J . Phys. Chem. 1988, 92, 6359-6367
6359
a bound state associated with the polar head groups of the surfactant or hydrated to the sodium ions4 Fremy’s salt appears to be freer than the water molecules, perhaps due to the repulsion between the charged head groups and the negatively charged SO< groups on the nitroxide. As the water content decreases, the dimension of the water pool becomes comparable to the size of Fremy’s salt. At wo = 2 the diameter of the water pool is estimated to be 6 &I9 which is close to the molecular diameter of Fremy’s salt. The rotational correlation time of Fremy’s salt of wo = 2 is still much shorter than that of the overall micelle (1 X 10-9 s, estimated from (4)4). These facts suggest that the water pool does not necessarily have a rigid structure but may vary in shape and size. It is known that an enzyme can exist in a water pool smaller than its volume.20 The same thing could happen in the present system. The probe expands the size of the water pool and thus gains more freedom of rotation than the micelle itself experiences.
Figure 2. Plot of the rotational correlation time rR of Fremy’s salt as a function of water content wo in AOT-heptane reversed micelles.
where r is the molecular radius and q is the viscosity of the solvent. This equation shows that smaller molecules have shorter rotational correlation times in a given solvent. The correlation times presented in Table I show that Fremy’s salt experiences a less viscous environment in the water pool than does the water itself. These results are interpreted by suggesting that most of the water molecules in the small water pool are in
Acknowledgment. Continuing support of ongoing research and a grant for the purchase of the ESR spectrometer from the National Sciences and Engineering Research Council for Canada are gratefully acknowledged. Registry No. AOT, 577-1 1-7; H20, 7732-18-5; Fremy’s salt, 1429370-0; heptane, 142-82-5. (19) Elwall, P.; Mandell, L.; Fontell, K. J . Colloid Inrerfuce Sci. 1970, 33, 215. (20) Luisi, P. L.; Meier, P.; Imre, V. E.; Pande, A. Reverse Micelles; Plenum: New York, 1984; p 323.
Cyclic Voltammetry at Semiconductor Photoelectrodes. 1. Ideal Surface-Attached Redox Couples with Ideal Semiconductor Behavior Patrick G. Santangelo, Gordon M. Miskelly, and Nathan S. Lewis* Department of Chemistry, Stanford University, Stanford, California 94305 (Received: February 12, 1988)
Working curves for the cyclic voltammetric behavior of semiconductor electrodes have been generated by consideration of a model electrode circuit. The circuit consists of an ideal photodiode in series with a metal electrode. The electroactive material is considered to be an ideally behaving, surface-attached redox couple. The solution for the diode/electrode current-voltage characteristic has been solved numerically. Simulations have been performed under varying levels of illumination and for different values of the diode barrier height, the voltage scan rate, and the amount of electroactive material. Chopped scans have also been simulated, where the forward scan is in the light and the reverse scan is in the dark. Emphasis has been placed on modeling cyclic voltammetric data under common experimental conditions, in order to provide a basis for comparison with experiments in the literature.
Introduction Cyclic voltammetry has become a popular technique for probing the properties of the semiconductor/liquid interface. The cyclic voltammetric response of semiconductor electrodes has been used for accurate determinations of the semiconductor flat-band potential,’ for measurement of photoelectrode barrier heights and open circuit and for identification of surface state densities and energies. Cylic voltammetry has also been used to yield information regarding Fermi-level pinning at semiconductorlliquid junctions8 and to identify cases in which semiconductors act as ideally polarizable electrode^.^^*^' Additionally, cyclic voltammetry has been used to identifygJOand to determine the kinetics” of mediated charge transfer processes at surface-modified *Address correspondence to this author at California Institute of Technology, 127-72, Pasadena, CA 91125.
0022-3654/88/2092-6359$01 SO10
semiconductor electrodes. Despite this widespread usage, no quantitative analytical solution or digital simulation has been (1) (a) Schneemeyer, L. F.; Wrighton, M. S. J.Am. Chem. Soc. 1979, 101, 6495. (b) Schneemeyer, L. F.; Wrighton, M. S.; Stacy, A.; Sienko, M. J. Appl. Phys. Lett. 1980, 36, 701. (2) (a) Baglio, J. A,; Calabrese, G. S.; Kamieniecki, E.; Kershaw, R.; Kubiak, C. P.; Ricco, A. J.; Wold, A.; Wrighton, M. S.; Zoski, G. D. J . Electrochem. SOC.1982, 129, 1461. (b) Kubiak, C. P.;Schneemeyer, L. F.; Wrighton, M. S. J. Am. Chem. SOC.1980, 102, 6898. (c) Calabrese, G. S.; Wrighton, M . S. J . Am. Chem. SOC.1981, 103, 6273. (d) Baglio, J. A,; Calabrese, G. S.; Harrison, D. J.; Kamieniecki, E.; Ricco, A. J.; Wrighton, M. S.; Zoski, G. D. J . Am. Chem. SOC.1983, 105,2246. (e) Simon, R. A.; Ricco, A. J.; Harrison, D. J.; Wrighton, M.S. J . Phys. Chem. 1983,87, 4446. (0 Aruchamy, A,; Wrighton, M. S. J. Phys. Chem. 1980, 84, 2848. (9) Tanaka. S.: Bruce. J. A: Wrinhton. M. S. J . Phvs. Chem. 1981.85, 3778. (h) Aruchamy, A.; Bruce, J. A.; Tanaka, S.; Wrighion, M. S. J . Elecrrochem. Soc. 1983, 130, 359.
0 1988 American Chemical Society
6360 The Journal of Physical Chemistry, Vol. 92, No. 22, 1988 presented for the cyclic voltammetric response of a semiconductor/liquid junction. This report describes our model for the general semiconductor/redox couple system under various conditions of illumination and with various values of the semiconductor/redox couple barrier height. The calculations described in this work are for the case of an ideal surface-attached redox couple on an ideal semiconductor; other common situations, including nonideal behavior and/or diffusive redox species, are somewhat different in response and will be described in separate publications. This paper reports simulated voltammetric working curves for numerous cases of experimental interest at semiconductor/surface-confined redox couple junctions and discusses previous experimental results in terms of the theoretical curves generated herein. Several common experiments that use cyclic voltammetry are of particular concern to our analysis. Of primary interest is the shape of the cyclic voltammogram at an “ideal” semiconductor electrode, and variations in this shape as a function of the light intensity, voltage scan rate, and potential limits. Also, we have investigated whether the difference in potential between a metal electrode and an illuminated semiconductor photoelectrode is a good approximation to the barrier height, the open circuit voltage, or some other system quantity. Finally, we have investigated whether the presence of cathodic current at potentials positive of the flat-band potential of an n-type semiconductor is always indicative of surface states and how the magnitude and position of this current relate to the surface-related processes. Although the present study is restricted to modeling the current-voltage characteristics for surface-attached electroactive films on semiconductor electrodes, this analysis does illustrate many of the key aspects of the general situation at semiconductor electrodes. In fact, surface-attached systems have been used in all of the representative semiconductor photoelectrode energetic and kinetic measurements and also have proven especially important in “molecular electronic” chemical sensing devices,’* in corrosion suppression at modified photoelectrode surface^,^.'^ and in mea-
(3) (a) Frank, S.N.; Bard, A. J. J . Am. Chem. SOC.1975, 97, 7427. (b) Kohl, P. A,; Bard, A. J. J . Am. Chem. SOC.1977, 99, 7531. (c) Laser, D.; Bard, A. J. J . Phys. Chem. 1976, 80, 459. (d) Kohl, P. A.; Bard, A. J. J . Electrochem. SOC.1979, 126, 59. (e) Di Quarto, F.; Bard, A. J . J . Electroanal. Chem. 1981, 127, 43. (f) Fan, F. R. F.; White, H. S.; Wheeler, B. L.; Bard, A. J. J . Am. Chem. SOC.1980, 102, 5142. (9) White, H. S.; Fan, F. R. F.; Bard, A. J. J . Electrochem. SOC.1981,128, 1045. (h) Koval, C. A.; Austermann, R. L. J . Electrochem. SOC.1985, 132, 2656. (i) Koval, C. A,; Austermann, R. L.; Turner, J. A.; Parkinson, B. A. J. Electrochem. SOC.1985, 132, 613. (4) Yeh, L.-S. R.; Hackerman, N. J . Phys. Chem. 1978, 82, 2719. (5) Singh, P.; Rajeshwar, K.; DuBow, J.; Job, R. J . Am. Chem. SOC.1980, 102, 4676. (6) Kautek, W.; Gerischer, H . Ber. Bunsen-Ges. Phys. Chem. 1980, 84, 645. (7) (a) Chazalviel, J. N.; Truong, T. B. J . Electroanal. Chem. 1980, 114, 299. (b) Byker, H.; Wood, V.; Austin, A. J . Electrochem. SOC.1982, 129, 1982. (c) Nadjo, L. J . Electroanal. Chem. 1980, 108, 29. (8) (a) Bard, A. J.; Bocarsly, A. B.; Fan, F. R. F.; Walton, E. G.; Wrighton, M. S. J . A m . Chem. SOC.1980, 102, 3671. (b) Bard, A. J.; Fan, F. R. F.; Gioda, A. S.; Nagasubramanian, G.; White, H. S. Faraday. Discuss. Chem. SOC.1980, 70, 19. (c) Bocarsly, A. B.; Walton, E. G.; Bradley, M. G.; Wrighton, M . S. J . Electroanal. Chem. 1979, 100, 283. (9) (a) Bruce, J. A,; Wrighton, M. S. J . Electrochem. SOC.1981, 122, 93. (b) Bocarsly, A. B.; Walton, E. G.; Wrighton, M. S. J. Am. Chem. SOC.1980, 102, 3390.
(10) (a) Lewis, N. S.; Wrighton, M. S. J . Phys. Chem. 1984, 88, 2009. (b) Bookbinder, D. C.; Bruce, J. A,; Dominey, R. N.; Lewis, N. S . ; Wrighton, M. S . Proc. Natl. Acad. Sci. U.S.A. 1980, 77, 6280. (c) Lewis, N. S.; Wrighton, M . S. Science (Washington, DC) 1981, 211,944. (c) Chao, S.; Robbins, J. L.; Wrighton, M. S. J . Am. Chem. SOC.1983, 105, 181. (d) Bookbinder, D. C . ; Lewis, N. S.; Wrighton, M. S. J . Am. Chem. SOC.1981, 103, 7656. (11) (a) Lewis, N. S.; Bocarsly, A. B.; Wrighton, M. S. J . Phys. Chem. 1980, 84, 2033. (b) Lewis, N. S.; Wrighton, M. S. ACS Symp. Ser. 1981, No. 146, 37. (12) (a) Thackeray, J.; Wrighton, M. S. J. Phys. Chem. 1986, 90, 6674. (b) Thackeray. J.; White, H.; Wrighton, M. S. J . Phys. Chem. 1985,89, 5133. (13) (a) Bolts, J. M.; Wrighton, M. S. J . Am. Chem. SOC.1978, 100, 5257. (b) Bolts, J. M.; Bocarsly, A. B.; Palazzotto, M. C; Walton, E. G.; Lewis, N. S.; Wrighton, M. S. J . Am. Chem. Soc. 1979, 101, 1378. (c) Wrighton, M. S.; Austin, R. G.; Bocarsly, A. B.; Bolts, J. M.; Haas, 0.; Legg, K. D.; Nadjo, L.; Palazzotto, M C. J . Am. Chem. SOC.1978, 100, 1602.
Santangelo et al. Working
Reference
Counter
Figure 1. Equivalent circuit used as a model for the semiconductor/liquid interface. V, is the voltage applied between the working electrode and the reference electrode, vd is the resulting voltage drop across the phod is the voltage appearing across the electodiode, and V, = V, - v trode/solution interface.
surement of mediated kinetic events at modified semiconductor surfaces.9-” Circuit Model. The calculations presented in this work are only relevant to “ideal” semiconductors in contact with “ideal” surface-attached electroactive species. The voltammetric model used for an “ideal” semiconductor/liquid junction consists of an “ideal” diode in series with an “ideal” metal/electrolyte interface (Figure 1). This model is justified by the equivalent circuit for a semiconductor/liquid interface presented by Gerischer, which consists of the impedances for interfacial charge transfer placed in series with impedance elements for the bulk semiconductor and for the junction space charge layer.I4 Our simplification of this equivalent circuit into a series diode and electrode resistance element should accurately reflect the behavior of the semiconductor electrode when the interfacial rates for electron transfer at the semiconductor/ liquid interface become extremely large relative to the rates of supply of carriers to the interface. The equivalent circuit approach to the system also allows for an experimental verification of the accuracy of the simulation, because the current-voltage (I-V) properties of the individual circuit elements and of their series combination can be readily evaluated with suitable electrochemical measurements. Additionally, these measurements can be compared to the response of actual semiconductor electrode surfaces to determine the relevance of the model system to actual photoelectrode interfaces. A similar approach to equivalent circuit analysis was adopted by Bruckenstein and Miller for steady-state voltammetry at rotating semiconductor e1ectrodes.l5J6 In our framework, an “ideal” diode is one whose steady-state current-voltage response is of the form The response of this “ideal” diode is assumed in our treatment to be described completely by a diode quality factor ( A ) of unity and by a reverse saturation current, I,. IL is the photogenerated (14) Gerischer, H. J . Electroanal. Chem. 1975, 58, 263. (15) Bruckenstein, S.; Rosamilia, J. M.; Miller, B. J . Phys. Chem. 1985, 89, 677. ( 1 6) Bruckenstein, S.; Miller, B. J . Electrochem. SOC.1982, Z29, 2029.
Cyclic Voltammetry at Semiconductor Photoelectrodes current. In actual systems, Io is determined by the nature of the transport at the electrical interface of the diode, and this parameter of the simulation thus reflects the barrier height and junction tranyort properties of the modeled semiconductor This treatment is quite satisfactory for well-behaved surface barrier devices under various rate-determining recombination conditions. In the semiconductor/electrolyte system, the value of Io represents the exchange current, and the diode quality factor describes the voltage dependence of the carrier concentration at the semiconductor surface (Le., the use of A = 1.0 implies that a Tafel slope of 1.O (RTIF) would be measured in the absence of concentration polarization or series resistance losses in the electrolyte).20 The steady-state I-V properties of an actual semiconductor/ electrolyte interface, measured under conditions that minimize concentration overpotentials and series resistance losses, can be used to experimentally test the validity of eq 1 in a particular system of experimental interest. Although superposition of the light and dark currents does not accurately describe the I-V properties of diodes at very low light intensity or at very high Io values, we have assumed a strict adherence to the above diode equation in order to simplify the calculations. This assumption does not affect any of the principal conclusions of this work. For the ideal electrode/redox couple, the analytical I-V expression is as follows:
The Journal of Physical Chemistry, Vof. 92, No. 22, 1988 6361 TABLE I: Values Used in Simulations system parameters total charge in film, Q = n l T 8 A , no. of electrons in reaction sweep rate
value
initial potential final potential
reverse saturation current of diode photogenerated current diode quality factor temperature peak current at metal electrode I p = n21%F,A8/4RT = nFuQJ4RT open circuit voltage VIl, = I ( k T / q ) In (M(47 + IL))l
1.00 x 10” c 1.oo 0.100 v/s Eo’ - 0.950 V Eo’ 0.250 V 1.00 X A 2.00 x 10-3 A 1.oo 25 O C 9.73 X 10” A
+
0.550 V
At was chosen so that the system voltage V, varied by 1 pV between each iteration. This yielded an equation of the form
I = (nFA,I’,/At)([l
+ exp[nF(VJt [1
- At) - EO’)/RTII-’-
+ exp[nF(V,(t)
- Eo’)/RT]]-’) (3)
The electrode voltage was obtained by equating eq 1 with eq 3 and assuming n = 1 and A = 1. The resulting quadratic equation was solved to give an expression for exp(nFVe(t)/RT) in terms of (Io IL), A,, r,, and the previous electrode voltage, Ve(t - At). The current was then determined by substituting the calculated value of V, (=V,- Ve)into eq 1. The pairs of V,(t)and I ( t ) values were then stored for analysis and V,(t) was used for the subsequent where rs is the coverage of electroactive material in moles per iteration. square centimeter and A , is the electrode area. For a surfaceThe runs in which the electrode was illuminated on the positive attached species, “ideal” in this work implies that the Nernst scan but not on the reverse scan required an additional step to equation describes the ratio of surface-attached oxidized to reduced calculate the electrode potential at the beginning of the reverse material at the electrode surface for all electrode p ~ t e n t i a l s . ~ l - ~ ~ scan. The relaxation in a series combination of a diode and This assumption was made to simplify the computations without electrode at constant applied voltage was calculated by solving reducing the generality of the treatment or affecting the coneq 4 with V,, I(initial), and r,(initial) determined by the final clusions of the simulation. Charge propagation through the RT kT surface-attached redox material, which can be assumed to be V, = Eo’ - In [ro/(rs- r,)]- - In [(lo- Z)/Io] (4) purely diffusional with a single value for the diffusion coefficient, F 4 is taken into account in a separate publication. values for the positive voltage sweep and I(t) = nFA, dI’,/dt. In When a voltage, V,, is applied to a series combination of the the present case, the system was allowed to relax for 1 ms before above two-circuit elements, the voltage that appears across the the reverse scan. It should be noted that this relaxation does not electrode/electrolyte interface, V,, will in general only be a fraction have any discernible effect if the potential across the electrode, of this voltage. The simulation therefore involves convoluting the V,, and the applied potential, V,, are greater than (EO’ + 0.2 V). I-V responses of a photodiode and an electrode to determine the These two conditions were satisfied for all the cases shown in this I-V response of our modeled photoelectrode. overall paper. Calculation Methods. Given the assumptions above and the The diode was oriented in the circuit so that photocurrent was model equivalent circuit, the analysis reduces to solving for the anodic, and the system therefore modeled an n-type semiconductor current I through the circuit as a function of the voltage applied photoanode. The key constraint for our simulations is I , = Id = to the system as a whole, V,. The series representation imposes I,; thus, to accommodate the case where the diode and electrode the constraints that V, = Vd + V, and 1, = Id = I.., where s, d, areas are not equal, we generally have used units of current instead and e refer to the system, diode, and electrode, respectively. The of current density throughout the text. However, the final results problem consists of circuit elements that have nonlinear responses displayed in the working curves (vide infra) represent ratios of to voltage, primarily because the diode element exhibits an excurrents, and thus are independent of the active area of the ponential I-V dependence. Consequently, the current-voltage electrode element. For the specific case of equal area diode and response of the system was solved numerically rather than anaelectrode elements, the discussion below can be read in units of lytically. current density instead of current, if desired. The I-Vresponse for the simulated metal electrode was obtained The calculations were performed by use of double precision directly by use of eq 2. The current for the simulated semiconVAX-11 FORTRAN on a Digital VAX 11/750 computer. ductor electrode was calculated by the following procedure. The current was approximated by I = nFAr,/At, where Ar0is the Results and Discussion change in the concentration of oxidized species on the surface and The cyclic voltammetric responses have been investigated for the model semiconductor electrode system with several different combinations of light intensity, barrier heights, etc. Table I shows (17) Sze, S. M. Physics of Semiconductor Devices, 2nd ed.; Wiley: New York, 1981. the values of experimental parameters that were chosen for our (1 8) Fonash, S . J. Solar Cell Deoice Physics; Academic: New York, 1981. initial calculations. These values are typical for modified semi(19) Fahrenbruch, A. L.; Bube, R. H. Fundamentals of Solar Cells; Acconductor electrode^."^ For all simulations, the parameters were ademic: New York, 1983. fixed at the values indicated in Table I unless stated otherwise. (20) Morrison, S. R. Electrochemistry at Semiconductor and Oxidized We note that only certain combinations of these parameters are Metal Electrodes; Plenum: New York, 1980. (21) Bard, A. J.; Faulkner, L. F. Electrochemical Methods; Wiley: New relevant to the details and conclusions of our analysis. In parYork, 1980. ticular, the quantity that represents that the peak current at a (22) Laviron, E. J . Electroanal. Chem. 1974, 52, 395; 1975, 63, 245. metal electrode, n2F2vr,A,/(4RT),provides a convenient scale (23) (a) Murray, R. W. Acc. Chem. Res. 1980, 12, 135. (b) Snell, K. D.; factor for the calculated I-V behavior of the equivalent area Keenan, A. G. Chem. Soc. Rev. 1979, 8, 259.
+
+
6362 The Journal of Physical Chemistry, Vol. 92, No. 22, 1988
Santangelo et al.
TABLE 11: Data for Cyclic Voltammetric Behavior of Model Electrode Circuit IL, A
0
metal 9.73 x 4.86 x 9.73 x 9.73 x 9.73 x 1.95 X 3.24 X 4.86 X 6.08 X 9.73 x 1.08 I .22 1.62 1.95 2.43 3.04 3.23 4.86
10-5 10-4 10-4 10-3 10-2
10-1 10-1 10-1 10-1
1.00 x 2.00 x 1.00 x 1.00 x 1.00 x 5.00 X 3.00 X 2.00 X 1.60 X 1.00 x 9.00 x 8.00 x 6.00 x 5.00 x 4.00 x 3.20 x 3.00 x 2.00 x
10-2 10-3 10-3 10-4 10-5
IOw6 10” IO” 10-7 10-7 10-7 10-7 10-7 10-7 10-7 10-7
Ip/[p
1.000 1.000 1.000 1.ooo 1.000 0.997 0.987 0.967 0.929 0.895 0.780 0.744 0.701 0.581 0.502 0.409 0.329 0.308 0.206
Ipc/Ip -1.000 - 1.000 -1.000
- 1.000 -1.000 -0.998 -0.994 -0.988 -0.979 -0.973 -0.960 -0.956 -0.952 -0.941 -0.935 -0.928 -0.920 -0.9 18 -0.905
4Ep,, v 0.000 0.508 0.550 0.532 0.473 0.409 0.385 0.364 0.343 0.330 0.292 0.282 0.269 0.229 0.197 0.148 0.087 0.066 -0.100
4EF, v 0.000 0.508 0.550 0.533 0.474 0.419 0.405 0.396 0.390 0.387 0.382 0.381 0.380 0.378 0.377 0.376 0.375 0.375 0.373
semiconductor electrode. All I-V figures in this paper therefore will utilize this scaled current on the ordinate. A. Metal Electrode with Surface-Attached Redox Species. The current-voltage characteristics of the metal electrode/surface attached redox species interface chosen for study are depicted in Figure 2 . The cyclic voltammetric response was obtained from the analytical solution for a surface-attached, Nernstian redox species (eq 2 ) . For all scan rates, this yields AE, = E, -E, values of 0 mV and full widths at half-maximum peak current (fwhm) of 91 mV at room temperature. The peak current Zpis linear with scan rate ( u ) . B. Illuminated Semiconductor Electrode. 1. General Working Curoes. At sufficiently high illumination levels, the cyclic voltammetric response of the semiconductor electrode is expected to be dominated by the charge transfer resistance and/or mass transfer resistance of the redox couple and not by the transport impedance of the semiconductor. Under these conditions, the wave shape is expected to be very similar to that at a metal electrode. Under lower light levels, a substantial fraction of the applied voltage will be dropped across the diode, implying that the wave shape will be distorted. A quantitative treatment of voltammetric waves under various conditions is presented below. The key variables for determining the wave shape and position are I,,, IL, and I,. From the qualitative discussion above, it is expected that the wave shape will not be noticeably affected by the presence of the series diode element when I , l.5), A E , provides a better approximation to V, than does AE,p (AI& always provides the worst estimate). This can be seen from Figure 3 (or Figure 4a) and from the data in Table 11. The reason for this behavior is readily seen by consideration of the voltage drop across the diode, Figure 4b. Once cathodic current starts to flow, the diode goes into the forward bias condition, and its impedance drops relative to the reverse bias impedance. This change results in a reduced dependence of the cathodic wave shape on the light level compared to that exhibited in the positive scan direction. Working curves expressing the voltage error in V, using AEllz,Up,and AE, as key parameters are given in Figure 6. It is also interesting to note that even though the open circuit voltage of the diode is proportional to In ((IL Zo)/Zo) = In (ZL/Io) (when IL>> Io), lowering the value of ILin general has a different effect on the resultant cyclic voltammograms than does increasing the value of Zo. As depicted in Figure 5, the diode V, determines the “offset” between the diode/electrode system and the metal electrode system. This is quite reasonable, because at low currents, V, is approximately equal to V,. However, for 0 > the wave shape is a function of ILand Io through the sum (IL Io). Put concisely, the wave shape at a given electrode coverage and scan rate is a function of (IL+ Io), while the wave position is a function of ULIIO). We emphasize that the constraint I, = Id = I, requires use of currents, not current densities, in the above calculations. A very complicated functional dependence is obtained when the diode and electrode areas (and therefore IL,I,,, and I p ) are varied independently, even if the current densities Jo and J L are held constant. For this reason, the cyclic voltammetry waves are most simply calculated for uniform intensity illumination across the entire photoelectrode area. Very different (and difficult to simulate) wave shapes are expected to occur under conditions where a small portion of the active electrode surface is illuminated with a non-uniform-intensity laser beam. Also, under these conditions, some areas of the electrode will have high illumination, so that AEI12approximates V,, while this condition will not hold for other areas. Deconvolution of this area-dependent measurement into readily interpretable parameters is beyond the scope of our treatment at present. 3 . Deducing V, from Cyclic Voltammetry-Changes with Scan Rate. Clearly, there will always be a high light intensity regime in which the cyclic voltammogram will provide a good direct estimate of V,. However, in practice, it is often desirable
+
+
-08
-06
-04
-02
L-EO
(1‘)
0 0
02
Figure 7. Effect of scan rate on cyclic voltammograms for a surfaceconfined redox couple on a metal electrode in series with an illuminated photodiode. The cyclic voltammogram of the electrode with no photodiode in the circuit is also shown (curve e). Curve a, u = 0.01 V/s, B = 1.95 X lo-*, curve b, u = 0.1 V/s, 8 = 1.95 X lo-’; curve c, u = 1 V/s, B = 1.95;curve d, o = 10 V/s, B = 1.95 X 10’. The values of all other parameters are given in Table I, except that 1, = 5 X 10” A.
to use the cyclic voltammetric scans to determine the Y , at a particular light intensity. Although a complete comparison of cyclic voltammetric data with the working curves in Figure 3 can always be used to obtain V,, it is often simpler to extract the desired value directly from the cyclic voltammetric data. This can be done when the wave shape is independent of 0, i.e., when 0< At a fixed IL,this condition can be attained experimentally by reducing Ip,Le., by reducing the scan rate. Figure 7 depicts the cyclic voltammograms as a function of scan rate for A). It is the diode/electrode system of Figure 4 (IL= 5 X seen that there will always be a sufficiently small scan rate such and that the wave shape will be independent of that 0 < further reductions in scan rate. When these conditions are attained, (or AE,) will provide an acceptable measure of V,. 4 . Deducing V, from Cyclic Voltammetry-Arbitrary Experimental Conditions. A full comparison of the cyclic voltammetric data with the working curves in Figure 3 allows extraction of V, for an ideally behaving system under any experimental the I-Vcurves also contain conditions. In addition, when 8 > information regarding the absolute values of I,, and I,. The recommended procedure to obtain values of these quantities is as follows. I p can be determined either directly from a metal electrode scan or indirectly from an integration of the total faradaic charge on the semiconductor electrode. Knowledge of rsand L‘ then allows calculation of Ip,by use of eq 2. Comparison of the cyclic voltammetric data to the working curves of Figure 3 then yields a value for 0, which allows determination of ( I o IL). Comparison of the data to the working curves also yields V,, which allows calculation of the ratio IL/Io. Combination of the latter two pieces of information provides a solution for the independent values of I , and Io. This procedure only can be performed when the I-V properties are sensitive to 0, i.e., when 0 > Otherwise, only Ipand V,, or equivalently, Zp and the ratio I L / I o ,can be obtained from the cyclic voltammograms. An additional verification that the system is obeying the ideal diode/electrode behavior is that the change in cyclic voltammetry with variation in scan rate should produce I-V data in accord with the working curves of Figure 3. The working curves can also be used to predict the cyclic voltammetric behavior of a given diode/electrode combination under arbitrary experimental conditions. Because IL and Io can be determined independently from I-V properties of the semiconductor/electrolyte interface in a regenerative cell mode (under conditions of high concentrations of A+ and A, rapid mass transport, low series resistance, etc.) and I, can be calculated merely from the amount of electroactive material on the electrode surface, the data in Table I1 provide a method for a priori calculation of entire cyclic voltammograms, as well as the error in
+
Cyclic Voltammetry at Semiconductor Photoelectrodes
% O S
-
L;,
I
The Journal of Physical Chemistry, Vol. 92, No. 22, 1988 6365
-1 0 -1 0
’
-0 6
-0 4
-0 2
Vs-V,,-Eo
00
02
(V)
0.0
Figure 8. Effect of 6 on the nonilluminated scans of chopped cyclic voltammograms for a surface-confined redox couple on a metal electrode in series with a photodiode. The response is plotted in terms of the dimensionlesscurrent function, If/& The entire surface-attached material was oxidized before initiation of the dark reverse scan and the positive potential limit is much greater than Eo’ (see text). Values of 0 are for the reverse (nonilluminated) scans. Curve a, 0 = 9.73 X IO6; curve b, 6 = 9.73 x IO5;curve c, 0 = 9.73 X IO4;curve d, 6 = 9.73 X IO3;curve e, 6 = 9.73 X lo2; curve f, 6 = 9.73 X 10’; curve g, 6 = 9.73; curve h, 0 = 1.95; curve i, 6 = 9.73 X IO4.
TABLE 111: Data for Cyclic Voltammetric Behavior of Model Electrode Circuit (Nonilluminated Cathodic Scan) 6 IJIm AE,. mV fwhm. mV 9.73 x 104 1.ooo 0 91 1.95 0.935 40 100 104 9.73 0.890 76 0.868 134 105 9.73 x 10’ 0.865 193 105 9.73 x 102 0.865 252 105 9.73 x 103 0.865 311 105 9.73 x io4 105 0.865 370 9.73 x 10’ 0.865 430 105 9.73 x 106
V , at a given scan rate, for a particular (ideally behaving) modified semiconductor electrode. C . Nluminated Positive Voltage Scan and Dark Reverse Scan. In many experimental situations, it has been useful to perform a cyclic sweep with the semiconductor photoelectrode under illumination during the forward scan direction, followed by elimination of the light source in the reverse scan direction. Such ”chopped” scans have been used to identify surface state locations2 and mediated charge transfer event^^,'^ and to measure heterogeneous electron transfer rates at semiconductor surfaces.” We discuss general working curves and specific examples of experimental interest in the following sections. 1 . General Working Curves. The anodic scan in the light will be given by exactly the same calculations as in Figure 3. The working curves of this figure also will yield the proper shape for the cathodic dark scan; however, because ZL is now zero, the 0 values are likely to be much larger than those presented in Figure 3 and Table 11. Figure 8 and Table 111 present working curves in the Z’/O vs V’-Ea’ format for the cathodic scan over a much larger range of 0 values. These curves were not presented as part of the general treatment in section B because very low light levels would be required in Figure 3 to obtain such high B values. This would have prevented the entire amount of electroactive material from being oxidized in the anodic scan, which is in contrast to the general situation expected for the chopped light experiments. For the calculations depicted in Figure 8 and Table 111, the anodic scan was treated with its own 0 value, and it was assumed that the entire surface-attached material was oxidized before initiation of the dark cathodic scan. It was also assumed that the positive potential limit was much greater than E”, so that there would be little faradaic 0 (Le., current immediately after the light is blocked and V, V, Vs). With these assumptions, the cathodic working curves
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Vs-Eo’ ( V ) Figure 9. (a) Chopped cyclic voltammograms for a surface-confined redox couple on a metal electrode in series with a photodiode. The photodiode is illuminated only during the forward scan. The cyclic voltammogram of the electrode with no photodiode in the circuit is also shown. All parameters are as given in Table I. The values of 6 are as follows: forward scan, 6 = 4.86 X IO4; reverse scan, 6 = 9.73 X IO5. (b) Plot of the voltage drop across the photodiode, V,, as a function of the applied voltage, V,, for the voltammograms shown in part a.
in Figure 8 were obtained simply by application of the general treatment presented in Figure 3 to the cathodic scan direction only. 2. Specific Applications of Experimental Interest. Figure 9 depicts the calculated cyclic voltammetric response and resulting vd for our model semiconductor photoelectrode system and for a metal electrode under our standard conditions of light intensity, sweep voltage, etc. as given in Table I. In Figure 9a, the anodic peak shapes for the metal and diode/electrode scans are identical, but the peak potentials are separated by V, (550 mV). This is expected from the discussion in section B and the low 0 value of the illuminated anodic scan. In contrast, as 0 increases, the cathodic peak for the diode/electrode system decreases in height and broadens, with the fwhm asymptotically approaching 105 mV (compared to 90.6 mV for the metal electrode). Furthermore, E , is usually positive of E,. The presence of substantial cathodic current at potentials positive of E , arises because the diode is under forward bias for any potential where I < 0, so that even when 0 >> the voltage dropped across the diode at the cathodic current peak can be less than V,, whereas the anodic peak is The extent to which the diode positioned at Eo‘ - IV,] (0 < is loaded in the specific simulation of Figure 9 is obtained by reference to Vd in Figure 9b. Figure 10 extends the calculations to increasing values of the diode Io. This would correspond, in our model, to lowering the electrode/solution barrier height. In this figure, the anodic peaks all have fwhm values of 91 mV (because 0 < and E,, shifts 59 mV positive for every decade increase in Io. Again this is consistent with the expectations of section B. In contrast, the cathodic peaks are identical with the metal electrode for Io > lo6 A but become broadened and shifted in potential at lower values of Io. For the dark cathodic scan, when ZJZ0 > in the dark. The data in Table 111show that E , shifts 59 mV for every decade increase in u (0 > lo), and that the cathodic fwhm increases as u (and therefore 0) increases until fwhm = 105 mV. Several interesting effects, that have direct bearing on experimental interpretation of cyclic voltammetry at semiconductor electrodes, are observed in the calculated voltammograms shown in Figures 9-12. First, we note that in all cases, cathodic current is observed a t potentials far positive of the flat-band potential of the diode, even though this diode does not have any surface state leakage pathways in its circuit. This cathodic current flow is simply a result of the forward bias current-voltage characteristic of the diode, which may arise from a number of “ideal” diode transport mechanisms depending on the physical origin of Io. Also, the position and shape of the cathodic peak depend on the interplay between the faradaic impedance of the electrode/ solution interface and the diode impedance under forward bias (Figure 8). Normally, the cathodic peak potential is more positive than the anodic peak potential. However, if the diode is loaded sufficiently (V, becomes large) in the cathodic scan direction and Io is moderate in magnitude ( V , is small), the cathodic peak potential can become more negative than the anodic peak potential. This special case of our simulation is similar to the expectations previously proposed for “ideal“ semiconductor photoelectrodes (without surface states) under all Another interesting aspect of the chopped cyclic voltammetry simulations is that if the coverage of electroactive material on the electrode is increased, the cathodic wave will broaden and shift negative in peak potential in an analogous manner to the waves in Figure 12. Such shifts have been previously observed in the literature for n-type silicon photoelectrodes in mediated charge transfer experiments1Iaand have been assigned to the preferential kinetic reaction of particular distributions of surface-attached redox centers. However, an alternative explanation that needs
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Figure 10. Effect of the reverse saturation current of the diode on chopped cyclic voltammograms for a surface-confinedredox couple on a metal electrode in series with a photodiode. The photodiode is illuminated only during the forward scan. The cyclic voltammogram of the electrode with no photodiode in the circuit is also shown. The values of Io and 9 during the forward scan are as follows: (a) Io = 1 X A, 9 = 4.86 X IO4; (b) 1 X A, 4.86 X (c) 1 X lo“, 4.86 X IO4; (d) 1 X IO-’ A, 3.24 X lo4, (e) metal. The values of Io and 9 during the dark reverse scan are as follows: a) Io = 1 X lo-’* A, 0 = 9.73 X IO5;b) 1 X A, 9.73 X IO2; c) 1 X IO” A, 9.73 X IO-’; d) 1 X A, 9.73 X IO4; e) metal. The values of all other parameters are as given in Table I .
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Vs-Eo’ (V) Figure 11. (a) Effect of the photogenerated current on chopped cyclic voltammograms for a surface-confinedredox couple on a metal electrode in series with a photodiode. The photodiode is illuminated only during the forward scan. The cyclic voltammogram of the electrode without the photodiode in the circuit is also shown (curve e). Curve a, I, = 5 X 10” A, B(forward) = 1.95 X lo-’; curve b, 1, = 1 X IOd A, O(forward) = 9.73 X IO-’; curve c, IL= 5 X IO-’ A, B(forward) = 1.95; curve d, IL = 1 X lo-’ A, B(forward) = 9.73. The value of 9 for all curves on the dark reverse scan is 9.73 X IOs. The values for all other parameters are given in Table I. (b) Plot of the voltage drop across the photodiode, V,, as a function of the applied voltage, V,, for the voltammograms shown in part a. 10
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Figure 12. Effect of scan rate on chopped cyclic voltammograms for a surface-confined redox couple on a metal electrode in series with a photodiode. The photodiode is illuminated only during the forward scan. The values of u and 0 are as follows: (a) u = 1 V/s, 9(forward) = 4.86 X B(reverse) = 9.73 X lo6;(b) 0.1 V/s, 4.86 X 9.73 X lo5; (c) 0.01 V/s, 4.86 X 9.73 X lo4; (d) 0.001 V/s, 4.86 X lo”, 9.73 X lo3. The values of all other parameters are given in Table I.
to be considered is that the wave shapes are in accord with those expected from Figure 12. In this interpretation, the variation in wave shape with reaction time would result from a single homogeneous distribution of redox sites and an ideal diode with V, changing as a function of the faradaic current at the electrode/solution interface. D. General Comments and Conclusions. The analysis presented above can serve as a guideline for comparison with experimental
Cyclic Voltammetry at Semiconductor Photoelectrodes data, However, to date, no published cyclic voltammograms have been collected under sufficiently controlled experimental conditions to allow a quantitative comparison with this theory. Such experiments are currently being pursued in our laboratory and will be published in a separate paper. The key interface parameter that needs to be determined is the “impedance ratio”, 8, which expresses the ratio of the open circuit impedance of the diode element to the maximum faradaic impedance in the circuit. For the model system, this is easily evaluated by measurement of the separate I-Vcharacteristics of each circuit element. For an actual experimental system, the diode properties can be determined under steady-state conditions when there are negligible concentration polarization, kinetic, and ohmic losses due to the electrolyte portion of the circuit. Such conditions can be obtained in some semiconductor photoelectrode systems through judicious control over the cell geometry and with the proper redox couple and electrolyte/solvent system.24 The cyclic voltammetric properties can then be correlated with the curves displayed in the figures and tables presented above, provided that uniform irradiation conditions are maintained on the electrode surface. Several general conclusions can be derived from these simulations. First, under sufficiently high illumination levels, the difference in cyclic voltammetric anodic peak potential between a metal electrode and our model semiconductor photoelectrode for the redox pair A+/A is a good approximation to the open circuit voltage of the semiconductor/liquid-A+-A/metalcell. This has been implicitly assumed in some previous treatments, but other workers have associated this quantity with barrier heights,’ band bending values:h and other interfacial properties. For the systems modeled in Figure 5 , the cyclic voltammetric AE,or AEl12yields a >0.4 V underestimate of the flat-band potential and >0.5 V underestimate of the barrier height &,. This is due to the discrepancy between the open circuit voltage of the system and the barrier height of the electrically important junction. For other dominant recombination mechanisms, the error in estimating &, may be different than this value, depending on the exact relationship between I#Jb and V,. Second, we observe that the wave shape for an illuminated semiconductor electrode should resemble the shape at a metal electrode only for certain values of 8. When this condition is not fulfilled, a more complicated wave shape will be produced, and simulation is necessary to reproduce these features of the photoelectrode interface. Under these conditions, a qualitative guide to the error in V, can be obtained by AE, for the semiconductor electrode. Also, under these conditions, AE, may be a more reliable estimate of V, than AE, or AEljz. Third, the “chopped” reverse scan voltammograms will in general display cathodic current at potentials well positive of the anodic peak potential, even for a system with no surface state leakage pathways. Thus, use of the chopped return wave to diagnose the location and density of surface state processes would require a careful comparison of the deviation of experimental voltammograms with the theoretical curves presented in this work. Finally, we conclude that variations in the cathodic “chopped” wave shape as a function of scan rate or coverage of electroactive material will occur for ideal diodes, and the use of this wave shape to diagnose reaction site heterogeneity and to measure interfacial kinetic processes requires a detailed comparison with the simulations presented in this work. The model system described in this work should apply rigorously to semiconductor/liquid interfaces where the diode voltage is not (24) (a) Gibbons, J. F.: Cogan, G. W.: Gronet, C. M.: Lewis, N. S. Appl. Phys. Lett. 1984, 45, 1095. (b) Parkinson, B. A. Solar Cells 1982, 6, 177. (c) Orazem, M. E.; Newman, J. J . Electrochem. SOC.1984, 131, 2582.
The Journal of Physical Chemistry, Vol. 92, No. 22, 1988 6367 dependent on the concentrations of redox species in the electrolyte. This model is clearly appropriate for metal-covered semiconductor surfaces in contact with electrolytes and for situations where surface-state recombination or depletion region recombination dominates the voltage produced by the diode circuit element. However, we note that within the Marcus-Gerischer model for electron t r a n ~ f e r , * ~ ,it~ is ~ -predicted ~’ that the interfacial carrier capture velocities will be quite small at low concentrations of redox species. If no other recombination process is possible, then the photogenerated carriers will build up until they recombine in the bulk semiconductor. Thus, the diode voltage will be dependent on the concentrations of A+ and A at the electrode surface, and a more complicated set of expressions would be needed to describe the steady-state current voltage characteristics and the cyclic voltammetric response of such junctions. Such a treatment requires a full description of the quasi-Fermi levels for both carriers as a function of distance in the solid, and we are currently attempting to construct a model to simulate this system. Results of these simulations, and comparisons of the theoretical predictions presented in this work to appropriate experimental data, will be presented in a separate paper.
Acknowledgment. We acknowledge the Department of Energy, Office of Basic Energy Sciences, Grant DE-FG03-84ER13222, for support of this work. We also acknowledge helpful discussions with Gail N. Ryba and Professor Hans Andersen of Stanford University, Dr. Steven Feldberg of Brookhaven National Laboratory, and Professor Carl Koval of the University of Colorado. N.S.L. also acknowledges support as a A. P. Sloan Fellow and a Dreyfus Teacher-Scholar.
electrode surface area anodic peak potential cathodic peak potential (Epa + E,)/2 Epa(metal) - E,(semiconductor) E,(metal) - E,(semiconductor) Ei/2(metal) - E,/2(semiconductor) E p a - E, photogenerated current of diode reverse saturation current of diode peak current at metal electrode (at a fixed scan rate) = n2F%r,As/ (4R T ) dimensionless current variable; I/(Io IL) total charge in film voltage relative to the open circuit volta: e voltage across diode voltage across electrode open circuit voltage voltage applied across diode/electrode circuit scan rate total coverage of electroactive material, mol/cm2 coverage of oxidized material, mol/cm2 dimensionless current ratio; Ip/(IL + I,) full width at half of maximum peak current barrier height formal potential of electroactive material
+
(25) (a) Gerischer, H. In Physical Chemistry-An Aduanced Treatise; Eyring, H., Henderson, D., Jost, W., Eds.; Academic: New York, 1973; Vol. IXA, p 463. (b) Gerischer, H. Adu. Electrochem. Electrochem. Engr. 1961, I , 139. (26) Myamlin, V. A,: Pleskov, Y u . V. The Electrochemistry ofSemiconductors; Plenum: New York, 1967. (27) Memming, R. Elecfroanal. Chem. 1979, 1 1 , 1.
