Capacitance space charge

Another characteristic electrochemical property of a semiconductor/electrolyte contact is the double-layer capacitance, which is an approximation of the space-charge capacitance (Chapter 4). The space-charge capacitance can be determined by impedance measurements. If no current flows in the depletion region, the impedance is given by the reciprocal value of the space-charge capacitance. For other conditions the capacitance can be calculated from the complex impedance measurements. How to measure the impedance and to evaluate the data was described in Chapter 4 as well as the influence of diffusion processes in Chapter 5. 

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

From the slope of the Mott-Schottky line one can determine the charge career density (donor or acceptor density) if the relative dielectric permittivity is known. 

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Thus, the expression for the total capacitance of the bare EIS structure, C(solution-insulator interface potential (cp) (the capacitances C([Pg.216]

Determination of e and nT(t) can be performed by measuring the reverse current through the diode, or the change in space-charge capacitance. For t > 0 the total current at the plane x = W can be calculated (Sah et al, 1970) as the sum of the conduction current caused by the emission of electrons from traps... 

Indeed, at high bias (Figure 1(d)) the transient current response appears to be solely determined by this pseudo-capacitance, for the capacitance values determined from these scans ( vlO F) are two orders of magnitude larger than typical semiconductor space charge capacitances (12). 

Figure 7. Equivalent circuit for interphase (Raei) resistance of semiconductor (Retec) electrolyte resistance, (Rfar) fara-daic resistance (Csc) space charge capacitance (CDl) double-layer capacitance and (z) parallel impedances associated with surface states, faradaic reactions, etc.

A related analysis follows from a more general consideration of the semiconductor-electrolyte interphase [149] (see Equation 5.14). Because of the usually much larger double-layer capacitance (Cdl > 20 pi 7cm2), the overall capacitance is typically of the same order of magnitude as the space charge capacitance (Csc < 1 pF/cm2). In ACs, the latter is expected to be much larger because of the contribution from surface states, and both contributions are expected to be important. 

It is instructive to recall here the argument offered early by Oren et al. [144] as an explanation for potential-independent space charge capacitance ... 

Fig. 8.11. Equivalent circuit for a photoelectrochemical cell under potentiostatic conditions. The externally measured photocurrent is less than the generated current at high frequencies because the space charge capacitance shunts the cell resistance.

Li and Peter assumed that the space charge capacitance is much smaller than the capacitance of the Helmholtz layer the more generalised theory of Ponomarev and Peter considers the case where the space charge capacitance and Helmholtz capacitances are of comparable magnitude [60]. The attenuated IMPS response is then given by... 

Figure 23. Theoretical space charge capacitance according to Bohnenkamp and Engell as a function of the voltage drop over the boundary - ( i - for intrinsic and doped semiconductors (donor...

During dissolution, if the space charge capacitance is smaller than the WdhtihchVL layer capacitance then a small change in the applied potential (At/appUed) will lead... 

Sah and coworkers have developed a quasi-analytic calculation that can be expressed as a detailed equivalent electrical circuit. " This development is summarized by Jansen et al. and used to justify the application of the simplified equivalent circuit shown in Figure 12.8 to the analysis of the impedance response of semiconductors containing deep-level electronic states. This circuit was used to analyze the impedance data presented in Section 18.2 (see, e.g.. Figure 18.4). In Figure 12.8, C is the space-charge capacitance, Rn is a resistance that accounts for a small but finite leakage current, " and the parameters Ri...Rk and Ci... Q are attributed to the response of discrete deep-level energy states. 

Figure 12.8 Electrical circuit corresponding to the model presented by Jansen et al. in which Cn is the space-charge capacitance, R is a resistance that accounts for a small but finite leakage current, and the parameters Ri... Rjt and Cj... Q are attributed to the response of discrete deep-level energy states.

Solution The circuit corresponds to the dielectric response of a semiconductor device. The term Csc represents the space-charge capacitance, and the terms Rt,i, Ct,i, Rt,i, and account for the potential-dependent occupancy cfdeep-leoel electronic states, which typically have a small concentration. The term Ri accounts for the leakage current, which would be equal to zero for an ideal dielectric. 

It can be shown that the small-amplitude potential-modulated microwave response under depletion conditions is related linearly to the space-charge capacitance Csd by... 

In ideal semiconductor/electrolyte junctions, the presence of an energetic barrier in the semiconductor phase, originated from the equilibrium of the Fermi level in the solid and liquid phases, can be approached by the semiconductor depletion layer capacitance or space charge capacitance, Cgc- Measurement of capacitance versus... 

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