Capacitance flatband potential

In addition to the use of open-circuit photopotentials, the variation in interfacial capacitance with electrode potential can be utilized to determine the flatband potential as well as the semiconductor dopant concentration. A discussion of the capacitance-potential response of the semiconductor-electrolyte interface is beyond the scope of this text. The reader is referred to Reference 7 for a more complete discussion of this subject. 

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. 

Oskam et al. [66] have used IMPS to investigate the role of surface states at the n-Si(lll)/NH4F interface. In this case, the redox reaction is simpler, and appears not to involve holes trapped at surface states. This is probably due to the presence of a surface oxide layer. Electron transfer is evidently exceptionally slow in this case, since these authors observed a modulated photocurrent even at potentials far from the flatband potential where recombination is expected to be negligible. Accumulation of holes modifies the potential drop across the Helmholtz (and presumably also surface oxide region), leading to a capacitive charging current. This effect has also been treated in more detail by Peter et al. [71]. 

Thus, a plot of (Csc) 2 vs. B should be linear with an intercept at the flat-band potential. This linearity can be used as an immediate test of the theory and an example is shown in Fig. 20 for p-GaAs [62]. The capacitance derived from the two-component circuit is almost independent of frequency for potentials more than 0.5 V from the flat-band potential and the intercept is clearly defined. Similar results for both n-GaAs and p-GaAs are shown in Fig. 21 [63] and an important check on the theory is that the flatband potentials for the n- and p-type electrodes differ by ca. 1.4 V, corresponding to a bandgap of 1.4 eV for GaAs. This is expected as the Fermi level will be very close to the band edges in the bulk for these wide band materials. 

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],...

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 capacitance of the depleted interface reaches a maximum in the flatband condition. Measuring the flatband potential t/g, of die elech ode on same scale as LJ ofdie redox couple, and knowing the forbidden gap and the offset (AE in Fig. 4.24) of the semiconductor Fermi level from the majority carrier band edge, enables andE p " to be placed on a common scale. 

Figure 12.17 compares the capacitance response of the sihcon/fluoride solution interface at pH 1.3 with the potential-modulated microwave response. The shoulder in the capacitance curve due to svface states is absent from the microwave reflectance curve. The Mott-Schottky plot for ARm extends to the flatband potential, whereas the plot of 1/C deviates in the region where the surface-state capacitance becomes important. Comparison of the capacitance and microwave responses allows deconvolution of the surface-state capacitance (Schlichthorl and Peter, 1994 and 1995). 

The use of Eq. (10.3) assumes that the semiconductor-electrolyte interface is ideally capacitive and can be represented by the solution resistance, and the interface capacitance, C, in series. However, such an interface is almost never purely capacitive and must be represented by the CPE. This leads to different slopes at different frequencies and sometimes different values of the flatband potential. An example of such a behavior is shown in Fig. 10.3. It is evident that measurements at different frequencies display different intercepts and slopes, and, as a consequence, different fb and Ad-... 

Capacitance-potential relationship to reveal information on the energetic position of semiconductor bands and surface states, especially the flatband... 

Helmholtz capacitance - For samples with very high donor densities, the space charge capacitance may become so large that it is no longer possible to ignore the Helmholtz capacitance, Ch, which has a constant value of 10-20 pF/cm. The effect on the Mott- chottky curve is a shift of its slope to more negative potentials (for photoanodes). This means that the slope itself is unaffected and can still be used to determine the donor density. The flatband, however, shifts by an amount given by [52]... 

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