Low-Frequency Raman Spectroscopy of Few-Layer 2H-SnS2

We investigated interlayer phonon modes of mechanically exfoliated few-layer 2H-SnS2 samples by using room temperature low-frequency micro-Raman spectroscopy. Raman measurements were performed using laser wavelengths of 441.6, 514.4, 532 and 632.8 nm with power below 100 μW and inside a vacuum chamber to avoid photo-oxidation. The intralayer Eg and A1g modes are observed at ~206 cm−1 and 314 cm−1, respectively, but the Eg mode is much weaker for all excitation energies. The A1g mode exhibits strong resonant enhancement for the 532 nm (2.33 eV) laser. In the low-frequency region, interlayer vibrational modes of shear and breathing modes are observed. These modes show characteristic dependence on the number of layers. The strengths of the interlayer interactions are estimated by fitting the interlayer mode frequencies using the linear chain model and are found to be 1.64 × 1019 N · m−3 and 5.03 × 1019 N · m−3 for the shear and breathing modes, respectively.


Introduction
Interest in two-dimensional (2D) materials such as hexagonal boron nitride (hBN), black phosphorus (BP) and transition-metal dichalcogenides (TMDs) since the discovery 1 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 limit [2][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 transistors [7][8] , fast photodetection 9 suitable for flexible photodetectors from UV to IR 10 , interesting gas sensing property 11 , and high optical absorption and photovoltaic activities 12 .
Although chemical vapor deposition 34 and molecular beam epitaxy 35 growths have been tried, large-area growth of few-layer SnS2 has not been realized yet.At the moment, mechanical exfoliation from bulk crystals yields the highest quality few-layer samples.Raman spectroscopy is one of the most widely used characterization tools for 2D layered materials to determine the number of layers as well as polytypes or strain effects.More importantly, one can use low-frequency Raman spectroscopy to study the interlayer interactions of few-layer materials by measuring the in-plane (shear) and out-of-plane (breathing) modes in the low-frequency region (<50 cm -1 ).In the literature, the measured data of the shear and breathing modes are used to estimate the interlayer spring constants of the studied materials such as MoS2 and WSe2 36 , MoSe2 37 , MoTe2 38 , WS2 39 , ReS(e)2 40 , Bi2Te3 and Bi2Se3 41 , black phosphorus 42 , and graphite [43][44] by fitting the experimental data to the linear chain model (LCM).Additionally, Luo et al. reported that the stacking sequence determines Raman intensities of observed interlayer shear modes 45 .However, experimental work on Raman properties of few-layer 2H-SnS2 remains lacking although results for less-common 4H-SnS2 have been reported 19 .The Raman spectrum of bulk 2H-SnS2 shows two phonon modes at 315 cm −1 ( 1g ) and 205.5 cm −1 ( g ), while that of 4H-SnS2 shows several more modes 26 .
This offers a clear distinction between 2H-and 4H-SnS2.For few-layer SnS2, Yuan et al. 19 recently reported a Raman study on mechanically-exfoliated monolayer and few-layer as well as bulk 4H-SnS2.Nevertheless, low-frequency shear and breathing modes are not considered, i.e., interlayer interactions of the material remains uncovered in the Raman studies of few-layer SnS2.In this work, we investigate the Raman spectra of mechanically-exfoliated few-layer 2H-SnS2 using four excitation energies.We also analyze the low-frequency Raman spectra to investigate the interlayer interaction in few-layer 2H-SnS2.and ~1.4 nm for 2L, which is reasonable as there usually is a small extra thickness for the first layer in AFM measurements of 2D materials.This is either due to trapping of absorbed H2O molecules between the 2H-SnS2 and the SiO2/Si substrate 19 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 fewlayer 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.mode at ~314 cm −1 is most prominent.The  g 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).

Results and Discussion
In the low-frequency region, the interlayer vibrational modes of in-plane shear (S) and out-ofplane breathing (B) modes are identified.Figure 2(b) shows the excitation energy dependence of the  1g mode for 1L to 14L 2H-SnS2.The 532 nm (2.33 eV) excitation laser provides the strongest intensity of the  1g 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 1L 16 .Figure 2(c) shows the dependence of the Raman spectrum on the number of layers.In addition to the  1g and  g modes, two other weak signals from  1u and  1g -LA (M) modes are observed for bulk or thick samples at ~353 cm −1 and ~140 cm −1 , respectively.The  1u mode is an infrared mode but appear probably due to activation by lattice disorders, whereas the two-phonon scattering [46][47] signal of  1g -LA (M) is weak due to the small scattering cross section.For 1L 2H-SnS2, there exist nine vibrational modes at the center of the Brillouin zone at the Γ point: Γ =  1g +  g + 2 2u + 2 u 20,26 .Among six optical phonon modes, there are three Raman active modes ( 1g and  g ) and three infrared-active modes ( 2u and  u ).The three acoustic modes belong to  2u and  u .The Raman scattering intensity is proportional to where  i represents the polarization vector of the incident light,  s that of the scattered light, and  ̃ the Raman tensor.The Raman tensors can be expressed as 48 , In the backscattering geometry with the laser propagating in the  direction, only the  g mode is observable in cross polarization, whereas both the  1g and  g 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  g and the breathing modes  1g .By using polarized Raman measurements, one can thus distinguish shear and breathing modes unequivocally.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 model 36,41,49 , assuming that only interactions between nearest-neighbor layers are important and by neglecting the substrate and surface effects, the angular frequency of the -th shear (breathing) mode in N-layer 2H-SnS2 is given by, where  = 2, 3, … ,  ( = 1 corresponds 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  = 2.63352 × 10 −26 kg • Å −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.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  1g (~314 cm −1 ) mode is most prominent, whereas in thick samples and bulk, the weak in-plane  g (~206 cm −1 ) mode as well as two additional modes such as  1g − LA(M) (~140 cm −1 ) and  1u (~353 cm −1 ) are resolved.The

Figures 1 (
Figures 1(b) and (c) show the optical and AFM images of a 2H-SnS2 sample, respectively.The

Figure 2 (
Figure 2(a) shows the low-and high-frequency Raman spectra of 5L 2H-SnS2 measured

Figure 2 (
d) shows the  g mode measured with the 441.6 nm excitation laser in cross polarization configuration since this excitation laser provided relatively stronger signals for the  g 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  1g 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 evolvesmonotonically with the number of layers up to ~11L.This mode also shows a slight blue-shift from 1L to 3L, which is in good agreement with recent theoretical results16 .

Figure 3 (
Figure 3(a) illustrates the polarization dependence of the Raman spectrum of 5L 2H-SnS2.

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 fewlayer 2H-SnS2.

2. 33
eV (532 nm) excitation laser provides the strongest Raman signals of intralayer  1g mode and interlayer shear and breathing modes, whereas the  g mode appears stronger for the 2.81 eV (441.6 nm) excitation.For the  1g 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.MethodsFew-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 photooxidation.AFM images [Supplementary Information Figure 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-coupledevice (CCD) detector.The spectral resolution was below 1 cm −1 .

Table 1 .
Force constants per unit area of 2H-SnS 2 obtained by fitting experimental data to the linear chain model and comparison with those of other TMD materials.