AgKTe: An intrinsic semiconductor material with high thermoelectric properties at room temperature

Accepted Manuscript AgKTe: An intrinsic semiconductor material with high thermoelectric properties at room temperature Hao Ma, Chuan-Lu Yang, Mei-Shan Wang, Xiao-Guang Ma PII:

S0925-8388(17)34401-8

DOI:

10.1016/j.jallcom.2017.12.205

Reference:

JALCOM 44291

To appear in:

Journal of Alloys and Compounds

Received Date: 23 September 2017 Revised Date:

13 December 2017

Accepted Date: 19 December 2017

Please cite this article as: H. Ma, C.-L. Yang, M.-S. Wang, X.-G. Ma, AgKTe: An intrinsic semiconductor material with high thermoelectric properties at room temperature, Journal of Alloys and Compounds (2018), doi: 10.1016/j.jallcom.2017.12.205. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

AC C

EP

TE D

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

ACCEPTED MANUSCRIPT

AgKTe: an intrinsic semiconductor material with high thermoelectric properties at room temperature Hao Ma, Chuan-Lu Yang*, Mei-Shan Wang, Xiao-Guang Ma School of Physics and Optoelectronics Engineering, Ludong University, Yantai, 264025, the

RI PT

People’s Republic of China

ABSTRACT

The good thermoelectric properties of AgKTe at room temperature are identified

SC

by using the first-principles density functional theory. Based on the optimized

M AN U

geometrical structure, electronic properties, we calculate the relaxation time with deform potential theory. The transport coefficients including electronic thermal conductivity, Seebeck coefficient, and electrical conductivity are obtained with semiclassical Boltzmann transport theory and relaxation time approximation. The

TE D

lattice thermal conductivity at room temperature is calculated by using the Debye-Callaway model. The thermoelectric figure of merit of AgKTe is determined

EP

and compared with other typical thermoelectric materials. The results demonstrate that for both the n-type and the p-type AgKTe, the maximum thermoelectric figure of

AC C

merit of 1.7 can be achieved at room temperature by means of tuning the carrier concentration. Therefore, AgKTe could be a promising candidate of thermoelectric materials.

Keywords: A. thermoelectric materials; C. electronic band structure; C. electronic properties; C. electrical transport; C. thermoelectric; D. computer simulations

*Corresponding author. Tel: +86 535 6672870. E-mail address: [email protected]. (C.L. Yang). 1

ACCEPTED MANUSCRIPT

1. Introduction As the environment pollution and energy crisis intensified, people are alert to energy limited and energy shortage, especially to rely on a single energy brought

RI PT

about by the social and economic risk. A large number of technical activities focus on the development of new energy and the comprehensive utilization of all kinds of energy. Therefore, mankind urgently needs to find more materials for the clean and

SC

renewable green energy resource. The thermoelectric materials are known as new

M AN U

materials which are able to use solid internal carrier movement and can realize the function of heat and electricity directly transformation [1]. It has great application value and has drawn worldwide attention. At present, the key factor in the development of thermoelectric materials is the conversion efficiency [2]. It is still

TE D

difficult to identify the materials with excellent thermoelectric properties. The dimensionless figure of merit (ZT) can be used to evaluate the efficiency of the

EP

thermoelectric materials, and calculated as follows. ZT =

S 2σ T κl + κe

(1)

AC C

Where S is the Seebeck coefficient, σ is the electrical conductivity, T is the

absolute temperature, κl and κe are the lattice thermal conductivity and electronic thermal conductivity [3-4]. As can be seen from Eq (1), to obtain a high ZT value, one need to enhance the power factor (S2σ), and to decrease the thermal conductivity (κl and κe) of the materials at the same time [5]. However, these parameters (S, σ, κe) are not independent of each other, and all depend on the electronic structure of materials and the transmission properties of the carrier. Because the three physical quantities 2

ACCEPTED MANUSCRIPT can not be adjusted synchronously, it is difficult to significantly improve the ZT value and thermoelectric conversion efficiency [6]. Therefore, to identify the excellent thermoelectric materials is still a very challengeable task.

RI PT

Half-Heusler (HH) compounds have been widely investigated in the last twenty years as admirable thermoelectric materials, because of their narrow gap band size, high thermal stability, relatively larger Seebeck coefficient and good mechanical

SC

performance, etc [7-9]. Some HH compounds such as ANiSn(A=Zr, Ti, Hf) and

M AN U

BCoSb(B=Zr, Ti, Hf) [10-14] have been studied as the promising thermoelectric materials. Shen et al. [14] found that the partially Pd-substituted ZrNiSn exhibit a ZT of about 0.7 at 800 K. Fu et al. [15] reported that about 1.5 of ZT can be achieved at 1200 K for the p-type FeNb0.88Hf0.12Sb and FeNb0.86Hf0.14Sb alloys. Obviously, these

TE D

ZT values are not ideal and still far from the target value of about 3.0 at room temperature, because most HH compounds present smaller ZT values due to limited lattice thermal conductivity. Therefore, one should do his best to find the materials

EP

with inherent low lattice thermal conductivity at first if he wants to obtain higher ZT

AC C

value. Carrete et al. [16] studied the thermal conductivity of a large number of semiconducting materials and report that AgKTe semiconductor exhibits a lower lattice thermal conductivity at room temperature. However, the lower lattice thermal conductivity is not everything for large ZT but only one of the several factors to determine the ZT. To fully evaluate the ZT of AgKTe, we first investigate the electronic properties and the thermoelectric performance of AgKTe by using the density functional theory (DFT) combined with the semiclassical Boltzmann transport

3

ACCEPTED MANUSCRIPT theory and deform potential (DP) theory. Considering the presently optimized lattice parameters show some differences from those of Carrete et al. [16], we also calculate the lattice thermal conductivity of the AgKTe at 300 K by using the Debye-Callaway

RI PT

model [17-19]. Finally, the systematical calculations demonstrate that 1.7 of ZT can be achieved for both the n-type system and the p-type system of AgKTe by tuning the carrier concentration at the room temperature, which implies that AgKTe could be a

M AN U

2. Computational methods

SC

promising thermoelectric material.

The calculations of the structural optimization and the related electronic properties for AgKTe are performed by using the Vienna Ab initio Simulation

the

treatment

way

TE D

Package (VASP) [20-22], with the project-augmented wave (PAW) potential [23]. For of

exchange

and

correlation

energy,

the

form

of

Perdew-Burke-Ernzerhof (PBE) parameterization [24] under the generalized gradient

EP

approximation (GGA) [25] is adopted. It is worthwhile mentioning that the

AC C

meta-GGA mBJ [26] potential has been used to improve the quality of PBE and give the accurate band gaps and electronic properties. The plane-wave cutoff energy is set to 400 eV. The Monkhorst-Pack scheme is adopted for the sampling of the Brillouin zone with a k mesh of 7×7×7 or 9×9×9 for the optimization of the structure and self-consistent calculations, respectively. The convergent threshold of the total energy is set to 10-4 eV. AgKTe is fully relaxed until the magnitude of the force acting on every atom is less than 0.01 eV/Å.

4

ACCEPTED MANUSCRIPT To calculate the electronic transport coefficients and transport distribution, we need to introduce a micro-physical model that describes transport process [27]. The semiclassical Boltzmann transport theory [28] with the relaxation time approximation

∂f k ∂t

= − vk ⋅

∂f k

∂f 1 e  ∂f −  E + vk × H  ⋅ k + k c  ∂ k dt ∂r h 

sactt

RI PT

is used. The solution of Boltzmann’s equation is given by [27] (2)

SC

here the rate of change of the population is dependent on diffusion, the effect of magnetic (H) or electric (E) fields, or scattering. The Boltzmann equation relates to

M AN U

the band structure with the field effect by introducing the distribution function, thus becomes the theoretical basis for studying the transport properties of solid electrons. To facilitate the description of electronic transport coefficients, we define the transport distribution (TD) function [29],

∑ k

v k v kτ

TE D

Ξ =

k

(3)

where v k is the group velocity, τ k is the relation time that calculated by the DP

EP

theory [30] and DFT.

AC C

Once the TD function is determined, S, σ and κe can be obtained easily as follows.

 ∂f 0  Ξ(ε )  ∂ε 

σ = e 2 ∫ dε  − S=

where

ek B

σ

0

 ∂f 0 

(4)

ε −µ

∫ dε  − ∂ε Ξ(ε ) k T

(5)

B

is Fermi distribution function, µ is the chemical potential and kB is

Boltzmann’s constant, e is the charge of the carriers. Moreover, κe is defined as

5

ACCEPTED MANUSCRIPT follows.

κe =

π 2  kB 

2

  σT 3  e 

(6)

From this equation, we can see that κe is proportional to the electronic

RI PT

conductivity and the absolute temperature(σT). One can call the part of the constant as the Lorenz number, i.e, L= (πkB/e)2/3 [31-32].

SC

The calculation of transport coefficients can be performed by the BoltzTraP code [33] within the constant scattering time approximation which has a wide range of

M AN U

applications in different types of thermoelectric materials, including doped semiconductors and oxides. It should be noted that the BoltzTraP code is originally interfaced to the WIEN2k code [34-35] although to VASP available. To obtain a credible result, we calculate the band structure and the Fermi energy level by using

TE D

the WIEN2k code with a k mesh of 17×17×17 to run the BoltzTraP code. In this work, the lattice thermal conductivity is calculated by using the

EP

Debye-Callaway model [17-19] that is proved to produce relatively accurate result [19,36]. The total lattice thermal conductivity can be expressed as a sum of two

AC C

transverses (κTA and κTA') and one longitudinal (κLA) acoustic phonon branches: [17-18]

κ l = κ TA + κ TA ' + κ LA

(7)

The partial conductivities κi (i represents TA, TA', and LA modes) are written as

[17,37] 2   Θi T τ ci ( x )x 4 e x     ∫0 τ i (e x − 1) 2 dx   i 4 x Θ i T τ ( x )x e 1 N   3 c dx +  κ i = CiT ∫  2 i 4 x 0 Θ i T τ ( x )x e 3 ex −1 c  dx ∫0 τ i τ i e x − 1 2   N U  

(

)

(

6

)

(8)

ACCEPTED MANUSCRIPT In above expression, Θi is the longitudinal (transverse) Debye temperature,

x = hω k BT , and Ci = k B 2π 2 h 3vi . h is the Planck constant, ω is the phonon 4

frequency, and vi is the longitudinal (transverse) acoustic phonon velocity.

processes, 1 τ Ci is

scattering

the

total

phonon

RI PT

Here, 1 τ Ni is the normal phonon scattering rate, 1 τ Ri is the sum of all resistive scattering

rate

[38],

and

1 τ Ci = 1 τ Ri + 1 τ Ni . The sum of resistive scattering rate involves the contributions

SC

from Umklapp phonon-phonon scattering ( 1 τ Ui ), boundary scattering ( 1 τ Bi ),

M AN U

mass-difference impurity scattering ( 1 τ mi ), and phonon-electron scattering ( 1 τ iph −e ), respectively. Considering the Umklapp phonon-phonon processes dominate the resistive scattering rate ( 1 τ Ri ≅ 1 τ Ui ), the total phonon scattering rate is mainly determined

by

the

normal

Umklapp

phonon-phonon

processes

TE D

( 1 τ Ci = 1 τ Ni + 1 τ Ui ).

and

The normal phonon scattering and the Umklapp phonon-phonon scattering can be given by [17,39]

k B γ LA V 2 5 xT 5 Mh 4vLA

τ NLA ( x )

2

(9)

=

(10)

k B γ TA TA' V 5

2

AC C

1

=

EP

5

1

τ

TA TA' N

(x )

4

Mh vTA TA'

5

xT 5

k γ = B 2i x 2T 3e −Θi i τ U ( x ) Mhvi Θi 1

2

2

3T

(11)

here, γ is the Grüneisen parameter, V is the volume per atom, and M is the average mass of an atom in the crystal. The Grüneisen parameter is defined as

γ i = − V∂ωi ωi ∂V , which characterizes the relationship between phonon frequency and volume change. 7

ACCEPTED MANUSCRIPT

3. Results and discussion 3.1 Geometrical and electronic properties of AgKTe

RI PT

Fig. 1 shows the optimized cubic structure of the semiconductor compound AgKTe with the space group of F 43m [40]. There are four K atoms, four Ag atoms, four Te atoms in the unit cell. K atoms are located at the position of 4a(0,0,0), Ag atoms at the

SC

4c(1/4,1/4,1/4), and Te atoms at the 4b(1/2,1/2,1/2) in Wyckoff coordinates,

M AN U

respectively. The present 7.12 Å of the optimized lattice parameter is larger than the theoretical 6.83Å of Carrete et al [16] but smaller than 7.1852 Å from the AFLOWLIB.org consortium repository of Curtarolo et al [40]. The transport coefficient of thermoelectric semiconductor materials is related to

TE D

the crystal structure, chemical composition and band structure of materials. The band structure of the HH compound AgKTe is presented in the Fig. 2. A direct band gap is observed because both the conduction band minimum (CBM) and valence band

EP

maximum (VBM) is located at the Γ point. The energy band gap Eg of 0.49 eV is in

AC C

good agreement with the 0.46 eV [16] and correspond to the feature of the narrow band gap of fine thermoelectric materials. 3.2 Relaxation time and mobility The relaxation time [41] is indispensable to calculate the electronic transport

coefficients of the thermoelectric materials based on the semiclassical Boltzmann transport theory with relaxation time approximation. Generally, the relaxation time is influenced by many scattering mechanisms, including impurities and defects

8

ACCEPTED MANUSCRIPT scattering, electron-phonon interaction, electron-electron interaction and magnetic scattering, etc. Therefore, the determination of relaxation time is usually a difficult task. In the present work, we calculate the relaxation time by using the DP theory

RI PT

which can describe the influence of acoustic phonon scattering on charge transport in detail. At temperature T, the expression of the relaxation time along the β direction for three-dimensional system is [5] 3(k BTmdos* ) Eβ 3/ 2

SC

τβ =

2 2π Cβ h 4

2

(12)

M AN U

here, τβ is the relaxation time of the carrier (electron or hole) moving along the transport direction (β), kB is Boltzmann’s constant, ћ is the Planck constant divided by 2π, and T is the absolute temperature. There are three important physical quantities C β , E β and mdos* in this Eq. (12). C β is the elastic constant, which can be expressed

as (E − E0 ) / V0 = C β (∆l / l0 ) / 2 , solving this equation, we can obtain C β as follows. Cβ =

TE D

2

1 ∂2E l = l0 V0 ∂ (∆l / l0 )2

(13)

EP

Where l0 is the lattice constant. V0 and E are the equilibrium volume and total

AC C

energy of the unit cell, respectively. ∆l is the change of the lattice length along the β direction.

E β is the DP constant, which is defined as

(

Eβi = Vi / ∆l / l0

)

(14)

The Vi is the change value of first i energy band when the crystal lattice is stretched to the deformation quantity of ∆l / l along the β direction. In order to simplify the calculation, we take the change value of CBM and VBM to calculate the

9

ACCEPTED MANUSCRIPT DP constants of electron and hole, respectively [42]. mdos* is the effective mass and

(

* calculated by mdos = m*x m*y m*z

)

13

. mi* (i = x, y, z ) is the effective mass of carriers

(electrons or holes) along the x, y, and z directions in the k space, respectively, and

( )

 d 2E k m* = h2  2  d k

RI PT

determined by the band dispersion relationship as the following formula [43]: −1

(15)

 E (k )= E f

SC

here, k is the wave vector.

M AN U

C β , Eβ and mdos* are calculated by first principles DFT in VASP. To be specific, the elastic constant C β can be obtained by exerting deformation quantity on the unit cell along the β direction, and we calculate the total energy differences of the system under different, and then the second-order differentiation is calculated through

TE D

the total energy change according to Eq. (13). For Eβ , we take the energy shift of band edge of VBM or CBM with respect to lattice deformation quantity along the β direction of external strain. The energy of band edge as a function of lattice constant

EP

is gained consequently. Finally, the DP constant Eβ is calculated by using Eq. (14)

AC C

described above. For the calculation of above two physical quantities( C β , Eβ ), it should be pointed out that the calculations of the total energy of band edge with lattice strain amplitudes of -0.1, -0.05, 0, +0.05, +0.1 percentage of ∆l / l , which simulate the deformation of the unit cell. Afterwards, we fit the curves of E and Eedge near the equilibrium configuration with Eq. (13) and (14) to determine C β and E β , respectively. Additionally, by means of the calculated band structure, the carrier effective mass mdos* also can be obtained by fitting the curves of the conduction

10

ACCEPTED MANUSCRIPT band and valence band to k near the Γ point. As can be seen in the Fig. 2, the effective mass mi* values of AgKTe at Γ point along x, y, z directions are evaluated respectively by using Eq. (15) as the effective mass of carrier (electron or hole),

RI PT

which is associated with the slope of the band edge. Furthermore, to better understand the transport properties of AgKTe, the carrier mobility µ also are calculated by using an effective mass approximation. µ is expressed by following formula [44]. eτ * mdos

SC

µ=

(16)

M AN U

The results for both hole and electron of AgKTe are collected in Table 1. The effective mass of the electron is smaller than that the hole, which can be understood through the degree of freedom of carrier. Because the motion of a hole represents the successive movements of a large group of valence electrons in the valence band, the hole is not

TE D

as free as the electron in conduct band, resulting in the effective mass of the hole is much larger. The size of mdos* can also be qualitatively evaluated from the band

EP

structure in Fig. 2. The energy level near the CBM is much sharper than that near the VBM, which also indicates the effective mass of the electron is smaller, which results

AC C

in the larger relaxation time and the carrier mobility of electron is in comparison with that of the hole. The present relaxation time and the carrier mobility of AgKTe are favorable to larger ZT because it is larger than those of some good thermoelectric materials such as MoS2 [45]and Bi2Te3 [27].

3.3 Transport coefficients and ZT

The transport coefficients are calculated by solving the Boltzmann’s equation by

11

ACCEPTED MANUSCRIPT using the BoltzTraP program [33]. The Seebeck coefficient S of AgKTe as a function of p-type and n-type carrier concentration at 300 K are shown in the Fig. 3. The S of the p-type AgKTe is positive, while that of the n-type is negative. The absolute values

RI PT

of the S decrease with the increase of carrier concentration, which means that one can obtain satisfactory S by tuning the carrier concentration. The absolute S of p-type at lower carrier concentration is larger than that of the n-type, however, the decrease

SC

scale is also larger. They both are close to zero at the 1022 cm-3 of the carrier

M AN U

concentration, which implies that AgKTe can not be appropriate for thermoelectric performance over the carrier concentration because the very small S will result in very small merit ZT according to Eq. (1).

The electrical conductivity σ as a function of carrier concentration is also

TE D

determined and shown in Fig. 4. One can find from the figure that σ increases along with the increase of carrier concentration. The σ is connected to carrier concentration (n) via the carrier mobility (µ) as σ = neµ . The equation can be used to understand

EP

that the conductivity of electrons is larger than that of holes due to the apparent large

AC C

carrier mobility of electrons as shown Table 1. In order determine the thermoelectric properties of the AgKTe, the thermal

conductivity including the κl of lattice and the κe of the electron needs to be calculated. The electronic thermal conductivity κe of p-type and n-type AgKTe as a function of carrier concentration is calculated by using Eq. (6) [31-32]. The results are presented in Fig. 5. The figure shows that κe becomes larger along with the increase of carrier concentration, which comes from the increasing of the electrical conductivity. One

12

ACCEPTED MANUSCRIPT can notice that the κes of both electron and hole are small below 1021 cm-3 of the carrier concentration. However, it increases rapidly when the carrier concentration furtherly increases. Especially for the electron, at 1022 cm-3 of the carrier

RI PT

concentration, its κe reaches more than 4 times of that at 1021 cm-3. It implies that the carrier concentration does not over 1021 cm-3 if the satisfactory thermoelectric performance is expected.

SC

For the lattice thermal conductivity κl, based on the Debye-Callaway formalism

M AN U

and the phonon dispersions by DFT calculations, we determined the longitudinal (LA) and transverse (TA/TA') Grüneisen parameters (γLA/TA/TA'), Debye temperatures (ΘLA/TA/TA') and their corresponding phonon velocities (νLA/TA/TA') for AgKTe. The phonon dispersions at the DFT equilibrium volume and the expansion cell (+3%) are

TE D

used to calculated Grüneisen parameters. The average Grüeisen parameter γ of each acoustic dispersion on the wave vector q by calculated by the method described in Ref. 17: γ =

(γ i )2 . The results are collected in Table 2. Based on the obtained results, κl

EP

can be calculated by Eq. (7) and (8). The calculated value of κl is 0.23 W m-1 K-1 at

AC C

300 K, which is good agreement with the theoretical calculation of 0.25 W m-1 K-1 calculated by Carrete et al [16]. Therefore, it is reliable to be used in the following calculations.

Now, we can calculate the ZT of AgKTe by Eq. (1) since the values of all the

physical quantities in the right parts of the equation are determined. The calculated ZTs of p-type and n-type AgKTe as a function of carrier concentration at 300 K are shown in the Fig. 6. The maximum value of the merit ZT of the n-type AgKTe can

13

ACCEPTED MANUSCRIPT reach about 1.7 at the carrier concentration of 1.24 × 1017 cm-3, while that of p-type AgKTe can also reach 1.7 at the carrier concentration of 1.73 × 1019 cm-3. The present merit ZT value at 300 K is better than those of some good thermoelectric materials,

RI PT

such as Bi1-xSbx(ZT ≤ 0.8), SnSe(ZT < 0.5), AgSbTe2(ZT < 1.0) [46], and also better than the thermoelectric performance of other HH compounds PtYSb(ZT ≤ 0.57)[47], ErPdX(X=Sb and Bi)(ZT< 0.2) [48] which have been experimentally reported.

SC

Therefore, AgKTe should be a kind of materials with good thermoelectric

M AN U

performance.

4. Conclusions

We have investigated the electronic structure and the transport properties of

TE D

AgKTe by using the first-principles calculations, the semiclassical Boltzmann transport theory, and DP theory. The relaxation time is obtained from C β , E β and mdos* which are determined by the DFT calculations. Based on the band energy of AgKTe, the electronic

EP

thermal conductivity κe, the Seebeck coefficient S and the conductivity σ are determined by

AC C

Boltzmann theory calculations. The lattice thermal conductivity κl at 300 K is only 0.23 W m-1 K-1 by the Debye-Callaway model. Then, we have calculated the ZTs of n-type and p-type AgKTe as a function with the carrier concentrations at room temperature. The

maximum ZTs of 1.7 for both n-type and p-type AgKTe are identified at the carrier concentration of 1.24 × 1017 cm-3 and 1.73 × 1019 cm-3 at room temperature, respectively. The ZTs are better than those of some reported thermoelectric materials. Therefore, AgKTe is a promising candidate for thermoelectric materials. It is expected that the present

14

ACCEPTED MANUSCRIPT prediction can encourage more investigations on the thermoelectric performance of AgKTe.

Acknowledgments

RI PT

This work was supported by the National Natural Science Foundation of China (NSFC) under Grant Nos. NSFC-11374132 and NSFC-11574125, as well as the Taishan Scholars

SC

project of Shandong Province (ts201511055).

M AN U

References

[1] F.J. DiSalvo, Thermoelectric cooling and power generation, Science 285 (1999) 703-706.

[2] H. Liu, J.Y. Wang, Progress of semiconductor thermoelectric materials, J. Funct.

TE D

Mater. 02 (2000) 116-118.

[3] G.J. Snyder, E.S. Toberer, Complex thermoelectric materials, Nat. Mater. 07 (2008) 105-114.

EP

[4] A.D. LaLonde, Y.Z. Pei, H. Wang, G.J. Snyder, Lead telluride alloy

AC C

thermoelectrics, Mater. Today. 14 (2011) 526-532. [5] Q.Y. Xue, H.J. Liu, D.D. Fan, L. Cheng, B.Y. Zhao, J. Shi, LaPtSb: A half-Heusler

compound

with

high

thermoelectric

performance.

Phys.Chem.Chem.Phys. 18 (2016) 17912-17916. [6] D.T. Morelli, T. Caillat, J.P. Fleurial, et al. Low-temperature transport properties of p-type CoSb3, Phys. Rev. B. 51 (1995) 9622-9628. [7] H. Hohl, A.P. Ramirez, C. Goldmann, G. Ernst, B. Wlfing and E. Bucher,

15

ACCEPTED MANUSCRIPT Efficient dopants for ZrNiSn-based thermoelectric materials, J. Phys: Condens. Matter. 11 (1999) 1697-1709. [8] J. Yang, H. Li, T. Wu, W. Zhang, L. Chen and J. Yang, Evaluation of

transport properties, Adv. Func. Mater. 18 (2008) 2880-2888.

RI PT

Half-Heusler compounds as thermoelectric materials based on the calculated electrical

[9] C. Yu, T.J. Zhu, R.Z. Shi, Y. Zhang, X.B. Zhao and J. He, High-performance −

x

ZrxNiSn1 ySby prepared by levitation −

SC

half-Heusler thermoelectric materials Hf1

M AN U

melting and spark plasma sintering, Acta Mater. 57 (2009) 2757-2764. [10] T. Sekimoto, K. Kurosaki, H. Muta, and S. Yamanaka, Thermoelectric properties of Sn-doped TiCoSb Half-Heusler compounds, J. Alloys Compd. 407 (2006) 326-329.

TE D

[11] L.L. Wang, L. Miao, Z.Y. Wang, W. Wei, R. Xiong, et al. Thermoelectric performance of Half-Heusler compounds TiNiSn and TiCoSb, J. Appl. Phys. 105 (2009) 013709(1)-013709(5).

EP

[12] T. Sekimoto, K. Kurosaki, H. Muta, and S. Yamanaka, High-Thermoelectric

AC C

figure of merit realized in p-type Half-Heusler compounds: ZrCoSnxSb1-x, Jpn. J. Appl. Phys. 46 (2007) L673-L675. [13] Y. Ono, S. Inayama, H. Adachi, and T. Kajitani, Thermoelectric properties of doped Half-Heuslers NbCoSn1-xSbx and Nb0.99Ti0.01CoSn1-xSbx, Jpn. J. Appl. Phys. 45 (2006) 8740-8743. [14] Q. Shen, L. Chen, T. Goto, T. Hirai, J. Yang, G.P. Meisner, and C. Uher, Effects of partial substitution of Ni by Pd on the thermoelectric properties of ZrNiSn-based

16

ACCEPTED MANUSCRIPT Half-Heusler compounds, Appl. Phys. Lett. 79 (2001) 4165-4167. [15] C.G. Fu, S.Q. Bai, Y.T. Liu, Y.S. Tang, L.D. Chen, X.B. Zhao and T.J. Zhu, Realizing high figure of merit in heavy-band p-type Half-Heusler thermoelectric

RI PT

materials, Nat. Commun. 06 (2015) 8144-8150. [16] J. Carrete, W. Li, N. Mingo, S.D. Wang and S. Curtarolo, Finding unprecedentedly

low-thermal-conductivity

Half-Heusler

semiconductors

via

SC

high-throughput materials modeling, Phys. Rev. X. 4 (2014) 011019(1)-011019(9).

M AN U

[17] D.T. Morelli, J.P. Heremans, G.A. Slack, Estimation of the isotope effect on the lattice thermal conductivity of group IV and group III-V semiconductors. Phys. Rev. B: Condens. Matter Mater. Phys. 66 (2002) 195304(1)-195304(9). [18] M. Asen-Palmer, K. Bartkowski, E. Gmelin, M. Cardona, A.P. Zhernov, A.V.

TE D

Inyushkin, A. Taldenkov, V. I. Ozhogin, K.M. Itoh, E.E. Haller, Thermal conductivity of germanium crystals with different isotopic compositions. Phys. Rev. B: Condens. Matter Mater. Phys. 56 (1997) 9431-9447.

EP

[19] Y. Zhang, E. Skoug, J. Cain, V. Ozoliņs, D.T. Morelli, C. Wolverton,

AC C

First-principles description of anomalously low lattice thermal conductivity in thermoelectric Cu-Sb-Se ternary semiconductors. Phys. Rev. B: Condens. Matter Mater. Phys. 85 (2012) 054306(1)-054306(6). [20] J.P. Perdew, A. Zunger, Self-interaction correction to density-functional approximations for many-electron systems, Phys. Rev. B. 23 (1981) 5048-5079. [21] G. Kresse, J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev. B. 47 (1993) 558-561.

17

ACCEPTED MANUSCRIPT [22] G. Kresse, J. Hafner, Norm-conserving and ultrasoft pseudopotentials for first-row and transition elements, J. Phys: Condens. Matter. 6 (1994) 8245-8257. [23] P.E. Blöchl, Projector augmented-wave method, Phys. Rev. B. 50 (1994)

RI PT

17953-17979. [24] J.P. Perdew, K. Burke and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Phys. Rev. Lett. 77 (1996) 3865-3868.

SC

[25] G. Kresse, D. Joubert, From ultrasoft pseudopotentials to the projector

M AN U

augmented-wave method, Phys. Rev. B. 59 (1999) 1758-1775.

[26] J.A. Camargo-Mart í nez, R. Baquero. Performance of the modified Becke-Johnson

potential

for

195106(1)-195106(8).

semiconductors,

Phys.

Rev.

B,

86

(2012)

TE D

[27] T.J. Scheidemantel, C. Ambrosch-Draxl, T. Thonhauser, J.V. Badding and J.O. Sofo, Transport coefficients from the first-principles calculation, Phys. Rev. B. 68 (2003) 125210(1)-125210(6).

EP

[28] G.K.H. Madsen, K. Schwarz, P. Blaha and D.J. Singh, Electronic structure and

AC C

transport in type-I and type-VIII clathrates containing strontium, barium, and europium, Phys. Rev. B. 68 (2003) 125212(1)-125212(7). [29] G.D. Mahan, J.O. Sofo, The best thermoelectric, Proc. Natl. Acad. Sci. USA. 93 (1996) 7436-7439.

[30] J. Bardeen, W. Shockley, Deformation potentials, and mobilities in non-polar crystals, Phys. Rev. 80 (1950) 72-80. [31] C. Kittel, Introduction to solid state physics, John Wiley and Sons, New York,

18

ACCEPTED MANUSCRIPT 2005. [32] L.D. Hicks, M.S. Dresselhaus, The effect of quantum-well structures on the thermoelectric figure of merit, Phys. Rev. B. 47 (1993) 12727-12731.

RI PT

[33] G.K.H. Madsen, D.J. Singh, BoltzTraP. A code for calculating band-structure dependent quantities, Comput. Phys. Commun. 175 (2006) 67-78.

[34] P. Hohenberg, W. Kohn, Inhomogeneous electron gas, Phys. Rev. 136 (1964)

SC

B864-B871.

M AN U

[35] D.D. Koelling, B.N. Harmon, A technique for relativistic spin-polarised calculations, J. Phys. C: Solid State Phys. 10 (1977) 3107-3114. [36] L.D. Zhao, S.H. Lo, Y.S. Zhang, H. Sun, G.J. Tan, C. Uher, C. Wolverton, V. P. Dravid, M.G. Kanatzidis, Ultralow thermal conductivity and high thermoelectric

TE D

figure of merit in SnSe crystals. Nature 508 (2014) 373-377.

[37] J. Callaway, Model for lattice thermal conductivity at low temperatures. Phys. Rev. B. 113 (1959) 1046-1051.

EP

[38] J. Zou and A. Balandin, Phonon heat conduction in a semiconductor nanowire. J.

AC C

Appl. Phys. 89 (2001) 2932-2938. [39] G.A. Slack and S. Galginaitis, Thermal conductivity and phonon scattering by magnetic impurities in CdTe. Phys. Rev. 133 (1964) A253-A268. [40] S. Curtarolo, W. Setyawan, S.Wang, J. Xue, K. Yang, R. H. Taylor, L. J. Nelson, G. L. W. Hart, S. Sanvito, M. Buongiorno Nardelli, N. Mingo and O. Levy, AFLOWLIB.ORG:

A

distributed

materials

properties

repository

high-throughput ab initio calculations, Comput. Mater. Sci. 58 (2012) 227-235.

19

from

ACCEPTED MANUSCRIPT [41] D. D'Humières, I. Ginzburg, M. Krafczyk, Multiple-Relaxation-Time lattice Boltzmann models in three dimensions, Phil. Trans. R. Soc. Lond. A 360 (2002) 437-451.

RI PT

[42] L. Tang, M.Q. Long, D. Wang, Z.G. Shuai, The role of acoustic phonon scattering in charge transport in organic semiconductors: a first-principles deformation-potential study, Sci. China. Ser. B: Chem. 52 (2009) 1646-1652.

SC

[43] Z.Z. Feng, J.M. Yang, Y.X. Wang, Y.L. Yan, G. Yang, X.J. Zhang, Origin of

M AN U

different thermoelectric properties between Zintl compounds Ba3Al3P5 and Ba3Ga3P5: A first-principles study, J. Alloys Compd. 636 (2015) 387-394. [44] I. Chung, J.H. Song, J. Im, J. Androulakis, C.D. Malliakas, H. Li, A.J. Freeman, J.T. Kenney and M.G. Kanatzidis, CsSnI3: Semiconductor or Metal? High electrical

TE D

conductivity and strong Near-Infrared photoluminescence from a single material. High hole mobility and phase-transitions, J. Am. Chem. Soc. 134 (2012) 8579-8587. [45] Y.Q. Cai, G. Zhang, Y.W. Zhang, Polarity-Reversed robust carrier mobility in

EP

monolayer MoS2 nanoribbons, J. Am. Chem. Soc. 136 (2014) 6269-6275.

AC C

[46] C. Gayner, K.K. Kar, Recent advances in thermoelectric materials, Prog. Mater. Sci. 83 (2016) 330-382. [47] G.H. Li, K. Kurosaki, Y. Ohishi, H. Muta, S. Yamanaka, High temperature thermoelectric properties of Half-Heusler compound PtYSb, Jpn. J. Appl. Phys. 52 (2013) 041804(1)-041804(4). [48] T. Sekimoto, K. Kuroakai, H. Muta and S. Yamanaka, Thermoelectric and thermophysical properties of ErPdX (X=Sb and Bi) Half-Heusler compounds, J. Appl.

20

ACCEPTED MANUSCRIPT

RI PT

Phys. 99 (2006) 103701-103707.

The elastic constant Cβ (eV/Å3), the DP constant Eβ (eV), the effective mass

Table 1

mi* (i = x, y, z ) (me) ,the density-of-states effective mass mdos* (me), the relaxation time τ (fs) and

Cβ

Eβ

m x*

m y*

mz*

Electron

0.35

11.72

0.095

0.099

0.099

Hole

0.35

9.84

0.627

mdos*

τ

µ

0.098

462

0.83×104

40

1.13×102

M AN U

Carrier type

SC

the carrier mobility µ (cm2 V-1 S-1) of the AgKTe semiconductor compound at room temperature.

0.629

0.629

0.628

TE D

Table 2 Average longitudinal (LA) and transverse (TA/TA') Gruneisen parameters ( γ LA TA TA '‘), Debye temperatures (ΘLA/TA/TA'), and phonon velocities (νLA/TA/TA') in AgKTe.

γ LA

γ TA

AgKTe

3.308

10.137

γ TA '

ΘLA

ΘTA

ΘTA'

νLA

νTA

νTA'

κl

(K)

(K)

(K)

(m/s)

(m/s)

(m/s)

W m-1 K-1

101.476

56.082

56.082

2557.188

1042.348

1146.883

0.23

EP

System

AC C

9.271

21

ACCEPTED MANUSCRIPT Captions Fig.1 - The optimized structure of AgKTe. The green, blue and magenta represent K, Ag and Te element, respectively.

RI PT

Fig. 2 - The energy band structure of AgKTe. The special k points Γ , X, W, K, L, and U in the figure represent the points (0, 0, 0), (1/2, 0, 1/2), (1/2, 1/4, 3/4), (3/8, 3/8, 3/4), (1/2, 1/2, 1/2), and(5/8, 1/4, 5/8), respectively.

SC

Fig. 3 - The Seebeck coefficient S of p-type and n-type AgKTe as a function of carrier

M AN U

concentration at 300K.

Fig. 4 - The electrical conductivityσ of p-type and n-type AgKTe as a function of carrier concentration at 300K.

Fig. 5 - The electronic thermal conductivity κe of p-type and n-type AgKTe as a function of carrier

TE D

concentration at 300K.

Fig. 6 - The calculated ZT values of p-type and n-type AgKTe as a function of carrier

AC C

EP

concentration at 300K.

22

RI PT

ACCEPTED MANUSCRIPT

AC C

EP

TE D

M AN U

SC

Fig. 1. The optimized structure of AgKTe. The green, blue and magenta represent K, Ag and Te element, respectively.

ACCEPTED MANUSCRIPT 5

Energy (eV)

4 3 2 1 0

Γ

X

W K

Γ

L

U

W

L

K

RI PT

-1

AC C

EP

TE D

M AN U

SC

Fig. 2. The energy band structure of AgKTe. The special k points Γ , X, W, K, L, and U in the figure represent the points (0, 0, 0), (1/2, 0, 1/2), (1/2, 1/4, 3/4), (3/8, 3/8, 3/4), (1/2, 1/2, 1/2), and(5/8, 1/4, 5/8), respectively.

ACCEPTED MANUSCRIPT 800

p-type n-type

600

S (µV/K)

400 200 0 -200 -400

1E17

1E18

1E19

1E20

1E21 -3

Carrier concentration(cm )

1E22

RI PT

-600

AC C

EP

TE D

M AN U

SC

Fig. 3. The Seebeck coefficient S of p-type and n-type AgKTe as a function of carrier concentration at 300K.

ACCEPTED MANUSCRIPT 10

p-type n-type

σ(107/Ω m)

8 6 4

0 1E17

1E18

1E19

1E20

1E21

Carrier concen tratio n ( cm -3 )

1E22

RI PT

2

AC C

EP

TE D

M AN U

SC

Fig. 4. The electrical conductivity σ of p-type and n-type AgKTe as a function of carrier concentration at 300K.

ACCEPTED MANUSCRIPT 70 0

p-type n-type

60 0

κe(W/mK)

50 0 40 0 30 0 20 0

0 1E1 7

1E1 8

1 E19

1 E20

1E21

Carrier concentration ( cm -3 )

1E22

RI PT

10 0

AC C

EP

TE D

M AN U

SC

Fig. 5. The electronic thermal conductivity κe of p-type and n-type AgKTe as a function of carrier concentration at 300K.

ACCEPTED MANUSCRIPT p -ty p e n -ty p e

1 .6

ZT value

1 .2 0 .8 0 .4

1E16

1E17

1E18

1E19

C a rrier co n cen tra tio n (cm -3 )

1E20

RI PT

0 .0

AC C

EP

TE D

M AN U

SC

Fig. 6. The calculated ZT values of p-type and n-type AgKTe as a function of carrier concentration at 300K.

ACCEPTED MANUSCRIPT Highlights ● AgKTe is identified as a promising candidate for thermoelectric materials. ● ZTs of 1.7 at 300 K for AgKTe is determined based on first-principles calculations.

RI PT

● ZTs of AgKTe are better than those of some reported thermoelectric materials.

AC C

EP

TE D

M AN U

SC

● The transport coefficients (S, σ, κe) are obtained by using Boltzmann transport theory.