Modeling Piezoresponse Force Microscopy for Low-Dimensional Material Characterization: Theory and Experiment

Piezoresponse force microscopy (PFM) is an atomic force microscopy-based approach utilized for measuring local properties of piezoelectric materials. The objective of this study is to propose a practical framework for simultaneous estimation of the local stiffness and piezoelectric properties of materials. For this, the governing equation of motion of a vertical PFM is derived at a given point on the sample. Using the expansion theorem, the governing ordinary differential equations of the system and their state-space representation are derived under applied external voltage. For the proof of the concept, the results obtained from both frequency and step responses of a PFM experiment are utilized to simultaneously identify the microcantilever parameters along with local spring constant and piezoelectric coefficient of a periodically poled lithium niobate sample. In this regard, a new parameter estimation strategy is developed for modal identification of system parameters under general frequency response. Results indicate good agreements between the identified model and the experimental data using the proposed modeling and identification framework. This method can be particularly applied for accurate characterization of mechanical and piezoelectric properties of biological species and cells.