using state-of-the-art ab initio methodsgdr-thermoelectricite.cnrs.fr/.../Botti-GDR2012.pdf ·...
Transcript of using state-of-the-art ab initio methodsgdr-thermoelectricite.cnrs.fr/.../Botti-GDR2012.pdf ·...
-
From band structures to thermoelectric propertiesusing state-of-the-art ab initio methods
Silvana Botti
1LPMCN, CNRS-Université Lyon 1, France2European Theoretical Spectroscopy Facility
December 6, 2012 – Lyon
Silvana Botti Thermoelectricity 1 / 15
-
Outline
1 Calculations of thermoelectric properties
2 How to obtain reliable band structures?
3 Disilicides
4 Conclusions and perspectives
Silvana Botti Thermoelectricity 2 / 15
-
Thermoelectric properties
Thermoelectric power generation
Seebeck effect: converts temperature differences in electric voltages
Seebeck coefficient S = ∆V∆T
Silvana Botti Thermoelectricity 3 / 15
-
Thermoelectric properties
Thermoelectric power generation
Seebeck effect: converts temperature differences in electric voltages
Seebeck coefficient S = ∆V∆T
Silvana Botti Thermoelectricity 3 / 15
-
Thermoelectric properties
Thermoelectric power generation
Seebeck effect: converts temperature differences in electric voltages
Efficiency (< 10 – 15%)
ηmax =Thot − Tcold
Thot
√1 + ZT − 1
√1 + ZT + TcoldThot
Figure of merit:
ZT̄ =(Sp − Sn)2T̄
[(ρpκp)1/2 + (ρnκn)1/2]2
Seebeck coefficient S = ∆V∆T
Large ZT̄ are needed for high efficiency
Silvana Botti Thermoelectricity 3 / 15
-
Thermoelectric properties
Electronic terms of the figure of merit
ObjectivesPredict accurate values for thermoelectric propertiesDeal with complexity (large cells, doping, nanostructuring, . . .)
⇒ Find efficient, cheap and environment-friendly new thermoelectrics!
Silvana Botti Thermoelectricity 4 / 15
-
Thermoelectric properties
Boltzmann theory of transport
Within linear response:ji = σijEj
The conductivity tensor is
σij =1
4π3∑
n
∫τn,kvi(n,k)vj(n,k)
(−∂f (n,k,T )
∂E(k)
)dk
in terms of the group velocity and the relaxation time
The group velocity is given by the dispersion of the bands
Constant relaxation time approximation: τS is independent on τσ is proportional to τ
Silvana Botti Thermoelectricity 5 / 15
-
Thermoelectric properties
Kohn-Sham band structure
Kohn-Sham (KS) equations[−∇
2
2+ vKS (r)
]ϕKSi (r) = ε
KSi ϕ
KSi (r)
ρ (r) =occ.∑
i
|ϕKSi (r) |2
It is common to interpret the solutions of the Kohn-Shamequations as one-electron statesOften one obtains good band dispersions but band gaps aresystematically underestimatedSometimes one gets bad band dispersions and band gaps!This happens, e.g., when there are localized d or f states
W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).Silvana Botti Thermoelectricity 6 / 15
-
Thermoelectric properties
Kohn-Sham band structure
Kohn-Sham (KS) equations[−∇
2
2+ vKS (r)
]ϕKSi (r) = ε
KSi ϕ
KSi (r)
ρ (r) =occ.∑
i
|ϕKSi (r) |2
It is common to interpret the solutions of the Kohn-Shamequations as one-electron statesOften one obtains good band dispersions but band gaps aresystematically underestimatedSometimes one gets bad band dispersions and band gaps!This happens, e.g., when there are localized d or f states
W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).Silvana Botti Thermoelectricity 6 / 15
-
Reliable band structures
State-of-the-art of theorycom
puta
tional cost
# atoms
2000
200
20
Standard DFT (LDA,GGAs): severeunderestimation of gaps, often good structuralproperties, bad localized (d and f ) statesDFT + model U: corrects localization of d states,usually better gaps, reliability depends too muchon the systemHybrid functionals: good gaps (unfortunatelyprecision not systematic), excellent structuralproperties, better localized statesGW: excellent band structures, excellent localizedstates, self-consistent screening, hard to accessto total energies
accuracy
Silvana Botti Thermoelectricity 7 / 15
-
Reliable band structures
State-of-the-art of theorycom
puta
tional cost
# atoms
2000
200
20
Standard DFT (LDA,GGAs): severeunderestimation of gaps, often good structuralproperties, bad localized (d and f ) statesDFT + model U: corrects localization of d states,usually better gaps, reliability depends too muchon the systemHybrid functionals: good gaps (unfortunatelyprecision not systematic), excellent structuralproperties, better localized statesGW: excellent band structures, excellent localizedstates, self-consistent screening, hard to accessto total energies
accuracy
Silvana Botti Thermoelectricity 7 / 15
-
Reliable band structures
State-of-the-art of theorycom
puta
tional cost
# atoms
2000
200
20
Standard DFT (LDA,GGAs): severeunderestimation of gaps, often good structuralproperties, bad localized (d and f ) statesDFT + model U: corrects localization of d states,usually better gaps, reliability depends too muchon the systemHybrid functionals: good gaps (unfortunatelyprecision not systematic), excellent structuralproperties, better localized statesGW: excellent band structures, excellent localizedstates, self-consistent screening, hard to accessto total energies
accuracy
Silvana Botti Thermoelectricity 7 / 15
-
Reliable band structures
State-of-the-art of theorycom
puta
tional cost
# atoms
2000
200
20
Standard DFT (LDA,GGAs): severeunderestimation of gaps, often good structuralproperties, bad localized (d and f ) statesDFT + model U: corrects localization of d states,usually better gaps, reliability depends too muchon the systemHybrid functionals: good gaps (unfortunatelyprecision not systematic), excellent structuralproperties, better localized statesGW: excellent band structures, excellent localizedstates, self-consistent screening, hard to accessto total energies
accuracy
Silvana Botti Thermoelectricity 7 / 15
-
Reliable band structures
Comparative test: kesterite Cu2ZnSnS4
T Γ N-16
-14
-12
-10
-8
-6
-4
-2
0
2
4
6
8
Ene
rgy
(eV
)
T Γ N-16
-14
-12
-10
-8
-6
-4
-2
0
2
4
6
8
self-consistent GW
standard DFT
hybrids
DFT+U
CBM
VBM
S3p-Cu3d
bonding
(Sn,Zn)-S
S 3s
S3p-(Zn,Sn)s
antibonding
SB, D. Kammerlander and M.A.L. Marques, APL 98, 241915 (2011)C. Sevik and T. Çağin, PRB 82, 045202 (2010)
Silvana Botti Thermoelectricity 8 / 15
-
Reliable band structures
Exploring new kesterites: Cu2ZnGe(S,Se)4
T Γ N-18
-16
-14
-12
-10
-8
-6
-4
-2
0
2
4
6
8
10
Ene
rgy
[eV
]
LDAscGW
Cu2ZnGeSe
2 kesterite
scGW gap (HSE geometry) = 1.44 eVscGW gap (GGA geometry) = 0.91 eV
T Γ N-18
-16
-14
-12
-10
-8
-6
-4
-2
0
2
4
6
8
10
Ene
rgy
[eV
]
LDAscGW
Cu2ZnGeS
2 kesterite
Silvana Botti Thermoelectricity 9 / 15
-
Reliable band structures
CuAlO2 delafossite
Γ F L Z Γ-2.0
0.0
2.0
4.0
6.0
8.0
Ene
rgy(
eV)
sc-GW
Γ F L Z Γ
HSE03
Γ F L Z Γ
LDA+U
Strong differences both in dispersion and energy gaps
J. Vidal, F. Trani, F. Bruneval, M.A.L. Marques, and S. Botti PRL 104, 136401 (2010)
Silvana Botti Thermoelectricity 10 / 15
-
Disilicides
Quality of the density of states
X-ray photoelectron spectroscopy (XPS) measured in BaSi2Calculated electronic density of states using GGA-PBE and thehybrid functional HSE06
J. Flores-Livas, Ph.D. thesis, University of Lyon 1 (2012).
Silvana Botti Thermoelectricity 11 / 15
-
Disilicides
Seebeck coefficient
GGA calculationsorthorhombicBaSi2 agrees withexp.S underestimatedfor SrSi2 (metallicin GGA)
Silvana Botti Thermoelectricity 12 / 15
-
Conclusions and perspectives
Conclusions and perspectives
In many cases the semi-classical theory of Boltzmann and therelaxation time approximation are reliable, provided that the banddispersions are good and the systems do not turn out metallic
Band-structure methods beyond ground-state DFT are well establishedand necessary for systems with d-states close to the Fermi energy
Hybrid functionals are often a reasonable compromise
Open problems:ab initio determination of the relaxation timesab initio determination of the thermal conductivity
Silvana Botti Thermoelectricity 13 / 15
-
Conclusions and perspectives
Conclusions and perspectives
In many cases the semi-classical theory of Boltzmann and therelaxation time approximation are reliable, provided that the banddispersions are good and the systems do not turn out metallic
Band-structure methods beyond ground-state DFT are well establishedand necessary for systems with d-states close to the Fermi energy
Hybrid functionals are often a reasonable compromise
Open problems:ab initio determination of the relaxation timesab initio determination of the thermal conductivity
Silvana Botti Thermoelectricity 13 / 15
-
Conclusions and perspectives
Conclusions and perspectives
In many cases the semi-classical theory of Boltzmann and therelaxation time approximation are reliable, provided that the banddispersions are good and the systems do not turn out metallic
Band-structure methods beyond ground-state DFT are well establishedand necessary for systems with d-states close to the Fermi energy
Hybrid functionals are often a reasonable compromise
Open problems:ab initio determination of the relaxation timesab initio determination of the thermal conductivity
Silvana Botti Thermoelectricity 13 / 15
-
Thanks!
Thanks to all collaborators at LPMCN
Miguel Marques, José Flores-Livas (theory)
Stéphane Pailhés, Régis Debord, Valentina Giordano(experiments)
More information on our group home page:http://www.tddft.org/bmg/
http://www.abinit.org http://www.yambo-code.org http://cms.mpi.univie.ac.at/vasp/
Silvana Botti Thermoelectricity 14 / 15
http://www.tddft.org/bmg/http://www.abinit.orghttp://www.yambo-code.orghttp://cms.mpi.univie.ac.at/vasp/
Calculations of thermoelectric propertiesHow to obtain reliable band structures?DisilicidesConclusions and perspectivesThanks!