Electronic properties of materials for solar cells:

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Silvana Botti 1 LSI, CNRS-CEA-École Polytechnique, Palaiseau, France 2 LPMCN,

1 Electronic properties of materials for solar cells: Which ab initio approaches can we trust? Silvana Botti 1 LSI, CNRS-CEA-École Polytechnique, Palaiseau, France 2 LPMCN, CNRS-Université Lyon 1, France 3 European Theoretical Spectroscopy Facility September 14, 2009 CONARES, Helsinki Silvana Botti Electronic excitations in solar cells 1 / 57

2 Collaborators Ecole Polytechnique Julien Vidal, Lucia Reining Universite Lyon 1 Fabio Trani, Miguel Marques EDF Paris Pa r Olsson, J.-F. Guillemoles CEA Saclay 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

3 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: Silvana Botti Electronic excitations in solar cells 3 / 57

4 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

5 Outline Thin-film photovoltaic materials 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

6 Thin-film photovoltaic materials Present state of photovoltaic efficiency from National Renewable Energy Laboratory (USA) Silvana Botti Electronic excitations in solar cells 6 / 57

7 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) ZnO:Al TCO contact Würth Elektronik GmbH & Co. Efficiency = 13 % Silvana Botti Electronic excitations in solar cells 7 / 57

8 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

9 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

10 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

11 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

12 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

13 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

14 What can we calculate within standard DFT? Kohn-Sham band structure Kohn-Sham (KS) equations ] [ v KS (r) ϕ KS i (r) = ε KS i occ. ρ (r) = ϕ KS i (r) 2 i ϕ KS i (r) 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

15 What can we calculate within standard DFT? Discontinuity in V xc ε.6 ε.6 E g = (E (N+1) E (N) ) (E (N) E (N 1) ).6 ε 1 ε 1.6 ;& ( JDS.6 ( JDS.6 ε 1 1 = ε KS N+1 (N + 1) εks N (N) E DFT g = ε KS N+1 (N) εks N (N) 1HOHFWURQV N 1HOHFWURQV N xc = E g E DFT g = V (N+1) xc (r) V (N) (r) xc Band gap error not due to LDA, but to the discontinuity in the exact V xc L. J. Sham and M. Schlüter, PRL 51, 1888 (1983); PRB 32, 3883 (1985) J. P. Perdew and M. Levy, PRL 51, 1884 (1983) R. W. Godby, M. Schlüter and L. J. Sham, PRL 56, 2415 (1986) Silvana Botti Electronic excitations in solar cells 14 / 57

16 What can we calculate within standard DFT? An intuitive Picture for Absorption c unoccupied states v occupied states Independent particle KS picture using ε KS i and ϕ KS i Silvana Botti Electronic excitations in solar cells 15 / 57

17 What can we calculate within standard DFT? An intuitive Picture for Absorption c unoccupied states v occupied states Photoemission process: hν (E kin + φ) = E N 1,v E N,0 = ε v Silvana Botti Electronic excitations in solar cells 16 / 57

18 What can we calculate within standard DFT? An intuitive Picture for Absorption c unoccupied states v occupied states Optical absorption: electron-hole interaction (excitons) Silvana Botti Electronic excitations in solar cells 17 / 57

19 What can we calculate within standard DFT? Software supporting DFT Abinit ADF AIMPRO Atomistix Toolkit CADPAC CASTEP CPMD CRYSTAL06 DACAPO DALTON demon2k DFT++ DMol3 EXCITING Fireball FSatom - list of codes GAMESS (UK) GAMESS (US) GAUSSIAN JAGUAR MOLCAS MOLPRO MPQC NRLMOL NWChem OCTOPUS OpenMX ORCA ParaGauss PLATO PWscf (Quantum- ESPRESSO) Q-Chem SIESTA Spartan S/PHI/nX TURBOMOLE VASP WIEN2k 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.

20 What can we calculate within standard DFT? The code ABINIT First-principles computation of material properties : the ABINIT software project. X. Gonze et al, Computational Materials Science 25, (2002). A brief introduction to the ABINIT software package. X. Gonze et al, Zeit. Kristallogr. 220, (2005). Silvana Botti Electronic excitations in solar cells 19 / 57

21 What can we calculate within standard DFT? LDA Kohn-Sham energy gaps calculated gap (ev) HgTe InSb,P,InAs InN,Ge,GaSb,CdO Si InP,GaAs,CdTe,AlSb Se,Cu2O AlAs,GaP,SiC,AlP,CdS ZnSe,CuBr ZnO,GaN,ZnS diamond SrO AlN :LDA CaO MgO experimental gap (ev) van Schilfgaarde, Kotani, and Faleev, PRL 96 (2006) Silvana Botti Electronic excitations in solar cells 20 / 57

22 What can we calculate within standard DFT? LDA Kohn-Sham energy gaps for CIS CuInS 2 DFT-LDA exp. E g In-S S s band In 4 d band CuInSe 2 DFT-LDA exp. E g In-Se Se s band In 4 d band Silvana Botti Electronic excitations in solar cells 21 / 57

23 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

24 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

25 How to go beyond standard DFT? GW approaches! Solution Π0 In the many-body framework, we know how to solve these problems: GW for quasi-particle properties Bethe-Salpeter equation for the inclusion of electron-hole interaction The first step can be substantially more complicated than the second, so in the following we will focus on GW Silvana Botti Electronic excitations in solar cells 24 / 57

26 How to go beyond standard DFT? GW approaches! Hedin s equations W W = v + vpw Σ = GWΓ P Σ P = GGΓ G=G 0 +G 0 Σ G Γ G Γ=1+(δΣ/δG)GGΓ L. Hedin, Phys. Rev. 139 (1965). Silvana Botti Electronic excitations in solar cells 25 / 57

27 How to go beyond standard DFT? GW approaches! Green s functions Green s function: propagation of an extra-particle G(r 1, r 2, t 1 t 2 ) = i N T [ ˆψ(r 1, t 1 ) ˆψ (r 2, t 2 )] N r 2 t 2 r 1 t 1 Electron density: ρ (r) = G(r, r, t, t + ) Spectral function: A(ω) = 1/πTr {Im G(r 1, r 2, ω)} Silvana Botti Electronic excitations in solar cells 26 / 57

28 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 G 0 is known Hartree-Fock Σ x (r 1, r 2 ) = ig(r 1, r 2, t, t + )v(r 1, r 2 ) GW Σ(r 1, r 2, t 1 t 2 ) = ig(r 1, r 2, t 1 t 2 )W (r 1, r 2, t 2 t 1 ) W = ɛ 1 v: screened potential (much weaker than v!) Ingredients: KS Green s function G 0, and RPA dielectric matrix ɛ 1 G,G (q, ω) L. Hedin, Phys. Rev. 139 (1965) Silvana Botti Electronic excitations in solar cells 27 / 57

29 How to go beyond standard DFT? GW approaches! Standard one-shot GW Kohn-Sham equation: H 0 (r)ϕ KS (r) + v xc (r) ϕ KS (r) = ε KS ϕ KS (r) Quasiparticle equation: H 0 (r)φ QP (r) + dr Σ ( r, r ) (, ω = E QP φqp r ) = E QP φ QP (r) Quasiparticle energies 1st order perturbative correction with Σ = igw : E QP ε KS = ϕ KS Σ v xc ϕ KS Basic assumption: φ QP ϕ KS Hybersten and Louie, PRB 34 (1986); Godby, Schlüter and Sham, PRB 37 (1988) Silvana Botti Electronic excitations in solar cells 28 / 57

30 How to go beyond standard DFT? GW approaches! Energy gap within standard one-shot GW calculated gap (ev) HgTe InSb,P,InAs InN,Ge,GaSb,CdO Si InP,GaAs,CdTe,AlSb Se,Cu2O AlAs,GaP,SiC,AlP,CdS ZnSe,CuBr ZnO,GaN,ZnS diamond SrO AlN CaO MgO 0 :LDA :GW(LDA) experimental gap (ev) van Schilfgaarde, Kotani, and Faleev, PRL 96 (2006) Silvana Botti Electronic excitations in solar cells 29 / 57

31 How to go beyond standard DFT? GW approaches! Quasiparticle energies within G 0 W 0 for CIS CuInS 2 DFT-LDA G 0 W 0 exp. E g In-S S s band In 4 d band CuInSe 2 DFT-LDA G 0 W 0 exp. E g In-Se Se s band In 4 d band Silvana Botti Electronic excitations in solar cells 30 / 57

32 How to go beyond standard DFT? GW approaches! Beyond Standard GW Looking for another starting point: DFT with another approximation for v xc : GGA, EXX,... (e.g. Rinke et al. 2005) LDA/GGA + U (e.g. Kioupakis et al. 2008, Jiang et al ) 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

33 How to go beyond standard DFT? GW approaches! Beyond Standard GW Looking for another starting point: DFT with another approximation for v xc : GGA, EXX,... (e.g. Rinke et al. 2005) LDA/GGA + U (e.g. Kioupakis et al. 2008, Jiang et al ) 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

34 How to go beyond standard DFT? GW approaches! Self-consistent COHSEX Coulomb hole: Σ COH (r 1, r 2 ) = 1 2 δ(r 1 r 2 )[W (r 1, r 2, ω = 0) v(r 1, r 2 )] Screened Exchange: Σ SEX (r 1, r 2 ) = i θ(µ E i )φ i (r 1 )φ i (r 2)W (r 1, r 2, ω = 0) 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

35 How to go beyond standard DFT? GW approaches! Self-consistent GW à la Faleev Make self-energy Hermitian and static ki Σ kj = 1 4 ( ki Σ(εkj ) kj + kj Σ(ε kj ) ki + ki Σ(ε ki ) kj + kj Σ(ε ki ) ki ) ki and ε ki 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 Silvana Botti Electronic excitations in solar cells 33 / 57

36 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

37 How to go beyond standard DFT? GW approaches! Energy gap within sc-gw QPscGW gap (ev) HgTe InSb,InAs InN,GaSb InP,GaAs,CdTe Cu2O ZnTe,CdS ZnSe,CuBr ZnO,GaN ZnS Si Ge,CdO P,Te AlN MgO CaO SrO diamond AlAs,GaP,SiC,AlP AlSb,Se experimental gap (ev) van Schilfgaarde, Kotani, and Faleev, PRL 96 (2006) Silvana Botti Electronic excitations in solar cells 35 / 57

38 How to go beyond standard DFT? GW approaches! Quasiparticle energies within sc-gw for CIS CuInS 2 DFT-LDA G 0 W 0 sc-gw exp. E g In-S S s band In 4 d band CuInSe 2 DFT-LDA G 0 W 0 sc-gw exp. E g (+0.2) In-Se Se s band In 4 d band sc-gw is here sc-cohsex+g 0 W 0 Silvana Botti Electronic excitations in solar cells 36 / 57

39 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

40 Outline How to compare with experiments? 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

41 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) ZnO:Al TCO contact Würth Elektronik GmbH & Co. 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.

42 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

43 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: E v = ev Lany et al., PRB 72, (2005) Metastability caused by the vacancy complex V Se -V Cu Lany et al., JAP 100, (2006) Silvana Botti Electronic excitations in solar cells 41 / 57

44 How to compare with experiments? Is the gap stable under lattice distortion? E g [ev] CuInS 2 Expt u CuInSe 2 Expt u DFT-LDA, G 0 W 0, sc-cohsex, sc-cohsex+g 0 W 0 The gap is not stable! Self-consistency enhances the gap variations Previous corrected-lda (dots) results have LDA slope sc-cohsex only in energies is enough for the gap Silvana Botti Electronic excitations in solar cells 42 / 57

45 How to compare with experiments? Shifts of CuInS 2 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 ρ COHSEX ρ LDA u = 0.2 u = 0.215 u = 0.235 u = 0.

46 How to compare with experiments? Cu-S bond under lattice distortion Contribution of the VBM to ρ COHSEX ρ LDA u = 0.2 u = u = u = 0.25 Small u: the Cu-S bond is weakened Large u: the Cu-S bond is strenghtened Once again V Cu formation is favored at small u Silvana Botti Electronic excitations in solar cells 44 / 57

47 Defects How to compare with experiments? a) Perfect crystal b) V Cu c) V Se d) 2V Cu In Cu (a) (b) DOS (c) (d) Energy (ev) The presence of V Cu opens up the gap! Silvana Botti Electronic excitations in solar cells 45 / 57

48 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 Å E g 0.5 ev Considering both variations of d(cu,s) and [V Cu ] E g 0.04 ev Silvana Botti Electronic excitations in solar cells 46 / 57

49 How to compare with experiments? Quasi-particle corrections for CuInS 2 E GW -E DFT (ev) 0 Bandgap region -2 In-S bond S 3s -4 Cu 3d S 3p In 4d T Conduction bands Cu 3d S 3p Γ N E DFT (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

50 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

51 How to compare with experiments? The long dispute about delafossite gaps The most studied compound is CuAlO 2 : E g [ev] E g indirect E g direct =E g direct -Eg indirect exp. direct gap exp. indirect gap Indirect gap Minimum direct gap at L: dipole allowed Experimental data far from sc-gw calculations! 0 LDA LDA+U B3LYP HSE03 HSE06 G 0 W 0 scgw scgw+p Is sc-gw wrong in this case? Silvana Botti Electronic excitations in solar cells 49 / 57

52 How to compare with experiments? The long dispute about delafossite gaps E g [ev] E g indirect E g direct =E g direct -Eg indirect exp. direct gap exp. indirect gap LDA LDA+U B3LYP HSE03 HSE06 G 0 W 0 scgw scgw+p Experimental data are for optical gap: exciton binding energy 0.5 ev [Laskowski et al. PRB 79, (2009)] Strong lattice polaron effects are expected 1 ev [Bechstedt et al. PRB 72, (2005)] Silvana Botti Electronic excitations in solar cells 50 / 57

53 How to compare with experiments? The long dispute about delafossite gaps All results for CuInO 2 are consistent with results for CuAlO 2 Energy [ev] E g indirect E g direct (Γ) E g direct (L) exp. indirect gap exp. direct gap LDA LDA+U B3LYP HSE03 HSE06 G 0 W 0 scgw Only 2 optical experiments Minimum direct gap at Γ: dipole forbidden [Nie et al. PRL (2002)] Silvana Botti Electronic excitations in solar cells 51 / 57

54 How to compare with experiments? Bands of CuAlO 2 from LDA+U Energy(eV) LDA+U direct gap close to experiment CB are rigidly shifted 0-2 Γ F L Z Γ Silvana Botti Electronic excitations in solar cells 52 / 57

55 How to compare with experiments? Bands of CuAlO 2 from sc-gw calculations 8 Energy(eV) GW corrections strongly k-dependent CBM moves from Γ to L gap becomes quasi-direct direct gap 1.5 ev larger than experiment -2 Γ F L Z Γ Silvana Botti Electronic excitations in solar cells 53 / 57

56 How to compare with experiments? Comparison with hybrid functional calculations Energy(eV) sc-gw HSE03 LDA+U -2.0 Γ F L Z Γ Γ F L Z Γ Γ F L Z Γ Strong differences both in dispersion and energy gaps Are hybrids a good compromise? Silvana Botti Electronic excitations in solar cells 54 / 57

57 How to compare with experiments? Next step: optical spectra... Preliminary results for CuInO 2 : RPA (NLF) scgw(nlf) solid lines: xy component, dashed: z component ε scgw+bse Energy (ev) Strong excitonic effects also for the In compound! Silvana Botti Electronic excitations in solar cells 55 / 57

58 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+G 0 W 0 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 G 0 W 0 ) 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.

59 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 Silvana Botti Electronic excitations in solar cells 57 / 57

60 Thanks! Post-doctoral positions in Lyon Two postdoctoral positions in theoretical and computational Physics are available at the Laboratoire de physique de la matière condensée 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 to Miguel Marques (marques@tddft.org). For more information or to apply please contact Miguel Marques (marques@tddft.org). Silvana Botti Electronic excitations in solar cells 58 / 57

Photoelectronic properties of chalcopyrites for photovoltaic conversion:

Photoelectronic properties of chalcopyrites for photovoltaic conversion: self-consistent GW calculations Silvana Botti 1 LSI, CNRS-CEA-École Polytechnique, Palaiseau, France 2 LPMCN, CNRS-Université Lyon