Microwave reflectance studies of photoelectrochemical kinetics at semiconductor electrodes. 3. Photoelectrochemical reduction of Ru(NH3)63+ at p-Si

Article abstract of DOI:10.1021/jp0311963

The reduction of Ru(NH₃)₆³⁺ at illuminated p-Si in ammonium fluoride solutions was studied by a light modulated microwave reflectivity method. Ru(NH₃)₆³⁺ was chosen as an example of a one electron outer sphere redox system that is expected to exhibit facile electron transfer kinetics. The results of the microwave measurements show that the transfer of photogenerated electrons to Ru(NH₃)₆³⁺ at an illuminated p-Si electrode is very slow compared to an order of magnitude estimate for outer sphere electron transfer. It is concluded that the reduction of Ru(NH₃)₆³⁺ does not involve direct electron transfer from the conduction band but is instead mediated by photogenerated hydrogen states.

Full text of DOI:10.1021/jp0311963

2660
J. Phys. Chem. B 2004, 108, 2660-2665
Microwave Reflectance Studies of Photoelectrochemical Kinetics at Semiconductor
3
+
Electrodes. 3. Photolectrochemical Reduction of Ru(NH3)6 at p-Si
Laurence M. Peter* and Shin Ushiroda†
Department of Chemistry, UniVersity of Bath, Bath BA2 7AY, United Kingdom
ReceiVed: October 28, 2003; In Final Form: December 16, 2003
3
+
The reduction of Ru(NH
modulated microwave reflectivity method. Ru(NH
sphere redox system that is expected to exhibit facile electron transfer kinetics. The results of the microwave
3
)
6
at illuminated p-Si in ammonium fluoride solutions was studied by a light
3
+
3
)
6
was chosen as an example of a one electron outer
3+
measurements show that the transfer of photogenerated electrons to Ru(NH
)
3 6
at an illuminated p-Si electrode
is very slow compared to an order of magnitude estimate for outer sphere electron transfer. It is concluded
3+
that the reduction of Ru(NH
3
)
6
does not involve direct electron transfer from the conduction band but is
instead mediated by photogenerated hydrogen states.
-5
Introduction
(LMMR) technique.3 The present paper describes the appli-
cation of LMMR to study the photoreduction of ruthenium(III)
hexaammine at illuminated p-Si under conditions where the
silicon surface is free of oxide. This system was chosen to test
the expectation that rapid capture of photogenerated electrons
Investigation of the kinetics of electron transfer at illuminated
semiconductor electrodes is complicated by the fact that only
limited information is available from the measured photocurrent.
In the case of a semiconductor electrode biased into strong
depletion, photogenerated carriers are swept to the interface by
the electric field in the space charge region, and the measured
current is simply proportional to the light intensity. Transient
photocurrent measurements in the photocurrent saturation region
at high band bending also contain no information about the rate
constants for electron transfer because it is not possible to
distinguish between the displacement current and the transfer
of electrons across the interface. Information about the kinetics
of interfacial electron transfer can be obtained by studying the
transient or periodic photocurrent response in the photocurrent
onset region at lower bias, where recombination competes with
electron transfer. An example of a technique that exploits this
competition is intensity modulated photocurrent spectroscopy
3
+
by Ru(NH3)6 should prevent the buildup of electrons and
hence effectively quench the microwave response completely,
as predicted by our recent theoretical modeling. In fact, the
4
study revealed that the microwave response is not quenched by
3
+
the presence of Ru(NH3)6 . Consequently, it proved possible
to measure the rate constant for electron transfer, which turns
out to be many orders of magnitude smaller than expected. The
reasons for this surprising result are explored.
Theory
Definition and Estimation of Rate Constants. Discussion
of electron transfer at semiconductor electrodes is complicated
by the fact that three different rate constants are commonly used.
The rate of electron transfer is first order in the concentration
of electrons or holes in the semiconductor and also first order
in the concentration of redox species in the electrolyte. The
starting point for the discussion is therefore the second-order
heterogeneous rate constant for interfacial electron transfer, k2
(cm s ). If the concentration of redox species in the interfacial
region is assumed to be constant, a pseudo-first-order hetero-
geneous rate constant for electron transfer, k (cm s ), can be
defined that is analogous to the rate constant used to describe
electron transfer at a metal contact. Finally, a phenomenological
(IMPS), which involves measuring the frequency-dependent
magnitude and phase of the photocurrent response to a sinuo-
soidally modulated photon flux.1,2 More recently, we have
developed an analogous modulation technique that involves
measuring the periodic change in microwave reflectivity caused
4
-1
by intensity modulated illumination.3-5 The use of microwave
reflectivity measurements for the characterization of semicon-
ductor electrodes was pioneered by Tributsch and co-workers.
-
1
6
-8
tr
The method is sensitive to changes in the conductivity of a
semiconductor sample brought about by illumination or changes
in applied voltage. In the case of photoelectrochemical reactions,
minority carriers are driven to the surface, where they may
accumulate in substantial concentrations if electron transfer to
redox species is a slow process. The buildup and decay of these
charge carriers when the illumination is switched on and off is
determined by the rate of interfacial charge transfer. The
accumulation of photogenerated carriers near the interface is
not evident in the current transient, but it can be followed by
-
1
10
electron transfer rate constant, k1 (s ), can be defined by
introducing the concept of an effective surface electron or hole
density (cm ). The relationship between the three rate constants
can be expressed in the form
-2
ktr
k2N
redox
k1 )
)
) VthσredoxNredox
(1)
δ
δ
9
Here δ is a nominal reaction layer thickness or tunneling length
for electron transfer at the interface, Vth is the thermal velocity
of minority carriers, and σredox is the capture cross section for
the reaction of minority carriers with redox species present with
the change in conductivity detected by microwave reflectance.
This is the basis of the light modulated microwave reflectivity
†
Current address: Department of Chemistry, Colorado State University,
Fort Collins, Colorado 80523.
1
1
a volume density of Nredox in the solution.
1
0.1021/jp0311963 CCC: $27.50 © 2004 American Chemical Society
Published on Web 01/27/2004

Photolectrochemical Reduction of Ru(NH3)63+ at p-Si
J. Phys. Chem. B, Vol. 108, No. 8, 2004 2661
Figure 2. Solid line: dependence of the change in mean conductivity
〈
∆σ〉 on the rate constant for interfacial charge transfer, calculated from
the excess carrier profiles in the photocurrent saturation region (see
ref 4 for details). Open circles: values of the microwave reflectance
change ∆R
M
calculated using a multilayer model and the Fresnel
Figure 1. Energy scheme for capture of photogenerated electrons from
the conduction band of low-doped p-Si in ammonium fluoride
electrolyte (pH 3.0). Note that the overlap between conduction band
states and Ru(III) states is expected to facilitate rapid electron transfer.
equations. Comparison of the two plots allows calculation of the
14
-2 -1
sensitivity factor, S. Incident photon flux (626 nm) 10 cm
that the microwave response will be difficult to measure at this light
intensity if ktr > 1 cm s
s . Note
-1
.
small in the presence of Ru(NH3)63+, and the time constant for
the transient and periodic responses should be correspondingly
short (on the submicrosecond scale). The present study has
shown that neither of these predictions is correct.
The Ru(III)/Ru(II) hexaammine redox system is relatively
substitution inert, and the homogeneous self-electron self-
1
2
exchange rate constant of the couple at 298 K is reported to
4
-1 -1
be 2.2 × 10 M s , which is consistent with values of the
-
1
standard heterogeneous rate constant of the order of 1 cm s
Origin and Magnitude of the Microwave Response. The
theoretical basis for microwave reflectivity measurements and
LMMR has been reviewed recently, and the results of numerical
calculations of the microwave reflectivity response for low-
doped silicon of the type used in the present experiments have
at metal electrodes. These rate constants correspond to a value
of about 0.9 eV for the reorganization energy for outer sphere
electron transfer from a semiconductor electrode. The standard
potential of the couple places the redox Fermi level close to
the center of the band gap of silicon in fluoride solutions at pH
4
been presented. Only the main points will be summarized here.
3, so that rapid transfer of photogenerated electrons from the
The microwave reflectivity change ∆RM brought about by
perturbation of a semiconductor electrode by light can be related
linearly to the change in mean conductivity, 〈∆σ〉, by
conduction band of p-Si to Ru(III) should be possible, as
illustrated by Figure 1.
The electron transfer rate constant k2 can be expressed in the
form13
∆Pr
∆Pr
∆
R )
) RM
) S〈∆σ〉 )
M
Pi
Pr
k ) Vκ κ
n el
(2)
2
Sq
d
d
∫
[µ ∆n(x) + µ ∆p(x)] dx (4)
n p
0
where κn is the (dimensionless) nuclear term related to the
4
Franck Condon factor for the process, and κel (units cm ) is
Here Pi and Pr are the incident and reflected microwave power,
respectively, ∆Pr is the change in reflected microwave power,
RM is the unperturbed microwave reflectivity, S is a sensitivity
factor, d is the sample thickness, q is the elementary charge,
determined by the electronic coupling between the reactants.
The nuclear term is given by the well-known expression
0
2
(
∆G ′ + λ)
∆n(x) and ∆p(x) are the position dependent excess electron and
κ ) exp -
(3)
n
[
]
4λkBT
hole densities resulting from illumination, and µn and µp are
the electron and hole mobilities. The density profiles of
photogenerated electrons and holes can be calculated for given
conditions (intensity and wavelength of illumination and rate
constant for interfacial electron transfer). Integration of the
profiles then gives the change in mean conductivity and hence
0
where ∆G ′ is the driving force for interfacial electron transfer
and λ is the reorganization energy. On the basis of this approach,
1
4,15
Royea et al.
have estimated an upper limit for the second-
order rate constant k2 for outer sphere reactions at semiconductor
-
17
4
-1
5
electrodes in the range (1-10) × 10 cm s . In the present
the microwave response. S can be measured or it can be
0
case, using ∆G ′) -0.5 eV (cf. Figure 1) and λ ) 0.9 eV for
the ruthenium hexaammine couple gives an estimate of 0.18
calculated using a filter stack model to represent the carrier
4
profiles.
13
for κn. On the basis of measurements of charge transfer at n-InP
Figure 2 indicates how the magnitude of the microwave
reflectivity response for the experimental conditions used in this
study is expected to decrease as the rate constant for electron
transfer increases (further details are given in ref 4). Because
and n-Si,16 Lewis and co-workers have estimated κel to be of
-
30
4
-1
13 -1
the order of 10 cm s , so that setting V ) 10
s
gives k2
-
18
4 -1
≈
2 × 10
cm s for electron transfer from the conduction
3+
3+
-2
-6
band of p-Si to Ru(NH3)6 at pH 3. For [Ru(NH3)6 ] ) 10
M and δ ) 10 cm, this value of k2 corresponds to ktr ) 12
cm s and k1 ) 1.2 × 10 s . As the next section shows, this
order of magnitude estimate of the electron transfer rate
constants predicts that the microwave response should be very
the practical detection limit lies around ∆RM ) 10 , it is clear
-
7
that the microwave response should become undetectable once
-
1
8
-1
-1
the rate constant ktr exceeds 1-10 cm s .
Periodic Microwave and Photocurrent Response to In-
tensity Modulated Illumination. The time constant for the

2662 J. Phys. Chem. B, Vol. 108, No. 8, 2004
Peter and Ushiroda
Figure 3. Comparison of LMMR and IMPS responses for the case
where half of the photogenerated electrons are lost by surface
recombination, i.e., k ) krec. It is important to note that the diameter
1
of the LMMR semicircles increases as the band bending increases,
whereas the IMPS semicircles become progressively smaller until all
Figure 4. Normalized photocurrent voltage plots for p-Si in ammonium
fluoride solution, pH 3.0 containing 0.33 mM Ru(NH3)63 . The values
of the saturation photcourrent are shown. The displacement evident at
the highest light intensity is attributed to exceeding the mass transport
+
information is lost when the photocurrent saturation condition (krec
) is reached.
,
k
1
3+
limited rate for reduction of Ru((NH
)
3 6
, leading to accumulation of
microwave response to step and sinusoidal illumination profiles
photogenerated electrons at the surface of p-Si.
4
is given by
5
-
1
detail elsewhere. Boron doped p-Si (111) samples (ITME, 10-
τ ) (k + k )
(5)
1
rec
1
4
-3
2
0 Ω cm doping density 7 × 10 cm ) were used in the
-
1
where k1 and krec are first-order rate constants (s ) for electron
transfer and electron-hole recombination, respectively, that arise
from a phenomenological formulation of kinetics in terms of
measurements. Samples were etched for 30 s in flowing CP-
4A solution (3:5:3 by volume 48% HF: concentrated HNO3:
100% CH COOH) and rinsed with Milli-Q water. Ohmic contact
3
-
2
the nominal surface concentrations (cm ) of electrons and
was made around the periphery of the wafer using Ga|In
holes.10 As we have shown elsewhere,
3-5
values of k1 and krec
eutectic. The 1 M fluoride (pH 3) background electrolyte
can be obtained by analysis of the light modulated microwave
reflectivity (LMMR) response. The real and imaginary com-
ponents of the normalized LMMR response are given by
solution consisted of 0.5 M NH F (40%, BDH, Aristar), 0.15
4
M NH Cl (Aldrich, ACS reagent), and 0.5 M HF (48%, BDH,
4
AnalaR). Hexaammine ruthenium(III) chloride (98%, Aldrich)
was used to prepare the solutions with Ru(III) concentrations
in the range 0.1-1.0 mM. The flow cell was designed to
continuously refresh the solution layer above the illuminated
p-Si electrode.The degassed electrolyte was circulated continu-
ously through the PTFE flow cell via a gravity-fed reservoir
by a nitrogen lift pump.
k (k + k )
1
S
1
1
rec
Re(∆R ) )
M
2
2
(
k + k ) + ω
1 rec
1
S
k1ω
Im(∆R ) ) -
(6)
2
M
2
(
k + k ) + ω
1 rec
Measurements were made in three-electrode PTFE flow cell
equipped with Pt wire counter and Ag/AgCl reference elec-
trodes. Intensity-modulated photocurrent spectroscopy (IMPS)
and light-modulated microwave reflectance (LMMR) measure-
ments were performed by illuminating the sample with a red
light emitting diode (LED: λ ) 626 nm). Sinusoidal intensity
modulation of the LED output was achieved by using a current
driver programmed by the lock-in amplifier. The current and
microwave responses were detected simultaneously by two
synchronized lock-in amplifiers (Stanford Research SR830). A
Stanford Research SR560 low-noise preamplifier was used to
amplify the signal from the microwave detector. The illumina-
tion intensity was controlled using a set of calibrated Schott
neutral density (NG) filters. Light intensities were measured
with a calibrated silicon diode. The frequency-dependent light-
modulated microwave and photocurrent responses were fitted
using a nonlinear least squares program (Solartron Z-View).
The flatband potential of the p-Si samples was determined from
iMl l uo mt t i nS ac t hi oo nt t. ky plots to be +0.2 V vs Ag|AgCl prior to
where ω ) 2πf. The LMMR response is a semicircular plot in
the complex plane with a low-frequency intercept determined
by the ratio k1/(k1 + krec), a high-frequency intercept of zero
and a minimum located at ωmin ) 1/(k1 + krec). It is worth noting
that in the absence of recombination (krec f 0), the normalized
plot has a low-frequency intercept of unity. By contrast, the
corresponding normalized IMPS response is described by the
1
,2
expressions
2
jphoto ω + k (k + k )
1
1
rec
Re
)
2
2
qI0
(k + k ) + ω
1
rec
jphoto
ωkrec
Im
)
(7)
2
2
qI0
(k + k ) + ω
1
rec
Here I0 is the absorbed photon flux. (For simplicity, it is assumed
that all photoexcited minority carriers are collected in the space
charge region.) The complex plane IMPS plots are characterized
by a low-frequency intercept determined by the ratio k1/(k1 +
krec) and a high-frequency intercept of unity. The difference
between the IMPS and LMMR responses is illustrated in Figure
Results and Discussion
3
for the particular case where k1 ) krec; i.e., the dc photocurrent
is half of the saturation value.
“Steady State” Photocurrent and Microwave Responses.
Figure 4 shows normalized photocurrent voltage plots for p-Si
Experimental Section
3+
in a pH 3 fluoride solution containing 0.33 mM Ru(NH3)6
.
Measurements were performed with a Ka-band microwave
system and an experimental setup that have been described in
At the two lowest light intensities, the photocurrent onset occurs
close to the flatband potential (0.2 V vs Ag|AgCl). By contrast,

Photolectrochemical Reduction of Ru(NH3)63+ at p-Si
J. Phys. Chem. B, Vol. 108, No. 8, 2004 2663
Figure 6. Normalized IMPS response plots at the potentials shown.
3+
The electrolyte contained 0.33 mM Ru(NH
3
k
3
)
6
. Saturation photocurrent
.6-3.9 µA cm . The intercepts and ωmin values were used to obtain
1
and krec as a function of potential.
-
2
Figure 5. Normalized microwave reflectance plots obtained by dividing
the microwave signal by the saturation photocurrent at each intensity
(
values shown). The higher response observed for the highest light
intensity is interpreted as evidence for the accumulation of photo-
generated electrons due to the onset of mass transport limitation in the
3
+
reduction of Ru(NH
3
)
6
(concentration 0.33 mM).
at the highest light intensity, the photocurrent onset is shifted
to more negative potentials. This indicates that the photocurrent
in this case is larger than the limiting current for the mass
transport controlled reduction of Ru(NH3)63+, so that hydrogen
evolution occurs giving rise to surface charging.5
Figure 7. Normalized LMMR response plots at the potentials shown.
3+
The electrolyte contained 0.33 mM Ru(NH
3
)
6
. Saturation photocurrent
.6-3.9 µA cm . The intercepts and ωmin values were used to obtain
1
and krec as a function of potential (see Figure 8).
The corresponding normalized plots of the photoinduced
microwave response are shown in Figure 5. It can be seen that
the normalized microwave response is independent of light
intensity at the lowest two illumination levels, but increases
significantly at the highest light intensity. This is consistent with
exceeding the mass transport controlled limiting current for
Ru(III) reduction in the flow cell configuration, so that hydrogen
evolution also occurs. To avoid mass transport limitations,
LMMR and IMPS measurements were carried out at low light
intensities, where the photocurrent in the plateau region was
-
2
3
k
-
2
3
.6-3.9 µA cm .
Comparison of the normalized magnitude of the measured
microwave response for the two lowest light intensities with
values predicted by numerical simulation as a function of ktr
-
3
-1
-1
(
cf. Figure 2) suggests that ktr ≈ 10 cm s , not ≈ 1 cm s
as estimated for an outer sphere electron transfer process. In
other words, the microwave response is much larger than
expected, which indicates that electron transfer to redox species
in solution is slow. (Note that Figure 1 shows the results of a
calculation for I0 ) 1014 cm s . The simulations showed that
the microwave response should be a linear function of light
intensity, so that normalization is straightforward.)
2 -1
LMMR and IMPS. Figures 6 and 7 contrast the LMMR
and IMPS plots obtained using a solution containing 0.33 mM
Ru(III). It can be seen that the diameters of the LMMR plots
become larger as the electrode potential is made more negative,
increasing the band bending in the p-Si. On the other hand, the
IMPS semicircles become smaller in diameter as the band
bending is increased, until only a point on the real axis is
observed in the limiting photocurrent region. It is noted here
that the low-frequency data for the IMPS plots converge on
the real axis, whereas in the case of the LMMR plots, the low-
frequency response (not shown in Figure 7) tends to broaden
along the real axis, suggesting an additional slow component.
The semicircular complex plane LMMR plots were fitted to
obtain values of the low-frequency intercept and values of ωmin.
These were used to obtain k1 and krec as a function of potential.
Figure 8. Potential dependence of k
data shown in Figure 8. The inset shows the potential dependence of
rec in a double logarithmic representation. Note that the rate constant
for interfacial charge transfer is independent of potential over the entire
range, whereas krec varies due to the change in hole density with
potential.
1
and krec derived from the LMMR
k
Figure 8 shows the result. Over the range of potential investi-
-
1
gated, k was found to be remarkably constant (230 ( 5 s ),
1
whereas k varied exponentially with potential with a slope of
rec
-
1
(180 mV) , as shown in the inset to Figure 7. Because surface
recombination in p-Si is first order in the concentration of holes,
-
1
one would expect a slope of (59 mV)
for krec if the
semiconductor|electrolyte junction behaved ideally and recom-
bination occurred at the surface. The fact that the experimental
slope is approximately 150 mV per decade could indicate that

2664 J. Phys. Chem. B, Vol. 108, No. 8, 2004
Peter and Ushiroda
slow component of the LMMR response noted earlier. The
process is described by the sequence
+
-
H O + e a H + H O
(8a)
(8b)
3
cb
surf
2
Hsurf a HSi
+
-
H a H + e
(8c)
(8d)
Si
Si
cb
3
+
+
2+
3 6
Hsurf + Ru(NH3)6 + H O f H O + Ru(NH )
2
3
In this scheme, hydrogen penetrates into the near surface of
the p-Si, where it can act as a “near surface state”. (Such near
surface states interact more strongly with the semiconductor than
with the solution because interfacial electron transfer is limited
by tunneling.) Atom exchange with the surface by eq 8b and
electron exchange with the conduction band are represented by
eq 8c. Alternatively, protons may penetrate into the Si lattice
so that electrons are captured before they reach the surface. In
this case, electron capture by protons would be favored as the
first step and the loci for the competing electron transfer
reactions would be different. Similar behavior has been observed
in the case of p-GaP, where the term “near surface state” has
been used to underline the importance of the spatial distribution
of electron acceptors. Such near surface states should be very
effective in intercepting electrons before they can be transferred
to redox species in solution. The subsequent transfer of the
trapped electron to redox species could be slow due to tunneling
effects or to diffusion of hydrogen atoms.
Figure 9. Concentration dependence of the phenomenological rate
constant for electron transfer. The slope of the plot allows calculation
of k and k (see text). The result confirms that the rate constants are
1 2
much lower than predicted for an outer sphere electron transfer process.
2
3
the potential drop in the Helmholtz layer varies as a consequence
of charging surface states.
The values of k1 and krec obtained from the IMPS plots for a
more restricted range of potential were similar to those obtained
from the LMMR data, but as Figure 7 shows, the contraction
of the IMPS plots with increasing band bending limited the
range of potential over which an analysis could be performed.
LMMR, by contrast, provides values of k1 even when in the
photocurrent saturation region, where recombination is negli-
gible.
Conclusions
The present study has shown how light modulated microwave
reflectivity measurements can be used to investigate electron
transfer at illuminated semiconductor electrodes. Comparison
of the measured rate constants for electron transfer with
theoretical predictions indicates that the mechanism of reduction
LMMR and IMPS measurements were repeated using dif-
3+
ferent concentrations of Ru(NH3)6 to check that the rate
constant k1 was first order in the concentration of redox species
As Figure 9 shows, k1 varies linearly with concentration as
3+
of Ru(NH3)6 cannot involve direct electron transfer from the
5
-1 -1
expected. The slope of the plot is 7.5 × 10 M s . Using eq
conduction band. Instead it appears that electron transfer is
mediated by hydrogen surface states.
-
7
-22
4
-1
1
with δ ≈ 10 cm, we obtain k2 ≈ 10
cm s , which is 4
orders of magnitude lower than the value estimated for the outer
sphere electron transfer process using eqs 2 and 3.
Acknowledgment. This work was supported by the UK
Engineering and Physical Science Research Council (EPSRC).
We thank Alison Walker, Michael Cass, and Steve Pennock
for assistance with the modeling of the microwave response as
well as Noel Duffy, Mike Bailes, and David Hatten for
assistance with the experimental system.
The very low value of k2 suggests that capture of electrons
at the surface of the illuminated p-Si involves a slow step. Our
previous microwave reflectivity study of hydrogen evolution
at p-Si in acidic fluoride media established that the electron
5
transfer process was unusually slow. Furthermore, there is a
considerable body of evidence for hydrogen incorporation into
17-21
silicon electrodes.
We have therefore proposed that conduc-
References and Notes
tion band electrons may be captured by protons to form
subsurface protons as the first step of the hydrogen evolution
(
1) Peter, L. M. Chem. ReV. 1990, 90, 753.
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5
3+
process. Ru(NH3)6 could then scavenge hydrogen atoms that
2
2
reach the surface. Navon and Meyerstein have studied the
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+
3+
(3) Schlichth o¨ rl, G.; Ponomarev, E. A.; Peter, L. M. J. Electrochem.
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6
-1 -1
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(
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+
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(
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(
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