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2017-05-22_JMFROST_MAPI-Polarons.pdf

 2017-05-22_JMFROST_MAPI-Polarons.pdf

As Presented at Spring EMRS2017, D.1.2.
I made it to slide 43!

F9278b7f6b5b5c4e09e6b5dec800660a?s=128

Jarvist Moore Frost

May 22, 2017
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  1. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Walsh Materials Design Group, Imperial College London, UK jarvist.frost@imperial.ac.uk Polarons in CH 3 NH 3 .PbI 3 : formation, transport and recombination Jarvist Moore Frost, Lucy Whalley, Jonathan Skelton, Pooya Azarhoosh, Scott McKechnie, Mark van Schilfgaarde, Aron Walsh
  2. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Perovskite (ABX 3 ) Crystal structure of the mineral CaTiO 3 A BX 3 Lev Perovski (Russia, 1839)
  3. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 A - Molecular Cation - '1+' charge B - {Pb, Sn} - '2+' charge X 3 - Halide {I, Br, Cl*} - '1-' charge Hybrid Halide Perovskites (ABX 3 ) Weber, Dieter. "CH3NH3PbX3, ein Pb (II)-System mit kubischer Perowskitstruktur/CH3NH3PbX3, a Pb (II)-System with Cubic Perovskite Structure." Zeitschrift für Naturforschung B 33.12 (1978): 1443-1445.
  4. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 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 (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Glazer Tilting - Glazer 1972
  6. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Glazer Tilting - Glazer 1972 Theorist health warning: • The atoms are heavy (Pb Z=82) • The material is static and dynamically disordered DFT fails in important ways. The central electronic structure theory ansatz (Born-Oppenheimer adiabatic approximation) is dubious. See: "Perspective: Theory and simulation of hybrid halide perovskites" LD Whalley et al. https://arxiv.org/abs/1703.09504
  7. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Why is solution processed MAPI (disorder) an efficient solar cell? ◆ Almost absent non-radiative recombination ◦ Few mid gap defects (fortitude? Linked to the negative deformation potential?) ◆ Slow radiative recombination • Unusual for a direct gap material • ? Slightly-indirect gap due to Rashba splitting • ? Electrostatic potential fluctuations reduce recombination ◆ Sufficient mobility to get charges out • But not that high considering effective mass (~50 cm2/Vs vs. 1000 cm2/Vs for CdTe)
  8. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 What is a Polaron? ➔ bare electron interacts with polar modes of lattice → polaron (the i.r. active lattice vibrations) ➔ becomes dressed in a cloud of excitations ➔ interactions energetically trap particle… ➔ And shield interaction between particles... (A Guide to Feynman Diagrams in the Many-body Problem, R.D. Mattuck) e + + + + + + A Quasiparticle!
  9. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Dielectric response… Fröhlich Polaron (static picture)
  10. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 • Consider linear dielectric response -outside- polaron Dielectric response… Fröhlich Polaron
  11. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Dielectric response… Site Energy (Polarisation) Self consistent response...
  12. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 S For an idealised 1D chain...
  13. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Effective mass polarons α GaAs: 0.068 CdTe: 0.29 AgCl: 1.84 SrTiO3: 3.77 (Devreese 2005) In effective mass approximation (NFE), 'electrons' are already a quasi-particle with a renormalised mass (effective mass). In a polar material, a major electron-phonon coupling is the long-ranged dielectric coupling. We can calculate this 'Frohlich' parameter with simply: ➔ Difference of dielectric constants ➔ Characteristic frequency of 'LO' mode ➔ Effective mass of electron (Original form Landau (1933); this follows Jones & March (1985), "Theoretical Solid State Physics Vol 2". See also Devreese (2016), arXiv:1611.06122. )
  14. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 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]
  15. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 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 large k-space grid for sufficient points for fit near extrema!)
  16. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Figure: Beau Lambert, Kenneth A. Mauritz. Dielectric function (not a constant) = +8.92 @ 300K (Onsager theory; See Wilsen 1939)
  17. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 LO-like modes @ 2.2 THz TO-like modes @ 1 THz Representation of i.r. activity from: Phys. Rev. B 92, 144308 (2015)
  18. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Free Charges or large Polarons or small Polarons? (Arguments for these follow Landau (1933); from Jones & March (1985), "Theoretical Solid State Physics Vol 2" ) MAPI: α GaAs: 0.068 CdTe: 0.29 AgCl: 1.84 SrTiO3: 3.77 (Devreese 2005) m h */m ~ 0.12 (holes)
  19. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Free Charges or large Polarons or small Polarons? (Arguments for these follow Landau (1933); from Jones & March (1985), "Theoretical Solid State Physics Vol 2" ) (Perturbation theory, small alpha limit, R.Feynman, 1955)
  20. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Free Charges or large Polarons or small Polarons? (Polaron Binding Energy) (Arguments for these follow Landau (1933); from Jones & March (1985), "Theoretical Solid State Physics Vol 2" ) (Jones & March, 1985)
  21. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Exciton binding from effective mass theory: Carrier mass & dielectric screening favour free carrier generation (t→infinity). But initial exciton is commensurate with polaron size! Where does the energy go? Radius = 36 Å = 5.75 Lattice Spacings (Epsilon infinity) Free charge generation or excitons? (MAPI; Iodine material)
  22. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Polarons in CH 3 NH 3 .PbI 3 : transport
  23. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017
  24. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017
  25. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017
  26. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017
  27. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 W
  28. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 M k (Feynman Polaron Model: "Slow Elcetrons in a Polar Crystal", Phys Rev, Feynman 1955)
  29. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 (Hellwarth et al. 1999 - an update to Feynman et al. 1962. Direct contour integration of mobility response function.)
  30. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 (Hellwarth 1999)
  31. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 (Hellwarth 1999)
  32. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 (Beta>1, means T<100 K for halide perovskites)
  33. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Variational codes validated against Hellwarth 1999 https://github.com/jarvist/PolaronMobility-FeynmanKadanoffOsakaHellwarth (Hellwarth 1999 PRB)
  34. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 [1.61] from Devreese 2016, based on: Boltzmann Equation for Polarons Leo P. Kadanoff Phys. Rev. 130, 1364 – Published 15 May 1963 Kadanoff 1963 - adds a term for the emission of phonons. BUT - is still meant for low-T. Feynman, Hellwarth et al.1962 "Dissipation at low temperatures" T=300 , β=0.36 : v= 19.82 w= 16.92; M=0.372 k=107 μ(Kadanoff) = 112 cm^2/Vs
  35. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Nb: Log scale! Dynamic disorder, phonon lifetimes, and the assignment of modes to the vibrational spectra of methylammonium lead halide perovskites AMA Leguy, et al. Physical Chemistry Chemical Physics 18 (39), 27051-27066 (2016)
  36. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Ship wakes: Kelvin or Mach angle? M. Rabaud and F. Moisy, Phys. Rev. Lett. 110, 214503 (2013). Editor's suggestion
  37. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Ship wakes: Kelvin or Mach angle? M. Rabaud and F. Moisy, Phys. Rev. Lett. 110, 214503 (2013). Editor's suggestion
  38. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 → Semonin et al.: The Journal of Physical Chemistry Letters 7, 3510 (2016) → Saidaminov et al.: Nature Communications 6, 7586 (2015) → Milot et al.: Advanced Functional Materials 25, 6218 (2015) μ(electron) = 136 cm^2/Vs μ(hole) = 94 cm^2/Vs μ(Saidaminov) = 67.2 cm^2/Vs μ(Milot/Herz) = 35 cm^2/Vs μ(Semonin) = 115 cm^2/Vs
  39. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Internal characterisation of polaron state. Direct prediction of (T-dep) scattering time and phonon mass.
  40. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Not the first to apply this model to halide perovskites... Optical Phonons in Methylammonium Lead Halide Perovskites and Implications for Charge Transport M. Sendner, P. Nayak, D. Egger, S. Beck, C. Müller, B. Epding, W. Kowalsky, L. Kronik, H. J. Snaith, A. Pucci and R. Lovrincic Materials Horizons, 2016, 3, pp 613-620
  41. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Cesium (inorganic halide perovskite) analogues: In comparison to methlyammonium, polaronic nature is reduced by the reduced (static) dielectric constant ( → mobility doubles). Stiffening of phonon modes in Sn based perovskites furthers this.
  42. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 PAPER: https://arxiv.org/abs/1704.05404 CODES: github.com/jarvist/PolaronMobility-FeynmanKadanoffOsakaHellwarth
  43. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Polaron mobility: • Fully ab-initio temperature-dependent prediction of mobility ◦ Great agreement to (single-crystal TRMC) data for MAPI and CsSnI3. ◦ Suggests optical phonon scattering limits mobility • Theory is based on effective-mass approximation, and only considers dielectric electron-phonon coupling • BUT, within those limits ◦ Coupled electron-phonon system is treated fully (correlation integrated out with path integration) ◦ Strong coupling regime + transition to weak ◦ In a polar material, the long range dielectric electron-phonon coupling is expected to be large (and perhaps dominate) PAPER: https://arxiv.org/abs/1704.05404 CODES: github.com/jarvist/PolaronMobility-FeynmanKadanoffOsakaHellwarth
  44. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Real space disorder: STARRYNIGHT codes Classical Metropolis algorithm simulation of cage:cage dipole interactions. Analytic Hamiltonian, interaction strength parameterised by DFT. ( Apl Materials 2 (8), 081506, 2014. Open source on GitHub https://github.com/WMD-Group/Starrynight )
  45. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 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!)
  46. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Parameters via DFT 25-75 meV (nearest neighbour) 25 meV (nearest neighbour) 1-5 meV at solar cell fields
  47. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 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!
  48. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 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.)
  49. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 T= 0 K (Ground State - but a bit out of eqm, due to MC) CageStrain = 50 meV / neighbour ---> Ferroelectric Ferroelectric order parameter tricked by disorder...
  50. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Cagestrain=25 meV → Semi-ordered Ferroelectric ground state; Intermediate long range order (dynamic) at finite T 0K 128K 64K 256K 384K
  51. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 0K 128K 256K 384K Cagestrain=25 meV → Semi-ordered Ferroelectric ground state; Intermediate long range order (dynamic) at finite T
  52. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 POLARON POLARON NORALOP Slightly indirect band gap. Real space potential fluctuations
  53. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Real space recombination model:
  54. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Simple Statistical Mechanics argument V h+ h+ h+ e- e- Recombination...
  55. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 POLARON POLARON NORALOP How to model polarons? POLARON
  56. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Gaussian blur!
  57. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Boltzmann / mid-gap Fermi Dirac Fermi level
  58. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Fermi-Dirac e- quasi Fermi level h+ quasi Fermi level Fermi Level
  59. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 (Boltzmann distribution of electrons, at 300 K) Recombination Reduction
  60. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Simple thermal de-trapping model (Boltzmann distribution of electrons, at 300 K) Mobility Reduction
  61. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Recombination vs. Mobility ? This is structureless disorder (just density of states), using models more suitable from low mobility materials (from amorphous silicon). At 300 K recombination is reduced by a factor of X 100 due to charge segregation. But the potential fluctuations also reduced the mobility by a factor of X 100. Further work will look at structure and see whether 'ferroelectric highways' allow for greater mobility than expected of Gaussian Disorder Model.
  62. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Real-space disorder Conclusions ➔ Ground state dependent on details of Hamiltonian terms. Our errors here could be +-200%. ➔ We observe exponentially decaying long range partial ferroelectric ordering. ➔ Continuous inter-converting domains at finite temperature. ➔ Considerable (+-150 meV) electrostatic potential fluctuations. Statistical mechanics models indicate what behaviour is possible. Experiment will show that which is present. https://github.com/WMD-Group/StarryNight
  63. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Collaborators:- Piers Barnes; Jenny Nelson + Groups - Imperial College London Mark van Schilfgaarde, Pooya Azarhoosh, Scott McKechnie - King's College London Piers Barnes Jenny Nelson Mark van Schilfgaarde Pooya Azarhoosh WMD Group, ICL/Bath Acknowledgments:- EPSRC - EP/K016288/1 EPSRC Archer - EP/L000202 University of Bath HPC Imperial College London HPC https://wmd-group.github.io
  64. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 The Back Pages - extra slides
  65. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Electron-phonon coupling for fun and the future ( Now published, Physical Review B 94 (22), 220301 - 2016 )
  66. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Florian Marquardt, Wikipedia, CC Lattice Dynamics (Phonons) MAPI Low-frequency dispersion (PCCP, AMA Leguy et al., 2016)
  67. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Lattice Dynamics (Phonons)
  68. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Leguy et al. Phys. Chem. Chem. Phys., 2016,18, 27051-27066 DOI: 10.1039/C6CP03474H
  69. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Quantum (an)Harmonic Oscillators & e-ph coupling Motivation: How to treat soft phonon modes? What is the repercussion for the electronic structure (and electron-phonon coupling) for such large tilting modes?
  70. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Adiabatic electron-phonon coupling Born-Oppenheimer approximation (full wavefunction is product of electronic and nuclear wavefunctions) Adiabatic approximation: treat Nuclear and Electronic degrees of freedom separately. Mean-field expectation. Solve Sch. Eqn. for nuclear degree of freedom. Solve electronic Sch. Eqn. varying nuclear degree of freedom (i.e. deformation potential). Combine in mean-field manner.
  71. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 The 1D Schrodinger equation is easy to solve!
  72. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017
  73. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 ~15 meV well persists in structure to > 600 K BE Distribution 600 K 1 K
  74. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 (Calculations: Lucy Whalley) Band-gap as a function of Q (Deformation Potential)
  75. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 (R acoustic mode at Brillouin-Zone boundary [tilt])
  76. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 R M
  77. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 “The previous methods for calculating the electron-phonon matrix element in a metal are neither rigorously formulated nor satisfactory in their results. From each method there is something to learn—usually that the method is unreliable in some important aspect.” —Ziman, 1960 ‘Electrons and Phonons’, § 5.7, page 197. MAPI soft modes • Soft modes at R and M Brillouin-Zone boundaries • Mode following for potential energy surface → 1D Sch. Eqn. solver → Nuclear p.d.f → mean-field temperature resolved el-ph band-gap renormalisation for soft modes • Values of ~35 meV per mode seem to agree with experimental linewidths from photo luminescence
  78. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Absorption: Spin-orbit-coupling flattens the valence band - leading to a large density of states available for direct excitation. A sudden “turn-on”, like 2D band structures. Emission: Holes and electrons quickly thermalise to bottom of band (densities at 1 sun solar flux are very low); indirect radiative recombination is slow. → Have your cake and eat it ← The Dresselhaus crystal field effect splits the CBM (more than VBM); a spin split indirect gap forms. 75 meV P. Azarhoosh et al., APL Materials 4, 091501 (2016) Spin-split indirect-gap:
  79. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 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
  80. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 → DFT, athermal structure; mainly spin texture → DFT, MD sampled structures; mainly k-space displacement
  81. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Calculate radiative recombination rate: QSGW band structure (120x120x120 K-point mesh). Direct transitions only. Fermi-Dirac distribution for the electrons / holes within their band (full thermalisation).
  82. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Strong T-dep at low fluence Direct gap at high fluence. Temperature insensitive dynamics.
  83. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017
  84. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017
  85. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Predictions: Spin-split indirect-gap leads to 300 X decrease in bi-molecular recombination. Weak indirect gap ~75 meV below direct; should not be present in Orthorhombic phase (~<150K). B coeff. varies strongly as a function of intensity (you can't do a 'global fit' to TRPL data over many decades) Faster recombination expected in Sn analogue due to reduced Spin Orbit Coupling - it should be more direct gap like. Lasing threshold can be directly explained by intensity dependence of B. Epitaxial / ferroelectric manipulation should affect optical properties. Spin split indirect gap → may be a new design feature for novel solar cell materials. Present where {Sb,Bi,Pb} + ferroelectric distortion. P. Azarhoosh et al., APL Materials 4, 091501 (2016)
  86. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 "It is typical of modern physicists that they will erect skyscrapers of theory upon the slender foundations of outrageously simplified models." J.M.Ziman, 1962 "Electrons in metals: a short guide to the Fermi surface" Most solid state (electronic structure) theory based on a fiction of periodicity • Infinite in all directions • Perfect registration • Crystallographic momentum is a good q number
  87. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 ( Videos on YouTube - search for 'MAPI molecular dynamics' ) https://youtu.be/K_-rsop0n5A Incredibly Soft crystal; large distortions of octahedra ➔ MA ion yaw ➔ ...and roll… ➔ ...CH3 clicks ➔ so does NH3 [2x2x2 Pseudo cubic relaxed supercell, lattice parameters held constant during MD (NVT simulation). PBESol Functional at the Gamma point (forces + energies should converge well). dt = 0.5 fs, T = 300 K ] Molecular Dynamics
  88. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Iodine location, MAPI, ~100 ps MD
  89. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Glazer Tilting - Glazer 1972
  90. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Project back onto the first unit cell by symmetry
  91. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Lead Iodine Pb: Lone pair / 2nd order Jahn-Teller distortion Carbon (Methylammonium)
  92. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Iodine 300K Iodine 200K
  93. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Timescale of MA orientation 2D infrared spectroscopy ~ 3 ps Bakulin et al. J. Phys. Chem. Lett., 2015, 6 (18), pp 3663–3669 Quasi-Elastic Neutron Scattering (QENS) ~14 ps ; Leguy et al., Nature Communications 2015, 6, 7124 ~5 ps (higher SNR); Chen et al. 2015 arXiv: 1506.02205v2 DFT Molecular Dynamics → 2x2x2 unit cell ~2.5 ps ; Bakulin et al. ~2 ps (FAPI) ; Weller et al. J. Phys. Chem. Lett., 2015, 6 (16), pp 3209–3212
  94. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 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.
  95. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017
  96. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017
  97. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 FACE (X) DIAGONAL (R) EDGE (M) FACE: 42% EDGE: 31% DIAG.: 26% (weighted by MC integration of random sphere points)
  98. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017
  99. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Preprint on the arXiv: 1504.07508
  100. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 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).
  101. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 i.r. Raman Cubic Tetra Ortho Cation Cage
  102. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 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 ?
  103. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 18 Cage Modes (3 acoustic, 9 cage (3N-3), 6 rovibrational (MA))
  104. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 18 MA high freq. molecular modes (3N-6)
  105. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 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.
  106. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 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
  107. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Cl Br I
  108. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Nudged elastic band activation energies, of vacancy mediated diffusion; from DFT / PBESol in MD equilibriated Supercells Iodine Vacancy mediated diffusion: Ea = 0.58 eV
  109. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017
  110. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017
  111. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 N. Onoda-Yamamuro et al, J. Phys. Chem. Solids. 2, 277 (1992)
  112. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 N. Onoda-Yamamuro et al, J. Phys. Chem. Solids. 2, 277 (1992) =+2%
  113. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 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
  114. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 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
  115. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 How non parabolic? Very! Implications for device models (i.e. Drift diffusion, assumptions of scattering)
  116. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Effect of disorder: x100 MD disorder → Rashba split increases Suggests Pb-I distortion is main crystal field over Pb(6p).
  117. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 This is a title (Montserret 48) And this is the text. Questrial 22. It was a bright cold day in April, and the clocks were striking 12. #^/?&
  118. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Walsh Materials Design (WMD) 2011–2016 : Department of Chemistry, University of Bath 2016– : Department of Materials, Imperial College London
  119. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Hybrid Halide Perovskites 2012–2016 → Relativistic electronic structure → Ferroelectricity and hysteresis → Dynamic structural disorder → Defect formation and transport → Anharmonic phonons and IR/Raman spectra "What Is Moving in Hybrid Halide Perovskite Solar Cells?" Jarvist Frost and Aron Walsh, Accounts of Chemical Research 49, 528 (2016)
  120. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Publications Citations Web of Science citation report: TOPIC: (hybrid perovskite OR MAPI OR CH3NH3PbI3 solar cell) 10% solution processed solar cell Why work / not work * on MAPI? * (This should encourage you if you are a Boson-type scientist, Discourage you if you are a Fermion-type!)
  121. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Why is the material interesting? Plus points: ➔ 22% power conversion efficiency solution processed solar cells ➔ Tunable band gap ➔ Easy to make Negative points: ➔ Degrades easily ➔ Sample variation Key question: • Why does it work? Henry Snaith, one of the early proponents
  122. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Step 1) Write down everything you know...
  123. Jarvist Moore Frost (Imperial College London, UK) D.1.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Step 2) Auto-differentiate and optimise function...