Mobility, charge-carrier constants

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. 

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. 

The effect of the electric field allows us to neglect cation movement in the reverse direction. The flux of cations in the oxide, N+, is then given by (6.21), where v corresponds to a frequency factor. The quantity c+ represents the concentration of mobile charge carriers, typically point defects, assumed constant within the film. 

The variations of dielectric constant and of the tangent of the dielectric-loss angle with time provide information on the mobility and concentration of charge carriers, the dissociation of defect clusters, the occurrence of phase transitions and the formation of solid solutions. Techniques and the interpretation of results for sodium azide are described by Ellis and Hall [372]. 

Such a chemical approach which links ionic conductivity with thermodynamic characteristics of the dissociating species was initially proposed by Ravaine and Souquet (1977). Since it simply extends to glasses the theory of electrolytic dissociation proposed a century ago by Arrhenius for liquid ionic solutions, this approach is currently called the weak electrolyte theory. The weak electrolyte approach allows, for a glass in which the ionic conductivity is mainly dominated by an MY salt, a simple relationship between the cationic conductivity a+, the electrical mobility u+ of the charge carrier, the dissociation constant and the thermodynamic activity of the salt with a partial molar free energy AG y with respect to an arbitrary reference state ... 

So far, very few attempts at improving ion conductivity have been realized via the salt approach, because the choice of anions suitable for lithium electrolyte solute is limited. Instead, solvent composition tailoring has been the main tool for manipulating electrolyte ion conductivity due to the availability of a vast number of candidate solvents. Considerable knowledge has been accumulated on the correlation between solvent properties and ion conductivity, and the most important are the two bulk properties of the solvents, dielectric constant e and viscosity rj, which determine the charge carrier number n and ion mobility (w ), respectively. 

Fig. 13 Experimental (symbols) and theoretical (lines) data for the current-density as a function of applied voltage for a polymer film of a derivative of PPV under the condition of space-charge-limited current flow. Full curves are the solution of a transport equation that includes DOS filling (see text), dashed lines show the prediction of Child s law for space-charge-limited current flow assuming a constant charge carrier mobility. From [96] with permission. Copyright (2005) by the American Institute of Physics...

Fig. 20 Charge carrier mobility in P3HT as a function of the charge carrier concentration. Squares refer to an experiment performed on a field effect transistor while circles refer to experiments done on an electrochemically doped sample. In the latter case the mobility is inferred from the steady state current at a given doping level. Solid and dashed lines have been fitted using the theory of [101]. The fit parameters are the site separation a, the prefactor Vq in the Miller-Abrahams-type hopping rate, the inverse wavefunction decay parameter y and the dielectric constant e. From [101] with permission. Copyright (2005) by the American Institute of Physics...

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