Theoretical limits for visibly transparent photovoltaics
Richard R. Lunt
Citation:
Applied Physics Letters
101, 043902 (2012); doi: 10.1063/1.4738896
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http://dx.doi.org/10.1063/1.4738896
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http://scitation.aip.org/content/aip/journal/apl/101/4?ver=pdfcov
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Theoretical limits for visibly transparent photovoltaics
Richard R. Lunt
a)
Department of Chemical Engineering and Materials Science, Michigan State University, East Lansing,
Michigan 48824, USA
(Received 31 March 2012; accepted 9 July 2012; published online 24 July 2012)
Transparent photovoltaics (PVs) provide a potentially facile route to building-integrated PVs and
seamless energy-harvesting within non-window surfaces such as electronic displays, autonomously
powered electronic-glazings, and mobile-electronic accessories. Such devices have been enabled by
manipulation of excitons in organic and molecular semiconductors that allow for selective
ultraviolet and near-infrared solar conversion. Here, the theoretical efficiency limits of transparent
photovoltaics are determined as a function of transparency. Power-production from ultraviolet and
near-infrared photons alone leads to a theoretical single-junction efficiency of 21% in transparent
structures, compared to 33% for opaque-junctions. Reducing thermal losses via transparent
multi-junction stacking these limits increase to 37%.
V
C
2012 American Institute of Physics.
[
http://dx.doi.org/10.1063/1.4738896
]
The development of transparent photovoltaics (PVs) can
enable seamless integration onto any already utilized transpar-
ent surfaces for PV deployment, such as on building windows,
skylights, greenhouses, sun-roofs, and mobile electronic devi-
ces without requiring additional structural framing or acquisi-
tion of undeveloped real estate. In general, the purpose of
windows and displays is to provide natural lighting or a clear
view. This problem can be approached with the development
of a visibly transparent PV technology that selectively har-
vests near-infrared (NIR) and ultraviolet (UV) light. A high
level of visible transmittance (VT) on the order of 70%–80%
for architectural and 55%–90% for automotive is necessary
for ubiquitous adoption of solar-active windows.
1
Transparent
solar cells designed for high-end device applications (e.g., mo-
bile electronics integration) require even greater transparency
>80%–90%, where display quality is paramount.
Recently, we have shown that by exploiting the excitonic
character of molecular and organic semiconductors, it is possi-
ble to produce near-infrared PV architectures that are selec-
tively absorptive in the UV and NIR, enabling visibly
transparent active-layer photovoltaics for optimization of both
efficiency and transparency.
2
These structures can also be
added ubiquitously to non-transparent surfaces without affect-
ing their underlying aesthetic, are capable of harvesting direct
and indirect light, and could be combined with spatially dis-
tributed inorganic cells
3
–
5
or semitransparent devices
6
–
17
to
further boost visible (VIS) external quantum efficiencies
(EQEs) for niche applications with less stringent transparency
requirements (e.g., fac¸ade, darkened, or colored glass applica-
tions). Although stringent transparency requirements could
create challenges for full module scale-up in large-area appli-
cations due to bus bar integration necessary to reduce resistive
losses,
18
,
19
this is likely surmountable with the recent develop-
ment of highly transparent and highly conductive metal nano-
wire grids,
20
–
23
carbon nanotube meshes,
24
or improved
transparent conducting oxides interconnects.
25
In this article, the theoretical efficiency limits are deter-
mined as a function of transparency to define the maximum
realizable goals for transparent single- and multi-junction
photovoltaics in a range of applications. The range of per-
ceptible visible light is first determined using color rendering
index (CRI) analysis and subsequently utilized in determin-
ing thermodynamic efficiency limits for visibly transparent
solar cells.
The CRI is a quantitative metric for evaluating the qual-
ity of lighting systems and can be utilized to evaluate the
level or perceptible color-tinting of a window. CRIs are cal-
culated based on ideal transmission profiles (step-functions)
in combination with CIE 1976 three-dimensional uniform
color space (CIELUV), CIE 1974 test-color samples, and
with correction for chromatic adaptation (non-planckian-
locus), when necessary, according to
26
CRI
¼
1
8
X
8
i
¼1
100
4:6
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðDL
i
Þ
2
þ ðDu
i
Þ
2
þ ðDv
i
Þ
2
q
; (1)
where D
L
i
*, Du
i
*, and Dv
i
*, are the difference in lightness
(
L*) and chromaticity coordinates (u*,v*) between each
color sample,
i (8 in total) "illuminated" with a fixed refer-
ence solar spectrum (AM1.5G) and the transmission sources
(
T(k)
AM1.5(k)). The weighted average VT is calculated
according to
26
VT
¼
ð
T
ðkÞPðkÞSðkÞdk
ð
V
ðkÞSðkÞdk
;
(2)
where k is the wavelength,
T is the transmission spectrum, P
is the photopic response of the human eye,
S is the solar
energy flux, and the integration is preformed over a sufficient
wavelength
range
to
completely
encompass
P
(e.g.,
300–900 nm) so that it is accordingly independent of any
defined visible wavelength range. Thermodynamic limiting
efficiencies are calculated via the Shockley ideal diode equa-
tion with radiative-limited recombination dark current, viz,
27
a)
rlunt@msu.edu.
0003-6951/2012/101(4)/043902/4/$30.00
V
C
2012 American Institute of Physics
101, 043902-1
APPLIED PHYSICS LETTERS 101, 043902 (2012)
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J
S
ffi qg
ð
1
E
G
E
2
=EQE
exp
ðE=nkTÞ 1
dE;
(3)
where
g
¼ 2p/(c
2
h
3
),
n is the ideality factor (n
¼ 1 here), c is
the speed of light,
h is Planck’s constant, and E
G
is the active
layer bandgap. For heterojunction devices,
E
G
is subse-
quently replaced in Eq.
(3)
with the interface gap,
I
G
, which
is the difference between the highest occupied molecular
orbital energy of the donor and the lowest unoccupied
molecular orbital energy. Practical laboratory efficiencies
(non-module) are then calculated as outlined in Ref.
28
for
excitonic and nanostructured semiconductors capable of ena-
bling transparent structures with fractional scaling of the
Shockley-Queisser (SQ) voltage, photocurrent, and fill fac-
tor. This scaling estimates,
a-posteriori, an upper limit volt-
age for heterojunction devices that accounts for replacing
E
G
with
I
G
that leads to increased dark-current recombination,
and therefore decreasing voltage scaling, due to the hetero-
junction energy offset required to dissociate excitons.
29
–
33
Resistive losses for full module scale-up can be further con-
sidered (but was not applied here) by multiplying the practi-
cal laboratory efficiencies with an upper limit heuristic
factor of
0.75 typical for other thin-film PV scale-
up.
28
,
34
,
35
Series-integrated tandem junction efficiencies are
calculated by constraining current-density (
J) matching in
each cell at every voltage,
J(V)
¼ J
i
(
V
i
,
E
i
)
¼ J
i
þ1
(
V
i
þ1
,
E
i
þ1
).
This equation was solved for the voltage in each cell (
V
i
) as
a function of
J, so that the total device voltage is V
¼
P
V
i
.
In evaluating the efficiency limits of transparent photo-
voltaics, it is first necessary to define the range of the visible
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