Schottky equation

This makes our mathematics simpler since we can rewrite the Schottky equation of Table 3-3 as ... 

In Eq. (4.5.5), describing an n-type semiconductor strongly doped with electron donors, the first and third terms in brackets can be neglected for the depletion layer (Af0 kT/e). Thus, the Mott-Schottky equation is obtained for the depletion layer,... 

Semiconductors that are used in electrochemical systems often do not meet the ideal conditions on which the Mott-Schottky equation is based. This is particularly true if the semiconductor is an oxide film formed in situ by oxidizing a metal such as Fe or Ti. Such semiconducting films are often amorphous, and contain localized states in the band gap that are spread over a whole range of energies. This may give rise... 

The interfacial capacity follows the Mott-Schottky equation (7.4) over a wide range of potentials. Figure 8.4 shows a few examples for electrodes with various amounts of doping [5]. The dielectric constant of Sn02 is e 10 so the donor concentration can be determined from the slopes of these plots. 

Equation (3.4.28) is commonly known as Mott-Schottky equation. 

Rearrangement yields the Mott-Schottky equation. This is used for evaluation of the doping concentration No from the plot of inverse square of C versus applied voltage V. 

Mott-Schottky plot — is a graphical representation of the relationship between the -> space charge layer - capacitance, and the potential of a semiconducting -> electrode (Mott-Schottky equation) ... 

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 ... 

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 an idealized case when the effect of the Helmholtz layer can be neglected, i.e., when Ch Csc, there is a negligible amount of surface states, that is. Css Qc. The total capacitance of the semiconductor/electrolyte interface described by Eq. (1.45) becomes C Csc. The interface capacitance as a function of the electrode potential then follows the Mott-Schottky equation ... 

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.,... 

Eq. (14.1) is known as the Mott-Schottky equation. We note that for a given //-type semiconductor, the barrier height increases as the work frmction of the metal increases. It is therefore expected that high work function metals will give a rectifying junction, and low work function metals an ohmic contact (it is the reverse for a p-type semiconductor). 

In the absence of electronic equilibrium established by a redox electrolyte, the potential difference across the semiconductor/electrolyte jimction can be controlled in a three electrode cell with a reference electrode. The variation of the depletion layer capacitance with potential, U, is described by the Mott-Schottky equation [1] ... 

Rearrangement yields a very useful relationship (first derived for the metal/semiconductor junction) called the Mott-Schottky equation (54, 55) ... 

Ti02 formed by electrochemical anodization on a polished titanium surface is usually an n-type semiconductor. In the potential window where it is passive, Ti02 is in a depletion condition. The capacitance of Ti02 is the space-charge capacitance described by the Mott-Schottky equation. 

Figure 11.15b also shows an interesting way of extrapolating the equilibrium hole fraction h T,P = 0) to lower temperatures. When considering the vacancies of the S-S lattice as Schottky point defects, their equilibrium concentration heq may be expressed by the Schottky equation. 

The capacitance is a function of the electrode potential E. The relation between capacitance and potential is called the Mott-Schottky equation... 

This is the so-called Mott-Schottky equation. Typical values for Csc are 10-1,000 nF/cm. By plotting HCsc as a function of the applied potential, the donor density of the semiconductor can be determined. 

Schottky (1914) emission is governed by the Richardson-Schottky equation of thermal emission over the image-force barrier... 

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). 

The Poole-Frenkel effect is the high-field assisted thermally-activated escape from traps. The derivation of an expression for the rate of escape from traps is similar to the derivation of the Schottky equation. Because the charge on the trap is fixed in position, the attractive force is proportional to l/x instead of to l/(2x). This gives an apparent difference of 2 in the slope of the plot of log / vs. E as compared with the Schottky mechanism. 

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