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Concentrating & Splitting Optics Toolkit
Owen D. Miller, Vidya Ganapati, Korok Chatterjee, Chi-Sing Ho &
Prof. Eli Yablonovitch
UC Berkeley Electrical Engineering & Computer Sciences Dept.
& Lawrence Berkeley Nat’l Lab.
Boulder, CO April 11, 2013
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-Summer: More hours of daylight.
Sun is higher in the sky
-Winter: Shorter days, increased
cloudiness, and sun is lower.
Need for seasonal, long term energy storage.
Time
Sunlig
ht Summer Sunlight Cycle: Longer Days
Sunlig
ht
Winter Sunlight Cycle: Shorter Days
Time
Therefore storable fuel,
not batteries
are needed.
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h
h
Solar Cell:
light trapping:
path length increased by 4n2=50
where n = refractive index
semi-
conductor
semiconductor
single pass only
h
h
h
Light Emitting Diode:
semi-
conductor
semiconductor
only 1/4n2 = 1/50 = 2%
of the light escapes.
all the light eventually escapes.
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3
2
c
8π
Density of
Optical Modes
per Unit Volume
in air
3
22
c
n8π
Density of
Optical Modes
per Unit Volume
in semiconductor
What is the ratio? …… n2
There is a factor 2 from double pass
and
There is a factor 2 from cos averaging
The net benefit is 4n2
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Light Trapping Requirement:
1. Either the high index material has to be textured,
or the photon recycling should be very efficient.
The Benefit:
a. 4n2 ~50 times thinner layer can be sufficient to absorb the
sunlight saving semiconductor cost.
b. In a thinner cell, there is less series resistance, and a
higher Fill Factor
c. The operating point voltage, (not just Voc), increases by
kT ln{4n2} ~ 0.1Volts.
Total Internal Reflection is completely compatible
with an Anti-Reflection Coating.
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What is the ideal voltage Voc to expect, i.e. the Quasi-Fermi
Level separation, chemical potential, or Free Energy?
In molecules and quantum dots:
qVoc=Free energy = kT ln
In semiconductors with mobile electrons & holes:
Free energy = EFc-EFv=2kT ln
darktheinpopulationstateexcited
lighttheinpopulationstateexcited
darktheindensityelectron
lighttheindensityelectron
darktheinpopulationstateexcited
lighttheinpopulationstateexcited
kT
EnergyFreeexp
Boltzmann Factor
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What is the voltage to expect, i.e. the Quasi-Fermi
Level separation, chemical potential, or Free Energy?
Shockley-Queisser Limit (1961):
qVoc = kT ln
But in quasi-equilibrium:
qVoc = kT ln
darktheinemissionbandtoband
sunlightincoming
darktheinemissionbandtoband
emissionnt Luminesceexternal
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qV =
Eg – kT{ln(/s) + ln(4n2) + ln(qVop/kT) –ln()-ln( )}
operating
point
Photon Free Energy = h - TS
Photon Free Energy = h - kT lnW
Yes photons have entropy, S
where s is the solid angle subtended by the sun
Entropy due
to loss of
directivity
information
Entropy
due to
incomplete
light
trapping
Free energy
loss due to
power-point
optimization
-0.28eV -0.1eV -0.1eV 0.0-0.3eV
Free energy
loss due to
poor
Quantum
Efficiency
nicest treatment:
R.T.Ross "Some Thermodynamics of PhotoChemical Systems", J. Chem. Phys. 46, 44590 (1967)
s
g
kT
E
s
T
T41
e.
+0.02eV
correction
for Planck
emission-
bandwidth
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Year
Eff
icie
ncy
(%
)
1990 1995 2000 2005 2010 24
25
26
27
28
29
30
1-sun, single junction,
solar cell efficiency record:
Alta Devices record, 28.8%
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Latest 1 sun
single-junction
results from
Alta Devices, Inc.
Expected to reach
34% dual junction,
eventually.
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Open
Cir
cuit
vo
ltag
e V
OC (
Vo
lts)
0.95
1.00
1.05
1.10
1.15
Year 1990 1995 2000 2005 2010
Open Circuit voltage for
record efficiency cells:
Alta Devices record cell, 1.122 volts
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What if the material is not ideal, and the electrons and
holes are lost to heat before they can luminesce?
qVoc = qVoc-ideal – kT|ln{ext}|
The external
fluorescence yield ext is what matters!
Only external
Luminescence can balance
the incoming radiation.
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e-
h+
h h h
25.1% efficiency
1990-2007
h h h hg
hg
e-
h+
28.8% efficiency
2011-2012
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For solar cells at 25%,
good electron-hole transport is already a given.
Further improvements of efficiency above 25% are
all about the photon management!
A good solar cell has to be a good LED!
Counter-intuitively, the solar cell performs best when
there is
maximum external fluorescence yield ext.
Miller et al, IEEE J. Photovoltaics, vol. 2, pp. 303-311 (2012)
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Paradox: Why is external luminescence is good for
solar cell efficiency?
Reason #5; Luminescence IS Voltage:
External luminescence is sometimes used as a type of
contactless voltmeter, indicating the separation of
quasi-Fermi levels in the solar material.
Luminescence =
(This is sometimes employed as a contactless, quality-
control-metric, in solar cell manufacturing plants. )
This viewpoint is tautological:
Good external luminescence actually is good voltage,
and therefore good efficiency.
}{BB kT/qVexpnnp 2
i
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Diffuse Light has lots of entropy:
S=k ln(/s) 12k
It cannot be focused in a concentrator
A Flat plate cell exploits diffuse light.
Direct rays from the sun have little entropy,
and are easy to focus
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Thin-Film flexible
GaAs solar cell
as a parabolic
reflector.
All photons
below h =1.4eV
are focused
for solar thermal
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GaAs Courtesy of
Alta Devices,
Inc.
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Simple
parabolic
reflector.
Electricity
+
process heat
+
save money
on smaller solar cell
but heat is traded for solar electricity
high temperature solar cell
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The Problem with Concentrators:
Percentage
Direct
SunLight:
Phoenix 76%
Los Angeles 65%
Houston 62%
New York 59%
(1-axis tracking)
Partly compensated by Voltage Boost:
(kT/q)ln{Concentration Ratio}
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Approaches to Ultrahigh Efficiency Solar Energy Conversion Webinar March 7, 2013
The Next Step: Split the Solar Spectrum for efficiencies >30%
Splitting:
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p-Al0.2Ga0.8As
n-GaAs Eg=1.4eV
n-Al0.5In0.5P
n+-Al0.5In0.5P Eg~2.35eV
p+-Al0.5In0.5P Eg~2.35eV
p-Ga0.5In0.5P Eg~1.9eV
n-Al0.5In0.5P Eg~2.35eV
n-Ga0.5In0.5P Eg~1.9eV
Tunnel
Contact
GaAs
VOC=1.1V
Solar Cell p-GaAs Eg=1.4eV
Ga0.5In0.5P
VOC=1.5V
Solar Cell
Tunnel
Contact
GaAs
VOC=1.1V
Solar Cell
Ga0.5In0.5P
VOC=1.5V
Solar Cell
>30%, dual Junction Series-Connected Tandem Solar Cell
h h
All Lattice-Matched ~34% efficiency should be possible.
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Latest 1 sun
dual-junction
results from
Alta Devices, Inc.
Expected to reach
34% dual junction,
eventually.
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Approaches to Ultrahigh Efficiency Solar Energy Conversion Webinar March 7, 2013
The Next Step: How to Split the Solar Spectrum for efficiencies >30%
Serial Splitting: The Tandem
25
p-Al0.2Ga0.8As
n-GaAs Eg=1.4eV
n-Al0.5In0.5P
n+-Al0.5In0.5P Eg~2.35eV
p+-Al0.5In0.5P Eg~2.35eV
p-Ga0.5In0.5P Eg~1.9eV
n-Al0.5In0.5P Eg~2.35eV
n-Ga0.5In0.5P Eg~1.9eV
hh
Lateral Splitting:
~3mm
solar cell stripes
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p-Al0.2Ga0.8As
n-GaAs Eg=1.4eV
n-Al0.5In0.5P
n+-Al0.5In0.5P Eg~2.35eV
p+-Al0.5In0.5P Eg~2.35eV
p-Ga0.5In0.5P Eg~1.9eV
n-Al0.5In0.5P Eg~2.35eV
n-Ga0.5In0.5P Eg~1.9eV
Tunnel
Contact
GaAs
VOC=1.1V
Solar Cell p-GaAs Eg=1.4eV
Ga0.5In0.5P
VOC=1.5V
Solar Cell
Tunnel
Contact
GaAs
VOC=1.1V
Solar Cell
Ga0.5In0.5P
VOC=1.5V
Solar Cell
The Voltage Boost due to
Luminescence Trapping only
occurs in the lower cell h h
All Lattice-Matched ~34% efficiency should be possible.
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Challenge: Achieve maximum transmission
for incident sunlight, and maximum total
internal reflection for luminescence
• An air-gap provides 98% total-internal-reflection of luminescence, based on angular selectivity rather than spectral selectivity.
• The anti-reflection coating provides 99% transmission of band-edge radiation.
InGaP
GaAs
Air, aerogel,.. n2=1
anti-reflection coating n3=1.9 150nm
150nm anti-reflection coating n3=1.9
98%
99%
h
h
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Lateral Splitting requires mild concentration
Glass index, n=1.5, provides sufficient focusing.
holographically patterned surface
~3mm
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24th European Photovoltaic Solar Energy Conference, 21-25 September 2009
B. Groß, G. Peharz, G. Siefer, M. Peters, J.C. Goldschmidt, M. Steiner, W. Guter, V.
Klinger, B. George, and F. Dimroth, Fraunhofer Institute for Solar Energy Systems
directivity entropy problem:
These solar cells
see only part
of the sky.
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Slice of Initial Surface
Calculate New Geometry “Shape Derivative”
Adjoint Conjugate Gradient Method 2 Electromagnetic FDTD Simulations
Shape Calculus for Inverse Design
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Image Courtesy of Luminescent Technologies, Inc.
SRAM 90nm Wafer
the mathematical solution is rather non-intuitive!
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holographic pattern
Figure-of-Merit
Spectral splitting
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Pearl Gas to Liquids (GTL) Plant from Shell – Largest GTL Plant in the world
Oryx GTL Plant from Sasol
Gases to Liquid
Fuels
Fischer-Tropsch;
Runs 24 hours a day
is already economic.
Qatar
Qatar
actual
reaction 8CO+17H2 C8H18+ 8H2O syngas
But
Electrolyzer
runs only
6 hours/day.
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Summary 1. Use mathematical “Inverse Design”--
One-time design of the spectral-splitting holographic pattern.—
Reproduce the hologram by stamping, indefinitely.
2. 30%-50% efficiency solar cell efficiency, at low cost, will
eventually be the norm.
3. Seasonal as well Nightly storage will be needed.
4. For seasonal storage, high-value fuels will be needed.
The petrochemical industry is poised for the conversion of solar
electricity to fuel.