Biaxial Strain Transfer in Monolayer MoS2 and WSe2 Transistor Structures

Monolayer transition metal dichalcogenides are intensely explored as active materials in 2D material-based devices due to their potential to overcome device size limitations, sub-nanometric thickness, and robust mechanical properties. Considering their large band gap sensitivity to mechanical strain, single-layered TMDs are well-suited for strain-engineered devices. While the impact of various types of mechanical strain on the properties of a variety of TMDs has been studied in the past, TMD-based devices have rarely been studied under mechanical deformations, with uniaxial strain being the most common one. Biaxial strain on the other hand, which is an important mode of deformation, remains scarcely studied as far as 2D material devices are concerned. Here, we study the strain transfer efficiency in MoS2- and WSe2-based flexible transistor structures under biaxial deformation. Utilizing Raman spectroscopy, we identify that strains as high as 0.55% can be efficiently and homogeneously transferred from the substrate to the material in the transistor channel. In particular, for the WSe2 transistors, we capture the strain dependence of the higher-order Raman modes and show that they are up to five times more sensitive compared to the first-order ones. Our work demonstrates Raman spectroscopy as a nondestructive probe for strain detection in 2D material-based flexible electronics and deepens our understanding of the strain transfer effects on 2D TMD devices.


■ INTRODUCTION
−24 Various modes of deformation have been successfully applied in atomically thin materials including uniaxial, 13,25,26 biaxial, 27−30 shear 31 or nonuniform mechanical strain fields 17 using a variety of techniques.Nevertheless, current literature has primarily studied monolayers that were either freestanding, 30,32 simply supported 13,25,33 or polymer-encapsulated. 34,35 In contrast, flexible 2D-TMDs-based devices typically involve several heterointerfaces that are required to not only withstand the externally applied mechanical strain but also efficiently transfer it to the TMD crystal to leverage straininduced behavior.For example, locally back-gated field-effect transistors contain multiple interfaces in the substrate-gatedielectric-channel stack as well as between the channel and electrical contacts.−40 In this work, we demonstrate that very high biaxial strain transfer efficiency can be achieved in 2D material-based flexible devices.In particular, for the first time, we subject several MoS 2 and WSe 2 monolayer transistors, fabricated on flexible polyethylene napthalate (PEN) substrates, to tensile biaxial strain.Raman spectroscopy is utilized to measure the imposed strain in situ.We show that despite the heterogeneity of interfaces occurring in a typical 2D material transistor, biaxial strains up to 0.55% can be efficiently and controllably imposed on the semiconducting TMD layers in the transistor channel.
Because the biaxial strain sensitivity of the main Raman modes of 1L-MoS 2 is well-established, 28,30 the efficient strain transfer is first verified for several MoS 2 devices through detailed Raman mapping over the transistor channel.An analysis of the Raman maps obtained in the undeformed state revealed a distribution of residual strain.Upon strain application, the magnitude of strain in the channel systematically increased in a relatively homogeneous manner, indicating efficient biaxial strain transfer.Furthermore, WSe 2 devices were investigated using 515 and 632 nm excitation, which offer different resonance conditions. 41We also probe the strain response of the higher-order Raman modes of WSe 2 between 350 to 400 cm −1 for the first time, finding a 5-fold strain sensitivity compared to the accidentally degenerate first-order A 1 ′/E′ Raman modes.−44 Finally, this work highlights the utility of Raman spectroscopy for strain detection in 2D material based flexible electronics and, furthermore, deepens our understanding of the strain transfer effects on 2D TMD devices, with potential implications for engineering transistor performance as it has been done for strained silicon in the past.

■ METHODS
Flexible Transistor Fabrication.Figure 1a shows the device structure of our 1L MoS 2 and WSe 2 field-effect transistors.We first pattern and evaporate 5 nm/40 nm Ti/Au local back gates onto 125-μm thick free-standing polyethylene naphthalate (PEN) substrates, then deposit ≈18 nm Al 2 O 3 using atomic layer deposition at 130 °C.We grow monolayer MoS 2 and WSe 2 onto Si/SiO 2 substrates with 100 nm thermal oxide via solid-source chemical vapor deposition.We then transfer the TMD onto the PEN substrate using a bilayer PMMA/polystyrene stamp, as described in ref 45, and pattern and evaporate 55 nm Au contacts.Lastly, we define the channel using an O 2 plasma etch.The flexible PEN film with transistors is attached to a 3 mm thick PMMA cruciform using commercially available cyanoacrylate adhesive (Logo Instant).Section 1 in the Supporting Information discusses in more detail the attachment procedure.
Application of Biaxial Strain.A custom-made strain jig allows the controlled application of biaxial strain on the cruciform while, at the same time, providing direct optical access to the samples.In particular, a micrometric precision screw (deflection screw) is used to gradually deflect the center of the cruciform in the out-of-plane direction.−29 This kind of bending induces tensile biaxial strain at the concave side of the cruciform.More details of the strain jig have been published elsewhere. 29aman Spectroscopy.All Raman measurements were conducted in the backscattering geometry using three different set-ups.The first setup is a Renishaw InVia Raman spectrometer equipped with a solid state Cobolt Fandango (515 nm) laser and a 2400 grooves/mm grating.The laser beam was focused on the samples using a 50 × (NA: 0.75) objective lens resulting in a spot-size of about 1 μm.Incident power on sample was less than 0.1 mW.High-resolution Raman spectra were recorded using a triple monochromator system (Dilor XY) equipped with a nitrogen-cooled CCD and a 514.5 nm Ar + laser.A 50× long working distance objective was used to focus the beam on the sample, at a power lower than 0.5 mW.Finally, the Raman measurements acquired with the 632.8 nm He−Ne laser line were recorded using a LabRam HR (HORIBA) system equipped with a Peltier-cooled CCD.The laser was focused on the sample with a 50× long working distance objective at a power lower than 0.1 mW.
■ RESULTS AND DISCUSSION MoS 2 Transistors.Figure 1b shows the forward and backward drain current (I ds ) vs gate voltage (V g ) sweeps of a representative MoS 2 device.The devices have a constantcurrent threshold voltage of about −3 V, extracted using the current threshold of 100 pA, consistent with the International Roadmap for Devices and Systems. 46We calculate the carrier concentration at V gs = 0 V from the I ds − V gs curves using n 2D = C ox •(V gs V T ), where C ox ≈ 350 nF/cm 2 is the gate oxide capacitance per unit area.This results in a charge density n 2D ≈ 6.6 × 10 12 cm −2 in the channel region.We note that device performance is suboptimal compared to state-of-the-art 2D material devices.This, however, is attributed mainly to the following three factors.First, the devices were electrically measured in air and were not encapsulated, thus the transistor channel was exposed to ambient conditions.This way water molecules and/or other adsorbates could adsorb in the channel during measurement, increasing the device hysteresis. 47econd, contact resistance may contribute to lower ONcurrent, as Au is known to cause Fermi level pinning near the midgap in MoS 2 and WSe 2 . 48Third, device fabrication involves a wet transfer process, which may cause additional damage to the TMD and introduce PMMA polymer residues onto the TMD surface. 49While other works have achieved more optimal contacts with other metals, contact resistance optimization is outside the scope of this work.After attachment of the flexible transistors onto a PMMA cruciform using a cyanoacrylate adhesive (Figure 1c), biaxial strain is applied on the cruciform (see Methods).Due to interfacial shear forces between PMMA/adhesive and adhesive/PEN film interfaces, this applied strain is then transferred to the PEN film.Note, however, that the strain imparted on the device-side of the PEN film is not necessarily of equal magnitude to the strain that is applied at the cruciform's top surface in the absence of the PEN film.The ratio between the strain at top of the PEN film, ε PEN , to the applied strain on the cruciform, ε PMMA , is known as the strain transfer efficiency and depends on the adhesive thickness and its mechanical properties.The strain transfer efficiency from cruciform to the PEN film was assessed using strain gauge sensors for several adhesives.Among the compounds that were tested, cyanoacrylate adhesive (CA) presented an average strain transfer efficiency of 87%, preserved the linearity of applied strains, and formed a thin adhesion layer with a nominal thickness of the order of 20 μm (see Supporting Information Section 1).
As a first step, MoS 2 devices were investigated under various levels of biaxial strain using Raman spectroscopy.Four devices were measured in total (labeled MT1 to MT4) all having a nominal channel width of 20 μm and channel length of 5 μm except for device MT4 with a channel length of 7 μm.Considering that the probed devices were located at different positions relative to the center of the cruciform, slightly different strains are imposed at each device which, however, can be determined from the methodology presented in a previous work. 29The probed devices were all between 1 up to 2 mm from the center of the cruciform and the corresponding strain level differed less than 5%.Figure 2a shows Raman spectra from the central region of an MoS 2 transistor channel as a function of applied strain.Both peaks shift to lower frequencies with increasing biaxial strain, with E′ being more sensitive to the A 1 ′, (Figure 2b).Importantly, no widening or splitting of the E′ peak is observed, as expected for biaxial strain.The dependence of the peak positions for the other transistors that were studied (devices MT1, MT2 and MT4) are shown in Figure S3, and exhibit similar trends.The average slopes for E′ and A 1 ′ peaks were determined at −4.3(1) and −2.5(3) cm −1 /%, respectively.Table 1 summarizes  , for all tested MoS 2 devices.The results are in very good agreement with the reported shift rates and Gruneisen parameters for CVD MoS 2 monolayers under biaxial tension. 28,30part from single point spectra per strain level, detailed Raman maps were collected at zero and maximum applied  strains on all four devices.Figure 2c shows the PosA 1 ′ − PosE′ correlation plot for device MT1 at zero and maximum applied strain as blue circles and orange triangles, respectively.Note that the mean position of the unstrained cluster was used as a reference point for the strain−doping axes.For both cases, the data form clearly distinguished clusters.The unstrained cluster presents an average Pos(E′), Pos(A 1 ′) value of 384.8 and 403.8 cm −1 with a standard deviation of 0.2 and 0.4 cm −1 , respectively.On the other hand, at the maximum applied strain of 0.43%, the cluster shifts to a new position with Pos(E), Pos(A 1 ′) = 383.4± 0.2 and 403.4 ± 0.4 cm −1 , respectively.Overlaying the strain and doping axes in the correlation plot with reference to the unstrained state, it is found that, at maximum applied strain, the MoS 2 experiences mainly mechanical strain with only slight change of the doping levels (roughly 2 × 10 12 cm −2 ).Importantly, the almost uniform shift of the cluster indicates homogeneous strain transfer across the channel region.As shown in the strain contour maps at zero and maximum strain presented in Figure 2d, mechanical strain in the channel region is increased but the initial strain distribution roughly remains unchanged.Specifically, the initial residual strain pattern, imparted to the monolayer due to the transferring and subsequent nanofabrication steps, can also be roughly discerned in the maximum strain contour.This phenomenon is observed in all four transistors studied.The corresponding strain maps and ε−n correlation plots for devices MT2, MT3 and MT4 are presented in Supporting Information Figure S4.This is an important result, indicating that mechanical strain can indeed be homogeneously transferred to the transistor channel, despite the complex interfaces and geometry of the transistors.WSe 2 Transistors.Representative I d − V g transfer curves at zero strain for five WSe 2 devices are presented in Figure S5 in the Supporting Information.Semiconducting behavior and ambipolarity are observed, confirming that the material quality is sufficient for field-effect transistor operation.Having established that mechanical strain can be transferred efficiently in the channel of an MoS 2 transistor, attention was shifted to monolayer tungsten diselenide (WSe 2 ) devices, because it has hardly been studied under biaxial deformations despite its significance as a potential p-type semiconductor in flexible electronics.Hence, a systematic strain-dependent Raman study was carried out on WSe 2 transistors having identical structure to the previously studied MoS 2 devices.Additionally, since the biaxial strain response of WSe 2 is not known, contrary to other TMDs such as MoS 2 28,30 two samples having a simpler structure were also tested under strain in order to establish a reference point.The first sample was fabricated by transferring as-grown CVD 1L-WSe 2 crystals directly onto a PEN film, which was then subsequently bonded to a PMMA cruciform.The second sample was identical to the first one except for an Representative Raman spectra of these two samples are compared to a spectrum obtained from the channel region of a 1L-WSe 2 transistor in Figure S6 in the Supporting Information.It is evident that the spectra from the reference samples (WSe 2 /PEN and WSe 2 /AlO x /PEN) exhibit strong background luminescence originating from the PEN film.In contrast, the spectrum from the 1L-WSe 2 in the transistor channel presents a very low background intensity.The background luminescence and prominent Raman bands around 520 and 780 cm −1 are attributed to the excitation of the PEN substrate.Unfortunately, their presence partially obscures accurate measurement of the WSe 2 Raman modes apart from the very prominent peak around 250 cm −1 .In contrast, the 40 nm thick Au layer in the gate electrode of the transistors effectively blocks the excitation beam from reaching the PEN film substrate, as its thickness is roughly twice as large as the penetration depth of λ = 515 nm radiation on Au (≈20 nm). 50his screening effect not only allows for the recording of excellent quality spectra free from extrinsic influences, but also enables the detection of additional Raman modes of WSe 2 in the 300 to 440 cm −1 spectral region (inset of Figure S6).Note that similar effects have been have been observed for FETs fabricated on polyimide instead of PEN. 12 This indicates that using an ultrathin film of gold (or any other noble metal) in a similar manner has the potential to enable the collection of high-quality spectra.Finally, the strain dependence of the A 1 ′ and 2LA modes for the reference samples is presented in Supporting Information Figure S7.The shift rate of the A 1 ′ mode was determined at −1.0(2) and −1.7(3) cm −1 /%, while the shift rate of the 2LA mode was determined at −1.5(3) and −1.8(4) cm −1 /%, for the WSe 2 /PEN and WSe 2 /AlO x /PEN sample, respectively.
Figure 3a,b show two spectral regions from representative Raman spectra of a WSe 2 transistor, obtained with λ = 515 nm excitation.The spectra were collected at increasing levels of tensile biaxial strain reaching up to about 0.5%.In the lower frequency region (Figure 3a), the most prominent feature is located around 249 cm −1 and is attributed to the out-of-plane, A 1 ′, and in-plane, E′, Raman-active zone-center optical phonons.The accidental degeneracy of the A 1 ′ and E′ phonon frequencies, which occurs only in the monolayer limit, 51 can make determining strain from Raman peaks challenging due to the much lower sensitivity of the A 1 ′ mode compared to the E′ mode.An alternative approach is to employ polarizationresolved Raman scattering (linear or circular), which enables the selection of only one of the E′ and A 1 ′ peaks depending on the polarization configuration. 52,53Note, however, that the almost identical frequency and similar widths of the E′ and A 1 ′ modes for the monolayer WSe 2 complicates the peak deconvolution and assignment process.
The comparatively weak feature around 260 cm −1 is known as the 2LA peak and is assigned to second-order two-phonon scattering involving two longitudinal acoustic (LA) phonons from the Brillouin zone boundary.Note that a closer inspection of the Raman line shape of the 2LA feature, as recorded with 515 nm excitation, hints to the contribution of at least two components.Indeed, the line shape of the 2LA mode can potentially include scattering from at least two critical points of the LA branch, specifically, a local maximum at the M point and a saddle point located along the MK high symmetry line. 54The frequency of the LA branch at the aforementioned critical points is around 130 cm −1 , indicating that the 2LA overtones are expected around 260 cm −1 .This is consistent with the detected broad and asymmetric feature detected close to 260 cm −1 as shown in Figure S8.However, in at least one work, the high frequency component of this feature close to ≈263 cm −1 is attributed to the defect-activated A 1 ′(M). 55This is reasonable since there is a large contribution to the phonon density of states near this frequency due to the A 1 ′ branch.It must nevertheless be stressed that while critical point analysis can provide interesting insights, a proper determination of the line shape of higher-order modes can be vastly more complex and demands a more rigorous analysis which is beyond the scope of this work. 43Note that in the spectra obtained with 515 nm excitation, this feature was fitted with only one Lorentzian component since attempts to fit this feature with two Lorentzians resulted in unstable fits.However, an additional experiment with 514.5 nm excitation and a higher resolution spectrometer resolved both 2LA and A 1 ′(M) peaks (see Supporting Information Figure S9).
In the higher frequency region between 300 and 440 cm −1 (Figure 3b), a bundle of five Raman peaks is detected.Since the highest phonon frequency in 1L-WSe 2 lies close to 300 cm −1 , these peaks can only be assigned to higher-order Table 2. Raman Peak Positions, Strain-Induced Shift Rates and Gruneisen Parameters for WSe 2 Devices Excited with λ exc = 515 nm scattering processes involving more than one phonon, i.e., overtones or phonon combinations.The exact assignment of those peaks is not yet clearly established.They are so far attributed to multiphonon combination or difference processes between optical and acoustic phonons. 51,55For this reason, the four high-order sharp peaks that were monitored successfully under strain are labeled as p 1 to p 4 , as shown in Figure 3b.The lowest frequency broader peak around 350 cm −1 is not discussed further in this study because large uncertainties occurred in determining its position during curve fitting.We note that while for peak p 1 the signal-to-noise ratio is rather low compared to other higher-order peaks, the peak position can nevertheless be extracted satisfactorily by multiple Lorentzian fitting as shown in Figure 3c.
Figure 3c shows the strain dependence of the frequencies of all six Raman bands that were adequately monitored in the spectra from a representative device.With increasing tensile strain, all recorded peaks are found to shift to lower frequencies.From each of the five WSe 2 transistors that were investigated with 515 nm excitation, up to four spectra were collected from the central region of the channel of each device at each strain level.The points in Figure 3c show the mean peak position and the error bars indicate the standard deviation of the measured frequencies.The determined shift rates for all Raman peaks and investigated devices (labeled WT1 to WT4) are summarized in Table 2.It is stressed that the A 1 ′ mode presents an average shift rate of −1.3(1) cm −1 /% which compares satisfactorily with the obtained shift rates of −1.0(2) and −1.8(3) cm −1 /%, respectively, for the WSe 2 /PEN and WSe 2 /AlO x /PEN reference samples presented earlier.Furthermore, the higher-order peaks (p 1 to p 4 ) are found to be up to five times more sensitive to strain compared to the A 1 ′ mode and, thus, appear as more appealing strain indicator compared to E′/A 1 ′.Importantly, these results are in very good agreement with the higher resolution Raman experiment presented in the Supporting Information section 7.
Two other WSe devices WT6, WT7 were also studied in a following experiment under λ = 632.8nm excitation.The evolution of the Raman spectra as a function of strain is presented in Figure 3d,e for the lower and higher frequency regions (as in (a) and (b)), respectively.Due to the different resonance conditions, new bands are now visible in the lower frequency region.Three new peaks are detected around 219, 223, and 239 cm −1 and are labeled a, b and c, respectively.The most notable difference, compared to the excitation with green laser (515 nm), is that the 2LA/A′(M) feature is now the most prominent one, with two clearly resolvable components.This time the A 1 ′(Γ) peak, indicated by the "*" symbol, is barely visible between the c and 2LA peaks.No new peaks were detected in the higher frequency region, and only the p 2 − p 4 peaks were of adequate intensity.Also, in contrast to what is observed with 515 nm excitation, the p 3 and p 4 peaks are now three to four times more intense than p 2 .
Note that in multiple-phonon scattering an excited carrier is scattered consecutively by two or more phonons.For excitation energies near the visible spectrum the selection rules relax and require that the wavevectors of the participating phonons sum to zero. 42In general, the intensity of higherorder Raman modes is expected to be weaker compared to first-order modes.However, when the intermediate states occupied by the excited carrier are real electronic states of the system instead of virtual states (resonance condition), a significant enhancement of the scattering cross-section for these participating phonons is observed. 43,44The process is said to be a single-, double-or multiple-resonance, depending on how many of the intermediate states satisfy the resonance condition.In some cases, the higher-order modes can be of comparable intensity to the first-order modes.An excellent manifestation of resonant Raman effects is the large enhancement of the intensity of the 2LA mode in semiconducting TMDs.For example, for 632.8 nm excitation in WSe 2 (see Figure 3), or for WS 2 monolayers with 514.5 nm excitation, as shown in ref 56.It must be noted that in a resonance Raman scattering process the electronic and phononic systems of the material are intimately coupled. 42If the matrix element for the process is not vanishing due other reasons (e.g., symmetry considerations), the scattering cross-section is strongly enhanced only for those phonons whose energy and wavevectors "connect" two (or more) real electronic states within the same or neighboring conduction or valence band valleys.For example, in semiconducting TMDs such as WSe 2 , a common intervalley scattering pathway occurs between the conduction band valleys located at the K/K′ point of the Brillouin zone that are connected by phonons with wavevectors near K. 43,57 Thus, under appropriate resonance conditions, certain phonons near the K point can contribute to the recorded Raman spectrum.Here we note that mechanical strain significantly impacts both the electronic band as well as the phonon band structure of the material. 13,29,30Hence, the strain-induced frequency shift of higherorder modes is ultimately influenced by both contributions.−60 Such a detailed treatment of resonance Raman effects in WSe 2 is out of scope of this work.Nevertheless, the strain dependence of the Raman modes of WSe 2 presented here, is valuable for future treatments of the phenomenon.
The strain dependence of the detected peak positions is presented in Figure 3f.Again, all peaks were observed to redshift with applied biaxial strain.Table 3 summarizes the determined shiftrates.Importantly, for both devices measured under 632.8 nm excitation, the strain-induced shift rates for most of the detected Raman peaks are similar.The larger uncertainties are mainly due to the lower spectral resolution of the Raman spectrometer for 632.8 nm excitation (see Methods) compared to the 515 nm.For example, the average shift rate for the features assigned to the 2LA/A 1 ′ mode with 515 nm excitation, is −2.3(1) cm −1 , while for 632.8 nm excitation the 2LA and A 1 ′(M) peaks presented shift rates of −2.4(7) cm −1 /% and −1.6(7) cm −1 , respectively.On the other hand, the average shift rate of peak p 2 under 632.8 nm excitation was found to be about −2.6(7) cm −1 /%, which is lower compared to average shift rate of −4.8(2) cm −1 /% observed for 515 nm excitation.This is not surprising, considering the significantly different excitation conditions which probe phonons from different regions of the BZ.Overall, peak p 2 under 515 nm excitation seems to be the best compromise between strain sensitivity and simplicity of peak fitting.
The strain-dependent Raman spectroscopy in 1L-MoS 2 devices provided strong evidence that biaxial strain can be effectively transferred through both the gate electrode and dielectric, as the detected Raman peak positions varied linearly with applied strain and at rates compatible with previously published data. 28In particular, the detected strain-induced shift rates of the first-order Raman modes of MoS 2 are on the high end of the reported values for simply supported CVD MoS 2 .This indicates that the various functional layers of the device (i.e., gate and gate dielectric) are robust in transferring the applied strain from PEN to MoS 2 (at least up to 0.5%).As such, the strain transfer efficiency from PEN film through the gate electrode, gate oxide and finally the MoS 2 layer is found to be very close to 100% for the transistor geometries used here.The Young's modulus of PEN (5.5 GPa) is one to 2 orders of magnitude lower than the moduli of Au, AlO x and MoS 2 .This is reminiscent to the reinforcement effect, 61 where a strain gauge bonded to a low modulus material (substrate) leads to inefficient strain transfer from the substrate to the strain gauge (the transistor in our case). 61To explore the mechanics of strain transfer further, we model the adhesive-PEN-TMD transistor stack using an integro-differential equation that captures the strain transfer efficiency in uniaxial loading based on previous work by Stehlin. 62For an MoS 2 /AlO x (18 nm)/ Au (40 nm)/Ti (5 nm) stack supported on a PEN substrate, the calculated strain transfer efficiency for various channel lengths is presented in Figure S11.The strain transfer efficiency as a function of the logarithm of the channel length (L) is a typical s-shaped curve with 50 and 90% efficiencies attained at 154 and 1150 nm, respectively.For the 5 μm long channels in the devices studied in this work, the strain transfer efficiency is 98%, justifying that the strain experienced by the 2D materials in the tested devices is essentially equal to the applied strain directly under the gate electrode.

■ CONCLUSIONS
Biaxial tensile strain can be successfully applied to flexible TMD devices fabricated on thin (125 μm) flexible PEN substrates.Using resistive strain gauges, we determined that the strain transfer from cruciform to the PEN film is efficiently mediated by the thin cyanoacrylate adhesive layer.Notably, this adhesive layer was found to form a mechanically robust interface capable of preserving the linearity of the externally applied strains up to at least 0.7%.Strain dependent Raman measurements were performed in single layer MoS 2 devices supported on PEN films for strains up to 0.5%.The detected strain-induced Raman peak redshifts for the zone center E′ and A 1 ′ modes were found to be in excellent agreement with the corresponding values obtained for simply supported 2D crystals on PMMA.Furthermore, the residual strain distribution, imposed due to device fabrication steps, was determined by Raman mapping in the channel region at zero external strain.A similar Raman mapping at maximum applied strain revealed that the externally applied strain is imposed in a rather homogeneous manner.This strongly suggests that the various interfaces formed between the substrate, the gate, and the gate dielectric are robust, and facilitate transferring of the applied strain all the way to the 2D material in the device channel.
Finally, using two different excitations of 515 and 632 nm, we performed strain-dependent Raman measurements on a set of 1L-WSe 2 devices and two reference samples with simpler structures (WSe 2 /PEN and WSe 2 /AlO x /PEN).For the 515 nm excitation, the strain dependence of the first-order A 1 ′/E′ Raman bands obtained for the devices is in good agreement with that of the reference samples.Very strong substrate luminescence was observed in the reference samples, which was, however, quenched in all devices due to the presence of the gate electrode (5/40 nm Ti/Au).This enabled us to determine the strain sensitivity of the higher-order Raman peaks of WSe 2 , which is reported for the first time and is found to be up to five times higher compared to the first-order Raman modes.Given that the first-order modes in 1L-WSe 2 are accidentally degenerate, the more sensitive higher-order Raman bands stand out as a more efficient strain indicator.
Our work sheds light on the strain transfer effects in 2D material based devices and highlights Raman spectroscopy as a versatile tool for the nondestructive strain sensing in 2D material flexible electronics.The strain dependence of the higher-order Raman modes sheds light to the intricate electron phonon coupling and resonance Raman scattering effects in 2D WSe 2 .Future work involves characterizing electrical device characteristics under different types of strain, such as uniaxial, and investigating the influence of interfacial defects and encapsulation layers on the strain response of TMD materials.
The determination of the strain transfer efficiency from PMMA to PEN; the strain dependence of additional MoS 2 transistors; correlation plots and strain maps for the rest of the investigated devices; transfer curves for representative WSe 2 devices; the WSe 2 /PEN and WSe 2 / AlO x /PEN samples; detail of the WSe 2 Raman spectrum near 260 cm −1 ; measurements with the high-resolution Raman spectrometer; details on the calculation of strain transfer efficiency based on strain transfer theory.(PDF) ■

Figure 1 .
Figure 1.(a) The structure of the transistors that were studied (not-to scale).The thickness of each layer is indicated.(b) Transfer curves I ds vs V gs for a representative MoS 2 device with a channel width of 20 μm (V ds = 1 V).(c) Image of a PEN film with transistors attached on a PMMA cruciform.
the phonon frequency at zero strain, ω o , strain-induced shift rate, d d , and the corresponding mode Gruneisen parameter, = 1 d d o

Figure 2 .
Figure 2. Strain-dependent Raman spectroscopy in an MoS 2 flexible transistor.(a) Evolution of the Raman spectra at various strain levels.(b) Strain dependence of the A 1 ′ and E′ peak frequencies.The error bars indicate the standard deviation of the measurements.(c) Pos (A 1 ′) -Pos (E′) plot and corresponding strain -doping axes for Raman maps at zero (blue) and maximum (orange) strain for transistor MT1.The grid size of the ε−n axes is 0.1% and 2 × 10 12 cm −2 , respectively.The black arrows indicate the positive direction of each axis.Inset: Optical microscope image of the probed device.(d) Contour plots of mechanical strain in the transistor channel region at zero strain (left panel) and maximum applied strain (right panel).

Figure 3 .
Figure 3. Evolution of the Raman spectrum of WSe 2 with strain and strain dependence of the peak frequencies for 515 nm excitation in panels (a)− (c), and 632.8 nm excitation in (d)-(f).In (a), (b), (d) and (e) dashed blue curves are the Lorentzian components fitted to the spectrum.The solid lines in (c), (f) are the best fit curves.The error bars indicate the standard deviation of the measurements.

Table 1 .
Raman Peak Positions at Zero Strain, Strain-Induced Shift Ratesand Mode Gruneisen Parameters for MoS 2 Devices

Table 3 .
Raman Peak Positions, Strain-Induced Shift Rates and Gruneisen Parameters for WSe 2 Devices Excited with λ exc = 632.8nm