Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Jarvist Moore Frost (a,b), Pooya Azarhoosh(c), Scott McKenzie(c), Lucy Whalley(b), Jonathan Skelton (a), Suzy Wallace(a,b), Mark van Schilfgaarde (c), Aron Walsh (a,b,d) a) University of Bath, UK b) Imperial College London, UK c) King's College London, UK d) Yonsei University, Seoul 120-749, Korea Walsh Materials Design Group, Imperial College London, UK [email protected] Polarons in CH3NH3.PBI3 — Formation, Transport and Recombination 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 What is a Polaron? ➔ bare electron interacts with lattice (particularly, with the i.r. active lattice vibrations) ➔ becomes dressed in a cloud of excitations ➔ interactions energetically trap particle… ➔ And shield interaction between particles... (A Guide to Feynman Diagrams in the Many-body Problem, R.D. Mattuck) e + + + + + + 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Dielectric response… Fröhlich Polaron 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 ● Consider linear dielectric response -outside- polaron Dielectric response… Fröhlich Polaron 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Dielectric response… Site Energy (Polarisation) Self consistent response... 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 S For an idealised 1D chain... 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Effective mass polarons α GaAs: 0.068 CdTe: 0.29 AgCl: 1.84 SrTiO3: 3.77 (Devreese 2005) In the limit of the effective mass approximation (NFE), can fold response of lattice into dimensionless coupling constant alpha ● Difference of dielectric constants ● Characteristic frequency of LO mode ● Effective mass of electron (Original paper Landau (1933); this follows Jones & March (1985), "Theoretical Solid State Physics Vol 2" ) 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 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] 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 F. Brivio et al, Physical Review B 89, 155204 (2014) Bands are not parabolic, but… m h */m ~ 0.12 (light holes) m e */m ~ 0.15 (light electrons) [sampled within k B T of band edges] Optical Absorption Hole Effective Mass [110] [112] [111] (Nb: requires sophisticated treatment of k-space grid for sufficient points for fit!) 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Figure: Beau Lambert, Kenneth A. Mauritz. 33 24 4.5 Dielectric function (not a constant) 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 LO-like modes @ 2 THz TO-like modes @ 1 THz Representation of i.r. activity from: Phys. Rev. B 92, 144308 (2015) 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Free Charges or large Polarons or small Polarons? (Arguments for these follow Landau (1933); from Jones & March (1985), "Theoretical Solid State Physics Vol 2" ) MAPI: α GaAs: 0.068 CdTe: 0.29 AgCl: 1.84 SrTiO3: 3.77 (Devreese 2005) 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Free Charges or large Polarons or small Polarons? (Polaron Binding Energy) (Arguments for these follow Landau (1933); from Jones & March (1985), "Theoretical Solid State Physics Vol 2" ) (R.Feynman, 1955) 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Real space disorder: STARRYNIGHT codes Classical Metropolis algorithm simulation of cage:cage dipole interactions. Analytic Hamiltonian, interaction strength parameterised by DFT. ( Apl Materials 2 (8), 081506, 2014. Open source on GitHub https://github.com/WMD-Group/Starrynight ) 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Display direction of Dipole by point on HSV sphere p (Nb: Simulation linear scaling + very fast; here I present 2D slices of ~20x20, as any larger and you can't see what's going on!) 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Parameters via DFT 25-75 meV (nearest neighbour) 25 meV (nearest neighbour) 1-5 meV at solar cell fields 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 https://github.com/WMD-group/StarryNight Metropolis (local spin move) Monte Carlo code written in C99. Efficient & on lattice → millions of moves per second. Analysis code built in, and additional Julia post processing tools. Open source! 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 T= 0 K (Ground State - but a bit out of eqm, due to MC) CageStrain = 0 ---> Anti-Ferroelectric (The potential at a site from the dipole on the nearest neighbour (= 1 in the internet units of Starrynight) is simply 0.165 V.) 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 T= 0 K (Ground State - but a bit out of eqm, due to MC) CageStrain = 50 meV / neighbour ---> Ferroelectric 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Cagestrain=25 meV → Semi-ordered Ferroelectric ground state; Intermediate long range order (dynamic) at finite T 0K 128K 64K 256K 384K 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 0K 128K 256K 384K Cagestrain=25 meV → Semi-ordered Ferroelectric ground state; Intermediate long range order (dynamic) at finite T 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 POLARON POLARON NORALOP Slightly indirect band gap. Real space potential fluctuations 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Real space recombination model: 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Simple Statistical Mechanics argument V h+ h+ h+ e- e- Recombination... 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 POLARON POLARON NORALOP How to model polarons? POLARON 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Gaussian blur! 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Boltzmann / mid-gap Fermi Dirac Fermi level 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Fermi-Dirac e- quasi Fermi level h+ quasi Fermi level Fermi Level 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 (Boltzmann distribution of electrons, at 300 K) Recombination Reduction 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Simple thermal de-trapping model (Boltzmann distribution of electrons, at 300 K) Mobility Reduction 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Recombination vs. Mobility ? This is structureless disorder (just density of states), using models more suitable from low mobility materials (from amorphous silicon). At 300 K recombination is reduced by a factor of X 100 due to charge segregation. But the potential fluctuations also reduced the mobility by a factor of X 100. Further work will look at structure and see whether 'ferroelectric highways' allow for greater mobility than expected of Gaussian Disorder Model. 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Real-space disorder Conclusions ➔ Ground state dependent on details of Hamiltonian terms. Our errors here could be +-200%. ➔ We observe exponentially decaying long range partial ferroelectric ordering. ➔ Continuous inter-converting domains at finite temperature. ➔ Considerable (+-150 meV) electrostatic potential fluctuations. Statistical mechanics models indicate what behaviour is possible. Experiment will show that which is present. https://github.com/WMD-Group/StarryNight 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Absorption: Spin-orbit-coupling flattens the valence band - leading to a large density of states available for direct excitation. A sudden “turn-on”, like 2D band structures. Emission: Holes and electrons quickly thermalise to bottom of band (densities at 1 sun solar flux are very low); indirect radiative recombination is slow. → Have your cake and eat it ← The Dresselhaus crystal field effect splits the CBM (more than VBM); a spin split indirect gap forms. 75 meV P. Azarhoosh et al., APL Materials 4, 091501 (2016) Spin-split indirect-gap: 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Spin-split indirect-gap: 75 meV Biggest contribution where Xi(r) is large, near the Pb (Z=82) nucleus. Driven by the crystal (electric) field. Weaker effect at I (Z=53) on 5p-orbital, flattens bands. → Electric field at nucleus 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 → DFT, athermal structure; mainly spin texture → DFT, MD sampled structures; mainly k-space displacement 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Calculate radiative recombination rate: QSGW band structure (120x120x120 K-point mesh). Direct transitions only. Fermi-Dirac distribution for the electrons / holes within their band (full thermalisation). 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Strong T-dep at low fluence Direct gap at high fluence. Temperature insensitive dynamics. 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Predictions: Spin-split indirect-gap leads to 300 X decrease in bi-molecular recombination. Weak indirect gap ~75 meV below direct; should not be present in Orthorhombic phase (~<150K). B coeff. varies strongly as a function of intensity (you can't do a 'global fit' to TRPL data over many decades) Faster recombination expected in Sn analogue due to reduced Spin Orbit Coupling - it should be more direct gap like. Lasing threshold can be directly explained by intensity dependence of B. Epitaxial / ferroelectric manipulation should affect optical properties. Spin split indirect gap → may be a new design feature for novel solar cell materials. Present where {Sb,Bi,Pb} + ferroelectric distortion. P. Azarhoosh et al., APL Materials 4, 091501 (2016) 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Are lead-halide perovskites Intermediate Band Solar Cells ? (Photon Ratchet) 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Red-dashed, without spin orbit coupling Black-full, with spin orbit coupling QSGW Band structure, Scott McKechnie 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Valence Band → Intermediate Band 1.6+ eV Valence Band → Conduction Band 3.1+ eV Intermediate Band → Conduction Band Photon Ratchet @ 1.5 eV Eigenvalues on 11x11x11 k-mesh, Pooya Azarhoosh 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Mulliken projected partial density of states, from QSGW calculation including spin orbit. VBM is almost perfectly I 5p. The Intermediate and Conduction bands have considerable 6p contribution, but are not pure. 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Can MAPI make an IBSC? ● Two necessary requirements: ○ Independent Quasi-Fermi levels ✔ ○ Selective-contacts CB (LiF, Ca, Ba, Fulleroid) ✔ ● Can't break Shockley-Queisser (Bg wrong) ● Will it make a useful photocurrent? ○ Requires further calculations, custom codes ○ Spin-split indirect-gap will reduce recombination, and produce a photon-ratchet effect ○ Transitions allowed between IB to CB? ● Rashba-split band extrema offer a lot of potential interesting device physics, exploitable for PV 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Collaborators:- Piers Barnes; Jenny Nelson - Imperial College London Mark van Schilfgaarde, Pooya Azarhoosh, Scott McKechnie - King's College London Piers Barnes Jenny Nelson Mark van Schilfgaarde Pooya Azarhoosh WMD Group, ICL/Bath Acknowledgments:- EPSRC - EP/K016288/1 EPSRC Archer - EP/L000202 University of Bath HPC Imperial College London HPC http://go.bath.ac.uk/wmd 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Back Pages 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Electron-phonon coupling for fun and the future 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Florian Marquardt, Wikipedia, CC Lattice Dynamics (Phonons) MAPI Low-frequency dispersion (PCCP Adv. Article., AMA Leguy et al., 2016) 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Lattice Dynamics (Phonons) 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Quantum (an)Harmonic Oscillators & e-ph coupling Motivation: How to treat soft phonon modes? What is the repercussion for the electronic structure (and electron-phonon coupling) for such large tilting modes? 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Adiabatic electron-phonon coupling Born-Oppenheimer approximation (full wavefunction is product of electronic and nuclear wavefunctions) Adiabatic approximation: treat Nuclear and Electronic degrees of freedom separately. Mean-field expectation. Solve Sch. Eqn. for nuclear degree of freedom. Solve electronic Sch. Eqn. varying nuclear degree of freedom (i.e. deformation potential). Combine in mean-field manner. 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 The 1D Schrodinger equation is easy to solve! 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 ~15 meV well persists in structure to > 600 K BE Distribution 600 K 1 K 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 (Calculations: Lucy Whalley) Band-gap as a function of Q (Deformation Potential) 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 (R acoustic mode at Brillouin-Zone boundary [tilt]) 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 R M 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 “The previous methods for calculating the electron-phonon matrix element in a metal are neither rigorously formulated nor satisfactory in their results. From each method there is something to learn—usually that the method is unreliable in some important aspect.” Ziman, 1960 ‘Electrons and Phonons’, § 5.7, page 197. MAPI soft modes ● Soft modes at R and M Brillouin-Zone boundaries ● Mode following for potential energy surface → 1D Sch. Eqn. solver → Nuclear p.d.f → mean-field temperature resolved el-ph coupling for soft modes ● Values of ~35 meV per mode seem to agree with experimental linewidths 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 "It is typical of modern physicists that they will erect skyscrapers of theory upon the slender foundations of outrageously simplified models." J.M.Ziman, 1962 "Electrons in metals: a short guide to the Fermi surface" Most solid state (electronic structure) theory based on a fiction of periodicity ● Infinite in all directions ● Perfect registration ● Crystallographic momentum is a good q number 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Perovskite (ABX 3 ) Crystal structure of the mineral CaTiO 3 A BX 3 Lev Perovski (Russia, 1839) 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 A - Molecular Cation - '1+' charge B - {Pb, Sn} - '2+' charge X 3 - Halide {I, Br, Cl*} - '1-' charge Hybrid Halide Perovskites (ABX 3 ) Weber, Dieter. "CH3NH3PbX3, ein Pb (II)-System mit kubischer Perowskitstruktur/CH3NH3PbX3, a Pb (II)-System with Cubic Perovskite Structure." Zeitschrift für Naturforschung B 33.12 (1978): 1443-1445. 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Methylammonium (CH 3 NH 3 +) ; MA A closed shell (18 e-) molecular cation with a large electric dipole (2.2 D) J. M. Frost et al, Nano Letters 14, 2584 (2014) Deprotonation (pK a ~ 10): CH 3 NH 3 + → CH 3 NH 2 + H+ 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Why is the material interesting? ➔ 22% power conversion efficiency solution processed solar cells ➔ Tunable band gap ➔ Easy to make ➔ Degrades easily ➔ Sample variation Henry Snaith, one of the early proponents 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Why is solution processed MAPI (disorder) an efficient solar cell? ◆ Almost absent non-radiative recombination ○ Few mid gap defects (fortitude? Linked to the negative deformation potential?) ◆ Slow radiative recombination ● Unusual for a direct gap material ● ? Slightly-indirect gap due to Rashba splitting ● ? Electrostatic potential fluctuations reduce recombination ◆ Sufficient mobility to get charges out ● But not that high considering effective mass (~50 cm2/Vs vs. 1000 cm2/Vs for CdTe) ○ ? Reduced by electrostatic fluct? 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 ( Videos on YouTube - search for 'MAPI molecular dynamics' ) https://youtu.be/K_-rsop0n5A Incredibly Soft crystal; large distortions of octahedra ➔ MA ion yaw ➔ ...and roll… ➔ ...CH3 clicks ➔ so does NH3 [2x2x2 Pseudo cubic relaxed supercell, lattice parameters held constant during MD (NVT simulation). PBESol Functional at the Gamma point (forces + energies should converge well). dt = 0.5 fs, T = 300 K ] Molecular Dynamics 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Iodine location, MAPI, ~100 ps MD 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Glazer Tilting - Glazer 1972 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Project back onto the first unit cell by symmetry 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Lead Iodine Pb: Lone pair / 2nd order Jahn-Teller distortion Carbon (Methylammonium) 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Iodine 300K Iodine 200K 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Timescale of MA orientation 2D infrared spectroscopy ~ 3 ps Bakulin et al. J. Phys. Chem. Lett., 2015, 6 (18), pp 3663–3669 Quasi-Elastic Neutron Scattering (QENS) ~14 ps ; Leguy et al., Nature Communications 2015, 6, 7124 ~5 ps (higher SNR); Chen et al. 2015 arXiv: 1506.02205v2 DFT Molecular Dynamics → 2x2x2 unit cell ~2.5 ps ; Bakulin et al. ~2 ps (FAPI) ; Weller et al. J. Phys. Chem. Lett., 2015, 6 (16), pp 3209–3212 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 A total of 58 ps (2319 frames) of data was used for analysis, after an equilibration run of 5 ps. This generated 18547 unique MA alignment vectors. 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 FACE (X) DIAGONAL (R) EDGE (M) FACE: 42% EDGE: 31% DIAG.: 26% (weighted by MC integration of random sphere points) 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Preprint on the arXiv: 1504.07508 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 a Baikie T., et al., Synthesis and crystal chemistry of the hybrid perovskite (CH 3 NH 3 ) PbI 3 for solid-state sensitised solar cell applications, J. Mater. Chem. A, 1, 5628-5641 (2013). b Stoumpos, C. C., Malliakas, C. D. & Kanatzidis, M. G. Semiconducting tin and lead iodide perovskites with organic cations: phase transitions, high mobilities, and near-infrared photoluminescent properties. Inorg. Chem. 52, 9019–9038 (2013). c Weller M. T., et al., Complete structure and cation orientation in the perovskite photovoltaic methylammonium lead iodide between 100 and 352K Chem. Comm., DOI:10.1039/c4cc09944c (2015) d Kawamura Y., Mashiyama H., Hasebe K., Structural study on cubic-tetragonal transition of CH 3 NH 3 PbI 3 , J. Phys. Soc. Japan. 71, 1694-1697 (2002). † Note: due to the manner in which orientational disorder is fitted to neutron diffraction data, this bond length represents an underestimate. To refine the orthorhombic structure, Weller et al use fixed bond lengths of 1.46Å (C-N), 1.13Å (C-H) and 1.00Å (N-H). 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 i.r. Raman Cubic Tetra Ortho Cation Cage 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Ortho. DFT, with 150 K Expt data. Cage Cation Experimental data: Oliver J. Weber, Mark T. Weller, (Bath) Alejandro R. Goni (ICMAB, Barcelona), Aurelien M. A. Leguy, Piers R. F. Barnes (Imperial, London) Aurelien Leguy ICMAB, Barcelona Imperial College London ? 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 18 Cage Modes (3 acoustic, 9 cage (3N-3), 6 rovibrational (MA)) 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 18 MA high freq. molecular modes (3N-6) 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 3 mid-energy range MA hydrogen modes Most molecular modes are the same in vacuum (by DFT calculation), as in the solid state. Low-frequency molecular modes (methyl clicker) seem highly affected by environment (900 → 300 cm-1 ). Good be a useful probe of local packing / ordering. 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Vacuum calculation describes eigenvectors well A; 282 cm-1 E; 886 cm-1 A; 922 cm-1 E; 1240 cm-1 E; 1451 cm-1 A; 1478 cm-1 E; 1621 cm-1 A; 1418 cm-1 E; 3119 cm-1 A; 3321 cm-1 E; 3395 cm-1 A; 3018 cm-1 Strong Raman Active ; Strongly i.r. active 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Cl Br I 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Nudged elastic band activation energies, of vacancy mediated diffusion; from DFT / PBESol in MD equilibriated Supercells Iodine Vacancy mediated diffusion: Ea = 0.58 eV 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 N. Onoda-Yamamuro et al, J. Phys. Chem. Solids. 2, 277 (1992) 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 N. Onoda-Yamamuro et al, J. Phys. Chem. Solids. 2, 277 (1992) =+2% 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Cubic? Tetragonal? Orthorhombic? Powder Neutron diffraction allows for a full solution (inc. hydrogens) ➔ 150K 1st order phase transition (Ortho-Tetra) ➔ 2nd order transition to cubic phase Weller et al. Chem. Commun., 2015, DOI: 10.1039/C4CC09944C Received 12 Dec 2014, Accepted 22 Jan 2015 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Exciton binding from effective mass theory: Carrier mass & dielectric screening favour free carrier generation (t→infinity) J. M. Frost et al, Nano Letters 14, 2584 (2014) Onsager theory; See Wilsen 1939 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 How non parabolic? Very! Implications for device models (i.e. Drift diffusion, assumptions of scattering) 

Jarvist Moore Frost (Imperial College London, UK) MRS Fall - Boston 2016 Tues 29th Nov 2016 Effect of disorder: x100 MD disorder → Rashba split increases Suggests Pb-I distortion is main crystal field over Pb(6p).