2017-03-PVCDT-CDT_JarvistMooreForst_MultiscalePhysicsOfPhotovoltaics

Jarvist Moore Frost (Imperial College London, UK) PV-CDT - 2017
Wed 8th Mar 2017 Walsh Materials Design Group, Imperial College London, UK [email protected] From atoms to solar cells Multiscale physics of Photovoltaics

Wed 8th Mar 2017 The physics of undergraduate textbooks 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), p. 40.

Wed 8th Mar 2017 Walsh Materials Design Group, Imperial College London, UK [email protected] From solar cells to atoms Multiscale physics of Photovoltaics

Wed 8th Mar 2017 http://www.treehugger.com/renewable-energy/striking-chart-showing-solar-power-will-take-over-world.html Solar is winning!

Wed 8th Mar 2017 76 GW new capacity in 2016 (Guardian, 7th March 2017)

Wed 8th Mar 2017 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. (i.e. twice as cheap; or twice as efficient.) Henry Snaith, Oxford So… what are we doing with our lives?

Wed 8th Mar 2017 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...

Wed 8th Mar 2017 Silicon grown by Czochralski process 1956 George E. Meyers, Raytheon Corp. semiconductor plant in Newton, Massachusetts, USA American Radio History

Wed 8th Mar 2017 1500 degrees celsius!

Wed 8th Mar 2017 Dye sensitised solar cell http://dx.doi.org/10.1590/S0103-50532003000600005

Wed 8th Mar 2017 What are the physics? Almost every area of physics outside the nucleus! • Solid State Theory → crystalline solids (Si, CZTS, MAPI ?) • Condensed Matter Theory → amorphous, polymer, liquid (a-Si, Dye SCs, MAPI ?) • Quantum Electrodynamics (QED) & Quantum Field Theory (QFT) → Matter / Light interaction • Statistical physics → structures, defects • Thermodynamics → device operation, light concentration & formation of active layer • Maxwell's equations → classical field theory of light • Group theory → useful for a lot of the above

Wed 8th Mar 2017 Ziman - 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

Wed 8th Mar 2017 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!)

Wed 8th Mar 2017 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.

Wed 8th Mar 2017 Life cycle of a PV material • New material! → a spec of dust ← • Contactless Material characterisation: ◦ Compositional (MALDI-ToF, NMR ) ◦ Optical (UV-Vis, PL, TRPL) ◦ Solution electrochemistry (EA,IP) ◦ Scattering (Neutrons, X-Rays) • Electrical Contacts: ◦ Guess at Work function? [or calculate!] ◦ Mobility via: FET, ToF, SCLC (!!! dodgy) • Devices: (Need good _films_ ; Ohmic contacts) ◦ Is it a diode? Transient response. EQE. EL. ◦ → Device efficiency! ←

Wed 8th Mar 2017 1.6 eV 1.0 eV AM1 AM1.5 θ=48° AM0

Wed 8th Mar 2017 Solving Models • Universal things are well implemented (DFT, etc.) ◦ BUT - opportunity cost (to you) to learn to use codes + methods. • Particular (to your project / scientific problems) are unlikely to be implemented • So you'll have to implement them yourself!

Wed 8th Mar 2017

Wed 8th Mar 2017 Labview! (The Horror, The Horror)

Wed 8th Mar 2017 Mathematician Theorist Numericalist (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

Wed 8th Mar 2017 "There is a computer disease that anybody who works with computers knows about. It's a very serious disease and it interferes completely with the work. The trouble with computers is that you 'play' with them! " -- Richard P. Feynman

Wed 8th Mar 2017 "Computers are bicycles for the mind." - Steve Jobs

Wed 8th Mar 2017 (UK) Children of the 80/90s had a head start...

Wed 8th Mar 2017 But you guys have open-source & the Internet!

Wed 8th Mar 2017 Programming languages compared (Potential) Computational Speed Algorithmic Expressiveness C Python Julia Fortran Assembly R Octave go Haskell Note - Turing completeness (universal computability): any Turing complete language can impersonate any other. Any program can be written in any programming language.

Wed 8th Mar 2017 Programming languages compared (Potential) Computational Speed Algorithmic Expressiveness C Python Julia Fortran Assembly R Octave go Haskell

Wed 8th Mar 2017 Static or Dynamically typed Compiled, JIT compiled or Interpreted Procedural or Functional Homoiconic, or not Mathematically expressive, or less so 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

Wed 8th Mar 2017 My recommendation... Everyone (particularly experimentalists) should use a Jupyter 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…

Wed 8th Mar 2017 Mathematical expressivity >> Python; Speed ~= C / Fortran

Wed 8th Mar 2017 Pairing Socks Effectively http://www.instructables.com/id/Orphan-Sock-Reunion-Device/

Wed 8th Mar 2017 Fastest approach... • Don't calculate anything! Flickr: Amy Jane Gustafson, Argyle mismatched socks

Wed 8th Mar 2017 Discussion and demonstration on the whiteboard • What algorithm to use? • What is the time complexity of this algorithm? • Is it rigorous to errors (single socks)? • Discussion of data structures, and how this can change the time-complexity of the algorithm, yet doing the same work.

Wed 8th Mar 2017 Big 'O' notation Constant time ~ O(1) Linear scaling DFT ~ O(N) Molecular Dynamics // Monte Carlo ~ O(N) Kohn-Sham DFT ~ O(N^3) Hybrid DFT / Hartree Fock ~ O(N^4) GW-approximation ~ O(N^5/N^6) Exact Schrodinger solution / Full CI ~ O(N!) ( N is usually: # of electrons; or # of atoms. )

Wed 8th Mar 2017 Programming Case Studies • Hellwarth 1999 PRB • Tight binding ◦ Sturm Sequences • Structures by Stat Mech

Wed 8th Mar 2017 Hellwarth 1999 PRB Interactive discussion of an iJulia/Jupyter notebook, which is available at: https://github.com/jarvist/ijulia-notebooks/blob /86fd5779710d5ffc55becb25f2d4e031fe03f4d 9/2017-02-10%20-%20Hellwarth%201999%20 PRB%20-%20Mobility%20of%20an%20electron %20in%20a%20multimode%20polar%20lattice. ipynb

Wed 8th Mar 2017

Wed 8th Mar 2017 Step 1) Write down everything you know...

Wed 8th Mar 2017 Step 2) Go and get some help...

Wed 8th Mar 2017 Step 3) Fiddle until it works!

Wed 8th Mar 2017 Step 4) Success! (For arbitrary Alpha and Beta) Hellwarth 1999 PRB

Wed 8th Mar 2017 Motivation Motivation: Why do organic solar cells work*? (* at all)

Wed 8th Mar 2017 A simple type of N-state model Basis of states on monomers… (orthogonal) Coupled with effective transfer-integrals

Wed 8th Mar 2017 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"

Wed 8th Mar 2017 Psi & E - results of our efforts

Wed 8th Mar 2017 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)

Wed 8th Mar 2017 Infinite polymer (10 units)

Wed 8th Mar 2017 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

Wed 8th Mar 2017 5K PL-spectra, Octamers

Wed 8th Mar 2017 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

Wed 8th Mar 2017 Perfectly ordered (+ with trap states) PFO polymer No site disorder... No J disorder...

Wed 8th Mar 2017 Disorder doesn't remove trap states

Wed 8th Mar 2017 Still not fast enough… (only ~1000 DoS points / s) Mostly empty Hamiltonian… yet spending a lot of time solving it Sparse matrix routines? → (10x speedup!) Break into sub problems & combine? Direct mathematical analysis - random matrices? Mathematical interlude

Wed 8th Mar 2017 Random Matrices... Random Matrix Theory...

Wed 8th Mar 2017 Tridiagonal Matrices? ( Reading maths paper on the ArXiv isn't always a complete waste of time. )

Wed 8th Mar 2017 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? )

Wed 8th Mar 2017 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 )

Wed 8th Mar 2017 ~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)

Wed 8th Mar 2017 Soft Modes Interactive discussion of solving the Time-independent Schrodinger equation, not as difficult as you might imagine. https://github.com/jarvist/ijulia-notebooks/blob /86fd5779710d5ffc55becb25f2d4e031fe03f4d 9/2016-05%20-%201D%20Schr.%20solver%20 -%20Soft%20Phonon%20Modes.ipynb

Wed 8th Mar 2017 Slithering Snakes: Structures by Stat Mech

Wed 8th Mar 2017 Generating Geometries Beyond Born-Oppenheimer Ab-initio MD Empirical MD Coarse grain MD Stat Phy Make stuff up 'optimised geom' Physical Accuracy? Time (exp)

Wed 8th Mar 2017 MD is quite a pain...

Wed 8th Mar 2017 ∇U = F F = ma At the core of MD...

Wed 8th Mar 2017 Statistical mechanics view At thermodynamic equilibrium, difference in population: (We don't need no trajectory (history, kinetics) - just ΔE )

Wed 8th Mar 2017 Polyfluorene - a 9 yr love / hate relationship

Wed 8th Mar 2017 Early PhD work… design a PFO MD forcefield

Wed 8th Mar 2017 Simulate molecular dynamics & analyse the result...

Wed 8th Mar 2017 Polyfluorene (by MD)

Wed 8th Mar 2017 Given a U, how to populate DoS?

Wed 8th Mar 2017 "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 1972 Feynman says...

Wed 8th Mar 2017 How to Z? Sum over configurations Continuous variable U(theta) → simple integral

Wed 8th Mar 2017 How to Z? Sum over configurations Continuous variable U(theta) → simple integral Transcendental function - an absolute pain to analytically integrate!

Wed 8th Mar 2017 I love Julia. Nb: Z is Z(T , U). Therefore need to reevaluate if they change...

Wed 8th Mar 2017 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)

Wed 8th Mar 2017 Zero pressure potential (U from QC, MP2 PFO dimer) eV Red = potential Green = distribution @ 300K

Wed 8th Mar 2017 Increasing (holding flat) sin potential [[ Pressure ]]

Wed 8th Mar 2017 Populate Density of States Hamiltonian... Distribution of thetas from stat mech... Model for transfer integral...

Wed 8th Mar 2017 Acknowledgments WMD Group (Imperial/Bath) James Kirkpatrick (Imperial, now Deepmind / Google) Beth Rice (Imperial) Jenny Nelson (Imperial)

Wed 8th Mar 2017 “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

Wed 8th Mar 2017 Supposed end of Slides

Wed 8th Mar 2017 "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

Wed 8th Mar 2017 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)

Wed 8th Mar 2017 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

Wed 8th Mar 2017 What we need is Fusion! [ E=mc2 ] Opération Canopus, Fangatuafa atoll, 1968. 2.6 MT

Wed 8th Mar 2017

Wed 8th Mar 2017 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)

Wed 8th Mar 2017 ~1000 kWh/m^2 per annum

2017-03-PVCDT-CDT_JarvistMooreForst_MultiscaleP...

2017-03-PVCDT-CDT_JarvistMooreForst_MultiscalePhysicsOfPhotovoltaics

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