Frontiers in materials modelling of perovskites: Electrons, phonons and dynamic disorder

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Frontiers in Materials Modelling of Perovskites: Electrons, Phonons and Dynamic Disorder Prof. Aron Walsh Department of Materials Imperial College London, UK https://wmd-group.github.io @lonepair

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First-Principles Materials Modelling Structure Properties Input: Output: William Hamilton (Dublin, 1805) Hamiltonian (ions and electrons) William Bragg (Wigton, 1862) X-ray Diffraction (unit cells) Physical Chemistry (stimuli) Neville Mott (Leeds, 1905)

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Supercomputers in 2017 (1017 FLOPS) Top500.org Ranking

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Thousands of Interacting Electrons “With DFT as your hammer, everything starts to look like a nail” Chris Pickard, 2009

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First-Principles Modelling in 2017 Remove Approximations length and times scales electron-electron interactions electron-phonon interactions phonon-phonon interactions

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First-Principles Modelling in 2017 Remove Approximations length and times scales electron-electron interactions electron-phonon interactions phonon-phonon interactions Accurate Solid-State Properties effective mass to carrier mobility phonon frequencies to lifetimes ground to excited states perfect crystals to defects and disorder

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Talk Outline A. Early Modelling of Halide Perovskites B. Latest Results

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A Long Time Ago in South Korea…

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A Long Time Ago in South Korea…

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Some Time Ago in Italy…

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Some Time Ago in Italy…

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2013 – The Awakening (Italy)

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2013 – The Awakening (UK)

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2013 – The Awakening (France)

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2013 – The Awakening (Japan)

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2013 – The Awakening (USA)

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2013 MRS Rump Session 15 speakers with 10 min talks on latest unpublished results

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2013 Post-MRS Idea Overload

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Talk Outline A. Early Modelling of Halide Perovskites B. Latest Results

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Why Hybrid Perovskites? Essentials for Solar Cells • Strong optical absorption (Eg ~ 1.6 eV) • Light electron and hole masses (conductive) • Easy to synthesise (cheap and scalable) Advanced Features • Large dielectric constants: carrier separation (weak excitons) and transport (low scattering) • Slow e-h recombination: low losses, large VOC o Relativistic effects – spin-orbit coupling o Polar domains – dynamic fluctuations

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Perovskites: Model vs Reality Plastic crystal behaviour probed by Quasi-Elastic Neutron Scattering (P. Barnes, DOI: 10.1038/ncomms8124); 2D IR Spectroscopy (A. Bakulin, DOI: 10.1021/acs.jpclett.5b01555); Inelastic X-ray Scattering (S. Billinge, DOI: 10.1021/acsenergylett.6b00381) with simulations

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Dynamic Processes in Perovskites Faster (fs) Slower (ps) Electrons and Holes Effective semiconductors Lattice Vibrations Symmetry breaking and carrier separation Molecular Rotations Large static dielectric constant Ions and Charged Defects “Self healing” and hysteresis

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Phonon Theory Refresh Collective vibrational excitation in crystal: N atoms vibrate as 3N phonon modes, ⍵(q) Essential for: • Free energy • Vibrational spectra • Thermal expansion • Phase transformations • Heat flow • Electrical conductivity Crystal momentum

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Phonon Theory Refresh Collective vibrational excitation in crystal: N atoms vibrate as 3N phonon modes, ⍵(q) Crystal Potential Static DFT model Anharmonicity Higher-order terms Harmonic Phonons Ionic Forces = 0 at equilibrium Crystal potential expanded with ion displacements (r)

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Phonon Theory for CH3 NH3 PbI3 Harmonic Phonon Dispersion, ⍵(q) Good comparison to IR and Raman spectra over full 0–3000 cm-1 range [PRB 92, 144308 (2015)] Quasi-Harmonic Phonons, ⍵(q,T) Thermal expansion 1.25⨉10-4/K compared to 1.32⨉10-4/K from neutron diffraction Three-Phonon Interactions, ⍵(q,T) with (⍵,T) Very strong interactions, with short lifetimes and ultra-low thermal conductivity (0.05 Wm−1K−1) [PRB 94, 220301 (2016)]

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Phonon Theory for CH3 NH3 PbI3 Rocking MA+ mode at 2.5 THz [Complete mode assignment] PCCP 18, 27051 (2016)

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Low-Frequency Dielectric Response

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Electronic Band Structure (MAPI) [QSGW with M. van Schilfgaarde, KCL] Physical Review B 89, 155204 (2014) Conduction Band Valence Band Pb 6p0 I 5p6 Pb 6s2 Relativistic spin-splitting Degeneracy removed by ΔCF and ΔSOC Eg QSGW = 2.7 eV à 1.7 eV (SOC)

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Rashba and Radiative Recombination Rashba splitting of conduction band reduces bimolecular recombination at low fluence Led by Mark van Schilfgaarde (KCL) 120⨉120⨉120 k-mesh [First-principles recombination rates] APL Materials 4, 091501 (2016)

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Support for Weakly Indirect Gap Validation from experiment is growing Indirect to direct band gap transition under pressure Led by Bruno Ehrler (AMOLF); Energy. Environ. Science (2017); DOI: 10.1039/c6ee03474h Indirect to direct band gap transition with fluence Led by Sam Stranks (Cambridge); Nature Materials (2016); DOI: 10.1038/nmat4765 Giant Rashba splitting in MAPbBr3 with ARPES Led by Thomas Fauster (Erlangen); Physical Review Letters (2016); DOI: 10.1103/PhysRevLett.117.126401

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Dynamic Rashba Effect Effect persists at room temperature SOC calculations on snapshots from MD (T = 300K ) Value from static model MD Simulations Jarvist Frost QSGW Scott McKechnie

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Giant Phonon Anharmonicity Phonon-phonon interactions 103 stronger in CH3 NH3 PbI3 than GaAs Mean free path of each phonon 41,544 displacements in a 96 atom supercell – Phono3py (PBEsol) Whalley, Skelton, Frost and Walsh, Physical Review B 94, 220301(R) (2016)

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MAPI is a Thermal Insulator Whalley, Skelton, Frost and Walsh, Physical Review B 94, 220301(R) (2016) T = 300K GaAs 38 (calculated) 45 (measured) CdTe 9 (calculated) 7 (measured) MAPI 0.05 (calculated)

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Next (Large) Steps Model for carrier cooling – informed by a combination of principles electronic and phonon density of states [Jarvist Frost] Model for non-radiative recombination – defect and surface states coupled to a phonon bath [Lucy Whalley]

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Re: Photo-induced Halide Separation Requires high local carrier concentrations and mobile ions (move before recombination)

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Conclusion and Outlook Materials modelling has been highly predictive for perovskite solar cells; many challenge remain Next Steps: Development of robust screening procedure for Pb-free materials Project Collaborators: Jarvist Frost, Federico Brivio, Jonathan Skelton, Lucy Whalley (ICL); Simon Billinge (Columbia); Mark van Schilfgaarde (Kings); Bruno Erhler (AMOLF); Mark Weller (Bath) Funding: ERC; EPSRC; Royal Society; Leverhulme Slides: https://speakerdeck.com/aronwalsh