The Pressure Response of Bulk and Two−Dimensional MoS₂ Crystals Studied by Raman and Photoluminescence Spectroscopy: Dimensionality and Pressure Transmitting Medium Effects

Abstract

The pressure response of bulk and two−dimensional (2D) MoS₂ crystals (monolayer, bilayer, and many–layered), directly transferred to the diamond surface of the diamond anvil cell (DAC) used for high−pressure application, is examined by means of Raman and photoluminescence (PL) spectroscopy. For the high–pressure experiments of 2D MoS₂, the Daphne 7474 oil and the 4:1 methanol–ethanol mixture are alternatively used as pressure-transmitting media (PTM), while the former is also used as PTM in the case of bulk MoS₂. Characteristic differences are observed in the pressure evolution of the Raman spectral profile and the pressure coefficients of the peak frequencies between the bulk and the 2D MoS₂ crystals of various thicknesses, which also depend on the PTM used. These observations, along with the pressure evolution of the PL spectrum of 2D MoS₂, are ascribed to the different stress conditions in each case (hydrostatic vs. uniaxial compression perpendicular to the MoS₂ layers), the adhesion of the 2D MoS₂ crystals on the diamond anvil, as well as the nature of the particular PTM used and its interaction with the studied system.

1. Introduction

Molybdenum disulfide (MoS₂) is an important member of the transition metal dichalcogenides (TMDs) family with the general formula MX₂ (where M is a transition metal, such as Mo, W, Ti, Zr, Hf, Nb or Ta, and X a chalcogen, such as S, Se or Te), having a wide range of current and potential applications both in its bulk and two–dimensional (2D) variant [1,2,3,4,5,6]. In the bulk form, it exhibits different structural polytypes (trigonal–T, hexagonal–H, and rhombohedral–R), with the most common one being the hexagonal 2H due to its stability [1,2,7,8]. It consists of triple atomic layers (S–Mo–S) with strong covalent bonding between Mo and S atoms. Each Mo atom is surrounded by six S atoms in a trigonal prismatic coordination around Mo, with the S atoms in the upper layer located directly above those of the lower layer. These MoS₂ layers are stacked along the c–axis with weak van der Waals interlayer interactions, facilitating their easy mechanical separation into 2D sheets [1,2,7,8,9].

The 2D MoS₂ crystals have attracted intense scientific interest due to their remarkable mechanical and electronic properties, including a thickness−dependent energy bandgap [1,2,10,11,12]. Namely, the bulk and few–layered (FL) hexagonal MoS₂ have an indirect energy gap of 1.2–1.6 eV, which turns into a direct one of 1.8–1.9 eV in the case of monolayer (1L) MoS₂ [12,13]. This indirect–to–direct bandgap transition causes the dramatic photoluminescence (PL) signal increase in the visible spectral region for 1L MoS₂ [2,12,14], while the bandgap can be tuned by mechanical strain and pressure application [15,16,17]. Apart from being an effective technique to modify the lattice and electronic structure of bulk and 2D materials, pressure application also enables the continuous increase in the interaction between a 2D system and its environment, thus constituting a method of choice to investigate such effects [18].

Because of their extreme sensitivity and ease of application, optical spectroscopic techniques are versatile tools for scientific investigations in the 2D materials field, both at ambient and high–pressure conditions. Therefore, apart from their common use for identifying the samples thickness at ambient conditions (see Section 3.2), there are several reports in the literature during the last decade dealing with the study of the pressure response of 2D MoS₂ crystals by means of PL and/or Raman spectroscopy [16,19,20,21,22,23,24,25,26,27,28,29]. These reports provided different results—contradictory in some cases—regarding the pressure evolution of the PL and the Raman peak energies and their interpretation. This is mainly due to the different conditions of the studied 2D crystals inside the diamond anvil cells (DACs) used for high pressure application, deposited on different substrates, usually on thinned SiO₂/Si, or even directly on the diamond anvil of the DAC (to eliminate the contribution of the additional substrate in the pressure response of the crystals) and different fluids as pressure transmitting media (PTM). Moreover, in some cases, the reported pressure coefficients of the Raman peak frequencies were extracted from the corresponding frequency vs. pressure data up to very high pressures (20–30 GPa), assuming a linear dependence. Additionally, for some of the PTMs used, the deviation from linearity is further enhanced because of the solidification of the PTM at much lower pressures, causing non-hydrostatic conditions inside the DAC.

Here, we report on a systematic high–pressure study of bulk and 2D MoS₂ crystals of various thicknesses, deposited directly on the diamond anvil of the DAC (the so–called ‘substrate–free’ 2D crystals), by means of Raman spectroscopy, alternatively using two different fluids as PTM in the case of the 2D crystals. In contrast to previous works that often extended to much higher pressures, our analysis is restricted to the low–to–moderate pressure regime, using only data collected before the solidification of the PTM and before the onset of structural/electronic transitions, so as to obtain reliable pressure coefficients and to unveil the effects of dimensionality, 2D crystal–substrate adhesion and PTM properties on the Raman response. The pressure evolution of the PL peaks of monolayer and bilayer MoS₂ is also examined under carefully controlled excitation conditions, with the laser power kept as low as possible and the signal averaged over a scanned area to minimize sample heating. Our approach reveals non–trivial layer– and PTM–dependent trends and is expected to shed light on the pressure response of 2D MoS₂ systems, contributing to a clearer interpretation of the existing literature.

2. Materials and Methods

The bulk hexagonal 2H–MoS₂ crystals (purity > 99.9%) used in the present work were purchased from HQ Graphene (Groningen, the Netherlands). The 2D (single– and few–layered) MoS₂ crystals were grown by chemical vapor deposition (CVD) on SiO₂/Si substrates, through the reaction between sulfur vapors and pre–deposited sodium molybdate (Na₂MoO₄) in solution at high temperature (800 °C) and atmospheric pressure. The concentration of the precursor Na₂MoO₄ solution was 10 mg·mL⁻¹, yielding a continuous MoS₂ film with single–, bi–, and few–layered domains epitaxially fabricated on the substrate. Further details can be found in the corresponding article by Michail et al. [30].

Raman and PL spectra were collected in the backscattering geometry by a LabRAM HR spectrometer equipped with a DuoScan^TM mapping system (HORIBA, Kyoto, Japan). The excitation laser beam (λ_exc = 514 nm) of a diode–pumped solid-state laser (Cobolt Fandango^TM, HÜBNER Photonics, Kassel, Germany) was focused on the sample by means of a 50× super long working distance objective (focusing spot diameter: ~2 μm). The elastically scattered light is eliminated by means of an appropriate edge filter. The laser power was set either to 1 mW (Raman measurements) or 10 and 100 μW (PL measurements), to minimize any laser–heating effects. To further reduce the heating of the samples by the excitation laser beam in the case of the PL measurements, the signal from the studied sample was averaged by continuously scanning a square area of 5 × 5 μm², taking advantage of the DuoScan^TM mapping system.

High pressure was generated by means of a gas membrane-type diamond anvil cell (DAC, Almax–easyLab, Diksmuide, Belgium) using a ~100 μm–thick drilled (~150 μm hole diameter) stainless steel gasket. Pressure was calibrated using the ruby fluorescence method [31,32]. To eliminate the effect of the SiO₂/Si substrate on the pressure response of the 2D MoS₂, the crystals were transferred directly onto the diamond anvil of the DAC (‘substrate–free’ 2D MoS₂ crystals), utilizing the ‘surface–energy’ assisted methodology with polydimethylsiloxane (PDMS) stamps [33]. The experimental setup and schematic representations of the diamond anvil cell and the crystalline structures of the studied 2D MoS₂ (monolayer—1L, bilayer—2L, and many–layered—mL [34,35]) are depicted in Figure S1 in the Supplementary Materials. In this study, two different fluids served as a pressure-transmitting medium to ensure hydrostaticity inside the sample chamber. Firstly, the high viscosity, non–polar Daphne 7474 oil, comprising large–sized molecules and solidifying above 3.7 GPa [36,37]. In order to exclude any sample–related strain and doping effects on the high–pressure response of the Raman spectrum, two different experiments were conducted in this case. Secondly, the low viscosity, polar 4:1 methanol–ethanol mixture, comprising small molecules with a solidification pressure of 10.4 GPa [38,39]. The choice of these two fluids was based not only on their distinct properties and hydrostatic behavior but also on their availability, ease of application, and widespread use (especially the alcohol mixture) for high−pressure experiments.

3. Results and Discussion

3.1. High-Pressure Raman Study of Bulk MoS₂

Firstly, we have examined, during the same experiment, the pressure response of the Raman spectrum of two bulk hexagonal MoS₂ crystals with slightly different orientations with respect to the incident excitation laser beam (bulk1 and bulk2 crystals in Figure 1a, where representative Raman spectra at various pressures are illustrated), utilizing Daphne 7474 oil as PTM. It is well–known that the number and the symmetry of the Raman active modes depend on the number of layers comprising the MoS₂ crystal (bulk, even– or odd–numbered few–layered and monolayer) and the corresponding point/space group symmetry [40,41]. The hexagonal bulk 2H–MoS₂, belonging to the P6₃/mmc space group (D_6h point group symmetry) [41,42], has four Raman active modes at the Γ point of the Brillouin zone with symmetries E_1g, E_2g (${\mathrm{E}}_{2\mathrm{g}}^1$ and ${\mathrm{E}}_{2\mathrm{g}}^2$) and A_1g [43,44]. Except for the ${\mathrm{E}}_{2\mathrm{g}}^2$ mode, which is assigned to relative displacements of two adjacent rigid MoS₂ layers (it appears at very low frequency, below 40 cm⁻¹, and is inaccessible due to the edge filter cut–off used in the present study), the other Raman modes are associated with intralayer vibrations [41,45]. The E_1g mode (in–plane motion of the S atoms) at ~287 cm⁻¹ is symmetry forbidden in the backscattering geometry perpendicular to the MoS₂ layers and appears only in the case of different crystal orientations with respect to the incident laser beam (bulk2 crystal in Figure 1a). Hence, the Raman spectrum of bulk MoS₂ is dominated by the ${\mathrm{E}}_{2\mathrm{g}}^1$ (in–plane motions of the S and Mo atoms to opposite directions) and the A_1g mode (out–of–plane motions of the S atoms) at ~384 and ~409 cm⁻¹, respectively [41,43,44]. Furthermore, a weak second-order Raman band, marked as 2LA in Figure 1a, also appears in the spectra in the frequency range 440–475 cm⁻¹ [46].

With increasing pressure, the observed first-order Raman peaks shift to higher frequencies, reflecting the bond hardening upon volume reduction. At the same time, pressure application also causes the reversible gradual intensity attenuation and moderate broadening of the in–plane ${\mathrm{E}}_{2\mathrm{g}}^1$ with respect to the out–of–plane A_1g Raman peak, without the appearance of any additional Raman peak (Figure 1a). The pressure evolution of the Raman peak frequencies for the two bulk MoS₂ crystals is illustrated in Figure 1b. All these pressure dependencies are quite smooth in the whole pressure range investigated (up to ~8 GPa) and fully reversible upon pressure release (solid symbols in the Figure). Note that previous Raman studies of bulk MoS₂ up to much higher pressures have shown the appearance of a new band on the high frequency side of the in–plane mode and/or changes in the pressure coefficients for both first–order Raman peak frequencies for P > 15 GPa [47,48,49,50]. These observations have been attributed to the beginning of a structural phase transition from 2H_c to 2H_a, caused by the interlayer sliding upon compression as suggested by the corresponding synchrotron XRD explorations for P > 20 GPa [51,52]. However, as expected, the experimental data presented in the current work do not show such anomalies because of the much lower pressure range investigated.

Above the solidification pressure of the Daphne 7474 oil (~4 GPa) [36], the frequency vs. pressure data is somewhat different (more pronounced for the in–plane). ${\mathrm{E}}_{2\mathrm{g}}^1$ mode) between the two bulk crystals (up and down triangles in the Figure). This deviation reflects the gradual development of non−hydrostatic pressure components in the sample chamber inside the DAC after the solidification of the PTM used [36]. Therefore, only data obtained up to 4 GPa were used for further analysis. The linear fit of the data yields the values of 2.1, 1.9, and 3.7 cm⁻¹GPa⁻¹ for the pressure coefficients of the E_1g, ${\mathrm{E}}_{2\mathrm{g}}^1$ and A_1g modes, respectively. The larger pressure coefficient for the out–of–plane mode compared to those of the in–plane ones suggests that the compression of MoS₂ on the c–axis is more effective compared to that of the a–axis [22,29]. Noticeably, the data for the main ${\mathrm{E}}_{2\mathrm{g}}^1$ and A_1g Raman peaks are better fitted by parabolic (sublinear) functions, resulting in linear pressure coefficient values of 2.0 and 4.1 cm⁻¹GPa⁻¹, respectively. This sublinear behavior is more pronounced for the out–of–plane A_1g mode, reflecting the important role of the much weaker van der Waals interlayer interactions compared to the strong intralayer covalent bonds in the pressure response of bulk MoS₂. The linear pressure coefficients obtained in this work using Daphne 7474 as PTM are lying closer to the upper limit of the corresponding values in the existing literature for bulk MoS₂ using different PTM (4:1 methanol–ethanol mixture, Silicone oil, NaCl, KBr, or Ar); 1.5–1.8 cm⁻¹GPa⁻¹ for the E_1g, 1.3–1.9 cm⁻¹GPa⁻¹ for the ${\mathrm{E}}_{2\mathrm{g}}^1$ and 2.6–4.0 cm⁻¹GPa⁻¹ for the A_1g mode, respectively [27,47,48,49,50,53,54].

3.2. Raman and PL Spectra of 2D MoS₂ at Ambient Pressure

Unlike bulk and even–numbered few–layer (FL) MoS₂, odd–numbered FL and 1L MoS₂ possess the $P\overline{6}m2$ space group (D_3h point group symmetry) due to the lack of inversion symmetry. Hence, the symmetry of the Raman active modes E_1g, ${\mathrm{E}}_{2\mathrm{g}}^1$ and A_1g becomes E’’, E’ and ${\mathrm{A}}_1^{\mathrm{\prime }}$, respectively, with identical Raman tensors because of the correlation between D_3h and D_6h [40,41,55]. Noticeably, as the number of layers in 2D MoS₂ crystals decreases, the frequency difference (Δω) between the out–of–plane A_1g ${(\mathrm{A}}_1^{\mathrm{\prime }})$ and the main in–plane ${\mathrm{E}}_{2\mathrm{g}}^1$ (E’) mode also decreases [40,41,44,56]. This Δω separation decrease is caused by the simultaneous redshift (frequency downshift) of the out–of–plane and blueshift (frequency upshift) of the in–plane mode with decreasing number of layers comprising a 2D MoS₂ crystal. The redshift of the A_1g ${(\mathrm{A}}_1^{\mathrm{\prime }})$ mode is attributed to the reduced restoring forces on the S atoms, resulting from the lesser interlayer interactions with decreasing number of layers [40,44]. On the other hand, it has been shown that the ‘anomalous’ blueshift of the ${\mathrm{E}}_{2\mathrm{g}}^1$ (E’) mode arises from the strengthening of the surface force constants for the Mo–S intralayer interactions due to the loss of neighbors in adjacent layers in the case of 2D MoS₂ [40,57]. Apparently, the particular Δω separation value can be exploited for the thickness determination of a 2D MoS₂ crystal. Figure 2a illustrates representative Raman spectra of the ‘substrate–free’ 2D MoS₂ sample inside the loaded DAC and prior to pressure application (nearly ambient pressure), as obtained from the three different areas shown in the optical image depicted in the inset of the Figure. The corresponding Δω values are also given in the Figure. Taking into account the corresponding literature data [41,43,56], the three areas examined can be identified as many–layered (mL), bilayer (2L), and 1L MoS₂.

Typical PL spectra obtained from the three aforementioned sample areas are illustrated in Figure 2b. The indirect–to–direct bandgap transition on going from 2L to 1L MoS₂ is clearly reflected in the PL spectral profile and signal intensity, being compatible with the assignment of the various sample regions to specific 2D MoS₂ crystals on the basis of the corresponding Raman spectra. In the 2L MoS₂, two rather weak bands appear in the spectrum. The lower energy broad one at ~1.52 eV, marked by ‘I’, is attributed to the indirect K to Γ point transition, while the higher energy band of excitonic origin at ~1.86 eV, labeled as ‘A’, results from the direct interband transition between the conduction band (CB) and the top of the valence band (VB) at the K point of the Brillouin zone (inset in the Figure) [19]. On the other hand, only a significantly strong excitonic A–band appears in the PL spectrum of 1L MoS₂ at a similar energy to that of the 2L and in agreement with the literature data [19,58].

3.3. High-Pressure Raman and PL Study of 2D MoS₂

Next, we studied, using again Daphne 7474 as PTM, the pressure response of the Raman spectra obtained from the three different regions of the ‘substrate–free’ 2D MoS₂ sample shown in the inset of Figure 2a, corresponding to 1L, 2L, and mL MoS₂. Representative Raman spectra of 1L (bottom panel) and 2L (top panel) MoS₂ crystals at various pressures up to 4 GPa, where the PTM still provides good hydrostatic conditions, are illustrated in Figure 3a. Similarly to the case of the bulk crystals, both the in–plane (E’ or ${\mathrm{E}}_{2\mathrm{g}}^1$) and the out–of–plane (${\mathrm{A}}_1^{\mathrm{\prime }}$ or A_1g) Raman peaks of the 2D MoS₂ crystals gradually shift to higher frequencies with increasing pressure. Contrary to the pressure evolution of the Raman spectral profile for bulk MoS₂, pressure application on 1L and 2L crystals causes a significant broadening and peak height decrease in the out–of–plane peak, indicating the gradual deformation of the crystals upon compression. This behavior, different from that of the bulk MoS₂, is an indication of the presence of non–hydrostatic compression components on the ‘substrate–free’ 1L and 2L crystals and their good adhesion to the diamond surface of the DAC (vide infra).

As it can also be inferred from the same Figure, there is no apparent splitting of the two first–order Raman peaks up to the highest pressure attained in our experiments, contrary to the cases of uniaxial strain application along the MoS₂ layer(s), resulting in the splitting of the doubly degenerate E’/${\mathrm{E}}_{2\mathrm{g}}^1$ mode, or to the presence of regions with stronger and weaker layer–substrate interaction that can also cause the splitting of the ${\mathrm{A}}_1^{\mathrm{\prime }}$/A_1g Raman peak [24,59,60,61]. In our case, the absence of splitting of the Raman peaks suggests that there is no significant differentiation in the in–plane strain and the MoS₂ layer–substrate interaction. Upon pressure release, only a partial recovery of the width and peak height of the out–of–plane peak in 1L and 2L MoS₂ takes place (Figure S2 in the Supplementary Materials), while pressure application has more detrimental effects and stronger irreversibility in the case of 2L MoS₂, possibly due to the additional presence of the interlayer coupling. On the other hand, pressure application on mL MoS₂ using Daphne 7474 as PTM does not have any profound effect on the overall Raman spectral profile (Figure S3 in the Supplementary Materials).

The pressure dependencies of the frequencies of the two Raman peaks observed for each of the three ‘substrate–free’ 2D MoS₂ crystals (1L, 2L, and mL) are illustrated in Figure 3b. All of them are quasi–linear and reversible, precluding the occurrence of any structural and/or electronic phase transition up to 4 GPa. The pressure coefficients of the Raman peak frequencies are smaller than those of the corresponding modes in the bulk crystals and increase with increasing number of layers for the out–of–plane mode (2.5, 3.2 and 3.6 cm⁻¹GPa⁻¹ for 1L, 2L and mL MoS₂, respectively), whereas they decrease for the in–plane mode (1.5, 1.2 and 1.0 cm⁻¹GPa⁻¹ for 1L, 2L and mL MoS₂, respectively). To understand the observed behavior, one should consider the stress/strain situation of the studied 2D samples inside the DAC, taking into account the nature of the PTM used, as well as the adhesion of the sample on the substrate, associated with their relative sliding [33,62].

In the case of the 2D MoS₂ crystals stuck on the diamond surface, pressure acts more or less—depending on their thickness—such as a piston along the c–axis, resulting in a predominantly uniaxial compression of the samples. Under these circumstances, the hydrostatic stress component acting on the sample (σ_H) is lower than that measured by the ruby gauge (P_R) [63,64]. Assuming pure uniaxial stress perpendicular to the sample surface with perfect adhesion on the highly stiff diamond, the hydrostatic part of the applied pressure is (Section S1 in the Supplementary Materials) [63,64,65,66]:

$${\mathsf{\sigma }}_{\mathrm{H}}={\displaystyle \frac{(2C_{13}+C_{33})}{3C_{33}}}{P}_{\mathrm{R}}$$

(1)

A rough estimation of σ_H can be obtained using Equation (1), the experimental bulk MoS₂ values for the elastic constants C₁₃ and C₃₃ [67], keeping in mind that this is not accurate for 1L MoS₂ because of the absence of weak van der Waals interlayer interactions [33]. Remarkably, this substitution yields σ_H = 0.63P_R, in very good agreement with the reduced linear pressure coefficients for the Raman peak frequencies of 1L (Figure 3b) with respect to those of the bulk crystals (Figure 1b).

As the number of layers increases, going from 1L to 2L and eventually to mL in the 2D MoS₂ crystals, the pressure will be applied more and more hydrostatically on the samples. This leads to an increase in the σ_H/P_R ratio and could explain the gradual increase in the pressure coefficient of the out–of–plane A_1g mode frequency observed in Figure 3b with increasing number of layers. On the other hand, the increase in the number of layers comprising a 2D MoS₂ crystal is also expected to cause its unbinding from the substrate due to the increase in its bending modulus [24,68,69]. The reduced adhesion of the sample to the substrate promotes their relative sliding, leading to a decrease in the pressure coefficient of the in–plane ${\mathrm{E}}_{2\mathrm{g}}^1$ mode frequency as long as pressure is applied predominantly perpendicular to the MoS₂ layers.

The pressure evolution of the PL peak energies in 1L and 2L ‘substrate–free’ MoS₂ crystals is also examined, reducing as much as possible the heating of the samples by the excitation laser beam (see Section 2). We stress that the pressure evolution of the PL spectrum is generally expected to be more complicated than that of the Raman peaks. Apart from the exact strain conditions of the sample in the DAC, it is affected by the different pressure dependence of the VB and the CB and their splitting, the possible electronic transitions, the presence of pressure–induced defects, and the sample heating by the excitation beam. As can be inferred from Figure 4, with 100 μW excitation power, the PL bands for both 1L and 2L shift initially with pressure (up to ~1.5 GPa) to lower energies at a rate of 13–15 meV∙GPa⁻¹ for the A– and ~66 meV∙GPa⁻¹ for the I–band, respectively. Subsequently, the position of the A–band for both 2D crystals remains nearly constant with further pressure increase up to ~4 GPa (the solidification pressure of Daphne 7474 used as PTM), while the weak I–band cannot be followed above 1.5 GPa because of its broad lineshape and its further intensity reduction with pressure.

In the case of the 2L MoS₂, the red shift in the I–band is compatible with the corresponding literature, where the decrease in the Γ–K energy gap is attributed to the large band splitting at the Γ point due to the interlayer electronic coupling upon compression [19,28,29,70]. On the other hand, the overall pressure evolution of the A–band in 2L MoS₂ deviates from the corresponding findings by Dou et al. and Li et al. [19,28]. Dou et al. used thinned SiO₂/Si substrates to support 2L MoS₂ inside the DAC, a 4:1 methanol–ethanol mixture as PTM, and much higher laser power for excitation compared to the present study (~20 times). They reported a blueshift of the A–band up to 1.5 GPa and a redshift at higher pressures, and they ascribed this discontinuity to a pressure–induced modification from a direct interband Κ–Κ to an indirect interband Λ–Κ transition at ~1.5 GPa [19]. On the contrary, Li et al. studied ‘substrate–free’ 2L MoS₂ with Ar or He as PTM and laser power ~10 times higher than the one used here [28]. They reported a continuous redshift of the A–band up to ~6 GPa at a much smaller rate (−1.6 meV∙GPa⁻¹), accompanied by an intensity decrease. At higher pressures, they observed an increase in the redshift rate (–3.8 meV∙GPa⁻¹), which they attributed to the same direct–to–indirect electronic transition reported by Dou et al. at ~1.5 GPa [19,28].

In the case of the 10 μW excitation power, which is more than two orders of magnitude lower than that typically used in the literature so far [16,19,20,21,24,25,28], the A–band for 1L MoS₂ does not practically shift with pressure in the whole pressure range investigated (0–4 GPa). Despite the special precautions taken in the present study, already using 100 μW for excitation (much lower power compared to that in the literature, and beam scanning on the sample), the different pressure response of the PL peak energy for the 10 μW laser power underlines its extreme sensitivity to the sample heating. The increase in pressure causes only the strong intensity reduction of this band, in agreement with other literature reports [19,20,25]. This intensity suppression could be ascribed to the pressure–induced intralayer hybridization between Mo d orbitals and the S p orbitals that could eventually lead to a crossover from direct to indirect transition at higher pressures and/or the pressure–induced increase in defects, as proposed in the literature [19,20,21,71]. The latter possibility is also compatible with the gradual deformation of the 1L and 2L MoS₂ crystals upon compression, inferred from the strong broadening and peak height decrease in the out–of–plane Raman peak (vide supra).

The essentially zero pressure shift in the A–band energy in ‘substrate–free’ 1L MoS₂ is in contrast to what was earlier reported in the literature for 1L MoS₂ on SiO₂/Si substrates [19,20,21,25] or transferred to the diamond anvil of the DAC using Ar or He as PTM [28]. In these studies, a rather strong blueshift of the A–band up to 4 GPa (the maximum pressure attained in our experiments) with rates 20–50 meV∙GPa⁻¹ was observed. Intriguingly, Fu et al. reported an alteration from blueshift to redshift (−15.3 meV∙GPa⁻¹) above ~2 GPa for the PL peak of 1L MoS₂ on SiO₂/Si with Silicone oil as PTM, which they attributed to a Κ–Λ crossover in the CB [25]. The pressure–induced blueshift of the A–band in 1L MoS₂ has been ascribed to the fact that both the VB and the CB mainly originate from the d_x²_–y², d_z² orbitals of Mo and the p_x, p_y orbitals of S, which may move away from the Fermi level by compression, leading to an increase in the energy band gap [28,72]. However, in these studies, either the substrate determines the strain of 1L MoS₂ upon compression, and hence the response of the PL peak energy [19,20,21,25], or the small–sized molecules of Ar and He allow for a more efficient lateral compression of the ‘substrate-free’ sample [28]. Our work reveals that uniaxial stress application—according to the high–pressure Raman data—up to 4 GPa in ‘substrate–free’ 1L MoS₂ with minimum sample heating does not practically affect the A–band energy.

The results of the present study are better correlated with the findings of Francisco–López et al., who studied the pressure response of the A and B excitons in ‘substrate–free’ 1L WSe₂ in comparison with that encapsulated into hexagonal boron nitride layers [33]. They observed that upon compression, the A and B exciton energies for the former sample decrease with rates −3.1 and −1.3 meV∙GPa⁻¹, respectively, whereas for the latter sample, they increase with rates 3.5 and 3.8 meV∙GPa⁻¹, respectively. They have ascribed these contradictory results to the essentially uniaxial stress situation, with the compressive stress component in the direction perpendicular to the plane of the ‘substrate–free’ WSe₂, with respect to the hydrostatic compression of the substantially thicker encapsulated sample [33]. In this context, Zhao et al. investigated the pressure response of ‘substrate–free’ 2D InSe crystals of various thicknesses [73]. They reported that for N > 20 layers of InSe, the lattice is compressed in all directions, and the intralayer compression leads to widening of the band gap, resulting in the blue shift in PL. In contrast, for N ≤ 15, they observed a redshift of PL, which is also attributed to the predominantly uniaxial interlayer compression because of the high strain resistance along the InSe–diamond interface [73].

3.4. The Effect of the Pressure Transmitting Medium

The aforementioned findings concerning the pressure evolution of the Raman spectral profile and the pressure coefficients of the Raman peak frequencies of ‘substrate–free’ 2D MoS₂ crystals (1L, 2L and mL) using Daphne 7474 as PTM have been further confirmed by another, independent high–pressure experiment (Run 2) on different 2D crystals (different local strain and doping [74]). Indeed, from this second experiment, very similar results to those of the first experiment are obtained (Figures S3 and S4 in the Supplementary Materials). In order to investigate the effect of the PTM on the observed behavior, we have also studied the pressure response of ‘substrate–free’ 2D MoS₂ crystals by Raman spectroscopy using the 4:1 methanol–ethanol mixture as PTM. Representative Raman spectra of 1L (bottom panel) and mL (top panel) MoS₂ crystals at various pressures up to 7 GPa are illustrated in Figure 5a.

In this case, pressure application on 1L and 2L causes a considerably smaller broadening and relative peak height decrease in the out–of–plane ${\mathrm{A}}_1^{\mathrm{\prime }}$ or A_1g peak, while the pressure evolution of the Raman spectral profile for mL MoS₂ is very similar to that of the bulk crystals (gradual intensity attenuation and moderate broadening of the in–plane ${\mathrm{E}}_{2\mathrm{g}}^1$ with respect to the out–of–plane A_1g Raman peak). Moreover, as can be inferred from Figure 5b, the pressure coefficients for the corresponding modes are similar, independently of the sample thickness (1L, 2L, or mL).

Overall, the high–pressure Raman results for the studied 2D MoS₂ samples using the alcohol mixture as PTM, the molecules of which are much smaller compared to those of Daphne 7474 [75] and can even penetrate with pressure the space between the sample and the diamond anvil [24], along with its polar nature that could lead to its stronger interaction with the samples [69], imply the more hydrostatic pressure conditions in this case. Thus, it is evident that the choice of PTM is crucial for the pressure response of ‘substrate–free’ 2D MoS₂ systems. Note, however, that for 2D systems on a substrate, the nature of the PTM does not appear to detectably affect its pressure response, at least in the hydrostatic pressure regime of the PTM [62]. Instead, in that case, the strain transferred from the substrate to the 2D material upon compression plays the dominant role [62,69,76].

4. Conclusions

In conclusion, we have presented our detailed high–pressure Raman and PL studies of bulk (three–dimensional, 3D) and ‘substrate–free’ 2D MoS₂ crystals using two different PTM in their hydrostatic pressure range. In the case of the Daphne 7474 PTM, apart from the different pressure evolution of the Raman spectral profile compared to that of the bulk, a considerable reduction in the pressure coefficients of the Raman peak frequencies in the ‘substrate–free’ 2D MoS₂ crystals is observed. Intriguingly, as the number of the MoS₂ layers comprising the 2D crystals increases, the pressure coefficient for the out–of–plane mode frequency increases, gradually approaching the corresponding value for the bulk, whereas for the in–plane mode it decreases on going from 1L to 2L and eventually to mL MoS₂. Furthermore, minimizing the sample heating effects, the PL peak energy in 1L MoS₂ appears to be pressure independent up to 4 GPa (close to the solidification pressure of the PTM). On the other hand, in the case of the alcohol mixture PTM, both the pressure evolution of the Raman spectral profile and the pressure coefficients of the Raman peak frequencies are more similar to those of the bulk, regardless of the number of layers comprising the ‘substrate–free’ 2D MoS₂ crystals. The present experimental findings and deviations can be understood in terms of the degree of uniaxial or hydrostatic stress application on going from 2D to 3D MoS₂ crystals, the degree of adhesion of the 2D crystals on the diamond surface of the high–pressure cell, as well as the properties of the PTM. It would also be interesting to extend the methodology of this study to other important—in terms of their potential applications—2D systems and/or their heterostructures, as long as 1L to FL sheets with satisfactory Raman and/or PL signal can be isolated and successfully transferred to the diamond anvil of the high–pressure cell.