  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.
