2020-01-10_JMFrost_York_NewHorizonsMaterialsModelling

 2020-01-10_JMFrost_York_NewHorizonsMaterialsModelling

Sustainable materials modelling for a sustainable future

Jarvist Moore Frost

Humanity needs new materials for power generation without reliance on fossil fuels, and for everyone (the earth's population is predicted to be nearly 10 billion by 2050) to enjoy a high standard of living. Ideally these materials would be made out of earth-abundant elements, would be non-toxic in extraction, use and disposal, and would not require much energy to process. Materials modelling is essential for the design of these materials, both in a purely predictive manner (suggesting a material to make), and more subtly in enabling the correct interpretation of measurements, and thereby the correct empirical design rules.

We also need sustainability both in our calculations, and in our careers. State of the art materials calculations require increasingly highfalutin physics, and eye watering amounts of computer time. Long gone are the prospects of a comfortable research career built on the application of standard density functional theory methods. As community codes have become more reliable, and computers have got bigger, large automated computational sifts of all materials have taken place.

But all is not lost! It is a much better application of our human brains to be dreaming up new models and interpretable explanations of observed behaviour, than debugging FORTRAN run-time errors. Many material properties of actual technical interest are phenomenological in nature: they are not direct observables.

I will take some examples from recent work on halide perovskite materials, to show how calculations with standard electronic structure theory codes can feed into modest (but bespoke) computational models to explain new data.

Halide perovskites are soft, polar, semiconductors [1]. As well as being materials of potential technological use, they are scientifically interesting in being a high performance yet solution processed semiconductor, and being a semiconductor composed of heavy (e.g. Pb Z=82) elements.

Anharmonicity in the phonon modes leads to extremely low thermal conductivity [2]. This anharmonicity has been observed by x-ray scattering [3] and neutron spectroscopy [4].

Strong dielectric electron-phonon coupling leads to correlated electron and phonon degrees of freedom, the formation of a polaron. We can describe this interacting system with path integrals, integrating out the (infinite) degrees of freedom associated with the phonon quantum field. We have recently implemented codes to calculate the finite-temperature Feynman polaron state, based on a Fröhlich electron-phonon Hamiltonian [5,6]. For a polar material, the long-range dielectric coupling can be expected to dominate the electron-phonon interaction. This model provides temperature dependent charge carrier mobility, with no free parameters. For halide perovskite systems, the predictions agree well with experiment, indicating that we are capturing the essential physics.

From a characterisation of this finite-temperature polaron state, we have proposed a model for the observed slow carrier cooling in halide perovskites [7]. The polaron state is stable at high temperature, and results in a limited density of states which the hot-electron is in thermal contact with. The very low lattice thermal conductivity retains the localisation of this transient hot-spot. This model explains cation and halide trends in observed cooling rates [8].

The fundamental enigma of the halide perovskite semiconductor is how a solution processed (and thus defective) semiconductor has such a slow minority carrier recombination rate. I propose this is due to a combination of the heavy elements leading to relativistic effects in the band-structure [9] (which persist when thermal disorder is present [10]), and the underlying device physics of polarons. Most device physics models (such as those used to fit experimental data) assume electrons scatter as plane waves, extending the models to include the Gaussian wavepacket localisation of a polaron changes the result considerably.

I will discuss the design principles which can be derived from studying the behaviour of the halide perovskite material, both for new defect tolerant semiconductors, and new solar cell device architectures.

[1] JM Frost et al. Acc.Chem.Res. 49 (3) pp 528–535 (2016).

[2] LD Whalley et al. "Phonon anharmonicity, lifetimes, and thermal transport in CH3NH3.PbI3 from many-body perturbation theory" Phys. Rev. B 94, 220301(R) (2016).

[3] AN Beecher et al. "Direct observation of dynamic symmetry breaking above room temperature in methylammonium lead iodide perovskite" ACS Energy Letters 1 (4), 880-887 (2016)

[4] A Gold-Parker et al. "Acoustic phonon lifetimes limit thermal transport in methylammonium lead iodide" Proceedings of the National Academy of Sciences 115 (47), 11905-1191 (2018)

[5] JM Frost. "Calculating polaron mobility in halide perovskites" Phys. Rev. B 96, 195202 (2017)

[6] https://github.com/jarvist/PolaronMobility.jl

[7] JM Frost et al. "Slow cooling of hot polarons in halide perovskite solar cells" ACS Energy Lett., 2017, 2 (12), pp 2647–2652

[8] T Hopper et al. "Ultrafast Intraband Spectroscopy of Hot-Carrier Cooling in Lead-Halide Perovskites" ACS Energy Lett., 2018, 3 (9), pp 2199–2205

[9] P Azarhoosh et al. "Research Update: Relativistic origin of slow electron-hole recombination in hybrid halide perovskite solar cells" APL Materials 4 (9), 091501 (2017)

[10] S McKechnie et al. "Dynamic symmetry breaking and spin splitting in metal halide perovskites" Phys. Rev. B 98 (8), 085108

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Jarvist Moore Frost

January 10, 2020
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  1. 1.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Imperial College London Email: jarvist.frost@ic.ac.uk Twitter: @JarvistFrost https://jarvist.github.io Sustainable materials modelling for a sustainable future Jarvist Moore Frost. Lucy Whalley, Federico Brivio, Jonathan Skelton, and Aron Walsh. Tom Hopper, and Artem Bakulin.
  2. 2.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Carbon cost of High Performance Computing epcc.ed.ac.uk 1.2 MW for 4920 compute nodes (each 24 cores) ⇒ 250 W / node, 6 kWhr in 24 hours Each 24-hour single-node job = 8.6 kAU ⇒ 700 kWhr / MAU But UK as a whole averages about 400 g / kWhr for the year ⇒ 280 kg CO2 / MAU on ARCHER (Flying to Boston and back Economy, for Fall MRS = 800 kg CO2, ~= 3 MAU calculations.) Provisos: • Electricity is (very quickly) decarbonising • South Scotland typically has a very low carbon intensity for their electricity (nuclear + wind) • ARCHER2 will be much more energy efficient Academic Research Computing High End Resource (Archer) Cray XC30
  3. 3.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 UK national supercomputer utilisation … by research area
  4. 4.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 UK national supercomputer utilisation … by language
  5. 5.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Doing what? 'B' term in the 2-electron integrals that make Hartree-Fock theory scale as O(N4)
  6. 6.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 "Computers are bicycles for the mind." - Steve Jobs A long way from the hippie ideals of personal computing...
  7. 7.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 J.M. Ziman ©1957 Gonville & Caius College, Cambridge "It is typical of modern physicists that they will erect skyscrapers of theory upon the slender foundations of outrageously simplified models." ~ J.M.Ziman, "Electrons in metals: a short guide to the Fermi surface", 1962 Is almost all by Fermi's golden rule! • 1st order perturbation theory (Time-dependent Schrodinger equation.) • Difficult to go beyond this Theorists (>1980) have mainly retreated into ever more involved methods of calculating matrix elements. Link solid state theory ⇔ experiment
  8. 8.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 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 Sustainable materials won't be periodic
  9. 9.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Thesis of this talk To model materials one should: • Build computationally lightweight models, often based on 1950s/1960s solid state theories • Use standard (DFT) packages to parametrise model • (preferably) develop in a modern language, that allows natural physical abstractions Why? • Make technically relevant predictions ◦ Many interesting measurements probe response functions ◦ Most materials are not single crystals ◦ Even single crystals have thermal vibrations • These predictions are by definition unique ◦ You won't get replaced by an exascale computer... • It's fun!
  10. 10.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Examples of this approach 1/ Hybrid lead halide perovskites (MAPI + friends) a/ Molecular dynamics interpretation b/ Exceeding the Born-Oppenheimer approximation with an 'undergraduate' 1D QM model 2/ Polarons a/ 1950s theories b/ beyond Fermi's golden rule mobilities 3/ Polaron devices physics a/ Explaining slow-cooling in hybrid halide perovskites b/ Scattering beyond the Born approximation c/ Polarons + large scale Monte-Carlo structural models
  11. 11.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 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.
  12. 12.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Solution processed → defective Soft → thermal disorder • Slow radiative recombination (for a direct gap material) • Sufficient mobility to get charges out (But not that high considering effective mass 0.12, ~50 cm2/Vs vs. 1000 cm2/Vs for CdTe) • Almost absent non-radiative recombination Why can we make efficient solar cells out of solution processed MAPI?
  13. 13.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 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+
  14. 14.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 ( 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
  15. 15.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 100 ps MD; 2x2x2 supercell; Iodine location
  16. 16.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Glazer Tilting - Glazer 1972
  17. 17.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Lead Iodine Pb: Lone pair / 2nd order Jahn-Teller distortion Carbon (Methylammonium) "It's as soft as jelly!" (Bulk modulus ~wood.)
  18. 18.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 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. Phys. Chem. Chem. Phys., 2015,17, 31278-31286 (2015) 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
  19. 19.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 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.
  20. 20.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Reduce to first octant… abs(r), r=[x,y,z]
  21. 21.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Apply reflection symmetry… sorted(abs(r)) , r={x,y,z} = 48 fold increase in SNR (Tom Ruen, Wikimedia Commons)
  22. 24.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 FACE (X) DIAGONAL (R) EDGE (M)
  23. 25.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 FACE (X) DIAGONAL (R) EDGE (M) FACE: 42% EDGE: 31% DIAG.: 26% (weighted by MC integration of random sphere points)
  24. 26.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Examples of this approach 1/ Hybrid lead halide perovskites (MAPI + friends) a/ Molecular dynamics interpretation b/ Exceeding the Born-Oppenheimer approximation with an 'undergraduate' 1D QM model 2/ Polarons a/ 1950s theories b/ beyond Fermi's golden rule mobilities 3/ Polaron devices physics a/ Explaining slow-cooling in hybrid halide perovskites b/ Scattering beyond the Born approximation c/ Polarons + large scale Monte-Carlo structural models
  25. 27.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Lattice Dynamics (Phonons)
  26. 28.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 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?
  27. 29.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 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.
  28. 30.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 The 1D Schrodinger equation is easy to solve!
  29. 32.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 ~15 meV well persists in structure to > 600 K BE Distribution 600 K 1 K
  30. 33.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Iodine 300K Iodine 200K
  31. 34.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 (Calculations: Lucy Whalley) Band-gap as a function of Q (Deformation Potential)
  32. 35.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 (R acoustic mode at Brillouin-Zone boundary [tilt])
  33. 36.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 R M Phonon anharmonicity, lifetimes, and thermal transport in CH 3 NH 3 PbI 3 from many-body perturbation theory LD Whalley, JM Skelton, JM Frost, A Walsh - Physical Review B, 2016
  34. 37.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Examples of this approach 1/ Hybrid lead halide perovskites (MAPI + friends) a/ Molecular dynamics interpretation b/ Exceeding the Born-Oppenheimer approximation with an 'undergraduate' 1D QM model 2/ Polarons a/ 1950s theories b/ beyond Fermi's golden rule mobilities 3/ Polaron devices physics a/ Explaining slow-cooling in hybrid halide perovskites b/ Scattering beyond the Born approximation c/ Polarons + large scale Monte-Carlo structural models
  35. 38.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 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!
  36. 39.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Dielectric response… Fröhlich Polaron (static picture)
  37. 40.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Fröhlich effective mass polarons α GaAs: 0.068 CdTe: 0.29 AgCl: 1.84 SrTiO3: 3.77 (Devreese 2005) We need: ➔ Difference of dielectric constants ➔ Characteristic frequency of 'Linear Optical' mode ➔ Effective mass of electron This is the long-range dielectric electron-phonon interaction (the 1/q divergence that causes issues in ab-initio calculations). (Original form Landau (1933); this follows Jones & March (1985), "Theoretical Solid State Physics Vol 2". See also Devreese (2016), arXiv:1611.06122. )
  38. 42.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Slow Electrons in a Polar Crystal, Phys. Rev. 97, Feynman 1955 Infinite quantum field of phonon excitations Path Integrals for Pedestrians (2016) https://doi.org/10.1142/9183
  39. 43.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 M k → Simple Harmonic Motion (ball and chain) An explicitly quasi-particle theory
  40. 44.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Free energy of polaron, by path integration. Optimisation by automatic-differentiation. Explicit contour integration of polaron self-energy on complex plane Mobility, polaron mass, spring constant, absorption profile etc.
  41. 45.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Examples of this approach 1/ Hybrid lead halide perovskites (MAPI + friends) a/ Molecular dynamics interpretation b/ Exceeding the Born-Oppenheimer approximation with an 'undergraduate' 1D QM model 2/ Polarons a/ 1950s theories b/ beyond Fermi's golden rule mobilities 3/ Polaron devices physics a/ Explaining slow-cooling in hybrid halide perovskites b/ Scattering beyond the Born approximation c/ Polarons + large scale Monte-Carlo structural models
  42. 46.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 julia> import Pkg; Pkg.add("PolaronMobility") julia> using PolaronMobility julia> MAPIe=polaronmobility(300, 4.5, 24.1, 2.25E12, 0.12) ... T: 300.000000 β: 2.41e+20 βred: 0.36 ħω = 9.31 meV Converged? : true VariationalParams v= 19.86 w= 16.96 || M=0.371407 k=106.835753 POLARON SIZE (rf), following Schultz1959. (s.d. of Gaussian polaron ψ ) Schultz1959(2.4): rf= 0.528075 (int units) = 2.68001e-09 m [SI] Polaron Free Energy: A= -6.448815 B= 7.355626 C= 2.911977 F= -3.818788 = -35.534786 meV Polaron Mobility theories: μ(FHIP)= 0.082049 m^2/Vs = 820.49 cm^2/Vs Eqm. Phonon. pop. Nbar: 2.308150 μ(Kadanoff1963 [Eqn. 25]) = 0.019689 m^2/Vs = 196.89 cm^2/Vs Tau=1/Gamma0 = 1.15751e-13 = 0.115751 ps μ(Hellwarth1999)= 0.013642 m^2/Vs = 136.42 cm^2/Vs ... https://github.com/jarvist/PolaronMobility.jl Open source! Please use / adapt.
  43. 47.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 → 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
  44. 48.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Effective mass + 40% (Phonon drag) (You could use this in a BTE calculation.) Time scale for scattering. Polaron wavefunction (Gaussian), and scale.
  45. 49.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Examples of this approach 1/ Hybrid lead halide perovskites (MAPI + friends) a/ Molecular dynamics interpretation b/ Exceeding the Born-Oppenheimer approximation with an 'undergraduate' 1D QM model 2/ Polarons a/ 1950s theories b/ beyond Fermi's golden rule mobilities 3/ Polaron devices physics a/ Explaining slow-cooling in hybrid halide perovskites b/ Scattering beyond the Born approximation c/ Polarons + large scale Monte-Carlo structural models
  46. 50.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Where does the hot-electron E go? 78 meV / ps Phonon band structure cm-1 ~15 nm
  47. 51.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 ACS Energy Lett., 2017, 2, pp 2647–2652. October 23, 2017. DOI: 10.1021/acsenergylett.7b00862
  48. 52.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 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!
  49. 54.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 (Final) experimental data
  50. 55.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Experiment : Theory • Computer environments are really built for hypothesis testing and model • Hybrid perovskite have ~twice the heat capacity of inorganic (count the modes! 16 vs. 9 in thermal window) Polaron scattering rate Heat capacity + polaron size
  51. 56.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Examples of this approach 1/ Hybrid lead halide perovskites (MAPI + friends) a/ Molecular dynamics interpretation b/ Exceeding the Born-Oppenheimer approximation with an 'undergraduate' 1D QM model 2/ Polarons a/ 1950s theories b/ beyond Fermi's golden rule mobilities 3/ Polaron devices physics a/ Explaining slow-cooling in hybrid halide perovskites b/ Scattering beyond the Born approximation c/ Polarons + large scale Monte-Carlo structural models
  52. 57.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 How do electrons scatter? Born approximation assumes: 1) Weak scattering (perturbation theory) 2) Input and output states of the charge-carrier are plane waves (Bloch states) These rates underly almost all device physics models (impurity scattering, non-radiative recombination, defect capture cross section etc.)
  53. 58.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 "Scattering of wave packets on atoms in the Born approximation" D.V. Karlovets, G.L. Kotkin, and V.G. Serbo PRA 92, 052703 (2015) A very similar problem explored recently in accelerator physics. (Airy beams - electron accelerators can focus to < 1nm.) Standard Born Approximation: Fourier-Transform of potential Karlovets2015: Multiply with transverse wavefunction before Fourier transform.
  54. 59.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Scattering of Gaussian wavepackets (polarons) Polaron scattering attenuated by: • Classical contribution from localising the electron • Quantum contribution from incoherency of Gaussian wavepacket Derivation follows: "Scattering of wave packets on atoms in the Born approximation" D. V. Karlovets, G. L. Kotkin, and V. G. Serbo Phys. Rev. A 92, 052703 (2015)
  55. 60.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Weighted for transport Effect further strengthened for transport-relevant scattering. Q) Why did the polaron cross the defective semiconductor? A) Because it was too incoherent to scatter.
  56. 61.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Examples of this approach 1/ Hybrid lead halide perovskites (MAPI + friends) a/ Molecular dynamics interpretation b/ Exceeding the Born-Oppenheimer approximation with an 'undergraduate' 1D QM model 2/ Polarons a/ 1950s theories b/ beyond Fermi's golden rule mobilities 3/ Polaron devices physics a/ Explaining slow-cooling in hybrid halide perovskites b/ Scattering beyond the Born approximation c/ Polarons + large scale Monte-Carlo structural models
  57. 62.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 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 )
  58. 63.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 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!)
  59. 64.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Parameters via DFT 25-75 meV (nearest neighbour) 25 meV (nearest neighbour) 1-5 meV at solar cell fields
  60. 65.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 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!
  61. 66.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 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.)
  62. 67.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 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...
  63. 68.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Cagestrain=25 meV → Semi-ordered Ferroelectric ground state; Intermediate long range order (dynamic) at finite T 0K 128K 64K 256K 384K
  64. 69.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 0K 128K 256K 384K Cagestrain=25 meV → Semi-ordered Ferroelectric ground state; Intermediate long range order (dynamic) at finite T
  65. 70.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 POLARON POLARON NORALOP Polarons ~6 lattice units (Frost2014), by Asymptotic Feynman solution Polarons ~4 lattice units (Frost2017) by finite-temperatur e numeric solution (Both numbers are the s.d. of the Gaussian wavefunction.) Real space potential fluctuations
  66. 71.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Real space recombination model:
  67. 72.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Statistical mechanic argument (thermalised population) V h+ h+ h+ e- e- Recombination...
  68. 73.

    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Boltzmann / mid-gap Fermi Dirac Fermi level
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    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Fermi-Dirac e- quasi Fermi level h+ quasi Fermi level Fermi Level
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    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 POLARON POLARON NORALOP How to model polarons in a static potential? POLARON
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    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Gaussian blur!
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    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Recombination Rate Polaron size (lattice units) ( Relaxor ferroelectric @ 300 K )
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    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Recombination Reduction
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    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Simple thermal de-trapping model (Boltzmann distribution of electrons, at 300 K) Mobility Reduction, from disorder?
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    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Conclusion ★ You can do a lot with a modest computation ★ Some of this may even have been useful! ★ Basing these calculations on the outputs of electronic structure theory, gives you chemical specificity Everyone in this room can program… Everyone in this room has a physic-y / chemistry-y background… So why not combine them?
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    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Collaborators:- Piers Barnes Aron Walsh Artem Bakulin WMD Group, Bath/ICL Acknowledgments:- EPSRC - EP/K016288/1 Royal Society - URF/R1/191292 Tom Hopper
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    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 2012-2019 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.
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    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Solution processed → defective Soft → thermal disorder • Slow radiative recombination (for a direct gap material) ▪ Slightly-indirect gap due to Rashba splitting (350x) ▪ Electrostatic potential fluctuations reduce recombination (10x-100x) • Sufficient mobility to get charges out (But not that high considering effective mass 0.12, ~50 cm2/Vs vs. 1000 cm2/Vs for CdTe) ⇒ Polarons! • Almost absent non-radiative recombination ▪ ? Few mid gap defects ▪ Lower (polaron) cross-section for recombination Why can we make efficient solar cells out of solution processed MAPI?
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    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 Fröhlich effective mass polarons Units: m/F (inverse of vacuum permittivity) • Usually viewed as some 'bulk' phenomenological quantity Units: F • Can view this as the capacitance of the phonon field Units: m^-1 • Scale the matrix element to make it dimensionless
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    Jarvist Moore Frost (ICL, UK) New horizons in materials modelling;

    Sustainable models 10th Jan 2020 General heading Section heading Orange goodness heading Close to dark-grey green thingy Style guide 36 Montserrat - SemiBold 22 Questrial // 22 Montserrat - SemiBold 14 Questrial