Space-charge-limited current theory for a spatially non-uniform trap distribution

Abstract

The theory of space-charge-limited current, including diffusion, is discussed for an insulator containing a shallow or exponential distribution of traps whose concentration varies with position, being higher near the insulator surface than in the bulk. Two simple step- function spatial distributions are considered-one symmetric and one asymmetric. Analytic treatments are given for the open-circuit situation in both cases. For the symmetric case simple formulae are derived for the current-voltage relation. The current may be bulk- or surface-limited or there may be a transition from the former to the latter as the voltage is raised, giving rise to considerable structure in the current-voltage curves not predicted by theory which neglects diffusion. An asymmetric distribution may give rise to rectification at low voltages. This can be treated by considering the region of high trap density near one electrode to make an effectively blocking contact to the bulk of the insulator. Comparison of open-circuit potential profiles for the step-function and exponential spatial trap distributions suggests that the system is insensitive at low voltage to the nature of the spatial distribution; only the trap density in the vicinity of the surfaces is important.