Mapping of Low-Frequency Raman Modes in CVD-Grown Transition Metal Dichalcogenides: Layer Number, Stacking Orientation and Resonant Effects

Layered inorganic materials, such as the transition metal dichalcogenides (TMDs), have attracted much attention due to their exceptional electronic and optical properties. Reliable synthesis and characterization of these materials must be developed if these properties are to be exploited. Herein, we present low-frequency Raman analysis of MoS2, MoSe2, WSe2 and WS2 grown by chemical vapour deposition (CVD). Raman spectra are acquired over large areas allowing changes in the position and intensity of the shear and layer-breathing modes to be visualized in maps. This allows detailed characterization of mono- and few-layered TMDs which is complementary to well-established (high-frequency) Raman and photoluminescence spectroscopy. This study presents a major stepping stone in fundamental understanding of layered materials as mapping the low-frequency modes allows the quality, symmetry, stacking configuration and layer number of 2D materials to be probed over large areas. In addition, we report on anomalous resonance effects in the low-frequency region of the WS2 Raman spectrum.

Transition metal dichalcogenides (TMDs), such as MoS 2 and MoSe 2 , have recently attracted significant attention from both industry and academia due to their wide range of fascinating properties [1][2][3] . Unlike graphene, these materials possess a sizable bandgap and many reports indicate that they could be suitable as active layers in logic electronics and optoelectronics [3][4][5][6] and as constituents in a variety of energy related applications [7][8][9][10] . High-quality monolayer flakes of TMDs have previously been obtained via mechanical exfoliation [1][2][3] ; however, this method is serendipitous and suffers from low-throughput. Chemical 11 and liquid-phase exfoliation [12][13][14][15] have greatly improved the prospect of scalability, however, the crystals produced by these methods typically have relatively small lateral dimensions rendering them ill-suited for many electronic applications. Large-scale TMD films have been obtained by sulfurization of metal oxide 16,17 or metal films [18][19][20] , but, the thus derived films are typically polycrystalline. Recently, there have been significant advances using chemical vapour deposition (CVD) [21][22][23][24][25][26][27][28] to produce large-area, high-quality crystals, which could facilitate the realization of industry-relevant devices. In the case of each of these aforementioned synthesis routes it is imperative that the composition, quality and thickness of the materials produced is assessed before they can be considered for use in applications. Techniques such as atomic force microscopy and transmission electron microscopy are useful in the characterization of layer number and crystalline quality, respectively, but suffer from low sample throughput and laborious sample preparation.
Raman spectroscopy is a widely used technique in materials science and can be used to study molecular vibrations in 2D materials, which can reveal a wealth of information about material properties in a fast and non-destructive manner. In the case of graphene, Raman spectroscopy can be used to investigate the number

Results and Discussion
TMDs can exist in 3 polytypes, depending on the co-ordination of chalcogen atoms around the metal atoms, and the stacking order of the layers. The first, 1T, is a metallic crystal with octahedral co-ordination that has recently been artificially synthesized for device applications 31 . However, since this polytype is metastable and not found in nature 32 , we will not discuss it here. The more common 2H and 3R polytypes are semiconducting, with trigonal prismatic coordination, with similar properties but differing stacking orders of metallic and chalcogen atoms. For example, 2H has a stacking order of AbA BaB AbA BaB, where capital letters indicate chalcogen atoms and lower-case letters indicate metal atoms, while 3R has a typical stacking order of AbA BcB CaC AbA, or the inverted AbA CaC BcB AbA 32 . The layers can also adopt a mixture of these stacking configurations, whereby, for example in a 3L sample, layers 1-2 obey 2H stacking, and layers 2-3 obey 3R stacking 33 . This means that a 3L 2H-3R sample could have the stacking configuration AbA BaB CbC, or AbA BaB AcA. The properties of 2H and 3R TMDs have been reported to be almost identical 32 , with little observable change in the high-frequency region of the Raman spectrum. However, recent reports indicate slight differences in band structures and absorption spectra between the two stacking types 34,35 . This shows that further investigation into the identification and properties of these stacking configurations is important both for fundamental studies of these materials and for future studies in the emerging field of van der Waals heterostructures 36 where the stacking order of two dissimilar layers could change the electronic and optical properties 37,38 of artificial 39 or grown 40 heterostacks. In this study, we refer to 2H stacked crystals unless explicitly stated otherwise.
The Raman spectra of 2H and 3R semiconducting TMDs generally display two main characteristic vibrational modes. These are the E'/E g /E 1 2g and A' 1 /A 1g first-order modes at the Brillouin zone centre, shown in Fig. 1, that result from the in-plane and out-of-plane vibrations, respectively, of metal (M) and chalcogen (X) atoms [41][42][43] . Different peak labels are used for different layer numbers due to the changing symmetry of the point group from D 3h (odd layer number) to D 3d (even layer number) to D 6h (bulk). These Raman active modes have been shown to shift in position with number of layers 26,[44][45][46] , allowing mono-and few-layer crystals to be identified. For example, in the case of MoS 2 , as the layer number increases, interlayer van der Waals (vdW) forces suppress atomic vibrations meaning higher force constants are observed 44 . This means that the out-of-plane A' 1 /A 1g mode becomes blue-shifted at higher layer numbers (~2 cm −1 from monolayer to bilayer), as the vibrations of this mode are more strongly affected by vdW forces between the layers. The in-plane E'/E g /E 1 2g mode in contrast shows a red shift as layer number increases (~2 cm −1 from monolayer to bilayer). This is attributed to structural changes in the material or to an increase in long-range Coulombic interlayer interactions affecting the atomic vibrations 30,44 . However, for the transition metal diselenides, such as MoSe 2 and WSe 2 , these changes in frequency for different layer numbers are not as dramatic (e.g. a shift of ~1 cm −1 in the A 1g peak from 2 to 3L MoSe 2 ) 45,47 , and may be below the instrumental spectral resolution of standard equipment. Furthermore, crystallite size 48 , doping and strain have been shown to significantly alter the Raman spectra of TMDs. Previous reports have shown a red shift and broadening of the A' 1 /A 1g peak in MoS 2 with n-doping 49 and a blue shift and enhancement of the A' 1 /A 1g peak with p-doping 50 . The Raman spectrum of MoS 2 is also highly sensitive to strain with the application of uniaxial strain resulting in the degeneracy of the E'/E g /E 1 2g mode being lifted 51 , whereas the introduction of localized wrinkles and folds has been shown to cause a red shift of both A' 1 /A 1g and E'/E g /E 1 2g modes 52 . Given the large number of factors that can affect the primary peaks in the Raman spectra of TMDs, an alternative method for the clear assessment of TMD layer numbers using Raman spectroscopy is desirable.
Investigation of the low-frequency SM and LBM has been suggested as a universal method of layer number (N) determination in TMD materials 30 , due to the fact that the layer-breathing mode vibrations are themselves out of plane and vary significantly as a function of layer number. The relative atomistic motions of the SMs and LBMs in TMDs are illustrated in Fig. 1, whereby the SM involves the in-plane motion of metal and chalcogen atoms, and the LBM involves the out-of-plane motion of metal and chalcogen atoms 43 . These SMs and LBMs are not present in single layers, but show a characteristic blue and red shift, respectively as layer number increases from 2L to bulk. While not commonly used as a metric for layer thickness in 2D materials currently, due their Raman shift position appearing in the ultra-low frequency region beyond the filter cut-offs for most commercial Raman spectrometers, ongoing developments in the use of components such as multiple notch filters 53 can allow measurement of these peaks with low excitation powers and short acquisition times. Full measurement and analysis of these modes is desirable for a more comprehensive understanding of the mechanical and electrical properties of TMDs 54 .
The low-frequency SMs and LBMs have been extensively studied in graphene 53,55 and have been reported for a number of mechanically exfoliated TMDs 30,54,56 . Unlike graphene, which consists of single atomic layers of carbon, TMD monolayers consist of three atomic layers of chalcogen/metal/chalcogen, resulting in a richer and more complex Raman spectrum. While previous reports have outlined the evolution of low-frequency peak positions with layer number 57 , this has not yet been comprehensively studied for all layered materials. In addition, recent reports have identified new peaks in the low-frequency region of MoSe 2 corresponding to different polytypes of the material, indicating that Raman shifts in this region are of interest for considering differences in interlayer interactions with stacking type 33 . Here, by means of Raman mapping, we image the peak intensities and positions of SMs and LBMs for different TMDs and highlight the efficacy of this technique for layer-number identification. We further outline the effectiveness of this technique for quickly distinguishing between different stacking configurations which are prevalent in transition metal diselenide layers.

MoS 2 Raman Mapping
In Fig. 2(a), a sample of CVD-grown MoS 2 with multiple distinct layers present is shown. In MoS 2 , the in-plane (E'/E g /E 1 2g ) and out-of-plane (A' 1 /A 1g ) peaks occur in the vicinity of ~385 and ~403 cm −1 , respectively. Figure 2(d) shows the evolution of Raman spectra (normalized to A' 1 /A 1g peak intensity) extracted from 1-5L MoS 2 , which display a characteristic red and blue shift of the E'/E g /E 1 2g and A 1 '/A 1g modes, respectively as the layer number increases 44,46 . Peak intensity maps are presented in Fig. 2

(b,c), showing an increase in intensity of
2g peaks as layer number increases from 1-5 layers, with a subsequent decrease as layer number increases towards bulk, attributed to optical interference occurring for the excitation laser and emitted Raman scattering 46 . The peak position maps for A' 1 /A 1g and E'/E g /E 1 2g are shown in the supporting information, with Figure S1(a) and S1(b) showing clearly the red and blue shift in E'/E g /E 1 2g and A' 1 /A 1g peaks, respectively, as layer number increases, allowing an initial assessment of layer number to be made. This assessment is supported by PL intensity maps of the same area, shown in Fig. 2(e,f), showing a maximum intensity of A1 excitons in monolayer regions, and an enhancement of B1 exciton intensity in multilayer regions. The corresponding shift in PL position as layer number increases, reflecting the changing bandgap of MoS 2 with layer number, is illustrated in the peak position maps in Figure S1(d) and (e) in the supplementary information, and in the corresponding spectra in Figure S1(f). Figure 3 presents the low-frequency SMs and LBMs of MoS 2 . Spectra of 1-5L MoS 2 are shown in Fig. 3(a), in close agreement with previous measurements of mechanically exfoliated MoS 2 30,54 . Figure 3(b-e) show peak intensity maps of SMs/LBMs for 2-5L MoS 2 . There is some overlap in peak intensity maps, due to peaks for different layer numbers appearing at similar Raman shifts; however, the relative intensity of these modes provides a strong indication of layer number. While peak intensity maps allow a step-by-step assignation of layer number, this can be better visualized by generating a map of the position of maximum peak intensity in the low-frequency regime as shown in Fig. 3(f). Such mapping represents a clear and facile method of assigning the layer number present in MoS 2 , by uniquely identifying the highest intensity SMs and LBMs present in 2-5 L MoS 2 by their position in the range of 10-50 cm −1 , noting that 1L MoS 2 has no peaks in this region.

MoSe 2 Raman Mapping
Raman analysis of CVD-grown MoSe 2 with a variety of layer numbers is shown in Fig. 4. In MoSe 2 , the in-plane (E'/E g /E 1 2g ) and out-of-plane (A' 1 /A 1g ) Raman active modes occur in the vicinity of ~287 and ~240 cm −1 , respectively. The significant red shift of peaks compared with MoS 2 occurs due to the larger mass of the selenium vs. sulfur atoms 54 . Similar to MoS 2 , the in-plane (E'/E g /E 1 2g ) and out-of-plane (A' 1 /A 1g ) modes exhibit a red and blue shift, respectively, with increasing layer thickness. In Fig. 4(a), an optical image of CVD grown layers is shown. A Raman map of A' 1 /A 1g (~240 cm −1 ) peak intensity is shown in Fig. 4(b), with the corresponding peak position map in Figure S2(a) in the supporting information. It is clear from these images that while the intensity varies significantly with thickness, following an initial jump from 1 to 2L, the A' 1 /A 1g (~240 cm −1 ) position does not change dramatically with layer number. A map of the E'/E g /E 1 2g (~287 cm −1 ) intensity is shown in Fig. 4(c), with the corresponding position map in Figure S2(b) in the supporting information. This Raman mode's intensity and position changes significantly from monolayer to bilayer, but shows no further significant change between 2, 3, and 4 layers, and is therefore not useful for layer number determination. Figure 4(d) shows spectra of 1 to 4 L 2 H MoSe 2 crystals extracted from different areas in Fig. 4(a), which are in good agreement with previously reported spectra 42,47,56 . We can also consider the intensity maximum and position maps of the A' 1 /A 1g /B 1 2g mode (~350 cm −1 ). This mode is inactive in bulk material, but has previously been observed to become weakly Raman active in bilayer and few-layer crystals due to the breakdown of translation symmetry 42 . To avoid confusion with other modes, this will henceforth be referred to as the B 1 2g mode. As this mode does not appear for monolayer MoSe 2 , as shown in the peak intensity map in Fig. 4(e), its absence (in combination with a characteristic PL signal) serves as a confirmation of monolayer presence. However, similar to E'/E g /E 1 2g (~287 cm −1 ), it does not shift significantly in intensity or position for 2 + layers as shown in the map of B 1 2g position in Figure S2(d) of the Supporting Information. A map of PL intensity is shown in Fig. 4(f), with the corresponding position map and spectra shown in Figure S2(e) and (f), respectively in the Supporting Information. The intense PL seen in certain areas serves as confirmation of monolayer presence, with some drop-off in intensity, as expected, in the regions of grain boundaries. The apparent lack of PL in other layers does not necessarily signify bulk behaviour -rather the signal for few-layer crystals is overshadowed by that of the monolayer.
We now focus on the study of low-frequency Raman modes in MoSe 2 . Figure 5(a) shows spectra of 1 to 4 L 2 H-MoSe 2 which have been extracted from different areas marked in the optical image in Fig. 4(a), and are in close agreement with spectra previously shown in the literature 47 . These spectra have been normalized to the intensity of the high-frequency A 1g mode, and offset for clarity, as have the rest of the MoSe 2 spectra in Fig. 5.   A Raman map of the maximum signal over the range 10-50 cm −1 is shown in Fig. 5(b). Interestingly, this map shows fractures and splitting in areas where no change is discernible in the optical image and therefore further investigation into the low-frequency modes was warranted. By analysis of various regions that appeared to be the same thickness according to optical contrast, it was possible to extract different low-frequency Raman signals correlating to different combinations of 2 H and 3R stacking of MoSe 2 layers. These different stacking configurations have previously been observed in CVD-grown transition metal diselenide layers and their formation attributed to the small difference in formation energy between the two different configurations 58 . It should be noted that there was no evidence of these different stacking configurations in our CVD-grown MoS 2 , with all areas probed displaying a purely 2 H signal. In Fig. 5(c), a map of position of peak intensity maximum in the low-frequency region is shown. Study of the differences in intensity maximum in Fig. 5(b) and the position of this intensity maximum for each layer shows that there is no direct overlap in each -rather, some areas have peaks of maximum intensity in the same position but of different intensity, while others have peaks of similar intensity but in different areas. To explain this observation, we will examine the low-frequency spectra for each layer number. In Fig. 5(d), low-frequency Raman spectra for different regions of 2 L MoS 2 are shown, corresponding to 2 H (max at 18 cm −1 ), 3R (max at 18 cm −1 , but significantly lower in relative intensity), and 3R* (max at 29 cm −1 ). The difference between 3R (max at 18 cm −1 ) and 3R* (max at 29 cm −1 ) is attributed to one being 3R, and the other being the vertically flipped 3R 33 , labelled as 3R* here, which would interact radically differently with incoming phonons. The intensity maximum for 2H and 3R (18 cm −1 ) is shown in Fig. 5(e), which shows (with some overlap with peaks present in 4L) the areas where these peaks are present. The difference in intensity between 2H and 3R here is consistent with previous reports 33 . Additionally, as shown in Fig. 5(f), we also observe experimentally for the first time a predicted Raman mode at ~29 cm −1 , attributed to the A 1 mode in the 3R* stacking configuration 33 . Similar evidence for different stacking configurations is seen in the 3L low-frequency Raman spectra in Fig. 5(g), where it is possible to identify a variety of 3L stacking configurations, including 2H-2H, 2H-3R, and 3R-3R. The trends in intensity for the peaks at ~13 cm −1 and ~24 cm −1 are clear when the peak intensity maps are considered. In Fig. 5(h), a peak intensity map of the SM at ~13 cm −1 is shown, which is present for 3R-3R stacking, but also present at higher intensities as the SM mode in 2H-3R stacking, where it appears in parallel with another SM mode at 24 cm −1 . Therefore, the relative intensity of this mode at ~13 cm −1 can be used to distinguish between 3R-3R and 2H-3R stacking, as labelled on the intensity scale bar in Fig. 5(h), with further verification of the 2H-3R mode afforded by the presence of a SM/LBM overlap peak at ~24 cm −1 , the intensity of which is mapped out in Fig. 5(i). This peak is highest in intensity in 2H-2H stacking, as is expected for pristine mechanically exfoliated 2H crystals 56 , and decreases as stacking configuration goes from 2H-2H to 2H-3R to 3R-3R. This is logical when considering the decreasing interlayer interactions and force constants present in 3R stacking in comparison to 2H stacking. The respective intensities for the different stacks, as shown in Fig. 5(i), indicate clearly that different intensities are present for this peak in different areas, allowing one to distinguish between 2H-2H, 2H-3R and different 3R-3R stacking configurations. The use of Raman intensity maps serves to highlight the ubiquitous nature of the different stacking configurations, which would not be readily apparent in comparing individual spectra of different crystals, or in the study of high-frequency point spectra, which show little change between 2H and 3R stacking configurations 32 , as shown in the extracted high-frequency spectra in Figure S4 and discussed in the Supporting Information. Low-frequency Raman mapping can distinguish between different stacking configurations rapidly and non-destructively, allowing TMDs in different stacking configurations to be identified and studied without the need for high-resolution imaging 59 . The peak positions of SMs and LBMs observed here are in good agreement with previously observed low-frequency modes in mechanically exfoliated 2H MoSe 2 56,60 and CVD-grown MoSe 2 stacking polytypes 33 . Raman spectra of different stacking configurations for 4L MoSe 2 are shown in Figure S3 and discussed in the Supporting Information. Layer number assignations have been confirmed using atomic force microscopy (AFM) as detailed in the Supporting Information, Figures S5 and S6.

WSe 2 Raman Mapping
A sample of CVD-grown WSe 2 with a variety of layer numbers present is shown in Fig. 6(a). The WSe 2 Raman spectrum displays the in-plane (E'/E g ) and out-of-plane (A' 1 /A 1g ) modes typical for layered TMDs. Under the experimental conditions used here, these appear as a single overlapping peak at ~250 cm −1 in mono-and few-layer WSe 2 . In the case of resonant excitation conditions, as applies when using a 532 nm excitation laser in resonance with the A' exciton peak of WSe 2 61,62 , the 2LA(M) phonon also appears. This is a second order resonant Raman mode that occurs due to LA phonons at the M point in the Brillouin zone 45 , similar to the case of MoS 2 and WS 2 in resonance 26,63,64 . Figure 6(d) shows spectra of 1 to 3L WSe 2 extracted from different areas marked in Fig. 6(a), which are in agreement with previous studies 56,58 . A peak intensity Raman map of the peak at ~250 cm −1 is shown in Fig. 6(b), with the corresponding position map in Figure S7(a) in the Supporting Information. This peak is a combination of contributions from the A' 1 /A 1g and E'/E g /E 1 2g modes that coincidentally overlap at this Raman shift. This mode shows a decrease in intensity with layer number, and a slight shift in position as shown and discussed in Figure S7(a) in the Supporting Information. The changing intensity of this peak between the two bilayer regions, as labelled on the optical image, indicates some change in stacking configuration, with one region appearing at a higher intensity than the other 58 . This is likely due to a decrease in in-plane contributions due to decreasing magnitudes of Raman tensors in 3R symmetry contributions, but high-frequency modes alone are not sufficient to assign a definitive stacking configuration to each region. The labels shown on the optical image will be discussed in the low-frequency analysis below. A Raman map of the 2LA(M) mode (~260 cm −1 ) intensity is shown in Fig. 6(c), with the corresponding position map in Figure S7(b). The 2LA(M) mode's intensity changes significantly from monolayer to bilayer, but shows no further significant change for 3L. It is clear that this mode, similar to the peak at 250 cm −1 , is also more intense for one bilayer region than another. The relative intensity of 2LA(M) increases with respect to the A' 1 /A 1g and E'/E g /E 1 2g combination peak, however, the overall intensity decreases sufficiently for this not to be apparent in the peak intensity maps. The B 2g (~310 cm −1 ) peak Scientific RepoRts | 6:19476 | DOI: 10.1038/srep19476 intensity map is shown in Fig. 6(e), with the corresponding peak position map shown in Figure S7(d). This mode, similar to the case for MoSe 2 , is inactive in bulk material, but becomes Raman active in few-layer samples 42 . However, the absence of a discernible change in the intensity or position for 2-3 layers means it is of little use for layer-number analysis. Interestingly, this mode is most intense in the case of one 2L stacking configuration, which we tentatively attribute to increased interlayer interactions in ideal (likely 2H stacking) in comparison to other (3R) configurations. The brightest areas in the PL intensity map in Fig. 6(f) signify the presence of monolayers. This is confirmed by the extracted PL spectra and position map shown in Figure S7(c) and (e), respectively in the Supporting Information. As layer number increases, the PL position shifts to higher wavelengths (lower bandgap), and decreases in intensity, as is expected due to the change in band structure 1,63 . No significant change in PL intensity or position is seen between the two different bilayer regions.
The low-frequency Raman modes of WSe 2 are shown in Fig. 7. Figure 7(a) shows spectra of 1 to 3L WSe 2 SMs and LBMs, which have been extracted from different areas marked in the optical image in Fig. 6(a), and are in close agreement with spectra previously reported 56,58 . A clear decrease in intensity of the SM from 2L-2H to 2L-3R stacking is observed, with a corresponding increase in the LBM. The low-frequency peaks shown here  agree well with different stacking configurations of 2L WSe 2 reported previously 58 . A Raman map of the 2L SM (~17 cm −1 ) intensity is shown in Fig. 7(b), which shows (with some overlap with peaks present in different layers) the areas where 2L-2H coverage is present. This is also shown for intensity maps of 2L-3R LBM (~27 cm −1 ) and 3L-2H SM/LBM peak overlap (~21 cm −1 ) shown in Fig. 7(c,d), respectively. A map of the position of maximum intensity in the low-frequency region is shown in Fig. 7(e), where the measurement of peak position over the range of 10-40 cm −1 allows for some clarification of each layer from a single Raman map.

WS 2 Raman Mapping
A sample of CVD grown WS 2 with a variety of layer numbers present is shown in Fig. 8(a). The WS 2 Raman spectrum with an excitation wavelength of 532 nm is characterized by the E'/E g /E 1 2g and A' 1 /A 1g modes at ~355 cm −1 and 417 cm −1 , respectively, and the resonant 2LA(M) phonon mode at ~352 cm −1 , similar to that discussed previously for WSe 2 . The resonance mode appears here due to the 532 nm laser wavelength used being in resonance with the B exciton peak of WS 2 61,62,64 . Resonant Raman spectroscopy is a powerful tool in the study of exciton-phonon interactions in 2D materials; through careful selection of the excitation wavelength certain modes can be enhanced and additional resonant contributions such as the 2LA(M) mode observed 65 . A Raman map of intensity of the peak centred at ~352 cm −1 is shown in Fig. 8(b), with the corresponding peak position map in Figure S8(a) in the supporting information. This peak is a combination of contributions from the resonant 2LA(M) and E'/E g /E 1 2g modes that coincidentally overlap at this Raman shift. This peak is most intense in monolayer crystals, correlating to the PL map in Fig. 8(e). A Raman map of the A' 1 /A 1g mode intensity is shown in Fig. 8(d), with the corresponding peak position map shown in Figure S8(b) in the Supporting Information. The Raman spectrum of these layers is shown in Fig. 8(c), with the spectra normalized to the peak at 352 cm −1 and offset for clarity. This shows changing behaviour from monolayer to few-layer crystals that is consistent with previous reports 26,66 . The remarkable PL in WS 2 monolayers is evident in the PL intensity map and spectrum in Figure S8(e) and (g) in the Supporting Information. The apparent absence of PL in this map for 2 + layers is simply due to the relative intensity of the PL in 2 + layers being dwarfed by the emission from the monolayer crystals, where the intensity ratio of PL to 2LA(M)/E 1 2g is ~25. Further changes in PL between mono and few-layer films are evident in the map of PL peak position in Figure S8(f) in the Supporting Information, which demonstrates the position shift from ~640 nm for monolayers to ~650 nm for few layers, as is expected as the addition of layers causes shifting of the band structure towards a smaller and more indirect bandgap.
While for MoS 2 , MoSe 2 and WSe 2 we have highlighted the practicality of low-frequency Raman spectroscopy for assessment of layer-number and stacking orientation, in the case of WS 2 we will now discuss the possible presence of resonant modes in the low-frequency region of the Raman spectrum. Low-frequency Raman spectra of WS 2 regions of different layer thickness are shown in Fig. 8(f). We observe a peak at ~27 cm −1 for all layer numbers, essentially obscuring SMs and LBMs at the Raman excitation wavelength used (532 nm). This peak is most intense in monolayer, as can be seen by the map in Fig. 8(e). A recent report has shown similar behaviour in the low-frequency region of the Raman spectrum of MoS 2 probed with a 633 nm excitation laser 67 and attributed this to strong resonance with excitons or exciton-polaritons, while previous reports have attributed this resonant Raman process to be reflective of a subtle splitting in the conduction band at K points 68 . We tentatively assign this new peak in WS 2 as a LA(M) related mode, due to the peak intensity maps appearing almost identical in relative intensity to the 2LA(M) peak intensity map shown in Fig. 8(b). It should be noted that these resonance effects are not seen in WSe 2 , with the laser wavelength used (532 nm), as this is only in resonance with the A' split exciton peak, and not an exciton absorption peak as is the case for WS 2 61 . This peak is seen in WS 2 for all layer thicknesses measured and while it is most intense in monolayer it does not vary significantly in intensity for other layer numbers. To further strengthen the link between this newly observed peak and the resonant modes, a comparison between Figure S8(c) in the Supporting Information, a peak intensity map of the LA(M) mode, and the low-frequency resonance peak shown here in Fig. 8(e), shows that these correlate in relative intensity. It is suggested that further exploration of WS 2 low-frequency modes with multiple wavelengths would confirm this assignment, as has held true for MoS 2 67,68 .

Conclusion
A comprehensive study of Raman scattering in CVD-grown mono-and few-layer MoS 2 , MoSe 2 , WSe 2 and WS 2 has been presented. Phonon modes for in-plane and out-of-plane vibrations show thickness dependent intensities and positions in both the high-and low-frequency regions. The general peak shift trends are similar for all materials studied due to their similar lattice structures, where a stiffening (blue shift) is observed in SMs, while a softening (red shift) is observed in LBMs, with increasing layer number. However, the intensity dependencies and Raman shifts vary in each material due to the different atomic masses of the metal/chalcogen in each crystal type, and due to the stacking order of the layers. The determination of layer number via systematic low-frequency mode mapping is a crucial development in the research and analysis of TMD thin films, as is the stacking configuration determination, which we have shown here by Raman mapping techniques. We further report a new peak observable in resonance conditions at ~27 cm −1 in WS 2 crystals.
In future, low-frequency Raman mapping could readily be applied to quickly assess the layer number of TMDs produced by other methods, such as liquid-phase exfoliation, to ascertain their suitability for specific applications. Importantly, this methodology could be extended to other TMD crystals that do not show significant changes in the high-frequency region of their Raman spectrum with layer number, such as ReS 2 69 . Furthermore, it is anticipated that this technique will be useful for investigating layer number and stacking orientation in 2D material alloys 70 and recently fabricated TMD heterostructures 39,40 .

Materials and Methods
CVD growth of TMDs. Precursor layers of MoO 3 (WO 3 ) were liquid-phase exfoliated and dispersed onto commercially available silicon dioxide (SiO 2 , ~ 290 nm thick) substrates as described previously 28,71 . The MoO 3 (WO 3 ) precursor substrates were then placed in a quartz boat with a blank 300 nm SiO 2 /Si substrate face down on top of them, creating a microreactor. This was then placed in the centre of the heating zone of a quartz tube furnace, and ramped to 750 o C under 150 sccm of forming gas (10% H 2 in Ar) flow at a pressure of ~0.7 torr. Sulfide and selenide films were grown in separate, dedicated systems to avoid cross contamination.
For MSe 2 growth. Se vapour was then produced by heating Se powder to ~220 o C in an independently controlled upstream heating zone of the furnace, and carried downstream to the microreactor for a duration of 30 minutes after which the furnace was cooled down to room temperature.
For MS 2 growth. S vapour was then produced by heating S powder to ~120 o C in an independently controlled upstream heating zone of the furnace, and carried downstream to the microreactor for a duration of 20 minutes after which the furnace was held at 750 o C for 20 minutes before being cooled down to room temperature.
A schematic of the growth setup used is shown in Figure S9 in the Supporting Information. While the described growth procedure can produce large-area monolayer coverage 28 , areas consisting of crystals with a variety of layer thicknesses were specifically chosen to highlight the capability of low-frequency Raman mapping for layer-number and stacking-orientation investigation.
Raman and PL Analysis. Raman and PL spectroscopy were performed using a Witec alpha 300R with a 532 nm excitation laser and a laser power of < 500 μ W, in order to minimize sample damage. The Witec alpha 300R was fitted with a Rayshield Coupler to detect Raman lines close to the Rayleigh line at 0 cm −1 . A spectral grating with 1800 lines/mm was used for all Raman spectra whereas a spectral grating with 600 lines/mm was used for PL measurements. The spectrometer was calibrated to a Hg/Ar calibration lamp (Ocean Optics) prior to the acquisition of spectra. Maps were generated by taking 4 spectra per μ m in both x and y directions over large areas. AFM measurements were carried out using a Veeco Dimension 3100 in tapping mode, with 40 N/m probes from Budget Sensors.