Optical constants and dispersion parameters of amorphous Se_65−xAs₃₅Sb_x thick films for optoelectronics

Abstract

Optical properties of amorphous Se_65−xAs₃₅Sb_x thin films with different compositions (x = 0, 2, 4, 6, 8 and 10 at%) deposited by evaporation technique have been investigated by measuring transmission (T) and reflection (R) in the wavelength range 400–2500 nm. An optical characterization method for uniform films based on Swanepoel’s method has been employed to extract the refractive index n and film thickness d, with high precision (better than 1%). The calculated thickness for all thin films was about 1 µm. In addition, the absorption coefficient was evaluated in the strong absorption region of T and R. The possible optical transition in these films is found to be allowed indirect transition with energy gap $E_{g}^{\text{opt}}$ decreases from 1.72 to 1.53 eV with increasing Sb content at expense of Se. The chemical bond approach has been applied to explain the decrease of the optical gap with increasing Sb content. The dispersion and oscillator energies were analyzed using the concept of the single oscillator by Wemple and Di-Domenico. The nonlinear refractive index was calculated and found to be increase with increasing Sb content.

1 Introduction

Chalcogenide glasses contain one or more chalcogen element (Se, S, Te) which produces covalent bonds with the network formers like As, Sb, Ge, etc. Because of the high atomic masses and hence the low phonon energies in these elements, the transmission range extends into infrared region making it a suitable candidate for many applications in medical imaging, telecommunication, bio-sensing, infrared waveguides, optical fibers [1,2,3,4]. These materials appear a continuous alteration in many physical properties with alteration in chemical composition [5]. Many investigations of the electrical properties [6, 7], photo-conductivity [8], glass formation [9], study of structure [10] and analysis of crystallization kinetics [11,12,13] of the glassy (As–Se–Sb) system have been made. To our knowledge, less detailed investigations have been performed on their optical properties. In addition, more efforts have been carried out to develop the mathematical formulation describing both the reflectance and the transmittance of different optical systems. In the present work, the optical properties of amorphous semiconductor Se_65−xAs₃₅Sb_x (0 ≤←x←≤←10) thin films are investigated. The straightforward method proposed by Swanepoel is applied which is based on the use of the extremes of the interference fringes of transmittance spectrum for calculation the refractive index and film thickness in the transparent region. For determination of the refractive index, the film thickness of the samples must be sufficient high (about 1 µm) in order to obtain several interference extremes and help us to avoid the effect of the film thickness on the optical constants of the films. The absorption coefficient therefore band gap is calculated in the strong absorption region of transmittance and reflectance spectra. The dispersion parameters are discussed using by Single-oscillator Wemple-Di Domenico model [14]. The compositional variation of optical band gap with Se-As-Sb thin films is discussed in terms of the chemical bond approaches present in the glassy compositions under study.

2 Experimental procedures

Bulk chalcogenide Se_65−xAs₃₅Sb_x with (0 ≤ x ≥ 10) at. % was prepared by the usual melt quench technique. Highly pure materials (99.999%) were weighted based on their atomic percentages, using an electrical balance type (Sartorius) with accuracy (± 10⁻⁴ g) and sealed in evacuated silica tube (10⁻³ Pa) and it was heated at 1000 °C with the temperature ramp about 5 °C/min for 24 h. During the melting process, the ampoule was inverted at regular time intervals (~ 1 h) so that the amorphous solid will be homogenous and isotropic. After the synthesis, the melt was quenched rapidly in ice water to obtain the Se_65−xAs₃₅Sb_x glassy alloy. Then the solid was broken along its natural stress line into smaller pieces suitable for grinding. The different compositions of Se_65−xAs₃₅Sb_x with (0 ≤ x ≥ 10 at%) thin films were deposited by evaporating the powdered chalcogenide samples from a resistance heating quartz glass crucible onto dried precleaned glass substrates kept at room temperature, using a conventional coating unit (Denton Vacuum DV 502 A). The films were deposited onto glass substrates at a pressure of about 1 × 10⁻⁶ Pa. Both the film thickness and the deposition rate (was about 20 Å/s) were monitored using FTM6 thickness monitor. The elemental composition of the films was analyzed using energy-dispersive X-ray spectrometer (EDX) interfaced with a scanning electron microscope, SEM (JOEL XL) operating an accelerating voltage of 30 kV. The relative error of determining the indicated elements does not exceed 2%. X-ray powder diffraction (XRD) Philips diffractometry (1710), with Cu-Kα1 radiation (λ = 1.54056 Å) has been used to examine the structure of the as-prepared thin films. The data collection was performed by step scan mode, in a 2θ range between 5° and 90° with step-size of 0.02° and step time of 0.6 s. The transmittance (T) and reflectance (R) optical spectra of the as-deposited films were performed at room temperature range using UV-Vis-NIR SHIMADZU UV-1700 double beam spectrophotometer. At normal incidence, the transmittance spectra were collected without substrate in the reference beam in the wavelength range 400–2500 nm, while the reflectance spectra were measured using reflection attachment close to normal incidence (~ 5^o).

3 Results and discussion

3.1 XRD analysis

Figure 1 demonstrates XRD patterns of different compositions of Se_65−xAs₃₅Sb_x with (0 ≤ x ≥ 10 at. %.) Such a figure revealed broad peaks without any sharp crystallization peaks, suggesting that the amorphous nature of such films.

Fig. 1

The XRD patterns of different composition of Se_65−xAs₃₅Sb_x thin films onto glass substrates

3.2 Optical studies

3.2.1 Interference fringes in transmittance spectra

The optical properties were studied for as-prepared Se_65−xAs₃₅Sb_x by optical transmittance [T (λ)] and the reflectance [R (λ)] data of wavelength range of (400–2500 nm). The spectra of T (λ) and R (λ) for Se_65−xAs₃₅Sb_x thin films are shown in Fig. 2. The thickness of the studied samples was deduced according to Swanepoel's method, which is based on the idea of Manifacier et al. [15] of creating upper and lower envelopes of the transmittance spectrum which showed the construction of the two envelopes T_M (λ), T_m (λ) (according to Eq. (1)) and then the geometric mean:

$$T_{\alpha } = \sqrt {T_{M} (\lambda )T_{m} (\lambda )}$$

(1)

Fig. 2

Transmission and reflection spectra of Se_65−xAs₃₅Sb_x with thin films

3.2.2 Envelope construction

The two envelopes construction T_M (λ) and T_m (λ) are expressing using by program origin version 2018 (Origin-Lab Corp.), where T_M and T_m are the transmission maximum and the corresponding minimum at a certain wavelength. Alternatively, one of these values is an empirical interference extreme and the other one is derived from the corresponding envelope; both envelopes were computer-generated using by the program origin version 2018 (Origin-Lab Corp.). T_M (λ) and T_m (λ) are displayed in Fig. 3 and their values are listed in Tables 1.

Fig. 3

Variation of the typical spectral transmittances and reflectance versus wavelength for different ratios Se_65−xAs₃₅Sb_x thin films

Table 1 Values of the wavelength of the incident photon, the two envelopes T_M and T_m for Se_65−xAs₃₅Sb_x with ((0 ≤ x ≥ 2 at. %) thin films. The calculated values of refractive index and film thickness are based on the envelope method

3.2.3 Estimation of the refractive index of the substrate

The refractive index of the film substrate was determined using the subsequent relation [16]:

$$S_{j} = (T_{sj} )^{ - 1} + \sqrt {((T_{sj} )^{ - 1} + 1)}$$

(2)

where T_s is the transmittance of the glass substrate which has been defined by the subsequent function:

$$T_{s(j)} = A + B\lambda_{j} + C\lambda_{j}^{2} + D\lambda_{j}^{3}$$

(3)

where j is a number refers to a specific wavelength and the values of the constants that appear in Eq. (3), namely A, B, C and D equal to 0.901414, 8.02369 × 10⁻⁵, 6.13838 × 10⁻⁸ and 1.38877 × 10⁻¹¹, respectively.

3.2.4 Estimation of crude refractive index

The crude refractive index (n_e) of the as-prepared films under investigation can be deduced based on the envelope method via transmission spectrum proposed by Swanepoel's [17, 18]. The values of n_e can be computed at any wavelength via the following Eq. [19]:

$$n_{e} = [N + (N^{2} - s_{j}^{2} )^{1/2} ]^{1/2}$$

(4)

where

$$N = 2s_{j} \frac{{T_{{M_{j} }} - T_{{m_{j} }} }}{{T_{{M_{j} }} T_{{m_{j} }} }} + \frac{{S_{j}^{2} + 1}}{2}$$

(5)

where s_j is the refractive index of the glass substrate. Values of crude refractive index, (n_e ≡ n₁) for two as-prepared thin films with (x = 0, x = 2), as only examples, are computed and listed in Tables 1.

3.2.5 Determination of the crude and accuracy films thickness

Values of n_e at any adjacent maximal (or minimal), that have been computed by Eq. (4) are used to calculate crude film thickness (d₁). If n_e1 and n_e2 are the refractive indices of two adjacent maxima or minima at wavelengths λ_e1 and λ_e2, then the crude thickness of the film is expressed as [20]:

$$d_{1} = \frac{{\lambda_{e1} \lambda_{e2} }}{2}[\lambda_{e1} n_{e2} - \lambda_{e2} n_{e1} ]^{ - 1}$$

(6)

To improve the accuracy of film thickness, there was a set of the order number (m_o) for the interference fringes was computed using by relation [20]:

$$m_{0} = \frac{{2n_{e1} \bar{d}_{1} }}{{\lambda_{e1} }}$$

(7)

where (n_e ≡ n₁)and λ_e1 are the values taken at the extreme point of the interference fringes and d₁ is the average of d₁ from Eq. (6) then by taking the approximate value of m_o produces a new order number m where m = 1, 2, 3… at the maximum points in the transmission spectrum and m = 1/2, 3/2, 5/2… at minimum points in the transmission spectrum after that the accuracy of refractive index $(n_{2} )$ in terms of accuracy of thickness thin film expresses, $(d_{2} )$ as the subsequent relation:

$$n_{2} = \frac{{m \cdot \lambda_{e1} }}{{2 \cdot \bar{d}_{2} }}$$

(8)

where $\bar{d}_{2}$ is the new average accuracy thickness of thin films after rounded m_o to m. The final values of new refractive index n₂ and other mentioned values are presented in Table 1. On the other hand, to compute the standard deviation values (σ_i) and deviation ratio (p_i) about the actual value for each of d₁ and d₂, we used the subsequent equations:

$$\sigma_{i} = \left\{ {\left[ {\frac{{\sum\nolimits_{1}^{n} {(d_{i} )^{2} } }}{n}} \right] - (\bar{d}_{1} )^{2} } \right\}^{0.5} ,\quad \bar{d}_{1} = \frac{{\sum\nolimits_{1}^{n} {(d_{i} )} }}{n},\quad P_{i} \% = \frac{{\sigma_{i} }}{{\bar{d}_{i} }} \times 100$$

(9)

where i is a number equals to 1 or 2, and n refers to the number of thicknesses.

3.2.6 Estimation of optical parameters

The absorption coefficient (α) can be deduced in the strong absorption region via both the empirical transmission (T) and reflection (R) spectra [21,22,23] as follows:

$$\alpha = \frac{1}{d}\ln\,\left[ \frac{{(1 - R)^{2} + \sqrt {(1 - R)^{4} + 4(TR)^{2} } }}{2T}\right]$$

(10)

where d is the thickness of the films that computed by Swanepoel's method and almost equals to 1 µm. Figure 4 shows the dependence of the absorption coefficient, α, on photon energy (hν) for amorphous Se_65−xAs₃₅Sb_x thin film with different composition, x = 0, 2, 4, 6, 8 and 10 at%).

Fig. 4

The dependence of the absorption coefficient on the incident photon energy for Se_65−xAs₃₅Sb_x thin films

It is clear that the absorption edge (α ≥10⁴) shifts toward the lower photon energy with increasing Sb content that is related to the decreasing of the optical bandgap. Based on the Tauc’s equation at the end of absorption edge region (α ≥ 10⁴ cm⁻¹), the optical energy band gap (E_g) can be determined via the values of the absorption coefficient using the following Equation [24,25,26]:

$$\alpha (hv) = A(hv - E_{g}^{\text{opt}} )^{r}$$

(11)

where A is a constant parameter and depends on the transition probability and (r = 2) for non-direct transition and (r = 1/2) for the direct transition. For investigated thin films we notice that the indirect transitions are valid. Figure 5 appears the (αhν)^1/2 against hν for investigated samples. E_g of the films was estimated from the intercept of the linear portion of each curve for the studied films with hν in the abscissa, i.e., at (αhν)^1/2 = 0 as presented in Fig. 5.

Fig. 5

The plot of (αhν)^0.5 versus photon energy (hν) for Se_65−xAs₃₅Sb_x thin films

On the other hand, the absorption coefficient at less than about α ~10⁴ cm⁻¹ near the absorption edge depends exponentially on hv as follows [26, 27]:

$$\alpha (hv) = \alpha_{0} \cdot \exp \left[ {\frac{hv}{{E_{e} }}} \right]$$

(12)

where α_o is a constant and E_e is the Urbach energy. (E_e) is computed from plotting ln(α) versus hν as illustrated in Fig. 6. The computed values of E_g and E_e are presented in Table 2. Apparently, the optical band gap $E_{g}^{\text{opt}}$ decreases from 1.72 to 1.53 eV with increasing Sb content at expense of Se content.

Fig. 6

The plot of ln(α) versus photon energy (hν) for Se_65−xAs₃₅Sb_x thin films

Table 2 Physical parameters of the Se_65−xAs₃₅Sb_x with ((0 ≤ x ≥ 10 at. %) thin films

3.3 Determination of the absorption constants

3.3.1 Estimation of the refractive index

Figure 7 shows the dependence of refractive index on wavelength for as-prepared thin films under investigation. In the strong absorption spectral region, the values of the refractive index can be fitted using the two-term Cauchy dispersion relationship, n (λ) = a + (b/λ²) which can be used to extrapolate the complete overall wavelengths [27]. It is clear that the refractive index increases with increasing Sb content as shown in Fig. 7. The values of Cauchy coefficients (a and b) are listed in Table 2. The increasing in refractive index is related to the increased polarizability of the larger Sb atoms (atomic radius, 1.53 Å), in comparison with Se atoms (atomic radius, 1.22 Å). One can see that the refractive index increases while optical band gap decreases, this behavior may be explained using Moss rule, which says n and $E_{g}^{\text{opt}}$ are in inverse relation.

Fig. 7

The spectral dependence of refractive index (n) for Se_65−xAs₃₅Sb_x thin films

The variation of energy gap ($E_{g}^{\text{opt}}$) with composition in amorphous ternary alloys can be described by the following simple relation [5]:

$$E_{g} \left( {AsSeSb} \right) \, = \, aEgAs + \, bEgSe + cEgSb$$

(13)

where a, b and c are the fractions of the element As, Se and Sb, respectively. EgAs, EgSe and EgSb are the corresponding optical gaps, which equal 1.15, 1.95 and 0.15, respectively. One can see that the Sb has an energy gap lower than Se, so the calculations of E_g based on the above equation for the present Se_65−xAs₃₅Sb_x alloys cause reduction in energy gap.

The absorption index, namely the extinction coefficient (k_ex.) has been computed using the following relation [28, 29]:

$$k_{ex.} = \varepsilon {}_{0}\,\alpha \lambda = \frac{\alpha \lambda }{4\pi }$$

(13)

The values of k_ex of investigated samples decrease with increasing the wavelength, whereas these values increase with increasing Sb content as shown in Fig. 8.

Fig. 8

Variation of extinction coefficient (k) versus wavelength (λ) for Se_65−xAs₃₅Sb_x with thin films

3.3.2 Determination of the loss factor

There is quantity frequently used to characterize the optical properties of thin films is called the dissipation factor ($\tan (\delta )$) which can be evaluated using the following relation [30]:

$$\tan (\delta ) = \frac{{\varepsilon_{i} }}{{\varepsilon {}_{r}}}$$

(14)

Here, $\varepsilon_{r}$ and $\varepsilon_{i}$ represent the real ($\varepsilon_{r} = n^{2} - k^{2}$) and imaginary ($\varepsilon_{i} = 2nk$) parts of the dielectric constant, respectively. The variations of dissipation factor as a function of photon energy were shown in Fig. 9. This figure appears that the dissipation factor increases with increasing photon energy.

Fig. 9

Variation of dissipation factor (tan(δ)) on the photon energy (hν) for Se_65−xAs₃₅Sb_x thin films

3.4 Determination of the dispersion parameters

The dispersion of refractive index (n (λ)) was analyzed using by the concept of the single oscillator and can be expressed by the Wemple-Didomenico relationship [14, 31] as:

$$n^{2} = 1 + \frac{{E_{o} E_{d} }}{{E_{o}^{2} - (h\nu )^{2} }}$$

(15)

where (hν) is the photon energy, E_o is the oscillator energy and E_d is the dispersion energy which measures the average strength of inter-band optical transitions. Figure 10 shows the relation between (n²− 1)⁻¹ versus (hν)² for the investigated films. The values of E_d and E_o have been deduced from the slopes and the intersection of the straight lines with (n²− 1)⁻¹ axis. The variations of E_o and E_d with Sb concentration of the studied samples are illustrated in Table 2. The values of E_d and E_o decrease with increasing the Sb content. The decrease in E_o and E_d could be attributed to the increase in the number of scattering center that due to the dissolving of Sb atoms in the glass film matrix [32]. Further analysis of the (n²− 1)⁻¹ against (hν)² allows to deduce the static refractive index, using the subsequent relation:

$$n_{o} = (1 + {{E_{d} } \mathord{\left/ {\vphantom {{E_{d} } {E_{0} )}}} \right. \kern-0pt} {E_{0} )}}^{1/2}$$

(16)

Fig. 10

The plot of the relation between (n²− 1)⁻¹ and (hν)² for the investigated compositions

The computed values are tabulated in Table 2.

3.5 Determination of nonlinear refractive index

The strong electric field of high intensity light may cause a medium’s refractive index to vary as the light passes through it, giving rise to nonlinearity. The nonlinear refractive index highly relies on incident intensity. When matter is exposed to intense electric field of incident light, polarization is no longer proportional to electric field and the change in polarizability has to be extended by terms proportional to square of electric field [33].

The nonlinear refractive index was deduced in terms of Tichy and Ticha relationship [34]. Tichy and Ticha relationship is a combination of Miller’s popularized rule and static refractive index obtained from WDD model as [34]:

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

(17)

where χ⁽³⁾ is third-order nonlinear susceptibility. χ⁽³⁾ is obtained from the equation [35, 36];

$$\chi^{(3)} = B[\chi^{(1)} ]^{4}$$

(18)

where χ⁽¹⁾ is linear susceptibility and is given as:

$$\chi^{(1)} = \frac{1}{4\pi }\left[ {\frac{{E_{d} }}{{E_{o} }}} \right]$$

(19)

where B = 1.7×10⁻¹⁰ (for χ⁽³⁾ in esu), χ⁽³⁾ is given as:

$$\chi^{(3)} = \frac{B}{{(4\pi )^{4} }}\left( {n_{o}^{2} - 1} \right)^{4}$$

(20)

Figure 11 shows plots of nonlinear refractive index, n₂ versus wavelength, λ. From this figure, it is found that the value of nonlinear refractive index decreases with increasing Sb content.

Fig. 11

Dependence of nonlinear the refractive index (n₂) on the wavelength for investigated films

4 Conclusions

In summary, bulk samples of Se_65−xAs₃₅Sb_x thin films with ((0 ≤ x ≥ 10) at. %) were successfully synthesized using a homogeneous precipitation method. The studied films were deposited using thermal evaporation technique. The optical characterization of different compositions of amorphous Se_65−xAs₃₅Sb_x films has been carried out using the transmittance and reflectance spectra. The envelope method suggested by Swanepoel has been applied to the films with larger thickness, which has a reasonable number of interference fringes. The results indicate that n gradually increases with increasing Sb content. The increase in the refractive index is explained in terms of the polarizability. The dispersion of the refractive index studied utilizing the WDD single-oscillator model. The oscillator and dispersion parameters were computed. The nonlinear refractive index of the studied films is well related to the linear refractive index. Low optical transmittance and small bandgap for Se_65−xAs₃₅Sb_x films render them hopeful candidate for optoelectronic devices and so for various light detection, modulation and manipulation functions.