Resolution-function theory in piezoresponse force microscopy: Wall imaging, spectroscopy, and lateral resolution

Piezoresponse force microscopy (PFM) has emerged as a primary tool for imaging, domain engineering, and switching spectroscopy on ferroelectric materials. Quantitative interpretation of PFM data, including measurements of the intrinsic width of the domain walls, determination of geometric parameters of the domain below the tip in local hysteresis loop measurements, as well as interpretation of local switching and coercive biases in terms of material properties and switching mechanisms, requires reliable knowledge on electrostatic and strain field structures produced by the tip. Using linear imaging theory, we develop a theoretical approach for the interpretation of these measurements and the determination of tip parameters from a suitable calibration standard. The resolution and object transfer functions in PFM are derived, and the effect of material parameters on resolution is determined. Closed-form solutions for domain-wall profiles in vertical and lateral PFM and signals from cylindrical and nested cylindrical domains in transversally isotropic piezoelectric are derived for point-charge and sphere-plane geometries of the tip.