Schottky surface charge layer

A more reliable method for the determination of the fb potential can be drawn from a thorough investigation of the complete impedance diagram equivalent to the space charge layer. In fact, the main difficulty encountered in the Mott-Schottky plot is the rather wide range potential for the C extrapolation, which necessarily lead to values where electrochemical reactions contribute to changing the surface properties of the substrate. Moreover, the expected linear relationship shows a significant deviation, which is explained... 

This result makes it impossible to predict theoretically the position of energy bands without further experiments, since Uh is unknown. Fortunately, however, the position of energy levels can be obtained experimentally by capacity measurements. The differential capacity of the space charge layer below the semiconductor surface can be derived quantitatively by solving the Poisson equation (see e.g. Ref. [6]). For doped semiconductors one obtains the so-called Mott-Schottky equation ... 

The Mott-Schottky regime spans about 1 V in applied bias potential for most semiconductor-electrolyte interfaces (i.e., in the region of depletion layer formation of the semiconductor space-charge layer, see above) [15]. The simple case considered here involves no mediator trap states or surface states at the interface such that the equivalent circuit of the interface essentially collapses to its most rudimentary form of Csc in series with the bulk resistance of the semiconductor. Further, in all the discussions above, it is reiterated that the redox electrolyte is sufficiently concentrated that the potential drop across the Gouy layer can be neglected. Specific adsorption and other processes at the semiconductor-electrolyte interface will influence Ffb these are discussed elsewhere [29, 30], as are anomalies related to the measurement process itself [31]. Figure 7 contains representative Mott-Schottky... 

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. ... 

In general, however, even at equilibrium, there may also be a double layer, called space charge, next to the surface extending into the oxide interior (Mott-Schottky layer). The width of the space charge layer will be of the order of the... 

However, the assumption of the Schottky barrier formation raises some complex questions regarding both the size of particles on the surface of which (in principle, in a region of less than 0.5 nm) a significant change of electron density may be expected, and the nature of the space charge layer on the oxide side of the barrier. 

Diagrams of electron depletion for oxide grains and the resistance of contact between grains, (a) Space charge layer model, (b) double Schottky barrier model, (c) regional and volume depletion model, (d) surface conductive grains contact model. 

Fig. 3.18 Mott-Schottky plots of Si-doped (curves a-c) and undoped (curve d) mesoporous hematite photoanode. The capacitances for curves a, b, and c are obtained from an Si-doped sample and models a, b, and c, respectively, shown in the inset of the left-hand plot. Curve d is obtained from the undoped film and model a (series RC). The dashed lines connecting the data points represent the variable active surface area fit. Sketches e-g depict the development of the space-charge layer in a mesoporous semiconductor as function of applied potential, illustrating a decrease in active surface area at advancing space-charge layer width in two dimensions, (e) Near flat band potential with maximum surface area, (f) Total depletion of smaller feature at increased bias potential, (g) Decreased active surface area in concave curved surface. Reprinted with permission from ref. [57], copyright, 2009 American Chemical Society...

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