Effect of the Intrinsic Width on the Piezoelectric Force Microscopy of a   Single Ferroelectric Domain Wall
  Intrinsic domain wall width is a fundamental parameter that reflects bulk ferroelectric properties and governs the performance of ferroelectric memory devices. We present closed-form analytical expressions for vertical and lateral piezoelectric force microscopy (PFM) profiles for the conical and disc models of the tip, beyond point charge and sphere approximations. The analysis takes into account the finite intrinsic width of the domain wall, and dielectric anisotropy of the material. These analytical expressions provide insight into the mechanisms of PFM image formation and can be used for quantitative analysis of the PFM domain wall profiles. PFM profile of a realistic domain wall is shown to be the convolution of its intrinsic profile and resolution function of PFM. 
Anna N. Morozovska, Eugene A. Eliseev, George S. Svechnikov,   Venkatraman Gopalan, and Sergei V. Kalinin