Effects of boron doping in InSe single crystals on optical limiting performance in the near-infrared region

Identification of photonic materials with high infrared transmittance and high nonlinear optical coefficients is one of the main emphases in material science as a result of the rapid advancement in infrared photonics. In this study, undoped and B (boron) -doped InSe single crystals were grown by using the modified vertical Bridgman method, and their nonlinear optical properties were investigated to reveal their usability as an optical limiter in the near-infrared region. The decreasing band gap energies and increasing defect states were determined with increasing B concentration in InSe single crystals. The effect of the B concentration on the nonlinear absorption (NA) and optical limiting properties of the InSe single crystals was investigated via open aperture (OA) Z-scan experiments under ultrafast laser excitation at 1200 nm wavelength with 100 femtosecond pulse duration. Two-photon absorption (TPA) was the dominant NA mechanism at 1200 nm excitation wavelength in the femtosecond domain. The results revealed that the NA became stronger with increasing input intensity and increasing amount of B dopant atoms in the InSe single crystal. The observed enhanced NA can be attributed to two possible events (i) increasing input intensity induced more excited electrons which led to more contribution to NA through TPA and (ii) increasing B dopant atoms in InSe single crystal induced more defect states. The NA may be more enhanced with the contribution of these defect states related NA mechanisms. The high transparency and strong NA behavior at the near-infrared region make these single crystals exceptional potential candidates for developing various optoelectronics and filters at the near-infrared spectral region.


Introduction
Indium Selenide (InSe), a complex layered (Se-In-In-Se) semiconductor compound, is an essential member of III-VI group compounds.In the literature, there are many studies on the determination of linear and nonlinear optical properties of InSe materials doped with various elements such as Ho, Dy, Er, Al, and Ag [1][2][3][4][5].Three forms of InSe (thin film, nanosheet, and single crystal) have been generally investigated for optoelectronic applications such as phase change memory, solar cells, diode, and photodetector [6][7][8][9].
Nonlinear optical responses of materials provide significant benefits for various applications such as Q-switched fiber laser, optical limiting, and mode-locking [10][11][12].In the nonlinear optical experiments, InSe materials are excited with beams in the infrared region due to their narrow band gap energies (∼1.3 eV) and exhibit two types of nonlinear response: (i) Nonlinear absorption (NA) which includes two-photon absorption (TPA), multi-photon absorption (MPA), and free-carrier absorption (FCA), and (ii) saturable absorption (SA) [1,13,14].The increase in the nonlinear absorption coefficient with increasing optical intensity causes NA.This behavior is an important property for materials to be used as an optical limiter.An optical limiter (OL) is used to protect human eyes and optical detectors from irreversible damage by highly intense laser pulses from visible to infrared range.The optical limiting property of a material is based on nonlinear optical phenomena such as NA, nonlinear scattering, nonlinear refraction, and TPA [15][16][17][18][19][20][21].An optical limiter allows light to pass through when the intensity of light is weak.If the intensity of light is sufficiently high, the optical limiter begins to absorb the light and causes a decrease in transmission.Considering the human eyes, a few μJ energy of light can lead to irreversible damage [22].Therefore, the limiting threshold of an optical limiter material should be as low as possible for protecting human eyes.With the development of infrared high-intensity lasers, especially at short wavelength infrared (SWIR) band, optical limiting (OPL) devices are in demand for many application fields such as biomedicine, remote sensing, eye-safe LIDAR (Light Detection And Ranging) systems, active imaging, telemetry, autonomous vehicles guiding systems, and molecular spectroscopy [23][24][25][26][27]. Therefore, infrared OPL devices are quite important for various technologies, and demands for them are increasing day by day.
Linear optical and electrocatalyst features of B-doped InSe materials were investigated as a single crystal and monolayer [28,29].However, although there is much research on the nonlinear optical properties of InSe materials [1,4,13,14,[30][31][32][33][34][35], there are no studies that make an effort to design InSe single crystal as an effective optical limiter in near-infrared (IR) region.This study reveals the effective composition of the B-doped InSe single crystal as an efficient optical limiter in near IR region.In this way, it was aimed to tune the band gap with B atoms to support TPA to facilitate their use in the near IR region.The open aperture (OA) Z-scan experiments were performed at 1200 nm with a femtosecond pulsed laser with increasing input intensity to examine the behavior of the optical limiting behavior in the near IR region.

Experimental processes 2.1. Growth of undoped and B-doped InSe single crystals
Undoped and different amounts (0.1%, 0.5%, 1.0%, and 1.8%) of B-doped InSe single crystals were grown by using the modified vertical Bridgman method.To grow undoped and B-doped InSe single crystals, a stoichiometric mixture of high purity In (99.9999%),Se (99.999%), and B (99.7%) in evacuated quartz ampoules (10 −4 Torr) whose inner walls were coated with carbon.Undoped and B-doped InSe compounds were synthesized at 800 °C for 48 h.After the synthesis, the quartz ampoules firstly were positioned vertically in the modified Bridgman furnace.The growth temperature of undoped and B-doped InSe single crsytals is 660 °C.The details are given elsewhere [28,[36][37][38].The prepared undoped and B-doped InSe single crystal ingots had no cracks and voids on the surface.No polishing and cleaning were made for all samples due to their perfect mirror-like surfaces.Ingots were cleaved perpendicular to the c-axis using a razor blade.The dimensions of all samples prepared from the bulk ingots for the nonlinear optical measurements were approximately 1 cm × 1 cm.Doping concentration of InSe single crystals are atomic percentage.Also, the elemental compositions of the single crystals were determined by Inductively Coupled Plasma (ICP) spectroscopy.InSe single crystals are labeled InSe for undoped and InSe/0.1B,InSe/0.5B,InSe/1.0B, and InSe/1.8Bfor 0.1%, 0.5%, 1.0%, 1.8% B-doped samples, respectively.

Characterization methods
The structure of undoped and B-doped InSe single crystals was previously studied by XRD [37].The thicknesses of the undoped and B-doped InSe single crystals were determined by scanning electron microscope (ZEISS EVO 40).The absorption spectra of the crystal materials were obtained through a Shimadzu UV-1800 model UV/VIS absorption spectrophotometer.The nonlinear optical absorption experiments were performed via the open aperture (OA) Z-scan technique by using an ultrafast laser at 1200 nm wavelength with 100 femtosecond (fs) pulse duration and 1 kHz frequency.The crystals were fixed on a computer-controlled translational stage and the laser beam focused via a 20 cm convex lens.The radius of the beam was measured to be 40 μm at the focal point.The transmitted beams from the samples were measured by silicon detector and boxcar average.

Structural and linear optical properties
The XRD pattern of the studied single crystals was reported in [37].It was reported that the crystallinity of the InSe single crystal decreased with the increase of the B doping concentration and this result was attributed to the increased structural defects.The strain values were calculated to be 4.766 for InSe, 4.818 for InSe/0.1B,4.931 for InSe/0.5B,and 5.947 for InSe/1.8Bcrystals.A decrease in d values were also observed with B addition [34].Similar change in the band gap with the addition of B in InSe, as observed in other layered crystal [39].The thicknesses of the InSe single crystals presented in figure 1 were determined as 91.3, 137.1, 74.32, 207.0, and 152.8 μm for InSe, InSe/0.1B,InSe/0.5B,InSe/1.0B, and InSe/1.8B,respectively.Nonlinear absorption mechanisms are closely related to the band gap energy and the defect density of the materials.Band gap energies of InSe, InSe/0.1B,InSe/0.5B,InSe/1.0B, and InSe/1.8Bsingle crystals calculated from Tauc plots (seen in figure 2) as given in [38], and its values are 1.274, 1.269, 1.225, 1.203 and 1.188 eV, respectively.Band gap energies of InSe single crystals decrease with increasing B concentration relative to the band gap energy of undoped InSe single crystals.In our previous papers, a similar decrease in band gap energy with B addition was observed from the CPM and photoluminescence measurements [28,40].In general, band gap energies of undoped and different elements doped InSe single crystal is reported to be in the 1.  interstitial positions which may have different effects on lattice parameters and unit cell volume.Similar variations in lattice parameters were also observe in boron doped GaSe single crystals [45].
Figure 3 shows a ln -n h plots of undoped and B-doped InSe single crystals.The distribution of the defect states localized inside the band gap of the crystals can be determined by the following equation [46], Where α is the absorption coefficient, a 0 is a constant, and E U is the Urbach energy.The distribution of the defect states inside the band gap is proportional to the Urbach energy.The Urbach energies of the crystals can be calculated from the inverse slope of the linear regions of the a ln -n h curves.The Urbach energy of the undoped single crystal was found to be 0.013 eV and it increased to 0.054 eV with increasing the B concentration in InSe single crystal which follows the results given in [40].The Urbach energy values represent that the defect states are distributed below the conduction band of the crystals.

Nonlinear optical properties
The nonlinear absorption behaviors of the undoped and B-doped InSe single crystals from the fits of OA Z-scan measurements under 1200 nm wavelength excitations at 100 fs pulse duration are given in figure 4. As seen in figure 4, the transmittance of all crystals decreased depending on increasing of the optical intensity, which is called NA.The optical nonlinearity can be defined in the following equation [45], where a 0 and b are linear absorption and TPA coefficients, respectively.The transmittance can be given by the equation (4),   2. It is seen that the b values increased with increasing intensity of the laser beam for each crystal.The increasing input intensity induces more excited electrons which leads to more contribution to NA through TPA.Yüksek et al investigated the nonlinear optical properties of Ho-doped InSe single crystals, and they observed that the Ho-doped InSe single crystals exhibit SA at low input intensities at 1064 nm with 65 ps pulse duration.It is due to the lifetime of the defect states is shorter than the pulse duration and defect states can fill at low intensities [1].X Yan et al observed reverse saturable absorption (RSA) in Al-doped InSe thin films from the results of transient absorption experiments.It is attributed that Al nanoparticles trap the excited electrons and inhibit the recombination process.Therefore, Al doping provides stronger excited state absorption (ESA) [4].The B-doped InSe single crystals have higher b values than that of undoped InSe single crystals as seen in table 2. As reported in [37], the doping of B atoms in InSe single crystal caused to decrease in the crystallite size and increasing defect states.As reported in our previous studies [14,47,48], the reaction of more localized defect states with doping of the crystal led to enhanced NA behavior.The energy of the excitation photons (1200 nm) was 1.03 eV which is not enough to excite the localized defect states inside the band gap.On the other hand, these localized defect states could be distributed to the larger energy region considering to their Urbach energies.In this case, the excess localized defect states created by increasing B concentration can contribute to NA through one-photon absorption.In our previous study, we pointed out that the TPA performance of the material was related to the ratio between the input energy and band gap energy, and it increased with the increasing the ratio of n h E g / [49,50].The changes in the b values of the crystals at the same input intensity with the ratios of n h E g / are listed in table 3.These results reveal that the TPA is the dominant NA mechanism among other NA mechanisms in the femtosecond time domain at 1200 nm excitation wavelength for these crystals.

Optical limiting properties
The optical limiting features of undoped and B-doped InSe single crystals were investigated under the excitations of 100 fs laser pulse at 1200 nm wavelength.The normalized transmittances of the crystals were plotted against laser fluence and given in figure 5. Fluence was calculated using the following expression depending on the distance [51], where Q is the fluence which is the energy per beam area and t is the pulse duration, E is the energy of incident beam per pulse, w ( ) z is the beam waist which depends on the distance.To determine the beam waist, the relations for the Gaussian beam are given in equations (8) and (9), where z R is the Rayleigh distance, λ is the wavelength of the incident beam, and w 0 is the beam waist at focus.As seen in figure 5, the transmittance of the crystals begins to decrease sharply when the fluence of the incident beam reaches a threshold value for the crystals.For this reason, the undoped and B-doped InSe single crystals behave as optical limiters at high intensities which correspond to fluence values higher than the limiting thresholds.The optical limiting threshold values of the crystals were found in the range of 0.106-0.027mJ/cm 2 at 398.1 GW cm 2 / laser intensity.The lower optical limiting threshold was found as 0.027 mJ/cm 2 for higher B-doped InSe single crystal.The decrease in the optical limiting thresholds with increasing B concentration can be attributed to the stronger NA behavior.Therefore, B doping in the InSe single crystals provides more effective results for near-infrared optical limiting applications than the undoped InSe single crystal.Additionally, the comparison of the limiting thresholds of the undoped and B-doped InSe single crystals and similar materials in the literature at different excitation wavelengths and pulse durations is listed in table 4. Further, 1.8% B-doped InSe single crystal has the lowest limiting threshold for near-infrared excitations compared with the other optical limiting materials given in the table.Consequently, B-doped InSe single crystals are quite useful nonlinear optical materials for near-infrared optical limiting applications.

Conclusion
Most commercially available lasers operate in the near-infrared region, so it is crucial to study optical nonlinearities in this spectral range as well as to achieve good optical performance at non-resonant wavelengths to successfully demonstrate the materials' potential for use in nonlinear optical devices.In addition, materials with large TPA capability are highly useful for optical limiting.For that reason, B atoms were doped in different concentrations to undoped InSe single crystal to tune band gap energies, which in turn increased TPA at 1200 nm excitation wavelength.The band gap energies decreased from 1.27 to 1.18 eV with increasing B concentration via the localized defect states just below the conduction band.On the other hand, more localized defect states were created by increasing doping of B in InSe single crystal.The results of the OA Z-scan experiments indicated that the NA behaviors of the crystals tend to increase with increasing input intensity.Besides, the increasing B atoms in the InSe single crystal led to increasing TPA contribution to NA.The higher NA coefficient was found for higher B-doped InSe single crystal as 11.75 × 10 −9 m W −1 at 597.1 GW cm 2 / input intensity.Further, the B effect on the optical limiting behavior of the InSe single crystals was also investigated.The lowest optical limiting threshold was found as 0.027 mJ/cm 2 for the highest B concentration in InSe single crystal.Considering the higher transmittance and stronger NA behavior, undoped and B-doped InSe single crystals can be used as an effective optical limiter in the near-infrared region.

Figure 1 .
Figure 1.SEM images of undoped and B-doped InSe single crystals.

Figure 3 .
Figure 3. a ln versus n h plots of undoped and B-doped InSe single crystals.
2-1.3 eV interval[2,28,[40][41][42][43][44].B-doped InSe materials have relatively lower band gap energies at room temperature compared to InSe materials doped with other elements such as Ho, Dy, Al, and Ag, as seen in table1.The band gap energies given in the present study are consistent with theliterature.The shifting of band gap energies to lower values in the B-doped InSe single crystals is obviously related to the B addition.However, we should note that there are several mechanisms for the incorporation of boron atoms into the lattice: they may substitute with greater size In atoms (r In = 0.94 Å, and r B = 0.41 Å), intercalate between the layers or occupy

Figure 4 .
Figure 4. Open aperture Z-scan traces of B-doped and undoped InSe single crystals at various input intensities.

/
position of the material and = z 0 at he focus, is the Rayleigh range, w 0 is the beam waist at focus, I 0 is the intensity of laser beam at the focus, and L eff is the effective thickness of the material and given as a L is the thickness of the material.The TPA coefficient values of all crystals at different input intensities are given in table

Table 1 .
Comparison of the band gap energies of B, Ho, Dy, Al, and Ag-doped InSe materials.

Table 2 .
I 0 and β values of InSe single crystals from the Z-scan curve fit with different laser intensities.

Table 3 .
NA coefficients of InSe single crystals dependent on B concentration at 99.5 GW cm2

Table 4 .
Optical limiting thresholds of undoped and B-doped InSe single crystals and different nonlinear optical materials in the literature with excitation wavelengths and pulse durations.