Flatband conditions

Now we see that the vacuum levels above the same metal M are not equal. The resulting difference is the flatband voltage Vfb which must be externally applied in order to maintain the flatband condition. Thus, the flatband voltage (multiplied by the test charge) equals the difference in the electron work function of Pd and Si. In the nonideal junctions there are other charges and dipoles in this structure that must be added to the overall Vfb. 

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. 

Fig. 5.19 Energy scheme of the n- (left) and p-type (right) semiconductor-liquid interface a) at equilibrium b) under flatband conditions...

It should be emphasized that the previous models only describe the current due to minority carriers. Under near-flatband conditions, the majority carriers start to contribute to the overall current. This can be recognized by an increase in the dark current, and under those conditions (2.64) and (2.65) are no longer useful. Another implicit assumption is the absence of mass transport hmitations in the electrolyte, but this is rarely an issue in photoelectrochemistry due to the high electrolyte concentrations and modest efficiencies reported thus far. Finally, it should be realized that the models described above cannot accormt for recombination at the semiconductor/electrolyte interface. Wilson pubhshed an extension of G tner s original model that included interfacial recombination effects [56]. Although this somewhat complicated model is not often used because it does not account for the dark current and recombination in the space charge, it is of value for metal oxides that show extensive surface recombination. 

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 energy levels in the solution are kept constant, and the applied voltage shifts the bands in the oxide and the silicon. The Gaussian curves in Figure 4b represent the ferrocyanide/ferricyanide redox couple with an excess of ferrocyanide. E° is the standard redox potential of iron cyanide. With this, one can construct (a) to represent conditions with an accumulation layers, (b) with flatbands, where for illustration, we assume no charge in interface states, and (c) with an inversion or deep depletion layer (high anodic... 

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... 

The band diagram of silicon electrode in an electrolyte can be drawn when the flatband potential of the interface is determined. Figure 2.34 shows the band diagrams for various silicon/electrolyte interfaces. As described above, the flatband potential depends on many factors specific to the silicon/electrolyte interface under a given set of experimental conditions, as does the band diagram. 

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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