Nanoelectromechanics of Piezoresponse Force Microscopy

TL;DR

This paper develops analytical models for electroelastic fields in Piezoresponse Force Microscopy, enabling quantitative interpretation of signals and understanding of resolution limits, by solving electroelastic problems for weak and strong tip indentation.

Contribution

It provides a comprehensive continuum mechanics framework for PFM contact mechanics and signal generation, improving upon simplified electrostatic models.

Findings

Electroelastic fields are analytically derived for weak and strong indentation cases.

The models establish limits for the applicability of point charge and sphere-plane electrostatic approximations.

Implications for ferroelectric polarization switching processes are analyzed.

Abstract

To achieve quantitative interpretation of Piezoresponse Force Microscopy (PFM), including resolution limits, tip bias- and strain-induced phenomena and spectroscopy, analytical representations for tip-induced electroelastic fields inside the material are derived for the cases of weak and strong indentation. In the weak indentation case, electrostatic field distribution is calculated using image charge model. In the strong indentation case, the solution of the coupled electroelastic problem for piezoelectric indentation is used to obtain the electric field and strain distribution in the ferroelectric material. This establishes a complete continuum mechanics description of the PFM contact mechanics and imaging mechanism. The electroelastic field distribution allows signal generation volume in PFM to be determined. These rigorous solutions are compared with the electrostatic point charge and sphere-plane models, and the applicability limits for asymptotic point charge and point force models are established. The implications of these results for ferroelectric polarization switching processes are analyzed.