Killer Defects in Kesterite Thin-Film Solar Cells Prof. Aron Walsh Imperial College London, UK Yonsei University, Korea Materials Design Group: https://wmd-group.github.io @lonepair

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+

• 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

Crystal defects that cause rapid non-radiative recombination even in low concentrations* Hunt for Killer Kesterite Defects Do specific bulk imperfections limit the performance of kesterite solar cells? *“Non Radiative Transitions” A. M. Stoneham, Rep. Prog. Phys. 44, 1251 (1981) A defect level sequentially captures a hole and electron, with the excess energy converted into phonons (heat loss)

Talk Outline: Cu2 ZnSnS4 (CZTS) A. Materials Theory B. Extended Defects C. Point Defects

Density Functional Theory (DFT) Hohenberg-Kohn (1964); Kohn-Sham (1965) Source: F. Bechstedt – Many-body Approach to Electronic Excitations (2015)

First-Principles Modelling in 2018 Remove Approximations length and times scales electron-electron interactions electron-phonon interactions phonon-phonon interactions Accurate Solid-State Properties effective mass to carrier mobility phonon frequencies to lifetimes ground to excited states defects and disorder

Finite Temperature Simulations Standard DFT calculations are athermal: temperature requires lattice vibrations B. Monserrat et al, Appl. Phys. Lett. 112, 193903 (2018) Calculated change in band gap of Cu2 ZnSnS4 Thermal expansion Total change Vibrations [HSE06/DFT total energy and phonons: Allen & Heine e-p interaction]

Lattice Vibrations (Phonons) Discrepancy in calculated and measured high- frequency phonon modes has been solved J. M. Skelton et al, APL Mater. 3, 041102 (2015) [PBEsol/DFT phonons including calculated Raman intensity using Phonopy] Values in cm-1

Lattice Vibrations (Phonons) Discrepancy in calculated and measured high- frequency phonon modes has been solved [Harmonic phonons of Cu2 ZnSnS4 calculated using two DFT functionals] Semi-local Exc Values in cm-1 Hybrid non-local Exc B. Monserrat et al, Appl. Phys. Lett. 112, 193903 (2018)

Talk Outline: Cu2 ZnSnS4 (CZTS) A. Materials Theory B. Extended Defects C. Point Defects

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 Semiconductors 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 Semiconductors 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 STEM-HAADF 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

Talk Outline: Cu2 ZnSnS4 (CZTS) A. Materials Theory B. Extended Defects C. Point Defects

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 Recombination SRH analysis: mid-gap defects are most active Beyond SRH: 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 Recombination 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 supercell calculations including finite-size corrections] 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

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 + (4×10−13 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

Conclusions: Kesterite Solar Cells Group contributions from: Ji-Sang Park, Sunghyun Kim, Suzy Wallace, Samantha Hood, Jarvist Frost, Jonathan Skelton, Adam Jackson Slides: https://speakerdeck.com/aronwalsh 1. Stacking faults may weakly scatter carriers, but are not active recombination centres 2. Redox reactions involving Sn (including VS ) may act as killer defects in operating solar cells