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Ferroelectric domain imaging with piezoresponse force microscopy (PFM) relieson the converse piezoelectric effect: a voltage applied to the sample leads tomechanical deformations. In case of PFM one electrode is realized by the tip,therefore generating a strongly inhomogeneous electric field distributioninside the sample which reaches values up to $10^8 $V/m directly underneath theapex of the tip. Although often assumed, this high electric field does not leadto an enhancement of the piezoelectric deformation of the sample. On thecontrary, internal clamping of the material reduces the observed deformationcompared to the theoretically expected value which depends only on the voltagethus being independent of the exact field distribution

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