Capacitance, voltage dependence

A distinctive feature of CCs based on titanium carbide as compared to CCs based on silicon carbide is a higher specific surface area under similar synthesis conditions. Figure 27.18 shows comparison of capacitance-voltage dependences (potentials are measured vs. a porous carbon electrode with high capacitance) for four CCs in a sulfuric acid solution for the range of maximum reversibility, that is, the range of EDL charging. 

Figure 27.25. Comparison of capacitance-voltage dependences for SWCNTs in aqueous electrolytes (1) 0.5 M H2SO4 (2) 1 M KOH.

Capacitive interference of pipelines is of minor importance. It arises in the immediate vicinity of overhead power lines or railway power lines in the construction of pipelines where the pipe is laid on a foundation that is well insulated from soil (e.g., on dry wood). The pipeline picks up a voltage with respect to the soil. The value of this voltage depends on the voltage of the interfering conductor at the time as well as the capacities between the conductors and the pipeline. 

Electrostriction dominates the voltage dependence of membrane capacitance. However, at low tensions ( 4 x 10 N/m) the contribution of undulations is also important. The latter is in good agreement with the results of [78] if the same membrane parameters are chosen. At higher tension undulations are damped and their role becomes less significant. 

Ionic screening has only a minor effect on the voltage dependence of the capacitance for the ionic strengths considered, > 0.01 M. 

The typical shape of a capacitance-voltage (C-V) curve for a p-type EIS structure is given in Fig. 7.4. As can be seen from Fig. 7.4, dependent on the magnitude and polarity of the applied gate voltage, VG, three regions in the C-V curve can be distinguished accumulation, depletion and inversion (an n-type EIS structure shows an identical... 

Ca2+ can enter cells via voltage- or ligand-dependent channels and by capacitative entry. These three fundamental mechanisms of regulated calcium ion entry across the plasma membrane involve, respectively, voltage-dependent Ca2+ channels, ligand-gated Ca2+ channels and capacitative Ca2+ entry associated with phospholipase C-coupled receptors. 

Important electrical informations about OLEDs, such as charge transport, charge injection, carrier mobility, etc., can be obtained from bias-dependent impedance spectroscopy, which in turn provides insight into the operating mechanisms of the OLED [14,15,73,75 78]. Campbell et al. reported electrical measurements of a PLED with a 50-nm-thick emissive layer [75], Marai et al. studied electrical measurement of capacitance-voltage and impedance frequency of ITO/l,4-Mv-(9-anthrylvinyl)-benzene/Al OLED under different bias voltage conditions [76], They found that the current is space-charge limited with traps and the conductivity exhibits power-law frequency dependence. 

The remarkable stability of the capacitance of the SIKO against variations in bias, temperature, frequency and time of operation is a consequence of the superior properties of its ONO dielectric. In contrast to aluminum and tantalum capacitors, the SIKO is a symmetrical device. It shows no significant voltage dependence of the capacitance, as the high s ceramic capacitors do. Only polymeric capacitors show a lower dependence of capacitance on bias than a SIKO. 

Sodium contamination and drift effects have traditionally been measured using static bias-temperature stress on metal-oxide-silicon (MOS) capacitors (7). This technique depends upon the perfection of the oxidized silicon interface to permit its use as a sensitive detector of charges induced in the silicon surface as a result of the density and distribution of mobile ions in the oxide above it. To measure the sodium ion barrier properties of another insulator by an analogous procedure, oxidized silicon samples would be coated with the film in question, a measured amount of sodium contamination would be placed on the surface, and a top electrode would be affixed to attempt to drift the sodium through the film with an applied dc bias voltage. Resulting inward motion of the sodium would be sensed by shifts in the MOS capacitance-voltage characteristic. 

For less highly-doped epi films, one can use the C-V method. In this case, use is made of the fact that a Schottky semiconductor diode has a voltage-dependent capacitance. In other words, when such a diode is reverse biased, a depletion layer forms which then has a capacitance determined by the depth of this layer (w) as well as the doping (N) at its edge. The doping profile can be determined from the following relations.9... 

From these observations, it became apparent that the frequency dependent capacitance must be due, at least partially, to gating particles, and, in particular, to those of sodium channels. If the capacitance change shown in Figure 6 is indeed due to sodium channels, then the change must be affected by TTX, which is known to block sodium channels selectively. Figure 7 shows the membrane capacitance at various potentials. As can be seen, TTX effectively eliminates the voltage dependence of... 

From these observations, we can draw the following conclusions. 1) The membrane capacitance of nerve axon is dependent upon frequency, indicating the presence of a relaxation process in themembrane even at rest. 2) The membrane capacitance decreases with hyperpolarization, when the membrane has a tightly packed structure. 3) The membrane capacitance increases with depolarization, when ionic channels are wide open. 4) The voltage dependent capacitance is due to sodium channels. 

Here, w = m, n, and S. V represents the membrane potential, n is the opening probability of the potassium channels, and S accounts for the presence of a slow dynamics in the system. Ic and Ik are the calcium and potassium currents, gca = 3.6 and gx = 10.0 are the associated conductances, and Vca = 25 mV and Vk = -75 mV are the respective Nernst (or reversal) potentials. The ratio r/r s defines the relation between the fast (V and n) and the slow (S) time scales. The time constant for the membrane potential is determined by the capacitance and typical conductance of the cell membrane. With r = 0.02 s and ts = 35 s, the ratio ks = r/r s is quite small, and the cell model is numerically stiff. The calcium current Ica is assumed to adjust immediately to variations in V. For fixed values of the membrane potential, the gating variables n and S relax exponentially towards the voltage-dependent steady-state values noo (V) and S00 (V). Together with the ratio ks of the fast to the slow time constant, Vs is used as the main bifurcation parameter. This parameter determines the membrane potential at which the steady-state value for the gating variable S attains one-half of its maximum value. The other parameters are assumed to take the following values gs = 4.0, Vm = -20 mV, Vn = -16 mV, 9m = 12 mV, 9n = 5.6 mV, 9s = 10 mV, and a = 0.85. These values are all adjusted to fit experimentally observed relationships. In accordance with the formulation used by Sherman et al. [53], there is no capacitance in Eq. (6), and all the conductances are dimensionless. To eliminate any dependence on the cell size, all conductances are scaled with the typical conductance. Hence, we may consider the model to represent a cluster of closely coupled / -cells that share the combined capacity and conductance of the entire membrane area. 

An extensive study has been performed to demonstrate a general approach to assess electrochemical capacitor reliability as a function of operating conditions on commercial capacitor cells [75,76], For the temperature dependency an Arrhenius law is used, whereas for the voltage dependency an inverse power law is used. Some electronic apparatus concepts are already available to estimate in situ the DLC residual life by monitoring the temperature and voltage constraints of the application [77], DLC capacitance lifetime expectancies are displayed in Figure 11.16 as a function of the temperature for different values of the applied DC voltage. 

Figure 7.31 demonstrates the very good rectifying behavior of such a Pd Schottky diode on undoped ZnO thin film. The current density ratio determined for bias voltages of +0.6 V and -3V is about 104 as shown in the inset of Fig. 7.31. The ideality factor n is about 1.5. The temperature-dependent current-voltage (IV, see Fig. 7.31) and capacitance-voltage (CV) measurements from 210 to 300 K explain the reason for the slight deviation of the ideality factor from unity and the dependence of the reverse current on the reverse bias. The barrier heights of the diode of Fig. 7.31 jy and

Figure 24. Voltage dependence of the boundary layer capacitance for C a-Agl at 175 °C. From Ref.102. (Reprinted from R. D. Armstrong and R. Mason, Double Layer Capacity Measurements involving Solid Electrolytes. J. Electroanal. Chem. 41, 231-241. Copyright 1973 with permission from Elsevier.)...

---