Convergent beam electron holography for analysis of van der Waals heterostructures.

The van der Waals heterostructures, which explore the synergetic properties of 2D materials when assembled into 3D stacks, have already brought to life a number of exciting phenomena and electronic devices. Still, the interaction between the layers in such assembly, possible surface reconstruction, and intrinsic and extrinsic defects are very difficult to characterize by any method, because of the single-atomic nature of the crystals involved. Here we present a convergent beam electron holographic technique which allows imaging of the stacking order in such heterostructures. Based on the interference of electron waves scattered on different crystals in the stack, this approach allows one to reconstruct the relative rotation, stretching, and out-of-plane corrugation of the layers with atomic precision. Being holographic in nature, our approach allows extraction of quantitative information about the 3D structure of the typical defects from a single image covering thousands of square nanometers. Furthermore, qualitative information about the defects in the stack can be extracted from the convergent diffraction patterns even without reconstruction, simply by comparing the patterns in different diffraction spots. We expect that convergent beam electron holography will be widely used to study the properties of van der Waals heterostructures.