The Electrochemical Impedance of One-Equivalent Electrode

at the n-GaAs electrode. On the basis of the experimental impedance spectra and of the theoretical equivalent circuit derived in part 1 (Hens, Z. J. P...
0 downloads 0 Views 106KB Size
Download PDF
130

J. Phys. Chem. B 1999, 103, 130-138

The Electrochemical Impedance of One-Equivalent Electrode Processes at Dark Semiconductor/Redox Electrodes Involving Charge Transfer through Surface States. 2. The n-GaAs/Fe3+ System as an Experimental Example Z. Hens* and W. P. Gomes UniVersiteit Gent, Laboratorium Voor Fysische Chemie, Krijgslaan 281, B-9000 Gent, Belgium ReceiVed: June 25, 1998; In Final Form: October 26, 1998

In this paper, an electrochemical study of the n-GaAs/Fe3+ system is presented. Combining the results of current density vs potential, Mott-Schottky, and electrochemical impedance measurements, it is shown that charge transfer through surface states is the most plausible reaction mechanism for the Fe3+ to Fe2+ reduction at the n-GaAs electrode. On the basis of the experimental impedance spectra and of the theoretical equivalent circuit derived in part 1 (Hens, Z. J. Phys. Chem. 1998, 103, 122), the charge-transfer mechanism is analyzed in detail. The Fe3+ reduction rate shows a marked evolution as a function of time which, basing upon the electrochemical impedance results, is attributed to an increase in the number of surface states.

1. Introduction In this paper, the electrochemical impedance spectrum of the n-GaAs/Fe3+ system in 1 M H2SO4 aqueous solution is analyzed on the basis of the theoretical impedance expression for charge transfer through surface states as derived in the preceding paper (Part 1).1 The electrochemical characteristics of the n-GaAs/ Fe3+ and the p-GaAs/Fe3+ systems in aqueous sulfuric acid have been studied before by several authors.2-6 However, their experimental results and conclusions do not agree on the nature of the charge-transfer mechanism. Using rotating ring-disk electrodes, Menezes et al.2 showed that the consumption rate of Fe3+ at dark n-GaAs electrodes in a 1 M H2SO4 solution is almost zero if the disk current is zero, in contrast to the case of Ce4+ (0.1 M H2SO43) and Fe(CN)63(1 M KOH2) at n-GaAs. At dark p-GaAs electrodes in 2 × 10-3 M Fe3+, these authors did not observe Fe3+ reduction. Decker et al.3 performed analogous experiments in 0.1 M H2SO4 + 6 × 10-3 M Fe3+ solution at n-GaAs, confirming the results of Menezes et al. Moreover, Decker et al. could measure only a very weak electroluminescence signal during cathodic reduction of Fe3+, lower by about a factor of 500 than the signal obtained during the reduction of Ce4+ or Fe(CN)63- at n-GaAs. Combining these two results, the authors of ref 3 concluded that no hole injection by Fe3+ occurs. Experiments at the p-GaAs electrode were also performed by Kelly et al.4 These authors observed diffusion-limited cathodic reduction of Fe3+ in 5 × 10-2 M Fe3+ solution if anodic potentials were avoided during the potential scan, suggesting Fe3+ reduction by hole injection. Furthermore, they reported that, after a step from anodic to cathodic potentials was applied to an electrode, prepolarized at anodic potentials, the diffusionlimited current was only reached after approximately 60 s. Schro¨der et al.5 published results of electrochemical impedance measurements at the n-GaAs/Fe3+ system in 0.1 M H2SO4 solution (unspecified Fe3+ concentration). They showed that in the limit of high frequencies of the sinusoidal potential perturbation, a resistance equal to kBT/e| j| stands in parallel with * Research assistant of the FWO-Vlaanderen (Fund for Scientific Research, Flanders, Belgium).

the capacitance of the semiconductor/electrolyte interface.20 As these authors considered such a resistance as being typical for a recombination step in the reaction mechanism, they concluded that Fe3+ is reduced by hole injection in the potential range of the cathodic reduction current. Plieth et al.6 published current density versus potential curves for the reduction of Fe3+ at n-GaAs as a function of the doping density of the semiconductor. These authors observed a very slow onset of the Fe3+ reduction curve in 0.5 M H2SO4 solution, especially for the lowest doping concentration considered (5 × 1016 cm-3). They suggested a reaction mechanism through surface states or, alternatively, a shift of the band edges to explain these results. In the present paper, we present the results of an electrochemical impedance spectroscopic study of the n-GaAs/Fe3+ system using a 1 M H2SO4 + 4 × 10-3 M Fe3+ solution. This study is combined with current density vs potential and MottSchottky measurements both at n- and p-GaAs electrodes. The results of the latter two types of measurements show that no simple charge-transfer mechanism such as direct hole injection or direct electron capture can explain the reduction of Fe3+ at GaAs. This idea is confirmed by the electrochemical impedance spectrum measured, which is successfully described by the equivalent circuit for surface-state mediated charge transfer. In addition, the reduction current of Fe3+ at n-GaAs increases markedly as a function of time when the electrode is polarized cathodically. This time dependent reduction rate is reflected by an evolution of the electrochemical impedance spectrum: qualitatively, the spectrum remains unaltered as a function of time, but the numerical values of the different circuit parameters show a systematic time-dependence. Moreover, it is shown that the Fe3+ reduction rate at n-GaAs is strongly influenced by the electrode pretreatment used. Finally, additional experiments were performed using a 1 M H2SO4 + 5 × 10-2 M Fe3+ solution, since the results of Kelly et al. were obtained at this Fe3+ concentration. In the discussion part of the paper, the correspondence between the theoretical impedance as derived in the previous paper (part 1)1 and the experimental results obtained here is thoroughly discussed. Combining the impedance data with the

10.1021/jp9827678 CCC: $18.00 © 1999 American Chemical Society Published on Web 12/15/1998

One-Equivalent Electrode Processes. 2

J. Phys. Chem. B, Vol. 103, No. 1, 1999 131

results of the current density vs potential and the Mott-Schottky measurements, it is concluded that charge transfer through surface states constitutes the most plausible reaction mechanism. The evolution in time of the reduction rate may then be explained as an increase in the number of these surface states. 2. Experimental Section All electrodes used were (100) faces of single-crystal GaAs obtained from MCP Electronics. The n-GaAs and p-GaAs samples were doped with Si (2.3 × 1016 cm-3) and Zn (1.4 × 1017 cm-3), respectively. They were mounted as disk electrodes with a diameter of either 3 or 4 mm. All solutions were prepared using reagent grade chemicals. The indifferent electrolyte was always a 1 M H2SO4 aqueous solution. The Fe3+ solutions were prepared by dissolving the appropriate amount of Fe2(SO4)3 into the indifferent electrolyte. The electrode pretreatment consisted either of simple mechanical polishing using Al2O3 powder (50 nm) (pretreatment 1) or of mechanical polishing followed by a short etch in a mixture of H2SO4(98%):H2O2(30%):H2O (3:1:1) (pretreatment 2) or of mechanical polishing followed by a diffusion-limited photoanodic etch in 0.01M KOH, removing a 10 µm thick layer from the electrode surface (pretreatment 3). Experiments were carried out in a conventional threeelectrode electrochemical cell, closed from air, using a saturated calomel electrode (SCE) as the reference electrode. To keep the cell oxygen free, nitrogen was bubbled through the electrolyte prior to and between all measurements while it was blown over the solution during the measurements. The cell potential was controlled by a Zahner IM6 impedance measurement system, which allows both current-potential and impedance measurements. The electrochemical impedance spectra were recorded in the so-called pseudo-galvanostatic mode, meaning that the dc current is kept constant within (user-defined) limits of (100 nA while an impedance spectrum is recorded. This is achieved by changing the dc potential if the current exceeds the predefined limits. We preferred this operation mode because we noticed that a potential drift during the time of the measurement influenced the resulting impedance spectrum less than a current drift. Furthermore, the dc potential could be monitored during the course of each impedance measurement, so that it was possible to evaluate the stability of the system during an impedance measurement. The amplitude of the smallsignal potential perturbation (root mean square) was set equal to 2 or 5 mV, depending on the measurement noise. 3. Experimental Results 3.1. Current-Potential Measurements. Current density vs potential measurements were performed at n-GaAs and p-GaAs rotating-disk electrodes. Figure 1 shows current density vs potential curves obtained at an n-GaAs electrode in a 4 × 10-3 M Fe3+ solution for the three different pretreatments used. A current density vs potential curve recorded in a 1 M H2SO4 solution containing 4 × 10-3 M Ce4+ is shown as well. Prior to recording the current density vs potential curves, potentials more negative than -600 mV vs SCE were avoided since we observed a time-dependent increase of the reduction current at potentials more negative than -600 mV vs SCE (cf. infra). Similarly as reported by Plieth et al.6 for n-GaAs with doping concentration 5 × 1016 cm-1, Figure 1 shows a slow onset of the Fe3+ reduction current density curve (compare Fe3+ curves to the Ce4+ curve). Moreover, the current density vs potential curves strongly depend on the electrode pretreatment, the least rigorous method (simple mechanical polishing) yielding the

Figure 1. Current density vs potential curves, obtained at n-GaAs rotating disk electrodes (frot ) 10 Hz, all 3 pretreatments). Sweep rate: 20 mV s-1. (s) 1 M H2SO4; (-‚-) 1 M H2SO4 + 4 × 10-3 M Fe3+, pretreatment 1; (- -) 1 M H2SO4 + 4 × 10-3 M Fe3+, pretreatment 2; (‚‚‚) 1 M H2SO4 + 4 × 10-3 M Fe3+, pretreatment 3; (- -) 1 M H2SO4 + 4 × 10-3 M Ce4+, pretreatment 2.

TABLE 1: Variation of the Current Density through the n-GaAs/Fe3+ Electrode as a Function of Time for Three Different Values of the Electrode Potentiala applied potential (mV vs SCE)

current density variation (nA cm-2 s-1)

-800 -700 -600

-390 -71 -8.3

a Measurements performed at n-GaAs rotating disk electrodes (f rot ) 10 Hz, pretreatment 2) in a 1 M H2SO4 aqueous solution containing 4 × 10-3 M Fe3+. The increase is a mean value, determined between 5 and 30 min after the potential was applied to the electrode.

largest current densities. However, in neither of the three cases, a diffusion-limited current plateau is reached at -800 mV vs SCE. If a potential step is applied to the rotating-disk electrode from an open-circuit potential to a potential at which Fe3+ is reduced, the absolute value of the current density decreases at first but increases systematically afterward. The average increase rates of (the absolute value of) the current density, measured between 5 and 30 min after the potential step was applied, are summarized in Table 1. Clearly, this rate of increase is potentialdependent, varying from 390 nA cm-2 s-1 at -800 mV vs SCE to a very small value (8.3 nA cm-2 s-1) at -600 mV vs SCE. These results show that no simple charge-transfer mechanism governs the Fe3+ reduction at n-GaAs in a 1 M H2SO4 + 4 × 10-3 M Fe3+ solution. As for the current density vs potential measurements performed in solutions containing 4 × 10-3 M Fe3+, no diffusionlimited reduction plateau is reached at -800 mV vs SCE during current density vs potential measurements at n-GaAs in 1 M H2SO4 + 5 × 10-2 M Fe3+ solutions. However, the current density at -800 mV is higher by a factor of 20-40 in this solution than in the solution containing 4 × 10-3 M Fe3+. At a rotating p-GaAs electrode, almost no Fe3+ reduction occurs in 4 × 10-3 M Fe3+ solution (cf Figure 2). Subtracting the current density vs potential curve recorded without Fe3+ from that with Fe3+ added yields, after correcting for the shift of the flat-band potential (cf. infra), a more or less constant current of approximately 1 µA cm-2 (solid line in Figure 2).

132 J. Phys. Chem. B, Vol. 103, No. 1, 1999

Figure 2. Current density vs potential curves, measured at a p-GaAs rotating disk electrode (pretreatment 2, frot ) 10 Hz). Sweep rate: 20 mV s-1. (-‚-) 1 M H2SO4; (- -) 1 M H2SO4 + 4 × 10-3 M Fe3+; (s) net Fe3+ reduction current.

Figure 3. Mott-Schottky plots determined at n-GaAs in a 1 M H2SO4 aqueous solution with (0) and without (9) Fe3+ and at p-GaAs in a 1 M H2SO4 aqueous solution with (O) and without (b) Fe3+. Electrode pretreatment, 2; electrode rotation rate, 10 Hz; Fe3+ concentration, 4 × 10-3 M; frequency of the potential perturbation, 50 kHz; stabilization time after each potential step, 5 s.

Polarizing the electrode at -800 mV vs SCE for half an hour did not lead to an increase of the cathodic current density. Hence, neither the diffusion-limited Fe3+ reduction nor the timedependent rise of the cathodic current density, as observed by Kelly et al. in 5 × 10-2 M Fe3 solutions,4 is observed in the 4 × 10-3 M Fe3+ solutions used here. 3.2. Mott-Schottky Measurements. The flat-band potential of the n-GaAs and p-GaAs electrodes was determined by measuring the interfacial capacitance as a funcion of the applied electrode potential. In Figure 3, Mott-Schottky plots for n-GaAs and p-GaAs obtained at 50 kHz in 1 M H2SO4 without and with Fe3+ are shown. The n-GaAs plots were recorded from anodic to cathodic polarization, the p-GaAs plots from cathodic to anodic polarization. From the figure, it follows that the flatband potential is approximately -950 mV vs SCE for n-GaAs and +325 mV vs SCE. for p-GaAs if no Fe3+ is added to solution. This means that the band edges of n-GaAs and p-GaAs are situated approximately at the same energy level. For both semiconductor types, the flat-band potential shifts anodically after 4 × 10-3 M Fe3+ is added to the indifferent electrolyte. Depending on the measurement, the extent of this potential shift varies between +50 and +150 mV. At n-GaAs, the Mott-

Hens and Gomes

Figure 4. Electrochemical impedance spectrum recorded at an n-GaAs rotating disk electrode under pseudo-galvanostatic control (pretreatment 2, frot ) 10 Hz) in a 1 M H2SO4 aqueous solution containing 4 × 10-3 M Fe3+. The electrode was polarized cathodically for 55 min (see ref 24). Current density, -350 µA cm-2; the electrode potential varied between -727 and -719 mV vs SCE during the experiment. The solid line represents a simulation based upon the equivalent circuit shown in the insert of the figure. The symbol Rs stands for the real part of the impedance, whereas Xs represents its imaginary part. Inset: equivalent circuit used to simulate the experimental data. The triple line indicates a constant phase element.

Schottky plot now indicates a displacement of the band edges in the potential range between -200 and -500 mV vs SCE. The slope of the Mott-Schottky plots at potentials lower than -500 mV vs SCE is approximately equal to the slope at potentials higher than -200mV, indicating that the band edges are fixed at those potentials. A correlation between the shift of the flat-band potential and the electrode pretreatment could not be established. In solutions containing 5 × 10-2 M Fe3+, the flat-band potential of the p-GaAs electrode is approximately +150 mV vs SCE hence showing, in contrast to the case of the 4 × 10-3 M Fe3+ solution, a cathodic shift as compared to the value measured in the indifferent electrolyte. At n-GaAs, the flatband potential shifts from 150 to 200 mV in the anodic direction if 5 × 10-2 M Fe3+ is added to the indifferent electrolyte. 3.3. Electrochemical Impedance Measurements. Since the dc conditions of the electrode (dc current density as a function of applied potential) shift appreciably as a function of time (cf section 3.1), we determined the electrochemical impedance pseudo-galvanostatically22 as a function of time. Such a time scan includes applying a dc current density through the electrochemical cell and recording regularly the electrochemical impedance spectrum together with the dc potential.23 The drift as a function of time was sufficiently slow to make the electrochemical impedance spectra obtained reliable, with the exception of measurements at low frequencies. Therefore, the frequency of the potential variation applied was limited between 250 kHz and 1 Hz. Qualitatively, all electrochemical impedance spectra obtained are identical to the spectrum shown in Figure 4. This spectrum was recorded at a rotating n-GaAs electrode which was polarized cathodically24 for 55 min. In the insert of Figure 4, we show the equivalent circuit for transfer of conduction band electrons through surface states as calculated in the preceding article (part 1).1 In this circuit, C1 stands for the capacitance of the semiconductor depletion layer whereas the subcircuit consisting of R1, R2, C2, and W describes the charge transfer. Differently from the circuit presented in part 1, the capacitance C2 is

One-Equivalent Electrode Processes. 2

J. Phys. Chem. B, Vol. 103, No. 1, 1999 133

replaced by a constant phase element (CPE) here, whereas the diffusion element for finite diffusion length is reduced to a Warburg impedance. In the fitting algorithm used, the impedance of the CPE is defined as (ω0 ) 2π1000 s-1):7

ZCPE )

( )

1 ω0 ω0C2 iω

a

(1)

This definition ensures that the CPE parameter C2 has units nF cm-2. Furthermore, since ω0 ) 2π1000 s-1, the expression 1 puts the magnitude of ZCPE at 1000 Hz equal to the magnitude of a perfect capacitance with capacity C2 at 1000 Hz.25 The reason a CPE yields a better fit to the experimental spectra than a true capacitance is not clear. Possibly, the assumption of charge transfer through identical, monoenergtic surface states is too much of an idealization. On the other hand, the Warburg impedance used to simulate the experimental spectra is defined as

ZW )

W xiω

(2)

This impedance makes up the high frequency limit of the diffusion impedance for finite diffusion length. Due to the drifting dc conditions, the latter impedance element could not be recorded properly since it requires frequencies equal to or below 100 mHz. In the limited frequency range which we used to avoid a major influence of the dc drift on the impedance spectra (250 kHz to 1 Hz), the Warburg impedance provides a good approximation for the diffusion impedance for finite diffusion length. The simulation of the experimental spectra recorded to the circuit containing a CPE and a Warburg impedance always proved to be very successful, as demonstrated, e.g., by the solid line in Figure 4. Quantitatively, the numerical values of the circuit parameters obtained by fitting the experimental spectra to the equivalent circuit exhibit a typical behavior as a function of the period during which a programmed current density was passed through the interface. The time evolution of the numerical values of the resistances R1 and R2 when a current density of -283 µA cm-2 passes through the electrode/electrolyte interface is represented in Figure 5a. Clearly, the value of the resistance R2 varies markedly with time. From a relatively large initial value, it decreases continuously after a short, transient increase,26 becomes smaller than the value of the resistance R1, and seems to reach a limiting value. The resistance R1 on the other hand is essentially constant, neither depending on time nor on dc potential. As shown in Figure 6a, its numerical value is equal to 1.01kBT/ e/j/. The insert of Figure 5a shows the time evolution of the applied potential. The observed increasing potential at constant current density is in accordance with the increasing current density (absolute value) at constant potential (cf. section 3.1.). Figure 5b shows the time evolution of the numerical values of the capacitance C1 and the CPE parameter C2 during the same experiment of Figure 5a. From Figure 5b, it follows that especially the value of the CPE parameter C2 increases with time toward a (more or less) limiting value. We observed this evolution systematically when recording impedance spectra as a function of time. Averaging the largest values of C2 measured over seven time scans yields a mean value of 7.1 ( 1.5 µF cm-2. On the other hand, the value obtained for the capacitance C1 varies only slightly with time. Numerically, it is approximately equal to the interfacial capacitance as obtained from Mott-Schottky measurements. The time dependence it exhibits

Figure 5. (a) Evolution of the numerical values of the resistances R1 (O) and R2 (b) as a function of the time during which a current density of -283 µA cm-2 was drawn through the electrochemical cell. Electrolyte solution, 1 M H2SO4 + 4 × 10-3 M Fe3+; rotation rate of the n-GaAs electrode, 10 Hz; electrode pretreatment, 2. The insert shows the evolution of the cell potential during the experiment as a function of time. (b) Evolution of the numerical values of the capacitance C1 (O) and the CPE parameter C2 (b). See caption of Figure 5a for experimental details.

(decreasing value) as compared to the time dependence of the dc potential (increasing value) is consistent with this interpretation as well. In Figure 6b, we again show the numerical value of the CPE parameter C2 as a function of time. However, the dc current is not constant for the successive impedance spectra recorded now but is varied in a nonsystematic way between two measurements. The cell potential applied during the impedance measurement is indicated in the figure. The evolution of the numerical value of C2 shows that it has a general tendency to increase with time, regardless of whether the dc potential increases or decreases. This fact could not be deduced from Figure 5a and b solely, since in the course of the experiments reproduced there, the dc potential decreases systematically with time as well. The numerical value of the Warburg parameter W is not depicted. Since most measurements occurred at current densities considerably smaller than the diffusion limit, this was the least reliable of all circuit element data. As a function of the pretreatment applied to the electrode, we observed a systematic difference between the numerical values of the CPE parameter C2 for the first impedance spectrum recorded after a dc current was applied to the working electrode. The smallest values of this circuit element are observed for the photoanodically etched samples, followed by the electrodes dipped in H2SO4:H2O2:H2O; the largest value (approximately 10 times larger than the value obtained after pretreatment 3) is

134 J. Phys. Chem. B, Vol. 103, No. 1, 1999

Figure 6. (a) Dependence of the inverse of the resistance R1 on the current density passing through the semiconductor/electrolyte interface. Different current densities are obtained by using different Fe3+ concentrations (varying between 1 × 10-3 M to 4 × 10-3 M) and different polarization times. The slope of the fitting line equals 1/25.6 [mV-1]. (b) Variation of the numerical value of the CPE parameter C2 and the cell potential as the current density is varied in a nonsystematic way between the recording of the different impedance spectra. At the beginning of this experiment, the electrode was polarized cathodically for 60 min. Time between two consecutive measurements: 4 min.

recorded for an electrode that was only polished mechanically. It should, however, be stressed that the dc current varies in a similar way as a function of the pretreatment. Hence, it is not clear whether a direct correlation between the value of this CPE parameter and the pretreatment exists, or only an indirect one, i.e., due to the cathodic current having a different value. Impedance spectra recorded between 500 kHz and 5 Hz in a 1 M H2SO4 + 5 × 10-2 M Fe3+ solution yield an impedance spectra similar to that of Figure 4: two succesive semicircles at high frequencies are followed by a Warburg impedance. The major difference between both spectra is the numerical value of the CPE parameter C2. Normalization at 1000 Hz yields now a corresponding capacitance from 20 to 30 µF cm-2, depending on the measurement. 4. Discussion 4.1. Charge-Transfer Mechanism. The impedance spectra corresponding to the Fe3+ reduction at n-GaAs are successfully

Hens and Gomes approximated by the equivalent electrical circuit for transfer of conduction-band electrons through surface states as derived previously.1 Nevertheless, this correspondence is not sufficient to prove that the charge transfer actually occurs through surface states, since hole injection followed by recombination may yield a similar impedance spectrum.1,8 However, the current density vs potential and Mott-Schottky measurements supply additional arguments suggesting a charge-transfer mechanism through surface states. From the literature we know that, in contrast with, e.g., the n-GaAs/Ce4+ system, no Fe3+ reduction occurs at the n-GaAs electrode when no cathodic current flows. Therefore, cathodic hole injection by Fe3+ constitutes a possible reaction mechanism only if an upward shift of the n-GaAs band edges between the anodic and the cathodic potential region occurs. From the MottSchottky plots measured in Fe3+-containing solutions, it follows that this band-edge shift mainly occurs between -200 and -500 mV vs SCE. At more negative potentials, the band edges appear to be fixed at the semiconductor surface again.27 If the bandedge position is to be a critical parameter for the Fe3+ reduction, one would expect a more or less pronounced current-plateau at potentials lower than -500 mV. However, the current density vs potential plots show a continuously increasing current starting at approximately -300 mV. This makes direct hole injection unlikely as a charge-transfer mechanism. Next, we observed a marked dependence of the Fe3+ reduction current on the electrode pretreatment, the more careful method yielding the lowest reduction rate. However, no indication of a systematic difference in position of the band edges as a function of the electrode pretreatment could be found. Hence, it is hard to explain the dependence of the reduction rate on the pretreatment by a direct hole injection mechanism. On the contrary, a plausible relation between the nature of the pretreatment and the density of surface statessa more careful pretreatment yielding less surface statessmay explain the observed dependence of the current density on the electrode pretreatment rather straightforwardly, if surface-state charge transfer is assumed. A third point in favor of a charge-transfer mechanism through surface states is the anodic shift of the flat-band potential observed when Fe3+ is added to the indifferent electrolyte. At p-type electrodes, a shift of the flat-band potential under cathodic polarization is not compatible with a direct hole injection mechanism. The strong electric field in the depletion layer at cathodic potentials prevents accumulation of directly injected valence-band holes at the semiconductor surface. This was, e.g., demonstrated at the p-InP/Fe(CN)63- system.9 In contrast, transfer of an electron from a surface state at the p-GaAs surface to an Fe3+ ion in solution results in a surface state occupied by a hole. Subsequent excitation of this hole to the semiconductor valence band causes dc current flow (which was actually observed although it was very small). This excitation rate being low, a considerable number of holes may be accumulated in localized states at the semiconductor surface, explaining the observed shift of the flat-band potential. In contrast with direct hole injection at p-type electrodes, hole injection at n-type electrodes does cause a shift of the band edges at the semiconductor surface in the anodic potential range. The electric field in the depletion layer keeps the injected holes at the surface of the n-type electrode, enabling dissolution of the semiconductor. This causes an accumulation of positive charge at the semiconductor surface (valence-band holes and intermediates of the anodic decomposition), resulting into an anodic shift of the flat-band potential. This phenomenon was reported, e.g., for n-GaAs/Ce4+,5 n-GaAs/Fe(CN)63-,10 and n-InP/Fe(CN)63-.9

One-Equivalent Electrode Processes. 2

J. Phys. Chem. B, Vol. 103, No. 1, 1999 135

However, the rate of hole injection by Fe3+ at an anodically polarized n-GaAs electrode is almost zero.2,3,28 Therefore, an explanation of the observed shift of the flat-band potential measured at n-type electrodes by hole injection and subsequent anodic dissolution is not obvious. These arguments make a reaction mechanism involving charge transfer through surface states clearly more plausible than direct hole injection for the Fe3+ reduction at n-GaAs in a 1 M H2SO4 aqueous solution. In light of this hypothesis, it is interesting to investigate more closely the numerical values of the circuit elements obtained by fitting the experimental spectra to the equivalent circuit valid for surface-state-mediated charge transfer. In this way, interesting details on the charge-transfer mechanism may be revealed. Resistance R1. According to formula 29 of part 1,1 this resistance is the inverse of the partial derivative of the current density at the semiconductor side of the interface with respect to the potential drop across the semiconductor:

(

)

sc ∂( j sc a + jc ) R1 ) ∂φsc

-1

)

kBT

(3)

e/j sc c/

The second equality, in which j sc c stands for the cathodic current density at the semiconductor side of the interface, is calculated using the current expressions of formula 21a in Part 1, together with the equality φsc ) -(kBT/e)ln(ns/ni). As discussed in ref 11, this resistance is typical for reaction steps, the rate of which is proportional to the density of majority charge carriers at the surface of the semiconductor. From the experimental spectra, it follows that R1 is equal to 1.01kBT/e/j/, with j the net current density passing through the interface. This result is in agreement with eq 3 (within an error of 1%) if29 j sc a ) 0. Hence, from the value of this resistance, we may conclude that the transfer of an electron from the conduction band to the surface state30 is irreversible, which means that excitation of electrons from the surface states to the conduction band is negligible as compared to the capture of conduction band electrons by the surface states. Schro¨der et al.5 also reported that a resistance equal to kBT/ e/j/ stands in parallel with the interfacial capacitance at high frequencies. This observation is confirmed here but the interpretation that this resistance indicates a recombination process is probably not correct: irreversible transfer of conduction band electrons to surface states results into a similar resistance. Resistance R2. In part 1, this resistance was calculated as (cf. formula 31 in ref 1):

(

)( ) (

∂j sc

sc ∂j sc kBT ∂j + γs R2 ) ∂θ e ∂φsc ∂φsc

-1

)

H ∂j H kBT ∂j γs e ∂φH ∂φ

-1

(4)

In the (mathematical) limit of an infinite amount of surface states (density s), this expression simplifies to31

( )

∂j H lim R2 ) ∂φH sf∞

-1

)

kBT e[(1 - R)j Ha - ∂j Hc ]

(5)

Furthermore, as shown in Appendix A, the partial derivative of R2 with respect to the density of surface states is negative for all finite values of s. Let us assume now that the transfer of electrons between the surface states and the Fe3+ ions is only possible in the cathodic direction, which means that an electron may be transferred from an occupied surface state to an Fe3+ ion in solution but not

from an Fe2+ ion to an empty surface state. In that case, the fact that the partial derivative ∂R2/∂s is negative yields, in combination with eq 5, a lower limit for the resistance R2 at a given current density:

Rmin 2 )

1 kBT R e/j/

(6)

Experimentally, we observed that the resistance R2 becomes smaller than the resistance R1 after a certain time. It was shown that the latter resistance is equal to kBT/e/j/. Therefore, eq 6 is contradicted by the experimental results, since R e 1. This means that the exchange of charge between a surface state and an electroactive species in solution must be bidirectional, in the sense that Fe3+ may capture an electron from an occupied surface state and that Fe2+ may inject an electron into an empty surface state. This conclusion is in accordance with photoanodic stabilization experiments performed at n-GaAs in 0.1 M H2SO4 solution, showing that Fe2+ may donate an electron to certain intermediates of the photoanodic dissolution reaction.12 This conclusion remains valid if charge transfer occurs by hole injection into the valence band. However, the exchange of holes between the valence band and the electroactive species in solution is bidirectional now. Capacitance C2. According to formula 32 of part 1, the capacitance C2 equals

C2 )

( )( ∂j sc

∂φsc

sc sc 1 ∂j 1 ∂j + es ∂θ CH ∂φsc

)

-1

(7)

It follows from this formula that C2 may be considered as the series connection32 of the capacitance of the Helmholtz layer (CH) and a capacitance Css given by

Css )

( )( ) ∂j sc

∂φsc

sc -1

1 ∂j es ∂θ

)s

e2 βnns(1 - θ) kBT βnns + n

(8)

In the final expression, βn [cm3 s-1] and n [s-1] are the rate constants for capture of a conduction band electron by an empty surface state and for excitation of an electron from an occupied surface state to the conduction band, respectively. The capacitance Css is equal to the one calculated by Cardon.1,13 If the excitation of electrons from an occupied surface state to the conduction band is negligible, this capacitance is simply proportional to the number of unoccupied surface states. Two limiting cases for the capactitance C2 can be considered: C2 becomes equal to Css in the limit s f 0; on the other hand, it becomes equal to CH if s f ∞, as concluded previously by Vanmaekelbergh.8 Since C2 is always smaller than either of its constituting elements, the value of CH constitutes an upper limit for the capacitance C2. This means that the highest value of the capacitance C2 measured provides a lower limit for the capacitance of the Helmholtz layer at the n-GaAs/electrolyte interface. The experimental results yield a lower limit15 of 7.1 µF cm-2, a value which is comparable to previously reported values of the capacitance of the Helmholtz layer at semiconductor electrodes: 7.0 µF cm-2 for the R-Fe2O3/electrolyte system,33 5 µF cm-2 for the p-GaP/electrolyte system,15 and 4 µF cm-2 for n-Si(111) in 1 M NH4F.16 This result supports the physical interpretation of the proposed equivalent circuit. For the first spectra recorded during each time scan, the capacitance C2 is much smaller than this estimated value of CH. Thus, for those spectra, C2 is approximately equal to Css. Since Css is proportional to the density of surface states, the observed

136 J. Phys. Chem. B, Vol. 103, No. 1, 1999 dependence of the initial value of C2 on the electrode pretreatment is consistent with the assumption that a more careful pretreatment will yield less surface states. However, one should not consider this correspondence as a definite proof, since other variables, e.g., the occupancy θ, have an influence on Css as well. Finally, the question arises whether the contradictory results found in the literature can be interpreted in terms of the reaction mechanism proposed here. The results of Menezes et al.2 and of Decker et al.3 indicating a direct conduction band process, i.e., a lack of Fe3+ consumption in the anodic polarization range and of electroluminescence during cathodic reduction, are clearly in accordance with a reaction mechanism involving transfer of conduction band electrons through surface states. As shown previously,11 the resistance kBT/e/j/ which was found in parallel with the capacitance of the semiconductor/electrolyte interface at high frequencies by Schro¨der et al.5 does not necesseraly indicate a recombination step in the reaction mechanism. This resistance is part of the equivalent circuit of surface-state mediated charge transfer as well, if the transfer of electrons between the conduction band and the recombination level is irreversible. Hence, by assuming charge transfer through surface states, the contradiction between these interpretations is solved. According to Plieth et al.,6 the slow onset of the Fe3+ reduction is caused by a shift of the semiconductor band edges. However, this hypotheses cannot explain all experimental results presented here. First of all, the Mott-Schottky curve recorded in a solution containing 4 × 10-3 M Fe3+ only show a shift of the band edges in the potential range between -200 and -500 mV vs SCE. Next, a shift of the flat-band potential solely is insufficient to explain the observed time-dependence of the system. If this were the case, a unique current density vs potential curve should exist for every value of the flat-band potential and, inversely, a given value of the flat-band potential is associated to every j-V working point of the electrode. Therefore, a particular working point should always yield the same impedance spectrum. Now, looking at Figure 5a, it is clear that the working point of the first and the fourth measurement is approximately the same. The values of the impedance elements C1, C2, and R2, however, are clearly different. Thus, a shift of the flat-band potential solely is insufficient to account for the time-dependence of the Fe3+ reduction at n-GaAs. On the other hand, the results of Kelly et al.5 do not seem to fit into the proposed reaction mechanism. However, the results of our measurements indicate that the behavior of the GaAs electrode in Fe3+-containing solutions depends strongly on the Fe3+ concentration. The time-dependent rise of the reduction current toward the diffusion limited value at the p-GaAs electrode as observed by Kelly in 5 × 10-2 M Fe3+ solutions is completely absent in 4 × 10-3 M Fe3+ solutions. Moreover, the position of the flat-band potential of p-GaAs is markedly different for both Fe3+ concentrations, showing a cathodic shift in 5 × 10-2 M Fe3+ and an anodic shift in 4 × 10-3 M Fe3+, respectively. The electrochemical impedance measurements at n-GaAs in 1 M H2SO4 + 5 × 10-2 M Fe3+ yield a value of the CPE parameter C2 which is much higher than expected for the capacitance of the outer Helmholtz layer at n-GaAs. This indicates that the reaction mechanism in solutions containing 5 × 10-2 M Fe3+ might be complicated by adsorption of Fe3+ and/or Fe2+ on the GaAs surface. It remains however unclear whether adsorption is the clue to a better understanding of the different behavior of GaAs in solutions of low (4 × 10-3 M) as compared to high (5 × 10-2 M) Fe3+ concentration.

Hens and Gomes 4.2. The Time Evolution of the n-GaAs/Fe3+ Electrode Behavior. The measurements of the current density vs time and of the electrochemical impedance vs time show a systematic evolution in time of the n-GaAs/Fe3+ system. If the electrode is polarized for half an hour at -800 mV vs SCE, the current density (in absolute terms) increases markedly. However, this increase strongly depends on the applied potential. Analogously, the elements of the equivalent circuit R2 and C2 decrease and increase respectively as a function of the time during which a given current passes through the n-GaAs/electrolyte interface. The question arises whether this evolution can be analyzed in more detail, using the electrochemical impedance spectra recorded and the theoretical equivalent circuit calculated. In Appendix A, it is shown that for all finite values of the density of surface states, the partial derivative of R2 with respect to this density is strictly negative, whereas that of C2 with respect to this density is strictly positive. These results suggest that the time evolution observed is caused by an increase of the number of surface states. However, other variables, especially the occupancy θ, influence the value of the circuit elements R2 and C2 as well. From dc considerations, using eqs 15 and 21a-d from part 1 and the experimental fact that j ica is equal to zero, the occupancy θ may be written as

θ)

βnns + lacred βnns + lacred + lccox

(9)

Similar to their definitions given in part 1, la [cm3 s-1] and lc [cm3 s-1] represent the rate constant of the electron transfer between Fe2+ and an empty surface state and between an occupied surface state and Fe3+, respectively, whereas cred and cox stand for the concentration of reducing and oxidizing species at the interface, respectively. Using eq 9, it is easily shown that the partial derivative ∂θ/∂ns is given by

βnlccox ∂θ ) ∂ns (β n + l c + l c )2 n s a red c ox

(10)

Since this partial derivative is positive, the partial derivative ∂θ/∂φsc is negative. Furthermore, if thermal excitation of electrons from the surface state to the conduction band is negligible (as demonstrated experimentally), Css is simply proportional to (1 - θ). Therefore, if the density of surface states is constant, Css should increase when θ decreases, hence if φsc increases ()more anodic potentials) and, the other way round, Css should decrease when φsc decreases34 ()more cathodic potentials). However, from Figure 6b, it follows that C2 (and thus Css) has a general tendency to increases as a function of time, regardless of the value of the electrode potential. The most plausible explanation of the observed time-dependence is hence an increase of the number of surface states, which causes C2 to become larger and R2 to become smaller as a function of time. Using the measurements performed here, no decisive answer can be given about the cause of the increasing number of surface states. Is it caused by the Fe3+ reduction itself? Is it inherent to the n-GaAs electrode at cathodic potentials? A speculative explanation might be the formation of Ga0 at the n-GaAs surface at cathodic potentials, as recently observed by Erne´ et al.17 Since Ga0 is stable at the n-GaAs surface only at potentials negative from -750mV vs SCE,18,19 this process might indeed account for the observed potential-dependence of the time evolution. 5. Conclusion Combining the results of current density vs potential measurements, Mott-Schottky measurements and electrochemical

One-Equivalent Electrode Processes. 2

J. Phys. Chem. B, Vol. 103, No. 1, 1999 137

impedance spectroscopy at the n-GaAs and p-GaAs electrode during cathodic reduction of Fe3+, we showed that surface-statemediated charge-transfer constitutes the most plausible reaction mechanism for this electrode reaction. Moreover, from the results of studying the electrochemical impedance in detail, it follows that the charge-transfer step between the semiconductor conduction band and the surface states is irreversible in the sense that no significant excitation of electrons from the surface states to the conduction band occurs. On the other hand, the chargetransfer step between the surface states and the electroactive species in solution is shown to be possible in both directions, i.e., electron transfer from an occupied surface state to an Fe3+ ion in solution as well as from an Fe2+ ion in solution to an empty surface state. Finally, the electrochemical impedance measurements yield an experimental lower limit of the capacitance of the Helmholtz layer, equal to approximately 7 µF cm-2. In agreement with the idea of charge transfer through surface states, the Fe3+ reduction rate strongly depends on the electrode pretreatment. Using three different kinds of pretreatment, we showed that the most careful pretreatment yields the lowest reduction rate, probably corresponding to the lowest density of surface states. This property makes the Fe3+ reduction reaction a possible tool for investigating the efficiency of a surface pretreatment procedure. The reduction of Fe3+ at n-GaAs shows a marked dependence on the time during which a given current passes through the interface. On the basis of the electrochemical impedance results and of the theoretical treatment, we interpreted this time evolution as an increase of the surface-state density at the semiconductor surface. An explanation of this phenomenon could not be given. However, it should be clear that electrochemical impedance spectroscopy is an adequate tool to monitor this kind of time evolution. Acknowledgment. One of the authors (W.P.G.) wishes to thank the FWO-Vlaanderen (Fund for Scientific Research, Flanders, Belgium) for a research grant (Krediet aan Navorser). Appendix A In eq 4, the resistance R2 is written as:

∂j sc R2 )

sc kBT ∂j + γs ∂θ e ∂φsc

( )( ∂j sc

∂φsc

H ∂j H kBT ∂j γs e ∂φH ∂θ

)

(a1)

To simplify the notation, we will denote the four different partial derivatives in this Appendix as A (∂j sc/∂θ), B (∂j sc/∂φsc), C (∂j H/∂φΗ), and D (∂j H/∂θ), respectively. One can easily verify that A, B, and C are positive, whereas D is negative. From the expressions for the current densities at the semiconductor and the electrolyte side of the interface as given by eqs 21a-d in part 1,1 it follows that all terms in the expression for the resistance R2 (eq 4) are linear in the density of surface states, except for the terms containing a factor γs, which are quadratic in s. Therefore, the numerator of the partial derivative35 ∂R2/∂s is given by

(

)( ) (

) ( )(

)( ) )

kBT kBT 1 1 2 kBT A + γs B B γs C - D - A + γs B B × s s e e e s kBT kBT 2 kBT 1 γs C - D - A + γs B B γs C - D (a2) e e s e s

(

This expression may be simplified to

1 kBT kBT 2 kBT 1 - γs γ BBC - γs ABC + ABD s e s e s e s

(a3)

From this latter equation, it immediately follows that the numerator is strictly negative, yielding a negative partial derivative. In the mathematical limit s f ∞ the partial derivative becomes zero since the denominator contains a sixth power term of s whereas the numerator contains a fourth order term only in the density of surface states. Analogously, the capacitance C2 is given by the expression (eq 7)

C2 )

( )( ∂j sc

∂φsc

)

sc sc 1 ∂j 1 ∂j + es ∂φ CH ∂φsc

-I

(a4)

Using the same notation, the numerator of the partial derivative ∂C2/∂s becomes

(

) ( )

1 1 1 1 1 B + B A+ B -B s es CH s CH

(a5)

From this, it may be concluded that the partial derivative ∂C2/ ∂s is positive, except, again, in the mathematical limit s f ∞ where a partial derivative equal to zero is obtained. References and Notes (1) Hens, Z. J. Phys. Chem. B 1999, 103, 122. (2) Menezes, S.; Miller, B. J. Electrochem. Soc. 1983, 130, 517. (3) Decker, F.; Pettinger, B.; Gerischer, H. J. Electrochem. Soc. 1983, 130, 1335. (4) Kelly, J.; Notten, P. H. L. Electrochim. Acta 1984, 29, 589. (5) Schro¨der, K.; Memming, R. Ber. Bunsen-Ges. Phys. Chem. 1985, 89, 385. (6) Plieth, W.; Wetzenstein, S. Electrochim. Acta, 1994, 39, 1237. (7) IM6 Owner’s Manual; Zahner Elektrik: Kronach, Germany. (8) Vanmaekelbergh, D. Electrochim. Acta 1997, 42, 1135. (9) Vermeir, I. E.; Gomes, W. P. J. Electrochem. Soc. 1994, 365, 59. (10) Notten, P. H. L. Electrochim. Acta 1987, 32, 575. (11) Hens, Z.; Gomes, W. P. J. Electroanal. Chem. 1997, 437, 77. (12) Vanmaekelbergh, D.; Gomes, W. P.; Cardon, F. Ber. Bunsen-Ges. Phys. Chem. 1985, 89, 987. (13) Cardon, F. Physica, 1972, 57, 390. (14) Horowitz, G. J. Electroanal. Chem. 1983, 159, 421. (15) Goossens, H. H.; Gomes, W. P.; Cardon, F. J. Electroanal. Chem. 1990, 278, 335. (16) Oskam, G.; Hoffmann, P. M.; Searson, P. C. Phys. ReV. Lett. 1996, 76, 1521. (17) Erne´, B. H.; Stchakovsky, M.; Ozanam, F.; Chazalviel, J. N. J. Electrochem. Soc. 1998, 145, 448. (18) Park, S. M.; Barber, M. E. J. Electroanal. Chem. 1979, 99, 67. (19) Perrault, G. G. J. Electrochem. Soc. 1989, 136, 2845. (20) |j| stands for the absolute value of the net electrical current density passing through the electrochemical cell; kB indicates the Boltzmann constant, T the absolute temperature, and e the elementary electric charge. (21) Hence, the two current density curves are subtracted at the same band bending for both, not at the same potential. (22) In the pseudo-galvanostatic mode, the potentiostat contols the dc current and the ac potential. This means that after each single impedance measurement the dc current is adjusted to the value required if it has exceeded predefined current limits by changing the dc potential.7 (23) Prior to this current step, cathodic potentials more negative than -600 mV vs SCE were avoided except sometimes for a short time during a current-density vs potential measurement. (24) The cathodic polarization for 55 min consisted of: 40 min at -140 µA cm-2, potential increasing from -869 mV to -681 mV, frot ) 10 Hz and 15 min at -350 µA cm-2, potential increasing from -760 mV to -719 mV, frot ) 10 Hz; frot stands for the rotation frequency of the disk electrode. (25) This “normalization” makes the characteristic frequency of the parallel connection of a resistance R and a CPE with parameter C2 approximately equal to the characteristic frequency of a parallel connection of a resistance R and a perfect capacitance with capacity C2 if the normalization frequency ω0 is of the same order of magnitude as this characteristic frequency and the exponent R does not deviate too much from 1. Since both conditions are satisfied for the impedance spectra recorded

138 J. Phys. Chem. B, Vol. 103, No. 1, 1999 here (cf. Figure 4), the normalization 1 provides a physical basis to associate the CPE parameter C2 with the perfect capacitance obtained in the model of part 1. (26) This transient behavior of the resistance R2 (Figure 5a) is also observed in the initial decrease of the applied potential (Figure 5a), the decrease of the capacitance C2 (Figure 5b) and the increase of the capacitance C1 (Figure 5b). Probably, it is caused by the sudden change from OCP to cathodic polarization. The initial decrease of the reduction current after a potential step is applied to the electrode (cf. section 3.1.) is an analogous manifestation of this effect. (27) The position of the band edges at the semiconductor surface depends on the previous history of the electrode. The current density vs potential curves and the Mott-Schottky measurements are performed at electrodes with a similar history and at a comparable sweep rate (20 mV s-1 and steps of 100 mV every 5 s respectively). (28) The current density recorded at p-GaAs is as small as 1 µA cm-2 in a 4 × 10-3 M Fe3+ solution. Since the band edges of n-GaAs and p-GaAs

Hens and Gomes are situated at the same energy, this value is an indication of the equivalent current of the Fe3+ reduction rate at n-GaAs under anodic polarization in the same solution. (29) If jasc ) 0, then jcsc ) jc. (30) Recombination level using the hole injection terminology. (31) This is valid for hole injection as well. (32) Hence C2-1 ) CH-1 + Css-1. (33) One should remember that this value is indicative since it is obtained by normalization of the constant phase element to an ideal capacitance at a frequency of 1000 Hz (cf. supra). (34) This evolution of the capacitance Css as a function of the potential φsc is caused by the changing occupation of the surface states. At cathodic potentials, most surface states are filled with electrons, yielding a small value of the capacitance Css whereas at anodic potentials, most surface states are empty, yielding a large value of Css. (35) Since the denominator of this partial derivative is strictly positive, only the numerator determines the sign.