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Abstract
This work systematically investigates the third-order nonlinear optical (NLO) properties and ultrafast carrier dynamics of layered indium selenide (InSe) obtained by mechanical exfoliation (ME). The two-photon absorption (TPA) effect of layered InSe was tested using micro-Z/I-scan techniques. The results indicate that InSe flakes undergo the TPA response under the excitation of both 520 nm and 1040 nm fs pulses, and that InSe is more likely to achieve TPA saturation under visible light excitation. Furthermore, ultrafast carrier dynamics revealed that InSe flakes in the visible region undergo a transition from photoinduced absorption to photobleaching and exhibit a fast recombination time of ∼0.4–1ps, suggesting a high optical modulation speed as high as ∼1–2.5 THz.
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1. Introduction
Two-dimensional (2D) layered materials, pioneered by graphene, have been widely explored and deeply investigated by virtue of their huge application potential in nonlinear optics [1–5], optoelectronics [6–9], biomedicine [10–12], and photocatalysis [13–15], as well as in other fields, owing to their ultrathin size, thickness-dependent bandgap, and ultrafast optical response. During this process, it is fundamental but significant to study the intrinsic characteristics of these 2D materials. However, there are some property differences even in the same type of material because of differences in the preparation method, sample treatment, etc. For instance, the two-photon absorption (TPA) coefficient of monolayer MoS2 obtained by the mechanical exfoliation (ME) and chemical vapor deposition (CVD) method may differ by nearly two times, which can be ascribed to the large difference in the defect concentration between them [16]. The two-photon fluorescence of MoS2 improved after treatment with bis-(trifluoromethane) sulfonimide as the defect density decreased during the defect repair process [17]. Black phosphorus (BP) has unique photoelectric and biocompatibility properties, but also poor stability, which needs to be improved to realize its application [18–21]. Consequently, it is of profound implications to study the intrinsic characteristics and further realize the controllable modification engineering of these optical and physical properties in 2D materials.
Indium selenide (InSe) is a typical layered III–VI group semiconductor with exceptional electronic and optical properties, such as a broad adjustable bandgap [22,23], large electron mobility [24,25], and high photoresponsivity [26,27]. InSe has a wide tunable bandgap (1.25 ∼ 2.6 eV) as bulk InSe is reduced to a monolayer [22]. The field-effect electron mobility of InSe of ∼${10^3}$ and ∼${10^4}\; c{m^2}{V^{ - 1}}{s^{ - 1}}$ can be achieved at room temperature and liquid-helium temperature respectively, by choosing suitable contact metals and appropriate thicknesses [24,25]. The vertical and planar graphene/InSe and BP/InSe heterojunctions exhibit an ultrahigh photoresponsivity of ∼${10^5}\; A{W^{ - 1}}$ and a broad range of spectral responses from visible to near-infrared [26,27]. In our previous work [28], we have studied the third-order nonlinear optical (NLO) responses of InSe nanosheet dispersions. However, their intrinsic properties are hard to obtain due to the presence of organic solvents. In this study, we focus on the pure properties of InSe nanosheets, and the ME technique is a more appropriate sample preparation method than liquid-phase exfoliation.
In this work, we prepared a series of InSe flakes with different thicknesses using the ME method. X-ray diffraction (XRD), atomic force microscopy (AFM), temperature-dependent Raman spectroscopy, and high resolution transmission electron microscopy (HRTEM) were used to characterize the quality of the obtained flakes. The third-order NLO properties of the InSe nanosheets were investigated using home-made micro-Z-scan ($\mu $-Z-scan) and micro-I-scan ($\mu $-I-scan) setups, both at 520 nm and 1040 nm fs laser excitation. The transient absorption spectrum technique was utilized to investigate the carrier relaxation processes.
2. Characterizations
InSe crystals have a hexagonal structure, with the space group of $P{6_3}/mmc$ (No. 194). As shown in Fig. 1(a), InSe is a 2D material consisting of layers of Se-In-In-Se atoms stacked based on weak van der Waals forces, with the lattice parameters of a = b = 0.394 nm and c = 1.731 nm. For each layer, the In and Se atoms are strongly chemically bonded to form honeycomb rings. XRD measurement was performed to identify the crystal structure of the bulk InSe, as shown in Fig. 1(b). Obvious diffractions from the (002), (004), (006), (008), and (0012) crystal planes can be observed, which are in good accordance with the Bragg position of InSe (PDF#34-1431, red line). The absence of impurity peaks in the XRD pattern confirmed the high purity of the sample.
Fig. 1. (a) Schematic atomic structure of β-InSe with the side view (left) and top view (right). Brown and yellow spheres represent indium and selenium atoms, respectively. (b) Typical XRD pattern of bulk InSe. (c) Optical image of the single InSe nanosheet exfoliated onto a fused quartz substrate. Atomic force microscope measurement position marked by the red line, with a thickness of ∼387.4 nm. (d) Temperature-dependent Raman spectra and (e) room-temperature Raman spectrum of the ∼387.4 nm InSe nanosheet obtained under CW laser excitation at 520 nm. (f) Temperature dependence of the peak positions of $A_{1g}^1$, $E_{2g}^1$, and $A_{1g}^2$ Raman modes, respectively.
The layered structure of InSe makes it easy to obtain few- and/or mono-layer films through the ME method, which has been widely used in a large number of 2D crystals, such as graphene [29,30], MoS2 [31,32], BP [18,19] and h-BN [33]. Furthermore, ME technology has been recognized as an efficient method for obtaining fresh atomic/molecular layers, which are ideal candidates for studying their intrinsic electronic [34], optical [35], and mechanical properties [36]. Therefore, InSe nanosheets with several thicknesses of ∼7.0 nm, 8.8 nm, 10.5 nm, 23.2 nm, 30.3 nm and 387.4 nm were prepared with the ME technique. Figure 1(c) exhibits the optical image and AFM measurement of the flake at ∼387.4 nm. The corresponding information for the other thicknesses is shown in Fig. S1. Since InSe crystals are direct bandgap semiconductor materials at few layers and bulk [37], the optical bandgap of InSe at different thicknesses can be estimated by photoluminescence (PL) [22], as shown in Fig. S2. Temperature-dependent Raman spectroscopy, which is an effective tool to investigate the fine structure and properties of 2D materials [38–40], was performed in the range of 77 to 300 K with a 532 nm continuous wave (CW) laser (Fig. 1(d)). The Raman spectrum at room temperature was extracted as illustrated in Fig. 1(e); herein, we can find three Raman modes: $A_{1g}^1$ (115.48 cm-1), $E_{2g}^1$ (176.51 cm-1), and $A_{1g}^2$ (226.43 cm-1). No new Raman peaks appeared, thereby indicating the high stability of the InSe nanosheets, i.e., no phase transition or decomposition exists. Furthermore, we find that both the intensity and width of all three Raman modes increase with increasing temperature, which is very common in layered samples. The variation in the width of the Raman modes with temperature can be rationalized by phonon dispersion and many-body theoretical calculations [41]. In addition, the positions of the peaks exhibit a redshift with increasing temperature, which can be attributed to lattice thermal expansion and related anharmonic vibrations [42]. However, the three Raman vibrational modes are differently sensitive to temperature. We explored the variations in Raman modes with temperature in the InSe films, as shown in Fig. 1(f), based on the Grüneisen model [43]:
where ${\omega _0}$ is the Raman mode frequency at 0 K, and $\chi $ is the first-order temperature coefficient of the Raman mode. The fitted $\chi $ values of $A_{1g}^1$, $E_{2g}^1$, and $A_{1g}^2$ were -0.00617, -0.01399, and -0.01735 $c{m^{ - 1}}{K^{ - 1}}$, as depicted in Fig. 1(f), respectively. The three Raman modes have different temperature dependences. Among them, the $A_{1g}^2$ mode is the most sensitive, with a Raman peak position varying from 230.42 cm-1 at 77 K to 226.43 cm-1 at 300 K. The $A_{1g}^1$ mode has the smallest variation of 116.76 cm-1 at 77 K to 115.48 cm-1 at 300 K. Moreover, the $\chi $ of InSe flake is similar to that of MoS2 [41] and graphene [38], which again confirms the layered structure of InSe are packed by weak van der Waals interaction.Furthermore, HRTEM characterization was performed to demonstrate the morphologies and microstructures of the exfoliated InSe flakes. Figure 2(a) displays an HRTEM image of InSe, and the ordered lattice structure in the red frame region is shown in Fig. 2(b). Lattice spacings of 0.365 nm and 0.380 nm correspond to the (010) and (100) planes, respectively, with an interfacial angle of 60°. From the selected area electron diffraction pattern in Fig. 2(c), we can see that the InSe nanosheet has a hexagonal lattice structure with [001] zone axis. The clear Bragg spots of the (100) and ($\bar{1}10$) planes indicate the high crystallinity of InSe. As shown in Fig. 2(d-f), the low-magnification TEM image and the elemental energy dispersive X-ray spectroscopy (EDS) diagrams demonstrate that the layered InSe flake has a flat surface, and the Se, In elements are uniformly distributed throughout the sample with a molar percent ratio close to 1:1.
Fig. 2. (a) In-plane HRTEM image of InSe flakes. (b) The higher-magnification view of the section marked with the solid red box in (a). (c) Selected area electron diffraction pattern of InSe. (d) Transmission electron microscopy image of InSe nanosheet. (e, f) Distribution of Se and In atomic elements in energy dispersive X-ray spectroscopy.
3. Results and discussion
From the above characterizations, we found that high-quality single-crystal InSe flakes were prepared by the ME method. However, the sample size of exfoliated 2D materials is usually in the range of a few micrometers to tens of micrometers. The small size restricts the application of the famous Z-scan technique, as it is for macroscopic samples. $\mu $-Z-scan, which can be used to study nonlinear absorption and nonlinear refraction, and $\mu $-I-scan, which can be used to study nonlinear absorption, provide solutions to investigate the NLO properties of these small size samples. Figure 3 shows a schematic of our home-built µ-Z/I-scan setup. The excitation laser sources were 380-fs pulses at 1040 nm, and its second harmonic at 520 nm with a pulse repetition rate of 1 kHz. The incident light was tightly focused onto the sample with a waist radius of ∼2 µm ($\lambda = 520 \;nm$) through an objective lens (20×, N.A.: 0.3). To ensure that the beam was accurately focused on the target flakes during the measurement, another objective lens combined with a CCD camera was utilized to monitor the transmitted laser beam. For the $\mu $-Z-scan, the sample was mounted on a platform that enabled movement in and out of the focal region in the range of -150 to +150 µm, and the corresponding laser beam diameter was in the range of 4–40 µm. For the $\mu $-I-scan, the sample was fixed at the focal point of the laser, and an electronically controlled adjustable attenuation filter was used to adjust the incident light intensity. Meanwhile, an automatic control program was employed to synchronize the movement of the motorized stage/adjustable attenuation filter, and collect data. In this case, for samples smaller than 40 µm, we could only explore the $\mu $-I-scan method. For samples larger than 40 µm, like the InSe flake in Fig. 1(c) with a lateral size ∼86.55 µm, both $\mu $-Z-scan and $\mu $-I-scan techniques can be applied.
Figure 4 shows the NLO properties of the thicker InSe flake. During the measurement, the nanosheet was placed on a 10 mm × 10 mm × 1 mm quartz substrate, and its linear transmittance was ∼48.1% at 520 nm and ∼98.8% at 1040 nm. The normalized open-aperture $\mu $-Z-scan transmittances exhibit a symmetrical “valley” with respect to the laser focused at 520 nm (Fig. 4(a)) and 1040 nm (Fig. 4(b)), thus indicating a typical reverse saturable absorption (RSA) response. In addition, the transmittance “valley” depth increases gradually as the input laser pulse energy increases. For example, the valley value of the RSA response reduced from ∼92.4% at 0.4 nJ to ∼90.2% at 0.8 nJ, and ∼99.4% at 5 nJ to ∼97.7% at 9 nJ under 520 nm and 1040 nm excitation, respectively. The closed-aperture $\mu $-Z-scan results, which have been divided by the open-aperture Z-scan data, are displayed in Fig. 4(c) and 4(d). The “peak-valley” signals indicate a self-defocusing effect with a negative nonlinear refractive (NLR) index at 520 nm. However, no obvious nonlinear refraction response was observed before the sample was destroyed at 1040 nm, which could be attributed to the low incident fluence in our experiment. It is worth noting that no discernible NLO signal was tested in the quartz substrate, which indicates that the RSA and NLR responses originated primarily from the InSe flake.
Fig. 4. NLO property investigation of the 387.4 nm InSe nanosheet. (a, b) The open-aperture $\mu $-Z-scan results, (c, d) the closed-aperture $\mu $-Z-scan results, and (e, f) the µ-I-scan results under the excitation of 520 nm and 1040 nm fs pulses, respectively. The solid lines represent the corresponding fitting results.
To investigate the mechanism inducing the RSA response, we obtained the relationship between ln(1-T(z)) and ln(I) (insets of Fig. 4(a) and 4(b)), showing a slope of∼1.01 at 520 nm and ∼0.99 at 1040 nm. The detailed fitting data for different excitation energies are shown in Fig. S3 and S4. The results show that the slopes are always close to 1, which demonstrates that the degenerate TPA effect occurred in InSe flakes at both 520 nm and 1040 nm [44–46].
We fitted these Z-scan results using the light propagation equation given by [47]:
where I is the incident light intensity, $z^{\prime}\; $ is the propagation depth of the excitation light in the sample, ${\alpha _0}\; $ is the linear absorption coefficient, and β is the TPA coefficient. The well-fitted data confirmed the speculation of TPA, as shown in Fig. 4(a) and 4(b). In addition, the imaginary part of the third-order NLO susceptibility $Im{\chi ^{(3 )}}$, and figure of merit (FOM) are listed in Table 1.
Table 1. Linear and NLO parameters of InSe flake
In addition to β, we also focused on the NLR index ${n_2}$ of the InSe flake. We fitted the closed-aperture Z-scan data, as shown in Fig. 4(c) and 4(d), using the analytic formula in previous studies [48,49]. In addition, the NLR index ${n_2}$ increased with increasing excitation energy, which may be attributed to higher-order NLO effects at higher excitation energy. According to previous report [50], we fitted $\varDelta n/{I_0}$ and ${I_0}$ with a linear relationship, as shown in Fig. S5, which is caused by the contribution of free carriers. The fitting parameters of the InSe flake are listed in Table 2. Meanwhile, we performed comparisons to recognize the parameters of different low-dimensional materials for further comprehension. Under fs laser excitation, the β value of InSe flake was ∼1–3 orders of magnitude smaller than that of WS2, WSe2 [48], and BP [51]. This is probably because the InSe flakes are thicker than these 2D materials. This possibility was also demonstrated in subsequent I-scan tests of different thicknesses. Meanwhile, the nonlinear refractive index n2 is of the same order of magnitude as WS2, one order of magniutude smaller than WSe2 and four orders of magnitude smaller than BP.
Table 2. β and ${{n}_2}$ in different low-dimension materials
We also conducted μ-I-scan tests on the same single-crystal InSe flake (Fig. 4(e) and 4(f)). Based on the light propagation equation (Eq. (2)), the change in the TPA coefficient β with the incident intensity (I) can be expressed as [52]:
Table 3. Fitting results of ${\beta }$ by μ-Z-scan and μ-I-scan
The NLO effects of other InSe flakes (lateral size < 40 µm) were tested by µ-I-scan, Fig. 5(a)-(d), S6, and S7. The fitting parameters are summarized in Table 4. It is easily evident that the TPA coefficient (β0) excited by 520 nm is two orders of magnitude larger than that excited by 1040 nm, and Is,520 nm is one order of magnitude smaller than Is,1040 nm, thereby indicating that InSe nanosheets are more likely to achieve TPA saturation under visible light excitation. In addition, the two parameters show obvious thickness dependence, as shown in Fig. 5(e) and 5(f), where β0 decreases and Is increases with increasing thickness at both 520 nm and 1040 nm. This illustrates the weakening of the TPA in InSe as the thickness increases, which also occurs in TMDCs [52,53].
Fig. 5. (a, b) Optical images and AFM results of few-layered InSe. (c, d) The µ-I-scan results of InSe flakes of thicknesses 7.0 nm and 23.2 nm at the excitation of 520 nm and 1040 nm fs pulses, respectively. (e, f) TPA coefficient and TPA-induced saturable intensity of InSe flakes with different thicknesses both at 520 nm and 1040 nm. The shaded areas are the standard deviations from the fitting data.
Table 4. Fitting parameters of single crystal InSe flakes.
To study the ultrafast carrier dynamics of the InSe flakes, the transient absorption spectrum was acquired using a fs transient absorption spectrometer. A white light source derived from the nonlinear crystal CaF2 was applied as the probe light. A 200-fs pulsed laser at 400 nm was used as the pump source. Figure 6(a) shows the transient absorption spectrum of the 387.4 nm InSe flake. Because the bandgap of the 387.4 nm InSe flake is much smaller than the pump photon energy (${\lambda _{ex}} = 400\; nm,$ 3.1 eV), the electrons in the valence band can be effectively excited into the conduction band. In the 500–560 nm region, the transient absorption kinetics manifested photoinduced absorption (PIA, positive change of differential absorption signal) within 1 ps after pump excitation, corresponding to light red areas near zero delay time. The rapid process of PIA may be caused by the bandgap renormalization (BGN) effect. When a large number of electrons are transferred from the valence band to the conduction band, the accumulation of electrons in the conduction band often causes an instantaneous redshift of the bandgap, thereby resulting in a positive change in the differential absorption signal. As shown in Fig. 6(b), the absorption peaks with different pump-probe time delays are red-shift after excitation, and then remain stable over time, suggesting a process of moving from BGN to steady state [54–56]. The following behavior is photobleaching (PB, negative change of differential absorption signal) caused by Pauli blocking and a slow relaxation process. Meanwhile, for the 600–660 nm range, the transient absorption spectrum only exhibits a PB component and a corresponding long recovery process.
Fig. 6. (a) Visible transient absorption spectrum of ∼387.36 nm InSe flake under a 200 fs-pulsed laser excitation at 400 nm. (b) Transient absorption spectra with different pump-probe time delays. (c) Decay profiles of transient differential absorption monitored at different wavelengths. The solid lines represent the corresponding fitting results. (d) Evaluated lifetimes of the fast and slow components in the recovery of the transient differential absorption spectra, plotted versus probe wavelengths. (e) Schematic diagram of carrier relaxation process.
The carrier relaxation process (first 40 ps) with several representative probe wavelengths is shown in Fig. 6(c). The transient absorption decay curves in the 500–560 nm and 600–660 nm regions, which have different carrier relaxation processes, were fitted with tri- and double-exponential models, respectively [57], such that
Table 5. Fitting results of ultrafast transient absorption spectrum measurement
4. Conclusion
In summary, we prepared high-quality InSe flakes using the ME method and characterized them via XRD, AFM, HRTEM, and temperature-dependent Raman spectroscopy. $\mu $-Z-scan and $\mu $-I-scan measurements demonstrated that InSe has a TPA response at both 520 nm and 1040 nm fs laser excitations. The TPA coefficient of InSe of same thickness excited by 520 nm is two orders of magnitude larger than that excited by 1040 nm, and ${I_{s,520\; nm}}$ is one order of magnitude smaller than ${I_{s,1040\; nm}}$, indicating that the InSe nanosheets are more likely to achieve TPA saturation in the visible range. Furthermore, ultrafast carrier dynamics revealed that the InSe flake in the visible regime has a transition from PIA to PB and a fast recombination time of ∼0.4–1 ps, thereby suggesting a high optical modulation speed as high as ∼1-2.5 THz. Our work presents the intrinsic NLO and carrier dynamic properties of InSe nanosheets and provides inspiration for other 2D materials.
Funding
National Natural Science Foundation of China (11904375, 12174414, 61975221); China Postdoctoral Science Foundation (2020M680732); Guangdong Basic and Applied Basic Research Foundation (2020A1515110433).
Disclosures
The authors declare no conflicts of interest.
Data Availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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