We report the experimental determination of the elastic properties of suspended multilayer WSe2, a promising two-dimensional (2D) semiconducting material combined with high optical quality. The suspended WSe2 membranes have been fabricated by mechanical exfoliation of bulk WSe2 and transfer of the exfoliated multilayer WSe2 flakes onto SiO2/Si substrates pre-patterned with hole arrays. Then, indentation experiments have been performed on these membranes with an atomic force microscope. The results show that the 2D elastic modulus of the multilayer WSe2 membranes increases linearly while the prestress decreases linearly as the number of layers increases. The interlayer interaction in WSe2 has been observed to be strong enough to prevent the interlayer sliding during the indentation experiments. The Young's modulus of multilayer WSe2 (167.3 ± 6.7 GPa) is statistically independent of the thickness of the membranes, whose value is about two thirds of other most investigated 2D semiconducting transition metal dichalcogenides, namely, MoS2 and WS2. Moreover, the multilayer WSe2 can endure ∼12.4 GPa stress and ∼7.3% strain without fracture or mechanical degradation. The 2D WSe2 can be an attractive semiconducting material for application in flexible optoelectronic devices and nano-electromechanical systems.

Two-dimensional (2D) materials have triggered great interest in the application of flexible electronic devices and nano-electromechanical systems (NEMS) in recent years, due to their unique physical properties (ultralow weight, high Young's modulus, and high strength) and flexibility. The most widely studied 2D material so far is graphene because of its extraordinary physical properties (Young's modulus of ∼1 TPa and breaking strength of 100–120 GPa)1,2 and high mobility,3 and there has been a great quantity of research related to graphene based flexible devices4,5 and NEMS.6–8 However, pristine graphene does not have a bandgap,9 which limits its applications in certain fields requiring a semiconducting material. As a potential substitute material of graphene, the 2D semiconducting transition metal dichalcogenides (TMDs) with an intrinsic bandgap,10,11 such as MoS2, WS2, and WSe2, attract increasing attention, especially in electronic and optoelectronic applications.12–15 

2D WSe2 (normally exfoliated from the synthetic WSe2 crystals grown by chemical vapor transport method), as a semiconductor with high optical quality (much higher electroluminescence efficiency than natural MoS2;16,17 higher photoluminescence (PL) intensity than synthetic WS2 and natural MoS2;10 higher photo-conversion efficiency than natural MoS218,19), is a promising 2D material for application in optoelectronic devices, such as photodetectors, photovoltaics, and light-emitting diodes (LEDs). Simultaneously, under tensile strain, monolayer WSe2 remains a direct bandgap material with a bandgap decrease rate of ∼8 meV/% and multilayer WSe2 undergoes an indirect to direct bandgap transition,20 while monolayer MoS2 shows a direct to indirect bandgap transition with a higher bandgap decrease rate of ∼45 meV/% (PL intensity decreases rapidly with strain).21 Since the strain induced bandgap change will influence the resistivity of 2D materials,22 the smaller rate of bandgap change under strain of 2D WSe2 makes it a great contender for flexible electronic/optoelectronic device applications. Although a lot of research has been done to study the electrical and optical properties of the 2D TMDs,23–28 the investigations relevant to quantifying their mechanical properties experimentally (MoS229–31 and WS231) are still quite few. So far, the experimental measurement of elastic properties of 2D WSe2 has not been reported yet. In this work, we report the in-plane elastic properties of exfoliated multilayer WSe2 extracted from nanoindentation experiments. Our experiment aims to pave the way for the design and fabrication of a 2D WSe2 based flexible device and NEMS.

The indentation experiments have been performed on multilayer WSe2 membranes suspended over circular holes with an atomic force microscope (AFM). First, 280 nm SiO2 has been grown on Si substrates by thermal oxidation, which gives the optimal color contrast between WSe2 flakes and the substrates.32,33 Then, the SiO2 layers have been patterned with circular hole (1.55 μm and 2.6 μm in diameter, 220 nm in depth) arrays by photolithography and reactive ion etching (see Fig. S1 of the supplementary material).34 After etching, the photoresist has been stripped by sonication in acetone, isopropyl alcohol (IPA), and de-ionized (DI) water sequentially. Then, the substrates have been soaked in Piranha solution for 30 min and rinsed in DI water to remove organic residues, followed by O2 plasma treatment to increase the interaction between WSe2 flakes and SiO2 surface by removing the ambient adsorbates on SiO2 surface.35,36 Thereafter, multilayer WSe2 flakes have been exfoliated mechanically from bulk WSe2 crystals (supplied by 2D Semiconductors, Inc.) and transferred onto the hole arrays in SiO2/Si substrates with a polydimethylsiloxane (PDMS) stamp37,38 (see Fig. S2 of the supplementary material).34 Contact mode AFM (Bruker: MultiMode, Nanoscope IIIa) with a set-point force of ∼25 nN has been used to obtain the topography of WSe2 flakes on substrates and determine the thickness of the flakes. The reason why contact mode instead of tapping mode has been chosen is to provide accurate results for the thickness measurement.39 The number of layers of the corresponding flakes has been derived by dividing the measured thickness by the interlayer distance. An interlayer distance of 0.70 nm for WSe240,41 has been adopted for calculation.

Fig. 1(a) shows the multilayer WSe2 flakes, which have been transferred onto the substrate pre-patterned with an array of holes, forming several suspended WSe2 membranes over the holes. Fig. 1(b) presents the AFM image of the corresponding WSe2 flake in the square area of Fig. 1(a), while Fig. 1(c) shows the magnified AFM topography image of a suspended area of a 6-layer WSe2 membrane over a 1.55 μm diameter hole. No visible bubbles, wrinkles, or residue particles have been found on the membranes, which benefits from the appropriate pressure control during the all-dry transfer process.37 The height profile superimposed in the AFM image of Fig. 1(c) shows a uniform height around the edge of the hole, indicating that the membrane adheres tightly to the edge of the hole possibly by van der Waals interactions (dispersion forces or dipole interactions or both) with the substrate. The Raman measurements have been performed in a confocal Raman spectrometer (inVia Renishaw) with a 100× magnification objective in air environment. The wavelength of the laser is 514 nm, and the laser power has been kept at ∼0.2 mW. The Raman spectra of the transferred multilayer WSe2 flakes suspended over the holes are shown in Fig. 1(d). The in-plane mode E2g1 (248.7 cm−1), out-of-plane mode A1g (259.6 cm−1),42 and a weak peak at 308.2 cm−1 arising from the interlayer interaction40 have been observed. No Raman splitting of the E2g1 mode has been observed, indicating no large strain (>1%) exists in the transferred WSe2 flakes.20 The inset of Fig. 1(d) compares the Raman spectra of supported area and suspended area of a 5-layer WSe2 flake. Peak position shift of E2g1 and A1g modes has not been found, which suggests similar strain exists in the supported and suspended areas.

FIG. 1.

(a) Optical image of WSe2 flakes transferred onto pre-patterned SiO2/Si substrate. (b) AFM image of the corresponding WSe2 flake inside the square area of (a). (c) AFM image of a WSe2 membrane suspended over a hole and a superimposed height profile (along the dashed line) shows a step height of ∼30 nm. (d) Raman spectra of the suspended WSe2 flakes with different number of layers in the range of 100–500 cm−1. The inset shows the Raman spectra of supported area and suspended area of a 5-layer WSe2 flake in the range of 200–350 cm−1. Spectra are offset vertically for clarity.

FIG. 1.

(a) Optical image of WSe2 flakes transferred onto pre-patterned SiO2/Si substrate. (b) AFM image of the corresponding WSe2 flake inside the square area of (a). (c) AFM image of a WSe2 membrane suspended over a hole and a superimposed height profile (along the dashed line) shows a step height of ∼30 nm. (d) Raman spectra of the suspended WSe2 flakes with different number of layers in the range of 100–500 cm−1. The inset shows the Raman spectra of supported area and suspended area of a 5-layer WSe2 flake in the range of 200–350 cm−1. Spectra are offset vertically for clarity.

Close modal

To obtain the elastic properties of the suspended membranes, indentation experiments have been conducted. Prior to the indentation, the samples have been scanned for 1 h under AFM in order to minimize the thermal drift of the piezoelectric scanner. Then, the tip of an AFM probe with a radius rtip of 81 nm (NuNano: Scout 350 LowRes) has been located in the center of a suspended area of a membrane, and the membrane has been indented with a loading/unloading rate of 100 nm/s repeatedly for several cycles (as illustrated in Fig. 2(a)). During the measurement, no hysteresis has been found in the loading and unloading curves, which indicates that no plastic deformation has occurred to the membranes and the membranes have not slid over the margin of holes. The indentation depth at the center of a membrane has been determined by δ=ΔZd, where ΔZ is the displacement of the piezoelectric scanner as the AFM probe starts to contact with the membrane (see the supplementary material for the determination of contact point),34 and d is the deflection of the AFM probe. The force applied from the AFM tip onto the membrane has been derived from F=k×d, where k is the spring constant of the corresponding AFM probe (35.7 N/m), which has been calibrated via a reference cantilever with a known spring constant (Bruker: CLFC-NOBO). Representative force F versus displacement ΔZ curves on a suspended WSe2 membrane and SiO2/Si substrate are shown in Fig. 2(b). When the AFM probe indents towards the stiff substrate, the probe deflection d is assumed to be equal to the displacement of the scanner ΔZ, which has been used to calibrate the sensitivity of the photodetector of AFM.

FIG. 2.

(a) Schematic of the indentation experiment on a suspended WSe2 membrane. (b) Force-displacement curves obtained on a suspended WSe2 membrane and SiO2/Si substrate. (c) Representative force-deformation curves for suspended WSe2 membranes with different number of layers. The symbols correspond to the experimental data and the solid lines are fitted curves, agreeing well with the experimental results.

FIG. 2.

(a) Schematic of the indentation experiment on a suspended WSe2 membrane. (b) Force-displacement curves obtained on a suspended WSe2 membrane and SiO2/Si substrate. (c) Representative force-deformation curves for suspended WSe2 membranes with different number of layers. The symbols correspond to the experimental data and the solid lines are fitted curves, agreeing well with the experimental results.

Close modal

Since WSe2 owns three-fold rotation symmetry and the suspended area of WSe2 has circular symmetry, each WSe2 membrane has been modelled as a film with isotropic in-plane mechanical properties. Fig. 2(c) shows the representative force-deformation curves obtained from WSe2 membranes with different number of layers, which can be approximated with the Schwering-type solution as2,43,44

F=(σ02Dπ)δ+(E2Dq3r2)δ3,
(1)

where σ02D is the pretension, r is the radius of the hole, E2D is the 2D elastic modulus, v is the Poisson's ratio (0.19 (Refs. 45 and 46) for WSe2), and q is a dimensionless constant determined by q=1/(1.050.15v0.16v2). With a least square fitting of the experimental data using Eq. (1), the pretension σ02D and 2D elastic modulus E2D of the membranes can be derived. The fitted curves (solid lines in Fig. 2(c)) show good agreement with the experimental data, demonstrating the suitability of the chosen mechanic model. From this model, we can see the applied load has an approximate linear relationship with the indentation depth when the membrane deformation is small, while significantly follows a cubic relationship under large deformation.

To determine the variation of the mechanical properties of the suspended WSe2 membranes, a statistical analysis has been conducted on several WSe2 flakes with 5, 6, 12, and 14 layers. For each set of layers, the test has been done on 5 membranes with 3 different indentation depths twice, and therefore, 30 force-deformation curves have been obtained, which derives 30 values of σ02D and E2D by fitting Eq. (1) to the corresponding force-deformation curves. The results show that both the extracted 2D elastic modulus E2D and pretension σ02D are independent of the indentation depth (as shown in Fig. S5 of the supplementary material),34 which verifies the WSe2 membranes present an elastic deformation during the indentation experiments. The histograms of the derived 2D elastic modulus E2D and pretension σ02D for WSe2 membranes with different number of layers are shown in Figs. 3(a)–3(d) and Fig. S6 (see the supplementary material),34 respectively, which can be fitted with the Gaussian distribution. The mean 2D elastic modulus and their standard deviations are 596 ± 23, 690 ± 25, 1411 ± 61, and 1615± 56 N/m for 5, 6, 12, and 14-layer thick WSe2 membranes, respectively, as shown in Fig. 3(e). The deviations are attributed to different defect densities, stacking faults in the membranes, offset of the AFM tip from the center of a membrane, and the curve fitting errors. The 2D elastic modulus of the multilayer WSe2 membranes has been observed to increase statistically linearly as the number of layers increases. As described previously, the membranes have been found to clamp tightly over the edges of holes (no sliding over the substrates), which indicates interlayer sliding has not happened during the indentation experiments due to the interlayer interaction originating from van der Waals interactions.47 

FIG. 3.

Histograms of 2D elastic modulus E2D acquired from the curve fitting with Eq. (1) for (a) 5-layer, (b) 6-layer, (c) 12-layer, and (d) 14-layer thick WSe2 membranes. The dashed lines indicate the fitted Gaussian distributions. (e) 2D elastic modulus E2D of WSe2 membranes as a function of the number of layers. The error bars represent the standard deviations.

FIG. 3.

Histograms of 2D elastic modulus E2D acquired from the curve fitting with Eq. (1) for (a) 5-layer, (b) 6-layer, (c) 12-layer, and (d) 14-layer thick WSe2 membranes. The dashed lines indicate the fitted Gaussian distributions. (e) 2D elastic modulus E2D of WSe2 membranes as a function of the number of layers. The error bars represent the standard deviations.

Close modal

In order to compare the elastic properties of 2D WSe2 with the bulk materials and other materials, the 2D elastic modulus has been converted to the normal 3D Young's modulus EY by dividing the 2D value by the thickness of the membranes. Fig. 4(a) shows the box chart of Young's modulus EY for WSe2 membranes with different number of layers. No statistical difference of EY among the 4 different WSe2 membranes has been observed in our results, which indicates the Young's modulus EY of the WSe2 membranes is independent of the thickness. The corresponding values are 170.3 ± 6.7, 166.3 ± 6.1, 167.9 ± 7.2, and 164.8 ± 5.7 GPa for 5, 6, 12, and 14-layer thick WSe2 membranes, respectively, which is close to the first principle simulation result.48 Moreover, the mean value of EY (167.3 ± 6.7 GPa) for the multilayer WSe2 membranes is smaller than that of multilayer MoS2 (∼330 GPa),29 monolayer MoS2 (∼270 GPa),30,31 monolayer WS2 (∼270 GPa),31 roughly equal to one sixth of graphene (∼1.0 TPa)1,2 and carbon nanotube (∼1.0 TPa),49 and larger than that of MoS2 nanotube (∼120 GPa).50 The possible reason for smaller Young's modulus of WSe2 compared with 2D MoS2 and WS2 is that the charge transfer decrease and lattice constant increase in WSe2 induces the weakening binding between the metal and chalcogen.46 For a given geometry of NEMS, the resonant frequency will be lower if the Young's modulus of beam is lower or density is higher.51,52 Thus, 2D WSe2 with a relatively higher density value (9.32 g/cm3)53 and lower Young's modulus compared with other 2D materials can be put into application of NEMS with lower resonance frequency, such as acoustic sensor54 and loudspeakers.55 In addition, when flexible electronics composed of 2D materials are bent or stretched, extra stress will be formed at the interface between the 2D material and soft polymeric substrates, due to the mismatch of their mechanical properties, which may weaken the reliability of the devices. 2D WSe2 with lower Young's modulus will reduce this kind of stress under a certain amount of strain of devices and may therefore be more suitable for flexible electronics applications.

FIG. 4.

(a) The box chart of Young's modulus EY for WSe2 membranes with different number of layers. Each plot includes the minimum, lower quartile, median (horizontal line), mean (hollow square), upper quartile, maximum, and discrete data at the left. (b) Pretension and prestress for the corresponding multilayer WSe2 membranes.

FIG. 4.

(a) The box chart of Young's modulus EY for WSe2 membranes with different number of layers. Each plot includes the minimum, lower quartile, median (horizontal line), mean (hollow square), upper quartile, maximum, and discrete data at the left. (b) Pretension and prestress for the corresponding multilayer WSe2 membranes.

Close modal

During the whole indentation experiments, the maximum force applied on these WSe2 membranes is ∼3200 nN. None of the membranes have been fractured and all still kept their original elastic properties under this force. The maximum stress for a circular and linear elastic membrane during an indentation experiment with a spherical indenter in the case of rtip/r ≪ 1 can be derived with the expression as56 

σmax2D=FmaxE2D4πrtip.
(2)

Thus, the maximum stress for a 5-layer WSe2 membrane is calculated to be ∼43 N/m, corresponding to ∼12.4 GPa. Assuming the stress of multilayer WSe2 has a linear relationship with its strain (σ=EYε) results in the maximum strain of approximate 7.3%. Thus, the multilayer WSe2 can at least withstand ∼12.4 GPa stress and ∼7.3% strain without breaking. (The breaking stress/strain is larger than ∼12.4 GPa/∼7.3%.) This means the breaking strain of 2D WSe2 is at least three times larger than that of silicon (0.4%–2.2%)57 and comparable with the common materials used for substrates of flexible electronics, namely, polyimide (PI) or PDMS (∼7%),58 implying that 2D WSe2 is compatible with most of flexible electronic devices.

Fig. 4(b) shows the relationship between the extracted pretension and prestress (pretension divided by the thickness of the membranes) and the number of layers of WSe2 membranes. As can be seen, in our experiments, the pretension σ02D varies with the thickness of WSe2 membranes and is in the same scale as the reports of Refs. 29 and 31, which employ a similar 2D materials transfer method. In addition, the prestress that originates from the mechanical exfoliation and transfer process decreases approximately linearly as the number of layers increases. During the transfer process, the pressing of PDMS stamp together with WSe2 would have resulted in the PDMS stamp expanding laterally (see Fig. S2(c) of the supplementary material),34 due to the softness of the PDMS,59 which could have stretched the WSe2 flakes to a certain extent. When the PDMS stamp has been peeled off from the substrate, it is likely that the stretched WSe2 flakes adhering to the substrate by van der Waals force result in the positive pretension formed in the transferred flakes.

In conclusion, we have fabricated multilayer WSe2 membranes suspended over circular holes. The elastic properties of WSe2 membranes with different number of layers have been determined employing nanoindentation experiments. The results show that although the prestress decreases approximately linearly as the number of layers increases, the Young's modulus is independent of the number of layers, which indicates the interlayer interaction is strong enough to prevent the interlayer sliding. The Young's modulus of multilayer WSe2 is about two thirds of other most investigated 2D semiconducting TMDs, namely, MoS2 and WS2, and one sixth of graphene and carbon nanotube. During the experiments, the WSe2 membranes have withstood ∼12.4 GPa stress and ∼7.3% strain without breaking or mechanical degradation. 2D WSe2 can be an attractive alternative for graphene in some applications requiring flexible semiconducting materials, such as bendable transistors, photodetectors, photovoltaics, and NEMS.

We would like to thank the financial support of UK Engineering and Physical Sciences Research Council (EPSRC) for this work. We acknowledge Atif Syed's assistance with the AFM tip characterization.

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Supplementary Material