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Intensity modulated photocurrents on an anodically oxidized lead electrode in sulfuric acid solution
165
J. Electroanal. Chem., 316 (1991) 165-174 Elsevier Sequoia S.A., Lausanne
JEC 01679
Intensity modulated photocurrents on an anodically oxidized lead electrode in sulfuric acid solution Z.A. Rotenberg and O.A. Semenikhin A.N. Frumkin Institute of Electrochemistry, (Received
Academy of Sciences of the USSR, Moscow (USSR)
8 April 1991; in revised form 28 May 1991)
Abstract
The real and imaginary components of photocurrent on a semiconductor electrode illuminated simultaneously with light of constant and sinusoidally modulated intensity were calculated on the assumption that the rate coefficient of surface recombination can depend on the light intensity. Theory was compared with experimental data for an anodically oxidixed lead electrode in 0.5 M H,SO,. The frequency response of photocurrent in a complex plane is represented by overlapped elliptical arcs showing a uniform relaxation time distribution. The main kinetic coefficients of the photoprocess have been determined. It was shown that charge transfer through the interface can proceed via the surface states and directly from the valence band. The rate ratio of the two processes depends on potential.
1. INTRODUCT
ION
The intensity modulation method has already been considered as a new approach to investigation of surface recombination processes on the semiconductor-electrolyte interface [l-4]. In the case of illumination of the electrode with sinusoidally modulated light, the non-steady photocurrent is analyzed using either a complex plane or Bode plots. The frequency response analysis gives information about the surface state relaxation times and provides direct access to the kinetics of interfacial processes involving photoexcited minority carriers. The simplest approach [2,4], however, does not provide information about the mechanism of minority carrier injection at the interface. This process can proceed either directly from the corresponding band or via the surface states. To solve this problem for a Fe,O, electrode (n-type semiconductor) Pajkossy [S] measured the non-steady photocurrents as a function of the reducing agent concentration and found that holes were injected into solution directly from the valence band, but not via the surface states. This approach is not valid, however, for systems where hole injection into solution 0022-0728/91/$03.50
0 1991 - Elsevier Sequoia S.A. All rights reserved
166
proceeds effectively without additional reductants (e.g. TiO, electrode in aqueous solutions). When the rate coefficient of surface recombination (or the relaxation time) depends on the light intensity the mechanism of charge transfer can be investigated without adding a special acceptor to the solution. The influence of the light intensity on the rate coefficient of surface recombination was found recently for a TiO, electrode [6] and for an anodically oxidized lead electrode [7,8]. In the present paper the frequency response analysis of photocurrents is conducted in the case when the electrode is illuminated simultaneously with light of constant intensity and sinusoidally modulated light taking into consideration that the rate coefficient of surface recombination depends on the light intensity. Theory is compared with experimental data for an oxidized lead electrode containing a photoactive n-type semiconductor PbO film [9-111. THEORY
Let us consider an n-type semiconductor (Fig. 1) illuminated simultaneously with light of constant and sinusoidally modulated intensity. If the phase shift due to diffusion and migration can be neglected, the net time-dependent charge flux g(r) of minority carriers into the surface will follow the excitation function, i.e. g( t ) = g + Age’“’ where g and Ag are the dc and ac components of the flux respectively being proportional to the corresponding light intensities Z and AZ, o = 2rf is the circular frequency, i is the imaginary unit, t is time. In the following discussion we assume that Ag +z g. We also take into account that only the fraction y of the hole flux is captured by the surface states, the remaining fraction (1 - y) is injected directly into the solution. The holes captured by the surface states take part in the recombination with conduction band electrons (the rate coefficient k,) and are injected into the solution with the rate coefficient k,. We have assumed that k, is independent of the
Fig. 1. Kinetic
scheme of the photoelectrochemical
processes
at the semiconductor-electrolyte
interface.
167
light intensity the density of light intensity g(f), contains
and k, is a function of the electron density at the interface including photoexcited electrons. So this coefficient must be dependent on the or on the charge flux g. Thus the coefficient k,, just as the net flux the ac component
Ak = Ag(dk/dg)e’” where k = k, + k,. Let the surface charge denoted by p, then
density
of the holes captured
= y [ g + Age’“‘] - [k + (dk/dg)
dp/dt
by the surface
states
Age’“‘] p
be
0)
Using the solution of eqn. (1) in the form p(t) =p + Ape’“’ and assuming that (dk/dg) Ag +z k and Ap -=cp, after separation of the harmonic terms from the time-independent ones, one obtains P = YO
Ap =
(2)
y[l - g(d lnk/dg)l
The alternating equal to j = Ag - k,Ap Using j =
Ag/(k
photocurrent
+ iw) at the fundamental
frequency
of modulation
-pAk.
YB - y(l-
(w) is
(4)
eqns. (2) and (3) and introducing
Ag[l -
(3)
B&J@
parameter
B = g(dlnk/dg)
+ io)]
one finds (44
Here we have omitted the phase term eiwr. As follows from eqn. (4a), this system has a single relaxation time constant 7 = l/k. The real (Re). and imaginary (Im) components of the photocurrent then become Re( j) = Ag[l
- yfi - y(1 - j3)k,k/(k2
+ a’)]
(5)
and Im( j) = Agy(1 - jS)k,o/(k’+
w2)
The photocurrent response predicted by these (curve 1). The high frequency and zero frequency real axis follow from eqns. (5) and (6) as Re(j),
= Ag(I
- YB)
(6) equations intercepts
is illustrated in Fig. 2 of the semicircle on the
(7)
and Re(j),
= Ag[I
- Y + ~(1 - P)ki/k]
(8)
The high frequency limit of Re( j) is less than the generation flux Ag and depends on the light intensity through the coefficient fi_ When k is independent of the light intensity (fi = 0) we have Re(j), = Ag [3].
168
Ret j/Ag Fig. 2. Complex plane plots of the normalized ac photocurrent y = 1, k, = 0 (1) s = 0; (2) s = 0.6 k; (3) s = 0.9 k; (4) s = k.
calculated
1 using eqns. (9) and (10)
for
The coexistence of several surface states or the presence of their relaxation time distribution about a mean value results in deformation of the photocurrent semicircle [3]. For the uniform distribution of k from k - s to k + s about the mean value k with the density (2 s)-‘, the expressions for Re(j) and Im(j) can be obtained in the explicit form Re(j)
=Ag
l-up-~(l-P)kz/k+ 1
X[arctg(+$)-arctg(+)])
Im( j) = Ag
Y(I -I%+ 4sk
ln[ j;‘$:$]
~(1-
P)k,w 2sk
(9)
(10)
In this case the semicircle degenerates into an elliptical arc depending on s (Fig. 2, curves 2-4) with the same low and high frequency limits (see eqns. (7) and (8)). Frequency response analysis of photocurrents at various light intensities provides a possibility for the determination of the main kinetic coefficients (Ag, k,, k,, y and 8) of the photoprocess as shown below. 3. EXPERIMENTAL
The intensity modulated light was produced by a helium-cadmium laser (X = 440 nm) equipped with an optical modulator. In some experiments the electrode was irradiated with the polychromatic light from two independent light sources (100 W tungsten lamps). The beam of one of them was mechanically chopped. The amplitude of the alternating light intensity was significantly less than the constant
169
Re(j)/PE 0.4
0.:
0.2
0.1
0 -0.2
0.0
0.2
0.4
E/v
-0.1 Q/O 30
20
10
0 Fig. 3. Dependencies of the photocurrent amplitude and phase on electrode potential. Modulation frequency 288 Hz. (1) without constant intensity illumination; (2) under constant intensity illumination.
intensity, which was changed by applying dc voltage to the modulator or by using calibrated meshes. The measurements of the real and imaginary components of the photocurrent using a lock-in technique are described elsewhere [7]. Measurements were carried out on an anodically oxidized lead electrode in 0.5 M H,SO,. All potentials are given with respect to a mercury sulfate reference electrode in the same solution. The preliminary electrode preparation was carried out according to [7,8,10]. After photoactivation at 0.6 V the electrode was kept at -0.7 V under the highest light intensity till a steady state photocurrent was obtained. Then the electrode was treated by rapid cycling from -0.6 to 0.6 V. The potential dependence of the amplitude and phase of the photocurrent for such an electrode is shown in Fig. 3. Hysteresis of the j, E and +,E-curves indicates that surface changes take place during the potential scanning. Therefore the electrode was kept
170
at the corresponding measured.
potential
for 20 min
before
the
frequency
spectra
were
4. RESULTS
The frequency photocurrent spectra were measured in the potential range where the photocurrent phase differs significantly from zero (Fig. 3). The photocurrent plots in a complex plane for two light intensities are shown in Fig. 4. Both plots can be described as two overlapping elliptical arcs. The characteristic frequency corresponding to the maximum value of Im(j) for the high frequency region of the spectrum increases with the light intensity. In the low frequency region the maximum of Im( j) is less pronounced. This form of frequency dependence indicates that the surface state relaxation times are distributed about two mean values, corresponding to the frequencies at the maximum of the imaginary component of the photocurrent. To obtain the kinetic coefficients of the photoprocess we restricted ourselves to the high frequency region (f> 30 Hz) of the spectrum, neglecting the slow state participation in the reaction within this frequency range. From comparison of the experimental data with theory using the non-linear least squares method we obtained the values of the low (ignoring the slow states) and high frequency limits of photocurrent (Re(j), and Re(j)m) and the values of the kinetic coefficient k at the various light intensities which are listed in Tables l-3. From the tables one can see that Re( j), and Re( j), decrease with the light intensity and Fig. 5 illustrates this tendency for Re( j),, which is in accord with the limiting expressions (7) and (8) for fi # 0. The rate coefficient k which is equal to the reciprocal of the relaxation time increases with the light intensity (Fig. 5). The generation current Ag was obtained by extrapolation (Fig. 5) of the Re( j),, Z-dependence to Z = 0, where the coefficient /3 was assumed to be equal to zero. To obtain the other coefficients (y, fi, k, and k, = k - k,) we used a consequent approximation method assuming the intensity independence of coefficients y and k,. At the first stage the dependence of Re( j), on l/k was plotted and the
MJVPA
1
2
630 1.3k 1.3 IQ/-(-fq1 0.1
I 0.2
6.3k 0.3
Fig. 4. Complex plane photocurrent plots obtained for Pb/PbO/PbSO,, in 0.5 M H,SO, at various light intensities I (a.u.). Modulation frequency range l-6300 Hz. Electrode potential is equal to 0.0 V. (1) I = 6.5; (2) Z = 35.
171 TABLE
1
High frequency limits of photocurrent and the kinetic coefficients potential: E = -0.2 V, Ag = 0.31 pA, y = 0.96, k, = 251 s-l I/arbitrary
units
170 470 750 1310 2600 5200
TABLE
at various
W_&JPA
W.&/PA
k s-’
k,/s-’
B
0.31 0.29 0.29 0.29 0.26 0.16
0.13 0.11 0.09 0.07 0.04 0.02
603 905 1037 1596 2086 4040
352 654 786 1345 1835 3789
0.00 0.06 0.06 0.06 0.12 0.45
I/arbitrary
units
170 470 750 1310 2600 5200
170 470 750 1310 2600 5200
at various
light intensities
W&,/PA
WiWaA
k s-’
k,/s-’
P
0.49 0.44 0.42 0.39 0.36 0.31
0.23 0.17 0.15 0.12 0.08 0.05
528 584 729 1370 1980 3150
324 377 522 1163 1773 2943
0.02 0.12 0.17 0.23 0.30 0.40
for
3
High and low frequency limits of photocurrent and the kinetic coefficients the potential: E = 0.0 V, Ag = 0.50 PA, y = 0.68, k, = 820 s-’ I/arbitrary
for the
2
High and low frequency limits of photocument and the kinetic coefficients the potential: E = 0.1 V, Ag = 0.50 PA, y = 0.90, k, = 207 SC’
TABLE
light intensities
units
Btij),/~A 0.48 0.45 0.43 0.41 0.31 0.29
0.36 0.33 0.29 0.26 0.22 0.17
at various
fight intensities
k/s-’
k,/s-’
B
1345 1540 1710 2700 3520 5700
525 720 890 1880 2700 4880
0.06 0.12 0.20 0.25 0.43 0.56
for
coefficient y was obtained using its linear extrapolation to l/k = 0. This value can be considered as the first approximation because we have postulated that j? is independent of the light intensity. Using this coefficient it is easy to calculate the corresponding values of #3 from the values of j3y = 1 - Re(j),/Ag at differing light intensities. To correct the coefficient y (the second approximation) the dependencies of Re(j),/Ag on (1 - fi)/k (in accordance with eqn. (8)) were plotted (Fig. 6). They are represented by straight lines thus supporting the assumption that y and k, are independent of the light intensity. The corrected values of y were obtained from
172
k/s-’
0.6
- 4000
- 2000 0.2
0
A0 10
30
50 I/a.u.
Fig. 5. Dependencies of the high frequency limit of photocurrent Re(j), and the rate coefficient light intensity for variouselectrodepotentialsE/V: (1) E = -0.2; (2) E = -0.1;(3) E = 0.0.
0.8
0.2 -
0 0
0
2
A
3
k on
e
L 5
I 10 2i’tiOOO(173)/ks-
Fig. 6. Graphical determination of coefficients E=-0.2;(2) E=-0.1;(3)E=O.O.
y and k, for various
electrodepotentials
E/V:
(1)
the intercepts of these lines with the Re(j),/Ag axis and the rate coefficients k, were determined from the slopes of the lines. The values of both coefficients are listed in Tables l-3. 5. DISCUSSION
As follows from the experimental results, the photoelectrochemical behavior of an oxidized lead electrode can be described by the general scheme shown in Fig. 1. That the photoexcited holes can transfer through the interface either directly from the valence band or via the surface states, has been taken into consideration by
173
introducing the coefficient y. At the potential E = -0.2V y = 0.96 and thus the photoprocess proceeds mainly via the surface states. At more positive potentials the holes can also transfer onto the acceptors directly from the valence band (y = 0.7 at E = 0.0V).It is natural to connect such potential dependence of y with changing of surface state occupancy in equilibrium. When band bending increases at more positive potentials the surface state occupancy becomes smaller and the probability of hole capture by the surface states decreases. It can be concluded that at the most positive potentials (E > 0.2 V), when the photocurrent amplitude is frequency independent and its phase is equal to zero, the main fraction of photoexcited holes transfer through the interface directly from the valence band. On the other hand, in the region where the photocurrent changes its direction (E -e-0.2V) the reaction proceeds mainly via the surface states (y = 1). As one can see from Tables 1-3, the rate coefficient k, is approximately proportional to the light intensity. So we can conclude that photoexcited electrons participate in the surface recombination process. This conclusion is also supported by the results of pulse and second harmonic measurements [8,9]. The contribution of equilibrium (“dark”) electrons to the surface recombination must become significant only at a very low light intensity near the zero photocurrent potential ( - 0.5 V approximately), where their concentration in the conduction band near the surface increases. It should be mentioned that the electrode is unstable at these potentials, and long time measurements of the photocurrent spectra are impossible. As has been noted, the electrode state changes with potential, which is supported by the hysteresis on the j, E and $, E dependences (Fig. 3) and by the absence of a clear correlation between the measured kinetic coefficients and the potential (Tables l-3). In most systems, including an anodically oxidized lead electrode, the chemical and physical identity of the surface states remains obscure. The fast surface states are assumed to be related to the surface recombination of minority carriers, and the slow ones may be identified as photoelectrolysis products (e.g. non-stoichiometric oxygen) which are reduced in the dark. The low frequency plot of the photocurrent (Fig. 4) corresponds to this process. We could not perform a quantitative analysis of the whole photoprocess including the reduction of photoelectrolysis products because of the low frequency limitation of the apparatus used. The existence of the relaxation time distribution found for the surface states on an oxidized lead electrode in sulfuric acid solution is in agreement with the impedance data for the same system. As was shown earlier [12], the impedance complex plots either in the dark or under illumination could be represented by depressed semicircles typical for the systems with distributed electrical parameters. It is natural to connect this correlation with the properties and structure of the electrode itself, which is covered by a semipermeable sulfate membrane. Different parts of the PbO film surface being in contact with electrolyte through the membrane channels are physically unequal. In particular, the pH of the solution inside the membrane and the corresponding potential drop between the different parts of the PbO film on the membrane channel bottom and the solution can vary
174
depending distribution
on the channel size, which could result of the surface state relaxation times.
in the existence
of a certain
6. CONCLUSION
A new approach to the investigation of non-linear photoelectrochemical systems was developed in order to obtain direct information about the mechanism and kinetic parameters of the photoprocess. Theoretical expressions for the real and imaginary components of photocurrent on a semiconductor electrode irradiated simultaneously with light of constant and sinusoidally modulated intensity were compared with the experimental data for an anodically oxidized lead electrode in sulfuric acid solution. It was shown that this system possesses two different types of surface states with distributed relaxation times due to the physical inequality of different parts of the electrode surface covered by the sulfate membrane. The dependencies of the kinetic parameters of the photoprocess on the electrode potential were obtained. It was shown that near the zero photocurrent potential the photoexcited holes transfer onto acceptors mainly via the surface states, while at more positive potentials it is possible for holes to be injected into solution directly from the valence band. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12
W.J. Albery and P.N. Bartlett, J. Electrochem. Sot., 129 (1982) 2254. E. Kamienieski, J. Appl. Phys., 54 (1988) 6481. J. Li and L.M. Peter, J. Electroanal. Chem., 199 (1986) 1. R. Peat and L.M. Peter, J. Electroanal. Chem., 209 (1986) 307. T. Pajkossy, J. Electrochem. Sot., 130 (1983) 632. O.A. Semenikhin, Z.A. Rotenberg and G.L. Teplitskaya, Sov. Electrochem., 27 (1991) 209. Z.A. Rotenberg and B.I. Monakhov, Sov. Electrochem., 24 (1988) 332. Z.A. Rotenberg, Sov. Electrochem., 27 (1991) 202. V.A. Izvozchikov and G.A. Bordovsky, Doklady Akad. Nauk, USSR, 145 (1962) 1253. D. Pavlov, S. Zanova and G. Papazov, J. Electrochem. Sot., 121 (1977) 1253. M. Dimitrov, K. Kochev and D. Pavlov, J. Electroanal. Chem., 156 (1983) 165. Z.A. Rotenberg and N.V. Nekrasova, Sov. Electrochem., 25 (1988) 728.
J. Electroanal. Chem., 316 (1991) 165-174 Elsevier Sequoia S.A., Lausanne
JEC 01679
Intensity modulated photocurrents on an anodically oxidized lead electrode in sulfuric acid solution Z.A. Rotenberg and O.A. Semenikhin A.N. Frumkin Institute of Electrochemistry, (Received
Academy of Sciences of the USSR, Moscow (USSR)
8 April 1991; in revised form 28 May 1991)
Abstract
The real and imaginary components of photocurrent on a semiconductor electrode illuminated simultaneously with light of constant and sinusoidally modulated intensity were calculated on the assumption that the rate coefficient of surface recombination can depend on the light intensity. Theory was compared with experimental data for an anodically oxidixed lead electrode in 0.5 M H,SO,. The frequency response of photocurrent in a complex plane is represented by overlapped elliptical arcs showing a uniform relaxation time distribution. The main kinetic coefficients of the photoprocess have been determined. It was shown that charge transfer through the interface can proceed via the surface states and directly from the valence band. The rate ratio of the two processes depends on potential.
1. INTRODUCT
ION
The intensity modulation method has already been considered as a new approach to investigation of surface recombination processes on the semiconductor-electrolyte interface [l-4]. In the case of illumination of the electrode with sinusoidally modulated light, the non-steady photocurrent is analyzed using either a complex plane or Bode plots. The frequency response analysis gives information about the surface state relaxation times and provides direct access to the kinetics of interfacial processes involving photoexcited minority carriers. The simplest approach [2,4], however, does not provide information about the mechanism of minority carrier injection at the interface. This process can proceed either directly from the corresponding band or via the surface states. To solve this problem for a Fe,O, electrode (n-type semiconductor) Pajkossy [S] measured the non-steady photocurrents as a function of the reducing agent concentration and found that holes were injected into solution directly from the valence band, but not via the surface states. This approach is not valid, however, for systems where hole injection into solution 0022-0728/91/$03.50
0 1991 - Elsevier Sequoia S.A. All rights reserved
166
proceeds effectively without additional reductants (e.g. TiO, electrode in aqueous solutions). When the rate coefficient of surface recombination (or the relaxation time) depends on the light intensity the mechanism of charge transfer can be investigated without adding a special acceptor to the solution. The influence of the light intensity on the rate coefficient of surface recombination was found recently for a TiO, electrode [6] and for an anodically oxidized lead electrode [7,8]. In the present paper the frequency response analysis of photocurrents is conducted in the case when the electrode is illuminated simultaneously with light of constant intensity and sinusoidally modulated light taking into consideration that the rate coefficient of surface recombination depends on the light intensity. Theory is compared with experimental data for an oxidized lead electrode containing a photoactive n-type semiconductor PbO film [9-111. THEORY
Let us consider an n-type semiconductor (Fig. 1) illuminated simultaneously with light of constant and sinusoidally modulated intensity. If the phase shift due to diffusion and migration can be neglected, the net time-dependent charge flux g(r) of minority carriers into the surface will follow the excitation function, i.e. g( t ) = g + Age’“’ where g and Ag are the dc and ac components of the flux respectively being proportional to the corresponding light intensities Z and AZ, o = 2rf is the circular frequency, i is the imaginary unit, t is time. In the following discussion we assume that Ag +z g. We also take into account that only the fraction y of the hole flux is captured by the surface states, the remaining fraction (1 - y) is injected directly into the solution. The holes captured by the surface states take part in the recombination with conduction band electrons (the rate coefficient k,) and are injected into the solution with the rate coefficient k,. We have assumed that k, is independent of the
Fig. 1. Kinetic
scheme of the photoelectrochemical
processes
at the semiconductor-electrolyte
interface.
167
light intensity the density of light intensity g(f), contains
and k, is a function of the electron density at the interface including photoexcited electrons. So this coefficient must be dependent on the or on the charge flux g. Thus the coefficient k,, just as the net flux the ac component
Ak = Ag(dk/dg)e’” where k = k, + k,. Let the surface charge denoted by p, then
density
of the holes captured
= y [ g + Age’“‘] - [k + (dk/dg)
dp/dt
by the surface
states
Age’“‘] p
be
0)
Using the solution of eqn. (1) in the form p(t) =p + Ape’“’ and assuming that (dk/dg) Ag +z k and Ap -=cp, after separation of the harmonic terms from the time-independent ones, one obtains P = YO
Ap =
(2)
y[l - g(d lnk/dg)l
The alternating equal to j = Ag - k,Ap Using j =
Ag/(k
photocurrent
+ iw) at the fundamental
frequency
of modulation
-pAk.
YB - y(l-
(w) is
(4)
eqns. (2) and (3) and introducing
Ag[l -
(3)
B&J@
parameter
B = g(dlnk/dg)
+ io)]
one finds (44
Here we have omitted the phase term eiwr. As follows from eqn. (4a), this system has a single relaxation time constant 7 = l/k. The real (Re). and imaginary (Im) components of the photocurrent then become Re( j) = Ag[l
- yfi - y(1 - j3)k,k/(k2
+ a’)]
(5)
and Im( j) = Agy(1 - jS)k,o/(k’+
w2)
The photocurrent response predicted by these (curve 1). The high frequency and zero frequency real axis follow from eqns. (5) and (6) as Re(j),
= Ag(I
- YB)
(6) equations intercepts
is illustrated in Fig. 2 of the semicircle on the
(7)
and Re(j),
= Ag[I
- Y + ~(1 - P)ki/k]
(8)
The high frequency limit of Re( j) is less than the generation flux Ag and depends on the light intensity through the coefficient fi_ When k is independent of the light intensity (fi = 0) we have Re(j), = Ag [3].
168
Ret j/Ag Fig. 2. Complex plane plots of the normalized ac photocurrent y = 1, k, = 0 (1) s = 0; (2) s = 0.6 k; (3) s = 0.9 k; (4) s = k.
calculated
1 using eqns. (9) and (10)
for
The coexistence of several surface states or the presence of their relaxation time distribution about a mean value results in deformation of the photocurrent semicircle [3]. For the uniform distribution of k from k - s to k + s about the mean value k with the density (2 s)-‘, the expressions for Re(j) and Im(j) can be obtained in the explicit form Re(j)
=Ag
l-up-~(l-P)kz/k+ 1
X[arctg(+$)-arctg(+)])
Im( j) = Ag
Y(I -I%+ 4sk
ln[ j;‘$:$]
~(1-
P)k,w 2sk
(9)
(10)
In this case the semicircle degenerates into an elliptical arc depending on s (Fig. 2, curves 2-4) with the same low and high frequency limits (see eqns. (7) and (8)). Frequency response analysis of photocurrents at various light intensities provides a possibility for the determination of the main kinetic coefficients (Ag, k,, k,, y and 8) of the photoprocess as shown below. 3. EXPERIMENTAL
The intensity modulated light was produced by a helium-cadmium laser (X = 440 nm) equipped with an optical modulator. In some experiments the electrode was irradiated with the polychromatic light from two independent light sources (100 W tungsten lamps). The beam of one of them was mechanically chopped. The amplitude of the alternating light intensity was significantly less than the constant
169
Re(j)/PE 0.4
0.:
0.2
0.1
0 -0.2
0.0
0.2
0.4
E/v
-0.1 Q/O 30
20
10
0 Fig. 3. Dependencies of the photocurrent amplitude and phase on electrode potential. Modulation frequency 288 Hz. (1) without constant intensity illumination; (2) under constant intensity illumination.
intensity, which was changed by applying dc voltage to the modulator or by using calibrated meshes. The measurements of the real and imaginary components of the photocurrent using a lock-in technique are described elsewhere [7]. Measurements were carried out on an anodically oxidized lead electrode in 0.5 M H,SO,. All potentials are given with respect to a mercury sulfate reference electrode in the same solution. The preliminary electrode preparation was carried out according to [7,8,10]. After photoactivation at 0.6 V the electrode was kept at -0.7 V under the highest light intensity till a steady state photocurrent was obtained. Then the electrode was treated by rapid cycling from -0.6 to 0.6 V. The potential dependence of the amplitude and phase of the photocurrent for such an electrode is shown in Fig. 3. Hysteresis of the j, E and +,E-curves indicates that surface changes take place during the potential scanning. Therefore the electrode was kept
170
at the corresponding measured.
potential
for 20 min
before
the
frequency
spectra
were
4. RESULTS
The frequency photocurrent spectra were measured in the potential range where the photocurrent phase differs significantly from zero (Fig. 3). The photocurrent plots in a complex plane for two light intensities are shown in Fig. 4. Both plots can be described as two overlapping elliptical arcs. The characteristic frequency corresponding to the maximum value of Im(j) for the high frequency region of the spectrum increases with the light intensity. In the low frequency region the maximum of Im( j) is less pronounced. This form of frequency dependence indicates that the surface state relaxation times are distributed about two mean values, corresponding to the frequencies at the maximum of the imaginary component of the photocurrent. To obtain the kinetic coefficients of the photoprocess we restricted ourselves to the high frequency region (f> 30 Hz) of the spectrum, neglecting the slow state participation in the reaction within this frequency range. From comparison of the experimental data with theory using the non-linear least squares method we obtained the values of the low (ignoring the slow states) and high frequency limits of photocurrent (Re(j), and Re(j)m) and the values of the kinetic coefficient k at the various light intensities which are listed in Tables l-3. From the tables one can see that Re( j), and Re( j), decrease with the light intensity and Fig. 5 illustrates this tendency for Re( j),, which is in accord with the limiting expressions (7) and (8) for fi # 0. The rate coefficient k which is equal to the reciprocal of the relaxation time increases with the light intensity (Fig. 5). The generation current Ag was obtained by extrapolation (Fig. 5) of the Re( j),, Z-dependence to Z = 0, where the coefficient /3 was assumed to be equal to zero. To obtain the other coefficients (y, fi, k, and k, = k - k,) we used a consequent approximation method assuming the intensity independence of coefficients y and k,. At the first stage the dependence of Re( j), on l/k was plotted and the
MJVPA
1
2
630 1.3k 1.3 IQ/-(-fq1 0.1
I 0.2
6.3k 0.3
Fig. 4. Complex plane photocurrent plots obtained for Pb/PbO/PbSO,, in 0.5 M H,SO, at various light intensities I (a.u.). Modulation frequency range l-6300 Hz. Electrode potential is equal to 0.0 V. (1) I = 6.5; (2) Z = 35.
171 TABLE
1
High frequency limits of photocurrent and the kinetic coefficients potential: E = -0.2 V, Ag = 0.31 pA, y = 0.96, k, = 251 s-l I/arbitrary
units
170 470 750 1310 2600 5200
TABLE
at various
W_&JPA
W.&/PA
k s-’
k,/s-’
B
0.31 0.29 0.29 0.29 0.26 0.16
0.13 0.11 0.09 0.07 0.04 0.02
603 905 1037 1596 2086 4040
352 654 786 1345 1835 3789
0.00 0.06 0.06 0.06 0.12 0.45
I/arbitrary
units
170 470 750 1310 2600 5200
170 470 750 1310 2600 5200
at various
light intensities
W&,/PA
WiWaA
k s-’
k,/s-’
P
0.49 0.44 0.42 0.39 0.36 0.31
0.23 0.17 0.15 0.12 0.08 0.05
528 584 729 1370 1980 3150
324 377 522 1163 1773 2943
0.02 0.12 0.17 0.23 0.30 0.40
for
3
High and low frequency limits of photocurrent and the kinetic coefficients the potential: E = 0.0 V, Ag = 0.50 PA, y = 0.68, k, = 820 s-’ I/arbitrary
for the
2
High and low frequency limits of photocument and the kinetic coefficients the potential: E = 0.1 V, Ag = 0.50 PA, y = 0.90, k, = 207 SC’
TABLE
light intensities
units
Btij),/~A 0.48 0.45 0.43 0.41 0.31 0.29
0.36 0.33 0.29 0.26 0.22 0.17
at various
fight intensities
k/s-’
k,/s-’
B
1345 1540 1710 2700 3520 5700
525 720 890 1880 2700 4880
0.06 0.12 0.20 0.25 0.43 0.56
for
coefficient y was obtained using its linear extrapolation to l/k = 0. This value can be considered as the first approximation because we have postulated that j? is independent of the light intensity. Using this coefficient it is easy to calculate the corresponding values of #3 from the values of j3y = 1 - Re(j),/Ag at differing light intensities. To correct the coefficient y (the second approximation) the dependencies of Re(j),/Ag on (1 - fi)/k (in accordance with eqn. (8)) were plotted (Fig. 6). They are represented by straight lines thus supporting the assumption that y and k, are independent of the light intensity. The corrected values of y were obtained from
172
k/s-’
0.6
- 4000
- 2000 0.2
0
A0 10
30
50 I/a.u.
Fig. 5. Dependencies of the high frequency limit of photocurrent Re(j), and the rate coefficient light intensity for variouselectrodepotentialsE/V: (1) E = -0.2; (2) E = -0.1;(3) E = 0.0.
0.8
0.2 -
0 0
0
2
A
3
k on
e
L 5
I 10 2i’tiOOO(173)/ks-
Fig. 6. Graphical determination of coefficients E=-0.2;(2) E=-0.1;(3)E=O.O.
y and k, for various
electrodepotentials
E/V:
(1)
the intercepts of these lines with the Re(j),/Ag axis and the rate coefficients k, were determined from the slopes of the lines. The values of both coefficients are listed in Tables l-3. 5. DISCUSSION
As follows from the experimental results, the photoelectrochemical behavior of an oxidized lead electrode can be described by the general scheme shown in Fig. 1. That the photoexcited holes can transfer through the interface either directly from the valence band or via the surface states, has been taken into consideration by
173
introducing the coefficient y. At the potential E = -0.2V y = 0.96 and thus the photoprocess proceeds mainly via the surface states. At more positive potentials the holes can also transfer onto the acceptors directly from the valence band (y = 0.7 at E = 0.0V).It is natural to connect such potential dependence of y with changing of surface state occupancy in equilibrium. When band bending increases at more positive potentials the surface state occupancy becomes smaller and the probability of hole capture by the surface states decreases. It can be concluded that at the most positive potentials (E > 0.2 V), when the photocurrent amplitude is frequency independent and its phase is equal to zero, the main fraction of photoexcited holes transfer through the interface directly from the valence band. On the other hand, in the region where the photocurrent changes its direction (E -e-0.2V) the reaction proceeds mainly via the surface states (y = 1). As one can see from Tables 1-3, the rate coefficient k, is approximately proportional to the light intensity. So we can conclude that photoexcited electrons participate in the surface recombination process. This conclusion is also supported by the results of pulse and second harmonic measurements [8,9]. The contribution of equilibrium (“dark”) electrons to the surface recombination must become significant only at a very low light intensity near the zero photocurrent potential ( - 0.5 V approximately), where their concentration in the conduction band near the surface increases. It should be mentioned that the electrode is unstable at these potentials, and long time measurements of the photocurrent spectra are impossible. As has been noted, the electrode state changes with potential, which is supported by the hysteresis on the j, E and $, E dependences (Fig. 3) and by the absence of a clear correlation between the measured kinetic coefficients and the potential (Tables l-3). In most systems, including an anodically oxidized lead electrode, the chemical and physical identity of the surface states remains obscure. The fast surface states are assumed to be related to the surface recombination of minority carriers, and the slow ones may be identified as photoelectrolysis products (e.g. non-stoichiometric oxygen) which are reduced in the dark. The low frequency plot of the photocurrent (Fig. 4) corresponds to this process. We could not perform a quantitative analysis of the whole photoprocess including the reduction of photoelectrolysis products because of the low frequency limitation of the apparatus used. The existence of the relaxation time distribution found for the surface states on an oxidized lead electrode in sulfuric acid solution is in agreement with the impedance data for the same system. As was shown earlier [12], the impedance complex plots either in the dark or under illumination could be represented by depressed semicircles typical for the systems with distributed electrical parameters. It is natural to connect this correlation with the properties and structure of the electrode itself, which is covered by a semipermeable sulfate membrane. Different parts of the PbO film surface being in contact with electrolyte through the membrane channels are physically unequal. In particular, the pH of the solution inside the membrane and the corresponding potential drop between the different parts of the PbO film on the membrane channel bottom and the solution can vary
174
depending distribution
on the channel size, which could result of the surface state relaxation times.
in the existence
of a certain
6. CONCLUSION
A new approach to the investigation of non-linear photoelectrochemical systems was developed in order to obtain direct information about the mechanism and kinetic parameters of the photoprocess. Theoretical expressions for the real and imaginary components of photocurrent on a semiconductor electrode irradiated simultaneously with light of constant and sinusoidally modulated intensity were compared with the experimental data for an anodically oxidized lead electrode in sulfuric acid solution. It was shown that this system possesses two different types of surface states with distributed relaxation times due to the physical inequality of different parts of the electrode surface covered by the sulfate membrane. The dependencies of the kinetic parameters of the photoprocess on the electrode potential were obtained. It was shown that near the zero photocurrent potential the photoexcited holes transfer onto acceptors mainly via the surface states, while at more positive potentials it is possible for holes to be injected into solution directly from the valence band. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12
W.J. Albery and P.N. Bartlett, J. Electrochem. Sot., 129 (1982) 2254. E. Kamienieski, J. Appl. Phys., 54 (1988) 6481. J. Li and L.M. Peter, J. Electroanal. Chem., 199 (1986) 1. R. Peat and L.M. Peter, J. Electroanal. Chem., 209 (1986) 307. T. Pajkossy, J. Electrochem. Sot., 130 (1983) 632. O.A. Semenikhin, Z.A. Rotenberg and G.L. Teplitskaya, Sov. Electrochem., 27 (1991) 209. Z.A. Rotenberg and B.I. Monakhov, Sov. Electrochem., 24 (1988) 332. Z.A. Rotenberg, Sov. Electrochem., 27 (1991) 202. V.A. Izvozchikov and G.A. Bordovsky, Doklady Akad. Nauk, USSR, 145 (1962) 1253. D. Pavlov, S. Zanova and G. Papazov, J. Electrochem. Sot., 121 (1977) 1253. M. Dimitrov, K. Kochev and D. Pavlov, J. Electroanal. Chem., 156 (1983) 165. Z.A. Rotenberg and N.V. Nekrasova, Sov. Electrochem., 25 (1988) 728.