Schottky Injection Currents in Insulators: The Effect of Space Charge on the Time Dependence

When a particle current is injected into an insulator, and the charge is trapped in the insulator, the field at the injecting electrode decays with time t. Consequently, both the particle current and the total current density j also decay. If the trapping is complete, the time dependence is hyperbolic, i.e. j ∝ (t + τ)-1, where τ is a time constant. We show that this holds both when the traps are distributed in space, and also when the potential maximum of the Richardson-Schottky barrier lies within this space charge region. Therefore it is not possible to discriminate between the effect of spatially distributed traps and of an idealized thin sheet of traps. We suspect that this also holds even when the trapping is incomplete.