High temperature thermoelectric properties of Zr and Hf based transition metal dichalcogenides: A...
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High temperature thermoelectric properties of Zr and Hf based transition metal dichalcogenides: A first principles study George 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 MX 2 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 a temperature gradient and vice versa. I The efficiency of a thermoelectric material is determined by the figure of merit ZT = S 2 σ T/κ, where S, σ , κ and T are the thermopower, electrical conductivity, thermal conductivity and operating temperature, respectively. Fig. 1: A typical TMD: WS 2 I We explore the thermoelectric properties of Zr/Hf based TMDs which has much lower κ, with high thermopower, electrical conductivity. Computational methodology I Ab initio Density Functional Theory using linear augmented plane wave method including local orbitals (LAPW+lo) - WIEN2k I Electronic transport is calculated by Boltzmann transport equations under CSTA (BoltzTraP) I κ latt (PBTE) I IFCs - PBE-GGA (VASP) I The linearized PBTE - ShengBTE (a) Γ K A L H M k y k z k x a H b H c H (b) 0 0.5 1 1.5 2 Experimental (eV) 0.0 0.5 1.0 1.5 2.0 Theoretical (eV) WTe 2 MoTe 2 MoSe 2 HfSe 2 ZrSe 2 WSe 2 RuS 2 MoS 2 WS 2 ZrS 2 HfS 2 RuSe 2 RuTe 2 (c) Fig. 2: (a) Unit cell (MX 2 ), (b) Symmetric K- path in FBZ. (c) Comparison of E theo g and E calc g . Electronic structure (Band structure) Γ Γ MK A LH A -2 0 2 4 Energy(eV) Γ Γ MK A LH A HfS 2 HfSe 2 -2 0 2 4 Energy(eV) VBM CBM ZrS 2 ZrSe 2 (a) (b) (c) (d) Fig. 3: Electronic band structure I Conduction band: . Heavy ( ˆ z)- d yz , d xz . Light ( ˆ x, ˆ y )- d x 2 -y 2 , d z 2 . I Valence band: . Heavy - ( ˆ x, ˆ y )- p x , p y . . Light - ( ˆ z)- p z . -2 0 2 4 Energy (eV) Γ MK Γ A L A -2 0 2 4 -2 0 2 4 Zr d x 2 -y 2 Zr d z 2 Zr d xy Zr d yz Zr d xz S p x S p y S p z (a) (b) (c) (d) (e) (f) (g) (h) H Γ MK Γ A L A H Γ MK Γ A L A H Γ MK Γ A L A H Γ MK Γ A L A H Γ MK Γ A L A H Γ MK Γ A L A H Γ MK Γ A L A H Energy (eV) Energy (eV) Fig. 4: Orbital-resolved band structure of ZrS 2 . Electronic structure (DOS, Fermi surface) 0 1 2 3 4 5 DOS 0 1 2 3 4 5 DOS Zr - total Zr - d S - total S - p E - E F (eV) E - E F (eV) -3 -2 -1 0 1 2 3 4 -3 -2 -1 0 1 2 3 4 Hf- total Hf - d S - total S - p Zr - total Zr - d Se - total Se - p Hf - total Hf - d Se - total Se - p (a) (b) (c) (d) ZrS 2 ZrSe 2 HfS 2 HfSe 2 Fig. 5: (A) DOS (B) Fermi surface in FBZ Electronic transport properties I Huge anisotropy in the electrical conductivity provides the option of tuning the electronic transport in the desired direction. I Large thermopower (S) results in very high power-factor (S 2 σ ). 0.5 1.5 2.5 x = y z 0 0.5 1 1.5 0.5 1.5 2.5 0.5 1 1.5 2 σ ii /σ avg σ ii /σ avg 10 18 10 19 10 20 10 21 10 18 10 19 10 20 10 21 n, p (cm -3 ) n, p (cm -3 ) (a) (c) (b) (d) ZrS 2 HfS 2 ZrSe 2 HfSe 2 Fig. 6: Electrical conductivity -600 -400 -200 0 200 400 600 -600 -400 -200 0 200 400 600 T = 600K T = 900K (a) (b) 0 2 4 6 0 2 4 6 8 10 (c) (d) Carrier conc. (cm -3 ) 10 18 10 19 10 20 10 21 Carrier conc. (cm -3 ) 10 18 10 19 10 20 10 21 T = 600K T = 900K S avg (μV/K) S avg 2 σ avg /τ ×10 11 (W/m-K 2 s) HfS 2 HfSe 2 ZrS 2 ZrSe 2 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 Γ MK A LH A 0 100 200 Γ Γ MK A LH A Freq (cm -1 ) Freq (cm -1 ) (a) (b) (c) (d) ZrS 2 HfS 2 HfSe 2 ZrSe 2 A 1g E g A 1g E g A 1g E g A 1g E g Fig. 8: Phonon dispersion curve I Ultra low lattice thermal conductivities arises from the low group velocity and high phonon scattering rates. 600 900 1200 T (K) 0 5 10 15 20 25 κ latt (W/m-K) ω (rad/ps) 0.01 0.1 1 10 100 T = 300K (a) (b) W anhar (ps) -1 0 20 40 60 300 HfS 2 HfSe 2 ZrS 2 ZrSe 2 Fig. 9: (a) Lattice thermal conductivity (b) Anharmonic scattering rate at room temperature. I Less anisotropy in κ latt 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 ZrS 2 ZrSe 2 HfS 2 HfSe 2 (a) p-type 0 400 800 1200 1600 T (K) (b) n-type Fig. 10: Figure of merit (ZT) I The n-type doping exhibits ZT > 1 at T > 1200 K (Bi 2 Te 3 - ZT∼ 1, T∼ 300 K) I n-type doped HfSe 2 emerge as an efficient material for high temperature thermoelectric application, with ZT = 1.1 at T=1300 K. I This confirms the suitability of the n-type doping of these TMDs for high temperature 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. Singh High temperature thermoelectric properties of Zr and Hf based transition metal dichalcogenides: A first principles study J. Chem. Phys. 143, 234704 (2015) Contact Information I Email: [email protected] Yumnam et.al. J.Chem.Phys. 143, 234704 (2015) [email protected]
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Transcript of High temperature thermoelectric properties of Zr and Hf based transition metal dichalcogenides: A...
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: [email protected]
Yumnam et.al. J.Chem.Phys. 143, 234704 (2015) [email protected]
