2018-03-05_JMFrost_SolidStatePhysicsOfHybridHalidePerovskites

Presented at APS March 2018, invited talk (36 minutes in total - I skipped over the real-space Starrynight stuff!)

B32.00004 : Semiconductor physics of halide perovskite solar cells*
1:03 PM–1:39 PM

Authors:
Jarvist Frost
(Materials, Imperial College London)

Aron Walsh
(Materials, Imperial College London)

Perovskites are the wonder compounds of materials science, with recent applications in high-efficiency solar cells. This talk will address the physical properties that make halide perovskites unique. After five years of intensive research, there has been a number of breakthroughs in understanding, but many challenges remain.

Our research has addressed the origin of the success of methylammonium lead iodide photovoltaics from multi-scale materials modelling [1-4]. These organic-inorganic materials satisfy the optoelectronic criteria for an active photovoltaic layer, i.e. spectral response in the visible range combined with light electron and hole effective masses. In addition, these systems are structurally and compositionally flexible with large dielectric constants, and the ability to alloy on each of the lattice sites.

I will discuss issues ranging from disorder associated with molecular vibrations and rotations within the inorganic network, to microscopic polarisation arising from correlations in cell dipole orientations. The temporal behaviour of hybrid perovskites has recently been validated through a combination of neutron scattering, time-resolved vibrational spectroscopy, and kinetic measurements of the current-voltage response. The implications for electron-hole recombination and new models for the cooling of hot carriers in operating solar cells will be discussed.

1. “Atomistic origins of high-performance in halide perovskite solar cells” Nano Letters, 14, 2584 (2014)
2. “Self-regulation mechanism for charged point defects in halide perovskites” Angewandte Chemie Int. Ed. 54, 1791 (2015)
3. "Direct observation of dynamic symmetry breaking above room temperature in methylammonium lead iodide" ACS Energy Lett. 1, 880 (2016)
4. "Slow cooling of hot polarons in halide perovskite solar cells" ACS Energy Letters 2, 2647 (2017)

*This research has been supported by the Royal Society, and the European Research Council (Grant no. 277757).

Transcript

1. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 King's College London / Imperial College London, UK @JarvistFrost jarvist.frost@imperial.ac.uk https://jarvist.github.io Semiconductor physics of halide perovskite solar cells Jarvist Moore Frost, and Aron Walsh
2. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 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.
3. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 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+
4. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 ( 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 ] ~2 ps timescale to MA rotation, And octahedra tilting / distortion Molecular Dynamics
5. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 Experimental validation... 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
6. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 Iodine location, MAPI, ~100 ps MD
7. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 Glazer Tilting - Glazer 1972
8. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 Lead Iodine Pb: Lone pair / 2nd order Jahn-Teller distortion Carbon (Methylammonium) "It's as soft as jelly!" (Bulk modulus ~wood.)
9. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 Theorist health warning: → The atoms are heavy (Pb Z=82) → The material is statically and dynamically disordered → DFT fails in important ways. → The solid-state physics expectation of a well behaved periodic structure is dubious. See: "Perspective: Theory and simulation of hybrid halide perovskites" LD Whalley et al. ArXiv: 1703.09504 ; The Journal of Chemical Physics 146, 220901 (2017); https://doi.org/10.1063/1.4984964
10. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 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)
11. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 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: RECIPROCAL SPACE
12. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 QSGW SOC spin-texture (12 atom pseudo-cubic structure)
13. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 → DFT, athermal structure; mainly spin texture → → DFT, MD sampled structures; mainly k-space displacement
14. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 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 (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 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
16. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 Strong T-dep at low fluence Direct gap at high fluence. Temperature insensitive dynamics.
17. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 Is this effect robust? Dynamic Symmetry Breaking and Spin Splitting in Metal Halide Perovskites. Scott McKechnie et al. ArXiv: 1711.00533 2x2x2 CsPbI3 supercell Ab-inito MD @ 300 K; 5 ps ⇒ 200 correlated frames 2x2x2 MAPbI3 supercell Ab-inito MD @ 300 K; 5 ps ⇒ 200 correlated frames
18. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 3D band extrema wanderings Band extrema location (antipodal, around the R-point)
19. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 3D Spin Texture Spin-texture (vector of spins of extrema)
20. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 Predictions: Spin-split indirect-gap leads to 300 X decrease in bimolecular recombination. Weak indirect gap ~75 meV below direct; should not be present in Orthorhombic phase (~<150K). Faster recombination expected in Sn analogue due to reduced Spin Orbit Coupling - it should be more direct gap like. Spin split indirect gap → may be a new design feature for novel solar cell materials. Present where {Sb,Bi,Pb} + ferroelectric distortion. The effect is robust to finite temperature ; Similar behaviour for the organic ion (methlyammonium) and Cesium analogue. Finite temperature fluctuations locally break symmetry. P. Azarhoosh et al., APL Materials 4, 091501 (2016) S. McKechnie et al., ArXiv: 1711.00533
21. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 SOC renormalised & split conduction band Straddle solar spectrum Spin-split indirect gaps protect from recombination Are lead-halide perovskites Intermediate Band Solar Cells ?
22. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 • 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 Necessary conditions for IBSC
23. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 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]
24. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 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)
25. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 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 → antibonding (and s → p). (mainly) PbII [6p0] (mainly) I-I [5p6] Dipole transitions
26. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 Selection rules… ? VB CB1 CB2 CB3 PbII [6p z 0] ? PbII [6p y 0] ? PbII [6p x 0] ? (mainly) I-I [5p6] Dipole transitions
27. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 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.
28. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 Why think when you can calculate? QSGW 'fixed' LDA Full SOC (out of eqm) Spin-dep. matrix elements Out-of-equilibrium rate model
29. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 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
30. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 [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
31. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 (QSGW) Multi-valley effective mass
32. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018
33. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018
34. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 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! JM Frost et al., ArXiv:1611.09786
35. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 W
36. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 Representation of i.r. activity from: Phys. Rev. B 92, 144308 (2015) Soft as wood ∴ Frequencies small Ionic ∴ Born-Effective-Charges large
37. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 Free energy of polaron, by path integration. Variational solution, by autodifferentiation. Explicit contour integration of polaron self-energy on complex plane Mobility, polaron mass, spring constant, absorption profile etc.
38. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 → 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 (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 Polaron mobility: • Fully ab-initio temperature-dependent prediction of mobility ◦ (No fitted / empirical / free parameters.) ◦ Good 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 PAPER: JM Frost, PRB 96 (19), 195202. Arxiv:1704.05404 CODES: github.com/jarvist/PolaronMobility.jl TALK: Thur, March 8, 1:15 PM. S29.00009
40. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 ACS Energy Lett., 2017, 2, pp 2647–2652. October 23, 2017. DOI: 10.1021/acsenergylett.7b00862 Low thermal conductivity...
41. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 Where does the hot-electron E go? 78 meV / ps
42. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 By bulk thermal conductivity... MAPI has extremely low thermal conductivity: a phonon glass. MAPI: κ = 0.05 W m−1K−1 CsPbI3: κ = 0.5 W m−1K−1 CdTe: κ = 9 W m−1K−1 GaAs: κ = 38 W m−1K−1 ( Phono3py RTA; PBESol VASP DFT ) MAPI: 41,544 displacements!
43. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 Track phonon-phonon-phonon DoS? Beyond relaxation time approximation, one should be able to directly track the phonon decay processes, modelling non-equilibrium phonon density of states. (Stochastic / Master equation approach.) A work in progress! (Using phono3py.)
44. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 ACS Energy Lett., 2017, 2, pp 2647–2652. October 23, 2017. DOI: 10.1021/acsenergylett.7b00862 Low thermal conductivity... • We had calculated thermal conductivity by a 3-phonon scattering perturbation techniques. • It was as low as you can go - MAPI is a phonon glass. • From our polaron models, we had an idea of the extent of the exciton + polaron. • Transient absorption experiments show unusually slow cooling of above bandgap excitation. • Can we explain this with a simple mechanistic polaron model? • The answer is a (qualified) yes.
45. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 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 )
46. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 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!)
47. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 Parameters via DFT 25-75 meV (nearest neighbour) 25 meV (nearest neighbour) 1-5 meV at solar cell fields
48. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 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!
49. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 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.)
50. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 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...
51. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 Cagestrain=25 meV → Semi-ordered Ferroelectric ground state; Intermediate long range order (dynamic) at finite T 0K 128K 64K 256K 384K
52. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 0K 128K 256K 384K Cagestrain=25 meV → Semi-ordered Ferroelectric ground state; Intermediate long range order (dynamic) at finite T
53. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 POLARON POLARON NORALOP Slightly indirect band gap. Real space potential fluctuations
54. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 Real space recombination model:
55. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 Simple Statistical Mechanics argument V h+ h+ h+ e- e- Recombination...
56. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 Boltzmann / mid-gap Fermi Dirac Fermi level
57. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 Fermi-Dirac e- quasi Fermi level h+ quasi Fermi level Fermi Level
58. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 (Boltzmann distribution of electrons, at 300 K) Recombination Reduction
59. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 Simple thermal de-trapping model (Boltzmann distribution of electrons, at 300 K) Mobility Reduction
60. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 POLARON POLARON NORALOP How to model polarons? POLARON
61. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 Gaussian blur!
62. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 Recombination Rate Polaron size (lattice units) ( Relaxor ferroelectric @ 300 K )
63. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 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
64. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 2012-2018 What has theory told us? The fundamental question from 2012: ⇒ Why is a solution-processed material such a good photovoltaic? Does not yet have a definitive answer. But there are lots of suggestions! • Soft crystal structure. Dynamic local disorder, even for Cs. • Spin-split indirect-gap reduces recombination rate • Relativistic band structure could potentially support an IBSC • Polaron theories of mobility predict predict experimental values • Slow cooling can be explained by bulk thermal conductivity and polaron model • Relaxor ferroelectric structure generates local fluctuations in electric potential - affecting recombination and transport. Simple theories sometimes have the most to say. Theory tells us what is possible; experiment tells us what is present.
65. Jarvist Moore Frost (King's College London, UK) APS March - Los Angeles 2018 5th March 2018 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