Electronic excitations in materials for photovoltaics

Transcription

1 Electronic excitations in materials for photovoltaics Self-consistent GW and Bethe-Salpeter equation Silvana Botti 1 LSI, École Polytechnique-CNRS-CEA, Palaiseau, France 2 LPMCN, CNRS-Université Lyon 1, France 3 European Theoretical Spectroscopy Facility September 7, 2012 Journée CFCAM Silvana Botti Electronic excitations & photovoltaics 1 / 37

2 Outline 1 Cu-based absorbers for thin-film solar cells 2 Why do we need to go beyond standard DFT? 3 Examples of calculations Stability of the CIGS band gap Optical spectra of CIGS from Bethe-Salpeter Engeneering direct gap silicon 4 Conclusions and perspectives Silvana Botti Electronic excitations & photovoltaics 2 / 37

3 Outline thin-film solar cells 1 Cu-based absorbers for thin-film solar cells 2 Why do we need to go beyond standard DFT? 3 Examples of calculations 4 Conclusions and perspectives Silvana Botti Electronic excitations & photovoltaics 3 / 37

4 thin-film solar cells Chalcogenide thin-film solar cell Devices have to fulfill 2 functions: Photogeneration of electron-hole pairs Separation of charges to generate a current Würth Elektronik GmbH & Co. Efficiency = 13 % Molybdenum back contact CIGS layer (p-type layer) CdS layer (n-type layer) ZnO:Al TCO contact Silvana Botti Electronic excitations & photovoltaics 4 / 37

5 thin-film solar cells Chalcogenide thin-film solar cell Devices have to fulfill 2 functions: Photogeneration of electron-hole pairs Separation of charges to generate a current Würth Elektronik GmbH & Co. Efficiency = 13 % Molybdenum back contact CIGS layer (p-type layer) CdS layer (n-type layer) ZnO:Al TCO contact Silvana Botti Electronic excitations & photovoltaics 4 / 37

6 thin-film solar cells Chalcogenide thin-film solar cell Devices have to fulfill 2 functions: Photogeneration of electron-hole pairs Separation of charges to generate a current Cu(In,Ga)(S,Se) 2 (CIGS) optimal bandgap for high efficiency high optical absorption self-doping with native defects extraordinary stability under operating conditions Würth Elektronik GmbH & Co. Efficiency = 13 % Molybdenum back contact CIGS layer (p-type layer) CdS layer (n-type layer) ZnO:Al TCO contact Silvana Botti Electronic excitations & photovoltaics 4 / 37

7 thin-film solar cells Chalcogenide thin-film solar cell Devices have to fulfill 2 functions: Photogeneration of electron-hole pairs Separation of charges to generate a current Cu 2 ZnSn(S,Se) 4 (CZTS) very similar electronic and optical properties only abundant and non-toxic elements Würth Elektronik GmbH & Co. Efficiency = 13 % Molybdenum back contact CIGS layer (p-type layer) CdS layer (n-type layer) ZnO:Al TCO contact Silvana Botti Electronic excitations & photovoltaics 4 / 37

8 thin-film solar cells Modeling electronic excitations in complex systems Objectives Predict accurate values for fundamental opto-electronical properties: gap, absorption spectra, e-h pairs,... excited states Simulate real materials: d-electrons, nanostructured systems, defects, doping, interfaces large unit cells Cu-based absorbers are not simple sp compounds! Find a compromise between accuracy and computational effort Silvana Botti Electronic excitations & photovoltaics 5 / 37

9 thin-film solar cells Modeling electronic excitations in complex systems Objectives Predict accurate values for fundamental opto-electronical properties: gap, absorption spectra, e-h pairs,... excited states Simulate real materials: d-electrons, nanostructured systems, defects, doping, interfaces large unit cells Cu-based absorbers are not simple sp compounds! Find a compromise between accuracy and computational effort Silvana Botti Electronic excitations & photovoltaics 5 / 37

10 Outline Theoretical approaches 1 Cu-based absorbers for thin-film solar cells 2 Why do we need to go beyond standard DFT? 3 Examples of calculations 4 Conclusions and perspectives Silvana Botti Electronic excitations & photovoltaics 6 / 37

11 Theoretical approaches State-of-the-art of theory computational cost # atoms Standard DFT (LDA,GGAs): severe underestimation of gaps, often good structural properties, bad localized (d and f ) states DFT + model U: corrects localization of d states, usually better gaps, reliability depends too much on the system Hybrid functionals: good gaps (unfortunately precision not systematic), excellent structural properties, better localized states GW: excellent band structures, excellent localized states, self-consistent screening, hard to access to total energies accuracy Silvana Botti Electronic excitations & photovoltaics 7 / 37

12 Theoretical approaches State-of-the-art of theory computational cost # atoms Standard DFT (LDA,GGAs): severe underestimation of gaps, often good structural properties, bad localized (d and f ) states DFT + model U: corrects localization of d states, usually better gaps, reliability depends too much on the system Hybrid functionals: good gaps (unfortunately precision not systematic), excellent structural properties, better localized states GW: excellent band structures, excellent localized states, self-consistent screening, hard to access to total energies accuracy Silvana Botti Electronic excitations & photovoltaics 7 / 37

13 Theoretical approaches State-of-the-art of theory computational cost # atoms Standard DFT (LDA,GGAs): severe underestimation of gaps, often good structural properties, bad localized (d and f ) states DFT + model U: corrects localization of d states, usually better gaps, reliability depends too much on the system Hybrid functionals: good gaps (unfortunately precision not systematic), excellent structural properties, better localized states GW: excellent band structures, excellent localized states, self-consistent screening, hard to access to total energies accuracy Silvana Botti Electronic excitations & photovoltaics 7 / 37

14 Theoretical approaches State-of-the-art of theory computational cost # atoms Standard DFT (LDA,GGAs): severe underestimation of gaps, often good structural properties, bad localized (d and f ) states DFT + model U: corrects localization of d states, usually better gaps, reliability depends too much on the system Hybrid functionals: good gaps (unfortunately precision not systematic), excellent structural properties, better localized states GW: excellent band structures, excellent localized states, self-consistent screening, hard to access to total energies accuracy Silvana Botti Electronic excitations & photovoltaics 7 / 37

15 Theoretical approaches Band structures of kesterite Cu 2 ZnSnS Energy (ev) S3p-(Zn,Sn)s CBM VBM antibonding S3p-Cu3d bonding self-consistent GW standard DFT -16 T Γ N (Sn,Zn)-S S 3s hybrids DFT+U T Γ N -16 SB, D. Kammerlander and M.A.L. Marques, APL 98, (2011) Silvana Botti Electronic excitations & photovoltaics 8 / 37

16 Solution Theoretical approaches 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 However, these many-body approaches are computationally expensive! Silvana Botti Electronic excitations & photovoltaics 9 / 37

17 Theoretical approaches Green s function and Hedin s equations W Σ = GWΓ Σ G=G 0 +G 0 Σ G G Hedin s equations should be solved self-consistently W = v + vpw P P = GG P = GGΓ Γ Γ=1+(δΣ/δG)GGΓ sccohsex+g 0 W 0, QPscGW V. Faleev et al., PRL 93, (2004); Bruneval et al. PRB 74, (2006) Silvana Botti Electronic excitations & photovoltaics 10 / 37

18 Theoretical 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 & photovoltaics 11 / 37

19 Theoretical approaches Perturbative GW: best G, best W 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&Louie, PRB 34 (1986); Godby, Schlüter&Sham, PRB 37 (1988) Silvana Botti Electronic excitations & photovoltaics 12 / 37

20 Theoretical approaches Perturbative GW: best G, best W 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&Louie, PRB 34 (1986); Godby, Schlüter&Sham, PRB 37 (1988) Silvana Botti Electronic excitations & photovoltaics 12 / 37

21 Theoretical 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 ) Hybrid functionals (e.g. Fuchs et al. 2007, Rödl et al. 2009) Self-consistent approaches: GWscQP scheme (Faleev et al. 2004) sccohsex scheme (Hedin 1965, Bruneval et al. 2005) Our choice is to get a better starting point for G 0 W 0 using sccohsex Also working on improved hybrids! (Marques et al. 2011) L. Hedin and S. Lundqvist, Solid State Phys. 23, 1 (1969) Silvana Botti Electronic excitations & photovoltaics 13 / 37

22 Theoretical 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 ) Hybrid functionals (e.g. Fuchs et al. 2007, Rödl et al. 2009) Self-consistent approaches: GWscQP scheme (Faleev et al. 2004) sccohsex scheme (Hedin 1965, Bruneval et al. 2005) Our choice is to get a better starting point for G 0 W 0 using sccohsex Also working on improved hybrids! (Marques et al. 2011) L. Hedin and S. Lundqvist, Solid State Phys. 23, 1 (1969) Silvana Botti Electronic excitations & photovoltaics 13 / 37

23 Theoretical 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 ) Hybrid functionals (e.g. Fuchs et al. 2007, Rödl et al. 2009) Self-consistent approaches: GWscQP scheme (Faleev et al. 2004) sccohsex scheme (Hedin 1965, Bruneval et al. 2005) Our choice is to get a better starting point for G 0 W 0 using sccohsex Also working on improved hybrids! (Marques et al. 2011) L. Hedin and S. Lundqvist, Solid State Phys. 23, 1 (1969) Silvana Botti Electronic excitations & photovoltaics 13 / 37

24 Theoretical approaches COHSEX: approximation to GW self-energy Statically 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) Induced classical potential due to an extra point charge: 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 )] L. Hedin and S. Lundqvist, Solid State Phys. 23, 1 (1969); Bruneval et al. PRL 97, (2006); Gatti et al. PRL 99, (2007) Silvana Botti Electronic excitations & photovoltaics 14 / 37

25 Theoretical approaches Technical problem: convergence with bands GW codes usually require sums over virtual states. To speed-up convergence we use the trick of Bruneval and Gonze. Not just a technical point. Without any tricks the convergence is very slow, leading to an underestimation of the gaps. Using a value of 9.5 Ha, we could do our calculations using only 200 bands for CuInO 2. F. Bruneval and X. Gonze, PRB 78, (2008) A. Berger, L. Reining and F. Sottile, PRB 82, (R) (2010) F. Trani, J. Vidal, SB, M.A.L. Marques, PRB 82, (2010) Silvana Botti Electronic excitations & photovoltaics 15 / 37

26 Outline Examples of calculations 1 Cu-based absorbers for thin-film solar cells 2 Why do we need to go beyond standard DFT? 3 Examples of calculations Stability of the CIGS band gap Optical spectra of CIGS from Bethe-Salpeter Engeneering direct gap silicon 4 Conclusions and perspectives Silvana Botti Electronic excitations & photovoltaics 16 / 37

27 Examples of calculations Stability of the CIGS band gap Anion displacement of CuInS 2 Body-centered tetragonal cell The anion displacement u defines the position of the anion (S,Se) in the conventional cell u = a 2 (R 2 Cu (S,Se) R2 (In,Ga) (S,Se) ) u 1 4 Silvana Botti Electronic excitations & photovoltaics 17 / 37

28 Examples of calculations Stability of the CIGS band gap Anion displacement of CuInS 2 a [Å] GGA LDA GGA+U B3LYP HSE03 HSE06 PBE u 0.23 HF+c Experiments: large dispersion of values of u Theory: even larger dispersion! b u Hybrids and GGA+U in experimental range J. Vidal, S. Botti, P. Olsson, J-F. Guillemoles, L. Reining, PRL 104, (2010) Silvana Botti Electronic excitations & photovoltaics 17 / 37

29 Examples of calculations Dependence of the gap on u Stability of the CIGS band gap 3 2 CuInS 2 DFT-LDA G 0 W 0 scgw HSE06 HSE06 ε 0 E g [ev] 1 0 The self-consistent screening is the essential ingredient to describe the variation of the gap u J. Vidal, S. Botti, P. Olsson, J-F. Guillemoles, L. Reining, PRL 104, (2010) M.A.L. Marques, J. Vidal, M.J.T. Oliveira, L. Reining, SB, PRB 83, (2011) Silvana Botti Electronic excitations & photovoltaics 18 / 37

30 Hybrid functionals Examples of calculations Stability of the CIGS band gap The experimental values of some quantities lie often between they Hartree-Fock and DFT (LDA or GGA) values. So, we can try to mix, or to hybridize both theories. 1 Write an energy functional: E xc = ae Fock [ϕ i ] + (1 a)e DFT [n] 2 Minimize energy functional w.r.t. to the orbitals: v xc (r, r ) = av Fock (r, r ) + (1 a)v DFT (r) Silvana Botti Electronic excitations & photovoltaics 19 / 37

31 Examples of calculations What is the mixing parameter? Stability of the CIGS band gap Let us look at the quasi-particle equation: ] [ v ext(r) + v H (r) φ QP i (r)+ d 3 r Σ(r, r ; ε QP i COHSEX: occ Σ = Hybrids occ Σ = i i φ QP i φ QP i )φ QP i (r ) = ε QP (r)φ QP (r )W (r, r ; ω = 0) + δ(r r )Σ COH (r) i i φ QP (r)φ QP (r )a v(r r ) + δ(r r )(1 a) v DFT (r) i i (r ) = a 1/ɛ Silvana Botti Electronic excitations & photovoltaics 20 / 37

32 Examples of calculations Does it work (a = 1/ɛ )? Stability of the CIGS band gap 1/ε PBE y=x optimal mixing Optimal mixing obtained with a PBE0 form. Silvana Botti Electronic excitations & photovoltaics 21 / 37

33 Examples of calculations Does it work (a = 1/ɛ )? Stability of the CIGS band gap Errors: PBE (46%), Hartree-Fock (230%), PBE0 (27%), PBE0ɛ (16.53%) Theoretical gap (ev) y=x PBE PBE0 PBE0ε Experimental gap (ev) Silvana Botti Electronic excitations & photovoltaics 22 / 37

34 Can we do better? Examples of calculations Stability of the CIGS band gap Screening is related to the gap. So, if we have an estimator of the gap of the material, we can also get an estimator of the dielectric constant. There are several local estimators on the market: G = 1 8 n 2 /n 2 (Gutle et al. 1999) n /n (Heyd et al. 2003; Krukau et al. 2008) τ W = n 2 /8n (Jaramillo et al. 2003) These are however, local estimators and we need a global estimator. The solution is averaging. We follow the idea of the Tran and Blaha meta-gga and define ḡ = 1 d 3 r V cell cell F. Tran and P. Blaha, Phys. Rev. Lett. 102, (2009) n(r) n(r) Silvana Botti Electronic excitations & photovoltaics 23 / 37

35 Examples of calculations Is there a correlation? Stability of the CIGS band gap optimal mixing fit g Fit: ḡ. Error in the gaps: 14.37% Can one also do it with HSE? Silvana Botti Electronic excitations & photovoltaics 24 / 37

36 Results - Summary Examples of calculations Stability of the CIGS band gap exp. PBE HF+c PBE0 PBE0ɛ PBE0 mix HSE06 HSE06 mix TB09 G 0 W 0 Ne Ar Kr Xe C Si Ge LiF LiCl MgO SiC BN GaN GaAs AlP ZnS CdS AlN SiO MoS ZnO (%) Other properties (structural, band dispersions, etc.)? Silvana Botti Electronic excitations & photovoltaics 25 / 37

37 Examples of calculations Density-based mixing for hybrids Stability of the CIGS band gap The ab-initio determination of the mixing constant is: Cheap and easy to calculate Physically motivated Improves considerably electronic-gaps obtained with hybrid functionals Both small-gap and large-gap (rare-gases) materials can be well-described It is an energy functional all properties can be in principle calculated The solution to the size-consistency problem not yet implemented and tried Need to obtain more properties to get a better working knowledge of the functional Still has problems with d-electron systems Silvana Botti Electronic excitations & photovoltaics 26 / 37

38 Examples of calculations Density-based mixing for hybrids Stability of the CIGS band gap The ab-initio determination of the mixing constant is: Cheap and easy to calculate Physically motivated Improves considerably electronic-gaps obtained with hybrid functionals Both small-gap and large-gap (rare-gases) materials can be well-described It is an energy functional all properties can be in principle calculated The solution to the size-consistency problem not yet implemented and tried Need to obtain more properties to get a better working knowledge of the functional Still has problems with d-electron systems Silvana Botti Electronic excitations & photovoltaics 26 / 37

39 Examples of calculations Density-based mixing for hybrids Stability of the CIGS band gap The ab-initio determination of the mixing constant is: Cheap and easy to calculate Physically motivated Improves considerably electronic-gaps obtained with hybrid functionals Both small-gap and large-gap (rare-gases) materials can be well-described It is an energy functional all properties can be in principle calculated The solution to the size-consistency problem not yet implemented and tried Need to obtain more properties to get a better working knowledge of the functional Still has problems with d-electron systems Silvana Botti Electronic excitations & photovoltaics 26 / 37

40 Examples of calculations Stability of the CIGS band gap Measurements of band gap in Cu-poor CuInSe 2 Experiments: the band gap decreases slightly for Cu/In < 1 Theory: the band gap increases when [V Cu ] increases L. Gütay, D. Regesch, J.K. Larsen, Y. Aida, V. Depredurand, A. Redinger, S. Caneva, S. Schorr, C. Stephan, J. Vidal, SB, S. Siebentritt, PRB 86, (2012) Silvana Botti Electronic excitations & photovoltaics 27 / 37

41 Examples of calculations Stability of the CIGS band gap What are we missing? Structural variations! The feedback loop model can explain the stability of the band gap: u E g H f (V Cu ) [V Cu ] E g J. Vidal, SB, P. Olsson, J-F. Guillemoles, L. Reining, PRL 104, (2010); L. Gütay, D. Regesch, J.K. Larsen, Y. Aida, V. Depredurand, A. Redinger, S. Caneva, S. Schorr, C. Stephan, J. Vidal, SB, S. Siebentritt, PRB 86, (2012) Silvana Botti Electronic excitations & photovoltaics 28 / 37

42 Examples of calculations Stability of the CIGS band gap What are we missing? Structural variations! E g (u, [V Cu ]) = { Eg [V Cu ] + E } g u [V Cu ] u [V Cu ] We extract the partial derivatives from ab initio calculations for the primitive cell and 15, 32, 63 atom supercells: For 0.95 < Cu/In < 1 (experimental range): Considering only the variation of [V Cu ] E g 0.13 ev Considering variations of u and [V Cu ] E g ev J. Vidal, SB, P. Olsson, J-F. Guillemoles, L. Reining, PRL 104, (2010); L. Gütay, D. Regesch, J.K. Larsen, Y. Aida, V. Depredurand, A. Redinger, S. Caneva, S. Schorr, C. Stephan, J. Vidal, SB, S. Siebentritt, PRB 86, (2012) Silvana Botti Electronic excitations & photovoltaics 28 / 37

43 Examples of calculations Optical spectra of CIGS from Bethe-Salpeter Bethe-Salpeter equation: electron-hole interaction Absorption can be obtained from the 4-point reducible polarizability L: ɛ M = 1 lim v(q)λ drdr e iq (r r ) L(r, r, r, r ; ω) q 0 that satisfies the Bethe-Salpeter equation (BSE) rapidly varying L = L 0 + L 0 (4 v 4 W ) L slowly varying with 4 v(1, 2, 3, 4) = δ(1, 2)δ(3, 4) v(1, 3) and 4 W (1, 2, 3, 4) = δ(1, 3)δ(2, 4)W (1, 2) The ingredients are: Kohn-Sham or quasiparticle states (sc)gw corrected energies RPA screening matrix ε 1 GG (q) Salpeter and Bethe, Phys. Rev. 84, 1232 (1951) Silvana Botti Electronic excitations & photovoltaics 29 / 37

44 Examples of calculations Optical spectra of CIGS from Bethe-Salpeter Bethe-Salpeter equation: electron-hole interaction Absorption can be obtained from the 4-point reducible polarizability L: ɛ M = 1 lim v(q)λ drdr e iq (r r ) L(r, r, r, r ; ω) q 0 that satisfies the Bethe-Salpeter equation (BSE) rapidly varying L = L 0 + L 0 (4 v 4 W ) L slowly varying with 4 v(1, 2, 3, 4) = δ(1, 2)δ(3, 4) v(1, 3) and 4 W (1, 2, 3, 4) = δ(1, 3)δ(2, 4)W (1, 2) The ingredients are: Kohn-Sham or quasiparticle states (sc)gw corrected energies RPA screening matrix ε 1 GG (q) Salpeter and Bethe, Phys. Rev. 84, 1232 (1951) Silvana Botti Electronic excitations & photovoltaics 29 / 37

45 Examples of calculations Optical spectra of CIGS from Bethe-Salpeter Optical absorption of CuGaSe 2 Need for speed-up in solving Bethe-Salpeter equation: we use a double-grid method using Wannier interpolation 20 Absorption ε exp. Alonso et al. Bethe-Salpeter exp. Levcenko et al. 5 GW-RPA Energy [ev] D. Kammerlander, SB, M.A.L. Marques, A. Marini, C. Attaccalite, accepted in Phys. Rev. B (2012) Silvana Botti Electronic excitations & photovoltaics 30 / 37

46 Examples of calculations Engeneering direct gap silicon New low-energy sp 3 phases of silicon Structural search using minima hopping method (MHM) Imma (2) R8 BC8 P-1 Energy/atom (ev) C222 1 P2 1 /c Cmcm M-10 Z M-12 clathrate R8 and BC8 phases observed and calculated Si-VIII, Si-IX, Si-XIII observed but not yet fully characterized BCT, ST12, Ibam predicted in literature diamond Volume/atom (A 3 ) SB, J.A. Flores-Livas, M. Amsler, S. Goedecker, M.A.L. Marques, submitted (2012) Silvana Botti Electronic excitations & photovoltaics 31 / 37

47 Examples of calculations Minima hopping method Engeneering direct gap silicon The system is moved from one configuration to the next by consecutive molecular dynamics escape steps and geometry relaxations Initial velocities for dynamics are aligned along soft-mode directions to favor the escape to low-enthalpy configurations Revisiting already known structures is avoided by a feedback mechanism S. Goedecker, J. Chem. Phys. 120, 9911 (2004) M. Amsler and S. Goedecker, J. Chem. Phys. 133, (2010) Silvana Botti Electronic excitations & photovoltaics 32 / 37

48 Examples of calculations 3 Engeneering direct gap silicon New low-energy sp phases of silicon P2/m Cmcm C2221 P-1 P21 /c Imma Silvana Botti Electronic excitations & photovoltaics 33 / 37

49 Examples of calculations Engeneering direct gap silicon Optical absorption of the new phases Absorption (ε 2 ) AM 1.5 diamond M-10 C222 1 Imma Cmcm P-1 P2 1 /c strong absorption in the visible indirect band gaps of more than 1 ev absorbed irradiance close to CIGS E (ev) SB, J.A. Flores-Livas, M. Amsler, S. Goedecker, M.A.L. Marques, submitted (2012) Silvana Botti Electronic excitations & photovoltaics 34 / 37

50 Outline Conclusions and perspectives 1 Cu-based absorbers for thin-film solar cells 2 Why do we need to go beyond standard DFT? 3 Examples of calculations 4 Conclusions and perspectives Silvana Botti Electronic excitations & photovoltaics 35 / 37

51 Conclusions and perspectives Conclusions and perspectives Interpretation of experiments is not straightforward coupled effects! Methods beyond ground-state DFT are well established and absolutely necessary for systems with d-electrons Improvement of efficiency of scgw + BSE calculations New frontiers: structural search to design better materials and study phase diagrams with minima hopping method Silvana Botti Electronic excitations & photovoltaics 36 / 37

52 Thanks! Thanks to all collaborators Miguel Marques, David Kammerlander (LPMCN, Lyon) Micael Oliveira (University of Coimbra, Portugal) Claudio Attaccalite (Néel, Grenoble), Andrea Marini (CNR, Rome) Lucia Reining (LSI - ETSF, Ecole Polytechnique, Palaiseau) Julien Vidal (King s college, London) Jean-François Guillemoles (IRDEP, CNRS/EDF/ENSCP, Paris) Pär Olsson (Royal Institute of Technology, Stockholm) Susanne Siebentritt and coworkers (University of Luxembourg) Visit our group home page: Silvana Botti Electronic excitations & photovoltaics 37 / 37