Abstract
Based on the coupled theory, a simple explicit solution of piezoresponse force microscopy (PFM) in determining the effective piezoelectric coefficient for an ultra-thin transversely isotropic piezoelectric film bonded to a rigid conducting substrate is obtained, using the Taylor expansion and homogeneous assumption. And it is found to be exactly the same as the well-known result for the case of piezoelectric thin film clamped between flat rigid electrodes for homogeneous external electric field. The electric charge and the distance from the image charge model are also derived and the influences of the film thickness and substrate permittivity on the effective piezoelectric coefficient are then discussed. The obtained results can be used to quantitatively interpret the PFM signals and directly detect the piezoelectric constant through PFM for an ultra-thin film or supply important information for constructing a reliable formula to describe the thickness effect.
Highlights
Making use of the converse piezoelectric effect, piezoresponse force microscopy (PFM), has emerged as a widely used technique for investigating ferroelectric and piezoelectric samples to characterize material properties at the nanometer scale [1,2]
Instead of solving the piezoelectric equations, an alternative decoupled method, which is based on the assumption that the electric field under which the surface deformation is induced is purely calculated for the rigid dielectric, was originally proposed by Ganpule et al [6] to account for the effect of 90o domain walls on PFM image
We investigate the PFM problem of an ultra-thin transversely isotropic piezoelectric film with the coupled theory presented in Refs. [14,15,16]
Summary
Making use of the converse piezoelectric effect, piezoresponse force microscopy (PFM), has emerged as a widely used technique for investigating ferroelectric and piezoelectric samples to characterize material properties at the nanometer scale [1,2]. The obtained results for the effective piezoelectric coefficient from the coupled theory for half space are implicit and complicated combinations of material constants and very difficult to use to detect piezoelectric constants directly. MATEC Web of Conferences without considering the effect of the film thickness In this contribution, we investigate the PFM problem of an ultra-thin transversely isotropic piezoelectric film with the coupled theory presented in Refs. The influences of the film thickness and substrate permittivity on the effective piezoelectric coefficient are analyzed
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