Fundamentals of hybrid halide perovskites Semiconductors with a twist Sustainable Centre for Chemical Technologies Prof. Aron Walsh Department of Chemistry University of Bath, UK Adjunct Professor Yonsei University, Korea a.walsh@bath.ac.uk Fall MRS 2014 – Invited Talk

Perovskite (ABX 3 ) Crystal structure of the mineral CaTiO 3 A BX 3 Lev Perovski (Russia, 1839)

Hybrid Perovskite Perovskite structured materials containing organic and inorganic ions Dieter Weber (Germany, 1978)

Fundamentals of Hybrid Perovskites I. Structure & Composition II. From Inorganic to Hybrid III. Electronic Structure IV. Dynamic Dielectric Screening V. Challenges & Open Questions

Perovskite Stoichiometry (ABX 3 ) For charge neutrality, the formal oxidation states must obey A + B = 3X X = II (Oxides; A+B=VI) • A=I, B=V (e.g. KTaO3 ) • A=II, B=IV (e.g. SrTiO3 ) • A=III,B=III (e.g. GdFeO3 ) X = I (Halides; A+B=III) • A=I, B=II (e.g. CsSnI3 ) Note: quaternary and quinternary extensions, e.g. double perovskites, are possible

Conventional behaviour 0.7 < α < 1.1 Perovskite can be formed α > 1 B site is too small (off-site) α < 1 A site is too small (tilting) ABX 3 Radius Ratio Rules B X A α = r A +r X 2(r B +r X ) Structure tolerance factor V. M. Goldschmidt, Naturwissenschaften 14, 477 (1926)

along this direction oscillating in antiphase. It is for this reason that, when the mode condenses at the transition temperature, a°a°c - results. On the other hand, NaNbOa(T2) possesses the a°a°c + structure (determined with the present technique, using three reflexions), and condensation of an M3 soft- phonon mode at q = ½,½,0 has been postulated to explain the transition from the cubic phase (Glazer & Megaw, 1972). This mode consists of successive octahedra along [001] oscillating in phase about this direction, thus giving rise to the a°a°e + structure on condensation. modes in connexion with phase transitions in perov- skites, since rigid oscillations of the octahedra con- stitute important modes near the transitions. As mentioned earlier, there are not many known examples of compound tilts. Actually, only NaNbOa is definitely known to possess such complicated tilt systems, although it is very likely that AgNbO3 is isomorphous with it. The evidence for this (Francombe & Lewis, 1958) is based on the presence of superlattice lines corresponding to a unit cell of 2ap × 4bp × 2cp, with ap=cp and fl>90 °, as is found in NaNbOa(P). Table 1. Complete list of possible simple tilt systems Serial Lattice Multiple Relative pseudocubic number Symbol centring cell subccll parameters 3-tilt systems (1) a+b+c + I 2apx2bpx'.cp ap~bpq:cp t2) a+b+b + I ap~bp=cp (3) a+a+a + I ap=bp=cp (4) a+ b + c - P apv~bp~cp (5) a+a+c - P ap=bp~cp (6) a+b+b - P a~v~bp=cp (7) a + a + a- P ap = bp = cp (8) a+ b- c - A ap~bp~cx, o~ 90 ° (9) a + a- c- A ap = bp ~ cp~ ~ 90 ° (10) a + b-b - A ap v~ bp=cpoc ~ 90 ° (11) a+ a-a - A ap=bp=cp~t~90 ° (12) a-b-c- F ap v~ bp ~ cpo~-C fl-¢ ? ~ 90 ° (13) a-b-b- F " ap~bp=cp~,O~Tv~90 ° (14) a a a- F ap=bp=cpo~=fl=Tv~90 ° 2-tilt systems (15) a°b + c + I 2ap x 2bp x 2cp ap < bp ~ cp (16) a°b + b + I ap < bp = cp (17) a°b + c - B ap < bp ~ cp (18) a°b + b - B ap < bp = cp (19) a°b- c- F ap < bp ~ cpct ~ 90 ° (20) a°b- b- F ap < bo = c~ct ~ 90 ° 1-tilt systems (21) a°a°c + C 2ap × 2bp x cp a. = bp < cp (22) a°a°c- F 2ap x 2bp x 2cv ap = bp < cp Zero-tilt system (23) a°a°a ° P ap x bp x c~ ap = bp = ct, * These space group symbols refer to axes chosen according to the matrix transformation ½ - Space group Immm (No. 71) lmmm (No. 71) Im3 (No. 204) Pmmn (No. 59) Pmmn (No. 59) Pmmn (No. 59) Pmmn (No. 59) A2~/ml 1 (No. 11) A21/ml 1 (No. 11) Pnma (No. 62)* Pnma (No. 62)* FI (No. 2) I2/a (No. 15)* R~c (No. 167) lmmm (No. 71) 14/m (No. 78) Bmmb (No. 63) Bmmb (No. 63) F2/mll (No. 12) Imcm (No. 74)* C4/mmb (No. 127) F4/mmc (No. 140) Pm3m (No. 221) Perovskite Polymorphs Rotation and tilting of octahedra Accessible ferroelectric and antiferroelectric phases A. M. Glazer, Acta. Cryst. B 28, 3384 (1972) Mike Glazer (Oxford)

Fundamentals of Hybrid Perovskites I. Structure & Composition II. From Inorganic to Hybrid III. Electronic Structure IV. Dynamic Dielectric Screening V. Challenges & Open Questions

From Inorganic to Hybrid Perovskites A B X 3 a (Å) E g (eV) H+ Pb I 6.05 0.53 NH 4 + Pb I 6.21 1.38 CH 3 NH 3 + Pb I 6.29 1.67 Choice of counter ion: • Size • Shape • Polarisation Isolvalent ‘A’ substitution: metal to molecule F. Brivio et al, APL Materials 1, 042111 (2013) Ratio rules: A. K. Cheetham, Chem. Sci. 5, 4712 (2014)

Methylammonium (CH 3 NH 3 +) A closed shell (18 electron) molecular cation with a large electric dipole J. M. Frost et al, Nano Letters 14, 2584 (2014) Deprotonation (pK a ~ 10): CH 3 NH 3 + à CH 3 NH 2 + H+

From 3D to 1D Hybrids D. B. Mitzi et al, Science 267, 1473 (1995) Modular homologous series [100], [110] & [111] perovskite building blocks

Fundamentals of Hybrid Perovskites I. Structure & Composition II. From Inorganic to Hybrid III. Electronic Structure IV. Dynamic Dielectric Screening V. Challenges & Open Questions

CH 3 NH 3 PbI 3 (MAPI for short) Configuration: PbII [5d106s26p0]; I-I [5p6] F. Brivio et al, Physical Review B 89, 155204 (2014) Relativistic QSGW theory with Mark van Schilfgaarde (KCL) Conduction Band Valence Band Dresselhaus Splitting (SOC) [Molecule breaks centrosymmetry]

“Natural” Valence Band Alignments Similar to other thin-film PV materials Band gap engineering through A, B or X site modification K. T. Butler et al, Materials Horizons 2, 228 (2015)

Optical Absorption & Transport F. Brivio et al, Physical Review B 89, 155204 (2014) Bands are not parabolic (QSGW), but… m h */m ~ 0.12 (light holes) m e */m ~ 0.15 (light electrons) [sampled within k B T of band edges] 1 2 3 4 10−3 0.01 0.1 1 10 GaAs NH3 CH3 PbI3 NH4 PbI3 α (104 cm-1) E (eV) 0.01 0.1 0.01 0.1 1 E k (b) 0 0.02 0.04 0 0.1 0.2 0.3 m*/m E (c) Optical Absorption Hole Effective Mass [110] [112] [111]

Free Carriers or Excitons? Exciton binding from effective mass theory: E b = m*e4 !2ε2 ≈ 45 meV (ε ∞ ) ; 1.6 meV (ε0 ) The situation is different to organic PV where the dielectric constants are small and effective masses are heavy. Semiconducting perovskites are distinct from passive dyes in sensitised cells. Carrier masses & dielectric screening favour free carrier generation J. M. Frost et al, Nano Letters 14, 2584 (2014)

Fundamentals of Hybrid Perovskites I. Structure & Composition II. From Inorganic to Hybrid III. Electronic Structure IV. Dynamic Dielectric Screening V. Challenges & Open Questions

Dielectric Response of MAPbX 3 Strong screening; response is sensitive to frequency and T (eg. Poglitsch & Weber 1987) M. Maeda et al, J. Phys. Soc. Jap. 66, 1508 (1997) CH 3 NH 3 PbBr 3 Dielectric study of CH,NH,PbX, 937 se, following a Curie-Weiss type temperature ence down to the transition temperature where 6’ showed a discontinuity at the tetra- I-orthorhombic II transition. and tetragonal I pha.se.s these phases, the 6‘ curves show a l/T (or T,))-like temperature dependence. This indi- hat the dipoles are disordered in these phases. atic permittivity Q of the pure polar liquid is ed by the Kirkwood-Fr~hlich equation 193, (60 ---m)(2%+&) 1 Np= t,,& + 2)= = KgkeT’ (1) L, denotes the permittivity at the high- fl CHdHaPbI3 a CHNaPbBr3 0 CH3NH3PbCl3 150 2&l 250 300 350 TIK Fig. 4. Temperature dependence of the dielectric constant of the tetragonal (M/mm) phase and cubic phases of CH,NH,PbX, (X = Cl, Br, I) taken at 100 kHz. The best fit curves representing the modified Kirkwood-Frbhlich eqn (I) are shown as solid lines. 100 kHz T dependence is described by Kirkwood-Fröhlich equation

Multi-scale Dielectric Relaxation F. Brivio et al, APL Materials 1, 042111 (2013)

Multi-scale Dielectric Relaxation F. Brivio et al, APL Materials 1, 042111 (2013)

Molecular Orientation from Diffraction N. Onoda-Yamamuro (PhD Thesis, Osaka University, 1990)

Perovskite Cage from Diffraction Y. Kawamura et al, J. Phys. Soc. Jap. 71, 1964 (2002) Large anharmonic thermal displacements

First-principles Dynamics (300 K) “MAPI is as soft as jelly” 25 fs per frame J. M. Frost et al, APL Materials 2, 081506 (2014) Jarvist http://dx.doi.org/10.6084/m9.figshare.1061490 ß Focus on one CH 3 NH 3 ion 3D periodic boundary (80 - 640 atoms)

Molecular Orientation from Simulation J. M. Frost et al, APL Materials 2, 081506 (2014) Temperature: 300 K Production: 58 ps Timestep: 0.5 fs

Perovskite Cage from Simulation J. M. Frost (Unpublished); See Poster in Thursday Session Analysis code: SMASH (following POTATO & SPUDS) for kinematics of cage deformations

Current-Voltage Hysteresis H. J. Snaith et al, J. Phys. Chem. Lett. 5, 1511 (2014) Operation voltage and history affect recombination: sensitive to J-V scan rate 0.0 0.2 0.4 0.6 0.8 1.0 1.2 -20 -10 0 10 20 FB-SC SC-FB Current density (mAcm-2) Applied Bias (V) Scan rate: 0.15 V/s Direction Jsc (mA/cm2) η (%) Voc (V) FF FB-SC 22.9 15.5 1.05 0.66 SC-FB 22.8 10.2 0.97 0.46 9 of 17 The Journal of Physical Chemistry Letters

Domains of Molecular Dipoles Ferroelectric Hamiltonian (Monte Carlo solver) Regions of high (red) and low (blue) electrostatic potential J. M. Frost et al, APL Materials 2, 081506 (2014)

Impact of Built-in Electric Field Changes in polarisation of the hybrid perovskite layer: e-h recombination rates J. M. Frost et al, APL Materials 2, 081506 (2014)

Recent Experimental Evidence Direct Observation of Ferroelectric Domains in Solution-Processed CH3 NH3 PbI3 Perovskite Thin Films Yasemin Kutes,†,∥ Linghan Ye,†,∥ Yuanyuan Zhou,‡,∥ Shuping Pang,§ Bryan D. Huey,*,† and Nitin P. Padture*,‡ † Department of Materials Science and Engineering, University of Connecticut, Storrs, Connecticut 06269, United States ‡ School of Engineering, Brown University, Providence, Rhode Island 02912, United States §Qingdao Institute of Bioenergy and Bioprocess Technology, Chinese Academy of Sciences, Qingdao 266101, People’s Republic of China * S Supporting Information ABSTRACT: A new generation of solid-state photovoltaics is being made possible by the use of organometal-trihalide perovskite materials. While some of these materials are expected to be ferroelectric, almost nothing is known about their ferroelectric properties experimentally. Using piezoforce microscopy (PFM), here we show unambiguously, for the first time, the presence of ferroelectric domains in high-quality β-CH3 NH3 PbI3 perovskite thin films that have been synthesized using a new solution-processing method. The size of the ferroelectric domains is found to be about the size of the grains (∼100 nm). We also present evidence for the reversible switching of the ferroelectric domains by poling with DC biases. This suggests the importance of further PFM investigations into the local ferroelectric behavior of hybrid perovskites, in particular in situ photoeffects. Such investigations could contribute toward the Letter pubs.acs.org/JPCL olution-Processed D. Huey,*,† icut 06269, United States ngdao 266101, People’s Republic of Experimental dynamic structural collaboration: Inelastic neutron scattering (Piers Barnes – ICL) Tue 16:00 2D photon echo (Artem Bakulin – AMOLF) Wed 16:30

Fundamentals of Hybrid Perovskites I. Structure & Composition II. From Inorganic to Hybrid III. Electronic Structure IV. Dynamic Dielectric Screening V. Challenges & Open Questions

Challenge: Dynamic Disorder 1. Displacive Structural Instability Crystal structures reported from diffraction studies represent an average. The octahedral networks exhibit a dynamic local instability. 2. Orientational Disorder Molecular orientations display a wide distribution, but are sensitive to both internal strains and the external environment. 3. Defect Formation (“Entropy Saturation”) Standard analysis assumes perfect crystals (free energy minimisation); these materials are not!

Important Questions • Ion diffusion – evidence from impedance spectroscopy. What is moving? • Domain structure – sensitivity to synthesis, device operation, domain walls. • Surface & interface structure – clean interface with TiO 2 ? • n-type & p-type semiconducting samples – what is the origin and how can type conversion be controlled? • Device model that reproduces J-V hysteresis.

Conclusion Hybrid perovskites are interesting materials with complex solid-state chemistry & physics. Presentation: http://people.bath.ac.uk/aw558/presentations References: Mendeley group “Hybrid Perovskite Solar Cells” Group Members: PV – Suzy, Adam, Federico, Keith, Jarvist; MOF – Ruoxi, Chris, Jess; META – Jonathan, Rachel, Lora Collaborators: PV – Xingao Gong & Shiyou Chen (Fudan); Su-Huai Wei (NREL); David Scanlon (UCL); Piers Barnes (ICL); Mark van Schilfgaarde (KCL); Laurie Peter (Bath)

Group Hybrid Perovskite Publications Principles of chemical bonding and band gap engineering in hybrid organic–inorganic halide perovskites (2015) http://dx.doi.org/10.1021/jp512420b Ferroelectric materials for solar energy conversion: photoferroics revisited (2015) http://dx.doi.org/10.1039/C4EE03523B Self-regulation mechanism for charged point defects in hybrid halide perovskites (2015) http://dx.doi.org/10.1002/anie.201409740 The dynamics of methylammonium ions in hybrid organic– inorganic perovskite solar cells (2015) http://dx.doi.org/10.1038/ncomms8124 Ionic transport in hybrid perovskite solar cells (2015) http://dx.doi.org/10.1038/ncomms8497 Role of microstructure in the electron–hole interaction of hybrid lead halide perovskites (2015) http://dx.doi.org/10.1038/nphoton.2015.151

Group Hybrid Perovskite Publications Structural and electronic properties of hybrid perovskites for high-efficiency thin-film photovoltaics (2013) http://dx.doi.org/10.1063/1.4824147 Atomistic origins of high-performance in hybrid halide perovskite solar cells (2014) http://dx.doi.org/10.1021/nl500390f Molecular ferroelectric contributions to anomalous hysteresis in hybrid perovskite solar cells (2014) http://dx.doi.org/10.1063/1.4890246 Band alignment of the hybrid halide perovskites CH 3 NH 3 PbCl 3 , CH 3 NH 3 PbBr 3 and CH 3 NH 3 PbI 3 (2015) http://dx.doi.org/10.1039/C4MH00174E Assessment of polyanion (BF 4 − and PF 6 −) substitutions in halide perovskites (2015) http://dx.doi.org/10.1039/C4TA05284F