Resolution Function Theory in Piezoresponse Force Microscopy: Domain Wall Profile, Spatial Resolution, and Tip Calibration

TL;DR

This paper develops a theoretical framework for interpreting Piezoresponse Force Microscopy data, focusing on resolution, domain wall profiles, and tip calibration, to improve quantitative analysis of ferroelectric materials.

Contribution

It introduces a linear imaging theory approach for PFM, deriving resolution functions and domain wall profiles, aiding accurate measurement and tip calibration.

Findings

Derived resolution and object transfer functions for PFM

Provided closed-form solutions for domain wall profiles

Analyzed effects of material parameters on resolution

Abstract

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, geometric parameters of the domain below the tip in local hysteresis loop measurements, as well as interpretation of switching and coercive biases in terms of materials properties and switching mechanisms, requires reliable knowledge on electrostatic field structure produced by the tip. Using linear imaging theory, we develop a theoretical approach for interpretation of these measurements and determination of tip parameters from a calibration standard. The resolution and object transfer functions in PFM are derived and effect of materials parameters on resolution is determined. Closed form solutions for domain wall profiles in vertical and lateral PFM and signal from cylindrical domain in transversally isotropic piezoelectric are derived for point-charge and sphere-plane geometry of the tip.