The multilayer β-GaS thin films with a thickness of 800 nm were deposited on a 500 μm thick sapphire substrate by atomic layer deposition (ALD) technique (Nanjing MKNANO Technology Co., Ltd). The size of β-GaS film and the sapphire substrate was 5 × 5 and 10 × 10 mm, respectively. The deposited β-GaS films have a hexagonal crystal structure. And the XRD and Raman characterization of β-GaS films can be found elsewhere (Mukenano, 2021).

In our theoretical calculation, we used the experimental hexagonal lattice constant of a = 3.626 Ȧ and c = 17.425 Ȧ. The electronic band structure was based on the DFT with the generalized gradient approximation (GGA) (Perdew et al., 1996), The accurate projector-augmented wave (PAW) method (Blöchl, 1994), as implemented in the Vienna abinitio simulation package (VASP) (Kresse and Furthmüller, 1996), was used. The valence configurations of Ga and S atoms adopted in the present calculations were 3d¹⁰4s²4p¹ and 3s²3p⁴, respectively. A large plane wave cutoff of 550 eV and the small total energy convergence criterion of 10^–5 eV were used throughout. Fine Monkhorst-Pack k-meshes of 24 × 24 × 8 were used for the Brillouin zone integrations.

The ultrafast nonlinear absorption properties of the multilayer β-GaS thin films were measured by open-aperture Z-scan technique. The Z-scan system in this study is similar to the pervious report (Shen et al., 2020). In brief, the laser was emitted from an optical parametric amplifier (Light Conversion ORPHEUS) pumped with a Yb:KGW femtosecond fiber laser (Light Conversion PHAROS-SP). The pulse duration and laser repetition rate of the OPA were 190 fs and 20 Hz, respectively. The laser wavelength used in Z-scan measurement were tuned to 532 and 650 nm. The sample placed on the mobile stage was moved along the z-axis with respect to the focal point of a 200 mm focal lens. The laser beams were measured by two energy detectors (Laser probe, Rjp-765) connected to an energy meter (Laser probe, Rj-7620). The Z-scan system was calibrated using a 2 mm thick ZnSe semiconductor.

The ultrafast carrier dynamics in the multilayer β-GaS thin films were measured by femtosecond transient absorption (TA) spectroscopy. The TA spectroscopy was performed in the two-beam transmission geometry. The laser source was the same in the Z-scan measurements. We used pump wavelengths of 355 nm with photon energy of 3.49 eV, which is larger than the bandgap of β-GaS (∼2.5 eV). The pump fluence was kept below 50 μJ/cm² to avoid high-order carrier relaxation processes and thermal damage of the GaS thin films. The probe beam was a white light supercontinuum generated using a sapphire crystal. The pump and probe beam illuminated the films on the front side. The time resolution of the TA measurement system was ∼280 fs. Details of our TA measurement can be found in the previous report (Li et al., 2021).

Figure 1A shows the atomic structure of bulk β-GaS. It is shown that the β-GaS has a hexagonal lattice, and the stacking type of β-GaS comprises with monolayer consisting of Ga and S in the stacking sequence of S-Ga-Ga-S along the c axis. Therefore, the layered atomic structure of β-GaS is clearly shown. Because of the comparatively large thickness of our β-GaS film (∼800 nm), the quantum confinement effect is negligible in the DFT calculation. Therefore, the DFT result of bulk GaS is also applicable to the β-GaS film in this study. The calculated scalar-relativistic band structure of β-GaS is shown in Figure 1B. The DFT results demonstrate that the β-GaS is an indirect bandgap semiconductor, which agrees well with pervious experimental report (Ho and Lin, 2006).

The open aperture Z-scan curves of the multilayer β-GaS thin films measured under 532 and 650 nm excitation were shown in Figures 2A,B, respectively. The pulse energy used in Z-scan measurements was 3 and 12 nJ for 532 and 650 nm, and corresponding laser intensity at beam focus was 1.45 GW/cm² and 3.43 GW/cm² for 532 and 650 nm, respectively. The sapphire substrate was also measured under the same experimental condition and found to has negligible nonlinear response. The Z-scan curves in Figure 2 show that multilayer β-GaS thin films have saturable absorption (SA) behavior at 532 nm, while reverse saturable absorption (RSA) appears under 650 nm excitation. Due to the short pulse duration (190 fs) and low repetition rate of our laser system, the thermal nonlinearity can be negligible in our measurement. The photon energy of light at 532 and 650 nm is 2.33 and 1.91 eV, respectively. Therefore, the β-GaS film (E _g ∼ 2.5 eV) was unable to be excited with one photon with energy of 1.91 eV (650 nm). Hence, the RSA behavior at 650 nm can be attributed to the two-photon absorption mechanism. On the other hand, laser excitation at 532 nm was near-resonant with the bandgap of β-GaS. As a result, the SA behavior at 532 nm could be attributed to the state bleaching of band edge state or shallow defect state in β-GaS. (Christodoulides et al., 2010). The Z-scan curves were fitted using the standard Z-scan theory (Sheik-Bahae et al., 1990), and the effective nonlinear absorption coefficients were determined to be −1.8 × 10^–8 m/W and 4.9 × 10^–8 m/W for 532 and 650 nm, respectively. Pervious results demonstrate that the film thickness has a significant influence on the NLO response of 2D material (Zhang et al., 2018; Verrone et al., 2020). However, the experimental data of β-GaS thin film with different thickness was not available due to the limitation of film deposition system and the low laser damage threshold of few-layer thin film.

The NLO parameters of multilayer β-GaS thin films and various metal monochalcogenide and 2D layered materials reported in recent literatures (Kürüm et al., 2010; Isik et al., 2013; Dong et al., 2016; Ren et al., 2016; Karatay, 2019; Ertap, 2018; Jia et al., 2020) are summarized in Table 1. Note that it should be cautious to compare the definite value of NLO coefficients measured at different wavelength and different pulse duration. However, the data in Table 1 clearly demonstrates that the multilayer β-GaS thin films have excellent nonlinear absorption response. A large β on the order of 10^–8 m/W is observed, which is comparable to the reported values of PdSe₂ and WS₂ and higher than that of electrochemical graphene oxide (GO) (Dong et al., 2016; Ren et al., 2016; Jia et al., 2020), highlighting the strong NLO effect in the β-GaS film. The large NLO coefficient of β-GaS film could be ascribed to (a) homogeneously deposited film with improved crystalline compared to the amorphous or polycrystalline forms (Kumar et al., 2016), and (b) the ratio of photon energy to bandgap at 650 nm (532 nm) is 0.76 (0.93), which is close to the maximum value of the dispersion curve of β based on two parabolic-band model in semiconductors (Christodoulides et al., 2010). According to the Z-scan data, the imaginary part of the third-order nonlinear susceptibility can be deduced through the equation Im χ ( 3 ) = n 2 c 2 240 π 2 ω β ( m / W ) . And the figure of merit (FOM) for the third-order optical nonlinearity ( F O M Im = | Im χ ( 3 ) / α 0 | ) (Dong et al., 2016) can be determined to be −2.7 × 10^–13 (esu cm) and 8.9 × 10^–13 (esu cm) for 532 and 650 nm, respectively. The FOM of β-GaS film is higher than the reported values of WS₂ and Sb₂Te₃ thin films (Dong et al., 2016; Verrone et al., 2020), indicating the β-GaS is a promising candidate for applications in optical limiting and ultrafast saturable absorber.

To understand the origin of strong light absorption, ultrafast carrier dynamics in β-GaS thin films were studied with femtosecond TA spectroscopy. Figure 3 a and b shows the two-dimensional (2D) contour plot of TA and one-dimensional (1D) slice of TA spectra for the β-GaS thin films under 355 nm excitation, respectively. All TA spectra show periodical interference fringes, which are the characteristics of a highly homogeneous film thickness. Similar results were reported from the measurements of the TA spectra in GaN thin films (Fang et al., 2016). The TA spectra show strong photo-induced absorption (PIA) band around 650 nm, while the amplitude of TA is rather weak below 520. These results agree well with the Z-scan measurements, while could be attributed to the state bleaching around bandgap of β-GaS (∼2.5 eV). Moreover, a careful inspection of TA spectra in Figure 3B reveals that the TA signals remains almost the same at 1 and 10 ps, then the TA signals decay within hundreds of picoseconds. These results indicate that the β-GaS thin films have long carrier lifetime.

To elucidate the carrier relaxation dynamics in multilayer β-GaS thin films, we have chosen the probe wavelength at 645.6 nm (near the peak of PIA band). The normalized TA decay curve at 645.6 nm of β-GaS thin films under 355 nm excitation is shown in Figure 4. It is found that the TA signal rises instantaneously and reaches the maximum at ∼0.3 ps, which is limited by our instrument response. The TA signal remains almost constant from 0 to 10 ps, followed by an exponential decay. To analyze the TA results, we used the multi-exponential decay model (Li et al., 2017): Δ T ( t ) = Δ A 0 + [ ∑ i A i ⁡ exp ( − t τ i ) ] where τ _i and A _i are the time constants and amplitudes of the decay components, respectively and A ₀ is the offset (set as zero in the fitting). The fitting curves are shown as the solid lines in Figure 4. The exponential decay analysis indicates that the decay processes in β-GaS thin films consist of two kinetic components with time constants of 85 ± 19 ps and 450 ± 50 ps, respectively. The fast and slow decay components could be attributed to the defect trapping and inter-band carrier recombination in β-GaS thin films, respectively. These results are analogous to that reported for other semiconductor materials (Fang et al., 2016; Li et al., 2017; Kong et al., 2018; Yan et al., 2020; Li et al., 2021). Our TA measurements sheds light on the carrier relaxation mechanism in GaS materials, which could be helpful to develop a clear understanding on the carrier dynamics in Group-III metal monochalcogenide semiconductors.