Fundamental Limits in “nano” photovoltaics
Jenny Nelson
Department of Physics and Grantham Institute for Climate Change
Imperial College London
Thanks to: Ned Ekins-Daukes, UNSW
Thomas Kirchartz, FZ Juelich
Amsterdam,
18th June 2019
AMOLF International Nanophotonics Summer School
Solar energy conversion
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00
100
200
300
400
500
600
Irra
dia
nce / W
m-2 e
V-1
Photon energy / eV
Energ
y
Heat
Light
Solar thermal
Light Dm Chemical
potential
energy
Solar chemical
Light Dm
Electric
work
Solar photovoltaic
Photons in, electrons out
eV
• Photovoltaic energy conversion requires:
– photon absorption across an energy gap
– separation of photogenerated charges
– asymmetric contacts to an external circuit
Photons in, electrons out
p type silicon
n t
yp
e
sil
ico
n
p type silicon
n t
yp
e
efficiency
~ 15-20%
power rating
~ 100-200 Wp
Applications
CIS Tower, Manchester
0.4 MWp
(Solar Century) Solar powered refrigeration
~100 Wp ~1 mWp
Blackfriars Bridge
~1.1 MWp
- +
Voltage
Eg Light
DEF = eVoc
scE
inc JdEEAbsEbeg
Voltage
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00
100
200
300
400
500
600
Irra
dia
nce
/ W
m-2 e
V-1
Photon energy / eV
Power Conversion Efficiency =
Power converted into electrical work (J x V)
Radiant Power received from the Sun
Electrical work and efficiency
Efficiency from the Current density – Voltage (J-V) curve
• Short circuit current density Jsc,
• Open circuit voltage Voc
• Fill factor FF
7
200 400 600
-30
-20
-10
10
20
cu
rre
nt
de
nsity J
[m
Acm
-2]
voltage V [mV]
Jsc
Voc
po
we
r d
en
sity P
[m
Wcm
-2]
Pmpp
Jmpp, Vmpp
• J(V) measured under Standard Test Conditions (AM1.5, 1000 Wm-2, 25C)
• Approximately:
Power conversion efficiency:
http://upload.wikimedia.org/wikipedia/commons/3/35/Best_Research-Cell_Efficiencies.png
8
http://upload.wikimedia.org/wikipedia/commons/3/35/Best_Research-Cell_Efficiencies.png
9
Future directions in solar photovoltaics
Crystalline Silicon
“PV + X” Integrate solar panels with other functions
e.g. Electricity / heat
PV / fuels PV / storage
“Silicon + X” Add a layer to silicon to improve
performance
High efficiency designs Stack different solar cells together in
a multi-junction
Low cost, low energy manufacture Flexible, solution processible materials
Outline
• Photovoltaic energy conversion
• Limiting efficiency of solar cells
• Nanostructures in photovoltaics
• Routes to more work per photon
• Nanomaterials to approach the efficiency limit
• Nanomaterials to reduce costs
Detailed balance limit
(i) One electron hole pair per photon with h > Eg,
(ii) Carriers relax to form separate Fermi distributions at lattice temperature Tambient with quasi Fermi levels separated by Δm.
(iii) All electrons extracted with same electrochemical potential Δm = eV
(iv) Only loss process is spontaneous emission
Band gap
Solar cell absorbs visible light, emits IR light
0 1 2 3 4
1017
1018
1019
1020
1021
1022
5760 K
300 K
pho
ton
flu
x
bb [
cm
-2s
-1eV
-1]
energy E [eV]
5760 K
x 2.16 10-5
AM1.5G
AM1.5G spectrum sun
Ambient spectrum ambient
Co
nve
ntio
na
l so
lar
ce
ll
Ωemit >> Ωabs
Ts, Dm
Ts, 0
Dm N
Tsun,0
Ts, 0
Xb
1 - Xb
N
Particle flux
Calculation of limiting efficiency
0 1 2 3 4
10-1
100
101
p
ho
ton
flu
x
[1
01
8cm
-2s
-1]
energy E [eV]
AM1.5G
Emission of sun and solar cell at open circuit
The same integrated photon flux goes from the sun to the solar cell as back.
Graph: courtesy Thomas Kirchartz
Practical and limiting efficiencies
current
Radiative recombination
In the ideal (detailed balance) case: Energy is lost through transmission, relaxation and radiative recombination Limiting efficiency depends only on the band gap (and the concentration factor of the light)
0.00
0.10
0.20
0.30
0.40
0.50 1.00 1.50 2.00 2.50
Eff
icie
ncy
Band Gap / eV
current
Practical and limiting efficiencies
Radiative recombination
Non-radiative recombination
In practice: Energy is lost through transmission, reflection, relaxation, radiative and non-radiative recombination
0.00
0.10
0.20
0.30
0.40
0.50 1.00 1.50 2.00 2.50
Eff
icie
ncy
Band Gap / eV
c-Si GaAs
perovskite
OPV
Practical and limiting efficiencies
In the ideal (detailed balance) case: Energy is lost through radiative recombination. Part of the loss is due to the difference in angular range of absorbed and emitted light. Restricting the angular range of emission brings efficiency closer to the maximal concentration limit
Efficiency: 24.8 %
Spire Corp, IEEE Tr. Electron Dev. 37, 469 (1990)
Efficiency: 28.8 %
Alta Devices, Prog. Photovoltaics 20, 606 (2012)
Optical confinement in a thin-film
structure
Absorbing substrate
Hav
erko
rt e
t al
, Ap
pl.
Ph
ys. R
ev. (
20
18
)
How bad are the assumptions?
(i) One electron hole pair per photon with h > Eg,
(ii) Carriers relax to form separate Fermi distributions at lattice temperature Tambient with quasi Fermi levels separated by Δm.
(iii) All electrons extracted with same electrochemical potential Δm = qV
(iv) Only loss process is spontaneous emission
Overestimate current by 10-20%
~ OK
Overestimate eVoc by O(0.1 eV)
Overestimate qVoc by several 0.1 eV Overestimate fill factor
Assumptions in the Shockley Queisser limit
20 Slide: courtesy Thomas Kirchartz
Outline
• Photovoltaic energy conversion
• Limiting efficiency of solar cells
• Nanostructures in photovoltaics
• Routes to more work per photon
• Nanomaterials to approach the efficiency limit
• Nanomaterials to reduce costs
Nanostructures in Photovoltaics
First International conference on “Nanostructures in Photovoltaics”
Max Planck institute for Complex Systems
Dresden, 2001
conjugated
polymer
1 nm
Photovoltaic “nano”-materials 10 n
m
quantum well
dye
conjugated molecule 1 n
m
5 nm
nanocrystal
2D transition metal
chalcogenide
Properties of nanomaterials for use in photovoltaics
1-10 nm
Energ
y
• Control of the electronic density of states
• Control of the phonon density of states
• Anisotropy in electronic and optical properties
• Access new spectral ranges
• Manipulate the optical response
How can nanomaterials help PV efficiency?
• Surpass the SQ efficiency limit (?)
• Approach the SQ efficiency limit with imperfect
materials
• Reduce the cost of reaching a given efficiency
Outline
• Photovoltaic energy conversion
• Limiting efficiency of solar cells
• Nanostructures in photovoltaics
• Routes to more work per photon
• Nanomaterials to approach the efficiency limit
• Nanomaterials to reduce costs
Routes to more work per photon
0
200
400
600
800
0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00
Photon Energy (eV)
Irra
dia
nc
e (
W m
-2 e
V-1
)
Optimum cell
converts 31% of power
Power spectrum from
black body sun at 5760K
Lost by thermalisation
Lost by
transmission
1. More band gaps
3. Slow carrier
cooling
2. Spectral
conversion
Band gap
L. H
irst
Pro
g. P
V (
20
11
)
Route 1. Higher efficiency via multiple band gaps
IR IR
red
red
blue blue
Single band gap Two band gaps
0
200
400
600
800
0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00
Photon Energy (eV)
Irra
dia
nc
e (
W m
-2 e
V-1
)
Black body sunOne band gapTwo band gapsThree band gaps
• Multi-junction structures or spectral splitting
III-V Multi-Junction Solar Cells
1 2 3
This works, but multijunction III-V structures are expensive to grow
4
= 46.5% at 300 Suns
Tib
bit
s et
al,
29
th E
U P
VSE
C (
20
14
)
• Limiting efficiency around 46% for a monolithic four-junction cell under concentration
Using nanostructures to achieve multiple band gaps
• Strained layer quantum well solar cell: effectively a single junction device
Peak efficiency: 28.3%
• Quantum well structures could be used to achieve target band gaps for monolithic multi-junctions on selected substrates
N. J
. Eki
ns-
Dau
kes,
et.
al.,
Ap
pl.
Ph
ys. L
ett.
, 75
, p 4
19
5, (
19
99
)
Route 2. Reshaping the spectrum by up and down-conversion
E~Eg
E~Eg
E>2Eg
0
200
400
600
800
0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00
Photon Energy (eV)
Irra
dia
nc
e (
W m
-2 e
V-1
)
Optimum cell
converts 31% of power
Power spectrum from
black body sun at 5760K
Lost by thermalisation
Lost by
transmission
Singlet fission (image: NREL)
Tim Schmidt, U. Sydney
Singlet fission as a downconversion strategy
• Singlet fission: high energy singlet excitons converted efficiently into triplet pairs in some molecular materials
– Separate triplets into e – h pairs OR
– Convert into IR luminescence by energy transfer to nanoparticles
• Goal of an optical coating on silicon
Ra
o a
nd
Fri
end
, Na
ture
Rev
iew
s M
ate
ria
ls (
20
17
);
Da
vis
et a
l. J.
Phy
s. C
hem
. Let
t. (
20
18
) 9
61
45
4-1
46
0
Reducing the photon entropy loss
• Approach the ‘ultimate’ efficiency by restricting the angular range of emission to match the range of absorption.
• May be possible by engineering the optical modes of semiconductor nanowires
Haverkort et al., Appl. Phys. Rev. 5, 031106 (2018)
Route 3: More work per photon by slowed cooling
generation equilibriation cooling recombination
3/2 kT h 3/2 kT
a
0
200
400
600
800
0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00
Photon Energy (eV)
Irra
dia
nc
e (
W m
-2 e
V-1
)
Optimum cell
converts 31% of power
Power spectrum from
black body sun at 5760K
Lost by thermalisation
Lost by
transmission
Reduced thermalisation in solar cells
• Eliminating thermalisation of charge carriers with environment could increase efficiency to 85% but not physically achievable
• Approaches that have been studied:
– Multiple exciton generation
– Slow cooling via “phonon bottleneck”
Hardman et al., PCCP 2011 DOI: 10.1039/c1cp22330e; Schaller Phys. Rev. Lett 92, pp.186601 (2004)
ELO
Gre
en
an
d B
rem
ner
Nat
. Mat
er 2
01
7
Outline
• Photovoltaic energy conversion
• Limiting efficiency of solar cells
• Nanostructures in photovoltaics
• Routes to more work per photon
• Nanomaterials to approach the efficiency limit
• Nanomaterials to reduce costs
Nanostructures to improve charge collection
B.Kayes et al. Journal of Applied Physics (2005) vol. 97 (11) pp. 114302
• Radial nanowire solar cells can outperform planar junctions only when diffusion length << absorption depth
• Helps to approach limiting efficiency in poor quality semiconductors
• Comparable to the use of ‘bulk heterojunctions’ in molecular photovoltaics
Nanostructures to reduce light reflection
Spinelli et al., Nat. Comm. 2012
• Array of low geometrical cross section nanowires results in low refractive index and weak refection
Ch
en
et a
l. A
pp
lied
Ph
ysic
s L
ett
ers
(2
00
9)
vo
l. 9
4 (
26
) p
p. 2
63
11
8
• Exploit forward Mie scattering into high index substrate to reduce reflection
Nanostructures to improve the radiative efficiency N
at. P
ho
ton
ics,
7, 3
06
–31
0 (
20
13
)
• Nanowires can show optical cross section > 10x geometrical
• If recombination is proportional to bulk volume can enhance generation relative to non-radiative recombination
Gre
en
an
d B
rem
ner
Nat
. Mat
er 2
01
7
Use of Plasmonics in Photovoltaics
Internal Scattering Field Enhancement Surface Plasmon
Polariton
Propagation
Use of Plasmonics in Photovoltaics
• Design of nanostructures for plasmonic enhancement depends strongly on accurate knowledge of the dielectric function of the metal used!
See poster by Phoebe Pearce at this meeting
P. P
ea
rce
et a
l., S
ola
r E
ne
rgy M
ate
ria
ls a
nd
So
lar
Ce
lls 1
91
(2
01
9)
13
3–140
Outline
• Photovoltaic energy conversion
• Limiting efficiency of solar cells
• Nanostructures in photovoltaics
• Routes to more work per photon
• Nanomaterials to approach the efficiency limit
• Nanomaterials to reduce costs
Printable photovoltaics
contacts active layer
Current and
voltage output
flexible substrate
barrier coatingLight
contacts active layer
Current and
voltage output
flexible substrate
barrier coatingLight
contacts active layer
Current and
voltage output
flexible substrate
barrier coatingLight
Perovskite 2012-
~ 22%
Other new materials and new processes ...
2001- Organic (polymer:C60)
~ 16%
1990- Dye sensitised
~ 13%
e-
e-
e- e
-
e-
TiO2
Particle slurry CZTS 2010-
~ 13%
2007- Organic tandem
~ 17%
UC
LA
Summary
• Photovoltaic energy conversion efficiency is limited to 33% in unconcentrated sunlight
• To approach this efficiency need to maximise radiative efficiency; to surpass it we need to reduce losses to light transmission and charge carrier thermalisation
• Nanostructures have capability to modify the electronic and optical density of states
• Several approaches proposed to achieving more work per photon
– Upconversion, downconversion, multiple gaps, slowed cooling
– Only multi-junctions are currently practically useful
• Most effective uses of nanostructures to raise efficiency are in manipulating light absorption and emission to approach the theoretical limit