Materials Research Society (Fall Meeting 2018) UnsolvedMysteries of Halide Perovskites Prof. Aron Walsh Imperial College London, UK Yonsei University, Korea Materials Design Group: https://wmd-group.github.io @lonepair From @KamatlabND

Halide Perovskites – What we Know Introduction to underlying physics in 2014 MRS talk: https://speakerdeck.com/aronwalsh ABX3 compounds with strong optical absorption, light carrier masses, efficient dielectric screening Device consequences • Weak exciton binding (EB

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 ~ 10-12cm2s-1 at T = 300 K [PBEsol/DFT in 768 atom supercell with nudged-elastic band] Bulk diffusion barrier

Mysteries of Perovskites A. Charge Carrier Localisation B. Spontaneous Lattice Strain C. Defects and Doping

Nature of Electron and Hole Carriers Charge carriers in crystals are quasi-particles defined by electron-lattice interaction: polarons Effective mass (Bohr) radius

Nature of Electron and Hole Carriers Charge carriers in crystals are quasi-particles defined by electron-lattice interaction: polarons Polaron radius

Nature of Electron and Hole Carriers Fröhlich electron-lattice interaction ! = 1 2 1 %& − 1 %( ) ℏ+ 2,+ ℏ - . GaAs = 0.1 CdTe = 0.3 CH3 NH3 PbI3 = 2.4 SrTiO3 = 3.8 Intermediate coupling regime: Large polaron Variational solution for Feynman polaron model rP = 4 unit cells mP * = 0.2 me (+30%) µP < 100 cm2V-1s-1 Jarvist Frost APL Materials 2, 081506 (2014); ACS Energy Lett. 2, 2647 (2017)

Real-Space Hot Polaron Cooling Excess excitation energy contained in polaron, with slow exchange to the bulk crystal Frost, Whalley, Walsh, ACS Energy Letters 2, 2647 (2017) Low Density n < 1018 cm-3 High Density n > 1018 cm-3 (Laser source) Notebooks: https://github.com/WMD- group/hot-carrier-cooling

Ultra-Low Thermal Conductivity Phonon-phonon interactions 103 stronger (shorter lifetimes) in CH3 NH3 PbI3 than GaAs Whalley et al, PRB 94, 220301(R) (2016); Gold-Parker et al, PNAS, Online (2018) Calculated lattice thermal conductivity (Phono3py; PBEsol) T = 300K GaAs (!) 38 (calculated) 45 (measured) MAPI (!) 0.05 (calculated) ~0.5 (measured)

Open Question: Rashba Polarons Does symmetry breaking (non-centrosymmetry) alter the physics of polarons in perovskites? CH3 NH3 PbI3 CsPbI3 QSGW+SOC calculations on ab initio MD trajectory QUESTAAL Code With Mark van Schilfgaarde McKechnie et al, Phys. Rev. B 98, 085108 (2018) Rashba-Dresselhaus splitting of valence & conduction bands (300 K) ↑ ↓

Open Question: Rashba Polarons Sensitive to material form and quality? Carrier concentrations? Length and time scale of measurements? Does symmetry breaking (non-centrosymmetry) alter the physics of polarons in perovskites?

Mysteries of Perovskites A. Charge Carrier Localisation B. Spontaneous Lattice Strain C. Defects and Doping

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

“Ferroelectric” Pb Halide Perovskites Paper titles from the literature on one material! Many reports misled by polarisation signatures of interface charging, ion transport and/or lattice strain

Ferroelastic Domain Formation [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

Ferroelastic Domain Formation “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

Scales of Disorder in Perovskites Lattice strain patterns have a complex heterogeneity across multiple length scales “Supergrain” <110> quiver plot Nanofocus XRD at ESRF Micro-XRD at ALS Over 20 µm: 0.3% strain [Led by Sam Stranks] T. Jones et al, arXiv 1803.01192 (2018)

Open Question: (Photo)Electrostriction New perspective on ferroic effects: J. N. Wilson et al, arXiv 1811.01832 (2018) No convincing explanation or model for what drives lattice expansion up to Δa/a = 1% Reversible changes with timescales of ms to hours, suggests defect formation and redistribution

Mysteries of Perovskites A. Charge Carrier Localisation B. Spontaneous Lattice Strain C. Defects and Doping

Point Defects in Photovoltaic Materials Good Bad Population of Charge Carriers Shallow donors and acceptors Limit Charge Carrier Mobility Ionised and neutral impurity scattering Non-radiative e-h Recombination Deep level defects Coupled ion & electron transport, defect aggregates, and redox reactions Ugly Defect Tolerance: A. Walsh and A. Zunger, Nature Materials 16, 965 (2017)

Many Defects but Few Carriers Lead halide perovskites are intrinsic – low carrier concentrations, resistant to extrinsic p or n doping Carrier Conc. Technique Reference 109 cm-3 Hall effect on pressed pellets of CH3 NH3 PbI3 Stoumpos et al, Inorg Chem 52, 9019 (2013) 109 cm-3 Impedance measurements on photovoltaic devices Pockett et al, J Phys Chem C 119, 3456 (2015) 1014 cm-3 Hall effect on thin films of CH3 NH3 PbI3 Bu et al, J Mat Chem A 2, 18508 (2014) 1014 cm-3 = 1 carrier every 10 million unit cells (high purity CdTe)

Iodine Vacancy: High Concentration Low formation energy of VI + implies a high equilibrium donor concentration n = N exp −ΔGDefect k B T ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ Defect concentration 0.2 eV (VI + for EF = midgap) Lattice sites in MAPI If this was the sole defect: n = 1019 cm-3 Calculations by groups of Y. Yan (2014), M.-H. Du (2014), D.O. Scanlon (2015)…

Electronic (Carrier) Compensation If the only defect present is VI + then a high electron concentration would be expected Concentration of ionised donors Concentration of conduction electrons Charge neutrality expression

Charge compensation by ionic defects determine the doping limits of most semiconductors Ionic (Defect) Compensation Defect self-compensation: G. Mandel, Phys. Rev. 134, A1073 (1963) Decades of literature: Kröger, Walukiewicz, Wei, Zunger; van de Walle, Catlow Recent review: Walsh and Zunger, Nature Materials 16, 965 (2017) Electronic regime Ionic regime Overall charge neutrality Donors Holes Acceptors Electrons

Self-Regulation of Charge A. Walsh et al, Angewandte Chemie 54, 1791 (2015) A high population of charged defects with overall charge neutrality – few excess electrons or holes Schottky disorder Frenkel disorder Two limits Both forms of stoichiometric disorder – common in oxide perovskites

High concentration of charged defects from equilibrium thermodynamics ≥ 1018 cm-3 Perovskites: Soup of Charged Defects + + + + - - - - - ++ ++ - - - Quantitative predictions difficult as beyond dilute defect limit and description of solution processing / precipitation reactions

Open Question: Deep Defects Non-radiative recombination rates are low, but still represent loss of 100–200 mV from ideal Ji-sang Park et al, Nature Reviews Materials 3, 195 (2018) Technique Trap Levels (eV) DLTS (Yang, Science 2017) 0.46, 0.78, 0.82 below conduction band TSC (Baumann, JPCL 2015) 0.5 from a band edge DLTS (Heo, EES 2017) 0.62, 0.75 below conduction band Sensitive to growth but ≲ 1015 cm-3 traps

Open Question: Deep Defects 2X# + h& → X( # V centre X# + X) # + h& → X( # H centre Whalley, Crespo-Otero, and Walsh, ACS Energy Letters 2, 2713 (2017) Halide redox: Hole trapping in V and H centres studied in metal halides since the 1950s Predicted excited-states TDDFT (PBE0 with SOC) in DALTON2016 On-going work: Carrier trapping rates by Lucy Whalley (ICL)

Group Talks at #f18mrs Lone Pair Engineering for Polar Semiconductors Me again! Today 11:15 - EP01.01.09 Effect of Stacking Disorder in Cu2 ZnSn(S,Se)4 Jisang Park, Wed 08:45 - ET11.09.02 Charge Separation in Organic Solar Cells Samantha Hood, Wed 14:15 - EP05.10.03 Extended Defects in Earth Abundant Inorganic Materials Jisang Park, Wed 14:15 - ET12.06.03 Origin of Green-Light Emission in Cs4 PbBr6 Youngkwang Jung, Friday 8:30 AM - ET05.13.03

Conclusion and Outlook We learned a lot about halide perovskites since 2012. Challenges remain for understanding structural & electronic properties, e.g. will there ever be a perovskite p-n homojunction? Project Collaborators: Lucy Whalley, Jarvist Frost, Jonathan Skelton, Jacob Wilson, Youngkwang Jung; Mark van Schilfgaarde (Kings); Keith Butler (ISIS); Sam Stranks (Cambridge); Chol-Jun Yu (Kim Il Sung) Piers Barnes (ICL); Mike Toney (SLAC) Slides: https://speakerdeck.com/aronwalsh