of 11
A sensitivity analysis to assess the relative
importance of improvements in electrocatalysts,
light absorbers, and system geometry on the
e
ffi
ciency of solar-fuels generators
Yikai Chen, Shu Hu, Chengxiang Xiang
*
and Nathan S. Lewis
*
A sensitivity analysis has been performed for a variety of generic
designs for solar-fuels generators. The analysis has revealed the
relative importance of reductions in the overpotentials of electro-
catalysts, of improvements in the materials properties of light
absorbers, and of optimization in the system geometry for various
di
ff
erent types of solar-fuels generators, while considering operation
at a range of temperatures as well as under a variety of illumination
intensities including up to 10-fold optical concentration.
Introduction
Most concepts for a solar-fuels generator include components
for light absorption and charge separation, electrocatalysts for
one or both of the half-reactions involved in the production of
fuels from H
2
O or from H
2
O and CO
2
, and a membrane or other
physical separation barrier to ensure separation of the prod-
ucts.
1
3
All of these envisioned system components are the basis
for active areas of research, with the goal of improving the
activity, stability, and mutual compatibility of the various
components for use in a fully operational, e
ffi
cient, robust,
intrinsically safe, scalable, demonstration of a solar-fuels
generator.
1
11
In the discipline of systems engineering, a sensitivity anal-
ysis is a routine, critical tool used to identify the main levers,
i.e.
the components of the system for which improvements in
performance will have the most impact on improving the
performance of the system as a whole.
12
In general, a sensitivity
analysis can only bene
cially be performed when a system
design is in hand, because the architecture of the system will
play a signi
cant, if not dominant, role in the outcome and will
determine the inputs and outputs of the system-based sensi-
tivity analysis. For example, di
ff
erent sensitivity analyses would
be needed to ascertain the key levers in optimizing the
ight
speed or
ight time of a jet-powered,
xed-wing aircra
relative
to optimizing the speed or
ight time of a helicopter.
The theoretical, and practically realizable, e
ffi
ciencies of a
solar-driven water-splitting device based on theoretical mate-
rials properties, or on current state-of-the-art materials and
components, have not been presented in the literature for a
speci
c system design concept in hand.
13
15
Recently, several
generic systems-level concepts for solar-fuels generators have
been presented
16
20
in su
ffi
ciently speci
c detail to enable a
meaningful sensitivity analysis to identify the key levers that
will produce the largest performance improvements within the
overall design space of the systems of interest. The state-of-the-
art performance values of many classes of electrocatalysts for
key reactions of interest, including the hydrogen-evolution
reaction (HER), the oxygen-evolution reaction (OER), and
possible CO
2
-reduction reactions (CO
2
RR), have also recently
been compiled and documented.
11,21,22
Additionally, the state-of-
the-art performance of individual light absorbers, as well as the
performance of combinations of light absorbers for use in
Beckman Institute, Kavli Nanoscience Institute, and Joint Center for Arti
cial
Photosynthesis, 210 Noyes Laboratory, 127-72, Division of Chemistry and Chemical
Engineering, California Institute of Technology, Pasadena, CA 91125, USA. E-mail:
cxx@caltech.edu; nslewis@caltech.edu
Cite this:
Energy Environ. Sci.
,2015,
8
,
876
Received 23rd July 2014
Accepted 23rd December 2014
DOI: 10.1039/c4ee02314e
www.rsc.org/ees
Broader context
A solar-driven water-splitting cell is generally comprised of light
absorbers, electrocatalysts, membrane separators and an electrolyte
solution in a speci
c system geometry. The overall solar-to-hydrogen
conversion e
ffi
ciency of such a system depends on the performance and
materials properties of all the individual components as well as the design
of the system. Signi
cant research e
ff
orts are being devoted to improving
the performance of all of the system components, yet some improvements
will result in larger gains in the overall system e
ffi
ciency than others. We
describe herein a sensitivity analysis of the solar-to-hydrogen conversion
e
ffi
ciency with respect to the materials properties of light absorbers,
electrocatalysts, and the geometric design parameters, for a series of
speci
c but generic designs for solar-fuels generators. Such a sensitivity
analysis provides a quantitative framework within which to assess the
gains in system performance that can be attained as a result of improving,
relative to the current state-of-the-art, the performance of di
ff
erent
components of the system, and provides a useful framework for setting a
forward R&D agenda for such systems.
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tandem structures, have been recently reviewed.
1
Extensive
modeling and simulation e
ff
orts, using validated multi-physics
modeling approaches, have also been performed recently on a
variety of system geometries and for a variety of operating
temperatures, illumination intensities, and optical concentra-
tion factors.
16
20
We report herein a
one factor at a time
sensitivity anal-
ysis
23
25
for several types of generic designs of solar-fuels
generators. In this study, the sensitivity of the e
ffi
ciency of the
generation of solar fuels to the properties of the various system
components was evaluated as a function of the total over-
potential of the electrocatalysts for a variety of light absorbers
having a range of band gaps and having varying materials
quality. An additional sensitivity analysis has been performed to
determine the key levers for improving the e
ffi
ciency of solar-
fuels generation over a range of operating temperatures and
under concentrated illumination. The sensitivity analysis
clearly shows the extent to which improvements, relative to the
state-of-the-art, in the overpotential of the electrocatalysts, in
the system geometry and design, in the properties of the light
absorbers, and in the properties of the membranes will provide
gains in overall attainable system e
ffi
ciency. In this respect, the
sensitivity analysis serves to survey the possible system design
space and highlights areas that will have the largest impact on
improving the performance of the system as a whole.
Modeling
Device designs
The generic design of the solar-driven water-splitting device
investigated herein contained a photoabsorber component,
electrocatalyst layers for the OER and for the HER, a membrane
separator, and liquid electrolytes. The generic design includes
several speci
c cell constructs. The detailed geometric param-
eters of these cell constructs have been described previ-
ously.
16
18,20
The photoabsorber component contained a
tandem-junction photoelectrochemical cell, in which 100% of
the incident solar photon
ux arrives at the photoabsorber
surface in either an unconcentrated, planar design or in a
concentrated design coupled with a 10

optical solar concen-
trator. The optical obscuration due to the liquid electrolyte,
electrocatalyst layers, and membrane separators were neglected
in the calculation. The OER and HER electrocatalyst layers were
located directly on the top and the bottom of the anode and
cathode sides of the photoabsorber component, respectively, in
which the geometric surface area of the HER catalyst and OER
catalyst were identical and were bounded to the geometric area
of the tandem photoabsorber. The membrane separator was
employed to provide the required ion-transport pathways
between the cathode and anode compartments as well as to
provide e
ff
ective barriers to the crossover of products. The
liquid electrolyte contained strong acid or strong base (
e.g.
,1M
H
2
SO
4
(aq) or 1 M KOH(aq)), which produced negligible pH
gradients at the surfaces of the electrocatalysts under operating
conditions. The transport of ions through the membrane and in
the liquid electrolyte was the source of any additional resistive
losses in the device.
Although other solar-fuel generators,
e.g.
,CO
2
-reduction
reactors, contain some components in common with the solar-
driven water-splitting device described above, the speci
c cell
designs and operational constraints of a CO
2
-reduction reactor
could vary signi
cantly from those of a water-splitting reactor,
due to di
ff
erent system-level constraints. Moreover, depending
on the speci
c reduction products, the thermodynamic poten-
tials for other fuel-forming reactions can vary signi
cantly from
those of water splitting. Thus, the modeling and simulation
results and associated sensitivity analysis described herein are
only explicitly directed towards, and applicable, to solar-driven
water-splitting systems of the general design classes evaluated
herein.
Solar-to-hydrogen (STH) conversion e
ffi
ciency
The operating current density,
J
op
, of an integrated set of light
absorbers arranged in a tandem con
guration was calculated by
the following equation:
V
op
(
J
op
)
¼
f
0
+
h
OER
(
J
op
)+|
h
HER
(
J
op
)| +
R
eff
(
J
op
)
(1)
where
V
op
(
J
op
) is the current
voltage relationship of the tandem
photoabsorbers,
f
0
is the thermodynamic potential for the
water-splitting reaction,
R
e
ff
is the e
ff
ective transport resistance
in the membrane separator and the liquid electrolyte, and
h
OER
(
J
op
) and
h
HER
(
J
op
) are the overpotentials for the OER and
HER, respectively.
The STH conversion e
ffi
ciency,
h
STH
,isde
ned as:
F
STH
¼
1
:
23
ð
V
Þ
J
op
ð
mA cm

2
Þ
S
ð
mW cm

2
Þ
(2)
with
J
op
the operating photocurrent density (mA cm

2
) and
S
the
total incident solar irradiance (mW cm

2
).
Shockley
Queisser limit for light absorbers
The ideal limiting case,
i.e.
the Shockley
Queisser (S
Q) limit, in
which the current
voltage relationship for a tandem photo-
absorber is determined by use of a detailed-balance calculation,
is obtained when the current density at the operating photo-
voltage is equal to the sum of the incident solar radiation (
J
ph
)
and the thermal radiation (
J
th
) minus the radiative emission
(
J
rad
):
26
J
¼
J
ph
+
J
th

J
rad
(3)
J
ph
,
J
th
and
J
rad
were determined by:
26
J
ph
¼
C

e
ð
N
E
g
d
ħ
u
L
d
ħ
u
;
(4)
J
rad
¼
e

n
top
2
þ
n
bottom
2

4
p
2
c
2
ð
N
E
g
=
ħ
u
2
exp

eV

ħ
u
kT

d
u
;
(5)
and
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,2015,
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886 |
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J
th
¼

n
top
2
þ
n
bottom
2

4
p
2
c
2
ð
N
E
g
=
ħ
u
2
exp


ħ
u
kT

d
u
:
(6)
where
e
is the unsigned charge on an electron,
L
is the wave-
length-dependent solar
ux in the Air Mass (AM)1.5 solar spec-
trum,
ħ
is an abbreviation for
h
/2
p
(with
h
being Planck's
constant),
u
is the frequency of the incident light,
n
top
and
n
bottom
are the refractive indices of the top and the bottom of the
tandem absorber,
T
and
V
are the operating temperature and the
operating voltage, respectively, and
E
g
is the band gap of the top
or bottom light absorber, as indicated by the appropriate
subscript.
Several approaches have been proposed to e
ff
ectively utilize
even highly optically absorbing electrocatalysts in solar-fuels
generators, including deposition of catalysts on the back side of
the structure to re
ect light back into the absorbers, deposition
of catalysts along the surfaces or at the bases of microwire
arrays to re
ect light into the internal volume of the light-
absorber structure, or deposition of catalysts in pre-determined
islands on planar photoelectrode structures to minimize
obscuration.
27
31
Any optical obscuration by the electrocatalysts
would lower all of the e
ffi
ciencies calculated herein by approx-
imately the ratio of transmitted light to the light re
ected
outside of the speci
c light-absorber structure of concern. A
more speci
c analysis of the variation of e
ffi
ciency with light
intensity has been performed separately for several speci
c
system geometries.
17
The numerical relationship between the current density and
voltage obtained from the Shockley
Queisser model was
tted
using the ideal diode relationship:
J
¼
J
th

J
0

exp

eV
g
kT


1

(7)
where
J
0
is the reverse saturation current density and
g
is the
diode ideality factor. In the sensitivity analysis, the value of
J
ph
was not changed for a given light absorber, because
J
ph
is given
by the relationship between the wavelength-dependent
absorption behavior of the semiconductor and the spectral
irradiance of incident sunlight, as expressed by eqn (4)
(6). In
contrast, the value of
J
0
was increased by as much as 21 orders of
magnitude from the Shockley
Queisser limit, to account for a
range of materials properties of the light absorbers of interest.
This variation in
J
0
produced lower open-circuit voltages for a
given light absorber at a given value of
J
ph
, with the relationship
between
J
0
and
V
oc
given explicitly by eqn (7).
Behavior of electrocatalysts, membrane separator and
solution electrolyte
The current density,
J
OER/HER
as a function of the overpotential,
h
, for the OER and HER can be described by the Butler
Volmer
equation:
32
J
OER
=
HER
¼
J
0
;
OER
=
HER

exp

a
a
;
OER
=
HER
F
h
RT


exp


a
c
;
OER
=
HER
F
h
RT

(8)
where
J
0,OER/HER
is the exchange
current density for the OER or
HER, respectively, and
a
a,OER/HER
and
a
c,OER/HER
are the anodic
and cathodic transfer coe
ffi
cients for the OER or the HER,
respectively. Note that use of the Butler
Volmer equation to
describe the overpotential of the electrocatalysts as a function of
current density produces a di
ff
erent overvoltage at each current
density in the operational system, as opposed to assuming a
xed voltage drop for a given set of light absorbers independent
of whether the system is operating at open circuit (no current
passed), at the light-limited current density, at the maximum
power point of the system, or with additional ohmic resistance
drops due to the cell design.
The exchange
current density for the OER or the HER is
dependent on temperature, and was calculated using:
J
0
;
T
;
OER
=
HER
¼
J
0
;
T
ref
;
OER
=
HER
exp

E
a
;
OER
=
HER
RT
ref

exp


E
a
;
OER
=
HER
RT

;
(9)
where
E
a,OER/HER
is the activation energy for the OER or HER,
respectively, and
J
0,
T
ref
,OER/HER
is the exchange
current density
for the OER or HER, respectively, at the reference temperature.
E
a,OER/HER
was set to 42 560 J mol

1
and 28 900 J mol

1
for
iridium oxide and platinum catalysts, respectively, in 1 M
H
2
SO
4
(aq).
33
The behavior of each electrocatalyst and of each anodic/
cathodic electrocatalyst system was described by reference to a
gure-of-merit,
h
10 mA cm

2
overpotential
, which speci
ed the overpotential
required by that electrocatalyst (or electrocatalyst system) on an
otherwise ideally nonpolarizeable electrode (or anode and
cathode combination) to provide a current density of 10 mA
cm

2
. This
gure-of-merit allowed for a concise description of
the relevant Butler
Volmer properties of the electrocatalysts
according to eqn (8) and (9).
The temperature dependence of the e
ff
ective transport
resistance,
R
e
ff
, was de
ned as:
R
eff
;
T
¼
R
eff
;
ref

1
þ
a
T

T
ref
;
(10)
where the reference temperature,
T
ref
, is 300 K and the coe
ffi
-
cient
a
was taken to be 0.019 K

1
,by
tting the experimental
data for 1.0 M sulfuric acid.
34
Based on eqn (1)
(10), a zero-dimensional (0-D) analysis of
the STH conversion e
ffi
ciency was obtained, in which the
tandem photoabsorbers, electrocatalysts, liquid electrolyte and
membrane separators were coupled in series and the optical
absorption, photo-carrier transport and ionic transport were
coupled in parallel. The electrode surfaces were assumed to be
isopotential surfaces, and the spatial inhomogeneity of the
current
density distribution along the electrodes was approxi-
mated by the use of a 0-D e
ff
ective transport resistance. Note
that while the 0-D load-line analysis captures the key perfor-
mance characteristics of an integrated photoelectrolysis system,
the detailed device construct and geometrical parameters, and
their in
uence on the current density and potential distribution
in an actual three-dimensional operating system, are not
elucidated in such an analysis.
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,876
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The 0-D current
voltage model could also be employed to
evaluate
h
STH
for a system constructed using a discrete photo-
voltaic device connected in series to a discrete electrolyzer (PV +
electrolyzer), in which the e
ffi
ciencies of the photovoltaic device
and of the electrolyzer were optimized independently. A
comparison between the dependence on temperature and illu-
mination intensity dependence of
h
STH
for an integrated pho-
toelectrochemical system and for a stand-alone PV + electrolyzer
system has been described previously.
17
The low resistive loss
due to a lower operating current density in the integrated
system, or
distributed internal electrolyzer
, especially at low
illumination intensities, and the enhanced kinetics and trans-
port at elevated temperatures in the integrated designs are the
main reasons that an integrated system outperformed a stand-
alone PV + electrolyzer system under the conditions evaluated in
that work.
Results and discussion
State-of-the-art component properties
(a) Electrocatalysts.
The polarization behavior for the
overall water-splitting process is dependent on the combined
interfacial kinetics of the HER and the OER catalysts.
32
A
reduction in the overpotential for the HER and/or for the OER
has been one of the major research goals of electrocatalyst
development.
21
Some of the most active electrocatalysts repor-
ted to date operate in aqueous alkaline media, including Ni
Mo
alloys for the HER (overpotential of 75 mV at 10 mA cm

2
with a
Tafel slope of 40 mV dec

1
) and (Fe
Ni)O
x
alloys for the OER
(overpotential of 280 mV at 10 mA cm

2
with a Tafel slope of 40
mV dec

1
).
35,36
In acidic aqueous solutions, the state-of-the-art
electrocatalysts for HER and OER contain noble metals and
metal oxides, such as Pt and IrO
x
, which operate at 55 mV and
270 mV overpotential at 10 mA cm

2
for the HER and OER,
respectively,
5,37
although recent work with transition-metal
phosphides has shown overpotentials for the HER that
approach that of Pt.
38
40
Recent benchmarking work
21
has
shown that in aqueous alkaline solutions, many active non-
noble metal electrocatalysts for the OER exhibit mutually
similar overpotentials, of between 350 mV and 430 mV, at an
operating current density of 10 mA cm

2
. In addition, under
acidic conditions, no reported active OER electrocatalyst is
stable under anodic operational conditions except for IrO
x
.
21
The total kinetic overpotential,
h
10 mA cm

2
overpotential
, used to charac-
terize the behavior of the electrocatalysts was the sum of the
overpotentials for the OER and HER at 10 mA cm

2
, and was
dependent on the exchange
current density and the Tafel
slopes for the OER and HER, all of which were varied system-
atically in this analysis. For example, the current
voltage rela-
tionship for the HER was
xed, and the exchange
current
density for the OER,
J
0,OER
, was varied from 1.1

10

2
mA cm

2
to 1.1

10

46
mA cm

2
. This procedure resulted in total elec-
trocatalyst overpotentials ranging from 194 mV to 1965 mV at
the current density of 10 mA cm

2
. The total overpotential at 10
mA cm

2
of current density was a concise, useful
gure-of-merit
used herein to di
ff
erentiate between, and identify, the various
di
ff
erent electrocatalyst combinations, but the actual operating
current densities of each tandem absorber/electrocatalyst
combination in the operating system of interest were calculated
individually for each system using the load-line analysis of eqn
(1). Because the total overpotential is the important system-level
quantity, the procedure used herein to designate and vary the
behavior of the electrocatalysts was general for variation in
either the exchange
current density of the OER or the HER, or
both.
(b) Light absorbers.
For light absorbers, a tandem struc-
ture can produce signi
cantly higher solar energy-conversion
e
ffi
ciencies than a single-junction system. The optimal solar-to-
hydrogen conversion e
ffi
ciency is highly dependent on the
combination of band gaps of the tandem light absorbers.
14,19
For instance, under 1 Sun illumination with an Air Mass (AM)
1.5 solar spectrum, the optimal top/bottom semiconductor
band-gap combination is 1.65 eV/0.95 eV, which could yield, at
the detailed-balance limit, a solar-to-hydrogen conversion e
ffi
-
ciency of 31.1% in a system using Pt and IrO
x
electrocatalysts
and an optimized system design that minimizes the solution
resistance (0.1 ohm cm

2
).
19
However, the discovery of stable and high-performing light-
absorber materials that are comprised of earth-abundant
elements and that have a band gap of

1.6
1.8 eV has proven
challenging. The reported energy-conversion e
ffi
ciency and
current
voltage performance of state-of-the-art light-absorber
materials for the top cell,
i.e.
, BiVO
4
, FeO
x
, and WO
3
, are far
below the S
Q limit. Additionally, the band gaps of these
materials are far from the ideal band gap for the top cell of a
system. For instance, state-of-the art WO
3
prepared by electro-
deposition or sputtering exhibits a solar energy-conversion
e
ffi
ciency of
#
1.3% in contact with 1 M H
2
SO
4
(aq).
41,42
The
misalignment between the conduction band of the WO
3
and the
Nernstian potential for the OER, as well as charge
carrier
recombination at the surface and in the bulk, result in an open-
circuit voltage, 650 mV, that is low considering the large band
gap of WO
3
(2.6
2.7 eV).
41,42
(c) System design space.
The detailed geometry of the cell
construct, as well as the choice of the solution electrolyte, also
can have a signi
cant impact on the overall solar-to-hydrogen
system e
ffi
ciency.
18
Targeted geometric parameters for various
types of cells, including a vapor-feed solar-driven water-splitting
system and a 10

solar concentrator-assisted water-splitting
system, have been explored in detail.
16,20
The resistive loss,
concentration overpotential and e
ff
ects of electrodialysis of
di
ff
erent electrolytes, including strong base/acid and bu
ff
ered
solutions has also been investigated.
43
When an optimal cell
con
guration and strongly acidic or alkaline electrolytes are
employed, the average resistive loss in the membrane separator
and solution electrolyte can be limited to less than 100 mV at an
operational current density of 10 mA cm

2
.
17,18
In this work, the
e
ff
ective transport resistance was set to 10 ohm cm

2
, which
resulted in 100 mV potential loss at 10 mA cm

2
. These resistive
losses were accounted for in the calculation of
h
STH
in this
study, along with the kinetic overpotential losses due to the
water-splitting reaction. The voltage losses were not
xed rela-
tive to the band gap regardless of the actual system operating
conditions,
14,44
but instead, as given by eqn (1)
(10), the voltage
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,2015,
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,876
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losses were explicitly a function of the operating voltage and
current, in conjunction with the current-dependent ohmic-
based voltage losses and kinetically based electrocatalyst over-
potential losses, in the speci
c system being evaluated.
The sensitivity analysis investigated herein is applicable to
several speci
c device designs, including a
closed-sandwich
design in which the photocathode and photoanode are assem-
bled back-to-back,
18
an
open-sandwich
design with suitable
spectral-splitting in which the photocathode and photoanode
are assembled side-by-side,
18
a one-dimensional
trough
design and two-dimensional
bubble-wrap
design for the
photoelectrochemical cells coupled to solar concentrators,
16
and a membrane-enclosed, vapor-feed design.
20
The analysis is
not applicable to device designs in which the geometric area of
the electrolyzing components is signi
cantly di
ff
erent from that
of the light absorbers.
(d) Membranes/separators.
Depending on the speci
c
device designs, the permeability and conductivity of the
membrane separator could impact the overall
h
STH
of the
device. Ion transport through the separator is necessary and
results in a resistive loss in the system. Nevertheless, many
highly conductive polymers,
e.g.
,Na
on (10 S m

1
), exhibit
minimal resistive loss at 10 mA cm

2
in optimized device
geometries.
17,18
Another primary function of a membrane
separator is to block the di
ff
usive and convective crossovers for
the product gases. In certain microstructured cell designs,
h
STH
is highly dependent on the permeability of the membrane
materials.
45
Through use of a thick membrane separator (50
m
m
to 100
m
m) and/or with an optimized cell geometry, the e
ffi
-
ciency loss due to product crossover can be negligible.
17,18,45
Optimal STH conversion e
ffi
ciency at di
ff
erent total
overpotentials
In the
one factor at a time
sensitivity analysis performed
herein, the performance that can be obtained for various
families of tandem light absorbers has been investigated in
detail, with the families of tandem light absorbers designated
either by operation at the S
Q limit or by containing various
levels of defects that will degrade the photovoltage by increasing
the
J
0
of the absorbers away from the S
Q limit. In this process,
for a given set of electrocatalysts (denoted by their total over-
potential at 10 mA cm

2
of current density,
h
10 mA cm

2
overpotential
,asa
concise
gure-of-merit descriptor, but not constrained to
operate at 10 mA cm

2
in the actual system of interest), the
band gaps of the tandem light absorbers were varied to ascer-
tain the optimally performing tandem light-absorber combi-
nation for a given set of OER and HER electrocatalysts.
Hence, for a given set of electrocatalysts, the analysis iden-
ti
ed the maximum system e
ffi
ciency,
h
STH,opt
, that could be
obtained through use of the set of light absorbers that were
identi
ed as optimal with those speci
c electrocatalysts. In
addition, for that same speci
c set of electrocatalysts, the
optimization process was repeated, and a separate tandem-
absorber combination was identi
ed to give the optimum
system e
ffi
ciency, but with the light absorbers having their
photovoltage degraded by a speci
ed amount from the S
Q
limit, as described by an increased exchange
current density
(and consequently decreased photopotential at constant
charge
carrier injection level) for this separate set of tandem
light absorbers. Thus, a di
ff
erent set of tandem light absorbers
produced optimal system e
ffi
ciencies for each speci
ed
combination of electrocatalysts and for each family of light
absorbers (as quanti
ed by the increase in
J
0
of the light
absorbers relative to the S
Q limit).
Note that this process produces a fundamentally di
ff
erent
outcome, and answers a fundamentally di
ff
erent question, than
evaluating the degradation in e
ffi
ciency of a speci
c set of
tandem light absorbers as a function of increases in the over-
potentials of the electrocatalysts. In the latter approach, the
optimum band-gap combination for a tandem structure is
identi
ed in the absence of any system losses, and then the
decrease in e
ffi
ciency is evaluated in response to increases in
assumed voltage losses in the system.
14,44
In such a situation,
modest increases in the electrocatalyst overpotential can
produce large decreases in the resulting system e
ffi
ciency,
especially when the tandem structure is designed to barely
provide su
ffi
cient photovoltage to drive the electrocatalysts at
near the light-limited current density during operation at
optimal performance. In practice, such higher overpotential
catalysts would instead optimally be utilized in conjunction
with light absorbers that themselves had higher band gaps, to
yield higher system e
ffi
ciencies by allowing for operation at or
near the light-limited current density with the speci
c set of
electrocatalysts of interest. The optimized e
ffi
ciency,
h
STH,opt
,of
the latter system would be lower than that of the former system,
due to the a slight decrease in the light-limited current density
arising from the required increase in band gaps of the newly
optimized tandem light absorbers, but the optimized e
ffi
ciency
would not be nearly as low as the e
ffi
ciency of a system in which
the tandem-absorber band gaps were
xed in the design and
implementation phases and thus did not drive the electro-
catalysts being used in that system at the highest possible
current densities during system operation.
The process used herein is speci
cally illustrated in Fig. 1a
d. Using the electrocatalytic performance of the state-of-the-art
electrocatalysts as described by the B
V relation (for an elec-
trocatalyst system described concisely by the
gure-of-merit
having a value of
h
10 mA cm

2
overpotential
¼
355 mV), the band-gap combi-
nation of the tandem photoabsorbers was optimized and yiel-
ded
h
STH,opt
at the S
Q limit for absorbers having a tandem
band-gap combination of 1.7 eV/1.0 eV. In this
photocathode +
photoanode
optimization process, for each combination of
light absorbers and electrocatalysts, a load-line analysis based
on two half-cell current
voltage characteristics was used, and
the intersection point described the operating current of the full
cell derived from these two half-cells. The green curves in Fig. 1a
represent the resulting current
voltage relation of the photo-
cathode and the photoanode, in which the operating current
density produced
h
STH,opt
¼
h
STH,a
¼
27.5%.
The electrocatalytic performance of the HER catalyst was
then
xed, and the overpotential of the OER catalyst was
increased by decreasing the exchange
current density
880
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(
h
10 mA cm

2
overpotential
¼
757 mV). As shown in black in Fig. 1a, the new
operating point that resulted from this increase in catalyst
overpotential produced a very large decrease in system e
ffi
-
ciency, to
h
STH,b
¼
7.1%. However, for this new set of electro-
catalysts, the original tandem light-absorber structure no longer
provides the band-gap combination that provides the highest
possible system e
ffi
ciency. When the band gaps of the tandem
system were reoptimized in response to the increased over-
potential of this new electrocatalyst system, with the constraint
that the absorbers were still performing at the S
Q limit, the
half-cell behavior in Fig. 1a in blue was obtained, and the
resultant operating point yielded
h
STH,opt
¼
h
STH,c
¼
22.4%. The
light-limited current density of these new tandem absorbers is
lower than the light-limited current density of the absorbers
that were used to obtain the curves in green (and yield operating
points a or b) in Fig. 1, because the band gaps of the new
optimally performing system were increased (and thus
J
ph
decreased for a given illumination intensity and spectral
distribution from the sun) relative to the band gaps of the
original system (in a and b). However, the system e
ffi
ciency with
the speci
ed electrocatalysts is much higher for the newly
optimized system, because the increased band gaps provide a
su
ffi
cient increase in photovoltage to overcome the increased
catalyst overpotentials, and therefore allow system operation at
point c, near the light-limited current density of the newly
optimized tandem light absorber combination, with band gaps
of 1.8 eV/1.2 eV. Reoptimization of the band gaps of the tandem
structure therefore allowed the design of a system with a much
higher system e
ffi
ciency for these degraded electrocatalysts
than the system e
ffi
ciency obtained by
xing the properties of
the tandem structure based on negligible system losses, and
then absorbing the entirety of any real system voltage losses
directly in the form of decreases to the resulting system
e
ffi
ciency.
In a subsequent step, the overall optimum system e
ffi
ciency
h
STH,opt
was recalculated for each speci
c electrocatalyst system
of interest, but with the constraint that the light absorbers were
degraded in performance from the S
Q limit by a speci
ed
increase in
J
0
. For example, for the original electrocatalyst
behavior corresponding to the blue half-cell curves in Fig. 1a,
the green curves in Fig. 1b described the half-cell characteristics
of the tandem structure in which
J
0
was increased by 10
21
relative to the values of
J
0
obtained from the S
Q limit. For this
speci
c combination of electrocatalysts, the optimal system
e
ffi
ciency was very low, corresponding to
h
STH,opt
¼
h
STH,d
¼
7.7%. Due to the low photovoltage of the degraded light
absorbers relative to the values of their band gaps, the optimal
system e
ffi
ciency for this set of electrocatalyst properties
required a very signi
cant increase in the band gap of the
absorbers, to values of 2.5 eV/1.9 eV, to drive the electrocatalysts
and thus produced low overall optimal system e
ffi
ciencies. For
these tandem light-absorber systems, the same increase in
Fig. 1
Analysis of the operating current density of solar-driven water-splitting cells using a photocathode + photoanode analysis (a and b) and a
tandem photoabsorber + overall loading curve analysis (c and d). The photoabsorbers performed at the S
Q limit in (a) and (c) and performed at
the reverse-saturation current density of 10
21
J
0
in (b) and (d).
This journal is © The Royal Society of Chemistry 2015
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,2015,
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electrocatalyst overpotential as that represented in Fig. 2a
produced operating point e in Fig. 2b, with a corresponding
decrease in e
ffi
ciency to
h
STH,e
¼
0.4%. Reoptimization of the
band gaps, however, produced a system having signi
cantly
higher e
ffi
ciencies, as represented by the intersection of the red
and the green curves in Fig. 1b at operating point f (
h
STH,op
¼
h
STH,f
¼
6.0%).
Adi
ff
erent approach, the
tandem photoabsorber + overall
loading curve
con
guration (Fig. 1c and d), was also employed
to obtain the
h
STH
of the system, which yielded identical results
to the half-cell load-line analysis depicted in Fig. 1a and b. In
Fig. 1c and d, the blue and the green curves represent the overall
water-splitting loading curves with
h
10 mA cm

2
overpotential
¼
355 mV and
h
10 mA cm

2
overpotential
¼
757 mV, respectively. The red curve represents the
current
voltage characteristic of the tandem photoabsorbers, in
which the band-gap combination was optimized (1.7 eV/1.0 eV)
for the blue loading curve. The resulting
h
STH,opt
¼
h
STH,g
was
27.5%, which corresponds to the operating current density at
point g. The
h
STH,h
decreased to 7.1%, which corresponds to the
operating point h, when the activity of the electrocatalysts
decreased (blue loading curve) without the reoptimization of
the band-gap combination. When the band-gap combination
was optimized (1.8 eV/1.2 eV) for the green loading curve, the
resulting
h
STH,opt
¼
h
STH,i
was increased to 22.4%, which
corresponds to the operating point i. The same trend was
observed in Fig. 2d, in which the quality of the tandem photo-
absorber was varied by changing the reverse-saturation current
density to 10
21
J
0
(
h
STH,j
¼
7.7%,
h
STH,k
¼
0.4% and
h
STH,l
¼
6.0%).
Fig. 2a plots
h
STH,opt
for the system design space of interest,
incorporating the optimized tandem-cell arrangement, as a
function of the behavior of various di
ff
erent combinations of
electrocatalysts. As described above, at each value of the total
overpotential, the entire suite of band-gap combinations for the
tandem cell was explored to identify the combination that
produced the optimum e
ffi
ciency,
h
STH,opt
, at the speci
ed total
system overpotential. In this process, the band gap of the top
light absorber was varied from 1.3 eV to 3.0 eV, and band gap of
the bottom light absorber ranged between 0.6 eV and 2.0 eV.
The numerical current
voltage characteristic of the light
absorbers in the tandem cell under the Shockley
Queisser (S
Q)
limit (blue curve) was obtained using the ideal photodiode
relationship. As shown in the top-most data set plotted in
Fig. 2a, for light absorbers operating at the detailed-balance
limit, the slope of
h
STH,opt
as a function of the total over-
potential,
D
h
STH
;
opt
D
h
10 mA cm

2
overpotential
;
was

0.01% mV

1
. Hence, decreases in
the total overpotential by 100 mV, from 400 mV to 300 mV,
would result in 1 percentage-point change in
h
STH,opt
. State-of-
the-art electrocatalysts in alkaline solution, such as Ni
Mo alloy
Fig. 2
(a) Optimal STH conversion e
ffi
ciency,
h
STH,opt
, at all band-gap combinations as a function of the electrocatalyst characteristics described
by the total electrocatalytic overpotential at 10 mA cm

2
for the hydrogen-evolution reaction (HER) and the oxygen-evolution reaction (OER).
The actual operating current densities for each system were obtained using a load-line analysis, as described in Fig. 1. The reverse-saturation
current densities for the photoabsorbers were swept from the Shockley
Queisser (S
Q) limit,
J
0
,to10
21
J
0
. (b)
h
STH,opt
as a function of the top
and bottom band-gap combinations when the reverse-saturation current density and the total overpotential at 10 mA cm

2
were set to
J
0
and
355 mV and (c)
J
0
and 959 mV and (d) 10
5
J
0
and 355 mV, respectively.
882
|
Energy Environ. Sci.
,2015,
8
,876
886
This journal is © The Royal Society of Chemistry 2015
Energy & Environmental Science
Communication
Published on 24 December 2014. Downloaded by California Institute of Technology on 30/04/2015 16:33:20.
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