Influence of the inhomogeneous field at the tip on quantitative piezoresponse force microscopy

Ferroelectric domain imaging with piezoresponse force microscopy (PFM) relies on the converse piezoelectric effect: a voltage applied to the sample leads to electromechanical deformations. In the case of PFM one electrode is realized by a tip, therefore generating a strongly inhomogeneous electric field distribution inside the sample which reaches values up to 10(8) V/m directly underneath the apex of the tip. Although often assumed, this high electric field does not lead to an enhancement of the electromechanical deformation of the sample. On the contrary, internal clamping of the material reduces the deformation as compared to the theoretically expected value which depends only on the voltage applied to the tip, thus being independent of the exact field distribution.