2015-12-02_JMFROST_MRS_Perovskite

Dynamic disorder and electron-hole recombination in hybrid halide perovskites

Transcript

1. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Jarvist Moore Frost, Federico Brivio, Jonathan Skelton, Aron Walsh (University of Bath, UK) Pooya Azarhoosh, Scott McKechnie, Mark van Schilfgaarde (King’s College London, UK) Walsh Materials Design Group, University of Bath, UK j.m.frost@bath.ac.uk Dynamic disorder and electron-hole recombination in hybrid halide perovskites
2. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Perovskite (ABX 3 ) Crystal structure of the mineral CaTiO 3 A BX 3 Lev Perovski (Russia, 1839)
3. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 A - Molecular Cation B - {Pb, Sn} X 3 - Halide {I, Br, Cl*} 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.
4. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 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+
5. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Figure: Beau Lambert, Kenneth A. Mauritz. 33 24 4.5 Dielectric function (not a constant)
6. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 LO-like modes @ 2 THz TO-like modes @ 1 THz Representation of i.r. activity from: Phys. Rev. B 92, 144308 (2015)
7. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Timescale of (microscopic) MA motion 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
8. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Lead Iodine Pb: Lone pair / 2nd order Jahn-Teller distortion Glazer Tilting - Glazer 1972 Methylammonium
9. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 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
10. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Free Charges or large Polarons or small Polarons? (Fröhlich polarons) (Polaron Binding) (Arguments for these follow Landau (1933); from Jones & March (1985), "Theoretical Solid State Physics Vol 2" ) MAPI: (Feynman, 1955) α GaAs: 0.068 CdTe: 0.29 AgCl: 1.84 SrTiO3: 3.77 (Devreese 2005)
11. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 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) MRS Boston - NN14.02 Wed 2nd Dec 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); a spin split indirect gap forms. 75 meV
13. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 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
14. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Calculate radiative recombination rate: QSGW band structure. Direct transitions only. Fermi-Dirac distribution for the electrons / holes within their band (full thermalisation).
15. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Strong T-dep at low fluence Direct gap at high fluence. Temperature insensitive dynamics.
16. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Effect of disorder: x100 MD disorder → Rashba split increases Suggests Pb-I distortion is main crystal field over Pb(6p).
17. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Predictions: Spin-split indirect-gap leads to 300 X decrease in bi-molecular recombination 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. ( Pooya Azarhoosh et al.; in press )
18. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Back to real space: STARRYNIGHT 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 )
19. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Parameters via DFT 25-75 meV (nearest neighbour) 25 meV (nearest neighbour) 1-5 meV at solar cell fields
20. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 POLARON POLARON NORALOP Slightly indirect band gap. Real space potential fluctuations
21. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 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!
22. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Cagestrain=25 meV → Semi-ordered Ferroelectric ground state; Intermediate long range order (dynamic) at finite T Increasingly long range partial ferroelectric ordering as T drops. Reaches the orthorhombic phase transition before full ordering. 0K 128K 64K 256K 384K Radial order parameter ( Ziman 1979 ) [ R→ infinity value is equal to the Landau order ]
23. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 0K 128K 256K 384K
24. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Real space recombination model:
25. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Basic Stat. Mech. V h+ h+ h+ e- e- Recombination...
26. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Boltzmann / mid-gap Fermi Dirac Fermi level
27. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Fermi-Dirac e- quasi Fermi level h+ quasi Fermi level Fermi Level
28. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 (Boltzmann distribution of electrons, at 300 K) Recombination
29. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Mobility (Boltzmann distribution of electrons, at 300 K) Simple thermal de-trapping model, with assumed percolation threshold.
30. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Recombination vs. Mobility ? This is stucture less disorder (just density of states), using models more suitable from low mobility materials (from amorphous silicon). At 300 K the reduction in recombination (x 100) due to charge segregation is balanced by an estimate of the reduction in mobility (x 100) caused by trapping / detrapping. Further work will look at structure and see whether 'ferroelectric highways' allow for greater mobility than expected of Gaussian Disorder Model.
31. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Polarisation Response • Sinusoidally vary Efield • Calculate polarisation response of material Applied field
32. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 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?
33. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 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
34. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Starrynight 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
35. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Collaborators:- Piers Barnes, Aurel Leguy, Andrew McMahon - Imperial College London Mark van Schilfgaarde, Scott McKechnie, Pooya Azarhoosh - King's College London 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 http://go.bath.ac.uk/wmd
36. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 The backpages
37. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Cagestrain=0 → Antiferroelectric (AFE) ground state. No easy definition of AFE order parameter? ??? 0K
38. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 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
39. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Sinusoidal potential variation...
40. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Reproduce Adriaenssens 1997 result (numerically) Sum of rates (proport. to densities) Direct evaluation via partition functions
41. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015
42. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 STARRYNIGHT code (live 'user interface') Dipole alignment Resultant electostatic potential
43. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 → Expect anti-ferroelectric behaviour 25 meV (Frost, APL Mater 2014)
44. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 0K 100K 300K 1000K
45. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Zero field Dipole alignment .04% aligned (noise)
46. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Zero field Dipole potential Frost, APL Mater 2014 2D AFE model & further analysis
47. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Zero field Dipole potential POLARON POLARON
48. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Zero field Dipole potential Zero field Dipole potential (2D FFT) Zero frequency origins
49. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 → Solar Cell at SHORT CIRCUIT (built in field)
50. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Short-circuit field Dipole alignment .5% aligned
51. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Short-circuit field Dipole potential
52. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Short-circuit field (10MV/m) Dipole potential Dipole potential (2D FFT)
53. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Zero field (open circuit) Dipole potential Short Circuit Field Dipole potential Same figures, presented side by side...
54. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Zero field (open circuit) Dipole potential (2D FFT) Short Circuit Field Dipole potential (2D FFT) Same figures, presented side by side...
55. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Viktor & Rolf, Autumn 2015, 2015 Haute Couture Fall-Winter collections It's not just a fashionable material, I'd argue it is Haute Couture We may never see it on the street - but we can learn from it.
56. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 N. Onoda-Yamamuro et al, J. Phys. Chem. Solids. 2, 277 (1992)
57. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 N. Onoda-Yamamuro et al, J. Phys. Chem. Solids. 2, 277 (1992) =+2%
58. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 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
59. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 “Natural” 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
60. 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
61. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Preprint on the arXiv: 1504.07508
62. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015
63. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 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).
64. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 i.r. Raman Cubic Tetra Ortho Cation Cage
65. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 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 ?
66. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 18 Cage Modes (3 acoustic, 9 cage (3N-3), 6 rovibrational (MA))
67. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 18 MA high freq. molecular modes (3N-6)
68. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 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.
69. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 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
70. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Cl Br I
71. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Nudged elastic band activation energies, of vacancy mediated diffusion; from DFT / PBESol in MD equilibriated Supercells Iodine Vacancy mediated diffusion: Ea = 0.58 eV
72. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 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!)
73. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 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.)
74. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Anti Ferroelectric --- increase in temperature sees a slow broadening of density of states T 1 V 1 V
75. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 R→ infinity value is equal to the Landau order (but SNR has increased by R^2 !)
76. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Electric field (scalar) and dipoles alignment
77. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Ordered anti-ferroelectric domain wall (starting config) Sampled electric field at 300 K realisation
78. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Spatial variation of Boltzmann statistics cancel totally… (recombination a fn (Z) ) exp. terms cancel Ze=Zh if evenly distributed potential ?
79. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 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 sophisticated treatment of k-space grid for sufficient points for fit!)
80. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 How non parabolic? Very! Implications for device models (i.e. Drift diffusion, assumptions of scattering)
81. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Band Gap variation (Gamma, PBESol) during MD Fluctuation in the eigenvalues → motion coupling into energy levels. This is a thermodynamically sampled renormalisation of the electron energies (electron-phonon coupling)
82. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Iodine Location Need 2Nx2Nx2N supercell for tilting!
83. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 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.
84. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 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.)
85. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 FACE (X) DIAGONAL (R) EDGE (M) FACE: 42% EDGE: 31% DIAG.: 26% (weighted by MC integration of random sphere points)
86. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 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)
87. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 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)
88. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 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. = 25-75 meV / nearest neighbour [[ with significant error bars ]]
89. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 ➢ Optimised on-lattice C99 code ; ◦ up to ~10 million MC moves / second ➢ 2D version released May 2014; (Frost, APL Mater 2014) ◦ 3D version + many extra analyses, ~June 2015 ◦ OPENMP ~July 2015 (doesn't help much…) STARRYNIGHT
90. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 On lattice Statistical Physics Hamiltonian
91. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Ferroelectric; low disorder, which then melts to give sudden increase in variance T 1 V 1 V
92. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Landau Order Param Naive definition poor for dipoles: <<<<<>>>>> = 0 Replace with radial distribution function based order param: ( Ziman 1979 ) [ R→ infinity value is equal to the Landau order ]
93. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Why is radiative recombination so slow? POLARON POLARON NORALOP Slightly indirect band gap. Hypothesise slow recombination due to:- 1) Electrostatic potential fluct (proposed Nanoletters, Starrynight model APLMater, now studying rates) 2) Indirect gap recombination due to SOC (Pooya Azarhoosh, KCL; calculating rates)
94. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Electrostatic Pot. Fluct. Recombination Model • Thomas-Fermi model of electron density… ◦ Not ready for presentation... • Monte-Carlo (classical) model of electro hopping; conceptual issues with defining rates and motion, but coupled dipoles:electron transport would be easy. • First step: Classical Stat. Mech. population of charge carriers → effective slow down of bimolecular recombination
95. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Basic Stat. Mech. V Assumptions: • Slowly varying potential c.f. size of the polaron
96. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Basic Stat. Mech. V h+ h+ h+ e- e- Recombination... Recombination proportional to electron and hole densities at a site (Langevin).
97. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Basic Stat. Mech. V h+ h+ h+ e- e- Recombination...
98. Jarvist Moore Frost (University of Bath, UK) MRS Boston - NN14.02 Wed 2nd Dec 2015 Why is MAPI an efficient solar cell? ◆ Almost absent non-radiative recombination ◦ Few mid gap defects (fortitude?) ◆ 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?