The Piezoresponse Force Microscopy of surface layers and thin films: effective response and resolution function

TL;DR

This paper analyzes the signal formation and resolution in Piezoresponse Force Microscopy of thin piezoelectric films, deriving models for effective response and resolution limits considering substrate effects and film thickness.

Contribution

It provides exact series and Pade approximations for analytical calculation of the effective piezoresponse in thin films on various substrates, highlighting thickness and substrate permittivity effects.

Findings

Effective piezoresponse depends on film thickness for low-permittivity substrates.

Thickness dependence is suppressed for high-permittivity or metallic substrates.

Implications for ferroelectric data storage and device applications are discussed.

Abstract

Signal formation mechanism of Piezoresponse Force Microscopy of piezoelectric surface layers and thin films on stiff and elastically matched substrates is analyzed and thickness dependence of effective piezoelectric response, object transfer function components and Rayleigh two-point resolution are derived. Obtained exact series and simple Pade approximations can be applied for the effective piezoresponse analytical calculations in the case of films capped on different substrates. The effective piezoresponse is thickness dependent for piezoelectric films on substrates with low dielectric permittivity (extrinsic size effect), whereas the thickness dependence is essentially suppressed for giant permittivity or metallic substrates. Thus implications of analysis for ferroelectric data storage and device applications are discussed.