Picometer-Precision Strain Mapping of Two-Dimensional Heterostructures using an Electron Microscope Pixel Array Detector (EMPAD)

Abstract

Strain fields and dislocations play an important role in determining the electronic properties of atomically-thin two-dimensional (2D) crystals, especially laterally-stitched 2D heterojunctions 1-3. Conventional TEM can identify defects and dislocations using the diffraction contrast from two-beam analysis or the diffuse scattering from electron beam dechanneling along a column of atoms. However, these methods fail in 2D materials, which are confined to atomic dimensions in the direction of beam propagation. While geometric phase analysis (GPA) on atomic-resolution images can provide strain maps for 2D materials 4 , the field-of-view is limited to a few tens of nanometers. When heterostructures or grains of 2D materials reach the more typical micron scales, measuring strain and dislocations at atomic resolution is arduous and inefficient, requiring thousands of images. Here, we developed a method using an electron microscope pixel array detector (EMPAD) 5 to map the strain and topological defects in 2D crystals with high precision spanning at length scales from atomic to multimicron. The EMPAD is a high-speed, high dynamic range diffraction camera designed at Cornell that functions as a universal STEM detector 5. Specifically, in STEM, a diffraction pattern is acquired at each scan position (Fig. 1a) at 0.86 ms/frame. It has a high sensitivity that can detect a single electron, allowing quantitative analysis of diffraction from a single atom 6. In addition, its high dynamic range enables collection of all transmitted electrons, with primary beam unsaturated and diffracted beams clearly resolved (Fig. 1b). We show this by integrating the center beam (or one diffracted spot) to plot bright field (or filtered dark field) images, as shown in Fig. 1c and 1d. This high dynamic range provides high accuracy and simultaneous center-of-mass measurements (CoM) of all spots. In addition to mapping the mean inner potential of the monolayer from the CoM, we extract lattice information from the diffraction patterns at each scan position, obtaining lattice, strain and rotation maps in real space from the EMPAD's four-dimensional dataset (x and y in real space and k x and k y in momentum space). We examined strained (Fig. 1d) and relaxed (Fig. 2a) WS 2-WSe 2 lateral heterojunctions. At the relaxed junction, the lattice constant (Fig. 2b) and uniaxial strain map (Fig. 2e) cleanly distinguish the two materials, showing the 4.5% lattice mismatch. The intensity histograms (Fig. 2c and 2f) show a resolution of better than three picometers and elucidate strain variations to below 0.18%, with local samples distortions placing an upper limit on the spread. The rotation map in Fig. 2d shows that the lattice strain is released by the periodic misfit dislocations appearing at the interface. In contrast, rather than forming misfit dislocations as in wide heterojunctions, narrow heterojunctions remain coherent and instead exhibit uniaxial strain parallel to the interface (Fig. 2g and 2h).