Electrochemical Interface Studied - American Chemical Society

5974

J. Phys. Chem. B 2000, 104, 5974-5985

GaAs/H2O2 Electrochemical Interface Studied In Situ by Infrared Spectroscopy and Ultraviolet-Visible Ellipsometry Part II: Chemical Origin of Cathodic Oscillations B. H. Erne´ ,*,† F. Ozanam,† M. Stchakovsky,‡ D. Vanmaekelbergh,§ and J.-N. Chazalviel† Laboratoire de Physique de la Matie` re Condense´ e (U.M.R. 7643 du C.N.R.S.), EÄ cole Polytechnique, 91128 Palaiseau, France, I. S. A. Jobin-YVon-Spex, Groupe Instruments S. A., 7 route d'Egly, 91290 Arpajon, France, and Debye Institute, Utrecht UniVersity, P.O. Box 80000, 3508 TA Utrecht, The Netherlands. ReceiVed: February 1, 2000; In Final Form: April 8, 2000

Changes in the interfacial chemical composition of n-GaAs(100) electrodes during cathodic reduction of H2O2 solutions (pH 0) at fixed potential are monitored in real time using in situ infrared spectroscopy and in situ spectroscopic ellipsometry. Under conditions in which the current density spontaneously oscillates, synchronous oscillations are observed in the thickness of a porous layer of solid arsenic hydride, with typical variations of a few hundred Å. A physical and chemical model is proposed that accounts mathematically for the detailed time- and potential-dependent behavior and gives intuitive understanding of the chain of events occurring during an oscillation cycle. The periods of slow current rise correspond to the growth of the electroactive arsenic hydride phase, on which H2O2 is cathodically reduced. The current peaks coincide with the sudden dissolution of arsenic hydride, when the local potential reaches a value at which the phase is no longer cathodically protected, due to ohmic potential drop; surface H atoms are then replaced by OH groups, at which H2O2 adsorbs at a much higher rate. The model not only accounts for the current oscillations under potentiostatic conditions but also for the potential oscillations observed under galvanostatic conditions.

Introduction Two aspects of the GaAs/H2O2 electrochemical system were extensively studied in the past: the technological surface preparations of GaAs using H2O2-based electrolyte solutions1 and the periodic oscillations obtained under cathodic conditions.2-5 In the preceding paper (part I), chemical species at the n-GaAs/ aqueous H2O2 interface (pH 0) were identified using in situ spectroscopic techniques, and their effects on current density were discussed. Here, it will be seen that the kinetic model proposed for the interfacial chemical changes and charge transfers also accounts for the oscillatory behavior. Koper et al.2 revealed that spontaneous harmonic current oscillations occur at GaAs cathodes in H2O2 solutions (pH 0) when the series resistance is sufficiently large. Electrical impedance spectroscopy indicates that the current oscillations at constant applied potential result from a negative faradaic impedance in conjunction with the series resistance (electrolyte resistance, external resistance, and so forth).3 A model was proposed on the assumption that the oscillations are related to changes in the GaAs surface coverage by adsorbed hydrogen, which affect semiconductor bandbending.3 Although it gives a possible origin of the oscillations, the model does not account for several electrochemical observations. Moreover, in situ spectroscopic information acquired since the model was proposed has considerably improved our understanding of the surface chemistry. One shortcoming of the previous oscillation model3 is that it explains potentiostatic current oscillations but is unable to * To whom correspondence should be addressed. E-mail: ben.erne@ chimie.uvsq.fr. Fax: +33 1 3925 4381. Present address: Institut Lavoisier (IREM, UMR CNRS C 8637), Universite´ de Versailles Saint-Quentin-enYvelines, 45 Avenue des Etats-Unis, 78035 Versailles, France. †E Ä cole Polytechnique. ‡ I. S. A. Jobin-Yvon-Spex. § Debye Institute.

explain galvanostatic potential oscillations.2 The hysteresis in the current-potential curve (see preceding paper1) is not explained either. The same holds for the origin of inductive behavior observed at low frequency in the electrical impedance spectrum.3 Moreover, the model does not seem to account for the usual shape of the oscillations under monoperiodic conditions,4 a regular saw tooth with extremely sharp spikes at the tooth edges. Since the previous oscillation model3 was proposed, two important new pieces of information were acquired regarding the surface chemistry: the presence of an electrochemically active arsenic hydride phase (As2H2) and the detailed mechanism by which H atoms adsorb at GaAs surfaces.6,7 The presence of As2H2 and its effect on the electrochemistry were revealed in the preceding paper.1 Under cathodic conditions, chemical dissolution of GaAs by H2O2 is never completely suppressed, and the dissolution product HAsO2 is reduced in the form of a porous layer of solid arsenic hydride (As2H2). The cathodic current density corresponding to H2O2 reduction was found to be affected by variations in the amount of As2H2 and by the fractional surface coverages of GaAs and As2H2 by adsorbed H and OH groups. Hydrogen adsorption at GaAs cathodes had never been studied by in situ chemical methods when the previous oscillation model3 was proposed. Since then, hydrogen adsorbed at GaAs surfaces was detected by in situ infrared (IR) spectroscopy, and the effect of hydrogen adsorption on the flatband potential was determined quantitatively.6,7 The kinetics of cathodic hydrogen adsorption are quite different from previous assumptions3 because the hydrogen surface coverage does not result from a reversible adsorption-desorption equilibrium, and reaction of surface hydrogen with strong oxidants such as H2O2 cannot be neglected at all. Cathodic hydrogen adsorption and chemical hydrogen desorption are two processes

10.1021/jp000390b CCC: $19.00 © 2000 American Chemical Society Published on Web 06/03/2000

GaAs/H2O2 Electrochemical Interface Part II

J. Phys. Chem. B, Vol. 104, No. 25, 2000 5975

that occur separately, depending on the size of the cathodic current compared to the flow rate of oxidants such as H2O2 toward the surface.6,7 As indicated in the preceding paper,1 the hysteresis of cyclic voltammograms in the presence of H2O2 suggests that the hydrogen surface coverage is controlled by the same mechanism as that in acidic solutions without H2O2. The previous oscillation model3 also assumed a specific dependence of charge-transfer rates on the potential drop across the Helmholtz layer, but such a dependence is not supported either by in situ IR spectroscopy performed in combination with capacitance measurements, at least not for the hydrogen gas evolution reaction on GaAs.7 Here, in situ IR spectroscopy and in situ spectroscopic ellipsometry are used to monitor changes in chemical composition of the interface in real time during potentiostatic current oscillations. The potential dependence of the oscillation period is examined in greater detail than that found in previous works.2,3 The mechanism proposed in the preceding paper1 accounts for the evolution of the complex surface chemistry during an oscillation period and the detailed shape of the potentiostatic current oscillations. The potential dependence of the oscillation period is accounted for using a new model that includes a description of the geometric distribution of the local potential at the surface of the As2H2 phase, while simplifying some aspects of secondary importance in the oscillation process. On the basis of the in situ chemical information and the mathematical test of the model by numeric simulation, an intuitive explanation is proposed in terms of the events taking place sequentially during an oscillation cycle. Experimental Section Most of the experimental methods are detailed in the preceding paper.1 The series resistance plays an important role in the occurrence of the periodic oscillations. Two of the contributions to the series resistance are the electrolyte resistance and the resistance of the relatively low-doped GaAs samples required for in situ IR measurements (to limit IR absorption by free charge carriers8). In addition, an external resistor could be connected in series with the working electrode to increase the series resistance. The total series resistance Rs in Ω cm2 was determined by scanning the applied potential negatively until the current density versus potential curve reached a practically constant slope, equal, within negligible error, to Rs-1. In all cases, Rs was chosen to be sufficiently large to obtain monoperiodic oscillations. In contrast to previous reports,2,3 we found that an elevated temperature (40-50 °C) is unnecessary for spontaneous oscillations with the GaAs/H2O2 (pH 0) system. All of the measurements here are carried out at room temperature (20-25 °C). In preliminary experiments, chloride addition was found to affect the oscillation period, stopping the oscillations altogether when the concentration is sufficiently high (about 1 M). Chloride ions probably react with H2O2 to form chlorine, which is known to dissolve GaAs at a diffusion-limited rate9 and should thus significantly affect surface chemistry. A similar effect is not seen when phosphates are added to the solution. In Situ IR Spectroscopy Results. As seen in the preceding paper,1 in situ IR spectroscopy allows one to detect the As-H bonds inside the arsenic hydride phase (As2H2) present under cathodic conditions (at 2000 cm-1), the As-H bonds at the surface of As2H2 (at 2040 cm-1), the H2O molecules inside the porous As2H2 layer, the changes in sulfate concentration near the surface following the production of Ga3+ ions during GaAs dissolution, and the roughening of the surface.

Figure 1. Evolution of an n-GaAs electrode during cathodic reduction of 1 M H2O2 in 0.5 M H2SO4 at different potentials (Rs ) 28 Ω cm2): (a) current density, (b) total IR absorbance by As-H inside As2H2 (at 2000 cm-1) and at its surface (2040 cm-1), and (c) change in absorbance by H2O (3400 cm-1 band), (d) change in absorbance by sulfate groups in the vicinity of Ga3+, and (e) change in absorbance at 2500 cm-1, a measure of surface roughness. The scale on the right-hand side gives the thickness of the As2H2 layer calculated on the basis of As-H absorbance at 2000 cm-1, the calibration in the preceding paper1, and a layer porosity of 75%.

Figure 1 presents an experiment in which 1 M H2O2 is reduced at a few different applied potentials. At -0.75 V versus Ag/AgCl, the electrode roughness and the sulfate absorbance, due to the production of Ga3+ ions near the surface, increase rapidly. As soon as the applied potential is stepped to -0.80 V versus Ag/AgCl, arsenic hydride (As2H2) is observed and current density starts to oscillate. The potential at which As2H2 is first seen is more negative than in the experimental current-potential curves of the preceding paper1; this is because of a higher current density (higher H2O2 concentration), leading to an ohmic potential drop of about 0.25 V. The As2H2 layer thickness oscillates synchronously with current density. The experimental observations are summarized schematically in Figure 2. During an oscillation cycle, absorbances by As-H at 2000 cm-1 and by H2O at 1650 and 3500

5976 J. Phys. Chem. B, Vol. 104, No. 25, 2000

Figure 2. Schematic summary of experimental results concerning the chemical evolution of the interface during oscillatory cathodic reduction of H2O2 on GaAs. Different points of a typical current vs time plot correspond to different thicknesses of the porous As2H2 layer and different surface coverages of GaAs and As2H2 by adsorbed H and OH groups.

cm-1 (Figure 1) indicate that the thickness of the porous arsenic hydride layer increases slowly (Figure 2, points 1 to 2) until just before a peak in current density, at which the thickness of the layer drops rapidly (Figure 2, points 3 to 4). At the peak in the cathodic current density, the sulfate absorbance shows a slight, rapid increase (Figure 1d), indicating enhanced GaAs dissolution. As schematized in Figure 2 (points 3 and 4), IR spectroscopy in the absence of H2O2 indicates that GaAs is fully OH-covered under dissolution conditions (see the preceding paper1 and refs 6 and 7). Baseline absorbance increases continuously, except for brief moments in which the amount of elemental arsenic decreases abruptly (Figure 1e), whereas the amount of As2H2 comes back to the same value at the end of each oscillation period. The baseline increase is ascribed to irreversible surface roughening. The slight decrease in baseline absorbance when elemental arsenic disappears is probably an optical effect associated with the disappearance of this phase. The maximal thickness of the porous arsenic layer, just before a peak in the current density, increases with the oscillation period. This is shown in Figure 3, parts a and b. It demonstrates that the rate at which the layer grows is only a weak function of the oscillation period. At a peak in the current density, the layer thickness drops sharply, although not completely to zero, as shown in Figure 3a. On the basis of the calibration in the preceding paper,1 the rate at which layer thickness rises corresponds to about -60 µA cm-2, on the order of 0.5% of the total current as found in the preceding paper1 at lower H2O2 concentrations in the absence of oscillations. The ratio of absorbances by surface As-H at 2040 cm-1 and bulk hydride As-H at 2000 cm-1 is about 0.35 when a layer is present and much higher when the layer has almost disappeared

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Figure 3. Maximum and minimum absorbances measured under potentiostatic oscillation conditions at n-GaAs/1 M H2O2 (average j ) -8 mA cm-2) as a function of the oscillation period (at -0.85, -0.90, -0.945, and -0.995 V vs Ag/AgCl; Rs ) 28 Ω cm2): (a) total absorbance by As-H inside As2H2, (b) change in absorbance by H2O, and (c) ratio of absorbances by As-H at the surface and in the bulk of As2H2. The right-hand scale was calculated as in Figure 1.

Figure 4. Integrated charge measured during an oscillation cycle as a function of the time-averaged potential at the GaAs/electrolyte interface under different conditions (rotating disk electrodes at room temperature, except when indicated otherwise): b: 0.1 M H2O2, Rs ) 100 Ω cm2; 9: 0.2 M H2O2, Rs ) 44 Ω cm2; 2: 1 M H2O2, Rs ) 10 or 20 Ω cm2; [: 1 M H2O2, Rs ) 1.5 Ω cm2 (40-50 °C)2; 1: 1M H2O2, Rs ) 28 Ω cm2 (IR spectroscopy flow cell).

(Figure 3c). The surface coverage of the remaining As2H2 by adsorbed H atoms seems much higher than that found during As2H2 deposition, but part of the absorbance of surface As-H groups at 2040 cm-1 is due to the GaAs surface, whose contribution is relatively high when almost no As2H2 is left. A ratio of 0.35 indicates that the arsenic hydride phase has a very high specific surface area. A rough estimate suggests characteristic feature sizes in the nanometric range. The oscillation period τ strongly depends on the applied potential. In Figure 4, the current density integrated during one oscillation period (-τ) is plotted against the time-averaged interfacial potential U-Rs. Figure 4 combines measurements obtained under various conditions of H2O2 concentration (0.1-1.0 M) and average current density (-1 to -10 mA cm-2), cell geometry (flow cell or rotating disk electrode), series



Figure 6. Time evolution of (a) current density and (b,c) the in situ ellipsometric angles ψ and ∆ at 1.55 eV during cathodic reduction at n-GaAs in 1 M H2O2 (0.5 M H2SO4) at -0.955 V vs Ag/AgCl (Rs ) 23 Ω cm2). Thicknesses are based on the composition found in the preceding paper1 (22 vol % As2H2, 20 vol %. GaAs).

Figure 5. Evolution of an n-GaAs electrode during cathodic reduction of 0.75 M H2O2 in 0.5 M H2SO4 at -0.815 V vs Ag/AgCl before and after start of circulation of the electrolyte (Rs ) 16 Ω cm2): (a) current density, (b) total IR absorbance by As-H inside As2H2 (at 2000 cm-1, full line) and at its surface (2040 cm-1, dotted line), (c) change in absorbance by H2O (3400 cm-1 band), and (d) change in absorbance by sulfate groups in the vicinity of Ga3+. The right-hand scale was calculated as in Figure 1.

resistance (1.5-100 Ω cm2), and temperature (20-25 °C here and 40-50 °C in the measurements of Koper et al.2). All of the data seem to obey a general and linear relationship between -τ and U-Rs. The reciprocal slope is about 180 mV per decade. No such correlation was found for the charge measured during a current peak, typically about -5 10-3 C cm-2. Electrolyte circulation has an effect on the oscillations, as can be seen in Figure 5. The oscillations occurring during the reduction of 0.75 M H2O2 in 0.5 M H2SO4 at an applied potential of -0.815 V versus Ag/AgCl are shown before and after starting to circulate the solution in the flow cell. The circulation rate was such that the diffusion layer thickness was =200 µm.10 Without circulation, the absorbance by sulfate groups (which compensate the charge of Ga3+ ions released during the dissolution of GaAs, see the preceding paper1) has a strong peak just after a peak in the current density, whereas the peak is much weaker with circulation. At a current peak, chemical dissolution of GaAs by H2O2 appears to be enhanced, causing a rise in Ga3+ concentration near the surface, stronger when convection of Ga3+ away from the surface is slower. The abrupt start of circulation in Figure 5 itself causes a peak in current density and a simultaneous drop in layer thickness. More subtle effects of circulation are also observed on the shape

and duration of the oscillations. An important observation is that both with and without circulation, absorbance at 2040 cm-1 by As-H bonds at the surface of As2H2 stops increasing before absorbance at 2000 cm-1 by As-H bonds inside elemental arsenic reaches a maximum. This suggests that the last deposited As2H2 before a current peak has a surface that is no longer covered with adsorbed H atoms but instead is covered with OH groups (Figure 2, point 3). In Situ Ultraviolet-Visible (UV-Vis) Ellipsometry Results. The reduction of H2O2 at GaAs was also studied by in situ UV-vis ellipsometry. Figure 6a shows oscillations in current density during the reduction of 1.0 M H2O2, and Figure 6, parts b and c, shows the simultaneous changes in the ellipsometric angles ψ and ∆ measured at hV ) 1.55 eV (λ ) 800 nm). At this low energy, the layer is relatively transparent and ellipsometry mainly yields information about the thickness of the arsenic hydride surface layer. Between two peaks in current density, layer thickness increases more or less linearly. Assuming that the layer consists of 22% As2H2 and 20% GaAs (see preceding paper1), the layer thickness oscillates between about 250 and 450 Å. The slight curvatures of the graphs of ψ and ∆ as a function of time are probably due to the changing optical properties of the layer: arsenic hydride grows on top of a rough GaAs surface, so that the fraction of GaAs to be included in an effective medium model of the interface decreases as layer thickness increases. At a peak in the current density, the layer thickness drops abruptly, but it does not drop to zero. Measurements with a time resolution of 50 ms indicate that the layer thickness always starts to decrease slightly before the current density peak, as seen with lower time resolution by in situ IR spectroscopy (Figure 1). The time during which the layer thickness drops depends on the oscillation period and is typically 2 orders of magnitude shorter than the oscillation period. The ellipsometric spectra were measured under conditions in which oscillations have the same sawtooth shape as in Figure


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Figure 7. In situ ellipsometric spectra (angles ψ and ∆) just before and just after a current peak during the oscillatory reduction of 1 M H2O2 (0.5 M H2SO4) at n-GaAs at -0.855 V vs Ag/AgCl (Rs ) 23 Ω cm2, oscillation period 40 s, average j ) -10 mA cm-2). Thickness oscillates between about 450 and 550 Å.

5 (with circulation) and the oscillation period τ has a constant value of 40 s. Dynamic measurements were carried out with 50 ms resolution at different monochromatic wavelengths. Figure 7 shows the ellipsometric angles ψ and ∆ measured just before a peak in current density, when the thickness of the layer is maximal, and those measured just after a peak in current density, when the thickness of the layer is minimal. The spectra are relatively featureless, and the shifts occurring at a peak in current density are more or less independent of energy. This feature indicates that although layer thickness oscillates, the optical properties of the interface are relatively constant. Here, the spectroscopic dependence of the ellipsometric signal appears to be largely determined by the important and more or less constant surface roughness (GaAs and electrolyte solution dominate the effective optical medium). Discussion The discussion consists of four parts. (1) The model developed in the preceding paper1 to simulate cyclic voltammograms is used to simulate oscillations. (2) On the basis of this model and the in situ spectroscopic results, the events occurring at the surface during an oscillation cycle are discussed chronologically. (3) A more refined model is proposed for the oscillatory behavior of the arsenic hydride layer, a model that accounts for the potential dependence of the oscillation period. (4) Finally, the cause of the system’s oscillation is examined, as opposed to its going to a steady state. Oscillations Simulated using the Model for the Cyclic Voltammograms. According to Koper and Vanmaekelbergh,3 the oscillations at the GaAs/H2O2 (pH 0) interface are related to the presence of a negative slope region in the currentpotential curve, which destabilizes the interface when the series resistance is sufficiently high. The model proposed in the preceding paper1 accounts for the negative slope region in the current-potential curve and could, therefore, be expected to account for the oscillations when the series resistance is sufficiently large. Figure 8 shows simulations performed for a constant applied potential in the cathodic range using the model of the preceding paper.1 With the exception of the series resistance, which was taken as zero in the preceding paper1 and is now 10 Ω cm2, and the values for jadsOH and jadsH, taken higher by a factor of 10 (here, simulating a higher H2O2 concentration and facilitating

Figure 8. Simulated oscillations at n-GaAs/1 M H2O2 (pH 0) under potentiostatic conditions at -0.70 V vs Ag/AgCl. The simulation model and parameters are the same as in the preceding paper1, except for jadsOH ) 10 mA cm-2, jadsH ) 1 mA cm-2, and Rs ) 10 Ω cm2; (a) total current density; (b) partial current density corresponding to cathodic H2O2 reduction at As2H2, (c) thickness of the As2H2 layer, and (d) fractional surface coverages of GaAs and As2H2 by adsorbed H atoms. The local potential at the GaAs/electrolyte interface evolves from -0.59 to -0.53 V vs Ag/AgCl during the slow part of an oscillation cycle and reaches -0.44 V vs Ag/AgCl at a current peak.

comparison with the experiments), the parameters have the same values as in the simulations of the cyclic voltammograms.1 Oscillations are obtained, and their shape is remarkably similar to that usually observed in experiments. Between two current peaks, the amount of As2H2 rises slowly, and a current peak coincides with the sudden, although incomplete, disappearance of As2H2. The coverage of the As2H2 surface by adsorbed H atoms is close to 1 between current peaks and drops significantly during the current peaks. The coverage of the GaAs surface by adsorbed H atoms drops practically to zero during the current peaks, when the potential Uint at the GaAs/electrolyte interface is the most positive. Partial current densities due to hydrogen gas evolution and H2O2 reduction at GaAs (not shown) are minimal during the current peaks, when the electron concentration ns at the GaAs surface is minimal. Current peaks result from a maximum in the H2O2 reduction rate at the As2H2 surface

GaAs/H2O2 Electrochemical Interface Part II when the amount of As2H2 just reaches a maximum and the As2H2 surface is mainly OH-covered. The growth and dissolution of As2H2 and the reduction of H2O2 at its surface clearly play a predominant role in the oscillatory behavior (compare the total current density j in Figure 8a with the contribution j* of current at As2H2 in Figure 8b). In the computation, it is assumed that band bending responds instantaneously to a change in GaAs surface potential (U jRs) and that other parameters such as surface coverages of GaAs and As2H2 by adsorbed H and OH groups are approximately constant on the time scale of the time increment dt. At each time step, the various contributions to the current density are determined through a self-consistent iterative scheme based on the model in the preceding paper.1 Changes in the density of free surface sites of GaAs due to lateral growth of the As2H2 phase are not taken into account, but this is not expected to have a fundamental effect because the amount of As2H2 phase never decreases completely to zero. Figure 9 shows that the model accounts not only for current oscillations under potentiostatic conditions but also for potential oscillations under galvanostatic conditions. It will be seen in the following section that the sequence of events occurring under galvanostatic conditions is much the same as under potentiostatic conditions. Chronological Discussion of Events During an Oscillation Cycle. On the basis of the proposed model and the in situ spectroscopic results under oscillation conditions, the potential dependence of surface chemical composition is summarized and events occurring during a potentiostatic oscillation cycle are examined chronologically (see Figure 2). At open circuit potential, the GaAs surface is covered with adsorbed OH groups; H2O2 adsorbs and attacks GaAs surface bonds, leading to fast chemical dissolution because GaAs oxidation products are highly soluble at pH 0. At more negative potentials, H2O2 is reduced cathodically, so that chemical attack of GaAs is inhibited. However, dissolution of GaAs is never completely suppressed, and the dissolution product HAsO2 is electrodeposited in the form of a solid As2H2 phase. The electrodeposited As2H2 is covered with adsorbed H atoms as long as the potential of the As2H2 surface is sufficiently negative (cathodic protection, e.g., from point 1 to point 2 in Figure 2). This potential is not constant at constant applied potential: the potential at the GaAs surface varies with current density due to the ohmic drop in Rs, and the potential difference between the GaAs surface and the As2H2/electrolyte interface increases with arsenic layer thickness, due to the ohmic drop inside As2H2. The latter ohmic drop mainly results from the resistivity of As2H2 and from the current due to cathodic reduction of H2O2 at the H-covered As2H2 surface. The current increases as the thickness and surface area of the porous As2H2 layer increase. This slow rise in current density at constant applied potential could well correspond to the inductive loop that is observed at low frequency in the electrical impedance spectrum.3 The simulations show that the layer grows until the potential at the As2H2 surface reaches a certain value, of the order of -0.5 V vs Ag/AgCl (at point 2 in Figure 2). This is approximately the least negative interfacial potential at which oscillations are observed (Figure 4) and the potential negative of which As2H2 is electrodeposited from an HAsO2 solution without H2O2 (see the preceding paper1). As the applied potential becomes more negative, the As2H2 layer obtained before the threshold potential is reached at the As2H2 surface becomes thicker. Figure 5b indicates that the last-deposited arsenic hydride is no longer H-covered but OH-covered: at the end of


Figure 9. Simulated oscillations at n-GaAs/0.1 M H2O2 (pH 0) under galvanostatic conditions with j ) -1.2 mA cm-2. The simulation model and parameters are the same as in the preceding paper1, except for Rs ) 100 Ω cm2: (a) applied potential, (b) partial current densities corresponding to cathodic H2O2 reduction at As2H2 and cathodic hydrogen gas evolution at GaAs, (c) thickness of the As2H2 layer, and (d) fractional surface coverages of GaAs and As2H2 by adsorbed H atoms. The potential at the GaAs/electrolyte interface is U+0.12 V.

the increase in absorbance at 2000 cm-1, the absorbance at 2040 cm-1 levels off. It was concluded in the preceding paper1 that H2O2 adsorbs at a higher rate at OH sites than at H sites of the As2H2 surface, so that as the H2O2 reduction rate increases, the ohmic potential drop inside As2H2 rises even further, and the potential at the surface of As2H2 becomes even more positively shifted. This is the positive-feedback mechanism responsible for the abruptness of the changes at the end of the oscillation cycles. The switch toward OH coverage of As2H2 can thus be seen as autocatalytic, but As2H2 dissolves quickly because it is no longer cathodically protected at the positively shifted surface potential. During the short time when much OH-covered As2H2 is present, the current density is much enhanced, and a current peak is observed (points 3 and 4 in Figure 2). The potential at the GaAs surface can briefly leave the cathodic plateau range

5980 J. Phys. Chem. B, Vol. 104, No. 25, 2000 as a result of the ohmic drop, so that GaAs dissolves at an increased rate, leading to enhancement of the Ga3+-related sulfate signal (Figure 5d). After the current peak, the As2H2 thickness has decreased, and its surface is again H-covered (point 5 in Figure 2). Similar events are likely to occur during the galvanostatic oscillations observed with the same system in ref 2 (see the simulations in Figure 9). Current flow through As2H2 increases as the amount of As2H2 increases, which must be compensated by a decrease in current density at the GaAs/electrolyte interface. To this end, hydrogen gas evolution at GaAs is decreased by a positive shift of the interfacial potential; this continues until As2H2 is no longer cathodically protected. The switch of the As2H2 surface from H to OH coverage then enhances the current density at As2H2, so that the current at GaAs must briefly be diminished further by leaving the range where GaAs is cathodically protected. When much of the As2H2 has dissolved, the initial situation is obtained again. The oscillation period corresponds to the time required to grow the As2H2 layer until the local potential at its surface is no longer in the range where As2H2 is H-covered and cathodically protected. This is why the integrated charge measured during an oscillation period as a function of the time-averaged potential at the GaAs/electrolyte interface falls along a similar curve for different H2O2 concentrations and series resistances (Figure 4). The period increases as potential is made more negative because an increasing amount of As2H2 is required before the threshold potential is attained at the As2H2 surface and because the rate at which the As2H2 layer grows decreases. At increasingly negative potential, cathodic protection of GaAs is improved, so that the rate at which HAsO2 is released decreases. Nevertheless, the rate at which HAsO2 is released does not depend strongly on potential because variations in applied potential are largely accommodated by a change in the potential drop across the dipole layer at the GaAs surface resulting from the associated change in surface composition.6,7 As a result, the potential drop across the semiconductor spacecharge layer and the surface electron concentration do not depend strongly on potential. At a given potential, the oscillation period is essentially determined by the maximum thickness for which the As2H2 layer is cathodically protected. This indicates that growth and dissolution of the As2H2 layer play a dominant role in the oscillations, whereas other processes, such as hydrogen gas evolution at GaAs, are of secondary importance (at least in the potentiostatic mode). The present model describes the As2H2 layer in a very crude way, in terms of an average thickness and an average potential at its surface. A new model is proposed below that improves the description of the spatial potential distribution across the As2H2 surface while simplifying less important aspects of the system. Local Model for the Oscillatory Behavior of the Arsenic Hydride Layer. In the local model, whose detailed presentation is given in the Appendix, all of the parameters describing the As2H2 surface now represent local values, which depend on the position in the layer: U* is the local potential at the As2H2/ electrolyte interface, θOH* and θH* are the local coverages by adsorbed H and OH groups, jH2O2* is the local cathodic reduction rate of H2O2, jdiss* the local As2H2 dissolution rate, P* the local porosity, F* the local effective resistivity (which depends on P*), and ξ* is also defined locally. From now on, we will consider potentiostatic oscillations only. As in the first model, competition between chemical dissolution of GaAs or As2H2 by H2O2 and cathodic H2O2 reduction

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Figure 10. (a) Fractional coverages of the GaAs and As2H2 surfaces by adsorbed H atoms (Appendix, eqns 8,9) and (b) the competition factors ξ and ξ* (Appendix, eqns 3,4) in the local model for the oscillations (the simulation parameters are given in the Appendix).

at GaAs or As2H2 is described by the factors ξ and ξ* (ξ and ξ* are 1 when H2O2 is reduced cathodically at GaAs and As2H2, respectively1), but these factors are now given by explicit functions of the potential Uint at the GaAs/electrolyte interface and the local potential U* at a site of the As2H2/electrolyte interface. The potential Uint at the GaAs/electrolyte interface depends on Rs, just as in the previous model.1 The local potential U* at a site of the As2H2/electrolyte interface and at a distance r* from GaAs differs from the potential Uint at the GaAs/electrolyte interface. The difference is due to ohmic drop across the part of the layer within a distance r* from GaAs, with the local As2H2 resistivity F* depending on the position inside the layer. In the preceding model,1 the kinetics of hydrogen adsorption at GaAs and As2H2 were discussed in terms of reaction rate constants. Here, the potential and time dependences of θH and θH* are simplified in the following way. The steady-state values of θH and θH* are taken as simple functions of potentials, chosen according to the results of the previous model.1 The actual values of θH and θH* evolve toward the steady-state values within a characteristic time τθ. Figure 10 shows how the steady-state surface coverages of GaAs and As2H2 by adsorbed H atoms and the factors ξ and ξ* depend on the applied potential. Just as in the previous model,1 GaAs dissolution yields HAsO2, and in the potential range in which the present model applies, all HAsO2 is assumed to be deposited at the GaAs/ electrolyte interface as 50% porous As2H2. However, dissolution of As2H2 now occurs everywhere across the layer, at a local rate determined by the local potential U*, which affects the local porosity P*. Figure 11 illustrates how layer porosity gradually changes as one is more distant from GaAs: the local potential is increasingly positive due to ohmic drop inside the As2H2 bulk, so that cathodic protection deteriorates. P* is 50% at the GaAs surface because it is assumed that As2H2 is deposited at the GaAs surface with P* ) 50%. How porosity changes as one becomes more distant from the GaAs surface depends on electrode history (the profile in Figure 11 was calculated for t ) 11 s in Figure 12a,b). The simulated oscillations (Figure 12) closely resemble the experimental oscillations. Between two current peaks, current and layer thickness increase at an approximately constant slow rate, and at a current peak, layer thickness drops at a high rate but not to zero. Figure 13 illustrates that local potential is always somewhat more positive at the outermost part of As2H2 than it


Figure 11. Schematic illustration of the local model for the oscillations. The local current density at the As2H2/electrolyte interface depends on the distance from GaAs. Ohmic drop across the layer is obtained by an integration which takes into account the variations in local current density. Due to the gradient in local potential at the As2H2/electrolyte interface, outermost parts are not as well cathodically protected against dissolution as innermost parts, so that porosity varies across the layer (the profile was calculated on the same basis as Figure 12a,b, at t ) 11 s).

is at the GaAs/As2H2 interface, due to ohmic drop, which suggests that the current peak is initiated by H to OH surface conversion at the outermost part of the As2H2 layer. The switch from H to OH surface coverage starts at the outermost As2H2, causing a rise in current and ohmic drop across the entire layer, which further accelerates the process. Across a wide potential range, the simulated oscillation period increases by a factor of 10 for every 180 mV negative shift of the time-averaged potential at the GaAs/H2O2 interface (Figure 14), in agreement with experimental observations (Figure 4). Although the slope is not completely constant, it is practically the same for different values of Rs, jadsOH, and jadsH, as long as 0 < jadsH , jadsOH. The curves in Figure 14 do not exactly coincide with each other; it is difficult to say whether this trend is supported by the experiments, because of the scatter in the measurements (Figure 4). As mentioned before, the potential dependence of the oscillation period is due to the potential dependence of the As2H2 growth rate and to the potential dependence of the amount of As2H2 that must grow at a given potential at the GaAs/electrolyte interface to reach the surface potential at which H coverage switches to OH coverage. The potential dependence of the As2H2 growth rate results from the potential dependence of the electron concentration at the GaAs surface, which affects the production rate of HAsO2 and depends on how flatband potential shifts with changing hydrogen surface coverage of GaAs. If flatband potential was taken to be constant, the


Figure 12. Simulated evolution of current density and As2H2 layer thickness at n-GaAs/H2O2 (pH 0) under potentiostatic oscillation conditions (a,b) at -0.75 V vs Ag/AgCl and (c,d) at -0.85 V vs Ag/ AgCl with Rs ) 10 Ω cm2 (see Appendix for the other parameters).

Figure 13. Simulated time evolution of the local potentials at the GaAs/ electrolyte interface and at the outermost part of the As2H2 layer under potentiostatic oscillation conditions (parameters as in Figure 12c,d).

oscillation period could vary by one decade per 30 mV instead of one decade per 180 mV. The amount of As2H2 which must grow before the dissolution potential is locally reached at the As2H2 surface increases as the potential at the GaAs/electrolyte interface becomes more negative, because the required ohmic drop increases. Simulations were also carried out with different values for the resistivity F° of bulk As2H2 because its experimental value is unknown. As long as F° is chosen to be ,108 Ω cm, the numerical simulations are not sensitive to its exact value. For higher values (e.g., 108 Ω cm), oscillations occur even in the absence of a series resistance, in contrast to experimental observations. This suggests that such high values are excessive for the porous As2H2 phase at the GaAs/H2O2 interface. It is also concluded that the series resistance Rs plays a more


Figure 14. Simulated dependence of (a) the integrated charge measured during an oscillation cycle and (b) the maximum and minimum layer thicknesses during a cycle as a function of the time-averaged potential at the GaAs/electrolyte interface under potentiostatic oscillation conditions: jadsOH/jadsH ) 10 for all curves, and jadsOH ) 10 mA cm-2 with Rs ) 10 Ω cm2 for curve 1, jadsOH ) 10 mA cm-2 with Rs ) 20 Ω cm2 for curve 2, jadsOH ) 1 mA cm-2 with Rs ) 100 Ω cm2 for curve 3, and jadsOH ) 1 mA cm-2 with Rs )200 Ω cm2 for curve 4 (other parameters as in Figure 12). Part (b) corresponds to curve 1 in part (a).

important role than the resistivity of As2H2 in rendering the GaAs/H2O2 system unstable. Why the System Oscillates. It is not obvious from the discussion of the chain of events occurring during an oscillation cycle why the system oscillates, rather than reaching a steady state in which the As2H2 deposition rate equals the As2H2 dissolution rate. As a matter of fact, the interface is unstable only if a positive-feedback mechanism takes place, resulting in a real negative contribution to the Faradaic impedance.3,11,12 In a previous work,3 it was concluded that oscillations in the GaAs/ H2O2 (pH 0) system can occur only if the negative impedance is caused by an anomalous dependence of semiconductor band bending on the electrode potential, i.e., if an increase of the Fermi level of n-GaAs results in increased band bending. In the present work, it was demonstrated that such a band bending anomaly is not a necessary requirement because potentiostatic and galvanostatic oscillations can be accounted for without assuming such an anomaly. The growth and dissolution of the As2H2 layer play a predominant role. We propose an intuitive explanation for the instability of the interface in a picture inspired from Degn.13 Figure 15a shows schematically how current density depends on the potential at the GaAs/electrolyte interface for different thicknesses of the As2H2 layer. A large thickness of the As2H2 layer corresponds to a large developed surface area of the porous layer, thus to a large current associated with H2O2 adsorption. For all of the curves, two potential ranges can be distinguished, that on the negative side of the current peak where As2H2 is covered with adsorbed H atoms (Uint j -0.5 V vs Ag/AgCl, θH* ≈ 1, low H2O2 adsorption rate) and that where As2H2 is covered with adsorbed OH groups (Uint J∼ -0.5 V vs Ag/AgCl, θH* ≈ 0, high H2O2 adsorption rate). On each curve, a sharper distinction

Erne´ et al.

Figure 15. Schematic illustration of the origin of oscillatory behavior in the GaAs/H2O2 system (see the text). (a) Current density is plotted against the potential Uint at the GaAs /electrolyte interface for several different thicknesses (0-800 Å) of the As2H2 layer (calculated on the basis of the simulation parameters given in the Appendix, except for no series resistance). The line with slope -Rs-1 corresponds to possible (j,Uint) values at applied potential U and actual series resistance Rs. The dotted line indicates would-be stationary states of the system (i.e., such that ∂δ*/∂ t ) 0). The As2H2 surface is covered with adsorbed H atoms in the more negative potential range and with adsorbed OH groups in the less negative potential range. (b) Time evolution of As2H2 layer thickness and current density under potentiostatic oscillation conditions. Points 1 to 5 in parts (a) and (b) correspond to the same points as in Figure 2.

can also be made: on the negative potential side, the As2H2 thickness δ* tends to increase, and on the positive side δ* tends to decrease. These two potential ranges are separated on the drawing by the dotted line that corresponds to the points where dδ*/dt ) 0, i.e., those points for which the layer thickness would be stationary. An implicit assumption for the physical relevance of Figure 15a is that the kinetics of changes in surface coverage by adsorbed H atoms are much faster than those of changes in layer thickness, as suggested by the experiments. A given thickness and a given potential Uint at the GaAs interface correspond to a single value of current density, at least for typical parameter values. However, in the presence of a series resistance Rs, Uint is no longer equal to the applied potential U. The intersections of the j(Uint) curves with the line having a slope of Rs-1 and passing at (j ) 0,U) (the so-called “load line”) give the possible (j,Uint) values at applied potential U. In a certain As2H2 thickness range, as a result of the sigmoidal shape of the j(Uint) function in the negative slope region, three possible current densities correspond to U, two of which (the extreme ones) are electrically stable.14 Numbers 1 through 5 in Figure 15 trace the trajectory of the system during one oscillation cycle and correspond to the same points as indicated in Figure 2. From point 1 to 2, the thickness of the As2H2 layer increases slowly in the range where As2H2

GaAs/H2O2 Electrochemical Interface Part II is covered with adsorbed H atoms. As a result of the increased surface area of the As2H2 layer, current density increases and the interfacial potential Uint shifts due to ohmic drop. Even if three current densities are now possible at potential U, the system remains in the range where the As2H2 is H covered for continuity reasons: the local potential at the As2H2 surface is insufficient for conversion to OH coverage. The thickness of the As2H2 layer continues to rise until the local potential at the As2H2 surface is no longer sufficiently negative for electrodeposition of H-covered As2H2, so that the Rs-1 line loses its intersection with the j(Uint) curve in the θH* ≈ 1 range. The system “jumps” to the only remaining available state at potential U, on the positive edge of the j(Uint) curve (Figures 2 and 15, point 3); there, current density is higher because the As2H2 surface is OH-covered. In practice, the transition of the system is neither instantaneous nor discontinuous; experiments indicate that As2H2 briefly continues to grow, but that its surface is now OH-covered (Figure 5b). In the OH-coverage range, As2H2 is no longer cathodically protected, As2H2 dissolves at a high rate, and other possible states of the system reappear at lower current densities. The system remains in the θH* ≈ 1 range for continuity reasons: because the current density is high, the interfacial potential is too positive for a rise in H coverage of As2H2, due to ohmic drop. The system remains in the OH-covered state until As2H2 layer thickness and current density have decreased to such an extent that the interfacial potential is no longer sufficiently positive for OH coverage and As2H2 dissolution (Figures 2 and 15, point 4). The system then jumps to the only remaining state, in the θH* ≈ 1 range (Figures 2 and 15, point 5). Again, the jump is, in practice, not discontinuous. In the H-coverage range, As2H2 thickness starts to grow again. The system comes back to its initial state (Figures 2 and 15, point 1) and a new oscillation cycle starts. The reason the system oscillates rather than reaching a steady state is further illustrated in Figure 15a by the dotted line. If the system were to arrive on the dotted line, it would be in a steady state, and oscillations would stop. However, at such a point, the constant-thickness j(Uint) curve exhibits a slope steeper than that of the load line, i.e., it corresponds to an electrically unstable working point.14 Therefore, in practice, during the oscillations, the system can never reach the dotted line: it jumps from point 2 to point 3 (Figure 15a) when δ* increases, and from point 4 to point 5 when δ* decreases. To summarize, the oscillations are related to the sigmoidal shape of the j(Uint) curve, the time evolution of layer thickness, and the series resistance. Without a series resistance, a given applied potential and As2H2 layer thickness would correspond to only one state of the system, and As2H2 layer thickness would increase until the local potential at the As2H2 surface is such that the As2H2 growth rate is compensated by the As2H2 dissolution rate. With a sufficiently large series resistance,13 no steady state is attained: As2H2 layer thickness and current density increase slowly until the feedback mechanism leads to dissolution of a large part of the As2H2 and the cycle starts again. The periodicity of the observed oscillations indicates that the system attains a stable limit cycle, as illustrated in Figure 16, which plots current density as a function of As2H2 layer thickness and is based on the simulations in Figure 12a,b. The oscillation is asymmetric because the system evolves much more rapidly in the θH* ≈ 0 range than in the θH* ≈ 1 range. At this point, only “potentiostatic” current oscillations have been discussed (quotation marks because this is actually in the


Figure 16. Evolution of current density as a function of As2H2 layer thickness under oscillation conditions at GaAs/ H2O2 (pH 0) plotted for the data in Figure 12(a,b). The dots are equidistant in time (∆t ) 0.1 s), so that the system evolves at the highest rate when the dots are the most widely spaced.

presence of a series resistance), but galvanostatic potential oscillations are observed experimentally with the same system2 and can be simulated on the basis of the same interfacial model (see Figure 9). A system showing “potentiostatic” oscillations does not necessarily show galvanostatic oscillations because additional conditions are required: both types of oscillations require a negative contribution to the real electrical impedance (at least at intermediate frequencies), and galvanostatic oscillations also require a positive low-frequency limit of the real impedance (observed experimentally for GaAs/H2O2 in ref 3). The negative contribution to the real impedance is due to the same processes responsible for the negative slope of the dynamic current-potential curve (see Figure 15a and the preceding paper1). The positive low-frequency limit of the real impedance corresponds to the positive slope of the dotted curve in Figure 15a, which represents the system under steady-state conditions.15 This explains why the present model accounts for galvanostatic as well as “potentiostatic” oscillations. Conclusions Cathodic oscillations at the GaAs/H2O2 (pH 0) interface have been studied by in situ IR spectroscopy and in situ UV-vis ellipsometry. At the origin of the oscillations, a predominant role is played by an arsenic hydride layer formed by electroreduction of HAsO2 resulting from chemical dissolution of GaAs. Current oscillations coincide with synchronous oscillations of the thickness of this layer. A model is proposed for the growth and dissolution of the layer, and it accounts for the current oscillations under potentiostatic conditions and for the potential oscillations under galvanostatic conditions. The feedback mechanism of the system is explained, as well as the spiked sawtooth shape of the oscillations and the dependence of the oscillation period on experimental conditions. In a certain sense, oscillations of an electrochemical system are just a manifestation of its mathematical behavior. In the present case, the essential elements are the sigmoidal currentpotential curve, its evolution in time, the series resistance, and the feedback mechanism. Koper and Sluyters16 once warned against presenting a chain of expected chemical and physical events as an explanation for electrochemical oscillations because such a reasoning often does not pass the mathematical test for oscillatory behavior. However, oscillating experimental systems should not be reduced to mere illustrations of general oscillation theories either. The physical and chemical description is essential, notwithstanding the need to test the mathematical validity of a proposed model, as done in the present work by numerical simulations. Oscillatory behavior is a valuable piece


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of information about a system because a complete description must also account for the oscillations, putting an additional constraint on the development of a model. The results illustrate the importance of in situ chemical characterization to improve understanding of electrochemical mechanisms. A major contribution of the in situ results is the discovery that the number of degrees of freedom of the cathodic GaAs/H2O2 system is higher than expected. Interfacial kinetics and oscillations are often discussed using models with just two degrees of freedom, the interfacial potential and the fractional surface coverage by an adsorbed species. However, the degrees of freedom of the cathodic GaAs/H2O2 system are not only the potential at the GaAs/H2O2 interface and the surface concentration of H atoms adsorbed at GaAs but also the thickness of the As2H2 layer as well as its own surface concentration of adsorbed H atoms, at least in the oversimplified description of As2H2 in terms of uniform surface properties (one average U*, one average θH*). The acquired chemical insights could not have been deduced on the basis of electrochemical measurements alone. Investigating electrode surfaces by in situ spectroscopic chemical methods requires a major time investment. Prior to the present study of cathodic oscillations at GaAs/H2O2, first the chemical surface species in the absence of H2O2 had to be identified,17 the dynamics of hydrogen adsorption at GaAs cathodes had to be clarified,6,7 and then the chemical species in the presence of H2O2 had to be investigated.1 Parallel examples are the study of oscillations during cathodic H2O2 reduction at CuInSe218,19 and during anodic oxidation of silicon;20-24 in the latter system, an oxide layer grows under an electric field, becomes permeable upon reaching a critical thickness, dissolves rapidly, and starts to grow again. But at the cost of such studies, one obtains detailed physical and chemical understanding of the dynamics of a complex electrochemical system. Instead of a formal description of mathematical behavior, one can then propose a model that accounts for kinetics in terms of experimentally observed surface reaction intermediates. For the observation of such intermediates, chemical surface characterization must be performed in situ because species with a key mechanistic role such as As2H2 at the GaAs/H2O2 interface are present only at applied potential and because their presence and chemical identity are difficult to infer from electrochemical data alone. This is why in situ methods such as IR spectroscopy or UV-vis ellipsometry are highly desirable in the study of complex electrochemical systems. Appendix: Local Model for Oscillations. The local model presented here uses many of the same symbols introduced in the preceding paper,1 but all of the parameters describing the As2H2 surface now represent local values, which depend on the position in the layer: U* is the local potential at the As2H2/ electrolyte interface. θH* and θOH* are the local coverages by adsorbed H and OH groups. jH2O2* is the local cathodic reduction rate of H2O2, jdiss* the local As2H2 dissolution rate, P* the local porosity, and F* the local effective resistivity (which depends on P*). ξ* is also defined locally. Competition between chemical dissolution of GaAs or As2H2 by H2O2 and cathodic H2O2 reduction at GaAs (jH2O2) or As2H2 (jH2O2*) is described in the same way as in the previous model1

jH2O2 ) - (jadsOH θOH + jadsH θH ) ξ

(1)

jH2O2* ) - (jadsOH θOH* + jadsH θH*) ξ*

(2)

For simplicity, the factors ξ and ξ* are now given by explicit functions of the potential Uint at the GaAs/electrolyte interface

and the local potential U* at a site of the As2H2/electrolyte interface

ξ ) {1 + exp[e(Uint - U0 - βθH)/kBT]}-1

(3)

ξ* ) {1 + exp[e(U* - U0)/kBT]}-1

(4)

where U0 resembles U° of the previous model.1 The potential Uint at the GaAs/electrolyte interface depends on Rs, just as in the previous model1

Uint ) U - j Rs

(5)

The local potential U* at a site of the As2H2/electrolyte interface and at a distance r* from GaAs differs from the potential Uint at the GaAs/electrolyte interface. The difference is due to ohmic drop across the part of the layer within a distance r* from GaAs, with the local As2H2 resistivity F* depending on the position inside the layer. The ohmic drop increment between a distance r* and a distance r* + dr* depends not only on the local current density jH2O2* but also on the current flowing on to more remote points of the layer

U* ) Uint -

∫0r* dr*′ F*(r*′) ∫r*′δ* dr*′′ jH O *(r*′′) S*(r*′′) 2 2

(6)

where δ* is the total thickness of the layer. The local resistivity F* of As2H2 depends on the resistivity F° of bulk As2H2 and the local porosity P*

F* ) F°/(1 - P*)

(7)

The specific surface area S* could also be considered to depend on porosity, as found in many systems; here, however, the experimental observations (Figure 2c) support using a constant value. In the preceding model,1 the kinetics of hydrogen adsorption at GaAs and As2H2 were discussed in terms of reaction rate constants. Here, the potential and time dependences of θH and θH* are simplified in the following way. The steady-state values of θH and θH* are expressed as ΘH and ΘH*. ΘH is the solution of

ΘH ) {1 + exp[e(Uint - U1 - βΘH)/kBT]}-1

(8)

and ΘH* is taken as

ΘH* ) ξ*

(9)

The actual values of θH and θH* evolve toward the steady-state values within a characteristic time τθ

dθH/dt ) (ΘH - θH)/τθ

(10)

dθH*/dt ) (ΘH* - θH*)/τθ

(11)

A single τθ value is used even though experimental studies of hydrogen adsorption indicate that the kinetics depend on the interfacial potential.6,7 This simplification is made because the behavior simulated here is found to be insensitive to the potential dependence of τθ. Just as in the previous model,1 the rate at which GaAs dissolves is

jdiss ) (jadsOH θOH) (1 - ξ)

(12)



GaAs dissolution yields HAsO2, and in the potential range where the present model applies, all HAsO2 is assumed to be deposited at the GaAs/electrolyte interface as 50% porous As2H2

jdep ) - jdiss

(13)

Dissolution of As2H2 can occur everywhere across the layer, at a local rate determined by the local potential U*

jdiss* ) (1 - ξ*) jadsOH θOH*

(14)

Due to local dissolution, the local porosity P* increases, according to

dP*/dt ) jdiss* S* M*/(8F d*)

(15)

Of course, the molar mass M* and the density d* of bulk As2H2 are invariant across the layer. The total current density due to H2O2 reduction at the As2H2/electrolyte interface is the integral of the local current density jH2O2* across the layer. Hydrogen gas evolution is neglected here not only on As2H2 (as in the previous model1) but also on GaAs. Thus, the current density j through the external circuit is the sum of cathodic H2O2 reduction at the As2H2 surface and of cathodic H2O2 reduction at the GaAs surface

j ) jH2O2 + S*

∫0δ* dr* jH O * 2 2

(16)

Except when indicated otherwise, the numerical calculations (Figures 10 to 16) are carried out using jadsOH ) 10 mA cm-2 (eqs 1,2), jadsH ) 1 mA cm-2 (eqs 1,2), U0 ) -0.5 V vs Ag/ AgCl (eqs 3,4), U1 ) -0.6 V vs Ag/AgCl (eq 8), τθ ) 0.1 s (eqs 10,11), S* ) 0.03 Å-1 and F° ) 105 Ω cm (eq 7). The 100 mV negative shift of U1 with respect to U0 ensures that θH does not start to rise before GaAs dissolution is largely suppressed, as seen in the experiments.1 References and Notes (1) see the preceding paper, “part I”.

(2) Koper, M. T. M.; Meulenkamp, E. A.; Vanmaekelbergh, D. J. Phys. Chem. 1993, 97, 7337. (3) Koper, M. T. M.; Vanmaekelbergh, D. J. Phys. Chem. 1995, 99, 3687. (4) Koper, M. T. M.; Chaparro, A. M.; Tributsch, H.; Vanmaekelbergh, D. Langmuir 1998, 14, 3926. (5) Chaparro, A. M. J. Electroanal. Chem. 1999, 462, 251. (6) Erne´, B. H.; Ozanam, F.; Chazalviel, J.-N. Phys. ReV. Lett. 1998, 80, 4337. (7) Erne´, B. H.; Ozanam, F.; Chazalviel, J.-N. J. Phys. Chem. B 1999, 103, 2948. (8) Pankove, J. I. Optical Processes in Semiconductors; Prentice Hall: Englewood Cliffs, 1971. (9) Notten, P. H. L.; van den Meerakker, J. E. A. M.; Kelly, J. J. Etching of III-V Semiconductors: An Electrochemical Approach; Elsevier: Oxford, 1991. (10) Erne´, B. H.; Maroun, F.; Ozanam, F.; Chazalviel, J.-N. Electrochem. Solid-State Lett. 1999, 2, 231. (11) Wolf, W.; Lu¨bke, M.; Koper, M. T. M.; Krischer, K.; Eiswirth, M.; Ertl, G. J. Electroanal. Chem. 1995, 399, 185. (12) Berthier, F.; Diard, J.-P.; Montella, C. Electrochim. Acta 1999, 44, 2397. (13) Degn, H. Trans. Faraday Soc. 1968, 64, 1348. (14) The intersect of the load line with the j(Uint) curve at a point where its slope is negative and steeper than Rs-1 is electrically unstable. In a gedanken experiment, adding a small probe charge at the connecting point of the two electrical elements Rs and Uint(j) will result in a small change of the potential drops across each element. For the case that dj/dUint < Rs-1, the resulting change in the currents through the two elements will tend to enhance the probe charge; hence, the system will rapidly switch to another (stable) intersect. (15) The positive slope can be understood as follows: at more negative potential, the fractional surface coverage of As2H2 by adsorbed H atoms becomes still closer to unity, so that the local current density decreases, but this is more than compensated by the increasing thickness (and surface area) of the layer, i.e., the total current increases. (16) Koper, M. T. M.; Sluyters, J. H. J. Electroanal. Chem. 1994, 371, 149. (17) Erne´, B. H.; Stchakovsky, M.; Ozanam, F.; Chazalviel, J.-N. J. Electrochem. Soc. 1998, 145, 447. (18) Cattarin, S.; Tributsch, H.; Stimming, U. J. Electrochem. Soc. 1992, 139, 1320. (19) Cattarin, S.; Tributsch, H. J. Electrochem. Soc. 1992, 139, 1328. (20) Chazalviel, J.-N.; da Fonseca, C.; Ozanam, F. J. Electrochem. Soc. 1998, 145, 964. (21) Cattarin, S.; Chazalviel, J.-N.; da Fonseca, C.; Ozanam, F.; Peter, L. M.; Schlichtho¨rl, G.; Stumper, J. J. Electrochem. Soc. 1998, 145, 498. (22) Lehmann, V. J. Electrochem. Soc. 1996, 143, 1313. (23) Carstensen, J.; Prange, R.; Fo¨ll, H. J. Electrochem. Soc. 1999, 146, 1134. (24) Lewerenz, H. J. J. Phys. Chem. B 1997, 101, 2421.

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