2018 CAMD Summer School Materials Modelling for Solar Cells: Perovskites and Beyond Prof. Aron Walsh Imperial College London, UK Yonsei University, Korea Materials Design Group: https://wmd-group.github.io @lonepair

Solar Electricity & Fuel Electricity Solar Cells Chemical Energy Solar Fuels High efficiency (20–50%) Low efficiency (< 10%) Physics (electron–hole separation) is easier than chemistry (oxidation/reduction reactions) Fusion Reactor 174,000 Terawatts reaches the Earth’s surface

Fundamentals of Solar Cells • Electromagnetism (light) • Quantum Electrodynamics (light/matter interaction) • Solid State Physics (electronic band theory) • Solid State Chemistry (optimising materials) • Soft Matter Physics (glasses and polymers) • Statistical Mechanics (defects and disorder) • Thermodynamics (device operation and limits) • Electrical Engineering (devices, systems, and grids) • Economics and Politics (realise solar electricity) Slide adapted from J. M. Frost: https://speakerdeck.com/jarvist

Many Photovoltaic Technologies Shockley and Queisser (1961); Polman et al, Science 352, 307 (2016) High performance “Established” Fundamental research Theoretical limit for single-junction cell (2018)

Challenge for Emerging Solar Cells GaAs efficiency is close to the theoretical limit, while Si is cheap. New materials must perform! Metal oxides Cu2 O (6%) Bi2 FeCrO6 (8%) Co3 O4 (<1%) Metal sulphides SnS (5%) Cu2 ZnSnS4 (13%) FeS2 (3%) Metal halides CsSnI3 (10%) CH3 NH3 PbI3 (23%) BiI3 (1%) Examples of materials studied for thin-film photovoltaics (% sunlight to electricity conversion in photovoltaic devices) M. A. Green et al, Solar cell efficiency tables (version 52)

Talk Outline: Solar Energy A. Role of Materials Modelling B. Thin-Film Photovoltaics: • Kesterites (A2 BCX4 ) • Perovskites (ABX3 ) C. Outlook for Materials Design

Thin-Film Solar Cells Cu(In,Ga)Se2 CdTe From indirect (Si) to direct bandgap semiconductors for enhanced light absorption Light absorbing layer is a p-type semiconductor

From Materials to Devices Existing technologies benefited from decades of materials and device optimisation Complex chemical processes in CdTe solar cells: • Cu diffusion • CdCl2 annealing • Cd(S,Te) formation • (Cd,Zn)S formation http://www.nrel.gov/pv/cadmium-telluride-solar-cells.html Cu S,Te mixing Cd,Zn mixing

Modelling Thin-Film Solar Cells Active Solar Absorber • Optical response • Electronic structure • Electron transport • Defect levels Front Electrical Contact • Band offsets • Interfacial states • Interfacial dipoles • Modification layers Back Electrical Contact • Band offsets • Ion diffusion • Interfacial reactions • Modification layers Device Modelling • Efficiency losses • J–V behaviour • Carrier collection • Layer optimisation

Open-Source Community Software http://www.solcore.solar; https://github.com/dalonsoa/solcore5

Reproducible Analysis in Publications https://github.com/WMD-group/hot-carrier-cooling Global movement of #openscience for transparency, reproducibility, and data-sharing

Talk Outline: Solar Energy A. Role of Materials Modelling B. Thin-Film Photovoltaics: • Kesterites (A2 BCX4 ) • Perovskites (ABX3 ) C. Outlook for Materials Design

Brief History of Kesterite Solar Cells Cu2 CdSnS4 cell (1977); Cu2 ZnSnS4 cell (1988); 12.6% Cu2 ZnSn(S,Se)4 record by IBM (2014) Wagner & Bridenbaugh (1977); Ito & Nakazawa (1988); Wang, Mitzi et al (2014)

Kesterite Quaternary Semiconductors 2 4 2 1a×1a×2a zincblende superlattice Charge-conserving substitutions to construct multi-component semiconductors “High-throughput” Density Functional Theory: Phys. Rev. B 79, 165211 (2009) 2+ 2- 1+ 3+ 4+ 2 4 2

• Mixed phases e.g. Cu2 ZnSnS4 à Cu2 SnS3 + ZnS • Cation disorder e.g. Cu-Zn, Cu-Sn, Zn-Sn mixing • Deep level defects i.e. fast non-radiative recombination • Interface reactions e.g. MoS2 and SnS/SnS2 formation Challenging for theory, simulation, and experiment! Issues Facing Kesterite Solar Cells Wallace, Mitzi and Walsh, ACS Energy Letters 2, 776 (2017) Champion solar cells suffer from large voltage deficit, e.g. for CZTS (Eg ~ 1.50 eV), VOC < 0.75 V

Defects in Photovoltaic Materials Point defects in solar cells: J. Park et al, Nature Rev. Mater. 3, 194 (2018) Good: population of charge carriers required for p-n junctions; Bad: voltage loss by e- h+ recombination Defect-mediated recombination often dominates under “1 sun”. Described by 1st order kinetics of the Shockley-Read-Hall (SRH) process (more on this later…)

Polytypes and Stacking Faults SiC and ZnS have a large number of known polytypes Image from: M. Grundmann, Physics of Semiconductors (2006) Labelled with Ramsdell notation ΔE between cubic (ABC) and hexagonal (AB) polytypes is small for tetrahedral semiconductors

Polytypes for Multernary Systems S. Chen et al, Physical Review B 82, 195203 (2010) “Cubic” ABC-derived “Hexagonal” AB-derived Binary AX Zincblende (!" #$%) Wurtzite (P6 3 mc) Ternary ABX2 Chalcopyrite (I" #2d) BeSiN2 (Pna2 1 ) Quaternary A2 BCX4 Kesterite (I" #) Stannite (I" #2m) WZ-Kesterite (Pc) WZ-Stannite (Pmn2 1 )

Polytypes for Multernary Systems S. Chen et al, Physical Review B 82, 195203 (2010) “Cubic” ABC-derived “Hexagonal” AB-derived Binary AX ZnS ZnO Ternary ABX2 CuFeS2 BeSiN2 Quaternary A2 BCX4 Cu2 ZnXS4 Ag2 ZnXS4 (X = Si, Ge, Sn) Cu2 CdXS4 Ag2 CdXS4 (X = Si, Ge, Sn)

Stacking Faults in Kesterites Kattan et al, Nanoscale 8, 14369 (2016); Appl. Mater. Today 1, 52 (2015)

Stacking Faults in Kesterites TEM image of CZTS. Inset atomic model is of CZTS oriented along [110] zone axis. From the group of Klaus Leifer at Uppsala University using samples from Edgardo Saucedo at IREC

Atomic Models of Extended Defects J. Park et al, Phys. Rev. Mat. 2, 041602 (2018) 3D atomic models to describe stacking faults (a-c), a grain boundary (d), and anti-site boundary domains [Cu-Zn à Zn-Cu] (e-f) Jisang Park

DFT Calculation of Extended Defects Formation energy (eV/nm2) J. Park et al, Phys. Rev. Mat. 2, 041602 (2018) Formation energy from an Ising model Shifts in valence (VBO) & conduction (CBO) bands [weak electron barriers] Se HSE06; PAW / plane wave basis in VASP

Types of Point Defects in Kesterites Lattice imperfections formed in thermodynamic equilibrium and/or through materials processing Vacancies VCu , VZn , VSn , VS Interstitials Cui , Zni , Sni , Si Antisites CuZn , CuSn , ZnCu , etc. The copper vacancy and Cu-on-Zn antisite are the dominant acceptor defects responsible for native p- type behaviour of CZTS S. Chen et al, Adv. Mater. 25, 1522 (2013)

Point Defects: Theory and Experiment Calculable from DFT Observable Energy change ΔE/ΔH/ΔG • Heats of formation and concentrations • Diffusion barriers Defect ionisation level (Optical) Optical absorption; photoluminescence; photoconductivity Defect ionisation level (Thermal) Deep-level transient spectroscopy; thermally stimulated conductivity Defect vibrational modes ⍵(q,T) • IR / Raman spectra • Diffusion rates • Recombination rates

SRH: Shockley & Read, Phys. Rev. 87, 835 (1952); Hall, Phys. Rev. 87, 387 (1952) Non-Radiative Carrier Capture SRH analysis: mid-gap defects are most active Beyond: defects levels are not fixed, but vary with the charge state. Non- radiative recombination is a multi-level phonon-emission process

Structural relaxation (electron-phonon coupling) is a critical component of carrier capture Non-Radiative Carrier Capture Q = configuration coordinate [change in local structure with charge state] Huang & Rhys, Proc. RS 204, 406 (1950); Henry & Lang, Phys. Rev. 15, 989 (1977) Radiative recombination [Defect luminescence] Defect in charge states E1 and E2 Non-radiative recombination [Phonon emission]

Revisit: Deep Defects in Cu2 ZnSnS4 [HSE06/DFT supercells including finite-size effects: sxdefectalign] S. Kim et al, ACS Energy Lett. 3, 496 (2018) Defects involving Sn produce the deepest levels. The sulfur vacancy is low energy. It should act as a double donor [VS 2+ + 2e-], but produces no levels in the band gap… inert? Sunghyun Kim Note: quasi-particle energies, not single-particle eigenvalues

VS Assisted Recombination S. Kim et al, ACS Energy Lett. 3, 496 (2018) Kim Recombination Model 1. Population of VS + formed in thermal equilibrium 2. Hole capture VS + to VS ++ under illumination 3. Electron capture to recover VS + (10−13 cm2)* IR Photon Assisted (~0.6 eV) Static approximation: Alkauskas et al, Phys. Rev. B 90, 075202 (2014)

VS Assisted Recombination S. Kim et al, ACS Energy Lett. 3, 496 (2018) Testable Model? 1. Recombination rate should be enhanced by IR light (~2000 nm) 2. Role of VS + could be confirmed by spin (EPR) VS + is associated with Sn(III) species. EPR signal for Sn(III) in ZnS matches a brief 2010 report for CZTS. C. Chory et al, DOI: 10.1002/pssc.200983217 Sn lone pair associated with sulfur vacancy (excess electrons) IR Photon Assisted (~0.6 eV)

Beyond Dilute Defects in Kesterites Cross-section of typical cell [IBM] Cd/Zn mixing Cu/Zn mixing MoS2 /SnS2 formation

Talk Outline: Solar Energy A. Role of Materials Modelling B. Thin-Film Photovoltaics: • Kesterites (A2 BCX4 ) • Perovskites (ABX3 ) C. Outlook for Materials Design

Hybrid Organic–Inorganic Perovskites Brief History (1958) – Photoconductivity in CsPbI3 (Møller) (1978) – Synthesis of CH3 NH3 PbI3 (Weber) (1994) – Metallic transition in CH3 NH3 SnI3 (Mitzi) (2009) – Perovskite dye cell (Miyasaka) (2012) – Planar thin-film solar cell (Snaith) Inorganic CsPbI3 Hybrid CH3 NH3 PbI3 or MAPI

Why Halide Perovskites? Essentials for Solar Cells • Strong optical absorption (Eg ~ 1.6 eV) • Light electron and hole masses (conductive) • Easy to synthesise (cheap and scalable) Advanced Features • Dielectric screening: carrier separation (weak excitons) and transport (low scattering rates) • Slow e-h recombination: low losses, large VOC o Relativistic effects – spin-orbit coupling o Polar nano-domains – dynamic fluctuations o Phonon scattering – limit non-radiative events

Perovskites: Model vs Reality Plastic crystal behaviour probed by Quasi-Elastic Neutron Scattering (P. Barnes, DOI: 10.1038/ncomms8124); 2D IR Spectroscopy (A. Bakulin, DOI: 10.1021/acs.jpclett.5b01555); Inelastic X-ray Scattering (S. Billinge, DOI: 10.1021/acsenergylett.6b00381) with simulations

Intersection of Hard and Soft Matter Jarvist Frost CH3 NH3 PbI3 3D periodic boundary (80–640 atoms) 25 fs per frame 0.5 fs timestep based on PBEsol forces at T=300K “As soft as jelly” J. M. Frost, K. T. Butler, A. Walsh, APL Mater. 2, 081506 (2014) Combination of density functional theory, GW theory, lattice dynamics, molecular dynamics, classical Monte Carlo, continuum device models

Dielectric Response Standard Inorganic Dielectric Organic-Inorganic Dielectrics Microstructure Conductivity Contacts Lattice dynamics Optical response Stat. mechanics Sum of:

Dielectric Response High-frequency from QSGW+SOC Low-frequency from harmonic phonons (DFT/PBEsol) With Mark van Schilfgaarde

“Giant Dielectric Constant” JPCM 20, 191001 (2008) JPCL 5, 2390 (2014) J. M. Frost and A. Walsh, Acc. Chem. Res. 49, 528 (2016)

“Giant Dielectric Constant” JPCM 20, 191001 (2008) JPCL 5, 2390 (2014) J. M. Frost and A. Walsh, Acc. Chem. Res. 49, 528 (2016)

Bananas are Lossy Dielectrics J. F. Scott, J. Phys. Conden. Matter 20, 2 (2007)

Mixed Ion–Electron Conductors Current-voltage hysteresis [Snaith et al, JPCL (2014); Unger et al, EES (2014)] Rapid chemical conversion between halides [Pellet et al, CM (2015); Eperon et al, MH (2015)] Photoinduced phase separation [Hoke et al, CS (2015); Yoon et al, ACS-EL (2016)] Electric field induced phase separation [Xiao et al, NatM (2015); Yuan et al, AEM (2016)] Photo-stimulated ionic conductivity [Xing et al, PCCP (2016); Kim et al, NatM (2018)]

Mixed Ion–Electron Conductors Nature Comm. 6, 8497 (2015); ACS Energy Lett. 3, 1983 (2018) Reservoir of charged point defects (site vacancies) in thermodynamic equilibrium: V- MA , V2- Pb , V+ I A. Walsh et al, Angewandte Chemie 54, 1791 (2015) Figure 3. Iodide ion vacancy migration from DFT calculations (a) Calculated migration Vacancy Ea (eV) I- 0.6 CH3 NH3 + 0.8 Pb2+ 2.3 D ~ 10-12cm2s-1 at T = 300 K [PBEsol/DFT in 768 atom supercell with nudged-elastic band]

Talk Outline: Solar Energy A. Role of Materials Modelling B. Thin-Film Photovoltaic Technologies: • Kesterites (A2 BCX4 ) • Perovskites (ABX3 ) C. Outlook for Materials Design

Solar Absorber Shopping List • Low-cost and non-toxic elements • Direct optical bandgap (1–2 eV) • Easy to deposit and scale-up production • Semiconductor with low carrier concentrations • Tolerant to impurities and microstructure • Chemically stable at interfaces • Workfunction matched to electrical contacts

Solar Absorber Shopping List • Low-cost and non-toxic elements • Direct optical bandgap (1–2 eV) • Easy to deposit and scale-up production • Semiconductor with low carrier concentrations • Tolerant to impurities and microstructure • Chemically stable at interfaces • Workfunction matched to electrical contacts What can we reliably calculate from first-principles modelling?

Does it Absorb Sunlight? Simple descriptor: Eg . Advanced: optical absorption and detailed-balance for a thin-film SLME metric: Yu and Zunger, Phys. Rev. Lett. 108, 068701 (2012) Detailed balance: Blank et al, Phys. Rev. App. 8, 024032 (2017) Materials Chemistry Structure/Composition o Orbital character o Band widths o Band degeneracy o Selection rules

Is it Stable? Experiment (Scragg) Kesterite Unstable CZTS Stable Simple descriptor: ΔHf . Advanced: secondary phases under realistic growth conditions (ΔGf ) Materials Chemistry Structure/Composition o Choice of elements o Stoichiometry o Synthetic routes o Metastability Kesterites: Jackson and Walsh, J. Mat. Chem A 2, 7829 (2014) Perovskites: Zhang et al, Chin. Phys. Lett. 3, 036104 (2018) [arXiv 2014] Cu2 ZnSnS4 à Cu2 S + ZnS + SnS +S(g)

Does it Conduct (p–i–n)? CZTS Stable Simple descriptor: me * and ΔH(q,q’) for key defects. Advanced: self-consistent EF analysis Materials Chemistry Structure/Composition o Band energies o Growth conditions o (Co-)dopants o Solid-solutions Analysis of SnS: Y. Kumagai et al, Phys. Rev. Appl. 6, 014009 (2016) Defect review: J. Park et al, Nature Rev. Mater. 3, 194 (2018) Self-consistent defect cycle

Will Carriers Live or Die? Defect tolerance : Walsh and Zunger, Nature Mater. 16, 964 (2017) Defect review: J. Park et al, Nature Rev. Mater. 3, 194 (2018) Simple descriptor: ΔH(q,q’) point defect levels. Advanced: prediction of carrier capture rates Materials Chemistry Structure/Composition o Redox active ions o Lattice vibrations o Passivation o Post-processing

How to Extract Charge? CZTS Unstable CZTS Stable Simple descriptor: ɸ (workfunction). Advanced: structure matching and interfacial effects Materials Chemistry Structure/Composition o Atomic levels o Coordination o Reactivity o Interface layers QM/MM band energies: D. O. Scanlon et al, Nature Mater. 12, 798 (2013) ELS for perovskites: K. T. Butler et al, J. Mater. Chem. C 4, 1129 (2016) Electronic matching Lattice strain Site overlap for A find B with low Schottky barrier & small lattice mismatch & high atomic overlap

Evolution of Computational Materials CZTS Unstable CZTS Stable Quick-start machine learning guide: K. T. Butler et al, Nature 559, 547 (2018) Can we build a robust figure-of-merit and virtual screening procedure for thin-film solar cells? Potential for combining first-principles predictions with experiments and databases for data-driven materials discovery

Conclusions: Modelling for Solar Cells • Many simulation approaches required to describe range of processes (length and time scales) • First-principles techniques are having impact on emerging photovoltaic technologies • Further developments needed for quantitative predictions to enable true materials discovery Slides: https://speakerdeck.com/aronwalsh news & views e spoiled for urally occurring iodic table give y compounds ry compounds ompounds, each element inations exceed nent system. the number of ALS uest for new functionality tanding of the chemical bond, advances in synthetic chemistry, and large-scale computation, ow become a reality. From a pool of 400 unknown compositions, 15 new compounds have pt the expected structures and properties. Structural prediction Property simulation Targeted synthesis Chemical input Figure 1 | A modular materials design procedure, where an initial selection of chemical elements is subject to a series of optimization and screening steps. Each step may involve prediction of the crystal Near future: