Multiwavelength excitation Raman Scattering Analysis of bulk and 2 dimensional MoS2: Vibrational properties of atomically thin MoS2 layers

In order to deepen in the knowledge of the vibrational properties of 2-dimensional MoS2 atomic layers, a complete and systematic Raman scattering analysis has been performed using both bulk single crystal MoS2 samples and atomically thin MoS2 layers. Raman spectra have been measured under non-resonant and resonant conditions using seven different excitation wavelengths from near-infrared (NIR) to ultraviolet (UV). These measurements have allowed to observe and identify 41 peaks, among which 22 have not been previously experimentally observed for this compound, characterizing the existence of different resonant excitation conditions for the different excitation wavelengths. This has also included the first analysis of resonant Raman spectra that are achieved using UV excitation conditions. In addition, the analysis of atomically thin MoS2 layers has corroborated the higher potential of UV resonant Raman scattering measurements for the non destructive assessment of 2 dimensional MoS2 samples. Analysis of the relative integral intensity of the additional first and second order peaks measured under UV resonant excitation conditions is proposed for the non destructive characterization of the thickness of the layers, complementing previous studies based on the changes of the peak frequencies.


Introduction
Molybdenite or molybdenum disulfide (MoS 2 ) is one of the first two-dimensional (2D) materials which showed that graphene is not more alone competing in the world of future ultrathin 2D devices. Although mostly used as additive in oils for automotive application, MoS 2 is a semiconductor that has recently gained interest due to its similitude with graphene but also to its intriguing and improved properties when reduced to 2D layers. One of them, which boosted the research on MoS 2 and more recently enlarged on transition metal dichalcogenide (TMD) materials, has been the indirect-to-direct bandgap transition when the thickness is reduced to one single layer [1]. The presence of a direct bandgap, absent in graphene, has opened the way to a plethora of possible applications, some of them already demonstrated, such as field effect transistors [2], [3], logic operation [4], integrated circuits [5], photodetectors [6], [7], LEDs and solar cells [8], [9] using MoS 2 atomically thin layers.
The next promising step relies on the fabrication of 2D heterostructure devices consisting on a layer-by-layer building which recently demonstrated interesting functionalities [10]- [12].
However, constructing new 2D heterostructures directly implies to clearly identify the different materials forming the devices. Usually, the identification of layered materials is always accompanied of Raman peaks study, which also allows determining the number of layers [13]- [15]. For MoS 2 , this has been mostly done with the standard green excitation (514-532 nm) or in resonant conditions (633 nm) [16]- [20] and the studies have been mainly centered in the analysis of the two main 2 1 and 1 Raman peaks. However, up to know there is very scarce information in the literature on the Raman scattering analysis of MoS 2 atomically thin layers using other excitation wavelengths [20], [21] and only some old works on bulk or MoS 2 nanoparticles materials can be found [22]- [27]. Li et al. [20] reported a study involving other laser lines (325 and 488 nm) for MoS 2 atomically thin layers with the detection of other peaks at resonance conditions. Similarly more recently a work reported on several excitation wavelengths study [21] with the detection of some peaks but unfortunately no complete experimental identification of the MoS 2 peaks has been performed.
The use of several excitation wavelengths allows the coupling of the Raman scattering process with real energy bands and thus also producing resonant conditions. The applicability of different (non-resonant, resonant) excitation conditions presents a strong interest from the point of view of a complete characterization of a material, allowing the enhancement of weak peaks by breaking the Raman selection rules and activating forbidden and/or inactive modes that are non-detected in standard non-resonant conditions [28].
In this framework, and to analyze the potential of Raman scattering for the assessment of atomically thin MoS 2 layers, a complete and systematic Raman scattering analysis has been performed using seven excitation wavelengths covering a wide spectral range from UV to IR regions. In a first stage, and in order to deepen in the knowledge of the vibrational properties of these materials, the study has been centered on bulk single crystal MoS 2 samples, studying the included the first analysis of resonant Raman spectra that are achieved using UV excitation conditions. For atomically thin MoS 2 layers, the analysis performed shows the higher potential of UV resonant Raman scattering measurements for the non destructive characterization of the samples. This is based on the strong dependence of the relative integral intensity of the additional first and second order peaks in the UV resonant Raman spectra with the number of layers.

Bulk MoS 2
Bulk 2H-MoS 2 belongs to the space group 6ℎ 4 ( 6 3 ⁄ ) with the unit cell containing two Mo and four S atoms. The correlation method gives the following irreducible representations of the Brillouin zone-center phonons (Γ point): where A 1g , E 1g and two E 2g are the Raman active modes, A 2u and E 1u are infrared active acoustic modes; and B 2g , B 1u and E 2u are inactive phonon modes.
In order to understand the potential appearance of resonant excitation conditions when using different excitation wavelengths, room temperature photoluminescence measurements have been performed on the bulk MoS 2 single crystal. Figure 1 shows the room temperature    Table I. In this table, data from the experimental peaks that are identified for the first time in single crystal MoS 2 are indicated in red. Table I also contains theoretical calculations [31] and previously reported experimental data [23], [22], [27] for this compound. The deconvoluted spectra for the ultraviolet (325 nm) and near-infrared (785 nm) are shown in the supporting information.
All the experimental spectra are dominated with two very intense peaks at 382.9 and 408.1 cm-1, which are attributed to E 2g 1 (Γ) and A 1g (Γ) vibration modes [23]. Besides these, a low frequency fundamental peak is observed at 32.0 cm -1 and identified as E 2g 2 (Γ) [23]. Additionally, very intense and narrow peaks are observed at 285.0 and 469.8 cm -1 under the 325 nm excitation wavelength and are assigned to E 1g (Γ) and B 2g 1 (Γ) symmetry modes [23]. Interestingly both modes are not expected to be observed in the standard measurement conditions. In the first case, the E 1g (Γ) is forbidden in the used backscattering configuration. Observation of this peak is In addition, weak and slightly broader contributions detected at 395.8 and 462.3 cm -1 under 633 nm excitation could be attributed to contributions from infra-red active modes E 1u (Γ) and A 2u (Γ) as was explained in [22]. Activation of these modes is again explained by the use of resonant excitation conditions. Additionally, it should be mentioned another possible identification of the peak at 462.3 cm -1 , which is identified as E 1g (Γ)+XA band in the reference [27]. All other peaks detected in the Raman spectra measured with 633 nm excitation wavelength are assigned to second order modes as presented in Table 1. It should be noted that in all these cases the symmetry identification proposed for the second order modes is consistent with the crystal momentum conversation principle. The symmetry selection rules [23] exclude that these peaks could be assigned to one-or two-phonon allowed modes. Additionally their half-widths (8 cm -1 ) are comparable with that of first-order allowed modes (6 -8 cm -1 ), suggesting that they are due to one-phonon forbidden modes. Comparison of the frequencies of the bands with the phonon dispersion simulations [31] and inelastic neutron scattering measurements [33] leads to the assignment of the four Raman structures to one phonon forbidden TA, ZA and LA modes of the M and K points around the M and K gaps. It is not so surprising to observe these modes in resonance Raman scattering near an indirect bandgap, since it is well known that the transitions in this case are dominated by two-step processes mainly involving phonons with the same symmetry of the gap [34]. The main contribution to one-phonon forbidden resonant scattering is due to a second-order extrinsic process in which a free exciton 10 scatters inelastically the phonon via the Fröhlich electron-phonon interaction and elastically the defect via electron-impurity interaction [35]. In this case the momentum conversation law is not preserved, since the extra momentum of the phonon is being taken by the defect [36]. Defects in this case are probably planar native defects in the form of stacking faults with the direction of growth in the c axis, which are often found in layered materials due to very low formation energy [37]. Having in mind this, one-phonon indirect resonance Raman scattering could be explained by two-step process: (1) an electron excited by photon, is taking up the momentum needed to reach the allowed indirect band gap by being elastically scattered by a stacking fault; (2) the electron is inelastically scattered by a zone-edge phonon with the symmetry of the resonant gap, before recombination. This interpretation agrees with the identification proposed in the literature for the peak at 231.9 cm -1 (which is the only one from this structure previously reported in the literature, as shown in Table 1). It is interesting to remark that the lack of observation of these features in the spectra measured in standard off-resonant conditions and in direct band-gap resonant conditions confirm the good crystal quality of the natural single crystal sample used in this study.
Finally, Table I includes also four peaks in the 760 -820 cm -1 second order spectral region.
Even if this is the first time these peaks are observed in single crystal MoS 2 , similar peaks identified with E 1g (Γ)+E 2 2g (Γ), 2 x E 1 2g (Γ) and A 1g (Γ)+E 1 2g (Γ) have been previously reported in atomically thin MoS 2 samples [38]. In addition, there is a peak located at 780 cm -1 , labeled as "X"peak in Table I (Fig.   6a), the observed behavior has already been reported and explained in the literature [18], [20], [29]. As shown in Fig. 6b, the two first order additional peaks appearing in the UV resonant Raman spectra, identified with the , E 1g (Γ) and B 2g 1 (Γ) modes, tend to show a behavior similar to that of the 2 1 : This is especially true for the E 1g (Γ) peak, which shows a softening of ~2 cm A similar behavior is observed for B 2g 1 (Γ) mode, except that in this case the maximum intensity is achieved for L = 3 as presented in Figure 7 18 going to be more pronounced in the case of L=1 and L=2. The decrease in the intensity of these modes for L > 3 would be mainly due to the changes in the electronic structure with the layer thickness, as reported in [42]. In addition, a lowering of the intensity of these modes is also expected as the symmetry of the bulk is achieved, taking into account that they correspond to quasi-forbidden or inactive Raman modes, in agreement with their low relative intensity in the UV resonant Raman spectra from single crystal MoS 2 (as shown in Figure 2). On the other hand, the enhancement in the relative intensity of the second order peaks for layers with L ≤ 3 has been interpreted in terms of TRRS effect [38], as previously indicated.
The analysis of the intensity and the frequencies of the Raman modes from atomically thin MoS 2 layers have been proposed in the literature for the non destructive assessment of the number of atomic layers in 2D samples, as reported in [18], [42]. In these cases, non resonant  Table I. Frequency (in cm -1 ) of peaks from simultaneous fitting of Raman spectra measured with different excitation wavelengths, excitation condition under which the peak is best resolved, and proposed mode symmetry assignment. These are compared with theoretical predictions [31] and other reported experimental data [23,22,27].

Raman spectra
The deconvoluted spectra obtained for the ultraviolet (325 nm) and near-infrared (785 nm) excitation wavelengths are shown in the figure S1 and S2 respectively. Only the Raman peak positions which are the most intense under the excitation wavelength are here reported.