  The image formation mechanism in Piezoresponse Force Microscopy (PFM) of
capacitor structures is analyzed. We demonstrate that the spatial resolution is
a bilinear function of film and top electrode thicknesses, and derive the
corresponding analytical expressions. For many perovskites, the opposite
contributions of d31 and d33 components can result in anomalous domain wall
profiles. This analysis establishes the applicability limits of PFM for
polarization dynamics studies in capacitors, and applies to other structural
probes, including focused X-ray studies of capacitor structures.
