Space Mott-Schottky relation

Due to the great extension of the space-charge region, almost all the potential drop occurs across it. So we can measure its capacity, Csc, and calculate from the Mott-Schottky relation... 

The general method for the determination of the flat band potential is based on the Mott-Schottky linear plot based on ca-pacitance/voltage relation. Starting from Eq. (9) the space charge distribution was calculated, and its potential dependence lead to the derivation of a model equivalent to a capacitance, given by ... 

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. ... 

Two distinct differences can be seen in the relation for the space charge width in the Mott-Schottky compared to the Gouy-Chapman boundary conditions. When the majority defect carmot redistribute, the space charge width is dependent on the space charge potential, and the depletion width is greater in spatial extent due to a reduced charge screening ability. 

The capacity-potential relation, given by Eq. (10), is the so-called Mott-Schottky equation which is strictly valid only in the exhaustion region, i.e., for space charges in which the majority carrier density at the surface is smaller than the corresponding bulk concentration < o for n-type and Ps < po for p-type electrodes). 

Another simple case is the depletion layer in semiconductors with a wide band gap where no equilibrium is maintained between electrons cuid holes due to a too slow rate of electron-hole pair generation. In this case/ we have a parabolic relation between space charge capacity and A())g/ the so-called Mott-Schottky equation [7/8]. ... 

The capacitance of the space charge region can be related to A(/> by the Mott-Schottky equation... 

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