Materials contrast in piezoresponse force microscopy

Piezoresponse force microscopy (PFM) contrast in transversally isotropic material corresponding to the case of c+-c− domains in tetragonal ferroelectrics is analyzed using Green’s function theory by Felten et al. [J. Appl. Phys. 96, 563 (2004)]. A simplified expression for PFM signal as a linear combination of relevant piezoelectric constant is obtained. This analysis is extended to piezoelectric material of arbitrary symmetry with weak elastic and dielectric anisotropies. These results provide a framework for interpretation of PFM signals for systems with unknown or poorly known local elastic and dielectric properties, including nanocrystalline materials, ferroelectric polymers, and biopolymers.