Figure 1 show the XRD patterns of In₂S₃ thin films on ITO and fluorine-tinoxide FTO coated glass substrates with various thicknesses before vacuum annealing. From Figure 1, it can be also seen that, all the layers are amorphous, the reflexions marked by (*) in the patterns are assigned to the ITO and FTO coated glass substrates. This result was in agreement with those results in the literature [14] [15] [16] [17].

The XRD patterns of the different samples are shown in Figure 2(a). The In₂S₃/ITO and FTO films are annealed at 300˚C and 400˚C. The first observable effect is the appearance of the characteristic basal reflections of In₂S₃. The diffraction maxima of 2θ at 27.55, which correspond to the (109) reflection ascribed to In₂S₃ quadratic (JCPDS Card no. 782486) appear with hight intensity in all the samples. After annealing, all the XRD patterns just show the diffraction maxima of the quadratic spinel phase (JCPDS id. 78-2486) with (109) preferential orientation. This result is in good agreement with other studies [18] [19] [20] [21]. However, herein, the annealing of films at different temperature affects the crystallization of In₂S₃. Pointing out the intensity and shape of the In₂S₃ reflection maxima, it is clear that the crystallinity of the In₂S₃ formed varies depending on the nature of substrate ITO and FTO (Figure 2(a)).

Figure 2(b) depicts the diffractograms of indium sulfide on ITO and FTO layers with about 650 nm thickness. We can observe that the (103) peak becomes sharper in the films deposited on ITO substrates compared to the deposited on FTO substrates. In other side, the crystallinity of the In₂S₃ is enhanced with the temperature of annealing increase (400˚C) and the best crystallinity is obtained for a deposition on ITO substrate. Also, it can be also noticed, a slight shift of the main diffraction maxima when the annealing temperature increases from 300˚C to 400˚C (Inset Figure 2(b)). It can be attributed to a decrease in stress with generates a decrease in the dislocation [22]. This result can be explained by the rearrangement of the atoms into a lower energy state corresponding to a more orderly arrangement.

The average crystallite size can be estimated using Scherer’s formula:

D = 0.9 λ β cos θ (3)

where λ (0.1541 nm) is the wavelength of Cu Kα radiation, θ is the Bragg angle, and β is the half-width at half maximum (HWHM) of the diffraction maxima (109). Table 1 collects the In₂S₃ crystal size values estimated by the Scherrer’s equation.

Figure 3 displays the transmission and reflexion spectra of the prepared samples before annealing.

The results show that the transmission value varying from 80% to 70% correspond to In₂S₃ deposited on ITO and FTO coated glass substrates, respectively. As well as, the total reflexion value at 45% and 40% correspond to ITO and FTO coated glass substrates respectively.

Figure 4(a) and Figure 4(b) displays the transmission and reflxion of the samples annealing at 300˚C and 400˚C for 1 hours of the In₂S₃ deposited on ITO and FTO coated glass substrates.

From Figure 4, it can be also seen that, the low variation of transmittance after thermal treatment showing interference fringes, can be attributed to the homogeneity of In₂S₃ thin films.

Transmission spectra for layers deposited on the ITO show interference fringes, indicating good homogeneity. The transmission reaches 95% in the visible and near infrared range (Figure 4(b)). It is most important for the 300 nm thick layer. For those deposited with FTO, the transmission decreases dramatically indicating an aspect of inhomogeneity. We also note a decrease in the transmission values for the layers deposited at the FTO by about 25% compared to the layer deposited at the ITO. We explain the decrease in transmittance values for layers deposited at FTO compared to those deposited on ITO by the difference in structural condition and surface condition for each substrate.

The relation between the absorption coefficient, α, and the incident photon energy, hν, can be written as:

( α h ν ) = A ( h ν − E g ) n (3)

where A is a constant and n is a number which characterizes the transition process. The value, n = 1/2, characterizes a direct allowed optical transition. Plotting of (αhυ)² versus photon energy, hυ, yields a straight line indicating direct optical transition. The band gap values were obtained from the transmission spectra of In₂S₃ thin films for different thickness on ITO and FTO-coated glass substrates. The values of the direct band gap E_g are collected in Table 2. These values show that the optical gap decreases with the thickness of the layers for both types of substrates. This related to the degree of non-stoichiometry of In₂S₃ for low thicknesses and to the increase in crystallinity for large thicknesses. The corresponding E_g values calculated for the thin films of ITO and FTO decreases according to the thickness of the layers from 2.01 to 2.8 eV, which is close to that reported in the bibliography [23] [24] [25] [26] (2.5 eV).

Also, the refractive index, n of In₂S₃ films was calculated through the transmission maxima, T_M and minima, T_m of the envelopes of the transmission spectra, by using the Swanepoel method [27] [28].

n = [ N + ( N 2 − n s 2 ) 1 / 2 ] 1 / 2 (3)

With

N = 2 n s ( T M − T m ) T M T m + n s 2 + 1 2 (4)

s is the refractive index of the glass substrate and T_M and T_m represent the envelopes of the maximum and minimum positions of the transmission spectra.

The variations of refractive index n(λ), with Cauchy fitting for In₂S₃ thin films with different thicknesses are shown in Figure 5 and Figure 6, respectively. It is clear seen, that the refractive indices variations obey to the Cauchy decreases with increase of wavelength and remains constant above 1000 nm showing normal dispersion law for all the films [29]. The initial sharp decrease of n with wavelength indicated a rapid change in the absorption energy of the material [30], which depends on the surface and volume imperfections [31]. The average refractive indices values were in range 1.79 - 3.02 for the all the films (Table 3). These refractive indices values were taken for wavelengths greater than 1000 nm which corresponds to the spectral transparency region. The increase of refractive index indicates the improvement in the crystallinity of the films that could be decreased during the deposition process itself with the increase of thickness at different annealing deposed on ITO and FTO coated glass substrates so that the films had a better crystallinity leading to higher refractive index. Also, the variation in refractive index can be attributed to the changes occurring in the strain and dislocation density of the layers [32].

The Cauchy’s formula of the refractive index n, as a function of the wavelength λ, is [33] [34].

n ( λ ) = n 0 + A λ 2 + B λ 4 (5)

where n₀, A and B are the Cauchy’s parameters and λis the wavelength.

According to the Cauchy distribution, the refractive index depends on the material and the wavelength. The best fit of experimental data was added in Figure 6. The values of Cauchy’s parameters are gathered in Table 3.

According to Cauchy’s formula, we can noticed that a non-dispersive medium, A = B = 0 and that a medium is less and less dispersive if these constants tend towards zero at the same time. As well as, it is observed that for these constants are very far from zero despite the fact that some decrease slightly in some layers deposited on FTO substrates. This proves the dispersive character of these materials.

Wemple and DiDomenico [35] [36] have developed a model where the refractive index dispersion is studied in the region of transparency below the gap, using the single effective oscillator approximation. It is well known from the dispersion theory that in the region of low absorption the refractive index n described to a very good approximation, by the following formula,

n 2 ( h ν ) = 1 + E d E 0 E 0 2 − ( h ν ) 2 (6)

where, hν is the photon energy, E₀ is the single oscillator energy and E_d is the dispersion energy.

Plotting (n² − 1)⁻¹ against (hν)² (Figure 7) allow us to determine the oscillator parameters by fitting a straight line to the points. The values of E₀ and E_d can be determined directly from the slope (E₀E_d)⁻¹ and the intercept on the vertical axis, (E₀/E_d). It was found that E_d varies between 4.29 and 36.8 eV and E₀ varies from 2.23 to 7.74 eV for the different substrate.

The high-frequency dielectric constant ε_∞ is obtained by the Wemple-Didomenico model by stretching hν→ ∞:

ε ∞ = 1 + E d E 0 (7)

The different values of the oscillator parameters were summarized in Table 4.

The effect of the nature of the substrate reveals that the E_d dispersion energies are marked by a drop for layers deposited on FTO substrates (e.g. from 36.8 eV for unannealed layers deposited on ITO substrates to 6.7 eV for layers deposited on FTO substrates). Similarly for the average energy E₀ describes a decrease for layers deposited on FTO compared to ITO.

The effect of the nature of the substrate reveals that the Ed dispersion energies are marked by a drop for layers deposited on FTO substrates (e.g. from 36.8 eV for unannealed layers deposited on ITO substrates to 6.7 eV for layers deposited on FTO substrates). Similarly for the average energy E₀ describes a decrease for layers deposited on FTO compared to ITO.

The optoelectronic properties investigated by Hall Effect shows very intersting result. In fact, the nature of the substrate as well as the heat treatment under vaccum plays an essential role. The electrical properties of the samples with different annealing temperature and thickness are shown in Table 5. The Hall Effect study confirmed that layers have a very significant density out of carrier’s loads indicating a semiconductor n-type, which shows that the thermal treatment and substrate type do not change the type of the majority carriers in β-In₂S₃ [37] - [43]. Before annealing, they films deposited at FTO substrats present the highest resistivity and mobility. But after annealing treatment at 300˚C - 400˚C, on notice another behavior of the resistivity of the β-In₂S₃ thin films deposited at ITO. In fact, it can be observed that the ITO substrate is more stable and gives layers that have the lowest, resistivity. This resultas, it is on correlation with the XRD investigation wich shows that they films deposited at ITO

N.B: d: carriers density; ρ: resistivity and μ: mobility.

substrats present the high crystallinity compared to FTO substrates. Indeed the influence of the substrate is better felt for the indium sulfide layers on ITO. We also notice that the carrier concentration is important for both series of samples.