Thermoelectric properties of quaternary (Bi,Sb)2(Te,Se)3 compound

Journal of Alloys and Compounds 584 (2014) 13–18

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Thermoelectric properties of quaternary (Bi,Sb)2(Te,Se)3 compound Pengfei Lu a,⇑, Yiluan Li a, Chengjie Wu a, Zhongyuan Yu a, Huawei Cao a, Xianlong Zhang a, Ningning Cai a, Xuxia Zhong a, Shumin Wang b,c a State Key Laboratory of Information Photonics and Optical Communications, Ministry of Education, Beijing University of Posts and Telecommunications, P.O. Box 72, Beijing 100876, China b State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050, China c Photonics Laboratory, Department of Microtechnology and Nanoscience, Chalmers University of Technology, 41296 Gothenburg, Sweden

a r t i c l e

i n f o

Article history: Received 27 June 2013 Received in revised form 12 August 2013 Accepted 24 August 2013 Available online 15 September 2013 Keywords: Electronic structure Thermoelectric properties Figure of merit

a b s t r a c t The quaternary (Bi,Sb)2(Te,Se)3 compounds are investigated using first-principles study and Boltzmann transport theory. The energy band structure and density of states are studied in detail. The electronic transport coefficients are then calculated as a function of chemical potential. The figure of merit ZT is obtained assuming a constant relaxation time and an averaged thermal conductivity. Our theoretical result agrees well with previous experimental data. Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction Due to the increasingly serious environmental pollution and energy shortages, thermoelectric materials have attracted considerable attention in recent years. The advantages of thermoelectric devices can be attributed to long operating lifetime, solid-state operation and no pollution [1–3]. The energy conversion efficiency of thermoelectric materials is expressed by a dimensionless figure of merit ZT = rS2T/(je + jL), which is related with material parameters such as Seebeck coefficient S, electrical conductivity r, absolute temperature T, thermal conductivities of electron component je and lattice component jL, respectively. Generally, a good thermoelectric material should possess a high ZT value, and much effort has been expended to improve the ZT by increasing the electrical conductivity, Seebeck coefficient while decreasing the thermal conductivity [4,5]. However, until very recently, ZT value is still limited because there is a constraint on the constant relationship between the transport coefficients contributed from charge carriers at a given temperature. Many thermoelectric materials have a value of ZT around 1 or lower, which limits the widespread of thermoelectric applications. Nevertheless, high efficient thermoelectric material can be obtained by reducing the

⇑ Corresponding author. Address: P.O. Box 72, Beijing University of Posts and Telecommunications, Xitucheng Road No.10, Beijing 100876, China. Tel.: +86 10 61198062. E-mail address: [email protected] (P. Lu). 0925-8388/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jallcom.2013.08.141

lattice thermal conductivity via substitution elements [6] or bulk nanostructuring approach [7]. Among the various candidates of thermoelectric materials, Bi2Te3 based materials have attracted considerable attention and are widely used in thermoelectric industry. A series of experimental methods and theoretical calculations have been proposed to improve the ZT of Bi2Te3 and its derivative compounds. Chemical doping approach is found to be an effective way to enhance the thermoelectric performance. Sb and Se are two elements which have been widely used in experiments of Bi2Te3 doping, as Sb/Bi, Se/Te are in the same chemical group and both heavy elements. Caillat et al. [8–9] investigated the transport properties of (BixSb1x)2Te3 single crystals both in theoretical and experimental methods, and a maximum room temperature figure of merit Z = 3.2  103 K1 was determined for the solid solution. Kim et al. [10] have processed the p-type (Bi,Sb)2Te3 and the n-type Bi2(Te,Se)3 thermoelectric nanocomposites and reported the maximum room temperature Z of 3.52  103/K for (Bi0.2Sb0.8)2Te3 and 3.5  103/K for Bi2(Te0.9Se0.1)3. Theoretical investigations are mainly conducted in the framework of first principles, and the substitution method is used to reveal thermoelectric properties of Sb/ Se-doped Bi2Te3 [11–13]. Keawprak et al. [12] have investigated that Bi2SexTe3x crystal at x = 0.36, shows the lowest thermal conductivity and the highest ZT at room temperature. It is usually concluded that the main effect of Se/Sb substitution is to reduce the lattice thermal conductivity without adversely affecting the electrical resistivity [14].

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discussion are given in Section 3. Finally, the conclusion is made in Section 4. 2. Theoretical models and computational method 2.1. Theoretical models

Fig. 1. Crystal structure of Bi2Te3: (a) layered structure and (b) supercell of (Bi2Te3)3. Blue ball is Bi atom, and red ball is Te atom. In quaternary compound, Bi is replaced by Sb atom, while Te is substituted by Se atom. Model1: (Bi1–Sb,Te1–Se); Model2: (Bi1–Sb,Te2–Se); Model3: (Bi2–Sb,Te1–Se); Model4: (Bi2–Sb,Te2–Se). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

The primitive Bi2Te3 cell contains five atoms and has a rhombohedral structure with space group D53d ðR3mÞ. As shown in Fig. 1, the structure can be visualized in terms of a hexagonal lattice cell with three quintuple layer and five-atom thick lamellae alternatingly stacked in the sequence (Te1–Bi–Te2–Bi–Te1). Te1–Bi layer is combined with covalent bond and ionic bond, Te2–Bi layer is a combination of covalent bond, and the bond between layers (Te1–Te1) is of weak van der Waals interaction [17]. To insure the accuracy of calculations, a larger 1  1  3 supercell is built, and four models of different substitutions are introduced, where one Bi atom is replaced by Sb atom, and one Te atom is substituted by Se atom, respectively. The experimental lattice constants of primitive cell are a = b = 4.386 Å and c = 30.497 Å corresponding to the hexagonal unit cell [18]. After geometry optimizations, the calculated lattice constants are a = b = 4.424 Å and c = 31.359 Å, which are very close to the experimental data. In order to verify the stability of Bi5SbTe8Se compound, the heat of formation is calculated, which is defined by H = E(Bi5SbTe8Se) + E(Bi) + E(Te)  3  E(Bi2Te3)  E(Sb)  E(Se). A value of 1.26 eV is obtained to indicate that the Bi5SbTe8Se compound is energetically stable and may be synthesized under appropriate experimental conditions. 2.2. Computational method

Recently, the Bi–Sb–Te–Se quaternary compound has attracted much attention. Zhu and Wang [15] have report that the p-type Bi–Sb–Te–Se thermoelectric thin films have been prepared and exhibited the Seebeck coefficients of 116–133 lV/K and a maximum power factor of 0.62 mW K2 m1. André et al. [16] have produced n-type doped (Bi(1x)Sbx)2(Te(1y)Sey)3 thermoelectric alloys and showed the highest ZT for applications of (Bi0.97Sb0.03)2(Te0.93Se0.07)3 at TC = 295 K and TH = 420 K. This average ZT is further optimized for values of carrier concentrations close to 3.4  1019 cm3. Generally, the introduction of substitution elements leads to an increase in the electronic equivalent density of states compared with Bi2Te3, which has a direct impact on the transport coefficients. However, to the best of our knowledge, there is few theoretical work of (Bi,Sb)2(Te,Se)3 quaternary compound. In order to expand the previous theoretical research and provide a guidance to experimental results, a multiscale approach is used to investigate the structural, electronic, and thermoelectric properties of (Bi,Sb)2 (Te,Se)3 compound. Based on the structural and electronic properties from first-principles method, the electronic transport properties are calculated by using the Boltzmann transport theory. We describe the specific theoretical models and the details of our computational method in Section 2. Our result and

Our calculations have been performed by using the full-potential linearized augmented plane-wave (FP-LAPW) method within the density functional theory (DFT), which is implemented in the WIEN2K package [19–21].The exchange-correlation potential is in the form of Perdew–Burke–Ernzerhof (PBE) with generalized gradient approximation (GGA) [22]. The plane-wave cutoff is determined by Rminkmax = 7.0, where Rmin is the minimum LAPW radius and kmax is the plane-wave cutoff. The muffin tin radii are chosen to be 2.5 a.u. for all atoms. The Brillouin-zone integration is performed by directly increasing the density of the k-point meshes until convergence was reached. Self-consistent field calculations are done with a convergence criterion of 0.0001 Ry on the total energy. Since Bi and Te atoms are heavy elements, the effect of spin–orbit (SO) coupling is introduced in the calculations. The transport coefficients were calculated by using the Boltzmann transport theory as implemented in the BoltzTraP code and relaxation time approximation [23–24]. Within this method, the Seebeck coefficient S is independent of the relaxation time s, while the electrical conductivity r, the thermal conductivity due to electrons ke, and the power factor rS2 can only be evaluated with respect to the parameter s.

3. Results and discussion 3.1. Electronic properties There is a close relationship between band structure and thermoelectric properties of material. The Seebeck coefficient can be obtained from the derivatives of the electronic density of states

Fig. 2. The band structure of Bi5SbTe8Se is shown with (a) and without (b) SO coupling.

P. Lu et al. / Journal of Alloys and Compounds 584 (2014) 13–18

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Fig. 3. The band structure of Bi5SbTe8Se is shown with Bi (a), Te (b), Sb (c), and Se (d) SO coupling, respectively.

at the Fermi surface and the band velocity, which depends on the details of the electronic band structure [25]. This is particularly true for very flat bands which are associated with high density of states and therefore large Seebeck coefficients. Fig. 2 shows the band structure of Bi5SbTe8Se compounds. Model 2 is presented for illustration. SO coupling is introduced for comparison. Without SO coupling, Bi5SbTe8Se is shown in a direct band gap semiconductor with a value of 0.247 eV. After the introduction of SO coupling, the electronic states are redistributed and the bands split, which makes the degeneracy of band structure lower. The conduction band at C point becomes flat and the valence band here is squeezed down, then generating a new vertex of valence band. It shows that Bi5SbTe8Se with SO coupling shows indirect band gap semiconductor characteristics. Our calculations indicate that the SO coupling is very important and necessary to describe the band structure for these materials. Moreover, in order to give a comprehensive study of the band structure of Bi5SbTe8Se, SO couplings for each atom in the compound have been presented separately. In Fig. 3(a)–(d), the band structure of Bi5SbTe8Se is shown in the condition of Bi, Te, Sb and Se SO coupling, respectively. In Fig. 3(a), Bi SO coupling cannot affect the band structure at C point except to reduce the band gap. In Fig. 3(b), the valence bands at C point are obviously depressed, and the valence bands near k point rise, which make the system become indirect band gap structure. In Fig. 3(c)–(d) of Se and Sb SO coupling, both show that the valence bands at C point are further squeezed down and form a saddle-like shape. The concave conduction bands at K point turn to be convex and the adjacent bands are significantly close to the Fermi level, which leads to new valence band maximum and conduction band minimum. It

Fig. 4. The calculated total DOS of Bi5SbTe8Se. The partial DOS from four atoms are shown, respectively.

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Fig. 5. The calculated thermoelectric properties of Bi5SbTe8Se compound as a function of chemical potential l at 300 K. (a) Electrical conductivities relative to relaxation time. (b) Seebeck coefficient. (c) Power factor relative to relaxation time. Note here the relaxation time is included as a parameter.

indicates that the introduction of Se, Sb elements has a great influence on the band structure of the system. Fig. 4 shows the total DOS and partial DOS of model 2 with the replaced Bi and Te in adjacent positions. The total DOS mainly consists of the Se 4p, Te 5p, Sb 5p, and Bi 6p orbitals, respectively. The valence bands between 2 eV and 0 eV are primarily derived from Te 5p and Se 4p orbitals, while Bi 6p and Sb 5p states have more distinct peaks in the upper valence bands between the range of 4 eV–2 eV. Moreover, the p states component at Se site in the conduction bands from 0 eV to 4 eV are significantly larger than that of other elements of Bi5SbTe8Se compound, and have an apparent peak in 1.8 eV. Sb doping will affect the conduction band, while Se doping will affect the valance band obviously. This affection on DOS of the optimized alloys will lead to an impact on thermoelectric properties of Bi5SbTe8Se compound [16,26]. In total, the prediction of electronic band structure from first-principles is relatively effective and accurate, and the current electronic band structures can be applied for the Boltzmann

transport theory to calculate the transport properties of semiconductor alloys. 3.2. Thermoelectric properties The electronic conductivity r, Seebeck coefficient S are obtained by means of processing electronic structures with the solution of Boltzmann transport equation in the condition of constant relaxation time approximation. The main expressions are listed as follows [27]:

rab ðT; lÞ ¼ Sab ¼

X

1

Z

X



rab ðeÞ 

 @fl ðT; eÞ de @e

ðr1 Þac v bc

ð1Þ ð2Þ

c

v ab ðT; lÞ ¼

1 eT X

Z



rab ðeÞðe  lÞ 

 @fl ðT; eÞ de @e

ð3Þ

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where e is charge of electron; l is chemical potential; T is absolute temperature; fl is Fermi distribution function; e is band energy, and s is relaxation time. Based on the calculated band structure and the above expressions, some known thermoelectric properties can be predicted for the optimal doping levels [28–29]. Fig. 5 presents Seebeck coefficient, electrical resistivity relative to relaxation time, and power factor at 300 K as a function of chemical potential l for all four kinds of Bi5SbTe8Se compounds. The positive and negative l correspond to n-type and p-type doping of the system, respectively. In Fig. 5(a), r/s increases smoothly with the changing chemical potential in the vicinity of Fermi level, and reaches two apparent peaks at l = 0.85 eV and l = 0.77 eV, respectively. It is obviously shown that r/s varies with different models in n-type doping, which suggests that different atomic substitution will affect the conductivity of Bi5SbTe8Se alloy. In Fig. 5(b), Seebeck coefficient

has a sharply change along with two opposite peaks around the Fermi level. Fig. 5(c) shows the power factor relative to relaxation time as a function of chemical potential. There are plenty of peaks within the scope of chemical potential range, which suggests that thermoelectric performance of Bi5SbTe8Se compound can be enhanced by appropriate doping amount [30]. Generally, the calculations are appropriate when the chemical potential is not far away from the Fermi level where the relaxation time approximation is still in application. Therefore, the peaks around the Fermi level are considered. The appropriate doping amount can be achieved by previous experimental works [31,32]. Bi2Te3 is a typically anisotropic material. In Fig. 6, the anisotropic properties of model 3 are presented both in xx (in-layer) and zz (cross-layer) direction. For the parameters of conductivity and Seebeck coefficient, a slight difference is shown between xx and zz direction, which may be attributed to the layered structure

Fig. 6. The calculated thermoelectric properties in xx and zz direction of Bi5SbTe8Se compound as a function of chemical potential l at 300 K. (a) Electrical conductivities relative to relaxation time. (b) Seebeck coefficient. (c) Power factor relative to relaxation time. (d) Total power factor relative to relaxation time.

Table 1 The peaks of Seebeck coefficient (lV/k), power factor relative to s (1011 W/K2ms), relaxation time (1014 s) and the ZT in the vicinity of Fermi level for all models. Model

1 2 3 4

Seebeck coefficient

Power factor

Relaxation time

ZT

p-type

n-type

p-type

n-type

p-type

n-type

p-type

n-type

230 225 237 218

237 220 233 233

0.91 1.0 0.98 0.95

0.86 0.80 0.79 0.90

1.95 1.53 1.64 1.76

3.11 3.13 3.45 2.68

0.89 0.77 0.81 0.83

1.33 1.26 1.36 1.20

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by van der Waals interactions. Furthermore, the anisotropy of r and S will account for the difference of power factor of Bi5SbTe8Se compound. The total power factor is applied to calculate the ZT by using the constant relaxation-time assumption, and all the peak values of transport coefficients for four different Bi5SbTe8Se alloys around the Fermi level are also listed in Table 1. In order to fit available experimental electrical conductivity [16,28] with our calculated values, the relaxation time at 300 K is estimated to be 1.64  1014 s for p-type and 3.45  1014 s for n-type doping, respectively. In our calculation, an averaged thermal conductivity k = 0.6 W m1 K1 is adopt according to the reliable experiment [16], and the ZT values are predicted with 0.81 and 1.36 for the p-type and n-type doping of the Bi5SbTe8Se compound, respectively. The result indicates that n-type doping in the Bi5SbTe8Se compound may be more favorable than p-type doping to enhance the thermoelectric performance, which is consistent with the experimental result. The results of other models are also listed in Table 1. Our results agree well with previous experimental values [16], which mean that our simulation may provide an effective and suitable method to describe the thermoelectric properties in future research. In addition, future work should be addressed to investigate nanostructured models where the ZT value can be also enhanced by a sharper density of states near the Fermi level, as well as the reduced lattice thermal conductivity caused by the increased phonon scattering. 4. Conclusion In summary, we have performed multiscale calculations to study the thermoelectric properties of Bi5SbTe8Se compound in several substitutions. At electronic scale, the density of states and the energy band of these structures are investigated using first-principles calculations. The electronic transport coefficients are then calculated within the semiclassical Boltzmann theory and further evaluated as a function of chemical potential. The figure of merit ZT is obtained assuming a constant relaxation time and an averaged thermal conductivity. Acknowledgments This work is supported by the National Natural Science Foundation of China (Grant No. 61102024), and the Fundamental Research Funds for the Central Universities (Grant No. 2012RC0401).

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