  The rapid development of nanoscience and nanotechnology in the last two
decades was stimulated by the emergence of scanning probe microscopy (SPM)
techniques capable of accessing local material properties, including transport,
mechanical, and electromechanical behavior on the nanoscale. Here, we analyze
the general principles of electromechanical probing by piezoresponse force
microscopy (PFM), a scanning probe technique applicable to a broad range of
piezoelectric and ferroelectric materials. The physics of image formation in
PFM is compared to Scanning Tunneling Microscopy and Atomic Force Microscopy in
terms of the tensorial nature of excitation and the detection signals and
signal dependence on the tip-surface contact area. It is shown that its
insensitivity to contact area, capability for vector detection, and strong
orientational dependence render this technique a distinct class of SPM. The
relationship between vertical and lateral PFM signals and material properties
are derived analytically for two cases: transversally-isotropic piezoelectric
materials in the limit of weak elastic anisotropy, and anisotropic
piezoelectric materials in the limit of weak elastic and dielectric
anisotropies. The integral representations for PFM response for fully
anisotropic material are also obtained. The image formation mechanism for
conventional (e.g., sphere and cone) and multipole tips corresponding to
emerging shielded and strip-line type probes are analyzed. Resolution limits in
PFM and possible applications for orientation imaging on the nanoscale and
molecular resolution imaging are discussed.
