1 Introduction

Chalcogenides are potential candidates in various technological applications, such as optoelectronics [1], IR fiber [2], memory devices [3] and xerography [4]. The high-quality multilayer and bilayer films of such amorphous semiconductors provide potential applications in the field of micro and optoelectronics. The chalcogenide multilayer films are an attractive system having many potential applications in various modern technologies. For example, the holographic gratings can be prepared from Ag/As30Se70 bilayer films [5], whereas Sb/As2S3 metal–chalcogenide layer can be used as an efficient media for the optical, amplitude-phase recording of patterns for optoelectronics [6]. The binary metal/chalcogenide compounds offer a lot of scope for various application-oriented studies due to their layered structure. The ternary Ag–Sb–S films are potential candidates for rewritable optical data storage applications which can be prepared from the heterogeneous structure of Ag/Sb2S3 with laser-induced or heat-induced effects as in other films, such as Te/As2Se3and Bi/As2Se3. [7, 8]. The family of Ag-doped chalcogenides includes interesting materials that focused on various studies such as the fabrication of photonic crystal waveguides from Ag/As2Se3 films [9] and tuning of optical bandgap by top layer Ag/Bi deposition onto Sb2S3 thin films [10]. Apart from the above discussed important applications based on their linear properties, the chalcogenide films possess high nonlinear behavior which makes them more efficient materials for application point of view. However, to build a useful device and estimate its potential performance, it is necessary to know its nonlinear properties. To design nonlinear optical devices, it is very important to examine nonlinear optical properties, such as the third-order nonlinear susceptibility (χ3), second-order nonlinear refractive index (n2) and two-photon absorption coefficient (β2). [11].

The third-order nonlinear optical effects in the infrared region allow for all-optical high-capacity communication networks, tunable mid-infrared light sources that are hard to reach by other means, remote sensing and medical diagnostics [12,13,14]. The key parameter to such applications is the availability of an appropriate nonlinear medium, and chalcogenide films with high conversion efficiencies are the best candidate at present time. As compared to silica, the chalcogenide films possess a high order of nonlinearity, approximately 100 times greater than that of silica [15]. High nonlinear refractive index along with moderate to low nonlinear absorption can be used in all-optical signal-processing devices to empower telecommunication systems [16]. The nonlinear constants, such as χ3 and n2, are utilized for the fabrication of optical waveguides, diffractive optical elements and micro-optical elements [17,18,19]. The nonlinear optical behavior of such films is of special interest due to their optical switching ability [20]. The parameter χ3 which explains the third harmonic generation and two-photon absorption is an important parameter that decides the applicability of that material in the nonlinear optical device [21]. The 3rd order nonlinearity was enhanced by the doping of Ag atoms into alloys for suitable nonlinear applications [22]. So, it is desirable to form thin films that exhibit high nonlinear optical properties. There are several ways to make the desired film, but we have fabricated the bilayer films with high nonlinear values by deposition of Ag and Te layer onto As50Se50 film.

The aim of the present work was to investigate the effect of the Ag and Te top layer on the linear and nonlinear optical properties change in bilayer Ag/As50Se50 and Te/As50Se50 thin films as compared to the host As50Se50 film. The optical properties, including transmission, absorption, optical bandgap (Eg), linear refractive index (n), dispersion energy, oscillator energy, n2, χ3 etc., were determined from UV–Visible transmission spectra, and the nonlinear parameters were evaluated by the semiempirical formula. The structural investigation was carried out by X-ray diffraction (XRD) and the surface morphology was investigated from the field emission scanning electron microscopy (FESEM).

2 Experimental details

Thin films of As50Se50, Ag/As50Se50 and Te/As50Se50 were made from bulk As50Se50 (prepared by melt quenching method), Ag and Te (99.999% high purity elements from Aldrich and Sigma Chemical Company) by thermal evaporation method at a pressure of about 10−5 Torr. The films were deposited on glass substrates at 300 K, and the substrates were rotated slowly during the deposition process to obtain the homogenous and smooth film. The thickness of the thin film was 800 nm (As50Se50), 808 nm (Ag/As50Se50) and 808 nm (Te/As50Se50), respectively, which was measured by the crystal quartz monitor during the deposition process and the rate of deposition was 2 nm/s.

The structural information was obtained from XRD (Philips, CuKα,  = 1.54 Å). The XRD measurements were taken at 40 mA current and 40 kV voltage with a scan speed of 1° min−1, a step value of 0.02° in 2θ range of 10° - 80° at a grazing angle of 1°. The surface morphology of the films was taken in FESEM (Sirion XL 40) with the scan at 20 kV with 40 μA emission current exposing a sample of 1 cm2 size at 2 × 10−7 Torr pressure. The optical transmission spectra of the three films were taken by UV–Visible spectrometer (Bruker Optics (IFS66v/S) in the visible wavelength range 500–1200 nm. The measurement was done inside the sample chamber of the spectrometer in dark conditions. The linear optical quantities, such as absorption coefficient (α), optical bandgap (Eg), and Tauc parameter (B1/2), were calculated from Tauc relation, whereas the Swanepoel method was used to calculate the linear refractive index. The dispersion parameters were obtained from a single oscillator Wemple–Di Domenico model. The nonlinear parameters, such as n2 and χ3, were evaluated by Miller’s formula.

3 Results and discussion

3.1 Structural and surface morphology study

The XRD patterns of the studied thin films are presented in Fig. 1. The absence of any crystalline peaks and the presence of a broad hump confirms the amorphous nature of the prepared films. The three patterns look alike so that no differences can be noticed among the thin films. This infers that there is no structural change in the bilayer film due to Te and Ag deposition onto the As50Se50 host matrix.

Fig. 1
figure 1

XRD patterns of As50Se50, Ag/As50Se50 and Te/As50Se50 thin films

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However, the surface morphology change is visible in the FESEM images of As50Se50, Ag/As50Se50 and Te/As50Se50 thin films which are presented in Fig. 2. The surfaces of As50Se50 and Te/As50Se50 films are smooth and homogenous, whereas it is different in the case of Ag/As50Se50 film. The small agglomerate type structure is clearly noticed in the Ag/As50Se50 film and such wrinkle-like structure might be due to the Ag particles at the interface of the bilayer film. The wrinkle-like formations are interconnected with each other and do not have a particular orientation as found by also other studies [23]. The wrinkle-like formations are of various sizes as noticed and their length extends up to 2 μm.

Fig. 2
figure 2

FESEM images of As50Se50, Ag/As50Se50 and Te/As50Se50 thin films

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3.2 Linear optical parameters

3.2.1 Transmission, absorption and extinction coefficient

The optical transmission spectra give necessary information about the band structure of the semiconducting materials and other useful parameters. The transmittance spectra as recorded for As50Se50, Ag/As50Se50 and Te/As50Se50 thin films in the wavelength () range 500–1200 nm are presented in Fig. 3. The nonshrinking interference fringes observed in the transmittance spectra at a higher wavelength (700–1200 nm) indicate the homogeneity and smoothness of the deposited films [24]. It has been observed that the transmission  % decreased from 78% (As50Se50) to 64% for the Ag/As50Se50 film and 48% for the Te/As50Se50 thin film. We have shown the spectra for Ag/As50Se50 thin film up to 950 nm due to the appearance of noise after 950 nm. Furthermore, the absorption edge of the deposited films shows a shift which indicates the change of the optical bandgap for Ag/As50Se50 and Te/As50Se50 thin films.

Fig. 3
figure 3

Transmittance plot of As50Se50, Ag/As50Se50 and Te/As50Se50 thin films

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The absorption coefficient in the strong absorption region was calculated by using the formula [25]

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

where d is the thickness of the film, and T is the transmission of the films. The absorption coefficient is more for Ag/As50Se50 and Te/As50Se50 film than As50Se50 film as shown in Fig. 4.

Fig. 4
figure 4

α vs plot of As50Se50, Ag/As50Se50 and Te/As50Se50 thin films

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The mass extinction coefficient (k) measures how strongly the film absorbs the light at a given which is related to the absorption coefficient and wavelength by [26].

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

The variation of k with is shown in Fig. 5 that depicts the increase in k value, with Te and Ag deposition onto As50Se50 thin film. However, the value is more for the Te deposited film than the Ag layer film. Since k is related to the surface defects and disorder parameter, it infers the increase in density of defect states leading to the decrease in Eg which is discussed in the following section.

Fig. 5
figure 5

Variation of k with of studied thin films

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3.2.2 Optical bandgap (E g), Tauc parameter (B 1/2) and Urbach energy (E u)

The fundamental absorption edge in most amorphous semiconductors follows an exponential law. In the high absorption region, the photon energy dependence of the absorption coefficient in allowed indirect transition can be described by Tauc’s relation [27].

$$ \left( {\alpha h\vartheta } \right)^{{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-0pt} \!\lower0.7ex\hbox{$2$}}}} = B^{{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-0pt} \!\lower0.7ex\hbox{$2$}}}} \left( {h\vartheta - E_{\text{g}} } \right), $$
(3)

where B is the Tauc parameter which depends on transition probability and measures the degree of disorder and Eg is the optical bandgap [27]. By plotting the linear portions of the dependence of (αhν)1/2 versus hυ will give a straight line and the X-intercept gives the optical bandgap as shown in Fig. 6. The slope of the fitting gives the degree of disorder value (B1/2). The optical bandgap of As50Se50 was 1.71 ± 0.01 eV which decreased to 1.68 ± 0.01 eV for the Ag/As50Se50 film with Ag deposition. This decrease in Eg was due to the increase in density of localized states which reduced the optical bandgap. With the deposition of Te onto As50Se50, the Eg value was 1.60 ± 0.02 eV which is 0.08 eV less than that for Ag/As50Se50 film. This difference might be due to the less electronegativity of Ag (1.93) than Te (2.1) [28].

Fig. 6
figure 6

(αhν)1/2 vs hν for As50Se50, Ag/As50Se50 and Te/As50Se50 thin films

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The decrease in Eg after Te and Ag deposition is well understood by the Mott and Davis model [29] which proposes that the number of defects and degree of disorder influences the width of the localized states near the mobility edge in an amorphous structure. The localized states have a strong influence on the optical absorption and thus on the optical bandgap. The deposition of Ag and Te onto As50Se50 film formed a greater number of homopolar bonds at the interface which enhanced the degree of disorder in the new bilayer films. Therefore, the magnitude of the density of defects increased which increased the width of the localized states, and consequently, the Eg value decreased for the bilayer films [26, 30].

The degree of disorder is noticed from the B1/2 values which are 793 ± 3 cm−1/2 eV−1/2 (As50Se50), 759 ± 2 cm−1/2 eV−1/2 (Ag/As50Se50), and 698 ± 2 cm−1/2 eV−1/2 (Te/As50Se50), respectively, as shown in Table 1. The decrease in B1/2 value infers the increase in disorder in the films due to more homopolar bond formation at the interface of the two layers. So, the degree of disorder is more in Te deposited film than that of Ag deposited film.

Table 1 Optical parameters of the studied films
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The width of the localized states Eu (Urbach energy) also measures the amount of disorder in a system. This parameter is being evaluated in the weak absorption region of the absorption spectrum from an exponential dependence on photon energy [31]

$$ \alpha \left( {h\nu } \right) = \alpha_{0} \exp \left( {\frac{h\nu }{{E_{\text{u}} }}} \right) ,$$
(4)

where ν is the frequency of the radiation, α0 is a constant that corresponds to the absorption coefficient at bandgap, h is Planck’s constant. The Eu value was calculated from the reciprocal of the slope of the linear portion of the dependence of ln \( \left( {\alpha /\alpha_{0} } \right) \) versus hν. The calculated Eu values for the as-deposited As50Se50, Ag/As50Se50and Te/As50Se50 thin films are presented in Table 1. The increased Eu values confirm the increase of disorder in the Ag/As50Se50 and Te/As50Se50 films. The greater value in the case of Te/As50Se50 film than Ag/As50Se50 one clearly showed more disorder in Te film than that of Ag film. The presented values of B1/2 and Eu showed the inverse relation between them as studied in various other films [32, 33].

3.2.3 Linear refractive Index (n), oscillator energy (E o), dispersion energy (E d)

The linear refractive index was calculated from the transmission spectrum by using the Swanepoel method [34]. The required equation for the linear refractive index (n) is given by

$$ n = \left[ {N + \left( {N^{2} - s^{2} } \right)^{{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-0pt} \!\lower0.7ex\hbox{$2$}}}} } \right]^{{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-0pt} \!\lower0.7ex\hbox{$2$}}}}, $$
(5)

where

$$ N = 2s\left( {\frac{{T_{\text{M}} - T_{\text{m}} }}{{T_{\text{M}} T_{\text{m}} }}} \right) + \frac{{s^{2} + 1}}{2} $$
(6)

TM and Tm are the maxima and minima of the transmission curve at a particular wavelength; s is the refractive index of the glass substrate (1.51). The refractive index was found to be increased with Ag and Te deposition onto As50Se50 film as shown in Fig. 7 which is due to the increase of the number of unsaturated defects. These defects increased the density of localized states in the band structure thus increasing the refractive index. The red or blue shift of the bandgap values is related to the increase or decrease in the refractive index as stated by Moss’s rule (Egn4 ~ constant) as found in other studies [35, 36]. The change in ‘n’ value is more in Te/As50Se50 film than that of Ag/As50Se50 film.

Fig. 7
figure 7

n versus plot of As50Se50, Ag/As50Se50 and Te/As50Se50 thin films

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The single effective oscillator model (Wemple and Di Domenico) for the dispersion of refractive index [37] is given by the formula

$$ n^{2} \left( {h\upsilon } \right) = 1 + \frac{{E_{0} E_{\text{d}} }}{{E_{0}^{2} - \left( {h\upsilon } \right)^{2} }}, $$
(7)

where h is Planck’s constant, Eo is the average excitation energy for electronic transition which is empirically related to the optical bandgap, while Ed is the dispersion energy that measures the average optical transition strength. The value of Eo and Ed was obtained from the slope (EoEd)−1 and intercept (Eo/Ed) on the vertical axis (Fig. 8). The value of Eo for As50Se50, Ag/As50Se50 and Te/As50Se50 thin films are 3.94, 3.89 and 3.99 eV, respectively. Similarly, the Ed value for As50Se50, Ag/As50Se50 and Te/As50Se50 thin films are 27.85, 27.75 and 30.32 eV, respectively. This variation is due to the variation of scattering centers. The static refractive index (n0) was calculated from the relation

$$ n_{0}^{2} = \left( {1 + \frac{{E_{\text{d}} }}{{E_{0} }}} \right) $$
(8)
Fig. 8
figure 8

\( (n^{2} - 1)^{ - 1 } \) versus \( \left( {h\nu } \right)^{2} \) plot of As50Se50, Ag/As50Se50 and Te/As50Se50 thin films

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The high-frequency dielectric constant ε∞ = n 20 was calculated and presented in Table 2.

Table 2 Optical parameters of the studied films
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3.2.4 High-frequency dielectric constant and carrier concentration

The calculated value of the linear refractive index was used to obtain the high-frequency dielectric constant (εL) according to the relation [38]

$$ \varepsilon_{1} = n^{2} = \varepsilon_{\text{L}} - \left( {\frac{{e^{2} N}}{{4\pi^{2} C^{2} \varepsilon_{0} m^{*} }}} \right)\lambda^{2}, $$
(9)

where \( \varepsilon_{1} \) is the real part of dielectric constant, e is the charge of the electron, N is the free charge carrier concentration, \( \varepsilon_{0} \) is the permittivity of free space, m* is the effective mass of charge carrier, and c is the velocity of light. The intercept of the plot between n2 vs \( \lambda^{2} \) gives the value of εL and the value of N/m* was obtained from the slope of the linear portion of straight-line fitting (Fig. 9). The ε∞ increased from 8.05 to 8.11 with Ag deposition and to 8.59 for the Te/As50Se50 bilayer film. The εL was found to be 11.94 for As50Se50, 12.03 for Ag/As50Se50 and 12.37 for Te/As50Se50 thin film. The value of εL is more than that of ε∞ is due to the increase in free charge carrier concentration [39].

Fig. 9
figure 9

n2 versus 2 plot of As50Se50, Ag/As50Se50 and Te/As50Se50 thin films

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3.3 Nonlinear optical susceptibility and nonlinear refractive index

The nonlinear optics is used to describe the phenomena that occur when the interactions occur between very high light intensities and the materials. The nonlinear optical quantities are internally connected with the nonlinear polarization and the incident energy [40]. The third-order harmonic generation, two-photon absorption and nonlinear refractive index (n2) are evaluated from the third-order nonlinear optical susceptibility χ(3) for nonlinear optical applications [41]. The linear refractive index is related to the linear optical susceptibility (χ1) through the equation [42]

$$ \chi^{\left( 1 \right)} = \frac{{n^{2} - 1}}{4\pi } $$
(10)

Then, the relation between the linear susceptibility χ(1) and nonlinear susceptibility χ(3) involving an average energy gap (Eo) and single oscillator strength parameter (Ed) is given by generalized Miller’s rule [43, 44]

$$ \chi^{\left( 3 \right)} \cong A\left( {\chi^{\left( 1 \right)} } \right)^{4} ,$$
(11)

where A = 1.7 × 10−10 (χ measured in esu) is an amount that is expected to be frequency independent and approximately the same for all materials.

In the long-wavelength limit (hν → 0), the above equation becomes

$$ \chi^{\left( 1 \right)} = \frac{{n_{0}^{2} - 1}}{4\pi } $$
(12)

This makes Eq. 11 to the form

$$ \chi^{\left( 3 \right)} \cong A\left[ {\frac{{n_{0}^{2} - 1}}{4\pi }} \right]^{4} = A\left[ {\frac{{E_{0} E_{\text{d}} }}{{4\pi \left( {E_{0}^{2} - \left( {h\vartheta } \right)^{2} } \right)}}} \right]^{4} $$
(13)

The χ(1) value for As50Se50, Ag/As50Se50 and Te/As50Se50 film are presented in Table 2. The χ(3) values were calculated using Eq. 13, and it is observed that χ(3) value is more for the Te/As50Se50 film than the Ag/As50Se50 film as presented in Table 2. The susceptibility increased monotonically with decreasing bandgap which is observed for the studied films as shown in Tables 1 and 2 like other studies [45,46,47]. The nonlinear refractive index is related to the third-order susceptibility χ(3) by the relation [48]

$$ n_{2} = \frac{{12\pi \chi^{\left( 3 \right)} }}{{n_{0} }}, $$
(14)

where no is the static refractive index. The variation of n2 follows the same trend as χ(3).

The increase of Ed/Eo leads to an increase in the values of n2 and χ(3). The change in nonlinear parameters is very useful for UV nonlinear optical materials [49]. The deposition of Ag on the As2Se3 layer influences the optical parameters of the metal–chalcogenide (Ag/Se) interface due to the interaction among the elements as stated by Popescu et al. [50]. The large values of the nonlinear parameters for the Ag and Te deposited thin films are very important for the formation of low-power devices for nonlinear optical applications.

4 Conclusion

The thermally deposited thin films of Ag/As50Se50 and Te/As50Se50 undergo no structural change after deposition of Ag and Te onto As50Se50. The optical transmittance decreased, whereas the absorption coefficient increased for the bilayer thin films. The optical bandgap was found to be decreased with the increase in disorder as reflected from the B1/2 and Eu values. The homopolar bonds that formed at the interface increased the density of defect states which decreased the bandgap. The linear and nonlinear refractive index was increased along with the increase in χ(3). However, the change is more for the Te/As50Se50 film than that of Ag/As50Se50 film. The change in such optical constants can be used to design specific types of optoelectronic and integrated optical elements, which need high local changes of optical parameters.