The order of transition of a ferroelectric thin film on a compliant substrate Original Research Article

The characteristics of ferroelectricity depend on a myriad of factors, including boundary conditions, sample dimensions, and misfit epitaxial stresses, etc. For this reason, ferroelectric thin films generally exhibit characteristics that may be substantially different from their bulk counterparts. Existent theoretical studies on ferroelectric thin films consider either free-standing films or films on rigid substrates. In this paper, films on compliant substrates are considered. Treating the para/ferro-electric transition as a point of instability of the time-dependent Ginzburg–Landau equation, the order of the transition is shown to depend sensitively on the relative thickness of the film and substrate. It is interesting that a critical thickness of the substrate can be found, above which the transition of a thin film of first-order bulk materials may become second-order.