IEEE TRANSACTIONS ON MAGNETICS, VOL. 50, NO. 1, JANUARY 2014 1000904

Effect on the Electronic, Magnetic and Thermoelectric Properties of Bi Teby the Cerium SubstitutionTran Van Quang and Miyoung Kim

Department of Physics, Ajou University, Suwon 443-749, Republic of KoreaDepartment of Nano Physics, Sookmyung Women’s University, Seoul 140-742, Republic of Korea

We investigated the effect of the Ce substitution in Bi Te on its electronic, magnetic, and thermoelectric properties in first-principlesusing the precise full-potential linearized augmented plane-wave (FLAPW)method. Results revealed that CeBiTe is amagnetic semicon-ductor with a very narrow energy band gap in the spin-polarized phase within GGA U. The calculation of thermoelectric coefficients,which is determined by utilizing the Boltzmann’s equation in a constant relaxation-time approach using the FLAPW wave-functions,shows that the Ce substitution causes a reduction of the thermoelectric power, as a result of the change in Seebeck coefficient and elec-trical conductivity due to the strongly localized bands and the reduced band gap. The maximum figure of merit ZT is found to beabout 0.29 at 450 K, which is in good agreement with the experiment.

Index Terms—Electronic structure calculation, first-principles, rare earth, thermoelectric (TE).

I. INTRODUCTION

F OR many decades, thermoelectric (TE) technology hasbeen studied intensively in theory and experiment, aiming

for the practical application. Various TE application devicessuch as TE energy conversion, heat pump, space power gener-ation, thermocouple, deep-space probe, solid state refrigeratorusing semiconductor lasers, and seat cooler have been feasiblyinvestigated. Examining and optimizing materials to improvethe TE efficiency is a critical and fundamental key to intro-ducing the practical application. The TE efficiency of a mate-rial or a device is characterized by a dimensionless figure ofmerit, , in which is the Seebeck coefficient orthermopower, is the electrical conductivity, is the thermalconductivity determined from the lattice ( ) and the electronic( ) thermal conductivities by , and T is the tem-perature. With no obvious upper bound of ZT value claimed, thehighest ZT reported are 2.4 at room temperature (RT) [1] and 3.2at 300 C [2], which are still far from the value for the TE ef-ficiency factor to achieve ideal Carnot’s efficiency. To improveZT, the power factor has to be high or and have tobe large while is kept simultaneously low. Bismuth telluride(Bi Te ) and its alloys are well known as the best TE materialsoperating with ZT at RT [3]. Various efforts to improve ZThave beenmade by optimizing the carrier concentration and alsoby making nanostructures or supperlattices. One of the methodsto optimize the TE efficiency is introducing the rare earth ele-ments into the material, resulting in the beneficial TE propertiesby lowering the thermal conductivities. It has been reported thatthe rare earth chalcogenides are potentially brilliant TE candi-dates for the high temperature application [4]. It has been alsoshown recently that lanthanum telluride in bulk n-type material

Manuscript received May 06, 2013; revised July 14, 2013; accepted August18, 2013. Date of current version December 23, 2013. Corresponding author:M. Kim (e-mail: mykim.nu@gmail.com).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TMAG.2013.2279854

has a high ZT performing above 1000K [5]. One of the al-leged reasons for the improved TE efficiency in this class of ma-terials is the contribution of the strong localized - and -stateslocated near the Fermi level affecting on the TE transport prop-erties at high temperature. Similar properties are also observedin the cerium compounds [6], [7]. In addition, exploiting theMahan-Sofo theory with assumption of -shape of the densityof states, it has been suggested lately that ZT can be huge at hightemperature in cerium telluride [7], [8]. Therefore, taking ad-vantage of the localized -states near Fermi level by introducinga cerium atom into the conventional TE material to improveZT could be of great interest. In this paper, employing the pre-cise full-potential linearized augmented plane-wave (FLAPW)method [9], we examine the effect of the Ce substitution into theBi Te on its transport properties. We study the influence of thestrongly localized -states and its role on the TE transport prop-erties by analyzing the electronic structures and computing thethermoelectric transport coefficients utilizing the Boltzmann’sequation in the constant relaxation-time approach.

II. COMPUTATIONAL METHODS

The crystal structure of CeBiTe is rhombohedral with thespace group of with broken inversion symmetry andbroken time reversal symmetry. The experimental lattice con-stants in hexagonal form are and [10].In the framework of the density functional theory (DFT), theelectronic structure calculations are performed within the gen-eralized gradient approximation (GGA) for the exchange po-tential [11]. The strong correlation is additionally treated by theHubbard U correlation, via GGA U [12].The U and J values of 6.1 and 0.7 eV, respectively, are

adapted in our calculation as widely used in other studies forCe compounds [13]–[16]. Spin-orbit coupling (SOC) is in-cluded in the second variational way to describe the relativisticeffect of valence electrons [17], [18]. The Brillouin zone (BZ)integration is performed using Monkhorst-Packspecial k-points [19].In the structural aspect, CeBiTe is obtained by replacing one

of the two Bi atoms in Bi Te crystal substitutionally with a Ce

0018-9464 © 2013 IEEE

1000904 IEEE TRANSACTIONS ON MAGNETICS, VOL. 50, NO. 1, JANUARY 2014

Fig. 1. Primitive rhombohedral cell of CeBiTe . Big grey ball stands for Bi,dark ball Ce, and small bright ball Te.

atom as shown in Fig. 1. All atoms are fully relaxed by calcu-lating the atomic forces [18] to obtain the equilibrium positionsemploying the experimental lattice constants. It is well knownthat the single crystal Ce can exist in two phases depending onthe pressure. The -Ce phase has the Curie-Weiss susceptibilitywhile the -Ce phase has the Pauli paramagnitism with a col-lapse of volume [14], [20]. It has been shown that the -phasecould be well described using LDA while the -phase needs toadapt a beyond LDA approach to describe the strong exchangecorrelation effect. Therefore, we have shown the calculated re-sults by both GGA and GGA U approaches in this work.

III. ELECTRONIC STRUCTURE

The calculated total spin magnetic moments of CeBiTe arefound to be 0.9 and 1.0 per formula unit cell in the GGAand GGA U approaches, respectively. However, the calcu-lated electronic structures exhibit the big change obviously dueto U as can be seen from Figs. 2 and 3, where we showedthe band structure and density of states (DOS) of CeBiTe cal-culated in GGA and GGA U. It was found that CeBiTe ismetallic in GGAwhile its DOS at Fermi level ( ) reduces dras-tically, tending to be a semiconductor with a very narrow energyband gap of 48 meV in GGA U.Within the GGA, the -elec-trons of Ce contribute dominantly to the total DOS around theFermi energy. A single flat band right below is found con-tributed mostly by the electron of Ce atoms, which turns outto contribute meaningfully in the TE transport properties (willbe shown later). Except for this single band, most of the spin-mi-nority electrons are found unoccupied and widely ranged upto 2 eV above . As a result, the spin magnetic moment isfound to be 0.9 . With the contribution of the sharp -peak,the total DOS at is much greater than that of Bi Te , whichcould be a good sign promoting CeBiTe to be a potential can-didate for TE application according to Mahan-Sofo theory [8].When we invoke the strong correlation by GGA U, the

states split into two distinct peaks located far away from eachother in energy as can be seen from Fig. 3. The single -bandwhich was observed just below in GGA is now shifted deep

Fig. 2. Calculated results of (a) the electronic band structure and (b) the totaldensity of states of CeBiTe within GGA. Shaded DOS stands for the 4f-pro-jection of DOS.

Fig. 3. Calculated results of (a) electronic band structure and (b) density ofstates of CeBiTe within GGA U. Shaded DOS stands for the 4f-projectionof DOS.

below Fermi energy and localized at - - eV. The un-occupied -states are shifted up to the energy region of 1 eVfrom and above. As a result, the spin magnetic moment isslightly enhanced to 1.0 . Now with the -bands far from, we expect that the contribution to the transport properties is

mainly by and states of both Te and Bi, and states of Ce in-stead of the localized Ce -states. Compared with the Bi Te ,the magnitude as well as the slope of the DOS for CeBiTenear is found to be smaller than that of Bi Te , which maycause a reduction of the TE coefficients. Another distinct ef-fect of U correction is an opening of the energy band gap of48 meV. Therefore, the band gap is reduced due to the Ce sub-stitution from the value of Bi Te (0.162 eV in experiment [20]and 0.154 eV in first-principle calculation [21]). Opening of theband gap along with the strong localization is known to be bene-ficial for the improved TE properties. We also note that the shiftof -states due to the strong correlation effect is similar to whatwas observed in the electronic structure change of the -phaseCe due to the external pressure [14], [22]. The pressure wasfound to govern the behavior of the spin-minority -states forthe -phase Ce resulting in a band split and the enhanced bandlocalization which were not observed in the -Ce. Therefore,while the distinct band localization at is not explicitly foundin our GGA U calculation, our observation of a metal-to-semi-conductor transition through a band gap opening upon the strongcorrelation-effect correction implies that the strong correlationeffect via Ce substitution, probably together with the applyingan external strain effect, can be used to tune the TE properties.

QUANG AND KIM: EFFECT ON ELECTRONIC, MAGNETIC AND THERMOELECTRIC PROPERTIES OF Bi Te 1000904

In this context, we found that the precise geometry optimiza-tion is important for an accurate determination of the TE prop-erties; our test calculation using the hypothetical atomic struc-ture without full relaxation of the atomic positions within boththe GGA and the GGA U showed that the CeBiTe is con-ducting, which would reduce the figure of merit due to the de-creased thermopower. Also, the band structure of CeBiTe isfound similar to those of LaBiTe and GdBiTe [23]. The con-duction band minimum (CBM) and the valence band maximum(VBM) locate off the highly symmetric k-points; hence, the de-generacy which directly increases ZT remains [24].

IV. THERMOELECTRIC PROPERTIES

To determine the TE transport coefficients, the solution ofsemi-classical Boltzmann transport equation within the constantrelation time approximation is employed to compute the elec-trical conductivity, , and Seebeck coefficient, , which are ex-pressed via the so-called transport distribution function (TD)[24]. In our calculation, TD is determined by the group velocitywhich is estimated by mean of the full intraband optical ma-trix elements calculated using the FLAPWwave functions [25].The power factor is defined as a product of the electrical con-ductivity and the square of the Seebeck coefficient, that is, .In GGA without considering the additional correlation

interaction, our calculated results showed that the ceriumsubstitution results in a severe decrease of Seebeck coefficientand, thereby, markedly decreased power factor (we do notshow here). This reflects the usual unfavorable influence onTE properties of a metallic material. However, in this case,the -orbitals are strongly localized near the Fermi level.According to the Mahan-Sofo theory [8], it would potentiallycontribute to enhance the Seebeck coefficient. Therefore, theresult implies that while the heavy electrons strongly local-ized at may have favorable influence in increasing Seebeckcoefficient, the overall effect of the simultaneously significantreduction of the mobility of charged carriers can result in theless favorable TE property.Now, upon the additional strong correlation effect invoked by

GGA U, the calculated values of are found to be 44 and-18 VK- for p-type and n-type doping, respectively, at RTand carrier concentration of 10 cm- . With the relaxation timeconstant of - - , we obtain the electrical conductivityof cm . These calculated and values are inexcellent agreement with experimental values, VKand cm [10].We showed our calculated power factors as the function of

temperature and the carrier concentration in Fig. 4 for bothp-and n-type dopings. Again, the power factor of CeBiTe isfound to be drastically reduced compared to that of Bi Te .At RT and the typical doping level of cm- , forexample, the calculated power factors are 0.57 Wcm- K-

for p-type doping and 0.09 Wcm- K- for n-type doping,which are several hundred times smaller than those of Bi Te .In variations of temperature up to 600 K and the doping levelof up to cm- , the maximum power factor still doesnot exceed 6 Wcm- K- in n-type doping and 8 Wcm- K-

in p-type doping. The maximum power factor for p-type isfound to be 6.5 Wcm- K- achieved above 450 K (Fig. 4).

Fig. 4. Calculated power factor of CeBiTe as a function of the temperatureand carrier concentration in (a) p-type doping and (b) n-type doping calculatedwith the relaxation time constant of - - .

Assuming the same thermal conductivity as the Bi Te , namelyWm- K- [26], the ZT value estimated at the max-

imum power factor at 450 K is 0.29 at the optimized carrierconcentration of cm- , which is in good agreementwith the experiment [27]. At RT, the maximum value of ZT iscalculated to be 0.11, still far from the value of Bi Te , that is,0.78 [26].

V. CONCLUSION

From the first-principles calculation in the framework of thedensity functional theory, the CeBiTe is found to be metallicin GGA while it is a semiconductor with a tiny band gap of48 meV in the GGA U approach. We found that both metallicand semiconducting phases indicate the reduction of the ther-moelectric figure of merit due to the Ce substitution while thephysical origins are different. When the localized bands ap-pear near Fermi level in GGA, the Seebeck coefficient is foundto be enhanced while the mobility of the heavy electronic trans-port carriers is decreased more drastically resulting in the reduc-tion of the electrical conductivity by order of two, which overallcauses the decrease of the power factor compared to Bi Te .When the strong correlation correction is adapted, by GGA U,the power factor of CeBiTe is also found severely reduced dueto the decreases in both the Seebeck coefficients as well as theelectrical conductivity. From the electronic structure analysis,it is attributed to the reduced energy band gap and DOS nearthe Fermi level while a direct effect of the localized bands isnegligible since the bands are shifted further from the Fermilevel of CeBiTe in the GGA U approach.

1000904 IEEE TRANSACTIONS ON MAGNETICS, VOL. 50, NO. 1, JANUARY 2014

ACKNOWLEDGMENT

This work is supported by the Basic Science Researchunder Grant NRF-2013R1A1A3013348 through the NationalResearch Foundation of Korea..

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