Raman Spectra Shift of Few-Layer IV-VI 2D Materials

Raman spectroscopy is the most commonly used method to investigate structures of materials. Recently, few-layered IV-VI 2D materials (SnS, SnSe, GeS, and GeSe) have been found and ignited significant interest in electronic and optical applications. However, unlike few-layer graphene, in which its interlayer structures such as the number of its layers are confirmed through measurement of the Raman scattering, few-layer IV-VI 2D materials have not yet been developed to the point of understanding their interlayer structure. Here we performed first-principles calculations on Raman spectroscopy for few-layer IV-VI 2D materials. In addition to achieving consistent results with measurements of bulk structures, we revealed significant red and blue shifts of characteristic Raman modes up to 100 cm−1 associated with the layer number. These shifts of lattice vibrational modes originate from the change of the bond lengths between the metal atoms and chalcogen atoms through the change of the interlayer interactions. Particularly, our study shows weak covalent bonding between interlayers, making the evolution of Raman signals according to the thickness different from other vdW materials. Our results suggest a new way for obtaining information of layer structure of few-layer IV-VI 2D materials through Raman spectroscopy.

atomic layer deposition 18,51 , and spray pyrolysis 52 . Heterostructures with MX have also been studied as field-effect transistor device materials 48 .
However, like graphene and transition metal dichalcogenides, verifying the number of layers in few-layer MX structures is crucial when they are used as device materials. In stacking a layer, we average the length of all similar direction bonding. While MX has attracted great interest, verifying the number of layers of MX sample has not yet been sufficiently studied. For example, there has only been one case verifying the thickness of a sample using an electronic bandgap 10 ; that is a good method for figuring out the thickness. However, measuring a bandgap has too many more steps than Raman and can ruin an exfoliated crystal sample. Therefore, nondestructive Raman method might be the best method, but there are no relevant reference data. In this paper, we performed Raman simulation for MX as the number of layers varied from a monolayer to bulk in order to provide standard Raman spectroscopy data. We focus on SnS, SnSe, GeS, and GeSe as representative examples for MX. Our calculations show that the Raman spectroscopy for metal monochalcogenides depends on the number of layers. We found that the red shift and blue shift occur continuously as the number of layers increases by ~100 cm −1 . This can be explained by the fact that the shifts come from the change of the bond lengths between the metal atoms and chalcogen atoms by the change of the interlayer interaction, leading to the slight modification of a vibration mode. These results provide benchmarks for determining the number of layers of metal monochalcogenides by Raman spectroscopy analysis.
All of the calculations were carried out using density functional theory (DFT) and density functional perturbation theory (DFPT) 53 , as implemented in the PWSCF package of the QUANTUM-ESPRESSO 54 . The DFT is employed for the geometry optimization of the IV-VI layers, and the DFPT is employed for calculations of the Raman spectra, phonons, and dynamical matrices. We used norm conserved local density approximation (LDA) for pseudopotentials 55,56 , which gives consistent results with PBE-D3. The kinetic energy cutoff was taken to be 30 Ry. We use 9 × 9 × 3 and 9 × 9 × 1 k-point for the bulk and layered structures, respectively. Geometrical optimizations are performed for every single structure until the Hellman-Feynman force is below 10 −8 Ry/Bohr. All of our calculations were converged to ~10 −4 Ry/atom. Detail information for the optimization of the lattice vectors and the lattice constants is described in supporting information Figure S1, Figure S2, and Table S1.
We first performed calculations on the geometry optimizations for AB staked multilayered MXs (Fig. 1a) because it has been confirmed that, for MX bulks, AB stacked MX layers in bulks are the energetically most favorable configuration 57,58 . Figure 1 shows the optimized atomics structures of AB-stacked multilayer MX structures, where L 1 and L 2 denote the bonding lengths for out of plane and in-plane, respectively. The calculated values of the L 1 and L 2 and the interlayer distances for AB stacked MX multilayers are presented in Table 1, which are consistent with the values in the literature for a multi-layer 59 . For instance, L 1 and L 2 were calculated to be 2.56 and 2.70 Å for bilayer SnS, respectively. The bond lengths are increased as the atomic numbers of M and X increase. However, the interlayer distance, d is 2.64 Å (Supporting information Figure S3), slightly dependent on the type of MX layers, which corresponds to the equilibrium distance of ~3.4 Å via vdW interaction. Furthermore, the calculated values of L 1 , L 2 , and d as the number of layers varied from 1 to 3 are also presented in Table 1. We also carried out the calculations on the interlayer binding energy of bilayer and trilayer MXs in Table 2. For comparison, the interlayer binding energy and the interlayer distance were also calculated with other functional, i.e., meta-GGA 60 . The binding energy and the interlayer distance obtained with the LDA is slightly larger and smaller than those with the meta-GGA, respectively. We found that there are small changes in L 1 and L 2 as well as interlayer distance, similar to other 2D materials 12,61 .
We performed calculations on the Raman spectra of multilayer MX using DFPT calculation. In order to verify the computational accuracy of the DFPT, the calculated results were compared to the experimental data for AB stacked multilayer SnS 18 . We focused on the four characteristic peaks in the spectra of 53, 76, 104, and 244 cm −1 for monolayer SnS, because their Raman signals are remarkable and have been observed in experiments 18,62 . Remarkably, the calculated Raman spectra for SnS is strongly consistent with the experimental data ( Fig. 2) 18 . Thus, we believe that our calculations on the Raman spectra for other MX layers are reliable for predicting their properties. Moreover, it was verified that there is high accuracy in Raman simulations for monolayer using the ab initio method 63 .
We further analyzed the lattice vibrational modes of AB-stacked multilayer SnS corresponding to the characteristic Raman peaks in order to determine how the peaks are generated. We found that the phonon modes of  Table 1. Calculated local geometry information for AB stacked MX layers as the number of layers. Δ 1 (Δ 2 ) denotes L 1 (L 2 ) for a given layer minus L 1 (L 2 ) of monolayer presented in Fig. 1 Table 2. Calculated binding energy (E b ) between interlayers for few-layer MXs and interlayer distance (d).
The exchange-correlation functional is treated using LDA and strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation (meta-GGA).

Figure 2.
Calculated and experimental Raman spectroscopy for AB stacked multilayer SnS. The experimental data was in ref. 62 .  Fig. 3(e-h), respectively, are associated with the peaks for 91, 166, 196, and 221 cm −1 for multilayer SnS, respectively. Hereafter, we refer to the four peaks in the Raman spectra as B 1u , A g 2 , B 2g , and B 3g 2 , respectively. Monolayer SnS has the same phonon modes in Fig. 3(a-d). For the B 1u phonon mode, Sn atoms move out of plane and S atoms move in the oblique plane ( Fig. 3(a,e)). For the A g 2 phonon mode, Sn and S atoms move in the oblique plane ( Fig. 3(c,g)). For the B 2g , and B 3g 2 phonon modes, the Sn and S atoms move in the same plane in the opposite direction ( Fig. 3(b,d,f,h)). These modes can be approximately classified by atomic moving direction into three kinds: vertical of the MX plane, horizontal of the MX plane, and hybrid. B 2g is horizontal while B 3g 2 is vertical of the SnS plane. B 1u looks like a hybrid of the two. In A g 2 mode, atoms have a vibration in both directions, out of plane and in-plane. However, moving in out of plane appears to be negligible. Therefore, we can classify A g 2 as the horizontal mode. In order to investigate how the Raman spectra of few-layer MX materials depend on the number of layers, we performed calculations for few-layers MX as the number of layers varied. An attractive feature is that the Raman spectrum of SnS is dependent on the number of layers. For SnS, we found that B 1u , B 2g , and A g 2 are a blue shift by ~40 cm −1 , ~90 cm −1 , and ~92 cm −1 , respectively, while B 3g 2 are red shift by ~23 cm −1 . (Fig. 4(a)) Since Raman peaks are naturally split by stacking layers, we selected the most significant peak among several split peaks. If certain peaks are degenerate in the same position, the measured intensity is higher than that of the theoretical prediction. Increasing the number of layers yields a red shift for B 3g 2 and a blue shift for B 2g and A g 2 . These trends appear in all four MX except for B 1u . For the SnS and GeS layers, the B 1u mode shows a blue shift. For GeSe, the B 1u mode has a red shift trend, while it does not show any shift trend for SnSe. For other peaks, the changes appear to be sufficient to distinguish the number of layers of samples. On the other hand, the interaction addition as the number of layers is significant in a vertical direction compared with a horizontal direction because The thickness with respect to the vertical to the plane of MXs is increased as the number of their layers increases because L 1 increases as the number of layers increases (see Table 1). Therefore, the frequency shift in a complete vertical mode, i.e., B 3g 2 is more significant than that other modes as shown in Fig. 4. Moreover, we observe that the tendency depends on the direction of phonon mode, horizontal or vertical. In Fig. 5, the horizontal modes (such as B 2g ), in-plane modes, appear as the blue shift tendency, while the vertical modes (such as B 3g 2 ), out of plane modes, appear as the red shift trend when increasing the number of layers for SnS. This relation is consistent across the four kinds of MX.
We investigate what causes the difference between red and blue shift trends. In order to determine the blue and red shifts of the Raman spectroscopy, we investigated the local geometry of them with varying numbers of layers. The calculated values of the bond lengths (L 1 , L 2 ) between L 1 , L 2 , and interlayered distance as the number of layers varies are presented in Table 1. Importantly, we found that there is a small change of length for unit cell vectors, as in other 2D materials 12,61 . Further, there are certain changes of atomic bonding length from interlayer interactions. This can change the lattice vibration motion, which might be one of the causes of the shift tendency. We can understand that the change of bond lengths can be interpreted by the change of the spring constant using a simple harmonic approximation. Hence, when a bonding length is decreasing, a frequency is increased. This is the reason for why Raman shift frequency, a peak position, is changed according to the number of layers. According to the number of layers, the changes for L 1 and L 2 are shown in Table 1. With increasing the number of layers, L 1 , an average bond length of the vertical direction, is increasing, while L 2 , an average bond length of the horizontal direction, is decreasing. In other words, with increasing the number of layers, the vertical mode has a red shift and the horizontal mode has a blue shift. This relation holds for all our studied MXs.
In order to understand the origin of the bond lengths of few-layer MXs resulting in the shift of the phonon energy, we investigate the bond between layers. We found that this change of the lattice parameter via the interaction between layers stems from the weakly covalent bonding between interlayers, as shown in Fig. 6, where the charges transfer between interlayers. This differs from the bond between interlayer of few-layer vdW materials like graphene or MoS 2 . In addition, the binding energy of the layers is calculated to range from 0.2 eV to 0.5 eV, slightly dependent on the type of sheets (Table 2), which is greater than the value of a few ten meV in graphite and MoS 2 64-66 . This result is consistent with those of previous studies 67, 68 . Therefore, we believe that, because of the stronger interaction between layers than other vdW materials, the Raman shifts as the number of layers occur.   www.nature.com/scientificreports www.nature.com/scientificreports/ The relation between Raman shifts (Δv (cm −1 )) and the number of layers for MXs is shown in Fig. 4. We confirmed that this relationship remains very consistent for A g 2 , B 3g 2 , and B 2g . The data could almost be fitted linearly by a reciprocal number of layers as follows: where the subscript i indicates the index of phonon modes, a i and b i are fitting coefficients for a given i and N indicates the number of MX layers. The calculated coefficients for MX layers were calculated by a linear fitting (Supporting information Figure S1), which are presented in Table 3. The negative and positive values of a i mean red and blue shifts as N increases, respectively. This will be very beneficial in experiments to know the number of layers for a sample. Even though some shifts are of a small value per layer, like GeSe, modern Raman equipment has sufficient resolution (<1 cm −1 ) in room temperature to identify them 69 . In addition, for all examples, there are more than two rapid shift peaks, enough to identify thickness. The blue shift peaks, the horizontal modes, might be useful indicators for verifying the number of layers for almost MX. Another important point is that we propose a method of distinguishing the number of layers by comparing predicted Raman shift using Eq. (1) with experimental results of the Raman spectrum.
In conclusion, we have done the first-principles calculations for Raman spectroscopy based on the density functional theory. We found important things for a shift of the Raman peaks of metal monochalcogenide (MX), as its the number of layers. (1) Raman spectroscopy is considerably dependent upon the number of layers. (2) We have discovered the shifting or red trend of Raman peaks as the number of layers due to the change in atomic bonding length along with the direction of phonon. (3) We believe that our graphs for Raman peaks are useful benchmarks for identifying the number of layers of an arbitrary MX sample. Our results propose a method for distinguishing the number of layers in recently-reported few-layer MXs.    Table 3. Coefficients (a i , b i ) to Eq. (1) for each phonon mode. The unit of the values below is cm −1 .