Evaluation of the Flat-band Potentials by Measurements of Anodic/Cathodic Photocurrent Transitions BY HANS R. SPRUNKEN, ROLF SCHUMACHER AND RALPH N. SCHINDLER Institut fur Physikalische Chemie, Universitat Kiel, Olshausenstrasse 40-60, 2300 Gel, West Germany Received 2nd May, 1980 The photoprocesses on semiconducting n-Ti02 and n-SrTiO, electrodes in the presence of reducible surface species are described. These species are generated by pre-illumination with the band-gap light of the electrodes being operated under reverse bias. The amount formed in the course of this pre- illumination can be re!ated to the negative charge required to reduce them. This charge correlates proportionally with V,,, the voltage at which transition from anodic to cathodic photocurrent occurs. The influence on Vt, of the parameters surface coverage as function of pre-illumination time, wave- length, photon flux and pH of the electrolyte is investigated. The occurrence of the cathodic photoprocess is discussed in terms of an electron-tunnelling mechanism through the space-charge barrier to the solution and a joint model proposed by Bard and Gerischer.The influences of the cathodic photoeffect on the onset potential of the usual anodic photoprocess may affect flat-band potential determinations from curves of iph against V. Experimental evidence is provided that the most reliable values of Vfb from this method can be obtained by scanning from cathodic to anodic potentials. Also irradiation with long-wavelength light, close to the band-gap energy, and high light intensity are recommended.The increased interest in fundamental processes occurring on semiconductor electrodes is well documented in a number of publications which have appeared over the last decade. Further insight into the process is required because of its significance in the field of energy research. One important feature, the determination and evaluation of flat-band potentials Vfb, has attracted particular,research as the knowledge of this parameter is of essential importance for the energy calibration of the semi- conductor-liquid junction.lV2 Various techniques have been suggested for measuring VfbeS7 The most common method utilizes the capacitance shift as a function of the potential drop inside the semiconductor interface. Another method suggested by Butler connects photocur- rent against voltage measurements with the theory of Gartner.g In this case the flat- band position is defined as the potential where the photocurrent starts to flow.The determination of Vfb can be then obtained from plots (iP,J2 against V where iph denotes the photocurrent. The energy position of the flat-band potential has been shown in many cases to be dependent on the nature of the electrolytic solution, e.g., the pH, and on additives such as chalcogenides.l0V1l Because of variation of the pH and the sulphide ion concentration in both cases a shift of 60 mV per concentration decade of [H+] and [S2-] has been found. It is generally agreed that these shifts are caused by surface adsorption of these species. In this paper we report on complications which one may face using the method suggested by Butler to determine Vfb.It will be shown that an additional photo- process occurs when n-TiO, electrodes are operated in the reverse-bias mode and in the presence of reducible species. This cathodic photoprocess may give rise to an apparent onset potential V,, for the appearance of the anodic photoprocess. It will56 FLAT-BAND ANODIC/CATHODIC PHOTOCURRENTS be shown that the cathodic photocurrent is affected by experimental parameters such as light intensity, wavelength, electrolyte pH and the amount of the reducible species present. Influences on V,, of this cathodic process can be minimised by scanning from negative to positive potentials and using long-wavelength light, close to the band-gap energy, of high intensity. The occurrence of the cathodic photo- process is discussed in terms of an electron tunnelling mechanism through the space- charge barrier to the solution and a joint model proposed by Bard and G e r i ~ c h e r .~ * ~ ~ Finally, it should be noted that cathodic photoeffects on n-semiconductors have been reported p r e v i ~ u s l y . ' ~ ~ ~ EXPERIMENTAL Polycrystalline Ti02 electrodes were prepared by oxidation of Ti-foils (Metallwerk Plansee) in an air stream at temperatures between 700 and 800 "C. Before oxidation the specimens were cleaned in acetone, concentrated HzS04 and in HF (5%). Finally they were washed in doubly-distilled water. Different doping densities ND were made by vacuum annealing at temperatures ranging from 600 to 800 "C.TiO, single crystals, purchased from Hrand Djevahirdjian S.A., Monthey were vacuum treated in the same way. Polycrystalline SrTiO, doped with Nb was provided by Philips Research Laboratories, Aachen. Some of the Ti02 and SrTiO, single crystals were kindly supplied by Sandia Laboratories, Albuquerque. The oxides were made semiconducting by hydrogen reduction. Ohmic contacts were obtained with Ga/In. The rear sides of the single-crystal electrodes were insulated by epoxy cement. The electrochemical experiments were performed in a closed-cell arrangement. In order to avoid perturbation of the processes occurring at the working electrode by species generated at the counter electrode (platinized Pt) the compartments were separated with the aid of porous fritted glass discs.IA drops were made negligible by placing the reference electrode close to the working electrode. Flushing of the working electrode compartment with various gases could be arranged through a glass valve placed at the bottom of the cell. The measurements were carried out in 0.05 or 0.5 mol dm-3 H2S04 and 1 mol dm-3 NaOH, respectively, prepared with doubly-distilled water. Measurements at around pH 7 were carried out in 0.5 mol dm-3 Na,S04 solutions which were adjusted by adding H2S04 or NaOH. All chemicals used in this study were reagent grade. The potential of the semiconductor electrode was adjusted and scanned by a Wenking potentioscan POS 73 (Bank Elektronik). The usual scan rate was 2 mV s-l. The illumination of the exposed sample area (0.2 cm2) was performed by a 450 W xenon light source (Osram).The light could be separated into its components using a grating mono- chromator (M 25, Jobin Yvon) and was focused by quartz lenses onto the semiconducting electrodes. For most of the experiments the light was chopped with frequencies ranging from 0.05 to 2 Hz. Photocurrents were amplified with an Ithaco model 391 A lock-in system. Absolute light intensities were measured with a photodiode model OSD 50-1 (Laser Optronic) calibrated to a standard of the U.S. National Bureau of Standards. RESULTS Unexpected changes in the photoresponse of n-TiO, and n-SrTiO, electrodes were observed when the potential of the electrodes was swept from positive values into the cathodic direction (referred to as sweep C ) compared with scans from negative to positive potentials (sweep A).The scan directions are indicated by arrows. The sweeps were recorded with the lock-in amplifier system. Using the calibrated photodiode the output signals were converted into quantum efficiencies, q. As can be seen from sweep C in fig. 1 the direction fo the recorded photocurrents reverses at potentials more negative than -0.1 and -0.5 V This behaviour is illustrated in fig. 1.H . R . SPRUNKEN, R . SCHUMACHER AND R . N . SCHINDLER 57 m F l " " " ' " " " ' 1 I * 0.04- P 0.02 1 , , , , 1 l , , , 1 , . , - 0.5 0 0.5 potential/V 0s. SCE FIG. 1 .-Typical anodic qa and cathodic q' quantum-efficiency-potential curves taken for poly- crystalline n-Ti02 and n-SrTi03 electrodes in H,SO, solution of pH 3 and pH 1, respectively.C and A denote the scan direction. (i) n-Ti02: ND N 2 x 1017 cm-', h = 340 nm. (ii) n-SrTi03: ND N 5 x 10'' crne3, h = 350 nm. During both experiments N, was bubbled through the electro- for Ti02 and SrTiO, electrodes, respectively. We refer to this reductive photo- current as cathodic photoeffect iEh. This photoresponse was observed only for the sweeps C. The decrease of i,"h at potentials more negative than -0.2 and -0.5 V recorded on TiOz and SrTiO, electrodes, respectively, indicates the depletion of species adsorbed on the electrode surface. The reverse anodic scans A taken immediately after sweeps C show no reductive photocurrent iih. These results strongly suggest that photo-oxidized products like oxygen play an important role in initiating this cathodic photoeffect.lyte. - 1 .o -0.5 potential/V us. SCE 0 FIG. 2.-Typical current-voltage diagrams of n-Ti02 (ND 21 5 x 1017 ~ r n - ~ ) in 0.1 mol dm-3 NaOH. Prior to scanning nitrogen was bubbled through the solution. Dashed curve taken in the dark. Solid curve taken under illumination with h = 380 nm. For completeness in fig. 2 current against potential curves are given recorded in the dark and under band-gap illumination. Comparing the results of fig. 1 and 2 differences in the photocurrent curves were found around potentials where reductive dark currents appear. In this context we refer to the literature16-20 on forward cur- rents recorded in the dark under reverse bias.58 FLAT-BAND ANODIC/CATHODIC PHOTOCURRENTS According to a number of author^^'-^^ values for flat-band potentials v f b can be evaluated from photocurrent against voltage (iph against V ) curves.The photo- current onset potential Yo, for the photoprocess is considered to be the true flat-band potential Vfb. However, our results reveal that two different V,, values are found when tracking sweeps A or C. Thus, the determination of v f b from iph measurements seems to be uncertain due to contributions from possible cathodic photoprocesses. For convenience we define the potential where the anodic photoprocess changes over to the cathodic one as the transition potential V,,. In the following we report on experimental parameters which influence Vtr. In order to elucidate the electrode processes leading to the cathodic photoeffect we will also present more experimental evidence on that subject.The growth of the reductive photoprocess is influenced by the time of illumination under depletion conditions. This observation is represented in fig. 3(a) where the potential/V us. SCE 4 illumination timelmin FIG. 3.-Growth of the reductive photoresponse of polycrystalline n-TiO, pretreated at 0.5 V in 0.1 mol dm-3 NaOH as function of illumination time. (a) Behaviour of the anodic i;h and cathodic i&, photocurrents. The illumination times before the scans (2)-(8) were 1,2,3,5, 10, 15 and 40 min. During the experiments N2 was bubbled through the electrolyte. ( b ) Plots of the peak area and the transition potential Iftr as function of the time of The scan directions are indicated by arrows. illumination. photoresponse of an n-Ti02 electrode in the potential range - 1 .O to-0.6 V for various illumination times is plotted.The peak areas obtained in 7 C sweeps are taken as a measure of the value of the reductive photocurrent and plotted as curve (1) in fig. 3(b). A shift of Vt, as a function of illumination time was found only after short-time irradiations The diagram shows rapid initial growth with subsequent saturation.H. R . SPRUNKEN, R. SCHUMACHER AND R . N . SCHINDLER 59 [curves (2) and (3) in fig. 3(a)]. All other sweeps yield identical Vtr values. The change in Vtr is plotted in fig. 3(b) curve (2) as well. The exponential behaviour of curve (1) suggests that the species generated under these conditions are adsorbed on the TiOz surface. From the saturation limit we can obtain some idea of the electrode coverage.Assuming a two-electron process and a particle diameter of 4 A, 0.10 - 0.05- I I I l l I I I I I 1 I , 300 350 400 1 Inm I I I I I 3 00 350 40 0 i /nm FIG. 4.-Normalized spectral responses q" and qc obtained under anodic and cathodic bias in an electrolyte of pH 13. The scan directions are indicated. (a) Ti02: ND FZ 5 x loi7 ~ m - ~ , curves (1) and (2) taken at potentials of 0.5 V, curve (3) at a potential of -0.9 V. (b) SrTi03: ND z 2 x 1017 ~ m - ~ , curve (1) taken at a potential of A0 V, curve (2) obtained at a potential of -1.1 V.60 FLAT-BAND ANODIC/CATHODIC PHOTOCURRENTS an estimate of the number of adsorbed species per unit area yields 8 x lOI3 ~ m - ~ , which corresponds to a coverage of 0.5 monolayer. The valuations are based on coulometric data.Although the description of iih as function of coverage is ade- quately represented by measurements of the peak areas we preferred V,, as appropriate alternative. Fig. 3(6) indicates a reasonable correlation between peak area and Vtr. The stable nature of the species attached to the electrode surface could be proved. Even after a long delay at rest potential between light-off and the beginning of the 0.02 0.01 7 .+ E $ 0 .1. 0.01 c- 0.02 I I I l l l 1 I l l , : I 300 3 50 400 ;i/nm FIG. 5.-Normalized anodic qa and cathodic q" spectral response for polycrystalline n-Ti02 (ND z 5 x 10'' C M - ~ ) recorded at a potential of -0.85 V in 1 mol dm-3 NaOH. The light intensities were increased from time to time [curves (3) to (I)] by a factor of 4.scan into the negative direction the reductive photocurrent remained constant. Also vigorous stirring of the solution close to the electrode before the run did not affect the reduction peak intensity. The wavelength dependence of the photoprocess for polycrystalline n-Ti02 and SrTiO, at potentials positive and negative to Vt, is given in figs. 4(a) and (6). The photocurrents obtained were converted into quantum efficiencies q" and q" and plotted on the ordinate. Pre-treatment of the TiO, electrode for 15 min at - 1.5 V yielded curve (l), fig. 4(a). Electrodes not pre-treated this way showed the behaviour given in curve (2). This behaviour did not change in repetitive scans, whereas the influence of the pre-treated electrodes was of transient nature only. Curve (3) in fig.4(a) describes the cathodic photoresponse at -0.9 V obtained in the same wavelength region as curve (1) and (2). Reproducible cathodic quantum efficiencies were obtained for both scan directions if oxygen was bubbled through the electrolyte. From thisH . R . SPRUNKEN, R . SCHUMACHER AND R . N . SCHINDLER 61 we conclude that the cathodic photoeffect can be stabilized by dissolved oxygen which is supplied to the working electrode. Comparing curves (1) and (2) it is interesting to note that the presence of oxygen on the electrode generated by the anodic photo- process leads to a lowering of qa at short wavelengths whereas qc in the same wave- length region remained considerably higher. As in the case of TiOz the wavelength characteristics of polycrystalline n-SrTi03 were taken when oxygen was bubbled through the electrolyte. The figure shows that SrTiO, behaves qualitatively in the same way as TiO,. However, polarization at -1.8 V did not alter the anodic quantum efficiency at all.Fig. 4(a) and (b) reveal that separation of the photo-oxidation processes can be established by record- ing the spectral response at potentials considerably more cathodic or anodic, respectively, than the transition potential Vtr. Using an We next consider the influence of wavelength and photon flux on V,,. 1’ 1 I 1 - 0.90 - 0 . 8 5 - 0.80 potential/V us. SCE FIG. 6.-Transition potential Vt, of polycrystalline n-Ti02 (ND M 5 x 10’’ ~ m - ~ ) as function of the light intensity at the wavelengths: h(1) = 330, h(2) = 350, h(3) = 370, h(4) = 390 nm.iPh against Vscan obtained at J. = 345 nm the potential V,, was identified as -850 mV. Polarization of the electrode with that potential and illumination with J. = 380 nm resulted in an anodic photoeffect. Fig. 5 demonstrates the photoresponse at V,, = -850 mV recorded with the lock-in amplifier system in the spectral range 280-420 nm. The figure also reveals the influence of light intensity on the photoresponse. As shown the anodic process rises proportionally with the light intensity whereas for the cathodic process saturation was found. More detailed information on the dependence of Vt, on wavelength, photon flux62 FLAT-BAND ANODIC/CATHODIC PHOTOCURRENTS and pH is provided in fig. 6 and 7.Each curve in fig. 6 was obtained for one wave- length but for various intensities. The wavelengths of curves (1)-(4) are given in the figure captions. All measurements were carried out with the lock-in amplifier system. I I I I I I -1 .o 0 2 4 6 0 10 12 14 PH FIG. 7.-Dependence of Von and V,, on pH. Yon represents the onset potential of the anodic photo- current whereas V,, denotes the transition potential obtained on polycrystalline n-Ti02. The differ- ence between Yo, and Vtr depends on experimental conditions. DISCUSSION An evaluation of the flat-band potentials V,, taken from the onset potential of the commencing anodic photocurrent on semiconductor electrodes encounters unexpected difficulties because of an extra photoprocess which can occur under reverse bias.The following discussion is divided into two sections. In the first the experimental results will be discussed in order to elucidate the processes which are responsible for the occurrence of the cathodic photoeffect. The influences of that cathodic photo- process on the determination of the flat-band potential as suggested by Butler* are then discussed in the second section. As most of the results are obtained on poly- crystalline n-TiO, the discussion is centred on that material. However, the results show that the phenomena described can also be observed on polycrystalline n-SrTi03 and on single crystals of both materials as well. CATHODIC PHOTOPROCESSES UNDER REVERSE BIAS EFFECT OF SURFACE AREA As mentioned above, the phenomenon of the cathodic photoeffect observed on polycrystalline n-TiO, and n-SrTiO, also appears on both single-crystal materials.H.R . SPRUNKEN, R . SCHUMACHER AND R . N. SCHINDLER 63 We assume that the less pronounced effects on single crystals compared with the poly- crystalline materials arise from the smaller surface areas. This is supported by the results of fig. 3(a) and (b). Assuming a planar n-TiO, surface which is covered with one monolayer, the calculation for the number of adsorbed particles for the exposed area yields 1.6 x Coulometric determination of the generated species on the same area yields 8 x 1013 particles corresponding to a coverage of 50%. As reported in the 1iteratu1-e~~’~’ coverages in the range 0.5-20% are observed with the solid-gas interface. This discrepancy with our result of 8 x 1013 particles suggests a consider ably higher surface area of the polycrystalline materials used.EFFECT OF REDUCIBLE ADSORBATES DISCUSSED FOR OXYGEN To elucidate the effect of oxygen on the semiconductor-liquid interface we turn first to results found on semiconductor-gas interfaces. Electron transfer from the conduction band of a semiconductor such as TiO, to adsorbed electronegative species has been studied extensively. It seems generally agreed that after oxygen adsorption 0, molecules are f~rmed.~’-~O This species and further reduction products such as OH., H02* were identified in e.s.r. investigation^.^^^^^ On hydrated surfaces in addi- tion OH- and HO, were The formation of negative ions on the surface reduces the mobile electron density [el which affects the space-charge region of the semiconductor.It was demonstrated from conductivity measurements that charge transfer from TiO, to adsorbates, e.g. oxygen, results in a surface p-type c h a r a ~ t e r . ~ ~ ~ ~ ~ As a consequence the work function increases, resulting in an upward band bending. At the same time the electric field at the surface E, strengthen^.^^ This p-type be- haviour could be avoided by additional surface doping using electron donors such as vanadium and niobium.37 The photogenerated forward current in the electrochemical system was only observed when reducible species resulting from either anodic photoproduction or from diffusion of dissolved electrolyte oxygen were adsorbed on the electrode surface. We therefore conclude that in electrochemical systems also electrons are trans- ferred from the conduction band of n-TiO, to reducible adsorbates as discussed for the solid-gas interface.For electrochemical systems further oxygen reduction products and intermediates, especially H202, are discussed in the l i t e r a t ~ r e . ~ ~ * ~ ~ ~ TRANSITION POTENTIAL (Vtr) SHIFTS DUE TO CHANGES I N ELECTRON DENSITY [el AND THE ELECTRIC FIELD E , AT THE SURFACE In this section we explain the observed shifts of V,, in both potential directions by means of changes in [el and E, on the electrode surface. We recall that at the transi- tion potential, V,,, by definition no photoprocesses are observed because all the photogenerated carriers recombine. The concentration of mobile electrons within the depletion region of the elec- trodes can be changed by the following three methods: (i) different adsorbate con- centrations, (ii) illumination with various light intensities using monoenergetic photons and (iii) by varying the wavelength of the incident radiation.All three treatments resulted in a shift of the transition potential V,, (see fig. 3 and 6). We first deal with case (i) where the initial [el is lowered by increasing the adsorbate concentrations at the surface. As mentioned above this successive lowering of [el causes at the same time a rise in E,. It is obvious from the adsorption experiments where E, is increased that the cathodic photoprocess is favoured. This results in64 FLAT-BAND ANODIC/CATHODIC PHOTOCURRENTS a Yt,-shift to more positive potentials, as indeed was observed.According to the results of fig. 3(a) taken from curve (2) the potential V,, (2) = -780 mV was found for the lowest electrode coverage. For the next higher coverage at this potential the electrode showed a cathodic photoprocess [see curve (3)]. This results in a more positive potential V,,(3) = -705 mV. To understand the independence of V,, for higher coverages [curves (4)-(8)] we refer to the Results section. The observations found for case (i) are supported by experiments where [el was changed by illumination, case (ii) (see fig. 6). In contrast to the coverage experiments where [el was successively lowered, the experiments with increased photon fluxes lead to an increase in [el and thus to a reduction in E,. Hence, the potential V,, should move in the opposite direction as compared with case (i), as is supported by the results.The wavelength and intensity dependence of V,, as demonstrated in fig. 6 reveals that V,, is more strongly affected by wavelength than by photon flux. At short wavelengths [A(l) = 330 nm], [el at the surface can be changed considerably by varying the light intensity because all electrons are produced within the penetration depth ( 1 / ~ ) of 30 nm. Increasing the photon flux per unit area from1 x 1013 to 12 x lOI3 hv s-l shifts the potentials Vt, by 65 mV. On the other hand at A(4) = 390 nm this shift yields only 20 mV. At this wavelength the electrons are produced within an ex- tended penetration depth of l/rc = 3000 nm which alters the electron density [el close to the surface only slightly.It then follows that V,, shifts to more negative values for long wavelengths as compared with shorter wavelengths. Of course this is only valid for comparable photon fluxes. It seems to be conclusive that electron generation in deeper regions of the semiconductor does not show up as forward current, because of the reduced probability with which electrons reach the surface. The effect of extra surface doping by niobium and vanadium, 37 as well as by hydro- gen, 41 confirms this tendency. The doping procedures were similar to those noted in the literature. Surface doping caused by in-diffusion of hydrogen as reported re- ~ e n t l y ~ ' . ~ ~ influences qc in the same way as do the electron donors V5+ and Nb5+. Hydrogen can also leave the electrode by diffusion.Accordingly, reversible behaviour of the cathodic photoeffect should be restored, as indeed was observed. These addi- tional dopants increase the electron concentration at the surface and thus diminish the cathodic photoprocess and intensify the anodic one. Our conclusion is that surface doping may also result in a reduction of the E, initially caused by adsorption case (i). This result is unexpected in that an increase in E, which is connected to a higher potential drop at the semiconductor interface favours a forward current and diminishes the anodic photoresponse. One may suggest an electron tunnelling mechanism through the space-charge barrier as being responsible for this cathodic photoeffect. TRANSITION POTENTIAL (Vtr) SHIFTS OWING TO SURFACE STATES The observed shifts of Ytr given in fig.6 can be explained alternatively by models proposed by Bard and Gerischer and used by ~ t h e r ~ . ~ ~ ~ ~ * ~ ~ * ~ ~ In the model of Bard intermediate levels and/or surface states are included to mediate charge transfer from semiconductor to solution states. At V,, the number of electrons which flow from the conduction band via surface states to solution species is equal to the sum of holes which are lost by recombination or in oxidation processes. If the intensity of the light is increased [see case (ii) above] according to Gerischer the quasi-Fermi level of holes is much more affected than isH . R . SPRUNKEN, R . SCHUMACHER AND R . N. SCHINDLER 65 the quasi-Fermi level of electrons.As a consequence the anodic photocurrent is favoured, which results in the observed V,, shift to more negative potentials. To explain the wavelength dependence [case (iii)] using this model we assume that the population probability of the surface states is increased due to electrons photogenerated close to the surface. Electrons generated in deeper regions of the semiconductor (i.e., by low-energy photons) must first diffuse to the surface to be trapped there by the empty surface states. In our case surface states were produced either by anodic photogeneration or by adsorption of dissolved oxygen. The density of these states alters also the cathodic photoeffect (see fig. 3) and simultaneously the qa in the short- wavelength range [see fig. 4(a)]. EVALUATION OF THE FLAT-BAND POTENTIAL As shown in the previous sections the determination of flat-band potentials V f b taken from (iph,V) measurements as proposed by Butler' may lead to significant errors in the present system.In this method the onset potential Yon of the anodic photocurrent determines Vfb. It seems to be established that only in the absence of reducible species produced by illumination under strong depletion conditions does this method yield reliable values of Von and thus of Vfb. Sweeping from positive to negative potentials under illumination leads to an apparent Yon as demonstrated by fig. 1. We referred to this apparent Von as the transition potential Vtr. This V,, was found to depend very strongly on the experimental conditions such as surface coverage with reducible adsorbates, e.g., oxygen, illumination intensity, wavelength and pH-value of the electrolyte.As shown in fig. 7 for Y,, and Yon potentials a shift of 60 mV per pH unit was found, which coincides with the well-known pH shift of Vfb. The difference between Yon and V,, depends on the conditions during the measurement. It seems to be indicated that the most reliable values of V f b can be determined in the absence of reducible adsorbates and using high light intensities and long wavelengths. The former can be verified for n-type material when sweeping from negative to positive potentials. Utilizing photocurrent against voltage measurements according to the methodof Butler 'the flat-band potential is determined by the potential where (iph)2 is zero. This evaluation is restricted to wavelengths much longer than the space-charge barrier and the diffusion length.The above restrictions eliminate the influence on Vfb determinations initiated by the wavelength dependence of the cathodic photoprocess. Additionally, capacity measurements carried out to deter- mine Vf, yielded values close to Van. Note that the plots of 1/C2 against Vwere found not to be linear in most cases. Non-linear behaviour of Mott-Schottky plots has often been described and discussed in the l i t e r a t ~ r e . l ' ~ ~ ~ - ~ ~ Finally note that flat- band potentials for TiO, given in a recent paper of T o r n k i e ~ i c z ~ ~ were found to be ca. 200 mV more negative than the results taken from i:, against Y measurements. The work is supported in part by the Bundesminister fur Forschung und Tech- nologie (BMFT) Bonn, within project ET 4274 A.H. Gerischer, Topics Appl. Pltys., 1979, 31, 1 1 5. R. Memming in ElectroanaIyticaI Chemistry, ed. A. J. 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