#
Broadband Optical Constants and Nonlinear Properties of SnS_{2} and SnSe_{2}

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## Abstract

**:**

_{2}and SnSe

_{2}have recently been shown to have a wide range of applications in photonic and optoelectronic devices. However, because of incomplete knowledge about their optical characteristics, the use of SnS

_{2}and SnSe

_{2}in optical engineering remains challenging. Here, we addressed this problem by establishing SnS

_{2}and SnSe

_{2}linear and nonlinear optical properties in the broad (300–3300 nm) spectral range. Coupled with the first-principle calculations, our experimental study unveiled the full dielectric tensor of SnS

_{2}and SnSe

_{2}. Furthermore, we established that SnS

_{2}is a promising material for visible high refractive index nanophotonics. Meanwhile, SnSe

_{2}demonstrates a stronger nonlinear response compared with SnS

_{2}. Our results create a solid ground for current and next-generation SnS

_{2}- and SnSe

_{2}-based devices.

## 1. Introduction

_{2}[17], and hBN [18] have received the most attention, as they were the first [19,20,21] to catch researchers’ interest during the “two-dimensional” revolution [22] in material science. However, the number of known layered materials has increased exponentially over the last decade, with more than 1000 layered compounds being isolated and identified [23]. As a result, their properties are largely unexplored, which considerably impedes their application. In particular, the optical properties of tin-based dichalcogenides SnS

_{2}and SnSe

_{2}[24,25] are mostly unknown, with rare reports [26,27,28,29,30] on their absorption properties. Nonetheless, SnS

_{2}and SnSe

_{2}have already demonstrated their huge potential in optoelectronic applications, such as field-effect transistors [31,32,33], solar cells [34,35], saturable absorbers [36,37,38], photonic crystals [39,40], and photodetectors [41,42]. Hence, broadband linear and nonlinear optical properties are highly desired for the acceleration of the development of SnS

_{2}and SnSe

_{2}-based devices.

_{2}and SnSe

_{2}. Using spectroscopic ellipsometry and first-principle calculations, we determine the full broadband dielectric tensor of SnS

_{2}and SnSe

_{2}from ultraviolet to mid-infrared wavelengths (300–3300 nm). The results demonstrate a high dielectric response (n > 3) with zero losses in a wide spectral range: 560–3300 nm for SnS

_{2}and 1300–3300 nm for SnSe

_{2}. Moreover, we measured the second-order nonlinear optical susceptibility of SnS

_{2}and SnSe

_{2}at wavelengths ranging from 750 to 1050 nm. Finally, our results revealed that SnS

_{2}is a high refractive index material, which fills the important gap in the visible spectrum between bandgap energies of GaP and TiO

_{2}, which makes SnS

_{2}a promising material for all-dielectric nanophotonics.

## 2. Results and Discussion

#### 2.1. Surface and Structural Morphology Study

_{2}and SnSe

_{2}were synthesized by the chemical vapor deposition (CVD) method and transferred on a quartz substrate. Figure 1a schematically illustrates the crystal structure of 1T-SnS

_{2}or SnSe

_{2}viewed along c- axis and the a-axis. This crystal configuration is the most common atoms’ arrangement for SnS

_{2}and SnSe

_{2}, where layers stack directly above one another [43,44]. Optical microscopy photographs in Figure 1b,f show the uniform substrate’s coverage of synthesized SnS

_{2}and SnSe

_{2}films. Likewise, scanning electron microscopy (SEM) images in Figure 1c,g confirm the films’ full-area coverage and homogeneity at the microscale. In addition, we checked the films’ surface by atomic force microscopy (AFM), demonstrating an atomically smooth surface with root mean square (RMS) roughness of less than 1.6 nm and 0.5 nm for SnS

_{2}and SnSe

_{2}, respectively. Ultimately, we accurately measured the films’ thickness via AFM topographical scans (Figure 1e,i). They yielded 20.0 ± 1.8 nm and 6.5 ± 0.7 nm thicknesses for SnS

_{2}and SnSe

_{2}films, correspondingly.

#### 2.2. Analysis of the Crystal Structure and Raman Characterization

_{2}and SnSe

_{2}exist in several phase modifications [45,46], including 1T, 2H, 4H, and 18R polytypes. To identify the phase of our samples, we performed X-ray diffraction (XRD), whose spectra are displayed in Figure 2a,b. According to the Joint Committee on Powder Diffraction Standards (card No. 23-0677 and 89-2939) and previous publications [27,47,48], the obtained XRD patterns reveal the hexagonal lattice configuration, which could be 1T or 2H, for SnS

_{2}and SnSe

_{2}with lattice parameters a = b = 3.6486 Å and c = 5.8992 Å for SnS

_{2}and a = b = 3.811 Å and c = 6.137 Å for SnSe

_{2}.

_{2}reveals out-of-plane vibration mode A

_{1g}at ~314 cm

^{−1}and in-plane vibration of E

_{g}at ~205 cm

^{−1}, corresponding to 1T polytype [44,49,50]. Similar to SnS

_{2}, SnSe

_{2}Raman spectrum has two characteristic phonon modes: A

_{1g}mode at ~185 cm

^{−1}and E

_{g}mode at ~116.5 cm

^{−1}, associated with 1T-phase [36,51]. Moreover, Raman spectra at numerous locations of our samples demonstrate the same A

_{1g}and E

_{g}peak positions, additionally validating the homogeneity of the studied SnS

_{2}and SnSe

_{2}thin films.

#### 2.3. Optical Properties of SnS_{2} and SnSe_{2} Films

_{2}and SnSe

_{2}films through spectroscopic ellipsometry. We employed a two-layer optical model for ellipsometry data analysis: quartz substrate with SnS

_{2}or SnSe

_{2}film with the thickness determined from AFM (Figure 3e,i). Similar to other TMDCs [52,53], we describe SnS

_{2}and SnSe

_{2}dielectric function by the Tauc–Lorentz oscillator model (see Methods) [54,55]. Figure 3a,b shows the resulting optical constants n and k for SnS

_{2}and SnSe

_{2}films. Interestingly, we did not observe excitons for SnS

_{2}and SnSe

_{2}, which can be explained by their indirect bandgap, in contrast, to the direct bandgap in MoS

_{2}and WS

_{2}[56,57]. Apart from the dielectric function, Tauc–Lorentz oscillator parameters allow us to obtain the positions of critical points of joint density of states: 3.91 eV (317 nm) for SnS

_{2}; 2.87 eV (432 nm) and 3.98 eV (311 nm) for SnSe

_{2}. Furthermore, SnS

_{2}and SnSe

_{2}both have zero absorption (k ~ 0) at a broad wavelength range, starting from 560 and 1300 nm (Figure 3a,b), respectively. For reference, we also plotted in Figure 3a,b refractive indices and bandgap transitions of SnS

_{2}and SnSe

_{2}, determined by Domingo and coworkers [26]. As expected, the fundamental absorption edge coincides with the forbidden indirect transitions (Figure 3a,b), supporting our results in Figure 3a,b. For additional verification, we also measured the transmittance spectra of our samples (Figure 3c,d) and compared them with the transfer matrix calculations [58], based on optical constants from Figure 3a,b. Evidently, calculated and measured transmittance agree well, thereby validating our n and k in Figure 3a,b.

_{ab}and k

_{ab}) and c-axis (n

_{c}and k

_{c}). The first-principle calculations reproduce the shape of the experimental dielectric function and render the major optical features: a wide zero-absorption spectral range and high dielectric response. However, first-principle calculations overestimate values of dielectric function since the computations were performed assuming the ideal crystalline structure, whereas the studied CVD-grown films have a polycrystalline structure. Nevertheless, first-principle calculations provide access to the full dielectric permittivity tensor, allowing us to estimate the anisotropic optical properties, which are the most noticeable for SnS

_{2}with birefringence Δn = n

_{ab}− n

_{c}≈ 0.3 and almost negligible for SnSe

_{2}. In contrast, ellipsometry is nearly insensitive to optical constants along the c-axis, as explained by Ermolaev and colleagues [56,59]. Thus, our computations reveal for the first time the optical anisotropy in SnS

_{2}and SnSe

_{2}, which could be relevant in next-generation anisotropic nanophotonics [60].

_{2}and SnSe

_{2}[36,37,61], we also measured their nonlinear optical response (Figure 5). Specifically, we measured the second harmonic generation (SHG) in transmission geometry using 150 fs laser pulses focused into a 50 µm spot in diameter (see Methods). Figure 5a shows the SHG power dependence with the expected slope of 2 (2.01 ± 0.02 for SnS

_{2}and 2.02 ± 0.04 for SnSe

_{2}), confirming the second-order nonlinear process and the absence of saturation effects. SHG spectra of SnS

_{2}and SnSe

_{2}are shown in Figure 5b. For SnSe

_{2}, SHG resonance is at 415 nm (2.98 eV), associated with the 2 photon direct transition at the critical point (2.87 eV) found above from ellipsometry measurements. The presence of SH signal at large pump wavelengths indicates the contribution of direct transitions with lower energies, meaning that the direct transition of SnSe

_{2}is less than 2.36 eV. In contrast, for SnS

_{2}, the SH signal is negligible at large wavelengths. Therefore, the SHG resonance observed at the SH wavelength of 420 nm (2.95 eV) can be associated with the lowest energy direct transition of SnS

_{2}in agreement with Domingo and colleagues’ work [26].

_{2}and from 450 to 600 nm for SnSe

_{2}), which significantly exceeds the thickness of the films (Figure 1e,f). Thus, we can assume that the SHG is phase-matched and, hence, ${\mathrm{sin}\mathrm{c}}^{2}\left(\mathsf{\Delta}kL/2\right)=1$. It allows us to evaluate SnS

_{2}and SnSe

_{2}nonlinear optical susceptibility, displayed in Figure 5c.

_{2}is a promising material for all-dielectric nanophotonics [63,64], demanding a high refractive index and low absorption. As shown in Figure 6, SnS

_{2}meets both requirements since it possesses a refractive index n ≈ 2.8 and zero extinction in the visible and infrared ranges. More importantly, SnS

_{2}could even compete with classical high refractive index materials such as Si, GaP, and TiO

_{2}[65,66,67,68]. In particular, SnS

_{2}has a wider transparency region compared with GaP and Si and a larger refractive index than TiO

_{2}(Figure 6). More surprisingly, when we use the refractive index from first-principle calculations (Figure 4a) for monocrystalline SnS

_{2}, it perfectly fits into the correlation line between the refractive indices and optical bandgaps of high refractive index materials (Figure 6c). Therefore, SnS

_{2}enables the essential spectral range of all-dielectric nanophotonics between GaP and TiO

_{2}.

## 3. Materials and Methods

#### 3.1. Materials

_{2}and SnSe

_{2}samples of thin films were purchased from 2d Semiconductors Inc. (2d Semiconductors Inc., Scottsdale, AZ, USA). The samples with an area of 1 × 1 cm

^{2}were grown by CVD on sapphire substrates and subsequently transferred on quartz substrates.

#### 3.2. Surface Morphology Characterization

_{2}and SnSe

_{2}thin films was analysed by an optical microscope (Nikon LV150, Tokyo, Japan) with a digital camera DS-Fi3, as well as the scanning electron microscope (SEM) using the acceleration voltage of 30 kV and different magnifications (JEOL JSM-7001F, Tokyo, Japan) to prove films homogeneity. The film surface morphology was studied by atomic force microscopy (AFM, notegra, Nt-MDT Spectrum Instruments, Moscow, Russia) in semi-contact mode using a silicon tip with a radius <10 nm and resonance frequency of ~250 kHz (HA_NC Etalon, Tipsnano, Tallinn, Estonia) to determine surface roughnesses and films thicknesses.

#### 3.3. Crystal Structure Characterization

_{α1}radiation line (λ = 1.54 Å) to analyze the crystal structure of the films using a regime of 2θ-scan with angles range of 5°–75° with a step of 0.05° and accumulation time of 2 s.

#### 3.4. Raman Characterization

^{−1}. The spectra were recorded with 3.5 mW incident laser power, with an integration time of 10 s and 10 spectra accumulation.

#### 3.5. Ellipsometry Analysis

_{2}and SnSe

_{2}were measured using a variable-angle spectroscopic ellipsometer (VASE, J.A. Woollam Co., Lincoln, NE, USA), working at room temperature, at variable incidence angles 30°–75° with a step of 5° and wide spectral range from 300 to 3300 nm with a step of 1 nm, having the spotlight of size ~1 mm around the center of the sample, utilizing the high precision optical alignment. To fit the measured ellipsometric parameters Ψ and Δ, we used the Tauc–Lorentz oscillator model was used, defined by the following formula:

_{2}, we used one Tauc–Lorentz oscillator with the following parameters: $A=$ 54.613 eV; $C=$ 1.626 eV; ${E}_{0}=$ 3.911 eV; ${E}_{g}=$ 1.970 eV and ${\epsilon}_{\infty}=$ 5.031. For SnSe

_{2}, we used two Tauc–Lorentz oscillators with the following parameters: ${A}_{1}=$ 14.435 eV; ${C}_{1}=$ 1.345 eV; ${E}_{01}=$ 2.870 eV; ${A}_{2}=$ 20.432 eV; ${C}_{2}=$ 0.875 eV; ${E}_{02}=$ 3.981 eV; ${E}_{g}=$ 0.736 eV and ${\epsilon}_{\infty}=$ 4.445.

#### 3.6. Optical Properties Characterization

_{2}and SnSe

_{2}films on quartz were measured with a spectrophotometer (Cary 5000 UV-Vis-NIR, Agilent Tech., Santa Clara, CA, USA) at a wavelength range of 300–3300 nm.

#### 3.7. First-Principle Calculations

_{2}and SnSe

_{2}were calculated using density functional theory (DFT) implemented in the Vienna Ab Initio Simulation Package [70,71]. Core electrons, their interaction with valence electrons, and exchange correlation effects were described within generalized gradient approximation [72] (Perdew–Burke–Ernzerhof functional) and the projector-augmented wave pseudopotentials [73]. The unit cell parameters were a = b = 3.6486 Å and c = 5.8992 Å for SnS

_{2}and a = b = 3.811 Å and c = 6.137 Å for SnSe

_{2}. The calculation was performed in two steps: first, the atomic positions of SnS

_{2}and SnSe

_{2}were relaxed in until the interatomic forces were less than 10

^{−3}eV/Å, and a 1-electron basis set was obtained from a standard DFT calculations. Second, the real and imaginary parts of frequency-dependent dielectric function were calculated using the GW approximation [74]. Cutoff energy of the plane waves basis set was set to 600 eV, and the Γ-centered 11 × 11 × 7 k-points mesh was used to sample the first Brillouin zone.

## 4. Conclusions

_{2}and SnSe

_{2}in a wide spectral range (300–3300 nm). Our findings reveal a strong dielectric response of SnS

_{2}and SnSe

_{2}and their broad range with zero absorption. More importantly, for SnS

_{2}, this range includes visible frequencies, which makes SnS

_{2}a novel high refractive index material, which complements the classical high refractive index materials Si, GaP, and TiO

_{2}. Additionally, we measured the second-order nonlinear susceptibility of SnS

_{2}and SnSe

_{2}. From a broader perspective, our research enables a foundation for advanced optical engineering with SnS

_{2}and SnSe

_{2}.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

SnS_{2} | SnSe_{2} | |||
---|---|---|---|---|

λ (nm) | n | k | n | K |

300 | 3.8943 | 1.0436 | 2.8895 | 2.5984 |

350 | 3.5319 | 0.8434 | 3.8561 | 1.3915 |

400 | 3.3828 | 0.3664 | 3.5830 | 1.1143 |

450 | 3.1896 | 0.1537 | 3.6856 | 0.9836 |

500 | 3.0450 | 0.0599 | 3.7271 | 0.7105 |

550 | 2.9415 | 0.0180 | 3.6563 | 0.4900 |

600 | 2.8674 | 0.0021 | 3.5609 | 0.3480 |

650 | 2.8171 | 0.0000 | 3.4737 | 0.2566 |

700 | 2.7841 | 0.0000 | 3.4004 | 0.1950 |

750 | 2.7602 | 0.0000 | 3.3399 | 0.1515 |

800 | 2.7420 | 0.0000 | 3.2897 | 0.1195 |

850 | 2.7277 | 0.0000 | 3.2477 | 0.0952 |

900 | 2.7163 | 0.0000 | 3.2122 | 0.0762 |

1200 | 2.6782 | 0.0000 | 3.0787 | 0.0190 |

1500 | 2.6621 | 0.0000 | 3.0115 | 0.0021 |

1800 | 2.6537 | 0.0000 | 2.9751 | 0.0000 |

2100 | 2.6488 | 0.0000 | 3.6446 | 0.0000 |

2400 | 2.6456 | 0.0000 | 3.6001 | 0.0000 |

2700 | 2.6434 | 0.0000 | 3.5663 | 0.0000 |

3000 | 2.6419 | 0.0000 | 3.5400 | 0.0000 |

3300 | 2.6408 | 0.0000 | 3.5194 | 0.0000 |

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**Figure 1.**Morphology of SnS

_{2}and SnSe

_{2}. (

**a**) Crystal lattice structure of 1T-SnS

_{2}(or 1T-SnSe

_{2}) [44], optical microscopy images of (

**b**) SnS

_{2}and (

**f**) SnSe

_{2}. SEM images of (

**c**) SnS

_{2}and (

**g**) SnSe

_{2}. AFM scan images of (

**d**) SnS

_{2}and (

**h**) SnSe

_{2}. AFM thickness measurements of (

**e**) SnS

_{2}and (

**i**) SnSe

_{2}films with characteristic step height profiles.

**Figure 2.**Structural characterization of SnS

_{2}and SnSe

_{2}. XRD patterns of (

**a**) SnS

_{2}and (

**b**) SnSe

_{2}. Raman spectra for (

**c**) SnS

_{2}and (

**d**) SnSe

_{2}thin films.

**Figure 3.**Linear optical properties of SnS

_{2}and SnSe

_{2}

**.**Dielectric function of (

**a**) SnS

_{2}and (

**b**) SnSe

_{2}. For comparison, we included refractive indices (red circles) and electronic transitions (dashed lines) determined by Domingo et al. [26]. Measured and calculated transmittance for (

**c**) SnS

_{2}and (

**d**) SnSe

_{2}on quartz. Tabulated optical constants for SnS

_{2}and SnSe

_{2}are collected in Table A1.

**Figure 4.**First-principle calculations of SnS

_{2}and SnSe

_{2}

**.**Optical constants for (

**a**) SnS

_{2}and (

**b**) SnSe

_{2}, including in-plane n

_{ab}, k

_{ab}and out-of-plane n

_{c}, k

_{c}parts of dielectric tensor.

**Figure 5.**Nonlinear optical properties of SnS

_{2}and SnSe

_{2}. (

**a**) Power-dependent nonlinear optical response of SnS

_{2}and SnSe

_{2}thin films, plotted in double logarithmic scale, and its linear approximation with slope p = 2.01 ± 0.02 for SnS

_{2}and p = 2.02 ± 0.04 for SnSe

_{2}. Pump wavelength is 830 nm. (

**b**) SHG spectroscopy of SnS

_{2}(red line) and SnSe

_{2}(blue line) thin films at 40 mW pump power. (

**c**) Wavelength-dependent, second-order, nonlinear optical susceptibility of SnS

_{2}(red line) and SnSe

_{2}(blue line).

**Figure 6.**SnS

_{2}as a high refractive index material. (

**a**) Refractive index n and (

**b**) extinction coefficient k of SnS

_{2}compared with other high refractive index materials—Si, GaP, and TiO

_{2}. (

**c**) The dependence of refractive index and optical bandgap for high refractive index materials.

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## Share and Cite

**MDPI and ACS Style**

Ermolaev, G.A.; Yakubovsky, D.I.; El-Sayed, M.A.; Tatmyshevskiy, M.K.; Mazitov, A.B.; Popkova, A.A.; Antropov, I.M.; Bessonov, V.O.; Slavich, A.S.; Tselikov, G.I.;
et al. Broadband Optical Constants and Nonlinear Properties of SnS_{2} and SnSe_{2}. *Nanomaterials* **2022**, *12*, 141.
https://doi.org/10.3390/nano12010141

**AMA Style**

Ermolaev GA, Yakubovsky DI, El-Sayed MA, Tatmyshevskiy MK, Mazitov AB, Popkova AA, Antropov IM, Bessonov VO, Slavich AS, Tselikov GI,
et al. Broadband Optical Constants and Nonlinear Properties of SnS_{2} and SnSe_{2}. *Nanomaterials*. 2022; 12(1):141.
https://doi.org/10.3390/nano12010141

**Chicago/Turabian Style**

Ermolaev, Georgy A., Dmitry I. Yakubovsky, Marwa A. El-Sayed, Mikhail K. Tatmyshevskiy, Arslan B. Mazitov, Anna A. Popkova, Ilya M. Antropov, Vladimir O. Bessonov, Aleksandr S. Slavich, Gleb I. Tselikov,
and et al. 2022. "Broadband Optical Constants and Nonlinear Properties of SnS_{2} and SnSe_{2}" *Nanomaterials* 12, no. 1: 141.
https://doi.org/10.3390/nano12010141