Electronic structure and thermoelectric properties of orthorhombic SrLiAsLi Bin Guo, Yuan Xu Wang, Yu Li Yan, Gui Yang, Jue Ming Yang, and Zhen Zhen Feng Citation: Journal of Applied Physics 116, 033705 (2014); doi: 10.1063/1.4890516 View online: http://dx.doi.org/10.1063/1.4890516 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/116/3?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Structural, optical, and electrical properties of strained La-doped SrTiO3 films J. Appl. Phys. 116, 043705 (2014); 10.1063/1.4891225 Thermoelectric properties of epitaxial ScN films deposited by reactive magnetron sputtering onto MgO(001)substrates J. Appl. Phys. 113, 153704 (2013); 10.1063/1.4801886 Composition dependence of thermoelectric properties in polycrystalline type-I Ba8Ga x Si46-x (nominal x=14-18) AIP Conf. Proc. 1449, 259 (2012); 10.1063/1.4731546 Thermoelectric properties of p -type LiZnSb: Assessment of ab initio calculations J. Appl. Phys. 105, 063701 (2009); 10.1063/1.3091267 Induced electric fields in anisotropic thermoelectric materials J. Appl. Phys. 86, 5065 (1999); 10.1063/1.371480

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Electronic structure and thermoelectric properties of orthorhombic SrLiAs

Li Bin Guo, Yuan Xu Wang,a) Yu Li Yan, Gui Yang, Jue Ming Yang, and Zhen Zhen FengInstitute for Computational Materials Science, School of Physics and Electronics, Henan University,Kaifeng 475004, People’s Republic of China

(Received 20 June 2014; accepted 7 July 2014; published online 17 July 2014)

The electronic structure and the transport properties of orthorhombic SrLiAs were investigated

using first-principles calculations and the semiclassical Boltzmann theory. It is found that the

electrical conductivity along the y-direction is higher than those along other two directions, which

is most likely originated from the covalent ladder-like structure formed by the Li and As atoms.

Moreover, the transport properties of n-type SrLiAs are better than those of p-type one, due to the

large band dispersion along the y-direction near the Fermi level. Further, the value of power fac-

tor with respect to relaxation time achieves 9.2� 1011 W K�2 m�1 s�1 for n-type SrLiAs along

the y-direction at 1000 K with an optimal carrier concentration of 6.5� 1020 cm�3. The obtained

minimum lattice thermal conductivity is comparable to those of other Zintl phase compounds.VC 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4890516]

I. INTRODUCTION

Thermoelectric materials can directly and reversibly con-

vert heat energy into electrical energy.1 Thus, waste heat re-

covery using thermoelectric power generation is attracting

great interest over the past few decades.2 The thermoelectric

performance of a material is characterized by the material’s

dimensionless figure of merit, ZT ¼ rS2T=ðje þ jlÞ, where

r, S, T, je, and jl are the electrical conductivity, the Seebeck

coefficient, the absolute temperature, the electronic thermal

conductivity, and the lattice thermal conductivity, respec-

tively. Therefore, a good thermoelectric material should have

a large Seebeck coefficient, a high electrical conductivity,

and a low thermal conductivity.3–5 Zintl phase compounds

consist of electropositive cations which donate electrons to

electronegative anions, forming ionic bonds to satisfy va-

lence. They have recently emerged as promising thermoelec-

tric materials. This has been demonstrated by many

synthesized Zintl phase compounds, such as Ca5Al2Sb6,

Yb14AlSb11, and Sr3AlSb3.4–6 In Zintl compounds, the coex-

istence of ionic and covalent bonds leads to complex crystal

structures with large unit cells, which is helpful to obtaining a

low lattice thermal conductivity. The interconnected covalent

substructure can form paths for high-mobility charge trans-

port. Because both Seebeck coefficient and electrical conduc-

tivity have a strong, but opposite dependence on carrier

concentration, it is necessary to find an optimal carrier con-

centration to achieve the highest thermoelectric performance.

However, the energy conversion efficiency of these

Zintl phase compounds is relatively low, and their ZT values

are smaller than 1. For instance, Sr3AlSb3 exhibits a peak ZTof approximately 0.15, though it has a large Seebeck coeffi-

cient (>300 lV/K).6 Therefore, it is valuable to optimize the

carrier concentration to achieve high electrical conductivities

and large Seebeck coefficients. Experimentally synthesized

SrLiAs is a Zintl phase compound with an orthorhombic

structure and is stable in a limited temperature range from

550 to 826 �C.7 Our calculations showed that SrLiAs is a

semiconductor with a direct band gap of 1.3 eV. To find an

optimal carrier concentration, the thermoelectric properties

of n-type and p-type SrLiAs were investigated using the

semiclassical Boltzmann theory. It is found that the value of

the power factor with respect to relaxation time reaches

9.2� 1011 W K�2 m�1 s�1 for n-type SrLiAs along the

y-direction at 1000 K.

II. COMPUTATIONAL DETAIL

The structure optimization of SrLiAs was carried out

using the Vienna ab initio simulation package (VASP)8–10

based on the projector augmented wave (PAW) method of

Bl€ochl11 in the implementation of Kresse and Joubert.12 It is

convenient to simultaneously optimize lattice constants and

atomic positions using VASP. The Perdew-Burke-Ernzerhof

generalized-gradient approximation (PBE-GGA) was used to

deal with the exchange correlation potential. The plane-wave

cutoff energy of 400 eV was set, and the k-point sampling

7� 8� 6 points were chosen. The atomic positions and lat-

tice constants were optimized using the conjugate-gradient

algorithm. The Hellmann-Feynman forces on each ion are

less than 0.02 eV/A.

The electronic structure of SrLiAs was calculated using

the full-potential linearized augmented plane waves

(FLAPW) method,13 as implemented in the WIEN2k.14–16

FLAPW method is more beneficial for obtaining accurate

electronic properties of semiconductors in order to achieve

exciting properties.4–6,17 The Engel-Vosko with generalized-

gradient approximation (EV-GGA) correlation potential was

used to accurately mimic the action of orbital dependent

potential around the band gap. It is very significant for

obtaining an accurate band gap. An accurate electronic struc-

ture is important for estimating thermoelectric properties.

The muffin-tin radii were selected to be 2.5 for the Sr atoms,

2.47 for the Li and As atoms. The convergence of the basis

set is controlled by a cutoff parameter Rmt � Kmax ¼ 7, in

which Kmax is the magnitude of the largest k vector and the ka)E-mail: wangyx@henu.edu.cn

0021-8979/2014/116(3)/033705/5/$30.00 VC 2014 AIP Publishing LLC116, 033705-1

JOURNAL OF APPLIED PHYSICS 116, 033705 (2014)

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points are 1000 in the irreducible Brillouin zone.

Furthermore, we used the semiclassical Boltzmann theory

and the rigid band approach18 to calculate the Seebeck coef-

ficient and electrical conductivity concerning the relaxation

time r=s. The constant scattering time approximation is

employed, which is usually used for metals and degenerately

doped semiconductors. It is based on hypothesis that the

scattering time determining the electrical conductivity does

not vary greatly with energy on the scale of kBT.

III. RESULTS AND DISCUSSION

The optimized structure of SrLiAs (Fig. 1) belongs to

the TiNiSi type structure (space group Pnma). There are

twelve atoms in one unit cell. Two Li atoms and two As

atoms in the middle of unit cell form a parallelogram. There

are same atoms at both ends of diagonal. As seen from Fig.

1, each Li atom is combined with four As atoms, and Sr

atoms are embedded in both sides of framework formed by

Li and As atoms. All Sr atoms are equivalent, as the same to

all Li atoms and all As atoms on crystallography. The opti-

mized lattice constants (a¼ 7.6722 A, b¼ 4.5470 A, and

c¼ 8.0847 A) agree well with the experimental results

(a¼ 7.6458 A, b¼ 4.5158 A, and c¼ 8.0403 A).7

The electronic structure is important to understand the

transport properties. The heavy band can enhance Seebeck

coefficient, and the light band is helpful for increasing elec-

trical conductivity.19–23 ZT also relies on group velocity of

carrier via electrical conductivity.24 The transport coeffi-

cients of SrLiAs were calculated using the semiclassical

Boltzmann theory. The calculated band structure (Fig. 2)

predicts that SrLiAs is a semiconductor with a direct gap of

1.3 eV, which is in accordance with the results in Ref. 7. The

band gap of SrLiAs is much larger than that of Ca5Ga2As6

(indirect band gap of 0.37 eV).25 The direct band gap is more

advantageous for the electron transition than the indirect

band gap under the same condition. The extremum simulta-

neously appears at the C point on the valence bands and the

conduction bands. For p-type doping, the Fermi level will

decline. When the Fermi level shifts to the valence bands by

0.381 eV, there is a valley degeneracy at the C point,

corresponding to a carrier concentration of 1020 cm�3. In the

conduction bands, the valley degeneracy of Nv ¼ 2 appears

along the Y-T direction. It is well known that the high valley

degeneracy can increase Seebeck coefficient and is beneficial

for thermoelectric performance.25–27

For the conduction bands, the calculated effective masses

are m�x ¼ 4:0me, m�z ¼ 6:5me, and m�y ¼ 0:6me. The stronger

band dispersion along a certain direction means that the

larger group velocity, which is helpful for increasing electri-

cal conductivity. The band dispersion along the y- (C-Y)

direction is larger than that along the x- (C-X) and z- (C-Z)

directions, indicating a light band along the y- (C-Y) direc-

tion. For the valence bands, m�x ¼ 2:4me, m�y ¼ 2:2me, and

m�z ¼ 3:4me, the difference in hole effective mass is little.

The detailed transport properties will be discussed in the fol-

lowing part. To see clearly the states of the valence bands

and the conduction bands near the Fermi level, the total den-

sity of states (DOS) of SrLiAs and the projected density of

states (PDOS) of atoms were calculated and are shown in

Fig. 3. As seen from Figs. 3(a) and 3(b), the top of the va-

lence bands are mainly derived from As p states, and the bot-

tom of the conduction bands is primarily dominated by Sr dstates. The carrier effective masses of SrLiAs are much

greater than those in graphene systems. Kaloni et al. theoreti-

cally found that the carrier effective masses in BN-doped gra-

phene systems increase with an increasing band gap. The

obtained effective masses for these systems are between

0.007 me and 0.209 me.28 The previous calculated electronic

structure of graphene/BN heterobilayers also confirmed that

the effective mass is proportional to the band gap.29

Electron localization function (ELF) is a useful tool for

describing the degree of electron localization and under-

standing the nature of chemical bonding.30 The range of ELF

value is between 0 and 1. The value ELF¼ 0 represents that

electrons are hardly appeared in the area. ELF¼ 0.5 indi-

cates the situation in a homogeneous electron gas duringFIG. 1. Crystal structure of SrLiAs. The green, red, and blue spheres repre-

sent Sr, Li, and As atoms, respectively.

FIG. 2. Calculated band structure of SrLiAs.

033705-2 Guo et al. J. Appl. Phys. 116, 033705 (2014)

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atoms. The upper value of 1 notes the ideal localization of

electrons. As seen from Fig. 4, there appears homogeneous

electron gas between Li and As atoms, indicating a covalent

interaction between them. The electronegativity of the Li

atom is weak. Generally, it forms ionic bond combining with

other atoms. For example, Wang et al. found that boron

doped graphene is an efficient Li-ion storage material due to

an attractive interaction between Li ions and boron atoms.31

The density-function-theory study by Kaloni et al. reveals

that Li intercalation in graphene forms a strong ionic bond-

ing between Li ions and C atoms.32 Moreover, Li intercala-

tion not only increases the intrinsic stiffness of graphene

systems and but also enhances dramatically their charge car-

rier density. In Li-decorated graphene, the charge transfer

from Li to C can induce a strong electron-phonon coupling,

and its superconductivity can be enhanced by application of

a h-BN substrate.33 Wang et al. predicted that, for Li doped

B2C graphene, the charge transfer from the Li ions to the B

and C atoms results in partially filled B p and C p orbitals,

and then the split empty Li p orbitals accept electrons from

the B2C graphene.31 However, the value of ELF between Sr

and Li (As) atoms is small. Thus, the Li and As atoms form a

covalent bond, and an ionic bond is formed between Sr

atoms and Li (As) atoms. As seen from Fig. 1, there exists a

framework composed of covalent Li-As bonding along the

y-direction, which benefits the carriers transport. It can

improve the electrical conductivity.

For degenerate semiconductors and metals, the Seebeck

coefficient is given34 by

S ¼ 8p2k2B

3eh2m�T

p3n

� �2=3

; (1)

where h is the Planck constant, kB is Boltzmann constant, m�

is the effective mass. T is the temperature, and n is the carrier

concentration. The effective mass is defined by

m� ¼ �h2 d2E kð Þdk2

� ��1

E kð Þ¼Ef

; (2)

which shows the relation of effective mass and band disper-

sion near the Fermi level. Thus, m� is inversely proportional

to the dispersion. The electrical conductivity is defined by

r ¼ nel; (3)

where l is the carrier mobility. Thus, the electrical conduc-

tivity is proportional to carrier mobility and carrier concen-

tration. The mobility is defined by

l ¼ se

m�: (4)

From above equations, the large effective mass is beneficial

for Seebeck coefficient. Additionally, electrical conductivity

is proportional to the carrier concentration, however, is

inversely proportional to effective mass. Next, we study the

carrier concentration dependence of transport properties.

The calculated transport properties of p-type and n-type

SrLiAs are depicted in Fig. 5. We calculated S, r=s, and

S2r=s as a function of carrier concentration at 1000 K. As

seen from Fig. 5(a), the values of Seebeck coefficient are

greater than 109 lV/K with the carrier concentration from

1� 1019 cm�3 to 1� 1021 cm�3. The values of Seebeck coef-

ficient for p-type SrLiAs decrease with increasing carrier

concentration, and the difference in S along the three direc-

tions is reduced from 1� 1019 cm�3 to 1.2� 1021 cm�3. Fig.

5(b) shows that r=s of p-type SrLiAs increases with increas-

ing carrier concentration. Further, at the low carrier concen-

tration, the difference in r=s along the x-, y-, and z-

directions is little. It can be seen from Fig. 5(c) that the larg-

est value of S2r=s for p-type doping is 5.4� 1011 W

K�2 m�1 s�1 along the y-direction, mainly due to the large

Seebeck coefficient. Therefore, the thermoelectric perform-

ance along the y-direction is probably better than those along

the x- and z-directions.

For n-type SrLiAs, Fig. 5(a) shows that the absolute val-

ues of Seebeck coefficient also decrease with increasing car-

rier concentration. We can see from the Fig. 5(b) that the

values of r=s increase with increasing carrier concentration

when n< 6� 1021 cm�3, and the values of r=s along the

FIG. 3. Calculated density of states (DOS) of SrLiAs: (a) total DOS; (b) pro-

jected DOS of atoms.

FIG. 4. Electron localization function of SrLiAs. The slice is parallel to the

(010) plane and passes through the center of Sr, Li, and As atoms.

033705-3 Guo et al. J. Appl. Phys. 116, 033705 (2014)

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y-direction are significantly larger than those along the

x- and z-directions at the same carrier concentration. The ori-

gin of the high r=s can be analyzed from the band structure.

Along the y- (C-Y) direction, the value of the effective

mass (m�y ¼ 0:6me) is much smaller than those along the

x-direction (m�x ¼ 4:0me) and z-direction (m�z ¼ 6:5me).

According to Eqs. (3) and (4), the values of r=s along the

y-direction should be the largest at the same carrier

concentration. As seen from Fig. 5(c), the maximum value of

S2r=s along the y-direction for n-type doping reaches

9.2� 1011 W K�2 m�1 s�1 with the carrier concentration of

6.5� 1020 cm�3. That is mainly attributed to the large elec-

trical conductivity along the y-direction, i.e., stronger disper-

sion along the y- (C-Y) direction of the conduction bands.

As seen from the ELF (Fig. 5) of SrLiAs, the ladder-like

structure composed of covalent Li-As bonding along the y-

direction may lead to a high electrical conductivity along the

y-direction.

Comparing p-type and n-type doping, we can see that

the values of r=s of n-type doping along the y-direction are

larger than those of p-type doping. The values of Seebeck

coefficient for p-type and n-type doping are similar at the

same carrier concentration. Therefore, the difference in

S2r=s is mainly derived from the difference in the electrical

conductivity with respect to the relaxation time for p-type

and n-type doping. The largest value of S2r=s for p-type

doping is 5.4� 1011 W K�2 m�1 s�1 with the carrier concen-

tration of 8.5� 1020 cm�3. However, the maximum value of

S2r=s for n-type doping is 9.2� 1011 W K�2 m�1 s�1, corre-

sponding to the carrier concentration of 6.5� 1020 cm�3.

Therefore, the transport properties of n-type doping are prob-

ably better than those of p-type doping.

To improve thermoelectric performance, it is important

to decrease the thermal conductivity. It is difficult to estimate

the lattice thermal conductivity using first-principles calcula-

tions. However, the minimum thermal conductivity (jmin)

can be calculated using a model proposed by Slack.35 jmin is

calculated under the assumption that the minimum lifetime

of a defined lattice vibrational mode is half the period of the

vibration.36 The lattice thermal conductivity in glasses and

complex crystal (such as Zintl compounds) may approach

jmin at relative low temperature, compared with the melting

temperature at which the jmin is reached for simple crystal

structures. Therefore, it is possible to calculate jmin of the

Zintl compound SrLiAs using this method. Such method has

been applied to estimate the jmin of the Zintl compound

Ca5M2Sb6 (M¼Al, Ga, In).37 Above the Debye temperature,

the lattice thermal conductivity is generally limited by

Umklapp scattering leading to jl / 1=T. But this continues

until jmin is reached. At high temperature (T>H), jmin can

be approximated by

jmin ¼1

2

p6

� �1=3

kBV�2=3 2vs þ vlð Þ; (5)

where kB is the Boltzmann constant, V is the average volume

per atom, and vs and vl are the transverse and longitudinal

elastic wave velocity.

As a fundamental parameter, the Debye temperature

correlates with many physical properties. One of the standard

methods to calculate the Debye temperature (H) is from elas-

tic constant data, given by

H ¼ h

kB

3n

4pNAqM

� �� �1=3

vm; (6)

where h is the Planck constant, kB is the Boltzmann constant,

n is the number of atoms in the molecule, NA is Avogadro

number, q is the density, M is the molecular weight, and vm

is the averaged sound velocity, which is given by

vm ¼1

3

2

v3s

þ 1

v3l

� �� ��1=3

: (7)

Here, vs and vl are related to the material’s stiffness and den-

sity according to

vs ¼G

q

� �1=2

; (8)

vl ¼Bþ 4

3G

q

0@

1A

1=2

; (9)

where G and B are the shear and bulk moduli, respectively. qis the theoretical density. Furthermore, the elastic constants

were obtained from the stress of the strained structure and

the strains. The calculated matrix of the elastic constants of

SrLiAs is

FIG. 5. Calculated transport coefficients of p-type and n-type doping for

SrLiAs as a function of carrier concentration. (a) Seebeck coefficients, S(unit in 10�6 V K�1); (b) Electrical conductivity relative to relaxation time,

r=s (unit in 1020 X�1 m�1 s�1); (c) Power factor with respect to relaxation

time, S2r=s (unit in 1011 W K�2 m�1 s�1).

033705-4 Guo et al. J. Appl. Phys. 116, 033705 (2014)

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129.22.67.107 On: Sat, 22 Nov 2014 06:58:14

cij ¼

86 19 20 0 0 0

19 91 28 0 0 0

20 28 65 0 0 0

0 0 0 41 0 0

0 0 0 0 31 0

0 0 0 0 0 36

0BBBBBB@

1CCCCCCA:

The significance of the Debye temperature is that only

under T>H (331.5 K) condition, phonon scattering is domi-

nant position, and the calculation of the lattice thermal con-

ductivity is significant. From the elastic constants (cij), we

can simulate the values of the bulk and the shear moduli (Band G). According to Eqs. (5), (8), and (9), the calculated

value of jmin (0.71 W/mK) is obtained, which is comparable

to that of the Zintl compound Ca5Al2Sb6 (0.53 W/mK).37

Thus, SrLiAS is expected to have a relative low thermal

conductivity.

IV. CONCLUSION

The band structure, the density of states, and the trans-

port properties of SrLiAs were studied using first-principles

calculations and the semiclassical Boltzmann theory. The

covalent Li-As bonding along the y-direction induces a larger

dispersion in the conduction bands along the y- (C-Y) direc-

tion, which leads to a high electrical conductivity along the

y-direction. The transport properties of n-type doping are

most likely better than those of p-type doping. Further, the

peak value of power factor with respect to relaxation time for

n-type SrLiAs appears along the y-direction at 1000 K, with a

carrier concentration of 6.5� 1020 cm�3. The calculated the

minimum lattice thermal conductivity (0.71 W/m K) is com-

parable to those of other Zintl phase compounds.

ACKNOWLEDGMENTS

This research was sponsored by the National Natural

Science Foundation of China (Nos. 51371076 and

U1204112) and Program for Innovative Research Team (in

Science and Technology) in University of Henan Province

(No. 13IRTSTHN017).

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