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Techno-economic analysis of tandem photovoltaic
systems
I. M. Peters,*S. Sofia, J. Mailoa and T. Buonassisi*
Tandem solar cells offer the potential of conversion efficiencies exceeding those of single-junction solar
cells, but also incur higher fabrication costs. The question arises under which conditions a tandem solar
cell becomes economically preferable to both of the single-junction sub-cells it comprises. We present
an analysis based on cost and efficiency relations to answer this question for a double-junction tandem
solar cell. We find that combining two ideally band-gap-matched single-junction solar cell technologies
into a tandem should be a “marriage of equals”: the sub cells should be produced at similar $ per W
costs, both sub cells should have similar efficiencies when operated independently, and the costs to turn
both cells into a system should be similar. We discuss examples of different hypothetical and actual
tandem solar cell technologies and show the intricacies of imbalances in the mentioned factors. We find
that tandem-solar-cell-based PV power stations for existing solar-cell technologies offer the potential to
reduce the levelized cost of electricity (LCOE), provided suitable top cells are developed.
1. Introduction
“Efficiency”is the technical variable that most strongly inu-
ences the cost of electricity provided by solar cell modules and
systems.
1
With established technologies like Si
2–4
and GaAs
4–6
approaching their practical efficiency limits, non-concentrating
tandem solar cell
7–10
technology has gained renewed interest.
Tandem solar cells offer a path to increase efficiencies beyond
the Shockley–Queisser limit
11
by stacking multiple junctions
made from different absorber materials, thus reducing ther-
malization losses.
12
Tandem technology is appealing because it
can leverage well-established technologies with AM1.5 effi-
ciencies >20%. Resulting tandem efficiencies exceed single-
junction efficiencies by several percent absolute. Highest effi-
ciencies were achieved with III–V materials;
13–15
recently reach-
ing 29.8% with GaInP on Si.
16
Pathways to practical efficiencies
exceeding 33% (ref. 17) exist. Notable are also results for hybrid
organic lead halide perovskites
18,19
on silicon tandem solar
cells
20
that offer a potential path to low-cost manufacturing and
have recently exceeded 20% efficiency.
21
Other thin-lm tech-
nologies like CdTe
22,23
and CIGS
24
also offer low-cost and high
efficiency potential.
A tandem solar cell is economically viable if and only if the
cost of the electric power provided by the tandem is lower than
that of either the top or bottom single-junction cell operating
independently. At rst glance, tandems require only a “small”
additional areal cost associated with a few thin-lm layers to
achieve the aforementioned efficiency gain. However, tandems
have hitherto failed to gain market traction, because the bene-
ts of efficiency improvements to date have not exceeded the
cost of the additional fabrication steps, balance of systems, and
power electronics.
In this work, we conduct a techno-economic analysis with
parametric cost relations, to identify the circumstances under
which tandems are economically preferable to single-junction
constituent devices. Cost modelling is a valuable method to
determine innovation pathways to achieve cost reductions for
PV electricity.
1,25–31
We use a bottom up cost-model and the
minimum sustainable price (MSP) methodology to calculate $
per W, as formulated by Doug Powell and Alan Goodrich
1
for
silicon and by Sin Cheng Siah
32
for CdTe. To calculate levelized
cost of electricity (LCOE), we use the System Advisor Model
(SAM) from the National Renewable Energy Laboratory.
33
Once baseline models are established, we explore a wider
techno-economic parameter space by developing parametric
cost relations, thus identifying under which circumstances it is
economically benecial to combine two single-junction solar
cell technologies at AM1.5 conditions into a tandem. Our
simplied parametric cost relation requires only two inputs: the
ratio of solar cell to system related costs, and the efficiency of
the three solar cells (one tandem and two single-junction
devices). Denition of the cost relations is formulated, and an
efficiency calculation for tandem solar cells is described in the
“Methodology”section. The cost breakdown for PV modules
and PV installations is discussed in the section entitled
“Breakdown of system costs”. We then describe the impact of
different technical and economic parameters on the cost-
effectiveness of tandems and show the negative effects of
imbalances for these parameters. We nd that tandems make
Massachusetts Institute of Technology, Cambridge, MA 02139, USA. E-mail:
impeters@mit.edu; buonassisi@mit.edu
Cite this: RSC Adv.,2016,6, 66911
Received 22nd March 2016
Accepted 7th July 2016
DOI: 10.1039/c6ra07553c
www.rsc.org/advances
This journal is © The Royal Society of Chemistry 2016 RSC Adv.,2016,6, 66911–66923 | 66911
RSC Advances
PAPER
economic sense only when three conditions are satised
simultaneously: (1) the band-gaps are well matched to enable
a high efficiency potential, (2) the areal manufacturing costs ($
per m
2
) of top and bottom single-junction devices are similar,
and (3) both sub-cells have a similar efficiency when operated
independently (marriage of equals). We conclude with
a recommendation for future research, including the need for
a wider range of low-cost ($ per m
2
), high-efficiency, low-capex,
and highly reliable absorbers with band-gaps in the 1.4–1.9 eV
range.
2. Methodology
The presented methodology aspires to relate the cost of energy
for a tandem solar cell with the cost of energy of the two single-
junction solar cells it comprises. For this purpose we estimate
(i) the cost of a tandem solar cell system from the cost of the two
comprising single-junction solar cell systems, and (ii) the effi-
ciency of a tandem solar cell from the efficiencies of the two
single-junction solar cells it is made of.
2.1 Relation of single-junction solar cell and tandem solar
cell system costs
First we need to dene the term “PV system”. In the context of
this analysis, the term PV system is used in a broad sense and
refers to any arrangement of components that may include solar
cells, a supporting structure, electronics to convert DC elec-
tricity into AC, and other system costs. We intentionally dene
the term “PV system”broadly, so it comprises both PV modules
and PV power stations, which serve as exemplary systems in our
analysis.
For any such system, it is possible to break down the system
costs C
sys
into one part that is associated with the cost of
making the solar cells C
cell
and one part associated with the cost
of making the supporting structure C
str
. Fig. 1 shows a sche-
matic sketch of this approach, with more detailed explanations
in Sections 3.1 and 3.3.
For a single-junction (sj) solar cell the break down is then
given by
C
sys,sj
¼C
cell
+C
str,sj
.(1)
In the following section, we discuss how these values are
determined for a PV module and a PV power station. For
a double junction (dj) tandem solar cell PV system, costs can be
split up in an analogous way
C
sys,tan
¼C
cell,top
+C
cell,bot
+C
str,tan
,(2)
where C
cell,top
(C
cell,bot
) is the cost to fabricate the top (bottom)
junction. In the following, we will abbreviate this term as C
top
(C
bot
). In general, the breakdown dened in (1) and (2) is
ambiguous as some elements could be counted as part of the
cell or part of the structure. In the present analysis, the break-
down will be made such that the cost for fabricating a junction
of a certain material is the same for the single-junction- and the
tandem solar-cell fabrication processes. In this way, the break-
down becomes unique and the generality of the presented
results is not affected. Differences between the single-junction
and the tandem fabrication process are now summarized in
the costs of the supporting structure C
str
. For example, if
a tunnel junction
34
is required, the additional cost of the tunnel
junction is embedded in C
str
.
Depending on the specics of the fabrication process, C
str,sj
could differ signicantly from C
str,tan
. This is particularly the
case for PV modules and for highly integrated tandem fabrica-
tion processes. For PV power stations, the differences will be
smaller, as many of the components will be required regardless
of the specics of the solar cell. In the following, we will assume
whichever structure cost of the two single-junction solar cells is
higher as an approximation for the structure cost of the tandem.
C
str,tan
zMax[C
str,top
,C
str,bot
]. (3)
This approximation can be turned into an equation by
introducing a factor DC,
C
str,tan
¼Max[C
str,top
,C
str,bot
]+DC.(4)
The factor DCsummarizes all differences between the single-
junction and the tandem fabrication process. We discuss these
differences and what values DCcan take later in this section.
Finally, we dene the relative cost-benet function as
RCsys;top;Csys;bot ¼
MinCsys;top
Ptop
;Csys;bot
Pbot Csys;tan
Ptan
MinCsys;top
Ptop
;Csys;bot
Pbot (5)
where C
sys,top
and C
sys,bot
are the costs of making PV systems
using only single-junction top or bottom cell respectively, P
top
and P
bot
are the powers generated by PV systems made from
single-junction top or bottom cell, and P
tan
is the power
generated by the tandem PV system. The function Ris unitless
and its entries are deliberately ambiguous, as the analysis
encompasses different types of PV systems. While Cis always in
unit of $, Pdepends on the type of system investigated. For a PV
module, Pis power in units of watts, whereas for a PV power
station, Prepresents work in units of kilowatt hours. Both
quantities are ultimately calculated from the efficiency of the
Fig. 1 Schematic sketch of the definition for a PV system used in this
study.
66912 |RSC Adv.,2016,6, 66911–66923 This journal is © The Royal Society of Chemistry 2016
RSC Advances Paper
corresponding solar cell, but the later involves assumptions that
ultimately lead to energy-yield calculations.
35
Ris positive if the cost per output is lower for a given tandem
PV system than for each of the single-junction PV systems it
comprises –hence, if the tandem PV system is economically
preferable. The value of Rstates how much the cost per output
of the tandem PV system is lower (in percent) than the cost per
output of the less expensive single-junction PV system. The term
“output”can refer to power or work, depending on the system
considered.
2.2 Relation of single-junction solar cell and tandem solar
cell efficiencies
In a second step, we need to relate the power or work generated
or done by the tandem solar cell PV system to that of the single-
junction solar cells it comprises. Work and power can both be
calculated from the solar cell power-conversion efficiency. As
arst-order approximation, we use solar-cell efficiencies as
proxies for power and work. Consequently, we need to relate the
efficiencies of the tandem solar cell h
tan
and the efficiencies of
the two single-junction solar cells h
top
and h
bot
. Note that when
mentioning a single-junction solar cell efficiency, we always
refer to the efficiency generated by this solar cell on its own and
under standard testing conditions.
The radiative efficiency limit of a single-junction solar cell
h
SQ
was determined by Shockley and Queisser.
11
In this limit,
the efficiency is completely determined by the band-gap E
g
of
the material used. The limiting efficiency of a double-junction
solar cell can be calculated by a modication of this
approach
7
and is completely determined by the band-gaps of
the two sub-cells, E
g,top
and E
g,bot
. The tandem solar cell is,
however, not uniquely dened by the two band-gaps. It also
dependsonhowthetwosub-cellsareintegrated.Mainly,
there are two possible congurations:atwo-andafour-
terminal conguration. In the four-terminal conguration,
both sub-cells are contacted independently. Efficiencies for
top and bottom cell are calculated separately and are added to
obtain the tandem efficiency. In the ideal case, all solar
photonswithenergiesuptohy<E
g,top
are utilized by the top
cell, which is identical to the top cell being operated as
a single-junction cell. The bottom cell efficiency is calculated
with an altered spectrum, containing all photons with ener-
gies E
g,top
<hy<E
g,bot
.
In the two-terminal conguration, the sub cells are mono-
lithically integrated and electrically separated by a tunnel
junction. The sub-cell with lower current generation limits the
current of the tandem device. If the bottom cell is limiting,
current generation in the top cell, j
top
can be reduced, within
limits, by thinning
36,37
or by area adjustment.
38
Thus
jtan ¼8
<
:
jtop if jtop \jbot
1
2jtop þjbotif jtop .jbot
;(6)
with j
tan
(j
bot
) the current generated by the tandem (bottom)
solar cell. The voltages generated by the two sub-cells are added
to obtain the tandem solar cell efficiency.
The efficiency of a non-ideal single-junction solar cell h
sj
can
be dened by two parameters: the band-gap of the material used
and the fraction f
SQ
of the radiative limit at which the solar cell
is operating. Thus,
h
sj
(E
g
,f
SQ
)¼h
SQ
(E
g
)f
SQ
.(7)
The efficiencies of two non-ideal single-junction solar cells
can then be linked to the efficiency of a tandem solar cell. The
tandem solar cell efficiency is given as a function of E
g,top
,
f
SQ,top
,E
g,bot
and f
SQ,bot
. The scaling factors f
SQ,top
(f
SQ,bot
)
provide no freedom of breaking down losses into parts corre-
sponding to current, voltage and ll factor. As different distri-
butions into these parts are possible, the tandem solar cell
efficiency is not uniquely given if the single-junction efficiencies
are known. Furthermore, the approach does not take into
account any additional losses that occur by tandem integration.
The used approach can, therefore, only serve as a rst-order
approximation. The approximation works the better, the
closer to the radiative limit the two single-junction cells operate.
For a more detailed analysis, a complete device simulation is
required.
The broad view presented in this analysis necessarily ignores
some aspects that will affect the comparison of single junction
and multi junction solar cells. This topic has been discussed in
the context of PV LCOE.
39
Examples for such factors are differ-
ences in the energy yields of single junction and multi-junction
solar cells
35
and degradation.
2.3 Cost regimes
An example of R(C
1
,C
2
) is plotted in Fig. 2; we will refer to this
type of plot as “cost-regime plot”. Parameters used in the plot
Fig. 2 Exemplary cost-regime plot. The tandem solar cell comprises
a top cell with a band-gap of E
g,top
¼1.74 eV, and a single-junction
efficiency of h
top
¼21.8% (f
SQ,top
¼76%). The bottom solar cell (E
g,bot
¼
1.124 eV) has a single-junction efficiency of h
bot
¼21.8% (f
SQ,bot
¼
64%). The calculated tandem efficiency is h
tan
¼32.7% in the four-
terminal configuration. The two-terminal efficiency would be h
tan
¼
32.3%. Structure costs for all three solar cells are equal (C
sys,top
¼
C
sys,bot
¼C
sys,tan
).
This journal is © The Royal Society of Chemistry 2016 RSC Adv.,2016,6, 66911–66923 | 66913
Paper RSC Advances
are stated in the gure caption. The used parameters do not
correspond to any fabricated solar cell system; they were chosen
because they represent an ideal example of a tandem solar cell
from a cost relation point of view. It will be discussed in the
following sections, in what sense this example can be consid-
ered ideal. Axes in the cost-regime plot are given as the ratio of
solar cell C
cell
to supporting structure C
str
cost. A ratio of one
signies equal cost shares and corresponds to 50% contribution
of each cost to the system cost C
sys
.
The plot in Fig. 2 marks three regimes, separated by the
black and white lines. In each regime either of the three solar
cell systems, using only the top cell (upper le), using only the
bottom (lower right) cell and using the tandem (lower le
corner) has the lowest cost per output. The lines mark the
conditions under which two of the three solar cell systems have
the same cost per output. The triple point marks the condition
for which all three solar cell systems are at the same cost per
output. In the depicted ideal case the triple point is located at (1,
1).
The white line additionally marks the gradient and the ridge
in relative cost-benet. Approaching the extension of the white
line within the tandem regime is, therefore, desirable. From
this we draw the rst conclusion about under which conditions
two solar cells should be combined into a tandem: both solar
cells, operated in a system independently, should be at a similar
cost per output level.
Another point of interest is the maximum relative cost
benet (MRCB). The MRCB is located numerically by analysing
the cost-relations plot. It will later be used to compare impacts
of different parameters on the nancial competitiveness of the
tandem PV system. In Fig. 2, the MRCB is located in the origin.
However, this is not generally the case.
3. Breakdown of system costs
As indicated earlier, the term “system”in this work is used in
a broad sense. The presented method for analysing cost regimes
is valid for any arrangement that includes solar cells and sup-
porting structural components. We will in the following discuss
two classes of systems of interest: PV modules and PV power
stations. These examples address the economic interest of
different trades: module manufacturers for which we will use
the MSP as a gure of merit, and PV installers or yieldcos for
which we will use the total system costs and LCOE as a gure of
merit. As these two system types include different components,
also the breakdown of system costs will be different. We will
show how such a break down can be made and indicate what
values for C
cell
/C
str
can be expected in each case. Note that the
presented analysis uses data for cases within the United States,
and numbers would have to be adapted for other locations.
3.1 PV modules
We analyse two PV module fabrication processes: mono-
crystalline silicon and CdTe, as an example for a thin-lm
technology. Bottom-up cost analyses for these processes are
presented in ref. 1 and 32. Table 1 shows a cost breakdown for
these fabrication processes in three categories: feedstock &
absorber, absorber to cell and cell to module. Each of those
categories can be further broken down into material, labour,
electricity, maintenance and capex related costs (not shown).
For CdTe we included two examples: one process for a module
with frame and one process for a frameless module. C
cell
includes feedstock & absorber and absorber to cell costs. C
str
includes all cell to module costs. As indicated earlier, we per-
formed the break down such that C
cell
would be similar in
a tandem fabrication process and all variations are subsumed
under C
str
. One example for which this issue this has an effect is
the glass substrate for the thin-lm solar cell. Usually, the glass
would be considered part of the absorber to cell process. Here,
we consider it as part of the cell to module process. This has two
reasons: (i) in a silicon PV module, glass is used as a cover and
we wanted the two processes to be as close as possible, and (ii)
in a tandem solar cell, one of the cells would be deposited on an
existing junction and not on glass. The results of our analysis
are summarized in Table 1. The rst column for each tech-
nology states the fabrication cost, the second column the MSP.
Using this cost breakdown, we can project the costs for
a hypothetical tandem fabrication by combining different
materials. In Table 2 we show the combination for a hypothet-
ical thin-lm on silicon tandem PV module, and a hypothetical
frameless thin-lm on thin-lm tandem PV module. Initially we
assume that all processes steps are similar to single junction,
i.e.,DC¼0. The table again states fabrication costs and MSP.
Table 1 Cost breakdown for different single-junction solar cell module technologies
CdTe single-junction,
frameless
CdTe single-junction, with
frame Silicon single junction
Cost
[$ per m
2
]
MSP
[$ per m
2
]
Cost
[$ per m
2
]
MSP
[$ per m
2
]
Cost
[$ per m
2
]
MSP
[$ per m
2
]
Feedstock & absorber C
cell
17.98 30.77 17.98 30.77 42.08 56.16
Absorber to cell C
cell
17.76 26.22 17.76 26.22 27.12 39.64
Cell to module C
str
21.43 25.29 25.39 29.93 33.81 42.94
Total 57.16 82.27 61.13 86.92 103.01 138.74
C
cell
/C
str
1.67 2.25 1.41 1.90 2.04 2.23
66914 |RSC Adv.,2016,6, 66911–66923 This journal is © The Royal Society of Chemistry 2016
RSC Advances Paper
3.2 Discussion of DC
In the breakdown shown in Table 2, single-junction and tandem
solar cell PV module fabrication processes use the exact same
process steps. While feedstock and absorber costs should
remain largely unaffected, differences can be anticipated in the
absorber to cell process in actual fabrication. These differences
will depend on the tandem solar cell architecture. In the
following we will give a brief discussion on DCfor a two-
terminal and a four-terminal tandem PV module.
Two-terminal conguration. In the two-terminal congura-
tion, the cell process can be assumed to be highly integrated.
The top thin-lm solar cell is deposited onto the silicon- or the
thin-lm bottom cell. The cells are electrically connected by
a tunnel junction. Consequently, the rear contact of the top cell
and the front contact of the bottom cell become obsolete. We
estimate the corresponding savings to be up to 5 $ per m
2
.
While the tunnel junction is an added feature of the tandem
solar cell, other features of the single-junction solar cell become
also obsolete. Among them is the antireection (AR) coating of
the bottom cell. We hypothesize that the tunnel junction
deposition replaces the AR coating deposition and that the
tunnel junction can be integrated in fabrication with the front
passivation of the bottom cell and the rear passivation of the top
cell. As a result, we don't assume any additional cost for the
tunnel junction.
A further factor to consider is fabrication yield. As the inte-
grated fabrication process requires more fabrication steps, yield
will likely decrease. A decreased yield would result in higher
cost. Following the processes described in ref. 1 and 32, a yield
reduction of 1% absolute for the tandem PV module was
assumed.
Further potential costs could be related to the higher power
generated by the tandem solar cell PV module. This could have
implications on the modularization process; different wiring or
different junction boxes could be required. This is not consid-
ered here.
Following the given discussion, we expect DCfor the 2-
terminal conguration to be up to 5 $ per m
2
. This corre-
sponds to 15% of the cell to module costs for a silicon PV
module and 23% for a thin-lm PV module.
Four-terminal conguration. In the four-terminal congu-
ration, the two sub cells are fabricated and operated indepen-
dently. We will assume here that they are mechanically stacked.
Fabrication procedure and yield remain largely unaffected;
though, the four-terminal tandem requires some changes in the
design of top and bottom cell.
As the top cell needs a translucent rear contact, the full-area
metal contact needs to be replaced by a transparent contact and
a rear AR coating. AR coatings can potentially be deposited on
both sides of the cell at the same time. The full area metal
contact could be replaced by a metal grid. Ensuing costs are
marginal and we neglect additional cost for these changes.
Mechanical stacking will, most likely, require an additional
polymer layer between the two sub-cells. An air layer is,
however, possible. An additional EVA layer would come at an
additional cost of 1.8 $ per m
2
.
Potential design changes in the bottom cell include AR
coating thickness and junction prole. Foreseeable changes in
process costs are small and are ignored here.
Independent contacts for the two sub cells require inde-
pendent circuitry, an additional junction box and additional
cables. We estimate ensuing costs at $7.5 per module (4.6 $ per
m
2
). Integration could reduce this cost and a customized
junction box and cable design could be envisioned that includes
contacts for both cell types and could reduce this cost factor.
Considering these changes, DCfor the 4-terminal congu-
ration would be 6.4 $ per m
2
, corresponding to 19% of the cell to
module cost for a silicon module and 30% for a (frameless) thin-
lm module.
Relative changes in the cell to module process correspond
directly to changes in MSP. We have plotted the impact of
a change in DCof 25% relative on the cost regime in Fig. 3.
Note that this analysis was conducted for a specic case and
location and that all results are likely to vary as a result of the
variation in PV module manufacturing by geography/
manufacturer.
40,41
3.3 PV power stations
The cost breakdown for PV power stations requires a general-
ization of the approach used for PV modules. The cost of a PV
power station includes more cost components than that of a PV
module, including costs for PV module, racks, mounting,
wiring, land, permits, labor, and inverters. Replacing single-
junction solar cells in a PV power station by more efficient
tandem solar cells results in the station generating more power.
Consequently, all components that scale with a higher power
Table 2 Cost breakdown for two hypothetical tandem module technologies
TF on silicon tandem TF on TF tandem (frameless)
Cost [$ per m
2
] MSP [$ per m
2
] Cost [$ per m
2
] MSP [$ per m
2
]
Feedstock & absorber (top) 17.98 30.77 17.98 30.77
Absorber to cell (top) 17.76 26.22 17.76 26.22
Feedstock & absorber (bot) 42.08 56.16 17.98 30.77
Absorber to cell (bot) 27.12 39.64 17.76 26.22
Cell to module 33.81 42.94 25.39 25.29
Total 138.76 195.72 92.90 139.25
This journal is © The Royal Society of Chemistry 2016 RSC Adv.,2016,6, 66911–66923 | 66915
Paper RSC Advances
output for a constant area or number of PV panels need to be
considered as a part of C
cell
. Apart from the solar cells, this
includes especially inverters and cables. C
str
includes all other
components. We used ref. 1 and 32 again for the solar cell and
module costs and material published within the solar advisory
model (SAM) from ref. 33 to establish C
str
and C
cell
.AsC
str
changes with the size of the installation, we have considered
three different station sizes for each residential scale and utility
scale. Additionally, for each solar cell technology, CdTe and Si,
we considered three different efficiencies. These efficiencies will
later be used to investigate the impact of different parameters
on the cost regimes. The results of the calculations are
summarized in Table 3.
Comparing Tables 1 and 3, the signicant difference
between C
cell
/C
str
for PV modules and power stations becomes
clear. Whereas in a PV module this ratio is between 1.4 and 2.3,
for power stations the ratio is between 0.06 and 0.5. From this
result it can be concluded that, whether a tandem solar cell is
economically attractive, will be judged differently by a module
manufacturer and a system installer or yieldco. The smaller
ratios for power stations show that tandem solar cell technology
will become interesting to installers before it will become
interesting to manufacturers.
It also becomes obvious that the main share of the cost in
a PV power station is not related to solar cells. This has impli-
cations on DC. It can be argued that fabrication differences
between two- and four-terminal solar cells are exhausted at the
module level. For example, as cables and inverters scale with
power, wiring in four-terminal tandems could be imagined that
connects different inverters to different cells. Therefore, most of
C
str
becomes independent of the solar cell technology and the
relative differences become much smaller. We estimated DCat
3% of C
str
at the power station level.
4. Impact of different parameters on
cost relations
4.1 Impact of different pairings of band-gaps (E
g
)
The combination of band-gaps of top and bottom cell deter-
mines the limiting efficiency for the tandem solar cell. This
limit is different for the two- and four-terminal conguration, as
the former requires current matching. We calculated the
limiting efficiencies for a range of different band-gap pairs
according to the method described in the methodology section
for the two- and four-terminal conguration. The results of this
calculation are shown in Fig. 4 and are plotted as contour lines.
We also calculated which band-gap pairing gives the highest
efficiency for a given top cell/bottom cell band-gap (blue dotted
line). For each band-gap pairing, we calculated the MRCB,
which is represented by the color code. Finally, we calculated
the band-gap pairing that gives the highest MRCB for a given
bottom/top cell band-gap (black and red line, respectively).
Generally, the band-gap pairings that result in the highest
efficiency also result in the highest MRCB. This is strictly true
for the two-terminal conguration. For the four-terminal
conguration, there is an ambiguity for small bottom-cell
Fig. 3 Effect of a relative change in DCon the cost regimes. The black
lines border conditions in which the tandem solar cell provides
a positive cost benefit. A change in DCscales the corresponding area
and moves the triple point along the (white) line for equal cost per
output of the top and bottom cell.
Table 3 Cost breakdown for different single-junction solar power stations. The 1 kW residential and the 600 MW utility scale system mark the
smallest and largest value in each row
Cell type h[%] MSP [$ per W]
C
cell
/C
str
Residential Utility
1 kW 5 kW 13.5 kW 50 MW 186.7 MW 600 MW
CdTe 14.0 0.62 0.077 0.168 0.206 0.313 0.332 0.338
16.4 0.53 0.069 0.160 0.202 0.319 0.331 0.337
20.8 0.40 0.059 0.148 0.197 0.308 0.337 0.345
Si 12.2 1.14 0.139 0.283 0.339 0.499 0.524 0.531
16.4 0.85 0.114 0.260 0.326 0.488 0.521 0.530
24.7 0.56 0.084 0.224 0.301 0.467 0.514 0.527
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RSC Advances Paper
band-gaps (E
g,bot
< 1 eV). The result depends on whether in the
calculation the top- or the bottom-cell band-gap is xed.
The reason for the peculiar behavior of the four-terminal
conguration lies in the relative nature of the metric. A single-
junction solar cell with either a very small or a very large
band-gap generates a very small efficiency on its own. In the
four-terminal conguration, the efficiencies of a top cell with
a large band-gap and a bottom cell with a small band-gap nearly
add up. The relative cost benet compared to either of the
single-junction solar cells is then very large, but the absolute
price per output is very high, so that these combinations are not
actually desirable. To avoid these solutions, it is necessary to
look at both, the E
g,top
that results in the highest MRCB for
axed E
g,bot
(black line) and the E
g,bot
that results in the highest
MRCB for a xed E
g,top
(red line).
To illustrate the effect of different band-gap pairings on cost
regimes, we compare a close to ideal band-gap pairing on
silicon (E
g,bot
¼1.124 eV, E
g,top
¼1.74 eV) to a non-ideal one
(E
g,bot
¼1.124 eV, E
g,top
¼1.42 eV). The results are shown in
Fig. 5. For the close to ideal band-gap pairing (Fig. 5a), we used
a top cell efficiency of h
top
¼20.8%, corresponding to a value of
f
SQ,top
¼72%. This efficiency was chosen with the current record
efficiency for GaInP
42
in mind. The band-gap of GaInP can be
tuned by a variation of In and P content. The current record
efficiencies were achieved with a material that had a slightly
higher band-gap (1.81 eV). A silicon solar cell with the same cell
quality (f
SQ,bot
¼72%) is at h
bot
¼24.7%, which is about 1%
below world record.
43
The calculated tandem solar cell efficiency
for this combination would be h
tan
¼33.2% (four terminal) or
h
tan
¼32.6% (two terminal).
Fig. 4 Maximum relative cost benefit as a function of top cell band-gap E
g,top
and bottom cell band-gap E
g,bot
for the four-terminal (a) and two-
terminal (b) configuration. The contours show the limiting efficiencies for the corresponding band-gap combination. The blue dotted line
represents the band-gap pairing with the highest efficiency for a given E
g,top
,E
g,bot
. The black line represents the band-gap pairing with the
highest relative cost benefit for a given E
g,bot
. For the four-terminal tandem, we also show the band-gap pairing with the highest relative cost
benefit for a given E
g,top
(red line).
Fig. 5 Illustration of the impact of ideal and non-ideal band-gap combination on the cost regimes. A close to ideal band-gap pairing is shown on
the left (a), a non-ideal band-gap pairing on the right (b). The blue line at the top of each graph represents the C
cell
/C
str
value for a silicon PV
module (Table 1), the blue band at the bottom represents the range of C
cell
/C
str
values for different silicon PV power stations (compare Table 3).
The lower boundary corresponds to a small residential system, the upper boundary to a large utility scale system. $ per W values show at what
MSP levels the module would be.
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Paper RSC Advances
The non-ideal case corresponds to a GaAs on Si tandem solar
cell.
35
GaAs on silicon was chosen as an example as these
materials represent mature technologies with a clear path
toward 30% at panel tandem efficiency.
44
For consistency, we
also used a top cell with f
SQ,top
¼72%, which corresponds to h
top
¼24.4% efficiency, about 4% below world record
45
but still at
a competitive level.
46
The calculated combined efficiency for this
tandem solar cell is h
tan
¼30.7% (four terminal) and h
tan
¼
28.5% (two terminal). The two-terminal efficiency takes
a stronger penalty due to the non-ideal band-gap pairing.
Fig. 5 also shows $ per W values that are obtained from MSP
calculations. Values from Table 1 were used with C
str,top
¼
C
str,bot
¼C
str,tan
¼42.94 $ per m
2
. As the cost regimes depends
on h
top
and h
bot
, which are different in both cases, the lines for
equal cost per output for top and bottom cell are not diagonal
anymore. Looking at C
cell
/C
str
for a silicon PV module (blue
dotted line), there is no path with current technology in which
the tandem is preferable, regardless of the band-gap of the III–V
top cell. At the power-station level, an ideal band-gap combi-
nation has the possibility for an economically attractive
tandem, provided C
top
/C
str
is smaller than 0.5 for a utility-scale
system or smaller than 0.4 for a residential system.
For the non-ideal band-gap combination of GaAs and silicon,
current technologies are not cost-advantageous as a tandem,
even for utility-scale stations. For residential power stations,
tandems become preferable, provided C
top
/C
str
is smaller than
0.3. In either case, III–V solar cells would have to become very
inexpensive. A rough estimate for a split according to (1) and (2)
can be made using.
47
At least with current fabrication proce-
dures, III–V technology is at a signicantly higher cost level than
Si. Technological solutions for reducing cost have been sug-
gested, e.g., in ref. 48 and 49. Further opportunities for GaAs-on-
silicon solar cells lie in areas where the solar cell contributes an
even smaller fraction of the entire system costs or where other
factors, like weight or size, are important. Examples are
outdoor, concentrator
50
and space applications.
51
From this analysis we conclude that ideal band-gap pairings
are very desirable for the commercialization of tandem solar
cells. This is especially true for tandem solar cells in a two-
terminal conguration, as these cells take a larger efficiency
hit if they are not current matched.
4.2 Impact of different pairings of solar cell qualities f
SQ
As a measure for the quality of a solar cell we use the fraction of
the radiative limit f
SQ
at which the cells operate. To gauge the
impact of different cell qualities on the cost-benet, we assess
the MRCB as a function of f
SQ,top
and f
SQ,bot
. The results of this
calculation are shown in Fig. 6. We use a close to ideal band-gap
pairing with a silicon bottom cell (E
g,bot
¼1.124 eV, E
g,top
¼1.74
eV). Results are similar for other ideal band-gap pairings,
though absolute efficiency numbers change.
The combination of f
SQ,top
and f
SQ,bot
that yields the highest
improvement of tandem solar cell efficiency over the
comprising single-junction solar cell efficiency for a given f
SQ,top
or f
SQ,bot
coincides with the combination that yields the highest
MRCB. The ideal combination of f
SQ,top
and f
SQ,bot
is given if h
top
¼h
bot
. This not only true for the shown band-gap combination
but holds generally. The slope of the line in Fig. 6 is given by the
ratio of the radiative limits of bottom and top cell h
SQ,bot
/h
SQ,top
.
To illustrate the effect of ideal and non-ideal cell quality
pairings, we show the cost relations for a perovskite on silicon
tandem solar cell with two different silicon bottom cells. The
result of this calculation is shown in Fig. 7.
Perovskite on silicon solar cells are of interest as perovskite
solar cells have achieved high efficiencies up to 21%,
21
are
potentially inexpensive, and can be fabricated with band-gaps
that are close to the ideal pairing with silicon.
In the presented calculation (Fig. 7a) we have used parame-
ters taken from an in-house study.
52
The top cell has an effi-
ciency of h
top
¼12.0% (f
SQ,top
¼41%) at E
g,top
¼1.7 eV band-
gap. The bottom cell had a similar efficiency of h
bot
¼12.2%
(f
SQ,bot
¼38%) at E
g,top
¼1.124 eV. The calculated tandem solar
cell efficiency is 17.8% (comparing to 17.0% for a 1.6 eV top cell
in ref. 24; a different band-gap was used in order to vary only
one parameter at a time). While the achieved efficiencies are
low, they provide a good case study for similar efficiencies. It
can be seen that the regime in which the tandem is preferable is
comparably large. At the module level, there is, also here, no
scenario in which the tandem is preferable to either top or
bottom cell alone. On the power station level, the tandem
becomes preferable if C
cell
/C
str
for the perovskite solar cell are
below 0.7 for utility-scale stations and 0.5 for residential-scale
stations. Given the currently unknown but potentially low
fabrication cost of perovskite solar cells, these goals seem
achievable. The shown $ per W values in Fig. 7a are comparably
high because of the low efficiencies of the comprising solar
cells. Increasing h
top
and h
bot
simultaneously will reduce those
Fig. 6 Surplus tandem solar cell efficiency (h
tan
max[h
top
,h
bot
]) over
the higher of the comprising single-junction solar cell efficiencies as
a function of f
SQ,top
and f
SQ,bot
. The top cell has a band-gap of E
g,top
¼
1.74 eV, and a radiative efficiency of h
SQ,top
¼28.4%. The bottom cell
has a band-gap of E
g,bot
¼1.124 eV and a radiative efficiency of h
SQ,bot
¼33.0%. The tandem solar cell efficiency is shown by the contour
lines. The maximum efficiency is h
SQ,tan
¼44.5%. Also shown are lines
representing the highest efficiency benefit (blue, segmented) and the
highest cost benefit for a given f
SQ,top
or f
SQ,bot
(black). Note that these
lines coincide. They also mark the case for which h
top
¼h
bot
.
66918 |RSC Adv.,2016,6, 66911–66923 This journal is © The Royal Society of Chemistry 2016
RSC Advances Paper
numbers while not changing the rest of the plot. Of course,
resolving the reliability issue is a precondition for commer-
cialization at any scale.
In Fig. 7b we show the effect of replacing the 12.2% bottom
cell by a 20.5% bottom cell (f
SQ,bot
¼60%). The calculated
tandem solar cell efficiency in this case is h
tan
¼21.7% and is
still higher than the single-junction efficiency of the silicon
solar cell. However, the efficiency benet of the tandem solar
cell has reduced from 5.6% for case (a) to 1.2% in case (b). As
a consequence, the top cell has to be fabricated for virtually zero
cost (C
cell
/C
str
< 0.05) for the tandem solar cell to become pref-
erable. This case is of interest because it is frequently argued
that an existing solar cell system could be improved by adding
an inexpensive top cell. Our analysis does not support this
argument but indicates that both sub cells should operate at
similar efficiencies to achieve a cost benet from the tandem.
C
str
for silicon were taken from Table 1 for PV modules
(C
str,top
¼C
str,bot
¼C
str,tan
¼42.94 $ per m
2
) and from Table 3 for
power stations. At the current stage of technology, C
str
for
perovskite solar cells is unknown. Structure costs for perovskite
solar cells can be anticipated to be lower than those for silicon,
especially for modules, yet reliability concerns may require use
of additional encapsulants. Differences were omitted as the
intent of the example was to illustrate the effect of an imbalance
in cell quality. The impact of different system costs is discussed
in the next section.
It is worth mentioning here again that the presented analysis
only determines which of the three options, a system made only
from the top cell, a system made only from the bottom cell or
a system made from the tandem solar cell is at the lowest cost
per output level. Comparison to other solar cells requires
comparing $ per W or ¢ per kW per h values for the respective
systems.
4.3 Impact of different pairings of structure costs C
str
A third important factor that we want to highlight in this study
is the impact of differences in structure costs. C
str
for a module
is given by the costs of cell to module processing. As shown in
Table 1, the difference in costs required to make a module out
of a fabricated solar cell can be as high as 50% relative when
comparing a frameless thin-lm PV module with a silicon wafer
PV module. As discussed earlier, these differences are strongly
attenuated when looking at PV power stations. Differences in
C
str
due to differences in technology here are in the range of
10% relative. Variations in structure costs due to the size of the
PV power station, its location and the cost of permits has
a much stronger impact. To illustrate the impact of differences
in C
str
, we calculated the MRCB as a function of C
str,bot
and
C
str,top
using eqn (4) for C
str,tan
and DC¼0. The results are
shown Fig. 8.
Fig. 7 Illustration of the impact of similar and different single-junction solar cell efficiencies on the cost regimes. A similar efficiency pairing is
shown on the left (a). A pairing with different efficiencies is shown on the right (b). C
cell
/C
str
for a silicon PV module and PV power stations are
again indicated.
Fig. 8 Maximum relative cost benefit as a function of C
str,bot
and
C
str,top
. The top cell has a band-gap of E
g,top
¼1.74 eV, and a radiative
efficiency of h
top
¼28.4% (f
SQ,top
¼1). The bottom cell has a band-gap
of E
g,bot
¼1.124 eV and a radiative efficiency of h
bot
¼33.0% (f
SQ,bot
¼
1). The resulting tandem solar cell efficiency is h
tan
¼44.5%. Also
shown is the line representing the highest MRCB for a given C
str,bot
or
C
str,top
.
This journal is © The Royal Society of Chemistry 2016 RSC Adv.,2016,6, 66911–66923 | 66919
Paper RSC Advances
As the two sub-cells contribute to the tandem with different
efficiencies, the highest cost benet is not a diagonal. The
system costs enter the calculation twice, consequently the
position of the highest MRCB has a slope of ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
htop=hbot
q.
To highlight the impact of C
str
, we investigate a module and
a PV power station made of hypothetical thin-lm on silicon
tandem solar cells and made of hypothetical thin-lm on thin-
lm tandem solar cells. In both cases we use a top cell efficiency
of h
top
¼14.0% (E
g,top
¼1.74 eV, f
SQ,top
¼49%), a bottom cell
efficiency of h
bot
¼16.4% (E
g,bot
¼1.124 eV, f
SQ,bot
¼49%),
which results in a tandem efficiency of h
tan
¼21.8% for two-
terminal and 22.2% for the four-terminal conguration. These
numbers were chosen having recent efficiencies of commer-
cially available CdTe and screen-printed multicrystalline silicon
solar cells in mind (we are aware that both technologies are
capable of higher efficiencies but believe that the ratio of both
efficiencies is representative, which is the key variable in the
analysis). The cost breakdown of the corresponding modules is
shown in Table 2. Cost regimes are shown in Fig. 9.
As Fig. 9 shows, differences in C
str
result in a reduction of
size of the tandem regime. The further the size is reduced, the
larger the difference is. As shown in Fig. 9a and b, the cost
structures of the thin-lm and silicon solar cells make the
tandem PV module a non-preferred option. Only fundamental
reduction in the cost of solar cell fabrication, to about a third of
the current cost, can change this. However, when looking at PV
power stations, (Fig. 9a and c) tandems made out of these
hypothetical solar cells are preferable to their single-junction
counterparts. As C
str
for power stations is very similar (1.61 $
per W for thin-lm and 1.73 $ per W for silicon), there is little
difference between the cost regimes for the two tandems. For
a 50 MW utility scale station, the difference is 7.5% relative and
varies between 7% for a large utility scale station and 11% for
a small residential station.
We calculated the LCOE for different power station sizes
using.
33
We used default parameters, neglected degradation,
and avoided use of advanced nancial mechanisms. The
reference location was Boston, MA. We calculated the LCOE for
all power stations from Fig. 9a and c. These include two resi-
dential and three utility-scale stations of different sizes. Results
are shown in Table 4. The LCOE calculations conrm that the
hypothetical tandem PV power stations operate at a lower LCOE
than either comprising single-junction technology. The relative
improvement is between 5% and 7.5% relative to each single-
junction technology.
Fig. 9 Cost regimes for different PV systems: (a) the cases for both PV modules and PV power stations made from a hypothetical pair of thin-film
solar cells. C
str
are identical for top and bottom cell and are 29.9 $ per m
2
(see Table 1) for a module and 1.61 $ per W for a reference power
station.
20
(b) The case for a hypothetical thin-film on silicon tandem PV module. C
str
for top and bottom cells differ significantly. (c) The case for
a hypothetical thin-film on silicon tandem PV power station. C
str
for top and bottom cell were chosen for a reference (50 MW, utility) power
station. C
cell
/C
str
values for modules (blue segmented line) and different size PV power stations (the blue band again marks the range for stations
of different size as specified in Table 3) are indicated.
Table 4 LCOE calculations for the different solar cell technologies discussed in this section
Cell type h[%] MSP [$ per W]
Nom. LCOE [¢ per kW per h]
Residential Utility
5 kW 13.5 kW 50 MW 186.7 MW 600 MW
TF top 14 $0.62 11.31 10.02 11.89 11.54 11.45
TF bot 16.4 $0.53 10.51 9.18 10.82 10.46 10.37
TF on TF 21.8 $0.66 9.88 8.63 10.31 9.95 9.86
Rel. LCOE benet [%] 5.99 5.99 4.71 4.88 4.92
TF top 14 $0.62 11.31 10.02 11.89 11.54 11.45
Si bot 16.4 $0.85 11.35 10.02 12.12 11.76 11.67
TF on Si 21.8 $0.90 10.52 9.26 11.28 10.93 10.84
Rel. LCOE benet [%] 6.98 7.58 5.13 5.29 5.33
66920 |RSC Adv.,2016,6, 66911–66923 This journal is © The Royal Society of Chemistry 2016
RSC Advances Paper
5. Summary and discussion
In this work, we aspired to answer the following question: given
two single-junction solar cell technologies A and B, under which
circumstances is it economically benecial to combine these
technologies into a tandem solar cell C? To answer this ques-
tion, we rst related the costs and efficiencies of the two single-
junction technologies to the tandem. Tandem costs were esti-
mated by breaking down the costs of the fabrication processes
for the single-junction solar cells and constructing the costs for
fabricating the tandem solar cell from this breakdown. Two
types of PV systems were considered: PV modules and PV power
stations. The ratio between the cost to make the solar cell and
the cost to make the supporting structure C
cell
/C
str
is a key
parameter in this study; we calculated this parameter for
a range of different modules and power stations. Tandem effi-
ciencies were estimated via the radiative limit and the fraction
of the radiative limit at which each single-junction solar cell
operates.
Using these numbers, we introduced the cost-regime plot,
which shows under which conditions a PV system using either
of the three solar cell technologies A, B, or C generates power or
work at the lowest cost. The plot also shows the relative cost-
benet of C towards A and B. Generally, we nd that tandems
become the more favourable the smaller the fraction of the solar
cell-related cost in the entire system is. As a rule of thumb,
tandem solar cells can become attractive if C
cell
/C
str
for A and B
are below 50%.
We investigated the impact of different parameters on the
cost regimes using the described methodology. Our results
suggest that a tandem solar cell should be a “marriage of
equals”. By this we mean that:
(i) The tandem solar cell should be made using two solar-cell
technologies that, when operated independently as single-
junction solar cells, should be at a similar cost per unit
output power or energy. Matching this condition ensures that
the tandem solar cell has the highest cost-benet over the
comprising single-junction solar cells. This was discussed in the
context of Fig. 2.
(ii) The tandem solar cell should be made from two materials
that form an ideal band-gap pairing. Matching this condition
ensures that the tandem solar cell has the highest potential
efficiency benet over the comprising single-junction solar
cells. We have illustrated this with the example of different
hypothetical III–V on silicon tandem solar cells (Fig. 5).
(iii) The tandem solar cell should be made from two solar
cells that, when operated independently as single-junction solar
cells, should be at a similar efficiency. Matching this condition
ensures that the tandem solar cell has the highest efficiency
surplus over the comprising single-junction solar cells. This
condition is different from (ii) as it addresses non-idealities and
losses in the cell architecture. We have illustrated this with the
example of different perovskite on silicon tandem solar cells
(Fig. 7).
(iv) The tandem PV system should be made from two tech-
nologies with similar costs for supporting structure. This
condition is more relevant for PV modules than for PV power
stations. Matching this condition ensures that the tandem PV
system has the highest cost benet compared to PV systems
made of the comprising single-junction solar cells. We have
illustrated this with different hypothetical thin-lm on thin-lm
and thin-lm on silicon tandem solar cells (Fig. 9).
Moreover, we compared different tandem solar cell archi-
tectures (two terminal and four terminal). The two-terminal
architecture offers the greater potential for reducing the
number of fabrication steps and material, while the four-
terminal tandem allows greater exibility in terms of band-
gap pairings and, hence, material choice. Whereas we nd
some differences on the module level that favour the two-
terminal architecture, we don't see a clear trend toward either
architecture on the power station level. A ner analysis of energy
yield will be able to offer a clearer picture here.
A further conclusion of this work is that a module manu-
facturer and a PV installer or a yieldco will give different
answers to the posed question. The structural cost component
C
str
inamoduleismuchsmallerthaninaPVpowerstation.In
none of the investigated examples did we nd a case in which
a tandem PV module could be produced at a lower $ per W
level than either of the comprising single-junction PV
modules. Solar cell fabrication costs in current technology
would have to be reduced signicantly in order to achieve this.
ForPVpowerstations,ontheotherhand,thecurrentcost
structure of silicon and thin-lm solar cells make tandems an
attractive option with lower LCOE values for the tandem than
for either single junction cell (provided cells with suitable
characteristics are available). This difference creates a conun-
drum; an installer may be interested in tandem PV modules
while a module producer may want to avoid a higher-cost
product. Stable market conditions and clear regulations can
help solve this conundrum, as they will allow module
producers to foresee the value of tandem PV modules to the
customer and charge a premium on high efficiency solar cell
technologies.
Finally we want to give suggestions for future research
directions that are motivated by this study:
(i) Established single-junction solar cells target band-gaps
between 1.0 eV and 1.4 eV band-gap, as these band-gaps merit
the highest single-junction efficiencies. This band-gap range is
also suitable for the bottom cell in a double-junction tandem.
However, top cells with appropriate band-gaps (1.6–2.0 eV) and
efficiencies (>20%) are far less developed and available. We,
therefore, recommend research for the development of suitable
top cells. We believe that high lifetimes are a prerequisite for
this.
53
(ii) Additionally, suitable deposition techniques for top cells
are required, as fabrication should be as integrated as possible.
We therefore also recommend research on equipment design to
accelerate throughput without sacricing quality.
(iii) While this point has been made before, it is worth
repeating that in today's PV power stations the solar cell
generates 100% of the power, yet the contribution to the total
system cost is small. Under this condition, increasing the solar
cell efficiency, even at increased cost, is worthwhile. However,
This journal is © The Royal Society of Chemistry 2016 RSC Adv.,2016,6, 66911–66923 | 66921
Paper RSC Advances
there is an equal or even larger opportunity in reducing LCOE by
reducing system related costs, which requires efforts on the
technological as well as on the policy side.
Acknowledgements
We thank Dirk Weiss (First Solar) and BJ Stanbery for very
helpful discussion and suggestions. Research presented in this
work was nancially supported by the Department of Energy
under Award Number DE-EE0006707 and by the National
Research Foundation Singapore through the Singapore MIT
Alliance for Research and Technology's Low Energy Electronic
Systems research program.
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