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Thermoelectric properties of Bi-doped SnS: First-principle study
Journal of Physics and Chemistry of Solids 137 (2020) 109182
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Thermoelectric properties of Bi-doped SnS: First-principle study Jingyu Guan, Zhengping Zhang, Meiling Dou, Jing Ji, Ye Song, Jingjun Liu, Zhilin Li *, Feng Wang ** State Key Laboratory of Chemical Resource Engineering, Beijing Key Laboratory of Electrochemical Process and Technology for Materials, Beijing University of Chemical Technology, Beijing, 100029, PR China
A R T I C L E I N F O
A B S T R A C T
Keywords: SnS Bi doping Thermoelectric materials First-principle calculation Electron transport Phonon
Although tin sulfide (SnS) is a potential thermoelectric material, it has not been applied commercially because of its low intrinsic electrical conductivity. Doping is a possible method to improve the thermoelectric properties by promoting its electron and phonon transport characters. In this work, we constructed calculation models for SnS and Sn1-xBixS to investigate their thermoelectric properties. Calculations of phonon and Grüneisen spectra show that Bi doping can reduce the lattice thermal conductivity by affecting lattice vibration in the temperature range of 300–800 K. After Bi doping, the electrical conductivity is enhanced tremendously by the huge promotion of carrier concentration, leading to a significant increase in the power factor PF. The results and analyses indicate that the influence of electron thermal conductivity on the ZT value is important. Although Bi doping increases PF by promotion of electrical conductivity, it simultaneously raises the electron thermal conductivity. However, Bi doping decreases lattice thermal conductivity, which can partially compensate for the negative effect of the increase in electron thermal conductivity on ZT values. The ZT value along the a axis increases from 0.16 to 0.36 after Bi doping at the Bi concentration of 1.56%. Such high ZT values can be attributed to the lowest thermal conductivity and the highest PF along the a axis. The calculation method and model can be extended to predict the thermoelectric performance of other materials.
1. Introduction Thermoelectric generators have the ability to directly produce elec tric power from waste heat, which is expected to play an important role in environmental protection. The exploration of thermoelectric mate rials with high efficiency has attracted much attention [1–3]. In prac tical applications, the performance of thermoelectric materials is typically expressed by the dimensionless thermoelectric figure of merit ZT ¼ S2σT/(κl þ кe), where S represents the Seebeck coefficient, σ rep resents electrical conductivity, T represents temperature, and κl and кe represent the lattice and electron thermal conductivities, respectively. An excellent thermoelectric material should have both high S and σ, represented by the power factor PF ¼ S2σ . Moreover, it is necessary for such materials to possess low thermal conductivity. However, these parameters compete with each other, except for κl which is independent [4–7]. Therefore, optimizing the contradictory parameters and reducing κl are the two paths to improving thermoelectric properties. Recently, the highest ZT value of known thermoelectric materials
was discovered in single-crystal tin selenide (SnSe). The intrinsic reason for the high ZT value is its special orthogonal layered crystal structure [8–11]. The toxicity and high cost of Se limit the large-scale application of SnSe. Tin sulfide (SnS) has the same orthogonal layered crystal structure, and S should have similar atom characteristics to Se because it belongs to the same group. Thus, SnS should also have good thermo electric performances. In addition, S is more resource-abundant, inex pensive, innocuous, and environmental friendly compared with Se [12–15]. Therefore, SnS is expected to be a potential thermoelectric material. Although SnS has received much attention for a long period, research has mainly focused on its photoelectric properties and few researchers have examined its thermoelectric performances. Paker et al. [16] pre dicted theoretically that the indirect semiconductor SnS had a high S. However, the ZT value of pure SnS is low because of its low electrical conductivity. Its highest measured value of electrical conductivity is only 10 S/m [17], and the ZT value of pure SnS is only 0.16 at 823 K [18]. As a consequence, pure SnS is not a favorable thermoelectric
* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (Z. Li), [email protected] (F. Wang). https://doi.org/10.1016/j.jpcs.2019.109182 Received 25 January 2019; Received in revised form 3 September 2019; Accepted 4 September 2019 Available online 5 September 2019 0022-3697/© 2019 Elsevier Ltd. All rights reserved.
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Journal of Physics and Chemistry of Solids 137 (2020) 109182
Fig. 1. Calculation model of pure SnS with Pnma crystal structure: projections along (a) a axis, (b) b axis, and (c) c axis.
self-consistency steps required a high precision of 10 8 eV and the convergence criterion for the forces on atoms was 10 6 eV Å 1. The system volume was expanded by þ2% from the DFT relaxed volume. The Grüneisen parameter γ describes the relationship between phonon frequency and the volume change, which is described by the finite dif ference method:
material, despite having a high S. Because the low electric conductivity of SnS is determined by the low intrinsic carrier concentration, doping might be a feasible method to improve its thermoelectric properties by increasing the carrier concentration [19,20]. There have been some attempts to improve the thermoelectric properties of SnS by doping. Sun et al. [21] explored the doping effect by theoretical calculation and found that the ZT value can be improved by the synergistic effect of temperature and carrier concentration. Chaki et al. [22] found that SnS single crystals were still p-type semiconductors after indium or antimony doping. Tan et al. [18] found that the crystal structure of SnS did not change after silver doping. Because the radii of silver and Sn ions are approximately the same, electrical conductivity was remarkably improved and the maximum ZT value reached ~0.6 at 923 K. Zhou et al. [23] reported that sodium doping reached the highest carrier concentration for SnS, which led to a significant enhancement in PF. Although doping has been shown to improve thermoelectric prop erties, suitable doping elements and their contents are extremely diffi cult to determine experimentally as they require an enormous amount of work. Therefore, theoretical calculation is an effective tool for compo sition design of doping materials. Motivated by the above issues, we used first-principle calculation based on the density functional theory (DFT) to investigate the influence of bismuth (Bi) doping on the thermoelectric performance of SnS. We calculated the change of phonon and electron transport properties after doping. The electric conductivity was greatly increased by doping, and lattice thermal conductivity decreased due to the lattice vibration character change. The thermoelectric properties of SnS were effectively improved by Bi doping. Moreover, our results demonstrated the importance of electron thermal conductivity on the ZT value, which was generally neglected in approximate predictions in previous research.
γi ¼
V ∂ωi ωi ∂V
(1)
where ω and V represent phonon frequency and volume, respectively. The lattice thermal conductivity κl is described in the following formula: κl ¼
1 Cv νλ 3
(2)
where Cv, λ, and v represent the specific heat capacity, mean free path, and velocity of phonon, respectively [28]. We also utilized the Cahill [29] model to calculate the minimum lattice thermal conductivity κmin: κmin ¼
�π�13 6
2
kB n3
Θ X � T �2 Z Ti x3 ex νi dx Θi ðex 1Þ2 0 i
(3)
where kB, n, Θ, and T represent the Boltzmann constant, the number density of atoms, Debye temperature, and temperature, respectively. The electronic transport property calculations were carried out by the BoltzTraP code [30,31], which adopted the semi-classical Boltzmann transport theory. In this method, rigid band approximation (RBA) and constant relaxation time approximation were used to calculate the transport properties. The σ , кe, and S are given by � � Z 1 ∂fμ ðT; εÞ σ αβ ðT; μÞ ¼ σαβ ðεÞ (4) dε Ω ∂ε
2. Computational procedure For the structural and electronic approaches, we calculated via a plane-wave pseudopotential formulation within the framework of DFT, and implemented the code in the Vienna Ab initio Simulation Package. The projector-augmented wave potentials were used to describe the interaction between electrons and ions. The generalized gradient approximation of Perdew–Burke–Ernzerhof was used for the exchange correlation function [24–27]. Before the calculations were performed, k-point sampling and cutoff energy convergence were tested. Then we set a 450-eV energy cutoff and 4 � 12 � 12 Monkhorst-Pack k-points to optimize the structure for a pure SnS unit cell. The atomic positions were relaxed until the forces on the atoms were smaller than 0.01 eV Å 1. We constructed the supercell and replaced some Sn atoms with Bi atoms in the calculations corresponding to the Bi-doped SnS. A temperature range of 300–800 K was adopted, in which the Pnma structure could be maintained stably. Such a range is just suitable for low temperature applications, such as for waste heat in power plants. In the quasi-harmonic DFT phonon calculations, we used the Pho nopy code [28] to construct a 2 � 3 � 3 supercell for the phonon dis persions, Grüneisen dispersions, and other lattice vibration characteristics. The total energy difference between two successive
κ0αβ ðT; μÞ ¼ Sij ¼ σ
1
�
1
2�
Z
e2 TΩ
σ αβ ðεÞðε
μÞ
�
∂fμ ðT; εÞ dε ∂ε
(5) (6)
αi ναj
where μ, εi,k, Ω, fμ, and σ αβ(ε) represent the chemical potential, electronband energies, volume, the Fermi distribution function, and the energy projected conductivity tensors, respectively. The σ αβ(ε) and the conductivity tensors σαβ(i,k) can be obtained by
σ αβ ðεÞ ¼
1X δðε εi;k Þ σαβ ði; kÞ N i;k dε �
σ αβ ði; kÞ ¼ e2 τi;k vα i; k vβ ði; kÞ
(7) (8)
where N, τ, and v represent the number of k-points sampled, relaxation time, and group velocity, respectively. All calculations were under the assumption that τ is directionindependent and S is independent of τ. 2
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Journal of Physics and Chemistry of Solids 137 (2020) 109182
Fig. 2. Calculation model of Bi-doped SnS with Pnma crystal structure: (projections along (a) a axis, (b) b axis, and (c) c axis. Table 1 Calculation results of phonon group velocity v, Debye temperature Θ and Grü neisen parameters γ along different axes of pure SnSa. Axis
Branch
v (m/s)
Θ(K)
γ
Г-X/a
TA TA0 LA Average
1832 1833 2064 1910
37 37 38 37
5.67 1.87 2.07 3.20
Г-Y/b
TA TA0 LA Average
1781 1772 3417 2323
75 75 84 78
0.68 1.93 2.15 1.59
Г-Z/c
TA TA0 LA Average
1988 2210 3046 2415
63 63 74 67
2.07 2.19 1.28 1.85
a
The Debye temperature Θ was calculated by Θ ¼
ωD
, where ωD represents kB the largest vibration frequency in each acoustic branch. The phonon group ve dω locity v was the derivation of the wave vector by the frequency, v ¼ . The dK Grüneisen parameters of each acoustic dispersion was evaluated from the rootpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi < γi >. Additionally, mean-square value of γi along each direction, γ ¼ average values were obtained from the three acoustic branches.
such doping. The stable crystal structure of Sn1-xBixS maintained the Pnma type (Fig. 2). 3.2. Vibration properties and lattice thermal conductivity
Fig. 3. (a) Phonon dispersions of pure SnS. (b) Grüneisen dispersions of pure SnS. In figures, TA, TA’, transverse acoustic phonon scattering branches; LA, longitudinal acoustic phonon scattering branch; and X, Г, Y, P, Г, A, Z, Г, and T describe the (1/2 0 0), (0 0 0), (0 1/2 0), (1/2 1/2 0), (0 0 0), (1/2 0 1/2), (0 0 1/2), (0 0 0), and (1/2 1/2 1/2) high-symmetry points, respectively.
3.2.1. Vibration properties and lattice thermal conductivity of pure SnS The phonon transport properties have a vital influence on lattice thermal conductivity, so we computed the phonon and Grüneisen dis persions. The results for pure SnS are shown in Fig. 3. In the phonon dispersion, there is no imaginary frequency in the whole Brillouin zone, which indicates that the SnS crystal structure was optimized with good stability. The acoustic modes along the Г–X Brillouin zone direction (a axis) are softer than those along both Г–Y (b axis) and Г–Z (c axis) di rections. The calculation results of v, Θ, and γ along different axes of pure SnS are shown in Table 1. The Θ and v along the a axis are the smallest. Such results are due to the weak interatomic bonding and strong anharmonicity along the a axis, which implies κl along the a axis. The weak interatomic bonding and strong anharmonicity along the a axis are further verified by the Grüneisen dispersion (Fig. 3b) and the Grüneisen parameters (Table 1). The γ value along a axis is larger than those along both the b and c axes. We further calculated the κl with formula (2), where λ used the calculated value of 1 nm at 300 K by Huang et al. [33]. The results of κl along a, b and c axes are 1.17, 1.42 and 1.48 Wm 1K 1, respectively. The average value is 1.36 Wm 1K 1 which is close to the experimental value [18]. At other temperatures, we attempted different mean free paths of phonon and obtained a series of κl which also agree well with experi mental values. This consistency is the foundation of our further
3. Results and discussion 3.1. Geometry optimization Fig. 1 shows the calculation model of the pure SnS with the Pnma crystal structure. The b–c plane has two-atom-thick SnS slabs, which are corrugated and creates a zig-zag accordion-like projection along the c axis. The slabs are connected with weak Sn–S bond along the a axis. The relaxed lattice constants are a ¼ 11.42 Å, b ¼ 4.02 Å, and c ¼ 4.42 Å for SnS, which are close to the experimental results and some previous ab initio calculations [21]. For the Bi doping model, we constructed a similar 1 � 2 � 2 supercell and replaced a Sn atom with a Bi atom in the calculation. Doping con centration was defined as the ratio of the number of Bi atoms to the total number of Bi and Sn atoms in a supercell. In this case, the doping con centration of the 1 � 2 � 2 supercell was 6.25%. In other words, we constructed a Sn1-xBixS model on x ¼ 6.25%. Structural optimization showed that the Pnma crystal structure of SnS remained unchanged after 3
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Journal of Physics and Chemistry of Solids 137 (2020) 109182
Table 2 Calculation results of phonon group velocity v, Debye temperature Θ and Grü neisen parameters γ along different axes of Bi-doped SnS (Sn93.75%Bi6.25%S). Axis
Branch
v (m/s)
Θ(K)
γ
Г-X/a
TA TA0 LA Average
1487 1636 1860 1661
29 33 36 33
2.43 5.91 1.51 3.28
Г-Y/b
TA TA0 LA Average
1810 1915 2970 2232
51 54 56 54
0.38 2.10 2.47 1.65
Г-Z/c
TA TA0 LA Average
1536 1993 2348 1959
41 46 48 45
1.14 2.55 1.47 2.06
Fig. 4. Specific heat capacity Cv, the calculated lattice thermal conductivity κl along three axes, and their average values of pure SnS at different temperatures.
Fig. 6. Specific heat capacity Cv, the calculated lattice thermal conductivity кl along three axes and their average values of Bi-doped SnS (Sn93.75%Bi6.25%S) at different temperatures.
instance, the thermal conductivity along a axis is still the lowest, and decreases with increase in temperature. Therefore, the lattice structure remains stable but the lattice vibration character changes with the Bi doping. However, all values of v, Θ, and κl of Bi-doped SnS are less than corresponding values of pure SnS. The Grüneisen parameters of Bidoped SnS are larger than those of pure SnS. The calculated values of κmin along the a, b, and c axes of Bi-doped SnS are 0.321, 0.428, and 0.376 Wm 1K 1, respectively, and are all lower than corresponding values for pure SnS. Therefore, Bi doping obviously changes the lattice vibration parameters of v, Θ, and γ in a similar vibration behavior, so that it effectively reduces κl. Because κl is independent of electronic conductivity, such decreases caused by Bi doping promote the ZT value.
Fig. 5. (a) Phonon dispersions of Bi-doped SnS (Sn93.75%Bi6.25%S). (b) Grü neisen dispersions of Bi-doped SnS (Sn93.75%Bi6.25%S).
calculations. The κl is smaller along the a axis than along both the b and c axes, and all values decrease with increasing temperature (Fig. 4). We also calculated κmin using the Cahill model of formula (3). The κmin along the a, b, and c axes are 0.339, 0.431, and 0.432 Wm 1K 1, respectively. The κmin along the a axis is also smaller than along the b and c axes, consistent with the calculated regulations of Debye temperature and Grüneisen parameters along different axes in Table 1.
3.3. Electronic structures, electron transport, and thermoelectric properties 3.3.1. Electronic structure of pure SnS The calculation results of electronic structure of pure SnS (Fig. 7) form the background for the further discussion of Bi-doped SnS. The band structure and electronic density of state (DOS) are similar to pre vious results with other methods [11,28], further confirming reliability of our calculations. The DOS plot (Fig. 7a) shows that the top of the valence band is mainly determined by the hybridization of s- and p-states of Sn and the p-state of S, whereas the bottom of the conduction band is formed primarily by the p-states of Sn and S. Previous work and
3.2.2. Vibration properties and κl of Bi-doped SnS The phonon and Grüneisen dispersions of Bi-doped SnS are shown in Fig. 5. No imaginary frequency exists in the whole Brillouin zone, indicating that the structure is still very stable after Bi doping. The calculation results for v, Θ, and γ of Bi-doped SnS are shown in Table 2, and for Cv and κl in Fig. 6. The lattice variation parameters of Bi-doped SnS along different axes have the same trends as those of pure SnS. For 4
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Fig. 7. (a) Total and partial densities of state and (b) band structure of pure SnS.
Fig. 8. (a) Total and partial densities of state and (b) band structure of Bi-doped SnS (Sn93.75%Bi6.25%S).
defect calculations suggest that the intrinsic p-type conductivity is due to the easy formation of Sn vacancies which act as shallow acceptors [32].
the highest Bi doping concentration of 6.25%, are quite different from their model of Sn0.5Bi0.5S, which is a different compound. This explains the different conclusions. However, our structural optimization and phonon dispersion also showed that the structure can exist stably. The electrons with the energy from the bottom of valence band to EF should be free electrons, which can directly participate in electron transport without excitation. Therefore, the density of transport electrons should increase greatly with Bi doping, which can promote σ and PF. Furthermore, the band gap of SnS is narrowed by Bi doping, indi cating the easier intrinsic excitation of the carrier. So the carrier con centration might be promoted by Bi doping at high temperatures, which also aids in promoting σ and PF.
3.3.2. Electronic structures of Bi-doped SnS The calculation results of electronic structure of Bi-doped SnS are shown in Fig. 8. The DOS close to the top of valence band is mainly determined by the hybridization of the s- and p-states of Sn and the pstate of S (Fig. 8a), so Bi doping has little effect on the top of the valence band. However, the p-state of Bi has a relatively large DOS near the bottom of the conduction band, which significantly affects the bottom of the conduction band of Bi-doped SnS. More notable is that Bi doping not only dramatically changes the p-states of Sn and S but also greatly changes the DOS distribution near the bottom of the conduction band. Xiao and co-workers performed DFT calculations to examine n-type doping of SnS, and found that Bi doping was not an effective route [33]. However, our calculation models, based on a solid solution of SnS with
3.3.3. Electron transport and thermoelectric properties Based on the electronic structures, we calculated the electron transport properties of pure SnS and Bi-doped SnS by Boltzmann theory (Fig. 9). In the BoltzTraP calculations, constant relaxation time 5
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Journal of Physics and Chemistry of Solids 137 (2020) 109182
Fig. 9. Calculation results of electron transport and thermoelectric properties of SnS and Bi-doped SnS (Sn93.75%Bi6.25%S) at various temperatures: (a) electrical conductivity, (b) absolute value of Seebeck coefficient, (c) power factor, (d) electron thermal conductivity and (e) ZT value.
approximation was used to calculate the transport properties. We adopted the relaxation time from the experimental measurements and deductions by Nassary et al. [14]; the values are 15.1 � 10 16 and 7.44 � 10 16 s for the pure and doped SnS, respectively. The σ of pure SnS is quite small although it increases with rising temperature. After Bi doping, σ increases significantly, although it decreases slightly with increasing temperature (Fig. 9a). This can be attributed to the change in electron structure after Bi doping which we analyzed above. Calculation results show that the S values of Bi-doped SnS are negative, providing further proof of the formation of an n-type semiconductor after Bi doping. Because the ZT value is determined by S2, we show |S| in Fig. 9b. The |S| decreases obviously after Bi doping, which is unfavorable for promotion of PF and ZT value. However, the significant increase in σ could compensate for the decrease in |S|, so Bi doping can still result in a significant increase in PF (Fig. 9c). The κe increases after Bi doping (Fig. 9d), which is disadvantageous for promotion of ZT value. However, Bi doping causes obvious decrease of κl, which can partially compensate
for the negative effect of doping on ZT value. The complex effect of Bi doping on electron transport and phonon transport causes a complex change in ZT value (Fig. 9e). The Bi doping increases the ZT value below 700 K, but decreases it at 800 K. Although this improved ZT value in the temperature range of 300–700 K can satisfy most application circum stances of waste-heat power generation, the increment is quite limited by such Bi doping and needs further improvement. For calculation convenience, previous approximate prediction usu ally paid much attention to the positive effect of doping on σ and PF, and unintentionally neglected its negative effect on κe. However, the results in Fig. 9d and e indicate that κe plays an important role in the thermo electric properties, which should not be ignored. For instance, a too high value of κe causes a decrease of ZT at 800 K after Bi doping. Therefore, the content of Bi should be optimized to decrease the density of transport electrons and κe.
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be neglected. Therefore, only the Bi concentration should be considered in the following calculations. The calculation results show that σ increases with the increase in doping concentration in all temperature ranges (Fig. 10a), owing to the increase in carrier concentration caused by Bi doping. When x ¼ 1.56–6.25%, the |S| decreases with the increase in doping concen tration (Fig. 10b), which is opposite to the relationship between σ and T. However, such a relationship is not maintained when x ¼ 0.78%. The opposite relationships of σ and |S| vs Bi doping concentration causes complex changes of PF when x ¼ 1.56–6.25% (Fig. 10c). The PF order for different Bi doping concentrations changes at different temperature, and PF for x ¼ 0.78% is the lowest among all Bi doping concentrations. However, the thermal electric properties of different Bi content could still be compared reasonably by κe and ZT value analyses. The κe de creases significantly for doping concentration of 1.56% (Fig. 10d), leading to a remarkable increase in ZT value (Fig. 10e). On the whole, the ZT value at x ¼ 6.25% is low because of the excessive κe resulting from the very high carrier concentrations. For
Table 3 Different supercells and doping concentrations of Bi-doped SnS. Supercell 1�1�1 1�2�2 2�2�2 2�2�4 2�4�4
Atom number Sn
S
Bi
Total
4 15 31 63 127
4 16 32 64 128
0 1 1 1 1
8 32 64 128 256
Doping concentration
Type of conduction
0 6.25% 3.13% 1.56% 0.78%
p-type n-type n-type n-type n-type
3.4. Optimization of doping concentration We constructed larger supercells of Sn1-xBixS (x ¼ 0.78, 1.56, and 3.13%) to accomplish different doping concentrations (Table 3). We calculated electron transport properties of Sn1-xBixS with different Bi positions in a supercell, and found that substitutional sites of Bi atom have no effect on electron transport properties. Such results can be attributed to the periodic model in which the effect of crystal surface can
Fig. 10. Calculation results of electron transport and thermoelectric properties of Sn1-xBixS (x ¼ 0.78, 1.56, 3.12, and 6.25%) at various temperatures: (a) electrical conductivity, (b) absolute value of Seebeck coefficient, (c) power factor, (d) electron thermal conductivity and (e) ZT value. 7
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much larger along the b and c axes [34]. 4. Conclusions We constructed calculation models for SnS and Sn1-xBixS using different x values. The models were confirmed by experimental facts and previous calculations, such as the calculations of crystal structure, lattice constants, band structures, and DOS. We further investigated the ther moelectric properties of SnS and Bi-doped SnS in the aspects of electron transport and phonon transport. In our calculation range, the Pnma crystal structure of pure SnS remained stable after Bi doping. Through calculations of phonon and Grüneisen spectra which are related to lat tice vibration, we found that Bi doping reduced the lattice thermal conductivity by the effect on the lattice vibration in the temperature range of 300–800 K. Furthermore, both the pure and Bi-doped SnS had the lowest lattice thermal conductivity along the a axis because of their weak interatomic bonding and strong anharmonicity which were re flected by the largest Grüneisen parameters along the a axis. The calculation results of electronic DOS and band structure indicated that Bi doping effectively narrowed the band gap. The change of band gap can improve the thermoelectric performances as confirmed by subsequent calculations of electron transport. After Bi doping, electrical conduc tivity was greatly promoted by the large increase in carrier concentra tion, so that PF was significantly improved by Bi doping. Therefore, our results and analyses indicate that the influence of electron thermal conductivity on the ZT value was important. The Bi doping increased PF by increasing the electrical conductivity, but raised the electron thermal conductivity simultaneously to decrease the ZT value. However, Bi doping decreased lattice thermal conductivity which could partially compensate for the negative effect of the increase of electron thermal conductivity. We calculated the thermoelectric properties at different Bi doping concentrations and determined the optimum doping concentra tion of 1.56%. The peak ZT value at this doping concentration was 0.31 in the temperature range of 300–800 K. Considering the anisotropy, Bidoped SnS reached a larger ZT value of 0.36 along the a axis, which was a large increase compared with the value of 0.16 for SnS. The cause of such a high ZT value can be attributed to the lowest thermal conduc tivity and the highest PF along the a axis. Furthermore, our calculation methods and models are convenient tools for doping element selection and content determination for thermoelectric materials, and can be extended to prediction of the thermoelectric performance of other materials.
Fig. 11. ZT value at different temperature along different directions.
doping concentration of 1.56%, the low doping content causes low carrier concentration, low κe, and high |S|, which determines high ZT values. In this circumstance, the importance of the electron thermal conductivity on thermal electric properties is fully displayed. Although the κe for x ¼ 0.78% is the lowest among all doping concentrations, the PF is too low because of the low carrier concentration and σ at this Bi content. Therefore, the ZT value for x ¼ 0.78% is lower than that for x ¼ 1.56%. The ZT value reaches a maximum when x ¼ 1.56% in the whole temperature range, rising with increasing temperature and reaching 0.31 at 800 K. This is a significant promotion compared with the value of 0.16 for pure SnS. Sun et al. [21] evaluated the ZT value of n-type doping of SnS using the RBA method. They obtained a maximum ZT of 0.61 at 800 K, which is much higher than our result of 0.31. They simply adopted an exper iment thermal conductivity of 0.65 Wm 1K 1 of pure SnS at 800 K in their evaluation, so their final ZT value of doped SnS is doubtful because they neglected the effect of doping on κe. The doping increases the carrier concentration, and so definitely increases the electron thermal conductivity. We used our thermal conductivity result of Bi-doped SnS for x ¼ 1.56% (including phonon and electron thermal conductivities) into the model of Sun et al. [21] and produced a ZT value of 0.28, which is quite close to our calculation result of 0.31. The similarity between the ZT values obtained with different methods further demonstrates the reliability of our calculation.
Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant number 51472020) and CHEMCLOUDCOMPUTING.
3.5. Further optimization of ZT value by texture One notable characteristic of SnS is its highly anisotropic layered orthonormal structure [11], which is maintained after Bi doping in our circumstances. So the ZT value of Bi-doped SnS might be further improved by anisotropy. We calculated the ZT values along the a, b, and c axes of the Bi-doped SnS with optimal doping concentration of x ¼ 1.56%, respectively (Fig. 11). Unlike pure SnS which reaches a maximum ZT value along the b axis, the Bi-doped SnS reaches a maximum ZT along the a axis for all temperatures. At 300 K, the ZT value along the a axis reaches 0.06, which is a 100% increase with respect to the value of polycrystal of 0.03. At 800 K, the ZT value along the a axis reaches 0.36, which still represents a 16% increase. The reason why the highest ZT value appears along the a axis can be explained by our calculation results for σ, S, PF, κe, and κl. The κl is the lowest and PF is the largest along the a axis. The low κl along the a axis can be attributed to the weak interatomic bonding and strong anharmonicity, and the large PF can be attributed to the low effective mass along the a axis in the conduction band [34]. The Fermi level enters the conduction band to form an n-type semiconductor after Bi doping (Fig. 8b), so the effective masses of electrons become significantly smaller along the a axis but
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Journal of Physics and Chemistry of Solids journal homepage: http://www.elsevier.com/locate/jpcs
Thermoelectric properties of Bi-doped SnS: First-principle study Jingyu Guan, Zhengping Zhang, Meiling Dou, Jing Ji, Ye Song, Jingjun Liu, Zhilin Li *, Feng Wang ** State Key Laboratory of Chemical Resource Engineering, Beijing Key Laboratory of Electrochemical Process and Technology for Materials, Beijing University of Chemical Technology, Beijing, 100029, PR China
A R T I C L E I N F O
A B S T R A C T
Keywords: SnS Bi doping Thermoelectric materials First-principle calculation Electron transport Phonon
Although tin sulfide (SnS) is a potential thermoelectric material, it has not been applied commercially because of its low intrinsic electrical conductivity. Doping is a possible method to improve the thermoelectric properties by promoting its electron and phonon transport characters. In this work, we constructed calculation models for SnS and Sn1-xBixS to investigate their thermoelectric properties. Calculations of phonon and Grüneisen spectra show that Bi doping can reduce the lattice thermal conductivity by affecting lattice vibration in the temperature range of 300–800 K. After Bi doping, the electrical conductivity is enhanced tremendously by the huge promotion of carrier concentration, leading to a significant increase in the power factor PF. The results and analyses indicate that the influence of electron thermal conductivity on the ZT value is important. Although Bi doping increases PF by promotion of electrical conductivity, it simultaneously raises the electron thermal conductivity. However, Bi doping decreases lattice thermal conductivity, which can partially compensate for the negative effect of the increase in electron thermal conductivity on ZT values. The ZT value along the a axis increases from 0.16 to 0.36 after Bi doping at the Bi concentration of 1.56%. Such high ZT values can be attributed to the lowest thermal conductivity and the highest PF along the a axis. The calculation method and model can be extended to predict the thermoelectric performance of other materials.
1. Introduction Thermoelectric generators have the ability to directly produce elec tric power from waste heat, which is expected to play an important role in environmental protection. The exploration of thermoelectric mate rials with high efficiency has attracted much attention [1–3]. In prac tical applications, the performance of thermoelectric materials is typically expressed by the dimensionless thermoelectric figure of merit ZT ¼ S2σT/(κl þ кe), where S represents the Seebeck coefficient, σ rep resents electrical conductivity, T represents temperature, and κl and кe represent the lattice and electron thermal conductivities, respectively. An excellent thermoelectric material should have both high S and σ, represented by the power factor PF ¼ S2σ . Moreover, it is necessary for such materials to possess low thermal conductivity. However, these parameters compete with each other, except for κl which is independent [4–7]. Therefore, optimizing the contradictory parameters and reducing κl are the two paths to improving thermoelectric properties. Recently, the highest ZT value of known thermoelectric materials
was discovered in single-crystal tin selenide (SnSe). The intrinsic reason for the high ZT value is its special orthogonal layered crystal structure [8–11]. The toxicity and high cost of Se limit the large-scale application of SnSe. Tin sulfide (SnS) has the same orthogonal layered crystal structure, and S should have similar atom characteristics to Se because it belongs to the same group. Thus, SnS should also have good thermo electric performances. In addition, S is more resource-abundant, inex pensive, innocuous, and environmental friendly compared with Se [12–15]. Therefore, SnS is expected to be a potential thermoelectric material. Although SnS has received much attention for a long period, research has mainly focused on its photoelectric properties and few researchers have examined its thermoelectric performances. Paker et al. [16] pre dicted theoretically that the indirect semiconductor SnS had a high S. However, the ZT value of pure SnS is low because of its low electrical conductivity. Its highest measured value of electrical conductivity is only 10 S/m [17], and the ZT value of pure SnS is only 0.16 at 823 K [18]. As a consequence, pure SnS is not a favorable thermoelectric
* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (Z. Li), [email protected] (F. Wang). https://doi.org/10.1016/j.jpcs.2019.109182 Received 25 January 2019; Received in revised form 3 September 2019; Accepted 4 September 2019 Available online 5 September 2019 0022-3697/© 2019 Elsevier Ltd. All rights reserved.
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Fig. 1. Calculation model of pure SnS with Pnma crystal structure: projections along (a) a axis, (b) b axis, and (c) c axis.
self-consistency steps required a high precision of 10 8 eV and the convergence criterion for the forces on atoms was 10 6 eV Å 1. The system volume was expanded by þ2% from the DFT relaxed volume. The Grüneisen parameter γ describes the relationship between phonon frequency and the volume change, which is described by the finite dif ference method:
material, despite having a high S. Because the low electric conductivity of SnS is determined by the low intrinsic carrier concentration, doping might be a feasible method to improve its thermoelectric properties by increasing the carrier concentration [19,20]. There have been some attempts to improve the thermoelectric properties of SnS by doping. Sun et al. [21] explored the doping effect by theoretical calculation and found that the ZT value can be improved by the synergistic effect of temperature and carrier concentration. Chaki et al. [22] found that SnS single crystals were still p-type semiconductors after indium or antimony doping. Tan et al. [18] found that the crystal structure of SnS did not change after silver doping. Because the radii of silver and Sn ions are approximately the same, electrical conductivity was remarkably improved and the maximum ZT value reached ~0.6 at 923 K. Zhou et al. [23] reported that sodium doping reached the highest carrier concentration for SnS, which led to a significant enhancement in PF. Although doping has been shown to improve thermoelectric prop erties, suitable doping elements and their contents are extremely diffi cult to determine experimentally as they require an enormous amount of work. Therefore, theoretical calculation is an effective tool for compo sition design of doping materials. Motivated by the above issues, we used first-principle calculation based on the density functional theory (DFT) to investigate the influence of bismuth (Bi) doping on the thermoelectric performance of SnS. We calculated the change of phonon and electron transport properties after doping. The electric conductivity was greatly increased by doping, and lattice thermal conductivity decreased due to the lattice vibration character change. The thermoelectric properties of SnS were effectively improved by Bi doping. Moreover, our results demonstrated the importance of electron thermal conductivity on the ZT value, which was generally neglected in approximate predictions in previous research.
γi ¼
V ∂ωi ωi ∂V
(1)
where ω and V represent phonon frequency and volume, respectively. The lattice thermal conductivity κl is described in the following formula: κl ¼
1 Cv νλ 3
(2)
where Cv, λ, and v represent the specific heat capacity, mean free path, and velocity of phonon, respectively [28]. We also utilized the Cahill [29] model to calculate the minimum lattice thermal conductivity κmin: κmin ¼
�π�13 6
2
kB n3
Θ X � T �2 Z Ti x3 ex νi dx Θi ðex 1Þ2 0 i
(3)
where kB, n, Θ, and T represent the Boltzmann constant, the number density of atoms, Debye temperature, and temperature, respectively. The electronic transport property calculations were carried out by the BoltzTraP code [30,31], which adopted the semi-classical Boltzmann transport theory. In this method, rigid band approximation (RBA) and constant relaxation time approximation were used to calculate the transport properties. The σ , кe, and S are given by � � Z 1 ∂fμ ðT; εÞ σ αβ ðT; μÞ ¼ σαβ ðεÞ (4) dε Ω ∂ε
2. Computational procedure For the structural and electronic approaches, we calculated via a plane-wave pseudopotential formulation within the framework of DFT, and implemented the code in the Vienna Ab initio Simulation Package. The projector-augmented wave potentials were used to describe the interaction between electrons and ions. The generalized gradient approximation of Perdew–Burke–Ernzerhof was used for the exchange correlation function [24–27]. Before the calculations were performed, k-point sampling and cutoff energy convergence were tested. Then we set a 450-eV energy cutoff and 4 � 12 � 12 Monkhorst-Pack k-points to optimize the structure for a pure SnS unit cell. The atomic positions were relaxed until the forces on the atoms were smaller than 0.01 eV Å 1. We constructed the supercell and replaced some Sn atoms with Bi atoms in the calculations corresponding to the Bi-doped SnS. A temperature range of 300–800 K was adopted, in which the Pnma structure could be maintained stably. Such a range is just suitable for low temperature applications, such as for waste heat in power plants. In the quasi-harmonic DFT phonon calculations, we used the Pho nopy code [28] to construct a 2 � 3 � 3 supercell for the phonon dis persions, Grüneisen dispersions, and other lattice vibration characteristics. The total energy difference between two successive
κ0αβ ðT; μÞ ¼ Sij ¼ σ
1
�
1
2�
Z
e2 TΩ
σ αβ ðεÞðε
μÞ
�
∂fμ ðT; εÞ dε ∂ε
(5) (6)
αi ναj
where μ, εi,k, Ω, fμ, and σ αβ(ε) represent the chemical potential, electronband energies, volume, the Fermi distribution function, and the energy projected conductivity tensors, respectively. The σ αβ(ε) and the conductivity tensors σαβ(i,k) can be obtained by
σ αβ ðεÞ ¼
1X δðε εi;k Þ σαβ ði; kÞ N i;k dε �
σ αβ ði; kÞ ¼ e2 τi;k vα i; k vβ ði; kÞ
(7) (8)
where N, τ, and v represent the number of k-points sampled, relaxation time, and group velocity, respectively. All calculations were under the assumption that τ is directionindependent and S is independent of τ. 2
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Fig. 2. Calculation model of Bi-doped SnS with Pnma crystal structure: (projections along (a) a axis, (b) b axis, and (c) c axis. Table 1 Calculation results of phonon group velocity v, Debye temperature Θ and Grü neisen parameters γ along different axes of pure SnSa. Axis
Branch
v (m/s)
Θ(K)
γ
Г-X/a
TA TA0 LA Average
1832 1833 2064 1910
37 37 38 37
5.67 1.87 2.07 3.20
Г-Y/b
TA TA0 LA Average
1781 1772 3417 2323
75 75 84 78
0.68 1.93 2.15 1.59
Г-Z/c
TA TA0 LA Average
1988 2210 3046 2415
63 63 74 67
2.07 2.19 1.28 1.85
a
The Debye temperature Θ was calculated by Θ ¼
ωD
, where ωD represents kB the largest vibration frequency in each acoustic branch. The phonon group ve dω locity v was the derivation of the wave vector by the frequency, v ¼ . The dK Grüneisen parameters of each acoustic dispersion was evaluated from the rootpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi < γi >. Additionally, mean-square value of γi along each direction, γ ¼ average values were obtained from the three acoustic branches.
such doping. The stable crystal structure of Sn1-xBixS maintained the Pnma type (Fig. 2). 3.2. Vibration properties and lattice thermal conductivity
Fig. 3. (a) Phonon dispersions of pure SnS. (b) Grüneisen dispersions of pure SnS. In figures, TA, TA’, transverse acoustic phonon scattering branches; LA, longitudinal acoustic phonon scattering branch; and X, Г, Y, P, Г, A, Z, Г, and T describe the (1/2 0 0), (0 0 0), (0 1/2 0), (1/2 1/2 0), (0 0 0), (1/2 0 1/2), (0 0 1/2), (0 0 0), and (1/2 1/2 1/2) high-symmetry points, respectively.
3.2.1. Vibration properties and lattice thermal conductivity of pure SnS The phonon transport properties have a vital influence on lattice thermal conductivity, so we computed the phonon and Grüneisen dis persions. The results for pure SnS are shown in Fig. 3. In the phonon dispersion, there is no imaginary frequency in the whole Brillouin zone, which indicates that the SnS crystal structure was optimized with good stability. The acoustic modes along the Г–X Brillouin zone direction (a axis) are softer than those along both Г–Y (b axis) and Г–Z (c axis) di rections. The calculation results of v, Θ, and γ along different axes of pure SnS are shown in Table 1. The Θ and v along the a axis are the smallest. Such results are due to the weak interatomic bonding and strong anharmonicity along the a axis, which implies κl along the a axis. The weak interatomic bonding and strong anharmonicity along the a axis are further verified by the Grüneisen dispersion (Fig. 3b) and the Grüneisen parameters (Table 1). The γ value along a axis is larger than those along both the b and c axes. We further calculated the κl with formula (2), where λ used the calculated value of 1 nm at 300 K by Huang et al. [33]. The results of κl along a, b and c axes are 1.17, 1.42 and 1.48 Wm 1K 1, respectively. The average value is 1.36 Wm 1K 1 which is close to the experimental value [18]. At other temperatures, we attempted different mean free paths of phonon and obtained a series of κl which also agree well with experi mental values. This consistency is the foundation of our further
3. Results and discussion 3.1. Geometry optimization Fig. 1 shows the calculation model of the pure SnS with the Pnma crystal structure. The b–c plane has two-atom-thick SnS slabs, which are corrugated and creates a zig-zag accordion-like projection along the c axis. The slabs are connected with weak Sn–S bond along the a axis. The relaxed lattice constants are a ¼ 11.42 Å, b ¼ 4.02 Å, and c ¼ 4.42 Å for SnS, which are close to the experimental results and some previous ab initio calculations [21]. For the Bi doping model, we constructed a similar 1 � 2 � 2 supercell and replaced a Sn atom with a Bi atom in the calculation. Doping con centration was defined as the ratio of the number of Bi atoms to the total number of Bi and Sn atoms in a supercell. In this case, the doping con centration of the 1 � 2 � 2 supercell was 6.25%. In other words, we constructed a Sn1-xBixS model on x ¼ 6.25%. Structural optimization showed that the Pnma crystal structure of SnS remained unchanged after 3
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Table 2 Calculation results of phonon group velocity v, Debye temperature Θ and Grü neisen parameters γ along different axes of Bi-doped SnS (Sn93.75%Bi6.25%S). Axis
Branch
v (m/s)
Θ(K)
γ
Г-X/a
TA TA0 LA Average
1487 1636 1860 1661
29 33 36 33
2.43 5.91 1.51 3.28
Г-Y/b
TA TA0 LA Average
1810 1915 2970 2232
51 54 56 54
0.38 2.10 2.47 1.65
Г-Z/c
TA TA0 LA Average
1536 1993 2348 1959
41 46 48 45
1.14 2.55 1.47 2.06
Fig. 4. Specific heat capacity Cv, the calculated lattice thermal conductivity κl along three axes, and their average values of pure SnS at different temperatures.
Fig. 6. Specific heat capacity Cv, the calculated lattice thermal conductivity кl along three axes and their average values of Bi-doped SnS (Sn93.75%Bi6.25%S) at different temperatures.
instance, the thermal conductivity along a axis is still the lowest, and decreases with increase in temperature. Therefore, the lattice structure remains stable but the lattice vibration character changes with the Bi doping. However, all values of v, Θ, and κl of Bi-doped SnS are less than corresponding values of pure SnS. The Grüneisen parameters of Bidoped SnS are larger than those of pure SnS. The calculated values of κmin along the a, b, and c axes of Bi-doped SnS are 0.321, 0.428, and 0.376 Wm 1K 1, respectively, and are all lower than corresponding values for pure SnS. Therefore, Bi doping obviously changes the lattice vibration parameters of v, Θ, and γ in a similar vibration behavior, so that it effectively reduces κl. Because κl is independent of electronic conductivity, such decreases caused by Bi doping promote the ZT value.
Fig. 5. (a) Phonon dispersions of Bi-doped SnS (Sn93.75%Bi6.25%S). (b) Grü neisen dispersions of Bi-doped SnS (Sn93.75%Bi6.25%S).
calculations. The κl is smaller along the a axis than along both the b and c axes, and all values decrease with increasing temperature (Fig. 4). We also calculated κmin using the Cahill model of formula (3). The κmin along the a, b, and c axes are 0.339, 0.431, and 0.432 Wm 1K 1, respectively. The κmin along the a axis is also smaller than along the b and c axes, consistent with the calculated regulations of Debye temperature and Grüneisen parameters along different axes in Table 1.
3.3. Electronic structures, electron transport, and thermoelectric properties 3.3.1. Electronic structure of pure SnS The calculation results of electronic structure of pure SnS (Fig. 7) form the background for the further discussion of Bi-doped SnS. The band structure and electronic density of state (DOS) are similar to pre vious results with other methods [11,28], further confirming reliability of our calculations. The DOS plot (Fig. 7a) shows that the top of the valence band is mainly determined by the hybridization of s- and p-states of Sn and the p-state of S, whereas the bottom of the conduction band is formed primarily by the p-states of Sn and S. Previous work and
3.2.2. Vibration properties and κl of Bi-doped SnS The phonon and Grüneisen dispersions of Bi-doped SnS are shown in Fig. 5. No imaginary frequency exists in the whole Brillouin zone, indicating that the structure is still very stable after Bi doping. The calculation results for v, Θ, and γ of Bi-doped SnS are shown in Table 2, and for Cv and κl in Fig. 6. The lattice variation parameters of Bi-doped SnS along different axes have the same trends as those of pure SnS. For 4
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Journal of Physics and Chemistry of Solids 137 (2020) 109182
Fig. 7. (a) Total and partial densities of state and (b) band structure of pure SnS.
Fig. 8. (a) Total and partial densities of state and (b) band structure of Bi-doped SnS (Sn93.75%Bi6.25%S).
defect calculations suggest that the intrinsic p-type conductivity is due to the easy formation of Sn vacancies which act as shallow acceptors [32].
the highest Bi doping concentration of 6.25%, are quite different from their model of Sn0.5Bi0.5S, which is a different compound. This explains the different conclusions. However, our structural optimization and phonon dispersion also showed that the structure can exist stably. The electrons with the energy from the bottom of valence band to EF should be free electrons, which can directly participate in electron transport without excitation. Therefore, the density of transport electrons should increase greatly with Bi doping, which can promote σ and PF. Furthermore, the band gap of SnS is narrowed by Bi doping, indi cating the easier intrinsic excitation of the carrier. So the carrier con centration might be promoted by Bi doping at high temperatures, which also aids in promoting σ and PF.
3.3.2. Electronic structures of Bi-doped SnS The calculation results of electronic structure of Bi-doped SnS are shown in Fig. 8. The DOS close to the top of valence band is mainly determined by the hybridization of the s- and p-states of Sn and the pstate of S (Fig. 8a), so Bi doping has little effect on the top of the valence band. However, the p-state of Bi has a relatively large DOS near the bottom of the conduction band, which significantly affects the bottom of the conduction band of Bi-doped SnS. More notable is that Bi doping not only dramatically changes the p-states of Sn and S but also greatly changes the DOS distribution near the bottom of the conduction band. Xiao and co-workers performed DFT calculations to examine n-type doping of SnS, and found that Bi doping was not an effective route [33]. However, our calculation models, based on a solid solution of SnS with
3.3.3. Electron transport and thermoelectric properties Based on the electronic structures, we calculated the electron transport properties of pure SnS and Bi-doped SnS by Boltzmann theory (Fig. 9). In the BoltzTraP calculations, constant relaxation time 5
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Journal of Physics and Chemistry of Solids 137 (2020) 109182
Fig. 9. Calculation results of electron transport and thermoelectric properties of SnS and Bi-doped SnS (Sn93.75%Bi6.25%S) at various temperatures: (a) electrical conductivity, (b) absolute value of Seebeck coefficient, (c) power factor, (d) electron thermal conductivity and (e) ZT value.
approximation was used to calculate the transport properties. We adopted the relaxation time from the experimental measurements and deductions by Nassary et al. [14]; the values are 15.1 � 10 16 and 7.44 � 10 16 s for the pure and doped SnS, respectively. The σ of pure SnS is quite small although it increases with rising temperature. After Bi doping, σ increases significantly, although it decreases slightly with increasing temperature (Fig. 9a). This can be attributed to the change in electron structure after Bi doping which we analyzed above. Calculation results show that the S values of Bi-doped SnS are negative, providing further proof of the formation of an n-type semiconductor after Bi doping. Because the ZT value is determined by S2, we show |S| in Fig. 9b. The |S| decreases obviously after Bi doping, which is unfavorable for promotion of PF and ZT value. However, the significant increase in σ could compensate for the decrease in |S|, so Bi doping can still result in a significant increase in PF (Fig. 9c). The κe increases after Bi doping (Fig. 9d), which is disadvantageous for promotion of ZT value. However, Bi doping causes obvious decrease of κl, which can partially compensate
for the negative effect of doping on ZT value. The complex effect of Bi doping on electron transport and phonon transport causes a complex change in ZT value (Fig. 9e). The Bi doping increases the ZT value below 700 K, but decreases it at 800 K. Although this improved ZT value in the temperature range of 300–700 K can satisfy most application circum stances of waste-heat power generation, the increment is quite limited by such Bi doping and needs further improvement. For calculation convenience, previous approximate prediction usu ally paid much attention to the positive effect of doping on σ and PF, and unintentionally neglected its negative effect on κe. However, the results in Fig. 9d and e indicate that κe plays an important role in the thermo electric properties, which should not be ignored. For instance, a too high value of κe causes a decrease of ZT at 800 K after Bi doping. Therefore, the content of Bi should be optimized to decrease the density of transport electrons and κe.
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be neglected. Therefore, only the Bi concentration should be considered in the following calculations. The calculation results show that σ increases with the increase in doping concentration in all temperature ranges (Fig. 10a), owing to the increase in carrier concentration caused by Bi doping. When x ¼ 1.56–6.25%, the |S| decreases with the increase in doping concen tration (Fig. 10b), which is opposite to the relationship between σ and T. However, such a relationship is not maintained when x ¼ 0.78%. The opposite relationships of σ and |S| vs Bi doping concentration causes complex changes of PF when x ¼ 1.56–6.25% (Fig. 10c). The PF order for different Bi doping concentrations changes at different temperature, and PF for x ¼ 0.78% is the lowest among all Bi doping concentrations. However, the thermal electric properties of different Bi content could still be compared reasonably by κe and ZT value analyses. The κe de creases significantly for doping concentration of 1.56% (Fig. 10d), leading to a remarkable increase in ZT value (Fig. 10e). On the whole, the ZT value at x ¼ 6.25% is low because of the excessive κe resulting from the very high carrier concentrations. For
Table 3 Different supercells and doping concentrations of Bi-doped SnS. Supercell 1�1�1 1�2�2 2�2�2 2�2�4 2�4�4
Atom number Sn
S
Bi
Total
4 15 31 63 127
4 16 32 64 128
0 1 1 1 1
8 32 64 128 256
Doping concentration
Type of conduction
0 6.25% 3.13% 1.56% 0.78%
p-type n-type n-type n-type n-type
3.4. Optimization of doping concentration We constructed larger supercells of Sn1-xBixS (x ¼ 0.78, 1.56, and 3.13%) to accomplish different doping concentrations (Table 3). We calculated electron transport properties of Sn1-xBixS with different Bi positions in a supercell, and found that substitutional sites of Bi atom have no effect on electron transport properties. Such results can be attributed to the periodic model in which the effect of crystal surface can
Fig. 10. Calculation results of electron transport and thermoelectric properties of Sn1-xBixS (x ¼ 0.78, 1.56, 3.12, and 6.25%) at various temperatures: (a) electrical conductivity, (b) absolute value of Seebeck coefficient, (c) power factor, (d) electron thermal conductivity and (e) ZT value. 7
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much larger along the b and c axes [34]. 4. Conclusions We constructed calculation models for SnS and Sn1-xBixS using different x values. The models were confirmed by experimental facts and previous calculations, such as the calculations of crystal structure, lattice constants, band structures, and DOS. We further investigated the ther moelectric properties of SnS and Bi-doped SnS in the aspects of electron transport and phonon transport. In our calculation range, the Pnma crystal structure of pure SnS remained stable after Bi doping. Through calculations of phonon and Grüneisen spectra which are related to lat tice vibration, we found that Bi doping reduced the lattice thermal conductivity by the effect on the lattice vibration in the temperature range of 300–800 K. Furthermore, both the pure and Bi-doped SnS had the lowest lattice thermal conductivity along the a axis because of their weak interatomic bonding and strong anharmonicity which were re flected by the largest Grüneisen parameters along the a axis. The calculation results of electronic DOS and band structure indicated that Bi doping effectively narrowed the band gap. The change of band gap can improve the thermoelectric performances as confirmed by subsequent calculations of electron transport. After Bi doping, electrical conduc tivity was greatly promoted by the large increase in carrier concentra tion, so that PF was significantly improved by Bi doping. Therefore, our results and analyses indicate that the influence of electron thermal conductivity on the ZT value was important. The Bi doping increased PF by increasing the electrical conductivity, but raised the electron thermal conductivity simultaneously to decrease the ZT value. However, Bi doping decreased lattice thermal conductivity which could partially compensate for the negative effect of the increase of electron thermal conductivity. We calculated the thermoelectric properties at different Bi doping concentrations and determined the optimum doping concentra tion of 1.56%. The peak ZT value at this doping concentration was 0.31 in the temperature range of 300–800 K. Considering the anisotropy, Bidoped SnS reached a larger ZT value of 0.36 along the a axis, which was a large increase compared with the value of 0.16 for SnS. The cause of such a high ZT value can be attributed to the lowest thermal conduc tivity and the highest PF along the a axis. Furthermore, our calculation methods and models are convenient tools for doping element selection and content determination for thermoelectric materials, and can be extended to prediction of the thermoelectric performance of other materials.
Fig. 11. ZT value at different temperature along different directions.
doping concentration of 1.56%, the low doping content causes low carrier concentration, low κe, and high |S|, which determines high ZT values. In this circumstance, the importance of the electron thermal conductivity on thermal electric properties is fully displayed. Although the κe for x ¼ 0.78% is the lowest among all doping concentrations, the PF is too low because of the low carrier concentration and σ at this Bi content. Therefore, the ZT value for x ¼ 0.78% is lower than that for x ¼ 1.56%. The ZT value reaches a maximum when x ¼ 1.56% in the whole temperature range, rising with increasing temperature and reaching 0.31 at 800 K. This is a significant promotion compared with the value of 0.16 for pure SnS. Sun et al. [21] evaluated the ZT value of n-type doping of SnS using the RBA method. They obtained a maximum ZT of 0.61 at 800 K, which is much higher than our result of 0.31. They simply adopted an exper iment thermal conductivity of 0.65 Wm 1K 1 of pure SnS at 800 K in their evaluation, so their final ZT value of doped SnS is doubtful because they neglected the effect of doping on κe. The doping increases the carrier concentration, and so definitely increases the electron thermal conductivity. We used our thermal conductivity result of Bi-doped SnS for x ¼ 1.56% (including phonon and electron thermal conductivities) into the model of Sun et al. [21] and produced a ZT value of 0.28, which is quite close to our calculation result of 0.31. The similarity between the ZT values obtained with different methods further demonstrates the reliability of our calculation.
Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant number 51472020) and CHEMCLOUDCOMPUTING.
3.5. Further optimization of ZT value by texture One notable characteristic of SnS is its highly anisotropic layered orthonormal structure [11], which is maintained after Bi doping in our circumstances. So the ZT value of Bi-doped SnS might be further improved by anisotropy. We calculated the ZT values along the a, b, and c axes of the Bi-doped SnS with optimal doping concentration of x ¼ 1.56%, respectively (Fig. 11). Unlike pure SnS which reaches a maximum ZT value along the b axis, the Bi-doped SnS reaches a maximum ZT along the a axis for all temperatures. At 300 K, the ZT value along the a axis reaches 0.06, which is a 100% increase with respect to the value of polycrystal of 0.03. At 800 K, the ZT value along the a axis reaches 0.36, which still represents a 16% increase. The reason why the highest ZT value appears along the a axis can be explained by our calculation results for σ, S, PF, κe, and κl. The κl is the lowest and PF is the largest along the a axis. The low κl along the a axis can be attributed to the weak interatomic bonding and strong anharmonicity, and the large PF can be attributed to the low effective mass along the a axis in the conduction band [34]. The Fermi level enters the conduction band to form an n-type semiconductor after Bi doping (Fig. 8b), so the effective masses of electrons become significantly smaller along the a axis but
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