High temperature thermoelectric properties of Zr and Hfbased transition metal dichalcogenides:

A first principles studyGeorge Yumnam, Tribhuwan Pandey and Abhishek K. Singh

Materials Research Centre, Indian Institute of Science, Bangalore

Objective

I To study the electronic and thermal transport properties of bulk MX2

compounds (M = Zr, Hf and X = S, Se).I Quantify the thermoelectric figure of merit (ZT) at high temperature.

Introduction

I Thermoelectric effect is the generation of an electric voltage from atemperature gradient and vice versa.

I The efficiency of a thermoelectric material is determined by the figure ofmerit ZT = S2σT/κ, where S, σ, κ and T are the thermopower, electricalconductivity, thermal conductivity and operating temperature, respectively.

Fig. 1: A typical TMD: WS2

I We explore thethermoelectric propertiesof Zr/Hf based TMDswhich has much lower κ,with high thermopower,electrical conductivity.

Computational methodology

I Ab initio Density Functional Theoryusing linear augmented plane wavemethod including local orbitals(LAPW+lo) - WIEN2k

I Electronic transport is calculated byBoltzmann transport equations underCSTA (BoltzTraP)

I κlatt (PBTE)I IFCs - PBE-GGA (VASP)I The linearized PBTE - ShengBTE

(a)

Γ

K

A

L H

M

ky

kzk

x

aH

bH

cH(b)

0 0.5 1 1.5 2

Experimental (eV)

0.0

0.5

1.0

1.5

2.0

Theo

reti

cal

(eV

)

WTe2

MoTe2

MoSe2

HfSe2

ZrSe2

WSe2

RuS2

MoS2

WS2

ZrS2

HfS2

RuSe2

RuTe2

(c)

Fig. 2: (a) Unit cell (MX2), (b) Symmetric K-

path in FBZ. (c) Comparison of Etheog and Ecalc

g .

Electronic structure (Band structure)

Γ ΓM K A L H A

-2

0

2

4

Energy(eV)

Γ ΓM K A L H A

HfS2

HfSe2

-2

0

2

4

Energy(eV)

VBMCBM

ZrS2

ZrSe2

(a) (b)

(c) (d)

Fig. 3: Electronic band structure

I Conduction band:. Heavy (z) - dyz, dxz

. Light (x, y) - dx2-y2, dz2.

I Valence band:. Heavy - (x, y) - px, py.. Light - (z) - pz.

-2

0

2

4

En

erg

y (

eV)

Γ M K ΓA L A

-2

0

2

4

-2

0

2

4

Zr dx2

-y2 Zr d

z2

Zr dxy

Zr dyz

Zr dxz

S px

S py

S pz

(a) (b)

(c) (d) (e)

(f) (g) (h)

H Γ M K ΓA L AH Γ M K ΓA L AH

Γ M K ΓA L AH Γ M K ΓA L AH Γ M K ΓA L AH

Γ M K ΓA L AH Γ M K ΓA L AH

En

erg

y (

eV)

En

erg

y (

eV)

Fig. 4: Orbital-resolved band structure of ZrS2.

Electronic structure (DOS, Fermi surface)

0

1

2

3

4

5

DO

S

0

1

2

3

4

5

DO

S

Zr - totalZr - dS - totalS - p

E - EF (eV) E - E

F (eV)

-3 -2 -1 0 1 2 3 4 -3 -2 -1 0 1 2 3 4

Hf- totalHf - dS - totalS - p

Zr - totalZr - dSe - totalSe - p

Hf - totalHf - dSe - totalSe - p

(a) (b)

(c) (d)

ZrS2

ZrSe2

HfS2

HfSe2

Fig. 5: (A) DOS (B) Fermi surface in FBZ

Electronic transport properties

I Huge anisotropy in the electricalconductivity provides the option oftuning the electronic transport in thedesired direction.

I Large thermopower (S) results invery high power-factor (S2σ).

0.5

1.5

2.5

x = yz

0

0.5

1

1.5

0.5

1.5

2.5

0.5

1

1.5

2

σii/σ

avg

σii/σ

avg

1018 1019 1020 1021 1018 1019 1020 1021

n, p (cm-3) n, p (cm-3)

(a)

(c)

(b)

(d)

ZrS2

HfS2

ZrSe2

HfSe2

Fig. 6: Electrical conductivity

−600

−400

−200

0

200

400

600

−600

−400

−200

0

200

400

600T = 600K T = 900K

(a) (b)

0

2

4

6

0

2

4

6

8

10(c) (d)

Carrier conc. (cm−3)1018 1019 1020 1021

Carrier conc. (cm−3)1018 1019 1020 1021

T = 600K T = 900K

Sav

g (

µV

/K)

Sav

g

2σ

avg/τ

×10

11 (

W/m

-K2s)

HfS2

HfSe2

ZrS2

ZrSe2

Fig. 7: (a, b) Thermopower, (c, d) Power-factor.

Lattice dynamics and thermal conductivity

0

100

200

300

0

100

200

0

100

200

300

Γ ΓM K A L H A0

100

200

Γ ΓM K A L H A

Fre

q (

cm-1)

Fre

q (

cm-1)

(a) (b)

(c) (d)

ZrS2

HfS2

HfSe2

ZrSe2

A1g

Eg

A1g

Eg

A1g

Eg

A1g

Eg

Fig. 8: Phonon dispersion curve

I Ultra low lattice thermal conductivitiesarises from the low group velocity andhigh phonon scattering rates.

600 900 1200T (K)

0

5

10

15

20

25

κla

tt (W

/m-K

)ω (rad/ps)

0.01

0.1

1

10

100

T = 300K

(a) (b)

Wan

har

(ps)

-1

0 20 40 60300

HfS2

HfSe2

ZrS2

ZrSe2

Fig. 9: (a) Lattice thermal conductivity

(b) Anharmonic scattering rate at room temperature.

I Less anisotropy in κlatt due to isotropic group velocity.

Conclusion

0 400 800 1200 1600

T (K)

0

0.2

0.4

0.6

0.8

1.0

ZT

ZrS2ZrSe2

HfS2

HfSe2

(a)

p-type

0 400 800 1200 1600

T (K)

(b)

n-type

Fig. 10: Figure of merit (ZT)

I The n-type doping exhibitsZT > 1 at T > 1200 K(Bi2Te3 - ZT∼ 1, T∼ 300 K)

I n-type doped HfSe2 emerge asan efficient material for hightemperature thermoelectricapplication, with ZT = 1.1at T=1300 K.

I This confirms the suitability of the n-type doping of these TMDs for hightemperature thermoelectric application.

Acknowledgments

I I acknowledge SERC and MRC for providing computational facility.I I also acknowledge DST, INSPIRE for providing fellowships during the course

of this work.

Reference

George Yumnam, Tribhuwan Pandey and Abhishek K. SinghHigh temperature thermoelectric properties of Zr and Hf based transitionmetal dichalcogenides: A first principles studyJ. Chem. Phys. 143, 234704 (2015)

Contact Information

I Email: uggeorge@ug.iisc.in

Yumnam et.al. J.Chem.Phys. 143, 234704 (2015) uggeorge@ug.iisc.in