3.2.1 Absorption parameters
Linear optical analysis aimed to assess various optical parameters and constants and forecast their possible uses. The transmittance of a medium or a material is the fraction of light that passes through the other side of the medium or the proportion of the light energy hitting it to the light going through it. The estimated values of transmittance (T) and reflectance (R) provide a simpler method for calculating important optical parameters such as optical bandgap, localized state refractive index width, and other parameters. As the light travels through any medium, it can be transmitted, reflected, or absorbed. T and R characteristics of Ag/Ge25Se75 films were examined in relation to incident wavelength (λ). Figure 4 displays both T and R at different λ values from ultraviolet to near-infrared (200–2500 nm) for Ag/Ge25Se75 films at 573 K at different annealing times of 30, 60, 90, 180 and 210 min. it can be seen form that figure, in the ultraviolet region (200–500 nm), T values rose considerably with λ. However, as the λ increased more, the rate of rise in T became smaller, eventually stabilizing for the remaining λ range. The Ag/Ge25Se75 films at 573 K at different annealing times of 30, 60, 90, 180 and 210 min showed high transmittance values for wavelengths (500 ≤ λ ≤ 800 nm). As the annealing time went up from 30 to 210 min, the measured transmittance value also went up. In contrast, the R values of the prepared samples displayed a different pattern than T. The R values were lower throughout the examined λ range, with an average value around 4%. The annealing time shows a nonlinear variation when T or R is changed.
Ag/Ge25Se75 films can be used in applications that require transparent materials, such as packaging material for optoelectronic and microelectronic devices. Therefore, the estimated value of absorption coefficient (α) was calculated using[14]:
$$\:\alpha\:=\frac{1}{d}ln\left[\frac{(1-{R}^{2})}{2T}+\sqrt{{R}^{2}+\frac{(1-{R}^{2})}{4{T}^{2}}}\right]$$
1
d: thickness, T: transmittance and R: reflectance.
The absorption coefficient (α) is a measure of how well a substance can absorb light with a specific wavelength per unit length. It provides information about each absorber molecule or ion and the nature of the electronic transition. The absorption coefficient determines whether the electronic transition will occur directly or indirectly. Changes in the absorption coefficient can be attributed to annealing times of 30, 60, 90, 180 and 210 min. As shown in Fig. 5, the value of α increases as the photon energy increases, while in the range of (0.5-2.0 eV), a shoulder is observed. As the annealing time increases, the value of α decreases. Therefore, more Ag diffuse in layer of GaAs films, which enhance the absorption of the present films. Figures 6 and 7 show the plot of (αhν)1/2 and (αhν)2 against the photon energy (hν) for Ag/Ge25Se75 films at 573 K and different annealing times of 30, 60, 90, 180 and 210 min.
The first two plots are driven using[15] :
$$\:{\left(\alpha\:h\upsilon\:\right)}^{r}=const.(h\upsilon\:-{E}_{g})$$
2
The plots of (αhν)1/2 and (αhν)2 show linear relationships with photon energy at higher energy levels, indicating that Ag/Ge25Se75 films at 573 K and different annealing times of 30, 60, 90, 180 and 210 min exhibit indirect optical transitions. The more fitting relation indicate that indirect transition is the majority one in these samples due to Ag in Ge25Se75 which create localized states in Ge25Se75 samples. The intercepts of the lines yield estimated values for the direct and indirect optical bandgap (Eg) for the respective samples as listed in Table 1. It is well known that the Eg of a material can be affected by various factors, such as temperature, pressure, doping, and grain size, therefore it is changed due to gradually thermal diffusing of silver.
The amount of light that a material absorbs at a specific wavelength is measured by its extinction coefficient. The mass extinction coefficient, molar extinction coefficient, optical extinction coefficient, and other units can be used to express it. The size, shape, composition, and structure of the material are among the physical and chemical characteristics that affect the extinction coefficient. The extension coefficient (kex), using an equation[16]
$$\:{k}_{ex}=\frac{\alpha\:\lambda\:}{4\pi\:}$$
3
Figure 8 depict the extension coefficient (kex) versus photon energy (eV) for Ag/Ge25Se75 films at 573 K and different annealing times of 30, 60, 90, 180 and 210 min.
3.2.2 Dispersion parameters
The refractive index (n) versus the wavelength (λ) is illustrated in Fig. 7 for Ag/Ge25Se75 films at 573 K and different annealing times of 30, 60, 90, 180 and 210 min, respectively was estimated from[17]
$$\:n=\sqrt{\frac{4R}{{(R-1)}^{2}}-{k}_{ex}^{2}}+\frac{R+1}{R-1}$$
4
Both kex and n follow a similar trend to α. In the ultraviolet (UV) region, at wavelengths shorter than 275 nm (≤ 4.5 eV), their values abruptly drop from higher values before progressively increasing with additional wavelength. For Ag/Ge25Se75 films, kex values vary from 0 to 1 and get smaller as the annealing time increases. At 1000 nm, the refractive index reaches its maximum value of 6, with an average range of 2 to 6 [18].
Figures 9 and 10 illustrates the real part of the dielectric constant (εr) and the imaginary part of the dielectric constant (εi), respectively, as a function of the wavelength (λ) for Ag/Ge25Se75 films at 573 K and various annealing times of 30, 60, 90, 180 and 210 min.
The values of (εr) and (εi) were derived from the equation [19].
$$\:{\epsilon\:}_{r}={n}^{2}-{k}_{ex}^{2}$$
5
$$\:{\epsilon\:}_{i}=2n{k}_{ex}$$
6
An increase in the annealing times causes minor changes in the dielectric constants of (Ge25Se75)Ag, specifically the real part (εr) and the imaginary part (εi). For the same wavelength, εi is smaller than εr. When wavelengths surpass 450 nm, there is a slight increase in εi and a decrease in εr. While εi reaches a stable value, εr reaches its maximum value at 1200 nm[19]. A portion of the optical energy is lost when it drops below the optical bandgap. Dispersion parameters, such as the static refractive index, dispersion energy, and single oscillator energy, can be used to quantify this lost energy. The Wemple-DiDomenico model is used to compute these parameters[20].
Figure 11 displays a graph of (n2-1)−1 versus (hυ)2 for Ag/Ge25Se75 films at 573 K and various annealing times of 30, 60, 90, 180 and 210 min.
The experimental data was fitted to straight lines using a specific formula[21]
$$\:{({n}^{2}-1)}^{-1}=\frac{{E}_{a}}{{E}_{d}}-\frac{{\left(h\upsilon\:\right)}^{2}}{{E}_{o}{E}_{d}}$$
7
$$\:{\epsilon\:}_{\infty\:}={n}_{o}^{2}=1+\frac{{E}_{d}}{{E}_{a}}$$
8
Based on the slope and intercept of the straight lines, Table 2 presents the estimated values of the oscillator's average energy (Ea) and the inter-band optical transitions' average strength (Ed).
Table 2
Deduced optical parameters of as prepared and annealed Ag/Ge25Se75 films at 573 K at different times of 30, 60, 90 and 210 min.
Annealing time (min.)
|
Eing
|
Edig
|
Ea
|
Ed
|
\(\:{n}_{\infty\:}^{2}\)
|
\(\:{n}_{\infty\:}\)
|
M− 1
|
M− 3
|
\(\:{n}_{o}\)
|
\(\:{\epsilon\:}_{L}\)
|
\(\:\frac{N}{{m}^{*}}\)x1050
|
0
|
2.02
|
3.23
|
1.16
|
4.31
|
4.72
|
2.17
|
3.72
|
2.76254
|
3.33467
|
11.12
|
10.08
|
30
|
1.99
|
2.70
|
1.17
|
3.09
|
3.63
|
1.91
|
2.63
|
1.91
|
2.79
|
7.76
|
6.66
|
60
|
2.26
|
3.16
|
1.13
|
4.81
|
5.26
|
2.29
|
4.26
|
3.34
|
3.59
|
12.86
|
11.97
|
90
|
2.30
|
3.13
|
1.14
|
5.41
|
5.74
|
2.40
|
4.74
|
3.64
|
3.77
|
14.22
|
13.93
|
180
|
2.16
|
3.21
|
1.07
|
5.08
|
5.74
|
2.40
|
4.74
|
4.13
|
4.14
|
17.10
|
19.76
|
210
|
2.06
|
3.10
|
1.14
|
4.89
|
5.31
|
2.30
|
4.31
|
3.34
|
3.60
|
12.99
|
12.44
|
Table 2 revealed that ε ∞ and no were both dependent on annealing times of 30, 60, 90, 180 and 210 min. In addition, WDD [22]states that two additional optical dispersion parameters that describe the strength of the inter-band transition are the optical spectrum moments, M− 1 and M− 3. The following equations relate these parameters to the optical dispersion parameters Eo and Ed[23]:
$$\:{M}_{-1}=\frac{{E}_{d}}{{E}_{o}},\:{M}_{-3}=\frac{{M}_{-1}}{{E}_{o}^{2}}$$
9
The computed values for M-1 and M-3 are listed in Table 2. As the annealing times increased, the values of M− 1 and M− 3 increased. When the annealing times rises, the trends of Ed and Ea shift in the same directions[24]. The formula based on the Eo and Ed parameters can be used to determine the static refractive index[24]:
$$\:{n}_{o}=\sqrt{1+\frac{{E}_{d}}{{E}_{a}}}$$
10
The Ag/Ge25Se75 films ratio's value of no. In addition, the high-frequency dielectric constant and the ratio of charge carrier concentration (N) to the effective mass of the electron (m*) were determined using Sellmeier's model. The plot for Ag/Ge25Se75 films in Fig. 12 shows the relationship between n2 and λ2. Interestingly, the experimental data shows an amazing agreement with straight lines according to the previously mentioned equation[25].
The relationship between a transparent material's refractive index and light wavelength is represented by Sellmeier's model. Light bending as it enters or leaves a material is measured by the refractive index. An equation involving some experimentally determined coefficients is used in Sellmeier's model. If the material doesn't absorb light in that range, the formula can be used to determine the refractive index for any wavelength.
We can also learn more about how light disperses, or splits into different colors, when it passes through materials using Sellmeier's model. As the annealing time increases, the value of no for Ag/Ge25Se75 films decreases. In addition, the high-frequency dielectric constant and the ratio of charge carrier concentration (N) to the effective mass of the electron (m*) were determined using Sellmeier's model. The plot for Ag/Ge25Se75 films in Fig. 13 shows the relationship between n2 and λ2. The experimental data shows an agreement with straight lines according to the previously mentioned equation[14].
$$\:{n}^{2}={\epsilon\:}_{\infty\:}-\frac{{e}^{2}}{4{\pi\:}^{2}{\epsilon\:}_{o}{c}^{2}}\frac{N}{{m}^{*}}{\lambda\:}^{2}$$
11
The symbols for the high-frequency dielectric constant, vacuum permittivity, and speed of light in this equation are\(\:{\:\epsilon\:}_{\infty\:}\), \(\:{\epsilon\:}_{o}\), and c, respectively. In the composite, the free carrier concentration drops to 1.37 x1050 when the annealing time is raised. The estimated values of \(\:{\epsilon\:}_{\infty\:}\) and\(\:\:\frac{N}{{m}^{*}}\), are listed in Table 2, and the formula of \(\:{\epsilon\:}_{\infty\:\:}={n}_{o}^{2}\:\) is confirmed by the estimated values of no and \(\:{\epsilon\:}_{\infty\:\:}\).