CIGS photovoltaic technology The alternative to silicon solar cells Silvana Botti 1 LSI,

´ CNRS-CEA-Ecole Polytechnique, Palaiseau, France 2 LPMCN, CNRS-Universite ´ Lyon 1, France 3 European Theoretical Spectroscopy Facility

February 17, 2010 – Coimbra

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Collaborators Ecole Polytechnique Julien Vidal, Lucia Reining

Universite´ Lyon 1 Fabio Trani, Miguel Marques

EDF Paris ¨ Olsson, J.-F. Guillemoles Par

CEA Saclay Fabien Bruneval

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Outline

1

Thin-film photovoltaic cells

2

What can we calculate within standard DFT?

3

How to go beyond standard DFT? GW approaches!

4

How to compare with experiments for “real” materials?

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CIGS solar cells

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Thin-film photovoltaic cells

Outline

1

Thin-film photovoltaic cells

2

What can we calculate within standard DFT?

3

How to go beyond standard DFT? GW approaches!

4

How to compare with experiments for “real” materials?

Silvana Botti

CIGS solar cells

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Thin-film photovoltaic cells

Present state of photovoltaic efficiency

from National Renewable Energy Laboratory (USA) Silvana Botti

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Thin-film photovoltaic cells

Shockley-Queisser Limit Detailed balance limit of efficiency of a p-n junction solar cells The sun is assumed to be a blackbody at 6000K The solar cell is assumed to be a blackbody at 300K (cell is uniform in temperature throughout.) The active region is thick enough to absorb all light above the band gap One photon gives rise to one electron-hole pair All recombination is via radiative processes (detailed balance) All photoexcited carrier pairs that do not recombine radiatively are extracted All excited carriers relax to the band edge prior to extraction, relaxation is by creating phonons

Shockley and Queisser, J. Appl. Phys. 32, 510 (1961)

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Thin-film photovoltaic cells

Solar spectrum

Carriers below the gap are not absorbed

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Thin-film photovoltaic cells

Detailed balance limit depends on the gap

Optimum band gap is ≈ 1.2 eV Top efficiency for a single-junction cell at one-sun is ≈ 30% Thermodynamic limit is 68%. Shockley and Queisser, J. Appl. Phys. 32, 510 (1961) Silvana Botti

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Thin-film photovoltaic cells

Solar plant in Moura (2008-2010)

Polycrystalline silicon modules Portugal’s sunny location provides ideal conditions The plant provides 46 MW (62 MW in the 2nd phase), enough to supply approximatley 30,000 homes A windmill provides 2–5 MW Still, a nuclear power plant generates about 1–5 GW Silvana Botti

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Thin-film photovoltaic cells

Solar plants in Spain

In 2008, more than 1000 large-scale plants were constructed and put into service worldwide Spain is world leader in solar power plants Open-space CIS photovoltaic plant in Albacete (2008, 3.26 MW) Good outputs even when temperatures are high or when light is diffuse, e.g. in poor weather Cheaper (thin-films!), better than amorphous silicon and cadmium-telluride thin-films Silvana Botti

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Thin-film photovoltaic cells

Building-Integrated Photovoltaics Projects realised so far do not yet represent the full range of products available on the market: these include integratable crystalline modules, thin-layer modules, transparent and shading modules, solar roof tiles, photovoltaic roof foils or complete solar roofs Playing with light and glass: building-integrated photovoltaics opens new creative opportunities for architects

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Thin-film photovoltaic cells

CIGS properties Cu(In,Ga)(S,Se)2 are among the best absorbers: cheaper to manufact high optical absorption, direct gap ⇒ 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

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Thin-film photovoltaic cells

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

Silvana Botti

Wurth Elektronik GmbH & Co. ¨ Efficiency = 13 %

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Thin-film photovoltaic cells

Modeling photovoltaic materials

Objectives Predict accurate values for fundamental opto-electronical properties of materials Deal with complex materials (large unit cells, defects)

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What can we calculate within standard DFT?

Outline

1

Thin-film photovoltaic cells

2

What can we calculate within standard DFT?

3

How to go beyond standard DFT? GW approaches!

4

How to compare with experiments for “real” materials?

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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)?

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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).

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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).

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What can we calculate within standard DFT?

Kohn-Sham band structure Kohn-Sham (KS) equations   ∇2 KS KS − + vKS (r ) ϕKS i (r) = εi ϕi (r) 2 ρ (r) =

occ. X

2 |ϕKS i (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 =⇒ Kohn-Sham band structures

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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: one often obtains good band dispersions but band gaps are systematically underestimated

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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: one often obtains good band dispersions but band gaps are systematically underestimated

Silvana Botti

CIGS solar cells

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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: one often obtains good band dispersions but band gaps are systematically underestimated

Silvana Botti

CIGS solar cells

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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: one often obtains good band dispersions but band gaps are systematically underestimated

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What can we calculate within standard DFT?

2

MgO

4

CaO

calculated gap (eV)

6

diamond SrO AlN

8

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

LDA Kohn-Sham energy gaps

:LDA

0

experimental gap (eV) van Schilfgaarde, Kotani, and Faleev, PRL 96 (2006)

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What can we calculate within standard DFT?

LDA Kohn-Sham energy gaps for CIS

Eg In-S S s band In 4 d band

CuInS2 DFT-LDA exp. -0.11 1.54 6.5 6.9 12.4 12.0 14.6 18.2

Eg In-Se Se s band In 4 d band

CuInSe2 DFT-LDA exp. -0.29 1.05 5.8 6.5 12.6 13.0 14.7 18.0

www.abinit.org Silvana Botti

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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

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How to go beyond standard DFT? GW approaches!

Outline

1

Thin-film photovoltaic cells

2

What can we calculate within standard DFT?

3

How to go beyond standard DFT? GW approaches!

4

How to compare with experiments for “real” materials?

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How to go beyond standard DFT? GW approaches!

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Solution

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The first step can be substantially more complicated than the second, so in the following we will focus on GW

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!

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Bethe-Salpeter equation for the inclusion of electron-hole interaction

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How to go beyond standard DFT? GW approaches!

Hedin’s equations

Σ

W =G

Γ

Σ

G= G

0

+G

0

ΣG

G

P

P = GGΓ

Γ

Γ=1

+ vPW

+(δΣ

/δ G)

W=v

GGΓ

W

L. Hedin, Phys. Rev. 139 (1965).

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How to go beyond standard DFT? GW approaches!

Green’s functions

Green’s function: propagation of an extra-particle ˆ 1 , t1 )ψˆ† (r 2 , t2 )]|Ni G(r 1 , r 2 , t1 − t2 ) = −ihN|T [ψ(r r2 t 2

r1 t 1

Electron density: ρ (r) = G(r, r, t, t + )

Silvana Botti

Spectral function: A(ω) = 1/πTr {Im G(r 1 , r 2 , ω)}

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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 Σx (r1 , r2 ) = iG(r1 , r2 , t, t + )v (r1 , r2 )

Hartree-Fock

Σ(r1 , r2 , t1 − t2 ) = iG(r1 , r2 , t1 − t2 )W (r1 , r2 , t2 − t1 )

GW

W = −1 v : screened potential (much weaker than v !) Ingredients: KS Green’s function G0 , and RPA dielectric matrix −1 G,G 0 (q, ω) L. Hedin, Phys. Rev. 139 (1965)

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How to go beyond standard DFT? GW approaches!

Standard one-shot GW Kohn-Sham equation: H0 (r )ϕKS (r ) + vxc (r ) ϕKS (r ) = εKS ϕKS (r ) Quasiparticle equation: Z

H0 (r )φQP (r ) + dr 0 Σ r , r 0 , ω = EQP φQP r 0 = EQP φQP (r ) Quasiparticle energies 1st order perturbative correction with Σ = iGW : EQP − εKS = hϕKS |Σ − vxc |ϕKS i Basic assumption: φQP ' ϕKS Hybersten and Louie, PRB 34 (1986); Godby, Schluter and Sham, PRB 37 (1988) ¨ Silvana Botti

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How to go beyond standard DFT? GW approaches!

2

MgO

4

CaO

calculated gap (eV)

6

diamond SrO AlN

8

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

Energy gap within standard one-shot GW

:LDA :GW(LDA)

0

experimental gap (eV) van Schilfgaarde, Kotani, and Faleev, PRL 96 (2006)

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How to go beyond standard DFT? GW approaches!

Quasiparticle energies within G0 W0 for CIS

Eg In-S S s band In 4 d band

CuInS2 DFT-LDA G0 W0 -0.11 0.28 6.5 6.9 12.4 13.0 14.6 16.4

exp. 1.54 6.9 12.0 18.2

Eg In-Se Se s band In 4 d band

CuInSe2 DFT-LDA G0 W0 -0.29 0.25 5.8 6.15 12.6 12.9 14.7 16.2

exp. 1.05 6.5 13.0 18.0

www.abinit.org

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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)

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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)

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How to go beyond standard DFT? GW approaches!

Energy gap within sc-GW

MgO

8

QPscGW gap (eV)

6

4

2

HgTe InSb,InAs InN,GaSb InP,GaAs,CdTe Cu2O ZnTe,CdS ZnSe,CuBr ZnO,GaN ZnS

AlN CaO SrO diamond

AlAs,GaP,SiC,AlP AlSb,Se

Si Ge,CdO P,Te

0

0

2 4 6 experimental gap (eV)

8

van Schilfgaarde, Kotani, and Faleev, PRL 96 (2006) Silvana Botti

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How to go beyond standard DFT? GW approaches!

Quasiparticle energies within sc-GW for CIS

Eg In-S S s band In 4 d band

Eg In-Se Se s band In 4 d band

DFT-LDA -0.11 6.5 12.4 14.6

CuInS2 G0 W0 sc-GW 0.28 1.48 6.9 7.0 13.0 13.6 16.4 18.2

exp. 1.54 6.9 12.0 18.2

DFT-LDA -0.29 5.8 12.6 14.7

CuInSe2 G0 W0 sc-GW 0.25 1.14 6.15 6.64 12.9 13.6 16.2 17.8

exp. 1.05 (+0.2) 6.5 13.0 18.0

sc-GW is here sc-COHSEX+G0 W0 www.abinit.org Silvana Botti

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How to compare with experiments for “real” materials?

Outline

1

Thin-film photovoltaic cells

2

What can we calculate within standard DFT?

3

How to go beyond standard DFT? GW approaches!

4

How to compare with experiments for “real” materials?

Silvana Botti

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How to compare with experiments for “real” materials?

Stability of the gap Is the gap stable under lattice distortion? YES: Experiments measure a stable gap (within 10%) 5 4

Experiment

3 2

Large dispersion of u

1 0

Only hybrid-DFT calculations overlap with experiments

4 Theory Hybrids

3 2 1 0 0.2

0.21

0.22

0.23

0.24

0.25

u

  Anion displacement: u = 1/4 + R2Cu−(S,Se) − R2In−(S,Se) /a2 6= 1/4. Jaffe&Zunger, PRB 29, 1882 (1984); Merino, J. Appl. Phys. 80, 5610 (1996); Jaffe&Zunger, PRB 27, 5176 (1983); Jiang, Sem. Sci. Technol. 23, 025001 (2008). Silvana Botti

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How to compare with experiments for “real” materials?

Stability of the gap 3 DFT-LDA

Eg [eV]

2

CuInS2

Strong variations in DFT-LDA (in agreement with literature)

1

0

0.2

0.21

0.22

u

0.23

0.24

0.25

www.abinit.org

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How to compare with experiments for “real” materials?

Stability of the gap 3 DFT-LDA G0W0

Eg [eV]

2

CuInS2

G0 W0 does not change the slope . . .

1

0

0.2

0.21

0.22

u

0.23

0.24

0.25

www.abinit.org

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How to compare with experiments for “real” materials?

Stability of the gap 3 DFT-LDA G0W0

Eg [eV]

2

CuInS2

. . . except if the gap is already open

1

0

0.2

0.21

0.22

u

0.23

0.24

0.25

www.abinit.org

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How to compare with experiments for “real” materials?

Stability of the gap 3

Eg [eV]

2

DFT-LDA G0W0 scGW

CuInS2

sc-GW enhances the gap variation

1

0

0.2

0.21

0.22

u

0.23

0.24

0.25

www.abinit.org

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How to compare with experiments for “real” materials?

Stability of the gap 3

Eg [eV]

2

DFT-LDA G0W0 scGW HSE06

CuInS2

HSE06 hybrid gives an intermediate slope

1

HSE06 GGA 1 HF,sr 1 GGA,sr Exc = Exc + Ex − Ex 4 4

0

0.2

0.21

0.22

u

0.23

0.24

0.25

www.abinit.org

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How to compare with experiments for “real” materials?

Stability of the gap Is the gap stable under lattice distortion?

NON: sc-GW and hybrid calculations predict even stronger variations than LDA The gap is not stable under lattice distortion alone Note that CIS thin-films favour a non-stoichiometric Cu-poor phase

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How to compare with experiments for “real” materials?

Stability of the gap Is the gap stable under lattice distortion?

NON: sc-GW and hybrid calculations predict even stronger variations than LDA The gap is not stable under lattice distortion alone Note that CIS thin-films favour a non-stoichiometric Cu-poor phase

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How to compare with experiments for “real” materials?

Stability of the gap Is the gap stable under lattice distortion?

NON: sc-GW and hybrid calculations predict even stronger variations than LDA The gap is not stable under lattice distortion alone Note that CIS thin-films favour a non-stoichiometric Cu-poor phase

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How to compare with experiments for “real” materials?

Formation energy of Cu vacancies The formation energy of VCu varies under lattice distortion: ∆Ef = ∆EfDFT − ∆Esc−GW VBM

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How to compare with experiments for “real” materials?

Formation energy of Cu vacancies The formation energy of VCu varies under lattice distortion: ∆Ef = ∆EfDFT − ∆Esc−GW VBM

conduction band minimum (CBM)

valence band maximum (VBM) It is essential to go beyond DFT-LDA LDA+U (blue lines) gives only constant shifts Zhang et al. PRB 57, 9642 (1998); Lany et al. PRB 78, 235104 (2008). Silvana Botti

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How to compare with experiments for “real” materials?

Why is the experimental gap so stable?

A feedback loop can explain the stability of the band gap:

∆u  

Silvana Botti

{

∆VBM

∆Ef

∆[VCu]

∆Eg  

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How to compare with experiments for “real” materials?

Why is the experimental gap so stable?

A feedback loop can explain the stability of the band gap:

∆u  

{

∆VBM

∆Ef

∆[VCu]

∆Eg  

∆Eg '

∂Eg ∆u ∂u

Experimental variation of ∆u = 0.02 ⇒ ∆Eg ≈ 0.65 eV

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How to compare with experiments for “real” materials?

Why is the experimental gap so stable?

A feedback loop can explain the stability of the band gap:

∆u  

{

∆Eg '

∆VBM

∆Ef

∆[VCu]

∆Eg  

∂Eg ∂Eg ∆u + ∆[VCu ] ∂u ∂[VCu ]

Experimental variation of ∆u = 0.02 ⇒ ∆Eg ≈ -0.04 eV

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How to compare with experiments for “real” materials?

Conclusions and perspectives Interpretation of experiments is often not straightforward It is absolutely necessary to go beyond ground-state DFT for systems with d-electrons Methods that go beyond DFT are by now well established (sc)GW and BSE hybrid functionals can be a good compromise In progress now: Defects using VASP (hybrid functionals and G0 W0 ) – supercells up to 300 atoms Absorption spectra from the Bethe-Salpeter equation

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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”, Phys. Rev. Lett. 104, 056401 (2010). J. Vidal, F. Trani, F. Bruneval, M. A. L. Marques and S. Botti, “Effects of electronic and lattice polarization on the band structure of delafossite transparent conductive oxides”, submitted.

We are looking for Ph.D. students at the LPMCN, University of Lyon 1 Please contact us if you are interested! http://www-lpmcn.univ-lyon1.fr/site/ http://www.etsf.eu http://www.abinit.org

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