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The structure of a single antiparallel ferroelectric domain wall in LiNbO3 isquantitatively mapped by piezoelectric force microscopy (PFM) with calibratedprobe geometry. The PFM measurements are performed for 49 probes with theradius varying from 10 to 300 nm. The magnitude and variation of theexperimental piezoelectric coefficient across a domain wall matches theprofiles calculated from a comprehensive analytical theory, as well as3-dimensional finite element method simulations. Quantitative agreement betweenexperimental and theoretical profile widths is obtained only when a finitedisk-type tip radius that is in true contact with the sample surface isconsidered, which is in agreement with scanning electron microscopy images ofthe actual tips after imaging. The magnitude of the piezoelectric coefficientis shown to be independent of the tip radius, and the PFM profile width islinearly proportional to the tip radius. Finally we demonstrate a method toextract any intrinsic material broadening of the ferroelectric wall width.Surprisingly wide wall widths of 20- 200nm are observed.

Quantitative piezoelectric force microscopy: Influence of tip shape,  size, and contact geometry on the nanoscale resolution of an antiparallel  ferroelectric domain wall