Breaking the Defect Bottleneck in Halide Perovskite Semiconductors Prof. Aron Walsh Imperial College London, UK Yonsei University, Korea

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

Dynamic Processes in Perovskites Faster (fs) Slower (s) Electron Transport Effective semiconductors Crystal Vibrations Symmetry breaking and carrier separation Molecular Rotations Large static dielectric constant Ion Transport “Self healing” and hysteresis Dielectric Perspective: J. N. Wilson et al, APL Materials 7, 010901 (2019)

Point Defects in Perovskites Good Bad Population of Charge Carriers Shallow donors and acceptors Slow Charge Carrier Mobility Impurity scattering Non-radiative e-h Recombination Deep level defects Defect Tolerance: A. Walsh and A. Zunger, Nature Materials 16, 964 (2017) Bottlenecks: Decreasing trap concentrations; Increasing donor (n) and acceptor (p) density

Talk Outline: Imperfect Perovskites A. Defect Theory in a Nutshell B. Equilibrium Processes C. Beyond Equilibrium

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.

Point defects minimise the Gibbs free energy of a crystal – balance between enthalpic cost of bond breaking and entropic gain from disorder Frenkel (1925); Jost (1933); Mott & Littleton (1938), etc. Defect free energy of formation ΔGDefect = ΔH −TΔS vib Enthalpy [1–10 eV] Vibrational entropy [1–10 kB , ~ 0.1 eV at RT] Defects: Equilibrium Property of Crystals

ΔGDefect = ΔH −TΔS vib 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 Concentrations Fermi level [function of n, p, T] Defect free energy of formation Crystal strain [internal or applied]

Mott & Gurney “Electronic Processes in Ionic Crystals” (1941) Defects: Levels in the Band Gap Neutral donor Ionised donor Conduction electron Conduction Band Valence Band D(0/+) ΔE Optical level – fast (vertical) process Thermal level – slow ionic relaxation

Defects: Trapping vs Recombination " + ℎ% ⇋ ' " + ℎ% ⇋ ' + " ⇋ " Active for Trapping Acceptor A can capture a hole Active for Recombination Acceptor A can capture a hole and an electron ' Inert Defect D does “nothing”

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

Talk Outline: Imperfect Perovskites A. Defect Theory in a Nutshell B. Equilibrium Processes C. Beyond Equilibrium

Many Defects but Few Carriers Pb 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)

Many Defects but Few Carriers Pb 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: Ionised Donor Donor level is resonant in the conduction band – hydrogenic state that is thermally ionised (VI +) Conduction Band Valence Band VI (0/+) ΔE = 3 meV (Effective mass theory for shallow donor) L. W. Whalley et al, J. Chem. Phys. 146, 220901 (2017)

Iodine Vacancy: High Concentration The low formation energy of VI + implies a high equilibrium 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)

Tuning Chemical Potentials I- chemical potential insensitive to molar ratio

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 compensation by ionic defects determine the doping limits of a material Ionic (Defect) Compensation Decades of Literature: Kröger, Walukiewicz, Wei, Zhang, Zunger; van de Walle, etc. Electronic regime Ionic regime Overall charge neutrality Recommended: A. Walsh and A. Zunger, Nature Materials 16, 964 (2017)

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 Both limiting forms of stoichiometric disorder – common in oxide perovskites

Processing samples in an iodine atmosphere can change µi and alter the defect populations Iodine Vapour: Tip the Balance A. Zohar et al, ACS Energy Lett. 2, 2408 (2017) Iodine vacancies are filled, removing donors and the associated electrons, thus lowering the Fermi level (i to p) Mix of N2 /I2 at 0.5 atm

Process one perovskite layer under PbI2 -rich conditions and one under PbI2 -poor conditions Halide Perovskite Homojunction? P. Cui et al, Nature Energy 4, 190 (2019) By altering the PbI2 :CH3 NH3 I precursor ratio from 0.90 to 1.15, a hole concentration of 1010 cm–3 is converted to an electron concentration of 1013 cm–3 Q. Ions should gradually diffuse across to remove the gradient?

Talk Outline: Imperfect Perovskites A. Defect Theory in a Nutshell B. Equilibrium Processes C. Beyond Equilibrium

Influence of External Stimuli • Electric field (“Snaithing”) – E and qdefect • Chemical gradient – ∇µ and nion • Temperature gradient – ∇T and Qdefect • Light (“Hoking”) – hv and coupled to all stimuli • Strain – σ and coupled to all stimuli E + µ + T + hv + σ Walsh and Stranks, ACS Energy Lett. 3, 1983 (2018)

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

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

Photo-Stimulated Defect Generation Walsh and Stranks, ACS Energy Lett. 3, 1983 (2018) In most semiconductors, the bandgap is less than the defect formation energy: Eg < ΔEdefect For CH3 NH3 PbI3 , Eg = 1.6 eV, but ΔESchottky(MAI) ~ 0.2 eV For GaAs, Eg = 1.5 eV, but ΔESchottky(GaAs) ~ 5 eV

Conclusion Electron and defect distributions in halide perovskites are sensitive to many factors. A quantitative understanding has been slow to develop (due to complexity of processing and mixed-ionic/electronic transport signatures). More theory and experiment is required! Collaborations: Youngkwang Jung, Lucy Whalley, Youngwon Woo, Jacob Wilson, Sunghyun Kim, Jarvist Frost (ICL); Ji-Sang Park (Kyungpook), Sam Stranks (Cambridge); Bruno Ehrler (AMOLF); Mike Toney (SLAC) Slides: https://speakerdeck.com/aronwalsh @lonepair