The application of graphene in semiconducting devices is hindered by its lack of a bandgap. Up to now, two different strategies have been employed to fabricate semiconducting two-dimensional crystals: opening a bandgap in graphene 1 2 3 or using another two-dimensional crystal with a large intrinsic bandgap 4 . Atomically thin molybdenum disulphide (MoS₂), a semiconducting transition metal dichalcogenide, has recently attracted a lot of attention due to its large intrinsic bandgap of 1.8 eV and high mobility μ > 200 cm² V^-1 s^-1 5 6 . In fact, MoS₂ has been employed to fabricate field-effect transistors with high on/off ratios 5 , chemical sensors 7 and logic gates among other things 8 . Nevertheless, the study of the mechanical properties of this nanomaterial (which will dictate its applicability in flexible electronic applications) has just begun 9 10 . In a previous work, we studied the mechanical properties of freely suspended MoS₂ nanosheets using a bending test experiment performed with the tip of an atomic force microscope (AFM) 10 .

Here, we perform a more detailed characterization of the fabricated nanosheets by quantitative optical microscopy and high-resolution friction force microscopy, and we extend the study of the mechanical properties to a larger number of MoS₂ nanosheets (with thicknesses in the range of 5 to 25 layers) to improve the robustness of our statistical analysis. We present force versus deformation curves measured not only by pushing the nanosheets (as usual) but also by pulling them, demonstrating that for moderate deformations pushing and pulling the nanosheets are equivalent. These measurements allow for the simultaneous determination of the Young's modulus (E) and the initial pre-tension (T) of these MoS₂ nanosheets.

Although atomically thin MoS₂ crystals can be fabricated by scotch-tape-based micromechanical cleavage 11 , this procedure can leave traces of adhesive. Thus, it is preferable to use an all-dry technique based on poly (dimethyl)-siloxane stamps which have been successfully employed to fabricate ultra-clean atomically thin crystals of graphene 12 , graphene nanoribbons 13 , NbSe₂, MoS₂ 14 , and muscovite mica 15 . In order to fabricate freely suspended atomically thin MoS₂ flakes, the cleaved flakes are transferred to a pre-patterned oxidized silicon wafer 16 with circular holes 1.1 μm in diameter and 200-nm deep.

After fabrication, an optical microscope (Nikon eclipse LV100, Nikon Instruments Inc., Melville, NY, USA) is used to identify MoS₂ flakes at first glance. In fact, ultrathin MoS₂ flakes deposited onto a silicon wafer with a 285-nm-thick SiO₂ capping layer can be easily identified by optical microscopy. Figure 1a shows a chart of the expected color of MoS₂ flakes with different thicknesses when they are laying on the surface or covering a hole. The expected color has been calculated with a Fresnel law-based model, employing the refractive index of MoS₂ in 14 and the response of the camera as indicated in 17 . The topography of selected flakes is then studied by contact mode atomic force microscopy to avoid possible artifacts in the flake thickness measurements 18 . Figure 1b, c is an optical micrograph and a contact mode AFM topography, respectively, of an 8-layer-thick MoS₂ flake deposited onto a 285-nm SiO₂/Si pre-patterned substrate.

Additionally, high resolution contact mode AFM measurements can provide lattice resolution even in the suspended region of the MoS₂ flakes which demonstrates the very clean nature of our fabrication technique. Figure 1d, e shows two lateral force maps (friction images) obtained in the suspended and the supported parts of the MoS₂ flake shown in Figure 1c. The atomic resolution can be better resolved in the suspended region of the MoS₂ flake (Figure 1d), while in the supported part, the frictional force image mainly follows parallel stripes (Figure 1e). We have employed a two-dimensional Tomlinson model 19 to simulate the frictional force image measured in the supported part of the nanolayer (see inset in Figure 1e), finding a remarkable qualitative agreement. Interestingly, by reducing a 25% in the depth of the surface potential employed in the simulation the calculated friction force image qualitatively matches the one measured in the suspended part of the MoS₂ nanomembrane (Figure 1d). This difference in the frictional force image can be due to a slight modification of the MoS₂ lattice induced by the pre-tension of the suspended part of the sheet. However, a detailed analysis of the tension dependence of frictional force images and their interpretation, although interesting, is beyond the scope of this work.

Once the suspended nanosheet under study is identified and characterized, we measure its elastic mechanical properties using the AFM tip to apply a load cycle in the center of the suspended region of the nanosheet while its deformation is measured, as shown in the inset of Figure 2a. When the tip and sample are in contact, the elastic deformation of the nanosheet (δ), the deflection of the AFM cantilever (Δz _c), and the displacement of the scanning piezotube of the AFM (Δz _piezo) are related by the following equation:

δ = Δ z piezo - Δ z c

The force applied is related to the cantilever deflection as F = k _c·Δz _c, where k _c is the spring constant of the cantilever (k _c = 0.75 ± 0.20 N/m 20 ).

Figure 2a shows three different deformations versus force (F(δ) hereafter), measured for nanosheets with 5, 10, and 20 layers in thickness, not only by pushing the sheets but also by pulling them. For small deformations, these F(δ) traces are linear with a slope that defines the effective spring constant of the nanolayer (k _eff) 21 :

k eff = ∂ F ∂ δ δ = 0 = 4 π E 3 ( 1 - ν 2 ) ⋅ t 3 R 2 + π T

with ν the Poisson's ratio (ν = 0.125, 22 ), t the thickness, and R the radius of the nanosheet. As the effective spring constant depends on both the Young's modulus and the pre-tension constant, one cannot separately determine these values just from the slope of a F(δ) trace. To independently determine E and T, however, one can use the thickness dependence of the effective spring constant. Indeed, according to Equation 2, the first term (which accounts for the bending rigidity of the layer) strongly depends on the sheet thickness, while the second one (which accounts for the initial pre-tension) is thickness independent. Fitting the measured k _eff versus thickness to Equation 2, one can determine E and T. Figure 2b shows the measured k _eff as a function of the thickness of 31 different MoS₂ layers and the fit to the experimental data using the following:

E = 0 . 30 ± 0 . 10  TPa and T = 0 . 15 ± 0 . 15  N/m

This Young's modulus value is extremely high, only one third lower than exfoliated graphene (one of the stiffest materials on earth with E = 0.8 to 1.0 TPa) 23 24 and comparable to other 2D crystals such as graphene oxide (0.2 TPa) 25 or hexagonal boron nitride (0.25 TPa) 26 . It is also remarkable that the E value is restrained between 0.2 and 0.4 TPa, indicating a high homogeneity of the MoS₂ flakes, which is much smaller than the one observed for graphene (0.02 to 3 TPa) 27 or graphene oxide (0.08 to 0.7 TPa) 25 . The high Young's modulus of the ultrathin MoS₂ flakes (E = 0.30 ± 0.10 TPa compared to the bulk value E _bulk = 0.24 TPa 28 ) can be explained by a low presence of stacking faults. Indeed, the thinner the nanosheet the lower the presence of stacking faults, allowing the study of the intrinsic mechanical properties of the material.

We have studied the mechanical properties of ultrathin freely suspended MoS₂ nanosheets with 5 to 25 layers thick. The mean Young's modulus of these suspended nanosheets, E = 0.30 ± 0.07 TPa, is extremely high, and they present low pre-strain and high strength, being able to stand elastic deformations of tens of nanometers elastically without breaking. In summary, the low pre-tension and high elasticity and Young's modulus of these crystals make them attractive substitutes or alternatives for graphene in applications requiring flexible semiconductor materials.

AFM: Atomic force microscope; MoS₂: Molybdenum disulphide.

The authors declare that they have no competing interests.

AC-G carried out the transfer and characterization of MoS₂ nanolayers and the bending test measurements. MP fabricated the pre-patterned substrates. AC-G and GR-B participated in the design and coordination of the experiments and designed the manuscript layout. MP, GAS, HSJvdZ, and NA participated in the drafting of the manuscript and helped with the interpretation of the data. All authors read and approved the final manuscript.

AC-G and MP are post-doctoral researchers at the Kavli Institute of Nanoscience at Delft University of Technology and at the Department of Engineering Science of Yale University, respectively. GAS and HSJvdZ are assistant professor and full professor, respectively, at the Kavli Institute of Nanoscience at Delft University of Technology. NA and GR-B are associate professor and full professor, respectively, at the Department of Condensed Matter at Universidad Autonoma de Madrid. NA is also an associated senior researcher at the Madrid Institute for Advanced Studies in Nanoscience (IMDEA-Nanoscience).