Imaging mechanism of piezoresponse force microscopy of ferroelectric surfaces

In order to determine the origin of image contrast in piezoresponse force microscopy (PFM), analytical descriptions of the complex interactions between a small tip and ferroelectric surface are derived for several sets of limiting conditions. Image charge calculations are used to determine potential and field distributions at the tip-surface junction between a spherical tip and an anisotropic dielectric half plane. Methods of Hertzian mechanics are used to calculate the response amplitude in the electrostatic regime. In the electromechanical regime, the limits of strong (classical) and weak (field-induced) indentation are established and the relative contributions of electroelastic constants are determined. These results are used to construct “piezoresponse contrast mechanism maps” that correlate the imaging conditions with the PFM contrast mechanisms. Conditions for quantitative PFM imaging are set forth. Variable-temperature PFM imaging of domain structures in ${\mathrm{BaTiO}}_3$ and the temperature dependence of the piezoresponse are compared with Ginzburg-Devonshire theory. An approach to the simultaneous acquisition of piezoresponse and surface potential images is proposed.