Ferroelectric nanostructures can be formed by local switching of domains using techniques such as piezo-force microscopy (PFM). Understanding lateral size effects 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 to simulate localized switching of domains for a PFM type and parallel-plate capacitor configurations. Our investigations indicate that fringing electric fields lead to switching via 90 deg domain wedge nucleation for thicker films while at smaller thicknesses, the polarization switches directly by 180 deg rotations. 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. In all cases, the width of the switched region extends beyond the electrodes, due to fringing.
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