Determination of Flatband Potential

In practice, the determination of flatband potential according to the Mott-Schottky equation can be affected by a number of factors, e.g., high doping concentration (i.e., Ch Csc is not valid), the presence of a high density of surface states (i.e.,... 

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. 

G. Redmond D. Eitzmaurige, Spectroscopic determination of flatband potentials For polycrystalline... 

Enright B., Redmond G. and Fitzmaiffice D. (1994), Spectroscopic determination of flatband potentials for polycrystalline Ti02 electrodes in mixed solvent systems , J. Phys. Chem. 98, 6195-6200. 

Redmond G, Fitzmaurice D (1993) Spectroscopic determination of flatband potentials for polycrystalline titania electrodes in nonaqueous solvents. J Phys Chem 97(7) 1426-1430... 

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. 

Plots of C c vs. potential are used to determine the flatband potential, Ups, and the doping density N. ... 

Several techniques can be used to determine the flatband potential of a semiconductor. The most straightforward method is to measure the photocurrent onset potential, ( onset- At potentials positive of (/>fb a depletion layer forms that enables the separation of photogenerated electrons and holes, so one would expect a photocurrent. However, the actual potential that needs to be applied before a photocurrent is observed is often several tenths of a volt more positive than ( fb- This can be due to recombination in the space charge layer [45], hole trapping at surface defects [46], or hole accumulation at the surface due to poor charge transfer kinetics [43]. A more reliable method for determining ( fb is electrolyte electroreflectance (EER), with which changes in the surface free electron concentration can be accurately detected [47]. The most often used method, however, is Mott- chottky analysis. Here, the 1/ Csc is plotted as a function of the applied potential and the value of the flatband... 

According to these results, it is in principle possible to determine the flatband potential (Section 2) by measuring the electrode potential of an Illuminated electrode under open circuit conditions. This method, as will be shown later, can lead, however, to rather inaccurate results. 

Figure 24b. Butler has also suggested using this procedure for determining the flatband potential by extrapolating the linear plot of /ph vs. C/e to /ph 0. The flatband potential obtained from Figure 24b agrees quite well with the value derived from capacity measurements.

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. 

For an electrode with high interfacial rate constants, for example, relation (28) can be plotted, which yields the flatband potential. It allows determination of the constant C, from which the sensitivity factor S can be calculated when the diffusion constant D, the absorption coefficient a, the diffusion length L, and the incident photon density I0 (corrected for reflection) are known ... 

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 promise of photoelectrochemical devices of both the photovoltaic and chemical producing variety has been discussed and reviewed extensively.Cl,, 3,4) The criteria that these cells must meet with respect to stability, band gap and flatband potential have been modeled effectively and in a systematic fashion. However, it is becomirg clear that though such models accurately describe the general features of the device, as in the case of solid state Schottky barrier solar cells, the detailed nature of the interfacial properties can play an overriding role in determining the device properties. Some of these interface properties and processes and their potential deleterious or beneficial effects on electrode performance will be discussed. 

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... 

Equation (1.24) is the much-used Mott-Schottky equation, which relates the space charge capacity to the surface barrier potential Vs. Two important parameters can be determined by plotting versus Vapp the flatband potential Vn, at = 0 (where Vs = 0) and the density of charge in the space charge layer, that is, the doping concentration N. ... 

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