Elastic properties of suspended multilayer WSe 2

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.7][8] However, pristine graphene does not have a bandgap, 9 which limits its applications in certain fields requiring a semiconducting material.][14][15] 2D WSe 2 (normally exfoliated from the synthetic WSe 2 crystals grown by chemical vapor transport method), as a semiconductor with high optical quality (much higher electroluminescence efficiency than natural MoS 2 ; 16,17 higher photoluminescence (PL) intensity than synthetic WS 2 and natural MoS 2 ; 10 higher photo-conversion efficiency than natural MoS 2 18,19   ), is a promising 2D material for application in optoelectronic devices, such as photodetectors, photovoltaics, and light-emitting diodes (LEDs).Simultaneously, under tensile strain, monolayer WSe 2 remains a direct bandgap material with a bandgap decrease rate of $8 meV/% and multilayer WSe 2 undergoes an indirect to direct bandgap transition, 20 while monolayer MoS 2 shows a direct to indirect bandgap transition with a higher bandgap decrease rate of $45 meV/% (PL intensity decreases rapidly with strain). 21ince the strain induced bandgap change will influence the resistivity of 2D materials, 22 the smaller rate of bandgap change under strain of 2D WSe 2 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][24][25][26][27][28] the investigations relevant to quantifying their mechanical properties experimentally (MoS 2 [29][30][31] and WS 2

31
) are still quite few.So far, the experimental measurement of elastic properties of 2D WSe 2 has not been reported yet.In this work, we report the in-plane elastic properties of exfoliated multilayer WSe 2 extracted from nanoindentation experiments.Our experiment aims to pave the way for the design and fabrication of a 2D WSe 2 based flexible device and NEMS.
The indentation experiments have been performed on multilayer WSe 2 membranes suspended over circular holes with an atomic force microscope (AFM).First, 280 nm SiO 2 has been grown on Si substrates by thermal oxidation, which gives the optimal color contrast between WSe 2 flakes and the substrates. 32,33Then, the SiO 2 layers have been patterned with circular hole (1.55 lm and 2.6 lm in diameter, 220 nm in depth) arrays by photolithography and reactive ion etching (see Fig. S1 of the supplementary material). 34After 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 a) Author to whom correspondence should be addressed.Electronic mail: rui.zhang@ed.ac.uk 0003-6951/2016/108(4)/042104/5 V C Author(s) 2016 108, 042104-1 APPLIED PHYSICS LETTERS 108, 042104 (2016) solution for 30 min and rinsed in DI water to remove organic residues, followed by O 2 plasma treatment to increase the interaction between WSe 2 flakes and SiO 2 surface by removing the ambient adsorbates on SiO 2 surface. 35,36Thereafter, multilayer WSe 2 flakes have been exfoliated mechanically from bulk WSe 2 crystals (supplied by 2D Semiconductors, Inc.) and transferred onto the hole arrays in SiO 2 /Si substrates with a polydimethylsiloxane (PDMS) stamp 37,38 (see Fig. S2 of the supplementary material). 34Contact mode AFM (Bruker: MultiMode, Nanoscope IIIa) with a set-point force of $25 nN has been used to obtain the topography of WSe 2 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. 39The 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 WSe 2 40,41 has been adopted for calculation.Fig. 1(a) shows the multilayer WSe 2 flakes, which have been transferred onto the substrate pre-patterned with an array of holes, forming several suspended WSe 2 membranes over the holes.Fig. 1(b) presents the AFM image of the corresponding WSe 2 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 WSe 2 membrane over a 1.55 lm 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. 37The 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 100Â 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 WSe 2 flakes suspended over the holes are shown in Fig. 1(d).The in-plane mode E 1 2g (248.7 cm À1 ), out-ofplane mode A 1g (259.6 cm À1 ), 42 and a weak peak at 308.2 cm À1 arising from the interlayer interaction 40 have been observed.No Raman splitting of the E 1 2g mode has been observed, indicating no large strain (>1%) exists in the transferred WSe 2 flakes. 20The inset of Fig. 1(d) compares the Raman spectra of supported area and suspended area of a 5-layer WSe 2 flake.Peak position shift of E 1 2g and A 1g modes has not been found, which suggests similar strain exists in the supported and suspended areas.
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 r tip 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 d ¼ DZ À d, where DZ 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 ¼ k Â 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 DZ curves on a suspended WSe 2 membrane and SiO 2 /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 DZ, which has been used to calibrate the sensitivity of the photodetector of AFM.
Since WSe 2 owns three-fold rotation symmetry and the suspended area of WSe 2 has circular symmetry, each WSe 2 membrane has been modelled as a film with isotropic in-plane mechanical properties.Fig. 2(c) shows the representative force-deformation curves obtained from WSe 2 membranes with different number of layers, which can be approximated with the Schwering-type solution as 2,43,44 where r 2D 0 is the pretension, r is the radius of the hole, E 2D is the 2D elastic modulus, v is the Poisson's ratio (0.19 (Refs.45 and 46) for WSe 2 ), and q is a dimensionless constant determined by q ¼ 1=ð1:05 À 0:15v À 0:16v 2 Þ.With a least square fitting of the experimental data using Eq. ( 1), the pretension r 2D 0 and 2D elastic modulus E 2D 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 WSe 2 membranes, a statistical analysis has been conducted on several WSe 2 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 r 2D 0 and E 2D by fitting Eq. ( 1) to the corresponding force-deformation curves.The results show that both the extracted 2D elastic modulus E 2D and pretension r 2D 0 are independent of the indentation depth (as shown in Fig. S5 of the supplementary material), 34 which verifies the WSe 2 membranes present an elastic deformation during the indentation experiments.The histograms of the derived 2D elastic modulus E 2D and pretension r 2D 0 for WSe 2 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 6 23, 690 6 25, 1411 6 61, and 1615 6 56 N/m 5, 6, 12, and 14-layer thick WSe 2 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 WSe 2 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 order to compare the elastic properties of 2D WSe 2 with the bulk materials and other materials, the 2D elastic modulus has been converted to the normal 3D Young's modulus E Y by dividing the 2D value by the thickness of the membranes.Fig. 4(a) shows the box chart of Young's modulus E Y for WSe 2 membranes with different number of layers.No statistical difference of E Y among the 4 different WSe 2 membranes has been observed in our results, which indicates the Young's modulus E Y of the WSe 2 membranes is independent of the thickness.The corresponding values are 170.3 6 6.7, 166.3 6 6.1, 167.9 6 7.2, and 164.8 6 5.7 GPa for 5, 6, 12, and 14-layer thick WSe 2 membranes, respectively, which is close to the first principle simulation result. 48oreover, the mean value of E Y (167.3 6 6.7 GPa) for the multilayer WSe 2 membranes is smaller than that of multilayer MoS 2 ($330 GPa), 29 monolayer MoS 2 ($270 GPa), 30,31 monolayer WS 2 ($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 MoS 2 nanotube ($120 GPa). 50The possible reason for smaller Young's modulus of WSe 2 compared with 2D MoS 2 and WS 2 is that the charge transfer decrease and lattice constant increase in WSe 2 induces the weakening binding between the metal and chalcogen. 46For a given geometry of NEMS, the resonant frequency will be lower if the Young's modulus of beam is lower or density is higher. 51,52Thus, 2D WSe 2 with a relatively higher density value (9.32 g/cm 3 ) 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 sensor 54 and loudspeakers. 55In 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 WSe 2 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.During the whole indentation experiments, the maximum force applied on these WSe 2 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 r tip /r ( 1 can be derived with the expression as 56 Thus, the maximum stress for a 5-layer WSe 2 membrane is calculated to be $43 N/m, corresponding to $12.4 GPa. Assuming the stress of multilayer WSe 2 has a linear relationship with its strain (r ¼ E Y e) results in the maximum strain of approximate 7.3%.Thus, the multilayer WSe 2 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 WSe 2 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 WSe 2 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 WSe 2 membranes.As can be seen, in our experiments, the pretension r 2D 0 varies with the thickness of WSe 2 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 WSe 2 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 WSe 2 flakes to a certain extent.When the PDMS stamp has been peeled off from the substrate, it is likely that the stretched WSe 2 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 WSe 2 membranes suspended over circular holes.The elastic properties of WSe 2 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 WSe 2 is about two thirds of other most investigated 2D semiconducting TMDs, namely, MoS 2 and WS 2 , and one sixth of graphene and carbon nanotube.During the experiments, the WSe 2 membranes have withstood $12.4 GPa stress and $7.3% strain without breaking or mechanical degradation.2D WSe 2 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.

FIG. 1 .
FIG. 1.(a) Optical image of WSe 2 flakes transferred onto pre-patterned SiO 2 /Si substrate.(b) AFM image of the corresponding WSe 2 flake inside the square area of (a).(c) AFM image of a WSe 2 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 WSe 2 flakes with different number of layers in the range of 100-500 cm À1 .The inset shows the Raman spectra of supported area and suspended area of a 5-layer WSe 2 flake in the range of 200-350 cm À1 .Spectra are offset vertically for clarity.

FIG. 2 .
FIG. 2. (a) Schematic of the indentation experiment on a suspended WSe 2 membrane.(b) Force-displacement curves obtained on a suspended WSe 2 membrane and SiO 2 /Si substrate.(c) Representative force-deformation curves for suspended WSe 2 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. 4 .
FIG. 4. (a) The box chart of Young's modulus E Y for WSe 2 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 WSe 2 membranes.