2015-05-13_Rome_HOPV_JMFROST

Transcript

1. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Jarvist Moore Frost, Federico Brivio, Jonathan Skelton, Aron Walsh Chris Eames, Saiful Islam (Bath) Pooya Azarhoosh, Mark van Schilfgaarde (King’s College London) Aurelien Leguy, Brian O'Regan, Piers Barnes (Imperial College London) Artem Bakulin et al. (now at Cambridge) Walsh Materials Design Group, University of Bath, UK j.m.frost@bath.ac.uk Solid state physics of hybrid halide Perovskites
2. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Overview MAPI: Structure & basic solid state physics Phonons & Raman Molecular Dynamics Ionic conductivity (Iodine & MA) Classical Monte Carlo dipole simulator, STARRYNIGHT
3. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015
4. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015
5. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 N. Onoda-Yamamuro et al, J. Phys. Chem. Solids. 2, 277 (1992)
6. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 N. Onoda-Yamamuro et al, J. Phys. Chem. Solids. 2, 277 (1992) =+2%
7. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 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
8. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 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 + → CH 3 NH 2 + H+
9. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Free Carriers or Excitons? Exciton binding from effective mass theory: Carrier masses & dielectric screening favour free carrier generation J. M. Frost et al, Nano Letters 14, 2584 (2014) = +8.92 @ 300K Onsager theory; See Wilsen 1939
10. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Free Charges or large Polarons or small Polarons? (Frohlich polarons) r p = 32 Å ~= 5.2 Lattice units W = 0.25 eV (Polaron Binding) (Arguments for these follow Landau (1933); from Jones & March 1985, Theoretical Solid State Physics Vol 2 ) (w=9THz=270cm-1) GaAs: 0.068 CdTe: 0.29 AgCl: 1.84 SrTiO3: 3.77 (Devreese 2005) MAPI: [Feynman, 1955]
11. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 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]
12. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 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 ← Why MAPI is so great: The Dresselhaus crystal field effect splits the CBM (more than VBM); the band gap becomes slightly indirect. 50meV
13. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Role of the Crystal Field The Dresselhaus/Rashba effect is driven by the crystal field. ( To a first approximation, it is linear in it. ) Most DFT calculations are in a single unit cell with 100% of the MethylAmmonium aligned - this is probably an upper limit to the crystal field. Weller's <150K structure is Anti-ferroelectric. The MA dipoles are cancelled, Crystal field will be small. Much reduced Dresselhaus; do the cells still work the same? Does the diffusion length change?
14. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Where is the cryogenic data?
15. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Valence Band Alignments K. T. Butler et al, Materials Horizons, Advance Article (2015) Similar to other thin-film PV materials Band gap engineering through A, B or X site modification
16. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 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 extremely sophisticated treatment of k-space grid for sufficient points for fit!)
17. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 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 extremely sophisticated treatment of k-space grid for sufficient points for fit!)
18. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 How non parabolic? Very! Implications for device models (i.e. Drift diffusion, assumptions of scattering)
19. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Overview MAPI: Structure & basic solid state physics Phonons & Raman Molecular Dynamics Ionic conductivity (Iodine + MA) Classical Monte Carlo dipole simulator, STARRYNIGHT
20. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Preprint on the arXiv: 1504.07508 HOPV Poster on Monday by Federico Brivio.
21. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015
22. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 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).
23. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 i.r. Raman Cubic Tetra Ortho Cation Cage
24. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 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 ?
25. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 18 Cage Modes (3 acoustic, 9 cage (3N-3), 6 rovibrational (MA))
26. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 18 MA high freq. molecular modes (3N-6)
27. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 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.
28. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 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
29. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Cl Br I
30. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Overview MAPI: Structure & basic solid state physics Phonons & Raman Molecular Dynamics: Beyond the Harmonic Ionic conductivity (Iodine & MA) Classical Monte Carlo dipole simulator, STARRYNIGHT ( Initial work: Frost 2014, APL Materials 2 (8), 081506 ; Quasi-elastic Neutron Scattering, Nature Comms (Leguy, in press) 2D infrared spectroscopy (Bakulin, submitted))
31. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Incredibly Soft crystal; large distortions of octahedra ➔ MA ion yaw ➔ ...and roll… ➔ ...CH3 clicks ➔ so does NH3 Do electronic structure calculations on 'perfect' 'equilibrated' crystals have any real meaning for MAPI? [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 (MAPI is as soft as Jelly.)
32. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 There is nothing clever about doing MD... It just takes time… The challenge is doing something useful with the data...
33. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Unit cell (2x2x2) PbI 6 Octahedra 'Salt Cellars': 0.1 ps mean; integrates out hydrogen-vibrations Orange-Green tubes: 1 ps average of Carbon- Nitrogen bond; MA alignment
34. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Molecular Dynamics Challenge is getting useful science out of R{x, y,z}(t) ➔ {Static} ensemble information ➔ Dynamics ◆ Correlation (MA ion vs. Octahedra)
35. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Lead Iodine Carbon (Methylammonium)
36. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Lead Physicist: Second Order Jahn-Teller effect, large movement of Pb relative to I (If there is a degeneracy, the universe wants to break it.) Chemist: Pb Lone Pair (6s2) - of course it will be distorting! Octahedra distort and become polar themselves.
37. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Iodine Location Need 2Nx2Nx2N supercell for tilting!
38. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Glazer Tilting - Glazer 1972
39. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Y. Kawamura et al, J. Phys. Soc. Jap. 71, 1964 (2002)
40. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Traces in space over 200 ps of Molecular Dynamics of MAPI at 300 K.
41. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Weller, 2015; Powdered Neutron Diffraction solution (Orthorhombic | Cubic )
42. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Band Gap variation (Gamma, PBESol) during MD Qualitative only. Gamma point PBESol occ->unocc energy only! No fermi golden rule / overlap consideration Need a quasi-particle theory for proper absorption
43. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 MD: Extract methyl-ammonium alignment vectors... C-N C-N C-N
44. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 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.
45. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 FACE (X) DIAGONAL (R) EDGE (M) FACE: 42% EDGE: 31% DIAG.: 26% (weighted by MC integration of random sphere points) Molecular ferroelectric contributions to anomalous hysteresis in hybrid perovskite solar cells Jarvist M. Frost, Keith T. Butler, and Aron Walsh APL Mat. 2, 081506 (2014); DOI: 10.1063/1.4890246
46. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 (1 frame = 25 fs) Sampling both residence time (long tail) & time taken to move (short time peak) ~2.5 ps for average (mean) dynamics ~1.25 ps for first peak (fast) dynamics
47. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 2D photon echo anisotropy measurements Artem Bakulin
48. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 •Simulated 2DIR via Boson H propogation, by Thomas Jansen •Two decay processes: fast <0.3 ps; and a longer 3 ps process [expt window 6 ps] •Directly attribute to 'wobbling' and 'hopping' motion of MA ion •T-dep MD shows that at 150K (pseudo-cubic); motion is partially frozen. Pump 1470 cm-1 Probe 1445 cm-1 2D photon echo anisotropy measurements (MD)
49. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Are these motions described by Phonons? In Phonon eigenmodes, 117 cm-1 mode corresponds to MA constrained rotation = 3.5 THz = 0.285 ps Overall motion of MA not described in harmonic limit. (Slowest motion 1 ps .)
50. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Strong Temperature Dependence of MA align. Real-Time Observation of Organic Cation Reorientation in Methylammonium Lead Iodide Perovskites Artem A. Bakulin, Oleg Selig, Huib J. Bakker, Yves L.A. Rezus, Christian Müller, Tobias Glaser, Robert Lovrincic, Zhenhua Sun, Zhuoying Chen, Aron Walsh, Jarvist M. Frost, Thomas L. C. Jansen ( Submitted to Nature Communications )
51. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Overview MAPI: Structure & basic solid state physics Phonons & Raman Molecular Dynamics Ionic conductivity (Iodine + MA) Classical Monte Carlo dipole simulator, STARRYNIGHT ( Out to review with Nature Comms. )
52. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Nudged elastic band activation energies, of vacancy mediated diffusion; from DFT / PBESol in MD equilibrated (sampled) 'even expansion' Supercells (spurious results before we did this… strain + electrostatic energy of artificially aligned dipoles) Chris Eames et al, accepted Nature Comms May 2015
53. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Driving both ions, electrons, and dipoles all result in an electric field. Direct measure of species responsible for hysterisis?
54. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 New Spiro? Calculating Ionisation Potential of SPIRO-OMeTAD and twelve methoxy isomers and polymethoxy derivatives, simple vacuum hybrid DFT (Delta SCF) calculations. Modular design of SPIRO-OMeTAD analogues as hole transport materials in solar cells Alexander T. Murray, Jarvist M. Frost, Christopher H. Hendon, Christopher D. Molloy, David R. Carbery and Aron Walsh Chem. Commun., 2015, Advance Article DOI: 10.1039/C5CC02129D Received 12 Mar 2015, Accepted 23 Apr 2015
55. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Overview MAPI: Structure & basic solid state physics Phonons & Raman Molecular Dynamics Ionic conductivity (Iodine vacancies) Classical Monte Carlo dipole simulator, STARRYNIGHT
56. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Electrostatic potential projected onto electron density isosurface (iso value = 0.02) 0.6 0.375 0.3 Electrostatic Potential Vacuum calculation CCSD/cc-pVTZ on b3lyp/6-31g* geom. Gaussian09 2.2 Debye Φ E 18 electrons,closed shell = happy quantum chemical days (Frost, Nano Letters 2014) Hartrees (x 27.211 V)
57. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Interaction Energy Vacuum dielectric (effect through empty cage gap) On-lattice dipoles, spacing of 6.29Å. Point dipole approximation * = 25 meV * MA Dipole moment massively dominates in polarisation tensor, point approximation possibly not valid r=6.29Å 2.2 Debye (Frost, 2014, Nano Letters)
58. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Calculation of cage strain term (elastic response)... Rotating single MA in 4x4x4 supercell (+ relaxing intermediates) gives you a ~ near-neighbour dot product local strain / elastic response term. = 25-50 meV / nearest neighbour [[ with significant error bars ]]
59. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 MAPI domain Hamiltonian (Frost, APL Mater 2014) (25 meV)
60. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 MAPI domain Hamiltonian (Leguy, Nat Comms, 2015) 25-50 meV / nearest cofacial neighbour (25 meV)
61. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 • Optimised on-lattice C99 code ; ◦ millions - billions MC moves / second • 2D version released May 2014; (Frost, APL Mater 2014) ◦ 3D version + many extra analyses, ~June 2015 STARRYNIGHT
62. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 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!)
63. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Zero field Dipole alignment .04% aligned (noise)
64. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Zero field Dipole potential Frost, APL Mater 2014 2D AFE model & further analysis
65. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Zero field Dipole potential POLARON POLARON
66. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Ferroelectric --- increase in temperature sees a large broadening in density of states T 1 V 1 V
67. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Quantifying order: Where is the Physics? Landau Order parameter, gives useful metric when you have infinite range order - but doesn't describe partial ordering.
68. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 R→ infinity value is the same as the Landau order (but SNR has increased by R^2 !) Define a radially-dependent autocorrelation function of the dipoles Ziman - Models of Disorder, 1979
69. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Cagestrain=25 meV → Semi-ordered Ferroelectric ground state; Intermediate long range order (dynamic) at finite T 0K 128K 64K 256K 384K
70. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 0K 128K 256K 384K Cagestrain=25 meV → Semi-ordered Ferroelectric ground state; Intermediate long range order (dynamic) at finite T
71. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Polarisation Response • Sinusoidally vary Efield • Calculate polarisation response of material Applied field
72. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Polarisation Applied field Elastic Cage Strain = 25 meV No cage strain - columnar Anti- ferroelectric ~1GHz Scan 10 nm sample Nb: Time in Monte Carlo is ill defined Assume 3 ps / MC move Nb: Fields enormous! ~75 V Lossy Dielectric? Ferroelectric?
73. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 ~1MHz Scan 10 nm 2D sample Nb: Time in Monte Carlo is ill defined Assume 3 ps / MC move Polarisation Caveat: 2D simulation! - (simulation time limitations) ~2.5 V
74. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Electric field (scalar) and dipoles
75. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Electrostatic potential and dipoles
76. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Electrostatic potential and dipoles POLARON POLARON NORALOP
77. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Evidence from numerics... ➔ Excitons: not stable at RT. ➔ Polarons: ~5 lattice units; 0.25 eV binding ➔ MAPI is soft. Distorting / Tilting @ 300K ➔ MA is highly rotationally mobile… ◆ … with a large static dipole along it ◆ Cage:Cage dipole interaction ~25meV ➔ Dipole domains form correlated regions of electrostatic potential relevant for charge carrier mobility & recombination
78. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Is MAPI Ferroelectric? • Ferroelectric order parameter never ~1.0 ◦ i.e. not a true long range ferroelectric, ◦ anti-ferroelectric <150 K ground state • Distant dependent order param ◦ short range order possessed to high temperature ◦ Hysteretic polarisation due to domain wall creep • These domains form internal electric-fields ◦ Crystal field effect → Rashba splitting ◦ Exciton separation by E-field ◦ Segregation of electrons and holes
79. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Why is MAPI great?: Large SOC + crystal field ➔ Dresselhaus, Flattened VBM (+-5meV) → sharp, strong, absorption ➔ Split CBM (+-50meV) → reduced radiative recombination (lost in k-space) The benefits for PV of a direct AND indirect gap
80. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Why is MAPI great?: Defects don't harm Why is MAPI so electrically benign? Schottky analysis suggests 0.4 % defects! Ionic disorder is favoured - lattice defects are low energy to form & so they compensate. High dielectric constants screen effects; clustering of defects neutralises them. Self-Regulation Mechanism for Charged Point Defects in Hybrid Halide Perovskites Prof. Aron Walsh, Dr. David O. Scanlon, Prof. Shiyou Chen, Prof. X. G. Gong and Dr. Su-Huai Wei. Article first published online: 11 DEC 2014 DOI: 10.1002/ange.201409740
81. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Hysteresis? ➔ Ionic (Iodine + MA, vacancy mediated) conductivity is theoretically justified, with an activation energy that agrees with expt. ➔ Extremely rich ferroelectric, antiferroelectric & mixed phase behaviour expected; delayed Polarisation response ➔ My suspicion is that both processes are present; ◆ experiment is needed to differentiate ◆ Theory provides possibilities; Nature is empirical!
82. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Collaborators:- Barnes - Imperial College London, Bakulin, Jansen - Cambridge, Groningen Schilfgaarde - King's College London, Islam - Bath Piers Barnes Aurelien Leguy Mark van Schilfgaarde Pooya Azarhoosh WMD Group, Bath Acknowledgments:- EPSRC - EP/K016288/1 EPSRC Archer - EP/L000202 University of Bath HPC
83. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Papers & codes Atomistic Origins of High-Performance in Hybrid Halide Perovskite Solar Cells Jarvist M. Frost, Keith T. Butler, Federico Brivio, Christopher H. Hendon, Mark van Schilfgaarde, and Aron Walsh Nano Letters 2014 14 (5), 2584-2590 DOI: 10.1021/nl500390f Molecular ferroelectric contributions to anomalous hysteresis in hybrid perovskite solar cells Jarvist M. Frost, Keith T. Butler, and Aron Walsh APL Mat. 2, 081506 (2014); DOI: 10.1063/1.4890246 MD Videos - on YouTube: https://t.co/5z81WfUZhw https://github.com/WMD-Bath/StarryNight - Starrynight code (classical dipoles 2D MC code) https://github.com/jarvist/MAPI-MD-analysis - Analysis codes for MD (Python) https://github.com/WMD-Bath/Hybrid-perovskites - Hybrid perovskite DFT structures
84. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Additional slides...
85. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Ziman's "Models of Disorder" 1979
86. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 BUT - not the complete story; need higher order distribution functions → compactness / smoothness
87. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 T= 128 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.)
88. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 T= 128 K (Ground State - but a bit out of eqm, due to MC) CageStrain = 1 ---> Partial 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.)
89. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 T= 128 K (Ground State - but a bit out of eqm, due to MC) CageStrain = 2 ---> 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.)
90. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Perovskite (ABX 3 ) Crystal structure of the mineral CaTiO 3 A BX 3 Lev Perovski (Russia, 1839)
91. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 A - Molecular Cation B - {Pb, Sn} X 3 - Halide {I, Br, Cl*} Hybrid Perovskites (ABX 3 )
92. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 MAPI Solar Cells PbI 2 + CH 3 NH 3 .I (soln) → CH 3 NH 3 .PbI 3 ~20% efficient solar cell SQ limit Henry Snaith, University of Oxford, with a Hybrid Perovskite Film Image credit: Douglas Fry
93. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015
94. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 STARRYNIGHT code (live 'user interface') Dipole alignment Resultant electostatic potential
95. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 → Expect anti-ferroelectric behaviour
96. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 0K 100K 300K 1000K
97. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Zero field Dipole potential Zero field Dipole potential (2D FFT) Zero frequency origins
98. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 → Solar Cell at SHORT CIRCUIT (built in field)
99. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Short-circuit field Dipole alignment .5% aligned
100. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Short-circuit field Dipole potential
101. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Short-circuit field (10MV/m) Dipole potential Dipole potential (2D FFT)
102. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Zero field (open circuit) Dipole potential Short Circuit Field Dipole potential Same figures, presented side by side...
103. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Zero field (open circuit) Dipole potential (2D FFT) Short Circuit Field Dipole potential (2D FFT) Same figures, presented side by side...
104. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015
105. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 → 'strain' term from DFT calculation in 4x4x4 Cell
106. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Anti Ferroelectric --- increase in temperature sees a slow broadening of density of states T
107. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 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.)
108. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 T= 0 K (Ground State - but a bit out of eqm, due to MC) CageStrain = 2 ---> 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.)
109. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Cagestrain=0 → Antiferroelectric (AFE) ground state. No easy definition of AFE order parameter? ??? 0K
110. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015
111. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Hybrid Perovskites: The Bad News Extremely high efficiency for a solution processed solar cell technology ◆ c.f. ~10% for Dye solar cell, ~12% for organic Why? ◆ Small exciton binding energy (large ε r ~=25) ◆ Very long minority carrier diffusion lengths ◆ High ambipolar charge carrier mobility Lead (!); ◆ Tin is less stable <24 hrs lifetime Anomalous hysteresis in measurement? Snaith et al, Phys. Chem. Lett., 2014, 5 (9), pp 1511– 1515
112. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Deformation potential ➔ Large scale movement of ions considerably varies Hamiltonian used to calculate the electronic structure ➔ Disorder of movement means there is no longer a perfect lattice - Bloch states feel a disordered potential ➔ Consequence for band transport? (i.e. polaron localisation) ➔ For absorption? (losing dimensionality of bands increases absorption coefficient, i.e. as amorphous silicon vs. X'taline)
113. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Rotation and tilting of octahedra Accessible ferroelectric and antiferroelectric phases A. M. Glazer, Acta. Cryst. B 28, 3384 (1972) Mike Glazer (Oxford)
114. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Perovskite Distortions • DISTORTIONS of the octahedra • DISPLACEMENTS of cations (i.e. BaTiO3) • TILTING of the Octahedra Distortion & displacement driven by electronic instabilities of A-cation (Here, Pb) Tilting retains same 1st coordination sphere (octahedra), while cation-anion distance changes (After Woodward, 1997)
115. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 MAPI: Tilts, Distorts & Displaces • This is a problem; how to deconvolve? "Gauge kinematics of deformable bodies" Shapere, Wilczek Am. J. Phys. 57, 514 (1989); DOI: 10.1119/1.15986
116. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Experiment by Piers Barnes and Brian O'Regan to directly probe hysteresis in solar perovskite solar cells; transient current as a function of switched light and bias. (NB: Very little temperature dependent data in the literature. Due to the Sprio hole transport layer, devices 'freeze out' at relatively high temperature.)
117. Jarvist Moore Frost (University of Bath, UK) HOPV Rome - Solid state physics of hybrid Perovskites 13th May 2015 Ionic transport in hybrid lead iodide perovskite solar cells Christopher Eames, Jarvist M. Frost, Piers R. F. Barnes, Brian C. O’Regan, Aron Walsh and M. Saiful Islam (Nature Communications, accepted May 2015, in press.)