Charge localization and transport in disordered dielectric materials

The effect of disorder in solid insulators (ceramics and polymers) is to produce localized states (Anderson) from which results the localization of charge. To account for the conduction properties of these materials, the description of localized states in the conduction band tail is based on the Mott's formalism. The mobility edge E-c between localized and extended states is located in the conduction band and is a function of the degree of disorder N-c/N, where N and N, are, respectively, the number of atoms and the number of localized states per unit volume. For 10(-3) < N-c/N < 10(-1), E-c ranges from similar to 10(-2) to similar to 1eV. Conduction is deduced from calculation of the Fermi distribution of electrons on the extended and localized states of the conduction band. (The impurity band is not considered in the present work.) Conduction involves two processes: a hopping conduction through localized states below E-c, with an effective mobility mu (hop)*, and a conduction through extended states above E-c, with an effective mobility mu (ext)*. When N-c/N increases, mu (ext)*, decreases, whereas mu (hop)*, increases. The total effective mobility mu* exhibits a minimum, the value of which depends on the extension 1/alpha of the wave function which characterizes the localized states. At low disorder, conduction is mainly due to extended states, whereas at high disorder (greater than or equal to 3 x 10(-2)) it is the consequence of hopping through localized states. Conduction in crystallized alumina, amorphous SiO2, and amorphous polystyrene is discussed in relation to the present model. The temperature dependence of mobility is considered up to 400 degreesC. (C) 2001 Elsevier Science B.V. All rights reserved.