Lateral size and thickness dependence in ferroelectric nanostructures formed by localized domain switching

Ferroelectric nanostructures can be formed by local switching of domains using techniques such as piezo-force microscopy (PFM). Understanding the dependence of the switching behavior on the lateral size of the electrode is important to determine the minimum feature size for writing ferroelectric nanostructures. To understand these lateral size effects, we use the time-dependent Ginzburg–Landau equations in a two-dimensional square to rectangle ferroelectric transition to simulate localized switching of domains for PFM-type and parallel-plate capacitor configurations. Our investigations indicate that fringing electric fields lead to switching via intermediate 90° domains even in the absence of substrate or clamping effects for films of sufficient thicknesses, and via 180° rotations at smaller thicknesses. The voltage required to switch the domain increases by decreasing the lateral size, and at very small lateral sizes the coercive voltage becomes so large that it becomes virtually impossible to switch the domain.