Quantum Mechanochemical Coupling in Halide Perovskites Prof. Aron Walsh Imperial College London, UK Yonsei University, Korea Electric polarisation fields in CH3 NH3 PbI3 (MAPI)

Chemistry of Halide Perovskites ABX3 compounds with flexibility for atomic or molecular A, B, and X components Valence rules for 1:1:3 compounds X = 2- (Oxides; A + B = 6+) • A = 1+, B = 5+ (e.g. KTaO3 ) • A = 2+, B = 4+ (e.g. SrTiO3 ) • A = 3+, B = 3+ (e.g. GdFeO3 ) X = 1- (Halides; A + B = 3+) • A = 1+, B = 2+ (e.g. CsSnI3 ) Electrostatic analysis: J. M. Frost et al., Nano Letters 14, 2584 (2014) A = CH3 NH3 +

Chemistry of Halide Perovskites Double Perovskites (A2 BB’X6 ) e.g. 2Sn(II) à Ag(I) + Bi(III) e.g. 2Pb(II) à In(I) + Bi(III) Indirect band gaps / Phase competition / Order-disorder Layered Perovskites (Ax By Xz ) e.g. Sn(II) à Bi(III) • A3 B2 X9 , A2 BX4 types • <100>, <110> and <111> sequences Potential issues with double perovskites: ACS Energy Lett. 1, 949 (2016)

Physics of Halide Perovskites Principles of Chemical Bonding and Band Gap Engineering in Hybrid Halide Perovskites, J. Phys. Chem. C. 119, 5755 (2015) Semiconductors with strong optical absorption, light carrier masses, efficient dielectric screening Photovoltaic device consequences • Weak exciton binding (EB < kB T in 1:1:3 compounds) • High carrier mobility (phonon scattering limited) • Semiconductor alloys (on A, B, and X sites)

Semiconductors with a Twist Current-voltage hysteresis Snaith et al, JPCL (2014); Unger et al, EES (2014) Rapid chemical conversion between halides Pellet et al, CoM (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 Yang et al, AChemie (2015); Kim et al, NatM (2018)

Semiconductors with a Twist Mixed ionic-electronic charge transport Ionic Conduction of the Perovskite-Type Halides Ionic Conductivity of CsPbCl3 and CsPbBr3 Large Photoeffect on Ion Conduction in Perovskites

Semiconductors with a Twist Nature Comm. 6, 8497 (2015); ACS Energy Lett. 3, 1983 (2018) Reservoir of charged point defects in thermodynamic equilibrium, e.g. V- MA , V2- Pb , V+ I A. Walsh et al, Angew. 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 ~ 10-12 cm2s-1 at T = 300 K [PBEsol/DFT in 768 atom supercell with nudged-elastic band] Bulk diffusion barrier

Semiconductors with a Twist Phonon mode assignments: PCCP 18, 27051 (2016) Vibrations, librations, and rotations of molecular components inside the crystals Rocking MA+ mode at 2.5 THz Animation of calculated phonon eigenvector (PBEsol/Phonopy)

Semiconductors with a Twist Quasi-elastic neutron scattering [Piers Barnes]: N. Comm. (2015) 2D IR spectroscopy [Artem Bakulin]: JPCL (2015) Inelastic X-ray scattering [Simon Billinge]: ACS Energy Lett. (2016) Inelastic neutron scattering [Mike Toney]: PNAS (2018) Vibrations, librations, and rotations of molecular components inside the crystals 30HE, United Kingdom in ls. he nd ve py nic Librations Rotations Theory ✖ Experiment

Talk Motivation and Outline Does crystal strain influence the operation and performance of halide perovskite solar cells? A. Background B. Perfect crystal response C. Imperfect crystal response

Polarisation and Strain in Crystals Ferroelectricity – switchable crystal polarisation Ferroelasticity – switchable crystal strain Strain (ε) hysteresis Polarisation (P) hysteresis

Polarisation and Strain in Crystals Ferroelectricity – switchable crystal polarisation Ferroelasticity – switchable crystal strain Strain (ε) hysteresis Polarisation (P) hysteresis Can be coupled through the piezoelectric effect (where crystal symmetry allows) Material Ferroelectric Ferroelastic BaTiO3 Yes Yes LiH3 (SeO3 )2 Yes No YBa2 Cu3 O7-x No Yes Ferroelastic domains in YBa2 Cu3 O7-x Group theory can aid classification, but chemistry determines the magnitude Aizu, PRB 2, 754 (1970)

Ferroelectric Pb Halide Perovskites Paper titles from the literature on one material!

Ferroelectric Pb Halide Perovskites Paper titles from the literature on one material! Some analysis misled by polarisation signatures of interface charging, ion transport and/or crystal strain

Ferroelectric Pb Halide Perovskites Room T phase of CH3 NH3 PbI3 is tetragonal with reports of polar and non-polar space groups M. T. Weller et al, Chem. Comm. 51, 4180 (2015) Non-polar: I4/mcm Powder neutron diffraction (ISIS,UK) Molecular orientational disorder above 160K a0a0c- Glazer tilting pattern

Ferroelectric Pb Halide Perovskites Room T phase of CH3 NH3 PbI3 is tetragonal with reports of polar and non-polar space groups Garten et al, Science Advances 5, eaas9311 (2019) Single crystal XRD Averaged over space and time Local structure is hidden Polar Non-polar

Non-Ferroelectric Pb Halide Perovskites Local symmetry breaking (polar nanodomains) but paraelectric over longer ranges [Led by Simon Billinge] A. N. Beecher et al, ACS Energy Lett. 1, 880 (2016) Fits of pair-distribution function data to three space groups over two length scales CH3 NH3 PbI3 at T = 350 K

Crystal strain patterns have a complex heterogeneity across multiple length scales “Supergrains” <110> quiver plot Nanofocus XRD at ESRF Micro-XRD at ALS Over 20 µm: 0.3% strain [Led by Sam Stranks] T. W. Jones et al, Energy and Environ. Sci. 12, 596 (2019) Strain in Pb Halide Perovskite Films

Origins of Strain in Halide Perovskites • Transformational – variation in crystal orientation, e.g. following the cubic-to- tetragonal phase transition (a=b≠c) • Compositional – variation in distribution of A, B, or X species, e.g. Br-rich regions in (Br,I) solid-solutions • Interfacial – mesoporous metal oxide substrate likely to influence strain gradients in thin halide perovskite films

[Image] Nat. Comm. 8, 14547 (2017); J. Phys. Chem. C 120, 5724 (2016) Twin domains in CH3 NH3 PbI3 as a result of cubic- to-tetragonal phase transition around 57℃ Cubic (70℃) Tetragonal (25℃ ) 1µm 1µm (110) domains (TEM, SAED) Reversible with T Δa/a~0.3% Domains form to minimise stress Transformational Strain

Transformational Strain “Twinning in ferroelectric and ferroelastic ceramics: stress relief” G. Arlt, J. Mater. Sci. 25, 2655 (1990) Same features observed in BaTiO3 – domains vary with grain size and shape distribution; sensitive to electron beam intensity in halide perovskites BaTiO3 CH3 NH3 PbI3

Ferroelastic Response of Domains CH3 NH3 PbI3 Perovskites: Ferroelasticity Revealed E. Strelcov et al, Science Advances 3, e1602165 (2017) Response to applied stress (polarised light micrograph) Beyond stress, perovskite structure also responds to electric fields (electrostriction) and light (photostriction) – also reversible and reproducible?

Talk Motivation and Outline Does crystal strain influence the operation and performance of perovskite solar cells? A. Background B. Perfect crystal response C. Imperfect crystal response

Unusually, Pb and Sn halides have positive bandgap deformation due to filled cation s2 band Band Gap Deformation in CH3 NH3 PbI3 Deformation potential: J. M. Frost et al., Nano Letters 14, 2584 (2014) Pressure dependence: T. Wang et al, EES 10, 509 (2017) Deformation potential: • ⍺ V = 2.5 eV • Dilation increases Eg • Compression decreases Eg • Behaviour also seen with T and P 0.5% volume change: Eg ± 13 meV Ehrler group (AMOLF) HSE06+SOC

Band Gap Deformation in CH3 NH3 PbI3 Unixial behaviour Same magnitude of Eg change with uniaxial strain in CH3 NH3 PbI3 E&ES 12, 596 (2019) Unusually, Pb and Sn halides have positive bandgap deformation due to filled cation s2 band Youngkwang Jung

Talk Motivation and Outline Does crystal strain influence the operation and performance of perovskite solar cells? A. Background B. Perfect crystal response C. Imperfect crystal response

Defects: Equilibrium Property of Crystals Point defects minimise the Gibbs free energy of a crystal – balance between enthalpic cost of bond breaking and entropic gain from disorder n = N exp −ΔGDefect k B T ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ Defect concentration Defect energy Lattice sites Frenkel (1925); Jost (1933); Mott & Littleton (1938), etc.

Defect formation energies (concentrations and distributions) are functions that can be tuned F. A. Kröger “Chemistry of Imperfect Crystals” (1964) Atomic chemical potentials [growth & annealing conditions] Defects: Control Distributions Fermi level [function of n, p, T] Defect free energy of formation Crystal strain [internal or applied]

Vacancies in Strained CH3 NH3 PbI3 Crystal strain has a large (linear) effect on vacancy formation and distribution Formation of VI + calculated as a function of uniaxial strain up to 0.5% (DFT/PBEsol in tetragonal supercell) T. W. Jones et al, Energy and Environ. Sci. 12, 596 (2019) compressive tensile

Vacancies in Strained CH3 NH3 PbI3 Formation of VI + calculated as a function of uniaxial strain up to 0.5% (DFT/PBEsol in tetragonal supercell) T. W. Jones et al, Energy and Environ. Sci. 12, 596 (2019) T = 300 K equilibrium thermodynamics Crystal strain has a large (linear) effect on vacancy formation and distribution

Interstitials in Polycrystalline CsPbI3 Grain boundaries can act as sinks for excess iodine due to strain relief (large crystal relaxation) J. S. Park et al, ACS Energy Letters 4, 1321 (2019) 400 atom model of a Σ5 [130] tilt boundary in CsPbI3 . Formation energy: 0.23 J/m-2 Relative energy of excess iodine, Ii + Accumulation of charged iodine interstitials at the grain boundary (up to 1018 cm-3): linked to relaxation energy (I–I bond length)

Next Step: Carrier Capture Rates Group developers: Dr Sunghyun Kim Dr Samantha Hood Defectq=0 + eCB - Defectq=-1 Non-radiative recombination: defect concentrations and capture cross-sections are now accessible github.com/WMD-group/CarrierCapture.jl Solve the Schrödinger equation for each potential energy surface Building on approach of Alkauskas et al, Phys. Rev. B 90, 075202 (2014) Static coupling approximation

Next Step: Carrier Capture Rates Non-radiative recombination: defect concentrations and capture cross-sections are now accessible

Next Step: Carrier Capture Rates First PV applications to the “well behaved” tetrahedral semiconductor Cu2 ZnSnS4 (CZTS) SRH limit S-Q limit JSC 28.91 mA/cm2 28.91 mA/cm2 VOC 0.84 V 1.23 V FF 86.4% 90.0% Efficiency 20.9% 32.1% Theoretical Cu2 ZnSnS4 solar cell efficiency (“best case scenario”) CdS CZTS d(1+/0) d(2+/1+) 2 1 0 1 Energy (eV) 200 100 0 Position (nm) ϵ(2+/1+) E F ϵ(1+/0) Neutral trap Repulsive trap Giant trap V S -Cu Zn 1+ V S 2+ Sn Zn 1+ Sn Zn 2+ Cu Sn 1− 1000/T (1/K) σn (cm2) 0 2 4 6 8 10 10−30 10−27 10−24 10−21 10−18 10−15 10−12 (a ) (b) Giant traps (capture cross-section) Perovskites are coming soon (several technical challenges to overcome…) Work of Dr Sunghyun Kim, In Preparation (2019) [He is looking for a faculty position in 2020!] J. Mat. Chem. A 7, 2686 (2019)

Conclusion Electron and defect distributions in halide perovskites are sensitive to many factors. Strain even in single compositions can be important; the influence in mixed-anion systems is likely larger. More theory and experiment is required! Collaborations: Youngkwang Jung, Lucy Whalley, Youngwon Woo, Jacob Wilson, Sunghyun Kim, Samantha Hood; Jarvist Frost (ICL); Ji-Sang Park (Kyungpook); Sam Stranks (Cambridge); Bruno Ehrler (AMOLF); Mike Toney (SLAC) Slides: https://speakerdeck.com/aronwalsh @lonepair