Enhancement of Thermoelectric Performance in Na-Doped Pb0.6Sn0

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Enhancement of Thermoelectric Performance in Na-doped Pb0.6Sn0.4Te0.95-xSexS0.05 via Breaking the Inversion Symmetry, Band Convergence, and Nanostructuring by Multiple Elements Doping Dianta Ginting, Chan-Chieh Lin, Lydia Rathnam, Gareoung Kim, Jae Hyun Yun, Hyeon Seob So, Hosun Lee, Byung-Kyu Yu, Sung-Jin Kim, Kyunghan Ahn, and Jong Soo Rhyee ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b18362 • Publication Date (Web): 22 Mar 2018 Downloaded from http://pubs.acs.org on March 22, 2018

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ACS Applied Materials & Interfaces

Enhancement of Thermoelectric Performance in Na-doped Pb0.6Sn0.4Te0.95xSexS0.05

via Breaking the Inversion Symmetry, Band Convergence, and

Nanostructuring by Multiple Elements Doping Dianta Ginting, †,#,& Chan-Chieh Lin,†,& Lydia Rathnam,† Gareoung Kim,† Jae Hyun Yun,† Hyeon Seob So,† Hosun Lee,† Byung-Kyu Yu,‡ Sung-Jin Kim,‡ Kyunghan Ahn,*,† and Jong-Soo Rhyee*,† †

Department of Applied Physics and Institute of Natural Sciences, Kyung Hee University, YongIn, Gyong-gi 17104, Republic of Korea. #

Department of Mechanical engineering, Universitas Mercu Buana, Jalan Meruya Selatan No.1, Joglo, Kembangan, RT.4/RW.1, Meruya Selatan, RT.4/RW.1, Meruya Sel., Kembangan, Kota Jakarta Barat-Indonesia. ‡

Department of Chemistry and Nano Sciences, Ehwa Womans University, Seoul 03760, Republic of Korea

ABSTRACT

Topological insulators have attracted much interest in topological states of matter featuring unusual electrical conduction behaviors. It has been recently reported that a topological crystalline insulator could exhibit a high thermoelectric performance by breaking its crystal symmetry via chemical doping. Here, we investigate the multiple effects of Na, Se, and S alloying on thermoelectric properties of a topological crystalline insulator Pb0.6Sn0.4Te. The Na doping is known to be effective for breaking the crystalline mirror symmetry of Pb0.6Sn0.4Te. We demonstrate that simultaneous emergence of band convergence by Se alloying and nanostructuring by S doping enhance the power factor and decrease lattice thermal conductivity, respectively. Remarkably, the high power factor of 22.3 µW cm-1 K-2 at 800 K is achieved for Na

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1 %-doped Pb0.6Sn0.4Te0.90Se0.05S0.05 mainly due to a relatively high Seebeck coefficient via band convergence by Se alloying as well as the suppression of bipolar conduction at high temperatures by the increase of energy band gap. Furthermore, the lattice thermal conductivity is significantly suppressed by PbS nano-precipitates without deteriorating the hole carrier mobility, ranging from 0.80 W m-1 K-1 for Pb0.6Sn0.4Te to 0.17 W m-1 K-1 at 300 K for Pb0.6Sn0.4Te0.85Se0.10S0.05. As a result, the synergistically combined effects of breaking the crystalline mirror symmetry of topological crystalline insulator, band convergence, and nanostructuring for Pb0.6Sn0.4Te0.95xSexS0.05

(x = 0, 0.05, 0.1, 0.2, and 0.95) give rise to an impressively high ZT of 1.59 at 800 K for

x=0.05. We suggest that the multiple-doping in topological crystalline insulators is an effective to improve the thermoelectric performance.

Keywords: Thermoelectric, Topological crystalline insulator, Thermal conductivity, ZT, Power factor, Nano structure.


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1. INTRODUCTION Thermoelectric (TE) materials can switch heat into electricity when subjected to a temperature gradient, resulting in a waste heat power generation. The efficiency of TE materials is determined by the TE figure of merit ZT which is expressed by the following relation:1,2 =

where, T, S, σ, κe, and κl is the absolute temperature, the Seebeck coefficient, the electrical conductivity, the electrical thermal conductivity, and the lattice thermal conductivity, respectively. According to the above equation, a high performance TE material should have a high power factor (PF = S2σ) and a low thermal conductivity (κ = κe + κl). However, it is quite elusive to obtain them simultaneously because three parameters (S, σ, and κ) are closely interrelated. Consequently, a lot of research efforts have been performed to find highperformance TE materials. On the other hand, topological crystalline insulators (TCIs) are a new class of topological insulators (TIs) that the surface state is protected by the crystal mirror symmetry, while that of TIs is secured by the time reversal symmetry.3 TCIs could be promising to be good TE materials because TCIs generally shows common physical properties including narrow band gaps and heavy constituent elements with TE materials. The IV-VI semiconductor SnTe as well as the related alloys Pb1-xSnxTe and Pb1-xSnxSe have been well known as TCIs materials because of their robust surface states on the (001) plane by first-principles calculations.4 This has been also experimentally confirmed by a direct observation of topological surface states using the angle-resolved photoemission spectroscopy (ARPES).5 It has been recently reported that the Na doping in a TCI Pb0.6Sn0.4Te compound breaks its crystalline mirror symmetry, opens its bulk electronic band gap, and thereby


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suppresses its strong bipolar conduction that makes the absolute magnitude of S decrease with increasing temperature, resulting in a maximum ZT of 1 at 856 K compared to the undoped Pb0.6Sn0.4Te (ZT = 0.38 at 475K).6 However, the Na-doped Pb0.6Sn0.4Te compound still shows a relatively smaller ZT than the Na-doped PbTe compound (ZT = 1.2 at 750 K).7 The valence band of PbQ (Q = Se, Te) has been known to have dual bands (one light L band and the other heavy Σ band) showing different temperature-dependencies. Consequently, a valence band convergence of dispersive light L and heavy Σ band has shown an enhanced PF while decreasing the κlat in PbTe1-xSex system (ZT = 1.8 at 850 K)8 and PbTe1-xSx system (ZT = 1.55 at 773 K).9 Here, we investigate the effect of Se and S co-doping on TE properties of Na-doped Pb0.6Sn0.4Te system in order to further boost its TE performance via solid-solution with Se and S for Na 1 %-doped Pb0.6Sn0.4Te0.95-xSexS0.05 (x = 0, 0.05, 0.10, 0.20, 0.95). We fix the S composition of 0.05 to achieve a low κlat because the nano-precipitates, which are effective for phonon scattering, are naturally formed in the PbTe-PbSe-PbS system when the S content is less than 0.07.10,11 We try to control Se content in the composition to obtain a high PF via the valence band convergence. The 1% Na-doping can help place the Fermi level deeper within the first band, helping to position the Fermi level within ±2kBT for the valence band convergence. Furthermore, it has been already reported that the bulk electronic band gap is increased through the breaking of the crystalline mirror symmetry by Na doping, resulting in the suppression of bipolar conduction at high temperatures.6 Combined with the multiple beneficial effects caused by Na, Se, and S co-doping, the Na 1 %-doped Pb0.6Sn0.4Te0.95-xSexS0.05 for x= 0.05 shows a maximum ZT of 1.59 at 800 K, which is about 327 %, 59 %, and 23 % enhancement in ZT compared to Pb0.6Sn0.4Te6, Na-doped Pb0.6Sn0.4Te6 and Na-doped PbTe7, respectively.


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2. EXPERIMENTAL SECTION 2.1. Materials synthesis Starting material of PbSe and PbS ware synthesized by melting of high purity elements at 1100 oC using stoichiometric mixture of Pb (99.999 %), dried S (99.999 %), and Se (99.999 %) in an evacuated quart ampoules with residual pressure of 10-4 torr. Polycrystalline compounds Pb0.6Sn0.4Te0.95-xSexS0.05 (x = 0, 0.05, 0.10, 0.20, 0.95) were prepared by mixing of Pb, Te, Sn, and Na, PbSe, and PbS, with additional 1 % Na. The mixed Na-doped Pb0.6Sn0.4Te0.95-xSexS0.05 was sealed in carbon-coated quartz tubes and sealed under vacuum 10-4 torr and heated to 1100 oC for 10 hours, then samples ware quanched in cold water, followed by anneling at 500 o

C for 72 hours. The resulting ingots after anneling were pulverized in an agate mortar. Poweders

of Na-doped Pb0.6Sn0.4Te0.95-xSexS0.05 were sintered at 500 oC under vacuum in a graphite mold having 12.7 mm dameter by a hot press sintering machine.10,11

2.2. Characterization and measurement of thermoelectric properties Polycrystalline compounds of Pb0.6Sn0.4Te0.95-xSexS0.05 (x = 0, 0.05, 0.10, 0.20, 0.95) were characterized by powder X-ray diffraction (XRD) measurements with Cu Kα radiation (D8 Advance, Bruker, Germany). The lattice parameter of Pb0.6Sn0.4Te0.95-xSexS0.05 (x = 0, 0.05, 0.10, 0.20, 0.95) were calculated by using Rietveld analysis.10,11 The Seebeck coefficient S and electrical conductivity σ were measured using ZEM-3 ULVAC, Japan. The Hall carrier concentration was measured by five-point contact method with sweeping magnetic fields from −5 T to 5 T using a physical property measurement system (PPMS, Quantum Design, USA). The Hall coefficient RH, Hall carrier density nH, and Hall mobility µH were obtained using the

relations of = / , = −1/( ) , and = 1/() , respectively.10,11 Thermal ACS Paragon Plus Environment

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diffusivity was measured by laser flash method (LFA-447, NETZSCH, Germany). Total thermal conductivity κ was calculated by the relation κ = ρsλCp where ρs, λ, and Cp are sample density, thermal diffusivity, and specific heat. The ρs was calculated by Archimedes method. Cp were calculated by high temperature fitting of the Dulong-Petit law by measuring specific heat using a physical property measurement system (Quantum Design, USA), respectively.10,11 We measured the ellipsometric angels (∆, φ) of clean surface polycrystalline of Pb0.6Sn0.4Te0.95-xSexS0.05 (x = 0, 0.05, 0.1, 0.2, and 0.95) compounds in the spectral range between 0.7 eV and 6 eV at room temperature with tree angles of incidence (65o, 70o, and 75o) by means of spectroscopic ellipsometry (V-VASE, Woollam inc.).

3. RESULTS AND DISCUSSION X-ray diffraction (XRD) patterns of Pb0.6Sn0.4Te0.95-xSexS0.05 (x = 0, 0.05, 0.1, 0.2, and 0.95) samples are shown in Fig. 1. This reveals that all the samples crystallize in the NaCl-type cubic structure without any impurity phases (Fig. 1a). The lattice parameter a tends to decrease with increasing Se content because of smaller atomic radius of Se (1.15 Å) than that of Te (1.40 Å), which follows a Vegard’s law, indicating that a value of a solid solution is inversely proportional to its Se composition (Figure 1b). Figure 2 shows microstructural images of the Pb0.6Sn0.4Te0.95-xSexS0.05 at x=0.05 sample analyzed by high resolution transmission electron microscopy (HR-TEM), indicating that there are several homogeneous nano-precipitates with the size distribution of 2-10 nm in the matrix (Figures 2a, 2b, 2c and Figures S1 and S2 in supporting information). The electron diffraction pattern in Fig. 2d reveals the (200) plane with the zone axis of [012]. Furthermore, the bright


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field-scanning TEM (BF-STEM) images also demonstrate that the nano-precipitates are evenly distributed with a typical size of 2-5 nm (Figures 3a and 3b). The nano-precipitates are formed due to the decomposition boundary of PbTe-PbS in thermodynamic phase diagram at about 500 o

C, thereby the nano-precipitation of PbS is thought to be formed during the annealing at 500 oC

for 72 hours.7,11 The electron diffraction pattern of the compound shows clear cubic structure which also supports the PbS precipitation. These nano-precipitates embedded in the matrix should play a major role in reducing the κlat of the Pb0.6Sn0.4Te0.95-xSexS0.05 compound. We performed the ellipsometry measurements in order to measure energy band gaps of the compounds. From the linear fit of the optical absorption spectra, as shown in Fig. 4(a), the energy band gaps are systematically increased with increasing Se concentration in Na-doped Pb0.6Sn0.4Te0.95-xSexS0.05 from 0.15 eV (x = 0.0) to 0.49 (x = 0.95), which linearly increase of energy band gap with increasing Se concentration as shown in Fig. 4(c). This behavior is quite interesting because the Se substitution in Na-doped PbTe0.95-xSexS0.05 decreases the energy band gap with increasing Se concentration which presented in Fig. 4(d).7 The Sn-doped Pb1-xSnxTe (x ≥ 0.25) system is known as topological crystal insulator.12 It undergoes topological phase transition from conventional insulator PbTe to topological crystal insulator SnTe.5 Near the topological phase transition region (0.4 ≤ x ≤ 0.6), it is expected the

band inversion that the conduction band band edge in PbTe inverted to valence band and

valence band band edge becomes conduction band with increasing Sn concentration. Pb1-

xSnxTe

(x = 0.6) is the topological Dirac semimetal region that band touches with the band

edge.12,13


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We present the energy band gap with respect to Sn concentration in Fig. 4(b). Sn substitution in Pb-site decreases energy band gap and the conduction and valence bands are touched resulting in the Dirac semimetal near x = 0.6 region. Further increase of Sn concentration increases energy band gap entering into band inversion in the topological crystal insulating phase for Sn rich concentration region Pb1-xSnxTe (x > 0.6). On the other hand, the Pb0.6Sn0.4Te0.95-xSexS0.05 compounds exhibit the increase of energy band gap with increasing Se concentration, as shown in Fig. 5. Here, small perturbations of crystalline lattice by Na-, S-, and Se-doping and substitutions can break topological crystal insulating phase of pristine Pb0.6Sn0.4Te. The Pb0.55Sn0.45Se also exhibited nontrivial topological state with semimetallic electronic band structure from the angle resolved photoemission spectroscopy.14 It implies that the increase of energy band gap with Se substitution in Na-doped Pb0.6Sn0.4Te0.95-xSexS0.05 compounds may associated with the breaking non-trivial topological states. In spite of trivial band semiconductor of the compounds, the compounds of Pb0.6Sn0.4Te0.95-xSexS0.05 reside near the region of topological phase transition with band inversion. From the scanning tunneling microscopy (STM) measurements, it was reported that there is coexistence of massive and massless Dirac bands in Pb1-xSnxSe near the topological phase transition. The massive and massless Dirac bands with sizable bulk band gap can contribute to the enhancement of thermoelectric performance because of simultaneous emergence of high electrical mobility and relatively high Seebeck coefficient. It is well known that high band dispersion and high band degeneracy give rise to the enhancement of electrical mobility and Seebeck coefficient, respectively.8 The Seebeck coefficient and electrical conductivity are presented in Fig. 6(a) and 6(b), respectively. The sign of Seebeck coefficient S in this work is positive, indicating the majority


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charge carrier is hole for the Pb0.6Sn0.4Te0.95-xSexS0.05 samples. It reveals that there is a broad shoulder near 700 K for the compounds (x = 0.05 and 0.1) due to bipolar conduction of carriers due to small band gap of the compounds.7 The charge compensation between electron and hole charge excitations decreases Seebeck coefficient at high temperature region in narrow gap or semimetallic compound such as Pb0.6Sn0.4Te compound.6 The bipolar conduction behavior with broad shoulder shifts to a high temperature region with increasing Se content. For example, the temperature region of broad shoulder is increased to 800 K for x = 0.2 and finally, there is no broad shoulder in x = 0.95 compound in Fig. 6(a). The broad maximum of S is related with a unique character of two-valence bands of light L- and heavy Σ-bands in MQ-based systems (M = Sn, Pb; Q = Se, Te).15,16 Taking into account two kinds of holes from the light L-band and the heavy Σ-band, the hole carrier concentration pH and S can be expressed as the following equations:17-19 = %=

( ! " " ) $ # " "

" " "

(1)

(2)

where pL (pΣ) is the hole carrier concertation, µL (µΣ) the hole carrier mobility, σL (σΣ) the electrical conductivity, and SL (SΣ) the Seebeck coefficient of the L-band (Σ-band), respectively. For the two-band model, the band structure parameters including band edge effective masses m*L (m*Σ) for a light L-valence band and for a heavy Σ-valence band can be taken from the Rogers’ analysis. Here, the L-band is assumed to be non-parabolic while the Σ-band is considered to be parabolic. According to Roger’s analysis,17,18 the RT m*L, m*Σ, and band gap ∆E of Pb0.5Sn0.5Te is estimated to be 0.16me, 1.6me, and 0.09 eV, respectively.19


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The band inversions by topological nontrivial state generally leads to a non-parabolic behavior with almost linear Kane band type dispersion. From the Pisarenko’s plot assumed by a single parabolic band model, the Na-doped Pb0.6Sn0.4Te0.95-xSexS0.05 samples do not follow the single parabolic behavior (m* = 0.73me) as shown in Fig. 6(b). Such a non-parabolic band is frequently observed in high performance thermoelectric materials and more detailed discussion can be found in previous studies.20-22 On the other hand, as shown in Fig. 6(c), that a theoretical two-band model is in good agreement with the experimental data for the compounds of Nadoped Pb0.6Sn0.4Te0.95-xSexS0.05 with effective masses of m*L and m*Σ by 0.16me and 1.6me, respectively. The band convergence at high temperature should be effective for the Na-doped Pb0.6Sn0.4Te0.95-xSexS0.05 samples with a high pH value when the Fermi level lies deep inside the valence band. The distances of band edges (∆EL-Σ) between L- and Σ-bands are increases with increasing Se concentration in Pb0.6Sn0.4Te0.95-xSexS0.05 so that the temperature of band convergence is increased for increasing Se concentration because temperature-sensitive L-band goes deep inside to the temperature-insensitive Σ-band with increasing temperature.7 The electrical conductivity σ of the Na-doped Pb0.6Sn0.4Te0.95-xSexS0.05 samples decreases with increasing temperature, showing a metallic or degenerate semiconducting behavior (Fig. 6(d)). The RT σ is decreased with increasing Se content mainly due to the alloy scattering for x ≤ 0.1. Further increase of Se concentration increases room temperature electrical conductivity, which may come from the increase of energy band gap. From the Hall resistivity ρxy measurements, the Hall carrier concertation pH and Hall mobility are obtained and presented in Fig. 7(a). The Hall carrier density is initially decreased and tends to increase with increasing Se concentration. The Hall mobility µH inversely follows the Hall carrier density in that is


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initially increased and decreased with increasing Se concentration implying that the Hall mobility is governed by carrier scattering. The unusual behavior of Hall carrier concentration and Hall mobility for the x = 0.05 compound is not an experimental error but an intrinsic property. It can be understood by the weak disordering of the TCI state by the small Se substitution (5 %). Small Se substitution can induce massless and massive Dirac surface states by a small chemical perturbation which can simultaneously contribute to electrical transport properties. Therefore, a weak disordering of the crystal symmetry by 5 % Se substitution weakens the TCI state so that a partial gap opening of surface Dirac bands, resulting in a simultaneous highly dispersive and degenerated energy bands, cause significantly enhanced Hall mobility (by highly dispersive energy band) and decrease of Hall carrier concentration (by increase of energy band gap and alloy scattering of carriers). On the other hand, a heavy Se alloying (10 % and 20 %) eliminates a TCI state completely with the disappearance of massless Dirac surface states. Temperature-dependent power factor S2σ is presented in Fig. 7(b). The power factor of the TCI compound Pb0.6Sn0.4Te is shown in dashed line.6 The relatively small power factor of the Pb0.6Sn0.4Te compound is owing to the low electrical conductivity and significant decrease of Seebeck coefficient at high temperature region. The Se and S co-substitution significantly increases power factor at high temperature region, mainly attributed from the increase of Seebeck coefficient, as shown in Fig. 6. The maximum power factor PF of 22.3 µW cm-1 K-2 is achieved for x = 0.05 compound. The PF tends to decrease with increasing Se content. The significant increase of power factor is the result of simultaneous emergence of breaking of TCI state by disordered multiple elements doping and band convergence.6,7


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Figure 8(a) shows the temperature-dependent total thermal conductivity κT. The total thermal conductivity decreases with increasing temperature until 600 K and afterward there is a small upturn of thermal conductivity at high temperatures T ≥ 600 K. The small upturn of κT is also found in the Na-doped (PbTe)1-x(PbS)x compound, which is originated from a small bipolar contribution.23 Even though the Se alloying effect does not show any systematic behavior of total thermal conductivity, the lowest room temperature κT of 1.25 W m-1 K-1 is obtained for x = 0.1. The thermal conductivity is composed by the sum of the electrical thermal conductivity κel and the lattice thermal conductivity κL. The κel can be expressed as the Wiedemann-Franz relation κel = LσT, where L is the Lorentz number estimated by fitting the experimentally measured temperature-dependent S values based on a single parabolic band (SPB) model.24,25. The temperature-dependent κL of the samples is shown in Fig. 8(b). The lattice thermal conductivities are increased with increasing temperature for all samples at high temperature region, indicating the existence of bipolar diffusion effect. Several reasons can be considered the extremely low lattice thermal conductivity of the compound: (1) the Lorentz number calculation within the single parabolic model is not exact in topological materials, (2) an anharmonic phonon excitation, and (3) partial local collapse of the nanostructure with increasing temperature. This phenomenon also found in (PbTe)0.88(PbS)0.12 by multiple elements doping and (Pb0.95Sn0.05Te)1x(PbS)x.

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The lowest RT κL of 0.12 W m-1 K-1 is achieved for x = 0.05, which is impressively

lower than the glass limit of thermal conductivity for the bulk PbTe system (0.36 W m-1 K-1).26 Such a considerable reduction in κlat for Pb0.6Sn0.4Te0.9Se0.05S0.05 is originated from the alloy scattering by substituting multiple elements of Se and S for Te, which will be discussed in detail below.


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In order to clarify the effect of multiple elements doping on the κL for the compounds of Pb0.6Sn0.4Te0.95-xSexS0.05, we plot the RT κL values of Pb0.6Sn0.4Te0.95-xSexS0.05 in this work and those of PbTe0.95-xSexS0.057 as a function of Se content, which is shown together with theoretically estimated RT κL values based on an alloy model for PbTe-PbSe-PbS27 and PbTe1xSex.

6

Here, we applied model fitting based on the formalism by Klemens and Abeles.28,29 The

Klemens model applies to the phonon scattering in solid solution driven by Umklapp and point defect scattering.28 &'

())*+

= &'

,-./ 0(123 (-$ -

- 4 = 5 7 4 &' 4ℏ: 6 8

,-./

; = =(3 − =) >?

;

@A 4

(3)

(4) @E 4

B + D? E B F A

(5)

where ΘD is the Debye temperature, Ω is molar volume, v is sound velocity, and Γ is a disorder scaling parameter that depends on mass and strain field fluctuations (∆m/m and ∆α/α). When we take into account not only Umklapp and point defect scattering but also phonon scattering by a normal process, the alloy model lattice thermal conductivity has the form as in the following formula of the Abeles model.27,29 ())*+ &'

=

0(123 -

4

M 3L 3 0(123 ,-./ &' G H(J K - + 3N( -O -4 0(123- Q 3

L

3M I (

H

P

-

(6)

where a is the ratio of normal to Umpklapp processes.30,31 Figure 8(c) clearly shows that the κL values of Na-doped Pb0.6Sn0.4Te0.95-xSexS0.05 lie below the calculated lattice thermal conductivity of PbTe-PbSe-PbS and PbTe1-xSex, implying


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that much lower κL values should be attributed to other scattering sources including the point defect scattering caused by Pb/Sn disordering as well as the point defect scattering caused by Te/Se and Te/S mixed occupation. In this regard, it is presumable to consider nanostructuring induced by meso-scale grains and nano-precipitates for the reduction on κL in the Pb0.6Sn0.4Te0.95xSexS0.05

system. In general, the low-, mid-, and high-frequency phonons contribute to the κL

based on the frequency-dependenency of the κL.32 Among them, the κL is predominantly governed by the mid-frequency phonons. Here, in the Pb0.6Sn0.4Te0.95-xSexS0.05 system, the mesoscale grains can strongly block the low-frequency phonons as well as the mid-frequency phonons having the mean free path of a few hundreds of nanometer. Furthermore, the nano-precipitates with a characteristic length smaller than 10 nm, as shown in Fig. 2 and 3, could significantly scatter the long-wavelength phonons. In order to identify the phonon scattering mechanism by nano-precipitates, we analyze the κL of Pb0.6Sn0.4Te0.75Se0.2S0.05 using various scattering mechanisms based on a Callaway model of PbTe, and PbTe0.75Se0.20S0.05.7 We applied theoretical calculations of the lattice thermal conductivity based on Debye-Callaway’s model.33,34 The model describes the lattice thermal conductivity by various scattering centers. Here the theoretical lattice thermal conductivity is given by,

&' =

RS

454 :

?

RT U P ℏ

B

X W V

\7] =O /O Y^ U Z[ (/=3)4 _=

+

4 \7 ] Z[ =O /O U `Y^ _=b Za (/= 23)4

\7 ] 3 Z =O /O Y^ UZ L3Z [ M = 4 _= a a (/ 23)

e d c

where kB is the Boltzmann constant, ℏ is Plank’s constant, x = ℏω⁄kBT, T is

(7)

absolute

temperature, v is the sound velocity, and θD is Debye temperature, respectively. The model


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assumes the constant relaxation approximation, where the combined relaxation time τc is given by the Matthessen’s rule: Z[ 3 = Zf 3 + Za 3 + ZS 3 + Zg 3 + Z7 3 + Zh 3

(8)

where τU, τN, τB, τS, τD, and τP are the relaxation times corresponding to scattering from Umklapp process, normal process, grain boundaries, strain, dislocations, and the precipitate.34 Figure 8(d) shows the temperature-dependent lattice thermal conductivity κL of PbTe, PbTe0.75Se0.20S0.05, and Pb0.6Sn0.4Te0.9Se0.2S0.05 and their theoretical fitting to the κL of PbTe and PbTe0.75Se0.20S0.05, respectively (dashed line). The experimentally measured κL values of PbTe (solid square green) and those of PbTe0.75Se0.20S0.05 (solid square navy) are fitted well with the theoretical calculations, represented by dashed pink and red lines, respectively. On the other hand, we fail to fit of the experimental lattice thermal conductivity of Pb0.6Sn0.4Te75Se0.20S0.05 to the theoretical Callaway model. We can conclude that the low lattice thermal conductivity comes from the phonon scattering by nano-precipitation. Synergistic effect of an enhancement of PF and a low κL in the Pb0.6Sn0.4Te0.95-xSexS0.05 at x=0.05 compound gives rise to an impressive enhancement of thermoelectric figure-of-merit ZT of 1.59 at 800 K, which is 300 % enhanced value in ZT compared to the undoped TCI pristine Pb0.6Sn0.4Te compound (ZT = 0.4 at 460 K) as shown in Fig. 9. It demonstrates that combing effects of breaking a topological crystal insulating phase by disordering and opening a band gap, band convergence between heavy and light bands, and nano-structuring have synergistic enhancement of power factor and lowering of lattice thermal conductivity, resulting in the enhancement of thermoelectric performance.

4. CONCLUSIONS


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In summary, we present the effect of Na, Se, and S multiple elements doping on the TE performances of a TCI Pb0.6Sn0.4Te. Herein, the optimally multiple-doped compound of p-type Pb0.6Sn0.4Te0.95-xSexS0.05 (x = 0, 0.05, 0.1, 0.2, and 0.95) exhibits an exceptional enhancement of ZT 1.59 at 800 K for x =0.05. This is a result from the synergetic effects by breaking the TCI state and opening a band gap via multiple elements doping, band convergence, and a nano precipitation of PbS in a matrix. Increase of band gap and high band degeneracy give rise to high Seebeck coefficient while highly dispersive valence band and massive linear band, caused in the vicinity breaking a TCI, may guarantee high mobility and high electrical conductivity. Nano precipitation lowers lattice thermal conductivity which confirms the theoretical fittings with experiment. It shows that multiple synergistic approach can enhance thermoelectric performance. The inter-relationship of the combined effect on these compounds should be studied as a further research.

ASSOCIATED CONTENT Supporting Information High-resolution TEM images of x=0.05 compound, transmission electron microscope (TEM) images of x=0.05 compound at different regions, X-ray absorption spectra for Pb L1-edge and L3-edge of the Pb0.5Sn0.5Te1-xSex, and ratio of the absorption jump from the XAS spectra at Pb L1- to L3-edge with respect to Se concentration.

AUTHOR INFORMATION &

The authors equally contributed on this work.


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Corresponding authors *[email protected] (K.A.) *[email protected] (J.S.R.)

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT JSR was supported by the Samsung Research Funding Centre of Samsung Electronics under Project Number SRFC-TA1403-02 and SJK was supported by the Nano Material Technology Development Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (NRF-2015R1A5A1036133).

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Figure Legends Figure 1. (a) Powder x-ray diffraction (XRD) of Na-doped Pb0.6Sn0.4Te0.95SexS0.05(x=0, 0.05, 0.1, 0.20, and 0.95). (b) The lattice parameters with respect to Se concentration follows Vegard’s law in Pb0.6Sn0.4Te0.95SexS0.05 (x=0, 0.05, 0.1, 0.2, and 0.95). Figure 2. Transmission electron microscope (TEM) images at x = 0.05 for low magnified images show numerous nano-precipitation region (a) and its enlarged images (b). High-resolution TEM (HR-TEM) image of nano-precipitation (yellow circle) (c) and its electron diffraction pattern (d).


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Figure 3. Low magnified bright field images of the scanning transmission electron microscopy (STEM) for x = 0.05 showing numerous nano-precipitates at different regions (a) and (b). Figure 4. The optical absorption spectra of Pb0.6Sn0.4Te0.95SexS0.05

05

(x=0, 0.05, 0.1, 0.2, and

0.95) (a), A plot demonstrating the variation of band gap energies with the Sn concentration from reference35 (Reproduced with permission from Ref. 35, copyright from 2009 American Chemical Society) compare to experimental data (b). The band gap energies with Se concentration in Pb0.6Sn0.4Te0.95SexS0.05 (x=0, 0.05, 0.20, and 0.95) (c) and, (PbTe)0.95-x(PbSe)x(PbS)0.05 (x= 0.05, 0.15 and 0.207 (Reproduced with permission from Ref. 7, copyright from 2017 Elsevier)) (d). Figure 5. Schematic diagram of the band gap energy for and

band edges in

Pb0.6Sn0.4Te0.95SexS0.05. Figure 6. Temperature dependent Seebeck coefficient S(T) of Pb0.6Sn0.4Te0.95SexS0.05 (x=0, 0.05, 0.1, 0.2, and 0.95) compare to Pb0.6Sn0.4Te (a)6 (Reproduced with permission from Ref. 6, copyright from 2015 John Wiley-Verlag), room temperature Piaranko’s plot based on single parabolic band model with experimental data (b), Pisarenko’s plot based on two valance band model of Pb1-xSnxTe from Ref. 19 (Reproduced with permission from Ref. 19, copyright from 1969 Elsevier) with experimental data of Pb0.6Sn0.4Te0.95SexS0.05 (c), and temperature dependent electrical conductivity σ(T) of Pb0.6Sn0.4Te0.95SexS0.05 of (x=0, 0.05, 0.1, 0.2, and 0.95) comparing to Pb0.6Sn0.4Te6 (d) (Reproduced with permission from Ref. 6, copyright from 2015 John WileyVerlag). Figure 7. Hall carrier concentration nH (black line and symbol, left axis), Hall mobility µH (blue line and symbol, right axis) (a), and temperature dependent power factor S2σ of


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Pb0.6Sn0.4Te0.95SexS0.05 (x=0, 0.05, 0.1, 0.2, and 0.95) compare to Pb0.6Sn0.4Te6 (b) (adapted with permission from reference 6, copyright 2015 John Wiley-Verlag) Figure 8. Temperature-dependent total thermal conductivity κT (T) (a), lattice thermal conductivity κL(T) of Pb0.6Sn0.4Te0.95-xSexS0.05 (x=0, 0.05, 0.1, 0.2, and 0.95) comparing to Pb0.6Sn0.4Te6 (b) (Reproduced with permission from Ref. 6, copyright from 2015 John WileyVerlag) (c) Experimental (symbols) and theoretical (lines) lattice thermal conductivity κL(T) for PbTe-PbSe-PbS and PbTe-PbSe alloys with respect to Se concentration.8,27 (Reproduced with permission from Ref. 8, copyright from 2011 Springer Nature) (Reproduced with permission from Ref. 27, copyright from 2014 American Chemical Society) (d) Temperature-dependent lattice thermal conductivity of Pb0.6Sn0.4Te0.95-xSexS0.05 for x =0.05 comparing to other references for PbTe7 (Reproduced with permission from Ref. 7, copyright from 2017 Elsevier) and (PbTe)0.95-x(PbSe)x(PbS)0.05 at x = 0.207(Reproduced with permission from Ref. 7, copyright from 2017 Elsevier). The theoretical data (dashed lines) of PbTe and (PbTe)0.95-x(PbSe)x(PbS)0.05 at x=0.20 are calculated by Deybe-Callaway’s model (see text). Figure 9. Temperature-dependent ZT values for Pb0.6Sn0.4Te0.95-xSexS0.05 (x=0, 0.05, 0.1, 0.2, and 0.95) together with pristine Pb0.6Sn0.4Te6 (Reproduced with permission from Ref. 6, copyright from 2015 John Wiley-Verlag).


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Figure. 1


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Figure. 2


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Figure. 3


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Figure. 4


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Figure. 5


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Figure. 6


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Figure. 7


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Figure. 8


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Figure. 9


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Table of Contents


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Enhancement of Thermoelectric Performance in Na-Doped Pb0.6Sn0

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