Dielectric relaxation capacitance

An alternative approach that was used in the past was to treat the photoelectrochemical cell as a single RC element and to interpret the frequency dispersion of the "capacitance" as indicative of a frequency dispersion of the dielectric constant. (5) In its simplest form the frequency dispersion obeys the Debye equation. (6) It can be shown that in this simple form the two approaches are formally equivalent (7) and the difference resides in the physical interpretation of modes of charge accumulation, their relaxation time, and the mechanism for dielectric relaxations. This ambiguity is not unique to liquid junction cells but extends to solid junctions where microscopic mechanisms for the dielectric relaxation such as the presence of deep traps were assumed. 

In Eq. (5) r defines the dielectric relaxation time (r = e/cr) according to which obviously a charge perturbation decays exponentially in a conductor. This defines a parallel R-C circuit as a good approximation of a homogeneous conductor (see Section III). In the following part of this section we consider the steady state, in which the conduction current represents the total current and capacitive contributions have vanished. 

As expected, the capacitance of the cell increases when the frequency is decreased (Figure 1.25a) below the knee frequency, the capacitance tends to be less dependent on the frequency and should be constant at lower frequencies. This knee frequency is an important parameter of the EDLC it depends on the type of the porous carbon, the electrolyte as well as the technology used (electrode thickness, stack, etc.) [20], The imaginary part of the capacitance (Figure 1.25b) goes through a maximum at a given frequency noted as/0 that defines a time constant x0 = 1 lf0. This time constant was described earlier by Cole and Cole [33] as the dielectric relaxation time of the system, whereas... 

There are several complications in using this technique for a-Si H, first of which is the frequency dependence. The capacitance is measured by the response to a small alternating applied electric field. The depletion layer capacitance is obtained only when the free carriers within the bulk of the semiconductor can respond at the frequency of the applied field, dielectric relaxation time. 

Dielectric relaxation is a standard name for conductive-capacitive processes occurring in materials submitted to electric field and current under a dynamic regime. The two system constitutive properties involved are the permittivity e, also called dielectric constant, which is the spatially reduced capacitance, and the conductivity a, which is the spatially reduced conductance. The permittivity has been studied in Chapter 5 (dealing with space-distributed poles) in case studies B3 Electric Space Charges, B4 Poisson Equation, and B5 Gauss Equation. It relates the electric field E to the electric displacement ( electrization ) D... 

FIGURE 11.10 Electrical circuit of the parallel mounting of a capacitive common phase element and a resistor representing the generalized Cole-Cole model of nonideal dielectric relaxation. 

Dielectric relaxation means the adjustment of dielectric displacement (D) or polarization ( ) to the time-dependent electrical field (E). Relative permittivity (e) characterizes the capacitance ratio of a condenser filled with an insulating material and with vacuum. If the field is sinusoidal, the permittivity becomes a complex number ... 

Lipton and Koda i h ve also recently presented results on a CdSe TFT-liquid-crystal panel. They used relatively high-conductivity dynamic-scattering material consequently, they added a capacitor in parallel with each TFT and display element to obtain the required electrical decay time. Brody and co-workers were able to utilize the long dielectric relaxation time associated with the twisted nematic fluid and did not have to add the supplemental capacitance. 

Studies of capacitance-voltage characteristics were done on metal insulator semiconductor (MIS) structures. The MIS structure consists of PCBM spin-coated on top of DNA-CTMA. For the metal electrode in the MIS device Cr/Au was chosen as the bottom as well as top electrode. Similarly, MIM devices were also fabricated and studied. For the MIM devices characteristics of capacitance vs frequency show no significant change in capacitance throughout the measured frequency range (see Fig. 21). On the other hand, MIS devices show rise in capacitance between frequency ranges of 10 to 10 Hz, corresponding to the dielectric relaxation of the PCBM semiconductor. At lower frequencies, capacitance further increases to an... 

The Debye circuit has been described in the dielectric literature using the complex permittivity notation. The circuit serves as an expression for a "single dielectric relaxation" system, where transition occurs from high-frequency permittivity (or in this example capacitance Cj) to low-frequency permittivity Eij. (capacitance C,). As was shown above, in the Debye circuit the response is completely capacitive at high- and low-frequency extremes, making e = e (real permittivity) for both e and ,j. = -Ae (Section 1-2). 

The above dielectric (or complex capacitance) notation and Debye dispersion (Eq. 1-15) have often been used to describe a single bulk-media dielectric relaxation process in organic and polymeric (lossy) systems where at least two components with resistive and capacitive features exist [9, p. 33]. The permittivity of a lossy dielectric with negligible parallel DC conductance can be expressed on the basis of the Havriliak-Negami model (Eq. 1-16). Equivalent circuits representing a Debye model for lossy dielectric, where C, g = C g e, Cg - C j, R 1 /G [1, p. 65, p. 216], are shown in Figure 5-3. 

No attempt is made to summarize conductivity data. Conductivity increases similarly in several major steps symmetrical to the changes of the dielectric constant. These changes are in accord with the theoretical demand that the ratio of capacitance and conductance changes for each relaxation mechanism is given by its time constant, or, in the case of distributions of time constants, by an appropriate average time constant and the Kramers-Kronig relations. 

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