Permittivity semiconductors

Here, cv is the dielectric permittivity of the semiconductor. The charge density is given by... 

The basic difference between metal-electrolyte and semiconductor-electrolyte interfaces lies primarily in the fact that the concentration of charge carriers is very low in semiconductors (see Section 2.4.1). For this reason and also because the permittivity of a semiconductor is limited, the semiconductor part of the electrical double layer at the semiconductor-electrolyte interface has a marked diffuse character with Debye lengths of the order of 10 4-10 6cm. This layer is termed the space charge region in solid-state physics. 

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)... 

How does the electric potential change with respect to distance from the interface On the solution side the potential decays as described before. We have a Stern and a diffuse layer. For a semiconductor the potential variation at the solid side is also of interest. It also decays and this decay can be described as the decay of the diffuse layer. We only have to replace the salt concentration by the concentration of electrons ce and holes ch and we have to use the appropriate dielectric permittivity. 

Here q is the electronic charge, e is the dielectric constant of semiconductor, and eo is the permittivity of free space. The carrier density of holes1 is denoted by p and the electric field by F. Mott showed that the diffusion component of the current is negligible and... 

From condition (195), it follows that ILC will be observed only for relatively low currents at high electric fields with high mobility and large values dielectric permittivity (e) materials formed into high chemical and structural perfection (large value of ) thin layers. These are often met features of thin organic films sandwiched between metals or semiconductors with moderate work functions. The measured current... 

Applications that have received attention, and the material properties that enable them, are shown in Figure 27.1. These applications are reviewed in detail in Waser and Ramesh. Decoupling capacitors and filters on semiconductor chips, packages, and polymer substrates (e.g., embedded passives ) utilize planar or low aspect ratio oxide films. These films, with thicknesses of 0.1 to 1 J,m, are readily prepared by CSD. Because capacitance density is a key consideration, high-permittivity materials are of interest. These needs may be met by morpho-tropic phase boundary PZT materials, BST, and BTZ (BaTi03-BaZr03) solid solutions. Phase shifters (for phase array antennas) and tunable resonator and filter applications are also enabled by these materials because their effective permittivity exhibits a dependence on the direct current (DC) bias voltage, an effect called tunability. 

Technically useful properties of such perovskite ceramics are their high permittivities (relative dielectric constants), the semiconductor properties of certain chemical compositions and their piezoelectric properties. 

Electrostatic interactions are more important in organic semiconductors (partly because the relative dielectric permittivity is small, at typically 2-4) ... 

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