2016-06-07_ETSF-YRM Disorder in semiconductors for photovoltaics

Presented at the 2016 European Theoretical Spectroscopy Facility (ETSF) Young Researcher Meeting (YRM), on the 7th June 2016 at King's College London.

The meeting was really nice - quite a different dynamic with all the permanent contract academic (i.e. PIs) barred.
I had twice as many slides as I could fit into my 20 minute talk, so I skipped Case Studies III and IV when I presented.

Conference website:-
https://yrm2016.github.io/

Abstract:-
Title: Disorder in Semiconductors for Photovoltaics
Authors : Jarvist Moore Frost, Suzanne Wallace, Federico Brivio, Jonathan Skelton, Beth Rice, Jenny Nelson, Aron Walsh
Affiliations : University of Bath, United Kingdom
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Abstract:
Terawatt scale photovoltaics requires new semiconductors. Disorder will be pervasive. The low-energy and reduced-time synthesis, necessary to make a cheap material, are required by statistical physics to also make a disordered material.

Disorder poses a severe challenge for electronic structure theory. Emergent and statistical behaviour dominate device operation. The length and time scales preclude direct atomistic treatment of the system. Instead we are forced to attack the problem through model building - to carefully choose which aspect of the system to model explicitly, and to write custom codes that allow the evaluation of some experimentally relevant metric.

In this talk I will discuss some approaches to treating this disorder with computational methods. As case studies I will discuss work with a thin film photovoltaic material (Copper Zinc Tin Sulphide, CZTS), organic solar cells and hybrid halide perovskites.

Transcript

1. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 Jarvist Moore Frost, Federico Brivio, Jonathan Skelton, Aron Walsh (University of Bath, UK) Beth Rice, Jenny Nelson (Imperial College London, UK) Pooya Azarhoosh, Scott McKechnie, Mark van Schilfgaarde (King’s College London, UK) Walsh Materials Design Group, University of Bath, UK j.m.frost@bath.ac.uk Disorder in semiconductors for photovoltaics
2. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 "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
3. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 Why does disorder matter? Direct measurement of gap-state absorption in hydrogenated amorphous silicon by photothermal deflection spectroscopy Warren B. Jackson and Nabil M. Amer Phys. Rev. B 25, 5559(R) – Published 15 April 1982 'Exponential' band tailing from disorder / thermal fluctuations Discrete states merging at band edge Distinct states within the gap
4. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 Vast Power of the Sun Is Tapped By Battery Using Sand Ingredient; NEW BATTERY TAPS SUN'S VAST POWER Special to The New York Times. April 26, 1954, Monday MURRAY HILL, N. J., April 25 -- A solar battery, the first of its kind, which converts useful amounts of the sun's radiation directly and efficiently into electricity, has been constructed here by the Bell Telephone Laboratories. [~6% efficiency - PN Silicon Diode] Vanguard 1 (1958 – NASA) [Still in orbit...] ~5cm square silicon cells [transmitted for 7 years] We have the technology! → Cost is the key issue - the solar resource is low density (1kW / m^2)
5. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 Silicon grown by Czochralski process 1956 George E. Meyers, Raytheon Corp. semiconductor plant in Newton, Massachusetts, USA American Radio History 1500 degrees celsius!
6. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 http://www.treehugger.com/renewable-energy/striking-chart-showing-solar-power-will-take-over-world.html Still only ~0.1% of total energy consumption Photovoltaics is winning...
7. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016
8. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 Substitutional disorder driven by entropy gains
9. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 Disorder will be pervasive • Materials are always thermally disordered ◦ Even at 0 K → Zero-point-fluctuations • Most other disorder can be processed out ◦ But you're fighting entropy with enthalpy • Disorder tolerant or disorder exploiting Terawatt scale photovoltaics requires new semiconductors. Disorder will be pervasive. The low-energy and reduced-time synthesis, necessary to make a cheap material, are required by statistical physics to also make a
10. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 DFT is no longer enough DFT is no longer enough (for a paper, for a career) Many material screening databases appearing; Artificial agents are better at cranking the handle on vanilla electronic structure calculations.
11. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 Case Study I - Hybrid Halide Perovskites Relativistic origin of slow electron-hole recombination in hybrid halide perovskite solar cells P Azarhoosh, JM Frost, S McKechnie, A Walsh, M van Schilfgaarde arXiv preprint arXiv:1604.04500 What is moving in hybrid halide perovskite solar cells? JM Frost, A Walsh arXiv preprint arXiv:1601.05301 Lattice dynamics and vibrational spectra of the orthorhombic, tetragonal, and cubic phases of methylammonium lead iodide F Brivio, JM Frost, JM Skelton, AJ Jackson, OJ Weber, MT Weller, AR Goñi, ... Physical Review B 92 (14), 144308 Role of microstructure in the electron–hole interaction of hybrid lead halide perovskites G Grancini, ARS Kandada, JM Frost, AJ Barker, M De Bastiani, M Gandini, ... Nature photonics 9 (10), 695-701 Real-time observation of organic cation reorientation in methylammonium lead iodide perovskites AA Bakulin, O Selig, HJ Bakker, YLA Rezus, C Müller, T Glaser, ... The journal of physical chemistry letters 6 (18), 3663- 3669 Cubic Perovskite Structure of Black Formamidinium Lead Iodide, α-[HC (NH2) 2] PbI3, at 298 K MT Weller, OJ Weber, JM Frost, A Walsh The Journal of Physical Chemistry Letters 6 (16), 3209- 3212 (2015) Ionic transport in hybrid lead iodide perovskite solar cells C Eames, JM Frost, PRF Barnes, BC O’regan, A Walsh, MS Islam Nature communications 6 The dynamics of methylammonium ions in hybrid organic-inorganic perovskite solar cells AMA Leguy, JM Frost, AP McMahon, VG Sakai, W Kockelmann, CH Law, ... Nature communications 6 Molecular ferroelectric contributions to anomalous hysteresis in hybrid perovskite solar cells JM Frost, KT Butler, A Walsh Apl Materials 2 (8), 081506 Atomistic origins of high-performance in hybrid halide perovskite solar cells JM Frost, KT Butler, F Brivio, CH Hendon, M Van Schilfgaarde, A Walsh Nano letters 14 (5), 2584-2590
12. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 Perovskite (ABX 3 ) Crystal structure of the mineral CaTiO 3 A BX 3 Lev Perovski (Russia, 1839)
13. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 A - Molecular Cation B - {Pb, Sn} X 3 - Halide {I, Br, Cl*} 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.
14. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 MAPI makes a good solar cell. Why? MAPI makes a good solar cell. Why? ◆ Almost absent non-radiative recombination ◦ Few mid gap defects (fortitude?) ◆ 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 cm^2 / Vs vs. 1000 for CdTe) ◦ ? Reduced by the potential energy fluct?
15. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 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+
16. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 Figure: Beau Lambert, Kenneth A. Mauritz. 33 24 4.5 Dielectric function (not a constant)
17. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 LO-like modes @ 2 THz TO-like modes @ 1 THz Representation of i.r. activity from: Phys. Rev. B 92, 144308 (2015)
18. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 Lead Iodine Pb: Lone pair / 2nd order Jahn-Teller distortion Glazer Tilting - Glazer 1972 Methylammonium
19. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 Back to real space: STARRYNIGHT 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 )
20. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 Parameters via DFT 25-75 meV (nearest neighbour) 25 meV (nearest neighbour) 1-5 meV at solar cell fields
21. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 POLARON POLARON NORALOP Slightly indirect band gap. Real space potential fluctuations
22. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 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!
23. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 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.)
24. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 T= 0 K (Ground State - but a bit out of eqm, due to MC) CageStrain = 50 meV / neighbour ---> Ferroelectric
25. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 Anti Ferroelectric --- increase in temperature sees a slow broadening of density of states T 1 V 1 V
26. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 Ferroelectric; low disorder, which then melts to give sudden increase in variance T 1 V 1 V
27. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 Landau Order Param Naive definition poor for dipoles: <<<<<>>>>> = 0 Replace with radial distribution function based order param: ( Ziman 1979 ) [ R→ infinity value is equal to the Landau order ]
28. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 Cagestrain=25 meV → Semi-ordered Ferroelectric ground state; Intermediate long range order (dynamic) at finite T 0K 128K 64K 256K 384K
29. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 0K 128K 256K 384K Cagestrain=25 meV → Semi-ordered Ferroelectric ground state; Intermediate long range order (dynamic) at finite T
30. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 R→ infinity value is equal to the Landau order (but SNR has increased by R^2 !)
31. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 Case Study II - Quantum Harmonic Oscil. Motivation: How to treat soft modes? What is the repercussion for the electronic structure (and electron- phonon coupling) for such large tilting modes?
32. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 The 1D Schrodinger equation is easy to solve!
33. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016
34. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 ~15 meV well persists in structure to > 600 K BE Distribution 600 K 1 K
35. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 References Nothing published yet! See : https://github.com/jarvist/ijulia-notebooks 2016-05 - 1D Schr. solver - Soft Phonon Modes.ipynb For code.
36. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 Case Study III - Disordered Fullerene For some of this, see: Distinguishing the influence of structural and energetic disorder on electron transport in fullerene multi-adducts F Steiner, S Foster, A Losquin, J Labram… - Materials Horizons, 2015
37. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 Motivation Motivation: Why do organic solar cells work*? (* at all)
38. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 C60 Mono-PCBM Bis-PCBM Tris-PCBM
39. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 Coarse grained molecular dynamics; Atoms → Smarties, gives you a ~1000x (or more) speedup
40. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016
41. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 Consider the inter-adduct angles
42. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 8 Bis isomers; Angles: 36 72 60 90 180 144 120 108
43. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016
44. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 45 (unique) Tris Isomers 36.0 36.0 36.0 36.0 36.0 60.0 36.0 36.0 72.0 36.0 60.0 60.0 36.0 60.0 72.0 36.0 60.0 90.0 36.0 72.0 90.0 36.0 72.0 108.0 36.0 90.0 108.0 36.0 90.0 120.0 36.0 108.0 120.0 36.0 108.0 144.0 36.0 120.0 120.0 36.0 120.0 144.0 36.0 144.0 144.0 36.0 144.0 180.0 #All highly sterically hindered 60.0 60.0 108.0 60.0 60.0 120.0 60.0 72.0 72.0 60.0 72.0 90.0 60.0 72.0 120.0 60.0 90.0 108.0 60.0 90.0 144.0 60.0 108.0 108.0 60.0 108.0 144.0 60.0 120.0 144.0 60.0 120.0 180.0 60.0 144.0 144.0 72.0 72.0 108.0 72.0 72.0 144.0 72.0 90.0 120.0 72.0 90.0 144.0 72.0 108.0 120.0 72.0 108.0 180.0 72.0 120.0 144.0 72.0 144.0 144.0 90.0 90.0 90.0 # EEE 90.0 90.0 180.0 #E/T isomers 90.0 108.0 120.0 90.0 108.0 144.0 90.0 120.0 144.0 108.0 108.0 108.0 108.0 108.0 144.0 #Trans isomers 108.0 120.0 120.0 120.0 120.0 120.0
45. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 45 Unique Tris Isomers... (of 24360)
46. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 C60 (Bucky Balls) Mono PCBM Bis PCBM Tris PCBM
47. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 A simple type of N-state model Basis of states on monomers… (orthogonal) Coupled with effective transfer-integrals
48. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 Tight Binding Hamiltonian No correlation!
49. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 Psi & E - results of our (fairly minimal) efforts
50. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 Infinite polymer (10 units)
51. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016
52. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 3D Checkerboard
53. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 3D 10x10x10 simple cubic cell
54. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 "The systematic algebraic technique for the complete exploitation of such symmetry properties is called group theory, and is an essential tool for the theoretical physicist in this field. It can guide us to the form of the solution before we even consider the sordid details of atomic potentials, and enables us to squeeze the last drop out of an actual calculation." - J.M.Ziman, 1962 "Electrons in metals: a short guide to the Fermi surface" Characteristic lattices have particular Van Hove singularities associated with their density of states. These are symmetries induced in the DoS at the critical points in the Brillouin zone.
55. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 3D 10x10x10 simple cubic cell Schematic form of DoS for face-centred cubic lattice Figure 1.10, p 34, Jones & March - Theoretical solid state physics Volume 1
56. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 What is a polaron? • bare electron interacts with surrounding medium (Fermi sea) • becomes dressed in excitation cloud • interaction tends to self trap particle... (Diagram: A Guide to Feynman Diagrams in the Many-body Problem, R.D. Mattuck)
57. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 Frohlich Polaron • Consider linear dielectric response - outside- polaron Dielectric response…
58. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 Dielectric response… Site Energy (Polarisation) Self consistent response...
59. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 The SCF loop... Alpha is a 'response parameter'; almost identical to the Frohlich Electron-Phonon coupling (may even be formally identical!) Calculated as ~0.5 eV / e by assuming linear response of dielectric to electron fully localised on 1 nm fullerene molecule
60. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 Simple 1D chain case... S
61. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 Simple cubic lattice Tiny defect to break symm
62. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016
63. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016
64. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 Transfer between polarons Polaron transfer integral calculation
65. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 Unperturbed; C60 Simulated Annealing
66. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 Localised Polaron State Perturbed States Polaron; C60 Simulated Annealing
67. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 Case Study IV: Sturm sequences in 1D https://github.com/jarvist/Teclo See also: Parameter free calculation of the subgap density of states in poly (3-hexylthiophene) JM Frost, J Kirkpatrick, T Kirchartz, J Nelson - Faraday discussions, 2014
68. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 In 1D polymers; a tridiagonal Hamiltonian ( Reading maths paper on the ArXiv isn't always a complete waste of time. )
69. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 A 'Mathematical Trick'... ( For any tridiagonal matrix; technique of Sturm sequences is universal but it is slower for full matrix than traditional solvers. What about the intermediate regime w/ offdiagonals? )
70. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Sturm Sequences (in Julia) O(n) time complexity, for m bins (m<<n) ( vs O(n*n) time complexity, O(m) time complexity to bin eigenvalues & much much more memory use )
71. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 ~BOOM~ ( ~1'000'000 times faster) N=10'000; Tri-diagonal matrix Sturm sequence method: elapsed time: 9.4411e-5 seconds ( 86'912 bytes allocated) Standard dense eigensolver: elapsed time: 112.3307 seconds (803'281'176 bytes allocated)
72. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Polyfluorene (by MD)
73. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 ∇U = F F = ma Where to get structures? At the core of MD... HEAT BATH Rough potential energy landscape
74. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Statistical mechanics view At thermodynamic equilibrium, difference in population: (We don't need no trajectory (history, kinetics) - just ΔE )
75. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 PFO (some polymer) potential energy landscape
76. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Really need a free energy (including entropy)
77. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 "This fundamental law is the summit of statistical mechanics, and the entire subject is either the slide-down from this summit, as the principle is applied to various cases, or the climb-up to where the fundamental law is derived and the concepts of thermal equilibrium and temperature T clarified." Feynman says... Statistical Mechanics: A Set Of Lectures (Advanced Book Classics) by Richard Feynman
78. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 How to Z? Sum over configurations or Sum over energy (caring for degeneracy) Continuous variable U(theta) → simple integral
79. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 How to Z? Sum over configurations or Sum over energy (caring for degeneracy) Continuous variable U(theta) → simple integral Transcendental function - an absolute pain to analytically integrate!
80. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Nb: Z is Z(T , U). Therefore need to reevaluate if T or U change...
81. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016
82. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Populate Density of States Hamiltonian... Distribution of thetas from stat mech... Model for transfer integral...
83. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016
84. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 Sturm sequence in 1D • Effective torsional potential → integrate to partition function • Take these generate assemblies & with a model for the electron transfer (hopping) integral → Hamiltonian • Solve this Tridiagonal H via Sturm sequences • generates disordered DoS extremely efficiently • (everything is linear in time + space, O(n))
85. Jarvist Moore Frost (University of Bath, UK) ETSF - YRM June 2016 - King's College London Tues 7th Jun 2016 Collaborators:- Piers Barnes, Aurel Leguy, Andrew McMahon - Imperial College London Piers Barnes Aurelien Leguy WMD Group, Bath Acknowledgments:- EPSRC - EP/K016288/1 EPSRC Archer - EP/L000202 University of Bath HPC http://go.bath.ac.uk/wmd