1. Introduction

Raman spectroscopy has been widely used to characterize phonons in two-dimensional layered materials, which can afford information on stacking thickness [1], stacking order [2], strain [3], etc. ARP Raman spectroscopy is a very important branch of Raman spectroscopy to study the orientation of Raman modes [4–6] based on crystal symmetry or crystal orientation. The precise determination of crystal symmetry and orientation is an essential prerequisite for understanding and tuning the interplay between the geometrical structure of two-dimensional layered materials and its optical and electronic properties. X. L. Liu et al. [4] have presented ARP Raman measurements of G mode on the base plane and edge plane of highly oriented pyrolytic graphite (HOPG) and have demonstrated that polarized Raman measurements can be implemented by several different configurations. Recently, polarization-dependent anisotropic behaviors of phonons in other two-dimensional layered materials have been paid attention and studied. For example, in twisted MoS₂ layers, the polarized Raman intensity of ${E^1}_{2g}$ mode is strongly affected by the misorientation angle between adjacent layers [5]. MoS₂ is a promising layered material for optoelectronic applications because of its distinctive electronic and optical properties such as strong photoluminescence emission [7,8], light absorption [9,10], photocurrent [11], and valleytronics [12,13]. The success of ARP Raman scattering in characterizing HOPG prompted the feasibility to extend this technique to MoS₂. Ying Ding. et al. [6] have studied Raman tensor of layered MoS₂ by ARP Raman scatterings on basal and edge planes of layered MoS₂ using the geometry configuration of parallel polarization and have concluded that Raman scattering intensity of vibration modes in the edge plane shows a strong polarization dependence due to the anisotropy of the MoS₂ cross-section structure. In fact, the intensity of Raman signal depends on not only the Raman selection rule but also the relationship between the polarization direction of the incident/emitted light and the crystal direction for Raman modes with certain symmetries. In this paper, Raman scattering intensities of ${E^1}_{2g}$ and ${A_{1g}}$ modes of the basal and edge plane of 2H-MoS₂ were fully studied under the I and II type ARP Raman spectroscopy. The experimental configuration and the calculation method of X. L. Liu et al. [4] provide great help and reference for the research of this paper. Here, the polarization properties of phonon modes in different planes of bulk MoS₂ were discussed and their dependence on the polarization direction of incident/scattered light were presented with four kinds of polarization configurations according to horizontal and vertical Raman signal polarizations. Furthermore, the experimental results were confirmed and analyzed by theoretical analysis. This paper provides a complete and accurate optical method for identifying polarization-angle dependence of phonons of two-dimensional layered crystalline materials like MoS₂. The results lay the groundwork to determine atomic arrangement with different morphologies (including tiled and vertical arrangement) and to explore interlayer coupling related to crystallographic misalignments between adjacent layers in MoS₂ materials.

2. Experimental methods and theoretical calculations

2.1 Experimental methods

The CVT-grown high purity 2H-MoS₂ bulk crystal was obtained directly from commercial purchase (Shanghai Onway Technology Co., Ltd). The MoS₂ sample was attached to the side of a metallic cube to measure the basal and edge plane of MoS₂, as shown in Fig. 1(a). Figures 1(b) and 1(c) present the optical images of the basal and edge plane of MoS₂ with the ×20 objective lens. The surface of the basal plane is smooth while the edge plane has distinct layered stripes, which is consistent with the layered structure of MoS₂. For the basal plane, the laser is incident to the sample surface which is shown in Fig. 1(d). For the edge plane, the MoS₂ is rotated 90° and the laser is incident to the sample surface which is shown in Fig. 1(e).

 

Fig. 1. (a) the MoS₂ sample attached to the side of a metallic cube, (b, c) the optical images of the basal and edge plane of MoS₂, and (d, e) Schematic diagrams of the laser incident to the basal and edge plane of MoS₂.

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The Raman spectra at room temperature were measured in back-scattering scheme with a HR Evolution micro-Raman system, equipped with the unique SWIFT CCD, a ×100 objective lens (NA=0.90), and an 1800g/mm grating. The excitation wavelengths were 532 nm from a diode-pumped solid-state laser. The laser power was controlled to below 0.5 mW to avoid sample heating effect and the CCD integration time of 20s was adopted to ensure a good signal-to-noise ratio. Here, we use two ARP Raman configurations including Type I (to set a half-wave plate in the optical path of incident laser to change the polarization direction of the incident laser) and Type II (to set a half-wave plate in the common optical path of incident laser and Raman signal to simultaneously vary their polarization directions), as shown in Fig. 2. The laboratory coordinates are represented by black dotted arrows, in which Y and X correspond to vertical and horizontal directions. The initial polarization direction of the laser is parallel to Y axis. There are two typical Raman signal polarizations according to the analyzer selection: vertical and horizontal directions. The blue two-way arrows represent the polarization direction of the incident laser reaching the sample. The red two-way arrows represent the initial polarization of Raman signal from the sample surface corresponding to the analyzer-selected vertical or horizonal direction. Figure 2(a) presents the schematic diagram of Type I configuration, in which the laser polarization can be tuned by the half-wave plate. We denote laser polarization direction as α. In combination with the analyzer direction, the configurations of αY, αX were used for Type I configuration. Figure 2(b) presents the schematic diagram of Type II configuration, in which both the laser and Raman signal polarizations can be tuned by the half-wave plate. We denote laser polarization direction as β. In combination with the analyzer direction, the configurations of βY, βX were used for Type II configuration. α(β) varies from 0° to 360° by taking 10° as the step to record the Raman peak intensities in the I(II) type configurations.

 

Fig. 2. Schematic diagrams of Type I and II polarization configurations for angle-resolved polarized Raman spectroscopy: (a) αY and αX, and (b) βY and βX. Laboratory coordinates (xyz) are represented by black arrows. Blue two-way arrows stand for the incident laser polarization reaching at sample. Red two-way arrows represent the original polarization of Raman signal corresponding to vertically or horizontally polarized signal selected by the analyzer before spectrometer entrance.

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2.2 Theoretical calculation

The intensity of a Raman mode can be expressed as:$I \propto \mathop \sum \nolimits_j {|{{{\vec{e}}_R} \cdot {R_j} \cdot {{\vec{e}}_L}} |^2}$, where ${\vec{e}_R}$ and ${\vec{e}_L}$ are the unit polarization vectors of the Raman signal and the laser, and ${R_j}$ is the 3×3 Raman tensor, respectively.

The ${E^1}_{2g}$ mode of 2H-MoS₂ has two Raman tensors, ${R_1} = \left( {\begin{array}{ccc} {\; 0\; \; \; e\; \; \; 0\; }\\ {\; e\; \; \; 0\; \; \; 0}\\ {\; 0\; \; \; 0\; \; \; 0\; } \end{array}} \right)$, ${R_2} = \left( {\begin{array}{ccc} {\; e\; \; \; 0\; \; \; 0\; }\\ {\; 0\; \; - e\; \; 0}\\ {\; 0\; \; \; 0\; \; \; 0\; } \end{array}} \right)$, where e is a constant. The ${A_{1g}}$ mode of 2H-MoS₂ has one Raman tensor, $R = \left( {\begin{array}{ccc} {\; a\; \; \; 0\; \; \; 0\; }\\ {\; 0\; \; \; a\; \; \; 0\; }\\ {\; 0\; \; \; 0\; \; \; b\; } \end{array}} \right)$, where a and b are constants.

The intensities of ${E^1}_{2g}$ and ${A_{1g}}$ modes at the basal and edge plane of 2H-MoS₂ are denoted as ${I_b}({{E^1}_{2g}} )$, ${I_b}({{A_{1g}}} )$, ${I_e}({{E^1}_{2g}} )$, and ${I_e}({{\textrm{A}_{1g}}} )$ respectively. The initial polarization direction of the laser is parallel to Y axis. For the basal plane, the crystal coordinates coincide with the laboratory coordinates. The laser is incident at the basal plane along the -Z axis is shown in Fig. 3(a). However, for the edge plane, the crystal coordinates rotate by -90° around the Y axis of the laboratory coordinates, which is shown in Fig. 3(b). The Raman tensor needs to be transformed, which can be seen in Xuelu Liu's article [4] for details.

 

Fig. 3. (a, b) Schematic diagrams of the basal and edge plane of MoS₂ for theoretical calculation, (c-f) polar plot of theoretical intensities of the E¹_2g and A_1g modes as a function of α for αY and αX configurations with Type I configuration, and (g-j) polar plot of theoretical intensities of the E¹_2g and A_1g modes as a function of β for βY and βX configurations with Type II configuration.

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In Type I configuration, the initial polarization of the laser is ${\vec{e}_L}^T = ({0\,1\,0} )$ which becomes ${\vec{e}_L}^T = ({sin \alpha cos \alpha 0} )$ after the half-wave plate. Under αY polarization, the polarization of scattered light is ${\vec{e}_R} = ({0\,1\,0} )$, so ${I_b}{({{E^1}_{2g}} )_{\mathrm{\alpha }Y}} = {e^2}$, ${I_b}{({{A_{1g}}} )_{\alpha Y}} = {a^2}{cos ^2}\alpha $, ${I_e}{({{E^1}_{2g}} )_{\alpha Y}} = {e^2}{cos ^2}\alpha $, ${I_e}{({{A_{1g}}} )_{\alpha Y}} = {a^2}{cos ^2}\alpha $; Under αX polarization, the polarization of the scattered light is ${\vec{e}_R} = ({1\,0\,0} )$, so ${I_b}{({{E^1}_{2g}} )_{\mathrm{\alpha }X}} = {e^2}$, ${I_b}{({{A_{1g}}} )_{\alpha X}} = {a^2}{sin ^2}\alpha $, ${I_e}{({{E^1}_{2g}} )_{\alpha X}} = 0$, ${I_e}{({{A_{1g}}} )_{\alpha X}} = {b^2}{sin ^2}\alpha $. The results of ${E^1}_{2g}$ and ${A_{1g}}$ intensities changing with α are shown in Figs. 3(c)–3(f).

In Type II configuration, a Jones matrix $J = \left( {\begin{array}{ccc} {\; - cos \beta \; \; \; sin \beta \; \; \; 0\; }\\ {\; \; \; \; sin \beta \; \; \; cos \beta \; \; \; 0\; }\\ {\; \; \; \; \; \; 0\; \; \; \; \; \; \; \; 0\; \; \; \; \; \; \; 0\; } \end{array}} \right)$ is introduced and the Raman intensity formula becomes to $I \propto \mathop \sum \nolimits_j {|{{{\vec{e}}_R} \cdot J \cdot {R_j} \cdot J \cdot {{\vec{e}}_L}} |^2}$ because the half-wave plate simultaneously changes the polarization direction of the incident and scattered light, which can be seen in Xuelu Liu's article [4] for details. Under βY polarization, ${\vec{e}_L}^T = ({0\,1\,0} )$ and ${\vec{e}_R} = ({0\,1\,0} )$, so ${I_b}{({{E^1}_{2g}} )_{\mathrm{\beta }Y}} = {e^2}$, ${I_b}{({{A_{1g}}} )_{\mathrm{\beta }Y}} = {a^2}$, ${I_e}{({{E^1}_{2g}} )_{\mathrm{\beta }Y}} = {e^2}{cos ^4}\beta $, ${I_e}{({{A_{1g}}} )_{\mathrm{\beta }Y}} = {b^2}{sin ^4}\beta + {a^2}{cos ^4}\beta + \frac{1}{2}ab{sin ^2}2\beta $; Under βX polarization, ${\vec{e}_L}^T = ({0\,1\,0} )$ and ${\vec{e}_R} = ({1\,0\,0} )$, so ${I_b}{({{E^1}_{2g}} )_{\mathrm{\beta }X}} = {e^2}$, ${I_b}{({{A_{1g}}} )_{\mathrm{\beta }X}} = 0$, ${I_e}{({{E^1}_{2g}} )_{\beta X}} = \frac{1}{4}{e^2}{sin ^2}2\beta $, ${I_e}{({{A_{1g}}} )_{\beta X}} = \frac{1}{4}{(a - b)^2}{sin ^2}2\beta $. The results of ${E^1}_{2g}$ and ${A_{1g}}$ intensities changing with β are shown in Figs. 3(g)–3(j). (For better display, we multiply the ${I_e}{({{E^1}_{2g}} )_{\beta X}}$ and ${I_e}{({{A_{1g}}} )_{\beta X}}$ by 4.)

3. Results and discussions

3.1 Raman spectra of the basal and edge planes of MoS₂ under the YY, YX polarization configurations

We first measured the normal Raman spectra of the basal and edge plane of MoS₂ in the range of 100∼500cm^-1, as shown in Fig. 4(a). The ${E^1}_{2g}$ and ${A_{1g}}$ peaks are observed at 383cm^-1 and 407cm^-1 in both planes, respectively. However, there is an additional peak at 286cm^-1 in Raman spectra of MoS₂ edge plane, which is assigned to a defective mode and is activated by the broken MoS₂ boundary [6]. We then measured the simple polarized Raman spectra of the basal and edge plane of MoS₂ under the YY and YX (YY means the polarization direction of incident and scattered light are both Y, and YX means the polarization direction of incident light is Y, but the polarization direction of scattered light is X) configurations in the range of 370∼430cm^-1, as shown in Figs. 4(b) and 4(c). Normalizing the intensity of ${E^1}_{2g}$ peak, the Raman spectra under the YY, YX configurations are plotted by blue and red line, respectively. In Figs. 4(b), it can be found that at basal plane the intensity of ${A_{1g}}$ mode under YY configuration is significantly different from that of ${A_{1g}}$ mode under YX configuration. The intensity of ${A_{1g}}$ mode under YY configuration is obviously greater than that of ${E^1}_{2g}$ mode, while the intensity of ${A_{1g}}$ mode under YX configuration becomes very weak and is significantly smaller than that of ${E^1}_{2g}$ mode. In Fig. 4(c), it can be found that at edge plane the intensity of ${A_{1g}}$ mode under YY configuration is basically the same as that under YX configuration, both of which are greater than that of ${E^1}_{2g}$ mode.

 

Fig. 4. (a) the normal Raman spectra of the basal and edge plane of MoS₂, (b) the simple polarized Raman spectra of the basal plane of MoS₂ under the YY and YX, and (c) the simple polarized Raman spectra of the edge plane of MoS₂ under the YY and YX.

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3.2 ARP Raman spectra of the basal and edge planes of MoS₂

The simple YY and YX polarization configurations can only be used for Raman modes identification of different planes of MoS₂, while ARP Raman spectroscopy is beneficial to study the crystal orientation and phonon polarization properties of different planes of MoS₂. We measured ARP Raman spectra of the ${E^1}_{2g}$ and ${A_{1g}}$ modes at the basal and edge planes of MoS₂ under Type I and Type II configurations. According to the calculation results of ${I_b}{({{E^1}_{2g}} )_{\mathrm{\alpha }Y}} = {e^2}$, ${I_b}{({{E^1}_{2g}} )_{\mathrm{\alpha }X}} = {e^2}$, ${I_b}{({{E^1}_{2g}} )_{\mathrm{\beta }Y}} = {e^2}$, and ${I_b}{({{E^1}_{2g}} )_{\mathrm{\beta }X}} = {e^2}$, we know that all the intensities of ${E^1}_{2g}$ at MoS₂ basal plane under Type I and Type II configurations remain a constant, independent of α and β. All the spectra are normalized as the corresponding ${I_b}({{E^1}_{2g}} )$ under the same configuration and the angle-resolved $I({{E^1}_{2g}} )$ and $I({{A_{1g}}} )$ are depicted in Fig. 5. The corresponding fitting curves are also plotted in Fig. 5. The diagram of rotation angle α or β at the basal plane of MoS₂ under two configurations is shown in Fig. 5(a) and the diagram of rotation angle α or β at the edge plane of MoS₂ under two configurations is shown in Fig. 5(b).

 

Fig. 5. (a, b) Schematic diagrams of the basal and edge plane of MoS₂ for Raman measurements, (c-f) polar plot of experimental intensities of the E¹_2g and A_1g modes as a function of α for αY and αX configurations with Type I configuration, and (g-j) polar plot of experimental intensities of the E¹_2g and A_1g modes as a function of β for βY and βX configurations with Type II configuration. The corresponding fitting curves are also plotted.

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The experimental results of ${I_b}({{E^1}_{2g}} )$, ${I_b}({{A_{1g}}} )$, ${I_e}({{E^1}_{2g}} )$, and ${I_e}({{\textrm{A}_{1g}}} )$ under Type I configurations are plotted in Figs. 5(c)–5(f) by blue circles and red squares, respectively. For ${E^1}_{2g}$ mode as shown in Figs. 5(c) and 5(e), ${I_b}{({{E^1}_{2g}} )_{\mathrm{\alpha }Y}}$ and ${I_b}{({{E^1}_{2g}} )_{\mathrm{\alpha }X}}$ remain a constant when α increases from 0° to 360°, independent of $\alpha $. However, ${I_e}{({{E^1}_{2g}} )_{\mathrm{\alpha }Y}}$ and ${I_e}{({{E^1}_{2g}} )_{\mathrm{\alpha }X}}$ are different. ${I_e}{({{E^1}_{2g}} )_{\mathrm{\alpha }Y}}$ reaches maximum when α=0° and 180°, and reaches minimum when α = 90° and 270°, whose shape is like a dumbbell placed vertically. ${I_e}{({{E^1}_{2g}} )_{\mathrm{\alpha }X}}$ remains zero. For ${A_{1g}}$ mode, ${I_b}{({{A_{1g}}} )_{\mathrm{\alpha }Y}}$ shows the same trend with ${I_e}{({{A_{1g}}} )_{\mathrm{\alpha }Y}}$ and ${I_b}{({{A_{1g}}} )_{\mathrm{\alpha }X}}$ shows the same trend with ${I_e}{({{A_{1g}}} )_{\mathrm{\alpha }X}}$ as shown in Figs. 5(d) and 5(f). Both ${I_b}{({{A_{1g}}} )_{\mathrm{\alpha }Y}}$ and ${I_e}{({{A_{1g}}} )_{\mathrm{\alpha }Y}}$ reach maximum when α=0° and 180° and reach minimum when α = 90° and 270°, which are shaped like a dumbbell placed vertically. Both ${I_b}{({{A_{1g}}} )_{\mathrm{\alpha }X}}$ and ${I_e}{({{A_{1g}}} )_{\mathrm{\alpha }X}}$ reach maximum when α = 90° and 270° and reach minimum when α=0° and 180°, which are shaped like a dumbbell placed horizontally.

The experimental results of ${I_b}({{E^1}_{2g}} )$, ${I_b}({{A_{1g}}} )$, ${I_e}({{E^1}_{2g}} )$, and ${I_e}({{\textrm{A}_{1g}}} )$ under Type II configurations are plotted in Figs. 5(g)–5(j) by blue circles and red squares, respectively. Under the βY configuration, ${I_b}{({{E^1}_{2g}} )_{\mathrm{\beta }Y}}$ remains a constant when β increases from 0° to 360° as shown in Fig. 5(g), and ${I_b}{({{A_{1g}}} )_{\mathrm{\beta }Y}}$ also remains a constant as shown in Fig. 5(h). However, ${I_e}{({{E^1}_{2g}} )_{\mathrm{\beta }Y}}$ reaches maximum when α=0° and 180° and reaches minimum when α = 90° and 270°, which is shaped like a dumbbell placed vertically as shown in Fig. 5(g), but ${I_e}{({{A_{1g}}} )_{\mathrm{\beta }Y}}$ reaches maximum when α = 90° and 270° and reaches minimum when α=0° and 180°, which are shaped like a dumbbell placed horizontally as shown in Fig. 5(h). Under the βX configuration, ${I_b}{({{E^1}_{2g}} )_{\mathrm{\beta }X}}$ and ${I_b}{({{A_{1g}}} )_{\mathrm{\beta }X}}$ show almost the same polarization properties, and ${I_e}{({{E^1}_{2g}} )_{\mathrm{\beta }X}}$ and ${I_e}{({{A_{1g}}} )_{\mathrm{\beta }X}}$ show almost the same polarization properties as shown in Figs. 5(i) and 5(j). Both ${I_b}{({{E^1}_{2g}} )_{\mathrm{\beta }X}}$ and ${I_b}{({{A_{1g}}} )_{\mathrm{\beta }X}}$ are isotropic, independent of $\beta $. The small difference is that ${I_b}{({{E^1}_{2g}} )_{\mathrm{\beta }X}}$ remains a constant from 0° to 360° as shown in Figs. 5(i) but ${I_b}{({{A_{1g}}} )_{\mathrm{\beta }X}}$ remains zero as shown in Figs. 5(j). Both ${I_e}{({{E^1}_{2g}} )_{\mathrm{\beta }X}}$ and ${I_e}{({{A_{1g}}} )_{\mathrm{\beta }X}}$ are anisotropic, dependent of $\beta $. They reach maximum when β=45°, 135°, 225° and 315°, and reach minimum when β=0°, 90°, 180° and 270°, like a four leaf clover.

The experimental results of ARP Raman intensities of ${E^1}_{2g}$ and ${A_{1g}}$ modes are mainly in good agreement with theoretical calculations. However, there are still some errors between the experimental results and the theoretical results as shown in Fig. 3 and Fig. 5. For example, on the MoS₂ edge plane, both ${E^1}_{2g}$ and ${A_{1g}}$ modes are anisotropic under both βY and βX polarizations. Both ${I_e}{({{E^1}_{2g}} )_{\mathrm{\beta }X}}$ and ${I_e}{({{A_{1g}}} )_{\mathrm{\beta }X}}$ present the perfect four-leaf clover shape theoretically, however, in the experiments ${I_e}{({{E^1}_{2g}} )_{\mathrm{\beta }X}}$ is larger when β=135° and 315° than that when β=45° and 225° as shown in Fig. 5(i) but ${I_e}{({{A_{1g}}} )_{\mathrm{\beta }X}}$ is larger when β=45° and 225° than that when β=135° and 315° as shown in Fig. 5(j). The possible reason is that the edge plane of MoS₂ is not smooth enough and the laser and the edge surface cannot be perpendicular to each other in all directions when β varies from 0° to 360°, resulting in Raman intensities of ${E^1}_{2g}$ and ${A_{1g}}$ modes in some directions are greater than that in other directions in ARP Raman measurements. However, the angles at which the maximum intensities of ${E^1}_{2g}$ and ${A_{1g}}$ modes are perpendicular to each other, indicating that the polarizations of ${E^1}_{2g}$ and ${A_{1g}}$ modes are perpendicular to each other under the βY configuration.

The polarization properties of ${E^1}_{2g}$ and ${A_{1g}}$ modes are summarized as followed. In αY and αX polarization configurations, $I({{E^1}_{2g}} )$ and $I({{A_{1g}}} )$ change as the polarization angle of the incident laser changes. On the MoS₂ basal plane, the ${E^1}_{2g}$ mode is isotropic under both αY and αX polarizations, but the ${A_{1g}}$ mode is anisotropic with both αY and αX polarizations, which are perpendicular to each other. On the MoS₂ edge plane, the ${E^1}_{2g}$ mode is anisotropic with the αY polarization but zero with the αX polarization. The ${A_{1g}}$ mode is anisotropic with both αY and αX polarizations, which are perpendicular to each other. In βY and βX polarization configurations, $I({{E^1}_{2g}} )$ and $I({{A_{1g}}} )$ change as the polarization angle of both the incident laser and the scattered light change, equivalent to in-plane rotation of the sample [4]. On the MoS₂ basal plane, the ${E^1}_{2g}$ mode is isotropic under both βY and βX polarizations, and the ${A_{1g}}$ mode is also isotropic under both βY and βX polarizations but keeping a constant with the βY polarization and zero with the βX polarization. On the MoS₂ edge plane, both ${E^1}_{2g}$ and ${A_{1g}}$ modes are anisotropic which are perpendicular to each other under both βY and βX configurations.

In all, the ${E^1}_{2g}$ and ${A_{1g}}$ modes show different properties under different polarizations due to the Raman tensors and the atomic arrangements. On the MoS₂ basal plane, the ${E^1}_{2g}$ mode is isotropic under all polarizations, and the ${A_{1g}}$ mode is anisotropic with both αY and αX polarizations but isotropic under both βY and βX polarizations. The results mean that the ${E^1}_{2g}$ mode is independent of the polarization of the incident laser due to the symmetry of the Raman tensor on the MoS₂ basal plane and independent of the in-plane rotation of the sample due to the symmetry of the atomic arrangement on the MoS₂ basal plane. However, the ${A_{1g}}$ mode is independent of the in-plane rotation of the sample due to the symmetry of the atomic arrangement on the MoS₂ basal plane but dependent of the polarization of the incident laser as a polar vibration mode on the MoS₂ basal plane. On the MoS₂ edge plane, the properties of ${E^1}_{2g}$ and ${A_{1g}}$ modes are complicated because of the transformation of Raman tensors and atomic arrangements. The ${E^1}_{2g}$ mode is anisotropic with the αY polarization but zero with the αX polarization, which can be explained by the fact that the ${E^1}_{2g}$ mode vibrates within the plane of each layer. In addition, the polarization properties of ${E^1}_{2g}$ mode in MoS₂ is similar to G mode in HOPG. $I({{E^1}_{2g}} )$ reaches maximum when the laser polarization is parallel to the edge plane orientation, which is consistent with the conclusions obtained by Xuelu Liu [4] and can be used to determine the orientation of MoS₂ layers at its edge plane. The ${A_{1g}}$ mode is anisotropic with both αY and αX polarizations, which means that the ${A_{1g}}$ mode is also dependent of the polarization of the incident laser as a polar vibration mode on the MoS₂ edge plane. It means that the polarizations of ${A_{1g}}$ mode exist in x, y, and z directions and the direction of polarization of the scattered light is always the same as that of the incident light. Moreover, both ${E^1}_{2g}$ and ${A_{1g}}$ modes are anisotropic under both βY and βX configurations which reflect the asymmetry of the atomic arrangement on the MoS₂ edge plane. The polarizations of ${E^1}_{2g}$ and ${A_{1g}}$ modes are perpendicular to each other, which can be explained by the fact that the ${E^1}_{2g}$ mode vibrates perpendicular to the ${A_{1g}}$ mode.

4. Conclusions

In this paper, Raman intensities of ${E^1}_{2g}$ and ${A_{1g}}$ modes of the basal and edge plane of 2H-MoS₂ were measured under two ARP Raman configurations with four kinds of polarization: αY, αX, βY, and βX. By these four polarization configurations, we concluded that the ${E^1}_{2g}$ and ${A_{1g}}$ modes show different polarization properties on the MoS₂ basal and edge planes. The ${E^1}_{2g}$ mode is independent of the polarization of the incident laser and the in-plane rotation of the sample on the MoS₂ basal plane but dependent of the polarization of the incident laser and the in-plane rotation of the sample on the MoS₂ edge plane. The polarizations of ${A_{1g}}$ mode exist on two planes and the direction of polarization of the scattered light is always the same as that of the incident light. These results provide references for the study of other two-dimensional layered crystalline materials by ARP Raman spectroscopy.