2016-03 PVCDT JarvistMooreFrost From Atoms to Solar Cells

Slides from a talk to PhD students in the PVCDT at the University of Bath. Attempting to bridge the gap between the (mostly experimental) view of a solar cell, and the atomistic grasp of materials modelling developed by Aron Walsh and Keith Butler (the two previous lecturers).

Transcript

1. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Jarvist Moore Frost Walsh Materials Design Group, University of Bath, UK j.m.frost@bath.ac.uk From atoms to solar cells Multiscale physics of Photovoltaics
2. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Overview • Introduction & why Photovoltaics (PV) • What is a solar cell? • What are the physics? • Thermodynamics, PV, Shockley-Queisser limit, Light trapping • Semiconductor Device Physics • Drift Diffusion, Organic Charge Transport • Theory & Programming Case studies:- • Tight Binding • Beta-Phase PFO • Sturm Sequences • Geometries by statistical mechanics
3. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 "I'm afraid I can't put it more clearly," Alice replied very politely, "for I can't understand it myself to begin with." Lewis Carroll, Alice's Adventure in Wonderland Illustration by John Tenniel
4. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 The physics of undergraduate text-books is 90% true; the contents of the primary research journals of physics is 90% false. — John M. Ziman Reliable Knowledge: An Exploration of the Grounds for Belief in Science (1978, 1991), 40.
5. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Jarvist Moore Frost Walsh Materials Design Group, University of Bath, UK j.m.frost@bath.ac.uk From solar cells to atoms Multiscale physics of Photovoltaics
6. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 I really dislike seeing this ~hundreds of times at conferences! - the one utility is to look at the lower right point, and see how recently the speaker refreshed their slides (NREL refreshes this every 3 months)
7. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Not a CO2 Crisis - we have an Energy Crisis Each person in Britain:- 10'000kg CO2 → ~10MWh pa 10MWh → 36GJ pa 1142W → ~10 Cyclists The world (2008) = 18 TW = 18'000'000'000'000 W Art Installation, V&A museum, Christmas 2009
8. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 What we need is Fusion! [ E=mc2 ] Opération Canopus, Fangatuafa atoll, 1968. 2.6 MT
9. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016
10. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016
11. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016
12. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 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)
13. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 ~1000 kWh/m^2 per annum
14. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 What is a solar cell? ...a slab of P and N doped silicon... ...a bulk heterojunction of fullerene and conjugated polymer… ...a conversion of individual quanta of light (photons) to movement of quanta of charge (electrons... ...a thermodynamic engine driven between the heat bath of the sun and the ambient...
15. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Silicon grown by Czochralski process 1956 George E. Meyers, Raytheon Corp. semiconductor plant in Newton, Massachusetts, USA American Radio History
16. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 1500 degrees celsius!
17. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 a) Methylammonium lead iodide (CH3NH3I) and PbI2 (precursor solution) dissolves in γ-butyrolactone solution. b) Spin-coating process ofCH3NH3PbI3perovskite solution on indium tin oxide (ITO)/glass substrate. 8 August 2013, SPIE Newsroom. DOI: 10.1117/2.1201307.005033 Hybrid Halide Perovskite - low energy process
18. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Silicon has a 60 years head start. The engineers have done amazing things. As scientists, if we want to beat Silicon - we need to find something an order of magnitude better. Henry Snaith, Oxford
19. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Overview • Introduction & why Photovoltaics (PV) • What is a solar cell? • What are the physics? • Thermodynamics, PV, Shockley-Queisser limit, Light trapping • Semiconductor Device Physics • Drift Diffusion, Organic Charge Transport • Theory & Programming Case studies:- • Tight binding • Beta-Phase PFO • Sturm Sequences • Geometries by statistical mechanics
20. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 What are the phyiscs? Almost every area of physics outside the nucleus! • Solid State Theory → crystalline solids (Si, CZTS) • Condensed Matter Theory → amorphous, polymer, liquid (a-Si, Dye SCs, Perov?) • Quantum Electrodynamics (QED) & Quantum Field Theory (QFT)→ Matter / Light interaction • Statistical physics → structures, defects • Thermodynamics → device operation, light concentration & formation of active layer • Electromagnetism → classical field theory of light • Group theory → useful for a lot of the above
21. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Ziman - extremely clear and intuitive descriptions; a delight to read. 1960 - Electrons and Phonons - Great reference for transport 1969 - Elements of Adv. Quantum Theory - Very gentle Intro... 1972 - Theory of Solids (2nd Ed.) - Perhaps the best single Solid State Text 1980 - Models of Disorder - The only real 'disorder' textbook, slightly dated
22. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 If you read just one book… ( My PhD Supervisor ; I am biased ) Unapologetically physics-based view of solar cells Clear text, fairly well structured, some interesting 'advanced' topics covered (thin films, light trapping strategies) Diagrams a little coarse (but stylish in a 1980s Mac Paint kind of way!)
23. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Overview • Introduction & why Photovoltaics (PV) • What is a solar cell? • What are the physics? • Thermodynamics, PV, Shockley-Queisser limit, Light trapping • Semiconductor Device Physics • Drift Diffusion, Organic Charge Transport • Theory & Programming Case studies:- • Tight Binding • Beta-Phase PFO • Sturm Sequences • Geometries by statistical mechanics
24. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 A solar cell... ... is a light absorbing material connected to an external circuit in an asymmetric manner. Photogenerated charge carriers are driven towards one or other of the contacts by the built-in spatial asymmetry. - J.Nelson, Physics of Solar cells A heat engine that silently runs on sunlight and thermodynamics to produce electrical power.
25. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Thermodynamic Limit Sun: 5760 K Cell: 2470 K Bath: 300 K η PCE = 85%
26. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 1.5 eV 1.0 eV AM1 AM1.5 θ=48° AM0
27. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Shockley–Queisser limit (@ 1 sun) Maximum solar conversion efficiency around 33.7%, assuming a single junction with a band gap of 1.34 eV CC0 Wikipedia, Own work by User: Sbyrnes321
28. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Multi Junction solar cell, Fraunhofer institute, 2010 Have faith in your material! There are some weird and wonderful device architectures...
29. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Martin Green -- 1990s
30. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Silicon, 2000; 25 Yr life
31. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Silicon, 2016; 25+ Yr life Martin Green -- Prog. Photovolt: Res. Appl. 2001; 9:123-135 CIGS CdTe Both ~killed by Silicon
32. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Life cycle of a PV material • New material! → a spec of dust ← • Contactless Material characterisation: ◦ Compositional (MALDI-ToF, NMR ) ◦ Optical (UV-Vis, TRPL) ◦ Solution electrochemistry (EA,IP) ◦ Scattering (Neutrons, X-Rays) • Electrical Contacts: ◦ Guess at Workfunction? [or calculate!] ◦ Mobility via: FET, ToF, SCLC (!!! dodgy) • Devices: (Need good _films_ ; Ohmic contacts) ◦ Is it a diode? Transient response. EQE. EL. ◦ → Device efficiency! ←
33. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Nature Materials 13, 103–104 (2014) doi:10.1038/nmat3837 On the thermodynamics of light trapping in solar cells Uwe Rau & Thomas Kirchartz Etendue ratio of solar cell system - solid angle of incident radiation vs. outgoing radiation ( sort of an light-beam measure of entropy; in a system it can only increase or stay constant ) Solar cell efficiency increases with sunlight concentration
34. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Light Trapping (Ray Limit) Nothing + Back reflector Inverted Pyramids Randomised Surface d= 4 n^2 =~ 50 (Si) Lambertian emittance
35. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 PERL Silicon Solar Cell ~23.5% PCE
36. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Overview • Introduction & why Photovoltaics (PV) • What is a solar cell? • What are the physics? • Thermodynamics, PV, Shockley-Queisser limit, Light trapping • Semiconductor Device Physics • Drift Diffusion, Organic Charge Transport • Theory & Programming Case studies:- • PCBM-MD • Tight Binding with PCBM-MD • Polarons and Tight Binding • Beta-Phase PFO • Sturm Sequences… • Geometries by statistical mechanics
37. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Organic Solar Cells! (This one is Rubrene, also the highest mobility organic…)
38. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016
39. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016
40. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016
41. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 1.6 eV 1.0 eV AM1 AM1.5 θ=48° AM0
42. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Ideal Diode equation I 0
43. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 The electrical behaviour of the device is the same in the dark and light Light provides a photocurrent which builds up within the device into a photovoltage Key Concept
44. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Overview • Introduction & why Photovoltaics (PV) • What is a solar cell? • What are the physics? • Thermodynamics, PV, Shockley-Queisser limit, Light trapping • Semiconductor Device Physics • Drift Diffusion, Organic Charge Transport • Theory & Programming Case studies:- • PCBM-MD • Tight Binding with PCBM-MD • Polarons and Tight Binding • Beta-Phase PFO • Sturm Sequences… • Geometries by statistical mechanics
45. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Nabla electrical potential = charge density / dielectric constant Actually quite nasty to solve! (self consistency & BCs) The Poisson Equation
46. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Full Drift Diffusion Diffusion term - concentration gradients reduced by random walk of carriers Drift term - carriers accelerate with applied field
47. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Practical Drift Diffusion Electron Affinity (variations) Effective Band Densities of State
48. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Drift Diffusion (Assumptions) • e/h form quasi thermal equilibrium (T, Ef) • e/h temperature same as lattice (no hot / accelerated carriers) • relaxation time approximation (scattering within band dominates over defects) • e/h are well defined by quantum number k • Boltzmann approximation • Compositional invariance (band edge gradient replaced with general F) • Most calculations (quasi) equilibrium only in 1D
49. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Drift Diffusion Codes SCAPS: Solarcell CAPacity Simulator Used by the CIGS community. Intuitive + has a new manual. Has built in defects :) but rather poorly documented :( Good for CV analysis of real cells. Email Marc Burgelman to get a copy →
50. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016
51. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Optimisation of Thickness - a Goldilocks situation Thick enough / dark enough to absorb... Mobility sufficient to extract charges through this thickness... avoiding recombination Sub-gap states will eat your lunch Above-gap states will never hurt you Dispersion / traps reduce mobility → increased recombination
52. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Overview • Introduction & why Photovoltaics (PV) • What is a solar cell? • What are the physics? • Thermodynamics, PV, Shockley-Queisser limit, Light trapping • Semiconductor Device Physics • Drift Diffusion, Organic Charge Transport • Theory & Programming Case studies:- • PCBM-MD • Tight Binding with PCBM-MD • Polarons and Tight Binding • Beta-Phase PFO • Sturm Sequences… • Geometries by statistical mechanics
53. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Mathematician Theorist Numerics (Computational) Experimentalist PURITY UTILITY After taking a course in mathematical physics, I wanted to know the real difference between Mathematics and Physicists. A professor friend told me "A Physicist is someone who averages the first 3 terms of a divergent series". - Benjamin Jones
54. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 "The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation." - Paul Dirac, 1929 However, this is not computationally tractable for real (>15 electron) systems. Approximate theories, adapted to the material & problem of interest, combined with numerical solution, is necessary to make progress. → Programming is an ever more important part of science ←
55. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 "Computers are bicycles for the mind." - Steve Jobs
56. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 UK Children of the 80s had a head start...
57. Programming languages compared (Potential) Computational Speed Algorithmic Expressiveness C Python Julia Fortran Assembly R Octave go Haskell
58. Static or Dynamically typed Compiled, JIT compiled or Interpreted Procedural or Functional Homoiconic, or not Mathematically powerful, or not Fortran/C: Static, Compiled, Procedural; laborious Python: Dynamic, Interpreted, Procedural (+ fn), Matrices 'bolted on' Julia: Dynamic and Static, JIT'ed, Proc./fn., homoiconic, extremely strong maths support Programming languages discussed
59. Christoph Ortner - some nice teaching Julia examples
60. Unicode Compact high-level mathematics
61. Julia is fast ; Python is relatively slow (20x slower than C)
62. My recommendations... Everyone (especially experimentalists) should use a iPython or iJulia web notebook; plot data, manipulate, back of the envelope calculations etc. Julia is a lot of fun → responsive, quick, less frustrating; Python has an enormous set of libraries available for it From a professional skills development point of view, programming skills are probably the most valuable thing you can acquire during a PhD… "Well, Mr. Frankel, who started this program, began to suffer from the computer disease that anybody who works with computers now knows about. It's a very serious disease and it interferes completely with the work. The trouble with computers is you *play* with them. They are so wonderful. You have these switches - if it's an even number you do this, if it's an odd number you do that - and pretty soon you can do more and more elaborate things if you are clever enough, on one machine. " - Richard Feynman
63. The LIGO (gravitational wave) data
64. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Overview • Introduction & why Photovoltaics (PV) • What is a solar cell? • What are the physics? • Thermodynamics, PV, Shockley-Queisser limit, Light trapping • Semiconductor Device Physics • Drift Diffusion, Organic Charge Transport • Theory & Programming Case studies:- • Tight binding • Beta-Phase PFO • Sturm Sequences • Geometries by statistical mechanics
65. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Motivation Motivation: Why do organic solar cells work*? (* at all)
66. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 A simple type of N-state model Basis of states on monomers… (orthogonal) Coupled with effective transfer-integrals
67. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 1D polymer Tight Binding Hamiltonian "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"
68. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Psi & E - results of our efforts
69. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Density of States by Tight Binding Solve Density Matrix Hamiltonian → Eigenvalues (electronic wavefunction expectation energies) … Density of States is the key transport parameter for amorphous / defective devices (effective mass and scattering distance matters little when charges are being energetically trapped)
70. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Infinite polymer (10 units)
71. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016
72. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Actually quite boring for large polymers...
73. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 100 'polymer', PBCs, slight mid-chain defect
74. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 2D checkerboard… (without PBCs)
75. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 2D checkerboard… (with PBCs)
76. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016
77. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 3D Checkerboard
78. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 3D 10x10x10 simple cubic cell
79. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 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.
80. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 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
81. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Unperturbed; C60 Simulated Annealing (BCC)
82. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 What is β-Phase PFO? Poyfluorene-di-octyl (PF8) [but not the other polyfluorenes] sometimes exhibits noticeable green fluorescence. "Formation of the β-phase effectively corresponds to crystallization in one dimension, a remarkably uncommon phenomenon in nature." Nano Lett., 2007, 7 (10), pp 2993–2998
83. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 5K PL-spectra, Octamers
84. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Normal 'Wiggly' Polyfluorene...
85. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 HOMO Spin Density - centre crimped flat Hypothesis:- Is Beta Phase a hole trap? Are 'bubbles' of beta phase responsible for reduced mobility in processing?
86. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Auto-generated varying 'Beta phase' with ModRedundant Me Gusta [11:43:04]jmf02@login-0:> cat magicnumbers.txt 65 64 93 94 =180.0 F 86 85 114 115 =180.0 F 44 43 72 73 =180.0 F 107 106 135 136 =180.0 F 23 22 51 52 =180.0 F 128 127 156 157 =180.0 F 2 1 30 31 =180.0 F [11:43:07]jmf02@login-0:> cat daughters.sh for i in ` seq 7 ` do cat mother.com > "${i}.com" head -n "${i}" magicnumbers.txt >> "${i}.com" echo >> "${i}.com" done [11:43:12]jmf02@login-0:> cat mother.com %chk=tmp.chk %mem=8GB %nprocshared=8 #p opt=ModRedundant am1 01010101.pdb 0 1 ... Jarv, evidently pleased with himself circa. March 2012
87. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 0 1 2 3 4 5 6 7
88. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Ran into the limits of what we can do with QC... PFO minima at theta = 45 deg P3HT (+ most other polymers) minima at theta= 0 deg
89. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Perfectly ordered (+ with trap states) PFO polymer No site disorder... No J disorder...
90. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Disorder doesn't remove trap states
91. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Still not fast enough… (only ~1000 DoS points / s) Mostly empty Hamiltonian… yet spending a lot of time solving it Sparse matrix routines? Break into sub problems & combine? Direct mathematical analysis - random matrices? Mathematical interlude
92. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Random Matrices... Random Matrix Theory...
93. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Tridiagonal Matrices? ( Reading maths paper on the ArXiv isn't always a complete waste of time. )
94. 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? )
95. 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 )
96. 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; elapsed time: 9.4411e-5 seconds ( 86'912 bytes allocated) elapsed time: 112.3307 seconds (803'281'176 bytes allocated)
97. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Overview • Introduction & why Photovoltaics (PV) • What is a solar cell? • What are the physics? • Thermodynamics, PV, Shockley-Queisser limit, Light trapping • Semiconductor Device Physics • Drift Diffusion, Organic Charge Transport • Theory & Programming Case studies:- • PCBM-MD • Tight Binding with PCBM-MD • Polarons and Tight Binding • Beta-Phase PFO • Sturm Sequences… • Geometries by statistical mechanics
98. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Snakes Under Pressure
99. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Photoluminesence of PFO under Pressure
100. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Generating Geometries Ab-initio MD Empirical MD Coarse grain MD Stat Phy Make Stuff up 'optimised geom' Physical Accuracy? Time (exp)
101. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 MD is quite a pain...
102. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 ∇U = F F = ma At the core of MD...
103. 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 )
104. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Polyfluorene - a 9 yr love / hate relationship
105. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Early PhD work… design a PFO MD forcefield
106. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Polymers are freaky...
107. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Polyfluorene (by MD)
108. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Given a U, how to populate DoS?
109. 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...
110. 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
111. 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!
112. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 I love Julia. Nb: Z is Z(T , U). Therefore need to reevaluate if they change...
113. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Codes to take arbitrary potential function → integrate to get Z (=partition function) → populate configurational density of states → parameterise electron transfer Js from result → if tridiagonal, extremely fast Sturm sequence else, standard eigenvalue + histogram → DoS for band of interest Partition Functions are cool (and not scary, honest)
114. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Zero pressure potential (U from QC, MP2 PFO dimer) eV Red = potential Green = distribution @ 300K
115. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Increasing (holding flat) sin potential [[ Pressure ]]
116. 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...
117. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Feed to TB DoS machinery Pressure STURM! 10'000 sites < 0.1 s [ quite fast ]
118. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 "Kinda agreement" Effect 10x times too strong by calculation… Why? Approx form for U? Back of the envelope calc of Pressure? Intra-chain effects saturating < 0.8 GPa, effect is mainly inter-chain compression? (Pi-Pi stacking...) Might have to go do some MD after all (-.-)
119. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 U is not a Hamiltonian Assume no correlation Theta1-Theta2-Theta3 Sidechains & cohesive action weird (U not a simple function) Polymers are hard... Problems?
120. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 Acknowledgments WMD Group (Bath) James KP (Imperial, now Deepmind / Google) - for all the tutorage re: Wave Functions Beth Rice (Imperial) Jenny Nelson (Imperial)
121. Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 2nd March 2016 “It is simply this: do not tire, never lose interest, never grow indifferent—lose your invaluable curiosity and you let yourself die. It's as simple as that.” ― Tove Jansson, Fair Play