Finite element modeling of piezoresponse in nanostructured ferroelectric films

Patterning thin ferroelectric films into discrete islands is an effective way to release the constraint imposed by a substrate and the unpoled nonpiezoactive surrounding film to enhance the film piezoresponse. The converse piezoresponse measured by the surface displacement of ferroelectric islands, with lateral size changing from a nanoscale to a continuous film, has been modeled using three-dimensional finite element method. The modeling has shown that piezodeformation of the islands results in a local deformation of a substrate in the vicinity of island. The deformation is larger when the substrate is softer. The deformation, together with clamping strain in the film, decreases the effective d33 of the film island. The effect of the top electrode on d33 measured by surface displacement is also modeled. The piezoresponse of different size island capacitors with PbZr0.5Ti0.5O3/SrTiO3/Si and PbZr0.2Ti0.8O3/SrTiO3 heterostructures has been calculated. The results of modeling are in good agreement with experimental data on d33 obtained by piezoresponse force microscopy.