The effective point charge of probe tip in piezoresponse force microscopy

Abstract

Abrasions of the probe apexes always happen during piezoresponse force microscopy (PFM) experiments, resulting in variation of distribution of the electroelastic field in piezoelectric materials, which finally influences the spatial resolution of PFM. In this paper, we find the effective point charges coupled with the piezoelectric coefficients for three probe models including the modified point charge model, the sphere-plane model, and the disk-plane model, through the fully-coupled electromechanical method. It is proved that the wear of the probe apex induces spreading of electroelastic field from the contact area to the surrounding area, and the electroelastic fields computed using the coupled method are much more localized than that computed by the decoupled method. The piezoresponses underneath the probe apexes have no correlation with the geometries of the probes, yet strongly depend on the choices of calculation methods. This analysis paves new ways for studies of the piezoresponses in complicated domain structures in ferroelectric materials.