Lattice and strain analysis of atomic resolution Z-contrast images based on template matching

A real space approach is developed based on template matching for quantitative lattice analysis using atomic resolution Z-contrast images. The method, called TeMA, uses the template of an atomic column, or a group of atomic columns, to transform the image into a lattice of correlation peaks. This is helped by using a local intensity adjusted correlation and by the design of templates. Lattice analysis is performed on the correlation peaks. A reference lattice is used to correct for scan noise and scan distortions in the recorded images. Using these methods, we demonstrate that a precision of few picometers is achievable in lattice measurement using aberration corrected Z-contrast images. For application, we apply the methods to strain analysis of a molecular beam epitaxy (MBE) grown LaMnO₃ and SrMnO₃ superlattice. The results show alternating epitaxial strain inside the superlattice and its variations across interfaces at the spatial resolution of a single perovskite unit cell. Our methods are general, model free and provide high spatial resolution for lattice analysis.