H. Xu, V.P. Dravid, C. Uher, G.J. Snyder, C. Wolverton, M.G. Kanatzidis, Ultrahigh power factor and thermoelectric performance in hole-doped single-crystal SnSe, Science 351 (80-.) (2016) 141–144. http://dx.doi.org/10.1126/science.aad3749. [20] T.R. Wei, G. Tan, X. Zhang, C.F. Wu, J.F. Li, V.P. Dravid, G.J. Snyder, M.G. Kanatzidis, Distinct impact of alkali-ion doping on electrical transport properties of thermoelectric ptype polycrystalline SnSe, J. Am. Chem. Soc. 138 (2016) 8875–8882. http://dx.doi.org/ 10.1021/jacs.6b04181. [21] A.T. Duong, V.Q. Nguyen, G. Duvjir, V.T. Duong, S. Kwon, J.Y. Song, J.K. Lee, J.E. Lee, S. Park, T. Min, J. Lee, J. Kim, S. Cho, Achieving ZT=2.2 with Bi-doped n-type SnSe single crystals, Nat. Commun. 7 (2016) 13713. http://dx.doi.org/10.1038/ ncomms13713.371. [22] W. Liu, X. Tan, K. Yin, H. Liu, X. Tang, J. Shi, Q. Zhang, C. Uher, Convergence of conduction bands as a means of enhancing thermoelectric performance of n-type Mg2Si(1-x)Sn(x) solid solutions (https://link.aps.org/doi/)Phys. Rev. Lett. 108 (2012) 166601. http://dx.doi.org/10.1103/PhysRevLett.108.166601. [23] Y. Pei, H. Wang, G.J. Snyder, Band engineering of thermoelectric materials, Adv. Mater. 24 (2012) 6125–6135. http://dx.doi.org/10.1002/adma.201202919. [24] B. Abeles, Lattice thermal conductivity of disordered semiconductor alloys at high temperatures, Phys. Rev. 131 (1963) 1906–1911. http://dx.doi.org/10.1103/ PhysRev.131.1906. [25] S. Lee, K. Esfarjani, T. Luo, J. Zhou, Z. Tian, G. Chen, Resonant bonding leads to low lattice thermal conductivity, Nat. Commun. 5 (2014) 1–8. http://dx.doi.org/10.1038/ ncomms4525. [26] Y.K. Lee, K. Ahn, J. Cha, C. Zhou, H.S. Kim, G. Choi, S.I. Chae, J.H. Park, S.P. Cho, S.H. Park, Y.E. Sung, W.B. Lee, T. Hyeon, I. Chung, Enhancing p-type thermoelectric performances of polycrystalline snse via tuning phase transition temperature, J. Am. Chem. Soc. 139 (2017) 10887–10896. http://dx.doi.org/10.1021/jacs.7b05881. [27] K. Momma, F. Izumi, VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data1 K, J. Appl. Crystallogr. 44 (2011) 1272–1276. http://dx.doi.org/ 10.1107/S0021889811038970. [28] L.D. Hicks, M.S. Dresselhaus, Effect of quantum-well structures on the thermomagnetic figure of merit, Phys. Rev. B. 47 (1993) 727–731. http://dx.doi.org/10.1103/ PhysRevB.47.12727. [29] G. Kresse, J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B. (1996). http://dx.doi.org/10.1103/ PhysRevB.54.11169. [30] J. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77 (1996) 3865–3868. http://dx.doi.org/10.1103/PhysRevLett.77.3865. [31] G.K.H. Madsen, D.J. Singh, P. BoltzTra, A code for calculating band-structure dependent quantities, Comput. Phys. Commun. 175 (2006) 67–71. http://dx.doi.org/10.1016/ j.cpc.2006.03.007. [32] A. Togo, L. Chaput, I. Tanaka, Distributions of phonon lifetimes in Brillouin zones, Phys. Rev. B. 91 (2015) 94306. http://dx.doi.org/10.1103/PhysRevB.91.094306. [33] A. Togo, I. Tanaka, First principles phonon calculations in materials science, Scr. Mater. 108 (2015) 1–5. http://dx.doi.org/10.1016/j.scriptamat.2015.07.021. [34] G.I. Csonka, J.P. Perdew, A. Ruzsinszky, P.H.T. Philipsen, S. Lebègue, J. Paier, O.A. Vydrov, J.G. Ángyán, Assessing the performance of recent density functionals for bulk solids, Phys. Rev. B - Condens. Matter Mater. Phys. 79 (2009) 1–14. http:// dx.doi.org/10.1103/PhysRevB.79.155107. [35] L.-D. Zhao, S.-H. Lo, Y. Zhang, H. Sun, G. Tan, C. Uher, C. Wolverton, V.P. Dravid, M.G. Kanatzidis, Ultralow thermal conductivity and high thermoelectric figure of merit in SnSe crystals, Nature 508 (2014) 373–377. http://dx.doi.org/10.1038/nature13184. [36] A. Dewandre, O. Hellman, S. Bhattacharya, A.H. Romero, G.K.H. Madsen, M.J. Verstraete, Two-step phase transition in snse and the origins of its high power factor from first principles, Phys. Rev. Lett. 117 (2016) 276601. http://dx.doi.org/10.1103/ PhysRevLett.117.276601. [37] R. Guo, X. Wang, Y. Kuang, B. Huang, First-principles study of anisotropic thermoelectric transport properties of IV-VI semiconductor compounds SnSe and SnS, Phys. Rev. B - Condens. Matter Mater. Phys. 92 (2015) 115202. http://dx.doi.org/10.1103/ PhysRevB.92.115202. [38] M.Y. Ha, G. Choi, D.H. Kim, H.S. Kim, S.H. Park, W.B. Lee, Effect of lattice relaxation on thermal conductivity of fcc-based structures: an efficient procedure of molecular dynamics simulation, Model. Simul. Mater. Sci. Eng. 25 (2017) 055011. http:// dx.doi.org/10.1088/1361-651X/aa6a2d.
Fig. 7. The final calculated Figure of Merit (ZT).
projected density of states of Pb show different shape near the fermi level. From the results the electrical conductivity and Seebeck coefficient were presented. Meanwhile, a 43% reduction in the lattice thermal conductivity is calculated and the ZT of PbxSn1−xSe is enhanced by the addition of Pb due to the decrease in lattice thermal conductivity. Most of the calculation results are consistent with experiments. It was confirmed that our DFT+BTE simulation gives reasonable results of the thermoelectric properties. Our approach will shed a light on the works of predicting thermoelectric properties of alloys. Acknowledgements This work was supported by a National Research Foundation of Korea (NRF) grant funded by the Korean Government through the Ministry of Science, ICT and Future Planning (MSIP) (NRF-2015R1A5A1036133). References [1] S.J. Kim, J.H. We, B.J. Cho, A wearable thermoelectric generator fabricated on a glass fabric, Energy Environ. Sci. 7 (2014) 1959. http://dx.doi.org/10.1039/c4ee00242c. [2] L.E. Bell, Cooling, heating, generating power, and recovering waste heat with thermoelectric systems, Science 321 (80-.) (2008) 1457–1461. http://dx.doi.org/10.1126/ science.1158899. [3] M. Zebarjadi, K. Esfarjani, M.S. Dresselhaus, Z.F. Ren, G. Chen, Perspectives on thermoelectrics: from fundamentals to device applications, Energy Environ. Sci. 5 (2012) 5147–5162. http://dx.doi.org/10.1039/C1EE02497C. [4] G. Chen, Theoretical efficiency of solar thermoelectric energy generators, J. Appl. Phys. 109 (2011) 104908. http://dx.doi.org/10.1063/1.3583182. [5] D. Wu, L.-D. Zhao, X. Tong, W. Li, L. Wu, Q. Tan, Y. Pei, L. Huang, J.-F. Li, Y. Zhu, M.G. Kanatzidis, J. He, Superior thermoelectric performance in PbTe–PbS pseudobinary: extremely low thermal conductivity and modulated carrier concentration, Energy Environ. Sci. 8 (2015) 2056–2068. http://dx.doi.org/10.1039/C5EE01147G. [6] Y. Pei, A.D. LaLonde, N.A. Heinz, G.J. Snyder, High thermoelectric figure of merit in PbTe alloys demonstrated in PbTe-CdTe, Adv. Energy Mater. 2 (2012) 670–675. http:// dx.doi.org/10.1002/aenm.201100770. [7] M.G. Kanatzidis, Nanostructured thermoelectrics: the new paradigm?, Chem. Mater. 22 (2010) 648–659. http://dx.doi.org/10.1021/cm902195j. [8] Y. Lee, S.-H. Lo, C. Chen, H. Sun, D.-Y. Chung, T.C. Chasapis, C. Uher, V.P. Dravid, M.G. Kanatzidis, Contrasting role of antimony and bismuth dopants on the thermoelectric performance of lead selenide, Nat. Commun. 5 (2014) 1–11. http://dx.doi.org/ 10.1038/ncomms4640. [9] Y. Han, Z. Chen, C. Xin, Y. Pei, M. Zhou, R. Huang, L. Li, Improved thermoelectric performance of Nb-doped lead selenide, J. Alloy. Compd. 600 (2014) 91–95. http:// dx.doi.org/10.1016/j.jallcom.2014.02.077. [10] G. Tan, F. Shi, S. Hao, H. Chi, T.P. Bailey, L.D. Zhao, C. Uher, C. Wolverton, V.P. Dravid, M.G. Kanatzidis, Valence band modification and high thermoelectric performance in SnTe heavily alloyed with MnTe, J. Am. Chem. Soc. 137 (2015) 11507–11516. http:// dx.doi.org/10.1021/jacs.5b07284. [11] G. Tan, F. Shi, J.W. Doak, H. Sun, L.-D. Zhao, P. Wang, C. Uher, C. Wolverton, V.P. Dravid, Kanatzidis, Extraordinary role of Hg in enhancing the thermoelectric performance of p-type SnTe, Energy Environ. Sci. 8 (2015) 267–277. http://dx.doi.org/ 10.1039/C4EE01463D. [12] A. Banik, U.S. Shenoy, S. Anand, U.V. Waghmare, K. Biswas, Mg alloying in SnTe facilitates valence band convergence and optimizes thermoelectric properties, Chem. Mater. 27 (2015) 581–587. http://dx.doi.org/10.1021/cm504112m.
418
Contents lists available at ScienceDirect
Journal of Solid State Chemistry journal homepage: www.elsevier.com/locate/jssc
Thermoelectric transport properties of Pb doped SnSe alloys (PbxSn1-xSe): DFT-BTE simulations
MARK
⁎
Hyo Seok Kima, Garam Choia, Min Young Haa, Dong Hyun Kima, Sang Hyun Parkb, In Chunga, , ⁎ Won Bo Leea, a b
School of Chemical and Biological Engineering, Institute of Chemical Processes, Seoul National University, Seoul 08826, Republic of Korea Korea Institute of Energy Research, Daejeon 34129, Republic of Korea
A R T I C L E I N F O
A BS T RAC T
Keywords: Thermoelectric Doping Density functional theory Tin selenide
Thermoelectric transport properties of Pb doped SnSe alloys, PbxSn1-xSe, were systematically investigated by DFT-BTE simulations. The figure of merit is mainly enhanced by reducing lattice thermal conductivity which is estimated about 43% decrease with Pb addition. Electrical conductivity and Seebeck coefficient evaluated by using the Boltzmann transport equation with a constant relaxation time approximation. These electronic transport properties hardly changed with Pb addition, and did not make any significant change in electron transport. However, the considerable change in phonon transport and lattice thermal conductivity are shown. This investigation elucidates the electrons and phonons transport phenomena in alloys, leading the design of new high-performance thermoelectric materials.
1. Introduction The growth of world energy demands has triggered the exploration of alternative energy resources. Thermoelectric materials have been a major focus because of their potential in wearable devices [1], waste heat recovery [2], and other various applications [3,4]. To be commercially viable, raising the efficiency has been one of the most important challenges in this area. The efficiency, called the figure of merit (ZT), is determined by ZT = S2σT/(κe+ κL): S is the Seebeck coefficient, σ is electrical conductivity, κe is electrical thermal conductivity, κL is the lattice thermal conductivity, and T is temperature. A number of IV–VI compounds have been reported to be highperformance thermoelectric materials. PbTe [5–7], PbSe [8,9], SnTe [10–12], and their alloys have been main subjects of research. Their narrow band gap energy, large effective mass, and highly resonant levels enable these IV–VI compounds to have high-performances [13]. SnSe, another IV–VI compound, has recently been extensively studied because of the high thermoelectric efficiency of its bulk crystal form and economic competitiveness. SnSe has a Pnma structure (#62) at ~800 K, and its experimentally determined lattice constants are a = 11.49, b = 4.15, and c = 4.45 Å [14]. At around 800 K, a phase transition from the Pmma to Cmcm (#63) structure occurs; the Sn2+ state is preferred, and the d-orbitals are involved in long-range interactions. In the Pnma case, each Sn2+ atom is surrounded by seven Se atoms in a perturbed arrangement with a corresponding resonant structure [15]. ⁎
Recently, a value of ZT = 2.6 along the b-axis was measured by Zhao et al. [15], which was a great advance in thermoelectric research. Since then, SnSe has drawn the attention of many researchers and meaningful advances are being made. Its intrinsic high-performance is verified not only experimental approaches, but also theoretical and computational approaches. Zhao et. al. firstly investigated the highperformance thermoelectric properties of SnSe using band-structure analysis [16]. They presented all valence band maxima of SnSe and their effective mass, and indicated that multiple valleys enable a high Seebeck coefficient. Hong et. al. indicated that a weak hybridization exists between Sn 5 s-states and Se-4p states from projected density of states(pDOS) analysis, and a high Seebeck coefficient of SnSe can attribute to the hybridization [17]. In addition, Li et. al. reported the hybridization also cause a phonon anharmonicity, thereby an ultra-low lattice thermal conductivity of SnSe is achieved [18]. Based on these findings, there have been several attempts to improve the performance of SnSe through doping [13,19–21], increasing the band degeneracy [22,23], and decreasing the lattice thermal conductivity [10,24,25]. The attempts to optimize the performance through doping are especially noteworthy. It was revealed that heavily hole-doped SnSe showed an improved ZT at lower temperatures. One of the novel strategies to tune the optimum performance temperature of SnSe was proposed by Lee et al. [26]. They verified that ZT can be enhanced to ~1.2 at 773 K with hole-doped polycrystalline PbxSn1−xSe by changing the phase transition temperature. However,
Corresponding authors. E-mail addresses: [email protected] (I. Chung), [email protected] (W.B. Lee).
https://doi.org/10.1016/j.jssc.2018.12.003 Received 27 August 2018; Received in revised form 7 November 2018; Accepted 1 December 2018 Available online 04 December 2018 0022-4596/ © 2018 Elsevier Inc. All rights reserved.
Journal of Solid State Chemistry 270 (2019) 413–418
H.S. Kim et al.
calculated using PHONO3PY [32] and PHONOPY [33]. Harmonic and anharmonic interatomic force constants (IFCs) were calculated using VASP [28,29] and the PBEsol [34] exchange–correlation functional. The atomic displacement was set to 0.03 Å, and the k-meshes for the force calculations were set to 2 × 2 × 2. To calculate the lattice thermal conductivity, the q-meshes were set to 7 × 7 × 7. The lattice thermal conductivity was computed from a solution of the linearized phonon Boltzmann transport equation (LBTE) [32]. The equation can be written in a closed form,
there have still been leaving questions how electrons and phonons behave in an alloy in which these factors are intricately intertwined. Especially, there is little First-principles research on verifying the effect of Pb alloying on reducing lattice thermal conductivity, which is critical to define high figure of merit. Here, we investigated the thermoelectric properties of PbxSn1−xSe alloys based on first-principles calculations. First, the electronic band structures are calculated, and the differences between a pure SnSe and a Pb-doped SnSe are discussed. The transport properties are then provided by solving the Boltzmann transport equation (BTE). Finally, the ZT values are evaluated, and the influence of Pb doping on the thermoelectric transport properties is discussed.
κ=
All the density functional theory (DFT) calculations described in this work were performed by using the projector augmented wave (PAW) formalism, as implemented in the Vienna Ab–initio Simulation Package (VASP) [28,29]. The exchange–correlation functional, given by the generalized gradient approximation (GGA) suggested by Perdew, Burke, and Ernzerhof (PBE) [30], was selected. The potentials used for Sn, Se, and Pb include the 4d105s25p2, 4s24p4, and 5d105s25p2 valence electrons, respectively. The energy convergence threshold was set to 1 × 10−8 eV. The final total energies were calculated using 7 × 13 × 13 meshes and the tetrahedral k-point integration method. The cutoff energy was set to 500 eV for all calculations. Three kinds of PbxSn1−xSe alloy were studied: pure SnSe, Pb0.0625Sn0.9375Se, and Pb0.125Sn0.875Se. The crystal structures are shown in Fig. 1. Supercells consisting of 1 × 2 × 2 primitive cells containing 32 atoms were used. Pb atom dopants were introduced by replacing the atomic positions of Sn with Pb without relaxing the supercell. The thermoelectric properties were calculated using the semi-classical Boltzmann transport theory within the constant relaxation time and rigid band approximations, which was implemented with BoltzTraP code [31]. Within the rigid band approximation, the electronic band structure is assumed to be maintained with any change of carrier doping or temperature. The final integral forms of the electrical and thermal conductivity are
v (T ; μ ) = −
1 qT Ω
3.1. Crystal structures From the lattice relaxation calculations, the lattice constants are a = 11.77, b = 4.21, and c = 4.57 Å which agree with the previous calculations [35,36]. The experimental values are a = 11.58, b = 4.20, and c = 4.50 Å [26]. Typically, it is known that the GGA exchange– correlation functional overestimates the lattice constant [34], and this trend was also confirmed in this work. 3.2. Electronic structures We present electronic band structures in Fig. 2 to elucidate the change of the electronic transport properties with Pb addition. The first and second conduction band minima (CBM1 and CBM2) are shown in the Γ-Y and U-Z directions, respectively. The first and second valence band maxima (VBM1 and VBM2) are shown in the Γ-Z and Γ-Y directions, respectively. The positions of CBM1 and VBM1 are consistent with the previous result [37]. The band gaps of PbxSn1−xSe were 0.6022, 0.6183, and 0.6355 eV for x = 0, x = 0.0625, and x = 0.125, respectively. Such a change in band gap energy was not detected experimentally [26]. It was demonstrated by a density of states analysis that the p-states of Se are dominant in the valence band region, and the additional p-states of the Pb dopant only exist in the same states as those of the Se p-states. Thus, Pb cannot effectively increase the valence band energy [26]. In SnSe, it is important to consider the multi-valence band effect to understand its electronic structure. However, one of our previous results states that the change of the second valence band energy with Pb addition is too minor to affect the electrical transport properties of SnSe [26]. Thus we don’t discuss the multi-valence band effect in this paper. The projected density of states for x = 0.0625 are presented in Fig. 3. For SnSe, it is known that the highest pick in valence band from fermi level to − 4.0 eV is mainly occupied with the hybridization of Sn 5 s orbital and Se 4p orbitals. This bonding pick is unstable and it can contribute to the high Seebeck coefficient [17]. In Fig. 3, the doped sand p-states of Pb showed dos similar to the s, p states of Sn in most energy domains. However, near the Fermi level, both s- and p-states of Pb are significantly different from s- and p-states of Sn in the valence band. The s- and p-states of Sn were hybridized with Se p-states to form peaks, but Pb did not. Nevertheless, the overall shape of the valence band does not change. Because the Se 4p orbital is mainly contribute to the valence band, the contribution of doped Pb is limited. PbxSn1-xSe have a two-phase region at around x = 0.12 [14]. The spin-orbital interaction (SOI) was also considered. Pb 6p orbital is generally changed by SOI. However, any significant changes cannot be found in the result.
∫ σ (ε)(ε−μ) ∂f (ε∂, εμ, T ) dε
S = E (∇T )−1 = (σ −1) ν, κ 0 (T ; μ ) = −
1 q 2T Ω
∫ σ (ε)(ε − μ)2 ∂f (ε∂, εμ, T ) dε
where Ω is the volume of the cell. The σ(ɛ) is the transport distribution, which is expressed by
σ (ε ) =
1 N
∑ σ (k ) k
λ
3. Results and discussion
∫ σ (ε) ∂f (ε∂, εμ, T ) dε
1 Ω
∑ Cλ vλ ⊗ vλ τλSMRT
where V0 is the volume of a unit cell, and vλ and τλSMRT are the group velocity and single mode relaxation time (SMRT) of phonon mode λ , respectively.
2. Calculation details
σ (T ; μ ) = −
1 NV0
δ (ε − ε k ) dε
where N is the number of k-points and σ (k) is the conductivity tensor, which can be obtained by q2 τ υ2(k). The Phonon dispersion and lattice thermal conductivity was
Fig. 1. Crystalline structures of the SnSe compounds (Pb: black, Sn: gray, Se: green) generated with VESTA [27]: (a) pure SnSe, (b) Pb0.0625Sn0.9375Se, and (c) Pb0.125Sn0.875Se.
414
Journal of Solid State Chemistry 270 (2019) 413–418
H.S. Kim et al.
Fig. 2. Band structures of SnSe primitive cell (a), 1 × 2 × 2 supercell of SnSe (32 atoms) (b), Pb0.0625Sn0.9375Se(c), Pb0.125Sn0.875Se(d).
However, at 600 K, shown in Fig. 3(d), Seebeck coefficient of Pb-doped SnSe was less than that of prisitine SnSe under nH ≈ 1 × 1018. This suggests that the carrier concentration can change the Seebeck coefficient of PbxSn1-xSe in the high temperature region, although the effect is limited. In Fig. 4(e) and (f), the effect of Pb doping on the power factor of PbxSn1−xSe is marginal, since the electrical conductivity slightly decreases while the Seebeck coefficient slightly increases. These factors offset each other, and the power factor was almost constant at 600 K, which matches well with the experimental results [26]. At 300 K, the dependence on Pb doping is more obvious; the power factor slightly increases as the Pb concentration increases, though the change is not linearly proportional to the Pb concentration. The power factor is maximized at nH ≈ 1 × 1020, which is consistent with the previous paper [37].
Fig. 3. The projected density of states per atom of PbxSn1−xSe for x = 0.0625.
3.3. Electrical transport properties 3.4. Phonon transport properties The electronic transport properties were calculated from the band structures, both at 300 and 600 K. It is known that SnSe starts to change its phase to CmCm (#63) from 650 K, and complete the transition ~800 K, and doped Pb atoms change its transition temperature region [26]. Thus, it is difficult theoretically as well as experimentally to distinguish the electrical transport properties of Pb doping from the characteristic that is caused by the phase change at high temperature. Here, we focus on the transport properties in Pnma (#62) at high temperature. Electrical conductivity could be calculated per unit of relaxation time, given by the ratio σ/τ. In Fig. 4(a) and (b), the electrical conductivity slightly decreased as the Pb concentration increased. This trend agrees with the experimental data [26]. These results can be attributed to decreased hole mobility. However, the reduction of electrical conductivity in this result is limited, because we don’t consider the relaxation time, which is main contribution on mobility. In Fig. 4(c) and (d), the Seebeck coefficients slightly increase for the Pb-doped SnSe. This trend is more obvious at 300 K than at 600 K. At 300 K, the trend is observed regardless of carrier concentration.
To understand thermal transport, the phonon properties are calculated. The relaxed lattice constants obtained for SnSe using PBEsol are a = 11.43, b = 4.15, and c = 4.36 Å, which are close to the experimental data [26]. The experimental values are a = 11.58, b = 4.20, and c = 4.50 Å. In Fig. 5(a) and (b), the phonon dispersions of PbxSn1−xSe are shown. The calculated phonon dispersion of SnSe in Fig. 5(a) shows a good agreement with the previous ab initio calculations [37]. Fig. 5(b) shows the phonon dispersions for x = 0.0625. The eight atoms in the SnSe unit cell give 24 phonon branches in Fig. 5(a), while the 1 × 2 × 2 supercell in Fig. 5(b) gives 4 times more. The small group velocities of the optical phonons along the Γ–X direction indicate the weak interactions between the layers [37], and the softened acoustic modes along the Γ–X direction suggest weak interatomic bonding along the a-axis and a strong anharmonicity [15]. Both the small group velocities of the optical phonons and softened acoustic modes are observed in Fig. 5(a) and (b). Although numerous bands appear to be present in Fig. 5(b), the group velocities of the optical and acoustic phonons hardly change along the Γ–X direction. 415
Journal of Solid State Chemistry 270 (2019) 413–418
H.S. Kim et al.
Fig. 4. Calculated transport properties of PbxSn1−xSe (x = 0.0–0.125). (a, b) σ/τ, (c, d) S, and (e, f) σS2/τ against carrier concentration for undoped and p-doped SnSe at (a, c, f) 300 K and (b, d, e) 600 K.
be defined. The carrier concentration was set to 1.0 × 1020 to maximize the power factor, and the electronic relaxation time was set to a constant value of 1.0 × 10−15. It is difficult to determine the exact electronic relaxation time, so a constant value is usually used to estimate properties in the relaxation time approximation approach [17]. The seebeck coefficient increased when Pb is added in Fig. 6(a). It can be attributed to decreased chemical potential when Pb added, shown in Fig. 6(d). The chemical potential shifted down ~ 0.02 eV. It means that carrier drift velocity increases, because the drift velocity is the integral of chemical potential, as mentioned above. However, this result is not consistent with experiment, because chemical potential is constant, regardless of Pb content. Therefore, the enhancement of Seebeck coefficient upon Pb addition is hard to be realized. The power factor and ZT values are shown in Figs. 6c and 7. The power factor and ZT values found here are lower than the experimental values due to the lower calculated Seebeck coefficients [14,26]. In Fig. 6(c), the power factor slightly increases with the amount of Pb added. However, in Fig. 6(d), ZT is considerably improved with Pb addition, which indicates that the major factor in improving ZT is the reduction in the lattice thermal conductivity that occurs with Pb addition. These findings are consistent with the experimental results [26].
Instead, the acoustic phonons along the Γ–Y and Γ–Z directions are slowed down. That is, the Pb substitution mainly influences the b- and c-axis directions rather than the a-axis direction. In Fig. 5(c), the lattice thermal conductivities of SnSe were 0.61, 1.67, and 1.16 W m−1 K−1 at 300 K along the a-, b-, and c-axis, respectively. These results are lower than those of a previous calculation performed using the local density approximation (LDA), which found corresponding values of 0.69, 1.87, and 1.41 W m−1 K−1 at room temperature [37]. It should be noted that the different lattice constants obtained affect the calculated lattice thermal conductivities [38]. The relaxed lattice constants using PBEsol are different from those using LDA, so the lattice thermal conductivity can be different. In Fig. 5(d), the lattice thermal conductivities for x = 0.0 and x = 0.0625 were presented. For x = 0.0625, the lattice thermal conductivity decreased to 0.65 W m−1 K−1 at 300 K. The calculated lattice thermal conductivities agree with the experimental data on polycrystalline PbxSn1−xSe [14,26]. Each lattice thermal conductivity value of PbxSn1−xSe shown in Fig. 5(d) is the average of the value of a-, b-, and c- axis. Generally, lattice thermal conductivity decreases alloying by point defect [13]. Wei et al. employed the Debye approximation model to explain the reduction of lattice thermal conductivity by point defect [14]. They also revealed that the doping-induced mass fluctuation plays a key role in phonon scattering in PbxSn1-xSe. In Fig. 5(d), the reduction ratio by Pb doping is considerably similar with the result of Wei et al. Thus, our results from DFT+BTE simulations confirms that the reduction of lattice thermal conductivity is mainly due to the point defect in PbxSn1−xSe. Fig. 6 shows the changes in the thermoelectric properties with temperature. To compute the properties, some parameters needed to
4. Conclusions In summary, we analyzed the effect of Pb doping in PbxSn1−xSe, presented the thermoelectric properties of PbxSn1−xSe based on the DFT +BTE simulation, and compared the results to data obtained from experiments and other calculations. It was verified that band gap energy and total density of states does not change with Pb addition, but the 416
Journal of Solid State Chemistry 270 (2019) 413–418
H.S. Kim et al.
Fig. 5. Calculated phonon dispersions along the high-symmetry paths for PbxSn1−xSe for (a) x = 0.0 and (b) x = 0.0625, with (c) lattice thermal conductivities of SnSe (d) the lattice thermal conductivities of PbxSn1−xSe. Each calculated lattice thermal conductivity value is the average of the a-, b-, c- axis.
Fig. 6. Variations in the calculated thermoelectric properties with temperature. Seebeck coefficient (a), electrical conductivity (b), power factor (c), and Chemical potential (d).
417
Journal of Solid State Chemistry 270 (2019) 413–418
H.S. Kim et al.
[13] G. Tan, L.D. Zhao, M.G. Kanatzidis, Rationally designing high-performance bulk thermoelectric materials, Chem. Rev. 116 (2016) 12123–12149. http://dx.doi.org/ 10.1021/acs.chemrev.6b00255. [14] T.R. Wei, G. Tan, C.F. Wu, C. Chang, L.D. Zhao, J.F. Li, G.J. Snyder, M.G. Kanatzidis, Thermoelectric transport properties of polycrystalline SnSe alloyed with PbSe, Appl. Phys. Lett. 110 (2017) 053901. http://dx.doi.org/10.1063/1.4975603. [15] L.-D. Zhao, C. Chang, G. Tan, M.G. Kanatzidis, SnSe: a remarkable new thermoelectric material, Energy Environ. Sci. 9 (2016) 3044–3060. http://dx.doi.org/10.1039/ C6EE01755J. [16] L.-D. Zhao, S.-H. Lo, Y. Zhang, H. Sun, G. Tan, C. Uher, C. Wolverton, V.P. Dravid, M.G. Kanatzidis, Ultralow thermal conductivity and high thermoelectric figure of merit in SnSe crystals, Nature 508 (2014) 373–377. http://dx.doi.org/10.1038/nature13184. [17] A.J. Hong, L. Li, H.X. Zhu, Z.B. Yan, J.-M. Liu, Z.F. Ren, Optimizing the thermoelectric performance of low-temperature SnSe compounds by electronic structure design, J. Mater. Chem. A 3 (2015) 13365–13370. http://dx.doi.org/10.1039/C5TA01703C. [18] C.W. Li, J. Hong, A.F. May, D. Bansal, S. Chi, T. Hong, G. Ehlers, O. Delaire, Orbitally driven giant phonon anharmonicity in SnSe, Nat. Phys. 11 (2015) 1–8. http://dx.doi.org/ 10.1038/nphys3492. [19] L.-D. Zhao, G. Tan, S. Hao, J. He, Y. Pei, H. Chi, H. Wang, S. Gong, H. Xu, V.P. Dravid, C. Uher, G.J. Snyder, C. Wolverton, M.G. Kanatzidis, Ultrahigh power factor and thermoelectric performance in hole-doped single-crystal SnSe, Science 351 (80-.) (2016) 141–144. http://dx.doi.org/10.1126/science.aad3749. [20] T.R. Wei, G. Tan, X. Zhang, C.F. Wu, J.F. Li, V.P. Dravid, G.J. Snyder, M.G. Kanatzidis, Distinct impact of alkali-ion doping on electrical transport properties of thermoelectric ptype polycrystalline SnSe, J. Am. Chem. Soc. 138 (2016) 8875–8882. http://dx.doi.org/ 10.1021/jacs.6b04181. [21] A.T. Duong, V.Q. Nguyen, G. Duvjir, V.T. Duong, S. Kwon, J.Y. Song, J.K. Lee, J.E. Lee, S. Park, T. Min, J. Lee, J. Kim, S. Cho, Achieving ZT=2.2 with Bi-doped n-type SnSe single crystals, Nat. Commun. 7 (2016) 13713. http://dx.doi.org/10.1038/ ncomms13713.371. [22] W. Liu, X. Tan, K. Yin, H. Liu, X. Tang, J. Shi, Q. Zhang, C. Uher, Convergence of conduction bands as a means of enhancing thermoelectric performance of n-type Mg2Si(1-x)Sn(x) solid solutions (https://link.aps.org/doi/)Phys. Rev. Lett. 108 (2012) 166601. http://dx.doi.org/10.1103/PhysRevLett.108.166601. [23] Y. Pei, H. Wang, G.J. Snyder, Band engineering of thermoelectric materials, Adv. Mater. 24 (2012) 6125–6135. http://dx.doi.org/10.1002/adma.201202919. [24] B. Abeles, Lattice thermal conductivity of disordered semiconductor alloys at high temperatures, Phys. Rev. 131 (1963) 1906–1911. http://dx.doi.org/10.1103/ PhysRev.131.1906. [25] S. Lee, K. Esfarjani, T. Luo, J. Zhou, Z. Tian, G. Chen, Resonant bonding leads to low lattice thermal conductivity, Nat. Commun. 5 (2014) 1–8. http://dx.doi.org/10.1038/ ncomms4525. [26] Y.K. Lee, K. Ahn, J. Cha, C. Zhou, H.S. Kim, G. Choi, S.I. Chae, J.H. Park, S.P. Cho, S.H. Park, Y.E. Sung, W.B. Lee, T. Hyeon, I. Chung, Enhancing p-type thermoelectric performances of polycrystalline snse via tuning phase transition temperature, J. Am. Chem. Soc. 139 (2017) 10887–10896. http://dx.doi.org/10.1021/jacs.7b05881. [27] K. Momma, F. Izumi, VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data1 K, J. Appl. Crystallogr. 44 (2011) 1272–1276. http://dx.doi.org/ 10.1107/S0021889811038970. [28] L.D. Hicks, M.S. Dresselhaus, Effect of quantum-well structures on the thermomagnetic figure of merit, Phys. Rev. B. 47 (1993) 727–731. http://dx.doi.org/10.1103/ PhysRevB.47.12727. [29] G. Kresse, J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B. (1996). http://dx.doi.org/10.1103/ PhysRevB.54.11169. [30] J. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77 (1996) 3865–3868. http://dx.doi.org/10.1103/PhysRevLett.77.3865. [31] G.K.H. Madsen, D.J. Singh, P. BoltzTra, A code for calculating band-structure dependent quantities, Comput. Phys. Commun. 175 (2006) 67–71. http://dx.doi.org/10.1016/ j.cpc.2006.03.007. [32] A. Togo, L. Chaput, I. Tanaka, Distributions of phonon lifetimes in Brillouin zones, Phys. Rev. B. 91 (2015) 94306. http://dx.doi.org/10.1103/PhysRevB.91.094306. [33] A. Togo, I. Tanaka, First principles phonon calculations in materials science, Scr. Mater. 108 (2015) 1–5. http://dx.doi.org/10.1016/j.scriptamat.2015.07.021. [34] G.I. Csonka, J.P. Perdew, A. Ruzsinszky, P.H.T. Philipsen, S. Lebègue, J. Paier, O.A. Vydrov, J.G. Ángyán, Assessing the performance of recent density functionals for bulk solids, Phys. Rev. B - Condens. Matter Mater. Phys. 79 (2009) 1–14. http:// dx.doi.org/10.1103/PhysRevB.79.155107. [35] L.-D. Zhao, S.-H. Lo, Y. Zhang, H. Sun, G. Tan, C. Uher, C. Wolverton, V.P. Dravid, M.G. Kanatzidis, Ultralow thermal conductivity and high thermoelectric figure of merit in SnSe crystals, Nature 508 (2014) 373–377. http://dx.doi.org/10.1038/nature13184. [36] A. Dewandre, O. Hellman, S. Bhattacharya, A.H. Romero, G.K.H. Madsen, M.J. Verstraete, Two-step phase transition in snse and the origins of its high power factor from first principles, Phys. Rev. Lett. 117 (2016) 276601. http://dx.doi.org/10.1103/ PhysRevLett.117.276601. [37] R. Guo, X. Wang, Y. Kuang, B. Huang, First-principles study of anisotropic thermoelectric transport properties of IV-VI semiconductor compounds SnSe and SnS, Phys. Rev. B - Condens. Matter Mater. Phys. 92 (2015) 115202. http://dx.doi.org/10.1103/ PhysRevB.92.115202. [38] M.Y. Ha, G. Choi, D.H. Kim, H.S. Kim, S.H. Park, W.B. Lee, Effect of lattice relaxation on thermal conductivity of fcc-based structures: an efficient procedure of molecular dynamics simulation, Model. Simul. Mater. Sci. Eng. 25 (2017) 055011. http:// dx.doi.org/10.1088/1361-651X/aa6a2d.
Fig. 7. The final calculated Figure of Merit (ZT).
projected density of states of Pb show different shape near the fermi level. From the results the electrical conductivity and Seebeck coefficient were presented. Meanwhile, a 43% reduction in the lattice thermal conductivity is calculated and the ZT of PbxSn1−xSe is enhanced by the addition of Pb due to the decrease in lattice thermal conductivity. Most of the calculation results are consistent with experiments. It was confirmed that our DFT+BTE simulation gives reasonable results of the thermoelectric properties. Our approach will shed a light on the works of predicting thermoelectric properties of alloys. Acknowledgements This work was supported by a National Research Foundation of Korea (NRF) grant funded by the Korean Government through the Ministry of Science, ICT and Future Planning (MSIP) (NRF-2015R1A5A1036133). References [1] S.J. Kim, J.H. We, B.J. Cho, A wearable thermoelectric generator fabricated on a glass fabric, Energy Environ. Sci. 7 (2014) 1959. http://dx.doi.org/10.1039/c4ee00242c. [2] L.E. Bell, Cooling, heating, generating power, and recovering waste heat with thermoelectric systems, Science 321 (80-.) (2008) 1457–1461. http://dx.doi.org/10.1126/ science.1158899. [3] M. Zebarjadi, K. Esfarjani, M.S. Dresselhaus, Z.F. Ren, G. Chen, Perspectives on thermoelectrics: from fundamentals to device applications, Energy Environ. Sci. 5 (2012) 5147–5162. http://dx.doi.org/10.1039/C1EE02497C. [4] G. Chen, Theoretical efficiency of solar thermoelectric energy generators, J. Appl. Phys. 109 (2011) 104908. http://dx.doi.org/10.1063/1.3583182. [5] D. Wu, L.-D. Zhao, X. Tong, W. Li, L. Wu, Q. Tan, Y. Pei, L. Huang, J.-F. Li, Y. Zhu, M.G. Kanatzidis, J. He, Superior thermoelectric performance in PbTe–PbS pseudobinary: extremely low thermal conductivity and modulated carrier concentration, Energy Environ. Sci. 8 (2015) 2056–2068. http://dx.doi.org/10.1039/C5EE01147G. [6] Y. Pei, A.D. LaLonde, N.A. Heinz, G.J. Snyder, High thermoelectric figure of merit in PbTe alloys demonstrated in PbTe-CdTe, Adv. Energy Mater. 2 (2012) 670–675. http:// dx.doi.org/10.1002/aenm.201100770. [7] M.G. Kanatzidis, Nanostructured thermoelectrics: the new paradigm?, Chem. Mater. 22 (2010) 648–659. http://dx.doi.org/10.1021/cm902195j. [8] Y. Lee, S.-H. Lo, C. Chen, H. Sun, D.-Y. Chung, T.C. Chasapis, C. Uher, V.P. Dravid, M.G. Kanatzidis, Contrasting role of antimony and bismuth dopants on the thermoelectric performance of lead selenide, Nat. Commun. 5 (2014) 1–11. http://dx.doi.org/ 10.1038/ncomms4640. [9] Y. Han, Z. Chen, C. Xin, Y. Pei, M. Zhou, R. Huang, L. Li, Improved thermoelectric performance of Nb-doped lead selenide, J. Alloy. Compd. 600 (2014) 91–95. http:// dx.doi.org/10.1016/j.jallcom.2014.02.077. [10] G. Tan, F. Shi, S. Hao, H. Chi, T.P. Bailey, L.D. Zhao, C. Uher, C. Wolverton, V.P. Dravid, M.G. Kanatzidis, Valence band modification and high thermoelectric performance in SnTe heavily alloyed with MnTe, J. Am. Chem. Soc. 137 (2015) 11507–11516. http:// dx.doi.org/10.1021/jacs.5b07284. [11] G. Tan, F. Shi, J.W. Doak, H. Sun, L.-D. Zhao, P. Wang, C. Uher, C. Wolverton, V.P. Dravid, Kanatzidis, Extraordinary role of Hg in enhancing the thermoelectric performance of p-type SnTe, Energy Environ. Sci. 8 (2015) 267–277. http://dx.doi.org/ 10.1039/C4EE01463D. [12] A. Banik, U.S. Shenoy, S. Anand, U.V. Waghmare, K. Biswas, Mg alloying in SnTe facilitates valence band convergence and optimizes thermoelectric properties, Chem. Mater. 27 (2015) 581–587. http://dx.doi.org/10.1021/cm504112m.
418