BE PFM and BE CRF for functional studies of free-standing ferroelectric membranes and thin films*

Classical AFM based tools to study electromechanical phenomena with nanoscale resolution are challenging to be applied on free-standing membranes, due to the mechanical instability of the systems. In this framework, resonant contact modes, such as Contact Resonance Frequency (CRF) and DART Piezoresponse Force Microscopy (DART-PFM), couple to geometrically induced vibrational modes of the suspended membranes and interfere the measurement of piezoelectric properties. Here, I will show on one hand how all the mechanical information of CRF is embedded into the DART-PFM signal. Then, I will discuss the risks, signal artifacts and common experimental concerns arising in this type of measurements and how the application of BE PFM and BE CRF, in a single and multifrequency approach can be applied to overcome the exposed issues. I will show the results obtained on the study of free-standing BaTiO₃ membranes with thicknesses in the range of 20 nm to 70 nm with different suspended geometries as well as on corrugated membranes laying on conductive substrates. I will then discuss how the strain and more specifically the strain gradient induced by these geometries impacts on the configuration of ferroelectric domains and enhancement of polarization, and the opportunities this opens to create complex structures with pre-designed functionalities.