Real-space phase-field simulation of piezoresponse force microscopy accounting for stray electric fields

Piezoresponse force microscopy (PFM) is a powerful scanning-probe technique used to characterize important aspects of the microstructure in ferroelectrics. It has been widely applied to understand domain patterns, domain nucleation and the structure of domain walls. In this paper, we apply a real-space phasefield model to consistently simulate various PFM configurations. We model the PFM tip as a charged region that is external to the ferroelectric, and implement a boundary element method to efficiently and accurately account for the external stray fields that mediate the interactions between the tip and the ferroelectric. Our phase-field model and the solution method together are able to account for the electrical fields both within the specimen as well as those outside, and also consistently solve for the resulting electromechanical response with the same phase-field model. We apply this to various problems: first, the effect of crystal lattice orientation on the induced tip displacement and rotation; second, PFM scanning of a 90◦ domain wall that emerges at a free surface; third, the effect of closure domain microstructure on PFM response; fourth, the effect of surface modulations on PFM response; and fifth, the effect of surface charge compensation on PFM response. (Some figures may appear in colour only in the online journal)