Theory of Time-dependent Space-charge-limited Conduction

We have developed a theory of time-dependent space-charge-limited conduction in recent years to understand a hysteresis-shift phenomenon of graded ferroelectric films. The theory is a generalization of the conventional steady-state space-charge-limited conduction model to include (i) two carrier types (p-type and n-type), (ii) intrinsic conductivity and (iii) time dependence. Later, the theory was also applied to understand the hysteresis behaviour of homogeneous ferroelectric films. In this paper, a full and updated version of the theory is presented. At the limit of zero intrinsic conductivity, the theory implies the dominance of either carrier type. Accordingly, the independent assumptions of (i) a single carrier type and (ii) a negligible intrinsic conductivity in the conventional steady-state conduction model are interrelated.