1 Introduction

In the recent era of science and technology, the amorphous chalcogenide materials have a wide range of applications in optoelectronics, phase change memory device, solar cells, sensor technology, telecommunication sector, and many more [1,2,3]. These chalcogenide thin films have large nonlinear optical behavior than their oxide counterpart due to the presence of heavy chalcogen atoms which have vibrational bonding at low energy. This unique behavior brings large transparency in the mid-IR region that is useful for optical fibre [4]. Among the chalcogenide alloys, Se containing As-based chalcogenides has large third-order optical nonlinear behavior because of the available double lone pair electrons [5]. Such properties can be modified by changing the composition of the films [6], treating the films by energetic ions [7], annealing at different temperatures [8], photo-irradiation [9], gamma irradiation [10], and many more techniques.

Among the above methods, thermal annealing process is well-known for the study on the depletion of inherent defects present in the vitreous state as well as the phase transformation effects. Such method allows to diffuse the composite system and facilitates the change in the physical and chemical properties of the systems. Heat treatment is a simple method to measure the reduction in the inherent defects in the amorphous state and amorphous-crystalline phase transformation [11]. The relaxation of the film into equilibrium condition is accelerated by thermal annealing than the conventional room temperature. It is to be noted that the relaxation time at normal room temperature for non-annealed films is very high [12]. The relaxation time is less at a characteristic temperature called as glass transition temperature (Tg) which is an important parameter for characterization of glassy state. In a glassy material, the lowest temperature at which the defects anneal away from the system is the glass transition temperature (Tg). Thus, the density of defects depends upon the glass transition temperature. Tg is related to the rigidity of the glassy network which is associated with the physical parameters like mean coordination number, cohesive energy, fixed value of viscosity (μ(Tg)≈1013 poise) for chalcogenides, dissociation energy etc. [13]. Hence, for chalcogenide glassy materials, the annealing temperature was selected by considering Tg of the material. The annealing of As50Se50 at a temperature 150 °C (Tg for As50Se50 is 156 °C [14]) caused atomic rearrangements that facilitated the formation of more homogeneous surface compositions and enhanced the concentration of heteropolar bonds over homopolar ones [15]. Tsvetkova et al. have studied that annealing at a temperature near Tg, affected the optical reflectivity and created a rippled surface, which depends on the concentration of As [16]. Similarly, the increase in annealing temperature and duration leads to the transformation of structural properties by the formation of AsSe3 pyramidal units with low surface roughness [17]. In the PLD based As50Se50 system, the thermal annealing reduced the structural and electronic defects [18]. Annealing near Tg brings the structural polymerization through the conversion of the homopolar bond to the heteropolar bond. The non-linear optical and dispersion parameter in As–Se–Sb films got largely affected by the thermal annealing process [19]. Due to annealing near its Tg, enhances the linear optical properties of As2Se3 [20]. Annealing improves the performance of Ge–Se thin film which is used for device applications [21]. The femtosecond laser irradiation on As35Se65 thin films resulted in the submicron gratings used for optical devices [22]. Due to the lack of systematic study on the tailoring of the linear and nonlinear optical parameters of As35Se65 film by annealing below and above glass transition temperature encouraged us for the present study.

The present study is focused on the analysis of both nonlinear and linear optical parameters of As35Se65 thin film annealed at 150 °C (below Tg) and 250 °C (above Tg). The various experimental characterizations were done to study the structural, optical, morphological behaviors. The single oscillator Wemple Di-Domenico model was used to obtain the two energies such as oscillator and dispersion energy. The obtained linear parameters were used to deduce the nonlinear constants by applying the semi-empirical Miller’s formula. The various linear optical constants (oscillator energy, optical band gap, dispersion energy, extinction coefficient, refractive index, absorption coefficient, optical density) and nonlinear optical parameters (third-order nonlinear susceptibility, nonlinear refractive index) have shown opposite nature for the two-annealing temperatures.

2 Experimental procedures

2.1 Details of thin film preparation

Bulk As35Se65 alloy was prepared by melt quenching method through the mixing of As and Se by taking stoichiometric amount in a quartz ampoule. After that, the ampoule was sealed under high vacuum condition and was put inside a furnace. The ampoules were heated in the furnace till 900 °C, at a slower rate of about 3–4 °C/min, and held at that temperature for 20 h. At the time of heating, the ampules were constantly shaken to achieve homogeneity. Then the ampule was brought out from the furnace and was rapidly quenched with ice-cold water. After that, the ampule was broken and the bulk alloy was removed for the thin film preparation. In the thermal evaporation procedure, the thin films were prepared from the bulk using the vacuum coating unit (HIND–HIVAC Model 12A4D). The thickness of the film (~ 800 nm) and rate of deposition (0.5 nm/s) were regulated through the crystal thickness monitor. The deposition process took place on clean glass substrates under 10–5 Torr vacuum. The as-prepared thin film was subjected to thermal annealing at 150 °C (below Tg) and 250 °C (above Tg) for 2 h.

3 Experimental techniques

To get the structural information, the X-ray diffraction (XRD) was done by Bruker D8 Advance, Cu-Kα radiation (λ = 1.54 Å) for the three films. The Raman spectroscopy measurements were performed in the LabRAM HR system by 514.5 nm argon laser with a CCD detector in backscattering mode in a range of 50–400 cm−1 to get more structural details. The constituent elements in the film such as As and Se was checked by energy-dispersive X-ray analysis (EDAX) and the surface morphology of the films were studied by Field emission scanning electron microscope (FESEM). The scanning of the films was done at 1 cm2 size exposure area by 20 kV voltage and 40 mA emission current at a pressure of 2 × 10–7 Torr. The data was recorded 3–4 times at various positions to minimize the errors. The optical properties were studied from the reflectance and transmittance data obtained by UV–Vis spectrometer (IFS66v/S) in 500–1200 nm wavelength range at room temperature. The chemical bonding modifications induced by annealing at each temperature were recorded in XPS (Axis Ultra, Kratos Analytical, UK) measurement. The core-level XPS spectra were taken by Al Kα X-rays (1486.6 eV) with a vacuum of 2 × 10–9 Torr. As the prepared films are of insulating glassy nature, the required charge correction was done with C1s binding energy (BE) of 284.6 eV [23, 24]. The original BE data correction was done using the calibration factor. The scan was performed at different portions of the films to reproduce the data.

4 Results and discussion

4.1 Structural analysis

The XRD patterns of the three films (as-prepared and 150 °C, 250 °C annealed) are presented in Fig. 1 which shows the absence of any sharp crystalline peaks. This confirms the amorphous structure of the studied films from which we can conclude that the annealing the film at both below and above Tg does not bring any change in its amorphous form. The humps appeared at different θ values are due to the glass substrates used for the film preparation [25, 26].

Fig. 1
figure 1

XRD patterns of studied thin films

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The Raman spectra for the as-prepared and 150 °C, 250 °C annealed films show peaks at different wavenumbers, as shown in Fig. 2. The peak located at 220 cm−1 is due to the As–Se vibration of the pyramidal structure AsSe3/2 symmetric stretching units [27]. However, there is a shoulder peak at 234 cm−1 which is assigned to the vibrations of As–Se structural units [28]. The peak intensity of these two peaks increased for the 150 °C annealed film, while it decreased for the 250 °C annealed film. In addition, the position of 234 cm−1 peak shifted to 243 cm−1 for the 250 °C annealed film. Therefore, we have observed the opposite change in intensity for the two films annealed at below Tg and above Tg which clearly indicates the different amorphization in the two films. There is another low-intensity peak at 462 cm−1 which may be for Se–Se vibrational bonds which disappears at 250 °C annealing. The Se–Se homopolar bond acts as a defect state in the system. As temperature increases, the defect present inside the system annealed away which reduced the disorder. The intensity for 150 °C annealed film is more than that of 250 °C annealed one infers the less disorder in 250 °C annealing than 150 °C annealing.

Fig. 2
figure 2

Raman spectra of the studied thin films

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5 Morphology study

The constituent As and Se elements of both as-prepared, 150 °C and 250 °C annealed films were verified by EDAX picture as presented in Fig. 3. The respective peak corresponds to different elements and the corresponding film composition is approximately same and within 4% error as compared to the calculated value (Table 1).

Fig. 3
figure 3

EDAX picture of as-prepared, 150 °C and 250 °C annealed thin films

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Table 1 Composition of as-prepared and annealed As35Se65 films
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The FESEM pictures at 200 nm scale of the as-prepared and 150 °C, 250 °C annealed As35Se65 films are shown in Fig. 4. The picture shows the homogeneous and smooth nature of the as-prepared film. The annealing effect on surface morphology is visible from these pictures as we can see that the annealed film possesses some agglomerations. We have observed the dense granules in the 150 °C annealed film and less granules in the 250 °C annealed film. The agglomeration increased upon annealing. Therefore, the annealed films are rough in nature.

Fig. 4
figure 4

FESEM picture of as-prepared and annealed thin films

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5.1 Optical study

5.1.1 Linear optical property analysis

5.1.1.1 Transmittance (T) and reflectance (R)

The optical transmittance is the property of the material that relates the capability of transmitting the electromagnetic waves through the system. This property is contributed to several applications in the field of optical and electronic devices. The reflectance and transmittance spectra of as-prepared, 150 °C and 250 °C annealed films from the UV–Vis spectroscopic measurement are shown in Fig. 5.

Fig. 5
figure 5

T and R spectra of the films

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From Fig. 5, the equispaced oscillatory fringes in the transmission spectra over the longer wavelength region (700–1150 nm) give a quite clear indication regarding uniformity in the thickness throughout the film [29]. It was observed that the transmittance of the films increased with wavelength. Furthermore, annealing below glass transition temperature (Tg), i.e., 150 °C causes a slight decrease in transmittance from 61% (as-prepared) to 60%, whereas an increase in transmittance to 63% has been seen for annealing above the Tg, i.e., 250 °C.

Figure 5 also depicts the shifting of absorption edge towards the longer wavelength side (redshift) for the 150 °C annealed film, whereas it shifts towards lower wavelength region (blue shift) for 250 °C annealed film as compared to the as-deposited film. The reflectance spectra showed the opposite behavior as compared to the transmittance curve.

5.1.1.2 Absorption coefficient (α)

The absorption coefficient (α) provides information regarding the optical energy bandgap and band tailing parameters of the amorphous system. The α value of the thin films over strong absorption region was evaluated using both the T and R spectra by [30]:

$$\alpha = \frac{1}{d}\ln \frac{{\left( {1 - R} \right)^{2} }}{T},$$
(1)

where d represents the film thickness (~ 800 nm). The behavior of α for As35Se65 thin film at the two-annealing temperature with wavelength is shown in Fig. 6. It is found that the α value is of 104 cm−1 order and decreases with wavelength which indicates the better transparency of the films and radiation can travel at a much faster and easier way through it. The variation of α for the 150 °C and 250 °C annealed films are opposite in nature, i.e., 150 °C annealed film shows redshift, whereas 250 °C annealed film shows blue shift.

Fig. 6
figure 6

α and k of the studied films

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5.1.1.3 Extinction coefficient (k)

The parameter extinction coefficient measures the loss of light that got absorbed or scattered per unit volume. Using the value of absorption coefficient (α), the extinction coefficient of the system can be estimated through the relation given as [31]

$$k = \frac{\alpha \lambda }{{4\pi }}.$$
(2)

Figure 6 (inset plot) represents the behavior of k with the energy of incident radiation (hν). From the plot, it can be inferred that the high value of k at high energy region signifies the opaque-ness at this range. After the absorption edges, it can be seen that k has a very small value, which indicates better transmittance. Here also we have observed the increase and decrease in k value with annealing at 150 °C and 250 °C, respectively. The change in the value of the extinction coefficient leads to modify the non-linear parameters of the materials [32].

5.1.1.4 Optical density (OD)

There is another parameter that describes the ability to absorb the electromagnetic radiation, known as optical density. This term characterizes the propagation of electromagnetic radiation through the material system that can be used to manufacture several optoelectronic devices. Furthermore, the optical density is related to ‘α’ by the relation [33]:

$${\text{Optical}}\;{\text{density}}\;\left( {\rm OD} \right) = \alpha \, x \, d,$$
(3)

where α and d represent the absorption coefficient and film thickness (~ 800 nm).

The behavior of optical density with wavelength for as-deposited and the film annealed at 150 °C and 250 °C is shown in Fig. 7 which shows the decrease of optical density with wavelength up about 680 nm and then saturated. This abrupt decrease is almost the wavelength of the absorption edges of the studied film. Then the optical density systematically decreased with the increase in ‘λ’ for all the films. In addition, it was observed the opposite changes in the OD values with annealing at 150 °C and 250 °C, respectively.

Fig. 7
figure 7

Variation of OD with λ

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5.1.1.5 Skin depth (δ)

The change in the skin depth or penetration depth (δ) of the studied thin films upon incident radiation energy can be estimated from the reciprocal of the absorption coefficient (α):

$${\text{Skin depth}}\left( \delta \right) = 1/\alpha .$$
(4)

This behavior relates to the exponential behavior of the amplitude of the electromagnetic waves after overpassing the film thickness [33]. Then the skin depth of the film is defined by

$$\delta \left( {{\text{cm}}} \right) = d.\ln \left[ {\frac{T}{{\left( {1 - R} \right)^{2} }}} \right],$$
(5)

where d represents film thickness, T and R are the transmittance and reflectance data of the studied films. Figure 7 (inset) depicts that skin depth decreased for 150 °C annealed film, whereas increased with annealing temperature 250 °C. Furthermore, when the energy of the incident radiation increased the skin depth is dramatically decreased for all films near to zero value.

It is also noted that there is a directly proportional interrelation between skin depth (δ) and optical energy bandgap (Eg). This relation comes from the dependency over the optical conductivity as both are dependent on conductivity.

5.2 Optical bandgap (E g) and Tauc parameter (B 1/2)

Using the values of ‘α’, the optical bandgap (Eg) of the system was evaluated from the Tauc formula (for α ≥ 104 cm−1) [34]:

$$\alpha hv = B\left( {hv - E_{g}^{{{\text{Opt}}}} } \right)^{m},$$
(6)

where B represents the Tauc parameter and m is a parameter related to the kind of electronic transition responsible for electron and absorption in both the valence and conduction band. According to Mott and Davis model [35] for amorphous semiconductor ‘m’ has several values depending on the type of transitions taking place inside the system like m = ½, 3/2, 2, and 3 for direct allowed, direct forbidden, indirect allowed and indirect forbidden transition, respectively. Here, m = 2 fits for the analysis of As35Se65 thin film samples which represent an indirect allowed transition process.

Figure 8 represents the variations of (αhv)1/2 vs incident energy (hv) of as-deposited and annealed thin films from which energy bandgap (Eg) is obtained from intercept of the linear portion of spectra with the X-axis ((αhv)1/2 = 0). The obtained Eg values are tabulated in Table 2 that shows the decrease of bandgap from 1.66 eV (as-prepared) to 1.62 eV for 150 °C annealed film and increased to 1.68 eV for the 250 °C annealed film which was annealed above Tg.

Fig. 8
figure 8

(αhν)1/2 vs hν for the studied films

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Table 2 Optical parameters of the studied films
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The reduction of the optical energy bandgap upon annealing below Tg may be explained through the Mott and Davis model [35]. As per the model, annealing causes the breakdown of the weaker bonds to form surface dangling bonds which are responsible for the formation of localized states in the bandgap region. Such localized states form band-tail, that decreases the optical bandgap like other studies due to the annealing effect [36, 37]. However, the increase in Eg value for the 250 °C annealed film may be due to the reduction of defect states and an increase in structural ordering which is noticed from the B1/2 values. Due to annealing, dangling bond defects along with some unsaturated bonds gradually annealed out by forming more saturated bonds. Thus, the decrease of unsaturated bonds causes decrease in the density of localized states which consequently increases the optical bandgap [38, 39].

The observed Eg value shows a good correlation with the skin depth spectra as skin depth is less for 150 °C annealed film which has reduced the bandgap and skin depth is more for the 250 °C annealed film which has increased bandgap. The measurement of the degree of disorder (B1/2) has been done by calculating the slope from Fig. 8 fitting and shown in Table 2. It was observed that the value of Tauc parameter decreased for 150 °C annealed film and increased for 250 °C annealed film.

5.2.1 Urbach energy (E u)

In the amorphous chalcogenide system, the absorption edges observed differently by showing an exponential behavior with incident energy (hv) near the absorption edges as represented by Urbach relation [40]:

$$\alpha \left( {hv} \right) = \alpha_{0} e^{{\frac{hv}{{E_{{\text{u}}} }}}},$$
(7)

where α0 is a constant and Eu represents the Urbach Energy which was calculated from the slope of the straight line drawn in the plot ln(α/α0) vs (hv). The values of Eu, which was estimated from the slope (1/Eu) of the spectra are listed in Table 2. The Urbach energy is being interpreted as the width of the tails of the localized states present in the gap region and measures the degree of disorder in amorphous semiconductor systems. It is seen that the Urbach energy increased for 150 °C annealed film and decreased for 250 °C annealed film. The increase/decrease of Eu and decrease/increase of Eg with annealing temperature can be attributed to the increase/decrease of the degree of disorder which results in an increase/decrease of the band tailing, and consequently a decrease/increase of Eg values [41, 42].

5.2.2 Linear refractive index (n)

Most of the calculation of the refractive index and thickness of the films by Swanepoel’s envelope method [43] has been proved approximately correct. According to this method, the first approximation refractive index (n1) for the region of weak and moderate absorption can be estimated according to the equation:

$$n_{1}^{2} = \left[ {N + \left( {N^{2} - S^{2} } \right)^{1/2} } \right].$$
(8)

where

$$N = 2S\left( {\frac{{T_{{\text{M}}} - T_{{\text{m}}} }}{{T_{{\text{M}}} T_{{\text{m}}} }}} \right) + \left( {\frac{{S^{2} + 1}}{2}} \right),$$
(9)

where Tm and TM are the minima and maxima of transmittance at fixed λ and ‘S’ represents substrate refractive index (1.51). By following the procedures as detailed in Ref. [43], the actual refractive index of the films at different wavelengths was estimated and is shown in Fig. 9. It was observed that the refractive index decreased with increases of the wavelength which is attributed towards the normal dispersion of the studied films. It also shows that the refractive index increased for 150 °C annealed film from the as-prepared film, whereas decreased with annealing at 250 °C. This behavior of the refractive index satisfies the Moss rule, i.e., Egn4 ~ constant [44] and studied by other others in different materials [45, 46].

Fig. 9
figure 9

n vs λ plot of the studied films

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5.2.3 Single oscillator energy (E 0) and dispersion energy (E d)

Wemple-Di Domenico (WDD) single effective oscillator model [47] is based on refractive index dispersion of the system which gives an inherent physical explanation of the measured parameters by just fitting the experimental data [33]. This model provides two main outputs; dispersion energy (Ed) and effective single oscillator energy (E0). The E0 is also known as an average of the energy gap that describes the information regarding the overall band structure of the system which is completely different from Eg, but there exists an empirical relation between E0 and Eg, i.e., E0 ≈ 2Eg [48]. However, in our case, the E0 value is not exactly double of the Eg value. Similarly, the dispersion energy Ed signifies the oscillator strength that is related to the interband optical transition of the system.

According to the WDD dispersion theory, the ‘n’ value is related to hv, E0 and Ed through the relation:

$$(n^{2} - 1) = \frac{{E_{0} E_{{\text{d}}} }}{{E_{0}^{2} - \left( {h\vartheta } \right)^{2} }},$$
(10)

which can also be written as;

$$(n^{2} - 1)^{ - 1} = \frac{{E_{0}^{2} - \left( {h\vartheta } \right)^{2} }}{{E_{0} E_{{\text{d}}} }} = \frac{{E_{0} }}{{E_{{\text{d}}} }} - \frac{{\left( {h\vartheta } \right)^{2} }}{{E_{0} E_{{\text{d}}} }}.$$
(11)

The dependency of (n2 − 1)−1 with (hv)2 is graphically represented in Fig. 10. The slope of the straight lines in Fig. 10 represents (1/E0Ed) and the intercept with Y-axis represents (E0/Ed). From the value of slope and intercept, the energy value of E0 and Ed was evaluated and shown in Table 2. It is observed that for annealing at a temperature below Tg, i.e., at 150 °C, results in the increase of E0 and Ed, whereas the opposite behavior was observed in the case of annealing at 250 °C. This behavior is quite similar to the behavior shown by the optical energy bandgap.

Fig. 10
figure 10

(n2 − 1)−1 vs (hν)2 of the films

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The first and second moments of the optical spectra, i.e., M−1 and M−3 were evaluated from the obtained E0 and Ed values using the WDD model. These moments can be deduced as.

$$E_{0}^{2} = \frac{{M_{ - 1} }}{{M_{ - 3} }},\;{\text{and}}\;E_{{\text{d}}}^{2} = \frac{{M_{ - 1}^{3} }}{{M_{ - 3} }}.$$
(12)

The above equations can be written as,

$$M_{ - 1 } = \frac{{E_{{\text{d}}} }}{{E_{0} }},\;{\text{and}}\;M_{ - 3} = \frac{{M_{ - 1} }}{{E_{{\text{d}}}^{2} }}.$$
(13)

Using the above relations, the first order and third-order moment of optical spectra were calculated and listed in Table 2. It was observed that the value of the moments, first increased for 150 °C annealing and then decreased for 250 °C annealing.

Similarly, from the single oscillator effective model, the value of dielectric constant (ε∞), as well as static refractive index (n0), can also be evaluated using the value of E0 and Ed by the formula [49]:

$$\varepsilon_{\infty } = 1 + \user2{ }\frac{{E_{{\text{d}}} }}{{E_{0} }},\;{\text{and}}\;n_{0} = \sqrt {1 + \user2{ }\frac{{E_{{\text{d}}} }}{{E_{0} }}} ,$$
(14)

\(\varepsilon_{\infty } = (n_{0} )^{2}\), denoted as the real dielectric constant of the lattice.

The calculated dielectric constant (ε∞) and static refractive index (n0) are presented in Table 2. Like the other parameters, the value of ε∞ and n0 first increased for annealing at 150 °C and then decreased further for annealing at 250 °C. The oscillator strength of the films is given by [50]

$$F = E_{0} E_{{\text{d}}} .$$
(15)

The oscillator strength values are presented in Table 2 which shows the increase of strength with annealing at 150 °C and then decreased for annealing at 250 °C.

5.2.4 Carrier concentration (N/m *) and high-frequency dielectric constant (ε L)

Upon using the linear refractive index values, the dielectric constant (εL) and the ratio of carrier concentration per effective mass (N/m*) was calculated by plotting n2 with λ2 (Fig. 11) through the following equation:

$$n^{2} = \varepsilon_{1} = \varepsilon_{L} - \left( {\frac{{e^{2} }}{{4\pi^{2} c^{2} \varepsilon_{0} }}} \right)\left( {\frac{N}{{m^{*} }}} \right)\lambda^{2} ,$$
(16)

where εL represents the real part of dielectric constant, N is the free charge carrier concentration, ε0 is the permittivity of free space, m* is the effective mass of the free charge carriers and c is the velocity of light. The εL is related to free charge carrier concentration and its effect contributed to the polarization process inside the material [51]. Here, the slope and intercepts with the X-axis are represented as N/m* and εL. The obtained value of N/m* and εL are listed in Table 2. The value of N/m* first decreased for annealing below Tg, i.e., at 150 °C and then increased for annealing at 250 °C. However, the εL value increased for 150 °C annealed film and decreased for annealing at 250 °C film.

Fig. 11
figure 11

n2 vs λ2 plot of the studied films

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5.2.5 Oscillator wavelength (λ 0) and strength of oscillator (S 0)

As per the single oscillator model proposed by Sellmeier, the refractive index at low frequency applied for classical dispersion relation is given as [52]

$$\frac{{n_{0}^{2} - 1}}{{n^{2} - 1}} = 1 - \frac{{{\uplambda }_{0}^{2} }}{{{\uplambda }^{2} }}.$$
(17)
$$\frac{1}{{n^{2} - 1}} = \frac{1}{{n_{0}^{2} - 1}} - \frac{{{\uplambda }_{0}^{2} }}{{\left( {n_{0}^{2} - 1} \right){\uplambda }^{2} }}.$$
(18)

After rewriting Eq. (18) becomes:

$$(n^{2} - 1)^{ - 1} = \frac{1}{{s_{0} \lambda_{0}^{2} }} - \frac{1}{{s_{0} \lambda^{2} }},$$
(19)

where \((n_{0}^{2} - 1)\) has been replaced with \(s_{0}\). A graph between \((n^{2} - 1)^{ - 1}\) vs \((\lambda )^{ - 2}\) was plotted from Eq. (19), as shown in Fig. 12. From the straight-line fitting, we have obtained \(\frac{1}{{s_{0} \lambda_{0}^{2} }}\) as its Y-intercept and \(\frac{1}{{s_{0} }}\) as its slope. From the values of Y-intercept and the slope, the values of oscillator wavelength (\({\uplambda }_{0}\)) and oscillator strength (\(s_{0}\)) were obtained and shown in Table 2. It was observed that the value of λ0 and S0 are showing the opposite behavior with each other.

Fig. 12
figure 12

(n2 − 1)−1 vs 1/λ2 plot of the studied films

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5.2.6 Non-linear optical properties

5.2.6.1 Third-order non-linear susceptibility (χ(3))

The nonlinear effects come into action when there are sufficiently high and intense incident energy falls on the film that can alter the properties of the system. This nonlinearity expresses itself through the polarization of the material system. Furthermore, the amorphous chalcogenide system possesses higher value of the optical non-linear susceptibility which helps to manufacture several non-linear optical devices [53]. Ticha and Tichy [54] and Miller’s rule [55] combination with Wemple–DiDomenico model was used to estimate the χ(3), since Ed and E0 are related to the chemistry of the material. The expression for Miller’s principle is

$$\chi^{\left( 3 \right)} = \frac{{A\left( {n_{0}^{2} - 1} \right)^{4} }}{{\left( {4\pi } \right)^{4} }}.$$
(20)

It can be also expressed in the form of:

$$\chi^{\left( 3 \right)} = A \left[ {\chi^{\left( 1 \right)} } \right]{ }^{4} \;{\text{where}}\;\chi^{\left( 1 \right)} = \frac{{\left( {n_{0}^{2} - 1} \right)}}{4\pi }.$$
(21)

In the above-mentioned expressions, \(n_{0}\) is the static refractive index in the \(\mathop {\lim }\limits_{h\nu \sim 0} \left( {n = n_{0} } \right)\) and A is a constant equal to \(1.7 \times 10^{ - 10}\) esu. Equations (20) and (21) are the combined relation of Miller’s principle and WDD model suggested by Tichy et al. [54].

Table 2 presents the estimated χ(1), χ(3) values from which it was found that the susceptibility increased for annealing below Tg, i.e., at 150 °C, and decreased for annealing at 250 °C. This increase/decrease in susceptibility due to annealing can be explained by homogenization and polymerization [56]. The presence of lone pair orbitals in chalcogenides makes them polarized easily and plays an important role in nonlinear effects also.

5.2.7 Non-linear refractive index (n 2)

According to Miller’s relation, the non-linear refractive index (n2) can be written in terms of χ(3) which has the form:

$$n_{2} = \frac{{12\pi \chi^{3} }}{{n_{0} }}.$$
(22)

The obtained results indicate that the n2 value increased for 150 °C annealed film and decreased for 250 °C annealed film. It shows the same behavior as that of the linear refractive index (n). This increase in nonlinearity upon annealing below Tg (at 150 °C) indicates an increase in different defect density states which can be explained through an increase in polarization of the system. The higher values of non-linear parameters make these annealing induced thin films diffraction free and suitable for non-linear devices. Due to the increase in structural order, the number of various defects in gap states decreased which leads to the reduction of nonlinearity for 250 °C annealed film. The reduction of n2 and χ(3) upon annealing at 250 °C can be useful for UV nonlinear materials and solid-state laser.

5.3 X-ray photoelectron spectroscopy (XPS) analysis

XPS is a surface analytic technique from which the information about different bonding can be obtained from the core-level analysis. The alterations in chemical bonding are often realized through correlation with chemical shifts in the XPS binding energies of key elements from their core-level spectra. Though the survey spectra consist of various core level and Auger spectra, we have selected the As 3d and Se 3d core-level peaks for the analysis. The core-level spectra were deconvoluted into sub peaks using the XPS data analysis software called XPSPEAK1. The Shirley baseline was used for background removal and the deconvoluted peaks were assumed to have Voigt line shapes. The deconvolution spectra give the spin–orbit splitting characteristic of the As3d and Se3d core levels. The spectrum was deconvolved into two doublets, each of them related to a specific state. During deconvolution of the peak, two constraints were considered for the process (i) the peak-to-peak separation and (ii) the 3d orbital peak area [57].

Due to spin orbit splitting, the Se3d peak consists Se3d5/2 and Se3d3/2 doublets with a peak-to-peak separation of ΔSe ≈ 0.79 eV, a value close to that found by Zhu et al. [58]. The Se3d3/2 orbital which is generally at higher energy value corresponds to the Se atom bonded to two As atoms (As−Se−As), whereas the Se3d5/2 orbital refers to the Se atoms with Se−Se−As bond found to be at lower BE [59]. Thus Se3d5/2 orbital refers to the Se–Se homopolar bonds and Se3d3/2 orbital refers to the As–Se heteropolar bonds. The deconvoluted Se3d core-level peak of the as-prepared, 150 °C annealed and 250 °C annealed film is shown in Fig. 13. The Se3d5/2 and Se3d3/2 peaks for the as-prepared film were at 54.15 eV and 54.94 eV, respectively. After 150 °C annealing, the Se3d5/2 and Se3d3/2 peaks were found at 54.99 eV and 54.20 eV with the area 1783 and 2014 units, respectively. The intensity of the 3d5/2 peak is more than that of the 3d3/2 peak for the 150 °C annealed film. This clearly shows the increase in Se–Se homopolar bond density than the As–Se heteropolar bond density which brought more disorder in the film. But it was observed that the intensity of 3d5/2 peak is less than that of the 3d3/2 peak for the 250 °C annealed film with peak positions at 54.68 eV and 55.47 eV, respectively. The area of 3d5/2 and Se3d3/2 peaks is 338 and 464 units, respectively, which clearly shows the more heteropolar bond than the homopolar bond in 250 °C annealed film. The opposite nature of the peaks for the two annealed films is in accordance with the optical parameters as observed. The full width half maximum (FWHM) for the Se3d5/2 is more (0.99) than that of the Se3d3/2 (0.91) for the 150 °C annealed film, whereas the FWHM for Se3d5/2 is less (1.15) than that of the Se3d3/2 (1.26) for the 250 °C annealed film. The comparative value of peak intensity, FWHM and area under the peak for the two annealed films are opposite to each other.

Fig. 13
figure 13

Deconvoluted Se 3d core-level peak of the films

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The As3d spectra consists of two peaks corresponding to 5/2 and 3/2 spin states of the 3d orbital with a separation of ΔAs ≈ 0.70 eV, a value close to that found by Beiyuan et al. [60]. For As 3d, the different bonding states are Se−As−Se2 and As−As−Se2. The sub peak d3/2 in the deconvoluted As 3d is assigned as As atoms within AsSe3/2 pyramidal units (Se−As−Se2) at higher BE and the sub peaks d5/2 is assigned as As atoms within units containing As–As homopolar bonds at lower BE, as shown in Fig. 14. Because As (2.18) has a smaller electro negativity than Se (2.55), the homopolar As–As bond containing units contribute the lower BE peak [61]. The peak intensity of As3d5/2 (homopolar bond) is more than that of the As3d3/2 (heteropolar) in the 150 °C annealed film which was opposite for the 250 °C annealed film. After 150 °C annealing, the As 3d5/2 and As 3d3/2 peaks were found at 42.11 eV and 42.82 eV with the area 1653 and 1077 units, respectively. This clearly shows the increase in As–As homopolar bond density than the As–Se heteropolar bond density which brought more disorder in the film. But it was observed that the intensity of 3d5/2 peak is less than that of the 3d3/2 peak for the 250 °C annealed film with peak positions at 42.60 eV and 43.19 eV, respectively. The area of As3d5/2 and As3d3/2 peaks is 101 and 602 units, respectively, which clearly shows the more heteropolar bond than the homopolar bond in 250 °C annealed film. The full width half maximum (FWHM) for the As3d5/2 is more (0.78) than that of the As3d3/2 (0.69) for the 150 °C annealed film, whereas the FWHM for As3d5/2 is less (0.53) than that of the As3d3/2 (1.12) for the 250 °C annealed film. The opposite nature of the peaks for the two annealed films is in accordance with the optical parameters as observed.

Fig. 14
figure 14

Deconvoluted As 3d core-level peak of the films

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6 Conclusions

The optical measurements of as-prepared and annealed As35Se65 films was calculated and studied by several models. Both the linear and nonlinear optical parameters have shown the opposite change for 150 °C and 250 °C annealed films. The optical band gap decreased for 150 °C annealed film, whereas it increased for the 250 °C annealed film. The linear refractive index, nonlinear refractive index, third-order susceptibility increased/decreased for the 150 °C and 250 °C annealed films, whereas carrier concentration and oscillator wavelength showed opposite changes. The annealing at both the temperature, however, did not show any change in the amorphous structure, but the degree of disorder in the film altered which was noticed from the Tauc parameter, Urbach energy, and Raman spectra. The skin depth increased and optical density decreased for the 150 °C annealed film which showed opposite changes for the 250 °C annealed film. The dispersion energy and oscillator energy increased for the 150 °C annealed film which decreased for the 250 °C annealed film. The deconvoluted XPS core-level peak intensity and area change showed the homopolar and heteropolar bond concentration that affected the degree of disorder. Therefore, we have observed both decrease/increase in the optical parameters when annealed at 150 °C and 250 °C temperatures. Such types of dual changes in the film at two different temperatures can be used for the fabrication of various optical devices based on their requirement.