Interface lattice displacement measurement to 1pm by geometric phase analysis on aberration-corrected HAADF STEM images

In this work, the accuracy of geometric phase analysis (GPA) on aberration-corrected high-angle annular dark-field scanning transmission electron microscopy (Cs-corrected HAADF-STEM) images for lattice strain measurement at heterogeneous interfaces has been systematically investigated. Starting with an ideal crystal lattice of synthetic images, and then experimental HAADF images of a single-crystal lattice, we have quantitatively evaluated the inherent GPA processing artifacts and experimental errors due to STEM scanning distortions. Our results suggest that, with a properly chosen Fourier mask size and strain profile direction/width, 1 pm accuracy can be achieved for GPA strain quantification in the STEM fast-scan direction with a spatial resolution of <1 nm. To demonstrate the effectiveness and reliability of the STEM-based GPA strain profile, we have applied it to two experimental heterointerfaces: the strained LaAlO3/SrTiO3 (LAO/STO) and the relaxed SrTiO3/MgO (STO/MgO). Interestingly, GPA strain mapping reveals a novel secondary relaxation mechanism in the LAO/STO heterostructures. Essential limitations in GPA are also discussed using the example of a FeSe0.5Te0.5(FST)/SrTiO3 heterointerface. Although we focus on the interfacial lattice strain in this paper, the approaches for strain error estimation and the fundamental discussions on line profiles can also be applied, with some modifications, to other nanostructures.