The nonlinear absorption (NLA) properties of ITO thin films were performed by utilizing femtosecond (100 fs), a high-repetition rate (80 MHz), and near-infrared (NIR) (750–820 nm) laser pulses. A radio frequency (RF) magnetron sputtering system was used to prepare ITO thin films of two different thicknesses. A scanning electron microscope (SEM) was used to determine the film thickness, and a UV-Visible spectrophotometer was used to observe the linear optical properties of the thin films. The open aperture Z-scan technique's nonlinear absorption studies of ITO thin films exhibited a reverse saturable absorption. The NLA properties of the ITO films varied depending on ITO thickness, incident laser power, and excitation wavelength, attributed to the increasing localized defect states in the band gap. The nonlinear absorption coefficient of 6×10− 7 cm/W and 9.7×10− 7 cm/W were measured for 170 and 280 nm film thicknesses, respectively. In contrast to the film thickness, the nonlinear absorption coefficient was inversely proportional to the excitation laser wavelength. Additionally, the optical limiting of ITO thin films was investigated, and it was found that there is a clear correlation between optical limiting and thin film thickness.
Research Article
Thickness-dependent nonlinear optical properties of ITO thin films
https://doi.org/10.21203/rs.3.rs-2472691/v1
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Femtosecond laser
ITO thin films
Nonlinear optics
Nonlinear refractive index
Nonlinear absorption coefficient
Z-scan technique
Transparent conducting oxide
There was considerable interest in transparent conductors for the reason that Badeker (1907) [1] suggested the first obvious carrying out cadmium oxide films. Transparent conducting oxide (TCO) thin films have a wide band gap of 3 to 4.2 eV [2], and they show off exceptional electrical and optical properties. Furthermore, the TCO has negligible optical absorption in the visible region of the spectrum [5]. due to their incredible optical transmission inside the visible region, these materials are used in liquid crystal shows [6], solar cell transparent electrodes [7], gasoline sensors [8], photodetectors [9], and laser damage-resistant coatings in high-power laser technology [10]. Under both inter-band and intra-band excitations, TCO substances exhibit strong nonlinear properties [11]. Within the case of strength-absorbing nonlinear processes, the TCO substances may be classified into two kinds: saturable absorption (SA) (increased transmittance) or reverse saturable absorption (RSA) (reduced transmittance). The transition from the ground state to the excited state results in the SA behavior [12], wherein absorption decreases with increasing incident light intensity and culminates in saturation of the excited country or bleaching of the ground nation [13]. In contrast, the RSA behavior is caused by excited-state absorption (ESA), multiphoton absorption (MPA), and free-carrier absorption (FCA) [14], in which absorption increases with growing light intensity. The SA effect is crucial for generating an ultrashort pulse laser utilizing TCO in mode-locking [15] and passive Q-switching techniques [16]. At the same time, the most crucial application of RSA is as an optical limiting system for the safety of sensitive optical components, such as human eyes from laser-caused damage [17]. TCO substances have also demonstrated many nonlinear applications, such as optical image processing, optical data storage, optical modulation devices, optical waveguides, optical limiters, and nonlinear optoelectronic devices [18, 19].
TCO thin films are made from a range of materials, including indium, tin, cadmium, and zinc oxides, as well as mixtures of these metals [20]. In comparison to other transparent conducting oxides, indium-doped tin oxide (ITO) films have received a lot of attention [21]. The electrical resistance of indium tin oxide (ITO) films is generally low [22], with significantly high optical transparency (over 80%) in the visible wavelength range [23]. ITO is an electrically conductive substance made up of In2O3 doped with Sn, which replaces the In3+ atoms in the crystal lattice structure of indium oxide to enhance the conductivity [24, 25]. ITO's strong conductivity is due to substitutional tin and oxygen vacancies [24, 26–28]. The ITO film is an n-type semiconductor with a band gap greater than 3 eV, and it is employed in many applications [2, 29, 30].
The interaction of high-intensity laser pulses with optical materials results in nonlinear optical (NLO) processes. These nonlinear optical processes involve the nonlinear absorption (NLA) coefficient and the nonlinear refractive (NLR) index of the material [31, 32]. The most straightforward technique for investigating the NLO properties of materials is the z-scan technique, which is used to characterize various optical materials [33].
Previous studies of the nonlinear optical properties of ITO thin films included nonlinear absorption [34, 35], Kerr nonlinearity [36], and four-wave mixing [37]. Kumar et al. [38] used a femtosecond (80 fs) laser with a wavelength of 395 nm to study the NLO properties of the gold cluster on ITO. Tingzhen et al. [39] investigated the NLA of ITO/PVA composite materials by utilizing a high repetition rate (1 MHz) and femtosecond (80 fs) laser with a wavelength of 1550 nm. Tarek Mohamed et al. [40] used a femtosecond (100 fs) and a high repetition rate (80 MHz) laser with excitation wavelengths ranging from 720 to 900 nm to measure the NLO properties of ITO thin film.
In the current study, ITO films were deposited on glass substrates by using radio-frequency (RF) magnetron sputtering at room temperature. The effect of the excitation wavelength and laser power on the nonlinear optical characteristics of the ITO thin films was investigated for two different ITO thicknesses of 170 and 280 nm. This research aimed to examine the effects of various ITO film thicknesses and various laser parameters on the optical limiting properties of ITO thin films.
2.1 ITO sample characterizations
An RF sputtering deposition system was used to create ITO thin films of various thicknesses on pre-cleansed glass substrates at room temperature. The sputtering method was first evacuated to a base pressure of 9×10− 6 Torr and maintained at 3×10− 3 Torr during the deposition process by adding argon gas at a flow rate of 20 SCCM. Two distinct thicknesses of ITO film, 170 and 280, were achieved by changing the deposition period from 1000 to 2000 seconds. Other deposition parameters were held constant during the deposition process, including substrate rotation, substrate distance, and RF power of 15 rpm, 14 cm, and 200 W, respectively. A double-beam Perkin-Elmer UV-Vis spectrophotometer was utilized to measure the optical absorption of the ITO thin films. A scanning electron microscope [JEOL JAPAN Jsm 6510LA] was used to measure the ITO thin film thicknesses.
Figure 2 illustrates the optical absorption data of various thicknesses of ITO thin films in the wavelength range from 200 to 1100 nm. In the visible range, ITO samples have good optical transparency. It is also worth noting that the absorbance in this area increases proportionally with film thickness, which could be attributable to improved film crystallinity, as depicted in Fig. 3. Absorbance spectra clearly exhibit a significant shift in wavelength towards longer wavelengths (redshift) as thickness increases, which is attributed to the thickness effect as has been reported in [41]. The band gap energy can be estimated from optical absorption data of ITO thin films by presuming an indirect transition between the valence and conduction bands and using Tauc’s plot equation [42], which can be written as:
\({\left({\propto }_{0}\text{h}{\upsilon }\right)}^{1/2}=\text{a}\left({\text{h}{\upsilon }-{\text{E}}_{\mathfrak{g}})}^{ } \right[\) 1]
Where a is a constant, Eɡ is the energy band gap of the films, \(\text{h}{\upsilon }\) is the photon energy, and \({\propto }_{0}\) is the linear absorption coefficient. The absorbance (Α) is calculated using the relation\(, {\propto }_{0}=2.303\times \frac{\text{A}}{\text{L}} \left[43\right]\), where L is the ITO thin film thickness. The (\({\propto }_{0}\text{h}{\upsilon }\))1/2 versus \(\text{h}{\upsilon }\) curves are shown in the inset of Fig. 2. Extrapolating the linear part of the plot relating to \(({\propto }_{0}{\text{h}{\upsilon })}^{1/2}\)and \(\text{h}{\upsilon }\) to \({\propto }_{0}\)h\({\upsilon }\) = 0 obtains the Eɡ of the ITO films [39]. As the thickness of the ITO thin film increases from 170 to 280 nm, the Eɡ decreases from 3.27 eV to 3 eV. For a given ITO thin film with thickness of L, the change in the band gap (\(\varDelta {\text{E}}_{\mathfrak{g}})\)can be generally explained using [44] as:
\(\varDelta {\text{E}}_{\mathfrak{g}}=\frac{{\text{ħ}}^{2}}{2\text{m}{\text{L}}^{2}}\) [2]
where m is the effective carrier mass. The decreases in \(\varDelta {\text{E}}_{\mathfrak{g}}\) is mainly due to increases in L which subsequently caused increasing in m. This suggests that unsaturated bonds are created during the thin film’s formation. These bonds are responsible for some defects in the films, which result in localized states. The density of localized states increases as the film thickness increases, potentially decreasing the band gap [45]. Using the Swanepoel formalism, the linear refractive index n0 was calculated from the absorption data (see Fig. 2) [46]. The linear refractive indices at a wavelength of 800 nm were estimated to be 1.86 and 2.19 for ITO thicknesses of 170 and 280 nm, respectively.
The real permittivity (ε) indicates the degree to which a material can be polarized and can be estimated from the absorption data (see Fig. 2) using the following equation [46]:
\(\text{R}\text{e}\text{a}\text{l} \left({\epsilon }\right)= {{\text{n}}_{0}}^{2}-{\text{k}}^{2}\) [3]
Where k is the extinction coefficient, k = λ\({\propto }_{0}\)/4π. Figure 3 shows the relationship between wavelength and real permittivity in ITO films of varying thicknesses.
Figure 4 depicts the X-ray diffraction spectra of ITO thin films of various thicknesses. An X-ray diffractometer [PANalytical X'Pert PRO] was used to examine the structure and crystallinity of the ITO thin films. The peak intensity of the (003) plane was dominant among the other orientation planes as in Fig. 4, indicating the ITO film's preferential orientation. The intensity of the plane reflections increased as the film thickness increased, indicating that the crystallite size of the films increased. The crystallite size mainly relies on the thin film thickness and the chemical composition. This implies that the structural properties of the ITO thin films have improved.
Energy-dispersive X-ray spectroscopy (EDX) JSM6510LA Eds detector Oxford was used for elemental analysis of ITO thin films. The EDX used for determining the atomic composition of ITO film is implemented utilizing an electron beam with an acceleration voltage of 30 keV, and the counting time of the spectrum is 35 s. Figure 5 presents the EDX spectra of the ITO film. To estimate the atomic composition of ITO film, we used the ZAF method, where Z is the atomic number, A is the absorption, and F is the fluorescence. The results are summarized in Table 1, which shows a dopant concentration of 4% for Sn in ITO thin film.
|
Element |
KeV |
Atom% |
Error% |
Mass% |
|---|---|---|---|---|
|
O K |
0.525 |
66.5 |
2.98 |
21.6 |
|
In L |
3.28 |
29.39 |
0.98 |
68.49 |
|
Sn L |
3.44 |
4.11 |
0.81 |
9.91 |
2.2 Z-scan set up
The Z-scan experimental setup for studying the NLA coefficient of ITO film is depicted in Fig. 6. The laser pulses are delivered by the laser system (INSPIRE HF100) from Spectra-Physics, which a mode-locked femtosecond Ti pumps: a sapphire laser (MAI TAI HP) from Spectra-Physics with an average power of 1.5–2.9 W, a repetition rate of 80 MHz, and a wavelength range of 690 to 1040 nm. The laser system (INSPIRE HF100) operates at the fundamental IR pump wavelengths and two other modes of operation: (i) Second Harmonic Generator (SHG), (ii) Optical Parametric Oscillator (OPO) [13, 40]. These modes of operation allow the output wavelength range between 345 nm and 2500 nm, which is covered by four exit apertures. The ITO samples are irradiated with Gaussian laser pulses of 100 fs duration at different wavelengths ranging from 750 nm to 820 nm, selected by the fundamental IR pump aperture. The spatial profile of the laser beam is a Gaussian distribution with TEM00 spatial mode and M2 < 1.1. The Gaussian laser pulses are tightly focused by a convex lens with 5 cm. The ITO sample is placed on a micrometer translation stage to scan the sample around the focus. The power meter (PM, Newport 843 R) determines the transmitted intensity from the samples as a function of their position relative to the focus. The normalized transmittance is calculated by adjusting the linear transmittance "S" of the aperture size to S = 1 for OA. We can deduce the nonlinear absorption coefficient from the OA experimental curves. The current experimental investigation has a 10% uncertainty, which results mainly from the determination of the irradiance distribution used in the experiment, i.e., beam waist, pulse width, and laser power calibration.
3.1 Open aperture Z-scan Measurements
Figures 7 and 8 demonstrate the experimental open-aperture (OA) Z-scan of ITO thin film was performed using fs and an HRR laser at 80 MHz. The nonlinear optical properties of ITO film at different thicknesses of 170 and 280 nm were studied at various laser beam excitation powers ranging from 1.2 to 1.8 W and different excitation wavelengths of 750, 800, and 820 nm. The curves shown in Figs. 7 and 8 all show Reverse Saturable Absorption (RSA). The transmission is symmetric around the focus (Z = 0), indicating an intensity-dependent absorption effect with a minimum transmission at the focus (valley) [47, 48]. The nonlinear absorption coefficient of a sample, subjected to the high-intensity laser (I), is dependent on the intensity delivered to the sample., as indicated by the following equation [49, 50]:
\(\propto \left(\text{I}\right)={\propto }_{0}+{\beta }\text{I}\) [4]
Where \({\propto }_{0}\) is the linear absorption coefficient and ꞵ is the two-photon nonlinear absorption (2PA) coefficient, To determine the NLO absorption coefficient, the OA Z-scan data were fitted by the NLO absorption model given by [51–53]
\({\text{T}}_{\text{O}\text{A}} = 1-\) \(\left.\left( \frac{{\beta } {{\text{I}}_{0 }}^{(\text{n}-1) }{\text{L}}_{\text{e}\text{f}\text{f}}}{{\text{n}}^{\frac{3}{2}}{\left(1+\frac{{\text{Z}}^{2}}{{{\text{Z}}_{0}}^{2}}\right)}^{(\text{n}-1)}}\right.\right)\) [5]
Where I0 is the peak intensity at the focus (Z = 0), and n = 1 for two-photon nonlinear absorption and n = 2 for three-photon nonlinear absorption. Z0 is the Rayleigh length \({\text{Z}}_{0}=\frac{{\pi }{{{\omega }}_{0}}^{2}}{{\lambda }}\). The \({\text{L}}_{\text{e}\text{f}\text{f}} =1-({\text{e}}^{-\text{n}{\propto }_{0}\text{L}}/\text{n}{\propto }_{0}\)), where L is the thickness of the sample. The normalized transmittance (TOA) decreases when the excitation power decreases, as shown in Fig. 7, while in Fig. 8 the TOA decreases with an increase in excitation power.
The observed RSA in the ITO thin films can be explained using the energy levels diagram, as shown in Fig. 9. ITO is made up of indium oxide doped with tin, and indium oxide has a valence band of O2−: 2p and In3+: 3d. The conduction band is made up of 5s and 5p. The conduction band is dominated by indium 5s orbitals, while the valence band is dominated by oxygen 2p electrons [26]. Due to n-type doping of tin impurities, the Fermi energy (Ef) is found a few eV below the conduction band [54]. The majority of carriers in ITO are electrons, which come mostly from the doping of donor Sn and oxygen vacancies. The excited electrons move from the valence band (2p) to the conduction band (5s). RSA is related to excited-state absorption (ESA), free carrier absorption (FCA), two-photon absorption (2PA), and nonlinear scattering [55]. 2PA relies on the excitation wavelength and energy band gap [56]. When ESA takes place, molecules are excited from an already excited state (5s) to a higher excited state (5p). For this to happen, the population of excited states should be high enough to increase the probability of photon absorption from the state [57]. FCA is expected to occur in ITO film because ITO is an n-type semiconductor with free carriers in the 5s that absorb incident photons and excite them to a higher excited state in the conduction band (5p) shown in Fig. 9. When the number of O vacancies and donor levels increase, defect state absorption increases, improving the RSA [58]. From Fig. 9. N0, ND, N1, and N2 denote the population densities corresponding to ground-state (S0), defect state (SD), and first and second excited states. The σ0 is the ground state absorption cross-section; σ1, σ2 are the defect state cross-section and excited-state absorption cross-sections, respectively. The τ3, τ2, and τ1 are the excited-state lifetimes. The total absorption coefficient and pump intensity are used to define the nonlinear propagation and rate equations, which are represented as [59–64]:
\(\frac{\text{d}\text{I}\left(\text{z}\right)}{\text{d}\text{z}}=-\propto \left(\text{I}\right) \text{I}\) [6]
\(\frac{\text{d}{\text{N}}_{0}}{\text{d}\text{t}}=-\frac{{N}_{0 }{\sigma }_{0}I}{hʋ}+ \frac{{N}_{D}}{{\tau }_{1}}\) [7]
\(\frac{\text{d}{\text{N}}_{D}}{\text{d}\text{t}}=\frac{{N}_{0 }{\sigma }_{0}I}{hʋ}-\frac{{N}_{D }{\sigma }_{1}I}{hʋ}+ \frac{{N}_{1 }}{{\tau }_{2}}-\frac{{N}_{D}}{{\tau }_{1}}\) [8]
\(\frac{\text{d}{\text{N}}_{1}}{\text{d}\text{t}}=\frac{{N}_{D }{\sigma }_{1}I}{hʋ}-\frac{{N}_{1 }{\sigma }_{2}I}{hʋ}-\frac{{N}_{1 }}{{\tau }_{2}}+ \frac{{N}_{2 }}{{\tau }_{3}}\) [9]
\(\frac{\text{d}{\text{N}}_{2}}{\text{d}\text{t}}=\frac{{N}_{1 }{\sigma }_{2}I}{hʋ}- \frac{{N}_{2 }}{{\tau }_{3}}\) [10]
The transmitted intensity through the thin film in Eq. 6 can then be expressed as [64]:
\(\frac{\text{d}\text{I}\left(\text{z}\right)}{\text{d}\text{z}}=-[{N}_{0 }{\sigma }_{0}I+{N}_{D }{\sigma }_{1}I+{N}_{1 }{\sigma }_{2}I]\) [11]
According to the Runge-Kutta technique and the Eqs. from 6 to 11, RSA occurs when the σ1 and σ2 are larger than σ0. For simplicity, M1 = σ1/σ0, M2 = σ2/σ1 and M3 = σ2/σ0 are assumed. RSA happens when M1 and M3 are both greater than one [65].
The NLA coefficient as a function of excitation power was estimated from the best fit of the experimental OA data shown in Figs. 7 and 8 using Eq. 5. Figure 10 shows the effect of laser excitation power on the ꞵ of an ITO thin film at thicknesses of 170 and 280 nm and excitation wavelengths of 750, 800, and 820 nm. For each excitation wavelength, as the excitation power increases the ꞵ decreases, due to the many-body effect, and the relaxation time τ3, τ2, and τ1 of excited states gets shorter [65, 66]. When the excitation power increases, the number of free carriers (electrons and holes) also increases. The electrons in the conduction band (5s) and the holes in the valence band (2p) interact with one another. This interaction is called "many-body interactions" [67]. The terms simply describe the Coulomb repulsion between electrons and between holes, and the Coulomb attraction between electrons and holes [68]. As a result, collisions between free carriers in the 5s and 2p increase, scattering of photons and phonons increases, and ꞵ decreases.
As shown in Fig. 8, the normalized transmittance (TOA) decreased as the excitation power increased, but the values of the ꞵ decreased. The RSA represents the contribution from nonlinear absorption as well as nonlinear scattering. Nonlinear scattering increases when excited carrier declines through nonradiative relaxation processes [69]. As shown in Fig. 9, the nonradiative decay of excited carriers via intraband transitions in 5s and 5p results in thermal energy. The thermal energy generated in the ITO film can cause nonlinear scattering and affect the ꞵ. The equation gives the laser light attenuation inside the sample [69, 70].
\(\frac{\text{d}\text{I}\left(\text{z}\right)}{\text{d}\text{z}}=-{\propto }_{0}\text{I}\left(\text{z}\right)-{\beta } {\text{I}}^{2}\left(\text{z}\right)\) [12]
where I(z) is the intensity incident on the sample, and z is the optical path length along with the sample. The scattering coefficient \({\propto }_{s}\) can be used to modify the nonlinear scattering losses in Eq. 12 \(\left[71\right]\).
\(\frac{\text{d}\text{I}\left(\text{z}\right)}{\text{d}\text{z}}=-{\propto }_{0}\text{I}\left(\text{z}\right)-{({\propto }_{s}+{\beta }}_{ }\left){\text{I}}^{2}\right(\text{z})\) [13]
Because of the energy band gap and carrier density, nonlinear scattering occurs significantly more at an ITO thickness of 280 nm than 170 nm at high excitation power. Electrons in the 2p absorb incident photon energy and are excited to a highly excited state at a thickness of 280 nm, whereas, at a thickness of 170 nm, electrons are excited to a low excited level, so the thermal energy is lower than at a thickness of 280 nm, as illustrated in Fig. 9.
The NLO properties of soda–lime glass substrates at different wavelengths and peak intensities were reported in [72]. According to this study, the NLA coefficient of soda-lime glass is 1016 orders of magnitude lower than the NLA coefficient of ITO thin film. Consequently, the contributions of the 1 mm soda–lime glass utilized as a substrate in this study were negligible compared to the NLA coefficient of the ITO thin film.
3.2 Investigating the effect of excitation wavelength on the nonlinear absorption coefficient
Figures 7 and 8 presents the dependence of the NLA coefficient on excitation wavelength for ITO thin films at 750, 800, and 820 nm, as well as different ITO thicknesses of 170 and 280 nm. The absorbance drops as the excitation wavelength increases, indicating a decrease in RSA. Moreover, with increasing photon energy, the probability of 2PA increases, causing nonlinear absorption to vary significantly [73]. The experimental data in Figs. 7 and 8 are fitted using Eq. 5 to obtain the ꞵ at various excitation wavelengths. Figures 10a and b show the nonlinear absorption coefficient as a function of excitation wavelength at constant ITO thin film thicknesses of 170 and 280 nm, respectively. As the excitation wavelengths increase, the ꞵ decreases linearly. Excitation photon energy and ITO band structure can explain the dependence of ꞵ. Because the photon energy is much higher than the ITO thin film's band gap, the valence electrons absorb it and undergo indirect transitions [74]. As presented in Fig. 11, when the excitation wavelength reduced from 820 to 750, the ꞵ increases due to the increase in photon energies, resulting in an increase in RSA [33]. The dependency of the nonlinear absorption coefficients on the excitation wavelength is influenced by several parameters, such as σ1, σ2 and the ratio of σ1/σ2. As the excitation wavelength decreased, the ratio σ1/σ2 increased, resulting in increased sequential two-photon absorption (STPA), as reported in [74, 75]. This demonstrates that the NLO absorption response is strongly dependent on the excitation wavelength, implying that nonlinear absorption is equally sensitive to the wavelength of excitation as it is to the intensity of excitation.
3.3 The influence of different ITO thicknesses on the nonlinear absorption coefficient
The RSA response increases with ITO thickness, as shown in Figs. 7 and 8. The \({\beta }\) of ITO, thicknesses of 170 and 280 nm is 6\(\times\)10−7 cm/W and 9.7\(\times\)10−7 cm/W, respectively. Because of FCA, ECA, 2PA, and nonlinear scattering, the β of an ITO thin film with a thickness of 280 nm is approximately three times higher than that of a 170 nm thickness film. As explained by Fig. 9, the RSA can be improved by increasing ITO thickness, lowering the bandgap energy, and enhancing the defect state absorption. The experimental evidence indicates that these defect states can absorb excited electrons and participate in optical absorption. As the defect states increase, the VB becomes more populated, resulting in improved NLA. The optical limiting effect of the ITO film at a thickness of 280 nm is better than that of 170 nm.
3.4 Nonlinear optical susceptibility of ITO thin films
Using the experimental data of nonlinear refractive index n2 and nonlinear absorption coefficient \(\text{ꞵ}\), the real and imaginary components of the third-order susceptibility \({{\chi }}^{\left(3\right)}\) can be determined. A material's nonlinear susceptibility can be expressed by [76, 77] as:
\({{\chi }}^{\left(3\right)}=\text{R}\text{e}\left[ {{\chi }}^{\left(3\right)}\right]+\text{i} \text{I}\text{m}\left[{{\chi }}^{\left(3\right)}\right]\) [14]
Where the real part is associated to the nonlinear refractive index n2 and the imaginary part is associated with the nonlinear absorption coefficient ꞵ. The real nonlinear susceptibility \(\text{R}\text{e}\left[{{\chi }}^{\left(3\right)}\right]\) can be expressed as:
\(\text{R}\text{e}\left[ {{\chi }}^{\left(3\right)}\right]= \frac{{\text{n}}_{0}}{3{\pi }} {\text{n}}_{2}\) [15]
The imaginary nonlinear susceptibility \(\text{I}\text{m}\left[{{\chi }}^{\left(3\right)}\right]\) can be expressed as:
\(\text{I}\text{m}\left[{{\chi }}^{\left(3\right)}\right]\left(\text{e}\text{s}\text{u}\right)=\left[\frac{{10}^{-7}c{{{\lambda }\text{n}}_{0}}^{2}}{96{{\pi }}^{2}}\right] \text{ꞵ}\) \(\left[16\right]\)
where c is the speed of light, λ is the excitation wavelength of the laser light, and n0 is the linear refractive index of the ITO films. At an excitation wavelength of 800 nm and an excitation power of 1.6 W, the imaginary nonlinear susceptibility \(\text{I}\text{m}\left[{{\chi }}^{\left(3\right)}\right]\) was found to be 2.08 × 10− 10 esu and 5.53 × 10− 10 esu for ITO thicknesses of 170 and 280 nm, respectively. The third-order nonlinear optical properties of given materials can also be characterized by a figure of merit (FOM), which depends on the linear absorption 𝛼0 and can be expressed by [78, 79] as.
\(\text{F}\text{O}\text{M}=\left|\frac{ \text{I}\text{m}\left[{{\chi }}^{\left(3\right)}\right] }{{{\alpha }}_{0}}\right|\) [17]
Based on the data presented in Table 2, the figure of merit of ITO thin film at a thickness of 280 nm is approximately three times larger than that of 170 nm. The absolute value of the nonlinear susceptibility is expressed as:
\(\left|{{\chi }}^{\left(3\right)}\right|=\sqrt{\left({\text{R}\text{e}\left[ {{\chi }}^{\left(3\right)}\right]}^{2}+{\text{I}\text{m}\left[{{\chi }}^{\left(3\right)}\right]}^{2}\right)}\) [18]
The absolute values of \({{\chi }}^{\left(3\right)}\) are given in Table 2
Table 2 The nonlinear optical parameters of ITO thin films for different thicknesses at an excitation wavelength of 800 nm and an excitation power of 1.6 W.
3.5 The optical limiting effect of ITO thin film
The optical limiting effect of an ITO thin film sample at different thicknesses of 170 and 280 nm is investigated experimentally by scanning the input excitation power at an excitation wavelength of 800 nm. The ITO sample was placed at the focus of a 5 cm convex lens and the transmitted power was measured at different input powers. Figure 12 indicates the output power variation with input excitation power obeying Beer’s law\(\text{I}={\text{I}}_{0}{\text{e}}^{(-\propto \text{L})}\), where I, I0, \(\propto\), and L are the output intensity, incident intensity, the absorption coefficient, and the sample thickness, respectively. In the case of ITO thicknesses of 170 nm, the output power increases linearly with increasing input power, as presented in Fig. 12. In the case of ITO thicknesses of 280 nm, the output power begins to saturate at 1.4 W input power. The optical limiting behaviour of ITO has been found to be influenced by its thickness. ITO exhibits a good optical limiter at a thickness of 280 nm, making it appropriate for protecting fragile optical components.
In summary, the nonlinear absorption of ITO thin film was studied utilizing the OA z-scan method for different thicknesses, distinctive excitation wavelengths, and excitation powers for ITO thin films produced using the RF sputtering method. The results show that excited state, defect state, and ground-state absorption all compete to illustrate RSA behavior. The ITO thickness, excitation wavelength, and excitation laser power all had a linear relationship with the nonlinear absorption coefficient and third-order susceptibility. At a large ITO thickness (280 nm), the NLA coefficient and third-order susceptibility were found to be improved. The ITO thin films with a thickness of 280 nm had substantial optical limiting at an excitation wavelength of 800 nm
Acknowledgment
This study was supported by a Science and Technology Development Fund (STDF) through the Basic Sciences Research Program (30147).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data Availability Statement
The data that support the findings of this study are available from the corresponding author upon reasonable request.
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