Electronic properties of materials for solar cells: Which ab initio approaches can we trust?
Silvana Botti
1LSI, CNRS-CEA-Ecole´ Polytechnique, Palaiseau, France 2LPMCN, CNRS-Universite´ Lyon 1, France 3European Theoretical Spectroscopy Facility
September 14, 2009 – CONARES, Helsinki
Silvana Botti Electronic excitations in solar cells 1 / 57 Collaborators
Ecole Polytechnique Universite´ Lyon 1 Julien Vidal, Lucia Reining Fabio Trani, Miguel Marques
EDF Paris CEA Saclay Par¨ Olsson, J.-F. Guillemoles Fabien Bruneval
Silvana Botti Electronic excitations in solar cells 2 / 57 European Theoretical Spectroscopy Facility (ETSF)
The ETSF is a knowledge center for theoretical spectroscopy carrying out state-of-the-art research on theoretical and computational methods for studying electronic and optical properties of materials.
The ETSF gathers the experience and know-how of more than 200 researchers in Europe and the United States.
The ETSF offers its expertise to researchers, industry, and students in the form of collaborative projects, free scientific software and training.
Proposals can be submitted at any moment!
Further information: www.etsf.eu
Silvana Botti Electronic excitations in solar cells 3 / 57 Outline
1 Thin-film photovoltaic materials
2 What can we calculate within standard DFT?
3 How to go beyond standard DFT? GW approaches!
4 How to compare with experiments?
Silvana Botti Electronic excitations in solar cells 4 / 57 Thin-film photovoltaic materials Outline
1 Thin-film photovoltaic materials
2 What can we calculate within standard DFT?
3 How to go beyond standard DFT? GW approaches!
4 How to compare with experiments?
Silvana Botti Electronic excitations in solar cells 5 / 57 Thin-film photovoltaic materials Present state of photovoltaic efficiency
from National Renewable Energy Laboratory (USA)
Silvana Botti Electronic excitations in solar cells 6 / 57 Thin-film photovoltaic materials CIGS solar cell
Devices have to fulfill 2 functions: Photogeneration of electron-hole pairs Separation of charge carriers to generate a current
Structure: Molybdenum back contact CIGS layer (p-type layer) CdS layer (n-type layer) Wurth¨ Elektronik GmbH & Co. ZnO:Al TCO contact Efficiency = 13 %
Silvana Botti Electronic excitations in solar cells 7 / 57 Thin-film photovoltaic materials Modeling photovoltaic materials
Objectives Predict accurate values for fundamental opto-electronical properties of materials Deal with complex materials (large unit cells, defects)
Silvana Botti Electronic excitations in solar cells 8 / 57 What can we calculate within standard DFT? Outline
1 Thin-film photovoltaic materials
2 What can we calculate within standard DFT?
3 How to go beyond standard DFT? GW approaches!
4 How to compare with experiments?
Silvana Botti Electronic excitations in solar cells 9 / 57 What can we calculate within standard DFT? Ground state densities vs potentials
At the heart of density functional theory (DFT) Is there a 1-to-1 mapping between different external potentials v(r) and their corresponding ground state densities ρ(r)?
Silvana Botti Electronic excitations in solar cells 10 / 57 What can we calculate within standard DFT? Density functional theory (DFT)
If we can give a positive answer, then it can be proved that (i) all observable quantities of a quantum system are completely determined by the density. (ii) which means that the basic variable is no more the many-body wavefunction Ψ({r)} but the electron density ρ(r).
P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964).
You can find details in R. M. Dreizler and E.K.U. Gross, Density Functional Theory, Springer (Berlin, 1990).
Silvana Botti Electronic excitations in solar cells 11 / 57 What can we calculate within standard DFT? Density functional theory (DFT)
If we can give a positive answer, then it can be proved that (i) all observable quantities of a quantum system are completely determined by the density. (ii) which means that the basic variable is no more the many-body wavefunction Ψ({r)} but the electron density ρ(r).
P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964).
You can find details in R. M. Dreizler and E.K.U. Gross, Density Functional Theory, Springer (Berlin, 1990).
Silvana Botti Electronic excitations in solar cells 11 / 57 What can we calculate within standard DFT? Density functional theory
DFT in its standard form is a ground state theory: Structural parameters: lattice parameters, internal distortions are usually good in LDA or GGA Formation energies for defects calculated from total energies are often reliable ... but ... Kohn-Sham energies are not meant to reproduce quasiparticle band structures Kohn-Sham DOS is not meant to reproduce photoemission
Silvana Botti Electronic excitations in solar cells 12 / 57 What can we calculate within standard DFT? Kohn-Sham band structure
Kohn-Sham (KS) equations ∇2 − + v (r) ϕKS (r) = εKSϕKS (r) 2 KS i i i occ. X KS 2 ρ (r) = |ϕi (r) | i
The KS states are not one-electron energy states for the quasi-electrons in the solid However, it is common to interpret the solutions of the Kohn-Sham equations as one-electron states Often one obtains good band dispersions but band gaps are systematically underestimated
Silvana Botti Electronic excitations in solar cells 13 / 57 What can we calculate within standard DFT? Discontinuity in Vxc
.6 .6 E = (E − E ) − (E − E ) ε ε g (N+1) (N) (N) (N−1)
ε .6 1 1 KS KS ∆ = ε (N + 1) − ε (N) ;& N+1 N .6 (
ε JDS 1 .6 ( ε .6 JDS 1 DFT KS KS Eg = εN+1(N) − εN (N)
N N 1HOHFWURQV 1HOHFWURQV
DFT (N+1) (N) ∆xc = Eg − Eg = Vxc (r) − Vxc (r)
Band gap error not due to LDA, but to the discontinuity in the exact Vxc
L. J. Sham and M. Schluter,¨ PRL 51, 1888 (1983); PRB 32, 3883 (1985) J. P. Perdew and M. Levy, PRL 51, 1884 (1983) R. W. Godby, M. Schluter¨ and L. J. Sham, PRL 56, 2415 (1986) Silvana Botti Electronic excitations in solar cells 14 / 57 What can we calculate within standard DFT? An intuitive Picture for Absorption
unoccupied states
occupied states v
KS KS Independent particle KS picture using εi and ϕi
Silvana Botti Electronic excitations in solar cells 15 / 57 What can we calculate within standard DFT? An intuitive Picture for Absorption
c
unoccupied states
occupied states v
Photoemission process:
hν − (Ekin + φ) = EN−1,v − EN,0 = −εv
Silvana Botti Electronic excitations in solar cells 16 / 57 What can we calculate within standard DFT? An intuitive Picture for Absorption
c
unoccupied states
occupied states v
Optical absorption: electron-hole interaction (excitons)
Silvana Botti Electronic excitations in solar cells 17 / 57 What can we calculate within standard DFT? Software supporting DFT
Abinit EXCITING OpenMX ADF Fireball ORCA AIMPRO FSatom - list of codes ParaGauss Atomistix Toolkit GAMESS (UK) PLATO CADPAC GAMESS (US) PWscf (Quantum- CASTEP GAUSSIAN ESPRESSO) CPMD JAGUAR Q-Chem CRYSTAL06 MOLCAS SIESTA DACAPO MOLPRO Spartan DALTON MPQC S/PHI/nX deMon2K NRLMOL TURBOMOLE DFT++ NWChem VASP DMol3 OCTOPUS WIEN2k http://en.wikipedia.org/wiki/Density_functional_theory
Silvana Botti Electronic excitations in solar cells 18 / 57 What can we calculate within standard DFT? The code ABINIT
http://www.abinit.org
”First-principles computation of material properties : the ABINIT software project.” X. Gonze et al, Computational Materials Science 25, 478-492 (2002). ”A brief introduction to the ABINIT software package.” X. Gonze et al, Zeit. Kristallogr. 220, 558-562 (2005).
Silvana Botti Electronic excitations in solar cells 19 / 57 What can we calculate within standard DFT? LDA Kohn-Sham energy gaps
8 AlN SrO diamond 6 ZnO,GaN,ZnS 4 ZnSe,CuBr AlAs,GaP,SiC,AlP,CdS Se,Cu2O MgO InP,GaAs,CdTe,AlSb
2 Si InN,Ge,GaSb,CdO CaO calculated gap (eV) InSb,P,InAs HgTe 0 :LDA
experimental gap (eV) van Schilfgaarde, Kotani, and Faleev, PRL 96 (2006)
Silvana Botti Electronic excitations in solar cells 20 / 57 What can we calculate within standard DFT? LDA Kohn-Sham energy gaps for CIS
CuInS2 DFT-LDA exp. Eg -0.11 1.54 In-S 6.5 6.9 S s band 12.4 12.0 In 4 d band 14.6 18.2
CuInSe2 DFT-LDA exp. Eg -0.29 1.05 In-Se 5.8 6.5 Se s band 12.6 13.0 In 4 d band 14.7 18.0 www.abinit.org
Silvana Botti Electronic excitations in solar cells 21 / 57 What can we calculate within standard DFT? Why do we need to go beyond standard DFT?
For photovoltaic applications we are interested in evaluating quasiparticle band gap optical band gap defect energy levels optical absorption spectra
All these quantities require going beyond standard DFT
Silvana Botti Electronic excitations in solar cells 22 / 57 How to go beyond standard DFT? GW approaches! Outline
1 Thin-film photovoltaic materials
2 What can we calculate within standard DFT?
3 How to go beyond standard DFT? GW approaches!
4 How to compare with experiments?
Silvana Botti Electronic excitations in solar cells 23 / 57 How to go beyond standard DFT? GW approaches! Solution
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Silvana Botti Electronic excitations in solar cells 24 / 57 How to go beyond standard DFT? GW approaches! Hedin’s equations
Σ G=G Γ 0 GW +G 0 Σ Σ = G W G
Γ W = v + vPW
G)GG
Γ Γ=1+(δΣ/δ P P = GGΓ
L. Hedin, Phys. Rev. 139 (1965).
Silvana Botti Electronic excitations in solar cells 25 / 57 How to go beyond standard DFT? GW approaches! Green’s functions
Green’s function: propagation of an extra-particle
ˆ ˆ† G(r 1, r 2, t1 − t2) = −ihN|T [ψ(r 1, t1)ψ (r 2, t2)]|Ni
r 2 t2
r 1 t1
Electron density: Spectral function:
+ ρ (r) = G(r, r, t, t ) A(ω) = 1/πTr {Im G(r 1, r 2, ω)}
Silvana Botti Electronic excitations in solar cells 26 / 57 How to go beyond standard DFT? GW approaches! Self-energy and screened interaction
Self-energy: nonlocal, non-Hermitian, frequency dependent operator It allows to obtain the Green’s function G once that G0 is known
+ Hartree-Fock Σx (r1, r2) = iG(r1, r2, t, t )v(r1, r2)
GW Σ(r1, r2, t1 − t2) = iG(r1, r2, t1 − t2)W (r1, r2, t2 − t1)
W = −1v: screened potential (much weaker than v!)
Ingredients: −1 KS Green’s function G0, and RPA dielectric matrix G,G0 (q, ω)
L. Hedin, Phys. Rev. 139 (1965)
Silvana Botti Electronic excitations in solar cells 27 / 57 How to go beyond standard DFT? GW approaches! Standard one-shot GW
Kohn-Sham equation:
H0(r)ϕKS (r) + vxc (r) ϕKS (r) = εKSϕKS (r)
Quasiparticle equation: Z 0 0 0 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 = hϕKS|Σ − vxc|ϕKSi
Basic assumption: φQP ' ϕKS
Hybersten and Louie, PRB 34 (1986); Godby, Schluter¨ and Sham, PRB 37 (1988)
Silvana Botti Electronic excitations in solar cells 28 / 57 How to go beyond standard DFT? GW approaches! Energy gap within standard one-shot GW
8 AlN SrO diamond 6 ZnO,GaN,ZnS 4 ZnSe,CuBr AlAs,GaP,SiC,AlP,CdS Se,Cu2O MgO InP,GaAs,CdTe,AlSb
2 Si InN,Ge,GaSb,CdO CaO calculated gap (eV) InSb,P,InAs HgTe 0 :LDA :GW(LDA)
experimental gap (eV) van Schilfgaarde, Kotani, and Faleev, PRL 96 (2006)
Silvana Botti Electronic excitations in solar cells 29 / 57 How to go beyond standard DFT? GW approaches! Quasiparticle energies within G0W0 for CIS
CuInS2 DFT-LDAG 0W0 exp. Eg -0.11 0.28 1.54 In-S 6.5 6.9 6.9 S s band 12.4 13.0 12.0 In 4 d band 14.6 16.4 18.2
CuInSe2 DFT-LDAG 0W0 exp. Eg -0.29 0.25 1.05 In-Se 5.8 6.15 6.5 Se s band 12.6 12.9 13.0 In 4 d band 14.7 16.2 18.0 www.abinit.org
Silvana Botti Electronic excitations in solar cells 30 / 57 How to go beyond standard DFT? GW approaches! 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 31 / 57 How to go beyond standard DFT? GW approaches! 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 31 / 57 How to go beyond standard DFT? GW approaches! Self-consistent COHSEX
Coulomb hole: 1 Σ (r , r ) = δ(r − r )[W (r , r , ω = 0) − v(r , r )] COH 1 2 2 1 2 1 2 1 2 Screened Exchange:
X ∗ ΣSEX(r1, r2) = − θ(µ − Ei )φi (r1)φi (r2)W (r1, r2, ω = 0) i
The COHSEX self-energy is static and Hermitian Self-consistency can be done either on energies alone or on both energies and wavefunctions Representation of WFs on a restricted LDA basis set
Silvana Botti Electronic excitations in solar cells 32 / 57 How to go beyond standard DFT? GW approaches! Self-consistent GW a` la Faleev
Make self-energy Hermitian and static
1 hki|Σ˜|kji = hki|Σ(ε )|kji + hkj|Σ(ε )|kii∗ 4 kj kj ∗ +hki|Σ(εki )|kji + hkj|Σ(εki )|kii )
|kii and εki are self-consistent eigensolutions of the iterative procedure Representation of WFs on a restricted LDA basis set Requires sums over empty states
Faleev, van Schilfgaarde, and Kotani, PRL 93 2004
Silvana Botti Electronic excitations in solar cells 33 / 57 How to go beyond standard DFT? GW approaches! Self-consistent COHSEX
Advantages of COHSEX: Old approximation physically motivated: accounts for Coulomb-hole and screened-exchange Computationally “inexpensive”: hermitian, static (only sums over occupied states) sc-COHSEX wave-functions very similar to sc-GW Disadvantages of COHSEX: Dynamical correlations are missing Quasiparticle 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 34 / 57 How to go beyond standard DFT? GW approaches! Energy gap within sc-GW
8 MgO AlN
CaO 6 SrO diamond ZnO,GaN ZnS ZnSe,CuBr 4 ZnTe,CdS Cu2O InP,GaAs,CdTe
InN,GaSb AlAs,GaP,SiC,AlP
2 InSb,InAs AlSb,Se QPscGW gap (eV)
HgTe Si Ge,CdO 0 P,Te
0 2 4 6 8 experimental gap (eV) van Schilfgaarde, Kotani, and Faleev, PRL 96 (2006)
Silvana Botti Electronic excitations in solar cells 35 / 57 How to go beyond standard DFT? GW approaches! Quasiparticle energies within sc-GW for CIS
CuInS2 DFT-LDA G0W0 sc-GW exp. Eg -0.11 0.28 1.48 1.54 In-S 6.5 6.9 7.0 6.9 S s band 12.4 13.0 13.6 12.0 In 4 d band 14.6 16.4 18.2 18.2
CuInSe2 DFT-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 13.0 In 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 36 / 57 How to go beyond standard DFT? GW approaches! First remarks concerning the gap of CIS
Self-consistency in the energies suffices to correct the gap
Self-consistency in the wave-functions is necessary to correct deeper states
Spin-orbit coupling is important for Se compound → Can be added perturbatively within DFT → Experiment: 0.2 eV Calculation: 0.16 eV
Silvana Botti Electronic excitations in solar cells 37 / 57 How to compare with experiments? Outline
1 Thin-film photovoltaic materials
2 What can we calculate within standard DFT?
3 How to go beyond standard DFT? GW approaches!
4 How to compare with experiments?
Silvana Botti Electronic excitations in solar cells 38 / 57 How to compare with experiments? CIGS solar cell
Devices have to fulfill 2 functions: Photogeneration of electron-hole pairs Separation of charge carriers to generate a current
Structure: Molybdenum back contact CIGS layer (p-type layer) CdS layer (n-type layer) Wurth¨ Elektronik GmbH & Co. ZnO:Al TCO contact Efficiency = 13 %
Silvana Botti Electronic excitations in solar cells 39 / 57 How to compare with experiments? CIGS properties
Cu(In,Ga)(S,Se)2 are among the best absorbers: high optical absorption ⇒ thin-layer films optimal photovoltaic gap (record efficiency 19.9 %) self-doping with native defects ⇒ p-n junctions electrical tolerance to large off-stoichiometries: not yet understood benign character of defects: not yet understood
Silvana Botti Electronic excitations in solar cells 40 / 57 How to compare with experiments? State of the art for CuIn(S,Se)2
First ab initio calculation for chalcopyrites Jaffe et al., PRB 28,10 (1983)
Formation energies of intrinsic defects and defect levels Zhang et al., PRB 57, 9642 (1998)
Correction of the bandgap LDA+U: ∆Ev=- 0.37 eV Lany et al., PRB 72, 035215 (2005)
Metastability caused by the vacancy complex VSe-VCu Lany et al., JAP 100,113725 (2006)
Silvana Botti Electronic excitations in solar cells 41 / 57 How to compare with experiments? Is the gap stable under lattice distortion?
CuInS2 CuInSe2 2 2 The gap is not stable! Self-consistency enhances the
1 Expt 1 gap variations [eV] g E Expt Previous corrected-LDA (dots) results have LDA slope 0 0 sc-COHSEX only in energies is enough for the gap 0.2 0.22u 0.24 0.2 0.22u 0.24
DFT-LDA,G 0W0, sc-COHSEX, sc-COHSEX+G0W0
www.abinit.org
Silvana Botti Electronic excitations in solar cells 42 / 57 How to compare with experiments? Shifts of CuInS2 band edges under lattice distortion
Note: Zhang et al. showed that an upward(downward) shift of the VBM favors(inhibits) the formation of V Cu
conduction band minimum (CBM)
valence band maximum (VBM)
LDA+U (blue lines) gives only constant shifts self-consistency in energies (dashed) is not enough
Zhang et al. PRB 57, 9642 (1998)
Silvana Botti Electronic excitations in solar cells 43 / 57 How to compare with experiments? Cu-S 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-S bond is weakened Large u: the Cu-S bond is strenghtened
Once again VCu formation is favored at small u
Silvana Botti Electronic excitations in solar cells 44 / 57 How to compare with experiments? Defects
a) Perfect crystal b) VCu c) VSe d) 2VCuInCu
1000 (a) 500
10000 (b) 500
10000 DOS (c) 500
10000 (d) 500
0 -7 -6 -5 -4 -3 -2 -1 0 1 2 Energy (eV)
The presence of VCu opens up the gap!
Silvana Botti Electronic excitations in solar cells 45 / 57 How to compare with experiments? Why is the experimental gap so stable?
The feedback loop can explain the stability of the band gap:
Experimental variation of d(Cu,S) = 0.04 A˚ ⇒ ∆Eg ≈ 0.5 eV
Considering both variations of d(Cu,S) and [VCu] ⇒ ∆Eg ≈ 0.04 eV
Silvana Botti Electronic excitations in solar cells 46 / 57 How to compare with experiments? Quasi-particle corrections for CuInS2
0 Bandgap region Conduction bands (eV) -2 In-S bond Cu 3d S 3p DFT S 3s -E -4 Cu 3d S 3p GW E In 4d T
Γ
N -15 -10 -5 0 5 EDFT (eV) Corrections depend on the character of the band → Models for quasi-particle corrections for defects
Silvana Botti Electronic excitations in solar cells 47 / 57 How to compare with experiments? Delafossite TCO properties
Cu(Al,In,Ga)O2 thin-films are transparent and conducting: p-type or even bipolar conductivity combination of n- and p-type TCO materials allows → stacked cells with increased efficiency → functional windows → transparent transistors
Silvana Botti Electronic excitations in solar cells 48 / 57 How to compare with experiments? The long dispute about delafossite gaps
The most studied compound is CuAlO2:
6 indirect Eg direct Eg 5 direct indirect ∆=E -E g g Indirect gap exp. direct gap 4 Minimum direct gap at L: dipole 3 [eV] exp. indirect g gap
E allowed 2 Experimental data far from sc-GW 1 calculations!
0 LDA LDA+U B3LYP HSE03 HSE06 G0W0 scGW scGW+P
Is sc-GW wrong in this case?
Silvana Botti Electronic excitations in solar cells 49 / 57 How to compare with experiments? The long dispute about delafossite gaps
6 indirect E g Experimental data direct Eg 5 direct indirect are for optical gap: ∆=E -E g g exciton binding exp. direct gap 4 energy ≈ 0.5 eV [Laskowski et al. PRB 79, 3 [eV] exp. indirect g gap 165209 (2009)] E 2 Strong lattice polaron effects are 1 expected ≈ 1 eV [Bechstedt et al. PRB 72, 0 LDA LDA+U B3LYP HSE03 HSE06 G W scGW scGW+P 0 0 245114 (2005)]
Silvana Botti Electronic excitations in solar cells 50 / 57 How to compare with experiments? The long dispute about delafossite gaps
All results for CuInO2 are consistent with results for CuAlO2 8 indirect Eg 7 direct Γ Eg ( ) direct 6 Eg (L) Only 2 optical experiments 5 exp. direct gap
4 Minimum direct exp. indirect gap at Γ: dipole
Energy [eV] 3 gap forbidden 2 [Nie et al. PRL 066405 1 (2002)] 0 LDA LDA+U B3LYPHSE03 HSE06 G0W0 scGW
Silvana Botti Electronic excitations in solar cells 51 / 57 How to compare with experiments? Bands of CuAlO2 from LDA+U
8
6
4 LDA+U direct gap close to 2 experiment 1.97 2.89 Energy(eV) 2.60 CB are rigidly shifted 2.91 0
-2
Γ FLZ Γ
Silvana Botti Electronic excitations in solar cells 52 / 57 How to compare with experiments? Bands of CuAlO2 from sc-GW calculations
8
6 5.01 5.41
4 GW corrections strongly k-dependent CBM moves from Γ to L 5.05 2 1.97 2.89 7.16 gap becomes quasi-direct Energy(eV) 2.60 2.91 direct gap 1.5 eV larger than 0 experiment
-2
Γ FLZ Γ
Silvana Botti Electronic excitations in solar cells 53 / 57 How to compare with experiments? Comparison with hybrid functional calculations
8.0
6.0
4.0
Energy(eV) 2.0 sc-GW HSE03 LDA+U 0.0
-2.0 Γ FLZ Γ Γ FLZ Γ Γ FLZ Γ
Strong differences both in dispersion and energy gaps Are hybrids a good compromise?
Silvana Botti Electronic excitations in solar cells 54 / 57 How to compare with experiments? Next step: optical spectra...
Preliminary results for CuInO2:
solid lines: xy component, dashed: z component 20 RPA (NLF)
15
10
5
0 20 scGW(NLF)
15 2
ε 10
5
0 20 scGW+BSE
15
10
5
0 0 1 2 3 4 5 6 7 8 Energy (eV)
Strong excitonic effects also for the In compound!
Silvana Botti Electronic excitations in solar cells 55 / 57 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 established GW and BSE
A better starting point is absolutely necessary for d-electrons
Self-consistent COHSEX+G0W0 gives a very good description of quasi-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 progress now:
Defects using VASP (hybrid functionals and G0W0) – supercells up to 300 atoms Absorption spectra from the Bethe-Salpeter equation
Silvana Botti Electronic excitations in solar cells 56 / 57 Thanks! Thanks!
J. Vidal, S. Botti, P. Olsson, J.-F. Guillemoles and L. Reining, “Strong interplay between structure and electronic properties 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 delafossite transparent conductive oxides”, submitted. http://www.etsf.eu http://etsf.polytechnique.fr
http://www.abinit.org
Silvana Botti Electronic excitations in solar cells 57 / 57 Thanks! Post-doctoral positions in Lyon
Two postdoctoral positions in theoretical and computational Physics are available at the Laboratoire de physique de la matiere` condensee´ et nanostructures, located at the University of Lyon 1 in Lyon, France. The successful applicants will work under the supervision of Miguel Marques and Silvana Botti on the subjects of atto-second dynamics of electrons and strong-field phenomena.
We will favor candidates with background in any of the following topics: laser physics, real-time propagation, ab-initio calculations. Applications should include: (1) Curriculum Vitae, (2) Publication List, (3) Two reference letters, and are to be sent by email to Miguel Marques ([email protected]).
For more information or to apply please contact Miguel Marques ([email protected]).
Silvana Botti Electronic excitations in solar cells 58 / 57