Higher-order electromechanical response of thin films by contact resonance piezoresponse force microscopy

Piezoresponse scanning force microscopy (PFM) has turned into an established technique for imaging ferroelectric domains in ferroelectric thin films. At least for soft cantilevers, the piezoresponse signal is not only dependent on the elastic properties of the material under investigation but also on the elastic properties of the cantilever. Due to this dependency, the cantilever response and, therefore, the measured properties depend on the frequency of the small alternating current (AC) testing voltage. At the contact resonance, the cantilever response is maximum, and this increased sensitivity can be used to detect very small signals or to decrease the voltage applied to the sample. We have shown that by using the hysteretic ferroelectric switching, it is possible to separate the signal into its components (viz. electromechanical and electrostatic contributions). Additionally, the measurement frequency can be tuned such that the second and third harmonics of the electromechanical response can be detected at the cantilever resonance, providing information about the higher-order electromechanical coefficients. We assume that this nonlinear behavior seen in local and macroscopic measurements is rooted in the nonlinearity of the dielectric permittivity. Our results are of crucial importance for the study of ferroelectric and electromechanical properties of nanostructures