Interface capacitance

To understand the electrical behaviour of the LAPS-based measurement, the LAPS set-up can be represented by an electrical equivalent circuit (see Fig. 5.2). Vbias represents the voltage source to apply the dc voltage to the LAPS structure. Re is a simple presentation of the reference electrode and the electrolyte resistance followed by a interface capacitance Cinterface (this complex capacitance can be further simulated by different proposed models as they are described, e.g., in Refs. [2,21,22]). In series to the interface capacitance, the insulator capacitance Cj will summarise the capacitances of all insulating layers of the LAPS device. The electrical current due to the photogeneration of electron-hole pairs can be modelled as current source Ip in parallel to the... 

Fig. 16. Nyquist plot of the impedance response of an electrode. The equivalent electrical circuit is shown above the plot. Ra is the solution resistance, Cp the electrode/solution interface capacitance, and Rp the electrode/solution interface polarization resistance.

For polarized Interfaces, capacitances can be readily measured directly with great precision. For mercury, capacitance-applied potential curves constitute the basic information for double layer analyses, outweighing that from electro-capillary curves. 

Pry, W.C. Stagner, W.C. Wichman, K.C. Computer-interfaced capacitive sensor for monitoring the granulation process 1 granulation monitor design and application. J. Pharm. Sci. 1984, 73, 420-421. 

Figure 14.5 Experimental setup used to determine the variation of interface capacitance with a low frequency perturbing signal.

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 ... 

The recombination velocity, which characterizes the recombination process, may vary over a wide range, from 1 to lO cm/s, at room temperature. Surface recombination centers that can be described by the one discrete recombination center model have been found to exist in different sihcon/electrolyte systems. ° The states that can exchange charge carriers with only one of the bands are traps for electrons or holes. Surface states that contribute to the interface capacitance but do not act as the... 

R. L. Meek, n-t silicon-electrolyte interface capacitance. Surf. Sci. 25, 526, 1971. 

Note This technique does nothing to cancel the noise injected through the interface capacitance (i.e. between the primary to secondary windings). But despite that limitation, a 10 dBpV reduction in conducted EMI is still possible (at various points in the EMI spectrum). So this could certainly be worth trying out, if there is a last-minute problem and a major redesign of the board needs to be avoided. 

Figure 183 (a) The admittance spectrum of a typical film in the low-frequency range the darkened squares are the measured data and the open squares are derived from (fc) the circuit model for low-frequency characteristics containing the interface admittance, Ri, Cj, and the film admittance, Rf, Cj. For the curve fit, the interface capacitance, C,, is 0.25 /xF and the interface resistance, R, is 1 kQ the film capacitance, C/, is 0.1 /xF and the film resistance, Rf, is 2.5 M 2. 

With this assumption, the maximum capacitance can be written in terms of the initial interface capacitance and the initial charge concentration for = 0 at f = 0, so that... 

According to this analysis, the rate of change in sensor capacitance is proportional to the initial interface capacitance, Ci.o, and the triiodide generation rate at x =0, which is related to the amount of bound conjugate by equation (18.16). 

In equation (5.3), aU of the information concerning the EDL is hidden in the value of the capacitance, so that this equation may be directly used from experimental data to estimate the corresponding electric field rate, when the interface capacitance is available. The content of the present work suggests that this estimation is licit, i.e. that one may connect a uniform electric field having some well-suited value to experimental reality at an electrochemical interface, whatever the nature of the underlying metal. 

Finally, when both types of carrier (electrons and holes) contribute to the interface capacitance, it may be possible to separate the two contributions if their spectral shapes are sufficiently different This has indeed proved to be possible for germanium [11, 37]. 

The use of Eq. (10.3) assumes that the semiconductor-electrolyte interface is ideally capacitive and can be represented by the solution resistance, and the interface capacitance, C, in series. However, such an interface is almost never purely capacitive and must be represented by the CPE. This leads to different slopes at different frequencies and sometimes different values of the flatband potential. An example of such a behavior is shown in Fig. 10.3. It is evident that measurements at different frequencies display different intercepts and slopes, and, as a consequence, different fb and Ad-... 

A real electrode with some degree of reversibility will therefore allow a steady state current to pass in the sense that such a current obeys Faraday s laws, it is termed a faradic current. A completely polarizable electrode passes no faradic current. In transient or ac experiment however, a polarizable electrode and a reversible electrode both pass a nonfaradic current, corresponding to charging or discharging of the interface capacitance and perhaps changes in the nature and concentration of any adsorbed species. The distinction between the two types of current is important in developing expressions for the impedance of the electrode-electrolyte interface. 

Additional information about the semiconductor can be obtained from the interface capacitance C , which arises because each interface state stores a charge. A surface potential C can be defined as the potential at the semiconductor-insulator interface which causes the center of the band gap of the semiconductor [the Fermi level of the intrinsic material, ( /),] to shift to a new value (Figure 4.3.5). This surface potential arises whenever the applied potential causes charge to build up at the interface. For example, for an -type material when E = Ef- ( /)ref is very much less than zero, ( /), will cross Ef as shown in Figure 4.3.5, leading to an accumulation of holes at the interface, that is, inversion as described above for the MOS devices. Now yZj can be calculated from the capacitance data described above by means of (NicoUian and Goetzberger [1967])... 

Fig. 3 Qualitative potential dependence of interface capacitance resulting from series contributions of inner-layer and diffuse layer capacitance a, b and c show the effects of successively decreasing bulk ionic defect concentrations.

Perhaps most importantly, the use of symmetric-electrode cells in these studies did not allow the d.c. voltage dependence of the interface capacitance to be determined in an xmambiguous manner. The applicability of Eq. 2 could not be investigated. 

If electrostatic and chemisorptive forces are comparable, i.e., if the excess of qj[ is modest, separation of the associated capacitances would seem difficult. If chemisorption, however, is relatively strong, it should result in a substantial change in the interfacial-layer electrolyte composition over the voltage range of interest. The interface capacitance should then be dominated by it and should be simply related to the voltage derivative of the adsorption isotherm of the ion involved. In this case, the adsorptive charging resembles a large capacitance in parallel with other sources of interface capacitance, since the ions involved are free to distribute themselves between the electrolyte bulk and interface sites, irrespective of other capacitance sources. 

A iQ(ads)- or other voltages, resulting in qj > 0 or q <0, the voltage dependence of the measured interface capacitance agrees well with Eq. 14 for the case of AgBr Pt, but better agreement with observed capacitance values is obtained by introducing that amount... 

RALEIGH I agree that the electrostatic model breaks down when ion chemisorption is involved and said this in my lecture. The combined effects of ion concentration and degree of charge transfer in the chemisorbed species suggests one model for accounting for high capacitances in these systems. In my lecture, I offer a somewhat different model which I believe explains other aspects of the interface capacitance more satisfactorily. 

All the methods above cannot compare directly with experiments due to the difficulty in assigning the potential scale to the electrode. Rossmeisl et al. proposed a realistic atomic model for calculating reaction energies and activation energies for charge transfer reactions without finite-size errors [5]. It also provides a measure of the vacuum potential relative to the NHE and gives values for the interface capacitance in agreement with experiments. However, the calculations require several calculations for different unit cell sizes to extrapolate to the limit of an infinite surface unit cell. Therefore, it is computationally more expensive than the ordinary calculations for surface reactions. 

Pulse and Step Methods, Fig. 4 Simplified impedance between reference electrode and working electrode electrolyte resistance Rq, interface resistance / /, and interface capacitance C/... 

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