Mobile charge carriers

At lower frequencies, orientational polarization may occur if the glass contains permanent ionic or molecular dipoles, such as H2O or an Si—OH group, that can rotate or oscillate in the presence of an appHed electric field. Another source of orientational polarization at even lower frequencies is the oscillatory movement of mobile ions such as Na". The higher the amount of alkaH oxide in the glass, the higher the dielectric constant. When the movement of mobile charge carriers is obstmcted by a barrier, the accumulation of carriers at the interface leads to interfacial polarization. Interfacial polarization can occur in phase-separated glasses if the phases have different dielectric constants. 

Thus when an electric field is appHed to a soHd material the mobile charge carriers are accelerated to an average drift velocity v, which, under steady-state conditions, is proportional to the field strength. The proportionality factor is defined as the mobility, = v/E. An absolute mobility defined as the velocity pet unit driving force acting on the particle, is given as ... 

A linear regression was performed on the data, giving a slope of 1.08, an intercept of 1.922, and = 0.94. The fit of the data to the linear relationship is surprisingly good when one considers the wide variety of ionic liquids and the unloiown errors in the literature data. This linear behavior in the Walden Plot clearly indicates that the number of mobile charge carriers in an ionic liquid and its viscosity are strongly coupled. 

Conjugated polymers are generally poor conductors unless they have been doped (oxidized or reduced) to generate mobile charge carriers. This can be explained by the schematic band diagrams shown in Fig. I.23 Polymerization causes the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of the monomer to split into n and n bands. In solid-state terminology these are the valence and conduction bands, respectively. In the neutral forms shown in Structures 1-4, the valence band is filled, the conduction band is empty, and the band gap (Eg) is typically 2-3 eV.24 There is therefore little intrinsic conductivity. 

The continuity of the current inside the oxide requires that the concentration of mobile charge carriers varies with the variation of the field with distance from the interface, so that their product remains constant. 

When the two ends of a material containing mobile charge carriers, holes or electrons, are held at different temperatures, a voltage is produced, a phenomenon called the Seebeck effect (Fig. 1.11). The Seebeck coefficient of a material, a, is defined as the ratio of the electric potential produced when no current flows to the temperature... 

The Seebeck coefficient is frequently called the thermoelectric power or thermopower, and labeled Q or S. Neither of these alternatives is a good choice. The units of the Seebeck coefficient are not those of power. The symbol Q is most often used to signify heat transfer in materials. The designation S can easily be confused with the entropy of the mobile charge carriers, which is important because the Seebeck coefficient is equivalent to the entropy per mobile charge carrier (see Supplementary Material S3). 

The Seebeck coefficient for pure LaCo03 is +600 xVK-1. (a) What are the mobile charge carriers (b) Suppose these occur because the crystal contains a trace of an impurity, Co4+, calculate the defect concentration and the formula of the material (data from Robert et al., 2006). 

The mechanism of generation of the mobile charge carriers follows that described in the previous two sections. Donor doping is expected to result in ra-typc thermistors. The situation in which Fe203 is doped with TiC>2, analogous to the situation outlined above for TiC>2-doped Cr203, provides an example. The favored mechanism is the formation of electrons, comparable to Eq. (8.1) ... 

Rather surprisingly, an equal contribution to the conductivity will come from positive charge carriers equal in number to the electrons promoted into the conduction band. These are vacancies in the valence band and are called positive holes or more generally holes. Each time an electron is removed from the full valence band to the conduction band, two mobile charge carriers are therefore created, an electron and a hole. 

Electrons, holes, or other mobile charge carriers can be considered as chemically reactive species that can be allotted a thermodynamic chemical potential—the electrochemical potential, X, defined as... 

Note that the above model is for a simple system in which there is only one defect and one type of mobile charge carrier. In semiconductors both holes and electrons contribute to the conductivity. In materials where this analysis applies, both holes and electrons contribute to the value of the Seebeck coefficient. If there are equal numbers of mobile electrons and holes, the value of the Seebeck coefficient will be zero (or close to it). Derivation of formulas for the Seebeck coefficient for band theory semiconductors such as Si and Ge, or metals, takes us beyond the scope of this book. 

The mobile charge carrier species may either recombine or reach the semiconductor surface, where they can be trapped by the surface adsorbates or other sites. The lifetime of electron-hole (e /h+) pairs that are generated is important in determining the reaction yield. The holes are mainly trapped by water molecules or hydroxyl ions, giving rise to very reactive hydroxyl radicals ... 

The existence of two types of mobile charge carriers in semiconductors enables us to distinguish between a majority charge carrier transferred from the electrode into the electrolyte and a minority charge carrier injected from the electrolyte into the electrode. Minority carrier injection causes significant reverse currents, but may also contribute to the total current under forward conditions. 

Both electrons and holes are mobile charge carriers in semiconductors. The mobile charge carrier whose concentration is much greater than the other is called the majority carrier, and the minority carrier is in much smaller concentrations. In n-type semiconductors, the mcgority carriers are electrons in the conduction band and the minority carriers are holes in the valence band. The product of the concentrations of majority and minority carriers (electrons and holes) in a semiconductor of extrinsic type (containing impurities) equals the square of the concentration of electron-hole pairs, ni, in the same semiconductor of intrinsic type (containing no impurities) ... 

LD. ff is in the order of 100 nm. In contrast, the thickness of the accumulation and inversion layers, in which the mobile charge carriers (electrons or holes) are concentrated, is in the order of 5 to 10 nm and is much thinner than the thickness of the depletion layer. 

Application of an external electric field causes the charges generated in the bright regions of the pattern to migrate (in polymers mobile charge carriers are holes)... 

Classification of Mobile Charge Carriers in Mixed-Valence Compounds... 

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