Theory of small-signal ac response of solids and liquids with recombining mobile charge

Abstract

An exact, small‐signal theory of the impedance of an electrode/material/electrode system under quite general conditions is presented. The system, assumed flat band, consists of a slab of material between two identical plane‐parallel electrodes. The material may be a nondegenerate electronic semiconductor or an ionic conductor. Solid ionic conductors considered are Schottky and Frenkel defect materials, possibly containing neutral defect pairs and/or aliovalent impurities, and fast ion conductors such as Na‐β‐alumina. Liquid ionic conductors treated include unsupported strong, weak or potential electrolytes, and possibly fused salts and oxides. Both intrinsic and extrinsic conduction conditions are included, with a single species of negative mobile charge of arbitrary valence and mobility and a single species of positive mobile charge of arbitrary valence and mobility assumed present. Intrinsic and extrinsic equilibrium and dynamic generation and recombination processes are taken into account. The boundary conditions employed permit the charge carriers to react directly at the electrode, to be adsorbed without reaction, or to react after the formation of an adsorbed intermediate. The general solution and various simplified special cases are discussed in detail. The general solution in the form presented here is sufficiently simple that it can be used without approximation as the fitting function in a newly developed weighted nonlinear least squares fitting procedure which treats simultaneously the real and imaginary parts of a complex function such as impedance. A discussion is presented showing how fitting parameter estimates thus derived from experimental data may be used to obtain a set of basic physical parameters characterizing the experimental electrode/material system. Finally, the physical interpretation and significance of many of the basic parameters is discussed in detail.