One among many other possibilities is leakage. With the thin film parameters and magnitude of the current and a better description of the experiment, one can try to rationalize other contributions.

you want to know the cause for the dark current ferroelectrics

First of all there is no dark current and current under illumination for ferroelectrics.

Most ferroelectric are good insulators. Instead of dark current it is more appropriate to say leakage current (which can depend on the applied electric field).

If at all there is a measurable leakage current, and if it is low then it is a good insulator. If the current is high, there can be many reasons, non- stoichiometry, two phase material having a conducting phase, oxygen vacancies, or defects.

K. Sreenivas Thank you sir for your response. Some ferroelectrics display current under illumination which shows photovoltaic effect and there the term dark current arises.

Saptam Ganguly Thank you for your response. Since you are working on ferroelectric thin films, can you please discuss the current dependency on polarization ? and one more thing does the Remnant polarization value of a particular material varies with thin film to bulk ?

When you say polarization, do you mean dependence on the sign or the magnitude of polarization ? I do not see how you want to correlate dark current to that directly. Its really sample and material specific. There is no generic rule dictating that. Subhasri Subudhi