Threshold voltage theory

A complete and quantitative theory of the dependence of the flat-band or threshold voltage of an EIS structure on Vo can be found in (17) and (18), and need not be repeated here. It can be shown (17) that the expression of the flat-band voltage of an EIS structure is given by ... 

The theory of nematic liquid crystal deformation, forced by an electric field is well developed and permits to establish the relationship between the threshold voltage U, causing sample orientation, with Ae and elasticity constants of a liquid crystal (Kn). For the main S and B types of deformation the equation is the following27 ... 

The second major obstacle to application of molecular-orbital theory lies in the need to define the electronic state of the ion. Thus, it is possible to calculate groimd- and excited-state properties of molecules and compare the results with experimental observation, but there is no direct knowledge of the electron configimation in an ion produced by electron impact except perhaps immediately after ionization at threshold voltages. The quasi-equilibrium theory can be applied to any state the ion is known to exist in, but this knowledge is usually lacking. Some attempt has been made to define the electronic state of an ion as ground-state or excited-state from the appearance of metastable ions, as is... 

Yau, L.D. A simple theory to predict the threshold voltage of short-channel IGFET s. Solid State Electron 17, 1059-1063 (1974)... 

The analysis of an alternation of flexodomains and EC patterns at low AC frequencies discussed in Section 4.4 is much more complicated. For frequencies / /t, where the threshold voltages of both patterns are near to each other, one expects them to flash up independently at the onset. With increasing voltage the flexodomains and rolls will start to interact, apart from the fact that each pattern type might develop its own secondary instabilities. To disentangle these processes is certainly a very demanding task both in theory and in experiment. 

However, such barriers are used and are created by special technology (enhanced types of MISFET). In this case, a voltage difference between the gate and source, Uqs, lower than or equal to the positive value of the so-called threshold voltage, U-r, cannot overcome the barrier and the transistor is shut (drain current, I, is zero). On the other hand, the depleted types of MISFET have negative values of Ux and even if Uqs < 0 is applied, the current Id can flow (for Uqs > Uj). In first-order MOS transistor theory, the dependence of Id on Ugs is described by... 

FIGURE 5.7. Experimental dependences of the threshold voltage for Ka-pustin-Williams domains with a planar initial orientation (a) on the anisotropy of the electrical conductivity and (b) on the dielectric anisotropy for doped MBBA (circles) and for mixture A of azoxy compoimds (crosses). Calculation is according to a two-dimensional theory (curve 1) and a one-dimensional theory (curve 2). The threshold of the Prederiks effect for doped MBBA is shown in curve 3, which represents the theory, while the squares represent the experimental measurements [31]. 

Using the theory which allows for the boundary conditions at the electrodes, [31, 51] give calculated threshold voltages of the electrohydrody-namic instability in a homogeneously aligned nematic as a function of the... 

FIGURE 6.13. Thickness dependence of the reduced wave vector (d/2w) and threshold voltage (Uth/Uo) for the instabiUty shown in Fig. 6.12 [25] (m is number of the Grandjean zone). Crosses (experiment) and solid lines (theory) are threshold voltages circles (experiment) and dash Unes (theory) are wave vectors. 

Investigation of an electrohydrodynamic instability (Ae < 0) in a planar Grandjean texture shows [17] that, in this case also, the directions of the domains alternate with a transition from one Grandjean zone to another, while the domains are perpendicular to the director of the cholesteric liquid crystal in the middle of the layer in each case. This can be seen in Fig. 6.18. With an increase in d, one-dimensional deformations transform to a two-dimensional grid. The threshold voltages for the formation of a periodic instability and the period of the domains, in this case, oscillate with an increase in thickness (Fig. 6.19). In principle, this can be accounted for by the Helffich-Hurault theory [22, 23], developed with the approximation d Po, in the spirit of (6.20) and (6.21) where the forced pitch P is substituted for the equilibrium pitch Pq-... 

Nevertheless, recent studies by many groups have revealed that the bulk theories presented above need to be supplemented by considerations of surface effects, especially in cases involving photoactive surface alignment films ° and the formation of permanent orientational gratings. A recent study, for example, has shown that the photoinduced surface space-charge field contribution will result in an optical-intensity-dependent lowering of the threshold voltage required to initiate the pho-torefractive effect. 

Since the conductivity of electrolytes and the cross section and thickness of the membrane are known, a can be determined from the voltage drops across the three pairs of probe electrodes 1-2, 3-4 and 5-6. The sodium current efficiency (CE) can also be determined by titrating the amount of caustic soda generated over a given period of time. The confinement chambers around the working electrodes are used to eliminate free bubbles near the membrane. Our normalized transport data for sulfonate, carboxylate and sulfonamide ionomers are plotted In Figure 5 the universal percolative nature of perfluorinated ionomers can be clearly eeij. The prefactor sulfonate ionomers. The exponent t is 1.5 0.1 in reasonable agreement with theory and the thresholds are between 8 to 10 vol. %, which are consistent with the bimodal distribution in cluster size postulated by the cluster-network model (5.18). This theory has also been applied recently to delineate sodium selectivity of perfluorinated ionomers (20). 

The molecular mechanism operative in the change in ion channel conductances is not yet clearly understood. However, it is likely that these ion channels are composed of lipid-protein complexes. There are at least two theories for the opening of the sodium channel (1) Voltage-dependent ion channel conductance When the depolarization potential is greater than the threshold value, the sodium channel opens. (2) Ca " removal from the membrane outer surface (probably, from the outer part of the sodium channel) Such removal acts as a trigger for opening the sodium channel. It seems... 

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