  Piezoresponse Force Spectroscopy (PFS) has emerged as a powerful technique
for probing highly localized switching behavior and the role of microstructure
and defects on switching. The application of a dc bias to a scanning probe
microscope tip in contact with a ferroelectric surface results in the
nucleation and growth of a ferroelectric domain below the tip, resulting in
changes in local electromechanical response. Resulting hysteresis loops
contains information on local ferroelectric switching behavior. The signal in
PFS is the convolution of the volume of the nascent domain and the probing
volume of the tip. Here, we analyze the signal formation mechanism in PFS by
deriving the main parameters of domain nucleation in a semi-infinite material
and establishing the relationships between domain parameters and PFM signal
using a linear Greens function theory. The effect of surface screening and
finite Debye length on the switching behavior is established. In particular, we
predict that the critical nucleus size in PFM is controlled by the surface
screening mechanism and in the absence of screening, tip-induced switching is
impossible. Future prospects of PFS to study domain nucleation in the vicinity
of defects, local switching centers in ferroelectrics, and unusual polarization
states in low-dimensional ferroelectrics are discussed.
