1. Introduction

Two-dimensional transition-metal dichalcogenide (TMDC) materials, such as molybdenum disulfide (MoS₂), are promising for the next generation of electronic and optoelectronic devices [1] because of their unique electrical, optical, and mechanical properties [2–9]. In contrast to graphene, MoS₂ atomic layers have a band gap which transits from indirect 1.2 eV to direct 1.9 eV as the thickness of MoS₂ reduces from bulk to monolayer [3,5]. Those unique properties of MoS₂ make it very suitable for fabrication of electronic and optoelectronic devices. Single-layer MoS₂ field effect transistors [10–12], heterojunction [13] and ultrasensitive photodetectors [14], have been reported. Field emission and photoresponse of MoS₂ thin films are also detailed investigated [15].Even the integrated circuits based on bilayer MoS₂ transistors have also been demonstrated [16]. It may be predicted that the degree of integration of MoS₂ transistor-based integrated circuits will be much higher than one of current Si-based microelectronic integrated circuits because MoS₂ transistors are in nanometer scale. Heat dissipation or thermal conductivity has been one of the most significant constraints on design and fabrication of current Si-based integrated electronic circuits. Consequently, it may be predicted that heat dissipation or thermal conductivity will be critical in near future in design and fabrication of single layer MoS₂ integrated circuits. For thermal manipulation, it is very necessary to study electron-phonon interactions, dynamics and thermodynamics of phonons in MoS₂ thin films.

Raman spectroscopy is a powerful tool to access thermal properties of materials, especially nanomaterials, and has been extensively used to investigate thermal properties and microstructures of TMDC films and other materials [17–23], revaling their doping effect [24], electronic and structural properties [25], and the vibration property of nanoribbons and nanosheets [26–28]. Several comprehensive studies on the vibration frequency and peak width evolution of phonon modes of MoS₂ mono- and few-layers with temperature have also been reported so that thermal conductivity and phonon dynamics of MoS₂ could be revealed [29–35]. However, some controversial experimental results were reported [29–35]. Both Taube et al. [29] and Yan et al. [30] investigated the temperature dependence of Raman shifts of $E_{2g}^1$ and A_1g modes of monolayer MoS₂ within a low temperature range of 80 – 350 K, respectively on SiO₂/Si and sapphire (suspended) substrates. Although the MoS₂ monolayer samples studied by the two groups were all fabricated from mechanical exfoliation of MoS₂ single crystals, Taube et al. [29] found nonlinear temperature dependence of Raman shifts of both $E_{2g}^1$ and A_1g modes, while Yan et al. [30] observed linear temperature dependence for either a sapphire substrate or the suspended. Inversely, Lanzillo et al. [31] and Najmaei et al. [32] studied the temperature dependence of Raman shifts of $E_{2g}^1$ and A_1g modes of monolayer MoS₂ on SiO₂/Si substrates within a high temperature range of 300 – 500 K, respectively prepared by chemical vapor deposition (CVD) and mechanical exfoliation. Both groups observed linear temperature dependence of Raman shifts of both $E_{2g}^1$ and A_1g modes. Lanzillo et al. [31] obtained the first-order temperature coefficient of $E_{2g}^1$ mode as −0.013 cm⁻¹/K, but Najmaei et al. [32] gave out one as −0.0179 cm⁻¹/K. An obvious difference on the first-order temperature coefficient of $E_{2g}^1$ mode existed between the two reports. A more disputed conclusion given by Najmaei et al. [32] was that linear temperature dependence of Raman shifts of $E_{2g}^1$ mode was dominated by anharmonic four-phonon processes rather than three-phonon processes. It was unexpected physically because four-phonon processes were higher-order than three-phonon processes. Sahoo et al. [33] and Thripuranthaka et al. [34] studied the temperature dependence of Raman shifts of $E_{2g}^1$ and A_1g modes of CVD-grown few-layer MoS₂, respectively on SiO₂/Si substrates and without substrates (suspended) in a widely variable temperature range of 80 – 600 K. Both of them claimed Raman shifts of $E_{2g}^1$ and A_1g modes varied linearly with temperature. Two slightly different first-order temperature coefficients of $E_{2g}^1$ mode, −0.0132 cm⁻¹/K [33] and −0.016 cm⁻¹/K [34], were given out. Su et al. [35] studied temperature-dependent Raman shifts of mono- and bilayer MoS₂ on sapphire and Si substrates in the range of above room temperature, and found that the temperature dependence of Raman shifts of $E_{2g}^1$ and A_1g modes was complex, including linear and nonlinear, depending on not only the number of layer of MoS₂ films, but also substrate type. Thus more experimental studies are necessary very much to extract the accurate temperature coefficient of Raman shift of Raman active modes because the temperature coefficient directly reflects the strength change of Raman vibration bond with varying temperature. It is also an important parameter to differentiate layer number of layered films.

To distinguish the disputes mentioned above, it is very necessary to further study the temperature dependence of Raman shifts of mono- and bilayer MoS₂, especially the dependence of monolayer MoS₂ directly CVD-grown on a Si substrate over a wide temperature range over 80 – 600 K, because CVD growth can fabricate large-area monolayer MoS₂ and Si substrates have excellent compatibility with Si-based microelectronics. Consequently, monolayer MoS₂ directly CVD-grown on a Si substrate has widely potential applications. In addition, it was already reported Raman shift strongly depended on substrate type and bonding strength between films and substrates [35,36]. To our knowledge, no such data are available yet for mono- and bilayer MoS₂ directly grown on SiO₂/Si substrate over a wide temperature range of the below and above room temperature. In addition, physical mechanism of nonlinear temperature dependence of Raman shifts was absent and excitation mechanism of $E_{2g}^1$ and A_1g modes of monolayer MoS₂ was also unknown.

In this article, we present the temperature dependence of Raman shifts of $E_{2g}^1$ and A_1g modes of mono-, bi- and multilayer MoS₂ directly CVD-grown on SiO₂/Si substrates over a wide temperature range of 90-540 K. We observe nonlinear temperature dependence of Raman shifts for both $E_{2g}^1$ and A_1g modes. It is different from the reported temperature dependence of Raman shifts of CVD-grown MoS₂ transferred onto SiO₂/Si substrate [35]. The nonlinear temperature dependence of Raman shifts is analyzed with a semi-quantitative physical model [32,35,37], which includes thermal expansion and pure temperature effects. The analyzed results show that the nonlinear temperature dependence of Raman shifts mainly originates from anharmonic effects of three- and four-phonon processes. For $E_{2g}^1$ mode, the contribution of three-phonon process is much stronger than four-phonon process. For A_1g mode, the contributions of three- and four-phonon processes are comparable but the former is still stronger than the latter. Furthermore, we perform a temperature-dependent non-resonant Raman scattering experiment on monolayer MoS₂ with 785 nm laser whose photon energy is lower than the band gap (1.8 eV) of monolayer MoS₂, and only observe the Raman peak of $E_{2g}^1$ mode. Thus we deduce A_1g mode is active only via electron-phonon interaction. These findings cannot only enrich the knowledge on vibrational properties of optical phonons of MoS₂ films but also may be useful in thermal manipulation of MoS₂ integrated circuits in the future.

2. Experiment results with 514.5nm laser

The optical micrograph of CVD-grown MoS₂ films on SiO₂/Si substrate is shown in Fig. 1(a).

 

Fig. 1 (a) Optical micrograph of CVD-grown MoS₂ on SiO₂/Si substrate. (b) Raman spectra of mono-, bi- and multilayer MoS₂. (c) Temperature-dependent Raman spectra of monolayer MoS₂ under the excitation of 1.6mW laser at 514.5 nm wavelength.

Download Full Size | PDF

Monolayer MoS₂ is crystalline well and in triangular shape. Single crystal domain size is large up to 50 μm. The temperature-dependent Raman spectra are collected using a Renishaw InVia micro-Raman spectrometer with laser line of 514.5 nm and 785nm. It is a confocal micro-Raman spectroscope system with a 2400lp/mm grating. Spectral resolution of the system is up to 0.6 cm⁻¹. The maximum power of 514.5 nm and 785nm lasers used in our experiments are 1.6 mW and 7.5mW respectively. Laser spot is focused down to 1 μm which is much smaller than MoS₂ sample size.The number of MoS₂ layers can be roughly estimated by observing the color and shape of homogenous domain. Mono-, bi- and multilayer MoS₂ are indicated in Fig. 1(a). Raman spectrum is used quantitatively to differentiate the number of MoS₂ film layers. Figure 1(b) shows the Raman spectra of three regions in Fig. 1(a) labeled by monolayer, bilayer and multilayer. Raman spectra are collected first using 514.5 nm laser. The wave-number difference of 20 cm⁻¹ between Raman peaks of $E_{2g}^1$ and A_1g modes, calculated from the bottom Raman spectrum in Fig. 1(b), is obtained, agrees well with the value of 20.3 cm⁻¹ measured by Zhan et al. on CVD-grown monolayer MoS₂ [38]. Similarly, a 22 cm⁻¹ difference calculated from the middle Raman spectrum in Fig. 1(b) is acquired, which is also in accordance with 22.3 cm⁻¹ difference of CVD-grown bilayer MoS₂ reported by Zhan et al. [38].

The MoS₂ sample is mounted in a cryostat cooled by liquid nitrogen. Temperature-dependent Raman spectra are taken over a wide temperature range of 90 – 540 K for mono-, bi- and multilayer MoS₂. Typical Raman spectra of MoS₂ monolayer are plotted in Fig. 1(c) for different lattice temperature over 90 - 540 K.

3. Analyses of experimental results

3.1 First- and second-order temperature coefficients extracted by linear and quadratic polynomial fittings

The positions of Raman peaks of $E_{2g}^1$ and A_1g modes are extracted by Lorentzian function fitting to all Raman spectra recorded at different temperatures, as shown in Fig. 1(c). The peak positions of $E_{2g}^1$ and A_1g modes versus temperature are plotted in Fig. 2(a) by triangle, circle and square points, respectively for mono-, bi- and multilayer MoS₂ thin films. Error bars are not plotted out in Fig. 2(a) because they are smaller than 0.1 cm⁻¹ and too small to be displayed. It is very apparent that the Raman shifts of $E_{2g}^1$ and A_1g modes decrease nonlinearly with increasing temperature for all of mono-, bi- and multilayer MoS₂. However, they appear linear if one only looks the graph in the range of above room temperature. Therefore, the linear dependence reported in [31,35] is only an approximate of our results here in the range of above room temperature.

 

Fig. 2 (a) The temperature dependence of Raman shifts of $E_{2g}^1$ and A_1g modes of mono-, bi- and multilayer MoS₂ under the excitation of 1.6mW laser at 514.5 nm wavelength. (b) The temperature dependence of Raman shifts of $E_{2g}^1$ and A_1g modes of multilayer MoS₂ for three different laser powers at 514.5 nm wavelength.

Download Full Size | PDF

The following quadratic polynomial

Table 1. First- and second-order temperature coefficients extracted by linear and quadratic polynomial fittings.

View Table

However, if we ignore the nonlinearity of temperature-dependent Raman shifts, as done in some literatures [30,31,33,34], the following linear formula,

Because the band gap and absorption coefficient of MoS₂ are also temperature-dependent, laser heating effect may be different at different lattice temperature. In other words, the temperature dependence of the Raman shifts observed may contain the contribution from different heating effects of the same excitation laser power. In order to test the effect of possibly different laser heating on Raman shifts, we have performed the measurement of temperature-dependent Raman spectra under another two lower excitation powers of 0.16 and 0.6 mW. The temperature dependence of Raman shifts of $E_{2g}^1$ and A_1g modes of multilayer MoS₂ is plotted in Fig. 2(b) simultaneously for three excitation powers of 1.6, 0.6 and 0.16 mW. One can see almost the same Raman shifts at each lattice temperature with three different laser powers. That implies the temperature-dependent laser heating effect may be negligible in the range of our low laser power.

3.2 Physical origin of nonlinear temperature dependence

In order to understand the physical origin of the nonlinear temperature dependence of Raman shifts, a physical model including thermal volume expansion and pure temperature effects is used to analyze temperature-dependent Raman shift data [32,35,37]. Under the condition of constant atmospheric pressure, the model can be written as

Volume expansion-induced contribution to the change of Raman shift can be described by Gruneisen constant model [32,35]

Gruneisen parameter γ slightly depend on the layer number of material. However, here we take γ of bulk MoS₂ as an approximation of γ of mono- and few-layer MoS₂, as done in [32], because γ itself is weakly layer number-dependent and its accurate thickness-dependent relation is unavailable so far. The reported in-plane γ($E_{2g}^1$) = 0.21 and out-of-plane γ(A_1g) = 0.42 in bulk MoS₂ are used later in our fitting calculation [39]. The thermal expansion coefficient α of $E_{2g}^1$ and A_1g modes were given out by El-Mahalawy and Evans as [40]

Contribution of pure temperature effects to the change of Raman shift is mainly from anharmonic effects of three- and four-phonon processes, and was simply modeled by Kelmens [41], written as [32,37,41]

The best fittings to nonlinear temperature dependence of Raman shifts of $E_{2g}^1$ and A_1g modes of monolayer MoS₂ with Eq. (3) are plotted in Fig. 3(a) by black solid lines. One can see the model of Eq. (3) fits temperature-dependent nonlinear Raman shifts (open squares) quite well. Meanwhile, component contributions of thermal expansion, three- and four-phonon processes are also potted in Fig. 3(a) by color dashed lines. For $E_{2g}^1$ mode, one can discern nonlinear temperature dependence of Raman shift mainly originates from three-phonon process (red dashed line), while thermal expansion (green dashed line) and four-phonon process (blue dashed line) contribute very weakly. However, for A_1g mode, one can find that the contributions from three- and four-phonon processes are comparable though three-phonon contribution (Δω_A-3p) is slightly stronger than four-phonon one (Δω_A-4p). For either $E_{2g}^1$ or A_1g mode, thermal expansion mainly contributes a nearly linear weak temperature-dependent component. As a result, nonlinear temperature dependence of Raman shifts is mainly from anharmonic effect of three-phonon process plus a weak four-phonon process. A quantitative comparison of three- and four-phonon contributions to Raman shifts is plotted in Fig. 3(b) by the ratio ((Δω_A-3p–A)/ (Δω_A-4p-B)) of three to four phonon contributions. It is obvious that three-phonon contribution is at least thirty five times stronger than the contribution of four phonon process for $E_{2g}^1$ mode, whereas the contribution of three phonon process is only a few times stronger than one of four phonon process for A_1g mode. It is worth emphasizing that such ratios of three- to four-phonon contributions are reasonable physically because four-phonon process is a higher-order process than three-phonon process. Contrarily, the conclusion obtained in [32], the four-phonon process was dominant in temperature dependence of Raman shift, was disputed and inappropriate physically. One can also notice from Fig. 3(b) that the ratio of three- to four-phonon contributions first increases with lattice temperature below ~140 K, peaks at ~140 K, and then decreases beyond ~140 K, which imply that three-phonon contribution enhances faster than four-phonon contribution below 140 K, while above 140 K the enhancement trend of three- and four-phonon processes reverse.

 

Fig. 3 (a) The best fitting to experimental Raman shift data (open squares) of monolayer MoS₂ with Eq. (3) described in text. Component contributions from thermal expansion, three- and four-phonon processes are plotted by color dashed lines. (b) The ratio of three- to four-phonon process contributions of $E_{2g}^1$ and A_1g modes.

Download Full Size | PDF

In similar way, we also fit the nonlinear temperature dependence of Raman shifts of $E_{2g}^1$ and A_1g modes of bi- and multilayer MoS₂, as shown in Fig. 2(a). The strength coefficients, A and B, of three- and four-phonon processes are shown in Fig. 4. For $E_{2g}^1$ mode, one can still find three-phonon contribution (A) is much stronger than four-phonon one (B) for both bi- and multilayer MoS₂, but for A_1g mode A and B are comparable although B is smaller than A. Therefore, three-phonon process is the main contribution to nonlinear temperature dependence of Raman shifts of $E_{2g}^1$ and A_1g modes for either mono- and bilayer or multilayer MoS₂.

 

Fig. 4 Strength coefficients of three- and four-phonon processes versus layer number of MoS₂ films in temperature-dependent Raman shifts of $E_{2g}^1$ and A_1g modes.

Download Full Size | PDF

4. Experiment results with 785nm laser and analysis

To understand excitation mechanism of $E_{2g}^1$ and A_1g modes, we re-measure temperature- dependent Raman spectra of monolayer MoS₂ with 785 nm laser instead of 514.5nm laser. In this experiment, hot phonon excitation via electron-phonon exchange interaction is avoided because the photon energy (1.58 eV) of 785 nm laser is lower than the band gap (~1.82 eV at room temperature) of monolayer MoS₂. The measured temperature-dependent Raman spectra are plotted in Fig. 5(a). One can find that only the Raman peak of $E_{2g}^1$ mode occurs, whereas A_1g mode disappears. It seems to imply that A_1g phonon mode can only be excited by electron-phonon exchange interplay. To further test the electron-phonon exchange excitation of A_1g mode, we measure Raman spectrum of multilayer MoS₂ with 785 nm laser, and again observe the Raman peaks of $E_{2g}^1$and A_1g modes simultaneously. This provides direct evidence to support the electron-phonon exchange excitation mechanism of A_1g mode because the band gap of multilayer MoS₂ is about 1.2 eV which is smaller than the photon energy (1.58 eV) of 785 nm laser and hence electron excitation takes place via interband transition.

 

Fig. 5 (a)Temperature-dependent Raman spectra of monolayer MoS₂ measured with 785nm laser. (b) Nonlinear temperature dependence of Raman shifts of $E_{2g}^1$ mode measured with 514.5 nm (filled circles) and 785 nm (open squares) lasers. Black lines are the best fittings with the model of Eq. (3) in text.

Download Full Size | PDF

On the other hand, one can find in Fig. 5(b) that the Raman shifts measured with 785 nm laser are larger than those measured with 514.5 nm laser for $E_{2g}^1$ mode although the shift data measured with 785 nm laser are noisy a little because nonresonant Raman scattering by 785 nm laser is much weaker than resonant Raman scattering with 514.5 nm laser. The difference in Raman shift decreases with increasing lattice temperature of MoS₂, and approaches to zero above 500 K. This phenomenon can be explained by laser heating to MoS₂ via electron-phonon excitation. When Raman spectra are measured with 514.5 nm laser, a great amount of hot optical phonons are excited continuously via electron-phonon exchange due to interband transition of electrons so that the equilibrium temperature of optical phonon system is actually higher than the lattice temperature. Generally speaking, the lifetime of hot optical phonons (decayed into acoustic phonons) decreases with the increase of lattice temperature [33], and hence heat dissipation of optical phonon system becomes fast with the rise of lattice temperature so that the temperature difference between optical phonon system and lattices becomes smaller at higher lattice temperature, just as shown in Fig. 5(b). Actually, such double-wavelength Raman spectra can be used to detect the temperature of optical phonon system or the temperature difference between optical phonon system and lattices. For example, the Raman shifts at O and P points are measured at the same lattice temperature of 200 K but different laser wavelength, respectively at 785 nm and 514.5 nm. The Raman shift at P is smaller than that at O, which means the temperature of optical phonon system at P is actually higher than the lattice temperature of 200 K. The real temperature of optical phonon system can be read out from point N as ~311 K, which is the equilibrium temperature of optical phonon system that is 110K higher than lattice temperature due to heating of 514.5 nm laser via electron-phonon exchange.

Finally, we analyze the nonlinear temperature dependence of Raman shifts of $E_{2g}^1$ mode measured with 785 nm laser using Eq. (3). One can see the temperature-dependent nonlinear Raman shifts mainly originates from three-phonon process. Four-phonon process is very weak and negligible. This result is similar to one measured with 514.5 nm laser in Fig. 3.

5. Conclusion

In this work, we have studied the temperature dependence of vibrational properties of optical phonon modes of CVD-grown MoS₂ mono- and few-layer thin films over a wide temperature range of 90 - 540 K using backscattering micro-Raman spectroscopy under the excitation of 514.5 nm and 785 nm lasers. We have observed nonlinear temperature dependence of Raman shifts of $E_{2g}^1$ and A_1g modes for mono-, bi- and multilayer MoS₂. A semi-quantitative model including thermal expansion and anharmonic effects is adopted to analyze the nonlinear temperature dependence of Raman shifts. We have found the nonlinear temperature dependence of Raman shifts of $E_{2g}^1$ and A_1g modes can be fit well by the model for either mono-, bi- or multilayer MoS₂. The fitting results reveal that thermal expansion contribution is very weak and almost linear. The nonlinear temperature dependence of Raman shifts mainly originate from anharmonic contributions of three- and four-phonon processes. The nonlinear temperature dependence of Raman shift of $E_{2g}^1$ mode is dominated by three-phonon process, and the contribution of four-phonon process is very weak and negligible in comparison to one of three-phonon process. This result is much different from one reported in the literature where four-phonon process was considered as main origin of nonlinear temperature dependence of Raman shifts. In contrast, we have found that the nonlinear temperature dependence of Raman shift of A_1g mode originates from cooperative three- and four-phonon processes, but three-phonon process contributes still stronger than four-phonon process. For the excitation of 785 nm laser, we have observed only Raman peak of $E_{2g}^1$ mode but not A_1g mode over the whole range of 90~540 K. The fact that the Raman peak of A_1g mode is absent with 785 nm laser reveals electron-phonon exchange excitation mechanism of A_1g optical phonon mode for the first time. We have also found the temperature of optical phonon system is actually higher than lattice temperature. The temperature difference between them can be measured by double-wavelength Raman spectra, where photon energy of one wavelength laser is higher than band gap of MoS₂, and photon energy of the other wavelength laser is lower than band gap.