The large elastic strains that can be sustained by transition metal dichalcogenides (TMDs), and the sensitivity of electronic properties to that strain, make these materials attractive targets for tunable optoelectronic devices. Defects have also been shown to influence the optical and electronic properties, characteristics that are especially important to understand for applications requiring high precision and sensitivity. Importantly, photoexcitation of TMDs is known to generate transient strain effects but the associated intralayer and interlayer low-frequency (tens of GHz) acoustic-phonon modes are largely unexplored, especially in relation to defects common to such materials. Here, with femtosecond electron imaging in an ultrafast electron microscope (UEM), we directly observe distinct photoexcited strain-wave dynamics specific to both the ab basal planes and the principal c-axis crystallographic stacking direction in multilayer 2H-MoS 2 , and we elucidate the microscopic interconnectedness of these modes to one another and to discrete defects, such as few-layer crystal step edges. By probing 3D structural information within a nanometer−picosecond 2D projected UEM image series, we were able to observe the excitation and evolution of both modes simultaneously. In this way, we found evidence of a delay between mode excitations; initiation of the interlayer (c-axis) strain-wave mode precedes the intralayer (ab plane) mode by 2.4 ps. Further, the intralayer mode is preferentially excited at free basal-plane edges, thus suggesting the initial impulsive structural changes along the c-axis direction and the increased freedom of motion of the MoS 2 layer edges at terraces and step edges combine to launch in-plane strain waves at the longitudinal speed of sound (here observed to be 7.8 nm/ps). Sensitivity of the c-axis mode to layer number is observed through direct imaging of a picosecond spatiotemporal dephasing of the lattice oscillation in discrete crystal regions separated by a step edge consisting of four MoS 2 layers. These results uncover new insights into the fundamental nanoscale structural responses of layered materials to ultrafast photoexcitation and illustrate the influence defects common to these materials have on behaviors that may impact the emergent optoelectronic properties.

The structural anisotropy of layered materials leads to disparate lattice responses along different crystallographic directions following femtosecond photoexcitation. Ultrafast scattering methods are well-suited to resolving such responses, though probe size and specimen structure and morphology must be considered when interpreting results. Here we use ultrafast electron microscopy (UEM) imaging and diffraction to study the influence of individual multilayer terraces and few-layer step-edges on acoustic-phonon dynamics in 1T-TaS 2 and 2H-MoS 2 . In TaS 2 , we find that a multilayer terrace produces distinct, localized responses arising from thickness-dependent c-axis phonon dynamics. Convolution of the responses is demonstrated with ultrafast selected-area diffraction by limiting the probe size and training it on the region of interest. This results in a reciprocal-space frequency response that is a convolution of the spatially separated behaviors. Sensitivity of phonon dynamics to few-layer step-edges in MoS 2 and the capability of UEM imaging to resolve the influence of such defects are also demonstrated. Spatial frequency maps from the UEM image series reveal regions separated by a four-layer step-edge having 60.0 GHz and 63.3 GHz oscillation frequencies, again linked to c-axis phonon propagation. As with ultrafast diffraction, signal convolution is demonstrated by continuous increase of the size of the selected region of interest used in the analysis.

Key properties of two-dimensional (2D) layered materials are highly strain tunable, arising from bond modulation and associated reconfiguration of the energy bands around the Fermi level. Approaches to locally controlling and patterning strain have included both active and passive elastic deformation via sustained loading and templating with nanostructures. Here, by float-capturing ultrathin flakes of single-crystal 2H-MoS 2 on amorphous holey silicon nitride substrates, we find that highly symmetric, high-fidelity strain patterns are formed. The hexagonally arranged holes and surface topography combine to generate highly conformal flakesubstrate coverage creating patterns that match optimal centroidal Voronoi tessellation in 2D Euclidean space. Using TEM imaging and diffraction, as well as AFM topographic mapping, we determine that the substrate-driven 3D geometry of the flakes over the holes consists of symmetric, out-of-plane bowl-like deformation of up to 35 nm, with in-plane, isotropic tensile strains of up to 1.8% (measured with both selected-area diffraction and AFM). Atomistic and image simulations accurately predict spontaneous formation of the strain patterns, with van der Waals forces and substrate topography as the input parameters. These results show that predictable patterns and 3D topography can be spontaneously induced in 2D materials captured on bare, holey substrates. The method also enables electron scattering studies of precisely aligned, substrate-free strained regions in transmission mode.

Step edges are an important and prevalent topological feature that influence catalytic, electronic, vibrational, and structural properties arising from modulation of atomic-scale force fields due to edge-atom relaxation. Direct probing of ultrafast atomic-to-nanoscale lattice dynamics at individual steps poses a particularly significant challenge owing to demanding spatiotemporal resolution requirements. Here, we achieve such resolutions with femtosecond 4D ultrafast electron microscopy and directly image nanometer-variant softening of photoexcited phonons at individual surface steps. We find large degrees of softening precisely at the step position, with a thickness-dependent, straininduced frequency modulation extending tens of nanometers laterally from the atomic-scale discontinuity. The effect originates from anisotropic bond dilation and photoinduced incoherent atomic displacements delineated by abrupt molecular-layer cessation. The magnitude and spatiotemporal extent of softening is quantitatively described with a finite-element transient-deformation model. The high spatiotemporal resolutions demonstrated here enable uncovering of new insights into atomic-scale structure−function relationships of highly defect-sensitive, functional materials.

Defect sensitive etching (DSE) was developed to estimate the density of non-basal plane dislocations in hexagonal boron nitride (hBN) single crystals. The crystals employed in this study were precipitated by slowly cooling (2–4 °C/h) a nickel-chromium flux saturated with hBN from 1500 °C under 1 bar of flowing nitrogen. On the (0001) planes, hexagonal-shaped etch pits were formed by etching the crystals in a eutectic mixture of NaOH and KOH between 450 °C and 525 °C for 1–2 min. There were three types of pits: pointed bottom, flat bottom, and mixed shape pits. Cross-sectional transmission electron microscopy revealed that the pointed bottom etch pits examined were associated with threading dislocations. All of these dislocations had an a-type burgers vector (i.e., they were edge dislocations, since the line direction is perpendicular to the [211¯0]-type direction). The pit widths were much wider than the pit depths as measured by atomic force microscopy, indicating the lateral etch rate was much faster than the vertical etch rate. From an Arrhenius plot of the log of the etch rate versus the inverse temperature, the activation energy was approximately 60 kJ/mol. This work demonstrates that DSE is an effective method for locating threading dislocations in hBN and estimating their densities.