Decoupling competing electromechanical mechanisms in dynamic atomic force microscopy

Electromechanical coupling is ubiquitous in nature and piezoresponse force microscopy (PFM) has emerged as a powerful tool to probe electromechanical coupling with nanometer resolution. Electrostatic interference, however, is inevitable in dynamic atomic force microscopy (AFM), making the analysis and interpretation of PFM data challenging, especially in a quantitative manner. In this work, we propose a decomposition principle to quantitatively decouple intrinsic electromechanical strain from extrinsic electrostatic interaction in PFM measurement, utilizing the first two vibrational modes of AFM cantilever for which piezoelectric strain and electrostatic force show different dependence. The cantilever dynamics involving both electromechanical couplings is simulated first by finite element method (FEM), validating our decomposition principle numerically. The method is then implemented using data-intensive bimodal sequential excitation (SE) PFM and applied to periodically poled lithium niobate (PPLN), demonstrating substantial electrostatic interference that overwhelms piezoelectric strain even in the strong ferroelectric PPLN. The decomposition not only reconstructs ferroelectric domain pattern consistent with theoretical expectation, but also recovers piezoelectric coefficient accurately regardless of sample voltage applied, confirming the reliability of the method. The applicability of the decomposition in different materials is also demonstrated via PMN-PT crystal.