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
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+
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
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)
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)
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]
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:
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
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).
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)
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
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
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]
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)
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.
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
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
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
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!
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
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
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
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.
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).
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 ?
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.
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
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
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
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).
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. #^/?&
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
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)
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!)
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