Tailoring phonon modes of few-layered MoS2 by in-plane electric field

We discuss the effect of the in-plane electric field on the Raman spectroscopy for few-layered MoS2. The characteristic Raman modes of MoS2 show gradual red shift, while the intensity increases by 45–50% as the electric field is increased, showing a large electro-optical effect. Structural analysis suggests that our few-layered MoS2 belongs to P6/m2 space group with broken inversion symmetry. We attribute this gradual red shift to this broken symmetry-driven piezoelectricity in MoS2, which generates tensile strain along the perpendicular direction when the electric field is applied. The enhancement of the effect upon reversing the electric field direction adds credence to our interpretation. Our first principal density-functional theory calculation further substantiates the claim. This optical probing of the electromechanical coupling may lead to applications as a nonextensive technique for electric field/strain sensors in the nanoelectronics devices.


INTRODUCTION
Tunability of two-dimensional quantum materials (2DQM) through an external perturbation has strongly excited condensed matter research in recent years due to its possibility of applications, if not by the rich physics they offer 1 . Graphene and other 2DQMs 2-6 exhibit a wealth of unusual and fascinating properties, such as Dirac 2 or Weyl semimetal, topological insulator 7,8 , charge-density wave 9 , and superconductivity 7,10 . Among the vast library of 2DQM 6 , atomically thin semiconducting transition metal dichalcogenides (TMDCs) (having formula MX 2 , M = Mo and W and X = S, Se, and Te) have attracted particular interest in optoelectronic application due to their strong light-matter interaction owing to the presence of van-Hove singularity in their electronic structure 11,12 . The bulk 3D TMDCs are formed by the stacking of individual layers through a weak van der Waal's (vdW) force, making them easy to cleave and get a monolayer, whereas the atoms within each 2D plane are bound through a strong covalent bonding 12 . Thus, the huge difference between in-plane and outof-plane interatomic interaction strengths often results in highly anisotropic electronic and mechanical properties in these layered systems. Coupling of these anisotropic properties may lead to interesting phenomena.
Quasi-2D molybdenum disulfide (MoS 2 ) 13 is a prototype material to study the light-matter interaction, since it has shown promising optoelectronic applications 14 . MoS 2 crystallizes in hexagonal structure and belongs to the space group/point group P3m1/D 6h (with inversion symmetry). Similar to other vdW crystals, e.g., graphene, an atomically thin version of this naturally occurring MoS 2 has been successfully obtained by mechanical exfoliation [13][14][15] or liquid-phase exfoliation 16 . The anisotropic crystal structure, strong in-plane Coulomb interaction, and weak out-of-plane van der Waal's interaction of MoS 2 leads to several interesting anisotropic optical and electronic behavior [17][18][19][20][21][22] . Both monolayer and few-layered MoS 2 exhibit a number of intriguing physical properties, including a direct optical bandgap of about 1.8 eV 13,14 , strong photoluminescence (PL), electroluminescence 13,14,23,24 , and reasonably high mobility of the order of 0.2 m 2 /Vs 25,26 . Numerous studies indicate that monolayer MoS 2 exhibits large exciton-and trion-binding energies 27 , inversion symmetry breaking together with strong spin-orbit coupling 28 , and valley Hall effect 29 . These indicate the promising possibility of MoS 2 in next-generation nanoelectronics 15,30 and photonics 31 applications.
Raman spectroscopy, a powerful tool to probe the phonons in solids, has been used extensively as a nondestructive method to characterize electronic and vibrational properties of 2DQMs 32,33 . It has also been used for identification of a number of layers [33][34][35] , and the twist angle between the layers in 2DMs 36 . MoS 2 shows two distinct and well-defined types of Raman modes, one due to the stretching of S atoms along the c axis (A mode) and the other is from the in-plane breathing motion (E 1 2g mode) 12,20,33,37 . The resonance excitation (~1.8-2.0 eV) gives rise to a rich spectrum of second-order peaks and multiphonon bands 26,33 due to strong electron-phonon coupling, and is widely used as the fingerprint characterization of MoS 2 33 . However, the effect of external perturbation on the Raman spectrum of MoS 2 is not extensively reported. Although recently, a giant increase in the phonon modes' intensity has been observed in monolayer to bulk MoS 2 under a magnetic field 37 and electron irradiation 38 , the effect of the electric field (E) is still unknown. Recently, the gate voltage dependence on the optical properties in general, has been discussed for MoS 2 , along with its possibility as optical modulators 39 . The effect of the gate voltage on the Raman spectroscopy has also been discussed 39 .
In this paper, we describe the effect of moderate in-plane electric field on the phonon modes of few-layered MoS 2 , probed by Raman spectroscopy at room temperature. We have been able to correlate the effect of the applied electric field to the strain generated in MoS 2 , by density-functional theory (DFT)-based firstprincipal calculations of its phonon modes.

Structural characterization
The morphology of the as-prepared MoS 2 was observed in transmission electron microscopy (TEM) and shown in Fig. 1a. It possesses nanosheet-like structure. In the inset of Fig. 1a we show the thickness map by Energy Filter TEM imaging recorded at 300 keV. The higher magnification image of the yellow-colored highlighted area in Fig. 1a is shown in Fig. 1b. We calculate the interplanar spacing as 0.63 nm, which corresponds to (002) plane of MoS 2 from the high-resolution TEM image (Fig. 1b). The selected area electron diffraction (inset of Fig. 1b) shows the hexagonal lattice arrangement of MoS 2 . The line profile along the blue rectangular box (Fig. 1a, inset) gives a numerical value of the relative thickness ( t λx ) of the specimen (Fig. 1c), where t is the thickness and λ x is inelastic mean-free path of the electron 40,41 . The thickness of the material can be determined by knowing λ x , which is 119 nm 40 at 300 keV. This implies that the average thickness of one of the segments of the MoS 2 flake (highlighted in Fig. 1a, inset) is ≈1.8 nm, which is close to the thickness of a threelayered MoS 2 . A typical thickness distribution histogram, measured in a similar manner, is shown in Fig. 1d. The crystalline structure and phase of MoS 2 nanosheets were further confirmed by XRD as shown in Fig. 1e, with the respective planes shown in parenthesis 42,43 . In Fig. 1e, the dots represent the experimental points, while the blue line is the Rietveld refinement fit 44,45 and the red line is the difference between the two. The structural refinement suggests that our MoS 2 sample is of pure hexagonal structure (space group P63/mmc) with the lattice parameters a = b = 0.3117 nm and c = 0.127 nm. We observe a shrinkage along the a and b axes and an elongation along the c axis. Compared with the standard relative intensities of different peaks, it is found that (103) and (105) peaks are suppressed, indicating an irregular stacking arrangement of the atomic layers 46 . Since (h-k = 0) reflections are unaffected by the stacking fault broadening, the (110) reflection has a larger relative intensity than (103) and (105) peaks. Furthermore, it can be seen from the fitting parameters in Supplementary Table 1 (see supplementary information) that the fault probability is ≈14%, suggesting a disordered stacked system.

Raman spectra characterization of MoS 2
The Raman spectra of our few-layered MoS 2 at various in-plane electric fields are shown in Fig. 2. For zero field, the major characteristic Raman modes are observed at 382.5 and 406.7 cm −1 that belong to the in-plane E 1 2g and out-of-plane A 1g vibrations, respectively 35 . As an indirect measure, the position and the difference between the E 1 2g and A 1g evolves with the increase in the number of layers in MoS 2 until six layers before it gets saturated 12,34,35 . At zero electric field, we find that the difference between these two Raman modes is 24.2 cm −1 , which is close to what is observed earlier for the five-layered MoS 2 34,35 . Furthermore, the presence of a strong direct PL (and subsequent absence of an indirect PL) (see supplementary information) suggests that our MoS 2 is indeed a few-layered thick, as the bulk MoS 2 shows only indirect electronic transition 35,47 .
Electric field effect on Raman spectra of MoS 2 As the in-plane electric field is increased, both the Raman characteristic peaks showed gradual red shifts in frequency (Fig. 2). This can be seen more clearly in Fig. 3, where we show the (a) E 1 2g and (b) A 1g spectra measured at different electric fields. A clear change in the peak position for both the peaks with the changing electric field can be observed. Alongside the shift in the peak positions to a lower value, the peak intensity increases with the increase in the electric field (Fig. 3d), while the full-width-halfmaxima (FWHM) remain almost unchanged (Fig. 3c). Moreover, the difference between the E 1 2g and A 1g peak remains almost unaffected over the window of the applied electric field (see supplementary information). The intensity of the phonon modes increased substantially by 45-50% as the electric field is increased (Fig. 3d), implying a large electro-optical coupling. This gradual increase can be attributed to the manipulation of the MoS 2 electrons under the electric field as it in turn affects the Raman phonon intensity 37 . A more careful look at the Raman spectra reveals the presence of an asymmetry near 377 cm −1 48,49 , which appears due to the transverse optical phonon mode of MoS 2 . The presence of this asymmetry in the zero electric field spectra allows us to infer that this arises due to the quality of the sample and is not related to the effect of the electric field.

DISCUSSION
The intriguing red shift of principal phonon modes of MoS 2 under the electric field, can be attributed to the doping by source-drain bias due to the electric field or by an increase in temperature due to Joule heating. The effect of temperature, in this case, can be refuted as under increasing temperature, the Raman peak intensity decreases and the FWHM increases 50 , while we observe the opposite trend in our system. The electrostatic doping, due to band bending, on the other hand, can lead to the softening of the phonon modes. However, the moderate applied electric field, to our understanding, will not be able to induce doping in the fewlayered MoS 2 under consideration.
On the contrary, we believe that the red shifts in Raman spectra under the electric field can be due to the strain generated in the system. MoS 2 , with an even number of layers, belongs to the P3m1 space group and with an odd number of layers belongs to the P6m2 space group (without inversion symmetry) 51,52 . Interestingly, this broken inversion symmetry induces piezoelectricity in MoS 2 with an odd number of layers 51,52 . Notably, in a piezoelectric material, if an electric field is applied, a strain is generated along its perpendicular direction and vice versa. This piezoelectricity in MoS 2 develops and vanishes as the number of The plots of the Raman spectra of few-layered MoS 2 under various in-plane electric fields, measured at room temperature. A blue laser of 488-nm wavelength has been used for the excitation. The solid lines are the damped harmonic oscillator (Lorentzian) model fit to the experimental data to identify multiple peaks. The E 1 2g and A 1g peak respectively appears at 382.5 and 406.7 cm −1 for zero field. The difference between the peak position is 24.2 cm −1 . Under the application of successive in-plane electric field, the position of E 1 2g and A 1g shows gradual red shifts. The peak separation remains almost unaffected, whereas the intensity of the peaks increases with increasing the electric field (E). layers change from odd to even due to the breaking and the recovery of the inversion symmetry 51,52 . As our MoS 2 belongs to the space group P6m2, we believe that the applied in-plane electric field induces an out-of-plane tensile strain in it due to the broken inversion symmetry-driven piezoelectricity.
To substantiate our claim, we performed DFT-based firstprincipal calculations of the Raman active phonon modes of MoS 2 for different percentages of out-of-plane tensile strains on it (for calculation details, see "Methods" section).
The DFT-calculated, Raman active modes of MoS 2 , for zero tensile strain (or zero electric field) occur at 385.3 cm −1 (E 1 2g ), and 408.3 cm −1 (A 1g ), which is in agreement with the experimental results 12,33,53 . The plots for the calculated Raman modes are shown in the supplementary information.
In Fig. 4a, b, we show the experimental change in the Raman mode for E 1 2g and A 1g with the applied electric field, with respect to its zero electric field value. In the same figure, we show the corresponding change in Raman frequency with applied out-ofplane tensile strain with respect to its zero-strain value, calculated by first-principal calculation. With the applied electric field/tensile strain, both the E 1 2g and A 1g modes shift to lower frequencies. The frequency shift (Δω) is defined as the difference between the frequencies of Raman active mode E 1 2g (A 1g ) at a finite electric field/tensile strain and at zero electric field/tensile strain. Mathematically, Δω ph ¼ ω ph ðEÞ À ω ph ðE ¼ 0Þ where 'ph' stands for either E 1 2g or A 1g . It is found that the frequencies of E 1 2g and A 1g decrease with increasing tensile strain along [001] direction in a similar manner as it changes with the applied in-plane electric field. Our first-principal calculation results are in agreement with the experimental data within an acceptable limit, and show similar features as observed previously on DFT-based calculation of Raman modes of MoS 2 under tensile strain 16,26 . The tensile strain Plots of the Raman spectra of a E 1 2g and b A 1g mode under different inplane electric fields for the few-layered MoS 2 . The electric field values are color-matched with the plots. The peak positions gradually shift to a lower wave number as the electric field is increased. c The Raman peaks' full-width half-maxima (FWHM) as obtained from the Lorentzian fit to the experimental data shown in Fig. 2. The FWHM for E 1 2g (in red, left and bottom axis) and A 1g (in blue, right and top axis) stays fairly constant over the electric field window. The lines are to guide the eye. The error bars are obtained from the least-square fit of the experimental Raman spectroscopy data to the damped harmonic oscillator model (refer to Fig. 2). d The relative percentage change of the intensity (normalized with respect to the zero-field value) of E 1 2g (in red, left and bottom axis) and A 1g (in blue, right and top axis) mode increases gradually as the electric field is increased. A substantial change of about 45-50% is observed for both the characteristic peaks in the measurement window, suggesting a strong electro-optical coupling.
increases the interlayer distance between S-Mo-S layers, which weaken the vdW interactions between adjacent layers. This results in a red shift in both E 1 2g and A 1g modes. However, for a given tensile strain, a reduction in Raman shift of the A 1g mode is larger than that of the E 1 2g mode. In the A 1g mode (arises from out-ofplane vibration of S atoms in the opposite direction along the z direction), the change in atomic vibration is dominated by interlayer force. While for E 1 2g long-range coulombic interlayer force plays a key role 34 and thus explains the observations. Raman spectroscopy measurements by reversing the polarity of the electric field (Fig. 4c) add more credence to our claim of this electric field-controlled strain-mediated tailoring of the principal phonon modes of MoS 2 . Intuitively, we expect a similar outcome as before, and indeed observe similar red shifts of the phonon modes with respect to the electric field (Fig. 4c). However, the magnitude of the change in the phonon mode frequency under the electric field with respect to its zero-field value is different in two different directions of the electric fields (Fig. 4d). A simple diagrammatic approach (Fig. 4e) of the experimental situation can help us to understand this. Although it cannot be determined unambiguously, we consider that the left panel [(i) of Fig. 4e] denotes the negative electric field direction, whereas the right panel [(ii) in Fig. 4e] denotes the positive electric field direction in accordance with our previous analogy. For (i), the piezoelectric strain on the MoS 2 flake is along the out-of-plane (positive z) direction; however, for (ii), it is along the negative z direction. Now for situation (i), the strain is applied along the free surface, leading to a larger change in the phonon mode frequency in contrast to situation (ii) where the strain is acting along a direction of the supporting substrate and thus is being suppressed. This leads to the difference in the magnitude of the change in the phonon mode frequency on either direction of the applied electric fields. We presume that this would be symmetrical about the zero field, if the flake is freely standing or supported by the identical surfaces on both sides, although, for the latter, the effect of pressure might also complicate the outcome. Interestingly, this behavior of different magnitude of the effect by reversing the polarity of the electric field can possibly exploit odd-layered MoS 2 in switching applications.
In summary, we prepared few-layered MoS 2 nanoflakes by a chemical bottom-up approach and performed Raman spectroscopic measurements under a moderate in-plane electric field. The Rietveld analysis of the X-ray diffraction suggests that the prepared MoS 2 is of hexagonal phase with broken inversion symmetry. Under the increasing in-plane electric field, both the prominent characteristic Raman modes of MoS 2 show gradual red shifts (in frequency), which we believe is due to the out-of-plane tensile strain generated due to the intrinsic piezoelectricity in MoS 2 with an odd number of layers. Our first-principal calculation of the Raman modes of MoS 2 under different percentages of out- Fig. 4 Comparison of the successive shifts of the Raman modes under an electric field (tensile strain). The plots of the successive shift of Raman mode with respect to its zero-field (or zero-strain) value. The symbols are the experimental data (in red, left and bottom axis), and the solid line is the theoretical calculation (in blue, right and top axis). Δω ph ¼ ω ph ðEÞ À ω ph ðE ¼ 0Þ where 'ph' stands for either E 1 2g or A 1g . The variation of experimental (red, left axis) and theoretical (blue, right axis) Δω with the electric field (E) (red bottom axis) or tensile strain (blue, top axis) for a E 1 2g and b A 1g modes. Δω for both E 1 2g and A 1g decreases linearly with the electric field or tensile strain. The errors in determining Δω are obtained from the Lorentzian fit to the experimental data (see Fig. 2). c Raman spectra of few-layered MoS 2 under two different directions of the applied electric field along with the zero-field data. For both the directions of the applied electric field (E), the principal Raman modes show a red shift in frequency with respect to their zero-field value (indicated by black dashed lines). d The plots of the successive shift of Raman mode under different directions of the applied electric field with respect to their zero-field value. The lines are to guide the eye. e Cartoon describing the experimental situation for observance of a different amount of shifts of the phonon mode frequency by reversing the direction of the applied electric field. In case (i) the strain is applied along the free surface of MoS 2 flake, whereas for case (ii), it is toward the substrate. The substrate suppresses the effect of strain, leading to a lesser change in the Raman shifts under the electric field.
of-plane tensile strain shows a similar red shift and adds credence to our claim. Experimentally, our interpretation was further supported by the Raman spectroscopy measurements by reversing the polarity of the electric field. Such an optical probing of the electromechanical coupling may lead to diverse applications as a nonextensive technique for the electric field and (or) strain sensors in the nanoelectronic devices.

Sample preparation
The MoS 2 samples were prepared by a chemical bottom-up approach by using molybdic oxide and potassium thiocyanate as precursor materials. These were mixed in ≈1:5, in distilled water and stirred to get a homogeneous mixture. This was then transferred into a Teflon-lined stainless-steel autoclave and was heated at 493 K for 24 h. Following this, the mixture was brought back to room temperature, and the resultant precipitate was washed thoroughly by distilled water and collected using centrifugation at 4000 rpm. Finally, the sample was dried at 353 K for 6 h under N 2 gas flow to obtain the dark-gray MoS 2 powder.

Device fabrication
Reduced graphene oxide (rGO) was prepared by reducing GO (for details of preparation, see ref. 54 ) and spin-coated on Sapphire substrate with a predefined mask. After rGO deposition, the mask was removed and a narrow channel (≈110 μm) was observed. The prepared MoS 2 was spincoated on rGO/Sapphire substrate. The electrical connection was done by putting silver electrodes. A schematic diagram and optical image of a simple device are presented in Fig. 1f. Experiments X-ray diffraction (XRD) was performed using a Rigaku (MiniFlex II) diffraction instrument with CuK α radiation. Transmission electron microscopy (TEM) was done in FEI TECNAI G2 F30. Raman and photoluminiscence (PL) measurements were done using a micro Raman Spectrometer (LabRam HR, Jobin Yvon) equipped with Peltier cooled CCD detector (pixel size 1024 × 256) at room temperature. We used an Argon ion blue (488nm) laser as an excitation source, and a ×50 objective was used to focus the laser beam on the sample. The slit width of the spectrometer is 100 μm and grating of line 1800/mm is used. The spectral resolution of the spectrometer is 0.35 cm −1 /pixel. The integration time for taking the Raman spectra was 30 s. The laser power was maintained at 0.2 mW throughout the measurement. A Keithley 2400 source meter was used to apply the electric field. The experimental arrangement has been shown as a schematic in Fig. 1f.

DFT calculation
The first-principal calculations have been carried out in GGA framework as implemented in QUANTUM ESPRESSO [55][56][57] . The optimized lattice parameters are a = b = 0.314 and c = 1.240 nm, while the experimental lattice parameters are a = b = 0.3117 and c = 1.27 nm 58 . The primitive lattice vectors of MoS 2 are a ! ¼ ða; 0; 0Þ; b ! ¼ ða=2; ffiffi ffi 3 p a=2; 0Þ; and c ! ¼ ðc; 0; 0Þ. The tensile strain along the z direction is defined (%ϵ z ) as the ratio of elongation in the length of the c vector (Δc) to its original length ð ΔcX100 c Þ. After applying the strain along the z direction, selfconsistent calculations are performed on the geometry, and vibrational modes at the center (Γ) of Brillouin zone are calculated using densityfunctional perturbation theory. PBEsol 57 exchange and correlation functional is adopted with scalar-relativistic PAW pseudopotentials. This functional provides accurate phonon frequencies compared with experimental data 59 . The plane-wave basis cutoff is taken to be 55 Ry. Brillouinzone sampling has been done using Monkhorst-Pack-type k-point mesh of 23 × 23 × 23 for self-consistent calculations. The vdW interactions are treated via the semiempirical dispersion correction DFT-D2 proposed by Grimme 60 . The lattice constants are obtained by performing the structural optimization until the total force on atoms was <0.0001 Ry/au.

DATA AVAILABILITY
The data that support the findings of this study are available from the corresponding author on reasonable request to S.M. (email: sreemanta85@gmail.com) or A.S. (email: achintya@jcbose.ac.in).