Abstract for 25th European Photovoltaic Solar Energy Conference, Valencia, Spain, Sep. 6-10, 2010
Subject number: 1.1 Fundamental Studies
Full title:
Fundamental Efficiency Losses in Next-Generation Multijunction Solar Cells
*Author for correspondence: Richard R. King Spectrolab, Inc., 12500 Gladstone Ave., Sylmar, CA 91342 USA
Tel: Int'l -818-838-7404 Fax: Int'l-818-838-7474
Richard R. King*
[email protected]
William Hong
[email protected]
Dhananjay Bhusari
[email protected]
Christopher M. Fetzer
[email protected]
Andreea Boca
[email protected]
Daniel C. Law
[email protected]
Diane Larrabee
[email protected]
Nasser H. Karam
[email protected]
Xing-Quan Liu
[email protected]
Spectrolab, Inc., 12500 Gladstone Ave., Sylmar, CA 91342 USA Tel: Int'l-818-365-4611 Fax: 818-838-7474
Fundamental Efficiency Losses in Next-Generation Multijunction Solar Cells
R. R. King, D. Bhusari, A. Boca, D. Larrabee, X.-Q. Liu, W. Hong, C. M. Fetzer, D. C. Law, and N. H. Karam
Multijunction III-V photovoltaic cells for terrestrial concentrator systems are the highest efficiency solar cell technology
yet demonstrated, with conversion efficiencies over 40% since 2006. These high efficiencies are extremely leveraging for
reducing the cost of solar electricity, since they reduce all area-related costs of a photovoltaic system – balance-of-system
costs like encapsulation, support structures, concentrating optics and trackers, as well as the area and costs of the cells
themselves – needed for a given power output.
As high as III-V multijunction efficiencies are presently, practical cell efficiencies of 50% and higher are possible with
new solar cell architectures having theoretical efficiencies of 70% and above. The increase in efficiency from 40% to 50% is
an extremely important range, corresponding to a tipping point at which concentrator PV becomes the most economic solar
electricity option, and is competitive with conventional electricity generation in many geographic areas even without
government subsidies. In this paper, we quantify the controlling efficiency losses in next-generation multijunction cell
designs, using both theoretical and experimental input, to evaluate the real potential of transformative cell architectures
capable of 50% efficiency and above.
Fundamental physical principles dictate some of the directions necessary for reaching higher efficiencies than today's
state-of-the-art cells. Incorporation of four and even more junctions is important to reduce the carrier thermalization losses
that occur as electrons and holes relax back to their respective band edges, as illustrated in Fig. A1. Cells with 4 and more
junctions have the added, highly significant benefit of lowering current density and I2R series resistance power losses,
especially important for concentrator cells. High quality subcells in the 2.0-eV and 1.0-eV band gap ranges are needed to
avoid excessive carrier thermalization losses, while low band gap subcells in the 0.7-eV range are needed to capture as much
energy as possible from the broad solar spectrum. Higher optical concentrations are favored as they narrow the gaps between
the quasi-Fermi levels and their respective band edges, bringing the cell voltage closer to that defined by the band gap.
Solar cells with four or more junctions are not without technical challenges, which work against their theoretical
efficiency advantages. Additional tunnel junctions to connect the added subcells in series makes parasitic light absorption in
the tunnel junctions a greater concern. The finer division of the solar spectrum in a cell with more than 3 junctions can cause
greater susceptibility to a single subcell limiting the current of the overall stack, as the solar spectrum changes over the
course of the day and year due to atmospheric attenuation. This paper will quantify these non-ideal effects in high-efficiency
next-generation multijunction cells, together with their fundamental efficiency advantages, in order to determine the net
benefit in efficiency and energy production in terrestrial concentrator systems.
These advances in understanding are beginning to have an impact on experimental solar cell efficiencies. Upright
metamorphic 3-junction GaInP/GaInAs/Ge concentrator cells, of the type that were first to reach over the 40% efficiency
milestone, are now being inserted into production as the C4MJ cell. Pilot production runs of the C4MJ terrestrial
concentrator cell have demonstrated average efficiency of 39.4%, nearly an absolute efficiency point higher than the previous
cell generation, and are expected to reach 40% average efficiency in production. Inverted metamorphic terrestrial
concentrator cells with a more advantageous band gap combination have been built and tested, and the latest measurement
results will be presented in the paper. Lattice-matched GaInP/GaInAs/Ge cells built at Spectrolab have demonstrated an
independently confirmed efficiency of 41.6% under the standard terrestrial spectrum at 364 suns (36.4 W/cm2) concentration
as shown in Fig. A2, the highest efficiency yet demonstrated for any type of solar cell. These next generations of
multijunction concentrator cells, capable of 45% or even 50% efficiency, have the potential to transform the economics of
solar electricity generation.
2.
350
1200
300
1000
250
800
200
600
150
400
100
200
50
0
200
400
600
800
1000
1200
1400
1600
2
Wavelength (W/(cm μ m))
Power Per Unit Area, Per Unit
1400
400
Cumulative Losses (W/cm )
AM1.5D solar spectrum, ASTM G173-03, norm. to 1000 W/m2
Available after thermalization loss
Thermalization loss
Cumulative thermalization loss – 3-junction
Cumulative thermalization loss – 4-junction
1600
0
1800
Wavelength (nm)
Figure A1. Thermalization losses in an advanced 4-junction
solar cell, showing lower cumulative thermalization loss for this
4-junction case than for 3-junction cells. Fundamental losses and
non-ideal losses are quantified in the paper, to illuminate the
realistic potential of next-generation solar cells.
Figure A2. Light I-V characteristic for the record 41.6%efficiency concentrator solar cell, the highest efficiency yet
reached by any type of solar cell. This 41.6% cell was built
at Spectrolab with a lattice-matched 3-junction cell
structure, and has been independently verified at NREL.
Fundamental Efficiency Losses in Next-Generation Multijunction Solar Cells
R. R. King, D. Bhusari, A. Boca, D. Larrabee, X.-Q. Liu, W. Hong, C. M. Fetzer, D. C. Law, and N. H. Karam
Spectrolab, Inc., 12500 Gladstone Ave., Sylmar, CA 91342 USA
INTRODUCTION
AM1.5D solar spectrum, ASTM G173-03, norm. to 1000 W/m2
Available after thermalization loss
Thermalization loss
Cumulative thermalization loss – 3-junction
Cumulative thermalization loss – 4-junction
2.
1000
250
800
200
600
150
400
100
200
50
400
600
800
1000
1200
1400
2
Wavelength (W/(cm μ m))
Power Per Unit Area, Per Unit
300
0
1800
1600
Wavelength (nm)
Fig. 1. Thermalization losses in an advanced 4-junction
solar cell, and power available in the direct, terrestrial
solar spectrum after thermalization losses as a function of
wavelength. This 4-junction cell exhibits much lower
cumulative loss from carrier thermalization to the band
edges than in a typical 3-junction GaInP/GaInAs/Ge cell.
These and other fundamental aspects of new highefficiency cell designs will be treated in the paper, such
as the band gap-voltage offset (Eg/q) –Voc in the ideal
detailed balance model and empirical models [1,5,6],
series resistance and grid shadowing, and absorption
from non-current-producing layers in the cell and impact
on quantum efficiency, as for the experimental 4-junction
cell quantum efficiency plotted in Fig. 2.
MULTIJUNCTION CELL MODELING
Fundamental physical principles dictate some of the
directions necessary for reaching higher efficiencies than
in today's cells. Incorporation of four and even more
junctions is important to reduce carrier thermalization
losses as electrons and holes that are excited far into their
respective bands by high energy photons relax back to
the band edges. Cells with 4 and more junctions have the
added, highly significant benefit of lowering current
density and I2R series resistance power losses, especially
important for concentrator cells. Efficient subcells with
2.0-eV band gaps and higher are needed to avoid
thermalization loss in the top subcell. High quality
subcells with band gaps in the 1.0-eV range must be
incorporated in low cost multijunction designs, to avoid
high thermalization loss in the Ge bottom cell of today's
3-junction cells, while subcells with low band gaps in the
0.7-eV range must continue to be used in order to capture
as much energy as possible from the broad solar
spectrum. Finally, higher optical concentrations are
favored as they narrow the distance between the quasiFermi levels of each carrier type and their respective
band edges, allowing the cell voltage to come closer to
that defined by the band gap.
Figure 1 plots the AM1.5 Direct ASTM G173-03
terrestrial solar spectrum, and the thermalization losses
convoluted with the solar spectrum for a 4-junction
concentrator solar cell with a 1.88/ 1.40/ 1.00/ 0.70 eV
band gap combination, graphically showing the severity
of this fundamental loss as a function of wavelength, with
respect to the subcell band edges, and the intensity
available in different parts of the solar spectrum. The
cumulative thermalization losses are plotted for the 4junction design, and compared to a standard 3-junction
GaInP/GaInAs/Ge cell, showing the substantially lower
theoretical thermalization losses for the 4-junction cell.
350
1200
0
200
1600
100
External Quantum Efficiency (%)
2
1400
400
Cumulative Losses (W/cm )
1600
Multijunction III-V photovoltaic cells for terrestrial
concentrator systems are the highest efficiency solar cell
technology yet demonstrated, with conversion
efficiencies over 40% since 2006 [1-4]. These high
efficiencies are extremely leveraging for reducing the
cost of solar electricity, since they reduce all area-related
costs of a photovoltaic system – balance-of-system costs
like encapsulation, support structures, concentrating
optics and trackers, as well as the area and costs of the
cells themselves – needed for a given power output.
As high as III-V multijunction efficiencies are
presently, practical cell efficiencies of 50% and higher
are possible with new solar cell architectures having
theoretical efficiencies of 70% and above. The increase
in efficiency from 40% to 50% is an extremely important
range, corresponding to a tipping point at which
concentrator PV becomes the most economic solar
electricity option, and is competitive with conventional
electricity generation in many geographic areas even
without government subsidies. In this paper, we quantify
the controlling efficiency losses in today's state-of-the-art
cells, using both theoretical and experimental input, to
evaluate the real potential of transformative cell
architectures capable of 50% efficiency and above.
90
1400
80
1200
70
AlGaInP subcell 1
1.95 eV
GaInAs subcell 3
1.39 eV
All subcells
60
50
AlGaInAs subcell 2
1.66 eV
Ge subcell 4
0.72 eV
AM1.5D
ASTM G173-03
40
1000
800
600
30
400
20
200
10
0
300
500
700
900
1100
1300
Wavelength (nm)
1500
1700
0
1900
Fig. 2. Measured external quantum efficiency for the
individual subcells of a 4-junction terrestrial concentrator
AlGaInP/ AlGaInAs/ GaInAs/ Ge lattice-matched solar
cell. The intensity per unit wavelength of the standard
AM1.5D, ASTM G173-03 spectrum is plotted, to show
available power in the response ranges of each subcell.
Solar cells with four or more junctions are not
without technical challenges, which work against their
theoretical efficiency advantages. Additional tunnel
junctions to connect the added subcells in series makes
parasitic light absorption in the tunnel junctions a greater
concern. The finer division of the solar spectrum in cells
with 4 or more junctions makes it more likely for a single
subcell to limit the current of the entire multijunction cell
stack, as the spectrum changes over the course of the day
and year due to atmospheric attenuation, as illustrated in
Fig. 3.
Intensity Per Unit Wavelength
(W/(m2μ m))
1
2000
1
1500
0.75
1000
0.5
500
0.25
0
250
500
750
1000
1250
1500
1750
2000
1 - Transmittance (unitless)
Intensity Per Unit Wavelength
2
. (W/(m μ m))
3
AM0, ASTM G173-03
1.25
AM1.5D, ASTM G173-03
1 - transmittance for air mass 1.5
1 - transmittance for air mass 2.5
2500
EXPERIMENTAL RESULTS
These advances in understanding are beginning to
have an impact on experimental solar cell efficiencies.
Upright metamorphic 3-junction GaInP/GaInAs/Ge
concentrator cells, of the type that were first to reach over
the 40% efficiency milestone, are now being inserted into
production as the C4MJ cell. A schematic cross section
of this type of metamorphic cell is shown on the right
side of Fig. 5, compared to a lattice-matched 3-junction
cell on the left.
contact
contact
AR
AR
n+-Ga(In)As
n-AlInP window
n-GaInP emitter
0
2250
p
To
p-GaInP base
GaInP top cell
Wavelength (nm)
p-AlGaInP BSF
p++-TJ
n++-TJ
Wide-bandgap tunnel junction
W
n-GaInP window
n-Ga(In)As emitter
Fig. 3. Attenuation of light intensity due to the
atmosphere, for air mass 1.5 and 2.5 [7].
p-Ga(In)As base
Ga(In)As middle cell
0.5
g
el
nn
Tu
p-AlGaInP BSF
e
dl
p++-TJ
n++-TJ
ll
Ce
n
tio
nc
Ju
Bo
m
tto
30%
n++-TJ
nucleation
0.4
6J opt. for 3 PM, eff. norm. to expt.
5J opt. for 3 PM, eff. norm. to expt.
0.1
0.2
4J opt. for 3 PM, eff. norm. to expt.
tto
Bo
n+-Ge emitter
p-Ge base
and substrate
p-Ge base
and substrate
contact
contact
l
el
C
m
Ce
ll
ηavg = 38.5%
C1MJ Production
ηavg =
C3MJ Production
C4MJ Preliminary Data
ηavg = 37.7%
39.4%
ηavg = 36.9%
20%
% of Cells
0.2
Intensity Available in Spectrum .
[(kWhr/m2)/hr]
15%
10%
5%
3J opt. for 3 PM, eff. norm. to expt.
Intensity available in spectrum
Fig. 4. Energy production of multijunction cells with 3
to 6 junctions, with cell efficiency normalized to
correspond to experimental values.
The energy
production increases with each additional junction, for
the cases shown, due to reduced series resistance and
thermalization losses [7].
This paper will expand on these studies to quantify
crucial non-ideal effects in high-efficiency nextgeneration multijunction cells, such as current imbalance
due to spectrum variation and elevated temperature under
operating conditions, together with their fundamental
efficiency advantages, in order to determine the net
benefit in efficiency and energy production in terrestrial
concentrator systems.
Efficiency at 50 W/cm2 (%)
Fig. 6. Efficiency histograms of four generations of
Spectrolab terrestrial concentrator cell products, from the
C1MJ cell with 36.9% average production efficiency,
C2MJ with 37.7%, C3MJ with 38.5%, and preliminary
data for the next generation C4MJ cell, with 39.4%
efficiency in early pilot runs. Average efficiency for the
C4MJ cell is anticipated to reach 40%.
Lattice-matched GaInP/GaInAs/Ge cells built at
Spectrolab have demonstrated an independently
confirmed efficiency of 41.6% under the standard
terrestrial spectrum at 364 suns (36.4 W/cm2)
concentration, the highest efficiency yet demonstrated for
any type of solar cell [6].
The illuminated I-V
characteristic of this record cell, as verified by the
41.5%
41.0%
40.5%
40.0%
39.5%
39.0%
38.5%
0%
38.0%
20
37.5%
18
37.0%
16
36.5%
10
12
14
Time of Day (hour)
36.0%
8
35.5%
6
35.0%
0.0
4
34.5%
0
34.0%
Energy Per Unit Area Produced .
Per Hour [(kWhr/m2)/hr]
0.6
e
dl
id
As shown in Fig. 6, pilot production runs of the C4MJ
terrestrial concentrator cell have demonstrated average
efficiency of 39.4%, nearly an absolute efficiency point
higher than the previous C3MJ cell generation, and are
expected to reach 40% average efficiency in production.
Inverted metamorphic terrestrial concentrator cells with a
more advantageous band gap combination have been
built and tested, and the latest measurement results will
be presented in the paper.
25%
0.3
el
nn
Tu
n
tio
nc
Ju
el
nn
Tu
p++-TJ
ll
Ce
C2MJ Production
0.8
l
Lattice-Mismatched
Lattice-Matched (LM)
or Metamorphic (MM)
Fig. 5. Schematics of the layer structures of latticematched and upright metamorphic 3-junction solar cells.
1.0
0.4
M
p-GaInAs
step-graded
buffer
nucleation
n+-Ge emitter
Eg
eid
l
Ce
p-GaInP BSF
n++ -TJ
Ge bottom cell
W
n-GaInP window
n-GaInAs emitter
n-Ga(In)As buffer
Buffer region
p
To
p-GaInP base
p-GaInAs base
p++ -TJ
Tunnel junction
id
M
el
nn
Tu
p-GaInP BSF
Energy production from photovoltaic power plants
has been gaining increasing attention from researchers
for all types of solar modules, since it is the kilowatthours of electricity produced that has the most direct
impact on the cost effectiveness of a solar electricity
installation.
It is a particularly salient topic for
multijunction cells, since a shift in spectrum affecting the
current of one subcell not only reduces the output of that
subcell, but can limit the current of all the other subcells
as well, even though they may have ample
photogeneration. As shown in Fig. 4, preliminary
modeling indicates that this effect may indeed cause a
crossover in 3-junction and 4-junction efficiencies for
very high air masses, i.e., in the very early morning or
very late afternoon when there is limited solar insolation
available anyway, but that the higher efficiency of the
modeled 4-, 5-, and 6-junction cells over the majority of
hours in the day outweighs this effect, giving a
significantly higher energy production over the day for
the cell designs with more than 3 junctions [7].
E
eid
n+-GaInAs
n-AlInP window
n-GaInP emitter
ll
Ce
independent test lab at the National Renewable Energy
Laboratory (NREL) is plotted in Fig. 7, with measured
Voc = 3.192 V, Jsc/intensity = 0.1468 A/W, FF = 0.8874 ,
and efficiency = 41.6 % at 364 suns.
In Fig. 9, the illuminated I-V curve of a prototype 4junction terrestrial concentrator cell is plotted, showing
its high-voltage, low-current characteristics which lead to
lower resistive power loss compared with 3-junction cells
[6]. These early prototype 4-junction concentrator cells
have reached up to 36.9% efficiency at 500 suns (50
W/cm2) at Spectrolab in unconfirmed measurements.
The independently confirmed light I-V curves of the
earlier record 40.7%-efficient metamorphic 3-junction
cell [1], the present record 41.6%-efficient latticematched 3-junction cell at 364 suns [6], and the same cell
measured to have 40.1% efficiency at 822 suns, are also
plotted for comparison.
Current Density / Inc. Intensity (A/W) .
0.16
Fig. 7. Light I-V characteristic for record efficiency
41.6%-efficiency concentrator solar cell, built at
Spectrolab with a lattice-matched 3-junction cell
structure, and independently verified at NREL [6].
Efficiency
V oc
Jsc /inten.
V mp
FF
conc.
area
0.06
0.04
2.911
0.1596
2.589
0.875
240
0.267
LM, 822 suns
3.192 V
0.1467 A/W
2.851 V
0.887
364
suns
0.317 cm2
Eff. 40.7%
41.6%
AM1.5D,
low -AOD spectrum
0.02
3J Conc.
Cell
Lattice-matched
3.251
0.1467
2.781
0.841
822
0.317
4J Cell
4.398 V
0.0980 A/W
3.950 V
0.856
500 suns
0.208 cm2
40.1%
AM1.5D,
ASTM G173-03
4J Conc.
Cell
36.9%
AM1.5D,
ASTM G173-03
AM1.5D,
ASTM G173-03
Prelim. meas.
25°C
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Voltage (V)
Fig. 9. Light I-V measurements for a 4-junction
terrestrial concentrator cell with Voc of 4.398 V, and
preliminary efficiency of 36.9% at 500 suns. An earlier
record 40.7% MM 3J cell [1], the present record 41.6%
LM 3J cell at 364 suns, and a cell with 40.1% measured
efficiency at 822 suns, are plotted for comparison [6].
4
SUMMARY
By analyzing the fundamental efficiency losses in
multijunction cells, this paper aims to form a bridge
between today's state-of-the-art solar cells and future
designs. Identifying the loss mechanisms that are
fundamental and dictated by laws of physics, and those
that are not fundamental and can therefore be reduced,
allows one to make informed decisions on research
directions, leading to advanced cell architectures that
maximize efficiency and energy production. The next
generations of multijunction concentrator cells, capable
of 45% or even 50% efficiency, have the ability to
transform the economics of solar electricity generation.
REFERENCES
0.94
38
0.92
36
0.90
34
0.88
32
0.86
30
0.84
28
0.82
26
0.80
24
1.0
10.0
0.78
1000.0
100.0
2
Incident Intensity (suns) (1 sun = 0.100 W/cm )
Fig. 8. Measured light I-V parameters of the 41.6%efficient solar cell as a function of incident intensity.
The cell is still over 40% efficient at 820 suns, and has
39.8% efficiency at 940 suns [6].
Fill Factor (unitless)
Efficiency (%) and Voc x 10 (V)
3J Conc.
Cell
Metamorphic
0
0.96
FF
0.1
3J Conc.
Cell
0.08
Independently confirmed meas.
25°C
Voc fit, 100 to 1000 suns
.
40
0.10
0.98
41.6%
Voc x 10
42
0.12
0.00
The dependence of the performance of this record
41.6%-efficient cell on varying incident intensity is
shown in Fig. 8. The efficiency, Voc, and FF of this
record cell are plotted at concentrations from 0.9 to 940
suns. The efficiency peaks at 41.6% at 364 suns and
drops for higher concentrations due to series resistance,
but is still over 40% at 820 suns, and is 39.8% at 940
suns. The fill factor shows a broad plateau over ~2
decades in incident intensity, rising rapidly between 1
and ~4 suns due to increasing excess carrier
concentration, and decreasing above ~400 suns due to
series resistance. The Voc increases at an average rate of
~80 mV per decade in incident intensity, per junction, in
the intensity range from 1 to 10 suns. From 10 to 100
suns this rate is 75 mV per decade, while from 100 to
1000 suns it drops to 61 mV per decade. Thus over the
100 to 1000 sun range of interest, the average Voc
increase with concentration is fit fairly well by using
diode ideality factor n = 1 for each of the 3 subcells.
44
0.14
[1] R. R. King et al., Appl. Phys. Lett., 90, 183516, 4 May
2007.
[2] J. F. Geisz et al., Appl. Phys. Lett., 93, 123505 (2008).
[3] Fraunhofer ISE Press Release, Jan. 14, 2009.
[4] F. Dimroth et al., Proc. 34th IEEE Photovoltaic Specialists
Conf. (2009), Philadelphia, Pennsylvania, USA.
[5] R. R. King et al., "Pathways to 40%-Efficient Concentrator
Photovoltaics," Proc. 20th European Photovoltaic Solar
Energy Conf. (2005), Barcelona, Spain, pp. 118-123.
[6] R. R. King et al., "Band-Gap-Engineered Architectures for
High-Efficiency Multijunction Concentrator Solar Cells," 24th
European Photovoltaic Solar Energy Conf. (2009), Hamburg,
Germany.
[7] R. R. King et al., "New Horizons in III-V Multijunction
Terrestrial Concentrator Cell Research," Proc. 21st European
Photovoltaic Solar Energy Conf. (2006), Dresden, Germany,
pp. 124-128.