Dynamic behaviour in piezoresponse force microscopy

Frequency-dependent dynamic behaviour in piezoresponse force microscopy (PFM) implemented on a beam-deflection atomic force microscope (AFM) is analysed using a combination of modelling and experimental measurements. The PFM signal is comprised of contributions from local electrostatic forces acting on the tip, distributed forces acting on the cantilever, and three components of the electromechanical response vector. These interactions result in the flexural and torsional oscillations of the cantilever, detected as vertical and lateral PFM signals. The relative magnitudes of these contributions depend on geometric parameters of the system, on the stiffnesses and frictional forces of the tip-surface junction, and on the frequency of operation. The dynamic signal formation mechanism in PFM is analysed and conditions for optimal PFM imaging are formulated. An experimental approach for probing cantilever dynamics using frequency-bias spectroscopy and deconvolution of electromechanical and electrostatic contrast is implemented.