J . Phys. Chern. 1988,92, 6655-6660
6655
Photoelectrochemical and Impedance Characteristics of Specular Hematite. 1. Photoelectrochemical, Parallel Conductance, and Trap Rate Studies S. M. Ahrned,**+J. Leduc, and S. F. Haller Mineral Sciences Laboratories, Canada Centre for Mineral and Energy Technology, Ottawa, Ontario, Kl A OGl, Canada (Received: August 24, 1987; In Final Form: May 6, 1988)
Most of the samples of naturally occurring specular hematite (Quebec, Canada) containing 0.6 mass % Ti were found to be degenerate semiconductors due to oxygen deficiency in these samples and yielded negligible photocurrents ( i p h ) in a photoelectrochemical (PEC) cell. When heated in air to 900 OC for 1 h or more after polishing, these samples developed substantial photocurrents as photoanodes in a PEC cell. The PEC, solid-state, and optical properties have been investigated by current-voltage and impedance measurements and by photocurrent spectroscopy. Information has been derived on the trapping centers and surface states with energies within the band-gap region. Inherent bulk states at 1.5 eV optical (-0.5-0.7 eV below the conduction band edge) are responsible for trapping of the majority carriers and for electron-hole recombination and surface states. The trapping and detrapping effects due to surface states could be eliminated and iphgreatly enhanced by filling the surface states by pyrogallol adsorption. The deep impurity/donor levels are also responsible for the trapping and recombination effects and consequently the low photon conversion efficiencies. Methods of improving the efficiencies have been suggested.
Introduction The photoelectrochemical (PEC) properties of a-Fe2O3 have been extensively investigated in view of its possible application as a photoanode in the photoelectrolysis of water for hydrogen production. Several forms of iron oxide have been investigated, e.g., flame-oxidized and the polycrystalline@ and single-crystal forms.1° Although stable to photocorrosion, the main disadvantages of iron oxide as a photoanode in photoelectrolysis of water are (i) a flat-band potential (fbp) which is positive to the hydrogen evolution potential and hence there would be a need for a bias voltage; (ii) low electron mobilities -1 X cm2/(V.s) for pure FezOgll to 7 X cm2/(V.s) for Ti-doped Fe20312due to localized, narrow d-band conduction; and (iii) the presence of localized, intrinsic and impurity levels and surface states in the band-gap region acting as trapping and recombination centers in photoconduction. All these factors drastically reduce the photon conversion efficiencies (vph). The poor transport properties of carriers in Fez03 dictate that only the films with low iR drop, but with a large depletion layer with low doping density, could be of any practical use. Such films have been successfully made recently4 but the ?+,h are still low. The most probable causes for low vlphin these films are the presence of grain boundaries, traps, and surface states. The present work was undertaken to investigate the nature of such trapping centers and surface states, in particular those present in specular hematite, and to find suitable means of eliminating them, for example by using donor type organic adsorbents as was accomplished with M0S2.13 The work is comprised of photocurrent-voltage and photocurrent-spectrum measurements with band-gap and sub-band-gap illumination, impedance measurements, and studies of the effects on photocurrents of adding donor-type adsorbents to fill the surface states. Specular hematite is the black variety of the naturally occurring a-F%03 which is normally n-type and much more conducting than the red variety. The low resistivity (-2 ohmcm) obtained by four-point probe resistance measurement is most probably due to the oxygen deficiency in the natural samples and due to impurities. This corresponds to a carrier concentration of 4.5 X IOl9 cm-3 for a mobility of 0.07 cm2/(V.s).12 Although the thermo emf was measurable in these samples, no photocurrents were produced in the PEC cells without polishing or heat treatment of the samples. The present work was carried out with such samples that were heated in air at 900 OC and also certain other samples that gave photocurrents after polishing to remove the surface layer.
'Research Scientist, CANMET, Energy, Mines and Resources Canada. 0022-3654/88/2092-6655$01 SO10
Experimental Section Hand-picked samples of specular hematite from Quebec (Canada) were cut into thin slices and polished to a shining finish by using standard methods. Spectrographic and S E M analysis indicated presence of 0.1-176 of Ti as ilmenite partly in solid solution with Fez03 and traces of Mg, Cr, Ni, and V. These samples were heated in air at 900 OC for different durations ranging from 1 to 60 h before making ohmic contacts. Ohmic contacts were made after heat treatment using an In-Sn eutectic alloy. After sintering for 1 h in argon at 300 OC and by use of a three-point probe method, the ohmicity of these contacts was established. The contacts were given a first coat of Micromask stop-off lacquer (Michigan Chrome and Chemical Co.) and a second coat of transparent silicone sealant (General Electric) before making electrodes. General PEC investigations were carried out using a standard three-electrode system with a saturated calomel reference electrode (SCE) under potentiostatic conditions. A two-compartment cell with a porous glass frit diaphragm was used. Open-circuit photopotentials and short-circuit photocurrents with bias where necessary were measured by standard methods. The distribution of the bias voltage between the Fez03 anode and the platinum counter electrode was also followed relative to S C E during short-circuit experiments in dark and under illumination. This measurement gives the polarizability of the two electrodes and hence the band bending of the semiconductor electrode alone, in addition to measurement of photopotentials. The photocurrent spectra were recorded by using a motor-driven monochromator and a 450-WXe light source. The spectral studies were extended from the UV up to the visible-IR ( 1000 nm)
-
(1) Sammells, A. F.; Ang, P. G . P. J. Electrochem. Soc. 1979, 126, 1831. (2) Yeh, L . 4 . R.; Hackerman, N. J. Electrochem. SOC.1977, 124, 833. (3) Liou, F.-T.; Yang, C. N.; Levine, S. N. J. Electrochem. Soc. 1982,129,
342. (4) Schumacher, L. C., Mamiche-Afara, S.;Weber, M. F.; Dignam, M. J. J . Electrochem. SOC.1985, 132, 2945. (5) Itoh, K.; Bockris, J . 0 M . J. Electrochem. SOC.1984, 131, 1266. (6) Kennedy, J. H.; Frese,Jr., K. W. J. Electrochem. Soc. 1978,125,709. ( 7 ) Kennedy, J. H., Frese, Jr., K. W. J. Electrochem. Soc. 1978,125, 723. (8) Kennedy, J. H.; Anderman, M. J. Electrochem. SOC.1983, 130, 848. ( 9 ) Anderman, M.; Kennedy, J. H. J. Electrochem. Soc. 1984,131, 1565. (IO) Merchant, P.; Collins, R.; Kershaw, R.; Dwight, K.; Wold, A. J. Solid State Chem. 1979, 27, 307. ( 1 1) Morin, F. J. Phys. Reu. 1954, 93, 1195. (12) Morin, F. J. Phys. Reu. 1951, 83, 1005. (13) Ahmed, S. M.; Haller, S. F. Extended Abstract, Electrochemical Society, Spring Meeting, San Francisco, 1983; Vol. 83, p 790.
Published 1988 by the American Chemical Society
6656
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The Journal ofPhysica1 Chemistry, Vol. 92, No. 23, ...r~~~~T_~_._~.~
F e n O J ; 9 0 0 0 C 1 n 0 8 r - 60 a n d - - - I h , SCHCTTKY P L F S i - V PLOTS; I M NaOH
Ahmed et al.
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6
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Figure 1. (a) Mott-Schottky plots. (b) Photocurrentsvs potential plots for specular hematite; A and B refer to samples with and without Fermi
level pinning respectively. See text for details on sample preparation. for sub-band-gap illumination. The light intensity was measured at different wavelengths by a calibrated power meter (Photodyne, Model 44XL) and a UV-sensitive head (Model 450) with an analog output for the X-Y recorder. The photon conversion efficiencies (l)ph) were calculated where necessary. The ac impedance measurements were carried out using an LCR meter (Hewlett Packard, Model 4374-A) and a minicomputer (HP-85) with a modification of data acquisition and control software, described elsewhere in detail.14 The method of impedance analysis is discussed in the next section.
Results Current-Voltage Behauior. The specular hematite samples without preheating in air or without removal of the surface layer by grinding and polishing did not give any photocurrent, most probably because of the high carrier density in the surface layer as a result of oxygen loss in the natural deposits. However, if the original samples are heat treated in air at 900 OC for various times (1-60 h), then photocurrents are developed as shown in Figure 1 b, although the duration of heat treatment apparently had no effect on the magnitude of the photocurrents developed. Some samples (A) gave a high anodic threshold potential of --0.2-0.1 V (SCE) whereas others (B) showed -0.45 V (SCE) for this onset. This potential is much higher than the flat-band potential ( Vh,) of about -0.87 V (SCE) as determined from the Mott-Schottky (M-S) plot of Figure l a in 1 M N a O H by a curve-fitting method.15 The Vbp of a synthetic cu-Fe203single crystal, at pH 13 for the same carrier concentration, was measured by Horowitz'* to be -0.832 V (SCE). Photocurrents were also obtained without preheating provided the original surface layer was removed by grinding followed by final polishing to a mirror finish (a 0.25-pm diamond paste was used). The iph(not shown in Figure 1) for these samples (C) showed a much more positive threshold potential (-+0.325 V (SCE) for the onset of iph. The photocurrents were also found to vary linearly with the light intensity up to at least about 100 mW cm-*, indicating that photoexcition and charge collection processes are still rate controlling (slow) rather than the electron transfer from the solution to the photogenerated holes. The M-S plots for the first two types of samples (A and B) are shown in Figure la. Details of the impedance analysis for establishing these plots are given below. Impedance Analysis. For impedance analysis, the equivalent circuit for all the frequencies (0.1-40 kHz), except for the highest available (100 kHz), was taken to be a resistance (R,) in series with a parallel combination of a capacitance (C,)and a conductance (G,) as indicated in Figure 2. The value of R, was first evaluated by a simple series analysis of the impedance measured (14) Leduc, J.; Ahrned, S . M. 'Impedance Measurements at the Semiconductor-Solution Interface"; CANMET Report 84-15 E , Energy, Mines and Resources, Canada, 1985, pp 1-82. (15) Leduc, J.; Ahmed, S. M., part 2, following paper in this issue.
..-. 0.75
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1
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I
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Figure 2. Parallel conductance shown as a function of electrode potential. Samples A and B are the same as in Figure 1, Sample C, top layer
removed by polishing, no heat treatment, also shows Fermi level pinning. Equivalent circuit used (see text for details).
Inset:
at the highest frequency (100 kHz) available. This was justified for two reasons. The phase of the impedance at that frequency was -1 O or less compared to -60' at 100 Hz. This indicated that at the higher frequency the equivalent circuit was almost purely resistive. The second reason is that the series resistance thus calculated was a constant and independent of the applied voltage within 9%. This allowed identification of this resistance (R,) as the series combination of the solution resistance and the solid-phase resistance. From three- and four-point probe resistance measurements on the iron oxide sample and the known value of 20 R for the electrolyte resistance, an expected value of about 30 R for this resistance was obtained. The parallel combination of C, and G, was then evaluated by subtracting the value of R, from the measured impedance data a t lower frequencies. The M-S plots, A and B shown in Figure la, represent two types of behavior shown by samples A and B, respectively, with different surface heat treatment and impurity content. While type B samples do not show any Fermi level pinning in their M-S plot (Figure la), type A samples show pinned Fermi level below -0.25 V (SCE) as seen in Figure l a (curve A), where the capacitance does not change with potential [below -0.25 V (SCE)]. Under conditions of Fermi level pinning, the surface states start getting charged as the Fermi level reaches the corresponding energy levels of surface states. The band bending then remains unaltered and consequently the capacitance will be independent of potential.16 This situation can also give rise to several other effects such as potential drop in the Helmholtz layer and recombination of electrons and holes via surface states and thus result in low photopotentials. The type A samples also showed a much more positive threshold potential [V,, = -0.2 to -0.1 V (SCE)] for the onset of photocurrents compared to samples B [ V, = -0.45 V (SCE)] as shown in plots A and B, respectively, of Figure lb. Both samples A and B were heat treated with or without prepolishing. The differences, inherent in the nature of the samples, appeared to be due to the kind of recombination centers, whether traps due to impurities or surface states. This point will be further clarified from studies of conductance peaks and photocurrent spectroscopy in the subband-gap region, in the following sections. Samples which were not heat treated but only polished to remove the surface layer (sample C) showed Fermi level pinning at -0.35 V (SCE) in 1 M NaOH (not shown in the figure). It should be emphasized here that if the M-S plots are derived from a simple series analysis of the impedance data, instead of the complex parallel equivalent circuit analysis as described here, then the M-S plots would be linear with sharp breaks and changes in slopes (not shown in the figures). Such M-S plots have been reported by others4v7J7and may be attributed to the presences of (16) Morrison, S . R. Electrochemistry at Semiconductor and Oxidized Metal Electrodes; Plenum: New York, 1980; Chapter 5, p 168.
Photoelectrochemistry of Hematite -1.0
The Journal of Physical Chemistry, Vol. 92, No. 23, 1988 6657
c
c
-0.8
ED:
3.0-
I
-
B I A S VOLTAGE ( V I
I
I
I
Fe,03 Subgap Spectrum 0.6 V(SCE);----O.I
-
I
V(SCE);25X
Figure 3. Distribution of the bias potential between the Fe203anode (in the dark and illuminated) and R cathode (SCE) shown as a function of the bias voltage.
surface states or traps which cannot be distinguished in this kind of simple analysis'* whereas with the present analysis using a more complex equivalent circuit, a distinction can be made between the traps (Figure l a , B) and surface states (Figure l a , A). The parallel conductance is considered next. In the inset of Figure 2, the parallel components [C, Gp (=l/R,)] identified with a subscript p refer to those components which do not include surface-state effects. Those components that involve only surface states have subscript ss, while R , refers to the series resistance considered earlier. The measured values of the parallel conductance G,' and capacitance C,' (not shown in the figure) contain both contributions. They are given for monoenergetic surface states as"
css C,' = 1 W2T* + CP
(1)
G,' = G,, + G,
(3)
+
where
G, = 1/Rp; 7 = R,,C, (4) When C , is small, then G,' G,, the background values of the conductance. C, is small when IEF- E,I > 5kT. Otherwise the surface-state capacitance has a significant value and the G, vs bias voltage plots would show a peak for each value of EF E,,
-
as shown in Figure 2, for samples of type A and C. These plots show two peaks for sample A and one peak for sample C, both of which show Fermi level pinning, and no peak at all for sample B which does not show Fermi level pinning. When plotted for different frequencies, the peak heights increase with increasing frequencies (not shown in the Figure). For sample A, the positions of the peaks with respect to voltage (Figure 2) are constant within 50 mV up to 40 kHz. However, with increasing frequency, the peak at -0.2 V (SCE) is absorbed by the peak at -0.45 V (SCE) which becomes broader at frequencies >20 kHz. This behavior is characteristic of the surface states contribution to the parallel conductance above the b a c k g r ~ u n d ' ~ ~ ' ~ (17) Wilhelm, S. M.; Yun, K. S.; Ballenger, L. W.; Hackerman, N. J . Electrochem. Soc. 1979, 126, 419. ( 1 8) Horowitz, G. J . Electroanal. Chem. 1983, 159, 421. (19) Nagasubramanian, G.; Wheeler, B. L.; Bard, A. J. J . Electrochem. Soc. 1983, 130, 1680.
(20) Goodman, A. M. J . Appl. Phys. 1963, 34, 329. (21) Ahmed, S. M. Int. J . Hydrogen Energy 1986, 11, 627.
-
6658 The Journal of Physical Chemistry, Vol. 92, No. 23, 1988
Ahmed et al.
0 . 5 M K,SO..DorkBilluminofed
- - O o r k : t O . O 0 5 M Pyrogallol IIluminoled
300 wW/crn*
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I
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I
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Figure 7. Effect of adding (A) pyrogallol and (B) oxalic acid on photocurrents of Fe20, in K2S04(0.5 M) solutions.
0
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8.5
0
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SEC. Figure 6. Photocurrent transient behavior of Fe203anode under flashed illumination: (A) 0.5 M K2S0, solution (pH 2.0); (B) effect of pyrogallol on the transient behavior; note the difference in iph scale in A and B: ( C ) steady-state photocurrents in the presence of pyrogallol. conduction band electrons could occur via these surface states and traps. The photocurrent spectrum in the 2.0-3.6-eV range is shown in Figure 4 in terms of photon conversion efficiencies (T)ph) which are seen to be rather low, -5%. The sub-band-gap spectrum in the 1.9-1.2-eV range taken at bias voltages of 0.1 and 0.6 V (SCE) are shown in Figure 5. This spectrum shows a number of peaks at 1.35, 1.5, 1.63, 1.70, and 1.75 eV out of which the 1.5-eV peak is most distinct. The fundamental absorption edge is seen to occur at about 2 eV, beyond which a tail of photocurrent extends into the infrared range. This is in agreement with the reported band gap of 2.0-2.2 eV for a-Fe203. In subsequent discussion it will be shown that the 1.5-eV level is structural and intrinsic in nature and appears to be mostly responsible for the trapping centers and surface states encountered at -0.5-0.7 eV below the conduction band edge. Photocurrent Transients and Effects of Adsorbed Organic Reducing Agents. The photocurrent ( i p h ) vs time transients with “light on” and “light off“, at pH 2 in K2S04solution, are shown in Figure 6A. These transients show a rise (0.125 s) and fall (- 1 s) in the iphbefore a steady-state value is reached. Then with the light off a cathodic current starts flowing, before equilibrium is reached in the dark and the original, anodic current starts flowing. This effect, observed by others als0,2J7922is due to surface states
trapping of the majority carriers under illumination, recombination, and detrapping of the carriers in the dark, as discussed later. On addition of pyrogallol, a strong reducing agent and hence an electron donor, it is seen in Figure 6B that the above-noted effects due to trapping and electron-hole recombination via surface states are completely eliminated. Also, addition of pyrogallol led to an increase (Figure 6B) in photocurrents by 30 times and a steady photocurrent started to flow as shown in Figure 6C (see also Figure 7A,B). A less pronounced but similar effect is seen for oxalic acid (Figure 7B). This behavior is due to the filling of surface states through electron donation from the chemisorbed pyrogallol and the subsequent transfer of these electrons to the photogenerated holes in the valance band. Similar effects have been demonstrated in an earlier work on MoS2 by one of with xanthate and pyrogallol to fill the surface states at the surfaces parallel to the C axis of the crystals. Further evidence is presented in the next section on the role of pyrogallol. us13921
Discussion Photocurrent Spectra. Hematite (a-Fe203) has a trigonal structure, the oxygen atoms occupying a distorted hexagonal close packing with Fe3+in two-thirds of the octahedral positions, so that each iron has six oxygen and each oxygen has four iron neighbors. Specular hematite is antiferromagnetic due to alternate layers of iron atoms oppositely magnetized. However, it has a net weak magnetism which interferes with the measurement of the Hall coefficient. The electronic and band structures have been although no single model can throughly investigated,1°*11,23-2s explain all the conductivity and spectroscopy data observed. The valence band is derived from the occupied e, Fe 3d orbitals with a strong antibonding admixture of 0 2p23while the conduction band edge is derived from the tze levels of Fe 3d and 0 2p. The absorption spectrum10-23-25 consists of two broad, weak absorption peaks at 1.5 eV (826 nm) and -2.0 eV (619 nm), instead of a fairly sharp optical absorption threshold, characteristic of broad-band semiconductors. This is in fairly good agreement with the photocurrent spectra shown in Figures 4 and 5. Tandon and (22) Hardee, K. L.; Bard, A. J. J . Electrochem. Soc. 1977, 124, 215. (23) Shuey, R. T. “Semiconductor Ore Minerals”; Deuelopmenfs in Economic Geology; Elsevier: Amsterdam, New York, 1975; Vol. 4, p 360. (24) Wickersheim, K. A.; Lefever, R. A. J . Chem. Phys. 1962, 36, 844. (25) Tandon, S. P.; Gupta, J. P.Spectrosc. Lett. 1970, 3, 297.
The Journal of Physical Chemistry, Vol. 92, No. 23, 1988 6659
Photoelectrochemistry of Hematite pH:
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-
-0.8
-
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surface state level E,, which was previously identified as the 1.5-eV intrinsic and structural level from the photocurrent spectra (Figure 5). In comparison, the valence band edge at pH 2 lies at -+1.8 V (SCE) and therefore direct hole capture by parogallol at the valence band level is not favorable. Hence it is reasonable to state that electron transfer from pyrogallol to the photogenerated holes in the valance band occurs via these surface states which get filled up first. As a result, not only the transient effects observed in the iph(Figure 6) attributed to the surface states are eliminated, but also a large increase occurs in iph (Figure 7). This particular role of pyrogallol on photocurrents may be demonstrated from kinetic considerations as follows for Fez03assuming a given set of values for the solid-state properties such as surface barrier and carrier concentration at equilibrium conditions which are assumed to remain constant. Such dependence of PEC kinetics on the solid-state properties may be found in standard works. Let k , and kz represent the specific rate constants for the photoexcitation and direct bulk recombination processes, so that
Figure 8. Energy level diagram showing positions of the band edges, flat-band potential (fbp), and surface state levels (Ea, and EM2).For X and w; see text. Large separation between E, and Ehp at carrier concentration -10'' is based on Horowitz.'*
(5)
kQ V I P E,,
GuptaZ5have assigned a 2.16-eV level as a direct gap to the crystal field transition
%,
-
-
4~,(tz,)3(e,)z
and a 1.44-eV absorption level to 6Al,
4Tle(t2g)4(ee)
Intense absorption has also been in the shorter wave length (UV range) due to charge-transfer transitions (-3 eV) from 0 2p levels to the conduction band, which however does seem to contribute significantly to the photocurrent spectrum as shown in Figure 4. The other peaks at 1.63, 1.70, and 1.75 eV are probably due to certain impurity donor levels. Surface States and Photocurrent Transients. The 1.5-eV peak in Figure 5 is a structural (d-d) transition also reported by others2q1'J2 for high-purity Fe203which also showed the iphtransients, similar to those reported here in Figure 6A. Hence, these inherent levels must be responsible for the slow surface states with time constants of a millisecond to a second, which result in trapping of photoexcited electrons and recombination followed by detrapping in the light off condition. The back cathodic current (Figure 6A) soon after light off arises because of a slight but momentary increase in the quasi (local) Fermi level, at the surface, soon after detrapping of electrons, to a cathodic value in the surface layer, which results in electron injection in the forward direction and reduction of the oxidized species accumulated on the surface. These surface states also cause Fermi level pinning (Figure 1) and large threshold potentials for the onset of iph,described in the previous section (see Results), and the impedance behavior (Figure 2). The effects of adding pyrogallol, a strong reducing agent, on the surface states and iphare discussed below. Other sub-band-gap levels observed in the iph spectra, due to inherent and/or impurity levels, particularly introduced by replacing Fe by Ti in FeZO3can act as deep donor- or acceptorlike trapping centers. These could also be responsible for the impedance behavior noted in the Results section. FeZO3and FeTi03 have similar structures and are known to form solid solutions. Effects of Adding Pyrogallol. Pyrogallol is a strong reducing agent and can be oxidized much more readily than water. The E l ( - E o ) for the first oxidation state of pyrogallol is -0.062 PI-# + O.5Oz6 which would be 0.14 V (SCE) at the experimental pH 2. If the potential scale shown in the energy level diagram of a-Fe2O3 at pH 13 in Figure 8 is adjusted to pH 2, then the E l l z ( - E ) for pyrogallol (0.14 V (SCE)) lies very close to the
where [p+] and [n-] are the concentrations of photogenerated holes and electrons in the semiconductor surface, while [pn] is the nonexcited state of electrons and holes in the valance band and [p] alone refers to the captured hole at the surface. In a n semiconductor, the n- being the majority carriers, reaction 5 is first order in p+ and pseudo zero order in n-. In eq 5, kz represents direct electron-hole recombination while k3 represents recombination of n- and p+ via surface states Essl. Hence, the latter would also show first-order dependence on the number of vacant sites available in the surface states, say [C,]. If, [X,] and [X,] are the concentrations of the solution species before and after being photooxidized (e.g., OH-, H02-, and OH,02), respectively (assuming a cell with transport), [&-] is the concentration of the added reducing agent (e.g., pyrogallol) and, Z is the intensity of illumination, then using appropriate rate constants for the redox processes, we have at anode
at anode (7) at cathode
From eq 5 rate of formation of holes = k,Z rate of hole depletion:
Rate of oxidation of xw- and xR- are given as
Hence
For steady-state conditions (26) Kolthoff, I. M.; Lingane, J. J. Polarography, 2nd ed.; Interscience: New York, 1952; Vol. 2, p 705 (see also p 699).
(9)
Ahmed et al.
6660 The Journal of Physical Chemistry, Vol. 92, No. 23, 1988
'
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e
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From eq 12 and 16
L
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(k2 + k3[c,l)[n-l From eq 17, 18, and 19
+ k4[xw-1+ kS[XR-l[cssl
KklI(k4[xw-l + k5LXR-I
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25
3 LOO,,
f
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1
1
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3.5
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Figure 9. Capacitance vs frequency plot at anodic polarization, from which the trap rate (l/r)is derived from the time constant r.
(19)
(20)
If k5 >> k4, there will be a large increase in i, on the addition of xR- to the electrolyte; e.g., an increase in [XR-] by 1 order of magnitude (0.001-0.01 M) would increase the i, by 3 orders of magnitude, for the given set of conditions. This mode is also consistent with the following observations: 1. i, is proportional to the intensity of illumination in the absence of surface states in view of the fact that both [n-] for n semiconductor and [xw-] are large and the process is pseudozero-order in [n-] and [xw-]. In the absence of surface states, the slow and rate-determining step is still the hole generation process and diffusion to the reaction sites, rather than electron transfer from xw- (or xR-). 2. Photon conversion efficiencies are low particularly in the presence of surface states when (k2 k3[C,])[n-] >> k4[xW-]. If k5 >> k3, then the surface-state recombination effects in lowering the photocurrents are overcome by the filling of these states by pyrogallol and its subsequent photooxidation. However, this improvement in photocurrent is limited by the number of sites available in surface states for accepting electrons from pyrogallol and the corresponding increase in the photocurrent would reach a limit as A[Css] 0. The Interface Model. A model was developed by GoodmanZo for a Schottky barrier at a metal-semiconductor rectifying contact including trapping and edge effects. This mode120was modified with the inclusion of the voltage drop across the Helmholtz layer and applied to the present case under discussion. With the exception of that voltage drop, the model is illustrated in Figure 8. The parameters w, X, and Vbp refer to the space charge layer width, the region of filled traps (electron-hole recombination region), the ionization threshold potential for traps, and the flat-band potential, respectively. Other quantities relevant to the model are E F ,E,, Ec, and E". These are the energies of the Fermi level, the trap level, the bottom of the conduction, and the top of the valence band in the bulk, respectively. The positions E,, and Ess2do not enter in Goodman's model; they are the positions of the surface-state densities maxima as revealed in Fermi level pinned samples by the parallel conductance. There is no direct connection between the trap level and the maxima in the surface-state densities. A visual fitting procedure was used to extract the following parameters from the plot B in Figure la: the carrier ~ ] trap concentration, [2 concentration [ l (hO.l) X IO" ~ m - the (*0.2) X lo'' ~ m - ~the ] , V,,, -0.872 V (h50 mV) (SCE) and
+
I
\--/
From eq 13 and 16 -d[XR-l -dt
I
the VI,,, -0.42 V (h50 mV) (SCE) in this case (Figure lb). Another heated sample without Fermi level pinning had the same carrier and trap concentration within a factor of 2 and the same Vbp within 10 mV, but the V,,, was estimated to be -0.65 V ( f 5 0 mV) (SCE). The derivation of the modified Goodman model will be published e 1 s e ~ h e r e . l ~ Trap emission rates were estimated by the Horowitz method.18 This method consists of plotting the parallel capacitance measured at high anodic voltage [ 1 V (SCE)] (w >> A) as a function of frequency and comparing the behavior of the capacitance at intermediate frequencies with that measured at the lowest frequency (100 Hz). It was not possible to use voltages higher than 0.145 V (SCE) with our samples because of loss of the electrode polarizability and therefore the estimate of the rate is within a factor of 3. Comparison between theory and experiment is shown in Figure 9. The sub-band-gap spectrum of Zr-doped Fe203 studied by Horowitz is essentially identical with that expected for pure Fez03 and trap emission lifetimes are of the order of 985 ms.I8 In our case, the sub-band-gap spectrum (Figure 5) shows impurity bands apart from the 1.5-eV structural level with 1-ms trap emission lifetime. Since the major impurity in our samples is Ti, it is highly probable that Ti is not only a donor but produces fast traps. Also, the use of Goodman's model is justified at 100 ~, Hz. This model is valid only if the ac frequency w
