1571
J . Phys. Chem. 1990, 94, 1571-1575
Relation between Chemical and Electrochemical Steps in the Anodic Decomposhion of I I I-V Semiconductor Electrodes: A Comprehenslve Model D. Vanmaekelberght and W. P. Gomes*g* Buys Ballot Laboratory, University of Utrecht, P.O. Box 80.000, NL-3508 T A Utrecht, The Netherlands, and Laboratorium voor Fysische Scheikunde, Rijksuniversiteit Gent, Krijgslaan 281, B-9000 Gent, Belgium (Received: May 18. 1989; In Final Form: September 5. 1989)
An overview is given of the different mechanisms of anodic decomposition, observed at GaAs and GaP electrodes. A comprehensive model is proposed, in which a chemical reaction between a mobile surface intermediate and water molecules is crucial for the competition between different electrochemical decomposition steps. The model accounts for the changes in decomposition mechanism observed when varying the activity of water or of protons and the anodic current density.
1. Introduction
During the last decade, many investigations have been devoted to the potential use of 111-V semiconductor electrodes in electrochemical solar cells. One of the major problems with respect to the use of n-type electrodes in particular is the anodic decomposition of the semiconductor material by photogenerated holes. This process can in principle be prevented by the addition to the electrolyte of a reducing agent, the oxidation of which by holes competes effectively with decomposition (for a review, see e.g. ref 1). It appears that only reducing agents that are chemisorbed, such as Se2-, can totally prevent anodic decompositi~n?.~In most cases, the fraction of the total photocurrent corresponding to the oxidation of the reducing agent (i.e. the stabilization ratio s) decreases with increasing photocurrent density. The study of this phenomenon has led to the establishment of various mechanisms for the competing anodic decomposition and oxidation of the reducing agentS4g5The common point of these mechanisms is that the oxidation of the reducing agent occurs not by holes directly but by intermediates of the decomposition reaction. Furthermore two main mechanisms for the anodic oxidation of the semiconductor had to be proposed, one involving holes and the other one involving mobile decomposition intermediates in each electrochemical step. Recently, Gomes et aL5 have performed a thorough investigation on the origin of the difference in decomposition mechanisms for GaAs under various circumstances, resulting in the conclusion that the mechanism depends on the activity of protons and of water in the electrolyte solution and on the indifferent electrolyte concentration. These effects were interpreted qualitatively on the basis of a chemical equilibrium, established after the first electrochemical step. Two decades ago, Gerischer6 showed that the anodic decomposition of one GaAs unit involves six elementary charge carriers and that besides hole capture, electron excitation into the conduction band is also involved to a small extent in the overall reaction. The decomposition current corresponding to electron excitation can be measured as the limiting dark anodic current increase at an n-type electrode under addition of a hole-injecting reactant. Only recently was it realized7 that the relationship between the anodic excitation current and the cathodic hole injection current constitutes a powerful probe for investigating the decomposition mechanism. This method was applied to n-GaP as well as to n-GaAs electrodes in various electrolyte^.^^ The results are in agreement with those obtained from stabilization measurements and from current-potential measurements at ptype electrode^^^^ and confirm the conclusion that the decomposition mechanism of a given semiconductor depends on the composition of the electrolyte. The distinct decomposition mechanisms observed at GaAs and at GaPelectrodes are labeled and tabulated in section 2. In this 'University of Utrecht. To whom correspondence should be addressed. Rijksuniversiteit Gent.
*
0022-3654/90/2094- 157 1$02.50/0
paper, an attempt is made to give an overall interpretation for the observed changes in mechanism. The basic concept of the model is that these mechanisms are mutually in competition and that a chemical reaction proceeding after the capture of a hole in a surface bond is the key point that governs this competition. This concept is completed with an assumption that follows from simple statistical considerations. It will be shown in section 3 that the proposed competition model provides an explanation for almost all observed changes in the decomposition mechanism of GaAs and GaP anodes.
2. Overview of the Observed Decomposition Mechanisms at CaAs and GaP Electrodes Six elementary charge carriers and hence six consecutive electrochemical steps are involved in the anodic dissolution of one GaP or GaAs unit. Evidently also chemical reactions between decomposition intermediates and water occur, leading to a (partial) neutralization of the charge of the decomposition intermediates and to solvation of the products. The available experimental results only provide information on one chemical reaction in the early stage of the decomposition p r o c e ~ s . ~O,n~ly this first chemical reaction will be considered further. Experimental results of the types mentioned in section 1 have led to the conclusion that, depending on circumstances, different decomposition mechanisms may operate. The common feature of all these mechanisms is the first electrochemical step, in which a valence band hole is trapped in a surface bond (denoted at Xo) leading to one-electron bond XI+
kih
Xo + h+ XI+ In what follows, the symbol XI+stands for a positively charged surface intermediate that is mobile in a two-dimensional surface layer. Since Ga is the less electronegative atom in GaAs or Gap, the positive charge will be mainly located on the Ga, so that chemically, XI+can to a first approximation be considered to be Ga'. Firstly, two mechanisms have to be distinguished, in both of which the second electrochemical step occurs directly after the first one. If another valence band hole is involved in this second electrochemical step (eq 2), it is assumed that holes are also (1) Miller, B. J . Electroanal. Chem. 1984, 168, 91.
(2) Tufts, B. J.; Abraham, I. L.; Santangelo, P. G.; Ryba, G. N.; Casagrande, L. G.; Lewis, N. S.Nature 1987, 326, 861. (3) Allongue, P.; Cachet, H.; Horowitz, G. J . Electrochem. Soc. 1983, 130. 2352. (4) Cardon, F.; Gomcs, W. P.; Vanden Kerchove, F.; Vanmaekelbergh, D.; Van Overmeire, F. Faraday Discuss. 1980, 70, 153. (5) Gome-s, W. P.; Lingier, S.; Vanmaekelbergh, D. J . Electroanal. Chem. 1989, 269, 237. (6) Gerischer, H.; Wallem-Mattes, 1. Z . Phys. Chem. (Frunkjurt) 1969, 64, 187.
(7) Vanmaekelbergh, D.; Kelly, J. J. J . Electrochem. Soc. 1989,136, 108. (8) Vanmaekelbergh, D.; Kelly, J. J.; Lingier, S.;Gomes, W. P. Ber. Bunsen-Ges. Phys. Chem. 1988, 92, 1068. (9) Vanmaekelbergh, D.; Hogenkamp, R.; Kelly, J. J., submitted to J . Elertroanal. Chem.
0 1990 American Chemical Society
1572 The Journal of Physical Chemistry, Vol. 94, No. 4, 1990
Vanmaekelbergh and Gomes
TABLE I: Overview of Decomposition Mechanisms Observed at CaAs Electrodes [(jii)and (100) Face] in Various Aqueous and Mixed Electrolytes‘
B n-GaAs
A I
C
(iii) 2
n-GaAs
(iii) p-GaAs
3
(iii) 4 5
p-GaAs
S(ih9Y) with TMPD
(iff)
H2S04 + 0.25 m ~ l - d m - ~ LiC14 in H20/48% CH,OH or H20/80% C H 3 0 H same as 6
n-GaAs
6
(iii) 7
X?)
H2S04 0.25 mobdm” L E I 4 in 18% CH,OH/H,O pH = 2.5 same as 4
(iii)
p-GaAs
(iii) 8
HZSO4 + 0.25 mobdm-) LiCIOI in 13% C H , C N / H 2 0 1 5 pH 5 2.5 H2S04 + 4 mobdm-’ LiCl in H 2 0 29pH93 HISO, + 0.25 m ~ l . d m - ~ LiCI in H20/42% CH,CN 1.5 IpH 9 2.5 0.5-4 mobdm-’ H2S04 in H 2 0 1 m ~ l . d m -NaOH ~ in H 2 0 0.5-2 mol-dm-, + 4.5 mol-dm-, LiCl in H 2 0
n-GaAs
(iii) n-GaAs
9
(iii) IO
n-GaAs
(iii) n-GaAs
11
(100)
n-GaAs
12
(100)
n-GaAs
13
(100)
10
(0;
+
n-GaAs
F
E X-C(R)
D H,SOd + 0.25 mol-dm-’ -K2S04 in H 2 0 pH = 1 H 2 S 0 4 + 0.25 mol-dm-’ LiCIO, in H,O 1 5 pH 5 3.5 same as 2
X-C(R)
11
X-C(R)
12
X-C(R)
I1
X-C(R)
12
probably H-C(R)
11 13
probably H-C(R)
12
H-C(R)
13
X
13
X
13
x-C(I) x-C(1)
8 9 8
X
9
“Key: column A, identification number; column B, type of GaAs (n or p) and crystallographic face; column C, experimental method, s(ih,y) measurement of the stabilization ratio s as a function of the concentration of the reducing agent y and the hole current density ih, s(ih,y,pH) see above, but including the study of the influence of pH, ih(V,y) measurement of the forward current density-potential characteristics at p-type electrodes at different values of the reducing agent concentration, i,(ih,pH) measurement of the anodic excitation current density at an n-type electrode under conditions of hole injection as a function of the hole current density ih and the pH of the solution; column D, composition of the electrolyte; column E, observed mechanism; column F, reference.
involved in the further electrochemical steps (the latter will not be explicitly mentioned below as they are not relevant to the further discussion). This mechanism will be labeled by the letter H X I + + h+
k?
XI-OH
X22+(H mechanism)
(2)
An alternative mechanism, in which mobile XI+ intermediates are involved in the second and following electrochemical steps, will be denoted as X XI+
+ XI+
bX
+
XZ2+ Xo (X mechanism)
(3)
Secondly, two mechanisms have to be considered in which a chemical reaction between the mobile intermediate XI+and water molecules occurs X I ++ n H 2 0
e k‘
XI-OH
+ H+(H20),,-,
(4)
In this chemical process, a neutral and immobile decomposition intermediate X,-OH and a solvated proton are formed. The number of water molecules involved in this process is denoted by n (>1). In the decomposition mechanisms under consideration, the intermediate XI-OH is involved in the second electrochemical step. The intermediate X 1 4 Hmay be oxidized by a valence band hole (mechanism H-C); i t is then assumed that holes are also involved in the subsequent electrochemical steps XI-OH
Alternatively, the intermediate X,-OH and the intermediates of higher formal oxidation degree may be oxidized by the mobile surface intermediate XI+ (mechanism X-C)
+ h+
kib
X2+
(5)
+ XI+
klU
Xz+
+ Xo
(6) Since experimental evidence exists that chemical reaction 4 may proceed either under quasi-reversible or under irreversible conditions, the mechanisms involving chemical reaction 4 will be classified more in detail as H-C(R) (reaction 4 is reversible) or H-C(1) (reaction 4 is irreversible) and X-C(R) or X-C(I), respectively. In what follows, the decomposition mechanisms observed at GaAs and GaP electrodes (n type and p type) will hence be denoted by H, X, X-C(R), X-C(I), H-C(R), and H-C(I), respectively. 3. Interpretation of the Data on the Basis of a Model Involving Competition between Decomposition Mechanisms 3.1. The Model. From the enumeration of distinct decomposition mechanisms observed at GaAs (Table I) and GaP (Table 11) electrodes in various electrolytes, it can be concluded that there (IO) Vanmaekelbergh, D.; Gomes, W. P.; Cardon, F. Ber. Bunsen-Ges. Phys. Chem. 1985.89.981. ( 1 1) Lingier, S.; Vanmaekelbergh, D.; Gomes, W. P. J . Electroanal. Chem. 1981, 228, 11. (12) Lingier, S . ; Gomes, W. P.;Cardon, F. Ber. Bunsen-Ges.Phys. Chem. 1989, 93, 2 . (13) Lingier, S . ; Vanmaekelbergh, D.; Gomes,W. P. In Phorocatalyric Grassi, G., Eds.; Elsevier Production of Energy-rich Compounds; Hall, D . 0.. Applied Science Publishers: London, 1988; p 127.
Anodic Decomposition of Semiconductor Electrodes
The Journal of Physical Chemistry, Vol. 94, No. 4, 1990 1573
TABLE I 1 Overview of Decomposition Mechanisms Observed at GaP Electrodes in Various Apwous Electrolytesa A B C D E 14 n-GaP H2S04 0.25 mol.dm-) probably
(iii)
p-GaP (iii)
same as 14
16
n-GaP
0.5-4
17
n-GaP (1 11)
18 19
20
n-GaP (iii) n-GaP (iii) p-GaP (iii)
14
H-C(R)
KzSO4 in H 2 0 pH = 1
15
(111)
a
+
F
probably H-C(R)
mol.dm-) H2S04
H-C(R)
7 9
X-C(R)
9
in HzO
+
0.5-4 mol-dm-' H2S04 4.5 mobdm-' LiCl
in HzO 0.25 mobdm-' K2S04+
buffer pH = 4 0.25 moladm-) K2S04+ 0.1 mol-dm-' Na2B40, pH = 9 same as 19
15
X (or
15
X-C(R)?) X (or
16
X-C(R)?) X (or
16
X-C(R)?)
For the meaning of the columns and notations, see Table I.
is no experimental evidence for the Occurrence of the decomposition mechanism H (Le. no chemical reaction after the first electrochemical step, holes are involved in each electrochemical step). This fact can be understood on the basis of a simple statistical argument. It is reasonable to assume that the concentration of unbroken surface bonds Xo is much higher than that of the decomposition intermediates XI+, X,-OH, etc. Hence, the probability for a hole to be trapped in an unbroken surface bond (process 1) will be much higher than to react with a decomposition intermediate (process 2), even if the respective rate constants would be the same. In fact, for electrostatic reasons, the rate constant k t will be considerably lower than klh. As a consequence, (nearly) all free holes will be consumed in the formation reaction of mobile surface intermediates XI+ (reaction 1) which are then involved in the further decomposition step (mechanism of the type X). The foregoing reasoning leads to one of the main assumptions of the model presented here: if there is no chemical reaction resulting in a drastic reduction of the concentration of the mobile intermediates XI+, no valence band holes but XI+ intermediates are involved in each electrochemical step of the decomposition. This assumption means that the mechanism H does not occur, and that the mechanisms of the type H-C(R) or H-C(1) occur only if the concentration of mobile surface intermediates is reduced to a very small value as a result of chemical reaction 4, i.e. under circumstances where the generation of the products of this reaction is largely favored. Therefore, in the competition scheme presented below, the direct reaction between XI and a valence band hole (process 2) according to mechanism H is excluded. For simplicity, the electrochemical step 5 and subsequent hole steps according to mechanisms of the type H-C are not included in the scheme below nor in the basic calculation. It will be shown further that this simplification does not undermine the relevance of the model. The scheme in Figure 1 represents a competition model for the decomposition mechanisms X and X-C. After the first step (see reaction equation l ) , in which a hole is trapped by an unbroken surface bond X,and a mobile surface intermediates Xi+ is formed, two pathways for further decomposition are available. In pathway 1 (further denoted as the direct pathway) (see Figure l), mobile intermediate XI+ reacts directly with another XI+ (see reaction (14) Vanmaekelbergh, D.; Gomes, W. P.;Cardon, F. J . Electrochem. Soc. 1982, 129, 546. (15) Lu, S. Y.;Vanmaekelbergh, D.; Gomes, W. P.; Cardon, F. Ber. Bunsen-Ges. Phys. Chem. 1987, 91, 390. (16) Vanmaekelbergh, D.; Lu, S.Y.;Gomes, W. P.; Cardon, F. J . Electroanal. Chem. 1987, 221, 187.
XI'
fast, chemical)
-_ Figure 1. Competitive decomposition reaction scheme: ( I ) 'direct" pathway, partial current density ji; (2) "chemical" pathway, partial
current density j 2 . equation 3). A doubly charged positive intermediate X>+ is formed which is then converted by one or more chemical reactions into the intermediate X2+. The hole flux corresponding to this direct pathway is denoted as jl. If the entire hole flux is associated with this pathway, one has the decomposition mechanism X GI = j h / 6 ) . In pathway 2 (further denoted as the indirect or chemical pathway) (see Figure l), XI+ is neutralized and immobilized by a chemical reaction (eq 4). After this chemical reaction, the second electrochemical step takes place, in which the neutral Xi-OH intermediate is oxidized by a mobile intermediate, resulting in the intermediate X2+ (see eq 6). The hole flux corresponding to this chemical pathway is denoted as j 2 . If the entire current density is associated with this chemical pathway and XI is involved in each electrochemical step, one has the mechanisms X-C(R)or X-C(1).In view of the considerations in the beginning of section 3, holes can be assumed to be involved in the electrochemical steps after chemical reaction 4, only if the concentration of mobile intermediates is negligibly low. One has then the mechanism H-C(R) or H-C(1). Since XI-OH is immobile, reaction between two such species can be excluded. The direct and indirect pathways join in the intermediate X2+. Electron excitation steps are parallel branchings of the electrochemical (hole or XI) steps. As they are only contributing for
oh)
1574 The Journal of Physical Chemistry9 Vol. 94, No. 4, 1990
Vanmaekelbergh and Gomes
a small fraction of the overall decomposition current, they are omitted from Figure 1. Under steady-state conditions one has j h / 6 = jl + j2 = k2XX12
12/(ih/61
x - C ( ~ ) ( c a s c s1-5and 171
+ [(kZX’k&Z)/(k, + kp’xl)]
(7)
In eq 7, xlstands for the surface activity of the mobile intermediate XI+, k , for kl(aH20)nand k , for k,‘aH+, u~~~ being the activity of water and aH+that of the hydrated proton. The significance of the rate constants follows from the competition scheme (Figure 1). The use of activities instead of concentrations in the kinetic eq 7 is motivated by the activated complex theory, in which the equilibrium constant for formation of the activated complex from the reactants is expressed in terms of activities. The reaction order n in H 2 0 of the forward reaction 4 will be discussed below. When eq 7 is solved, j , and j , can be expressed as a function of the relevant variables j h , aH2o,and U H + , which contain the appropriate rate constants. As the cubic equation (7) has three real roots that can only be found geometrically, a more simple strategy will be followed here, in which two limiting cases related to chemical reaction 4 are considered. In the first case (case a), chemical reaction 4 is considered to proceed under quasi-reversible conditions, which means that the reverse reaction (4) is much faster than the subsequent electrochemical step ( 6 ) : k , >> k z x ‘ x l . In the second case (case b), the chemical reaction is considered to proceed under irreversible conditions: k , > kzx’xl and k , 1, respectively. Case a. Chemical reaction 4 proceeds under quasi-reversible conditions: y 1 and @ > 1 or 9 , >> 1 . This mechanism corresponds to the lower part of the functional surface in Figure 2. 3.2. Interpretation of the Results Reported in Section 2. The changes in the decomposition mechanism of GaAs (TIT) electrodes will be interpreted first on the basis of the model presented in section 3.1. In Figure 2, the identification numbers of Table I are represented on the functional surface according to the experimentally observed decomposition mechanism. The numbers 1 to 3 pertain to aqueous electrolytes in which H2S04was added up to pH I 3.5. The occurrence of an X-C(R) mechanism in these aqueous media corresponds to y 1 . It is found that j 2 / 0 ’ h / 6 ) = (2/8)((P +
b/
Anodic Decomposition of Semiconductor Electrodes mechanism is found (experiments 6-8). This change can be understood on the basis of the medium effect. Indeed, the equilibrium constant Kc,m in C H 3 0 H / H 2 0 is related to the equilibrium constant Kc,+0 in H20 by K,m=
&.H~O
exp[(-AG’t,~+ + ~ A G ’ ~ , H ~ O ) / R T (15) I
(see eq 4). In eq 15, AGO~,H+ stands for the change in standard free energy when 1 mol of protons is transferred from the pure aqueous solution to the mixed solution C H 3 0 H / H 2 0 . An analogous definition holds for AGot,~20. The values of AGot,H+ found in the literature are considerably negative.”J* The value of AGot,H20 was calculated from thermodynamic data and was found to be slightly negative. The value of K C , , / K c , ~ has then been calculated on the basis of eq 15 with values tor AGO,,+ obtained from ref 18. It was found that in the acidic C H 3 0 H / H 2 0 solutions corresponding to experiments 6 and 7, Kc,,, is at least 2 orders of magnitude larger than Kc,H20,even if the hydration number n is assumed to be large (n = IO). The change from an X-C(R) to a H-C(R) mechanism can hence be understood as being the result of a considerable shift in the equilibrium of reaction 4, leading to a deficiency in mobile XI+ intermediates. Hence, valence band holes take over the role of Xi+ in the subsequent electrochemical steps. The same argument holds to explain the change in decomposition mechanism when the aqueous solution is replaced by a H20/13% CH3CN solution. When 4.5 m ~ l - d m LiCl - ~ or 48% CH3CN is added to the acidic aqueous electrolyte (experiments 9 and lo), the decomposition mechanism changes from X-C(R) (0 1 or 0 >> I ) . As cr is proportional to ( u ~ ~(see ~ eq ) - 10) ~ and to ( ~ ~ ~(see 0 eq ) 12), - ~ the ~ decrease of U H 0 from 1 to about 0.7 due to the addition of 4.5 m ~ l - d m LiCllb -~ results in an increase of both a and 8. However, to explain the change in mechanism, it must be assumed that at least 10 molecules of water are involved in the forward chemical reaction (4). It may seem like a surprising conclusion that the order of reaction is so high; however the fact should be considered that the reactant is the solvent. Analogous cases are met in the literature. For example, recent work by Saakes et aL20 has shown the Occurrence of reactions of high order in water between electrochemical steps during the reduction of metal ions at mercury electrodes. At GaAs (100) electrodes (experiments 11-13), an X-C(1) mechanism (y >> 1 and @ > 1 or p >> 1) when 4.5 moldm-3 LiCl is added. This change in mechanism is related to the change from > 1 as a result of the reduced water activity. It must be assumed again that IO or more HzO molecules are involved in chemical reaction 4. If abstraction is made of the possible dependence of the parameters a and p on the crystallographic face exposed to the (17) Alfenaar, M.; De Ligny, C. L. R e d . Trav. Chim. Pays-Bas 1967,86, 929. (18) Case, B.; Parsons, R. Trans. Faraday SOC.1967, 63, 1224. (19) Robinson, R. A,; Stokes, R. H. Electrolyte Solutions; Butterworths: London. 1959. (20) ’Saakes, M.; Sluyters-Rehbach, M.; Sluyters, J. H. J . Elecrroanal. Chem. 1989, 259, 265.
The Journal of Physical Chemistry, Vol. 94, No. 4, 1990 1575 electrolyte, also the change from an X-C(R) mechanism (experiments 1-5) to a X-C(1) mechanism (experiment 1 1 ) can be understood on the basis of our model. As the electrolyte composition in experiments 1 to 5 and 11 is the same, the change in mechanism must be related to a change in the hole flux j h . Indeed, the experiments under number 11 are performed at decomposition current densities ( - j h ) which are 1 to 2 orders of magnitude higher than those labeled 1 to 5 (see Table I). At GaP electrodes, a H-C(R) mechanism is observed in H 2 0 + H2S04 (experiments 14-16), changing into an X-C(R) mechanism when 4.5 m o l ~ d m -LiCl ~ is added (experiment 17). According to our model, a H-C(R) mechanism operates when the concentration of X I +is low, i.e. when the position of equilibrium 4 is far to the right. Addition of LiCl shifts this equilibrium to the left, so that more XI+ intermediates are available. However, in order to explain the change from a H-C(R) to an X-C(R) mechanism quantitatively, a large value of n in reaction 4 must again be assumed. As in experiments 18-20, the activity of protons and water was not intentionally varied, it is not clear whether an X or an X-C(R) mechanism holds in electrolytes with pH I 4. However, our model predicts a H-C(R) or an X-C(1) mechanism to occur at higher pH values. It must hence be concluded that the observed decomposition mechanisms at pH = 4 (no. 18) and pH = 9 (no. 19 and 20) are not in agreement with the predictions of our model. This suggests that in the intermediate pH range or above, a chemical reaction of different nature than the one proposed here governs the competition between decomposition mechanisms. 4. Conclusions The changes in the anodic decomposition mechanism of GaAs, observed when varying the electrolyte composition, are interpretable on the basis of a competitive reaction scheme in which a chemical step, occurring after the trapping of a free hole in a surface bond, plays a crucial role. This chemical reaction, which involves several water molecules, leads to the immobilization and the neutralization of the mobile decomposition intermediates XI+. The conditions under which this chemical reaction proceeds determine almost entirely the nature of the decomposition mechanism. The pronounced change in mechanism due to lowering of the water activity can be explained by the model if it is assumed that at least 10 water molecules are involved in the chemical reaction. Also the changes in decomposition mechanism occurring when the aqueous electrolyte is replaced by a mixed H20/CH30H or H20/CH3CN electrolyte can be understood if the medium effect on the chemical reaction is taken into account. The applicability of the model to the results obtained on GaP is restricted to strong acid medium. Apart from this case, the proposed model appears to be general enough to explain the observed changes in anodic dissolution mechanism of 111-V semiconductors: the competing reaction scheme, complemented with an acceptable statistical argument, makes clear which variables are crucial to the dissolution mechanism.
Acknowledgment. W.P.G. wishes to thank the I.I.K.W. (Inter-University Institute for Nuclear Sciences, Belgium) for financial support.
