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

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Journal of Alloys and Compounds

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

0925-8388/$ - see front matter � 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.jallcom.2013.08.141

⇑ Corresponding author. Address: P.O. Box 72, Beijing University of Posts andTelecommunications, Xitucheng Road No.10, Beijing 100876, China. Tel.: +86 1061198062.

E-mail address: photon.bupt@gmail.com (P. Lu).

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, Beijing100876, Chinab State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050, Chinac 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 2013Received in revised form 12 August 2013Accepted 24 August 2013Available online 15 September 2013

Keywords:Electronic structureThermoelectric propertiesFigure 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 Boltzmanntransport theory. The energy band structure and density of states are studied in detail. The electronictransport coefficients are then calculated as a function of chemical potential. The figure of merit ZT isobtained assuming a constant relaxation time and an averaged thermal conductivity. Our theoreticalresult agrees well with previous experimental data.

� 2013 Elsevier B.V. All rights reserved.

1. Introduction

Due to the increasingly serious environmental pollution andenergy shortages, thermoelectric materials have attracted consid-erable attention in recent years. The advantages of thermoelectricdevices can be attributed to long operating lifetime, solid-stateoperation and no pollution [1–3]. The energy conversion efficiencyof thermoelectric materials is expressed by a dimensionless figureof merit ZT = rS2T/(je + jL), which is related with material param-eters such as Seebeck coefficient S, electrical conductivity r, abso-lute temperature T, thermal conductivities of electron componentje and lattice component jL, respectively. Generally, a good ther-moelectric material should possess a high ZT value, and mucheffort has been expended to improve the ZT by increasing theelectrical conductivity, Seebeck coefficient while decreasing thethermal conductivity [4,5]. However, until very recently, ZT valueis still limited because there is a constraint on the constant rela-tionship between the transport coefficients contributed fromcharge carriers at a given temperature. Many thermoelectricmaterials have a value of ZT around 1 or lower, which limits thewidespread of thermoelectric applications. Nevertheless, highefficient thermoelectric material can be obtained by reducing the

lattice thermal conductivity via substitution elements [6] or bulknanostructuring approach [7].

Among the various candidates of thermoelectric materials, Bi2-

Te3 based materials have attracted considerable attention and arewidely used in thermoelectric industry. A series of experimentalmethods and theoretical calculations have been proposed toimprove the ZT of Bi2Te3 and its derivative compounds. Chemicaldoping approach is found to be an effective way to enhance thethermoelectric performance. Sb and Se are two elements whichhave 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 (BixSb1-�x)2Te3 single crystals both in theoretical and experimental meth-ods, and a maximum room temperature figure of meritZ = 3.2 � 10�3 K�1 was determined for the solid solution. Kimet al. [10] have processed the p-type (Bi,Sb)2Te3 and the n-typeBi2(Te,Se)3 thermoelectric nanocomposites and reported the maxi-mum room temperature Z of 3.52 � 10�3/K for (Bi0.2Sb0.8)2Te3 and3.5 � 10�3/K for Bi2(Te0.9Se0.1)3. Theoretical investigations aremainly conducted in the framework of first principles, and the sub-stitution method is used to reveal thermoelectric properties of Sb/Se-doped Bi2Te3 [11–13]. Keawprak et al. [12] have investigatedthat Bi2SexTe3�x crystal at x = 0.36, shows the lowest thermalconductivity and the highest ZT at room temperature. It is usuallyconcluded that the main effect of Se/Sb substitution is to reducethe lattice thermal conductivity without adversely affecting theelectrical resistivity [14].

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 isreplaced 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). (Forinterpretation of the references to color in this figure legend, the reader is referredto the web version of this article.)

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

Recently, the Bi–Sb–Te–Se quaternary compound has attractedmuch attention. Zhu and Wang [15] have report that the p-typeBi–Sb–Te–Se thermoelectric thin films have been prepared andexhibited the Seebeck coefficients of 116–133 lV/K and a maxi-mum power factor of 0.62 mW K�2 m�1. André et al. [16] haveproduced n-type doped (Bi(1�x)Sbx)2�(Te(1�y)Sey)3 thermoelectricalloys and showed the highest ZT for applications of (Bi0.97-

Sb0.03)2(Te0.93Se0.07)3 at TC = 295 K and TH = 420 K. This averageZT is further optimized for values of carrier concentrations closeto 3.4 � 1019 cm�3. Generally, the introduction of substitution ele-ments leads to an increase in the electronic equivalent density ofstates compared with Bi2Te3, which has a direct impact on thetransport coefficients.

However, to the best of our knowledge, there is few theoreticalwork of (Bi,Sb)2(Te,Se)3 quaternary compound. In order to expandthe previous theoretical research and provide a guidance toexperimental results, a multiscale approach is used to investigatethe structural, electronic, and thermoelectric properties of (Bi,Sb)2

(Te,Se)3 compound. Based on the structural and electronicproperties from first-principles method, the electronic transportproperties are calculated by using the Boltzmann transporttheory. We describe the specific theoretical models and the de-tails of our computational method in Section 2. Our result and

Fig. 2. The band structure of Bi5SbTe8Se is sho

discussion are given in Section 3. Finally, the conclusion is madein Section 4.

2. Theoretical models and computational method

2.1. Theoretical models

The primitive Bi2Te3 cell contains five atoms and has a rhombohedral structurewith space group D5

3dðR3mÞ. As shown in Fig. 1, the structure can be visualized interms of a hexagonal lattice cell with three quintuple layer and five-atom thicklamellae alternatingly stacked in the sequence (Te1–Bi–Te2–Bi–Te1). Te1–Bi layeris combined with covalent bond and ionic bond, Te2–Bi layer is a combination ofcovalent bond, and the bond between layers (Te1–Te1) is of weak van der Waalsinteraction [17]. To insure the accuracy of calculations, a larger 1 � 1 � 3 supercellis built, and four models of different substitutions are introduced, where one Biatom is replaced by Sb atom, and one Te atom is substituted by Se atom, respec-tively. The experimental lattice constants of primitive cell are a = b = 4.386 Å andc = 30.497 Å corresponding to the hexagonal unit cell [18]. After geometry optimi-zations, the calculated lattice constants are a = b = 4.424 Å and c = 31.359 Å, whichare very close to the experimental data. In order to verify the stability of Bi5SbTe8Secompound, the heat of formation is calculated, which is defined by H = E(Bi5SbTe8-

Se) + E(Bi) + E(Te) � 3 � E(Bi2Te3) � E(Sb) � E(Se). A value of �1.26 eV is obtained toindicate that the Bi5SbTe8Se compound is energetically stable and may be synthe-sized under appropriate experimental conditions.

2.2. Computational method

Our calculations have been performed by using the full-potential linearizedaugmented plane-wave (FP-LAPW) method within the density functional theory(DFT), which is implemented in the WIEN2K package [19–21].The exchange-corre-lation potential is in the form of Perdew–Burke–Ernzerhof (PBE) with generalizedgradient approximation (GGA) [22]. The plane-wave cutoff is determined by Rmin-

kmax = 7.0, where Rmin is the minimum LAPW radius and kmax is the plane-wave cut-off. The muffin tin radii are chosen to be 2.5 a.u. for all atoms. The Brillouin-zoneintegration is performed by directly increasing the density of the k-point meshesuntil convergence was reached. Self-consistent field calculations are done with aconvergence criterion of 0.0001 Ry on the total energy. Since Bi and Te atoms areheavy elements, the effect of spin–orbit (SO) coupling is introduced in thecalculations.

The transport coefficients were calculated by using the Boltzmann transporttheory as implemented in the BoltzTraP code and relaxation time approximation[23–24]. Within this method, the Seebeck coefficient S is independent of the relax-ation time s, while the electrical conductivity r, the thermal conductivity due toelectrons ke, and the power factor rS2 can only be evaluated with respect to theparameter s.

3. Results and discussion

3.1. Electronic properties

There is a close relationship between band structure and ther-moelectric properties of material. The Seebeck coefficient can beobtained from the derivatives of the electronic density of states

wn with (a) and without (b) SO coupling.

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

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

P. Lu et al. / Journal of Alloys and Compounds 584 (2014) 13–18 15

at the Fermi surface and the band velocity, which depends on thedetails of the electronic band structure [25]. This is particularlytrue for very flat bands which are associated with high density ofstates and therefore large Seebeck coefficients.

Fig. 2 shows the band structure of Bi5SbTe8Se compounds.Model 2 is presented for illustration. SO coupling is introducedfor comparison. Without SO coupling, Bi5SbTe8Se is shown in adirect band gap semiconductor with a value of 0.247 eV. Afterthe introduction of SO coupling, the electronic states are redis-tributed and the bands split, which makes the degeneracy of bandstructure lower. The conduction band at C point becomes flat andthe valence band here is squeezed down, then generating a newvertex of valence band. It shows that Bi5SbTe8Se with SO couplingshows indirect band gap semiconductor characteristics. Our cal-culations indicate that the SO coupling is very important and nec-essary to describe the band structure for these materials.

Moreover, in order to give a comprehensive study of the bandstructure of Bi5SbTe8Se, SO couplings for each atom in the com-pound have been presented separately. In Fig. 3(a)–(d), the bandstructure of Bi5SbTe8Se is shown in the condition of Bi, Te, Sband Se SO coupling, respectively. In Fig. 3(a), Bi SO coupling cannotaffect 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 systembecome indirect band gap structure. In Fig. 3(c)–(d) of Se and SbSO coupling, both show that the valence bands at C point arefurther squeezed down and form a saddle-like shape. The concaveconduction bands at K point turn to be convex and the adjacentbands are significantly close to the Fermi level, which leads tonew valence band maximum and conduction band minimum. It

shown, respectively.

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.

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

indicates that the introduction of Se, Sb elements has a greatinfluence on the band structure of the system.

Fig. 4 shows the total DOS and partial DOS of model 2 with thereplaced Bi and Te in adjacent positions. The total DOS mainlyconsists of the Se 4p, Te 5p, Sb 5p, and Bi 6p orbitals, respectively.The valence bands between �2 eV and 0 eV are primarily derivedfrom Te 5p and Se 4p orbitals, while Bi 6p and Sb 5p states havemore distinct peaks in the upper valence bands between therange of �4 eV–�2 eV. Moreover, the p states component at Sesite in the conduction bands from 0 eV to 4 eV are significantlylarger than that of other elements of Bi5SbTe8Se compound, andhave an apparent peak in 1.8 eV. Sb doping will affect theconduction band, while Se doping will affect the valance bandobviously. This affection on DOS of the optimized alloys will leadto an impact on thermoelectric properties of Bi5SbTe8Secompound [16,26].

In total, the prediction of electronic band structure fromfirst-principles is relatively effective and accurate, and the currentelectronic band structures can be applied for the Boltzmann

transport theory to calculate the transport properties of semicon-ductor alloys.

3.2. Thermoelectric properties

The electronic conductivity r, Seebeck coefficient S are obtainedby means of processing electronic structures with the solution ofBoltzmann transport equation in the condition of constant relaxa-tion time approximation. The main expressions are listed as fol-lows [27]:

rabðT;lÞ ¼1X

ZrabðeÞ �

@flðT; eÞ@e

� �de ð1Þ

Sab ¼X

cðr�1Þacvbc ð2Þ

vabðT;lÞ ¼1

eTX

ZrabðeÞðe� lÞ � @flðT; eÞ

@e

� �de ð3Þ

P. Lu et al. / Journal of Alloys and Compounds 584 (2014) 13–18 17

where e is charge of electron; l is chemical potential; T is absolutetemperature; fl is Fermi distribution function; e is band energy, ands is relaxation time.

Based on the calculated band structure and the above expres-sions, some known thermoelectric properties can be predicted forthe optimal doping levels [28–29]. Fig. 5 presents Seebeck coeffi-cient, electrical resistivity relative to relaxation time, and powerfactor at 300 K as a function of chemical potential l for all fourkinds of Bi5SbTe8Se compounds. The positive and negative l corre-spond to n-type and p-type doping of the system, respectively. InFig. 5(a), r/s increases smoothly with the changing chemicalpotential in the vicinity of Fermi level, and reaches two apparentpeaks at l = �0.85 eV and l = 0.77 eV, respectively. It is obviouslyshown that r/s varies with different models in n-type doping,which suggests that different atomic substitution will affect theconductivity of Bi5SbTe8Se alloy. In Fig. 5(b), Seebeck coefficient

Fig. 6. The calculated thermoelectric properties in xx and zz direction of Bi5SbTe8Se comrelative to relaxation time. (b) Seebeck coefficient. (c) Power factor relative to relaxation

Table 1The peaks of Seebeck coefficient (lV/k), power factor relative to s (�1011 W/K2ms), relaxat

Model Seebeck coefficient Power factor

p-type n-type p-type n-ty

1 230 �237 0.91 0.862 225 �220 1.0 0.803 237 �233 0.98 0.794 218 �233 0.95 0.90

has a sharply change along with two opposite peaks around theFermi level. Fig. 5(c) shows the power factor relative to relaxationtime as a function of chemical potential. There are plenty of peakswithin the scope of chemical potential range, which suggests thatthermoelectric performance of Bi5SbTe8Se compound can beenhanced by appropriate doping amount [30]. Generally, the calcu-lations are appropriate when the chemical potential is not far awayfrom the Fermi level where the relaxation time approximation isstill in application. Therefore, the peaks around the Fermi levelare considered. The appropriate doping amount can be achievedby previous experimental works [31,32].

Bi2Te3 is a typically anisotropic material. In Fig. 6, the aniso-tropic properties of model 3 are presented both in xx (in-layer)and zz (cross-layer) direction. For the parameters of conductivityand Seebeck coefficient, a slight difference is shown between xxand zz direction, which may be attributed to the layered structure

pound as a function of chemical potential l at 300 K. (a) Electrical conductivitiestime. (d) Total power factor relative to relaxation time.

ion time (�10�14 s) and the ZT in the vicinity of Fermi level for all models.

Relaxation time ZT

pe p-type n-type p-type n-type

1.95 3.11 0.89 1.331.53 3.13 0.77 1.261.64 3.45 0.81 1.361.76 2.68 0.83 1.20

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

by van der Waals interactions. Furthermore, the anisotropy of rand S will account for the difference of power factor of Bi5SbTe8Secompound. The total power factor is applied to calculate the ZT byusing the constant relaxation-time assumption, and all the peakvalues of transport coefficients for four different Bi5SbTe8Se alloysaround 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 isestimated to be 1.64 � 10�14 s for p-type and 3.45 � 10�14 s forn-type doping, respectively. In our calculation, an averagedthermal conductivity k = 0.6 W m�1 K�1 is adopt according to thereliable experiment [16], and the ZT values are predicted with0.81 and 1.36 for the p-type and n-type doping of the Bi5SbTe8Secompound, respectively. The result indicates that n-type dopingin the Bi5SbTe8Se compound may be more favorable than p-typedoping to enhance the thermoelectric performance, which is con-sistent with the experimental result. The results of other modelsare also listed in Table 1. Our results agree well with previousexperimental values [16], which mean that our simulation mayprovide an effective and suitable method to describe the thermo-electric properties in future research. In addition, future workshould be addressed to investigate nanostructured models wherethe ZT value can be also enhanced by a sharper density of statesnear the Fermi level, as well as the reduced lattice thermal conduc-tivity caused by the increased phonon scattering.

4. Conclusion

In summary, we have performed multiscale calculations tostudy the thermoelectric properties of Bi5SbTe8Se compound inseveral substitutions. At electronic scale, the density of states andthe energy band of these structures are investigated usingfirst-principles calculations. The electronic transport coefficientsare then calculated within the semiclassical Boltzmann theoryand further evaluated as a function of chemical potential. Thefigure of merit ZT is obtained assuming a constant relaxation timeand an averaged thermal conductivity.

Acknowledgments

This work is supported by the National Natural Science Founda-tion of China (Grant No. 61102024), and the Fundamental ResearchFunds for the Central Universities (Grant No. 2012RC0401).

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