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2017-05-22_JMFROST_MAPI-IBSC.pdf

 2017-05-22_JMFROST_MAPI-IBSC.pdf

As Presented at Spring EMRS2017, E.II.2.

For the first ten minutes I had no slides due to projector issues, so made do with waving my hands to describe band structure...

Jarvist Moore Frost

May 22, 2017
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  1. Jarvist Moore Frost (Imperial College London, UK) E.II.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Walsh Materials Design Group, Imperial College London, UK [email protected] A photon ratchet route to high-efficiency hybrid halide perovskite intermediate band solar cells Jarvist Moore Frost, Pooya Azarhoosh, Scott McKechnie, Mark van Schilfgaarde, Aron Walsh
  2. Jarvist Moore Frost (Imperial College London, UK) E.II.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) E.II.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) E.II.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) E.II.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) E.II.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)
  9. 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]
  10. Jarvist Moore Frost (Imperial College London, UK) E.II.2 - EMRS

    Spring 2017 Mon 22nd May 2017 SOC Spin-texture of the extrema:
  11. Jarvist Moore Frost (Imperial College London, UK) E.II.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:
  12. Jarvist Moore Frost (Imperial College London, UK) E.II.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
  13. Jarvist Moore Frost (Imperial College London, UK) E.II.2 - EMRS

    Spring 2017 Mon 22nd May 2017 → DFT, athermal structure; mainly spin texture → DFT, MD sampled structures; mainly k-space displacement
  14. Jarvist Moore Frost (Imperial College London, UK) E.II.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).
  15. Jarvist Moore Frost (Imperial College London, UK) E.II.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Strong T-dep at low fluence Direct gap at high fluence. Temperature insensitive dynamics.
  16. Jarvist Moore Frost (Imperial College London, UK) E.II.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)
  17. Jarvist Moore Frost (Imperial College London, UK) E.II.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Are lead-halide perovskites Intermediate Band Solar Cells ? SOC renormalised & split conduction band Straddle solar spectrum Spin-split indirect gaps protect from recombination
  18. Jarvist Moore Frost (Imperial College London, UK) E.II.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Necessary conditions for IBSC • VB → IB and IB → CB transitions are bright • Independent quasi-Fermi levels in IB and CB ◦ Charges must not leak CB → IB ▪ CB and IB bands must not touch ▪ Phonon scattering (indirect) must be low ◦ Charges must not thermalise via electrodes • Lifetime of charges in IB must be sufficient for (relatively dim) light to excite charges to the CB
  19. Jarvist Moore Frost (Imperial College London, UK) E.II.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Red-dashed: no spin orbit coupling. Black-full: With spin orbit coupling. QSGW Band structure, Scott McKechnie Px,Py,Pz Configuration: PbII [5d106s26p0]; I-I [5p6]
  20. Jarvist Moore Frost (Imperial College London, UK) E.II.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Valence Band → Intermediate Band 1.6+ eV Valence Band → Conduction Band 3.1+ eV Intermediate Band → Conduction Band Photon Ratchet @ 1.5 eV Partial DoS on 11x11x11 k-mesh (Pooya Azarhoosh)
  21. Jarvist Moore Frost (Imperial College London, UK) E.II.2 - EMRS

    Spring 2017 Mon 22nd May 2017 VB CB Selection rules: • Wavefunction must change parity • Spin conserved • Orbital angular momentum: ◦ Δm l =0,±1 ◦ Δl=±1 Semiconductor gap excitations are usually bonding → anti-bonding (and s → p). Dipole transitions (mainly) PbII [6p0] (mainly) I-I [5p6]
  22. Jarvist Moore Frost (Imperial College London, UK) E.II.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Selection rules… ? Dipole transitions VB CB1 CB2 CB3 PbII [6p z 0] ? PbII [6p y 0] ? PbII [6p x 0] ? (mainly) I-I [5p6]
  23. Jarvist Moore Frost (Imperial College London, UK) E.II.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Mulliken projected partial density of states, from QSGW calculation including spin orbit. VBM is almost perfectly I 5p. The Intermediate and Conduction bands have considerable Pb 6p contribution, but are not pure.
  24. Jarvist Moore Frost (Imperial College London, UK) E.II.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Why think when you can calculate? QSGW 'fixed' LDA Full SOC (out of eqm) Spin-dep. matrix elements Out-of-equilibrium rate model
  25. Jarvist Moore Frost (Imperial College London, UK) E.II.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Why think when you can calculate? QSGW 'fixed' LDA Full SOC (out of eqm) Spin-dep. matrix elements Out-of-equilibrium rate model
  26. Jarvist Moore Frost (Imperial College London, UK) E.II.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Not there yet! Like most codes, Questaal has hard-coding to equilibrium properties...
  27. Jarvist Moore Frost (Imperial College London, UK) E.II.2 - EMRS

    Spring 2017 Mon 22nd May 2017 VB CB1 CB2 CB3 FHI-AIMS: PBEsol (a GGA) with scalar relativistic corrections. 6x6x6 k-point grid. Structure: c-MAPbI3 from WMD Phonon repo • DFT mis-orders states ◦ (An interesting issue for DFT optics calculations in this material, not mentioned much in the literature!) • Spin-orbit-coupling (spin-up // spin-down) matrix elements not (yet) accessible
  28. Jarvist Moore Frost (Imperial College London, UK) E.II.2 - EMRS

    Spring 2017 Mon 22nd May 2017 [isotropically averaged transition matrix element, @ R-point in B.Z.] CB1 -> CB3 = 0.183 eV CB2 -> CB3 = 0.007 eV CB1 -> CB2 = 0.001 eV VB -> CB1 = 0.157 eV VB -> CB2 = 0.050 eV VB -> CB3 = 0.101 eV VB CB1 CB2 CB3
  29. Jarvist Moore Frost (Imperial College London, UK) E.II.2 - EMRS

    Spring 2017 Mon 22nd May 2017 (QSGW) Multi-valley effective mass
  30. Jarvist Moore Frost (Imperial College London, UK) E.II.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Can MAPI make an IBSC? • Two necessary requirements: ◦ Independent Quasi-Fermi levels ✔ ◦ Selective-contacts CB (LiF, Ca, Ba, Fulleroid) ✔ • Can't break Shockley-Queisser (Bg wrong) • Will it make a useful photocurrent? ◦ Requires further calculations, custom codes ◦ Spin-split indirect-gap will reduce recombination, and produce a photon-ratchet effect ◦ Phonon (indirect) transitions between IB & CB? • Rashba-split band extrema offer a lot of potential interesting device physics, exploitable for PV Theory suggests what is possible; experimental tells us what is present!
  31. Jarvist Moore Frost (Imperial College London, UK) E.II.2 - EMRS

    Spring 2017 Mon 22nd May 2017 https://arxiv.org/abs/1611.09786
  32. Jarvist Moore Frost (Imperial College London, UK) E.II.2 - EMRS

    Spring 2017 Mon 22nd May 2017 HEAVY METAL PHOTOVOLTAICS {Pt,Au,Hg,Tl,Pb,Bi} + local field = interesting photo physics!
  33. Jarvist Moore Frost (Imperial College London, UK) E.II.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
  34. Jarvist Moore Frost (Imperial College London, UK) E.II.2 - EMRS

    Spring 2017 Mon 22nd May 2017 The Back Pages - extra slides
  35. Jarvist Moore Frost (Imperial College London, UK) E.II.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
  36. Jarvist Moore Frost (Imperial College London, UK) E.II.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
  37. Jarvist Moore Frost (Imperial College London, UK) E.II.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Iodine location, MAPI, ~100 ps MD
  38. Jarvist Moore Frost (Imperial College London, UK) E.II.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Glazer Tilting - Glazer 1972
  39. Jarvist Moore Frost (Imperial College London, UK) E.II.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Project back onto the first unit cell by symmetry
  40. Jarvist Moore Frost (Imperial College London, UK) E.II.2 - EMRS

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

    Spring 2017 Mon 22nd May 2017 Iodine 300K Iodine 200K
  42. Jarvist Moore Frost (Imperial College London, UK) E.II.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
  43. Jarvist Moore Frost (Imperial College London, UK) E.II.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.
  44. Jarvist Moore Frost (Imperial College London, UK) E.II.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)
  45. Jarvist Moore Frost (Imperial College London, UK) E.II.2 - EMRS

    Spring 2017 Mon 22nd May 2017 Preprint on the arXiv: 1504.07508
  46. Jarvist Moore Frost (Imperial College London, UK) E.II.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).
  47. Jarvist Moore Frost (Imperial College London, UK) E.II.2 - EMRS

    Spring 2017 Mon 22nd May 2017 i.r. Raman Cubic Tetra Ortho Cation Cage
  48. Jarvist Moore Frost (Imperial College London, UK) E.II.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 ?
  49. Jarvist Moore Frost (Imperial College London, UK) E.II.2 - EMRS

    Spring 2017 Mon 22nd May 2017 18 Cage Modes (3 acoustic, 9 cage (3N-3), 6 rovibrational (MA))
  50. Jarvist Moore Frost (Imperial College London, UK) E.II.2 - EMRS

    Spring 2017 Mon 22nd May 2017 18 MA high freq. molecular modes (3N-6)
  51. Jarvist Moore Frost (Imperial College London, UK) E.II.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.
  52. Jarvist Moore Frost (Imperial College London, UK) E.II.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
  53. Jarvist Moore Frost (Imperial College London, UK) E.II.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
  54. Jarvist Moore Frost (Imperial College London, UK) E.II.2 - EMRS

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

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

    Spring 2017 Mon 22nd May 2017 How non parabolic? Very! Implications for device models (i.e. Drift diffusion, assumptions of scattering)
  59. Jarvist Moore Frost (Imperial College London, UK) E.II.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).
  60. Jarvist Moore Frost (Imperial College London, UK) E.II.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. #^/?&
  61. Jarvist Moore Frost (Imperial College London, UK) E.II.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
  62. Jarvist Moore Frost (Imperial College London, UK) E.II.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)
  63. Jarvist Moore Frost (Imperial College London, UK) E.II.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!)
  64. Jarvist Moore Frost (Imperial College London, UK) E.II.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