Thermal expansion coefficient of few-layer MoS2 studied by temperature-dependent Raman spectroscopy

The thermal expansion coefficient is an important thermal parameter that influences the performance of nanodevices based on two-dimensional materials. To obtain the thermal expansion coefficient of few-layer MoS2, suspended MoS2 and supported MoS2 were systematically investigated using Raman spectroscopy in the temperature range from 77 to 557 K. The temperature-dependent evolution of the Raman frequency shift for suspended MoS2 exhibited prominent differences from that for supported MoS2, obviously demonstrating the effect due to the thermal expansion coefficient mismatch between MoS2 and the substrate. The intrinsic thermal expansion coefficients of MoS2 with different numbers of layers were calculated. Interestingly, negative thermal expansion coefficients were obtained below 175 K, which was attributed to the bending vibrations in the MoS2 layer during cooling. Our results demonstrate that Raman spectroscopy is a feasible tool for investigating the thermal properties of few-layer MoS2 and will provide useful information for its further application in photoelectronic devices.

www.nature.com/scientificreports/ MoS 2 , especially the TEC mismatch between MoS 2 and the substrate, is a key for studying the thermal stability and intrinsic optical properties of few-layer MoS 2 -based devices. Raman spectroscopy has been demonstrated to be a versatile tool for investigating 2D TMDs [21][22][23] . In the past decade, the temperature effects on the Raman modes of 2D TMDs have been widely investigated [24][25][26][27][28][29] . However, the temperature behaviors of the Raman peaks of TMDs are still controversial. Some researchers reported that the peak positions varied linearly with increasing temperature [24][25][26][27] . Late et al. reported that both monolayer and few-layer MoSe 2 and WSe 2 exhibit a linear temperature dependence 25 . A linear temperature dependence of Raman modes was also observed in monolayer Mo 1−x W x S 2 27 . In recent years, some studies have demonstrated that the temperature dependence of the Raman peak positions for TMDs can be fitted by a nonlinear function. Su and coauthors employed temperature-dependent Raman spectroscopy to study the substrate bonding effects on MoS 2 and WS 2 and expressed the temperature dependence of Raman modes using a third-order polynomial function [28][29][30] . Although the reported temperature dependences of Raman modes for 2D TMDs differ, the TEC mismatch between TMDs and substrates is widely accepted to play an important role in the temperature evolution of Raman modes. To eliminate the substrate effects, suspended TMDs have been used to study the intrinsic properties of TMDs in recent years [31][32][33][34][35][36] . Two-ten times improvement of the mobility and on/off ratio was observed in suspended monolayer MoS 2 31 . The elastic coefficients, including the 2D elastic modulus and Young's modulus, were obtained for suspended multilayer WSe 2 32 . Moreover, the intrinsic thermal conductivity has been investigated for monolayer and few-layer MoS 2 33,34 . However, to our knowledge, the TEC mismatch effect in few-layer MoS 2 has not been systematically studied, and the intrinsic TEC of few-layer MoS 2 has not yet been obtained.
In this work, suspended MoS 2 and supported few-layer (2-6 layer) MoS 2 was comprehensively investigated using Raman spectroscopy in the temperature range from 77 to 557 K. The temperature dependence of suspended MoS 2 exhibited different trends from that of supported few-layer MoS 2 , which could be attributed to the TEC mismatch between MoS 2 and the substrate. Moreover, the temperature dependence of the Raman modes varied with the number of layers. Removing the substrate effect by adopting suspended MoS 2 as a freestanding MoS 2 , the intrinsic TECs of few-layer MoS 2 was obtained. Prominent differences between our results and previous reports were observed and discussed in detail.

Results and discussion
The suspended and supported samples were fabricated by transferring MoS 2 with 2-6 layers onto microholes, which were prepared using a modified mechanical exfoliation method 37 (see "Methods"). Figure 1a presents the optical microscopy image of suspended 2-layer MoS 2 as an example.
Raman spectra were collected using a confocal micro-Raman spectrometer (Horiba Evolution) under backscattering geometry, as exhibited in Fig. 1b. Figure 2 presents the room-temperature Raman spectra of suspended and supported few-layer MoS 2 , which exhibit the typical spectral features of MoS 2 previously reported 22,23 . Two high frequency peaks appear at approximately 380 cm −1 and 405 cm −1 , originating from the lattice vibration of bulk MoS 2 . Due to the crystalline symmetry changes between bulk, monolayer and few-layer MoS 2 , the symmetric representations of these two Raman modes are different. For convenience, these two modes are identified as the E 2g and A 1g modes, respectively, following the assignments for bulk MoS 2 23 . The bulk-vibrational Raman modes shift to higher positions with increasing number of layers. In recent years, ultralow frequency (ULF) Raman spectroscopy has attracted the interest of more researchers because it has been demonstrated to be a feasible tool for studying the interlayer vibrational modes of TMDs [38][39][40] . The ULF Raman peaks originate from the in-plane (shear) and out-of-plane (breathing) vibrations of MoS 2 , which have been used to identify the number of MoS 2 layers 39,40 . The sharp peak is denoted as a shear mode (S1), while the broad peak is assigned as a breathing mode (B1), as shown in Fig. 2. Notably, the signal-to-noise ratio (SNR) of the Raman peaks, especially the ULF Raman peaks, of suspended MoS 2 is much better than that of supported MoS 2 , and more detailed spectral information can be clearly seen. Both the S1 and B1 modes are clearly observed on suspended MoS 2 , whereas only the S1 mode is detected on supported MoS 2 . The MoS 2 layer is pinned on the substrate through van der Waals forces. The dielectric environment created from by the substrate may have effect on the local electromagnetic field due to the multiple reflection inside the monolayer 16 . The enhanced Raman signal of the suspended MoS 2 can be attributed to the isolation from the substrate effect 35 . Moreover, the E 2g mode for the supported 2L MoS 2 is asymmetric, as shown in Fig. 2b. As Mignuzzi et al. reported, defects could induce not only an asymmetric line shape but also www.nature.com/scientificreports/ Raman peaks arising from zone-edge phonon modes 41 . In our work, no additional peak was observed in the spectrum for supported 2L MoS 2 , suggesting that the strain is the dominant effect rather than defects. The E 2g mode of monolayer MoS 2 has been demonstrated to split into two singlets as the external strain is increased 42,43 .
As presented in Fig. S1b, the E 2g mode can be well fitted using two peaks, which can be attributed to the strain introduced by the substrate-MoS 2 interaction. We assume that the substrate-induced strain is the same for all the supported MoS 2 flakes. Therefore, the strain effect on the supported 2L MoS 2 is the most obvious because 2L MoS 2 is thinner than the other samples.
To deeply investigate the substrate effect, supported MoS 2 and suspended few-layer MoS 2 were studied in the temperature range of 77 K-557 K, and the results are displayed in Fig. 3. Prominent redshift and broadening of Raman peaks are noted for both suspended and supported MoS 2 with increasing temperature, as exhibited in Fig. 3. These phenomena can be attributed to the thermal expansion of the crystal lattice of MoS 2 26,27 . To obtain deeper insight into the difference between suspended and supported MoS 2 , the Raman spectra were deconvoluted using a Lorentz/Gaussian mixed function. The peak positions of the E 2g and A 1g modes are plotted as a function of temperature in one figure for comparison. Figure 4 exhibits the fitting results for supported and suspended MoS 2 , in which several remarkable phenomena should be addressed, as discussed below.
First, the temperature-dependent evolutions of the supported MoS 2 samples are similar, varying approximately linearly with increasing temperature at first sight. This suggests that the substrate effect is exerted on the MoS 2 flakes as a whole, although the substrate is only in direct contact with the bottom layer of a MoS 2 flake. The mechanically exfoliated MoS 2 layer is transferred and pinned on the substrate by the van der Waals force. As the temperature changes, the biaxial tensile or compressive stress induced by the TEC mismatch increases and becomes a prominent factor that modulates the frequency shift of Raman peaks. In addition to TEC mismatch, charge transfer between the film and the substrate or through interfacial states can impact the temperature evolution of Raman peak. As Su et al. discussed that accelerated redshift of A 1g mode with increasing temperature is associated with the enhanced charge injection from the substrate into the film and decomposition of adsorbed contaminants 30 .
Second, the temperature-dependent evolutions of suspended MoS 2 are very different from those of supported MoS 2 , exhibiting nonlinear behavior with increasing temperature. Moreover, the temperature dependence trends for the different suspended MoS 2 samples differ. As discussed previously, the TEC mismatch gives rise to a Raman shift with increasing temperature. However, suspended MoS 2 , at least the part on the hole, is free of the substrate effect, suggesting that its Raman shift only originates from lattice expansion. Compared with the temperature dependence of supported MoS 2 , suspended few-layer MoS 2 exhibits the intrinsic thermal properties of MoS 2 as expected.
Third, the peak positions of supported MoS 2 are higher than those of suspended MoS 2 at each temperature, suggesting that the TEC mismatch induced compression of the crystalline lattice in supported MoS 2 . That the larger attached area of supported MoS 2 compared with suspended MoS 2 would introduce more strain into the www.nature.com/scientificreports/ MoS 2 layer is easy to explicate. As demonstrated previously, the strain in the MoS 2 layer is due to the TEC mismatch between the SiO 2 substrate and MoS 2 .
The results shown in Fig. 4 demonstrate that the TEC of MoS 2 is strongly correlated with the number of layers, which can only be obviously exhibited after isolating it the from the substrate effect.
Then, the peak positions of MoS 2 were fitted as a function of temperature to obtain the regularities of the temperature dependence of the peak positions. First, a linear function was employed to fit temperature evolution Raman peaks for the supported and suspended MoS 2 samples (see Fig. S2). The temperature evolution of Raman peaks for the supported MoS 2 shows a nearly linear behavior as a function of temperature. But there is a small deviation between the experimental results and fitting curve, as exhibited in Fig. S2. On the other hand, the temperature evolution for the suspended MoS 2 cannot be well fitted using a linear function, in which large discrepancies between the linearly fitted curves and experimental results are observed. According to previous literatures, the anharmonic effect caused by the phonon-phonon coupling leads to the nonlinear temperaturedependent behavior of the Raman peaks 28 .  www.nature.com/scientificreports/ Therefore, the polynomial function was adopted to fit the experimental results for the supported and suspended MoS 2 samples instead of the linear function. All the temperature dependence trends of the E 2g and A 1g modes were fitted using a second-order polynomial function of temperature T, where ω 0 is the frequency at 0 K and χ 1 and χ 2 are the first-and second-order temperature coefficients, respectively. The fitting results for supported and suspended MoS 2 with the same thickness are plotted in Fig. 4 for comparison, and the fitting parameters are listed in Table 1. As shown in Fig. 4, the polynomial curves better fit the experimental results for the supported and suspended MoS 2 , compared with the linear curves. Remarkably, for the supported MoS 2 , the residual sum of square (RSS) for the polynomial fitting is much smaller than that for the linear fitting (see Table S1 in the Supplementary Information). This implies that the polynomial function is a better and more reasonable choice for fitting the temperature-evolution of the Raman shifts for the supported MoS 2 , although it exhibits an approximate linear trace.
As exhibited in Table 1, the fitting parameters for suspended MoS 2 are very different from those for supported MoS 2 . The fitting parameter χ 1 for suspended MoS 2 is one order of magnitude larger than that for supported MoS 2 . Moreover, the fitting parameters exhibit a layer number dependence. As exhibited in Table 1, for the 2L-5L MoS 2 samples, the χ 2 of suspended MoS 2 is positive, whereas the χ 2 of supported MoS 2 is negative. Interestingly, χ 2 is negative for both suspended and supported 6L MoS 2 . This occurs because of the different temperature evolutions of 6L MoS 2 and thinner MoS 2 . One can see in Fig. 4e and j that the peak positions for the 6L suspended MoS 2 linearly shift to low frequency, similar as the peak evolution for the supported MoS 2 . Therefore, the fitting parameters for the curves are all negative. In contrast, the shift rates of the peak positions for the 2L-5L suspended MoS 2 vary in different temperature ranges. As exhibited in Fig. 4a-d, the peak positions shift faster in the low temperature range (< 350 K) than in the high temperature range (> 350 K). Therefore, the parameter χ 2 is positive to better fit the experimental results. The thermal stability of MoS 2 strongly depends on the competition between the energy barriers introduced by the MoS 2 -substrate interface and by the MoS 2 -MoS 2 interlayer interface 44 . The few-layer MoS 2 flake as a whole changes with increasing temperature, the influence of the intrinsic thermal expansion of MoS 2 on the frequency shift increases as the number of layers increases. As a result, the temperature evolutions of the Raman peaks of the suspended and supported 6L MoS 2 samples become similar. These results suggest that the thermal behavior of few-layer MoS 2 become similar as that of bulk MoS 2 with increasing thickness.
The results in Table 1 indicate that the discrepancy in the frequency shifts between the suspended and supported MoS 2 originates from the TEC mismatch between the substrate and MoS 2 . Taking advantage of the results shown in Figs. 3, 4 and 5, the TEC of few-layer MoS 2 can be obtained, and the details for the calculation of the TEC of few-layer MoS 2 will be discussed in the following section.
As has been reported, the temperature-dependent Raman frequency shift ( �ω MoS2 (T) ) of freestanding MoS 2 can be commonly attributed to the thermal expansion of the lattice ( �ω E (T) ) and the anharmonic effect ( �ω A (T) ), which changes the phonon self-energy 45 . �ω MoS2 (T) can be expressed as �ω MoS2 (T) can be obtained using the peak position at T (ω MoS2 (T)) subtracted by the peak position at T 0 = 300 K (ω MoS2 (T 0 )).
For the thermal behavior of the supported MoS 2 , both common thermal effects and strains induced by the TEC mismatch between the substrate and MoS 2 must be considered. As a result, the frequency shifts of supported MoS 2 can be written as www.nature.com/scientificreports/ The E 2g mode arises from the in-plane relative vibration between the Mo and S atoms, which is more sensitive to the temperature-induced lattice expansion/shrinkage of 2D MoS 2 . On the other hand, the frequency shift of A 1g mode not only closely depends on lattice variations, but also is related with the charge transfer from the substrate to MoS 2 46 . The electron doping effect can induce the frequency shifts of A 1g mode due to the strong electron-phonon interaction 47 . Consult to previous literature, the E 2g mode is not sensitive to the electron doping effect 47,48 . So it is assumed that the electron doping effect induced Raman shift of E 2g mode did not change with temperature, or the changes can be neglected. For simplicity, the doping effect induced Raman shift of E 2g mode is defined as a constant that is independent of temperature in this work. Thus, in the calculation of the Raman frequency differences ( �ω MoS2 (T) ) between the given temperatures and T = 300 K, the doping effect induced Raman shift is subtracted as a constant. So that there are still three terms in Eq. (3) when the doping effect induced Raman shift is not taken into consideration. Therefore, the �ω MoS2 (T) of E 2g mode was calculated and employed in the following equations.
The TEC mismatch-induced frequency shift can be obtained by subtracting the intrinsic frequency shift from the frequency shift of supported MoS 2 , To apply Eq. (4), the frequency shift of freestanding MoS 2 should be provided. However, real freestanding MoS 2 does not exist. Therefore, Raman frequency shifts from theoretical calculations or suspended TMDs have normally been employed as those of freestanding samples 31,35 . In this work, we assume that the strain induced by the substrate effect can be neglected in the center of the suspended MoS 2 layers, as the laser spot (1 μm) in the measurement is much smaller than the size of the hole (5 μm) below the suspended MoS 2 . Therefore, the Raman shifts of suspended MoS 2 is adapt as the intrinsic frequency of freestanding MoS 2 in this work.
Based on above discussion, the TEC mismatch-induced frequency shift �ω S (T) for the supported MoS 2 can be obtained by where �ω sup (T) and �ω sus (T) are the Raman shifts of supported and suspended MoS 2 , respectively.
In addition, the contribution to the Raman frequency shift from the substrate-induced strain ( �ω S (T) ) can be expressed as where β is the biaxial strain coefficient of the Raman mode and α SiO 2 (T) and α MoS 2 (T) are the temperaturedependent TECs of SiO 2 and MoS 2 , respectively. As has been reported, β depends on the number of MoS 2 layers 49 .
As the values of α SiO 2 and βare already known from previous literatures, the temperature dependence of α MoS 2 can be derived from Eqs. (5) and (6). The calculated α MoS 2 (T) can be expressed using a quadratic function, and then, the α MoS 2 (T) values for MoS 2 with different numbers of layers are plotted in Fig. 5.
As presented in Fig. 5, the curves of the calculated TECs of MoS 2 with different numbers of layers follow similar trends. Notably, the order of magnitude of the TECs is at the same level as those in previous reports 22,28 , implying the validity of the calculation methods employed in this work. For example, the TEC at room temperature observed in this work is approximately 0.5 × 10 -6 K −1 . Su et al. claimed that the in-plane TEC of MoS 2 is 2.48 × 10 -6 K −1 at room temperature 28  www.nature.com/scientificreports/ in the temperature range of 150-450 K. These results clearly suggest the feasibility of using Raman spectroscopy in the investigation of the TEC of MoS 2 , at least in the temperature range of 150-450 K.
In addition, the diversity in the TECs between the MoS 2 with different numbers of layers is also obvious. As presented in the inset figure of Fig. 5, the TECs of few-layer MoS 2 exhibit remarkable differences in the temperature ranges of 0-150 K and 450-600 K. Strikingly, the TEC becomes negative below 175 K. This is different from most previous reports 25,28,50,51 , in which the TEC is positive in the entire temperature range. In 2015, Wang et al. obtained a negative TEC below 31 K for monolayer MoS 2 using first-principles calculation by taking the stiffness and charge transfer effect into consideration 52 . The ZA bending vibrations (acoustic modes) may cause negative thermal expansion in few-layer MoS 2 52,53 . The negative value of the Grüneisen parameter for the transverse acoustic mode responds for the negative TEC 54 . The larger the absolute value of the negative Grüneisen parameter is, the larger the negative TEC. The negative TEC below 175 K observed in our work suggests a larger negative Grüneisen parameter.
Moreover, the TEC of few-layer MoS 2 increases gently in the temperature range over 450 K, as shown in Fig. 5. This evolution of the TEC observed in our work is similar to that in previous studies [50][51][52] . However, the high-temperature TECs for 4L and 5L MoS 2 exhibit a slight difference compared with the other thicknesses. Wang et al. reported that the threshold temperature for etching monolayer MoS 2 is lower than 513 K, which is closely related with defects 44 . The abnormal behavior of the TECs for 4L and 5L MoS 2 in the high temperature range can be attributed to the lower thermal stability due to the defects initially existed in these MoS 2 samples. Identification of the TEC of few-layer MoS 2 requires further experimental and theoretical studies. In the future, the temperature-dependent Raman study carried with controllable electronic doping concentration is called to deeply investigate the doping and dielectric environment effects on the frequency shifts of Raman modes, especially the A 1g mode.

Conclusion
In this work, a comprehensive Raman study was carried out on supported and suspended MoS 2 with different numbers of layers in the temperature range from 77 to 557 K. Strikingly, the temperature behaviors of the Raman frequency shift for suspended MoS 2 are significantly different from those for supported MoS 2 . The intrinsic TECs of 2-6-layer MoS 2 were calculated after eliminating the substrate effect. Strikingly, the TEC becomes negative below 175 K, which can be associated with the bending vibration in the MoS 2 layer as the temperature decreases. The TEC curves of MoS 2 with different numbers of layers follow similar evolution trends in the temperature range of 150-450 K. Compared with previous reports, the validity of the TEC obtained in this work suggests that Raman spectroscopy is a feasible tool for investigating the TEC of MoS 2 . Our results provide useful information for understanding the thermal properties of MoS 2 and its further application in devices.

Methods
To fabricate suspended MoS 2 samples, a periodic hole array was first fabricated on a SiO 2 (300 nm)/Si substrate by UV lithography and reactive ion etching technology, in which the holes were 5 μm in diameter and 2 μm in depth. MoS 2 flakes with different thicknesses were prepared from a natural MoS 2 single crystal using a modified mechanical exfoliation method onto the prepatterned SiO 2 /Si substrate previously cleaned by oxygen plasma.
The optical image of the suspended few-layer MoS 2 was obtained using an Olympus BX41 microscope equipped on the micro-Raman spectrometer, Horiba Evolution HR. In the Raman spectroscopy measurements, a solid-state laser with a 532 nm wavelength was used as the excitation source. The laser beam was focused using a 100 × long-working distance objective with numeric aperture NA = 0.8, and the spot size was approximately 1 μm. To avoid significant frequency shifts induced by the local heating effect and ensure a sufficient SNR, the laser power was set at ~ 0.9 mW on the surface of the heating stage. The numbers of layers of MoS 2 were identified using ULF Raman spectroscopy. The sample was placed inside a cryostat cell (Linkam, THMS 600), and the Raman spectra were measured in the temperature range from 77 to 557 K at an interval of 20 K.