Using 4D-STEM to Map 3D Morphologies of 2D Materials

In this study, we demonstrate that nanobeam 4D-STEM can be utilized to map the 3D morphology of two-dimensional (2D) materials’ out-of-plane deformations. Our sample is a monolayer MoSe2–MoS2 heterojunction. These materials lead to the formation of “ripples” due to their 4.1% hexagonal lattice mismatch [1]. Internal strains develop and are then relaxed when the 2D material undergoes buckling in a direction normal to the plane of the sample. The formation of ripples changes the properties of a 2D material (e.g., optoelectronic) [2]; mapping ripples is therefore crucial to understand the relationships between lattice mismatch, tilt, and other material properties. 4D-STEM allows capturing a full 2D diffraction pattern on each scan position over a 2D grid (Figure 1(a)). As displayed in Figure 1(b), simulations show that different lattice tilt angles will impact the intensity of diffraction spots at different locations. It has been reported that the out-of-plane symmetry of transition metal dichalcogenides (TMD) leads to distinct 3D structure in reciprocal space, which can be accurately predicted by simulation [3]. Aiming at solving the morphology of monolayer MoSe2–MoS2 heterojunction, we show a simulation-based 3D plot of all possible tilt, tilt axis rotation, and intensity combinations (θ, ϕ, I) for the (h = 0, k = 2) 3rd-order diffraction spot of MoSe2–MoS2 (Figure 1(c)). We interpret the simulation as a mapping f (θ, ϕ)→I. Given that our 4D-STEM data provides full diffraction patterns with large dynamic range, it was necessary to find a method that would yield f–1(I)→(θ, ϕ). We solved the problem by performing cross-sections (at constant intensities) of each of the 3D plots for each (h, k) spot (such as those in Figure 1(d))—the curves intersect at a single point (θ, ϕ). The example shown is based on simulation data for all the 3rd-order spots of MoSe2–MoS2. We applied the approach to the heterostructures that contain ripples (Figure 2(a)). The ADF image and tilt map indicate a series of MoSe2 ripples formed between MoS2 (Figure 2(b)). The diffraction patterns from flat and ripple region are shown in Figure 2(c). Diffraction patterns were averaged vertically (along ripple orientation) and the background was subtracted to reduce noise effect. Here we assume that the tilt axis remained constant in such direction. The diffraction pattern from flat areas shows that the intensity of the spots remains consistent, only fading the further the spots are from the center; the one from ripples demonstrates that, for each diffraction order, spot intensities are dramatically different even though their spot positions slightly change due to the small tilt angle [4]. (a) Acquisition of diffraction patterns via four-dimensional scanning transmission electron microscopy (4D-STEM). (b) The variation of diffraction spot intensities on different probe positions of a deformed surface. (c) Simulation-based 3D plot of possible (normalized 0 to 1) intensity values that a (0, 2) 3rd-order diffraction spot can have depending on lattice tilt (θ) and tilt axis rotation (ϕ) angles. (d) Method to determine lattice tilt and tilt axis rotation angles based on diffraction spots’ observed intensities. From (c), it is shown how a 2D slice at constant intensity yields a curve such as those in (d). (a) Schematic of ripples and a ripple cross-section showing the variation of lattice tilt angles at different positions. (b) ADF-STEM image and tilt map of MoSe2-MoS2 heterojunction showing the formation of ripples. (c) Two diffraction patterns (averaged vertically) at a flat and a tilted region (slightly left of ripple). Scale bar is 150nm.