Exceptional Elasticity of Microscale Constrained MoS2 Domes

The outstanding mechanical performances of two-dimensional (2D) materials make them appealing for the emerging fields of flextronics and straintronics. However, their manufacturing and integration in 2D crystal-based devices rely on a thorough knowledge of their hardness, elasticity, and interface mechanics. Here, we investigate the elasticity of highly strained monolayer-thick MoS2 membranes, in the shape of micrometer-sized domes, by atomic force microscopy (AFM)-based nanoindentation experiments. A dome’s crushing procedure is performed to induce a local re-adhesion of the dome’s membrane to the bulk substrate under the AFM tip’s load. It is worth noting that no breakage, damage, or variation in size and shape are recorded in 95% of the crushed domes upon unloading. Furthermore, such a procedure paves the way to address quantitatively the extent of the van der Waals interlayer interaction and adhesion of MoS2 by studying pull-in instabilities and hysteresis of the loading–unloading cycles. The fundamental role and advantage of using a superimposed dome’s constraint are also discussed.


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These latter react to the performed crushing procedure (indentation as large as the dome's height) with i) a full reversibility of the loading/unloading process (approach, and retract curves -black and red, respectively -overlap upon releasing the loading); ii) a stress-strain diagram qualitatively similar to the one of conventional superelastic materials -in our experiments, the stress  is applied through the loading force exerted by the tip, and the strain  is proportional to the distance travelled inside the dome (or displacement). Importantly, the similarity in shape (the two elastic branches separated by a large hysteresis) is driven by a similar underlying phenomenology: both in the case of conventional superelastic materials and engineered MoS2 domes, the hysteresis is driven by a structural transition, between the two different phases of the crystal in the first, and between the two different states of the system (suspended MoS2 monolayer, and bulk constituted by the MoS2 monolayer stuck on the parent substrate) in the second. The two linear branches are then the elastic response of the two crystalline phases in conventional superelastic materials, and that of the bulged MoS2 monolayer and of the bulk material in our system. Figure S1. (a) typical stress-strain (-) diagram of a conventional shape-memory alloy, as extracted from [1]; (b) typical FDC resulting from the indentation of a constrained MoS2 dome. S-3

AFM Nanoindentation of MoS 2 bulk crystal
To discriminate the contribution of the van der Waals (vdW) attraction between the AFM probe and the bulk MoS2, when performing large-range indentations on domes, we pursued atomic force spectroscopy (AFS) of an untreated MoS2 crystal. Figure S2 shows the comparison between loading and unloading force vs displacement curve (FDC) as acquired on both bulk and membrane MoS2, by using the same AFM probe. We used LTESP Si tips, from Bruker, having in average a resonance frequency of 175 kHz, a deflection sensitivity of 40 nm/V and a spring constant of about 50 N/m. As expected, no additional pull-in instabilities are ever measured when indenting on the bulk, besides the snap-to-contact at the tip-MoS2 contact point, due to the vdW attraction between the AFM probe and the crystal's surface. Noteworthy, the jump-to-contact force in this case varies in between 10-20 nN, more than one order of magnitude smaller than the second snap-to-contact (feature (2)) appearing when indenting on a dome, thus making the AFM probe-bulk MoS2 interaction negligible with respect to the membrane-bulk MoS2 counterpart. Interestingly, as shown in the inset of Figure S2, also the shape of the first snap-to-contact (feature (1)) appears much different between bulk crystal and dome, the latter exhibiting a much slower and smoother force variation when AFM probe and membrane get closer and closer to each other. Such a finding demonstrates the strong reciprocal interaction between the tip and the membrane, with the membrane getting attracted and physically moving toward the probe as soon as the vdW forces set up (10-20 nm distance). In addition to this, we evaluated the hysteresis (if any) between approach and retract FDCs, when indenting on MoS2 crystal, resulting in ~0.04-0.1×10 -14 J -more than one order of magnitude smaller than that found when indenting on domes (Figure 3f -main text). Obviously, we underline that the indentation on the crystal gets vertical much earlier compared to the domes, being i) the bulk much harder and less prone to deformation, and ii) the used cantilever proper to match and measure the elastic properties of the domes rather than that of the flake.
S-4 Figure S2. Main: typical FDCs acquired on untreated MoS2 crystal (approach and retract cruves are blue and green stars, respectively) and on the domes (approach and retract are black and red spheres, respectively). Inset: zoom on snap-to-contact (1).

Van der Waals potential and force simulation for H 2 -mediated MoS 2 -MoS 2 interaction
Figure S3 plots simulated vdW potential and force curves for a sphere-surface modelled interaction, = − 6 and = − = − 6 2 , respectively [2]. Here is the radius of the indenting AFM-probe, ideally assuming that the indented membrane acquires the same curvature, is the distance between top-most membrane and underneath bulk flake, and is the Hamaker constant. We  [3].
As shown by Figure S3, the vdW interaction strongly decays in the first 10 nm distance and becomes totally negligible at 20 nm and higher.