J. Phys. Chem. 1992, 96, 1310-1317
1310
Comparabillty of Redox Reactions at n- and p-Type Semlconductor Electrodes. 1. The Quasi-Fermi Level Concept R. Reineke and R. Memming' Inrtitut fur Solarenergieforschung, Sokelantstrasse 5, W-3OOOHannover 1, Germany (Received: March 6, 1991; In Final Form: September 18, 1991)
In the present paper, a quasi-Fermi level concept is derived which makes it possible to compare reactions at n- and p-type semiconductor electrodes quantitatively. Considering only valence band processes, the model implies that the same reactions with identical rates occur if the quasi-Fermi levels of the holes are equal at the surface of an n- and p-type electrodes. This model has been proved quantitatively by studying the anodic decomposition of GaAs and the oxidation of a few redox systems (Cu+;Fe2+)at n- and ptype GaAs electrodes. It is shown that the quasi-Fermi levels of majority and minority carriers can be determined experimentally. The advantages and possible applications of the model and the conditions under which it is valid are discussed in detail.
1. Introduction With respect to the development of photoelectrochemical solar cells, it is necessary to obtain sufficient insight into reaction mechanisms at the semiconductor electrode and into recombination processes. In these cells, minority camers are produced by light excitation, leading to a corresponding photocurrent. Since the latter is primarily determined by the light intensity, it is difficult to obtain reliable information on the kinetics of the charge-transfer process, especially if not only redox reactions are involved but also anodic photodecomposition. On the basis of fundamental theories on charge-transfer reactions at electrodes developed by Marcus' and Gerischer,2 various kinetic models have been derived concerning the competition between redox processes and anodic decomposition reactions at the semiconductor/electrolyteinterface.3-' The latter models were introduced in order to explain the light intensity dependence of the stabilization of photoanodes in the presence of a redox system, an experimental result frequently found by various authors. All these kinetic models have in common that they contain a large number of free parameters (e.g. rate constants), most of which are not accessible experimentally. In addition, a possible shift of the flatband potential due to a change of the Helmholtz double layer or to the formation of an insoluble film was also not considered. This aspect has been discussed only in a few publication^.'^-'^ ~
~~~
(1) Marcus, R. A. Annu. Rev. Phys. Chem. 1964, 15, 155. Marcus, R. A. J. Chem. Phys. 1965,43,679. (2) Gerischer, H. 2.Phys. Chem. (Munich) 1961, 27, 48. (3) Frese, K. W., Jr.; Madou, M. J.; Momson, S . R. J. Phys. Chem. 1980, 84, 3172. (4) Cardon, F.; Gomes, W. P.; Vanden Kerchove, F.; Vanmaekelbergh, D.; van Overmeire, F. Faraday Discuss. Chem. Soc. 1980, 70, 153. (5) Frese, K. W., Jr.; Madou, M. J.; Morrison, S.R. J. Electrochem. Soc. 1981, 128, 1527.
(6) Vanmaekelbergh,D.; Gomes, W. P.; Cardon, F. J. Electrochem. Soc. 1982, 129, 546. (7) Vanmaekelbergh, D.; Gomes, W. P.; Cardon, F. J. Chem. Soc., Faraday Trans. I 1983, 79, 1391. (8) Vanmaekelbergh, D.; Gomes, W. P.; Cardon, F. Ber. Bunsen-Ges. Phys. Chem. 1985,89,987. (9) Memming, R. In Photoelectrochemistry, Photocatalysis and Photo-
reactors; Schiavello, M., Ed.; D. Reidel Publishing Co.: Dordrecht, The Netherlands, 1985; p 107. (10) Lingier, S.;Vanmaekelbergh, D.; Gomes, W. P. J . Electroanal. Chem.
Interfacial Electrochem. 1987, 228, 77. (11) Memming, R. Top. Curr. Chem. 1988, 143, 81. (12) Lu Shou Yun;Vanmaekelbergh,D.; Gomes, W. P. Ber. Bunsen-Ges. Phys. Chem. 1987,91, 390. (13) Vanmaekelbergh, D.; Lu Shou Yun; Gomes, W. P. J. Electroanal. Chem. Interfacial Electrochem. 1987, 221, 187. (14) Allongue, P.; Cachet, H. J. Electrochem. Soc. 1984, 131, 2861. (15) Allongue, P.; Cachet, H.; Clechet, P.; Froment, M.; Martin, J. R.; Vernev. E. J. Electrochem. SOC.1987. 134, 620. (lB)'Allongue, P.; Cachet, H. Electrochim. Acta 1988, 33, 79.
Fewer problems arise for majority carrier processes at semiconductor electrodes because the potential dependence of the interfacial current gives further information concerning the kinetics. The question arises, however, whether reactions at n- and ptype electrodesare quantitatively comparable. Vanmaekelbergh et al$J2J3 have investigated this problem with respect to the competition between the oxidation of Fe2+and [Fe(CN),le and anodic decomposition at Gap and concluded that the same reaction mechanism occurs at n- and ptype electrodes. In the present paper, we derive a quasi-Fermi level concept, which will be the basis for a quantitative analysis. 2. Theory and Basic Concept Quasi-Fermi levels have frequently been used in the theory of nonequilibrium processes in semiconductors and corresponding solid-statejunctions (see e.g. ref 25). They have also been applied in the description of minority carrier reactions at semiconductor-liquid junctions," however only qualitatively. With use of the usual definition of a quasi-Fermi level, a concept for a quantitative analysis of reactions at n- and p-type electrodes can be derived as follows:2')-22 A variation of the doping level of up to 1016-10'8cm-3 in a crystal lattice containing about atoms/cm3 influences the electronic properties of a semiconductor but certainly not its physical and chemical properties. Accordingly, it is reasonable to assume that the positions of the conduction and valence band edges are identical for an n- and a p-type electrode; i.e. it is independent of doping. It is the aim of the present paper to introduce a concept which makes it possible to compare dark reactions at ptype electrodes and photoreactions at n-type electrcdes or vice versa. We restrict our consideration to valence band reactions. If the densities of holes p8-or equivalently the quasi-Fermi level E",,,-are equal at the surface of a n- and pdopcd semiconductor, then the same reaction with identical rates (Le. equal currents) takes place at both electrodes (Figure 1). Since holes are majority carriers in a ptype semiconductor,the position of the quasi-Fermi level EaF, is identical to the electrode potential (see right side of Figure 15 and therefore directly measurable. The surface hole (17) Gerischer, H. J. Electroanal. Chem. Interfacial Electrochem. 1977, 82, 133. (18) Reineke, R.; Memming, R. J. Phys. Chem., following paper in this
issue.
(19) Albcry, W. J.; Hitchman, M. L. Ring-disc Electrodes; Clarendon Press: Oxford, U.K., 1971. (20) Reineke, R. Ph.D. Thesis, University of Hamburg, FRG, 1988. (21) Reineke, R.; Memming, R. In PhotaconuersionProcesses for Energy and Chemicals; Hall, D. O., Grassi, G., as. Energy ; from Biomass, Vol. 5 ; Elsevier Science Publishers LTD: Easex. U.K.. 1989: D 129. (22) Reineke, R.; Memming, R. Extended Abstracts Meeting of the Electrochemistry Society, Los Angel-, May 7-12, 1989; p 534.
0022-3654/92/2096-1310$03.00/00 1992 American Chemical Society
The Journal of Physical Chemistry, Vol. 96, No. 3, 1992 1311
Redox Reactions at Semiconductor Electrodes. 1
Equation 1 can also be used to estimate the influence of a thin tunnel oxide or a thick noncapacitive interfacial layer on the electrode surface. In eq 1, when CHis replaced by the capacity of a tunnel oxide (Cox= eto/d,,,), an upper limit of the oxide thickness is given by I
(3) (Ox red
OX) red
the same rate of reat tion
n-type illuminated
P - tY Pe i n the dark
Figure 1. The principle of the comparability of n- and ptype electrodes. The same reactions with the same reaction rate (Le. also equal current density) occur at n- and p-type electrodes if the quasi-Fermi levels of holes, EF,pof both electrodes have equal positions at the interface.
density p , can be easily calculated, provided that the positions of the energy bands at the surface are known. The measurement of a current-potential curve also yields automatically the relationship between current and the quasi-Fermi level of holes. The basic concept implies that the position of the quasi-Fermi level GF,pat the surface of an n-type semiconductor and the corresponding hole density pacan be derived for a given photocurrent, since the same relationship between current and the quasi-Fermi level of holes holds. This model, however, is only applicable if three essential conditions are fulfilled: (i) At equilibrium, the conduction and valence band edges at the surface of the n- and ptype semiconductor have the same position. Thii requires that the oppositely charged space charges in the n- and ptype semiconductor QscBand do not influence significantly the potential drop across the Helmholtz double layer or the diffuse Gouy-Chapman layer. (ii) All reactions taking place at the electrode can be described as a function of the surface hole density pa. (ii) The holes at the surface of the ptype electrode are nearly in equilibrium with those in the bulk. Accordingly, the Fermi level of the majority carriers (holes) is constant within the electrode. Before illustrating the consequences of the basic concept, the meaning of conditions i-iii has to be analyzed in more detail. Criteria for Condition i. According to condition i, the relative position of energy states on both sides of the interface remains constant. This is necessary for kinetically controlled reactions at both types of electrodes. Since besides a potential drop across the space charge layer (&) also a potential occurs across the Helmholtz double layer ( t # ~ ~ ) condition , i can only be fulfilled if remains nearly constant within kT/e. This requires that Qw- Q=,P -< -kT CH e
with A =
(1)
in which C, is the capacity of the Helmholtz double layer and are the space charges of the n- and ptype electrodes, respectively. The latter are given byz3
,Q and
aP
Qsc,, = + ( 2 e ~ c & ~ & ) ' / ~
Using for instance values of c = 11.3 and tox= 3.4 being typical for Si and SO2, respectively, a doping density of N = 10'' ~ m - ~ , and t#~? = 1 V, one obtains 6, I 0.4 nm as a maximum to fulfill condition i. Even thicker noncapacitive films may be included, provided that the charges compensating the space charge in the semiconductor are located close to the interface and that the thickness of the correspondinglycharged layer is smaller than that given by eq 3. Certainly, the position of energy bands may be changed upon film formation, but it will be equal for n- and ptype electrodes. Criteria for Condition ii. This condition certainly excludes any charge transfer via the conduction band at the interface. On the other hand, not only a direct hole transfer via the valence band is allowed but a transfer via surface states or any other intermediates. Moreover, a current-induced change in the composition of a Helmholtz layer or the formation of an insoluble surface layer is permitted, because these effects will occur at the n- and pdoped electrodes in the same way. Also mass transport limitations in the electrolyte and purely chemical (currentless) reactions can be included. Even relaxation effects are allowed. According to our model, however, the same current time history is required for comparing n- and p-type electrodes. The latter condition is restricted only by the time interval for charging the different space charge layers of n- and ptype electrodes, which should be on the order of 50 ns, assuming e.g. 10 nF as a space charge capacity and 5 D cm2as a series resistance. According to condition ii, any tunnel processes through the space charge layer have to be avoided, because the band bending is different for n- and pelectrodes. As a consequence of excluding conduction band processes at the interface, current doubling effects and recombination at the interface cannot be considered here. Recombination processes via corrosion products and chemical short circuits via the electrolyte will be discussed ~ e p a r a t e l y . Recombination ~~ processes in the bulk or within the space charge layer of the semiconductor are permitted by condition ii and will be discussed in part 2.'* Criteria for Condition iii. The anodic current at a ptype electrode due to hole transfer via the valence band is usually controlled by the kinetics at the interface or the diffusion of ions. In the case of a very fast kinetics, the current is controlled by the transport of holes toward the surface, Le. by the thermionic emission model.2s The current is then given by
(2a)
Qr,p = - ( 2 e r ~ f l ~ @ ~ ) ~ / ~ (2b) in which t is the dielectric constant, the permitivity in vacuum, and ND and NA the donor and acceptor density, respectively. Assuming a Helmholtz capacity in the order of 10-20 pF cm-2, eq 1 is usually fulfilled for doping densities of NDand NA < lo'* ~m-~. (23) Memming, R. In Electroanalytical Chemistry; Bard, A. J., Ed.; Marcel Dekker, Inc.: New York and Basel, 1979; Vol. 11, pp 1-83.
4remekz
-- 120 A cm-2 K-z
h3 Condition iii is fulfilled, i.e. the quasi-Fermi level of holes in a ptype electrode is constant, if the interfacial anodic current is smaller than that given by eq 4. This is illustrated by a current-potential dependence as obtained with pGaAs in Figure 2. The dashed curve (anodic current) is calculated by using eq 4. Since the experimental current values (solid curves a and b) were much lower than those predicted by the thermionic emission model, condition iii is satisfied. The question arises, what happens to the quasi-Fermi level of the majority carriers if a large number of majority carriers are injected into the semiconductor? Again with use of a ptype electrode as an example, hole injection into the valence band leads to a corresponding cathodic current, as il(24) Reineke, R. Manuscript in preparation. (25) Sze, S.M. Physics ofSemiconducror Deuices; John Wilcy & Sons:
New York, 1981.
Reineke and Memming
1312 The Journal of Physical Chemistry, Vol. 96, No. 3, 1992
Figure 2. Typical current-potential curves in the dark at pGaAs in the presence of different redox systems: (a) pure anodic dccomposition; (b) oxidation of the reduced species of a redox system; (c) reduction of an oxidized species via the valence band. Dashed curves show the upper limit as determined by the thermionic emission model (see text). U, is the flatband potential of p-GaAs in acid solution and -E,/e the corresponding position of the upper valence band edge assuming a doping level of 10'' ~ m - ~ .
lustrated by curve c in Figure 2. This current can be either diffusion or kinetically limited. Varying the electrode potential toward cathodic values, the band bending is increased, which may lead to problems concerning the rate at which holes at the surface equilibrate with those in the bulk. If an equilibrium is not achieved, the quasi-Fermi level of the majority carriers will not be constant any more. The mirror image of the current-potential curve determined by the thermionic emission model (see cathodic dashed curve) can be taken as a limit; accordingly, in the potential range being anodic from this limit, equilibrium of holes can be assumed (solid part of curve c). Accordingly, condition iii holds if the absolute value of the electrode current is lower than the thermionic emission current. Finally it should be mentioned that condition ii does not follow from the validity of condition iii, because an anodic current (such as e.g. curve b in Figure 2) being smaller than that given by the thermionic emission model cannot be taken as sufficient proof for a valence band process. In principle, such a current could also be due to an injection of minority carriers into the conduction band. Accordingly, condition ii must be verified separately. Sigdcnnce of tbe M d The advantage of the model is 2-fold: The quasi-Fermi level of the majority carriers (holes in p-type) is identical to the electrode potential. Anodic and cathodic currents vary with the electrode potential and therefore with the majority quasi-Fermi level depending on the type of reaction. Accordingly, the relationship between hole current and the quasi-Fermi level of holes can be determined by measuring the current-potential curve at a p-type electrode. Since the same relationship should hold for processes at the n-type electrode, the position of the quasi-Fermi level of holes (minority carriers) at the surface can directly be related to the hole current measured at this electrode. Since processes occurring at n- and p-type electrodes are comparable, it is further advantageous to study majority carrier currents which vary with potential. Corresponding current-potential curves give more detailed information than photocurrents which are potential independent and vary only with light intensity. We tested the model with GaAs-electrodes using Cu+/Cuz+ as a redox couple in HCl solutions. This redox system is rather favorable, because no side reactions,such as ftlm formation, occur.
respectively. The crystals were purchased from MCP Electronics, U.K.Ohmic contacts were made by alloying indium at 380 OC in a hydrogen atmosphere for 10 min. The ohmic contacts were checked by resistance measurements. The semiconductor disks prepared by ultrasonic cutting were mounted in a rotating ring disk assembly (RRDE) by using an epoxy glue. These electrodes were polished by using 0.5-pm diamond powder and then etched in freshly prepared hot solutions of HzSO4 (98%), HzOZ(30%), and HzO (2:l:l) for about 10 s. In order to avoid any contaminations of the GaAs surface by the glue, the electrodes (RRDEs) were rotated during etching (100 rpm). The GaAs disk, the Pt ring, the Pt counter electrodes, and the reference electrode were controlled by a Tacussel potentiostat. The potentials and energy levels are given with respect to a saturated calomel electrode (SCE) without a correction of the diffusion potential occurring between the acid electrolyte and the SCE. The electrodes were illuminated by using a 100-Whalogen lamp. The collection efficiency N of the rotating ring disk electrode was calculated according to the methods of Albery and H i t ~ h m a n . 'It~ was verified experimentally by investigating the reduction of Fe3+in 1 M HzS04 at n-GaAs (after anodic prepolarization to avoid hole injection by Fe3+) and the oxidation of Eu2+at pGaAs (pure valence band reaction). The collection factor was N = 0.2-0.25. All chemicals were of Pro-analysis grade. Before each stabilization measurement with F$+ and Cu', the oxidized species was removed from the electrolyte by electrolyzing the solution in a separate two-compartment cell by using large Pt electrodes. 4. Results
Many semiconductor electrodes undergo anodic decomposition, p-type electrodes in the dark and n-type electrodes under illumination. The corresponding anodic currents depend on the hole density at the surface. In the presence of a redox couple in the solution, the holes created by light excitation may be preferably transferred to the reduced species of the redox system, so that the corrosion rate may be low. In the case of light-induced reactions at n-type semiconductor electrodes, the anodic photocurrent is determined by the light intensity and the quantum yield of the photocurrent is frequently unity if the penetration depth of the light is sufficiently small. It cannot be concluded from the photocurrent values whether one of the two p r m s e s , redox reaction or anodic decomposition, dominates. One way of distinguishing between the two processes is the use of a rotating Pt ring/semiconductor disk electrodes assembly (RRDE), a technique applied by many research groups. At the semiconductor disk, the total current j, and the current due to the oxidation of the redox system j,, derived from the Pt ring current, can be determined. The stabilization factor is given by
s = io, -
(5)
= iox + j,
(6)
hot
with
where icon is the partial current of anodic decomposition. Corresponding measurements have been performed with nGaAs electrodes in 6 M HCl, using Cu+/Cu2+(V' = +0.34 V vs SCE) as a redox couple. A stabilization factor of S 0.74 has been obtained at a Cu+ concentration of 1.1 X IO-' M. AS shown in Figure 3, S is independent of the photocurrent and therefore of light intensity over several orders of magnitude in intensity. The decrease in S at high light intensity is due to diffusion limitation in the electrolyte. In this case, S depends, of course, on the rotation speed w. Interestingly, however, S rises also with increasing w in the range where S is independent of light intensity, as shown in Figure 4. The stability factor is also a function of the Cu+ concentration, as shown in Figure 5 . It reaches unity (S 1) asymptotically. 3. Experimental Section Similar investigations have been performed with p-type GaAs electrodes. In this case, the total current can be increased by The experiments were performedwith n- and ptrpe [lo01 GaAs and N A = lo'* ~ m - ~ , varying the electrode potential as shown in Figure 6. It is inwith a doping of N D = 3 X 10l6
-
The Journal of Physical Chemistry, Vol. 96, No. 3, 1992 1313
Redox Reactions at Semiconductor Electrodes. 1 S 1
Figure 3. Stabilization factor S vs photocurrent j p hof a rotating n-GaAs electrode in 6 M HC1 and 1.1 mM CuCl at U, = 0.35 V (SCE) and a rotation velocity of lo00 rpm. J& indicates the diffusion limited current of the Cu+ oxidation Ci,,). The Pt ring potential is +0.05 V (SCE). -u
a/
0.2
0.3
0.4
0.5 IVISCEII
Figure 6. Current-potential curves at a rotating pGaAs electrode (6 M HC1, 2.47 mM CuCI, 1000 rpm). j - is the current of anodic decomposition, joxthe partial current of the Cut-oxidation, and jtn the total current.
OCl/
oy: 0 5
20
50
5
500
1000
-I$[
jM
15 ~.W[S-HI
10
S 1.01
0.5t 1.01.01
c
I . best f i t with
S --1-s
5
200
Figure 7. Stabilization factor S vs the total current j,, at pGaAs. The current data were taken from Figure 6. J&, indicates the diffusion-limited current of the Cu+ oxidation Go,).
Figure 4. Photostabilization vs rotation speed for an n-GaAs electrode plotted as S/(1 - S) vs u1/2for a low photocurrent density (6 M HCl, 0.5 mM Cult, jph = 30 PA cm-2). The arrow at wn indicates the low limit of w where the diffusion limited current of the Cu+ oxidation agrees with the photocurrent. a and b are theoretical lines.
01 0
100
10
15
/
J
Y
-
CCU.
-
20 Ccu+ Immollll
Figure 5. Stabilization factor S vs Cu+ concentration with an n-GaAs electrode in 6 M HCl. It was measured in the photocurrent range where S is constant (see Figure 1). Rotation velocity is 1000 rpm. The solid line represents the theoretical curve.
teresting to note here that all currents increase by about 60 mV/decade, as expected for a reaction controlled by a onecharge-transfer step. At potentials anodic from 0.3 V, the slope of the log jox-UEcurve decreases, because the oxidation of the redox system becoma diffusion limited. The oxidation of the redox system and correspondinglyalso of S depend on the rotation speed of the electrode even at lower current densities, a result indicating that this reaction is at least partially diffusion controlled (see also part 218). On the other hand, the anodic decomposition process is kinetically controlled, and its rate is proportional to the hole density at the surface. The stability factor for the p-type GaAs electrode can be determined directly from the partialcurrents given in F i i 6 and is plotted versus the total current in Figure 7. Due to the equal slopes of currents in Figure 6, S is independent of j,,,, up to 300 PA cm-2 and decreases at higher currents because
0
CC"+
0
5 [mmollll Figure 8. Stabilization factor S vs the Cu+ concentration at pGaAs (6 M HCl, 1000 rpm) determined in the range of current independent stabilization (low current densities). The solid line represents the theoretical curve.
of the diffusion limitation. The stability factor also depends on the Cu+ concentration, similarly as that found with n-GaAs (Figure 8). In addition, the corrosion of GaAs was studied in the presence of the Cu2+/Cu+ redox system in the dark. Curve a in Figure 9 shows the potential dependence of the pure corrosion current for a ptype GaAs electrode. Upon addition of the oxidized species of the redox couple (Cu2+)to the electrolyte, an additional cathodic current is found (curve b), corresponding to hole injection into the valence band. The total current, presented by the dotted curve = 0) at the mixed potential UM.1 3: 0.34 V, at which c, is zero the two partial currents compensate to zero. After addition of Cu+ (reducing agent), the anodic current occurs already at less anodic potentials (curve d), and the corrosion partial current is much smaller at = 0 (UMJ= 0.27 V). The same experiments have been performed with n-GaAs. Compared to pGaAs, the cathodic current (reduction of Cu2+) occurs at more cathodic potentials (Figure loa), whereas in the anodic range the total
o,,,
1314 The Journal of Physical Chemistry, Vol. 96, No. 3, 1992
Reineke and Memming
[mA/cmZ]
j
i tmucm21
'gorr
0.2
-0.6
1
t I
1
uY,1
0.1
jcorr
"M,2
Figure 9. Current-potential curves for a rotating (1000 rpm) p-GaAs electrode in 6 M HCl: (a) anodic decomposition current; (b) partial current of Cu2+reduction (0.7 mM); (c) total current (dotted line); (d) total current (dotted line) upon further addition of Cut ions (50 mM).
I'""
TABLE I: Values of the Flatband Potential (V,) at n-CaAs in 6 M HCl at Various Cu*+ and Cut Concentrations (lo00 rpm) [Cu2+1,mmol/L [Cut], mmol/L U,. V (SCE) 0 0 -0.98 0.936 0 -0.87 0.933 1.54 -0.89 0.831 54.8 -1.01
current is nearly zero. The latter current is composed, however, of two partial currents, anodic decomposition and reduction of Cu2+,as determined by RRDE measurements (seedashed curves in Figure loa). Upon addition of Cu+, these partial currents are decreased considerably (Figure lob). In addition, capacity measurements have been performed. The data were taken in the potential range where the interfacial currents are small or at least potential independent. The flatband potentials U,, as measured with n-GaAs under various conditions, are collected in Table I.m According to these results, the flatband potential was found at U, = -0.98 V in solutions free from any redox system. Since the Fermi level is located by 69 mV below the conduction band, the latter occurs at E, = -1.05 V, and the valence band at E, = +0.35 V. The same energy positions have been obtained with pGaAs. Upon addition of Cu2+ions, an anodic shift of the flatband potential at n-GaAs occurs, due to injection of minority camers, as we have reported earlier for other oxidizing agents.26 The same shift occurs upon an effect which was interpreted by trapping of minority carriers in surface states.27 This anodic shift disappears in the presence of Cu+ (Table I), because Cut is an efficient hole scavanger. 5. Mscussioa
The model presented in section 2 can be proved by measurements of the stability factor and by corrosion experiments as follows: Acmrdiig to the current-potential curve measured at a pGaAs electrode, the corrosion current increases exponentially with the electrode potential (Figure 6). Since the slope of this curve is about 60 mV/decade, a one hole transfer is the rate determining step, and the current is entirely determined by the surface hole density.
(26) Schrader, K.; Memming, R. Ber. Bunsen-Ges. Phys. Chem. 1985,89, 385.
(27) Kelly, J. J.; Memming, R. J. Electrochem. SOC.1982, 129, 720.
Figure 10. Current-potential curve for a rotating (1000 rpm) n-GaAs electrode in the dark in 6 M HC1 and 0.76 mM Cu2+:(a, top) the dashed curves are the partial currents of anodic decomposition Ci,)and of Cu2+ reduction (jrd); (b, bottom) the same as in (a) after addition of 51 mM cut.
In the presence of Cu+ in the electrolyte, the total current is
increased without any change of the slope. This oxidation reaction is also a pure valence band process, which is reasonable, because the standard potential of the Cu2+/Cu+system = +0.33 V) is located very close to the valence band edge (-E,/e = +0.4 V). At higher currents, however, the oxidation of Cu+ is entirely diffusion limited, so that the current-potential curve merges into that measured without Cu+.According to eqs 5 and 6, the stability factors can be determined for the p-GaAs electrode. Since the slopes of the curves, i.e. partial currents versus potential, are equal, the stabilization is independent of the electrode potential and consequently independent of the total current (Figure 7). At current densities above 0.3 mA/cm2, the oxidation of the redox system becomes diffusion limited, and the stability factor decreases significantly (compare Figures 6 and 7). On the basis of our model, the same behavior can be predicted for the n-type photoelectrodes, Le. equal currents occur if the quasi-Fermilevels of holes are identical for n- and p-type electrodes. The experimental result given in Figure 3 confirms this prediction. A further proof for the model can be obtained from the concentration and the rotation speed dependence. As will be discussed in part 218 in more detail, the oxidation of Cu+ is a very fast process at GaAs; it is not kinetically but only diffusion controlled; i.e. it is a (practical) reversible reaction. In this case, the currentpotential behavior is given by (see eq 18 in part 2 withjclh = 0)
with the diffusion-limited current jXm =
O.~~FWJ~V-%~J%$~ (74 (F = Faraday constant, D = diffusion coefficient, v the kinematic viscmity, o the angular velocity of the rotating electrode, and c$,, the bulk concentration of the reduced species).
Redox Reactions at Semiconductor Electrodes. 1
The Journal of Physical Chemistry, Vol. 96, No. 3, 1992 1315
It is important to realize that joxdepends on w1f2 in the whole potential range, even at low current densities. In this range, eq 7 can be approximated by
Since the corrosion current increases exponentially with the electrode potential (kinetically controlled) and is further independent of the oxidation of the redox couple, one has
Using eqs 5 , 6, 8, and 9, one obtains
''
+
with
'
+ corr
+ corr
red
-'red
(b)
i.e. clIFis the Cut concentration at which S = 1/2. This relationship has been used to fit the experimental data in Figures 5 and 8. The fit is rather good, although the clI2values differ for n- and p-GaAs (cII2= 0.37 mM for n-type and 1.7 mM for ptype), This difference, however, is rather small because it corresponds to values ofjam(L&ox) = 0.23 and 1.04 mA cm-2, respectively, (see eq 1l), i.e. to a potential shift of the j m =f(PF,p) relationship by 38 mV. These experiments are very critical, because j,, should be constant during the measurements. How sensitive they really are is illustrated by the results given in Figure 4. According to eqs 10 and 11, the stability factor should depend on the rotation speed of the electrode, even for low current densities, as confiied by Figure 4. It should be mentioned here that the chargetransfer process with Cut/Cu2+ is a reversible reaction at p and n-GaAs with respect to the quasi-Fermi level of holes; i.e. the charge-transfer overpotential is negligiblels (for details see part 2). All data in Figure 4 occur in a range limited by the two lines a and b. Their different slopes can be interpreted by a variation In one case we of the corrosion current parameter jwm(@cdox). have jmm( pdOx) = 136 PA cm-2 (a), and in the other jwm(GdOx) = 185 PA (b). This difference corresponds to a shift of the jwm(PF,) relationship by 8 mV. Using two different electrodes-and this is necessary for comparing n- and p-type constant. electrodes-it is even more difficult to keep joom(~dox) The question arises, however, whether conditions i and ii are really fulfilled. Since in a practically reversible reaction (eq 7) jox(PF,p) is not sensitive to a change of the kinetic parameters, but the kinetically controlled corrosion does depend on such a change, an anodic shift of the band edges of n-GaAs compared to those of ptype (in contradiction to condition i) or a tunneling of holes through the space charge layer of pGaAs (in contradiction to condition ii) are responsible for the different cll2values for n- and ince at small corrosion currents at n-electrodes the band pGaAs. S edge shift is caused by trapping of holes in surface states or by a change of the dipole moment of a surface bond, the same shift is expected for ptype. However, this is very difficult to prove experimentally,because then capacity measurements at p-type have to be performed in a potential range where the current increases strongly with potential. In such a case, the space charge capacity can only be analyzed by impedance spectroscopy. Even then it may be doubtful whether a change of AU, = 38 mV due to a corrosion current can be determined. We think this is within the experimental error. More insight into the quasi-Fermi level concept and its application can be obtained by analysis of the corrosion processes in the dark. According to Figure 9,the cathodic current, due to reduction of Cu2+,and the anodic decomposition current are equal;
-'red
Figure 11. Position of the quasi-Fermi levels in the presence of 0.7 mM Cuz+ according to data given in Figures 9 and 10: (a) pGaAs at the potential UM,l= +0.34 V (SCE); (b) n-GaAs at the potential UE= +0.6 V (SCE); (C) UE -0.1 V (SCE). (C)
1-1.0
+ 1c o r r
*
'
red
+
'
+
corr
Ired
Figure 12. Position of the quasi-Fermi levels in the presence of 0.7 m M Cu2+and 50 m M Cu+according to data given in Figures 9 and 10: (a) pGaAs at the potential UM,z= +0.26 V (SCE); (b) n-GaAs at the potential UE = +0.6 V (SCE); (c) U, = -0.1 V (SCE).
Le. j, = 0 at an electrode potential of UE= UM,!= 0.34 V. The position of the quasi-Fermi level of the holes which is equivalent to the electrode potential at jtot= 0 is illustrated in Figure 1la. Since at the n-type electrode j m = 0 in the whole potential range of WE > -0.1 V (see Figure lo), the quasi-Fermi level of the holes (minority carriers at the surface) should be constant and pinned to UM,,= +0.34 V and the anodic and cathodic partial currents should be identical to those found with pGaAs at j,, = 0. This has exactly been found, as shown in Figures 9 and 10. The situation is illustrated in the band scheme given in Figure 11b,c for two different electrode potentials, which are arbitrarily chosen in the range wherej,, = 0, i.e. where E"F,pis independent of the electrode potential WE (UE= -EF,Je for n-type). According to the current-potential curves measured with pGaAs (Figure 9),the potential at whichj,, = 0 is shifted to UE = UM.2 = 0.26 V after addition of Cu' to the electrolyte (Figure 12a). In this case the partial current, due to anodic decomposition, is much smaller. Measurements at the n-type electrode show the same effect, and again the partial currents are identical for nand ptype electrodes. Also here the quasi-Fermi level of the holes is pinned to 0.26 V, as illustrated in Figure 12b,c. It should be mentioned here that models which assume a corrosion potential or an intermediate surface state in the middle of the gap16,28-32 are not able to predict these results because of (28) Frcse, K.W.; Madon, M. J.; Morrison, S.R.J . Electrochem. Soc. 1981, 128, 1939. (29) Memming, R. J . Electroehem. Soe. 1987,125, 117.
1316 The Journal of Physical Chemistry, Vol. 96, No. 3, 1992
Reineke and Memming I
- * I
p.
0
5
1
10
50 100
131
'Ph
Figure 13. Stabilization factor S vs photocurrent at a rotating (IO00 rpm) n-GaAs electrode in the presence of 1.5 M Fe? (a) in 1 M HCI; (b) in 1 M HSO,. Crosses represent steady-statevalues, and circles first transient values (compare also with Figure 15).
1 1
0.1
91
As l o p e 2 2 0 mVldec.
I
0.2
the following reasons: From the cathodic diffusion-limited total current (Le. diffusion-controlled hole injection into n-type), these models would predict for the range of j, = 0 the same corrosion current. In addition, one would expect that the latter current would be independent of the Cu+ concentrations. Both of these predictions would be in contradiction to the experimentalresults (Figure 10). Our results prove very convincingly the quasi-Fermi level concept, and they show that processes at n- and ptype electrodes are directly comparable, provided that conditions i-iii are fulfilled. This model makes it possible to get quantitative information on the position of the quasi-Fermi level of minority carriers (such as holes in n-type) at the surface. Several scientists prefer to analyze charge-transfer processes in terms of surface electron and hole concentrations instead of using quasi-Fermi levels. Carrier concentrations at the surface, however, are easily calculated if the band positions are known by using the equations n
0.3
IVlSCEII
--
"E
Figure 14. Current-potential curves at a rotating (loo0 rpm) p-GaAs electrode in 6 M HCl in the presence of 1.1 mM Fez+.
Iight on off
T)
= Nc "P(
- EC
EF,n
P = N" exP( F EV - EF,p
)
4 2 0 s -)
+t which are good approximations if the differences between the quasi-Fermi levels and the corresponding energy bands are greater than 3kT. Otherwise one has to use more general formulas (see e.g. Szezs). Although the use of charge densities or quasi-Fermi levels is in principle equivalent, the quasi-Fermi level has several advantages: First of all, quasi-Fermi levels can be measured as shown above, even if layer formations, changes of the Helmholtz double layer, or time-dependent reactions occur. Second, the relative position of the quasi-Fermi level, with respect to that in the electrolyte, yields the thermodynamic force which drives an electrochemical reaction. This has frequently been overlooked, and instead it has been assumed that the driving force is simply provided by holes at the upper edge of the valence band or electrons at the lower edge of the conduction band. In view of thermodynamics, this is simply the difference of an electrochemical potential (Fermi level) and an electrical potential (conduction or valence band edge). The third advantage of using quasi-Fermi levels is the possibility to apply the overpotential concept, common in metal electrochemistry, in photoelwtrochemistry as illustrated in part 2.'* Applications to Other Systems. As already mentioned in the introduction, the competition between the redox process and the anodic decomposition at n-GaAs- and n-Gap electrodes has been studied in detail using various redox couples, such as Fe2+/Fe3+, Fe(EDTA), etc.4-6,8,'0~'2 In all these cases, the stability factor S decreased with increasing intensity. Vanmaekelbergh et ala" concluded that the same reactions occur at n- and ptype electrodes. The interpretation is based on kinetic models mentioned ~~~
~~
~
~
(30)Bard, A. J.; Fan, F.-R. F.; Gioda, A. S.Faraday Discuss. Chem. Soc.
1980, 70, 19. (31) Frese, K. W.; Momson, S. R. J . Vac. Sci. Technol. 1980, 17,609. (32) Memming, K.Ber. Bunsen-Ges. Phys. Chem. 1987, 91, 353.
Figure 15. Photocurrent vs time at a rotating n-GaAs disk electrode (upper curve) and ring current (lower curve) during illumination in 1 M H$O4 and 1.5 M Fe2+(compare with Figure 13). For details see text.
above. In contradiction to our results obtained with the Cu+/Cu2+ redox couple, they observed j--& curves of a rather low slope. They showed for p-GaP that the anodic current decreased upon addition of Fez+* and explained this result by their kinetic model. Their model, however, does not really explain the rather flat Tafel slopes. Therefore we repeated some of their experiments with GaAs by using Fez+as a reducing agent. Indeed, we also found such an intensity dependence of S, as shown in Figure 13. Current-potential measurements performed with pGaAs showed, however, that the slope of the curves changes considerably if Fe2+ ions were added to the solution (Figure 14). Especially, the change of slope from 60 mV/decade for Cu+ to 220 mV/decade and for Fez+is very significant. Comparing the two curves (jOx jtJ, one can see immediately that the stability factor S decreases with increasing current, as already found with the n-type electrode. A quantitative comparison between the data given in Figures 13 and 14 is not possible here, because the corresponding measurements were performed at different concentrations. It is much more important, however, to realize that the large change in slope indicates some pecuhities in the oxidation process which cannot be derived from measurements at n-type electrodes. Since this result cannot be explained by the kinetic models mentioned above, the low slope may be caused by the formation of a thin surface layer. Indeed we found by visual inspection that a brown-reddish film was visible on the electrode surface after anodic polarization (especially in sulfate solutions), which did not occur in experiments with Cu+. We verified this result by using chopped light in experiments with n-type GaAs. The photocurrent at the disk followed completely the light pulse; i.e. it remained constant during the time interval in which the light was on (Figure
J. Phys. Chem. 1992,96, 1317-1323 15). The ring current, however, showed some transient behavior; i.e. it decreased during the exposure to a lower value. Since our model should be valid even for time-depending reactions, such as transient behavior at n-GaAs, a similar time dependence is expected for corresponding reactions at pGaAs. We verified this quantitatively,and indeed a high rate of Fez+oxidation occurred after cathodic prepolarization, which decreased within a few seconds. This result indicated that the Fe3+formed at the GaAs disk is involved in some film formation on the GaAs surface, possibly some iron arsenite or arsenate, which is only slightly soluble in H20. The latter is slightly more soluble in HCl than in H2S04,which could be the reason for the higher stabilization obtained in HCl (Figure 13). We assume that a similar surface layer is formed on Gap. According to the latter results, the application of the rather complex kinetic models for explaining the intensity dependence of the stability factor seems to be doubtful. Nevertheless, the quasi-Fermi concept derived in the present paper is also applicable for comparison of redox reactions at n- and ptype electrodes, even if a surface layer is formed, as long as equal working conditions are used for both types of electrodes. This has actually been confirmed by the data published by Vanmaekelbergh et al. There are various results given in the literature which can be interpreted on the basis of the quasi-Fermi level concept. Expecially the investigation of reactions of [Fe(CNja)l3-/' at GaAs The quasi-Fermi and the etching behavior confirm our level concept also explains results obtained with redox processes in which a multiple charge transfer is involved. Examples are (33) Sinn, Ch.; Meissner, D.;Memming, R. J. Electrochem. Soc. 1990, 137, 168. (34) Notten, P. H. L. Electrochim. Acta 1987, 32, 575. (35) Notten, P. H. L.; Kelly, J. J. J . Electrochem. Soc. 1987, 134, 444.
1317
OCl-/C12,36H202/H20?' 1-3/1-,38 and Cr6+/Cr3+39,40 at GaAs and Br2/Br- at InP!',42 The model can also be used to compare the redox reactions at p and n-WSe2.33In this case, the stability factor for instance increased with increasing light intensity at n-WSe2. An analysis of the corrosion current-potential curve at pWSe, showed that the slope of the curve was rather low (80-100 mV/decade), probably due to the formation of some W 0 3 on the surface. In the presence of a redox system, such as e.g. Fehen)^*+, an ideal slope of about 60 mV/decade for the current-potential curve has been found, which explains the intensity dependence of S. F e ( ~ h e n ) ~ ~is+a/ ~reversible + redox system at pWSe2. Therefore, the ideal slope of thejoxcurve is insensitive to layer formation and a corresponding shift of the flatband potential.
Acknowledgment. The authors are indebted to Prof. B. Kastening (University of Hamburg), Dr. D. Meissner, Ch. Sinn, J. Rimmasch, I. Lauermann, and B. Muller for many stimulating discussions. Thanks are also due to A. Meier and C. Ott for repeating various experiments. This work was sponsored by the German Federal Minister for Research and Technology (BMFT) under Grant 0328686. Registry No. Gab, 1303-00-0; H2S04,7664-93-9; Fe, 7439-89-6; Cu, 7440-50-8; HC1, 7647-01-0. (36) Notten, P. H. L. J. Electroanol. Chem. Interfacial Electrochem. 1987, 224, 211. (37) Kelly, J. J.; Reynders, A. C. Appl. Surf.Sci. 1987. 29, 149. (38) van der Meerakker, J. E. A. M. Electrochim. Acta 1985, 30, 435. (39) van der Ven, J.; van der Meerakker, J. E. A. M.; Kelly, J. J. J . Electrochem. SOC.1985. 132. 3020. (40) van der Ven, J.; Weyher, J. L.; van der Meerakker, J. E. A. M.; Kelly, J. J. J . Electrochem. Soc. 1986, 133, 799. (41) Notten, P. H. L.; Damen, A. A. J. M. Appl. Surf. Sci. 1987,28,331. (42) Notten, P. H. L. J . Electrochem. Soc. 1984, 131, 2641.
Comparability of Redox Reactions at n- and p-Type Semiconductor Electrodes. 2. Electrochemical Overpotential and Recombination in View of the Quasi-Fermi Level Concept R. Reineke and R. Memming' Institut fiir Solarenergieforschung, Sokelantstrasse 5, W-3000 Hannover 1, Germany (Received: March 7, 1991; In Final Form: July 30, 1991)
In the present paper, majority carrier processes at p-type semiconductor electrodes and corresponding reaction mechanisms redox system as an example, the corresponding have been studied using classical electrochemicalmethods. Taking the &+/a2+ current-potential curves obtained with p-type GaAs electrodes have been analyzed in detail. It is shown that the kinetics of the oxidation and reduction process are very fast, and the currents are entirely diffusion controlled. In addition, current-potential curves for an n-type electrode in the dark and under illumination have been calculated from dark current-potential curves obtained with a p-type electrode on the basis of the quasi-Fermi level concept. A comparison with experimental data has proved this procedure and consequently the model. It is further shown that, in the case of hole injection from Cu2+into the valence band of n-type GaAs, the chargetransfer rate across the interface is also fast, but the resulting current is determined by the rdmbination rate of injected holes with electrons in the conduction band.
1. Iatroduction
In part 1 we have derived a quasi-Fermi level concept which makes it possible to compare reactions at n- and ptype electrodes.' We have shown there that the same reactions with identical rates occur at the n- and ptype electrodes, if the quasi-Fermi level of the holes is equal at the surface for both types of electrodes. The model was proved quantitatively for the anodic decomposition of ( 1 ) Reineke, R.; Memming, R. J. Phys. Chem., preceding paper in this
issue.
GaAs and the oxidation of few redox systems at n- and p-GaAs electrodes. The advantage of the concept is that the position of the quasi-Fermi level can be. determined experimentally if a redox process occurs only via one energy band at n- and ptype electrodes. We have also shown that more information on the reaction kinetics can be obtained by studying majority carrier processes. In the first part of the present paper, we analyzed corresponding current-potential curves at p-type electrodes in terms of the electrochemical overpotential concept, and in the second, we analyze injection and recombination pracesses for minority carrier reactions
0022-3654/92/2096-1317S03.00/00 1992 American Chemical Society
