Potential flat-band

The flat-band potential (Ufl,) is a very important parameter for a semiconductor in contact with an electrolyte. Ufl, is directly related to the conduction band (CB) level for an tt-type semiconductor or the valence band (VB) level for a p-type semiconductor. A classic method to determine Ufl, is by means of Mott-Schotky plot [99] according to  

The location of Up, can also be obtained by studying of the potential dependence of the photocurrent. Under monochromatic illumination for wavelengths close to the band 

For semiconductor colloidal particles pulsed radiolysis techniques [103] have also been used to derive the flat-band potential. 

Due to the simplicity to determine the onset potential (Uon) experimentally, it has been widely accepted to substitute Up, with Uon. Ideally, Um should coincide with Up, [61]. In most n-type semiconductors, however, Uon is shifted a few tenths of a Volt, to more anodic potentials than Up, [104]. This represents the situation when sufficient band bending has been established in the semiconductor space charge layer, which enables an efficient hole transfer to the reduced species in the solution. 

It can be concluded that the onset and flat band have a close to Nemstian shift with pH. Generally, the pH dependencies of onset and flat band for single crystals have higher slopes. Since a change of pH also changes the electrode potential of the H2/H+ couple according to  

The capacity of the space-charge region in a semiconductor Csc, under the formation of a depletion layer, is related to the potential drop in this region by  

This method has widely been used in electrochemical measurements. It should be stressed, however, that direct application of Eq. (29) to experimental determination of (p( is based on several assumptions (often accepted without proof) concerning the properties of the semiconductor/electrolyte junction. These assumptions have been analyzed, for example, in Reference 38). Here we formulate the most important of these assumptions  

It is assumed that the capacity measured, C, is not distorted due to the leakage effect at the interface, a finite value of the ohmic resistance of the electrode and electrolyte, etc. A correct allowance for these obstacles is an individual problem, which is usually solved by using an equivalent electrical circuit of an electrode where the quantity in question, Csc, appears explicitly. Several measurement techniques and methods of processing experimental data have been suggested to find the equivalent circuit and its elements (see, e.g.. Ref. 40). 

It is assumed that donors (acceptors) in the semiconductor are, first, completely ionized at the temperature of measurements and, second, uniformly distributed in the sample, at least within the space-charge region. (A non-uniformity whose scale is large in comparison with the space-charge region thickness can be determined by a special method see Section V.4). If the concentrations 

No and depend on the coordinate, more complicated relations for the dependence of Qc on are obtained instead of Eq. (29) (see, e.g.. Ref. 41). Deviations from Eq. (29) are also observed in the presence of deep donors (acceptors), which are not ionized in the semiconductor bulk at the temperature of measurements, but become ionized in the space-charge electric field, thereby contributing to the capacity 

As the Fermi level reaches the surface state level, the interfacial capacity is determined by the capacity of the compact layer (the maximum capacity of the surface state) and remains constant in a range of potential where the Fermi level is pinned. A further increase in anodic polarization leads again to the capacity of the depletion layer in accordance with another Mott-Schottky plot parallel to the former plot as shown in Fig. 5-61. The flat band potential, which is obtained from the Mott-Schottlo plot, shifts in the anodic direction as a result of anodic charging of the siuface state. This shift of the flat band potential equals a change of potential of the compact layer, (Q /C = Q./Ch), due to the anodic charging of the surface state. 

The electrode potential at which the electron energy band is flat in semiconductor electrodes is caUed the flat band potential, . The flat band potential is used as a characteristic potential of individual semiconductor electrodes in the same way as the potential of zero charge is used for metal electrodes. At the flat band potential the space charge, Ogc, is zero but the interfacial charge, + oh + o, is not zero. The electrode interface is composed of only the compact layer at the flat band potential if no diffuse layer exists on the solution side. 

The flat band potential cem be estimated from the Mott-Schottl r plot of electrode capacity in the range of electrode potential where a depletion layer is formed as shown in Fig. 5-47 and in Fig. 5-49. The flat band potential can also be estimated by measuring the photopotential of semiconductor electrodes as shown in Fig. 5-62 the photopotential is zero at the flat band potential. 

As is described in Sec. 2.4, the Fermi level of semiconductors approaches the band edge level with increasing impurity concentration in the semiconductors. The flat band potential, hence, is more cathodic in the n-type electrode, as the 

The potential of the compact layer at the flat band potential depends on the concentration of potential-determining ions in the electrolyte solution. For most semiconductor electrodes in aqueous solutions, the potential across the compact layer is determined by the dissociation of surface hydroxjd groups hence, the flat band potential is given as a linear function of pH. From Eqn. 5-87 we obtain Eqn. 5-90  

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Fig. V-14. Energy level diagram and energy scales for an n-type semiconductor pho-toelectrochemical cell Eg, band gap E, electron affinity work function Vb, band bending Vh, Helmholtz layer potential drop 0ei. electrolyte work function U/b, flat-band potential. (See Section V-9 for discussion of some of these quantities. (From Ref. 181.)...

Here, the flat-band potential was neglected.) A typical set of drain current-voltage curves for various gate voltages is shown in Figure 14-8. 

Flade potential, 247 Flame-annealed gold surfaces and the work of Kolb, 81 Flat band potential, 483 Fluctuations asymmetrical and unstable systems, 255 controlling progress in pitting, 299 in pitting dissolution, 251 and corrosion processes, 217 during dissolution, 252 at electrodes, theory, 281 during film breakdown, 233 and mathematical expressions thereof, 276... 

Photo effects, as a function of flat band potential, 481... 

Primarily connected to corrosion concepts, Pourbaix diagrams may be used within the scope of prediction and understanding of the thermodynamic stability of materials under various conditions. Park and Barber [25] have shown this relevance in examining the thermodynamic stabilities of semiconductor binary compounds such as CdS, CdSe, CdTe, and GaP, in relation to their flat band potentials and under conditions related to photoelectrochemical cell performance with different redox couples in solution. 

Added stability in PEC can be attained through the use of non-aqueous solvents. Noufi et al. [68] systematically evaluated various non-aqueous ferro-ferricyanide electrolytes (DMF, acetonitrile, PC, alcohols) for use in stabilizing n-CdSe photoanodes. Selection of the solvent was discussed in terms of inherent stability provided, the rate of the redox reaction, the tendency toward specific adsorption of the redox species, and the formal potential of the redox couple with respect to the flat band potential (attainable open-circuit voltage). On the basis of these data, the methanol/Fe(CN)6 system (transparent below 2.6 eV) was chosen as providing complete stabilization of CdSe. Results were presented for cells of the type... 

The strong photocorrosion effect on an electrodeposited CdSe film treated near short-circuit conditions (positive to the flat band potential) in a polysulfide media under intense illumination is shown in Fig. 5.5, as manifested by the formation of numerous, regularly arranged pinholes often reaching the substrate surface [99],... 

Efficient photoelectrochemical decomposition of ZnSe electrodes has been observed in aqueous (indifferent) electrolytes of various pHs, despite the wide band gap of the semiconductor [119, 120]. On the other hand, ZnSe has been found to exhibit better dark electrochemical stability compared to the GdX compounds. Large dark potential ranges of stability (at least 3 V) were determined for I-doped ZnSe electrodes in aqueous media of pH 0, 6.3, and 14, by Gautron et al. [121], who presented also a detailed discussion of the flat band potential behavior on the basis of the Gartner model. Interestingly, a Nernstian pH dependence was found for... 

C/pB estimated by both electrical (Mott-Schottky) and optical (photocurrent voltammetry) methods in the media studied, for (11 l)-oriented ZnSe electrode surfaces. A different variation was observed for the (110) orientation at pH >6. At pH 0, for both (110) or (11 l)-oriented electrode surface, the flat band potential value was -1.65 V (SHE) and the measured potential stability range (no detected current) was -0.35 to +2.65 V (SHE). A comparison of band levels with the other II-VI compounds as well as decomposition levels of ZnSe is given in Fig. 5.6. 

Fig. 5.8 The energy levels of n-type M0S2 at the flat band potential relative to the positions of various redox couples in CH3CN/[n-Bu4N]C104 solution. The valence band edge of the semiconductor as revealed by accurate flat band potential measurement is at ca. +1.9 V vs. SCE implying that photooxrdations workable at Ti02 are thermodynamically possible at illuminated M0S2 as well. (Reproduced with permission from [137], Copyright 2010, American Chemical Society)...

Lemasson P, Dalbera JP, Gautron J (1981) Flat band potential determination of an elec-trolyte/semiconductor junction by an electro-optical method. J Appl Phys 52 6296-6300... 

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