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

TL;DR

This paper investigates how the highly inhomogeneous electric field at the tip of a PFM influences the measurement of ferroelectric domains, revealing that internal clamping reduces the expected deformation despite high local fields.

Contribution

It demonstrates that the inhomogeneous electric field does not enhance piezoelectric deformation due to internal clamping effects, challenging common assumptions in PFM analysis.

Findings

High electric fields do not increase deformation as expected.

Internal clamping reduces observed deformation.

Deformation depends mainly on applied voltage, not field distribution.

Abstract

Ferroelectric domain imaging with piezoresponse force microscopy (PFM) relies on the converse piezoelectric effect: a voltage applied to the sample leads to mechanical deformations. In case of PFM one electrode is realized by the 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 piezoelectric deformation of the sample. On the contrary, internal clamping of the material reduces the observed deformation compared to the theoretically expected value which depends only on the voltage thus being independent of the exact field distribution.