Imaging mechanism of piezoresponse force microscopy of ferroelectric surfaces

Abstract

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 BaTiO 3 and the temperature dependence of the piezoresponse are compared with GinzburgDevonshire theory. An approach to the simultaneous acquisition of piezoresponse and surface potential images is proposed. In order to determine the origin of image contrast in piezoresponse force microscopy ͑PFM͒, 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 ͑classical͒ and weak ͑field-induced͒ 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 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.

Polarization Switching Ability Dependent on Multidomain Topology in a Uniaxial Organic Ferroelectric

“…Using piezoresponse force microscopy (PFM) [20][21][22] and P-E hysteresis loop measurements, we found that multidomain states that incorporate charged domain walls do not exhibit bulk polarization switching, whereas lamella domain structures consisting of neutral domain walls do. This result is further corroborated by real-space observations of pinned charged domain walls under an electric field.…”

Dynamic behaviour in piezoresponse force microscopy

“…28 Here, we extend this analysis to the frequency dependence of the dominant contrast. Frequency dependence of the VPFM signal including electromechanical and local and non-local electrostatic contributions is given in Section II.…”

“…In the linear model, the lateral spring constant of the tip-surface junction is 28 Similarly to electromechanical contributions, dynamic effects in the high-frequency regime will strongly affect the magnitude of local and distributed electrostatic responses.…”

Ferroelectrics at the nanoscale

“…A now thriving community for PFM research and development exists, pushing the technique forward and establishing good practice amongst the global research community [85][86][87][88][89]. However, PFM is unlikely to be the only probe needed for the characterisation of nanoscale ferroelectrics.…”