Theory of ac Space-Charge Polarization Effects in Photoconductors, Semiconductors, and Electrolytes

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Abstract
A linear theory is developed of the ac behavior of solid or liquid materials containing charge carriers which can move freely within the material but cannot leave it through the electrodes. The theory applies for any degree of dissociation of neutral centers and recombination of positive and negative charge carriers, but these carriers are assumed to have been produced by dissociation from only one species of neutral center. The mobile carriers may be electrons, positive holes, positive ions, negative ions, positive ion vacancies, or negative ion vacancies. The general solution for the admittance of the material is obtained for an arbitrary ratio between the mobilities of positive and negative carriers, but, because of the complexity of the result, it is only discussed in detail in the present paper for the following special cases: (a) charge carriers of only one sign mobile, arbitrary recombination time; (b) charge carriers of both signs mobile with the same mobility, arbitrary recombination time; and (c) charge carriers of both signs mobile with unequal mobilities and very short recombination time. In case (a), two dispersion regions may appear, with that at lower frequencies arising from recombination and the other from the finite mobility of the carriers. Both regions follow Debye dispersion curves accurately over a wide frequency range, making it possible to represent the electrical behavior of the material for any recombination time by means of a simple equivalent circuit containing only frequency-independent elements. In cases (b) and (c), only the motional dispersion region appears, and it again follows Debye curves. Finally, the results of the present theory are compared with those of other theories of ac space-charge effects in semiconductors and electrolytes.