Nanoelectromechanics of piezoresponse force microscopy

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 an 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.