Engineered Creation of Periodic Giant, Nonuniform Strains in MoS₂ Monolayers

Abstract

The realization of ordered strain fields in 2D crystals is an intriguing perspective in many respects, including the instauration of novel transport regimes and enhanced device performances. However, the current straining techniques hardly allow to reach strains higher than ≈3% and in most cases there is no control over the strain distribution. In this work, a method is demonstrated to subject micrometric regions of atomically thin molybdenum disulfide (MoS2) to giant strains with the desired ordering. Selective hydrogen‐irradiation of bulk flakes allows the creation of arrays of size/position‐controlled monolayer domes containing pressurized hydrogen. However, the gas pressure is ruled by energy minimization, limiting the extent and geometry of the mechanical deformation of the 2D membrane. Here, a protocol is developed to create a mechanical constraint, that alters remarkably the morphology of the domes, otherwise subject to universal scaling laws, as demonstrated by atomic force microscopy. This enables the realization of unprecedented periodic configurations of large strain gradients—estimated by numerical simulations—with the highest strains being close to the rupture critical values (>10%). The creation of such high strains is confirmed by Raman experiments. The method proposed here represents an important step toward the strain engineering of 2D crystals.

Nanoscale Measurements of Elastic Properties and Hydrostatic Pressure in H2‐Bulged MoS2 Membranes

“…Figure 1b,c compare tapping-mode AFM topographies, 15 µm × 15 µm in lateral size, of uncoated and HSQ-coated MoS 2 surfaces, revealing the evolution toward a fine control of dome size and position due to the engineering of the sample prior to H + irradiation (corresponding optical images are given in Note S1 in the Supporting Information). Furthermore, the spontaneously created domes have a typical aspect ratio h/R = 0.16 (where h is the maximum height and R the footprint radius of the dome), namely universal value, in agreement with previous measurements; [29,39,40] on the contrary, the presence of the HSQ mask favors an over-pressurization of the internal gas inside the engineered domes, making their aspect ratio higher than 0.16. [40] With this method we have thus intentionally created domes spanning over a wide range of aspect ratios in between 0.15 and 0.31, thus permitting studies under quite different conditions, otherwise unattainable.…”

“…The subsequent formation of hydrogen molecules in the crystal interlayer regions gives rise to localized protrusions appearing on the flake surface in the shape of domes. [36][37][38][39][40] Here, we engineer the dome formation process as follows: [40] first of all, MoS 2 flakes are mechanically exfoliated onto a Si/SiO 2 substrate (top panel of Figure 1a); subsequently, the sample is partially coated by hydrogen silesquioxane (HSQ) negative-tone e-beam resists, of thickness varying in the range 50-100 nm; then, octagonal openings of micrometer-scale radius (middle panel of Figure 1a) are created in the HSQ layer via electron-beam lithography (EBL); finally, a low-energy proton irradiation is performed (bottom panel of Figure 1a). Additional information on sample production, patterning, and irradiation is reported in the Experimental Section.…”

“…This leads to an aspect ratio of h/R = 0.265, remarkably higher than the universal value h/R = 0.16. [29,40]…”

“…[3][4][5] Moreover, it has attracted growing interest due to the great tunability of its electronic properties as a several strategies for artificially inducing nanoblistering in 2D materials have been developed and employed, such as surface etching, [32,33] low temperature growth, [34,35] and surface hydrogenation. [36][37][38][39][40] The growing interest into 2D material blisters relies on the possibility of using them as a tool to probe and study: 1) the induced strain occurring at the blister surface and its impact on the electronic and optical properties of 2D materials; 2) the elastic properties of the 2D crystal involved (stretching modulus, Young's modulus, adhesion and/or exfoliation energy); 3) the nanoscale confinement exerted on the enclosed material (e.g., hydrostatic pressure). These studies are particularly relevant for the field of straintronics and twistronics (e.g., applications of flexible and stretchable electronics and photonics based on 2D materials and vdW heterostructures).…”

“…The formation process is also engineered, allowing the creation of ordered arrays of domes, clamped at their edges and containing over-pressurized gas (engineered clamped domes). [40] The loading resistance of these structures is probed by AFM nanoindentation experiments, and the results are compared to the solutions of the Föppl-von Karman equation, [53,54] describing the mechanics of thin plates under large deformations.…”