Introduction

Interest in two-dimensional (2D) materials such as hexagonal boron nitride (hBN), black phosphorus (BP) and transition-metal dichalcogenides (TMDs) since the discovery1 of graphene in 2004 has significantly increased due to their unique structures and properties. Most TMD materials such as MoS(e)2 and WS(e)2 are indirect band gap semiconductors with band gap energies in the visible range but become direct in the monolayer limit2,3,4,5,6. Recently, tin disulfide (SnS2) has attracted much interest because it is recognized as earth-abundant, relatively cheap and low-toxic material. Additionally, it has been shown to have high on/off current ratios for field effect transistors7,8, fast photodetection9 suitable for flexible photodetectors from UV to IR10, interesting gas sensing property11, and high optical absorption and photovoltaic activities19 or imperfect adhesion of the sample on the substrate. We measured multiple sets of samples with thicknesses ranging from 1L to 14L and bulk. It is worth mentioning that no sign of degradation was observed after our few-layer 2H-SnS2 samples had been left in ambient condition for several weeks, but AFM measurements performed few hours after being exposed to the laser beam in the Raman measurements in ambient air showed degradation caused by photo-oxidation (see Supplementary Information). We therefore carried out all Raman measurements with the sample kept inside a vacuum chamber.

Figure 2(a) shows the low- and high-frequency Raman spectra of 5L 2H-SnS2 measured with four excitation energies. Vertical dashed-lines are guides for the eye. It is seen that the Raman signals are strongest for the 2.33 eV (532 nm) excitation laser. The out-of-plane A1g mode at ~314 cm−1 is most prominent. The Eg mode at ~206 cm−1 is extremely weak and is barely resolved only in the spectrum taken with the excitation energy of 2.81 eV (441.6 nm). In the low-frequency region, the interlayer vibrational modes of in-plane shear (S) and out-of-plane breathing (B) modes are identified. Figure 2(b) shows the excitation energy dependence of the A1g mode for 1L to 14L 2H-SnS2. The 532 nm (2.33 eV) excitation laser provides the strongest intensity of the A1g mode, which implies that the band gap of few-layer 2H-SnS2 may be smaller than the recent theoretical prediction of 2.41 eV for 1L16. Figure 2(c) shows the dependence of the Raman spectrum on the number of layers. In addition to the A1g and Eg modes, two other weak signals from A1u and A1g-LA (M) modes are observed for bulk or thick samples at ~353 cm−1 and ~140 cm−1, respectively. The A1u mode is an infrared mode but appear probably due to activation by lattice disorders, whereas the two-phonon scattering46,47 signal of A1g-LA (M) is weak due to the small scattering cross section. Figure 2(d) shows the Eg mode measured with the 441.6 nm excitation laser in cross polarization configuration since this excitation laser provided relatively stronger signals for the Eg mode. No clear shift is observed as the thickness increases. Figure 2(e) indicates the evolution of the Raman intensity and the peak position of the A1g mode as a function of the number of layers. The error bars indicate the spectral resolution of the setup. The intensity of the A1g mode evolves monotonically with the number of layers up to ~1 1L. This mode also shows a slight blue-shift from 1L to 3L, which is in good agreement with recent theoretical results16.

Figure 2
figure 2

Raman spectra of few-layer 2H-SnS2. (a) Low- and high-frequency modes of 5L 2H-SnS2 measured with 441.6, 514.4, 532 and 632.8 nm lasers. (b) Excitation-energy dependence of the intensity of the A1g mode for 1L to 14L. (c) High-frequency modes of few-layer 2H-SnS2 measured by using the 532 nm laser in parallel polarization configuration. The Raman intensity of A1g mode in bulk layer is multiplied by 1/4. Inset shows the A1g-LA (M), Eg, and A1u modes of bulk 2H-SnS2. (d) The Eg mode measured by using the 441.6 nm laser in cross polarization configuration. (e) Evolution of the Raman intensity and peak positions of the A1g mode as a function of number of layers. The error bars indicate the spectral resolution of the setup.

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For 1L 2H-SnS2, there exist nine vibrational modes at the center of the Brillouin zone at the Γ point: Γ = A1g + Eg + 2A2u + 2Eu20,26. Among six optical phonon modes, there are three Raman active modes (A1g and Eg) and three infrared-active modes (A2u and Eu). The three acoustic modes belong to A2u and Eu. The Raman scattering intensity is proportional to \(|{e}_{{\rm{i}}}\cdot \tilde{R}\cdot {e}_{{\rm{s}}}|\), where ei represents the polarization vector of the incident light, es that of the scattered light, and \(\tilde{R}\) the Raman tensor. The Raman tensors can be expressed as48,

$${A}_{1{\rm{g}}}=(\begin{array}{ccc}a & 0 & 0\\ 0 & a & 0\\ 0 & 0 & b\end{array})\,{\rm{a}}{\rm{n}}{\rm{d}}\,{E}_{{\rm{g}}}=(\begin{array}{ccc}c & 0 & 0\\ 0 & -c & d\\ 0 & d & 0\end{array}),\,(\begin{array}{ccc}0 & -c & -d\\ -c & 0 & 0\\ -d & 0 & 0\end{array})$$
(1)

In the backscattering geometry with the laser propagating in the z direction, only the Eg mode is observable in cross polarization, whereas both the A1g and Eg modes can be observed in parallel polarization configuration. For the low-frequency interlayer modes that exist in 2L or thicker 2H-SnS2, the shear modes correspond to Eg and the breathing modes A1g. By using polarized Raman measurements, one can thus distinguish shear and breathing modes unequivocally.

Figure 3(a) illustrates the polarization dependence of the Raman spectrum of 5L 2H-SnS2. As a function of the relative scattering polarization angle with respect to the incident polarization direction, the intensities of the intralayer A1g mode and the interlayer breathing modes are modulated, whereas the intralayer Eg mode and the interlayer shear modes are independent of the scattering polarization, which is consistent with the Raman tensor analysis above. Figure 3(b) illustrates the vibrations of in-plane shear and out-of-plane breathing. The evolution of the low-frequency interlayer vibrational modes as a function of the number of layers is shown in Fig. 3(c–e). The shear and breathing modes can be distinguished by using polarized Raman measurements as explained before. Figure 3(c) shows the shear modes measured in cross polarization, in which the breathing modes are suppressed. Up to 2 shear modes (S1 and S2) are identified, and their positions depend sensitively on the number of layers. Figure 3(d) shows similar spectra measured in parallel polarization. Here, both the shear and breathing modes are observed. By comparing with Fig. 3(c), one can unambiguously identify the breathing modes (B1 and B2). Figure 2(e) summarizes the evolution of the interlayer vibrational modes as a function of the number of layers. Since the high-frequency intralayer modes show little dependence on the number of layers beyond 3L, low-frequency Raman analysis would be the most reliable method to determine the number of layers of few-layer 2H-SnS2.

Figure 3
figure 3

(a) Scattering angle dependence of the Raman spectra of 5L 2H-SnS2 measured by using 2.33 eV (532 nm) excitation laser. Labels S (shear) and B (breathing) indicate the positions of shear and breathing modes resolved in 5L 2H-SnS2, respectively. (b) Schematics of interlayer in-plane shear and out-of-plane breathing modes. (c) Shear modes measured in cross polarization. (d) Shear and breathing modes measured in parallel polarization. The dashed curves are guides for the eye. (e) Peak positions as a function of number of layers. Solid curves are fitting results using the linear chain model.

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As the low-frequency interlayer modes reflect the strength of the interlayer interaction, one can estimate the interlayer spring constants in the in-plane and out-of-plane directions by analyzing the frequencies of the shear and breathing modes, respectively. In the linear chain model36,41,49, assuming that only interactions between nearest-neighbor layers are important and by neglecting the substrate and surface effects, the angular frequency of the α-th shear (breathing) mode in N-layer 2H-SnS2 is given by,

$${\omega }_{\alpha }=\frac{1}{\pi c}\sqrt{\frac{K}{2\mu }[1-\cos \,(\frac{(\alpha -1)\pi }{N})]},$$
(2)

where α = 2, 3, …, N (α = 1corresponds to the zero-frequency acoustic mode at Γ point in the Brillouin zone), c is the speed of light in vacuum, K is the in-plane (out-of-plane) force constant, and \(\mu =2.63352\,\times \,{10}^{-26}\,{\rm{kg}}\cdot {{\rm{\AA }}}^{-2}\) is the mass per unit area of monolayer of 2H-SnS2. The in-plane (K = KS) and out-of-plane (K = KB) force constants per unit area can then be obtained by fitting the experimentally obtained peak frequencies of the shear and breathing modes, respectively, to equation (2). Table 1 compares the force constants per unit area of 2H-SnS2 thus obtained with those of other layered materials found in the literature. The interlayer interaction in 2H-SnS2 is significantly weaker than in most materials compared.

Table 1 Force constants per unit area of 2H-SnS2 obtained by fitting experimental data to the linear chain model and comparison with those of other TMD materials.
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In summary, we investigated lattice dynamics of mechanically-exfoliated few-layer 2H-SnS2 by room temperature low-frequency micro-Raman spectroscopy using four different excitation energies. In monolayer, the intralayer out-of-plane A1g (~314 cm−1) mode is most prominent, whereas in thick samples and bulk, the weak in-plane Eg (~206 cm−1) mode as well as two additional modes such as A1g − LA (M) (~140 cm−1) and A1u (~353 cm−1) are resolved. The 2.33 eV (532 nm) excitation laser provides the strongest Raman signals of intralayer A1g mode and interlayer shear and breathing modes, whereas the Eg mode appears stronger for the 2.81 eV (441.6 nm) excitation. For the A1g mode, the Raman shift is slightly sensitive to thickness for 1L-3L, but not for thicker material. The shear and breathing modes show strong dependence on the thickness, which provides a robust criterion for determination of the thickness using Raman spectroscopy. The interlayer interactions obtained by analyzing the interlayer vibrational modes are weaker than in most other layered materials. These results provide valuable information on materials parameters for device designs using few-layer 2H-SnS2.

Methods

Few-layer 2H-SnS2 samples were prepared from a SnS2 single-crystal (HQ Graphene) onto SiO2/Si substrates with 280 nm-thick oxide layer by mechanical exfoliation. The thickness of the samples was determined by atomic force microscope (AFM) and further confirmed by Raman measurements. The AFM measurements were performed by using a commercial AFM system (NT-MDT NTEGRA Spectra). Room temperature micro-Raman spectroscopy was conducted in backscattering geometry using four different excitation energies: the 441.6 nm (2.81 eV) line of a He-Cd laser, the 514.4 nm (2.41 eV) line of a diode-pumped laser (Cobolt), the 532 nm (2.33 eV) line of a diode-pumped solid-state (DPSS) laser, and the 632.8 nm (1.96 eV) line of a He-Ne laser. The input laser beam was focused onto the samples by a 40× microscope objective lens (0.6 NA), and the scattered light was collected and collimated by the same objective lens. The laser of power below 100 μW was used. All measurements were performed with the sample in a vacuum chamber to prevent photo-oxidation. AFM images [Supplementary Information Fig. S1] taken after Raman measurements confirmed that there were no apparent damages. Volume holographic filters (Ondax and OptiGrate) were used to access the low-frequency range below 50 cm−1. The Raman scattering signals were dispersed by a Jobin-Yvon iHR550 spectrometer with a 2400 grooves/mm grating (400 nm blaze) and detected by a liquid-nitrogen-cooled back-illuminated charged-couple-device (CCD) detector. The spectral resolution was below 1 cm−1.