TMDs with tunable bandgaps have been widely studied in recent years. From the crystal structure point of view, there are three polytypes of TMDs: 1T, 2H, and 3R. The first Arabic number corresponds to the layer number in the unit cell of each polytype. The letters T, H, and R represent tetragonal, hexagonal, and rhombohedral symmetries, respectively. Each layer contains three atomic planes, where the metal atomic plane is sandwiched between two chalcogen atomic planes like X–M–X (X stands for chalcogens and M represents transition metals), while different layers are bound by the vdW force. In each layer, for the trigonal prismatic coordination, the positions of the upper and the bottom triangle planes are the same. For the octahedral coordination, the bottom triangle plane is rotated 180° relative to the upper plane. The metal atoms of both the 2H and 3R polytypes are in the trigonal prismatic coordination. The unit cell of the 2H polytype has two X–M–X planes, in which the metal atom of the first X–M–X plane overlaps with the chalcogen of the second X–M–X plane. The unit cell of the 3R polytype consists of three X–M–X planes, in which the second and the third X–M–X planes are obtained by translating the first X–M–X plane by a certain distance along the same direction. The metal atoms of the 1T polytype are in the octahedral coordination. The structure of the 1T polytype has a stacking of X–M–X formed tautologically along the c-axis at the position of the following planes, which is the same as the first X–M–X plane. The transition metal atom (or chalcogen atom) overlaps with another transition metal atom (or chalcogen atom). X atoms in the upper layer and lower layer are rotated by 60°. The different electronic structures in the monolayer MX₂ depend on the different coordination of metal atoms. For example, monolayer 2H-MoS₂ is semiconducting, whereas single-layer 1T-MoS₂ is metallic. The stacking order is also an important parameter for the symmetry of 2D materials. The 2H polytype has the stacking order of AbA BaB (the capital letters denote chalcogens, and the lower-case letters stand for metal atoms). For the bulk phase of these materials, the symmetry space group is .^[54] For few-layer structures, the symmetry space group for odd-number-of-layers 2D materials of the 2H polytype is with the horizontal reflection plane (without inversion symmetry).^[55] Crystals with an even number of layers belong to the group with inversion symmetry.^[55,56] The typical stacking order of the 3R polytype is AbA BcB CaC. The stacking of bulk TMDs of the 1T polytype is AbC AbC. The symmetry space group for TMDs of the 1T polytype belongs to .

The lattice vibrations of crystals are related to the irreducible representation of the symmetry group. In the following, 2D materials beyond graphene such as MX₂ (M =W, Mo; X = S, Se, Te) are mainly discussed.^[47,57–59] Figure 2 shows the representative symmetry and normal mode displacement of several Raman active modes of the 1T, 2R, and 3R polytypes of MX₂. The unit cell of bulk MX₂ consists of six atoms, and there are 18 phonon modes with 3 acoustic modes and 15 optical modes according to the irreducible representation. The lattice vibrational modes of bulk MX₂ at the center of the Brillouin zone can be expressed as:^[55,60–63] , where one A_2u and E_1u are transitional acoustic modes, and the other A_2u and E_1u are infrared (IR) active. A_1g, E_1g, and E_2g are Raman (R) active modes, and B_2g, B_1u, and E_2u are optically inactive (silent) modes. Here, A_1g corresponds to the out-of-plane relative motion of X atoms; E_1g corresponds to the in-plane relative vibration of X atoms. E_2g corresponds to the in-plane opposing motion of M and X atoms. B_2g corresponds to the out-of-plane vibration of M and X atomic planes relative to each other. These four modes are the origin of bilayer MX₂ Raman modes.^[26] One doubly degenerate E_2g mode denoted and one B_2g mode denoted are shear and layer breathing modes in the bulk MX₂, respectively (shear mode and layer breathing mode are discussed in details later in this review). For monolayer MX₂, the unit cell is composed of three atoms with nine normal vibrational modes (6 phonon and 3 acoustic branches) at the Γ point. For multiple-layer MX₂, NL-MX₂ (N stands for the number of layers) there are 9N−3 optical modes, which include 3N-1 vibrations along the c-axis and 3N-12-fold degenerate in-plane modes.^[18] The irreducible representations of MX₂ with odd and even number of layers at the Γ point can be written as^[55,56,62] where E″, , A_1g, and are R modes, , A_2u, and E_u are IR modes, and E′ is both R and IR active. These Raman modes are not a unique feature of TMDs, but are generally expected in all layered systems with an inversion symmetry center or a horizontal mirror plane. Active Raman modes in few-layer systems are Raman inactive in specific scattering geometries. For example, E_1g is inactive in the back-scattering Raman configuration.^[30]

Fig. 2.

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	Fig. 2. (color online) Symmetry and normal displacements of optical vibration modes for the 2H-, 3R-, and 1T polytypes of monolayer, bilayer, and bulk MX2.

In Raman studies, the laser power can be tuned. This provides a useful tool to study the properties of 2D materials related to temperature changes. Generally speaking, the Raman peaks of a suspended MoS₂ flake redshift with the increasing incident laser power (laser power ). This phenomenon is due to the thermal expansion of the sample lattice with local heating. Moreover, the thermal expansion of the sample lattice in the out-of-plane direction is more sensitive than in the in-plane direction. Yan et al.^[64] found that both the A_1g and peaks of suspended monolayer MoS₂ redshift with the laser power increasing from 0.04 to 0.164 mW (Fig. 3(a)). Meanwhile, they showed that the parameters of the two modes vary slowly and not in a linear way when the laser power is larger than 0.25 mW in their experiment due to the nonlinearity of absorption or the higher orders of temperature-dependent coefficients. However, Miller et al.^[65] found that the A_1g peak redshifts and broadens, whereas the frequency of the mode changes negligibly as the laser power increases from 25 to under 488 nm laser excitation for MoS₂ in an ambient environment. Najmaei et al.^[66] also found that both the A_1g and peaks of supported 1L MoS₂ redshift with the increasing laser power, and the change for is small. The redshifts of the Raman modes with increasing laser power was also found in other 2D materials such as WS₂ and BP. Peimyoo et al.^[67] found that the A_1g Raman modes of mono- and bilayer WS₂ redshift, and their peak intensities are increased with increasing power of a 532 nm laser (Fig. 3(b)). Luo et al.^[68] found that the Raman modes of BP redshift as the temperature increases. As seen from Fig. 3(c), the mode is more sensitive to the temperature. Different edge structures such as zigzag and armchair provide different Raman signal responses. The zigzag-polarized excitation temperature coefficient is larger than that for armchair-polarized excitation, as seen in Fig. 3(d). It may result in anisotropic thermal expansion during the heating process.

Fig. 3.

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Fig. 3. (color online) Effect of laser power on Raman spectra. (a) Raman spectra of monolayer MoS2 for different values of laser power. Both the and A1g modes redshift as the laser power increases. Reproduced with permission from Ref. [64]. Copyright 2014, American Chemical Society. (b) The A1g mode of WS2 redshifts with the increasing laser power. Reproduced with permission from Ref. [67]. Copyright 2013, Springer International Publishing. (c) Raman spectra of armchair-edged BP with polarized laser excitation under different temperatures of 24°C, 42°C, 57°C, and 72°C, respectively. The vibrational modes , B2g, and are redshifted with the increase of the laser power. (d) Raman shift of the mode as a function of temperature for both armchair- and zigzag-edged BP under polarized laser excitation. Open circles and rectangles indicate armchair- and zigzag-edged BP under polarized laser excitation, respectively. Reproduced with permission from Ref. [68]. Copyright 2015, Nature Publishing Group.

The degree of orbital interactions, mechanical properties, and electronic band dispersion of ultrathin materials are sensitive to strain. Raman scattering is an efficient tool to probe the strain applied to few-layer and monolayer 2D material films. In recent years, there have been many reports studying uniaxial and biaxial strain applied to few-layer materials theoretically and experimentally.^[69–83] Usually, strain is induced by bending the flexible substrates supporting 2D materials. In-plane mode such as E_2g is sensitive to external stimuli and split into two modes when the strain approaches the critical value, indicating the emergence of broken symmetry. Huang et al.^[81] reported that the 2D peak of single-layer graphene is split into two modes (2D⁺ and 2D⁻) under uniaxial strain of up to . The uniaxial strain is applied to graphene with a three-point bending method by bending the flexible PDMS substrate. The intensities of the two modes depend on the laser polarization and the sample orientation. Desai et al.^[84] found that the mode of WSe₂ (1–4 layers) splits into two peaks under uniaxial tensile strain of up to . The peak splitting increases as the strain increases. The uniaxial tensile strain is applied on the sample with a two-point bending method by directly bending the flexible polyethylene terephthalate glycol-modified (PETG) substrate. Wang et al.^[85] found that the mode of monolayer MoS₂ redshifts with the increasing strain and splits into two modes under uniaxial strain up to 1%. Zhu et al.^[86] studied the uniaxial tensile strain applied to monolayer and bilayer MoS₂. The employed apparatus for applying strain to MoS₂ is shown in Fig. 4(a). Uniaxial strain can be successfully applied to MoS₂ by bending the flexible polyethylene terephthalate (PET) substrate due to the van der Waals attraction between the sample and the substrate. As seen in Fig. 4(b), the E′ and modes split into A′(1)/A′(2) and peaks, respectively. This indicates that the isotropic symmetry of MoS₂ in the xy-plane has been broken. The A′ and A_1g modes barely shift with the increasing applied strain, illustrating that the vibration along the c-axis is not sensitive to tensile strain. By using the same method, Lloyd et al.^[87] studied the continuous and reversible tuning of the optical bandgap of a suspended monolayer MoS₂ film by applying biaxial strain. As seen from Fig. 4(c), the A_1g and modes both soften (redshift) with the increasing strain. However, the peak positions of 2L and 3L MoS₂ shift less than in the case of the monolayer. The redshifts of the Raman peaks with the increasing tensile strain in the described reports can be attributed to the reduction of the force constants in the 2D material flake. The atom bond length increases under tensile strain. Hui et al.^[88] found that both the A_1g and blueshift as the piezoelectricity-induced biaxial compressive strain increases (Fig. 4(d)). The blueshift of the Raman peaks can be attributed to the increase of the force constants. The atom bond length decreases under compressive strain. In addition, TMDs are more sensitive to the biaxial than uniaxial strain.^[83]

Fig. 4.

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Fig. 4. (color online) Effect of strain on MoS2 films and their Raman signals. (a) Schematic of the three-point bending method for strain measurement. (b) Raman spectra for mono- and bilayer MoS2 with strain applied. The mode splits into two modes under the applied tensile strain. Reproduced with permission from Ref. [86]. Copyright 2013, American Physical Society. (c) Peak positions of the and A1g modes as functions of biaxial strain for 1L, 2L, and 3L MoS2. The inset shows the and A1g Raman modes of unstrained MoS2. Reproduced with permission from Ref. [87]. Copyright 2016, American Chemical Society. (d) Raman spectra of trilayer MoS2 under varying compressive strain. Both the and A1g modes blueshift for the compressive strain increasing from 0 to . Reproduced with permission from Ref. [88]. Copyright 2013, American Chemical Society.

The interaction between the substrate and 2D materials varies depending on the type of substrate material. There are several reports studying the effects of substrates on 2D materials.^[47,89,90] Buscema et al.^[89] studied the differences in the parameters of MoS₂ on various conducting and insulating substrates. The results indicate that the position of the mode is insensitive to the substrate characteristics. However, the A_1g mode stiffens for some substrates. The intensities for both modes are different for different substrates. The stiffening of the A_1g mode is related to the vdW force between the 2D material flake and the substrate. For example, as the A_1g mode is the out-of-plane vibrational mode involving S atoms in MoS₂, the electrostatic environment changes when the motion occurs, which may affect the A_1g mode frequency. Shi et al.^[91] found that the frequency difference between the A_1g and peaks for samples transferred on SiO₂ and quartz are smaller than that before the transfer process due to the strong interface interaction.

Banszerus et al.^[90] found that h-BN, WSe₂, and MoS₂ are better substrates than SiO₂ and sapphire, as shown in Fig. 5. It indicates that the interaction between materials from the 2D family is smaller than for other solid-state crystal materials. Rough surfaces of SrTiO₃, AlN, and SU-8 are not suitable for high-quality graphene devices because these substrates introduce nanometer-scale strain variations and significant charge carrier doping in graphene. In summary, 2D materials are well suitable as substrates for graphene due to the lower values of (the FWHM of the 2D-peak) and little overall doping. At the same time, rough surfaces, especially oxides, are not suitable substrates for graphene as they introduce additional charge carrier doping.

Fig. 5.

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Fig. 5. (color online) Interaction of graphene with different substrates including various 2D materials. (a)–(k) Scatter diagrams of ω2D versus ωG acquired from the spatially resolved Raman maps on different substrates. The black solid lines represent the strain axes and the black dashed lines represent the doping axes. The black circles indicate the point corresponding to unstrained graphene. (l) Schematic of the influence of strain and strain-induced p- and n-doping on ω2D and ωG. Reproduced with permission from Ref. [90]. Copyright 2017, IOP Publishing.

The properties of 2D materials depend on the number of layers. For example, bulk MoS₂ has an indirect bandgap, which transforms into a direct bandgap in monolayer MoS₂. It is necessary to identify the number of layers of 2D materials. Atomic force microscopy, optical contrast, and Raman spectroscopy have been widely used to determine the number of layers of 2D materials. Among them, Raman spectroscopy is a rapid, non-destructive, and direct tool to identify the number of layers.

Different numbers of layers of 2D materials are associated with different Raman spectra. In recent years, there have been many reports on the identification of the thickness of 2D materials with Raman spectroscopy.^{[48,56,92–102]} High- and low-frequency Raman modes are mainly found in Raman spectra. The high-frequency modes are usually associated with in-plane and out-of-plane vibrations, such as the G mode (in-plane vibration of sp² carbon atoms) and out-of-plane 2D mode (stacking order) in layered graphene or the mode (in-plane vibration of M and X atoms) and A_1g mode (out-of-plane vibration of X atoms) in MX₂. The intensities of the in-plane R modes are independent on the angle θ (the polarization of the incident light and scattered photons), while θ affects the intensity of the out-of-plane modes.^[26] Generally speaking, the frequency of the mode redshifts, and that of the A_1g mode blueshifts with the increasing number of layers in layered MX₂.^{[30,53,93,103,104]} Zhao et al.^[93] reported that the A_1g mode blueshifts, and the mode redshifts when the number of layers increases for both WS₂ and WSe₂ films. The FWHMs of the two modes decrease with the increasing thickness. Since the interlayer vdW forces suppress atomic vibrations as the thickness increases, the out-of-plane A_1g mode blueshifts with the increasing number of layers. The redshift of is associated with the structural changes or the increase of the long-range Coulomb force in interlayer interactions.^[30] However, the typical Raman modes of WS₂ are less sensitive to the number of layers.^[27,52] Additionally, the frequency difference ( ) between the A_1g and modes can be used to identify few-layer MX₂ (when the number of layers is less than 6).^[55] The of the two modes is calculated as .^[55] Yu et al.^[48] found that the frequency difference between the A_1g and E_2g peaks for a MoS₂ film increases with the increase of the thickness. Li et al.^[105] reported the high-frequency Raman spectra of MoS₂ with 1–120 layers, as shown in Fig. 6(a). They found that the curve of the peak intensity as a function of thickness is not monotonous, and a new enhanced peak appears at ∼85 layers. The increased intensities of the peaks are due to interference effects.

Fig. 6.

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Fig. 6. (color online) High- and low-frequency Raman spectra of MoS2 with various thickness. (a) Typical Raman spectra of 1L to bulk MoS2 (left), and the positions of the , A1g, and Raman modes as functions of NL. Reproduced with permission from Ref. [105]. Copyright 2012, American Chemical Society. (b) Stokes and anti-Stokes Raman spectra of MoS2 with various thickness in a range from −60 to 60 cm−1 (left), and the frequency and FWHM of the C and LB modes as functions of the number of layers (right). Reproduced with permission from Ref. [18]. Copyright 2013, American Physical Society.

The restoring forces of the high-frequency Raman vibrational modes are dominated by the interaction associated with strong chemical bonds. The differences for high-frequency Raman modes are not very obvious as N increases. In contrast, the difference for the low-frequency Raman modes is more pronounced for different numbers of layers.

The low-frequency modes correspond to interlayer vibrations where each layer moves as a whole unit. This motion could be either perpendicular or parallel to the layers.^[18,106,107] There are two types of interlayer vibration modes, the shear (S) mode, where the oscillation is parallel to the layer plane, and the layer-breathing (LB) mode, where the oscillation is perpendicular to the layer plane,^[49] arising from the Davydov splitting of the zero-frequency acoustic modes.^[26] The shear mode is also called C mode in some papers.^[18,106] The LB mode is also known as the compression vibrational mode.^[18,61,108] Since the interlayer coupling in TMDs is associated with the weak vdW interaction, the frequencies of the LB and S modes are usually lower than 100 cm⁻¹.^[52,108,109] In bulk MX₂, the LB mode is defined as and is optically inactive. The S mode is defined as with the adjacent layers vibrating out-of-phase, which is Raman active. In MX₂ with an odd number of layers, the S modes are defined as E″ (R) and E′ (IR + R), and the LB modes are defined as (R) and (IR). In MX₂ with an even number of layers, the S modes are (R) and E_u (IR), and the LB modes are A_1g (R) and A_2u (IR). The S and LB modes do not exist in monolayer 2D materials due to their interlayer coupling properties. The S and LB modes are not detectable in the bulk layered materials with only one rigid layer in its unit cell (for example, ReS₂, ReSe₂, and Bi₂Se₃).^[52] The intensities of the S and LB modes are determined by the associated electron–phonon coupling effect. In NL 2D materials, there are N−1 doubly degenerate interlayer S modes and N−1 LB modes. The frequencies of the S and LB modes depend on the following equations ((1) for S and (2) for LB):^[52,109] 1 2 and are the S and LB frequencies of 2L 2D materials flakes.^[52] Low-frequency Raman spectroscopy is a direct, substrate-free and precise tool to identify the number of layers in few-layer 2D materials. The low-frequency Raman spectra of MoS₂ with 1–19 layers are shown in Fig. 6(b).^[55] The authors demonstrated that the C mode stiffens from ∼22.6 cm⁻¹ in 2L to 32.5 cm⁻¹ in 19L-MoS₂, while the LB mode softens from ∼40.1 cm⁻¹ in 2L to 4.7 cm⁻¹ in 19L-MoS₂. Most related materials exhibit similar Raman shifts: the LB modes soften, and the S modes stiffen when the number of layers increases; this is characteristic for WSe₂,^[56] MoTe₂,^[26] NbSe₂,^[110] MoSe₂,^[53] Mo_0.5W_0.5S₂ alloy,^[106] and MoS₂.^[61] Particularly, different stacking order results in different trends of low-frequency Raman modes. For example, the S mode of AB-stacked few-layer graphene (FLG) stiffens with the increasing number of layers, while that of ABC-stacked FLG softens.^[107] The LB modes soften with the increasing number of layers for both isotropic and anisotropic stacking of NL ReS₂, while the S modes stiffen for isotropic stacking of NL ReS₂ and soften for anisotropic stacking of NL ReS₂ as the number of layers increases.^[111]

Since the discovery of the novel physical properties and bandgap structures of 2D materials, many 2D-materials-based semiconducting devices emerged. Raman spectroscopy is an effective tool to study the carrier concentration in 2D-materials-based semiconducting devices. Das et al.^[112] studied Raman scattering in a top-gated graphene transistor. The results show that the G peak redshifts when the top-gate voltage (V_TG) increases from −2.2 V to 0.6 V and then blueshifts for the voltages from 0.6 V to 4.0 V. The Raman shift of the G peak increases for both hole doping and electron doping. However, the 2D peak decreases for V_TG below 3 V for electron doping. The FWHM of the G peak decreases for both hole doping and electron doping. This result indicates that the dependence of the G mode on V_TG is weaker than that of the 2D mode. For TMDs, the modes are more sensitive to than the modes. Since the mode is the out-of-plane vibrational mode of X atoms, it is sensitive to surface adsorption and doping. Therefore, all electronic states introduce a perturbation to the mode due to relatively strong large electron–phonon coupling. For example, Chakraborty et al.^[113] studied the effect of carrier concentration on Raman scattering in a single-layer MoS₂ top-gated FET. The mode significantly redshifts when increases from 0 to 2.0 V, whereas the E′ mode remains almost unchanged. Miller et al.^[65] found that the A_1g modes of 1L and 2L MoS₂ redshift as increases from −1.0 to 1.0 V. However, the mode changes only slightly in monolayer and negligibly in bilayer MoS₂ with the increasing . Xu et al.^[114] studied the properties of graphene contacted with various metals using Raman spectroscopy. Figure 77 shows the resulting Raman spectra of the graphene characteristic peaks. Chemisorbed metals Ni and Ti not only cause a dramatic blueshift of the 2D peak but also broaden it and transform into a sum of two Gaussians. Thus, the lowest contact resistivity of is measured when metal Ni is used as an electrode material in a graphene FET.

Fig. 7.

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	Fig. 7. (color online) Properties of graphene metal contact probed by Raman spectroscopy. Reproduced with permission from Ref. [114]. Copyright 2018, Elsevier.

A charge density wave (CDW) is a symmetry-reducing ground state with periodic modulations of charge densities and the associated lattice distortions in layered materials.^[31,115] CDWs are affected by electron–phonon interactions, Peierls instabilities, and fluctuation effects from finite temperatures and disorders.^[31] vdW materials provide an ideal platform to study CDWs and the associated superconductivity.^[25,31,115] Raman spectroscopic measurement is an effective tool to identify the transition temperature of the CDW phase. Goli et al.^[115] found that the temperature of the transition to the CDW phase of TiSe₂ can increase up to ∼240 K when the thickness is decreased to below ∼100 nm. They found a new mode appearing at ∼460 cm⁻¹ below 200 K in bulk TiSe₂. Hajiyev et al.^[30] found that the two-phonon peaks for 1L, 2L, and bulk TaSe₂ soften with increasing temperature, and the frequency of this mode exhibits a sudden drop at 120 K. It indicates that the temperature of the transition from the metallic phase to ICDW (incommensurate charge density wave) phase of 2H-TaSe₂ is ∼120 K. Xi et al.^[31] found that both the CDW and the superconducting phase exist down to the monolayer limit. The superconducting transition temperature decreases with decreasing thickness. However, the CDW transition temperature increases from 33 K in bulk to 145 K in a monolayer. The temperature dependence of Raman spectra for bulk, bilayer, and monolayer NbSe₂ are shown in Fig. 8. The soft mode of bulk NbSe₂ redshifts with decreasing temperature and stops changing when the temperature is down to 33.5 K (T_CDW). There are two new Raman modes emerging when the temperature is below T_CDW. One mode appears at ∼35 cm⁻¹, where the CDW fluctuations are strong, with frequency and intensity both dropping rapidly to zero when the temperature is increasing and approaching T_CDW due to the second-order phase transition. The other new mode is at ∼190 cm⁻¹. The frequency of this mode is independent of the number of layers N, whereas the frequency at zero temperature blueshifts for decreasing thickness. Both modes persist at much higher temperatures, indicating the higher associated CDW transition temperatures. This result shows that there is a strongly enhanced CDW order in atomically thin NbSe₂ driven by strong electron–phonon coupling. In summary, the sudden drops of the Raman mode intensities and emerging of the new Raman modes are characteristic for the CDW phase.

Fig. 8.

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Fig. 8. (color online) Raman study of CDW phenomena in 2D materials. (a)–(c), Temperature maps of the Raman scattering intensity of bulk, 2L, and 1L NbSe2, respectively, for the perpendicular polarization configuration. The two arrows in each map indicate the low-frequency feature and the weak high-frequency feature. Dashed lines approximately indicate TCDW. (d)–(f) Raman spectra of each sample at selected temperatures. Reproduced with permission from Ref. [31]. Copyright 2015, Nature Publishing Group.

Temperature-dependent Raman spectroscopy is an efficient tool to investigate the thermoelectrical properties of 2D materials.^[116–118] Sahoo et al.^[119] studied the thermal conductivity of few-layer MoS₂ by Raman spectroscopy. The schematic for the heat conduction process in suspended few-layer MoS₂ is shown in Fig. 9(a). Figure 9(b) demonstrates that both the A_1g and modes redshift as the temperature increases from 83 to 473 K under the 532 nm laser excitation. The observed data for the Raman peak positions versus temperature were fitted using the Grüneisen model^[116,120] 3 where ω₀ is the frequency of the Raman mode at 0 K, and χ is the first-order temperature coefficient of the relative Raman mode. T stands for the changed temperature. The first-order temperature coefficient corresponds to the slope of the Raman mode as a function of temperature. The FWHM of A_1g in few-layer MoS₂ decreases as the temperature increases from 83 to 523 K (Fig. 9(c)). The A_1g mode is selected for the evaluation of the thermal conductivity because the intensity of the A_1g mode is much higher than that of the mode. The thermal conductivity is calculated by the authors as follows: 4 Here, is the first-order temperature coefficient for the A_1g mode, and is the change of the frequency with the incident laser power. The parameter h represents the thickness of the sample (6.5 nm in the reported work). The value of obtained from the slope of the laser-power-dependent A_1g (Fig. 9(d)) is 5.7 cm⁻¹/mW. The first-order temperature coefficient for the A_1g mode is , as seen in Fig. 9(a). The thermal conductivity of the few-layer MoS₂ sample is ∼52 W/mK calculated using Eq. (2) and the existing data. Yan et al.^[64] found that both the A_1g and modes of exfoliated monolayer MoS₂ also redshift with increasing temperature (for 514.5 nm laser wavelength). However, the thermal conductivity was evaluated to be ∼34.5 W/mK, which is smaller than the result of Sahoo et al. (∼52 W/mK), where the MoS₂ sample was prepared by chemical vapor deposition. Thripuranthaka et al.^[117] found that the A_1g and Raman peak positions for single-layer WS₂ redshift when the temperature increases from 77 to 623 K under the 514.5 nm laser excitation. The behavior of Raman modes for varying temperature is similar to the case of MoS₂. Zhang et al.^[121] studied the low-temperature Raman response of few-layer BP and found that the , , and A_1g vibration modes stiffen as the temperature decreases from 20 to −160°C. They also found that, for few-layer phosphorene, the Raman shift is more sensitive to temperature than for graphene and MoS₂ due to the mechanical flexibility of phosphorene. Xia et al.^[122] reported that the Raman modes of anisotropic 2D SnS flakes blueshift when the temperature decreases from 25 °C to −195 °C under the 532 nm laser excitation. It is interesting that the result demonstrates that 2D SnS flakes exhibit a higher temperature sensitivity than black phosphorus (BP). Pawbake et al.^[120] found that the Raman peaks of titanium trisulfide (TiS₃) shift toward lower frequencies when the temperature increases from 88 K to 570 K. All the results described above prove that the frequencies of typical Raman modes could be used to study the thermal conductivity of 2D materials in a non-destructive way. Chen et al.^[123] applied an AC lock-in technique and successfully separated the thermoelectric voltage in a graphene/hBN/graphene heterostructure device. The Raman 2D and G peaks shift with temperature at a rate of −0.057 cm⁻¹/K and −0.022 cm⁻¹/K, respectively.^[124] The shifts of the 2D and G peaks are converted to the temperature gradient ( ). Then, the Seebeck coefficent ( of is obtained.

Fig. 9.

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Fig. 9. (color online) Raman study of thermoelectricity in 2D materials. (a) Schematic for the heat conduction process in suspended few-layer MoS2. (b) Raman spectra of suspended few-layer MoS2 at different temperatures (left). The A1g and peak positions as functions of temperature (right). Both modes redshift as the temperature increases. (c) FWHM of the A1g peak as a function of temperature. The FWHM increases as the temperature increases. (d) The A1g mode frequency as a function of laser power. Redshifts are found as the temperature increases. Reproduced with permission from Ref. [119]. Copyright 2013, American Chemical Society.

Combining materials with different work functions can generate photoexcited electrons and holes accumulated in different layers.^[125] The p–n junction devices are implemented by bringing p-doped and n-doped materials in contact. vdW heterostructures, which consist of different 2D materials held together by weak vdW forces, have wide applications in photovoltaic devices. The carrier transport in vdW heterostructures is dominated by the interfacial properties of the adjacent layers with lattice mismatch. The interlayer coupling, charge transfer, lattice vibrations, and interface diffusion in vdW heterostructures transform the band structure, shift the Fermi level, and introduce band offsets.^[55] The low-frequency Raman spectroscopy is a powerful tool to detect the interlayer coupling and polytypes of heterostructures because the S and LB modes are sensitive to the stacking order.

There have been many reports on vertical and in-plane heterostructures in recent years.^{[101,126–137]} Zhang et al.^[127] studied vertical MoS₂/WS₂ heterostructures with AA and AB stacking grown by chemical vapor deposition (CVD) and vertical MoS₂/WS₂ heterostructures obtained with the transfer technique. The structure of CVD-prepared MoS₂/WS₂ heterostructures is associated with more efficient interlayer charge transfer and spatially separated exciton recombination than the mechanically transferred heterostructures, which due to the strong coupling. Figure 10(a) shows the typical Raman modes of CVD-grown MoS₂/WS₂ heterostructures. As seen from Fig. 10(b), the Raman spectra of mechanically transferred MoS₂/WS₂ heterostructures show a simple superposition of the individual Raman modes of WS₂ and MoS₂, whereas the A_1g modes of CVD-grown MoS₂/WS₂ heterostructures blueshift by 3–4 cm⁻¹ comparing with the modes of WS₂ and MoS₂. This reveals strong interlayer coupling in the CVD-grown MoS₂/WS₂ heterostructures. As seen from Fig. 10(c), the frequency of the LB mode of an AB-stacked heterostructure is ∼2 cm⁻¹ higher than that of an AA-stacked heterostructure. This may be due to the shorter interlayer distance and stronger interlayer coupling of AB-stacked heterostructures compared to AA-stacked heterostructures. Moreover, the vibrational frequency of the LB mode of an as-grown AB stacked MoS₂/WS₂ heterostructure is 2–4 cm⁻¹ higher than that of a transferred twist MoS₂/WS₂ heterostructure, demonstrating the weak interlayer coupling and lower packing efficiency of the transferred twist heterostructure. In comparison, the S modes can be observed only when heterostructures have perfect commensurate stacking due to the restoring force of the lateral displacement. In addition to vertical heterostructures, Chen et al.^[138] studied lateral MoS₂/WS₂ heterostructures prepared by the CVD method. The obtained Raman mapping images of as-grown WS₂/MoS₂ heterostructures are shown in Fig. 10(d), which demonstrates the features of an in-plane WS₂/MoS₂ heterostructure, with a triangular monolayer MoS₂ domain as the core and WS₂ as the shell layer. Figure 10(e) shows the I_ds–V_ds curves of a p–n diode of the lateral WS₂/MoS₂ heterostructure in the dark (black line) and under illumination with a wavelength of 514 nm and power of 1 mW (red line), with the inset showing the photovoltaic effect. The open-circuit voltage V_OC is ∼0.15 V, and the short-circuit current I_SC is ∼5.2 pA under the laser illumination of the device. The current rectification observed in the figure indicates that there is a p–n diode formed in the WS₂/MoS₂ lateral heterostructure. The output current was found to increase with the increasing positive gate voltage under different back gate voltages of 0–80 V. This indicates that the n-type monolayer MoS₂ partly limits the charge transport in the p–n diode. Lateral heterostructures based on TMDs can dramatically enhance the performance of optoelectronic devices.^[125] Gong et al.^[136] studied both vertical and in-plane MoS₂/WS₂ heterostructures. The structures of vertical and lateral WS₂/MoS₂ heterostructures are shown in Fig. 10(f). The Raman spectra of vertical WS₂/MoS₂ heterostructures are the same as reported by Zhang et al. The Raman spectra of lateral WS₂/MoS₂ heterostructures are the same as reported by Chen et al. They show that the p–n junctions of in-plane WS₂/MoS₂ heterostructures without external electrical tuning exhibit a two orders of magnitude higher forward bias current compared to the the reverse current.

Fig. 10.

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Fig. 10. Raman study on a 2D heterostructure as a photovoltaic device. (a) Raman vibrational modes of a vertical bilayer WS2/MoS2 heterostructure. (b) Raman spectra of as-grown 1L WS2 and MoS2 and as-grown, as-transferred WS2/MoS2 heterostructures. (c) Raman spectra of the LB and S modes for as-grown MoS2 films on WS2, AA stacked, AB stacked, and transferred twisted stacked MoS2/WS2 heterostructures, respectively. Reproduced with permission from Ref. [127]. Copyright 2016, Wiley-VCH Verlag GmbH & Co. KGaA. (d) Raman mapping results for lateral WS2/MoS2 heterostructures, MoS2, and WS2, respectively. (e) I–V curve of a lateral WS2/MoS2 heterostructure diode in the dark (black line) and under illumination with a wavelength of 514 nm and power of 1 mW (red line). Inset shows the photovoltaic effect. Reproduced with permission from Ref. [138]. Copyright 2015, American Chemical Society. (f) Schematic of vertical and lateral WS2/MoS2 heterostructures. Reproduced with permission from Ref. [136]. Copyright 2014, Nature Publishing Group.

Currently, most 2D heterostructures are created by the micromechanical stacking technique with only certain combinations of interfaces, and the direct growth of heterostructures by CVD or vdW epitaxy with their own inherent limitations is not yet well developed. Therefore, further study of heterostructures is necessary.