Tin sulfide (SnS) thin films have been reported to show strong layer number dependence on their ferroelectricity and Raman spectra. Identifying the number of layers and stacking structures is crucial for optoelectronic device fabrication. Here, we theoretically study the electronic and phononic properties of SnS thin films using first-principles calculations. We identify the characteristic Raman active phonon modes and their dependence on the number of layers and stacking sequences. The clear separation between surface modes and bulk modes is clarified for SnS thin films. In addition, we have clarified the relation between stacking structures and Raman active modes for bilayer SnS. Our results will serve the experimental characterization of such thin monochalcogenide systems through Raman spectra and will expedite their device fabrication.
Ferroelectric materials are the fundamental building blocks for the application of nonvolatile memory, sensor, and nonlinear optoelectronic devices.1–19 In order to create transparent and flexible devices, it is necessary to search materials that can retain their physical properties even when made into thin films.20–24 Recently, materials with ferroelectricity in the out-of-plane direction (MoTe2,1,25 WTe2,2,25 and CuInP2S63,11,12,14) and the in-plane/out-of-plane direction (α − In2Se34–9,13,26 and SnTe10) have been studied. The out-of-plane ferroelectric materials that constituted of a small number of layers lost their ferroelectricity due to metal/ferroelectric interfaces.8
Orthorhombic group-IV monochalcogenides have attracted much attention as two-dimensional (2D) ferroelectrics because of their pure in-plane ferroelectricity by breaking the spatial symmetry of the crystal and their strong spontaneous polarization.4,15,16,18,27–38 From the viewpoint of crystal stability, SnX is more stable than GeX.39 The bulk space group of group-IV monochalcogenides is Pnma (No. 62), but when the temperature is raised, it becomes CmCm (No. 63) and loses its ferroelectricity. The Curie temperature is higher in SnS than in SnSe.29
Recently, Higashitarumizu et al. reported that SnS can maintain the ferroelectricity in the in-plane direction even with a few thin layers due to the asymmetry in the crystal structure, unlike three-dimensional ferroelectric materials.18 However, the ferroelectricity of SnS crucially depends on the number of layers and stacking structures.18,40 For transparent and flexible electronic device fabrication, precise control over the number of layers is necessary. From an experimental point of view, Raman spectroscopy is a useful tool to analyze the number of layers and stacking geometry by precise detection of phonon vibration modes of samples. Therefore, proper understanding of the structure–property relationship in SnS necessitates the systematic and detailed investigation of phonon modes.
Here, we report on the electronic structures and phonon vibration modes of bulk and single- and multi-layered structures of SnS as obtained from the first-principles calculations. Since SnS thin films are semiconducting in nature, the HSE06 hybrid functional is used to evaluate the correct energy bandgaps. In addition, we identify the layer number dependence of Raman active and inactive modes (infrared active modes) by analyzing the phonon modes of SnS. Our results will serve as identification of the layer number for experimentally synthesized SnS films. In the supplementary material, the numerical data of phonon frequency for bulk and few-layer SnS are given.
We perform first-principles calculations based on density functional theory as implemented in the Vienna Ab initio Simulation Package (VASP)41 to perform structural optimization and to investigate the electronic states and phonon modes. The exchange-correlation energy is described by the generalized gradient approximation (GGA) using the Perdew–Burke–Ernzerhof (PBE) functional.42 The kinetic energy cut off is set at 500 eV. The Brillouin zone (BZ) is sampled using a Γ-centered 16 × 16 × 4 grid following the scheme proposed by Monkhorst–Pack. Structural optimization is performed self-consistently with an energy and force tolerance of 10−5 eV and 0.02 eV/Å, respectively. In addition, a hybrid functional approximation for the exchange-correlation term Heyd–Scuseria–Ernzerhof 2006 (HSE06)43 is employed in order to obtain reliable results for the energy bandgap. The phonon properties and determination of irreducible representations are investigated using the Phonopy code.44 The images of crystal structures are generated using VESTA.45 For few-layer systems, sufficiently large vacuum spaces are set in the non-periodic direction to eliminate the interlayer interaction. A DFT-D3 semiempirical dispersion correlation approach is adopted to consider the van der Waals interactions.46,47
III. BULK AND MONOLAYER STRUCTURES
SnS is a layered-material with an orthorhombic crystal structure and possesses two different structural phases called α and β′, as shown in Figs. 1(a) and 1(b), respectively.48 The difference between them is the stacking sequences. The unit cell of both phases contains four tin and sulfur atoms. The consecutive layers interact through van der Waals force. The space group of the α phase is Pnma (No. 62), while that of the β′-phase is Cmc21 (No. 36). Figure 1(c) shows the first Brillouin zone (BZ) of bulk SnS. The energy band structures of α and β′ phases are shown in Figs. 1(d) and 1(e), respectively. Both of them exhibit semiconducting behavior with an indirect bandgap. The top of the valence band and the bottom of the conduction band for the α (β′) phase are located at high-symmetric points, X (the midpoint of the X − Γ line) and Y (Γ), respectively.
Both of these bulk phases are thermodynamically stable, with the α phase having slightly lower energy and hence higher stability than the β′ phase, as shown in Table I. The energy bandgaps of α and β′ phases are 1.33 and 1.09 eV, respectively. These results are consistent with those of the preceding report.49 In most of the experiments, the bandgap of bulk SnS has been found to be in the range of 1.20–1.37 eV.51–53 Since the structure of the β′ phase arises due to the structural phase transition caused by either the application of an electric field or the increase in temperature, it can be inferred that the samples in most of the experiments are in the α phase. Therefore, we mainly focus on the stacking sequences of the α phase type in this study.
|.||a (Å) .||b (Å) .||c (Å) .||ET (eV) .||Eg (eV) .||d1 (Å) .||d2 (Å) .|
|.||a (Å) .||b (Å) .||c (Å) .||ET (eV) .||Eg (eV) .||d1 (Å) .||d2 (Å) .|
Furthermore, we explore the electronic structure of single-layer SnS. The single-layer of SnS belongs to the space group of Pmn21 (No. 31) and shows indirect gap semiconducting behavior. The lattice constants are a = 4.26 and b = 4.05 Å, which are larger than those of the α phase of bulk SnS. Figure 1(f) shows the energy band structure of monolayer SnS. The bandgap is 2.15 eV, which is also larger than the bandgap of the α and β′ phases of bulk SnS.
Figure 1(g) shows the calculated phonon frequency for the α and β′ phases of bulk SnS. Numerical data are given in Table S1 in the supplementary material. In the frequency region from 100 to 300 cm−1, the frequency of in-plane vibration modes of the β′ phase becomes lower than that of the α phase. On the other hand, the frequency of out-of-plane vibration modes of the β′ phase becomes higher than that of the α phase. This frequency shift can be attributed to the difference in bond lengths between two phases. As shown in Table I, the bond length between S and Sn atoms in the in-plane direction (d1) is 2.680 Å in the α-phase and 2.728 Å in the β′ phase. Since d1 of the α phase is smaller than that of the β′ phase, the frequencies of in-plane vibration modes shift toward higher values in the α phase. The result of phonon frequency for the bulk α phase is consistent with that of the preceding report.54
On the contrary, the bond length between S and Sn atoms in the out-of-plane direction (d2) is 2.646 Å in the α phase and 2.612 Å in the β′ phase (see Table I). Since d2 of the α phase is longer than that of the β′ phase, the frequencies of out-of-plane vibration modes for the β′ phase shift toward higher values than those for the α phase.
IV. FEW-LAYER STRUCTURE
Next, we investigate the electronic states and phonon modes of few-layer SnS. The space group for 2, 6, 10, and 14 layers is P21/m (No. 11), while that for 3, 4, and 5 layers is Pm (No. 6). In general, the systems with 4n − 2 layers (n = 1, 2, 3, …) belong to the P21/m (No. 11) space group; otherwise, they belong to Pm (No. 6). We investigate the lattice parameters and the energy bandgaps for few-layer SnS systems by varying the layer number up to 10 and present the results in Table S2 in the supplementary material.
Figure 2(a) shows the layer number (N) dependence of phonon frequency in the range 265–290 cm−1. The precise numerical data and corresponding irreducible representations are given in Table S3 in the supplementary material. Although the increase in layer numbers produces more number of phonon modes, there is a characteristic phonon mode specific to the few-layer SnS system. This phonon mode is the surface phonon mode, which is marked as ▴ in Fig. 2(a). As indicated by the red dashed line in Fig. 2(a), the surface phonon mode shifts toward lower frequency with an increase in the number of layers and converges around 282 cm−1. Figures 2(b) and 2(c) show this surface phonon mode profile for N = 4 and 5, respectively. It is clearly seen that only the out-of-plane vibrations in the outermost layers give rise to this surface phonon mode. The shift in this phonon mode toward lower frequency with increasing N can be attributed to the increase in the vertical bond length d2 between S and Sn atoms of surface layers (). The corresponding numerical values are presented in Table S2 in the supplementary material.
The phonon modes below 280 cm−1 arise from the bulk vibrations. The highest frequency bulk phonon modes are marked by ▾ in Fig. 2(a), and the corresponding vibration modes for N = 4 and 5 are presented in Figs. 2(d) and 2(e), respectively. In these modes, the surface layers do not vibrate and behave as nodal layers. However, the S and Sn atoms show out-of-phase vibration in the layers that are sandwiched between two surface layers in either of the boundaries. The amplitudes of vibrations become maximum at the middle layer. The highest bulk phonon mode exhibits the global minimum at N = 4 and converges to 277 cm−1 as we increase the number of layers.
These observations indicate that the number of layers of the SnS system can be identified by analyzing the out-of-plane surface and bulk vibration modes in the range 265–290 cm−1.
V. BILAYER STRUCTURE
Next, let us focus on the phonic properties of bilayer SnS. Bilayer SnS has five different stacking types—AA, AB, AC, AD, and AE—as shown in Figs. 3(a)–3(e), respectively. The lower panels of Figs. 3(a)–3(e) show the corresponding energy band structures of bilayer SnS. Calculated numerical data for structural parameters and energy gaps of bilayer SnS can be found in Table S4 in the supplementary material. The AB stacking has the same structure of the minimum unit of the bulk α phase. Each structure has a different space group, i.e., AA is Pmn21 (No. 31), AB is P21/m (No. 11), AC is Pmm2 (No. 25), AD is Pm (No. 6), and AE stacking is Pma2 (No. 28). The side views of AA and AC stackings show close resemblance as it is in the case of AD and AE stackings. Similarly, the pairs of AA and AD and of AC and AE stackings appear to be same from their top views. However, all these stacking geometries are distinct from each other.
Figure 3(f) shows the phonon frequency for bilayer SnS. The numerical data can be found in Table S5 in the supplementary material. It can be seen that AA, AD, and AE stackings have large negative frequencies of about −50 cm−1. Thus, these stackings have lower stability. The in-plane phonon modes for AA- and AC-stacking appear above 180 cm−1, whereas in the case of AD- and AE-stacking, they appear in lower frequencies. Therefore, by analyzing the in-plane vibration modes in the range of 150–200 cm−1, it is possible to distinguish between the stacking sequences with similar top views.
As for the out-of-plane modes, AC and AE stackings show doubly degenerate modes in the region of 200–250 cm−1, while these degeneracies are lifted in AA and AD stackings. Therefore, the stacking sequences with indistinguishable side views can be identified precisely by analyzing the out-of-plane vibration modes in the range of 200–250 cm−1.
Furthermore, the AB-stacking can be identified by the appearance of in-plane vibration modes above 200 cm−1 and the appearance of only one out-of-plane vibration mode below 250 cm−1. All these observations clearly indicate that the stacking structures of the bilayer SnS system can be identified by analyzing the in-plane and out-of-plane phonon modes existing in the range 150–250 cm−1.
In summary, we have studied the electronic and phononic properties of bulk and few-layer SnS, especially focusing on the layer number dependence of Raman active modes. As for bulk SnS, it is found that α and β′ phases have different frequency shifts due to the different bond lengths between S and Sn atoms. The few-layer structures show strong layer number dependence of phonon mode frequencies. The out-of-plane vibration modes in the range of 265–290 cm−1 are split into surface and bulk modes with the increase in the layer number. Our study can guide in identifying the number of layers by analyzing the positions of the surface and bulk phonon modes. Our further exploration of the bilayer SnS system with varying stacking sequences can help distinguish the closely resembling side view and top view geometries. Our results will serve to identify the layer numbers and stacking sequences of experimentally synthesized SnS thin films by comparing with Raman spectroscopy, thereby facilitating the device engineering based on this unique ferroelectric material.
See the supplementary material for the detailed calculated data.
K.N. acknowledges the financial support by JSPS KAKENHI (Grant Nos. 19H00755 and 19K21956). K.W. acknowledges the financial support by JSPS KAKENHI (Grant Nos. JP21H01019 and JP18H01154) and JST CREST (Grant No. JPMJCR19T1). K.W. and S.D. acknowledge the financial support through the individual special research fund and the international collaboration fund from Kwansei Gakuin University.
The data that support the findings of this study are available from the corresponding author upon reasonable request.