the ultralow thermal conductivity and ultrahigh thermoelectric...

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Please cite this article as: Tingwei Li, Nano Energy, https://doi.org/10.1016/j.nanoen.2019.104283

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The ultralow thermal conductivity and ultrahigh thermoelectric performance of fluorinated Sn2Bi sheet in room temperature

Tingwei Li a, Jiabing Yu b, Ge Nie c, Bo-Ping Zhang d, Qiang Sun a,e,*

a Department of Materials Science and Engineering, Peking University, Beijing, 100871, China b College of Optoelectronic Engineering, Chongqing University, Chongqing, 400044, China c ENN Group, Langfang City, Hebei Province, 065001, China d The Beijing Municipal Key Laboratory of New Energy Materials and Technologies, School of Materials Science and Engineering, University of Science and Technology Beijing, 100083, Beijing, China e Center for Applied Physics and Technology, Peking University, Beijing, 100871, China

A R T I C L E I N F O

Keywords: Thermoelectric 2D materials Room temperature Computation

A B S T R A C T

It has been a grand challenge to develop efficient thermoelectric materials for room temperature applications. Here, motivated by the recent experimental synthesis of Sn2Bi sheet on silicon wafer [Phys. Rev. Lett. 121, 126801 (2018)], for the first time we find that fluorination not only can stabilize Sn2Bi sheet in free-standing condition but also can significantly enhance the thermoelectric performance. The fluorinated Sn2Bi sheet ex-hibits an enlarged three-phonon scattering phase space, reduced group velocity and enhanced anharmonicity, leading to an ultralow lattice thermal conductivity of 0.19 W m� 1 K� 1 and an ultrahigh ZT value of 2.45 (1.70) at 300 K for n- (p-) doping, which are much higher than the reported values for n-type Bi2Te2.79Se0.21 poly-crystalline alloy (ZT~1.2 at 357 K), and p-type nanocomposites Bi0.48Sb1.52Te3 (ZT~1.4 at 475 K), thus the fluorinated Sn2Bi sheet can be a promising candidate for room-temperature thermoelectric applications.

1. Introduction

Thermoelectric (TE) materials have attracted increasing attention [1–4]. Among them, the room-temperature (300 K–500 K) TE materials are of special importance because most industrial waste heat from automotive exhaust gas, fireplace, and steel industrial is in this tem-perature range [5]. To evaluate the conversion efficiency of TE mate-rials, the dimensionless figure of merit (ZT¼ S2σT=κÞ is used, where S, σ, T and κ are the Seebeck coefficient, electrical conductivity, absolute temperature and thermal conductivity, respectively [6]. It is required that the ZT must be higher than 1.0 for room temperature applications [2], and tremendous effort has been made in this direction [7,8]. Currently the commercially used TE materials are Bi2Te3-based alloys [9], including n-type Bi2Te2.79Se0.21 polycrystalline alloy (ZT~1.2 at 357 K) [10], p-type nanocomposites Bi0.48Sb1.52Te3 (ZT~1.4 at 475 K) [11]. However, these materials contain rare and toxic elements (Se and Te), resulting in high costs and toxicity.

Recently 2D Sn2Bi sheet has been synthesized on silicon wafer and exhibits a high band degeneracy [12], which is favorable for high TE

performance. Moreover, different from Se and Te, Sn is abundant in resources and nontoxic, suggesting Sn2Bi being more favorable than BiTe and BiSe. However, the Sn2Bi sheet is not stable in free-standing condition. In this work, for the first time we demonstrate that fluori-nation not only can stabilize Sn2Bi sheet but also can significantly improve the TE performance. In fact, fluorination has been widely used for the surface functionalization of 2D materials such as fluorographene [13], fluorinated boron nitride (BN) sheet [14]. Because fluorine has a heavier atomic mass and a larger electronegativity, which can lead to a lower phonon group velocity and larger anharmonicity, thus fluorine can be used to improve the thermoelectric performance as demonstrated by a recent experimental study [15], where F was introduced to LaO-BiPbS3 for enhancing the thermoelectric properties. Inspired by these advances, we show that fluorinating Sn2Bi sheet can significantly improve the thermoelectric performance at room temperature in this study.

* Corresponding author. Department of Materials Science and Engineering, Peking University, Beijing, 100871, China. E-mail address: [email protected] (Q. Sun).

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Nano Energy

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https://doi.org/10.1016/j.nanoen.2019.104283 Received 9 August 2019; Received in revised form 26 October 2019; Accepted 7 November 2019

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2. Computational details

Calculations are performed using the Vienna ab initio simulation package (VASP) based on the density functional theory (DFT) [16] with projector-augmented-wave potential (PAW) [17], Perdew-Burke-Ernzerh (PBE) exchange-correlation functional [18], and plane wave basis having an energy cutoff of 600 eV. A vacuum space of 20 Å in the direction perpendicular to the Sn2Bi plane is included for reducing the interlayer interaction. A dense 11 � 11 � 1 Monkhorst-Pack k-point mesh is used, the convergence criteria for energy and force are set as 10� 8 eV, and 10� 6 eV Å� 1, respectively. Electronic band structures including spin-orbital coupling (SOC) effect are calculated by employing Heyd-Scuseria-Ernzerhof (HSE06) exchange-correlation functional [19].

Based on the calculated band structures, electronic transport prop-erties are calculated in the framework of the Boltzmann transport theory [20] within the constant relaxation time approximation. Rigid band approximation [21] is adopted to treat doping, which assumes that the position of the Fermi level shifting up for n-type doping and down for p-type. The electrical conductivity σ can be calculated using an integral over the Brillion zone with energy, ε [22].

σ¼ e2Z �

�∂f0∂E

�

ΞðεÞdε (1)

where Ξ ¼P

k!

vvτ is the so-called transport distribution (TD) function as

obtained from the band structure, v represents the group velocities of the carriers with wave vector κ, and τ is the carrier relaxation time.

Seebeck coefficient (S) can be defined as the ratio of the voltage (built up when a small temperature gradient is applied) and the tem-perature difference [23],

S ¼2k2BT3eℏ2

m*� π

3n

�23(2)

The electrical conductivity and Seebeck coefficient are solved by using the BoltzTrap 2 code [20]. A dense 15 � 15 � 1 q mesh is intro-duced to enable accurate Fourier interpolation of the Kohn-Sham eigenvalues.

Carrier mobility (μ) can be calculated according to the deformation potential theory [24],

μ2D¼ 2eℏ3C2D

3kBTm*2E2d(3)

where e is the electron charge, ℏ is the reduced Planck constant, C2D is the 2D elastic modulus, kB is the Boltzmann constant, T is the temper-ature, and Ed is the deformation potential constant.

The thermal conductivity consists of two parts, electron thermal conductivity (κel) and lattice thermal conductivity (κl). The κel can be calculated from the Wiedemann-Franz law [25],

κel ¼LσT (4)

where L is the Lorenz number [26–28], while the κl can be expressed as [29],

καβl ¼1

kBT2ΩN

X

j;qf0ðf0þ 1Þ

�ℏωj;q

�2vαj;qLβj;q (5)

Where α and β denote x; y or z; kB is the Boltzmann constant, Ω is the unit cell volume, and N is the Г-centered q-point grids. f0 is the Bose-Einstein distribution function, ωj;q and vαj;q are phonon frequency and group velocity of the phonon mode with the branch index j and wavevector q. Lj;q compensates the phonon distribution deviated from f0 in the presence of the small temperature gradient.

The lattice thermal conductivity is calculated iteratively by solving the phonon Boltzmann transport equation with interatomic force con-stants as inputs. The interatomic force constants (IFCs) are obtained by finite displacement method (FDM) [30] using a 3 � 3 � 1 supercell with

Fig. 1. Structures and stability of Sn2Bi–F and Sn2Bi–H. (a) Top view and side view of geometry, the black dashed rhombus indicates a unit cell; (b) The energy fluctuations as well as the final configurations in molecular dynamics simulation at 500 K.(c) and (d) Phonon spectra with partial phonon DOS.

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a 3 � 3 � 1 q-mesh. The interactions with the sixth nearest-neighbor atoms are included by using ShengBTE package [29].

3. Results and discussion

It has been found that hydrogenation can stabilize Sn2Bi [31], then some questions arise: Since fluorination is expected to be more effective in tuning thermal conductivity than hydrogenation due to the larger mass and higher electronegativity of F, can fluorination also stabilize the Sn2Bi sheet? and how much of ZT value is enhanced in fluorinated Sn2Bi sheet (labelled as Sn2Bi–F) as compared to that of hydrogenated Sn2Bi sheet (labelled as Sn2Bi–H)? In the following we answer these questions by studying stability, band structure and thermal conductivity.

3.1. Stability

The structures of Sn2Bi–F and Sn2Bi–H are similar as shown in Fig. 1 (a), the black dashed rhombus indicates a unit cell, which includes two Bi atoms, four Sn atoms, and four H or F atoms. The optimized lattice constant of Sn2Bi–F is 7.52 Å. From MD simulation and phonon spec-trum as shown in Fig. 1(b) and (c), one can see that Sn2Bi–F is stable thermally and dynamically. Hence, both the hydrogenation and fluori-nation can overcome the problem of instability resulting from the dangling bonds of Sn atoms. We also calculate the binding energy of hydrogen/fluorine atom with isolated Sn2Bi sheet, which is defined by Eb ¼ � ðEtotal � ESn2Bi � 4EadatomÞ=4, where Etotal, ESn2Bi, and Eadatom stand for, respectively, the total energy of the ground state configuration of the fluorinated/hydrogenated Sn2Bi sheet, isolated Sn2Bi sheet, and isolated fluorine/hydrogen atom. Each unit cell contains four fluorine or hydrogen atoms, the average binding energy is found to be 5.04 eV/F and 2.36 eV/H for the fluorinated and hydrogenated Sn2Bi sheet, respectively, which suggest that the binding of F with the sheet is much stronger. Moreover, compared to the binding energy (2.71 eV) of F on graphene [32], the binding of F with Sn2Bi–F is much stronger. Since the

technique of fluorinating graphene is well-developed [33], we can expect that the similar methods can also be used to fluorinate Sn2BiF sheet in the future.

More importantly, as shown in the partial phonon DOS (Fig. 1(c) and (d)), obvious difference in phonon spectra exists between Sn2Bi–F and Sn2Bi–H. For Sn2Bi–F, the low frequencies modes are contributed by Sn and Bi and F atoms, while for Sn2Bi–H, the low frequency modes are related to the vibrations of Sn and Bi atoms, and the high frequency modes are related to hydrogen atoms. The phonon dispersion of Sn2Bi–F with the frequency range of 10–15 THz is much flatter than that of Sn2Bi–H, which will result in a lower phonon group velocity, thus leading to a lower lattice thermal conductivity in Sn2Bi–F.

3.2. Electronic properties

We then discuss the electronic transport properties of Sn2Bi–F. It is known that Bi element always has a strong SOC effect as evidenced by comparing band structures with and without SOC effects (see Fig. S1). In this work, we mainly focus on electronic and thermal transport prop-erties of Sn2Bi–F and Sn2Bi–H including the SOC effect. As shown in Fig. 2, we calculate the atom-projected band structures of Sn2Bi–F and Sn2Bi–H. It is found that the valence and conduction band near the Fermi level mainly contributed by Sn and Bi atoms, F and H atoms only affect the lowest valence band in K-M, shifting the bottom of conduction band from Γ for Sn2Bi–H to K for Sn2Bi–F, resulting in a smaller indirect band gap of 0.65 eV for Sn2Bi–F as compared to the quasi-direct band gap of 1.34 eV for Sn2Bi–H.

The different band structures of Sn2Bi–F and Sn2Bi–H would exhibit different effective mass for electron and hole, affecting the electrical and thermal transport properties. Physically, the effective mass m� in a band is related to the curvature of the band and can be modified by distorting the band. From Fig. 2(a) and (b), both the lowest conduction band and the highest valence band of Sn2Bi–F have smaller dispersions than those of Sn2Bi–H, thus leading to a larger electron effective mass (~0.38 m0)

Fig. 2. Atom-projected band structures of Sn2Bi-F and Sn2Bi–H sheets from HSE06 hybrid functional.

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as compared with the value of 0.20 m0 in Sn2Bi–H, the main results are given in Table 1 for details.

3.3. Thermoelectric properties

To solve the Boltzmann transport equation [34], a ratio σ= τ between electrical conductivity and carrier relaxation time can be obtained. Using μ ¼ eτm*, one knowthat a large τ can be achieved by increasing the

product of μ and m*. For electrons, the τ of Sn2Bi–F is much larger than that of Sn2Bi–H, thus leading to a higher σ in Sn2Bi–F. From the Mott relation (see Eq. (2)), one can see that S is related to the m� and n. For a given n, a larger m� leads to a larger S. As shown in Fig. 3, due to the larger m� of electrons, n-type Sn2Bi–F displays a larger value of S than that of Sn2Bi–H.

We then discuss the TE power factor which is defined as S2σ. Ac-cording to the above results, we find that both the Seebeck coefficient

Table 1 Predicted effective mass m*, deformation potential constants Ed, 2D elastic modulus C2D, carrier mobility μ and relaxation time τ of Sn2Bi–F and Sn2Bi–H.

Carrier type m*(m0Þ EdðeVÞ C2DðJ m� 2Þ μðcm2V� 1S� 1Þ τð � 10� 14sÞ

Sn2Bi–F Electron 0.38 3.41 31.11 264.03 5.70 Hole 0.27 3.70 421.27 6.46

Sn2Bi–H Electron 0.19 5.95 19.14 213.20 2.30 Hole 0.21 3.58 482.07 5.75

Fig. 3. Electrical conductivity σ, Seebeck coefficient S, and power factor PF changing with carrier concentration at 300 K for n- and p-type doped Sn2Bi–F and Sn2Bi–H.

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and electrical conductivity of n-type Sn2Bi–F are higher than those of n- type Sn2Bi–H, resulting a high TE power factor value of 4596 μW m� 1K� 2 for Sn2Bi–F, significantly different from 2630 μW m� 1K� 2 for Sn2Bi–H, which manifests that fluorination can enhance electron transport properties for Sn2Bi sheet.

Next, we focus on the impact of fluorination on the lattice thermal conductivity κl of Sn2Bi sheet. To understand the mechanism of fluorination-induced changes in lattice thermal conductivity of Sn2Bi–F, we calculate phonon properties that determine the lattice thermal con-ductivity. We focus on the three acoustic branches: longitudinal (LA), transverse (TA), and flexural mode (ZA), which are the main contribu-tion to the thermal conductivity as shown in Fig. S3, where the acoustic modes exhibit isotropic dispersions along the M-Г (armchair) and Г-K (zigzag) directions. Noting that Sn2Bi–F has a lower cut-off acoustic

phonon frequency (fcut) than that of Sn2Bi–H (lying below 1 THz), which is also lower than those of many high-performance TE materials such as SnSe (~1.5 THz) [35], SnS (~2 THz) [36]. Moreover, previous studies have shown that fluorination can effectively lower the phonon fre-quency as compared to hydrogenation, e.g., from hydrogenated penta-graphene to fluorinated penta-graphene, the fcut reduces from 18 THz to 7 THz [37], from hydrogenated boron phosphide to fluori-nated boron phosphide, the fcut decreases from 8 THz to 3 THz [38].

Then we calculate the group velocities vg of the three acoustic branches and optical branches varying with frequency in Sn2Bi–F. As shown in Fig. 4(a), the maximum phonon group velocity of Sn2Bi–F is about 1/8 of the value of Sn2Bi–H in the frequency range of 12–18 THz. As we mentioned above, the high-frequency optical branches of Sn2Bi–F and Sn2Bi–H are contributed by the light atoms, while fluorine atom is

Fig. 4. (a) phonon group velocities,(b) three-phonon scattering phase space (c) phonon anharmonic scattering rates and (d) gruneisen parameters of Sn2Bi–F and Sn2Bi–H at 300 K.

Fig. 5. (a) κl of Sn2Bi–F and Sn2Bi–H as a function of temperature, (b) cumulative κl of Sn2Bi–F and Sn2Bi–H at 300 K with respect to MFP.

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heavier than hydrogen atom, Sn2Bi–F shows much lower phonon group velocities in this high frequency range, while in the low frequency range (2–6 THz), its optical phonon group velocities are similar to that in Sn2Bi–H. However, the group velocities of the three acoustic branches (0.71, 1.01, and 1.79 km/s for ZA, TA, and LA mode, respectively) in Sn2Bi–F are lower than the corresponding values of 0.91, 1.89, 2.45 km/ s in Sn2Bi–H.

The thermal transport is closely related to phonon scattering that is governed by two main factors: the scattering probability and strength. The former can be quantitatively characterized by the so-called scat-tering phase space and scattering rates. The latter is determined by the anharmonicity of a phonon mode and can be characterized by the gru-neisen (GP) parameter. The calculated phase space (Fig. 4(b)) shows that the phase space of Sn2Bi–F is obviously larger than that of Sn2Bi–H in the frequency range of 0–6 THz, indicating that Sn2Bi–F has more three-phonon scattering channels. This can be easily understood when considering the fact that fluorine atoms have larger contribution to phonon dispersion at low frequency, thus providing more scattering channels. As shown in Fig. 4(c), anharmonic scattering rates of some optical phonons in Sn2Bi–F are much higher than that of Sn2Bi–H, which leads to shorter phonon relaxation time and lower lattice thermal con-ductivity. Fig. 4(d) shows the GP values of Sn2Bi–F and Sn2Bi–H, one can see that the absolute GP values of acoustic phonon modes are larger than that of Sn2Bi–H. Moreover, the absolute GP of Sn2Bi–F is 2.46 which is obviously higher than the value of 1.7 for Sb2Te3 [39], 1.5 for Bi2Te3 [39] and 1.96 for PbTe [40]. As shown in Fig. 5 for the changes of lattice thermal conductivity (κl) with temperature and mean free path (MFP), one can see that Sn2Bi–F exhibits an ultralow κl of 0.19 W m� 1 K � 1 that is lower than the value of 0.69 W m� 1 K � 1 for Sn2Bi–H at 300 K, and this value is remarkably lower than that of known TE materials including Bi2Te3 (1.1 W m� 1 K � 1) [41], and PbTe (2.4 W m� 1 K � 1) [42]. More-over, the κl of Sn2Bi–F reaches a half of the normalized value much faster than Sn2Bi–H does, demonstrating that Sn2Bi–F has stronger scattering effects and shorter MFP, both are responsible for the lower lattice thermal conductivity of Sn2Bi–F.

Based on the results of electronic properties and lattice thermal conductivity, we then calculate the figure of merit ZT, and the main results are given in Fig. 6 and Table S1. One can clearly see that Sn2Bi–F shows much better TE performance than Sn2Bi–H. At 300 K, the ZT value for n-, and p-type is 2.45 and 1.71, respectively, much higher than the corresponding value of 0.37 and 0.64 for Sn2Bi–H. Furthermore, the ZT value for n-type Sn2Bi–F can reach 4.31 at 500 K, showing great poten-tial of thermoelectric applications.

4. Conclusion

Inspired by the recent experimental finding that the thermoelectric property of LaOBiPbS3 can be considerably improved when fluorine is introduced [15], we carry out first-principles calculations combined with Boltzmann transport theory, and find that the thermoelectric per-formance at room temperature for Sn2Bi sheet synthesized recently [12] can be considerably enhanced by fluorination, leading to a high PF factor of 4596 μW m� 1K� 2; an ultralow κl of 0.19 W m� 1 K� 1, an ul-trahigh ZT value of 2.45 and 1.70 for n- and p-doped sheets, showing a great promise for thermoelectric applications at room temperature. One of the underlying reasons is the larger atomic mass of F as compared to H, which enhances the phonon scattering and softens the phonon modes. When going beyond F, one can expect that Cl, Br and I can also be used for this purpose through halogenation, thus providing an effective way to modulate the TE performance of Sn2Bi sheet. We hope that our findings can motivates experimental efforts on this subject.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work is partially supported by grants from the National Natural Science Foundation of China [No. NSFC-21573008 and -21773003], and from the Ministry of Science and Technology of China [No. 2017YFA0204902]. Calculations are performed on the High Perfor-mance Computing Platform of Peking University, China.

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi. org/10.1016/j.nanoen.2019.104283.

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Tingwei Li is a Ph.D. student at the Department of Materials Science and Engineering in the Peking University, China, under the supervision of Prof. Qiang Sun. He received his B.S. degree in Physics from Xiangtan University in 2018. Her current research focuses on computational design for energy storage and conversion materials including thermoelectric materials and novel thermal materials.

Dr. Jiabing Yu received his B.Sc. degree in 2013 from Uni-versity of Science and Technology of China and Ph.D. degree majored in materials in 2019 from Peking University, China. Now he is working at School of Optoelectronic Engineering at Chongqing University, China. His current research interest is in computational materials design for energy and sensing applications.

Dr. Ge Nie is a senior researcher at ENN Science & Develop-ment Co., Ltd. He received his Doctor degree from Harbin Institute of Technology in 2012. After graduation, he worked in Furukawa Co., Ltd, in Japan. In 2016. he joined Virginia Tech as a senior research associate. And then, in 2017, he moved to ENN Science & Development Co., Ltd in China. His research interests are in advanced energy materials, thermoelectric materials synthesis and module/device fabrication, and advanced alloy materials preparation and processing.

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Dr. Bo-Ping Zhang is a professor at University of Science and Technology Beijing (USTB), China. Her research focuses on thermoelectric, piezoelectric and photocatalytic materials. She has mentored 23 PhD students and published more than 310 papers.

Dr. Qiang Sun, Professor at Peking University, received his Bachelor degree in physics from Southwest University in 1984, Master degree in theoretical physics from Sichuan University in 1987, and Ph.D. degree in condensed matter physics from Nanjing University in 1996. His current research interest is in computational materials design for energy and environment applications. These include hydrogen storage, metal-ion bat-tery, thermoelectricity, CO2 capture and conversion.

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The ultralow thermal conductivity and ultrahigh thermoelectric performance of fluorinated Sn2Bi sheet in room temperature1 Introduction2 Computational details3 Results and discussion3.1 Stability3.2 Electronic properties3.3 Thermoelectric properties

4 ConclusionDeclaration of competing interestAcknowledgmentsAppendix A Supplementary dataReferences

the ultralow thermal conductivity and ultrahigh thermoelectric...

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