Moiré fringe imaging of heterostructures by scanning transmission electron microscopy.

A heterostructured crystalline bilayer specimen is known to produce moiré fringes (MFs) in the conventional transmission electron microscopy (TEM). However, the understanding of how these patterns form in scanning transmission electron microscopy (STEM) remains limited. Here, we extended the double-scattering model to establish the imaging theory of MFs in STEM for a bilayer sample and applied this theory to successfully explain both experimental and simulated STEM images of a perovskite PbZrO/SrTiO system. Our findings demonstrated that the wave vectors of electrons exiting from Layer-1 and their relative positions with the atomic columns of Layer-2 should be taken into account. The atomic column misalignment leads to a faster reduction in the intensity of the secondary scattering beam compared to the single scattering beam as the scattering angle increases. Consequently, the intensity distribution of MFs in the bright field (BF)-STEM can be still described as the product of two single atomic images. However, in high angle annular dark field (HAADF)-STEM, it is approximately described as the superposition of the two images. Our work not only fills a knowledge gap of MFs in incoherent imaging, but also emphasizes the importance of the coherent scattering restricted by the real space when analyzing the HAADF-STEM imaging.