Piezoresponse force microscopy of ferroelectric thin films: Frequency dependence of phase imaging

The objective of this work is an evaluation of quantitative measurements of piezoresponse force microscopy for nanoscale characterization of ferroelectric films. To this end, we investigate how the piezoresponse phase difference Δ between c domains depends on the frequency ω of the applied ac field much lower than the cantilever first resonance frequency. The main specimen under study was a 102 nm thick film of Pb (Zr_0.2 Ti _0.8)O₃. For the sake of comparison, a 100 nm thick PbTiO₃ film was also used. From our measurements, we conclude a frequency dependent behavior Δ∼ ω-1, which can only be partially explained by the presence of adsorbates on the surface.