Space charge in silver halides—Theory of surface charge and electrode charge

Abstract

It is suggested that the recent space-charge theory of Fatuzzo and Coppo omits consideration of several effects important in general space-charge situations and probably also important in these authors' experimental studies of silver halides. These effects are discussed in some depth and may explain, at least in part, why Fatuzzo and Coppo's theoretical analysis does not apply well to their experimental results. A detailed discussion is given of the diffusion potential and of surface and electrode charge in blocking and nonblocking electrode situations. Although a careful distinction between electrode and surface (absorbed) charge is usually made in the ideally polarized electrode (completely blocking) electrolyte case, the need for this necessary separation has apparently not been well recognized heretofore for situations where a solid material of interest is assumed to be contained between electrodes which are completely blocking for some or all types of mobile charge carriers in the solid. When this distinction is made for the problem considered by Fatuzzo and Coppo, quite different results than theirs are obtained. Three important improvements over the Fatuzzo-Coppo work are the present use of more appropriate general expressions for static and differential dielectric constants (or capacitances), the avoidance of their implicit assumption that surface charge is independent of total applied potential difference, and the avoidance of their assumption that the applied potential difference divides equally between the left and right crystal-electrode regions. The new analysis, appropriate for intrinsic materials with completely blocking electrodes, leads to expressions for the differential capacitance of such a system for a specific situation where surface charge may depend on the applied potential difference.