EMRS 2014 - AA4.7 - Jarvist Moore Frost - Hybrid halide perovskites: modelling crystal dynamics and devices

Slide deck presented at EMRS 2014 on the subject of modelling the molecular ferroelectric response of hybrid halide perovskites (as used recently to great effect in solar cells).

12 minute talk with questions; MD video was presented over slide #5:-
https://www.youtube.com/watch?v=Rr2DDiYUoNA

References / Links:-

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

Ferroelectric contributions to anomalous hysteresis in hybrid
perovskite solar cells
Jarvist M. Frost, Keith T. Butler, and Aron Walsh
Submitted to APLMater
ArXiv Preprint:-
http://arxiv.org/abs/1405.5810

Barnes, Leguy et al. - quasi-inelastic neutron scattering - in production

MD Videos - on YouTube: https://t.co/5z81WfUZhw
https://github.com/WMD-Bath/StarryNight - Starrynight code (classical dipoles MC code)
https://github.com/jarvist/MAPI-MD-analysis - Anaylsis codes for MD (Python)
https://github.com/WMD-Bath/Hybrid-perovskites - Hybrid perovskite DFT structures

Transcript

1. Jarvist Moore Frost, Federico Brivio, Christopher Hendon, Keith Butler, Aron Walsh Walsh Materials Design Group, University of Bath, UK j.m.frost@bath.ac.uk Hybrid halide perovskites: modelling crystal dynamics and devices EMRS-Lille - AA.4/7 2014-05-27
2. • solution processed • defect tolerant (electrically) • strong absorption onset • not air stable (but why not?) • Odd device physics Methylammonium lead iodide (MAPI)
3. Anomalous Hysteresis Operating voltage & history seem to affect recombination within the active material ( this is very strange behaviour - the opposite effect occurs in e.g. amorphous silicon ) Snaith et al. J. Phys. Chem. Lett., 2014, 5 (9), pp 1511–1515 DOI: 10.1021/jz500113x
4. Molecular Dynamics on MAPI (PBESol, Γ-point, VASP) Soft crystal; large distortions of octahedra Repercussions for grain boundaries? (fortuitous?) Accuracy of electronic structure calculations on 'perfect' 'equilibrated' crystals? Would fluctuations lead to polaron localisation? [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=0.5fs, T=300K]
5. Molecular Dynamics Video (hopefully...) • MA ion yaws • ...and rolls… • ...CH3 clicks • so does NH3 ( 25 fs / frame 0.625 ps / s )
6. Purple - Iodine Green - Lead Orange - Carbon (methylammoniu m) Disordered & soft! Tilting octahedra
7. Lead Iodine Carbon (Methylammonium)
8. 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)
9. 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
10. MD: Extract methyl-ammonium alignment vectors... C-N C-N C-N
12. Octahedral symmetry... Pseudo cubic, therefore Oh symmetry… But how to apply the reductions?
14. Reduce to first octant… abs(r), r=[x,y,z]
15. Apply reflection symmetry… sorted(abs(r)), r=[x,y,z] = 48 fold increase in SNR Wikipedia, Octahedral symmetry page
16. FACE (X) DIAGONAL (R) EDGE (M)
17. FACE (X) DIAGONAL (R) EDGE (M) FACE: 42% EDGE: 31% DIAG.: 26% (weighted by MC integration of random sphere points)
18. What effect do these rotating cations have? There are a lot of dynamic processes here... Monopoles moving (i.e. ions) will dominate dielectric response, dipole rotation will add an additional smaller contribution Now we build a model for electrostatic interacting dipole domains
19. Classic dipole model MAPI perovskite has competing interactions giving rise to geometric frustration i.e. similar to a spin glass, but with various electrostatic and cage distortion interactions rather than ferromagnetic and anti-ferromagnetic. Potts model (Potts, 1952), n-dimensional, generalisation of Ising (Ising, 1925) model. Simple 'dipole like' dot-product interaction energy:- See: F. Y. Wu, The Potts model Rev. Mod. Phys. 54, 235 – Published 1 January 1982
21. Ferroelectric domain Hamiltonian
22. 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 Hartrees (x 27.211 V)
23. Same data, volume slice projection 0.6 0.0 Hartrees (x 27.211 V)
24. 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
25. Display direction of Dipole by point on HSV sphere p
26. Dipole angle distributions Increasing (applied) electric field E=1 kBT (NB: Enormous applied electric fields!) E=2 kBT E=10 kBT
27. Red: Zero Field Green: Applied Field
28. 0K 100K 300K 1000K
29. Zero field Dipole alignment .04% aligned (noise)
30. Zero field Dipole potential
31. Zero field Dipole potential Zero field Dipole potential (2D FFT) Zero frequency origins
32. Short-circuit field Dipole alignment .5% aligned
33. Short-circuit field Dipole potential
34. Short-circuit field (10MV/m) Dipole potential Dipole potential (2D FFT)
35. Zero field (open circuit) Dipole potential Short Circuit Field Dipole potential Same figures, presented side by side...
36. Zero field (open circuit) Dipole potential (2D FFT) Short Circuit Field Dipole potential (2D FFT) Same figures, presented side by side...
37. Conclusions • MAPI as soft as Jelly • MA is highly rotationally mobile… • … with a large static dipole along it • Cage:Cage dipole interaction ~25meV • Very rich phase behaviour of 'Potts' style classical model • Dipole domains form regions of electro static potential which may be relevant for charge carrier mobility & recombination
38. Acknowledgments WMD Group (Bath) Petra Cameron, Laurie Peter (Bath - experimental Perovskites, hysteresis) Piers Barnes, Aurelien Leguy (Imperial - quasi-inelastic neutron scattering data & device operation & hysteresis / effect of built in fields) Hugo Bronstein, Robert Palgrave (UCL - discussing hybrid perovskites & the potential for alternative cations) Piers Aurelien Hugo Rob
39. 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 Ferroelectric contributions to anomalous hysteresis in hybrid perovskite solar cells Jarvist M. Frost, Keith T. Butler, and Aron Walsh Submitted to APLMater ArXiv Preprint:- http://arxiv.org/abs/1405.5810 Barnes, Leguy et al. - quasi-inelastic neutron scattering - in production MD Videos - on YouTube: https://t.co/5z81WfUZhw https://github.com/WMD-Bath/StarryNight - Starrynight code (classical dipoles MC code) https://github.com/jarvist/MAPI-MD-analysis - Anaylsis codes for MD (Python) https://github.com/WMD-Bath/Hybrid-perovskites - Hybrid perovskite DFT structures