Imaging Mechanism of Piezoresponse Force Microscopy in Capacitor   Structures
  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. 
Sergei V. Kalinin, Brian J. Rodriguez, Seung-Hyun Kim, S-K. Hong,   Alexei Gruverman and Eugene A. Eliseev