Theory-assisted determination of nano-rippling and impurities in atomic resolution images of angle-mismatched bilayer graphene

Ripples and impurity atoms are universally present in 2D materials, limiting carrier mobility, creating pseudo-magnetic fields, or affecting the electronic and magnetic properties. Scanning transmission electron microscopy (STEM) generally provides picometer-level precision in the determination of the location of atoms or atomic 'columns' in the in-image plane (xy plane). However, precise atomic positions in the z-direction as well as the presence of certain impurities are difficult to detect. Furthermore, images containing moire patterns such as those in angle-mismatched bilayer graphene compound the problem by limiting the determination of atomic positions in the xy plane. Here, we introduce a reconstructive approach for the analysis of STEM images of twisted bilayers that combines the accessible xy coordinates of atomic positions in a STEM image with density-functional-theory calculations. The approach allows us to determine all three coordinates of all atomic positions in the bilayer and establishes the presence and identity of impurities. The deduced strain-induced rippling in a twisted bilayer graphene sample is consistent with the continuum model of elasticity. We also find that the moire pattern induces undulations in the z direction that are approximately an order of magnitude smaller than the strain-induced rippling. A single substitutional impurity, identified as nitrogen, is detected. The present reconstructive approach can, therefore, distinguish between moire and strain-induced effects and allows for the full reconstruction of 3D positions and atomic identities.