Quantitative determination of tip parameters in piezoresponse force microscopy

One of the key limiting factors in the quantitative interpretation of piezoresponse force microscopy (PFM) is the lack of knowledge on the effective tip geometry. Here the authors derive analytical expressions for a 180 degrees domain wall profile in PFM for the point charge, sphere plane, and disk electrode models of the tip. An approach for the determination of the effective tip parameters from the wall profile is suggested and illustrated for several ferroelectric materials. The calculated tip parameters can be used self-consistently for the interpretation of PFM resolution and spectroscopy data, i.e., linear imaging processes.