Piezoresponse Force Spectroscopy of Ferroelectric Materials
  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. 
Anna N. Morozovska, Sergei V. Svechnikov, Eugene A. Eliseev, Stephen   Jesse, Brian J. Rodriguez, and Sergei V. Kalinin