Discharge currents following space-charge-limited current conditions in insulators

Abstract

We show that the decay of electric field and of charge density in a shorted dielectric, following fully saturated space-charge-limited flow, can be written very simply as a similarity transform of the original field. This is true for both planar and cylindrical geometries. A single integration is needed to find the time dependence, and both zero and finite injection fields can be readily handled. This discharge current decays monotonically to zero.