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J. Phys. Chem. 1980, 84, 3172-3178
(29) S.decheveigne, J. Klein, A. Leger, M. Belin, and D. DeFourneau, Pbys. Rev. 8,15, 750 (1977). (30) R. V. Coleman, J. M. Clark, and C. S. Korman, in “Inelastic Electron Tunneling Spectroscopy”, Springer-Verlag, New York, 1978. (31) K. W. Hipps, U. Mazur, and M. S. Pearce, Cbem. Pbys. Lett., 68, 433 (1979). (32) W. H. Weinberg, Annu. Rev, Pbys. Cbem., 29, 115 (1978). (33) P. K. Hansma, Pbys. Rep., 30C, 145 (1977). (34) E. L. Wolf, Solid State Physics, 30, 1 (1975). (35) K. H. Gundlach and J. Kadlec, Appl. Pbys. Lett., 20, 445 (1972). (36) G. M. Singal, S.K. Gupta, A. K. Kapil, and V. K. Srivastava, J . Appl. Phys., 49, 3402 (1978). (37)J. G. Simmons, Pbys. Rev. Lett., I O , 10 (1963). (38) J. G. Simmons, Pbys. Rev. Left., 23, 297 (1969). (39) W. F. Brinkman, R. C. Dynes, and J. M. Rowell, J . Appl. Phys., 41, 1915 (1970). (40)C. S.Korman, J. C. Lau, A. M. Johnson, and R. V. Coleman, Pbys. Rev. B , 19,994 (1979). (41) M. F. Muldoon, R. A. Dragoset, and R. V. Coleman, Pbys. Rev. B , 20, 416 (1979). (42) P. R. Bevington, “Data Reduction and Error Analysis for the Physical Sciences”, McGraw-Hill, New York, 1969. (43) G. Brauer, “Handbook of Preparative Inorganic Chemistry”, Translated by P. G. Stecker, Academic Press, New York, 1965. (44) W. G. Palmer, “Experimental Inorganic Chemistry”, Cambridge University Press, London 1954;U. Mazur and K. W. Hipps, J. Pbys. Cbem., 83, 1884 (1979). (45) H. E. Toma, E. Gieserecht, J. N. Malin, and E. Fluck, Inorg. Cbim. Acta, 14, 1 1 (1975).
(46) D. Nicholls, “The Chemistry of Iron, Cobalt, and Nickel”, Pergamon Press, New York, 1973. (47) A. G. Sharpe, “The Chemistry of Cyano Complexes of the Transition Metals”, Academic Press, New York, 1976. (48) W. P. Griffith and G. T. Turner, J . Cbem. SOC. A , 858 (1970). (49)K. Nakamoto, “Infrared and Raman Spectra of Inorganic and Coordination Compounds”, 3rd ed, Wlley, New York, 1978. (50) L. Tosi and J. Danon, Inorg. Chlm., 3 , 150 (1964). (51) U. Mazur and K. W. Hipps, J . Phys. Chem., 83, 2773 (1979). (52) J. F. Duncan and H. J. Percival, Aust. J . Cbem., 21, 2175 (1968). (53) G. M. Muha, J . Cafal. 58, 478 (1979). (54) G. M. Muha, J . Pbys. Chem., 82, 1843 (1978). (55) C. S.Korman and R. V. Coleman, Pbys. Rev. B , 15, 1877 (1977). (56) J. 0.Ayers and W. H. Waggoner, J . Inorg. Nucl. Chem., 33, 721 (1971). (57) N. G. Vannerberg, Acta Cbim. Scand., 26, 2863 (1972). (58) A. Tullberg and N. G. Vannerberg, Acta Cbim. Scand., 28A, 551 (1974). (59) D. F. Shriver, S. A. Shriver, and S. E. Anderson, Inorg. Cbem., 4, 725 (1965). (60) R. R. Ryan and B. I.Swanson, Inorg. Cbem., 13, 1685 (1974). (61) R. R. Ryan and B. I. Swanson, Inorg. Cbem., 12, 283 (1973). (62)R. M. Handy, Pbys. Rev., 126, 1968 (1962). (63) S.R. Pollack and C. E. Morris, J . Appl. Phys., 35, 1503 (1964). (64) P. K. Hansma, D. A. Hickman, and J. A. Schwarz, J . Catal., 48, 237 (1977). (65) Compare our results for junctions exposed to water after oxide growth to those of the pristine oxide given by Coleman in ref 40 and 41. (66)K. Knorr and J. D. Leslie, Solld State Commun., 12, 615 (1973).
Investigation of Photoelectrochemical Corrosion of Semiconductors. 1 K. W. Frese, Jr.,* M. J. Madou, and S. R. Morrison Materials Research Laboratory, SRI International, Menlo Park, California 94025 (Received: February 25, 1980; In Final Form: July 30, 1980)
Experimental results of photoinduced corrosion of n-GaAs are reported, and models to account for the behavior both in this material and in other semiconductorsare developed. Specifically the role of defects (dislocations in particular) and of light intensity are discussed. Experimentally it is shown that the presence of dislocations on GaAs leads to much greater sensitivity to photocorrosion. It is shown theoretically that at the points where dislocations emerge at the surface there is a more negative “microscopicdecompositionpotential”, and corrosive attack at these points, leading to highly reactive surface steps, will account for the increased sensitivity. Experimentally it is shown that the percent stabilization offered by reducing agents in solution decreases with increasing light intensity. Theoretically it is shown that the decrease can be explained if the hole capture leading to corrosion is second order in hole density and if the hole capture by the reducing agent is first order in the hole density. Such a behavior would be consistent with the need for the capture of two holes to eliminate one bond.
Introduction Although noteworthy progress has been made in the development of photoelectrochemical solar cells,*-4the photocorrosion of desirable anode materials such as nGaAs and n-Si remains a major difficulty in the vast majority of electrolytes. Ultimately, the goal is to make solar cells using polycrystalline materials: and such materials will contain defects such as grain boundaries and dislocations. Simple theory suggests that defective areas of the crystal surface will be more difficult to stabilize. From an experimental point of view, it has not been clear what effects these defects will have on the photoelectrochemical corrosion process. Therefore, important objectives of our work are to investigate the effects of dislocations and grain boundaries on the corrosion rate and stabilization efficiency and also to study the corrosion process from a theoretical point of view. Our discussion begins with a description of the effect of a dislocation-like defect on the decomposition potential of an n-type semiconductor such as n-GaAs. This will serve 0022-3654/80/2084-3172$0 1.OO/O
to show that from a theoretical thermodynamic point of view defective sites are harder to stabilize. According to the Bronsted rule5we may expect that the rate of corrosion at a defect will be faster. We will next discuss our experimental results on stabilization efficiency for n-GaAs with various reducing agents, using both well-etched and damaged surfaces. The studies have included the effect of the hole current (light intensity) on the stabilization efficiency, as well as the effect of dislocations. Finally we propose a possible kinetic model for the corrosion process which accounts for the observed loss of stabilization as the hole current increases for the 1-equiv n-GaAs/Fe”EDTA system. Theoretical Results A thermodynamic model of corrosion has been given by Bard and Wrighton6 and Geri~cher.~ A similar model is summarized for an n-type semiconductor in Figure 1. Note that the holes are assumed to be at an energy level 0 1980 American Chemical Society
Photoelectrochemical Corrosion of Semiconductors
The Journal of Physical Chemistry, Vol. 84, No. 24, 1980 3173
-PEA
GaAs($)
-
TASA
\
“de c orno.
+
2RT
-CS Ga(s)
+
+ As ( 5 )
AS(g)--%
AG
6H20
Ga(OH)3
+ As(OH13 +
3H2
Figure 2. Thermodynamic cycle to show the effect of bonding on corrosion decomposltlon potential.
TABLE I : Calculation of Decomposition Potentials atomization no. energy, AGdecornp, (Ga, As) kcal mol-’ kcal mol-‘ coord
SOLID
ELECTROLYTE
(4,4) (493) (492) (4,1)
154 121 89 54
-7.6 -40.6 -72.6 -107.6
Edecomp
vs. NHE, V - 0.06
-0.29 -0.52 - 0.78
the direct reaction of GaAs with HzO. An alternate path to the products is to first atomize the GaAs and then return the gaseous Ga and As to elements and allow them to react with H210 with free-energy change AG. The key difference in the cycle between ideal and defective crystals is in the calculation of the atomization energy. In essence, a pair of Ga and As atoms associated with a defect in the crystal will require less energy for atomization due to weakening or breaking of bonds at the defects. This ento become more negative thalpy change will cause AG,,,, and thus raise the decomposition level ED to ED’. The calculation of the atomization energy of a pair of Ga and As atoms was carried out by using the bonding model of Sanderson? This model is a semiempirical model of bond strengths based on Sanderson’s electronegativity and the principle of electronegativity equalization. The atomization energ for an AB solid is given by eq I, in units
of kcal mol-l. In this equation ti and t, are ionic and covalent blending coefficients, calculated from changes of electronegativity that accompany chemical bonding. 2 is the ionic charge, M is a Madelung constant, k is a repulsive constant, N is the number of electron pair bonds (e.g., 4 for ideal GaAs structure), Ro and R, are bond distances, and (EuEBB)l/’is the geometric mean of the appropriate homonuclear single bond energies of Ga and As. The essential features of eq I that distinguish a surface defect are the Madelung constant, M , and more importantly N . Both of these quantities are structure sensitive. For example M may be ?elated to the coordination number (CN) of Ga and of As, rmd N may be decreased by breaking or partially breaking: gallium-arsenic bonds. From the cycle in Figure 2, we have eq 11. The meaning of the thermodynamic symbols is evident. AGdecomp= AEA- TASA + 2RT - CS + AG (11) The decomposition level is given by eq 111, where n = EDdsmmp = AGdecomp/ (nF) (111) 6. Table I summarizes the results obtained by using the cycle in Figure 2. In this example a Ga atom in the lattice was assumed to be surrounded by four As atoms (CN = 4). The As atom adjacent to the Ga atom was allowed to have different numbers of Ga neighbors. This corresponded to different numbers of broken bonds; that is, N was decreased by one for each bond broken. As the data
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The Journal of Physical Chemistry, Voi. 84, No. 24, 1980
in Table I show, the decomposition level for the pair of Ga and As atoms is shifted -230 mV more negative for each broken bond. Thus atoms at the point of emergence of dislocations at the surface will be much more sensitive to photocorrosion,because they are incompletely coordinated ( N = 3). The actual number of susceptible atoms per unit area that have this high microscopic decomposition potential is a small fraction of the total atom density on the surface, and it is necessary to show how their presence leads to rapid corrosion. The removal of one of the susceptible atoms from the end of the dislocation results in an encircling surface step, a circle of atoms with one less bond to the solid than an atom on a terrace (perfectly planar) region of the surface. Atoms at surface steps are expected to be kinetically much more active in corrosion than atoms on the plane surface. Atoms at a kink site, where a step has a corner, should be even more active. Thus, with the help of a step, a plane of atoms is easily removed from the surface, and a high dislocation density, generating many steps, will stimulate rapid photocorrosion of the crystal. From these results we reached the important conclusion that for good corrosion suppression one must consider not only the decomposition level of the ideal lattice but also that of the defective sites in and on the crystal. We also conclude that relatively stronger reducing agents are required to suppress corrosion on defective electrodes such as polycrystalline thin films. From a kinetic point of view, where the surface state energy level of holes compared to solution redox energy level is of interest, the role of defects in capturing the holes and thus altering the surface state hole energy levels may be of considerable importance. For example, at a dislocation or at a step, one may have a surface atom whose bonds have a significantly different character than bulk bonds. This different bonding character could lead to both higher or lower energy levels for holes at the semiconductor surface. A Ga or As atom at a step can have two bonds to the underlying lattice (back-bonds) and two bonds involving species from the electrolyte such as OH- or . ' H We believe that it is possible to have perturbations in the back-bonds caused by the bonding to the electrolyte species. In certain cases it appears that the back-bonds can be weakened (higher hole energy level), thus making such surface steps more susceptible to corrosion or equivalently harder to stabilize. This effect is governed by the details of the surface chemistry. Energy level shifts of this nature, necessary to understand in order to develop a detailed kinetic model, are currently under study and will be reported in a future publication. Experimental Results and Discussion on GaAs A rotating ring-disk electrode (RRDE)gwas assembled by using a single crystal n-GaAs disk and an amalgamated copper ring. The samples were etched with H,S04:H,02:Hz0 (3:l:l v/v). The (T T T) face, the arsenic face, was exposed to the solution. The GaAs disk was illuminated with chopped light at -1 Hz from a 150-W xenon lamp. The electrode potential vs. SCE of the ring and disk was controlled by a Pine RDE 3 bi-potentiostat. The disk potential was normally +0.8 V SCE. The rotation speed was 800-1000 rpm. High-purity N2was continuously bubbled through the solutions. In RRDE studies of competitionlo between electron transfer from a redox component and photocorrosion of a semiconductor, a kinetic parameter of interest is the percent stabilization, 9%S, or the fractional equivalent, S. The photoproduced holes at the surface of the GaAs disk can oxidize the reducing agent or can corrode the GaAs.
Frese et al.
2oo
>
150
Q,
s Lu
2
100
3 V 0
za
50
0 0
100
300 400 DISC CURRENT FA Area = 0 20 cm*
200
500
600
Flgure 3. Determination of collection efficlency, y. n-GaAs (i i7 AS) (A) 0.1 M Fe(CIO4),/0.1 M Na,EDTA. pH 7.8. (0) 0.08 M Fe(CIO,),/I M Nacit. pH 10.4. Disk potential, 4-0.8V SCE. Ring potential at saturation ring current.
The stabilization is expressed as the ratio of the hole current that leads to oxidation of the reducing agent, i,, to the totalac hole current, i, through the GaAs disk. The value of io, is determined by measuring the periodic component of the ring current and dividing this value by a collection efficiency factor, y. Reasonable estimates of y may be made9 from the geometry of the ring-disk electrode. We have determined our collection efficiency by using a high concentration, 0.1 M, of an effective stabilizing agent such as FeIIEDTA or Fencit (cit = citrate). For unit stabilization efficiency we have 1 = iOx/(+,) When the Stabilization is close to 1,a plot of ioxvs. i, should be linear with slope y. Figure 3 shows such a plot for n-GaAs using both Fe"EDTA and Fe"cit. The calculated slope gave y = 0.315, whereas the geometrical calculation of y gave 0.33 for our apparatus. These results were reproducible for several different disks. When Fe"EDTA was used, y values were 0.315 and 0.317; when Fe"cit was used, y was 0.316. Figure 4 shows the effect of the pH on the percentage stabilization of the etched n-type GaAs for two different concentrations of Fe(C104)2in 0.1 M EDTA. The pH was adjusted with either HC104or NH40H. One region below pH 2.5 is inaccessible because precipitation of EDTA occurs in such a solution. The light intensity was found to influence the percentage stabilization in such a way that higher light intensities gave lower percentage stabilization. Therefore all points given in Figure 4 were taken for the same disk current of -1 mA/cm2. Another important observation is that, if the percentage stabilization were low, perhaps because of the presence of an oxide film, a cathodic current temporarily passed through the disk could result in the recovery of the initial higher percentage stabilization. The experiments in Figure 4 were always started after the disk had been held cathodic for a few minutes. Figure 4 shows that, for both concentrations and with the prevailing light intensities, the stabilization is complete in the intermediate pH region. Within the accuracy of our apparatus, we concluded that stabilization is >99% under these conditions. For hole currents of 1 mA/cm2, the stabilization at both high and low pH decreases rapidly. The highest stabilization occurs where the oxidation product, Ga(OH&, of the crystal itself is most insoluble.ll This result is analogous to the one found in the stabilization of n-GaP with Fe(CN)4k:2 although in this case we
The Journal of Physlcal Chemlstry, Vol. 84, No. 24, 1980 3175
Photoelectrochemical Corrosion of Semiconductors I
I
-0-03
100
/
-0
/
80
I
I
l
l
l
l
I .-Qr
3!ri
k
4-
m
4
ka
\O
m
60
0
a I-
\o \\\\
L3
60
w
\
W
z
40
UJ
u a
2 50
l
80
z
k
I
z
.-o .P
a
I
'\I x
I
l
100
-0
x r :
0
/
I
a u
40
a W
n.
20
0.04 M Fe (C1O4l2 t 0.1 M EDTA e : 0.1 M Fe(C104)2 t 0.1 M EDTA
3 :
20
\ n 0
0.05
01
[ F d l l ) EDTA]
0
M
~
0
2
6
4
8
10
PH
Flgure 4. Percent stabllization of n-GaAs vs. pH. Disk current mA/cm2. The pH is adjusted wlth NH40H or HCIO,.
=1
found that at lower light intensities in acid solution e.g., 0.04 M Fe"EDTA, pH 3, 100% stabilization can be found. Further investigation is required to fully explain this pH dependence of the percentage stabilization. Possible explanations are (1)a change in redox properties of the solutions with pH (in the case of FeIIEDTA), (2) a shift in energy levels of the n-GaAs relative to the Fe"EDTA level because of Helmholtz potential shift, or (3) a change in electrode stability toward holes because of a thin oxide layer on the GaAs surface. We have found evidence on silicon13that, when a thin oxide layer develops, the stabilizing action of reducing agents resisting further corrosion is dramatically enhanced. We attribute this to the development of a double layer across the oxide when photoproduced holes are captured at interface states. Then the energy levels of the reducing agent may be favorably shifted relative to the valence band edge. On GaAs in the intermediate pH range, thin GazO3 layer could behave similarly. Figure 5 shows the effect of surface damage on the stabilization. In the figure we plot percentage stabilization vs. concentration of' Fe(I1) in 0.1 M EDTA at constant photocurrent and an intermediate pH. Curve a was determined by using well-etched samples and showed reproducible levels of stabilization as long as fresh solutions and freshly etched (e.g., 10-s etch) electrodes were used. Curve b was determined on specimens etched and subsequently polished with 0.3-pm A1203 powder for 30 s. This treatment may be assumed to introduce unspecified surface damage, primarily dislocations. For conditions of constant concentration of FeIIEDTA and light intensity, the effect of surface damage is to lower the stabilization efficiency. We have also observed several times that, if corrosion is allowed to proceed on such a damaged surface, the stabilization will recover with time, reaching a value characteristic of a damage-free surface in 15 min. Presumably this represents the removal of the damaged layer. Curve c shows data taken with a more severely damaged electrode. This surface was prepared by successive polishing with Buehler 4/0 polishing paper, a 6-pm diamond paste, and 1-pm Alz03and 0.3-pm A1203 powders. Im-
-
0.01
Figure 5. Percent stabilization of n-GaAs vs. Fe"EDTA concentratlon In 0.1 M EDTA aqueous solutions: intermedlate pH range: (a) surface undamaged: (b and c) surface damaged. See text.
0.8
0.6
S 0.4
o.2
t t
0 0
0.5
I
1
10
15
I 2.0
25
maim2
Figure 6. Comparison of experlmental and calculated (solld line)!Laz billzation efficiency vs. disk current density for welktched n-GaAs (1 1 1 As) at two FeI'EDTN concentrations. The value of the parameter k,k,/k-,k,2 was 1.713and 1.40 for 0.02 and 0.04 M, respectiiely. See text.
portantly, the sample was not etched before measurement. The results show that lower stabilization was obtained at all concentrations and that the highest FeIIEDTA concentration was needed to reach values close to 100%. These results demonstrate that damaging single crystal surfaces leads to changes in the competition between oxidation of the redox component in solution and the crystal lattice. We have studied the stabilization efficiency w. the Gaks photocurrent, j,, for several Fe"EDTA concentrations at pH 8, as shown in Figure 6. The photocurrent was varied by changing the light intensity at the GaAs surface. At high Fe"EDTA concentration (0.1 M), the stabilization efficiency is unit:y for all light intensities studied. This follows from the data in Figure 3. However, for low Fe'IEDTA concentrations as shown in Figure 6, we found that S seemed to approach unity in the limit of low j,. These data could be fit to a theoretical expression for the variation of S with j , to be discussed later.
3178
The Journal
of Physical
Chemistry, Vol. 84, No. 24, 1980 1.o
t
0.8
Frese et ai. l
1 0.8
0.1 0.2 0.3 0.4 H2Q Molarity
l
1
1
1
1
1
1
0.5
1
l
l
1
HQ-
0.4
t
0.6
1
I/
7 0.6
0
0
1
.0:2
S 0.4
I
l l I 0.7 0.6 0.5 0.4 0.3 0.2 0.1
0
I
I
0
I I -0.1 -0.2
I
-03
I I - 0 4 -0.5 -06
Eo (SCE)
0.2
0
I
I
I
I
I
05
10
15
20
25
jP
Flgure 8. Plot of stabiiizatlon efficiency for well-etched n-GaAs (17 7 As) vs. standard redox potential. Reducing agents concentration, 0.04 M. pH 8.0. E,, = +0.10 V SCE from capacitance measurements.
mA/cm2
Figure 7. Stabilization efficiency for well-etched n-GaAs ( 7iiAs) vs. concentration (insert) and disk current for various concentrations of hydroqulnone, 0.1 M KCI, pH 8.8.
Other reducing agents have been studied for n-GaAs. Figure 7 (insert) shows our results for stabilization efficiency for undamaged n-GaAs vs. concentration of hydroquinone (H2Q). Hydroquinone is a weak dibasic acid (p-dihydoxybenzene) with pK, values of 9.76 and 11.4. The prodominant deprotonated species at pH 8.8 is the single deprotonated form, HQ-. This species appears to be a somewhat weaker reducing agent than FenEDTA, but strong enough to give reasonable stabilization efficiency. The remainder of Figure 7 shows the effect of j , on the stabilization efficiency for various hydroquinone concentrations at pH 8.8. The shape of these curves is qualitatively similar to those for Fe"EDTA, especially for the higher j , values in Figure 6. At a concentration of 0.05 M hydroquinone (HQ0.006 M), we observed what seemed to be a maximum in the S vs. j, plot (not shown). However, this maximum has not been satisfactorily reproducible to merit further discussion. We should note that such maxima have been observed in a study of n-ZnO corrosion using bromide ion as the reducing agent.14 Figure 8 shows the stabilization efficiency for n-GaAs vs. standard redox potential (SCE) at 0.04 M concentration. For I- and Fe(CN)$-, those data were interpolated from S values at higher concentrations. The curve shows that, as Eo becomes more negative, the stabilization efficiency increases. I t is usually assumed that, when the energy level of the reducing agent associated with Eo reaches the neighborhood of the valence band, reasonable stabilization will be found. This conclusion seems verified since we found from capacitance measurements that E V B was at --0.1 V (SCE). General Kinetic Model. A reaction scheme may be formulated for the corrosion7J6of a semiconductor such as GaAs, based on the assumption that corrosion occurs by stepwise breaking of chemical bonds between surface atoms of the semiconductor and the underlying crystal lattice. The breaking of one such bond is assumed to be the rate-limiting step. In covalent semiconductors such as 111-V and group IV materials, these bonds are mainly localized between pairs of atoms. In an ionic semiconductor, however, the surface atoms are bound by long-
-
range Coulombic interactions. It is assumed that the kinetics of corrosion is describable by focusing on the stepwise breaking of a single electron pair bond. For example, in the crystal AB we write eq 1 and 2 for the first bond to be broken, where k is a rate k
>AB< >A.B
A-B< >A+B
However, it is clear that the ligands as surface groups will affect the surface energy levels associated with the back-bonds. This effect will occur when the ligands are attached to A and B before the bonding electrons are removed and will depend on whether this surface group is ionized or not. In step 1 a hole is captured a t the surface and causes creation of the radical-like species A.B. This resulting one-electron bond is considerably weaker than the original two-electron bond. Consequently the donor level associated with this one-electron bond will be in the bandgap region. Methods for estimating the position of the donor and acceptor levels associated with the one-electron bond are currently under study. Considerable progress has been made for clean surfaces by using a method based on the bond energy models of Sandersons and Weinberg et al. (BEBO).16 When a reducing agent is introduced into the system, it may directly capture valence band holes or provide electrons that may restore the broken bond A.B. The holes in the valence bond are annihilated, or the partially broken bond in A.B is restored to its original state, A:B. If the reducing agent can react with most of the impinging holes,
Photoelectrochemical Corrosion of
The Journal of Physical Chemistry, Vol. 84, No. 24, 1980 3177
Semiconductors
the corrosion can be suppressed. Therefore, we must consider two possible parallel steps in which holes are consumed by the reducing agent in solution. These steps may be written
+ h+ -% Ox+ R i t A-B OX++ A:B R
(34
k4
(3b)
4
or if we assume that reaction 3a dominates j 3 = k3(R)(h+)
(4)
where R and Oxt s,tand for reduced and oxidized forms of a redox couple and k3 is a heterogeneous electrontransfer rate constant. According to Marcus17
k3 = ,pZe-AG*/kT (5) where K and p are assumed to be about unity, 2 is a velocity term (- lo4 cm/s), atnd AG* is the free energy of activation. This term includes the energy-level correlation between the hole and the reducing agent level. We now seek to find a relationship between the total hole current, j,, and the current due to the electron transfer from the reducing (agent,j,. The rate of change of formation and reaction of the surface radical A-B is given by
We now mak:e the steady-state approximation on (AaB). Then (A-B) = kl(h+)/[k-,
+ k2(hf)]
(7)
The rate of step 2 is
The rate of corrosion, which is assumed to be equal to the rate of step 2, is j2 = klk~(h+)~/[k-1 + kAh+)l
(9)
The net hole current j , when eq 3a applies is given by j , = k3(h+)(Cd+ klk2(h+)'/ tk-, + k2(h+)l (10)
We would like to find the quantity S, the stabilization of efficiency, defined by S =jdj, (11) We solve eq 10 for (h+) and insert this result into eq 4. Two limiting cases will be considered. If k2(h+)
