Strain Mapping of Two-Dimensional Heterostructures with Subpicometer Precision

Next-generation, atomically thin devices require in-plane, one-dimensional heterojunctions to electrically connect different two-dimensional (2D) materials. However, the lattice mismatch between most 2D materials leads to unavoidable strain, dislocations, or ripples, which can strongly affect their mechanical, optical, and electronic properties. We have developed an approach to map 2D heterojunction lattice and strain profiles with subpicometer precision and the ability to identify dislocations and out-of-plane ripples. We collected diffraction patterns from a focused electron beam for each real-space scan position with a high-speed, high dynamic range, momentum-resolved detector-the electron microscope pixel array detector (EMPAD). The resulting four-dimensional (4D) phase space data sets contain the full spatially resolved lattice information on the sample. By using this technique on tungsten disulfide (WS2) and tungsten diselenide (WSe2) lateral heterostructures, we have mapped lattice distortions with 0.3 pm precision across multimicron fields of view and simultaneously observed the dislocations and ripples responsible for strain relaxation in 2D laterally epitaxial structures.