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Transcript of Electronic properties of materials for solar cells: - Which ab initio ...
Electronic properties of materials for solar cells:Which ab initio approaches can we trust?
Silvana Botti
1LSI, CNRS-CEA-Ecole Polytechnique, Palaiseau, France2LPMCN, CNRS-Universite Lyon 1, France
3European Theoretical Spectroscopy Facility
June 19, 2009 – Donostia, “DIPC Seminars”
Silvana Botti Electronic excitations in solar cells 1 / 35
Collaborators
Ecole Polytechnique Universite Lyon 1Julien Vidal, Lucia Reining Fabio Trani, Miguel Marques
EDF Paris CEA SaclayPar Olsson, J.-F. Guillemoles Fabien Bruneval
Silvana Botti Electronic excitations in solar cells 2 / 35
Outline
1 Thin-film photovoltaic materials
2 Why do we need to go beyond standard DFT?
3 How to compare with experiments?
Silvana Botti Electronic excitations in solar cells 3 / 35
Thin-film photovoltaic materials
Outline
1 Thin-film photovoltaic materials
2 Why do we need to go beyond standard DFT?
3 How to compare with experiments?
Silvana Botti Electronic excitations in solar cells 4 / 35
Thin-film photovoltaic materials
Present state of photovoltaic efficiency
from National Renewable Energy Laboratory (USA)
Silvana Botti Electronic excitations in solar cells 5 / 35
Thin-film photovoltaic materials
CIGS solar cell
Devices have to fulfill 2 functions:Photogeneration of electron-hole pairsSeparation of charge carriers to generate a current
Structure:
Molybdenum back contactCIGS layer (p-type layer)CdS layer (n-type layer)ZnO:Al TCO contact
Efficiency = 13 %Wurth Elektronik GmbH & Co.
Silvana Botti Electronic excitations in solar cells 6 / 35
Thin-film photovoltaic materials
CIGS properties
Cu(In,Ga)(S,Se)2 are among the best absorbers:
high optical absorption⇒ thin-layer filmsoptimal photovoltaic gap (record efficiency 19.9 %)self-doping with native defects⇒ p-n junctionselectrical tolerance to large off-stoichiometries:not yet understoodbenign character of defects:not yet understood
Silvana Botti Electronic excitations in solar cells 7 / 35
Thin-film photovoltaic materials
Delafossite TCO properties
Cu(Al,In,Ga)O2 thin-films are transparent and conducting:
p-type or even bipolar conductivitycombination of n- and p-type TCO materials allows
→ stacked cells with increased efficiency→ functional windows→ transparent transistors
Silvana Botti Electronic excitations in solar cells 8 / 35
Thin-film photovoltaic materials
Modeling photovoltaic materials
ObjectivesPredict accurate values forfundamental opto-electronicalproperties of materials
Deal with complex materials(large unit cells, defects)
Silvana Botti Electronic excitations in solar cells 9 / 35
Why do we need to go beyond standard DFT?
Outline
1 Thin-film photovoltaic materials
2 Why do we need to go beyond standard DFT?
3 How to compare with experiments?
Silvana Botti Electronic excitations in solar cells 10 / 35
Why do we need to go beyond standard DFT?
Density functional theory
DFT in its standard form is a ground state theory
Structural parameters: lattice parameters, internal distortions areusually ok in LDA or GGAFormation energies for defects calculated from total energies arereliableKohn-Sham energies are not meant to reproduce quasiparticleband structures: often one obtains good band dispersions butband gaps are systematically underestimatedKohn-Sham DOS is not meant to reproduce photoemission
Silvana Botti Electronic excitations in solar cells 11 / 35
Why do we need to go beyond standard DFT?
LDA Kohn-Sham energy gaps
0
2
4
6
8
calc
ula
ted g
ap (
eV
)
:LDA
HgT
e
InS
b,P
,InA
sIn
N,G
e,G
aS
b,C
dO
Si
InP
,GaA
s,C
dT
e,A
lSb
Se,C
u2O
AlA
s,G
aP
,SiC
,AlP
,CdS
ZnS
e,C
uB
r
ZnO
,GaN
,ZnS
dia
mond
SrO A
lN
MgO
CaO
van Schilfgaarde, Kotani, and Faleev, PRL 96 (2006)
Silvana Botti Electronic excitations in solar cells 12 / 35
experimental gap (eV)
Why do we need to go beyond standard DFT?
LDA Kohn-Sham energy gaps for CIS
CuInS2DFT-LDA exp.
Eg -0.11 1.54In-S 6.5 6.9
S s band 12.4 12.0In 4 d band 14.6 18.2
CuInSe2DFT-LDA exp.
Eg -0.29 1.05In-Se 5.8 6.5
Se s band 12.6 13.0In 4 d band 14.7 18.0
www.abinit.org
Silvana Botti Electronic excitations in solar cells 13 / 35
Why do we need to go beyond standard DFT?
Beyond standard DFT
For photovoltaic applications we areinterested in evaluating
quasiparticle band gapoptical band gapdefect energy levelsoptical absorption spectra
All these quantities require going beyond standard DFT
Silvana Botti Electronic excitations in solar cells 14 / 35
Why do we need to go beyond standard DFT?
Solution
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In the many-body framework, we know how to solvethese problems:
GW for quasi-particle propertiesBethe-Salpeter equation for the inclusion ofelectron-hole interaction
The first step can be substantially more complicatedthan the second, so in the following we will focus onGW
Silvana Botti Electronic excitations in solar cells 15 / 35
Why do we need to go beyond standard DFT?
Hedin’s equations
Σ
G
ΓP
W
G=G 0+G 0 Σ G
Γ=1+
(δΣ/
δG)G
GΓ
P = GGΓ
W = v + vPW
Σ = GWΓ
L. Hedin, Phys. Rev. 139 (1965).
Silvana Botti Electronic excitations in solar cells 16 / 35
Why do we need to go beyond standard DFT?
Standard one-shot GW
Kohn-Sham equation:
H0(r)ϕKS (r) + vxc (r)ϕKS (r) = εKSϕKS (r)
Quasiparticle equation:
H0(r)φQP (r) +
∫dr ′Σ
(r , r ′, ω = EQP
)φQP
(r ′) = EQPφQP (r)
Quasiparticle energies 1st order perturbative correction with Σ = iGW :
EQP − εKS = 〈ϕKS|Σ− vxc|ϕKS〉
Basic assumption: φQP ' ϕKS
L. Hedin, Phys. Rev. 139 (1965)
Hybersten and Louie, PRB 34 (1986); Godby, Schluter and Sham, PRB 37 (1988)
Silvana Botti Electronic excitations in solar cells 17 / 35
Why do we need to go beyond standard DFT?
Energy gap within standard one-shot GW
0
2
4
6
8
calc
ula
ted g
ap (
eV
)
:LDA
:GW(LDA)
HgT
e
InS
b,P
,InA
sIn
N,G
e,G
aS
b,C
dO
Si
InP
,GaA
s,C
dT
e,A
lSb
Se,C
u2O
AlA
s,G
aP
,SiC
,AlP
,CdS
ZnS
e,C
uB
r
ZnO
,GaN
,ZnS
dia
mond
SrO A
lN
MgO
CaO
van Schilfgaarde, Kotani, and Faleev, PRL 96 (2006)
Silvana Botti Electronic excitations in solar cells 18 / 35
experimental gap (eV)
Why do we need to go beyond standard DFT?
Quasiparticle energies within G0W0 for CIS
CuInS2DFT-LDA G0W0 exp.
Eg -0.11 0.28 1.54In-S 6.5 6.9 6.9
S s band 12.4 13.0 12.0In 4 d band 14.6 16.4 18.2
CuInSe2DFT-LDA G0W0 exp.
Eg -0.29 0.25 1.05In-Se 5.8 6.15 6.5
Se s band 12.6 12.9 13.0In 4 d band 14.7 16.2 18.0
www.abinit.org
Silvana Botti Electronic excitations in solar cells 19 / 35
Why do we need to go beyond standard DFT?
Beyond Standard GW
Looking for another starting point:DFT with another approximation for vxc : GGA, EXX,...(e.g. Rinke et al. 2005)LDA/GGA + U (e.g. Kioupakis et al. 2008, Jiang et al. 2009 )Semi-empirical hybrid functionals (e.g. Fuchs et al. 2007)
Self-consistent approaches:GWscQP scheme (Faleev et al. 2004)scCOHSEX scheme (Hedin 1965, Bruneval et al. 2005)
Silvana Botti Electronic excitations in solar cells 20 / 35
Why do we need to go beyond standard DFT?
Beyond Standard GW
Looking for another starting point:DFT with another approximation for vxc : GGA, EXX,...(e.g. Rinke et al. 2005)LDA/GGA + U (e.g. Kioupakis et al. 2008, Jiang et al. 2009 )Semi-empirical hybrid functionals (e.g. Fuchs et al. 2007)
Self-consistent approaches:GWscQP scheme (Faleev et al. 2004)scCOHSEX scheme (Hedin 1965, Bruneval et al. 2005)
Silvana Botti Electronic excitations in solar cells 20 / 35
Why do we need to go beyond standard DFT?
Self-consistent COHSEX
Advantages of COHSEX:Old approximation physically motivated: accounts forCoulomb-hole and screened-exchangeComputationally “inexpensive”: hermitian, static (only sums overoccupied states)sc-COHSEX wave-functions very similar to sc-GW
Disadvantages of COHSEX:Dynamical correlations are missingQuasiparticle gaps are better (10-20% higher than experiment),but still not OK
One-shot GW on top of sc-COHSEX corrects the energy gap!
Silvana Botti Electronic excitations in solar cells 21 / 35
Why do we need to go beyond standard DFT?
Energy gap within sc GW
0 2 4 6 8
0
2
4
6
8
experimental gap (eV)
QP
scG
W g
ap
(e
V)
MgO
AlN
CaO
HgT
e InS
b,I
nA
sIn
N,G
aS
b
InP
,Ga
As,C
dT
eC
u2
O Zn
Te
,Cd
SZ
nS
e,C
uB
rZ
nO
,Ga
NZ
nS
P,Te
SiGe,CdO
AlSb,SeAlAs,GaP,SiC,AlP
SrOdiamond
van Schilfgaarde, Kotani, and Faleev, PRL 96 (2006)
Silvana Botti Electronic excitations in solar cells 22 / 35
Why do we need to go beyond standard DFT?
Quasiparticle energies within sc-GW for CIS
CuInS2DFT-LDA G0W0 sc-GW exp.
Eg -0.11 0.28 1.48 1.54In-S 6.5 6.9 7.0 6.9
S s band 12.4 13.0 13.6 12.0In 4 d band 14.6 16.4 18.2 18.2
CuInSe2DFT-LDA G0W0 sc-GW exp.
Eg -0.29 0.25 1.14 1.05 (+0.2)In-Se 5.8 6.15 6.64 6.5
Se s band 12.6 12.9 13.6 13.0In 4 d band 14.7 16.2 17.8 18.0
sc-GW is here sc-COHSEX+G0W0
www.abinit.org
Silvana Botti Electronic excitations in solar cells 23 / 35
How to compare with experiments?
Outline
1 Thin-film photovoltaic materials
2 Why do we need to go beyond standard DFT?
3 How to compare with experiments?
Silvana Botti Electronic excitations in solar cells 24 / 35
How to compare with experiments?
Is the gap stable under lattice distortion?
0.2 0.22 0.24u
0
1
2
Eg [
eV]
CuInS2
0.2 0.22 0.24u
0
1
2CuInSe
2
Expt
Expt
The gap is not stable!Self-consistency enhances thegap variationsPrevious corrected-LDA (dots)results have LDA slopesc-COHSEX only in energiesis enough for the gap
DFT-LDA, G0W0, sc-COHSEX, sc-COHSEX+G0W0
www.abinit.org
Silvana Botti Electronic excitations in solar cells 25 / 35
How to compare with experiments?
Shifts of the band edges under lattice distortion
Note: Zhang et al. showed that an upward (downward) shift of theVBM favors (inhibits) the formation of VCu
conduction band minimum (CBM)
valence band maximum (VBM)
LDA+U (blue lines) gives only constant shiftsself-consistency in energies (dashed) is not enough
Zhang et al. PRB 57, 9642 (1998)
Silvana Botti Electronic excitations in solar cells 26 / 35
How to compare with experiments?
Cu-Se bond under lattice distortion
Contribution of the VBM to |ρCOHSEX − ρLDA|
u = 0.2 u = 0.215 u = 0.235 u = 0.25
Small u: the Cu-Se bond is weakenedLarge u: the Cu-Se bond is strenghtened
Once again VCu formation is favored at small u
Silvana Botti Electronic excitations in solar cells 27 / 35
How to compare with experiments?
Defects
a) Perfect crystal b) VCu c) VSe d) 2VCuInCu
0
500
1000
0
500
1000
DO
S
0
500
1000
-7 -6 -5 -4 -3 -2 -1 0 1 2Energy (eV)
0
500
1000
(a)
(b)
(c)
(d)
The presence of VCu opens up the gap!
Silvana Botti Electronic excitations in solar cells 28 / 35
How to compare with experiments?
Why the experimental gap is stable
0.2 0.22 0.24u
0
1
2
Eg [
eV]
CuInS2
0.2 0.22 0.24u
0
1
2CuInSe
2
Expt
Expt
In conclusion:In experiments where u is smaller than in the bulk and the gap isstable we can expect the concentration of VCu to be higher andcompensate for the decrease of the gap
Silvana Botti Electronic excitations in solar cells 29 / 35
How to compare with experiments?
The long dispute about delafossite gaps
The most studied compound is CuAlO2:
LDA LDA+U B3LYP HSE03 HSE06 G0W
0scGW
0
1
2
3
4
5
6
Eg [
eV]
Eg
indirect
Eg
direct
∆=Eg
direct-E
g
indirect Indirect gapMinimum directgap at L: dipoleallowedExperimental datafar from sc-GWcalculations!
Is sc-GW wrong in this case?
Silvana Botti Electronic excitations in solar cells 30 / 35
How to compare with experiments?
The long dispute about delafossite gaps
LDA LDA+U B3LYP HSE03 HSE06 G0W
0scGW
0
1
2
3
4
5
6
Eg [
eV]
Eg
indirect
Eg
direct
∆=Eg
direct-E
g
indirect
Experimental dataare for optical gap:exciton bindingenergy ≈ 0.5 eV[Laskowski et al. PRB 79,
165209 (2009)]
Strong latticepolaron effects areexpected ≈ 1 eV[Bechstedt et al. PRB 72,
245114 (2005)]
Silvana Botti Electronic excitations in solar cells 31 / 35
How to compare with experiments?
Bands of CuAlO2 from LDA+U
Γ F L Z Γ
-2
0
2
4
6
8
Ene
rgy(
eV)
2.91
2.892.60
1.97
LDA+U direct gap close toexperimentCB are rigidly shifted
Silvana Botti Electronic excitations in solar cells 32 / 35
How to compare with experiments?
Bands of CuAlO2 from sc-GW calculations
Γ F L Z Γ
-2
0
2
4
6
8
Ene
rgy(
eV)
2.91
2.892.60
1.97
5.01
5.05
7.16
5.41
GW corrections stronglyk-dependentCBM moves from Γ to Lgap becomes quasi-directdirect gap 1.5 eV larger thanexperiment
Silvana Botti Electronic excitations in solar cells 33 / 35
How to compare with experiments?
Conclusions and perspectives
Interpretation of experiments is often not straightforward
Methods that go beyond ground-state DFT are by now well establishedGW and BSE
A better starting point is absolutely necessary for d-electronsSelf-consistent COHSEX+G0W0 gives a very good description ofquasi-particle states→ In all cases we studied this proved to be at the level of scGW→ Much more friendly from the computational point of view
In progressDefectsAbsorption spectra from the Bethe-Salpeter equation
Silvana Botti Electronic excitations in solar cells 34 / 35
Thanks!
Thanks!
J. Vidal, S. Botti, P. Olsson, J.-F. Guillemoles and L.Reining, “Strong interplay between structure and electronicproperties in CuIn(S,Se)2: a first-principle study”,submitted.
J. Vidal, F. Trani, F. Bruneval, M. A. L. Marques and S.Botti, “Accurate band structure calculations of delafossitetransparent conductive oxides”, in preparation.
http://www.etsf.euhttp://etsf.polytechnique.fr
http://www.abinit.org
Silvana Botti Electronic excitations in solar cells 35 / 35