Negative Differential Resistivity and Positive Temperature Coefficient of Resistivity effect in the diffusion limited current of ferroelectric thin film capacitors

We present a model for the leakage current in ferroelectric thin- film capacitors which explains two of the observed phenomena that have escaped satisfactory explanation, i.e. the occurrence of either a plateau or negative differential resistivity at low voltages, and the observation of a Positive Temperature Coefficient of Resistivity (PTCR) effect in certain samples in the high-voltage regime. The leakage current is modelled by considering a diffusion-limited current process, which in the high-voltage regime recovers the diffusion-limited Schottky relationship of Simmons already shown to be applicable in these systems.