GENERAL DISCUSSION Mr. M. P. Dare-Edwards (Oxford) said : The evidence put forward by Prof. Bard for “ Fermi-level pinning ” on p-type GaAs comes only from measurements and correla- tion of the photovoltage behaviour of the electrode in the various electrolytes. No correlation is demonstrated between the dark-current behaviour and the standard potentials of the redox couples. Indeed, similar work performed here in Oxford has shown that despite the similarity in standard redox potentials of the 13-/1- and Fe3+/ Fe2 + couples, there is totally different dark-current behaviour of electrodes immersed in the two media. The time-dependent responses of the electrodes towards illumina- tion is also markedly different for these two couples. Much of Prof. Bard’s work was carried out using chopped illumination which, unfortunately, masks much of the time- dependent behaviour.There are also no reported measurements of flat-band poten- tials of p-GaAs in these media which may provide important additional evidence for Prof. Bard’s theory. From the observed results, it would seem more important to correlate behaviour with the detailed chemical interactions at the electrode/electrolyte interface than to use a generalized “ Fermi-level pinning ” model. From our own work, there is an obvious chemical interaction between p-GaAs and the I:/I- medium, seen by the appearance of a clear surface film on the electrode even following short periods of use. Another more general point is that the minimum concentration of surface states required to achieve “ Fermi-level pinning ’’ will be highly dependent on the nature and quantity of compensating ionic charge adsorbed within the inner Helmholtz layer.Prof. Bard alludes to the behaviour of “ Fermi-level pinned ” electrodes as if coated with a monolayer of metal. A.c. cyclic voltammetry of p-GaAs following long periods of use at cathodic potentials in the dark or after illumination reveals the presence of surface species which may be considerably enhanced by deliberate addition of Ga3+ to the electrolyte. The beha- viour correlates well with literature results on pure gallium metal. Use of p-GaAs for periods of up to 24 h can produce bulk Ga metal at the surface, sufficient to be seen with the much less sensitive d.c. cyclic voltammetry. As a final point, in the reduction of PhN02 by p-WSe,- it should be made more clear what Prof.Bard means by the 0.095 mol dmY3 PhNOi- produced at the Pt electrode being a “ small amount ”. At such levels quoted in the paper, specific ion adsorption of the PhN0;- could produce a negative flat-band shift sufficient to explain the observed results. This allusion may, in fact, be a reality. Prof. A. J. Bard (Texas) said: The “ Fermi-level pinning ” model at GaAs is drawn from a number of different experiments, involving redox couples which probably do not involve specific adsorption, in aqueous and non-aqueous (e.g., MeCN and liquid NH3) solutions. For p-GaAs in aqueous solution, we find that the onset photopoten- tial, 0.75 V us. SCE, in the presence of the I-/I, couple, is far more positive than the reported flat-band potential, Vfb, in the absence of redox couples 0.1-0.75 V us.SCE, at pH 0.1-3 This positive shift of the flat-band potential cannot be explained by the specific adsorption of the negatively charged ions (I- or I;). As indicated above, the reported values of Vfb of p-GaAs in aqueous solutions show a good deal of scatter,94 GENERAL DISCUSSION probably because of surface effects. We have used impedance techniques to measure V,, of p-GaAs in supporting electrolyte with or without redox couples. The results are complicated, especially in the presence of redox couples, which show interferences because of Faradaic processes. Results on the dark currents for p-GaAs with these couples have been previously reported (see, e.g., fig. 1, 3 and 4 in Fan and Bard).4 Continuous illumination experiments (for up to 8 h in an I-/I< solution) are also re- ported in this paper.Of course a more detailed picture of the interface would be desirable and clearly kinetic factors and the double-layer structure play a role in the behaviour of redox couples at semiconductors. However, the Fermi-level pinning model appears to explain quite well a number of observations at G ~ A S ~ B ~ and Si,6 especially when compared with the ideal model usually employed. - O A - 06 I 4 8 4 4 \ 4 0 36 energy /eV FIG. 1 .-X-ray photoelectron spectra of two p-GaAs electrodes. Electrode A was maintained at 0 V. Electrode B was scanned to -2.1 V and illuminated in liquid NHs containing 0.1 mol dm-3 KI. (From unpublished work by R.Malpas, K. Itaya and A. J. Bard.) With respect to the question of formation of bulk Ga metal at the surface, small amounts of Ga formation can probably occur under some circumstances. For example Kohl has found production of less than monolayer amounts of Ga on photo- reduction of p-GaAs in aqueous solutions. It is unlikely, however, that bulk Ga metalGENERAL DISCUSSION 95 deposition can explain the behaviour in most of the experiments reported for GaAs. For example, we considered this possibility in our original work on the GaAs/CH,CN interface5 and rejected it based on X-ray (X.P.S.) and Auger electron spectroscopic analysis of the electrode following use. No evidence of an increase in the relative amount of Ga was observed in this case, nor in the case of p-GaAs used to photo- generate solvated electrons in liquid ammonia, which represents rather drastic reduc- ing conditions.8 In the latter case two identical p-GaAs electrodes were placed in a liquid NH3 + 0.1 mol dm-3 KI solution with electrode A maintained at 0.0 V and electrode B scanned under illumination to potentials where solvated electrons are generated.After washing the electrodes and dismantling the cell in an inert-atmo- sphere glove box, the electrodes were transferred to an X.P.S. spectrometer. The As 3d peaks in the X-ray photoelectron spectrum for these electrodes are shown in fig. 1. The peak at 41 eV on both spectra has been previously assigned to As in GaAs, with the shift in binding energy between this peak and that for pure As metal (-0.7 eV) caused by the increased negative charge on the As.The significant difference between the two spectra is the change in the ratio of this peak to that centred around 44 eV. The latter peak has been previously assigned to an arsenic-oxygen species (probably AS,^^).^ Thus at 0 V, where the As/As,O, peak ratio is small, it appears that a sur- face oxide film exists on the electrode, whereas at -2.1 V, where the largest photo- effects are observed, the peak ratio is large suggesting reduction of this oxide film, thus producing a cleaner GaAs surface. The removal of the oxide films from anod- ized GaAs, by etching with HC1 or aqueous NH, solutions, has previously been shown to yield a surface rich in elemental AS.^ The Ga peaks in the X.P.S. spectra of the two GaAs samples were essentially the same.Finally Ga metal would be thermodynamically unstable in the acidic aqueous solu- tions and in the presence of oxidants such as 1, or Fe3+. The concentration of electrogenerated PhN0;- in the p-WSe, experiment was 0.095 mmol dm-3. Thus the negative shift of the onset photopotential V,, of p-WSe, due to specific ion adsorption of the PhNOS- seems unlikely. An experiment has been performed by dipping a p-WSe, electrode in a PhNOi- solution for a few minutes. After rinsing the electrode with solvent, a photovoltammetric experiment was per- formed with this electrode in a PhNO, solution. No shift of Yo, was observed com- pared with an electrode which had not been pretreated with PhNOI-. L. J. Handley and A. J. Bard, J. Electrochem.Soc., 1980, 127, 338. W. H. Laflere, R. L. Van Meirhaeghe, F. Cardon and W. P. Gomes, Swface Sci., 1976,59,401. R. Memming in Semiconductor Liquid-Junction Solar Cells, ed. A. Heller, Proceedings of a Con- ference on the Electrochemistry and Physics of Semiconductor Liquid Interfaces under Illumi- nation held at Airlie, Virginia, 1977, p. 38. F. R. F. Fan and A. J. Bard, J. Amer. Chem. Soc., 1980, 102, 3677. P. A. Kohl and A. J. Bard, J. Electrochem. Soc., 1979, 126, 59. A. B. Bocarsly, D. C. Bookbinder, R. N. Dominey, N. S. Lewis and M. S . Wrighton, J . Amer Chem. SOC., 1980, 102, 3683. ’ P. A. Kohl and F. W. Ostermayer Jr, 158th Meeting, Electrochem. SOC., Sept. 1980, Abstr. 289 J. Electrochem. SOC., 1980, 127, 371C. * R. E. Malpas, K. Itaya and A. J. Bard, to be published.C. C. Chang, P. H. Citrin and B. Schwartz, J. Vac. Sci. Technol., 1977, 14, 943. Prof. L. R. Faulkner (Urbana) said : There has been discussion among investigators interested in chemically modified semiconductor electrodes about the possibility that electroactive groups chemically attached to the surface could serve as agents for pin- ning the Fermi level of the electrode. The idea is that these groups act essentially as a set of surface states. However, it is important to note a difference between that96 GENERAL DISCUSSION situation and the usual idea of a surface state as part of or at least a rigid termination of the lattice. The distinction is that most chemical modification schemes involve flexible connection of electroactive species to a surface, whereas surface states are generally considered as rigid.In order for a collection of surface states to pin the Fermi level, they must offer a significant capacity for accepting net charge into a surface layer, so that the voltage drop across the Helmholtz layer changes as the electrode potential. Conventional surface states have this property. On the other hand, electrodes modified with electro- active agents usually do not because their flexible connections allow charge compen- sating ions to mingle among the electroactive sites. Thus charge transfer into the layer does not necessarily result in either a net charge in the layer or a change in the potential drop across the Helmholtz layer. In order for electroactive species at a chemically modified electrode to act as agents for Fermi-level pinning the attachment scheme must not allow penetration of their plane by counter ions.Prof. A. J. Bard (Texas) said: Prof. Faulkner’s point is certainly well-taken. If the attached electroactive group is predominantly in the diffuse double layer, it will essentially behave as a solution reactant and not cause pinning. However, some modi- fied electrodes (e.g., those involving “ adsorptive attachment ”) probably have a signi- cant amount of the species at the surface which can exchange charge with the electrode. These would behave as surface states. Prof. J. O’M. Bockris and Dr. S. U. M. Khan (Texas) and Dr. K. Uosaki (Sapporo) said: We wish to comment on the roots of the idea of double-layer pinning, suggested by Bard et al.We consider this concept to have been contained in the work of Mino Green, who published the first treatment of the structure of the double layer at a semiconductor/ solution interface in 1959. Green’s version of the situation concerning the movement of potential within and without the semiconductor, during change of electrode potential, was, however, qual- itative.’ His paper shows a figure portraying the double layer at a semiconductor/ solution interface in the absence and presence of surface states. The double-layer pinning model which Bard et al. present is tantamount to that of Green in the presence of surface states. Green published numerical calculations of the degree to which a change of the electrode potential would be partitioned over the potential drop inside the semiconductor and over the Helmholtz double layer.Typically, at low surface state concentrations, and with an electrode potential change of several hundred mV, the change over the Helmholtz layer was a few mV. However, at higher surface states, e.g. (1/10 ionized), the p.d. in the double layer for a 1 V change of the electrode potential approached 1 V, with the corresponding change in the interior being reduced to a few mV. The small change of the p.d. within the semiconductor implies, for a doped semiconductor, a limitingly small change in the position of the Fermi level. One may call the stationary Fermi level pinned. However, we should like to suggest that the term “ double-layer pinning ” for these happenings does not indicate what is happening as well as the descriptions “ inner p.d.change dominant ” and “ Helmholtz change dominant ” (respectively, for the case for which the potential is pinned at the surface of the electrode, and for which the Fermi level is pinned). The former descriptions help understand the relevant model, particularly in respect to the electrode kinetics, which each limiting condition would imply. In nearly all the papers published in photoelectrochemistry to date, the first caseGENERAL DISCUSSION 97 treated by Green (internal potential difference dominant) has been gratuitously as- sumed to be the relevant one, and the possibility that there will be sufficient surface to make the second case relevant has been neglected.2 Which is the more general case ? Although the requisite experiments have not yet been done, it seems likely that the high surface state and Helmholtz p.d. dominant is more general than the case usually treated.The evidence is circumstantial, and suffers under our poor knowledge of the nature and concentration of surface states. These are assumed to arise from localized bonds on the surface. However, it seems likely that they could arise from bonds which arise from the solution side. For example, in hydrogen or oxygen evolution, and if the steady state of an intermediate adsorbed chemical radical is high, each bond of such a radical to the surface would be associated with a surface state. As the con- centration of these states would vary with potential, they would affect the Helmholtz p.d. during a variation of the electrode potential.Correspondingly, the specific adsorption of ions on the surface of semiconductors seems likely to occur, and could cause surface states to occur in the presence of redox systems. Specific adsorption has been measured, for example by Genshaw, Paik and Bockris, on the surface of so-called iron and chromium which was likely to consist of oxide films, and found to be far higher than the corresponding adsorption with which we are used to dealing on rner~ury.~ The attainment of full coverage was reached for small concentrations of ions in the solution. This suggests that specific adsorption occurs with a large degree of charge transfer so that there is little repulsion between the adsorbed anions and such a picture may apply to the semiconductor/solu- tion interfaces, implying surface states at more than 0.1 of full coverage.As specific adsorption is potential dependent, there may be a correspondence between the surface states implied and changes in the Helmholtz double layer. If these thoughts are applicable, then diagrams which are drawn in photoelectro- chemical models would have to be modified to take account of the change of Helmholtz potential with electrode potential. It would become more likely that the photocur- rent/potential relation at a semiconductor/solution interface would be rate controlled, at low biases, by transfer of holes and electrons through the double layer (the quan- tum efficiency being controlled by the ratio of the rate constant for this passage, com- pared with the rate constant for the surface recombination reaction). This was the position taken by us in interpretation of the (ip, u) relations for hydro- gen evolution at low biases in the photoelectrochemical behaviour of p-type electrode^.^ We calculated the magnitude of the potential difference in the Helmholtz layer from the slope of the Mott-Schottky plot and derived the magnitude of the potentials in the Helmholtz layer.Thus, the phrase such as “ double-layer pinning ” is perhaps quantitative, since each semiconductor/solution interface has to be evaluated (for a given change of electrode potential) in respect to the degree of change of potential within and without each solid for itself, and in respect to the solution it contacts. Double-layer pinning would refer to the extreme case where the changes of p.d.would be entirely in the Helmholtz plane (“ metallization ”). We have to wait until we get a better measure of the concentration of surface states to know how often we come to this situation. At this time, “ Helmholtz-layer dominant,” or “ inner-layer dominant ” seems more appropriate terms to describe these situations. M. Green, J. Chem. Phys., 1959, 31, 200. J. O’M. Bockris and K. Uosaki, J. Electrochem. Soc., 1977, 124, 1. W. Paik, M. A. Genshaw and J. O’M. Bockris, J. Phys. Chern., 1970, 74, 4266. J. O’M. Bockris and K. Uosaki, J. Electrochem. Soc., 1978, 125, 2.98 GENERAL DISCUSSION Prof. A. J. Bard (Texas) said: As we point out in our paper the roots of the con- cept of Fermi-level pinning are contained in considerations of the semiconductor/ metal interface dating back to Bardeen’s work in 1947 [ref.(3) of my paper]. How- ever, Green’s contribution in 1959 to the theory of the semiconductor/electrolyte interface was certainly of importance and we have referenced this work both in this paper [ref. (6)] and our original publication on Fermi-level pinning [ref. (7)]. At the time of Green’s publication, as he points out, no actual experimental examples of this effect were available, and the importance of such effects have generally not been recog- nized in more recent studies. An especially important aspect of the Fermi-level pin- ning phenomenon, not dealt with in the original work of Green, is the shifting of the level to energies corresponding to couples well outside the semiconductor conduction and valence band edges (as determined from measurements in the absence of redox couple).The term “ Fermi-level pinning ” has its origins in the semiconductor/metal litera- ture.’ Terms such as “ double-layer pinning ” or “ band-edge unpinning ” are less‘ descriptive. In terms of the nature of surface states, I prefer the distinction drawn by Gerischer [ref. (1 3), p. 4751 where those that contribute to Fermi-level pinning involve electron exchange rather than simple specific adsorption of ions. See, for example, S. M. Sze, Physics of Semiconductor Devices (Wiley, New York, 1969). Prof. H. Geriscber (Berlin) said: Fermi-level pinning has been found on semi- conductor surfaces in vacuo if surface states are present to large enough concentrations. This is caused there by the presence of dangling bonds.The same effect has often been observed at semiconductor heterojunctions owing to the presence of interfacial electronic levels within the band-gap generated by structural imperfections or chemical impurities at such interfaces. It is not surprising that similar problems will arise at semiconductor/electrolyte contacts. One particular reason is that the chemical com- position of the semiconductor surface deviates from the bulk, as is the case with ger- manium or silicon or many compound semiconductors which form either an oxidic monolayer or even a thin oxide layer at such a contact. However, there was some hope that the reactivity of the surface could also prevent the generation of electronic states within the energy range of the band gap, since very stable bonds formed on the surface should have energy levels within the valence band, and their antibonding counterparts may be located within the conduction band.Such a type of surface state would not influence the distribution of the electric charge at the contact. The enormous dependence of the electronic properties of these contacts on surface pretreatment and etching procedures indicate that there is an enormous variability of the surface properties. I believe, however, that not all the shifts of the band edges observed in electrochemical systems can be attributed to the presence of surface states. One should consider that semiconductors with not too wide a band-gap can easily form an inversion layer if minority carriers are generated by light absorption or can directly be injected into the surface from the electrolyte owing to the presence of a suitable redox system therein. If the energy position of surface states is very close to the band edges, as might often be the case, it will be very difficult to distinguish be- tween Fermi-level pinning owing to surface states and control of the space-charge layer by inversion.Both situations lead to an up- or down-shifting of the band edges at the interface, if the applied potential is varied. To demonstrate the similarity between both situations I would like to show in fig. 2 the situation where a p-type semiconductor is polarized cathodically to such an extent that the band-gap would be exceeded by the Schottky barrier height if a deple-GENERAL DISCUSSION 99 acceptor Ec sur t ace states Redox system Flat band potential no surface states with surface states energy terms in the absence of Red FIG.2.-Formation of an inversion layer or Fermi-level pinning by surface states. tion layer were formed with no minority carriers available on the surface. In contact with a very cathodic redox system, electrons can be injected into the surface and in the absence of surface states an inversion layer will be formed causing some upwards shift of the band edges owing to the resulting potential drop in the Helmholtz double layer. In the presence of surface states as shown on the right-hand side of the picture the Fermi level will be pinned to the surface states in equilibrium with the redox system.Assuming that these surface states have acceptor character and can pick up negative charge, the potential drop in the Helmholtz double layer will now be controlled by this charge and the band edges at the interface will be shifted upwards even further. If the semiconductor is illuminated, photocurrents will be found in both cases without much difference. This is shown in fig. 3 on the left-hand side for a semiconductor without surface states, and on the right-hand side for a semiconductor with surface states located somewhere in the Larger differences can be expected if the polarization is varied. I bias I anodic (forwardl 1 bias with inversion layer anodic (forwardl 1 bias with surface state control of lhe Fermi level FIG. 3.-Semiconductor-redox-electrolyte junction at cathodic and anodic bias.100 GENERAL DISCUSSION band-gap.Most conclusive should be the behaviour in the dark, which is indicated in this figure by the course of the Fermi levels of electrons and holes. Under cathodic bias, i.e. in the reverse direction, the electrode will show a blocking be- haviour in both cases. The current will be controlled by the rate of electron-hole pair generation in the depleted region of the inversion layer or, in the case of the presence of surface states, directly underneath the surface, where ,,EF and deviate from each other. In the forward direction, however, a larger current would be expected if an inversion layer is formed, in accordance with the normal behaviour of p-n junc- tions. This is indicated in fig.3 by the large deviation of the Fermi levels of electrons and holes in the transition range between the n-type surface and the p-type bulk. In the presence of surface states the forward current would be controlled by the injection of electrons from surface states into the conduction band, which can only reach a high level if these states are very close to the band edge. My conclusion is that a distinc- tion between Fermi-level pinning by surface states and the formation of an inversion layer will be possible if the surface states are not too close to the band edges. Other- wise one can hardly distinguish whether the shift of the band edges at the interface is caused by the presence of surface states or by the accumulation of minority carriers at the surface.I have the impression that the results shown in fig. 4 of Prof. Bard's paper can easily be interpreted by the formation of an inversion layer. The difference between the onset of the photocurrent and the standard potential of this redox system at the plati- num electrode is ca. 0.7 V. This is just the photovoltage one would expect for a semi- conductor with a band gap of 1.15 eV, if an inversion layer is formed in contact with a redox system.l Another reason for this interpretation is that one can hardly see why surface states of such high concentration should be formed on the surface of layered materials, where in the absence of large concentrations of dislocations or steps the surface should be perfect and have no dangling bonds. W. Kautek and H. Gerischer, Ber.Bunsenges. phys. Chem., 1980, 84, 645. Prof. A. J. Bard (Texas) said: In general, we agree with the comments of Prof. Gerischer on the difficulty of distinguishing between a shift of the band edges at the interface being caused by the presence of surface states or by inversion, when the surface states are close to the band edges. In addition to the differences pointed out by Prof. Gerischer in the forward-bias voltammetric curves, the reverse-bias voltam- metric curves can be very different for these two models if the density of surface states is high and they are also close to the conduction band edge (for n-type) or the valence band edge (for p-type) semiconductors. Majority charge-carrier injection from the redox species is possible based on the Fermi-level pinning model but not on the inver- sion model.The results with p-WSe, in non-aqueous solution can apparently be interpreted by the formation of an inversion layer. However, Fermi-level pinning still cannot be completely excluded, since capacitance measurements (fig. 4) taken in aqueous solu- tion show a frequency dispersion which cannot be interpreted simply by pure inversion. There are at least two ways of explaining this frequency dispersion, one involving sur- face states and the other inversion along with a Faradaic process. Further work is required to give a definitive answer. The variation of Vredox- V,,, with T/redox for p- and n-WSe, for electrodes with smooth and edge-free surfaces is shown in fig. 5 . ' q 2 Note that while p-WSe, shows a levelling of the photovoltage at Vredox values corres- ponding to the conduction band edge, for n-WSe, pinning occurs at potentials signi- ficantly negative of the valence band edge.The surface states that cause this pinning also lead to recombination effects in the p-WSe, and small photovoltages for couplesGENERAL DISCUSSION 101 V/V US. SCE 0.8 0.4 10 0.4 I I I I I I FIG. 4.-Plots of capacitance against potential on “ smooth ” p-WSe2 electrode at various frequencies in 0.5 mol dm-j Na2S04 aqueous solution (pH % 5 ) . Curve 1 : 10 kHz; curve 2: 5 kHz; curve 3: 4 kHz; curve 4: 3 kHz; curve 5: 2 kHz; curve 6: 1 kHz. 1 c, 00 4 6 0 3 5 0 7 2 / I / I -2.0 -1.2 P= +0.4 @yfbi+; . 2 ’f b(n1 f, - E , - f, Vr/dox/V US. SCE FIG. 5.-Plot of Yredox - Yo, against Vredox for various redox couples at n- and p-type WSez in CH3CN solution.1, anthracene (O/ - 1); 2, phthalonitrile (O/ - 1); 3, nitrobenzene (0/ - 1); 4, ruthenium 2, 2’-bipyridine (+2/ + 1) ; 5 , azobenzene (O/ - 1) ; 6, anthraquinone (O/ - 1) ; 7, benzoquinone (O/-1); 8, methyl viologen (+2/+1); 9 = tetracyanoquinone dimethane (+l/O); 10, NNN”’- tetramethyl-p-phenylene diamine (+ 1 /O) ; 11, NNN”’-tetraphenyl-p-phenylene diamine ( + 1/0) ; 12, idodide/iodine; 13, bromide/bromine; 14, chloride/chlorine; 15, thianthrene (+ l/O); 16, ruthenium 2,2’-bipyridine (+3/+2).102 GENERAL DISCUSSION located at these energies. Similarly for n-WSe, recombination effects appear for couples located very near the conduction band edge. Thus pinning in p-WSe, could occur by either inversion or surface states close to the conduction band edge.The results suggest that even on apparently smooth layer-type compound electrodes, surface states can exist. H. S. White, F. R. Fan, and A. J. Bard, J. Electrochem. SOC., in press. G. Nagasubramanian and A. J. Bard, J. Electrochem. SOC., in press. Dr. A. J. Nozik (Colorado) said: I would like to point out that an alternative mechanism to Fermi-level pinning can be invoked in certain cases to explain the photoelectrochemical behaviour described by Prof. Bard. This mechanism is based on the effects of inversion, whereby the charge density and capacitance in the semi- conductor space-charge region can become greater than that of the Helmholtz layer. Inversion occurs when the band bending is sufficiently large that the Fermi level at the semiconductor surface lies closer to the minority carrier band than to the majority carrier band.' The resulting large increase in charge density and capacitance near the semiconductor surface causes additional changes in the electrode potential (in the direction of increased reverse bias) to drop across the Helmholtz layer rather than the semiconductor space-charge layer. This situation destroys the constancy of the posi- tions of the semiconductor band edges with respect to the electrolyte redox potentials, and allows the semiconductor band edges to move with applied potential (in the inver- sion region) with respect to the electrolyte redox levels.We call this effect " band- edge unpinning ". Recent experiments 2-4 with p-Si in non-aqueous electrolytes show that the dependence of the capacitance as function of electrode potential, light inten- sity and surface-oxide thickness is totally consistent with the behaviour expected for p-Si in inversion.This mechanism for band-edge unpinning works best for small- band-gap semiconductors, where inversion can be readily achieved. It also predicts, of course, that the band edges only become unpinned in the potential regions where inversion exists; it does not depend upon the presence of surface states. S. M. Sze, Physics of Semiconductor Devices (Wiley-Interscience, New York, 1969), chap. 9. J. A. Turner, J. Manassen and A. J. Nozik, Appl. Phys. Letters, 1980, 37, 489. J. A. Turner, J. Manassen and A. J. Nozik, Photoefects at Semiconductor-Electrolyte Interfaces, ACS Symp.Ser (ACS, Washington D.C., in press). M. Klausner, J. A. Turner and A. J. Nozik, to be published. Dr. R. Schumacher (Kiel) said: We have recently found changes in the overall capacitance c,, of n-Ti02 single-crystal electrodes illuminated with band-gap light. These changes are given in fig. 6 as the difference between the illuminated and un- illuminated sample. The most interesting feature of this illustration is that in the anodic potential mode c,, is diminished, whereas at negative potentials c,, increases. At the transition potential V,, no photocapacitance is observed. These changes, how- ever, are only detectable on n-TiO, samples which have been operated for a certain time period in the anodic potential mode and simultaneously illuminated with band- gap light.For illustration the increase of the photocapacitance as function of the pretreatment time is given in fig. 7. Samples which had not been treated in that way do not show any detectable photocapacitance. We assume that this photoelectrochemical pretreatment procedure covers the ex- posed electrode area with states which can be reversibly filled with or emptied of elec- trons. This, of course, can be carried out either by varying the cell potential and/or by illumination. Assuming that the capacities of the Helmholtz layer cH and that of the semiconductor c,, are shunted in series the potential drop across the semiconduc-GENERAL DISCUSSION 103 tor-liquid junction controls the recorded overall capacitance cov. That means at positive potentials c,, determines c,, whereas at potentials close to Vfb the C, is the controlling factor.A rough estimation on the contributions of the photoinduced capacitance revealed that changes of ca. 50% with respect to the dark behaviour were I I * I .5 potential / V us SCE. FIG. 6.-The course of the anodic (c&) cathodic (cpch) photocapacitance recorded with a lock-in ampli- fier svstem operated with chopped light in 0.1 mol dm-j NaOH as function of the potential. observed. The changes of c,, in both directions are explainable assuming light- induced variations of the charge distribution within the surface states. More details on the charge-transfer mechanism involved are given elsewhere.’ We suppose these significant changes of c,, due to illumination to be a strong indi- cation that the existence of surface states in which electric charge can be trapped timelmin was operated for certain time periods under band-gap illumination in 0.1 mol dm-j NaOH.FIG. 7.--Increase in the anodic photocapacitance due to the pre-treatment procedure. The sample favours a situation where a possible shift of the bands relative to electrolyte states seems conclusive. This result is in agreement with the conclusions presented in Prof. Bard’s paper. H. R. Sprunken, R. Schumacher and R. N. Schindler, Ber. Bunsenges. Phys. Chem., 1980, 10,1040. Dr. A. J. Nozik (Colorado) said: In response to Prof. Bard’s informally expressed criticism of the term “ band-edge unpinning ” I believe it is a perfectly valid descrip- tion of the effect we are discussing.In the previous models of the semiconductor- electrolyte interface it was generally acceped that the positions of the semiconductor band edges were fixed (indeed pinned) with respect to the redox levels in the electrolyte,104 GENERAL DISCUSSION and independent of electrode potential. In our current understanding, we realize that under certain conditions (e.g. surface states, inversion) the positions of the band edges may become unfixed, or unpinned, and move with applied potential. These special conditions, therefore, lead to band-edge unpinning. Dr. S . U. M. Khan and Prof. J. O'M. Bockris (Texas) said: It will be of interest to have proof from the theoretical point of view of the experimental observation that : 1*2 We make an attempt to prove relation (1) by considering charge transfer at the semi- conductor-solution interface as the rate-determining step, and the potential drop mainly in the Helmholtz layer for a semiconductor having surface state^.^ We also assume that the acceptor and donor electronic states in redox ions in solution are Boltzmannian.We assume that the onset potential, Yonset, in photoelectrochemical kinetics of semiconductors arises when the cathodic photocurrent, e.g., of p-type semiconductors, equals the anodic dark current across the conduction band. Following the experi- mental observation of Bockris and Uosaki that the Yonset is independent of photon energy, and hence considering the photoexcited electron transfer from the bottom of the conduction band to the acceptor ion, e.g., M3+(aq) ion, in solution, we can ex- press the cathodic photocurrent as : VOnse, - YZedox 2: constant 2: 0.4 V.(1) C A UL CT O"t + l i b pTc i,,,,(cathodic) = - e, I, (1 - RA) x exP - [A&(3) + peoAP]/kT = A exp - [AE0(3) + j?eoAp]/kT (2) where e, is the electronic charge; C, is the acceptor concentration, M3+ (aq), in the reaction plane; CT is the concentration of total number of sites in reaction plane; Z, is the intensity of light; RL is the reflection coefficient of light; aA is the adsorption coefficient of light; LD is the diffusion length of electrons in the semiconductor; P$ is the WKB tunnelling probability across the interfacial barrier for a cathodic process ; /? is the symmetry factor; Ap is the potential drop at the semiconductor-solution interface and AE0(3) is the amount of energy needed to excite M3+ (as) from the ground state to the activated state, so that radiationless photoelectron transfer is possible from the bottom of the conduction band to activated M3+ (as) ion in solution.AE,(3) is obtained using a cycle for the process M3+(aq) + p-Sc(e) AE(3)t M:"+(aq) and becomes: where AFo is the free energy of the reaction and AFt(2) is the free energy of activation of the reverse reaction, AEo(3) = AF" + AFj(2) M3+(aq) + p-Sc(e) -+ M2+(aq), M2+(aq) + M3+(aq) + p-Sc(e). (3) The dark anodic current corresponding to electron transfer to the conduction band can be expressed as: kT h i,,,,(anodic) = eo - CD 6 P$e - [ A W ) - & W / k *GENERAL DISCUSSION 105 where k is Boltzmann's constant; h is Planck's constant ; CD is the concentration of the donor, M2+(aq), ion; 6 is the width of the double layer at the p-Sc-solution inter- face; Pa is the WKB tunnelling probability across the interfacial barrier for an anodic process and AE(2) is the amount of energy needed to excite M2+(aq) from the ground state to the activated state, so that the radiationless electron transfer is possible from the excited M2+(aq)* to the vacant levels of the bottom of the conduction band of p-Sc electrode, and is obtained from a cycle for the process M2+(aq) ____+ M3+(aq)* + p-Sc(e) AE(3) and becomes: AEo(2) = -AF" + AFt(3) = AF(2) where AFl(3) is the free energy of activation for the reaction M3+(aq) + p-Sc(e) -+ M2+(aq).At Yonset we use the equality of current densities from eqn (2) and (4), i.e., Ae- + Be&vl/kT = Be - [AE0(2) - Be0Avl/kT or, for /3 = 1/2, eoAq = kT In AIB - AE0(3) + AE0(2).Using eqn (3) and (5) for AE0(3) and AE0(2), respectively, we get (Aq)onset = 5 1 , AIB - AF"/eo e0 or ( 5 ) in potential scale, or (7) - kT Yonset - V'redox = - In A/B = constant. e0 Hence, relation (1) is proved in eqn (7). Putting the value of A and B from eqn (2) and (4) in eqn (7) and considering (1 - R,) 21 1, and P: 'v P;, Zo = 2.97 x 1017 photon cm-2 s-l for an intensity of 1 sun, having hv = 2.1 eV. C,/C, = 0.5 for 0.5 rnol dm-3 solution; cq = lo4 cm-'; LD-l = lo3 cm'l; kT/h = 1012-5; C,, = 0.5 mol dm-3 = 3.0 x lo2' molecule ~ m - ~ ; 6 = 5 A. We get: - _ - - kT In (9 x 10-9-5) e0 = 0.5 V which is comparable with the experimental value.'106 GENERAL DISCUSSION F.F. Fan and A. J. Bard, J. Amer. Chem. Soc., 1980, 102, 3677. V. Guruswamy and J. O’M. Bockris, Energy Research, 1979, 3, 389. M. Green, J. Chem. Phys., 1959, 31, 200. J. O’M. Bockris and K. Uosaki, J. Electrochem. Soc., 1977, 124, 1348, Prof. J. O’M. Bockris (Texas) said : The reaction of photoelectrochemical processes to pulses is a main path to the determination of the rate-determining step in the steady state. Hence, I advocate detailed examination of the (current, time) line under potentiostatic conditions, not only at very low (nanosecond) or intermediate (milli- second) ranges but also up to the range of seconds where slow surface states (lifetime ca. seconds) can still be coming into play, and until steady state is reached.The rate- determining step may change as the occupancy of the surface with surface radicals changes and from the point of view of device orientation, it is the rate-determining step in the steady state which is important. An initial reduction of a surface oxide may be important at p-type semiconductors and affect the course of the (current, time) transient. Prof. A. B. Ellis (Wisconsin) said: In their potentiostatic flash experiments Dr. Richardson and Prof. Perone suggest that oxygen is the detected photo-oxidation pro- duct based on a lifetime which exceeds 15 ms. Is there any other evidence that the product is O2 and not, perhaps, a species such as H202? Mr. Z. Harzion (Tel Auiv) said: I would like to describe results of some fast photo- current transient measurements performed on the CdSe/polysulphide system in which a slightly different approach was adopted. We measured at both closed and Rseries Rlood FIG.8.-Equivalent circuit for photoelectrochemical cell. open circuit conditions and analysed the results by plotting the decay time z against the resistance of the external load in a two-electrode cell. Small potential perturb- ations were employed so that constant values of the interfacial elements could be safely assumed. A linear dependence is found in the small-R, region, while at higher values of RL the slope falls gradually. This general behaviour could be simulated by a simple equivalent circuit shown in fig. 8. In this circuit the semiconductor-electrolyte inter- face is represented by a capacitor C, with a shunt resistor, Ri, across it.The rest of the cell and circuit is represented by a resistor Rout, where Rout = Rseries + Rload, Rseries being the total series resistance of the photoelectrochemical cell. A current source represents the source of illumination and is connected in parallel with C. The measured response of this circuit to a short light pulse can be simulated by its re-GENERAL DISCUSSION 107 sponse to a delta function of injected current, and is calculated by Laplace transform- ation as: AQ iout = R C exP(-t/z) out where z is given by z = (Ri,JIROut)C. T = (Rseries + Rload)C and a plot of z against Rlcad should be linear with slope C and intercept Rseries C. In the high-Riload region the decay will occur primarily via the internal route, Rin, and in terms of this equivalent circuit z = RinC.For example, measurements taken before and after surface etching revealed that etching resulted in higher photocurrent peaks, larger charge per pulse, shorter decay time and a lowered Rseries. This might might be due to the removal of a damaged layer rich in traps. (Note that even at small Rload values, " closed circuit," the resolution rise-time is limited by pulse width as in the case of '' open circuit ".) One question which remains open at this point is the possible contribution of the Faradaic impedance for photohole transfer to the measured decay time: In the CdSe/ polysulphide system, the measured Rseries for an etched electrode was found to be simply the sum of bulk SC and solution ohmic resistances. More experiments with different hole acceptors are required to clarify if RF can have any direct effect on such photocurrent decay curves, or if the larger Helmholtz capacitor acts as a short during fast transient measurements, Z .Harzion, N. Croitoru and S. Gottesfeld, (a) Bull. Israel Phys. Suc., April 1980, (b) extended abstract of the 3rd Int. Conf. on Photochemical conversion and storage of Solar Energy, Boulder, Colorado, August 1980. When Rout < Xi,, Prof. W. J. Albery (London) said: Although in this work Perone et al. have sim- plified the equivalent circuit in fig. 1 of their paper to that given in fig. 2, I would like to ask if these new techniques will be able to measure the different elements of the more complicated circuit in fig. 1. Results from a.c.impedance techniques are often difficult to interpret and it would be helpful if your more direct technique could be used to obtain values of C,, and C,, for instance. Prof. H. Gerischer (Berlin) said: The coulostatic technique is certainly the most powerful technique for studying fast electrode reactions at metals. In the case of semiconductors, however, I believe that a serious limitation arises from the presence of a Helmholtz double layer and a space-charge layer which act as capacitors in series with respect to the potential distribution. The potential changes which are observed directly during the light pulse must be attributed to the charge separation occurring in the space-charge layer of the semiconductor. Electron-hole pairs generated therein will be separated immediately and generate a counter-voltage which can be observed externally.If minority carriers drift from the charge-free bulk to the space-charge layer, there might consecutively be a further potential change in the same direction due to a further increase of the surface charge. However, I cannot see how one can distinguish whether the electric charge stays on the surface of a semiconductor or moves further through the Helmholtz double layer in connection with an electro- chemical reaction. Electrostatically, this means that the electric charge which acts as counter-charge to that one accumulated in the bulk of the semiconductor is moving only a few Angstrom further apart. If the space charge layer is extended over 100 and often more A, this latter step can only cause a negligible variation of the overall potential drop which can be measured externally.Therefore I believe that no con- clusion can be drawn from these experiments on the charge-transfer reaction occur- ring at the interface.108 GENERAL DISCUSSION Prof. R. S. Davidson (London) said: We have observed transient overshoots of photocurrent with photosensitive electrodes made by depositing powdered titanium dioxide on platinum meshes.' The magnitude of the overshoot was dependent upon the electrolyte. Has Prof. Perone found the magnitude of his transient phenomena to be affected by the type of electrolyte used? H. H. Chambers, R. S. Davidson, R. R. Meek and R. M. Slater, J.C.S. Faraday I, 1979, 75, 25 17. Prof. A. J. Bard (Texas) said: To amplify on the comments of Prof.Davidson on the effect of electrolytes on transients observed at Ti02, let me add the following. Such transients occur on a much longer time-scale than those discussed in the paper by Perone et al. They are more significant at polycrystalline Ti02 and largely arise from the effects of recombination processes caused by the reduction of photogenerated oxidants which are reduced via surface states at the Ti02. They are much less promi- nent when electrolytes which do not produce oxygen (e.g., oxalate, acetate) are em- ployed. Your work demon- strates that very short photocurrent pulses can be observed when the cell time-constant is very small. Your work also shows that the time-dependence of the photocurrent pulse is dictated by the cell internal RC time-constant if no longer-lived current- producing processes occur. Thus, your observations are completely consistent with our studies which state that time-resolved potentiostatic photocurrent measurements are limited (assuming infinitesimally short light pulses) by the cell internal time-con- stant, specifically by RUG',, when C,, < Cdl.In your work I believe the values for R, and C,, were ca. 10 SZ and 10-20 nF, respectively, and your observed photocurrent pulses exhibited half-widths of ca. 100 ns, which is totally consistent with our statement regarding limitations on potentiostatic photocurrent measurements. On the other hand, open-circuit measurements of photopotential transients (which we call '' coulo- static-flash " experiments) are not subject to the same limitations.If the cell is treated as a voltage source with internal resistance Ri, the limiting rise-time is defined by the time-constant, RiCM, where CM is the total capacitance in parallel with the measurement probe. CM includes stray interelectrode capacitance (typically 20 pF), cable capaci- tance and measurement amplifier input capacitance. In our studies to date, we have found CM to be ca. 50-100 pF, and have used cells with Ri < 100 R. Thus, we have conducted experiments where the measurement rise-time is < 10 ns and the time resolution is limited by the pulse width of the nitrogen laser source (ca. 10 ns). Secondly in response to Prof. Albery I comment that we did provide a derivation for the response of the more complicated circuit of fig.1 to a potential step or to the equivalent step induced by a pulse photocharge. The goal was not to provide a tool to obtain better measurements of C,, or C,,, but rather to define the cell time-con- stant limitations to potentiostatic photocurrent measurements with a pulsed-laser source. An additional fringe benefit of this work is pointed out by your comment. That is, we can estimate RC,, and (R + R,,)C,, from the shape of potential-step current-time curves. From our experience, the A.c.-bridge techniques provide much more precise measurements of cell component characteristics. However, the poten- tial-step measurements at least demonstrate the time domains over which the cell electrical characteristics remain constant and where the transitions occur.Such measurements provide a complementary perspective on cell characteristics and em- phasize the need for variable-frequency a.c.-bridge measurements. They are also directly meaningful for pulsed photocurrent measurements. Prof. S. P. Perone (Indiana) said: I turn first to Mr. Harzion.GENERAL DISCUSSION 1 09 Thirdly in reply to comments by Prof. Gerischer I would remark that: (A) With regard to possible problems related to high laser intensities, we have been guided by the following facts: (1) Even though peak power can be high for our 10 nS pulse (up to 1 mW cm-2), the equivalent C.W. power is kept low ( < 1 mW) with a repetition rate of ca. 1 Hz. (2) We confine our studies to regions of laser intensity low enough to avoid saturation or other non-linear effects.(For these studies the upper limit was 10 kW cm-2). (3) The potential dependence of the " photoeffect '' is the same with pulsed laser irradiation as for low level C.W. irradiation. (4) We do not observe any long-term deterioration in the electrochemical behaviour or physical appearance of the Ti02 electrodes. Thus, we conclude that, at least for these electrodes under the conditions employed here, no perceptible physical damage occurred due to pulsed laser irradiation. Also, we have avoided irradiation conditions in this work where saturation or non-linear effects might distort the results. (B) With regard to the possibility that the time dependence of observed photo- potential transients might reflect primarily hole-electron recombination, I believe that this certainly must contribute some part of the observed behaviour.However, several other processes may also contribute.' These might include: charge transfer, space- charge relaxation, and long-term re-equilibration of electrode/solution Fermi levels. (C) With regard to coulostatic-flash experiments we agree that the change in the open-circuit cell potential with a light pulse does not in itself indicate charge transfer to the solution. Indeed, an initial negative excursion would occur with a 10 ns light pulse due to the production of electron-hole pairs and their separation. Simultan- eously, the double layer at the electrode-solution interface would become re-oriented to reflect the new potential field. However, if charge transfer to solution occurs sub- sequently, additional negative charge will enter the space-charge region of the semi- conductor, causing a further negative excursion of the electrode potential.Because we do not observe this subsequent step with Ti02 electrodes, one might conclude that charge transfer to solution is simultaneous with the light pulse, giving only a single step. We have conducted coulostatic-flash experiments with Ti02, where current- doubling reducing agent (tiron) was added to the solution. We observed concentra- tion-dependent enhancement of the initial photopotential excursions (up to double the response), with essentially the same rise-time, equivalent to the rise-time of the laser pulse (< 500 ns). Because response enhancement could only result from charge transfer to solution, these experiments demonstrated that we could measure the effect as a further negative excursion of the photopotential. One cannot infer that the charge-transfer rate is large if the recombination rate is fast, because charge transfer might only be allowed to occur during the light pulse.Thus, the efficiency of charge transfer would be directly related to the rate constant(s), but no characteristic time dependence would be observed. Our results to date with CdS electrodes suggest that charge-transfer processes after a 10 ns pulse can cause a slower negative photopotential excursion beyond that related to initial light-induced charge separation. This conclu- sion is based on observed correlations between recombination luminescence decay and the time dependence of the coulostatic-flash photopotential.Dr. J. H. Richardson (California) said: Prof. Gerischer has a good point in asking if the laser coulostatic technique is only monitoring physical processes occurring within the semiconductor and not measuring the rate of charge transfer across the interface. So far we have interpreted our results largely within a framework of physical processes occurring within the semiconductor and at the surface [electron-hole generation, separation and recombination, hole drift and diffusion, surface reactions (" extrinsic holes ")I. However, with regard to his specific comment concerning the capacitance110 GENERAL DISCUSSION differences between the space-charge region and the double layer, we saw only one potential step (< 10 ns) even with highly doped TiOt electrodes where the space-charge capacitance approached that of the double layer (to less than an order of magnitude difference).This would imply that the rate constant for charge transfer is also <lo ns. A different approach to measuring charge-transfer rates would be by spectroscopic techniques. While not a direct measurement of the charge-transfer rate, our time- resolved luminescence measurements may be thought to monitor Faradaic processes which must kinetically compete with radiative and non-radiative recombination. The observed longer luminescence lifetimes with CdS electrodes at negative potentials where hydrogen is being evolved may reflect a slower rate of chemical reaction at the interface. If so, that result is also consistent with a rate of charge transfer being of the order of 10 ns.Prof. H. Gerischer (BerZin) said: I address my remarks to Dr. Spriinken and his co-authors. It is surprising that such a large cathodic photoeffect has been observed in these experiments. I suppose that in this cathodic potential range a considerable dark cur- rent was already flowing through the interface. My question is: Have you measured the transient during a light pulse and seen that there is no relaxation in it which could cause misleading interpretations of the effect seen with lock-in techniques. Have you a satisfying explanation for the occurrence of these cathodic photoeffects ? Dr. M. D. Archer (Cambridge) said: Taking up the same theme, I notice that you mention in your paper that you have observed cathodic photocurrents resulting from the diffusion of dissolved oxygen to the electrode, as well as those resulting from the presence at the electrode surface of adsorbed oxygen produced by prior photoanodic generation.We have also observed cathodic photocurrentswith a well-defined poten- tial-independent plateau that apparently result from reduction of dissolved oxygen at a titanium-doped n-cobalt ferrite electrode in oxygen-saturated 1 mol dm-3 KOH, and will shortly publish the results. A preliminary investigation of the mass-transport characteristics of this photocurrent, using a rotating-disc electrode and oxygen or ferri- cyanide in solution, shows that the photocurrent declines considerably as the rotation speed is increased from 0 to 2000 r.p.m., but it becomes virtually independent of rota- tion speed above 2000 r.p.m.Independence of photocurrent and rotation speed is predicted both by your hypothesis that oxygen adsorption on the electrode determines the photocurrent, and by the hypothesis of Vandermolen et al. [your ref. (17)], that the saturation photocurrent is determined by rate-limiting capture of electrons from the conduction band by electronic surface states. However, neither model accounts for a decline in photocurrent between 0 and 2000 r.p.m. The photothermal hypothesis of Decker et al.' does not fit the form of our transient data either. I wonder if you have any feeling as to the role of mass transport in your observa- tions ? F. Decker, J. F. Julioa and M. Abramovich, Appl.Phys. Letters, 1979, 35, 397. Dr. W. Gissler (Zspra) said: Questions have been asked concerning the origin of the " anomalous " cathodic photocurrent which was observed in n-type Ti02. Such anomalous photocurrents have also been observed with other semiconductors and were recently discussed for p-type trigonal selenium.' Anomalous photocurrents occur together with relatively large dark currents which are caused in n-type semi- conductors by an electron transfer from the conduction band to the interface uia tunnelling through the space-charge layer. The dark current is increased if the tunnel-GENERAL DISCUSSION 111 ling probability is increased by narrowing the space-charge layer. This occurs in potentiostatic experiments by illumination due to an increased space-charge carrier density and it might be caused also by a Fermi-level pinning effect.In both cases the resulting current increase is no real photocurrent. A better description might be " light-induced dark-current enhancement." W. Gissler, J. Electrochem. SOC., 1980, 127, 1713. Dr. P . Pichat (Villeurbanne) said: I would like to comment on the oxygen species occuring at the U.V. illuminated Ti02 surface in 02. From photoconductivity measurements as a function of oxygen pressure, we infer- red the existence of 0- adsorbed species in addition to that of 02- species.' More- over, these 0- species are also formed on other U.V. illuminated n-type semiconductors, such as Zr02, ZnO, Sb204 and CeO,. Support for the formation of these dissociated oxygen species and their importance in photocatalytic oxidation reactions was recently gained from a study of NO interaction with illuminated TiO,.' Nitrogen oxide, which captures surface free electrons, decomposes yielding N, and N20.The resulting oxygen atoms were evidenced by the photocatalytic oxidation of alcohols over Ti02 in the presence of NO. Furthermore, we found3 that the oxidation of I- and Br- ions in illuminated aqueous suspensions of Ti02 requires the presence of dissolved O2 and a mechanism involving 0- species was tentatively suggested. In conclusion, con- cerning the effects of oxygen on illuminated Ti02 we agree with the authors, but we think that 0- species must be considered. ' J-M. Herrmann, J. Disdier and P. Pichat, Proc. 7th Znt. Vac. Congr. and 3rd Znt.Conf. Solid Surfaces ed. R. Dobrozemsky et al. (F. Berger und Sohn, A-3580 Horn, Austria, 1977), vol. 11, P. Pichat, H. Courbon, J. Disdier, M-N. Mozzanega and J-M. Herrmann, 7th Int. Congr. Catal., Tokyo (Japan), 1980, preprint F 7. J-M. Herrmann and P. Pichat, J.C.S. Farday Z, 1980, 76, 1138. p. 951. Dr. A. J . Nozik (Colorado) said: With regard to the problem of determining the flat-band potential from Mott-Schottky (MS) data, I would like to report on some recent work done at SERI that shows one must be very careful in interpreting these types of plots. Mott-Schottky data obtained from TiO, crystals that were prepared by the usual method reported in the literature (polished, etched, reduced or just polished and reduced) invariably showed non-linear MS plots and dispersion effects.However, if these crystals were then re-ground with 600 grit Sic paper and etched in concentrated H2S04 at 150-160 "C, the MS plots became perfectly linear and showed no dispersion. The measured flat-band potentials were consistent with literature values, and showed the expected pH dependence. These ideal MS plots were found to be dependent on the electrolyte concentration. At concentrations of 0.10 mol dm-3, the MS plots showed large dispersion effects; the ideal behaviour was not ob- tained until the electrolyte concentration exceeded 1 .O mol dm-3. However, it was also possible to obtain linear Mott-Schottky plots that yielded very negative x-axis intercepts; this was achieved by just grinding the crystals after reduction, without the H2S04 etch.These types of plots always showed dispersion effects, but the intercepts were still always anomalously negative, These very negative flat-band potential values (up to 1 V more negative than expected) were found to have no signficance with respect to photocurrent-voltage curves. The onset potential for anodic photocurrent was found to be the same for crystals showing ideal MS plots and for those showing anomolous MS plots. The lesson to be learned here is that the flat-band potential from MS plots can only112 GENERAL DISCUSSION be considered valid if the plots are perfectly linear, show no significant dispersion effects, and also show a reasonable pH dependence. MS plots that are simply linear at one frequency cannot be used to define the flat-band potential.With regard to the pH dependence of the flat-band potential, it was found that for several types of boules (Al-free, prism grade, optical grade) it varied from 57 mV/pH unit to 67 mV/pH depending on the boule type. The scatter of flat-band potential data in the literature is believed to be related to this generally uncontrolled or un- reported variable. Prof. J. 0’ 111. Bockris (Texas) said: Does not the Butler and Ginley approach to the determination of the fiat-band potential (iL, V ) relation essentially imply that the surface states are sufficiently low so that one is the inner p.d. dominant state?’ This and other assumptions are tacitly behind the Butler and Ginley deduction of their approach to ffat-band determination. However, there is an increasing amount of evidence that surface states in high concentrations do frequently appear on certain crystal planes of the semiconductor-solution interface.Thus, I would like to draw attention to some unpublished work of my former graduate student, Dr. J. F. McCann, who found that for numerous cases of photo- electrochemical reactions involving oxides (e.g. , In,O,), the difference between the Mott-Schottky flat band potential and that indicated by the intersection of the iph with the potential axis differed by up to 900 mV.2 Nevertheless, one must be cautious of attributing the difference always to surface states. As McCann showed, it may be in- terpreted also in terms of the effect of surface recombination. This would be another reason for not accepting the results of the Butler and Ginley approach to flat-band potential determination until much prior knowledge had been gathered about the interface concerned. This situation draws attention to the poverty of our present possibilities for the measurement of flat-band potential.The Mott-Schottky plot (when it does not vary with frequency) offers no smooth path. Is it affected by fast surface states? Is the Helmholtz capacitance correctly allowed for? (This may be increasingly difficult with a higher degree of surface states. What of the true area?) One of our principal lacks is methods of determining the flat-band potential. There are some dozen methods of determining the potential of zero charge at solid- solution interface^.^ Some of these could be turned into flat-band potential deter- minations.Thus, Bard and Handley have shown that Gockhshtein’s piezoelectric method can be used for this p u r p o ~ e . ~ ~ ~ Would the friction method be applicable?6 But note that determination of the flat-band potential without a knowledge of the surface states is like a determination of the potential of zero charge without knowledge of specific adsorption. M. A. Butler, J. Appl. Phys., 1977, 48, 1914; D. S. Ginley and M. A. Butler, J. Electrochem. SOC., 1978, 125, 1968. J. F. McCann, Ph.D. Thesis (Flinders University of South Australia, 1980). J. O’M. Bockris and S. U. M. Khan, Quantum Electrochemistry (Plenum Press, New York, 1979). A. Yu. Gokhshtein, Elektrochim., 1966, 2, 1318; Electrochim. Acta., 1970, 15, 219; Doklad. Akad. Nauk S.S.R., 1971, 200, 20.J. O’M. Bockris and R. K. Sen, Surface Sci., 1972,30, 237. Dr. D. S . Ginley (New Mexico) said: As Prof. Bockris has mentioned, the measure- ment of flat-band potentials can be fraught with difficulty. This is true not only because of the difficulties of the measurement techniques themselves, but because even the most stable materials we seek to measure may in fact be time variant. This is * A. J. Bard and L. Handey, J. Electrochem. SOC., 1980, 127, 338.GENERAL DISCUSSION 113 due not only to changes in the species adsorbed on the surface but to actual changes in the near-surface stoichiometry. We have found that the electromigration of ions across the semiconductor-elec- trolyte interface can play a large role in determining electrode properties. The field in the depletion region is only ca.1 V but this potential is dropped over a distance <1 pm. This gives rise to electric fields of lo4 V cm-l and larger. These fields are large enough to promote the movement of ions across the interface. Both materials have Fig. 9 illustrates the crystal structures for TiOz and Gap. FIG. 9.-Crystal structures for (a) rutile [OOl] and (b) zincblende [110]. 0 0 0 0 0 0 I , O f 0 0 . . I 0 0.1 0.2 0.3 0.4 0.5 0.6 depth/pm Change in donor profile in the near surface region after ageing. FIG. 10.-Doping profile of TiOz wafer anodically aged (+5 V, 30 h).114 GENERAL DISCUSSION TABLE DEPENDENCE OF Vfb ON AGEING CONDITIONS FOR SrTi03 bias illumination conditions" V&' US. SCE anodic anodic cathodic cathodic virgin -1.11 on +5 V us.SCE -1.15 PCb 21 h PC 4 days on +1 V us. SCE - 1.15 virgin -1.17 Off 0.2 mA-CC" 25 h - 0.95 Off 0.2 mA-CC 21 h - 0.96 a The anodic and cathodic ageing experiments were done consecutively, PC, potential control; tromigration will be of consequence predominately for positive ions since the radii of all negative ions are too large to allow entrance into the channels. Fig. 10 illustrates the doping profile of an anodically aged TiO, wafer. When run anodically, the field in the depletion region is such so as to force the removal of Ti3+ interstitials. This ageing phenomenon gradually reduces the doping level in the near- surface region, widening the depletion region allowing for the collection of electron- hole pairs from photons with a longer wavelength and deeper penetration depth.This in effect red-shifts the photoresponse. The donor distribution can be restored by thermal annealing of the sample. Since the number of atoms removed from the depletion layer is small, no change in electron affinity and consequently flat-band poten- tial is associated with this form of ageing. Substitutional doping is the only obvious way to avoid this problem. CC, current control. I 300 350 wavelength Inm 400 FIG. 11 .-Changes in the photoresponse associated with the cathodic ageing of the electrode: 1 , virgin Sr-Ti03; 2, cathodically aged (2 mA-CC for 25 h); 3, 0.0 V us. SCE for 27 h.GENERAL DISCUSSION 115 Table 1 illustrates that under cathodic ageing conditions the situation is substanti- ally different.Here the potential is such as to drive small positive ions into the surface region. This is most pronounced for hydrogen, deuterium and lithium. The top half of the table substantiates that there are no changes in V f b associated with anodic ageing. In the lower half of table 1 for cathodic ageing there is a considerable change in Vfb upon the electroinjection of hydrogen. The initial ageing period is sufficient to saturate the surface so subsequent ageing does not alter Vfb. These re- sults clarify the problem some investigators have had in measuring reproducible flat- band potentials after cathodically cycling their electrodes. Fig. 11 illustrates the changes in the photoresponse associated with the cathodic ageing of the electrode, The overall quantum efficiency is significantly reduced, which suggests that the injected H + significantly increases recombination centre den- sities.Interestingly, anodically cycling the electrode removes a substantial portion of the hydrogen, restoring the photoresponse; thus a significant portion remains, al- though capable of altering Vfb but not the photoresponse. Clearly the effects shown here can significantly alter electrode properties and must be taken into account when measurements are made, especially if they are to take place over any appreciable time span. The forced electromigration of ions may as well be a potentially useful tech- nique for electrode modification. There is a question on the talk presented as well. Is it possible that the observed p-type photoeffect is due to an accumulation effect? Dr.H. S. Jarrett (Delaware) said: We found in our laboratory that the flat-band potential Vfb for pure ( 4 0 ppm impurity) Ti02 crystals as determined from Mott- Schottky plots is in acceptable agreement (<O. 1 eV, but always more cathodic) with the potential V,, where photocurrent begins to flow. These data are reproducible in the same electrolyte over several days providing the electrolyte is kept clean. We define V,, as the potential at which the photocurrent exceeds the dark background current by 0.1 pA for a light flux 2 10'' photons The current characteristics were obtained point by point allowing a few minutes at each potential to attain steady-state conditions. No V,, is seen by this method, although current characteris- tics of the type reported here were seen for scan rates as low as 5 mV s-l.For 0.1 % vanadium-doped crystals, however, the agreement between v f b and V,, is poor. For various samples of n-V:Ti02 cut from the same single-crystal boule, (Vfb - VOcI x0.5 5 0.1 eV with the flat-band potential being more cathodic (see fig. 12). From the analysis of surface capacitance for semiconductors with deep im- purities,' one expects that C-2 is not linear, but has a maximum2 at a potential below flat-band corresponding to the energy of the filled acceptor state. The figure indicates such behaviour, although a clear maximum is not found but only an inflection and change of slope. In addition, the theory predicts that the two straight line segments of C2 above and below the maximum should both extrapolate to v f b as they do in this figure, which is for a fresh electrolyte sample.However, we also find that this be- haviour is not always obeyed and that over a period of several hours the more shallow segment of C - 2 tends to curve and become even more shallow so that the potential ob- tained by extrapolation to Cm2 = 0 of this more shallow segment moves to more cathodic potentials. Extrapolation of the steeper segment remains within 0.1 eV of v f b of the fresh sample. Such behaviour seems also to have been observed by Kennedy and Frese3 for m-Fe203, which should also have deep levels caused by the various valence states of iron. Despite these variations in capacitance, VOc remains constant and the entire cur- In their case, I V,, - VOcI is of the order of 0.2 eV.116 GENERAL DISCUSSION rent characteristic remains unchanged.Note, however, that vanadium doping seems to increase electron-hole recombination, and the photocurrent quantum effi- ciency is reduced by about two orders of magnitude from pure TiO,. H. S. Jarrett, A. W. Sleight, H. H. Kung and J. L. Gillson, J. Appl. Phys., 1980, 51, 3916. J. F. Dewald, Bell Systems Tech. J., 1960, 39, 615. J. H. Kennedy and K. W. Frese Jr, J. Electrochem. SOC., 1978, 125, 723. FIG. 12.-Plot of C against V for 0.1 % vanadium-doped crystals. N = 1.2 x 1020, pH = 2.6. Dr. M. A. Butler (New Mexico) said: Several people have raised the question about the usefulness of photocurrent onset potential Yo, as a measure of the flat-band poten- tial Vfb. I would like to point out some of the limitations of using V,, and some of the advantages.After all we are interested in obtaining the maximum amount of information about a specific semiconductor-electrolyte interface rather than having a blind tool for measuring flat-band potentials. The use of an (I2, Y ) plot as previously proposed’ has built into it a number of assumptions: (1) monochromatic light, (2) optical absorption depth c(-l much larger than depletion layer thickness W and (3) a uniform donor distribution. This first assumption is important as white light results in a spectrally weighted photoresponse which will not necessarily satisfy condition (2) and should not be ex-GENERAL DISCUSSION 117 pected to yield a linear (Z', Y ) plot. The second condition allows expansion of the full expression for the photocurrent : leC(1 - GL} and thus fulfils the conditions necessary for a linear (Z2, V ) plot.It also restricts the light to energies just above the bandgap. The third condition has become more important since ion migration has been re- cognized as a mechanism which generates non-uniform donor profiles. Finally re- combination at midgap states in the near surface region of the semiconductor can also result in disagreements between Yo, and Vfb. The important point is to consider disagreement between V,, and v f b not as an insoluble problem but as new information which will provide better insight into the properties of the semiconductor-electrolyte interface. Here we assume that V,, is Perhaps this can be best illustrated by fig.13. I 2 / vo " vfb V FIG. 13.-Plot of I 2 against V : (A) surface region is depleted of donors; (B) near-surface recombina- tion processes. determined by a linear extrapolation of an (Z', V ) plot and that Y f b is determined by some other means such as Mott-Schottky plot. In (A) we show the kind of behaviour that is observed when the near-surface region is depleted of donors. While the actual photocurrent onset occurs at v f b , extrapolation of the linear part of ( I 2 , V ) gives an intercept at more negative (positive) potentials for N(P)-type semiconductors. In (B) we illustrate the kind of behaviour expected with near-surface recombination pro- cesses. Here Vf, and V,, determined from a linear extrapolation agree but the actual photocurrent onset is at more positive (negative) potentials for N(P)-type semiconduc- tors.Thus these kinds of comparisons can provide insight into the properties of the interfacial region. It should be pointed out that the breaks in the curves are not al- ways as clear-cut as illustrated. Care must be taken to make measurements over a large enough potential region so that one is not deceived as to what is the true linear portion of the curve. M. A. Butler, J. Appl. Phys., 1977, 48, 2019. M. A. Butler, J. Electrochem. SOC., 1979, 126, 338.118 GENERAL DISCUSSION Prof. N. Armstrong (Arizona) said: I address my remarks to Drs McAleer and Peter. It should be made more clear that the titanium surface, as these authors have pre- pared it, probably consists of a gradient of oxide phases, from Ti02 at the very surface, to sub-oxide phases beneath, and finally the pure metal itself.We initially pointed this out as the authors indicated in ref. (15) of their paper, but enlarged the discussion in J. Electrochem. SOC., 1978,125, 1790. The (current, voltage) behaviour in fig. 1 of their paper can therefore be interpreted as the oxidation of a sub-stoichiometric oxide region extending to a thickness of up to ca. 50-60 A, followed by the formation of a true oxide-metal interface. Our initial experiments indicated that this transition occurs at ca. 1.5-1.7 V us. SCE which is notable when one considers the change in photocurrent response that they observe in this same potential region. I think that this fact should lead to a certain degree of caution in the interpretation of film thicknesses, since these are based upon assumptions of film stoichiometry which are not always well-under- stood.Prof. W. P. Gomes (Gent) said: In fig. 7 of their paper, the authors find the inter- section of the Mott-Schottky plot with the Y-axis ( Yo) to be ca. 1 V more negative than the photocurrent onset: and attribute this discrepancy to the contribution of the Helm- holtz layer to the (capacitance, voltage) behaviour. Now, assuming that the Helm- holtz capacitance C, is voltage-independent, the relationship between Vo and the flat- band potential Vfb can be expressed by: kT &o&eNd Yo = Vf, + 7 - ___ 2 cg * Using the data from the paper, i.e., & = 60, Nd = lo2' C M - ~ and c, = 40 pF cm-2, one finds a value of ca.-25 mV only for the last term in the foregoing expression. Hence, if one wants to interpret the difference between Yo and the photocurrent onset in this manner, one would have to assume a much lower value for C, (2: 6 pF cm-2). Dr. L. M. Peter (Southampton) said: Prof. Gomes has pointed out that our calcu- lation of the double-layer capacity is in error; a value of 6 pF cmm2 is indeed obtained from fig, 7 of our paper if E f b is assumed to be -0.3 V us. SCE. However, the flat- band potential cannot be obtained from the extrapolation shown in the figure, even when the small shift due to the potential drop in the Helmholtz layer is allowed for. We neglected to point out that the plot changes slope close to the flat-band potential, and to illustrate this we have plotted in fig.14 more data obtained at potentials below 1.5 V us. SCE in the measurement. E f b is seen to be close to -0.3 v us. SCE. The change in the slope of the Mott-Schottky plot, which has also been noted by Potter' in this discussion, can be interpreted as evidence for a two-level donor system or alter- natively in terms of a spatially inhomogeneous distribution of donors. Both cases have been treated in detail elsewhere.2 R. Potter, Firudiy Disc. Chern. Soc., 1980, 70, 124. J. F. McAleer, Ph.D. Thesis (University of Southampton, 1980). Dr. D. S. Ginley (New Mexico) said: Two questions come to mind concerning the (1) Is it really possible to measure the film thickness by this technique if the doping Clearly there is a validity of the techniques employed to measure the film thickness.level and composition of the film change as a function of depth?GENERAL DISCUSSION 119 0 -0.5 0 0.5 1 .o V/V us. SCE FIG. 14.-Mott-Schottky plot for the oxide film grown at 1 mV s-l to 5.4 V us. SCE in 1 mol dm-3 H3P04. The plot includes additional data points not shown in fig. 7 of our paper, and shows clearly a change in slope close to Efb. whole region of suboxides at the growth interface. As well, one expects that Ti3+ interstitials will age out of the interface under mild conditions. Is there any observed increase in the long-wavelength response associated with depletion-layer widening ? (2) Many people have observed the ph,otostimulated instability of Ti02 films in acidic media at potentials <6 V. Have the authors evaluated their films for stability and how does this affect their other measurements? Dr.L. M. Peter (Southampton) said: The determination of the film thickness by the method outlined in our paper should be insensitive to the doping level in the oxide. In fact, we have shown that the doping distribution is essentially homogeneous for slowly grown films. The point is that the photocurrent is measured during film growth, i.e., under conditions where the depletion region extends throughout the en- tire film (an excess charge is necessary on the metal to bring about film growth in the first place). The donor density and distribution should not, therefore, influence the photocurrents directly. We agree that lower oxides are probably present adjacent to the metal, and this point is discussed in our paper (see fig.5). We have also studied the photostimulated breakdown and growth of TiO, films on titanium, but we do not believe that the effect is important at the low intensities used in our work. The intact nature of the films below 2 V us. SCE is adequately demonstrated by the ideal behaviour of the (l/C, E ) relationship. At higher potentials, the breakdown phenomena discussed in our paper are not sensitive to illumination at the low intensities used for photo- current spectroscopy. Dr. M. Froelicher (Paris) said: We are in fair agreement with the authors on the occurrence of some modification in the oxide at ca. 1-1.5 V, at least in the electrolytic medium with which we are working, i.e. 0.5 mol dm-3 sulphuric acid.We observe that the optical indices of thicker anodic films have been measured,' which could lead to a better choice for al. However, the main point under discussion is not this choice of at, but some discrepancies in the hypothesis and conclusion of the argu- ment. The authors assume that the film has the optical properties of Ti02, then that120 GENERAL DISCUSSION it is Ti02, and they conclude that it “ may not be TiO, at all ”. In this case, what can be the significance of the chosen a2. In fact, in sulphuric acid, we proved from electroreflectance data that the film keeps this TiO, nature down to the corrosion poten- tial, and probably, it is the growth law which is modified, maybe in relation to incom- plete disappearance of native oxide, the rutile modification of Ti02, which can then present a different electrochemical behaviour than does anodic anatase.G. B. Blondeau, M. Froelicher, M. Froment and A. Hugot-Le Goff, Thin Solid Films, 1977,42, 147. Dr. L. M. Peter (Southampton) said: We cannot agree with Dr. Froelicher that our argument is inconsistent. We have made it abundantly clear in our paper we set out to test whether the thickness could be determined using the a2 values for Ti02. The success of this approach is evident in fig. 5 of our paper which shows how the thickness data obtained by analysis at different wavelengths fall onto a common plot. There can be little doubt that we are dealing with Ti02 here. We introduced the hypothesis that a lower oxide may be present at lower potentials in order to explain the late onset of the photocurrent during the growth scan; apparently the first 2 nm or so of the film are photoinactive.It is this film which “ may not be TiO, at all ”. The change in growth law suggested by Froelicher as the origin of the break in slope of the (apparent thickness, potential) plot (fig. 5) should also give rise to a change of slope in the ( l / C , E ) plot at the samepotential. We have not found this to be the case, and prefer a model in which the “ TiOz film could . . . grow at the expense of the underlying photoinactive oxide ”. Dr. M. A. Malati (Chatham) (communicated): The results presented in some figures of Dr. Peter’s paper (e.g., fig. 6 might) have been affected by the presence of &Pod. In a continuation of our study of the photoinduced oxidation of normal primary alcohols by anatase,’ we have noticed that when a Degussa anatase P25 was pretreated with H3P04, the yield of Ti3+ ions produced in n-butanol dropped from 1.5 x loe3 mol to ca.mol in 60 min as a result of the pretreatment2 This has been ascribed to the adsorption of phosphate at the Ti4+ surface sites., The specific adsorption of phosphate and of sulphate by P25 has been previously rep~rted.~ The photoenhanced decomposition of KMn04 solution in presence of Ti02 (anatase or r ~ t i l e ) ~ has been also in~estigated.~ A Tioxide sample of rutile, CLDD/ 1124,6 was shaken with H3P04 (1 mol dmm3) and then washed and irradiated with Hanovia chromatolite lamp as a suspension in KMn04 solution (1.99 x mol dm-3). The rate of photodecomposition dropped from 2.2 to 0.86 pmol min-’ as a result of the pretreatment with H3P04.’ This may be also ascribed to the adsorption of phosphate on the rutile surface.A. D. Buss, M. A. Malati and R. Atkinson, J. Oil Colour Chem. ASSOC., 1976, 59, 369. M. A. Malati and N. J. Seager, J. Oil Colour Chem. Assoc., in press. R. Flaig-Baumann, M. Herrmann and H. P. Boehm, Z. Anorg. allg. Chem., 1970,372,296. V. V. Sviridov and L. V. Potanina, Dokl. Akad. Nauk Beloruss. SSR, 1968, 12, 813. M. W. Rophael and M. A. Malati, Chemie f i r Labor und Betrieb, 1981, in press. M. A. Malati and A. E. Smith, Powder Technol., 1979, 22, 279. ’ R. Cobb, unpublished results. Dr. L. M. Peter (Southampton) (communicated) ; Although the effects of pH changes on the flat-band potential of Ti02 have been widely investigated, less is known about the influence of anion absorption.The systems described by Dr. Malati are notGENERAL DISCUSSION 121 \ - Gaertner "<approximation - \ strictly comparable with ours since we are usually concerned with the saturation photo- current obtained when surface recombination processes are unimportant. However, we have observed that the stability of the films is sensitive to the anion present in acid and it is clear that further study of anion adsorption on oxides is needed. J. F. McAleer, Ph.D. Thesis (University of Southampton, 1980). * J. F McAleer and L. M. Peter, to be published. Dr. H S. Jarrett (Delaware) said: These comments are addressed to Dr. Gautron and his colleagues. I have obtained a theoretical expression for the photocurrent density at the surface of an illuminated Schottky barrier by first solving the diffusion equation for photo- injected minority carrier density with finite lifetime, 7,.The solutions are subject to the boundary conditions that at the surface the minority carrier current is proportional to the minority surface-charge density and that the carrier density and its gradient are continuous at the barrier/bulk interface. For sufficiently high potential, the photo- current efficiency is always unity, and the behaviour observed by Gautron et al. would not be observed. However, such potentials can never be attained because inversion or tunnelling would occur first. Therefore, one must consider the photocurrent effi- ciency at some practical potential below the onset of inversion, say, 1 V beyond fiat- band potential for a semiconductor such as Ti02. At such potentials, various intrinsic and extrinsic parameters defining the semi- conductor now play a role in the photocurrent efficiency.One important parameter that emerges from this analysis is a characteristic time T,, the transit time across the rl 0.4 0.3 0.2 0.1 0 lo-' 1 10 lo2 lo3 Ni IN1 FIG. 15.-Plot of q against Ni/Nl: aLp = 0.1, V = 0.1 eV. Schottky barrier, which is inversely proportional to the impurity concentration, Ni. As Ni increases, z,, which may exceed z, at low impurity concentration, can become shorter than z, at the higher concentrations. For Z,/z, B 1, photocurrent efficiency is low because minority carriers are lost by recombination within the barrier during the long time these carriers take to traverse the wide barrier.For z,/ z, - 1 , the barrier narrows, and the minority carriers now traverse the bar- rier in a time comparable with or shorter than the time to recombine. Thus, the photocurrent efficiency increases with increasing impurity concentration. However, this trend cannot continue without limit. For zt/z, < 1, my expression for the photocurrent reduces to that originally122 GENERAL DISCUSSION obtained by Gaertner.' At such high impurity concentrations, the barrier is so narrow that although all carriers generated within the barrier traverse it before recombining, most of the minority carriers are generated in the bulk of the semiconductor because the penetration depth of light into the semiconductor greatly exceeds the barrier width.The bulk is field-free, and these carriers do not contribute to the photocurrent but remain in the bulk where they are lost by recombination. Thus, the photocurrent efficiency becomes low again after having passed through a maximum at intermediate concentrations. This behaviour, which is demonstrated in fig. 15, is qualitatively similar to that found by Gautron et al. The efficiency is determined at 1 V into the depletion region. NJN, is the impurity concentration normalized to N,, the impurity concentration at which z,/ z, is unity. All intrinsic parameters, z,, carrier mobility, diffusion constant, optical absorptivity, and surface transfer coefficient are assumed to be independent of impurity concentration.' W. W. Gaertner, Phys. Rev., 1959, 116, 84. Dr. M. A. Butler (New Mexico) said: I would like to comment on the nature of the sub-band-gap response shown in fig. 6 of the paper by Lemasson et al. Recently1 we have considered this photoresponse in Ti02 and SrTi03 in some detail with respect to the mechanism responsible for it and its spatial origin. It exhibits the following characteristics : (1) a linear dependence on light intensity, (2) a square-root dependence on the potential across the semiconductor and (3) the quantum efficiency to the two- thirds power is linear in photon energy. The potential dependence has been inter- preted as indicating a bulk origin from states uniformly distributed throughout the depletion layer. This follows directly from the dependence of depletion-layer thick- ness on potential,' and supports the identification of these states with defect states.The linear dependence on light intensity, even under laser illumination at > 200 mW cm-2, suggests that a two-step photoexcitation process is likely since it is doubtful that impurity-band conduction through the deep levels would be large enough to sup- port the kind of photocurrents observed. Such a two-step process can give a linear dependence for real intermediate states with appropriate lifetimes. This simple idea has been further developed using density of states arguments with simple parabolic bands to explain the observed spectral dependence. M. A. Butler, M. Abramovich, F. Decker and J. F. Juliao, J . Electrochem. Soc., 1981, 128, 200.* M. A, Butler, J . Appl. Phys., 1977, 48, 1914. Dr. P. Lemasson (Meudon) said: The existence of a sub-band-gap photoresponse with a diminishing degree of reduction is correlated to a lower donor concentration together with a more important role of the acceptors. The latter influence the sub- band-gap photoresponse strongly. As a consequence of the method of sample pre- paration we used, these acceptors are certainly distributed uniformly in the bulk; this uniformity exists right up to the surface. From the above, it follows that our explanation of the observed sub-band-gap photoresponse by a tunnelling of holes inside the energy band (level) of acceptors can be considered as possible. However, as suggested by Butler, a two-step absorption mechanism is equally pos- sible.In all the cases the problem of positioning the level(s) concerned within the for- bidden gap remains.GENERAL DISCUSSION 123 Dr. S. Ginley (New Mexico) said: (1) Has an examination been made of the de- pendence of quantum efficiency on wavelength ? The longer wavelengths penetrate more deeply and should be a better probe of the depletion layer than the short wave- lengths employed in the study. (2) Is the added Cr in your Ti02 electrodes acting simply to increase the density of impurity levels? How is the above-band-gap photo- response for the TiO, affected by Cr addition? Dr. P. Lemasson (Meudon) said: The photocell efficiency has been measured for wavelengths up to 410 nm. However, at 335 nm, the wavelength at which the results presented above have been obtained, the penetration depth of the light is always suffi- cient in comparison with that of the space-charge region.for a band- bending V, = 1.8 V, corresponding to the measured V,, (this gives the minimum value of V, and consequently of W in our measurements). For all values ND > (ND)o, the penetration depth I is larger than W. Following our experimental results, doping by chromium does not seem to influence the sub-band-gap photoresponse. An interpretation of the above may be that incorporation of chromium in Ti02 is equivalent to a reduction of the solid: it leads to the creation of autocompensating oxygen vacancies and not to acceptors (titanium vacancies). The consequence of the preceding remark is that during the incorporation of chromium the density of the impurity levels concerned remains unchanged.The above-band-gap photoresponse has not been studied by us in detail and in the present state of our experiments we cannot give reliable information concerning the influence of doping by chromium. The usually assumed relation lo = l/cco leads to (ND)o = 3 X loL8 Prof. A. J. Bard (Texas) said: The reported flat-band potentials (and hence the location of the energy levels for Ti02) appear to be quite different from those given by most authors. For example, in 1 mol dme3 H2S04, the reported value of V,, in this paper is -1.6 V us. saturated mercury sulphate electrode which corresponds to ca. -0.95 V 21s. NHE. In most studies' the position of Vfb in 1 mol dm-3 acid has been located at ca.0 V us. NHE. This finding is important since production of hydrogen at counter-electrodes in n-TiO, cells does not occur very readily and the production of oxygen appears to occur via processes in the valence band involving the formation of hydroxyl radical. Based on the potentials and energy-level diagram given here, hydro- gen formation should occur quite easily but hydroxyl formation would not be possible. See, for example, W. P. Gomes and F. Cardon, in Semiconductor Liquid-Junction Solar Cells, ed. A. Heller (Electrochem. SOC. Proc., Princeton, N.J.), vol. 77-3, p. 120. Dr. P. Lemasson (Meudon) said : The flat-band potential value we assume and that usually assumed are both indicated in the energy diagram presented in fig. 16. The short-circuit and open-circuit potential values experimentally determined have been used in the determination both of the band bendings and of the position of the metal Fermi level.It then appears that the Fermi level in solution lies between the levels corresponding to the H+/H2 and OH-/02 couples. With both flat-band potential values, the working of such a photocell may similarly be explained by a photogalvanic pr0cess.l J. G . Mavroides, D. I. Tchernev, J. A. Kafalas and D. F. Kolesar, Mater. Res. Bull., 1975, 10, 1023.124 GENERAL DISCUSSION 2p++H20-1/20,+ 2H+ T i 0 2 - x e l e c t r o l y t e metal pH =14 FIG. 16.-Energy diagram of a photocell with TiOz anode with two different band bendings corres- ponding to V,, and Vs, and with two possible flat-band potential values: Vfb (our measurements) and V'fb (Gomes measurement).The latter corresponds approximately to the energy level of couple H+/H2. Reactions occurring both at the anode and at the cathode are mentioned as in ref. (l), previous page. Mr. R. Potter (Southampton) said: The use of Mott-Schottky plots to determine flat-band potentials is not without danger. In particular it is necessary to measure capacitance data over a range of frequencies and over a sensible range of potential. Fig. 17 illustrates a set of Mott-Schottky plots which we have obtained for a hydrogen- reduced rutile specimen which has been prepared by the methods described by Dare- Edwards and Hamnett.' The change in slope which is evident in the Mott- Schottky plots could well have remained undetected if data had not been taken at potentials below this point.An extrapolation of the upper part of the plots would clearly lead to an erroneous value of the flat-band potential. We attribute the change in slope of the Mott-Schottky plot to a two-level donor state; the ratio of the slopes is close to 2 : 1, suggesting that a two-stage ionisation of titanium interstitials or oxygen vacancies may be involved. We cannot completely exclude the possibility that the results may be due to a spatial inhomogeneity in the donor distribution, but the ratio of the Mott-Schottky slopes and the sharpness of the discontinuity make this unlikely. The quality of the crystal surface is demonstrated by the exact correspondence of the flat-band potential with the onset of the photocurrent (fig.18), and this proves that the flat-band potential of the rutile sample in 1 mol dm-3 H2S04 was +0.2 V vs. NHE. The unusually negative Efb values found by Gautron et al. may therefore result from the way in which the Mott-Schottky plots in fig. 2 of their papers are extrapolated. M. P. Dare-Edwards and A. Hamnett, J. Electoanalyt. Chern., 1979, 105, 283. Dr. A. Hamnett (Oxford) (partly communicated): I would like to make several comments on the paper by Gautron et al. The authors have reported studies on the effects of doping level on the photoelectrochemical properties of rutile in the sub- stoichiometric (TiOz.J region. Implicit in much of their interpretation is the assump-GENERAL DISCUSSION 3-01 125 0 0 o n I 2.5 2 .o N 1 . 5 z 2 . N rj 1 . O 0 .5 0 0.0 0.5 1 .o 1.5 2 .o V/V us. SHE FIG. 17.-Mott-Schottky plot for single-crystal rutile. Preparation: Etched 1 : 1 (NH4)2S04 + HzS04, reduced in H,at 650 "C. Electrolyte 1 mol dmd3 H2S04. Frequencies: 0,110; 0, 1 kHz. tion that the nature of the defect centre does not alter as x increases. However, there is little evidence for this assumption. Indeed, recently James' has reviewed at length the defect equilibria in TiOz and his conclusions are that in the very slightly sub- stoichiometric region (x lo-^) Schottky disorder dominates, the effective point defect being an oxygen-ion vacancy. At higher values of x , the dominant defects are (132) shear planes that order for x 2 0.02. It seems likely that such shear planes are in kinetic equilibrium with isolated Ti3+ interstitials, but that such ions are in rela- tively small concentration. The first point to be made is therefore that the multitude of equilibria possible in TiOzPx makes it unlikely that any conceptually simple model will suffice to explain all the data.The second point concerns the erroneous flat-band potential predicted from fig. 2 of the paper. In materials with complex defect structure, such as Ti02-x, the flat-band potential cannot be obtained by extrapolation of the Mott-Schottky plot from a poten- tial region remote from flat-band. In the presence of deep traps that may ionise in126 GENERAL DISCUSSION the surface region in the presence of an anodic bias, it can be shown2v3 that a kink in the Mott-Schottky plot is to be expected. The potential at which the change in slope occurs provides a rough estimate of the trap energy, and from the data of Gautron et al.an energy ca. 1 eV below the conduction band is found for the lightly reduced samples, reasonably 100- 90 - 8 0 - 70- 6 0 - 9 5 0 - e W 40 - 30 - 2 0 - 1 0 - close to that expected for a singly occupied oxygen vacancy. 0 0 0 0 0 0 0 0 0 0 1 I I I V/V us. SHE I 0 .o 0.5 1.0 1.5 2.0 FIG. 18.-Photocurrent conversion efficiency, a, as a function of voltage for the same crystal in 1 mol dm-3 H2S04. Wavelength 330 nm. Additional evidence for the presence of deep traps is provided by the authors’ own con- ductivity data which shows a drop of ca. 2 units as the temperature falls from 1100 to 300 K. The third point I wish to make concerns the efficiency curve plotted in fig.3 of the paper. The authors state that the optimal efficiency corresponds to a value of the depletion-layer width equal to the reciprocal absorption coefficient. This is greatly oversimplified. Transport of minority carriers depends on the interplay of mass and field-assisted mechanisms and the relative importance of these depends in turn on the minority-carrier diffusion length L, and the electrochemical rate constant ko at the surface. Recently we have treated this problem theoretically allowing for recom- bination in the depletion layer, and it has emerged that only for very restricted ranges of these parameters should a maximum in efficiency with ND be seen. The authors’ own data of fig. 3 cannot be fitted by this formula. Instead we have fitted the efficiencyGENERAL DISCUSSION 127 for ND values below ca.2 x 10l8 cm-3 and have obtained values of ca. 7 x cm for L, and 0.04 cm s-' for ko assuming Jarrett's value of cm2 s-' for the diffusion coefficient for holes. These values are quite reasonable, but they do not predict a maximum efficiency with ND. There are two possible explanations for the sharp fall- off. First, the maximum in efficiency corresponds quite well to the first unambiguous appearance of shear planes; in other words, the character of the defects is changing, and such a change will be reflected in the band structure and in such parameters as recombination rates that must be put into the model. This must become significant once the shear planes order. The second possibility is that majority-carrier tunnelling may become significant for large values of ND, The oxidation of water is not a one- electron process and easily-reduced high-energy intermediates are likely to be in- volved.The back reduction of these species by electrons tunnelling through the de- pletion layer from the bulk becomes increasingly likely as the depletion layer contracts with increasing donor density. The fourth point is that the effects of mechanical polishing can only be removed by high-temperature (700 "C) reduction and annealing followed by extensive etching using a strong etchant such as boiling concentrated sulphuric acid.' Finally, we have also observed small sub-bandgap photocurrents in lightly doped SrTiO,. Recent p.e.s. data from this laboratory on the spinel system Lil+x Ti2--x04 have revealed that the formation of oxygen vacancies gives rise to electronic states ca.1 eV above the 0 2p band. It is quite possible that holes created in such levels in TiOz and SrTiO, can tunnel to the surface more rapidly than electron recapture can occur. Above this doping level, the photocurrent vanishes in SrTi0, as well as Ti02, and since the dominant defect in SrTiO, remains an oxygen vacancy, this sug- gests that the authors are correct in assuming that recombination becomes too fast. We have seen much larger sub-bandgap photocurrents in Cr-doped SrTiO,, the initial optical process here being undoubtedly a Cr3 + -Ti4+ charge-transfer.6 However the structural chemistry of Cr doped into SrTi0, is quite different from Cr doped Ti02.In the latter case shear structures form even at very low concentrations of Cr. R. James, Disorder and Non-stoichiometry in Rutile and Corundum Structured Metal Oxides AERE Harwell, Technical Publication 814 (1979). V. A. Myamlin and Yu. V. Pleskov, Electrochemistry of Semiconductors (Plenum Press, New York, 1967). J. H. Kennedy and K. W. Frese, J. Electrochem. SOC., 1978, 125, 723. W. J. Albery, P. N. Bartlett, M. P. Dare-Edwards and A. Hamnett, J. Electrochem. SOC., to be submitted. M. P. Dare-Edwards and A. Hamnett, J. Electroanalyt. Chem., 1979, 105, 283. G. Campet, M. P. Dare-Edwards, A. Hamnett and J. B. Goodenough Nouv. J. Chim., 1980, 4, 501. Dr. P. Lemasson (Meudon) said: I thank Drs. Potter and Hamnett for their re- marks, and deal with the various points in sequence.A complete set of experimental results in KOH medium is presented in fig. 19. The following remarks can be made : (1) In the (i, Y ) characteristic, a cathodic current rises at potentials lower than - 1 .O V/e.s.m. As oxygen is present in solution, the corresponding plateau may be attributed to oxygen reduction.' (2) Hydrogen evolu- tion begins at potential values lower than - 1.8 V/e.s.m. ( 3 ) A change in slope appears below - 1 .O V/e.s.m. in the Mott-Schottky plot (capacities being measured at 100 kHz). An extrapolation of this portion of curve, which is indeed not a straight line, leads to a flat-band potential Vfb = - 1.6 V/e.s.rn.128 GENERAL DISCUSSION (4) In the (iph, V ) characteristic, the Yo, value is V,, = -1.5 V/e.s.m. From these observations, the following conclusions can be drawn : (a) The change in slope in the Schottky plot seems to be connected to the rise of a cathodic current.In such conditions, the main question is the validity of a Schottky model because of the perturbation of charge equilibrium. Furthermore, this model assumes the existence of a fully depleted layer and is not applicable for band bendings lower than 0.3 VS3 (arb. units) I - - - - r - - 1 1 * V1e.s.m. FIG. 19.-Dark current (idark) photocurrent (ipb) and Schottky (C2) plots (in arbitrary units) as func- tions of the applied voltage (0. These two reasons explain why we have not chosen to introduce two donor levels in our paper ; such changes in slope exist for many semiconductor-electrolyte junction Schottky plots even in cases where physical measurements indicate clearly the existence of only one donor level.(b) It seems possible to explain the difference that exists between the Yo, and the Vfb values with the help of recent theories concerning the current voltage characteris- tics of semiconductor-electrolyte junctions under ill~mination.~ Besides, in our particular case, suggestions concerning a possible influence of an inhomogeneity of our samples seem ruled out more easily than when samples are reduced in a hydrogen atmosphere. This particular point is developed in that part of our answer concerning the preparation of our samples. (c) If the flat-band potential is - 1.5 V/e.s.m. as usually assumed, it seems difficult to explain how hydrogen evolution takes place only at potentials more negative than - 1.8 V/e.s.m. The quality of the surface preparation for surface recombination rate is closely connected to the etching used after polishing.The etching procedure proposed by Dr. Hamnett, while leading to low surface recombination rates [as proved by the shape of the (photocurrent, potential) charac- teristics] is nevertheless inconvenient for us as it is oxidizing.GENERAL DISCUSSION 1 29 Because we needed an electrode surface with the same stoichiometry as the bulk, we used a poorly oxidizing etchant which was not sufficient to remove completely the mechanically damaged layer. As mentioned in our paper, there seems to be an incompatibility between obtaining a surface presenting the property we needed and obtaining a good efficiency, i.e., a low surface recombination rate.In this range, the shape of conductivity and thermogravimetry isotherms may be ex- plained, as usual, by means of a point defect m0de1.~ For x > 0.01, large discon- tinuities occur, both in conductivity and thermogravimetry isotherms, indicating the existence of new phases (Magneli From fig. 1 in our paper, it is clearly pointed out that we are not in this region. After the quenching of our samples, they were investigated with the electron microscope and it was shown that there are no shear planes in them.8 At room temperature, it is quite evident that shear planes exist only when passage from high to low temperature is sufficiently slow that a point defect reorganization is possible. It then seems logical to assume the existence at room temperature of point defects (donors + acceptors), in an ionization state different from that at high tem- perature and with relative amounts depending on the degree of reduction.Conse- quently, the samples of Ti02-x we have studied here are all included in the mono- phasic domain of rutile. Finally, the way in which our samples were prepared, as explained in our paper and completed by the previous explanation concerning the nature of defects, indicates that they have a very good spatial homogeneity during the high-temperature equili- brium. This is not true for samples reduced in vacuum or in a hydrogen atmosphere which are usually used in electrochemical experiments. At high temperature, the non-stoichiometry range lies between < x < ' P.Clkhet, C. Martelet, J. R. Martin and R. Olier, Electrochim. Acta, 1979, 24, 457. ' P. Lemasson, A. M. Baticle and P. Vennereau, Surface Sci., 1976, 59, 177. V. A. Myamlin and Yu. V. Pleskov, Electrochemistry of Semi-conductors (Plenum Press, New York, 1967). J. Reichman, Appl. Phys. Letters, 1980, 36, 574. P. Kofstad, Non-stoichiometry, Diflusion and Electrical Conductivity in Binary Metal Oxides (Wiley, New York, 1972). J. F. Baumard, D. Panis and A. M. Anthony, J. Solid State Chem., 1977, 43, 20. J. S. Anderson and A. B. Khan, J. Less Common Metals, 1970,22, 219. * M. G. Blanchin, P. Faisant, C. Picard, M. Ezzo and G. Fontaine Phys. Stat. Solidi (a), 1980,60, 357. Dr. H . R. Sprunken (Kiel) said: There appears to be an inconsistency concerning the relation between light penetration depth, " best " doping density (N,) and photo- efficiency.As shown in fig. 6 (c) of Gautron's paper the influence of the doping den- sity of photocurrent will be small for a wavelength A < 340 nm. In contrast a strong influence is shown in fig. 3 with a maximum efficiency around ND = 5 x 10'' cm-j. Similar dependences on doping densities have been observed previously by Tamura for ;1 = 400 nm irradiation' and by us using white light.2 On the other hand if the results shown in fig. 3 were obtained with A = 355 nm3 corresponding to the light penetration depth l/m0 = lom5 cm the authors used for their (ND)o calculation the observed efficiency should include a 30% contribution from diffusion provided Lp 21 2 x cm is assumed.This contribution would be negligible only for photon energies close to the band gap, i.e., around 400 nm. I wonder whether Gautron et al. have applied corrections for this diffusion. Do they agree that their calculated value of (ND)o = 3 x 10l8 cm-j is not the " best '' doping density for other photon energies, i.e., other penetration depths l/ao?130 GENERAL DISCUSSION If one calculates the " best " doping density ND for irradiation with light close to the band gap, a density of ND 2: 2 x 1014 is obtained'*2 in contrast to the experi- mental findings. Do the authors consider in their discussion in addition to weak electric fields in the space-charge layer also processes via surface states to be responsible for the small efficiency observed for the low doped materials? Reactions mediated by these surface states would become more pronounced the smaller the doping density of the semiconducting electrode and thus the electric field of the depletion layer.' H. Tamura, H. Yoneyama, C. Iwakura, H. Sakamoto and S. Murakami, J. Electrounulyt. Chem. Interfacial Electrochem., 1977, 80, 357. H. R. Sprunken, R. Schumacher and R. N. Schindler 2nd. Int. Conf. Photochem. Conversion and Storage of Solar Energy, Cambridge, (1978), extended abstracts. D. M. Eagles, J. Phys. Chem. Solids, 1964,25, 1243. Dr. P. Lemasson (Meudon) said: In the case of the work cited as ref. (2) in the above question, it seems that anodes are not constituted by well-defined oxides. Indeed, the electrodes are prepared by thermal oxidation of Ti foils in air and some comments can be made : (1) The electrode surface, essential to determine the Mott-Schottky slope, is not easy to determine with good precision.(2) The thickness of the layers is not precise but it does not seem impossible for a 400 nm wavelength, a value at which penetration depth of light is approximately 10 pm, that the metal background will be reached by light, thus leading to multiple reflexions in the oxide layer. (3) Homo- geneity for such samples is quite questionable. In our case, the materials 'are massive in form and, as previously indicated, the assumption of homogeneity seems realistic in regard to the preparation used (see the answer on this subject to Dr. Hamnett). During measurement at fixed potential value of the (photocurrent, wavelength) characteristic, no noticeable modification of the shape in relation to the Ti02-x substoichiometry has been observed: in each case, a smooth maximum is found around 340 nm.In these conditions, the arguments developed on this question regarding the ND value for the maximum efficiency are ruled out. So far as the influence of minority-carrier diffusion on the photocell efficiencies is concerned, we are not certain that it will be important in comparison with space- charge region generation. A model which includes bulk recombination has recently been developed1 leading to diffusion being less important. An influence of the wavelength value of incident light (corresponding to energies higher than the forbidden gap) on the position of the maximum may be expected but our purpose here was to locate this maximum, if it existed, given that for each N,, value the photocurrent is a maximum at a given potential value.Although some discrepancies exist between the different results, it is interesting that in three different works on Ti02 electrodes (this one and the two cited above) a maximum efficiency has been observed at relatively similar N,, values. The dif- ferences between the three sets of results may certainly be accounted for by the dif- ferent types of electrode preparation used by the respective authors. ' J. Reichman, Appl. Phys. Letters, 1980, 36, 574. Prof. W. J. Albery (London) said: I would like to comment on the explanation offered by Gautron et al. for the maximum shown in their fig. 3. In collaboration with Dr. Hamnett, we have recently solved the differential equation describing the transport and kinetics of photogenerated minority carriers, including recombinationGENERAL DISCUSSION 131 in the space-charge layer.’V2 A rigorous solution can be obtained in terms of confluent hypergeometric functions, but we have shown that a good approximate solution is:- where, in addition to the symbols in Gautron’s paper 8, = eV,/kT, k = D/Lp,2 and k’ (in cm s-l) describes the reaction of the holes at the surface of the semiconductor. In the denominator the term in L, describes loss of holes from the surface by recombi- nation in the field-free region. Because of the large value of 8, this term can be ig- nored. The term in W describes the loss of the holes in the space-charge region. For the reasons stated by Gautron et al., q can show a maximum as W is varied. However, the condition R,W = 1 suggested by them is too simple, since the position 20 g E- 10 0 0 0 I I I 1 0 ’ ~ 1 OI6 10” NDlCrn - FIG. 20.-Variation of q with ND. The points are taken from fig. 3 of the paper of Gautron et a/. The curve is calculated from eqn (1) using the values of the parameters in the text. of the maximum must also depend on k’, k, 8, and L,. It is also true that the maxima predicted by eqn (1) are not nearly as pronounced as are the experimental results in fig. 3 of their paper. Fig. 20 shows the best fit that I can obtain to the points in fig. 3 of the paper, where I have used the following parameters:- ROW = 0.50 UOL, = 0.04 and k’/cco D = 1.1. In this case the condition for R,W is similar to that suggested by the authors, L, is smaller and using the value of D suggested by Jarrett3 we obtain a plausible value of k’ of 10 cm s-l.132 GENERAL DISCUSSION W. J. Albery, P. N. Bartlett, M. P. Dare Edwards and A. Hamnett, J. Electrochem. SOC., sub- mitted for publication. H. Jarrett, Faruduy Disc. Chern. Soc., 1980, 70, 121. ’ W. J. Albery, Chem. SOC. Rev., to be published. Dr. P. Lemasson (Meudun) said: I now respond to comments by both Prof. Albery and Dr. Hamnett. For the reasons mentioned in the answer to Dr. Ginley on the penetration depth of light into the semiconductor, the whole space-charge region is penetrated by light in our photocell measurements. Of course, it is difficult to discuss the physical model proposed in the questions for the reason it is not yet published and not available to us. However, some further remarks can be made: (1) The experimental points plotted in fig. 3 of our paper are reliable and are not in question. (2) The observed maximum is less pronounced when efficiency is measursd with sintered photoanodes. This case corresponds to a very low L, value. (3) The L, value given by the fitting proposed by Prof. Albery which presents a maximum, seems unrealistic (L, = 4 x lo-’ cm) whereas the rate constant (ko = 10 cm s-’) seems probable. (4) In the calculation proposed by Dr. Hamnett, only a very small number of our experimental points is involved and if the L, value (7 x cm) is acceptable, the rate constant (ko = 0.04 cm sdl) seems too low. (5) The shape of the photocell characteristic reported in fig. 5 of our paper can be explained by means of the model proposed by Reichmanl in the case where recombinations in the space-charge region are negligible. The de- crease in efficiency with increasing ND values can then be accounted for by the increase of bulk recombinations as light penetrates more deeply than the space-charge region: this is the case for ND Concerning specifically the &, values, we measured them for the three different types of electrodes we used, following the method proposed by TyagaL2 The results are 3 x lo1’ ~ r n - ~ . single crystals etched: L, fi 2 x cm single crystals etched + polished: L, E 2 x cm sintered electrodes : Lp 21 8 x cm These results seems to indicate that even the L, value used by Dr. Hamnett in his fitting is inadequate as long as our efficiencies in fig. 3 correspond to the second type of electrodes. l J. Reichman, Appl. Phys. Letters, 1980, 36, 574. V. A. Tyagai, Fiz. Tverd. Telu, 1964, 6, 1602.