ARTICLES
PUBLISHED ONLINE: 11 NOVEMBER 2012 | DOI: 10.1038/NMAT3477
Resonant light trapping in ultrathin films for
water splitting
Hen Dotan
1
, Ofer Kfir
2
, Elad Sharlin
1
, Oshri Blank
1
, Moran Gross
1
, Irina Dumchin
1
, Guy Ankonina
3
and Avner Rothschild
1
*
Semiconductor photoelectrodes for solar hydrogen production by water photoelectrolysis must employ stable, non-toxic,
abundant and inexpensive visible-light absorbers. Iron oxide (α-Fe
2
O
3
) is one of few materials meeting these requirements,
but its poor transport properties present challenges for efficient charge-carrier generation, separation, collection and injection.
Here we show that these challenges can be addressed by means of resonant light trapping in ultrathin films designed as optical
cavities. Interference between forward- and backward-propagating waves enhances the light absorption in quarter-wave or, in
some cases, deeper subwavelength films, amplifying the intensity close to the surface wherein photogenerated minority charge
carriers (holes) can reach the surface and oxidize water before recombination takes place. Combining this effect with photon
retrapping schemes, such as using V-shaped cells, provides efficient light harvesting in ultrathin films of high internal quantum
efficiency, overcoming the trade-off between light absorption and charge collection. A water photo-oxidation current density of
4 mA cm
−2
was achieved using a V-shaped cell comprising ∼26-nm-thick Ti-doped α-Fe
2
O
3
films on back-reflector substrates
coated with silver–gold alloy.
T
he efficient conversion of solar energy to hydrogen by
means of water photoelectrolysis is a long-standing challenge
with promise for solar energy conversion and storage in
the form of synthetic fuels (so-called solar fuels)
1,2
. Important
advances in studying water photoelectrolysis by semiconductor
photoelectrodes
3
have been achieved in the past four decades,
since the seminal report
4
on photoinduced water splitting using
TiO
2
photoanodes. Despite these advances and intensive research
and development efforts worldwide no photoelectrochemical
system for solar hydrogen production has met the required
performance benchmarks for efficiency, durability and cost.
Numerous photoelectrodes were examined, but most of them were
ruled out owing to poor stability or low efficiency
5,6
. α-Fe
2
O
3
(haematite) is one of few materials with a favourable combination
of stability in aqueous solutions, visible-light absorption, non-
toxicity, abundance and low cost
7–9
. With an energy bandgap of
2.1 eV, α-Fe
2
O
3
photoanodes can theoretically reach water photo-
oxidation current densities as high as 12.6 mA cm
−2
under air
mass 1.5 global (AM1.5G) solar irradiation conditions
10
, potentially
enabling a maximum solar to hydrogen conversion efficiency of
15.5% to be reached in an ideal tandem cell configuration
11
.
However, because of the low internal quantum efficiency (IQE),
only a quarter of the theoretical limit has been achieved by the best
α-Fe
2
O
3
photoanode reported so far
12
.
The low IQE of α-Fe
2
O
3
photoanodes has been attributed to
the slow water oxidation kinetics
13
and short diffusion length of
the photogenerated minority charge carriers (holes)
14
resulting
in significant loss due to electron–hole recombination. Extensive
efforts have been directed towards enhancing the water oxidation
kinetics using catalysts
7,9,12
, and reducing bulk recombination by
developing nanostructured architectures that decouple the charge
transport and optical path lengths
7–9,15
. Nanostructuring thick
1
Department of Materials Science and Engineering, Technion—Israel Institute of Technology, Haifa 32000, Israel,
2
Physics Department, Technion—Israel
Institute of Technology, Haifa 32000, Israel,
3
Photovoltaics Laboratory, Technion—Israel Institute of Technology, Haifa 32000, Israel.
*e-mail: avnerrot@technion.ac.il.
layers has been the main route to balance the trade-off between light
absorption and collection of photogenerated holes
8,9,15
. This trade-
off limits the solar energy conversion efficiency of semiconductors
with poor transport properties wherein the minority charge-
carrier collection length is smaller than the light penetration
depth
16
. Despite these efforts, state-of-the-art nanostructured
α-Fe
2
O
3
photoanodes still exhibit excessive bulk recombination
that consumes three quarters, or more, of the photogenerated
charge carriers. On the other hand, the injection yield of holes that
have reached the surface exceeds 90% under sufficiently high anodic
potentials
17
. Recent studies on thick layers
18,19
as well as ultrathin
films
20
confirm that the efficiency of α-Fe
2
O
3
photoanodes is
mainly limited by the collection of photogenerated holes at the
surface. Thus, reducing bulk recombination is the key to improving
the IQE of α-Fe
2
O
3
photoanodes—an important step towards
efficient, sustainable, durable and potentially inexpensive solar
hydrogen production.
Whereas the conventional approach for balancing photogen-
eration and collection of minority charge carriers at the surface
of α-Fe
2
O
3
photoanodes centres around nanostructured porous
thick layers (≥0.5 µm) of high surface area, here we show a
radically different approach in which compact flat ultrathin films
are designed as light trapping structures. Such films can be easily
produced using thin-film deposition methods, and they do not
have a high surface area that enhances surface recombination and
may lower the surface photovoltage—the driving force for pho-
toelectrochemical processes on semiconductor photoelectrodes
21
.
Instead of decoupling the optical and charge transport path lengths
we exploit the wave-nature of light propagation in subwavelength
structures to tailor the light intensity distribution inside the film,
amplifying the intensity close to the electrode/electrolyte interface.
This enables maximization of the absorption in regions where the
158 NATURE MATERIALS | VOL 12 | FEBRUARY 2013 | www.nature.com/naturematerials
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NATURE MATERIALS DOI: 10.1038/NMAT3477
ARTICLES
photogenerated minority charge carriers can reach the surface and
minimization of the wasted absorption in regions where they are
lost to recombination.
Ultrathin film α-Fe
2
O
3
photoanodes
The rationale for using ultrathin (<50 nm) film α-Fe
2
O
3
photoan-
odes stems from their high IQE compared with their thick-layer
counterparts
22
. This is demonstrated in Supplementary Fig. S1,
which shows that the charge separation and collection yield of
photogenerated holes at the surface of Ti-doped α-Fe
2
O
3
thin films
(Supplementary Fig. S2) increases with decreasing film thickness,
reaching 58±6% for the thinnest film (16±5 nm). This exceeds the
collection yield found in state-of-the-art nanostructured Si-doped
α-Fe
2
O
3
thick layers
17
by a factor of three, approximately, demon-
strating the potential advantage of ultrathin films of high crystalline
quality (see Supplementary Figs S4–S8). The salient problem is that
their optical density is too small. The thinnest film, that is the one
with the highest collection yield, is nearly translucent (see Supple-
mentary Fig. S2-C). Thus, effective utilization of ultrathin α-Fe
2
O
3
films requires special means to enhance the probability of light–
matter interaction in subwavelength structures. The standard ap-
proach for trapping light in thin film solar cells works only for films
much thicker than a half wavelength
23
. This is too thick for α-Fe
2
O
3
because of the small collection length of the photogenerated holes in
this material
9,13,14
. To address this challenge we employ a resonant
light trapping strategy that surpasses the classical limits of statistical
ray optics
24
, enabling efficient photon harvesting well below the
minimum film thickness required for the standard approach.
Resonant light trapping in ultrathin films
Our strategy employs optical cavities comprising ultrathin absorb-
ing films on reflective substrates serving as current collectors and
back reflectors that give rise to interference between the forward-
and backward-propagating waves, as illustrated schematically in
Fig. 1. This enhances the absorption by increasing the photon
lifetime in the film, reaching maximum absorption in the cavity
resonance modes. For normal incidence on an ideal cavity the first
resonance mode occurs in quarter-wave films, that is, when the film
thickness (d) is a quarter of the wavelength (λ) of the light inside
the film. We note that λ = λ
0
n
−1
2
, where λ
0
is the wavelength in
vacuum and n
2
is the refractive index of the film. The quarter-wave
condition takes into account the π phase shifts on reflection from
the surface of the film (x = 0) and from the film/substrate interface
(x = d), and another π phase shift on traversing the film forth and
back. Consequently, the first-order reflection is in anti-phase with
the higher-order reflections, as shown in Fig. 1, thereby suppressing
the intensity of the back-reflected light. Moreover, the light inten-
sity increases near the surface owing to constructive interference
between the forward- and backward-propagating waves. For other
conditions such as oblique light or optical cavities employing
metallized substrates with complex refractive indices the optimal
film thickness is smaller than a quarter-wave, providing another
degree of freedom for optimization.
The quarter-wave resonance condition is well defined for
monochromatic light, but our goal is to harvest as many photons
as possible from the incident sunlight in a broad spectral range
between the absorption edge of the absorber (λ
max
0
= 590 nm for
α-Fe
2
O
3
) and the fall-off of the sunlight spectrum (λ
min
0
= 300 nm).
Therefore, we should find the optimal film thickness for trapping
sunlight in this spectral range. Moreover, owing to the strong
dependence of the collection efficiency of photogenerated minority
charge carriers on the distance from the surface
25
we must take into
account not only how many photons are absorbed but also where
they are absorbed. The photocurrent density can then be calculated
by integrating the product of the photogeneration distribution,
which scales with the squared optical electric field strength
26
, and
Substrate
Reflective coating
n^
3
= n
3
+
iκ
3
n
2
+ iκ
2
n^
2
=
Absorbing film
n
1
Incident
light
Reflected light
x
0
d
2
π
πππ
46
…
Water
Figure 1 | Resonant light trapping in quarter-wave films. Schematic
illustration of the light propagation in a quarter-wave (d = λ/4, for normal
incidence) absorbing film on a back-reflector substrate. The different
colours represent the light intensity distribution across the film (red, high;
blue, low).
the IQE distribution across the film over the entire film thickness
and over the solar irradiance spectrum.
To calculate the light intensity distribution inside the film we
take the plane-wave solution of Maxwell’s electromagnetic wave
equation and tailor it to fit the boundary conditions of our system
with incident solar radiation, at AM1.5G conditions, striking the
optical stack illustrated in Fig. 1. From these solutions we obtain
analytical expressions (see Supplementary Equations S1–S3) for the
spectral photon flux profiles (the number of photons of wavelength
λ
0
reaching a distance x from the surface per unit time, unit area and
unit wavelength) I
λ
0
(λ
0
,x) for normal incidence on α-Fe
2
O
3
films
on ideally reflective, transparent or partially reflective metallized
substrates with complex refractive indices ˆn
3
= n
3
+ iκ
3
, where
n
3
and κ
3
are the refractive and attenuation indices, respectively.
The metallized substrates give rise to complex reflection coeffi-
cients at the film/substrate interface
27
, ˆr
23
= (ˆn
2
− ˆn
3
)(ˆn
2
+ ˆn
3
)
−1
.
By integrating I
λ
0
(λ
0
, x) we obtain the photon flux profiles,
I(x) =
R
λ
max
0
λ
min
0
I
λ
0
(λ
0
,x) dλ
0
, as a function of depth (x) inside the film.
Photon flux profiles predicted for Ti-doped α-Fe
2
O
3
films on ideally
reflective (ˆr
23
= −1), transparent (ˆr
23
= 0) and metallized substrates
coated with silver or platinum are shown in Fig. 2. Further profiles
for films on aluminium- or gold-coated substrates are presented
in Supplementary Fig. S26. The optical constants of the Ti-doped
α-Fe
2
O
3
films were measured by spectroscopic ellipsometry (see
Supplementary Fig. S11) and the constants for the metallized
substrates were taken from the ellipsometer database.
The predicted photon flux profiles for films on reflective
substrates exhibit a periodic dependence on the film thickness.
The first resonance mode of the ideal cavity is predicted to occur
at a film thickness of 43 nm, reaching the maximal intensity at
the surface. Partially reflective metallized substrates give rise to
smaller photon fluxes, due to absorption in the metal coating, and
the resonance modes are shifted to smaller film thicknesses due
to phase shifts larger than π at the film/substrate interface (see
Supplementary Fig. S25). The optical loss due to absorption in
the metal coating is low for silver and aluminium, but quite high
for platinum and gold. The first resonance mode is predicted to
occur at a film thickness of 20, 20, 24 or 30 nm for silver, gold,
platinum or aluminium coatings, respectively. Thus, the selection of
the reflective coating material influences the optimal film thickness.
All in all, considerably larger photon fluxes are predicted in
films, of the optimal thickness, on reflective substrates compared
with their counterparts on transparent substrates wherein the
photons have only one pass through the film and their flux
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© 2013 Macmillan Publishers Limited. All rights reserved
ARTICLES
NATURE MATERIALS DOI: 10.1038/NMAT3477
Depth (nm)
0 50 100 150 200
Depth (nm)
0 50 100 150 200
Depth (nm)
0 50 100 150 200
Depth (nm)
0 50 100 150 200
8.5
8.0
7.5
7.0
6.5
6.0
8.5
Log (photons cm
¬2
s
¬1
) Log (photons cm
¬2
s
¬1
)
Log (photons cm
¬2
s
¬1
) Log (photons cm
¬2
s
¬1
)
8.0
7.5
7.0
6.5
6.0
8.5
8.0
7.5
7.0
6.5
6.0
8.5
8.0
7.5
7.0
6.5
6.0
Film thickness (nm)
200
150
100
50
0
a
Film thickness (nm)
200
150
100
50
0
c
Film thickness (nm)
200
150
100
50
0
d
Film thickness (nm)
200
150
100
50
0
b
Figure 2 | Light intensity maps. a–d, Predicted photon flux profiles as a function of film thickness and depth from the surface into the film for Ti-doped
α-Fe
2
O
3
films on ideally reflective (a), transparent (b) and metallized substrates coated with silver (c) or platinum (d).
decreases exponentially with x according to Lambert’s law with no
dependence on the film thickness.
Figure 2 shows that in the first resonance mode high photon
fluxes are concentrated close to the surface. This is critical for
efficient collection of the photogenerated minority charge carriers,
enabling them to reach the surface and drive the water splitting
reaction before bulk recombination takes place. Furthermore, the
photon flux close to the film/substrate interface is suppressed in
films on ideally reflective substrates because of the π phase shift
on reflection from an ideal reflector
27
. This is expected to reduce
the loss due to backward injection of minority charge carriers to
the substrate, which has been identified as a major source of loss in
ultrathin α-Fe
2
O
3
photoanodes
28
.
To verify our model calculations we deposited Ti-doped α-Fe
2
O
3
films of different thicknesses between 8 and 155 nm on platinized
and, for comparison, fluorinated tin oxide (FTO)-coated glass sub-
strates (see Supplementary Fig. S2). The absorptance spectra, a(λ
0
),
of the specimens were obtained from reflection and transmission
measurements (Supplementary Fig. S12). The absorbed photon
flux was calculated using the formula
29
I
abs
=
R
λ
max
0
λ
min
0
I
Sun
λ
0
(λ
0
)a(λ
0
) dλ
0
,
where I
Sun
λ
0
is the solar irradiance spectrum at AM1.5G conditions.
The results are shown in Fig. 3 in terms of I
abs
and the photogen-
erated current density, J
pg
= qI
abs
, where q is the elementary charge.
The black squares show the absorption in the platinized specimens.
The model calculations, shown by the dashed line black curve,
nicely fit the experimental results. We note that the absorptance
obtained by these measurements includes contributions from both
the α-Fe
2
O
3
film and the platinized substrate, and we cannot extract
directly the net absorption in the α-Fe
2
O
3
film. Instead, we show
(full line black curve) the predicted absorption in the α-Fe
2
O
3
films,
obtained by integrating the product of the photon flux profiles in
Fig. 2d and the absorption coefficient of the films (Supplementary
Fig. S11) over the entire film thickness. Similar calculations for
films on ideally reflective (R = 1, red curve), transparent (R = 0,
blue curve) and metallized substrates coated with silver (green
curve), aluminium (grey curve) or gold (orange curve) are also
shown in Fig. 3. For the translucent FTO-coated specimens we
obtain the net absorptance in the Ti-doped α-Fe
2
O
3
films from
transmission and reflection measurements of coated and uncoated
specimens (see Supplementary Fig. S14). These results are shown by
the blue circles in Fig. 3.
The absorption in α-Fe
2
O
3
films on platinized substrates is
predicted to reach the first maximum at a film thickness of 36 nm
with a photogenerated current density of 5.1 mA cm
−2
, that is 40%
of the ultimate limit for α-Fe
2
O
3
(ref. 10). For comparison, the same
film would absorb approximately half the photons (2.8 mA cm
−2
) if
it were on a transparent substrate. Calculations for films on ideally
reflective substrates (red curve) show that a 47-nm-thick film would
reach a photogenerated current density of 8.9 mA cm
−2
, that is 71%
of the theoretical limit. This demonstrates the effectiveness of our
light trapping strategy, as the same film on a transparent substrate
yields only 3.4 mA cm
−2
. Thus, the photon harvesting yield can be
nearly tripled by replacing the ubiquitous transparent substrates
with suitable back reflectors. Similar calculations for films on silver,
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NATURE MATERIALS DOI: 10.1038/NMAT3477
ARTICLES
Optical gain
0
1
2
3
4
Film thickness (nm)
0 50 100 150 200
Film thickness (nm)
0 50 100 150 200
R
= 0
AI
Pt
R = 0
AI
Pt
R = 1
Ag
Au
R
= 1
Ag
Au
0
2
4
6
8
10
12
Photogenerated current density (mA cm
¬2
)
Absorbed photon flux (× 10
16
photons cm
¬2
s
¬1
)
0
1
2
3
4
5
6
7
8
Figure 3 | Sunlight absorption in α-Fe
2
O
3
films on back-reflector
substrates versus their counterparts on transparent substrates. Absorbed
photon flux and the corresponding photogenerated current density as a
function of film thickness for specimens comprising Ti-doped α-Fe
2
O
3
films on platinized (black squares) or FTO-coated substrates (blue circles).
The error bars represent the range of (estimated) systematic errors in the
measurements. The dashed curves show the predicted absorption in the
entire specimen, comprising contributions from both film and substrate;
the solid line curves show the predicted net absorption in the α-Fe
2
O
3
films. The inset shows the predicted optical gain, that is, the amount of
photons absorbed in α-Fe
2
O
3
films on different substrates divided by the
absorption in films of the same thickness on FTO-coated substrates.
aluminium- and gold-coated substrates are predicted to yield high
optical gains (see Fig. 3, inset), with a maximum gain of 4.2 for a
16-nm-thick film on a silver-coated substrate (green curve). It is
noteworthy that the rest of the photons that are not absorbed in the
α-Fe
2
O
3
film are not necessarily lost. The back-reflected photons
that escape can be collected using photon retrapping schemes such
as using V-shaped cells
30
, thereby further boosting the absorption.
From light trapping to water photo-oxidation
The photocurrent density, J
photo
, is a product of the photogeneration
rate per unit time and unit volume at distance x from the
surface, g (x), and the IQE distribution function, P(x), integrated
over the entire film thickness: J
photo
(d) = q
R
d
0
g (x)P(x)dx. The
photogeneration rate is a product of the spectral photon flux
distribution inside the film, I
λ
0
(λ
0
,x), and the absorption coefficient
of the absorber, α(λ
0
), integrated over the wavelength range
between the absorption edge and the fall-off of the sunlight
spectrum
16
: g (x) =
R
λ
max
0
λ
min
0
I
λ
0
(λ
0
,x)α(λ
0
)dλ
0
. P(x) is the probability
for the photogenerated minority charge carriers to separate from
the majority carriers, reach the surface and drive the water splitting
reaction. Only those carriers that reach the front surface of the
film and are forward injected to the electrolyte contribute to
the water splitting process, whereas those reaching the backside
of the film and being backward injected to the substrate reduce
the photocurrent. Backward injection to the substrate may occur
by interfacial recombination with charge carriers of the opposite
charge arriving from the substrate (that is, the back electrode).
We designate by Φ the probability for charge separation and
transport in the forward direction, that is, minority charge carriers
going towards the surface. The collection probability of minority
charge carriers generated at a distance x from the surface scales
exponentially with −x/L, where L is their collection length
25
.
Designating by
→
P
F
the probability for forward injection to the
electrolyte, that is, the probability for minority charge carriers
that have reached the surface to drive the desired electrochemical
reaction, the fraction of photogenerated minority charge carriers
¬0.2
0.0
0.2
0.4
0.6
200
150
100
50
0
0 50 100 150 200
Depth (nm)
Film thickness (nm)
P (x)
Figure 4 | Internal quantum efficiency map. The predicted IQE distribution
inside the film as a function of film thickness and depth for α-Fe
2
O
3
films
with Φ = 0.75,
→
P
F
=
←
P
B
= 0.9 and L = 20 nm.
that end up with a positive contribution to the photocurrent is
→
P
F
Φe
−x/L
. Likewise, the fraction of their counterparts ending up with
a negative contribution due to backward injection to the substrate
is
←
P
B
(1 − Φ)e
−(d−x)/L
, where
←
P
B
is the probability for backward
injection. All in all, P(x) =
→
P
F
Φe
−x/L
−
←
P
B
(1 − Φ)e
−(d−x)/L
. We
note that this expression can be derived from the constituent
equations of solar cells
31
.
→
P
F
,
←
P
B
,L and Φ depend on the doping level, preparation and
operation conditions of the photoelectrode. Figure 4 shows P(x) as
a function of d and x for Φ = 0.75,
→
P
F
=
←
P
B
= 0.9 and L = 20 nm.
These values were found to fit quite well the photocurrent densities
obtained with our Ti-doped α-Fe
2
O
3
films on platinized substrates,
and they are within range of the expected values
13,17,32
. P(x) reaches
more than 60% close to the surface but it decays exponentially to
near zero values deeper than ∼20 nm from the surface, reaching
negative values close to the interface with the substrate.
Taking the product of g (x), obtained using the calculated photon
flux profiles in Fig. 2 and the measured absorption coefficient
of our films (Supplementary Fig. S11), and P(x) from Fig. 4 we
obtain the predicted photocurrent density per unit volume profiles,
dJ
photo
/dx = qg (x)P(x), for films on ideally reflective, transparent
or metallized substrates, as shown in Fig. 5. These profiles show
that mainly the front region down to ∼20 nm from the surface
contributes to the photocurrent. The rest of the film is inactive, for
the most part, owing to bulk recombination, whereas the backside
of the film has a negative contribution due to backward injection to
the substrate. The advantage of our optical cavity design is clearly
demonstrated by the hotspots of high photocurrent density close to
the surface of films whose thickness is close to the optimal thickness
for the first resonance mode. The highest photocurrent densities
are predicted for the ideal cavity, which is also effective in reducing
the backward injection to the substrate by suppressing the light
intensity close to the film/substrate interface (see Fig. 2a). Films on
partially reflective metallized substrates also exhibit hotspots of high
photocurrent densities, but the hotspots become weaker in going
from highly reflective metals such as silver to poorly reflective ones
such as platinum. We also note that the calculations suggest that the
metallized substrates do not reduce the backward-injection loss as
effectively as their ideally reflective counterparts.
The photocurrent density per unit area, J
photo
, is calculated by
integrating the photocurrent density per unit volume over the
entire film thickness. Figure 6a shows the predicted photocurrent
density as a function of film thickness for α-Fe
2
O
3
films on
different substrates, assuming ideal forward-injection conditions
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ARTICLES
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Film thickness (nm)
Depth (nm)
0 50 100 150 200
Depth (nm)
0 50 100 150 200
Depth (nm)
0 50 100 150 200
Depth (nm)
0 50 100 150 200
200
150
100
50
0
a
Film thickness (nm)
200
150
100
50
0
Film thickness (nm)
cd
Film thickness (nm)
150
100
50
0
b
¬0.05
(mA cm
¬2
nm
¬1
)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
¬0.05
(mA cm
¬2
nm
¬1
)
(mA cm
¬2
nm
¬1
)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
¬0.05
0.00
0.05
0.10
0.15
0.20
0.25
0.30
¬0.05
(mA cm
¬2
nm
¬1
)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
200
200
150
100
50
0
Figure 5 | Photocurrent distribution maps. a–d, Predicted photocurrent density distribution maps as a function of film thickness and depth for α-Fe
2
O
3
films on ideally reflective (a), transparent (b) and metallized substrates coated with silver (c) or platinum (d). Further profiles for aluminium- and
gold-coated substrates are presented in Supplementary Fig. S27.
(that is, Φ = 1 and
→
P
F
= 1). Such conditions may be realized
using sufficiently high potentials
17
and selective transport layers to
block the backward injection to the substrate
33
. Films on reflective
substrates are predicted to yield maximum photocurrents close to
the first resonance modes of the respective optical cavities. The
maxima are quite narrow and therefore the film thickness must be
precisely tuned to achieve the optimal performance, as an offset
of just a few nanometres significantly decreases the photocurrent.
A maximum of 4.8 mA cm
−2
is predicted for a 43-nm-thick
film on an ideally reflective substrate (red curve). This value
exceeds the record obtained with the best α-Fe
2
O
3
photoanode
reported so far
12
, demonstrating the potential advantage of our
approach. Photocurrent densities of 4.6, 4.3, 3.1 and 2.9 mA cm
−2
are predicted for 22-, 31-, 24- and 29-nm-thick α-Fe
2
O
3
films
on silver-, aluminium-, gold- and platinum-coated substrates,
respectively. The predicted photocurrent gain with respect to films
of the same thickness on transparent substrates is shown in the
inset of Fig. 6a. Optical cavities comprising ultrathin α-Fe
2
O
3
films are predicted to exhibit considerable gains reaching 3.6, 2.8,
2.3 and 2.0 for 14-, 28-, 18- and 24-nm-thick films on silver-,
aluminium-, gold- or platinum-coated substrates, respectively,
whereas the gain for films on ideally reflective substrates reaches 2.9
for a 42-nm-thick film.
To verify our model calculations the photocurrent density
of Ti-doped α-Fe
2
O
3
films on platinized or, for comparison,
FTO-coated substrates was measured in a 1 M NaOH solution
under 100 mW cm
−2
white-light illumination. Figure 6b shows
the photocurrent density, measured at an applied potential of
1.4 V against the reversible hydrogen electrode (V
RHE
), plotted as
a function of the film thickness. Further results are shown in
Supplementary Figs S15–S17. The photocurrent density reached a
maximum of 1.39± 0.03 mA cm
−2
for a 26± 2-nm-thick Ti-doped
α-Fe
2
O
3
film on a platinized substrate, 2.6 times higher than
the photocurrent density obtained with a film of about the same
thickness (32 ± 8 nm) on an FTO-coated substrate. Moreover, this
ultrathin film outperformed any of its counterparts on FTO-coated
transparent substrates, including much thicker films. These results
clearly demonstrate the advantage of our light trapping scheme,
even though these proof-of-concept tests were carried out with
structures far from the optimal design because of the high optical
loss due to absorption in the platinum coating as well as other losses
as described in the following.
The experimental results in Fig. 6b were fitted with model
calculations assuming L = 20 ± 2 nm, consistent with other
reports
13,32
, and taking
→
P
F
×Φ and
←
P
B
×(1 − Φ) as fitting
parameters. All the other parameters were obtained from optical
measurements of the specimens (Supplementary Fig. S11). An
excellent agreement was obtained with
→
P
F
×Φ = 0.70 ± 0.05 and
←
P
B
×(1 − Φ) = 0.25 ± 0.05, validating our model calculations.
The fitting results are consistent with
→
P
F
= 0.95 ± 0.05, close to
the injection efficiency of our films as measured by the method
described in ref. 17,
←
P
B
= 1±
0
0.3
, and Φ = 0.74 ± 0.07. Thus,
a significant fraction of the potentially achievable photocurrent
predicted for these structures is lost for backward injection to the
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