Flatband potential measurement

Stationary microwave electrochemical measurements can be performed like stationary photoelectrochemical measurements simultaneously with the dynamic plot of photocurrents as a function of the voltage. The reflected photoinduced microwave power is recorded. A simultaneous plot of both photocurrents and microwave conductivity makes sense because the technique allows, as we will see, the determination of interfacial rate constants, flatband potential measurements, and the determination of a variety of interfacial and solid-state parameters. The accuracy increases when the photocurrent and the microwave conductivity are simultaneously determined for the same system. As in ordinary photoelectrochemistry, many parameters (light intensity, concentration of redox systems, temperature, the rotation speed of an electrode, or the pretreatment of an electrode) may be changed to obtain additional information. 

The Helmholtz potential, [7h, which depends, of course, on the composition of the electrolyte, can be determined quantitatively by flatband potential measurements using Eq. (16). A strong pH dependence has been found for most semiconductors. Especially in the case of oxide semiconductors, the pH dependence has been measured quantitatively. Such experiments have yielded a shift of 0.059 V/pH as shown by various authors. These results indicate that the adsorption or bonding of hydroxyl groups determines the behavior of the Helmholtz layer. A pH dependence has also been observed for some III-V compounds " and II-IV compounds. In these cases, however, hydroxyl groups are not necessarily the potential-determining species. For instance, Ginley and Butler identified such species to be HS and H at CdS electrodes. ... 

Figure 26. Dependence of function 4K.AU) [relation (19)] and of /

This is a relation in which PMCfl, the photoinduced microwave conductivity signal at the flatband potential, is measured and the rest of the constants are known. 

Otherwise, the effect of electrode potential and kinetic parameters as contained in the relevant expression for the PMC signal (21), which controls the lifetime of PMC transients (40), may lead to an erroneous interpretation of kinetic mechanisms. The fact that lifetime measurements of PMC transients largely match the pattern of PMC-potential curves, showing peaks in accumulation and depletion of the semiconductor electrode and a minimum at the flatband potential [Figs. 13, 16-18, 34, and 36(b)], demonstrates that kinetic constants are accessible via PMC transient measurements, as indicated by the simplified relation (40) derived for the depletion layer of an n-type electrode. 

Roy AM, De GC, Sasmal N, Bhattacharyya SS (1995) Determination of the flatband potential of semiconductor particles in suspension by photovoltage measurement. J Hydrogen Energy 20 627-630... 

Frequently it has been observed with n-type as well as with p-type electrodes in aqueous solutions that the onset potential of the pure photocurrent differs considerably from the flatband potential. The latter can be determined by capacity measurements in the dark as illustrated by the dashed line in the ij — Ub curve in Fig. 8 a. This effect is usually explained by recombination and trapping of minority carriers created by light excitation at the surface. It is obvious that these effects have a negative effect... 

The magnitude of the photopotential is also related to light intensity and to the value of EDARK. The value of Elight cannot obviously exceed the flatband potential. At Dark = Efb, the photopotential drops to zero which can be used for a simple measurement of the flatband potential. 

Figure 28.3 The flatband potential of a semiconductor can be established by measuring the photopotential of the semiconductor as a function of illumination intensity. In the dark (left), the semiconductor Fermi level and the redox potential of the electrolyte are equal, providing an equilibrium condition. However, illumination of the semiconductor (right) generates charge carriers that separate the Fermi level and the redox potential. The difference in these two parameters is the observed photovoltage as shown for an n-CdS electrode immersed in a ferri/ferrocyanide electrolyte (bottom). The measured photovoltage is observed to saturate at the flatband potential. In this case, a value of -0.2 V vs. SCE is obtained. Note that the photovoltage response yields a linear functionality at low light intensity with saturation behavior occurring as the flatband potential is approached.

The photocurrent onset potential is often taken as the flatband potential, since the measurement of the flatband potential is typically only good to 100 mV and the onset of photocurrent is often observed with less than 100 mV of band bending. This practice is dangerous, however, since the onset potential is actually the potential at which the dark cathodic current and the photoanodic current are equal. Even though in the case of the p-GaP illustration, the observation of an anodic current and a photocathodic current are separated by several hundred millivolts, in many systems these two currents overlap. In those cases, the relationship between the flatband potential and the onset potential becomes unclear. 

PZZP), the flatband potential is a direct measure of the semiconductor electron affinity (EA). 

Electroreflectance spectra were measured for n-CdSe in the liquid junction configuration, and variations of the lineshape as a function of potential were observed. As the potential was reduced below the flatband potential, the electroreflectance signals changed sign. The potential at which this change occurs correlates well with the turn-on potential for light-induced photocurrent and with the intercept of the Mott-Schottky plot. 

Different from a single crystal electrode, it is more difficult to measure the flatband potential of a semiconductor powder, which is necessary to estimate the absolute positions of the valence and conduction band edges. However, the suspension method developed by Bard and co-workers (25,26) and modified by Roy et al. (27), allows to obtain this important potential. The method is based on the pH-dependence of the flatband potential of Ti02 [Eq. (2)]. 

Unfortunately, the redox potential of the Pt4 + /3+ couple is not known in literature. Although some stable Ptm compounds have been isolated and characterized (37), the oxidation state III is reached usually only in unstable intermediates of photoaquation reactions (38-40) and on titania surfaces as detected by time resolved diffuse reflectance spectroscopy (41). To estimate the potential of the reductive surface center one has to recall that the injection of an electron into the conduction band of titania (TH) occurs at pH = 7, as confirmed by photocurrent measurements. Therefore, the redox potential of the surface Pt4 + /3+ couple should be equal or more negative than —0.28 V, i.e., the flatband potential of 4.0% H2[PtClal/ TH at pH = 7. From these results a potential energy diagram can be constructed as summarized in Scheme 2 for 4.0% H2[PtCl6]/TH at pH = 7. It includes the experimentally obtained positions of valence and conduction band edges, estimated redox potentials of the excited state of the surface platinum complex and other relevant potentials taken from literature. An important remark which should be made here is concerned with the error of the estimated potentials. Usually they are measured in simplified systems - for instance in the absence of titania - while adsorption at the surface, presence of various redox couples and other parameters can influence their values. Therefore the presented data may be connected with a rather large error. 

The following data were obtained during interfacial capacitance measurements of a single-crystal n-Ti02 electrode in 0.1 MTBAP (tributylammonium phosphate) + CHjCN at a frequency of 500 Hz. Calculate the flatband potential on n-Ti02 in this electrolyte and the concentration ofmajority carriers. Assume e = 86. 

Fig. 11.12. The results of Hall measurements of mobility are shown in Table 11.3. The Mott-Schottky plot showed a flatband potential of -0.23 V on the NHS. Some electrode kinetic measurements (Miller, 1992) are shown in Fig. 11.13.

Fig. 1. Plot of flatband potential vs. pH for different iron(III) oxides in contact with aqueous electrolytes obtained by capacitance-potential measurements. O, Thermal a-Fe203 [24] , single crystal a-Fe203 [25] A, a, thermal a-Fe203 [26, 27] , passive iron [28] I, passive iron [29] x, passive iron [30],...

The measured potential Vm, and thus jEf and K. can be varied through external polarization. Vm is the applied potential when the electrode is externally polarized and is the open-circuit potential without external polarization. When the semiconductor has no excess charge, there is no space charge region and the bands are not bent. The electrode potential under this condition is called the flatband potential Vn,. The flatband potential is an important quantity for a semiconductor electrode because it connects the energy levels of the carriers in the semiconductor to those of the redox couple in the electrolyte and it connects the paramete s that can be experimentally determined to those derived from solid-state physics and electrochemistry. It can generally be expressed as... 

Therefore, by measuring the flatband potential at pzc, one can determine the energy level of the semiconductor band in an electrolyte relative to the absolute scale or the vacuum scale. The pzc of a silicon electrode in aqueous electrolyte is similar to that of SiOi, at about pH 2.2, since the silicon surface is generally covered with a thin layer... 

Flatband potential is a very important parameter for characterization of a semi-conductor/electrolyte interface as it correlates the band edges to the redox potentials in the electrolyte. It is most commonly determined by measuring the capacitance as a... 

FIGURE 2,25. Capacitance-voltage plot on n- and p-type silicon in a solution of saturated KCl buffered to pH 4. Measurement frequency is 500 Hz. The flatband potentials are also indicated. After Madou et... 

The difference between the flatband potentials ofp-Si and n-Si plus the differences between the bulk Fermi level to the corresponding band edges equal the band gap, 1.12eV when the band edges of the two materials are the same in the solution. Such situations have been observed." " However, in many situations the measurement of flatband potentials ofp-Si and n-Si does not yield the band gap. There are two possible explanations. In one the band edges of p -Si and n-Si may not have the same energy... 

Reaction intermediates are a special group of surface states that can cause band edge shift (or Fermi level pinning). When this occurs, the flatband potential tends to change with current. Figure 2.32 shows that the flatband potential of -type silicon in O.IM K4Fe(CN)6 + 0.5 M KCl changes with photocurrent which induces surface states. The shift of 0.55V shown in Fig. 2.32 corresponds to a density of 2 x 10 cm. This result can be used to explain the difference between the flatband potentials determined by Mott-Schottky plot and by measurement of the onset potential for photocurrent... 

A closely related matter is the measurement and use of the flatband potential. The existing data show that for a silicon/electrolyte interface the flatband potential is specific to the given surface condition. Also, the flatband potential generally drifts due to the fact that the surface of silicon in electrolytes changes constantly with time. Also, it changes with application of potentials which is generally required for the determination of flatband potential. Therefore, any theory which assumes a fixed value of flat-band potential will be limited in its scope of validity. 

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