Charge Transport in Thermoelectric SnSe Single Crystals - ACS

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Charge Transport in Thermoelectric SnSe Single Crystal Min Jin, Zhiwei Chen, Xiaojian Tan, Hezhu Shao, Guoqiang Liu, Haoyang Hu, Jingtao Xu, Bo Yu, Hui Shen, Jia-Yue Xu, Haochuan Jiang, Yanzhong Pei, and Jun Jiang ACS Energy Lett., Just Accepted Manuscript • DOI: 10.1021/acsenergylett.7b01259 • Publication Date (Web): 15 Feb 2018 Downloaded from http://pubs.acs.org on February 15, 2018

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ACS Energy Letters

Charge Transport in Thermoelectric SnSe Single Crystal Min Jin,1,⊥ Zhiwei Chen,2,⊥ Xiaojian Tan,1,* Hezhu Shao,1 Guoqiang Liu,1 Haoyang Hu,1 Jingtao Xu,1 Bo Yu,1 Hui Shen,3 Jiayue Xu,3 Haochuan Jiang,1 Yanzhong Pei,2,† Jun Jiang1,‡ 1

Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences,

Ningbo 315201, China 2

School of Materials Science and Engineering, Tongji University, Shanghai 201804, China

3

School of Materials Science and Engineering, Shanghai Institute of Technology, Shanghai

201418, China

*

Corresponding Authors. E-mail: [email protected]

†


‡


⊥These authors contributed equally.

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Abstract SnSe has increasingly attracted attentions as a promising thermoelectric material. In this work, a horizontal vapor transfer method was developed to synthesize high-quality, fully-dense and stoichiometric SnSe single crystal, which enables an evaluation on the transport properties inherent to SnSe along the bc-plane. The electronic transport properties can be well understood by single parabolic band (SPB) model with acoustic phonon scattering, enabling insights into the fundamental material parameters determining the electronic properties. The lattice thermal conductivity (κl) decreases from 2.0 Wm–1K–1 at 300 K to 0.55 Wm–1K–1 at 773 K. It is revealed that an increase in hole concentration, an involvement of low-lying bands for transport and a further reduction in κl would all enable p-type SnSe as a promising eco-friendly thermoelectric material. This work not only provides a fundamental understanding on the charge transport, but also guides the further improvement for thermoelectric SnSe. TOC GRAPHICS (5 cm × 7.5 cm)

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Thermoelectric (TE) materials have drawn increasing attention in the research community because of the capability of directly converting heat to electricity and vice versa.1 The conversion efficiency is largely determined by the materials’ dimensionless thermoelectric figure of merit, ZT = S2σT/(κe+κl), where S is the Seebeck coefficient, σ is the electrical conductivity, T is the absolute temperature, κe and κl are the electronic and lattice contributions to thermal conductivity.2 Efficient TE materials require high power factor (S2σ) and low thermal conductivity (κ) simultaneously. Because of the strong coupling effect between S, σ and κe, it is difficult to achieve significant enhancement of S2σ by simply improving one of these parameters.3 The lattice thermal conductivity, κl, is the only one independent property determining ZT, which needs to be minimized. This leads to an important strategy for achieving high ZT by seeking new TE materials with intrinsic low κl in addition to enhancing TE performance in the known materials.4-8 As a new TE material, single crystal tin selenide (SnSe) has recently been reported to exhibit a high ZT of 2.6 at 973 K (along the b axis), due to its ultralow κl of 0.3 Wm−1K−1.9 This attracts extensive attentions on this material because of its unprecedented TE performance and its eco-friendly constituent elements. With efforts to optimize the carrier concentration by Na or Ag doping on Sn site, the ZT of doped single crystal SnSe shows a large increase at moderate temperatures,10-11 and thus the corresponding average ZT (ZTave = 1.3 between 300 ~ 800 K) is much higher than that of pristine single crystal SnSe (ZTave = 0.2).9 In addition, polycrystalline SnSe has been reported to be promissing to show a ZT of 0.7 ~ 1.3.12-23 Recently, the reported ZT in this material has shown a large variation from different literatures, mainly due to the discrepancy on the measured lattice thermal conductivity.24 It is shown that the reported κl, at tempeatrues enabling a high ZT, can vary by a factor as large as 2 or more.12-19 Possible reasons are discussed in several literatures,24 and are mostly related to the crystallinity, including the stoichiometry, oxidation, microcracks, density and vacancies25. In addition, SnSe undergoes a phase transition (PT) from room-temperature Pnma phase to high-temperature Cmcm phase at ~ 700 K, which would further complicate the analyses of transport properties.9, 18 ACS Paragon Plus Environment

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Although this compound has been considered for a while as a thermoelectric material, detailed discussion on the charge transport inherent to this material such as the scattering mechanism, effective mass and deformation potential coefficient, the optimal doping level as well their temperature dependence, has rarely been seen. Therefore, it is important to synthesize high-quality single crystal materials for a detailed investigation on the transport properties. This could help understand the fundamental physics of this material for thermoelectric applications, and further help guide the further advancements. In this work, a horizontal vapor transport method is developed to grow a high-quality SnSe single crystal to evaluate its transport properties. The schematic diagram of this method can be seen in Figure 1a. Compared to the conventional techniques (vertical Bridgman method, modified Bridgman method, zone melting method, et al.),11, 16 such a horizontal vapor transport method has several advantages for SnSe single crystal growth: (1) Since SnSe compound can be melted congruently acording to the Sn-Se phase diagram,26 such a vapor transport technique could ensure the stoichiometry of the crystal grown; (2) SnSe single crystal is grown from the in-situ vapor of SnSe molecules, which helps prevent material from oxidation during growth; (3) A PBN crucible is adopted to effectively protect the crystal from contamination; (4) Thermal stress inside the crystal could be effectively eliminated through slow cooling to aviod cracking. More detailed experimental procedure can be seen in the supplementary.

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Figure 1. a) Schematic diagram of vapor transfer method for crystal growth of SnSe, b) bowl-like SnSe single crystals as grown, c) the obtained high-quality SnSe single crystals with cleavage surfaces; and d) the Xray diffraction patterns.

Figure 1b displays some cleaved SnSe single crystals grown by a horizontal vapor transport method, and Figure 1c shows a typical particle (15×15×10 mm3). Due to the layered crystal structure,9 nice cleavage surfaces (along the bc plane) can be obtained (Figure 1b and 1d). The X-ray diffraction (XRD) measurement shown in Figure 1d reveals that these cleavages are along the bc plane, and all the corresponding (200), (400), (600) and (800) diffractions can be detected. The diffraction patterns of polycrystalline SnSe can be well-indexed to the room temperature Pnma SnSe phase (JCPDS # 48-1224), and the crystal structural parameters (Table S1) are consistent with the literature.27 The measured average density (Table S1) is > 99.5% of the theoretical value, and the energy dispersive spectrum (EDS) analysis (Figure S1) shows that the cyrstals are nicely stoichiometric. All these results confirm that the SnSe single crystal grown in this work is of high-purity, stoichiometric, fullydense and crack-free. As previously reported, layered SnSe exhibits a much higher ZT parallel to the bc plane than that along the perpendicular direction.9-11 Therefore, this work focuses on the transport properties parallel to the bc plane. Figure 2 (Figure S3) plots the Seebeck coefficient (S) and electrical conductivity (σ) as a function of temperature for SnSe single crystal (The insert shows bar-shaped samples (2 × 2 × 12 mm3) for Seebeck and electrical conductivity measurements and square shapes (6 × 6 × 1.8 mm3) for Hall coefficient and thermal conductivity measurements). As shown, the Seebeck coefficient increases with increasing temperature from 300 to 600 K while the electrical conductivity decreases, showing a typical degenerated semiconducting behavior. At T > 600 K, the Seebeck coefficient decreases and the electrical conductivity increases, driven by the PnmaCmcm PT. It is observed that S agrees well with the previously reported results while σ in this work is slightly lower in the whole temperature range, which leads to a slightly lower power factor (S2σ) in this work (Figure 2c).9


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Figure 2. Temperature dependent Seebeck coefficient a), electrical conductivity b), power factor c), and lattice thermal conductivity d). Data for some single (SC) and poly (PC) crystalline SnSe are collected for comparison. The insert shows bar-shaped samples (2 × 2 × 12 mm3) for Seebeck and electrical conductivity measurements and square shapes (6 × 6 × 1.8 mm3) for Hall coefficient and thermal conductivity measurements. The shaded region indicates the Pnma-Cmcm phase transition (PT).

Tempereture dependent lattice thermal conductivity (κl) for SnSe single crystal is shown in Figure 2d. The κl is obtained by subtracting the electronic thermal conductivity (κe) from the total thermal conductivity (κ). The κe is estimated by κe =LσT according to the Wiedemanne-Franz law, where L is the Lorenz factor (Figure S2a) determined by a single parabolic band (SPB) model. The κe (Figure S2b) is nearly zero for SnSe single crystal in this work. The lattice thermal conductivity decreases as T–1 approximately, indicating a dominant phonon scattering due to Umklapp processes in this material. The room temperature κl is measured to be 2.0 Wm–1K–1, and decreases to 0.55 Wm–1K–1 at 773 K in this work. It should be noted that κl can be underestimated in the PT region using the heat capacity measured by the LFA apparatus (including this work), since a careful heat capacity measurement by DSC shows a noticeable increase in this region. Figure 2d also includes the κl reported for both single crystal9, 11, 28 and polycrystalline18 with and without doping16 for comparison. It can be seen that the measured κl in this work is well consistent with that of single ACS Paragon Plus Environment

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crystal SnSe with similar density.28 It seems that single crystal SnSe with a lower density9, 24 tend to show a much lower κl. It is also noticed that polycrystalline materials are reported to have a lower κl as well.

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these low κl are believed to be responsible for the high ZT reported. Figure 3a and 3b show the temperature dependent hall carrier concentration (nh) and hall mobility (µh) for SnSe single crystal, respectively. It is seen that the single-crystal SnSe exhibits a low Hall carrier concentration (nh) of ~ 5 × 1017 cm–3 at room temperature. The hall mobility shows a near T–1.5 tendency of temperature, indicating a dominant mechanism of charge scattering by acoustic phonons. When temperature increases to about 600 K, the Pnma phase starts to transform to Cmcm phase, leading to a drastically increase in nh to ~ 7×1018 cm–3 (Figure 3a). This indicates a much higher equilibrium concentration of native Sn-vacancy in the Cmcm phase as compared to that in the Pnma phase, which could also partially explains the decrease in Seebeck coefficient (Figure 2a) while an increase in electrical conductivity (Figure 2b) at T>600 K.29

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Figure 3. Temperature dependent Hall carrier concentration (nh) a), Hall mobility (µh) b), band effective masses (mb*) as well as density of state effective masses (md*) c), and deformation potential coefficient d) (Edef) for SnSe single crystal. mb*, md*, and Edef are estimated according to the single parabolic band (SPB) model. The shaded region indicates the Pnma-Cmcm phase transition (PT).


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It is known that, if the carrier concentration of a given material can be optimized without significantly changing the scattering, electronic or phonon structure, the maximum ZT of a given material is determined by its dimensionless quality factor (β). Within the deformation potential theory and the carrier is dominantly scattered by acoustic phonon, β∝Nv/(Edef2mb*κl).30 Here, Nv is the band degeneracy, Edef the deformation potential coefficient, mb* the band effective mass and the band is assumed to be isotropic for simplicity. According to the band structure calculations11, 31-33, 6, 20-22 Pnma and Cmcm phases show single band conduction behavior with Nv of 2 and 4 respectively, since the experimentally obtained hole concentration of < 1020 cm–3 is not sufficiently high to involve a strong contribution to the transport properties from the low-lying valence bands.11, 34 The measured optical band gap is ~ 0.96 eV for SnSe single crystal in this work (Figure S4), which is in good agreement with the previously reported.9, 11, 15, 35 Such a wide band gap suggests that the band can be approximated as parabolic due to the weak interaction between the valence and conduction band. Thus, densityof-state (DOS) effective mass md* and Edef can be estimated by a single parabolic band (SPB) model with acoustic scattering, as evident in Figure 3b.36 It should be noted that, the SPB model may involve some uncertainties in the temperature range of 600-800 K due to the phase transition. Figure 3c-d show the temperature dependent md*, mb* and Edef for SnSe single crystal. Both md* and mb* show a weak temperature dependence for both Pnma and Cmcm phases. Due to the lager band degeneracy of the Cmcm phase (Nv of 4) than that of Pnma phase (Nv of 2), mb* of Cmcm phase (~0.4me) is almost half of that of Pnma phase (~ 0.7me) while the md* maintains the same, which can explain the slightly enhanced hall mobility in Cmcm phase. This reduced mb* would lead to an expectation of a higher quality factor (β in Cmcm phase. However, this is largely compensated by the increased Edef of Cmcm phase, leading the quality factor for Pnma and Cmcm SnSe to be comparable. Figure 4a-c show the hall carrier concentration (nh) dependent Seebeck coefficient (S), hall mobility (µh) and power factor (S2σ) and at different temperatures. Solid lines represent the prediction by the SPB model according to the above estimated md* and Edef at each temperature (Figure 3c-d). Experimental results in this work as well as majority of the available literature data agree well with the model predictions. It should be


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noted that, the inconsistencies between the measured transport properties for poly-crystalline SnSe and the model prediction for single-crystalline one along the bc plane in this work, could be due to the existence of band anisotropy in this anisotropic material9, 11 and the existence of other types of charge scattering in polycrystalline SnSe.13, 17 As shown in Figure 4c, power factor reaches its maximum when the hole concentration is increased to ~ 4×1019 cm–3 at room temperature.10 With increasing temperature, S2σ decreases firstly due to the increased Edef, and then increases slightly due to the Pnma-Cmcm phase transition (PT). Note here the higher power factor reported by Zhao et al. as compared with the one reported here at T>800 K, is presumably due to the higher hole concentration resulting from the Sn vacancies.25 This is supported by the lower Seebeck coefficient and a higher conductivity reported by Zhao et al.35 With the measured lattice thermal conductivity for SnSe single crystal (Figure 2d) in this work, the SPB model further enables a prediction on the carrier concentration dependent ZT at a given temperature. Since the energy offset between transporting bands in p-type SnSe in the carrier concentration and working temperature range is sufficiently small32, it is valid to approximate as an effectively single band transport with a high band degeneracy, which can be evidenced from the decent agreement between the measurements and SPB predictions. A maximal ZT of 1.2 is predicted at 773 K (Figure 4d, blue solid line), if the carrier concentration can be increased to ~ 4 × 1019 cm–3. Most importantly, the prediction shows good agreement with the previously reported ZTs versus carrier concentration for SnSe by various doping at different temperature.9, 11, 13-14, 17-20, 33, 37 Such predictions could shed light on the further improvements of the TE performance of SnSe-based materials. It should be noted that the κl of some reported SnSe samples (0.2 ~ 0.32 Wm–1K–1 at 773 K) are much lower than that measured in this work, thus it is not surprised that their ZTs are much higher than the prediction (Figure 4d, blue dashed line).9, 13


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Figure 4. Hall carrier concentration dependent Seebeck coefficient a) and hall mobility b) at different temperatures; The predicted power factor S2σ c) and ZT d) value a function of hall carrier concentration at different temperatures. Literature results4, 6, 8, 9, 12-15, 24, 37 are also included for comparison.

Although a peak ZT of 1.2 at 773 K predicted in this work through an optimization of carrier concentration, is not as high as some literatures claimed previously, there is still room for improvements. Firstly, SnSe possesses a multiple-band structure, the energy differences between the principal and the low-lying valence bands are small.11, 29-31 It is resonable to expect an enhancement in the electronic performance once these bands are engineered to be effectively alligned.38 Secondly, κl in high-quality SnSe single crystal is relative high. A further introduction of multiple-scale defects13, 39-40 can be expected to reduce the κl., a careful optimization on carrier concentration, an effective band alignment41-44 as well as a reduction45-48 in κl are all believed to be effective for further advancing eco-friendly SnSe thermoelectrics in p-type. In summary, high-quality SnSe single crystal are grown through a horizontal vapor transfer method in order to evalulated the transport properties and underlying physics (including effective mass and deformation potential coefficient) inherent to SnSe along the bc plane. This work rationalizes a SPB model to understand and to predict the electronic transport properties of SnSe, which agrees well with existing measurements. With the measured lattice thermal conductivity, this work fruther enables a prediction on temperature and carrier ACS Paragon Plus Environment

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concentration dependent thermoelectric figure of merit (ZT). It is revealed that a careful carrier concentration optimization, a further band alignment as well as a reduction in κl all contribute to an even brighter future for ptype thermoelectric SnSe.


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Supporting Information Brief statement of experimental method for samples synthesis, crystal growth, and physical characterization. Structural parameters, EDS maps, electronic absorption spectra, stability evaluations and thermal properties for grown SnSe single crystal.

AUTHOR INFORMATION Corresponding Author *

Email: [email protected]

ORCID Yanzhong Pei: 0000-0003-1612-3294 Notes The authors declare no competing financial interest. Acknowledgment This work was supported by the National Key Research and Development Program of China (2016YFC0101801),

Zhejiang

Provincial

Science

Foundation

for

Distinguished

Young

Scholars

(LR16E020001), Public Projects of Zhejiang Province (2017C31006), Natural Science Foundation of Zhejiang Province (LY17A040012 and LY17E020013), and Ningbo Municipal Natural Science Foundation (2017A610009 and 2017A610107). ZC and YP acknowledge the National Natural Science Foundation of China (Grant No. 51422208, 11474219 and 51772215) for funding support.


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(44) Lin, S.; Li, W.; Chen, Z.; Shen, J.; Ge, B.; Pei, Y., Tellurium as a high-performance elemental thermoelectric. Nat Commun 2016, 7, 10287. (45) Li, W.; Zheng, L.; Ge, B.; Lin, S.; Zhang, X.; Chen, Z.; Chang, Y.; Pei, Y., Promoting SnTe as an EcoFriendly Solution for p-PbTe Thermoelectric via Band Convergence and Interstitial Defects. Adv Mater 2017, 29, 1605887. (46) Li, W.; Wu, Y.; Lin, S.; Chen, Z.; Li, J.; Zhang, X.; Zheng, L.; Pei, Y., Advances in EnvironmentFriendly SnTe Thermoelectrics. ACS Energy Letters 2017, 2, 2349-2355. (47) Chen, Z.; Ge, B.; Li, W.; Lin, S.; Shen, J.; Chang, Y.; Hanus, R.; Snyder, G. J.; Pei, Y., Vacancyinduced dislocations within grains for high-performance PbSe thermoelectrics. Nat Commun 2017, 8, 13828. (48) Chen, Z.; Jian, Z.; Li, W.; Chang, Y.; Ge, B.; Hanus, R.; Yang, J.; Chen, Y.; Huang, M.; Snyder, G. J., et al., Lattice Dislocations Enhancing Thermoelectric PbTe in Addition to Band Convergence. Adv Mater 2017, 29, 1606768.


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Charge Transport in Thermoelectric SnSe Single Crystals - ACS

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