  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.
