2015-09-29_JMFROST_IOP_PV

Dynamic disorder and electron-hole recombination in hybrid halide perovskites

Transcript

1. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 Jarvist Moore Frost, Federico Brivio, Jonathan Skelton, Aron Walsh Pooya Azarhoosh, Mark van Schilfgaarde (King’s College London) 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) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 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) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 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) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 MAPI makes a good solar cell. Why? MAPI makes a good solar cell. Why? ◆ 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 cm^2 / Vs vs. 1000 for CdTe) ◦ ? Reduced by the potential energy fluct?
5. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 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+
6. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 Figure: Beau Lambert, Kenneth A. Mauritz. 36 26 6
7. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 Free Carriers or Excitons? 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) = +8.92 @ 300K Onsager theory; See Wilsen 1939
8. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 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]
9. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 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]
10. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 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 ← (Pooya Azarhoosh; paper in prep. :) ) Why MAPI is so great: The Dresselhaus crystal field effect splits the CBM (more than VBM); the band gap becomes slightly indirect. 50meV
11. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 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.)
12. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 FACE (X) DIAGONAL (R) EDGE (M) FACE: 42% EDGE: 31% DIAG.: 26% (weighted by MC integration of random sphere points)
13. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 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
14. 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
15. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 2D photon echo anisotropy measurements • monoexponential decay ~2 ps reorientation time • This is the fastest estimate as energy transfer may be involved "Real-Time Observation of Organic Cation Reorientation in Methylammonium Lead Iodide Perovskites". A. Bakulin et al. JPCL 2015 6 (18), 3663-3669, DOI: 10.1021/acs.jpclett.5b01555 Pump 1470 cm-1 Probe 1445 cm-1
16. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 STARRYNIGHT • There is a methyl-ammonium dipole • The methyl-ammonium have some freedom to move → Simulate response with on-lattice Ising-like (Potts) model
17. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 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)
18. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 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)
19. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 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 ]]
20. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 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
21. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 On lattice Statistical Physics Hamiltonian
22. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 → 'strain' term from DFT calculation in 4x4x4 Cell 25-75 meV / neighbour 25 meV Nearest Neighbour 1-5 meV at solar cell fields
23. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 T= 0 K (Ground State - but a bit out of eqm, due to MC) CageStrain = 50 meV / neighbour ---> Ferroelectric
24. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 Ferroelectric; low disorder, which then melts to give sudden increase in variance T 1 V 1 V
25. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 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 ]
26. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 Cagestrain=25 meV → Semi-ordered Ferroelectric ground state; Intermediate long range order (dynamic) at finite T 0K 128K 64K 256K 384K
27. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 0K 128K 256K 384K Cagestrain=25 meV → Semi-ordered Ferroelectric ground state; Intermediate long range order (dynamic) at finite T
28. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 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)
29. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 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
30. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015
31. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 Basic Stat. Mech. V Assumptions: • Slowly varying potential c.f. size of the polaron
32. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 Basic Stat. Mech. V h+ h+ h+ e- e- Recombination... Recombination proportional to electron and hole densities at a site (Langevin).
33. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 Basic Stat. Mech. V h+ h+ h+ e- e- Recombination...
34. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 Basic Stat. Mech. V h+ h+ h+ e- e- Recombination...
35. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 Boltzmann e- Fermi level? h+ Fermi level?
36. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 Fermi-Dirac e- quasi Fermi level h+ quasi Fermi level Fermi Level
37. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015
38. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 Lifetime vs. Mobility ? • How much is mobility reduced by potential fluctuations? ◦ Balance of mu vs. tau. ◦ Need a model for polarons + charge transport. • If radiative recombination has been suppressed by the indirect gap, did we pay for it in reduced absorption? In driving some other loss pathway?
39. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 Collaborators:- Piers Barnes, Aurel Leguy, Andrew McMahon - Imperial College London Mark van Schilfgaarde, 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
40. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 The backpages
41. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 Polarisation Response • Sinusoidally vary Efield • Calculate polarisation response of material Applied field
42. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 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?
43. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 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
44. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 Cagestrain=0 → Antiferroelectric (AFE) ground state. No easy definition of AFE order parameter? ??? 0K
45. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 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
46. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 Sinusoidal potential variation...
47. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 Reproduce Adriaenssens 1997 result (numerically) Sum of rates (proport. to densities) Direct evaluation via partition functions
48. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015
49. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 STARRYNIGHT code (live 'user interface') Dipole alignment Resultant electostatic potential
50. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 → Expect anti-ferroelectric behaviour 25 meV (Frost, APL Mater 2014)
51. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 0K 100K 300K 1000K
52. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 Zero field Dipole alignment .04% aligned (noise)
53. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 Zero field Dipole potential Frost, APL Mater 2014 2D AFE model & further analysis
54. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 Zero field Dipole potential POLARON POLARON
55. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 Zero field Dipole potential Zero field Dipole potential (2D FFT) Zero frequency origins
56. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 → Solar Cell at SHORT CIRCUIT (built in field)
57. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 Short-circuit field Dipole alignment .5% aligned
58. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 Short-circuit field Dipole potential
59. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 Short-circuit field (10MV/m) Dipole potential Dipole potential (2D FFT)
60. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 Zero field (open circuit) Dipole potential Short Circuit Field Dipole potential Same figures, presented side by side...
61. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 Zero field (open circuit) Dipole potential (2D FFT) Short Circuit Field Dipole potential (2D FFT) Same figures, presented side by side...
62. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 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.
63. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 N. Onoda-Yamamuro et al, J. Phys. Chem. Solids. 2, 277 (1992)
64. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 N. Onoda-Yamamuro et al, J. Phys. Chem. Solids. 2, 277 (1992) =+2%
65. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 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
66. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 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
67. 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
68. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 Preprint on the arXiv: 1504.07508
69. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015
70. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 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).
71. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 i.r. Raman Cubic Tetra Ortho Cation Cage
72. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 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 ?
73. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 18 Cage Modes (3 acoustic, 9 cage (3N-3), 6 rovibrational (MA))
74. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 18 MA high freq. molecular modes (3N-6)
75. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 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.
76. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 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
77. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 Cl Br I
78. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 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
79. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 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!)
80. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 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.)
81. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 Anti Ferroelectric --- increase in temperature sees a slow broadening of density of states T 1 V 1 V
82. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 R→ infinity value is equal to the Landau order (but SNR has increased by R^2 !)
83. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 Electric field (scalar) and dipoles alignment
84. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 Ordered anti-ferroelectric domain wall (starting config) Sampled electric field at 300 K realisation
85. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 Spatial variation of Boltzmann statistics cancel totally… (recombination a fn (Z) ) exp. terms cancel Ze=Zh if evenly distributed potential ?
86. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 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!)
87. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 How non parabolic? Very! Implications for device models (i.e. Drift diffusion, assumptions of scattering)
88. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 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)
89. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 Lead Iodine Carbon (Methylammonium) ( Lone pair / 2nd order Jahn-Teller distortion - Pb-I bonds change length and flex)
90. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 Iodine Location Need 2Nx2Nx2N supercell for tilting!
91. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 2015 Glazer Tilting - Glazer 1972
92. Jarvist Moore Frost (University of Bath, UK) Institute of Physics - Advances in Photovoltaics Tues 29th Sept 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.