From Atoms to Solar Cells

Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 5th March 2015
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

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

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

"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

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 republishes this every 3 months)

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

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

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 7 years]
We have the technology!
→ Cost is the key issue - the solar resource is low density (1kW / m^2)

What is a solar cell?
...a slab of P and N doped silicon...
...a bulk heterojunction of fullerene and
conjugated polymer…
...a convert 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...

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

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

(old) mono-crystalline
high efficiency (~15%) but expensive...

modern mono-crystalline (better anti-reflective → black)
highest efficiency (~20%), really quite cheap…
Best lifetimes

SunPower E20
20.4% efficient module (!!!!!!!!!)
Full back-contacted cells
Commercially available >2013

polycrystalline silicon
good efficiency (~14-16%)
(used to be sig. cheaper than mono-crystalline)

CIGS / a-Si - Black Mirrors
Efficiencies 7-13%. Were relatively cheap...

CdTe
Your flexible,
slightly purple-y
friend
(poisonous, but apparently easiest
to make!)
~7-15% efficiencies

What are the phyiscs?
● Almost every area of physics outside the nucleus...
● Solid State → 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)

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

My PhD Supervisor's book
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 bit coarse

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.

Thermodynamic Limit
Sun: 5760 K
Cell: 2470 K
Bath: 300 K
ηPCE
= 85%

1.6 eV
1.0 eV
θ

Shockley–Queisser limit (@ 1 sun)
Maximum solar conversion efficiency around 33.7%, assuming a single junction
with a band gap of 1.34 eV

Silicon, 2012; 25 Yr life
CIGS
CdTe
Both ~killed by
Silicon

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 )

Light Trapping (Ray Limit)
Nothing + Back reflector Inverted Pyramids
Randomised Surface
d= 4 n^2 =~ 50 (Si)
Lambertian
emittance

PERL Silicon Solar Cell ~23.5% PCE

Organic Solar Cells!
(This one is Rubrene, also the highest mobility organic…)

Ideal Diode
equation
I0

PN Junction -
From: http://en.wikipedia.org/wiki/P%E2%80%93n_junction

Nabla electrical potential =
charge density / dielectric constant
Actually quite nasty to solve!
(self consistency & BCs)
Poisson's Equation

Full Drift Diffusion
Electron Affinity
(variations)
Effective Band
Densities of State

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)

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.

References
/ Scheme of Work
Thomas Kirchartz, Kaori Seino, Jan-Martin Wagner, Uwe Rau, and Friedhelm
Bechstedt. “Efficiency Limits of Si/SiO2 Quantum Well Solar Cells from
First-Principles Calculations.” Journal of Applied Physics 105, no. 10:
104511. Accessed November 18, 2013. doi:10.1063/1.3132093.
→ Combines first principles calculation with drift diffusion
to model performance of novel PV structures
+ Read Jenny's Chapter 3 in The Physics of Solar Cells (Imperial College
Press 2003)

Thomas Kirchartz, Kaori Seino, Jan-Martin Wagner, Uwe Rau, and Friedhelm Bechstedt. “Efficiency Limits of Si/SiO2 Quantum Well Solar Cells
from First-Principles Calculations.” Journal of Applied Physics 105, no. 10: 104511. Accessed November 18, 2013. doi:10.1063/1.3132093.

Optimisation of Thickness
- a Goldilocks situation
Thick enough / dark enough to absorb...
Mobility sufficient to extract charges through
this thickness...
avoiding Langevin recombination
Sub-gap states will eat your lunch
Above-gap states will never hurt you
Dispersion / traps are fairly bad

Organic materials are soft: 'effective mass' so high that KE negligible
→ Small Polaron / hopping regime
Transport occurs at 'resonance'
Marcus theory offers a useful description
Key transport parameter is the 'Electron Transfer Integral' or J (sometimes 't')
→ calculate by projective method (DFT) ~ hrs / calculation
OR Molecular Orbital Overlap (MOO) ~ ms / calculation

Modelling Charge
Transport (in Organics)
Following 5 slides of
figures & text reproduced
from Joe Kwiatkowski's
MPhil thesis (ICL, 2008)

Charge transport - the microscopic view

Effective potential energy surface

Marcus theory

Transfer integral

All this scary matrix maths (orbital projection)

Practically… 3 DFT calculations & a matrix inversion
Molecule
A
Molecule
B
Molecule
A + B

Monte Carlo model of charge transport…

Mathematician
Theorist
Numerics (Computational)
Experimentalist
The Lay Person

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
An engineer thinks that equations are an approximation to reality.
A physicist thinks reality is an approximation to equations.
A mathematician doesn't care.
--- (from CANONICAL LIST OF MATH JOKES )

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
We don't need any new physics (as in, extra forces,
processes, etc.) - we need computationally tractable
models, that are sufficiently accurate for what we are
experimentally probing.

"Computers are bicycles for the mind." - Steve Jobs

UK Children of the 80s had a head start...

Programming languages compared
(Potential) Computational Speed
AlgorithmicExpressiveness
C
Python
Julia
Fortran
Assembly
R
Octave
go
parallel
Haskell

Static or Dynamically typed
Compiled or Interpreted (JIT'ed)
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

From Christoph Ortner's excellent numerical
analysis Julia notebooks.. http://homepages.
warwick.ac.uk/staff/C.Ortner/index.php?
page=julia

My recommendations...
Everyone (probably 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 (than other
languages)
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

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

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"

Psi & E - results of our efforts

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)

Infinite polymer (10 units)

Motivation
Motivation: Why do organic solar cells work*? (* at all)

Actually quite boring for large polymers...

100 'polymer', PBCs, slight mid-chain defect

2D checkerboard… (without PBCs)

2D checkerboard… (with PBCs)

3D Checkerboard

3D 10x10x10 simple cubic cell

"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 the DoS at
the critical points in the
Brillion zone.

Overview
● Tight Binding
● PCBM-MD
● Tight Binding with PCBM-MD
● Polarons and Tight Binding

Atoms → Smarties, gives you a ~1000x (or more) speedup

Where to get parameters?
Girifalco
'smeared' C60
for the balls...
And a scaled
version for
PBM?

Atomistic view...
We have an OPLS PCBM model...
so let's use it!
2564 PCBMs
MD for ~20ps

Atomistic RDF via COM
(Center of Mass) of PBM
and C60 fragments

1000 Tris PCBM, CG
alter elem c, vdw=5.0
alter elem p, vdw=3.0
show spheres

Consider the inter-adduct
angles

8 Bis isomers; Angles: 36 72 60 90 180 144 120 108

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 Unique Tris Isomers... (of 24360)

C60 (Bucky Balls) Mono PCBM Bis PCBM
Tris PCBM

Transfer Integrals
(old AutoJ data)
MONO
6.5 meV
Bis:
10.5 meV
Tris:
4.4 meV
Sampling!!! Average of 1000 structures;
generated with Packmol

Transfer Integrals…
Amicable Separation

Degeneracy… :(
C60 is 3-fold LUMO degenerate Adducts?
DFT KS unoccupied orbitals
MONO 30A LUMOs 0 -0.060 -0.284 -1.184 -1.248 (eV)
BIS 30A LUMOs 0 -0.235 -0.284 -1.196 -1.443 (eV)
TRIS 30A LUMOs 0 -0.005 -0.023 -1.195 -1.215 (eV)
Arbitrary (?) 50 meV cutoff for degeneracy gives
M non degenerate, B non degenerate, T 3-degenerate.
Elephant in the room: does degeneracy influence
transport in Tris? How about in M/B/T mixes?

Blue = exponential fit
Prefactor = 1e6 (?)
Characteristic length:
0.597 A (MONO)
0.577 A (BIS - E1)
0.580 A (TRIS - EEE)

Summary...
● We have a CG FF for Mono, Bis, Tris…
● Simulated annealing on 1000 mole
samples…
● Transfer integrals - exponential (isotropic)
seems to be a good fit to full blown
projective method QC

(Histogram of 1000 eigenvalues)
High lying states
Low lying states

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)

Frohlich Polaron
● Consider linear dielectric response -
outside- polaron
Dielectric
response…

Dielectric
response…
Site
Energy
(Polarisation)
Self consistent response...

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

Simple 1D chain case...
S

Simple cubic lattice
Tiny defect
to break
symm

Transfer between
polarons
Polaron transfer integral
calculation

Unperturbed; C60 Simulated Annealing

Localised
Polaron State
Perturbed
States
Polaron; C60 Simulated Annealing

?

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

5K PL-spectra, Octamers

Normal 'Wiggly' Polyfluorene...

HOMO Spin Density - centre crimped flat
Hypothesis:-
Is Beta Phase a hole trap?
Are 'bubbles' of beta phase responsible for
reduced mobility in processing?

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

0
1
2
3
4
5
6
7

Energy of Increasing Beta Phase
eV
Enthalpically very uphill -
must be driven by a strongly
entropic / enthalpic process
external to the backbone.
Or perhaps chemistry?

TD-DFT Singlets (Absorption)
0.log: Excited State 1: Singlet-A 3.1101 eV 398.65 nm f=6.0596
Octamer model of flattened segments correctly
predicts green band formation...

TD-DFT Singlets (Absorption)
0
7

HOMO / LUMO Energy
eV

(Holes float... )
0 HOMO: -5.066416 eV +0 meV
1 HOMO: -5.028321 eV +38 meV
2 HOMO: -4.991586 eV +75 meV
3 HOMO: -4.964103 eV +102 meV
4 HOMO: -4.946688 eV +120 meV
5 HOMO: -4.934171 eV +132 meV
6 HOMO: -4.928456 eV +138 meV
7 HOMO: -4.923558 eV +143 meV

Inner Sphere Reorganisation Energy
eV
--> Losing a degree of freedom... -->

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

Jarvist Moore Frost (University of Bath, UK) From atoms to solar cells: Multiscale physics of photovoltaics 5th March 201550meV Gaussian Site Energy Disorder

Beta Phase Energetic Trap
(5 sites)
DFT Trap
Depth
Reproduced!

Beta Phase Energetic Trap
(10 sites)
For Wide Enough trap ~10 sites (no confinement),
Trap depth = site Energy change

Theta ~ 45 degrees for segment
Theta = 0 degrees for beta phase bit
--> 0.18eV change in J
--> 310 meV trap depth

Disordered (torsionally)
TWISTED (~PFO) polymer
596meV
PFO MODEL

Disordered (torsionally)
But FLAT (minima) polymer
70meV
P3HT MODEL

No site disorder...
No J disorder...

PFO trap states from J variation are persistent

Summary of TB-BetaPhase
Model of flattened Beta phase segments produces horrific hole traps
in TB model
We don't see these being so deep in QC - our system is too small, our
model for the distribution of thetas too primitive (athermal).
We're using highly devoid from reality distributions for Theta and
Sigma. (Because we don't know any better.)
PFO-type polymers (or other non flat minima systems) have a
fundamental propensity for generating polaron traps at finite
temperature / disorder.

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

Random Matrices...
Random Matrix Theory...

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

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? )

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 )

~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)

Snakes Under Pressure

Generating Geometries
Ab-initio MD
Empirical MD
Coarse grain MD
Stat Phy
Make Stuff up
'optimised geom'
Physical
Accuracy?
Time(exp)

MD is quite a pain...

∇U = F
F = ma
At the core of MD...

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

Polyfluorene - a 9 yr love / hate relationship

Early PhD work… design a PFO MD forcefield

Polymers are freaky...

Polyfluorene (by MD)

Given a U, how to populate DoS?

"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...

How to Z?
Sum over configurations
or
Sum over energy (caring for degeneracy)
Continuous variable U(theta) → simple integral

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!

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

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)

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

Increasing (holding flat) sin potential [[ Pressure ]]

Populate Density of States Hamiltonian...
Distribution of thetas from stat mech...
Model for transfer integral...

Feed to TB DoS machinery
Pressure
STURM!
10'000 sites
< 0.1 s
[ quite fast ]

U is not a Hamiltonian
Assume no correlation Theta1-Theta2-Theta3
Sidechains & cohesive action weird (U not a
simple function)
Polymers are hard...
Problems?

Acknowledgments
WMD Group (Bath)
James KP (Imperial, now Deepmind / Google) - for all
the tutorage re: Wave Functions
Beth Rice (Imperial)
Jenny Nelson (Imperial)

“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

From Atoms to Solar Cells

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