of 6
Experimental demonstration of enhanced photon
recycling in angle-restricted GaAs solar cells
Emily D. Kosten,
a
Brendan M. Kayes
b
and Harry A. Atwater
*
a
For cells near the radiative limit, optically limiting the angles of emitted
light causes emitted photons to be recycled back to the cell, leading to
enhancement in voltage and e
ffi
ciency. While this has been under-
stood theoretically for some time, only recently have GaAs cells
reached su
ffi
cient quality for the e
ff
ect to be experimentally observed.
Here, as proof of concept, we demonstrate enhanced photon recy-
cling and open-circuit voltage (
V
oc
) experimentally using a narrow
band dielectric multilayer angle restrictor on a high quality GaAs cell.
With angle restriction we observe a clear decrease in the radiative dark
current, which is consistent with the observed
V
oc
increase. Further-
more, we observe larger
V
oc
enhancements for cells that are closer to
the radiative limit, and that more closely coupling the angle restrictor
to the cell leads to greater
V
oc
gains, emphasizing the optical nature of
the e
ff
ect.
1 Introduction
For ideal solar cells where all recombination is radiative,
photons emitted from the cell are the sole source of carrier loss,
as in the well-known Shockley
Queisser or detailed balance
limit.
1
Cells approaching this radiative limit have signi
cantly
higher e
ffi
ciencies, as evidenced by recent world record GaAs
cells, and can also exhibit new e
ff
ects owing to the signi
cant
number of radiatively emitted photons.
2
4
For example, optically
limiting the angles of emitted light, as in Fig. 1a, causes emitted
photons to be recycled back to the cell, leading to enhancement
in voltage and e
ffi
ciency. Despite this theoretical prediction,
until recently even the highest e
ffi
ciency solar cells were not
close enough to the radiative limit for such an e
ff
ect to be
observed.
5
7
However, with the introduction of cells li
ed o
ff
the
growth substrate, GaAs cells have shown signi
cant gains in
e
ffi
ciency due to
V
oc
increases, indicating an increase in the
external radiative e
ffi
ciency (ERE) of the cell.
2
4
In these li
ed-
o
ff
GaAs cells radiatively emitted photons are re
ected from a
metallized back surface instead of being absorbed in the
substrate, resulting in a large increase in ERE and
V
oc
.
4,8
As
radiative recombination is dominant in high quality GaAs,
these li
ed-o
ff
cells perform near the radiative limit and are
therefore suitable for experimentally demonstrating enhanced
photon recycling and
V
oc
via
angle restriction of emitted light.
In fact, it was recently demonstrated that a voltage increase
could be observed in such cells by placing a re
ecting dome
above the cell to recycle emitted photons.
9
Here, as proof of concept, we demonstrate enhanced photon
recycling and open-circuit voltage (
V
oc
) experimentally using an
optical element with angle restriction only over the narrow
wavelength range of emitted light in GaAs placed on a high
quality GaAs cell. As in Fig. 1, we design a dielectric multilayer
angle restrictor with excellent normal incidence transmission
and high re
ectivity at oblique angles for radiatively emitted
wavelengths. Using this narrow band angle restrictor with a
high quality GaAs cell, we observe enhanced photon recycling
a
Thomas J. Watson Laboratory of Applied Physics, California Institute of Technology,
1200 E. California Blvd., Pasadena, CA 91125, USA. E-mail: haa@caltech.edu
b
Alta Devices, Sunnyvale, CA, USA
Electronic supplementary information (ESI) available. See DOI:
10.1039/c3ee43584a
Cite this:
Energy Environ. Sci.
,2014,
7
,
1907
Received 31st October 2013
Accepted 15th April 2014
DOI: 10.1039/c3ee43584a
www.rsc.org/ees
Broader context
Traditionally, solar cell research focused on absorbing light and collecting
the resulting carriers. In fact, only recently have III
V solar cells, partic-
ularly GaAs, achieved su
ffi
cient radiative e
ffi
ciency for the light emitted
from a solar cell to be a signi
cant factor in the cell performance. As cells
approach the radiative limit, where emitted light is the sole source of loss,
managing the emitted light becomes a promising route to increasing
e
ffi
ciencies beyond the 33% detailed balance limit. Using an optic to
restrict the light emission angles causes emitted photons to be recycled
back to the cell and could allow for substantial e
ffi
ciency and voltage
increases. In fact, limiting the angles of emitted light becomes a viable
at-plate alternative to concentration for cells near the radiative limit. As a
proof of concept for this approach, we use a dielectric multilayer to the
restrict emission angles on a high quality GaAs cell and demonstrate a
clear voltage increase due to enhanced recycling of emitted photons. We
also illustrate that the voltage increase is larger for cells closer to the
radiative limit, indicating that greater bene
ts to angle restriction are
possible as solar cells continue to more closely approach this limit.
This journal is © The Royal Society of Chemistry 2014
Energy Environ. Sci.
,2014,
7
,1907
1912 |
1907
Energy &
Environmental
Science
COMMUNICATION
Published on 15 April 2014. Downloaded by California Institute of Technology on 09/06/2014 15:38:28.
View Article Online
View Journal
| View Issue
and a resulting voltage increase. In other words, simply placing
an angle restrictor on the cell causes a voltage increase of 3.6
mV without a change in current. In addition, we observe a 12%
decrease in the radiative component of the dark current, which
is consistent with the observed
V
oc
increase. Considering a
variety of cells, the largest
V
oc
enhancements occur in cells that
are closest to the radiative limit, with maximum ERE values of
15.7%. Finally, we see that more closely coupling the angle
restrictor to the cell leads to greater
V
oc
gains, emphasizing the
optical nature of the enhancement.
The predicted voltage increase from angle restriction follows
directly from the principles of detailed balance.
1
For a solar cell
in the radiative limit at steady state and open circuit, detailed
balance requires that the number of photons leaving the cell
equal the number of photons entering the cell. Mathematically,
we express this as
ð
N
E
g
S
ð
E
Þ
a
ð
E
Þ
d
E
¼
ð
U
c
ð
N
E
g
a
ð
E
Þ
2
h
3
c
2
E
2
e
ð
E

qV
oc
Þ
=
kT

1
d
E
cos
ð
q
Þ
d
U
where
a
(
E
) is the fraction of photons at energy
E
absorbed by the
solar cell,
U
c
is the solid angle the cell emits into,
S
(
E
) is the
solar spectrum, and
qV
oc
equals the chemical potential of the
cell.
5
The le
-hand side of the equation gives the photon
ux
absorbed by the cell, and the right-hand side gives the emitted
photon
ux at open circuit.
Assuming the
V
oc
does not closely approach the bandgap, we
may approximate the
V
oc
under illumination as
V
oc
z
kT
ln
ð
N
E
g
S
ð
E
Þ
a
ð
E
Þ
d
E
ð
U
c
ð
N
E
g
a
ð
E
Þ
2
h
3
c
2
E
2
e
ð
E

qV
oc
Þ
=
kT

1
d
E
cos
ð
q
Þ
d
U
0
B
B
B
@
1
C
C
C
A
¼
kT
ln
ð
J
sc
=
J
0
Þ
(1)
where
J
sc
is the short-circuit current and
J
0
is the dark current,
which is solely due to radiatively emitted light in the detailed
balance limit. Restricting the emission angle causes photons
generated by radiative recombination to be recycled and reab-
sorbed within the cell rather than emitted. Thus, enhanced photon
recycling
via
angle restriction reduces
J
0
and increases
V
oc
.
For realistic cells, emitted light forms a larger fraction of
J
0
in
cells closer to the radiative limit. Thus, high ERE cells, like the
GaAs cells in these experiments, are required for
J
0
to be
reduced su
ffi
ciently with angle restriction that a voltage
increase may be observed. Furthermore, higher ERE cells
should show larger voltage increases. For this reason, though
the voltage increases in this proof-of-concept experiment are
modest, further improvements in GaAs cell technology could
signi
cantly increase the performance bene
ts from angle
restriction. In fact, for an Auger-limited GaAs cell, angle
restriction is predicted to give cell e
ffi
ciencies above 38%.
6
Fig. 1
Narrowband dielectric angle restrictor design and fabrication.
(a) Experimental set-up: a high quality GaAs cell is placed in optical
contact with either a dielectric angle restrictor deposited on fused
silica (left) or a bare fused silica control (right) using fused silica index
matching
fl
uid at the GaAs-fused silica interface. The emission angles
for each optic are shown schematically in yellow. For the experiments
in Fig. 2 and 3, the edges of the optics are coated with a gold re
fl
ector
to minimize light loss. (b) The refractive index at 800 nm as a function
of depth for the dielectric angle restrictor multilayer design. (0
represents the air interface). (c) Calculated re
fl
ectivity for the dielectric
angle restrictor design as a function of angle and wavelength. Angles
are denoted in air, as we are only concerned with light that is not totally
internally re
fl
ected. Spectrum of photoluminescence available for
photon recycling (white line) indicates the wavelengths where angle
restriction is desired. (d) Measured re
fl
ectivity for the dielectric angle
restrictor as deposited with spectrum of photoluminescence available
for photon recycling (white line). Re
fl
ections at the back surface of the
substrate have been subtracted, see ESI.
Angles are again denoted in
air. For both (c) and (d), we plot only wavelengths greater than 600 nm,
to correspond with the wavelengths of illumination in the experiment.
1908
|
Energy Environ. Sci.
,2014,
7
,1907
1912
This journal is © The Royal Society of Chemistry 2014
Energy & Environmental Science
Communication
Published on 15 April 2014. Downloaded by California Institute of Technology on 09/06/2014 15:38:28.
View Article Online
For terrestrial applications, we envision a
at plate, one sun,
angle restricting system with high quality GaAs cells. While
tracking may be bene
cial, high accuracy tracking is not
required as dielectric angle restrictors have a relatively large
acceptance angle. Furthermore, for cells in the ERE range
considered here, narrow angle restriction has limited bene
t, as
non-radiative recombination limits the possible voltage
increase. (The ESI
includes a calculation with the angle
dependence of
J
sc
.) Recent work has demonstrated the fabrica-
tion of high ERE cells in other III
V materials, notably GaInP,
suggesting that this approach will become more broadly
applicable with continued cell development, and could easily be
incorporated with multijunctions.
10
Use with these cell tech-
nologies also suggests early applications in military and space
solar, where e
ffi
ciency and weight are paramount.
While our previous work has considered broadband ray
optical angle restrictors with light trapping cells, the cells in this
experiment have high re
ectivity specular back re
ectors that
are metallic, with re
ectivity of 75.5%, or metallodielectric, with
re
ectivity of 99.7%. The calculated re
ectivity values refer to
band edge (873 nm) emission angle-averaged within the GaAs.
As the solar cells are planar and do not incorporate light trap-
ping, we utilize a dielectric multilayer that provides angle
restriction only over the narrow range of wavelengths at the
semiconductor band edge where the GaAs cells emit light
(see Fig. 1). This narrowband angle restriction allows di
ff
use,
non-normal incidence light to enter over most of the spectral
range (see ESI
). Capturing this di
ff
use light gives signi
cant
current enhancements relative to a broadband concentrator or
angle restrictor. In addition, potential losses due to tracking
errors are greatly reduced, and simpler, cheaper trackers may be
utilized. As in the ESI,
we envision depositing such an angle
restrictor in place of an anti-re
ective coating, so the cost
derives only from the added layers relative to a conventional AR
coat.
As shown in Fig. 1b, the angle restrictor design consists of
alternating high and low index layers with large refractive index
contrast to increase the angular range of re
ection.
11
13
While
the design is not strictly periodic, the angular properties can be
understood from the Bragg condition
cos
q
¼
m
l
2
G
where
q
is the angle of maximum re
ectivity,
l
is the wave-
length,
G
is the period of the multilayer, and
m
is an integer.
14
For shorter wavelengths maximum re
ectivity occurs away from
normal incidence, providing angle restriction for emitted light
and excellent transmission at normal incidence in both the
designed and fabricated structures. We note that total internal
re
ection owing to the high index of GaAs already provides
signi
cant photon recycling within the cell, and despite this,
there is still a substantial loss due to emitted light, as ERE
estimates indicate.
4
As the measured re
ectivity in air, see
Fig. 1d, demonstrates, the dielectric structure provides photon
recycling of light that would otherwise be emitted. This
enhanced photon recycling occurs in addition to the photon
recycling
via
total internal re
ection, which is una
ff
ected by the
dielectric structure.
2 Results and discussion
Theory clearly indicates that enhanced photon recycling
via
angle restriction will result in a reduction of the radiative dark
current. We therefore measured the dark current characteristics
of a single cell under both the angle restrictor and a bare fused
silica control optic, as in Fig. 1a, with fused silica index
matching
uid at the interface of the cell and the fused silica
substrate to avoid extraneous re
ections. In the high voltage
region near
V
oc
, where radiative emission contributes most
signi
cantly to the dark current, we see a clear decrease in dark
current with angle restriction, as in Fig. 2a. To quantify this we
t the dark current,
J
0
, over the high voltage 0.6 to 1.1 V region,
to the double diode equation
J
0
¼
J
01
e
q
½
V

J
dark
R
s

kT

1

þ
J
02
e
q
½
V

J
dark
R
s

nkT

1

Fig. 2
Dark current measurements and
fi
ts. (a) Representative dark
current curves and double diode
fi
ts for both the angle restrictor and
control cases. Inset: a clear reduction in dark current is evident near
V
oc
for the angle restrictor case. (b) Double diode
fi
tted parameter
results with each bar representing one of three trials on the same 15.7%
ERE cell for both the angle restrictor and fused silica control. The error
bars represent 95% con
fi
dence intervals derived from the
fi
t. Consis-
tent with reduced radiative loss,
J
01
shows a marked decrease with
angle restriction while all other parameters remain unchanged.
This journal is © The Royal Society of Chemistry 2014
Energy Environ. Sci.
,2014,
7
,1907
1912 |
1909
Communication
Energy & Environmental Science
Published on 15 April 2014. Downloaded by California Institute of Technology on 09/06/2014 15:38:28.
View Article Online
where
J
01
is the high voltage dark current component,
J
02
is the
low voltage component,
R
s
is the series resistance, and
n
is the
diode ideality factor.
15,16
For both the control and angle
restriction curves, the
t is excellent over several orders of
magnitude. The
t deviates somewhat at very low currents,
which we attribute to shunt resistance and has been previously
observed in similar cells.
2
As Fig. 2b shows,
J
02
,
R
s
and
n
are
unchanged with angle restriction and
n
is very close to two,
indicating that the double diode model is valid.
15,16
In contrast,
the
J
01
term, which has the same voltage dependence as radia-
tive recombination, shows a 12% decrease with angle restric-
tion, well beyond the error of the
t. Thus, by simply changing
the optic above the cell to an angle restrictor, we observe a
de
nite reduction in the dark current. Speci
cally, the reduc-
tion occurs in the high voltage dark current component attrib-
utable to radiative loss, indicating that angle restriction is
enhancing photon recycling within the cell.
In addition to a reduction in dark current, we also expect a
direct
V
oc
enhancement under illumination. Furthermore, this
voltage enhancement should be larger for cells with higher ERE,
as more photons are available to be recycled
via
angle restric-
tion. We therefore measured light current
voltage curves for a
set of four cells with di
ff
ering back re
ector and material quality
leading to signi
cant variations in ERE across the cells, as
determined from the
J
sc
and
V
oc
characteristics under the
control optic (see ESI
for further model details). Owing to a
re
ecting band in the optical coupler around 550 nm, we
limited the spectrum in this proof-of-concept experiment to
wavelengths longer than 605 nm. (As in the ESI,
this re
ecting
band can be eliminated with a rugate
lter optical design, but
for the initial coupler we did not pursue these structures as they
are more di
ffi
cult to fabricate.
17,18
) As shown in Fig. 3a, when we
directly compare the control and angle restrictor on the same
cell, current losses of 3.5 to 5.3% are observed with angle
restriction, consistent with the measured normal incidence
re
ectivity of the angle restrictor. Without a change in the dark
current, a reduction in
J
sc
would normally produce a corre-
sponding reduction in
V
oc
, as in eqn (1). However,
V
oc
increases
of up to 2.5 mV are observed under angle restriction for the
highest ERE cells, as dark current reduction is the dominant
e
ff
ect. Thus, angle restriction increases cell voltage without any
change in the illumination, and despite a reduction in
J
sc
.
Furthermore, as we expect for photon recycling, the voltage
change tracks the cell ERE.
Fortunately, these current losses are not intrinsic, and result
from the simplicity of our initial angle restrictor design
17,18
(see ESI
). To isolate the photon recycling e
ff
ect, we adjust the
solar simulator to equalize the currents between the control and
angle restrictor, as in Fig. 3b. Once
J
sc
values are matched for
the angle restrictor and control, voltage increases ranging from
1.2 mV to 3.6 mV are seen for all cells, with higher ERE cells
showing larger voltage increases. As the 15.7% ERE cell was also
used for dark current measurements, we can compare the
change in
J
01
to the observed change in
V
oc
. Since
V
oc
¼
kT
ln(
J
sc
/
J
0
) and the
J
01
term is dominant near
V
oc
, the change in
V
oc
should be approximately
kT
ln(
J
01
/
J
01
0
), where
J
01
0
indicates
the average
tted value with the angle restrictor. Using this
approach, we predict from the dark current
ts that the
V
oc
increase should be 3.0 mV, which is reasonably consistent with
the measured value of 3.6 mV for this cell. Thus, we observe a
clear
V
oc
increase with angle restriction that is consistent with
our dark current measurements, and an ERE trend that indi-
cates enhanced photon recycling as the mechanism.
We also develop a model that directly relates the voltage
increase to the optical characteristics of the angle restrictor.
While detailed balance is traditionally considered an idealized
Fig. 3
Voltage increase as a function of radiative e
ffi
ciency. Measured
changes in open-circuit voltage (dark blue line) and short-circuit
current (green line) with angle restriction. The set of four cells is
plotted as a function of external radiative e
ffi
ciency (ERE) determined
from
J
sc
and
V
oc
under the control optic. Variations in ERE occur
between cells owing to di
ff
erences in back re
fl
ectors and material
quality. The error bars are calculated from standard deviation of
fi
ve
measured trials. The dotted white line indicates the expected voltage
increase based on a modi
fi
ed detailed balance calculation. The light
blue area shows the expected range of the model based on uncer-
tainty in
J
sc
,
V
oc
, and temperature. (a) No solar simulator adjustment.
Cells with high external radiative e
ffi
ciency show a voltage increase
despite a reduction in current. (b) The solar simulator was adjusted so
that currents were equalized with the angle restrictor and control. With
this current equalization, all cells see a voltage increase, with high ERE
cells seeing a larger voltage increase.
1910
|
Energy Environ. Sci.
,2014,
7
,1907
1912
This journal is © The Royal Society of Chemistry 2014
Energy & Environmental Science
Communication
Published on 15 April 2014. Downloaded by California Institute of Technology on 09/06/2014 15:38:28.
View Article Online
model, we have developed a more realistic detailed balance
model that includes the cell thickness, anti-re
ective coating,
back re
ectors, and Auger and surface recombination (further
details are provided in the ESI
). To account for the optical
environment, we calculate the angle-averaged emissivity for
both the control and the angle restrictor based on measured
re
ectivity data as in Fig. 1d. For each cell, we use the values for
J
sc
and
V
oc
measured under the control optic to determine the
cell's ERE (see ESI
). We then predict the
V
oc
under angle
restriction based on the previously determined ERE and
measured
J
sc
. Finally, the observed temperature
uctuations of
0.1

C and uncertainty estimates for
J
sc
and
V
oc
are used to
determine the range of the prediction, as in Fig. 3. These
calculations agree quite well with the experimental results,
indicating that the reduction in emissivity with angle restriction
and the resulting photon recycling enhancement fully explain
the observed di
ff
erences in
V
oc
.
Lastly, we perform a series of experiments where we gradu-
ally increase the photon recycling and
V
oc
by coupling the angle
restrictor more closely to the cell. As shown in Fig. 4, we begin
by placing a large, uncoated fused silica cylinder above the cell
which allows light to escape unimpeded from both the sides
and the top of the cylinder. In essence, this fused silica spacer
facilitates the outcoupling of light emitted from the solar cell to
free space, similar to the glass sphere o
en used with light-
emitting diodes. As before, index matching
uid is used at the
fused silica
GaAs cell interface. Then, the angle restrictor is
placed on a series of fused silica spacers with non-re
ecting,
uncoated sides that allow light to escape, with index matching
uid between the spacer and the angle restrictor substrate. As
the height of the spacer is reduced, less light escapes through
the transparent sides of the spacers and more light is recycled
back to the cell by the dielectric angle restrictor. Finally, we use
an angle restrictor with re
ecting sides to prevent light escape
from the sides of the fused silica substrate and maximize the
photon recycling. As Fig. 4 illustrates, more closely coupling the
angle restrictor to the solar cell increases the observed
V
oc
,
demonstrating that more e
ff
ective angle restriction leads to
enhanced photon recycling and
V
oc
. We also
nd close agree-
ment between the experiment and realistic detailed balance
calculations, indicating that the coupling of the angle restrictor
explains the observed changes in
V
oc
.
3 Conclusion
We have performed a series of experiments that clearly
demonstrate enhanced photon recycling and resulting
V
oc
increases of up to 3.6 mV
via
angle restriction with a narrow-
band dielectric multilayer angle restrictor. Dark current
measurements show a 12% decrease in the radiative compo-
nent of the dark current consistent with the observed voltage
enhancement. In addition, measurements of the voltage
increase on several cells illustrate that cells closer to the radi-
ative limit show larger voltage enhancements, as we expect for
photon recycling. These measurements also show good agree-
ment with calculations based on the measured re
ectivity of the
angle restrictor. Finally, we have shown that more closely
coupling the angle restrictor to the cell leads to predictable
increases in voltage for several con
gurations, emphasizing
that this voltage increase is due to a purely optical photon
recycling e
ff
ect.
Thus, we have demonstrated as a proof of concept that angle
restriction with a narrowband dielectric multilayer leads to
enhanced photon recycling and a corresponding voltage
increase in high quality GaAs cells. The narrowband angle
restrictor approach has signi
cant advantages in admitting
di
ff
use light and in the relatively simple design that can replace
an existing anti-re
ective coating. While the voltage enhance-
ments shown here are relatively small, the e
ff
ect becomes much
larger as ERE increases and cells approach the radiative limit.
High ERE cells are already being developed for III
V materials
to achieve the highest possible voltage and e
ffi
ciency, and these
cells are ideal candidates for a broader applicability of the angle
restriction approach.
10
As further improvements are made in
III
V cell technology and other materials reach the high ERE
regime, this approach holds promise for signi
cantly
increasing cell e
ffi
ciencies in a
at plate geometry.
Fig. 4
Voltage increase as a function angle restrictor coupling.
Measured open-circuit voltage (dark blue line) and short-circuit
current (green line) as angle restriction is increased by coupling the
angle restrictor more closely to the 15.7% ERE cell. The
x
-axis labels
indicate the height of the fused silica spacer below the dielectric angle
restrictor, or bare fused silica control, as on the far left. For all but the
rightmost optical con
fi
guration, the sides of the fused silica spacers are
uncoated to so emitted light may escape. Thus, a taller spacer allows
more light to escape from the sides, reducing photon recycling to the 1
cm
2
cell. In the rightmost con
fi
guration, the sides of the fused silica
substrate are coated with a re
fl
ector to avoid side loss and maximize
photon recycling by the dielectric angle restrictor. The error bars are
calculated from standard deviation of
fi
ve measured trials. The dotted
white line indicates the expected
V
oc
based on a modi
fi
ed detailed
balance calculation. The light blue area shows the expected range of
the model based on uncertainty in
J
sc
,
V
oc
, and temperature. The solar
simulator was adjusted as necessary to equalize the currents across
the various optical con
fi
gurations.
This journal is © The Royal Society of Chemistry 2014
Energy Environ. Sci.
,2014,
7
,1907
1912 |
1911
Communication
Energy & Environmental Science
Published on 15 April 2014. Downloaded by California Institute of Technology on 09/06/2014 15:38:28.
View Article Online
Acknowledgements
Thanks to M. Sheldon, E. Warmann, J. Bosco, and C. Eisler for
useful discussions and comments and to J. Lloyd for assistance
with
gure preparation. This work was supported by the the
Light-Material Interactions in Energy Conversion
Energy
Frontier Research Center funded by the U.S. Department of
Energy, O
ffi
ce of Science, O
ffi
ce of Basic Energy Sciences under
Award Number DE-SC0001293. E.K. is also the recipient of a
Resnick Sustainability Institute Graduate Fellowship.
References
1 W. Shockley and H. J. Queisser, Detailed balance limit of
e
ffi
ciency of p-n junction solar cells,
J. Appl. Phys.
, 1961,
32
(3), 510
519.
2 B. M. Kayes, H. Nie, R. Twist, S. G. Spruytte, F. Reinhardt,
I. C. Kizilyalli and G. S. Higashi, 27.6% conversion
e
ffi
ciency, a new record for single-junction solar cells
under 1 sun illumination, Proceedings of 37th IEEE
Photovoltaic Specialists Conference, 2011, pp. 4
8.
3 M. A. Steiner, J. F. Geisz, I. Garc
́
ı
a, D. J. Freidman, A. Duda
and S. R. Kurtz, Optical enhancement of the open-circuit
voltage in high quality GaAs solar cells,
J. Appl. Phys.
, 2013,
113
, 123109.
4 M. A. Green, Radiative e
ffi
ciency of state-of-the-art
photovoltaic cells,
Prog. Photovoltaics
, 2012,
20
(4), 472
476.
5 A. Mart
́
ı
, J. L. Balenzategui and R. F. Reyna, Photon recycling
and Shockely's diode equation,
J. Appl. Phys.
, 1997,
82
(8),
4067
4075.
6 E. D. Kosten, J. H. Atwater, J. Parsons, A. Polman and
H. A. Atwater, Highly e
ffi
cient GaAs solar cells by limiting
light emission angle,
Light: Sci. Appl.
, 2013,
2
, e45.
7 J. N. Munday, The e
ff
ect of photonic bandgap materials on
the shockley-queisser limit,
J. Appl. Phys.
, 2012,
112
(6),
064501.
8 O. D. Miller, E. Yablonovitch and S. R. Kurtz, Strong internal
and external luminescence as solar cells approach the
Shockley
Queisser limit,
IEEE Journal of Photovoltaics
, 2012,
2
, 303
311.
9 A. Braun, E. A. Katz, D. Feuermann, B. M. Kayes and
J. M. Gordon, Photovoltaic performance enhancement by
external recycling of photon emission,
Energy Environ. Sci.
,
2013,
6
, 1499
1503.
10 J. F. Geisz, M. A. Steiner, I. Garc
́
ı
a, S. R. Kurtz and
D. J. Freidman, Enhanced external radiative e
ffi
ciency for
20.8% e
ffi
cient single-junction GaInP solar cells,
Appl.
Phys. Lett.
, 2013,
103
(4), 041118.
11 M. Deopura, C. K. Ullal, B. Temelkuran and Y. Fink,
Dielectric omnidirectional visible re
ector,
Opt. Lett.
, 2001,
26
(15), 1197
1199.
12 Y. Fink, S. Winn, J. N. ad Fan, C. Chen, J. Michel,
J. D. Joannopoulos and E. L. Thomas, A dielectric
omnidirectional re
ector,
Science
, 1998,
282
, 1679
1682.
13 E. Yablonovitch, Engineered omnidirectional external-
re
ectivity spectra from one-dimensional layered
interference
lters,
Opt. Lett.
, 1998,
23
(21), 1648
1649.
14 B. E. A. Saleh and M. C. Teich,
Fundamentals of Photonics
,
Wiley, 2nd edn, 2007.
15 S. P. Tobin, S. M. Vernon, C. Bajgar, S. J. Wojtczuk,
M. R. Melloch, A. Keshavarzi, T. B. Stellwag,
S. Venkatensan, M. S. Lundstrom and K. A. Emery,
Assessment of MOCVD- and MBE-grown GaAs for high-
e
ffi
ciency solar cell applications,
IEEE Trans. Electron
Devices
, 1990,
37
(2), 469
477.
16 M. T. Sheldon, C. N. Eisler and H. A. Atwater, GaAs
passivation with trioctylphosphine sul
de for enhanced
solar cell e
ffi
ciency and durability,
Adv. Energy Mater.
,
2012,
2
(3), 339
344.
17 S. Fahr, C. Ulbrich, T. Kirchartz, U. Rau, C. Rockstuhl and
F. Lederer, Rugate
lter for light-trapping in solar cells,
Opt. Express
, 2008,
16
(13), 9332
9343.
18 C. Ulbrich, S. Fahr, J. Upping, M. Peters, T. Kirchartz,
C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer and
U. Rau, Directional selectivity and ultra-light-trapping in
solar cells,
Phys. Status Solidi A
, 2008,
205
(12), 2831
2843.
1912
|
Energy Environ. Sci.
,2014,
7
,1907
1912
This journal is © The Royal Society of Chemistry 2014
Energy & Environmental Science
Communication
Published on 15 April 2014. Downloaded by California Institute of Technology on 09/06/2014 15:38:28.
View Article Online