Electrostrictive and electrostatic responses in contact mode voltage   modulated Scanning Probe Microscopies
  Electromechanical response of solids underpins image formation mechanism of several scanning probe microscopy techniques including the piezoresponse force microscopy (PFM) and electrochemical strain microscopy (ESM). While the theory of linear piezoelectric and ionic responses are well developed, the contributions of quadratic effects including electrostriction and capacitive tip-surface forces to measured signal remain poorly understood. Here we analyze the electrostrictive and capacitive contributions to the PFM and ESM signals and discuss the implications of the dielectric tip-surface gap on these interactions. 
Eugene A. Eliseev, Anna N. Morozovska, Anton V. Ievlev, Nina Balke,   Peter Maksymovych, Alexander Tselev, and Sergei V. Kalinin
cond-mat.mtrl-sci cond-mat.mes-hall