Capacitance versus frequency

Fig. 26. Capacitance versus frequency measurements at two temperatures for the sample described in Fig. 25. [From Weisfield et al (1981).)...

Figure 1. a. Illustration of the dipole layer formed at the palladium Silicon dioxide interface as a result of H interactions b. Schematic capacitance versus applied volt- age, (C-V), and parallel conductance at frequency 6 versus applied voltage, (G- V), for an n-type silicon based Pd MOSCAP in the presence of oxygen (solid line) and hydrogen (dashed line). 

FIGURE 2.27. Capacitance versus potential as a function of frequency both in the dark and under illumination. The dark curve was measured at 10 Hz and represents the low-frequency limit. The plateau photocurrent was 5 pAcm", and the modulation amplitude was 2 mV (rms) [measured in 0.1 M KiFetCN) -l-0.5 M KCl at pH 9]. After Oskam et alP (Reproduced by permission of The Electrochemical Society, Inc.)... 

High frequency capacitance versus voltage measurements showed that for both oxide thicknesses there was a 10A thickness increase at the highest implantation dose (1016/cm2). Since this can be caused by either a real thickness increase or by a decrease in dielectric constant, the actual thickness was verified using ellipsometry. The result was that there was a real thickness increase. More than a 200mV threshold voltage shift was observed ... 

For the measurements of the ferroelectric hysteresis of P(VDF-TrFE) via the flatband shift, we used capacitors with oxidised p-type (-lO cm ) silicon substrate (100-235 nm Si02) to prevent large amoimts of leakage current. The copolymer film was prepared as described above. We used films of thickness fiom 100 nm to 1 pm. The structiues were prepared in top electrode geometry , with thermal evaporated aluminium, patterned via a shadow mask. The measiuements of capacitance versus voltage (CV) were carried out with an Agilent 4284A LCR meter at a frequency of 1 MHz with sweep rates fiom... 

The most widely used of these methods in the study of a-Si H have been field-effect, capacitance, and deep level transient spectroscopy (DLTS) measurements. Capacitance measurements actually include quite a number of variations such as capacitance versus applied voltage (C- V), frequency (C- w), or temperature (C-T), and also several kinds of distinct capacitance profiling techniques. The technique referred to as DLTS normally includes both capacitance-transient as well as current-transient measurements and will also be used as a generic term for such recent variations as isothermal capacitance transient spectroscopy (ICTS), constant capacitance methods, and the like. 

Compared to field effect, the analysis of low frequency capacitance versus voltage measurements to yield a density of gap states in a-Si H is rather straightforward. Such stupes were first presented by Dohler and Hirose... 

Fig. 14. Density of states deduced from the low frequency (dc) capacitance versus voltage characteristics of glow-discharge a-Si H MOS devices (solid curves). Dashed curves are the result of an approximate analysis for field-effect measurements taken on the same MOS devices. [After Hirose et al. (1979).]...

Two final examples are for the densities of states shown in Fig. 20, one of which is very similar to those derived from low frequency C-V methods (see Fig. 14). The other is similar to those obtained from DLTS measurements on -type doped samples (see Part V). The capacitance versus temperature curves in Figs. 21 and 22 are both generally smooth but clearly distinct from each other. In Fig. 21, which corresponds roughly to the C- F derived den-... 

C ((o) and C"((o) are the real and imaginary parts of the capacitance, respectively. Figure 4.13a shows a typical curve of C td) versus frequency [39]. With the increasing of frequency, the value of C (( ) sharply decreases and then seans to be less frequency dependent. This result relates to the electrode/electrolyte structures and their interfaces [39], As presented in Figure 4.13b, the imaginary of C"(< ) reaches a maximum value at frequency of/o (corresponding to a time constant of to = 1/fo). The to is called the relaxation time constant which has also been introduced iu Sectiou 1.4 [50],... 

Where 7 is the solution resistance, 7 p is the polarisation resistance and Cji is the double-layer capacitance. Various electrochemical phenomena at the metal solution interface causes a time lag and a measurable phase angle 9. These processes will be simulated by resistive and/or capacitive electrical networks. The impedance behaviour of an electrode may be expressed in Nyquis plot of Zj g (imaginary part of impedance) as a function of Z eai (real part of impedance) or in Bode plots of mod Impedance and 9 versus frequency, where co — 2 nf. 

To evaluate a coating, along with / , 7 p, Cdi and W (Warburg impedance) two additional circuit elements, namely coating capacitance (C ) and resistance of coating pores (Tfpo) come into account. The presences of Cai or can be idealised by a constant slope in versus frequencies plot and peaks in 9 versus frequencies plots. 

The interpretation of impedance measurements, i. e. curves C = C(v) in adsorption equilibria, or capacitance versus time curves C = C(t) at constant frequency (v = const) for adsorption processes, is not easy and still a field for analytic and simulative investigations. Also the dielectric equation of state (EOS) (Cr = 8r(T, p, m ))of an adsorption system does not seem to have been investigated in a systematic way -except some virial like series expansions considered in [3.40]. Correspondingly interrelations between the dielectric EOS and the adsorption isotherm or the heat of adsorption are - though they must exist, cp. [6.16, 6.17] - unknown to the best knowledge of the authors. 

As an example of how Fricke s law may be applied, let us suppose that we have made a parallel measurement of electrolyte capacitance over the frequency range from 1 Hz to 100 kHz. We have found a measured value of capacitance for a parallel configuration as depicted in Figure 2.3c (shown simply as C rather than in Figure 2.3c). The experimental plot of versus frequency is shown in Figure 2.8b. Let us assume that the electrodes used have an effective surface area of 100 cm, and that = 160 Q approximately. The variation in R is too small to observe Rp. We would like to estimate Rp by using Fricke s law. 

If we extrapolate the data to infinite frequency, where Cp = 0, then we see that the true sample capacitance Q = 0.001 fiF. If we now plot Cp versus frequency on a double logarithmic basis, we obtain the result shown in Figure 2.8c. The slope of this line is 0.85 and is the coefficient m which appears in the expression of Fricke s law. Normally m varies from 0.3 to 0.5 for platinum electrodes with a saline electrolyte. For the hypothetical sample selected, m = 0.85. 

Figure 10.4 (a) SEM image of NBT ceramics structural transitions present in NBT, and (c) synthesized through solid-state reaction route, the derivative of capacitance versus tempera-(b) temperature-dependent dielectric studies ture curve at 1 MHz revealing the antiferro-at different frequencies revealing the multiple electric transition behavior around 220 °C [22]. 

Fig. 13 Imaginary part of the complex capacitance C" of a 110 mm P(VDF-TrFE) film (Piezotech SA) versus frequency and inverse temperature. Maxima correspond to the fundamental and the third harmonics of the thickness extension mode (Reprinted from Mellinger (2002) with permission)...

Figure 24 shows the differential capacitance versus bias voltage at various frequencies for a devices with a relatively thick polyacetylene layer (150 nm). Accumulation is seen at bias voltages below about +10 V, and at the lowest frequency shown (50 Hz), the value of capacitance in accumulation is close to the value of Q. There is no indication for the onset of inversion at even the lowest frequency used, and the variation of capacitance in the depletion regime is well modelled by equation 27, as shown in figure 25. The slope of the linear redon of (C/Ci) versus bias voltage gives a value of Na, which for this structure is... 

Figure 26 Differential capacitance versus bias voltage for a n-Si/Si02A>olyacetylene MIS device at various frequencies (Si02 thickness 200 nm, polyacetylene thickness 60 nm).

An appearance of such a minimum in the C/Co versus frequency plot allows the determination of the charge carrier mobility. From the drift current equation and the Poisson equation for Jao one can deduce that the admittance Y co) depends on the carrier transit time. Then, because also the differential susceptance AB, which is related to the differential capacitance... 

The most important non-faradaic methods are conductometric analysis and (normal) potentiometric analysis in the former we have to deal essentially with the ionics and in the latter mainly with the electrodics. Strictly, one should assign a separate position to high-frequency analysis, where not so much the ionic conductance but rather the dielectric and/or diamagnetic properties of the solution are playing a role. Nevertheless, we shall still consider this techniques as a special form of conductometry, because the capacitive and inductive properties of the solution show up versus high-frequency as a kind of AC resistance (impedance) and, therefore, as far as its reciprocal is concerned, as a kind of AC conductance. 

Because the response time of the detector depends on the thermal time constant of the detector element / electrode assembly, coupled with the electrical time constant of the device capacitance and load resistor - the response versus modulation frequency (f shows a typical l//m form. 

One of the more useful functions of the DC Sweep is to plot transfer curves. A transfer curve usually plots an input versus an output. A DC transfer curve plots an input versus an output, assuming all capacitors are open circuits and all inductors are short circuits. In a DC Sweep, all capacitors are replaced by open circuits and all inductors are replaced by short circuits. Thus the DC Sweep is ideal for DC transfer curves. The Transient Analysis can also be used for DC transfer curves, but you must run the analysis with low-frequency waveforms to eliminate the effects of capacitance and inductance. Usually a DC Sweep works better for a transfer curve. The one place where a transient analysis works better is plotting a hysteresis curve for a Schmitt Trigger. For a Schmitt Trigger, the input must go from positive to negative, and then from negative to positive to trace out the entire hysteresis loop. This is not possible with a DC Sweep. 

This complex capacitance model, even if simplified, gives precious quantitative information about the change of the capacitance of an EDLC device versus the frequency. The knowledge of the ac behavior is indeed important since EDLC, as power devices, are often used in ac modes. Finally, it must be precise that improvements of such approach have been recently developed in a series of papers [35,36], where the De Levie TLM is associated with the complex capacitance model to estimate the porous structure of the carbon electrodes using discrete Fourier transformation. 

Figure 5.13 (top) displays the frequency spectra of the measured capacitance for temperatures ranging from 20 K to 300 K for a standard cell (ITO/PEDOT/MDMO-PPV PCBM/Al). The arrow indicates increasing temperatures. One clearly observes a step which is shifted to higher frequencies as the temperature increases. In order to evaluate the position of the steps, it is better to plot wdC/dw versus w, rather than C(u>) versus w. Figure 5.13 (bottom) shows the normalised deviated frequency spectrum of the capacitance. The steps now appear as maxima within the individual curves, and the corresponding critical frequency wq can be derived more ac-... 

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