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

Abstract

defects, and intercalations, [14-18] charge carrier doping, [19-21] charge transfer, [22,23] and pressure. [24] In addition to this, due to its intrinsic atomically smooth surface, it has been regarded as an ideal barrier for tunneling junctions. [25] Single-layer MoS 2 has been theoretically predicted to withstand a critical intrinsic stress and strain of σ c ≈ 24GPa and ε c ≈ 20% for biaxial tensile deformations (and higher for uniaxial), by employing first-principle calculations and investigating the stress-strain (σ − ε) relations up to the failure point. [26,27] On the other hand, experimental estimates of ε c in MoS 2 sheets subjected to nanoindentation (which has the effect of a biaxial tensile stress), lead to lower values, ε c = 6%-13%, [27,28] for measured σ c close to the expected one. The discrepancy in the experimental value of ε c is caused by the use of a linear σ − ε relation, σ = Yε, where Y is the material Young's modulus, in a no-longer linear regime (close to the breaking point). Recently, the excellent robustness and flexibility of MoS 2 and other 2D crystals has led to a keen interest into 2D-material-blisters, such as bubbles, wrinkles, and tents. Their spontaneous formation has been observed after transferring 2D materials on top of a substrate, or on stacks of van der Waals (vdW) heterostructures, and it has been attributed to the trapping of adsorbed water and/or hydrocarbons inevitably present on the individual layers before assembly. [29-31] Moreover, The combination of extremely high stiffness and bending flexibility with tunable electrical and optical properties makes van der Waals transition metal dichalcogenides appealing both for fundamental science and applied research. By taking advantage of localized H 2-bulged MoS 2 membranes, an innovative approach, based on atomic force microscopy nanoindentation, is demostrated and discussed here, aiming at measuring elastic and thermodynamic properties of nanoblisters made of 2D materials. The results, interpreted in the membrane limit of the Föppl-von Karman equation, lead to the quantification of the internal pressure and mole number of the trapped H 2 gas, as well as of the stretching modulus and adhesion energy of the MoS 2 membrane. The latter is discussed in the limit of strong (clamped and fully bonded interlayer interface) shear, as experimentally achieved in the investigated H 2-bulged 2D blisters. Moreover, this approach allows to quantify the stress, and consequently the strain, locally imposed to the MoS 2 membrane by the bulging of the domes.

Mechanical, Elastic, and Adhesive Properties of Two‐Dimensional Materials: From Straining Techniques to State‐of‐the‐Art Local Probe Measurements

“…The excellent agreement between this formulation and the experimental results is exemplified in Figure 9a, where the experimental profile acquired along a diameter of a WSe 2 bubble was fitted by Equation (5). The fit (blue dashed line) perfectly captures the experimental data for q = 2.21.…”

“…Bubble patterns of the desired period and size can be thus created, with a consequent full control of the strain location. [5,6,39] If the mask is thick enough, it acts as an external constraint, so that the aspect ratio of the bubbles increases, allowing one to reach strains as high as 12%. [5,6] Figure 12d shows the AFM map of a regular square array of bubbles, with h 0 ≈ 300 nm and a diameter D ≈ 3 μm, protruding from the mask-coated surface of a MoS 2 bulk flake, produced with this approach.…”

“…Indeed, these materials are inherently flexible, and they can boast exceptional resilience to mechanical deformations. [3][4][5][6] Furthermore, in the monolayer limit, TMDs-and particularly MoS 2 -are known to display strong piezoelectricity, [7,8] due to the lack of central symmetry of the atomic arrangement in their unit cell. As such, 2D materials are excellent candidates for the realization of novel piezoelectric NEMS devices, displaying nmlevel sensing and actuation capabilities.…”

Universal shape of graphene nanobubbles on metallic substrate

“…19 Alternatively, a few experimental methods have been designed to gain finer control over bubble formation. These include formation by ions bombarding, 20–24 electrolysis, 25 laser irradiation, 13,26 or by selective adsorption of the substrate. 27 In such experiments, one can tune the size of bubbles by dose or by adsorbate pressure.…”

Deuterium Adsorption on Free-Standing Graphene

“…Hence, the C–C sp bonds of graphene are modified towards sp H–C bonds in graphane [ 1 ]. Graphane and nano-structured/functionalised graphene may constitute innovative systems for designing highly efficient electronic devices, thanks to the remarkable mechanical robustness and flexibility typical of 2D materials [ 4 , 5 , 6 ], coupled with a semiconducting character [ 7 , 8 , 9 , 10 ], unlike graphene. Recently, graphane as constituted by tritium (T)—the -unstable isotope of hydrogen—covalently bonded to graphene, has been also suggested to represent an ideal candidate for the realisation of a new detector able to measure the endpoint of the tritium -electron spectrum.…”