Dielectric space charge

The measurement of ion activities assumes chemical equilibrium between the PVC membrane and the electrolyte bearing solutions. The time domain chemical and dielectric space charge changes that occur are minimized by membrane composition and sensor design and are considered negligible during the measurement period. Hence, the potential dependence of the ion activity is characterized by the Nemst equation. The following thermodynamic expressions describe the potentials of the... 

Some electrical properties are shown in Table 3. Values of other parameters have been pubflshed (146). Polymorphism of the PVDF chains and the orientation of the two distinct dipole groups, —CF2— and —CH2—, rather than trapped space charges (147) contribute to the exceptional dielectric properties and the extraordinarily large piezoelectric and pyroelectric activity of the polymer (146,148,149). 

Dispersing a dielectric substance such as A1203 in Lil [34] enhances the ionic conductivity of Lil about two orders of magnitude. The smaller the particle size of the dielectrics, the larger is the effect. This phenomenon is explained on the basis that the space-charge layer consists of or Li, generated at the interface between the ionic conductor (Lil) and the dielectric material (A1203) [35],... 

As an example Fig. 6 shows the distribution of the ions for a potential difference of A(j) = 0(00) — 0(—00) = kT/cq between the two bulk phases. In these calculations the dielectric constant was taken as e = 80 for both phases, and the bulk concentrations of all ions were assumed to be equal. This simplifies the calculations, and the Debye length Lj), which is the same for both solutions, can be used to scale the v axis. The most important feature of these distributions is the overlap of the space-charge regions at the interface, which is clearly visible in the figure. 

A rigorous solution of this problem was attempted, for example, in the hard sphere approximation by D. Henderson, L. Blum, and others. Here the discussion will be limited to the classical Gouy-Chapman theory, describing conditions between the bulk of the solution and the outer Helmholtz plane and considering the ions as point charges and the solvent as a structureless dielectric of permittivity e. The inner electrical potential 0(1) of the bulk of the solution will be taken as zero and the potential in the outer Helmholtz plane will be denoted as 02. The space charge in the diffuse layer is given by the Poisson equation... 

Because of the likely high ionic concentration and the small dielectric constant of the oxide, the diffuse layer thickness is expected to be small, and hence this space charge is limited to a few nanometers. 

Every dielectric film, irrespective of the technology used for its formation, possesses a more or less pronounced space charge. A significant space charge is generated in oxide films produced by the thermal oxidation of materials,235 plasma deposition,236 and... 

The modeling of hopping conductivity of real amorphous dielectrics of limited thickness, with or without the incorporated space charge, has recently been done by Parkhutik and Shershulskii.62... 

Figure 37. Schematic energy diagram of biased disordered dielectric. W, energy zone for hopping electrons Q, energy zone for strongly localized species forming space charge Ns, surface states.61...

Figure 38. Calculated j-U curves for dielectric with negative space charge (solid curves) and reference uncharged one (dashed curve). The insets illustrate curve linearization in log j- U and log j-Ul/2 coordinates.62...

The Gouy-Chapman theory treats the electrolyte as consisting of point ions in a dielectric continuum. This is reasonable when the concentration of the ions is low, and the space charge is so far from the metal surface that the discrete molecular nature of the solution is not important. This is not true at higher electrolyte concentrations, and better models must be used in this case. Improvements on the Gouy-Chapman theory should explain the origin of the Helmholtz capacity. In the last section we have seen that the metal makes a contribution to the Helmholtz capacity other contributions are expected to arise from the molecular structure of the solution. 

We can further describe the polarization, P, according to the different types of dipoles that either already exist or are induced in the dielectric material. The polarization of a dielectric material may be caused by four major types of polarization electronic polarization, ionic (atomic) polarization, orientation polarization, and space-charge (interfacial) polarization. Each type of polarization is shown schematically in Figure 6.24 and will be described in succession. In these descriptions, it will be useful to introduce a new term called the polarizability, a, which is simply a measure of the ability of a material to undergo the specific type of polarization. 

Inhomogeneity of the field-induced change in the characteristics of the medium, the complex dielectric permittivity esc = ei + >n particular (here e1>2 are real quantities), is a distinguishing feature of electrooptic effects in the space-charge region. The ranges of such inhomogeneities (10 4-10 5 cm)... 

As an important example, let us consider the effect of electroreflection due to inhomogeneity of the distribution of free carriers in the space-charge region of a semiconductor (plasma electroreflection). The contribution of the electrons to the complex dielectric permittivity (an n-type semiconductor is considered for illustration and the contribution of the holes is neglected) is given by the expression (see, for example, Ziman, 1972)... 

Here d is the dielectric constant of the medium which we simply assume constant throughout (that is, concentration and electric field intensity independent). Furthermore, p in (1.4a) is the density of the space charge... 

Here fi is the electric field strength, the dielectric constant, and p the density of the space charge. Assuming the correlation... 

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