Modeling and measurement of surface displacements in $BaTiO3$ bulk material in piezoresponse force microscopy

Piezoresponse force microscopy (PFM) is applied to image ferroelastic formed c domains in a single crystal ferroelectric barium titanate bulk material. A simple model and an analytical approach are presented, which provides a basis to understand the complex tip-surface interactions responsible for the image contrast in PFM. In particular, the measured amplitude of the piezoresponse out-of-plane surface displacements of a $C−$ domain is compared with theoretical results based upon a three-dimensional Green’s function solution. The electric field distribution in the tip-surface contact is determined using image-charge calculations for a spherical tip separated by a thin water layer from a mechanically isotropic and electrically anisotropic dielectric half plane.