Reciprocal space-based method for quantitative mapping of strain, absolute and polarization related displacement fields in HR-STEM images of ferroelectrics

Complex oxides` ferroelectric and piezoelectric properties make it attractive to integrate them as thin films or nanostructures on a Si substrate for use in nanoelectronics, communication devices, electromechanical systems, or sensors¹. This epitaxial integration leads to the modification of various material properties. Strain and atom displacements are particularly concerned because they alter spontaneous polarization and may result in the polarization reversal². Complex oxides are made up of more than two types of sublattices, each of which can be strained and/or shifted differently, although sharing a common Bravais lattice³. Thus, strain and atomic displacements must be measured for each sub-lattice individually and in relation to others.

Here, we propose a method for the reciprocal space treatment of high-resolution scanning transmission electron microscopy (HR-STEM) images. Named “Absolute strain” (AbStrain), it allows for quantification and mapping of interplanar distances and angles, displacement fields and strain tensor components with reference to a user-defined virtual real lattice, as well as for their correction from the image distortions specific to HR-STEM imaging. The mathematical formalism for AbStrain will be presented. When a crystal is made up of two or more types of atoms, the technique for extracting images of the sub-lattices and measuring absolute and polarization related displacements will be described. We will demonstrate a successful application of AbStrain to HR-STEM images of functional oxide ferroelectric structures. The advantages of AbStrain with respect to existing methods like geometric phase analysis⁴ and “peak finding”⁵ will be discussed.

References:

1. L. Mazet et al. Sci. Technol. Adv. Mater. 16 (2015).

2. L. Baudry et al, Phys. Rev. B 91 (14) (2015).

3. D. P. Kumah et al, Appl. Phys. Lett. 97 (25) (2010).

4. M. J. Hÿtch et al, Ultramicroscopy 74 (3) (1998).

5. M. Nord et al, Adv. Struct. Chem. imaging 3(1), 9 (2017).