Microwave reflectance studies of photoelectrochemical kinetics at semiconductor electrodes. 2. Hydrogen evolution at p-Si in ammonium fluoride solution

Article abstract of DOI:10.1021/jp0300896

Microwave reflectance methods have been used to study the kinetics of photogeneration of hydrogen on p-Si in acidic fluoride solutions. To estimate the rate constant for interfacial electron transfer, the magnitude of the observed steady-state light-induced microwave reflectivity change has been compared quantitatively with theoretical predictions based on numerical calculation of the electron and hole profiles in the silicon sample. In addition, the transient and periodic microwave reflectivity responses to stepped and sinusoidally modulated illumination, respectively, have been analyzed to obtain information about the electrode kinetics. The time constants for relaxation of the light-induced conductivity derived from this analysis confirm that electron transfer during hydrogen evolution is slow. The apparent inconsistency in the values of the phenomenological electron-transfer rate constants derived from the steady-state and transient or periodic responses can be resolved if it is assumed that hydrogen evolution proceeds via electron capture by protons followed by a slow bimolecular step leading to molecular hydrogen. Surface charging as the result of slow kinetics is expected to lead to band edge unpinning even at low light intensities, and the existence of this effect has been confirmed by transient photocapacitance measurements.

Full text of DOI:10.1021/jp0300896

5864
J. Phys. Chem. B 2003, 107, 5864-5870
Microwave Reflectance Studies of Photoelectrochemical Kinetics at Semiconductor
Electrodes. 2. Hydrogen Evolution at p-Si in Ammonium Fluoride Solution
Michael J. Cass,† Noel W. Duffy,‡ Laurence M. Peter,*,‡ Stephen R. Pennock,§
Shin Ushiroda,‡ and Alison B. Walker†
Department of Physics, Department of Chemistry, and Department of Electrical Engineering,
UniVersity of Bath, Bath BA2 7AY, United Kingdom
ReceiVed: January 23, 2003; In Final Form: April 21, 2003
Microwave reflectance methods have been used to study the kinetics of photogeneration of hydrogen on p-Si
in acidic fluoride solutions. To estimate the rate constant for interfacial electron transfer, the magnitude of
the observed steady-state light-induced microwave reflectivity change has been compared quantitatively with
theoretical predictions based on numerical calculation of the electron and hole profiles in the silicon sample.
In addition, the transient and periodic microwave reflectivity responses to stepped and sinusoidally modulated
illumination, respectively, have been analyzed to obtain information about the electrode kinetics. The time
constants for relaxation of the light-induced conductivity derived from this analysis confirm that electron
transfer during hydrogen evolution is slow. The apparent inconsistency in the values of the phenomenological
electron-transfer rate constants derived from the steady-state and transient or periodic responses can be resolved
if it is assumed that hydrogen evolution proceeds via electron capture by protons followed by a slow bimolecular
step leading to molecular hydrogen. Surface charging as the result of slow kinetics is expected to lead to
band edge unpinning even at low light intensities, and the existence of this effect has been confirmed by
transient photocapacitance measurements.
Introduction
Theory
The theory of light-induced microwave reflectance changes
The mechanism and kinetics of the electrochemical hydrogen
evolution reaction (HER) at metal electrodes have been studied
extensively. Both the mechanism and the rate of the electrode
process depend strongly on the nature of the metal, since the
reaction involves an adsorbed hydrogen intermediate. Although
generation of hydrogen at illuminated semiconductor electrodes
has attracted attention as a possible route for the production of
hydrogen from solar energy,1,2 surprisingly little is known about
the mechanism and kinetics of the process. Illumination of
p-type semiconductors leads to the generation of excess electrons
that can, in principle, reduce protons to hydrogen in a two-step
reaction, provided that the energy of the conduction band lies
above the hydrogen redox level. In practice, modification of
the semiconductor surface by deposition of an electrocatalyst
such as platinum is often used to enhance the efficiency of the
process.3,4 It is known that the photogenerated hydrogen may
modify the properties of the semiconductor photocathode,
introducing near surface recombination centers, as in the case
of p-GaP,5 or a disordered compensated layer, in the case of
silicon.6-8
at the semiconductor|electrolyte junction was developed initially
by Kunst and Tributsch, together with their collaborators.9-15
In a preceding paper in this series,16 we have reviewed the
theoretical foundations for the interpretation of light-induced
microwave reflectivity measurements, including the responses
to transient and periodic illumination. Profiles of the electron
and hole concentrations computed numerically from a Hall
Shockley Read model of the semiconductor|electrolyte junction
were used to calculate the mean change in electronic conductiv-
ity, ∆σ , of the silicon sample as a function of photon flux,
band bending, and rate constant for interfacial electron transfer.
The corresponding normalized microwave reflectivity change,
∆RM, was calculated by solving the Fresnel equations for a
multilayer model to represent the calculated electron and hole
profiles. Comparison of the results of the conductivity and
reflectivity calculations confirmed that, to a good approximation,
the microwave reflectivity change ∆RM can be related linearly
to ∆σ , as proposed by Kunst and Tributsch:
∆P
∆P
∆RM )
r ) RM r ) S ∆σ )
Pi
Pr
In the present study, photoelectrochemical hydrogen evolution
on oxide free Si(111) surfaces has been studied by light-induced
microwave reflectivity methods. The results offer new insights
into the kinetics and mechanisms of the hydrogen evolution
reaction and illustrate the potential of the experimental approach
for wider application.
d[µ ∆n(x) + µ ∆p(x)] dx (1)
Sq
d
∫
n
p
0
Here Pi and Pr are the incident and reflected microwave power,
respectively, ∆Pr is the change in reflected microwave power,
R
M is the unperturbed microwave reflectivity, S is a sensitivity
factor, d is the sample thickness, q is the elementary charge,
∆n(x) and ∆p(x) are the position dependent excess electron and
hole densities resulting from illumination, and µn and µp are
the electron and hole mobilities.
* Corresponding author. E-mail: l.m.peter@bath.ac.uk.
† Department of Physics.
‡ Department of Chemistry.
§ Department of Electrical Engineering.
10.1021/jp0300896 CCC: $25.00 © 2003 American Chemical Society
Published on Web 05/24/2003

Kinetics at Semiconductor Electrodes. 2
J. Phys. Chem. B, Vol. 107, No. 24, 2003 5865
The interpretation of time and frequency resolved microwave
reflectance measurements was also reviewed in the first paper.16
Here it was shown that the time constant for the response to
step and sinusoidal illumination profiles is given by
τ ) (k1 + krec)-1
(2)
where k1 and krec are first-order rate constants (s-1) for electron
transfer and electron-hole recombination, respectively. These
first-order rate constants arise from a phenomenological for-
mulation of kinetics in terms of the nominal surface concentra-
tions of electrons and holes.17 In order of magnitude terms at
least, k1 (s-1) can be related to k2 (cm4 s-1), the second-order
heterogeneous rate constant for interfacial electron transfer, and
to ktr (cm s-1), the pseudo-first-order heterogeneous rate constant
for electron transfer (obtained by assuming a constant concen-
tration of redox species in the interfacial region):
Figure 1. Continuous line: potential modulated microwave reflectivity
calculated from the Fresnel equations using a four-layer model, air|bulk
Si|depleted Si|electrolyte. The broken line shows the ac potential
modulation. Wafer thickness ) 350 µm; acceptor density ) 1015 cm-3
.
Band bending ) 1.2 eV. Calculated dc reflectivity, RM(0) ) 0.50. ꢀSi
) 12.0. ꢀelectrolyte ) 20; σelectrolyte ) 10-6 Ω-1 cm-1 (this low value of
the conductivity was chosen to eliminate interference effects and to
represent the open waveguide configuration).
ktr k2N
k1 )
)
redox ) VthσredoxNredox
(3)
δ
δ
Experimental Section
Measurements were performed with a Ka-band microwave
system. The microwave source was a Gunn diode (33 GHz,
Atlantic Microwave limited) mounted on a rectangular Ka-band
waveguide (7 mm × 3 mm). The silicon wafer was mounted
on the end of the waveguide in the base of a PTFE flow cell
(see below). The reflected microwave power was measured
using a crystal detector (R422C, Agilent technology) via a
directional coupler (Flann Microwave). An isolator ensured that
the microwave field was not reflected back to the microwave
source, and a variable attenuator allowed adjustment of the
power of the microwave field. Addition of a second directional
coupler allowed measurement of RM, the absolute microwave
reflectivity of the sample.
Boron doped p-Si(111) samples (ITME, 8-12 Ω cm) were
used in the measurements. The acceptor doping density ob-
tained by analysis of Mott Schottky plots was 7 × 1014
cm-3. Cut samples were etched for 30 s in flowing CP-4A
solution (3:5:3 by volume 48% HF:concentrated HNO3:100%
CH3COOH) and rinsed with Milli-Q water. This procedure
removed about 20 µm from the front surface of the wafers,
eliminating the polishing damage created during wafer manu-
facture that was found to enhance hydrogen uptake. Ohmic
contact was made around the periphery of the wafer using the
Ga|In eutectic. The ohmic losses in this configuration are
negligible due to the small size of the Ka-band waveguide (7
mm × 3 mm).
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
a volume density of Nredox in the solution.18
Royea et al.19 have estimated an upper limit for the rate
constant k2 for outer sphere reactions at semiconductor electrodes
in the range (1-10) × 10-17 cm4 s-1. If we assume a con-
centration of redox species equal to 10-2 M, for example, the
upper limit of ktr is in the range 60-600 cm s-1, and the
corresponding range for k1 is 6 × 108 to 6 × 109 s-1. In practice,
such rapid electron transfer will effectively prevent the buildup
of minority carriers at the interface, and as shown in the
preceding paper,16 the light-induced microwave response will
be too small to measure.
For quantitative interpretation of the steady-state microwave
reflectivity response, it is necessary to determine the sensitivity
factor, S (cf. eq 1). This can be done using potential-modulated
microwave reflectance (PMMR).20,21 The mean conductivity of
a semiconductor electrode under depletion conditions can be
perturbed in the dark by changing the potential. Since the density
of electrons and holes in the depletion region can be neglected,
eq 1 can be simplified to
Sq
d
S
d
S
d
∆RM ) S ∆σ ) µpp0∆Wsc ) µp∆Qsc ) µpCsc∆V (4)
The 1 M fluoride (pH 3) solution contained 0.5 M NH4F
(40%, BDH, Aristar), 0.15 M NH4Cl (Aldrich, ACS reagent),
and 0.5 M HF (48%, BDH, AnalaR). The electrolyte was
degassed with nitrogen for 10 min before starting experiments
and was circulated continuously through the flow cell via a
gravity-fed reservoir with a nitrogen lift pump.
Measurements were made in a three-electrode PTFE flow cell
equipped with Pt wire counter and Ag/AgCl reference elec-
trodes. The cell was machined to fit the end of the Ka
waveguide, and the silicon sample was mounted in its base so
as to expose an area of 0.21 cm2 to the electrolyte. Kapton tape
was used to isolate the silicon from the waveguide. The working
electrode potential was controlled by a low-noise potentiostat
programmed by the analog output of a computer-controlled
Stanford Research SR830 lock-in amplifier. Steady-state ca-
pacitance and PMMR measurements were made using a
frequency of 270 Hz. Transient photocapacitance measurements
were made at a frequency of 10 kHz.
Here ∆Wsc is the change in the width of the space charge region,
p0 is the bulk hole concentration, ∆Qsc is the change in the space
charge, Csc is the space charge capacitance, and ∆V is the
amplitude of the ac potential modulation. The linear relationship
between the microwave and capacitance responses implied by
eq 4 allows the sensitivity factor, S, to be determined experi-
mentally and compared with theoretical calculations based on
the Fresnel equations for a four-layer model: air|bulk Si|depleted
Si|solution.
Figure 1 shows the potential modulated microwave response
calculated from the four-layer model for 100 mV rms modula-
tion and band bending of 1.2 eV (similar calculations for the
lower frequency X-band 10 GHz system have been reported
by Searson et al.22). The doping density used in the calculation
was 1015 cm-3. The unperturbed reflectivity of the silicon sample
is 0.50, and ∆RM (peak to peak) is 8.5 × 10-6. The sensitivity
factor calculated from ∆RM using eq 4 is 0.27 Ω cm.

5866 J. Phys. Chem. B, Vol. 107, No. 24, 2003
Cass et al.
Intensity-modulated photocurrent spectroscopy (IMPS) and
light-modulated microwave reflectance (LMMR) measurements
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).
For the time resolved microwave and photocurrent measure-
ments, the LED driver was programmed by a square pulse
generator to give a 2 s on period followed by a 12 s off period.
The microwave detector was connected to one channel of a
Stanford SR560 low noise differential preamplifier, and the other
channel was used to offset the dc microwave signal to zero using
a Zener-stabilized dc source. The offset output was then
averaged using a digital oscilloscope (Tektronix TDS3012). A
typical experiment involved accumulation and averaging of 160
samples. Transient photocapacitance measurements were made
using a Stanford lock-in amplifier at a modulation frequency
of 10 kHz. The rise and decay of the microwave and capacitance
signals were fitted using nonlinear fitting routines in SigmaPlot.
Results and Discussion
Experimental Determination of the Sensitivity Factor. The
sensitivity factor relating the microwave response to the change
in mean conductivity (cf. eq 1) was determined by measuring
the potential-modulated microwave response of the p-Si|NH4F
system in the dark. In this case, potential modulation under
depletion conditions changes the width of the space charge
region, and the modulated microwave reflectivity is linearly
related to the space charge capacitance, which can be measured
at the same time (cf. eq 4). This relationship is illustrated by
Figure 2a, which compares the potential dependence of the
microwave and capacitance responses for a freshly etched
p-Si(111) sample in ammonium fluoride (pH 3.0).
Figure 2. (a) Comparison of the potential dependence of the
capacitance and PMMR responses of p-Si(111) in 1.0 M ammonium
fluoride solution (pH 3). Modulation frequency ) 270 Hz. Modulation
amplitude ) 100 mV rms. (b) Microwave Mott Schottky plot
constructed from the ∆RM data for a freshly etched silicon sample.
RM, the unperturbed reflectivity of the silicon sample, was
found to be 0.6, which is 20% higher than the value calculated
from the four-layer model. The experimental sensitivity factor
determined from Figure 2a is 0.53 Ω cm, which is twice the
value calculated using the four-layer Fresnel model. The reason
for these differences is not clear, but it may arise from
simplifications made in the four-layer Fresnel calculation.
The linear relationship between ∆RM and Csc allows the
PMMR data to be used to construct a Mott Schottky plot,20,23
as shown in Figure 2b. The plot shown here was constructed
from data obtained for a fresh sample. The flatband potential
was found to move progressively to more positive potentials
following prolonged illumination of the electrode. This effect
has been reported elsewhere7,24 and attributed to the effect of
incorporation of photogenerated hydrogen into the near-surface
region of the silicon. Fresh samples and low light intensities
were used in the present work in order to minimize the effects
of hydrogen incorporation as far as possible.
Figure 3. Set of photocurrent voltage curves for p-Si(111) in 1.0 M
ammonium fluoride solution (pH 3). The plots have been normalized
to the incident photon flux. Modulation frequency ) 10 Hz. Values of
the saturation photocurrent density (in µA cm-2): (1) -0.7; (2) -7.6;
(3) -91. The photocurrent calculated from the Ga¨rtner equation is also
shown (4). Note the displacement of the photocurrent onset potential
away from the flatband potential with increasing light intensity.
(10 Hz). The normalized photocurrent voltage plots in Figure
3 illustrate the characteristic displacement of the photocurrent
onset potential that is observed as the illumination intensity is
increased. Possible reasons for this effect include surface
charging and enhanced surface recombination via photogener-
ated intermediates (in this case hydrogen atoms).
“Steady-State” Microwave Response under Illumination.
The photocurrent and microwave responses of p-Si(111) were
characterized as a function of potential and light intensity. For
these measurements, the light was modulated at a low frequency

Kinetics at Semiconductor Electrodes. 2
J. Phys. Chem. B, Vol. 107, No. 24, 2003 5867
Figure 5. (a) Comparison of the transient photocurrent (lower trace)
and microwave (upper trace) responses of p-Si(111) in 1.0 M am-
monium fluoride solution (pH 3). Potential ) -1.0 V vs Ag|AgCl.
Compare the square photocurrent response typical of the saturation
region with the much slower rise and fall of the microwave response.
(b) Light-induced microwave response under the same conditions as
those for part a, showing the slow decay component of the decay
following an illumination pulse.
Figure 4. (a) Set of “steady state” ∆RM plots for different illumination
intensities. The values of the saturation current densities are the same
as those shown in Figure 3. Note that the plots are not normalized
with respect to the incident photon flux. (b) Plot showing the nonlinear
intensity dependence of the light-induced microwave reflectivity. The
limiting linear slope shown by the broken line was used to estimate ktr
from the steady-state response.
surface scattering, ∆RM will be smaller, but this effect is not
be large enough to explain the difference of more than 2 orders
of magnitude between the ktr values derived from the steady-
state and time/frequency resolved measurements (see below).
Time Resolved Microwave and Photocurrent Responses.
Figure 5a contrasts the photocurrent and microwave responses
to a step light function in the photocurrent saturation region.
The photocurrent follows the illumination essentially instanta-
neously, since recombination is negligible. By contrast, the rise
and fall of the microwave response are much slower. Figure 5b
shows that there are two components in the decay of the
microwave signal when the light is switched off. Since the
recovery of the microwave signal is very slow in the dark, a 1
to 10 light/dark duty cycle was used in the measurements, which
were restricted to low light intensities (3.5 × 1013 cm-2 s-1) to
minimize buildup of hydrogen in the silicon.
The rise of the microwave response was fitted to a single
exponential, whereas the decay was fitted to a double expo-
nential to take into account the very slow relaxation process
that can be seen in Figure 5b. Figure 6a shows an example of
the satisfactory nonlinear least-squares fit to a single exponential
obtained for the rising part of the microwave transient. Since
recombination is negligible at the potential of the measurement,
the time constant is equal to the inverse of the rate constant k1,
which was found to be 28 s-1. An identical value of k1 was
obtained for the faster component of the microwave reflectivity
decay. The time constant of the slow decay was found to be
0.5 s. It is not clear what causes the slow decay of the microwave
reflectivity in the dark, but we attribute it tentatively to a change
in the dielectric constant of the sample due to the incorporation
The corresponding microwave-voltage plots shown in Figure
4a have not been normalized, since, as Figure 4b shows, ∆RM
varies nonlinearly with the saturation photocurrent. This non-
linearity could indicate that the mobility of electrons in the near
surface region is not constant but falls as the electron density
increases. This behavior had been noted for accumulation and
inversion layers.25-27 However, as shown below, it is more likely
that the nonlinearity arises predominantly from the kinetics and
mechanism of the two-step hydrogen evolution reaction, which
give rise to an intensity dependence of k1.
In principle, the magnitude of the microwave response can
be used to estimate the electron-transfer rate constant. A
calculation of ∆RM as a function of ktr for parameter values
(doping density, band bending, light intensity, wavelength)
corresponding to those used in the present experiments is shown
in Figure 5 in the first paper in this series.16 In view of the
nonlinearity of the experimental response as a function of
illumination intensity, the linear response seen at low photon
fluxes (cf. Figure 4b) was used to estimate the value of ktr of
around 5 × 10-4 cm s-1. If we assume a tunneling distance δ
of the order of 1 nm, this value of ktr should correspond to a k1
value of 5 × 103 s-1. However, as shown below, the time and
frequency resolved responses of the system suggest a substan-
tially smaller value of k1 of 20-30 s-1. It should be noted here
that the calculation of ∆RM as a function of ktr was made using
the electron mobility for bulk silicon. If the electron mobility
in the near surface region is lowered by processes such as

5868 J. Phys. Chem. B, Vol. 107, No. 24, 2003
Cass et al.
Figure 7. (a) Set of normalized LMMR plots showing the increase in
diameter of the semicircles with increasing band bending, tending
toward the limiting response in the photocurrent saturation region, where
electron-hole recombination is negligible. The arrow shows the
direction of increasing modulation frequency (range 0.45-4.5 kHz, 5
steps per decade). The value of the sum (k1 + ktr) is obtained from the
radial frequency at which the minimum of the semicircle occurs. In
the photocurrent saturation region, the radial frequency of the minimum
is equal to k1. Saturation dc photocurrent ) -3.6 µA cm-2. (b)
Corresponding set of normalized IMPS plots showing the decrease in
diameter of the semicircles with increasing band bending, tending
toward the limit of a point in the saturation current region. The sum
(k1 + ktr) is obtained from the radial frequency at which the maximum
of the semicircle occurs, but by contrast with part a, no analysis is
possible in the photocurrent saturation limit.
Figure 6. (a) Expanded plot of ∆RM data from Figure 5a, showing
the nonlinear least-squares fit of the rising part to a single time constant.
(b) Photocurrent and microwave responses at -0.35 V vs Ag|AgCl.
Note the decay of the photocurrent (lower trace) associated with
electron-hole recombination. The microwave response has been fitted
to a single exponential corresponding to a time constant corresponding
to (k1 + krec) ) 55 s-1
.
of subsurface hydrogen. The possibility that it is due to band
edge unpinning was excluded by the results of transient
photocapacitance measurements (see below).
In the onset region of the photocurrent-voltage curve, the
transient photocurrent response exhibits the decay and overshoot
characteristic of the competition between recombination and
interfacial charge transfer.28 The microwave response, by
contrast, still rises and falls exponentially. The time constant
in this case is determined by the sum k1 + ktr, rather than ktr as
is the case in the photocurrent saturation region. These differ-
ences are illustrated by Figure 6b, which compares the photo-
current and microwave responses observed at a potential of
-0.35 V vs Ag|AgCl when the light is switched on. In this
case, the rise and fall of the microwave were found to correspond
Figure 8. Values of k1 and krec derived from the LMMR and IMPS
for the same conditions as those for Figure 7. Note that k1 is only weakly
potential dependent, whereas krec decreases with increasing band
bending. The slope of the fitted line is 180 mV per decade.
to (k1 + krec) ) 55 s-1
.
Frequency Resolved Microwave and Photocurrent Re-
sponses. In a previous study we showed that light-modulated
microwave reflectivity measurements could be used to obtain
of the photocurrent onset region, whereas the response in the
saturation region contracts to a point at unity on the real axis
and all information about electron-transfer kinetics is lost. The
low-frequency intercepts and the angular frequencies at which
the maxima in the semicircles occur were used to obtain values
of ktr and k1, and good agreement was found with the values
obtained by LMMR.
Figure 8 shows that the values of k1 derived by analyzing
the low-intensity LMMR and IMPS data vary little with
potential. krec, on the other hand, varies with potential, since
the recombination rate depends on the surface hole concentra-
tion. In the simplest case where no band edge unpinning occurs
as the result of surface charging, the slope of the semilogarithmic
k1 and krec.
29 A typical set of LMMR plots obtained at low light
intensity is presented in Figure 7a. The plots have been
normalized to the limiting response measured in the photocurrent
saturation region where recombination is negligible. The plots
illustrate clearly the effect of band bending. In general, the radial
frequency at which the minimum in the semicircular plots occurs
is equal to (k1 + krec). In the photocurrent saturation region, the
radial frequency is equal to k1, since recombination is negligible.
IMPS can be used in the photocurrent onset region to obtain
k1 and ktr. Figure 7b shows a set of normalized IMPS plots
obtained at the light intensity used in the LMMR experiments.
In the case of IMPS, the largest semicircle is seen at the start

Kinetics at Semiconductor Electrodes. 2
J. Phys. Chem. B, Vol. 107, No. 24, 2003 5869
ka(8kcg)1/2
k1 )
(6a)
ka + (8kcg)1/2
Here ka and kc are the rate constants for steps 5a and 5c,
respectively, and g is the flux of electrons into the surface given
by the Ga¨rtner equation. In the limit that ka is much greater
than (8kcg)1/2, eq 6a simplifies to a square root dependence of
the phenomenological rate constant on light intensity given by
k1 ) (8k4g)1/2
(6b)
and the steady-state surface concentration of the H0 intermediate
is given by
Figure 9. Double logarithmic plot showing that k1 and the dc
microwave reflectivity response appear to depend on the square root
of the incident photon flux (the x axis corresponds to the magnitude of
the saturation photocurrent density). Both sets of data were derived by
analysis of the LMMR response.
1/2
g
k4
[H0] )
(6c)
[ ]
The surface concentration of electrons is given by
plot should be 59 mV per decade, corresponding to the Boltz-
mann equation describing the surface hole density in the
nondegenerate case. However, the experimental value of the
slope is 180 mV per decade, indicating a much weaker potential
dependence of the recombination rate. As shown below, sig-
nificant band edge unpinning occurs as the result of surface
charging, even at the very low light intensities used in this study.
Surface charging is a consequence of the very low rate constant
for electron transfer, and it leads to a less rapid variation of
surface hole density with applied potential than is the case for
an ideal junction.
LMMR measurements made over a range of intensities
revealed that the rate constant for interfacial electron transfer
increases with intensity, as shown in Figure 9. The results
suggest that k1 varies with the square root of intensity. Since
(in the absence of surface recombination) the electron concen-
tration at the surface is a linear function of k1 and of light
intensity, one would expect a square root dependence of k1 to
result in a square root intensity dependence of the steady-state
microwave response. The steady-state microwave response can
be derived from the low-frequency intercept of the LMMR plots
on the real axis. Figure 9 confirms that the low-frequency limit
of the microwave response also appears to follow the same
square root intensity dependence. This is not expected for a
simple one-electron-transfer process, but of course, the hydrogen
evolution reaction is a two-step process.
g
ka
nsurf
)
(6d)
However, if the first step (electron capture by protons) is not
only fast but also reversible, the electron concentration will also
depend on the square root of the illumination intensity. It
therefore appears possible to explain the observed intensity
dependence of the phenomenological rate constant by the
mechanism outlined above.
The value of k4 derived from eq 6b is 6 × 10-12 cm2 s-1
,
and the surface coverage with H0 derived from eq 6c is about
1012 cm-2 at a current density of 3 µA cm-2. The corresponding
surface electron density can be much lower, since it depends
on the forward and reverse rate constants of the first step
involving electron capture (and release) by protons and not on
the phenomenological rate constant that determines the LMMR
and IMPS responses. However, further work will be required
to establish the details of the mechanism unequivocally.
Transient Photocapacitance Measurements. The buildup
of H0 (and of electrons) at the surface will lead to surface
charging. In the case of H0, the charging arises from the capture
of an electron by a proton. We speculate that protons may be
located in the near-surface region in the same way as has been
observed for p-GaP in our previous work.30 The mechanistic
analysis in the preceding section suggests that the surface
concentration of H0 is greater than that of electrons, as a
consequence of step 5a. The surface (or near-surface) charge,
At the simplest level of analysis, two mechanisms can be
considered, depending on whether the hydrogen atom intermedi-
ate, H°, is mobile or not:
Q
surf, associated with the trapping of electrons by protons should
produce a measurable change, ∆VH, in the potential drop across
the Helmholtz layer given by
H+ + e f H0
(5a)
Followed by either (H0 not mobile)
Qsurf
∆VH )
(7)
CH
H+ + H0 + e f H2
(5b)
where CH is the Helmholtz capacitance. Under potentiostatic
conditions, the potential drop across the space charge must
decrease by an equal amount. The corresponding increase in
space charge capacitance can be detected. In the present study,
transient capacitance measurements were made at a modulation
frequency of 10 kHz using a small time constant on the lock-in
amplifier to allow adequate time resolution. Figure 10 illustrates
the rising part of the transient capacitance response to an
illumination step. The response can be fitted to a single
exponential with a time constant of 3.3 ms, which is identical
to the time constant for the microwave response.
or (H0 mobile)
H0 + H0 f H2
(5c)
We have analyzed the IMPS response for analogous two-
step mechanisms previously in considerable detail for the case
in which the steps are irreversible.17 If recombination is
negligible, it can be shown that the apparent or phenomenologi-
cal rate constant for the mechanism involving eq 5a followed
by eq 5c is given by

5870 J. Phys. Chem. B, Vol. 107, No. 24, 2003
Cass et al.
of the microwave technique, the mechanistic details of the
hydrogen evolution reaction at p-Si have not been fully estab-
lished, and further studies are required to identify the reaction
steps and intermediates.
Acknowledgment. This work was supported by the Engi-
neering and Physical Sciences Research Council. The authors
thank David Hatten and Michael Bailes for valuable technical
assistance.
References and Notes
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