Resolving the piezoelectric properties through differential evolution algorithm via piezoresponse force microscopy

Abstract

Piezoresponse force microscopy (PFM) has rapidly become an important tool for characterizing electromechanical properties in piezoelectric materials at the nanoscale. However, there remains a challenge on the accurate quantitative determination of the piezoelectric coefficients through the electromechanical responses in PFM experiments, due to the long-range electroelastic interactions between the charged scanning probe of the microscopy and piezoelectric mediums. In this paper, differential evolution algorithm (DEA) has been utilized to quantitatively analyze the piezoelectric properties of transversely isotropic piezoelectric mediums via PFM experiment. Considering the coupling between piezoelectric mediums and air, we first extend the fully coupled theory to calculate the electromechanical responses including surface displacements and potentials underneath the probe. We further observe the relations among electromechanical responses, intrinsic piezoelectric properties and measurement conditions, which point us to choose the proper measurement conditions and optimization strategy during the resolving process through DEA. Finally, all the components of the transversely isotropic piezoelectric coefficients are successfully resolved after two-step optimization through the DEA combined with the fully coupled theory. This study provides an important guidance for quantitative and high-throughput determination of the electromechanical properties via PFM experiments.