Modeling folding behavior in freestanding ferroelectric thin films

Freestanding ferroelectric thin films have been studied recently due to their enhanced properties over traditional thin films. After removing the substrate, the freestanding ferroelectric thin films tend to become folded below the ferroelectric transition temperature, and they may become unfolded under the electron beam from a transmission electron microscope (TEM). It was proposed that this folding behavior is caused by the electrostatic force produced by the bound charges on the thin film surface. In this work, a comprehensive model for explaining the folding behavior in freestanding ferroelectric thin films is presented as a synergy of mechanical bending theory and phase-field model of ferroelectrics. The model provides a validation for the proposed folding mechanism by demonstrating a semi-quantitative agreement with the observed film folding behavior. It is found for the first time that there exists a critical ratio between the length and thickness of the film beyond which the folding may happen. The model also shows that the unfolding transition under the TEM electron beam may be the result of electron beam-induced surface charge compensation.