Introduction

Cadmium sulfide (CdS) is a II–VI compound semiconductor of a wide bandgap of about 2.42 eV at room temperature. CdS has reasonable conversion efficiency, stability and mature low-cost deposition technique. In addition, it has high electron affinity and it is easy to make ohmic contact. CdS thin films have potential uses in optoelectronic device fabrication and in photovoltaic applications as a window layer in CdTe-based and CuInS2 solar cells. For use as window layers in thin-film solar cells, CdS must have n-type electrical conductivity. There are different dopants that can be used to obtain n-type CdS, such as In Refs.1–4, Ag,1 Al,1,5 Cl,6 etc. In this work, indium was used as the dopant to improve the n-type conductivity of CdS films.

There are different techniques to produce CdS thin films such as chemical bath deposition (CBD),1,7–9 thermal evaporation,10 and the spray pyrolysis (SP) technique.11,12 The SP technique is a simple and low-cost method, which enables intentional doping, and the production of large-area films. The study of the optical properties and optimizing the optical parameters of CdS is important for the use of this material in solar cells and optoelectronic devices. The aim of the present work is to pay more attention to studying the influence of annealing on the optical parameters of indium-doped cadmium sulfide (CdS:In) thin films prepared by the spray pyrolysis technique.

Experimental Procedure

Indium-doped cadmium sulfide (CdS:In) thin films were prepared by spraying an aqueous solution of approximately stoichiometric ratios of the hydrated cadmium chloride (CdCl2·H2O) and thiourea [(NH2)2CS] on glass substrates kept at 490°C. Indium chloride (InCl3) was used as a dopant source in the starting solution. The films thus produced were annealed in a nitrogen atmosphere for 30 min at 400°C. Transmission spectra of the prepared films were measured at room temperature by normal incidence of light, using a double-beam UV-1601 PC Shimadzu spectrophotometer, in the wavelength range 400–1100 nm. The structure of the films was explored using x-ray diffraction (XRD) with CuKα radiation (λ = 1.5405 Å) in the range of Bragg angles 2° ≤ 2θ ≤ 60° in steps of 0.04°. The morphology and composition of the films were investigated using FEI scanning electron microscope (Inspect F 50) equipped with a thin-window energy dispersive x-ray spectrometer (EDS). The films’ thickness was estimated using transmittance and Lambert’s law of absorption in a semiconductor.

Results and Discussion

XRD diffractograms of as-deposited and annealed CdS:In thin films are shown in Fig. 1. The figure reveals that the films are polycrystalline and they have a mixed phase (cubic and hexagonal). All the prominent peaks are indexed with Millar indices which are shown in the figure. The lines C(1 1 1), C(2 2 0), and C(3 1 1) belong to the cubic phase. However, the peaks H(0 0 2), H(1 0 1), H(1 0 2), H(1 0 3), H(1 1 2), and H(2 0 2) belong to the hexagonal phase. The as-deposited and annealed CdS:In films were preferentially oriented along the H(1 0 1), and the C(3 1 1)/H(1 1 2) planes, where the positions of the C(3 1 1) line of the cubic phase and that of the H(1 1 2) line of the hexagonal phase approximately coincide.

Fig. 1
figure 1

XRD diffractograms of two CdS:In thin films; as-deposited with thickness = 400 nm (a), and annealed with thickness = 230 nm (b)

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SEM micrographs of an as-grown and nitrogen annealed CdS:In thin films on glass substrates are shown in Fig. 2. The films are polycrystalline and the annealed film shows larger grains as can be seen in the Figure. The surfaces of the films appear compact and with good substrate coverage. There is no notable change in surface morphologies between the as-deposited and annealed films. This is because the films were deposited at a high temperature (490°C), so the crystal growth is complete. Figure 3 displays the EDS spectra for the as-deposited (Fig. 3a) and annealed (Fig. 3b) films. From these, it can be seen that the films contain cadmium, sulfur, and indium.

Fig. 2
figure 2

SEM micrographs of two CdS:In thin films of thickness about 140 nm: as-deposited (a), and annealed (b)

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Fig. 3
figure 3

The EDS plots for the as-deposited (a), and annealed (b) CdS:In thin films of SEM images shown in Fig. 2

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Figure 4 displays the transmittance of films of different thicknesses which are annealed in a nitrogen atmosphere at 400°C. The transmittance decreased with the annealing, and the absorption edge was shifted towards the longer wavelengths, which refers to the decrease in the optical bandgap energy. The decrease in transmittance is related to the improvement in crystallinity and the increase of the number of free charge carriers after annealing.

Fig. 4
figure 4

Transmittance spectra of as-deposited and annealed CdS:In thin films with different thickness t. (a) t = 335 nm. (b) t = 400 nm. (c) t = 730 nm. (d) t = 740 nm. (e) t = 800 nm. The legend contains the names of the samples, where as refers to the as-deposited, and ann to the annealed films

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Absorption coefficient values of the films were deduced from the transmittance data, and they are of the order of 104 cm−1 in the strong absorption region. Figure 5 depicts the relationship between the absorption coefficient α and the photon’s energy hν for CdS:In thin films before and after annealing. From the Figure, it is apparent that the absorption edge was shifted to the lower energy side after annealing. The absorption coefficient increased or stayed approximately constant after annealing in the region of weak absorption, while it increased in the strong absorption region for two films (a and c), decreased for two films (b and d), and stayed approximately constant for another film (e). The decrease of α after annealing may be related to the Cd:S ratios and the indium content in these films. It can noted that the film in (b) and the films in (d and e) have higher transmittance before and after annealing than the films in (a and c). This means that the films in (b, d, and e) have approximately the same or smaller number of free charge carriers after annealing.

Fig. 5
figure 5

Absorption coefficient of as-deposited and annealed CdS:In films as a function of the photon’s energy hν for films with different thickness. (a) t = 336 nm. (b) t = 401 nm. (c) t = 732 nm. (d) t = 741 nm. (e) t = 801 nm

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To estimate the value of the bandgap energy, a plots of (αhν)2 versus hν is displayed in Fig. 6, where the transition is assumed to be a direct one. Linear fits were made in the linear regions of the curves, and the optical bandgap energy E g was estimated from the intercepts with the energy axis. The obtained values of E g are shown in Fig. 6, and they are in the ranges 2.440–2.448 eV, and 2.414–2.443 eV before and after annealing, respectively. Thus, the annealed films have reduced bandgap values compared with the as-deposited ones.

Fig. 6
figure 6

The plot and linear fit of (αhν)2 against the photon’s energy hν for CdS:In films of different thickness before and after annealing. (a) t = 336 nm. (b) t = 401 nm. (c) t = 732 nm. (d) t = 741 nm. (e) t = 801 nm

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The absorption coefficient, α, near the fundamental absorption edge usually shows simple exponential energy dependence:13

$$ \alpha = \alpha_{0} \exp (h\nu /E_{\text{e}} ) $$
(1)

referred to as the Urbach tail, where α 0 is constant and E e determines the width of the tail. The tail, i.e., Urbach energy, is generally attributed to disorder in the material which leads to a tail in the valence and conduction bands. To find the value of E e, a plot of the natural logarithm of the absorption coefficient (ln α) against the photons energy hν was made and is shown in Fig. 7. Linear fits were performed in the linear parts of the curves; fit parameters were used to find E e and α0. The values are inserted in Table I. In general, it can be noticed that E e decreases with annealing. The decrease of Urbach energy with annealing could be due to a decrease of the defects density in the tail after heat treatment. The enlargement of grain size results in a narrowing of the grain boundaries and then a reduction in the defects density.

Fig. 7
figure 7

A plot and linear fits of ln (α) against the photon’s energy hν for CdS:In films of different thickness before and after annealing. (a) t = 336 nm. (b) t = 401 nm. (c) t = 732 nm. (d) t = 741 nm. (e) t = 801 nm

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Table I The optical bandgap energy E g, width of Urbach tail E e, α 0, and the refractive index n at λ = 550 nm for all films before and after annealing; the film thickness is also listed
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To find the refractive index and the extinction coefficient, the definition of the reflectance R of a film for a light wave incident normally from air, with refractive index n 0  = 1, on a medium of complex refractive index n* = n + ik is used.14

$$ R = \frac{{\left( {n^{*} - 1} \right)^{2} }}{{\left( {n^{*} + 1} \right)^{2} }} = \frac{{\left( {n - 1} \right)^{2} + k^{2} }}{{\left( {n + 1} \right)^{2} + k^{2} }} $$
(2)

where n is the refractive index and k is the extinction coefficient of the film. Figure 8 shows that the reflectivity R of the films against the photon’s energy hν for the whole set of films under study. As the figure shows, R increases with annealing, especially in the near-infrared and visible regions. This result is in good agreement with Ziabari and Ghodsi13 for CdS nanoscrystalline thin films prepared by sol–gel and incorporated in polyethyleneglycol.

Fig. 8
figure 8

The reflectivity R of CdS:In thin films of different thickness against the photon’s energy hν before and after annealing. (a) t = 336 nm. (b) t = 401 nm. (c) t = 732 nm. (d) t = 741 nm. (e) t = 801 nm

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Knowing the value of the absorption coefficient α from the transmittance, the extinction coefficient can be calculated using the relationship \( k = \frac{\lambda \alpha }{4\pi } \), where λ is the wavelength in free space. Solving Eq. 1 for the refractive index n gives;

$$ n = \frac{{\left( {1 + R} \right) + \left[ {\left( {1 + R} \right)^{2} - \left( {1 - R} \right)^{2} \left( {1 + k^{2} } \right)} \right]^{1/2} }}{1 - R} $$
(3)

Figure 9 shows the dependence of the extinction coefficient of the films on hν. It is restricted for all the films in the ranges 0.018–0.077 and 0.019–0.110 before and after annealing, respectively. It is also fairly constant in the regions before the absorption edge. A sharp increase of k occurs at the absorption edge, then it becomes approximately constant or decreases slowly with hν.

Fig. 9
figure 9

A plot of the extinction coefficient k against the photon’s energy hν for CdS:In films of different thickness before and after annealing. (a) t = 336 nm. (b) t = 401 nm. (c) t = 732 nm. (d) t = 741 nm. (e) t = 801 nm

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Refractive index n values for all films were calculated using Eq. 3 and plotted against the photon’s energy hν in Fig. 10. The Figure implies that the refractive index increases with hν, slowly before the absorption edge, then strongly after it. Annealing increases the refractive index for all films. For hν ≤ 2.3 eV, the refractive index of all the as-deposited films lies in the range 1.33–3.29, and of all annealed films in the range 1.51–4.64. The increase of the refractive index with annealing is an indication of the improvement of the crystallinity of the films. The values of n before and after annealing at wavelength λ = 550 nm for all films are inserted in Table I.

Fig. 10
figure 10

A plot of the refractive index n against the photon’s energy hν for CdS:In films of different thickness before and after annealing. (a) t = 336 nm. (b) t = 401 nm. (c) t = 732 nm. (d) t = 741 nm. (e) t = 801 nm

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Below the absorption edge, refractive index dispersion can be analyzed by the single oscillator model. The dispersion of incident photon energy plays the important role in determining the optical property of the material. Thus, the obtained data of refractive index n has also been analyzed to yield the long wavelength refractive index (n ∞) together with the average oscillator wavelength (λ 0) for CdS:In thin film before and after annealing using the following relationship.15

$$ \frac{{n_{\infty }^{2} - 1}}{{n^{2} - 1}} = 1 - \left( {\frac{{\lambda_{0} }}{\lambda }} \right)^{2} $$
(4)

The relationship between (n 2 − 1)−1 and λ −2 for the as-deposited and annealed films is shown in Fig. 11. which also shows the linear fits in the linear part of each curve, where λ 0, n ∞ and ɛ ∞ = n 2∞ are evaluated from the fit parameters and are listed in Table II. From these values, the average excitation energy for electronic transitions E 0 = hc/λ 0, and the dispersion energy which is a measure of the strength of interband optical transitions E d = E 0(n 2∞  − 1) are also calculated and also listed in Table II. In general, λ 0, n ∞, ɛ ∞ and E d increased with annealing, while E 0 decreased. The ratio of E 0 to E g was calculated and is shown in Table II where i It is found that (E 0/E g) ≈ 1.1. This ratio is close to 1.2, at which Ilican et al.16 reported that the oscillator energy E o is related to lowest direct bandgap empirically by E o = 1.2E g. So, the calculated values of E o satisfy the empirical relationship obtained approximately from the single oscillator model. A measure of interband transition strengths can be provided from the M −1 and M −3 moments of the optical spectrum. The M −1 and M −3 are expressed as13

$$ M_{ - 1} = E_{\text{d}} /E_{0} $$
(5)

and

$$ M_{ - 3} = \frac{{E_{\text{d}} }}{{E_{0}^{3} }}, $$
(6)
Fig. 11
figure 11

The plot and linear fits of (n 2 − 1)−1 against λ −2 for as-deposited and annealed CdS:In thin films of different thickness. (a) t = 336 nm. (b) t = 401 nm. (c) t = 732 nm. (d) t = 741 nm. (e) t = 801 nm

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Table II The oscillator parameters of CdS:In thin films of different thickness before and after annealing
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The calculated values are shown in Table II, from which it can be observed that both moments had increased with annealing.

The polarizability of any solid is proportional to its dielectric constant. The variation of the dielectric constant with the photon’s energy is an indication of interactions between photons and electrons in the films in this energy range. The real and imaginary parts of the complex dielectric constant are expressed as:13,17

$$ \varepsilon_{1} = n^{2} - k^{2} $$
(7)

and

$$ \varepsilon_{2} = 2nk $$
(8)

Figure 12 displays the relationship between ε 1 and the photon’s energy hν for all films before and after heat treatment. As seen in the Figure, ε 1 is constant or slowly increases with hν in the near-infrared and visible regions before the absorption edge, after which an abrupt increase occurs. The variation of ε 1 is restricted in the ranges 2.28–10.83 and 2.28–21.56 for hν ≤ 2.30 eV for the as-deposited and annealed films, respectively. This abrupt increase indicates that the interaction of photons and electrons is the strongest at the absorption edge. In general, the real part of the dielectric constant increased with annealing.

Fig. 12
figure 12

The plot of the real part of the dielectric constant ε 1 against the photon’s energy hν for CdS:In films of different thickness before and after annealing. (a) t = 336 nm. (b) t = 401 nm. (c) t = 732 nm. (d) t = 741 nm. (e) t = 801 nm

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Figure 13 depicts the relationship between the imaginary part of the dielectric constant ε 2 against hν for the whole set of films before and after annealing. The behavior of ε 2 follows the behavior of k since it represents the absorption associated with free carriers.10 The values of ε 2 before the absorption edge are constant (approximately equal to zero) before and after annealing. An abrupt increase in ε 2 occurs at the absorption edge before and after heat treatment, and the shift of the absorption edge towards longer wavelengths after heat treatment is obvious. Also, the abrupt increase in ε 2 refers to the fact that the interaction between photons and electrons is the strongest at this point.

Fig. 13
figure 13

The plot of the imaginary part of the dielectric constant ε 2 against the photon’s energy hν for CdS:In films of different thickness before and after annealing. (a) t = 336 nm. (b) t = 401 nm. (c) t = 732 nm. (d) t = 741 nm. (e) t = 801 nm

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Dielectric loss is a loss of energy that goes into heating a dielectric material in a varying electric field. The dielectric loss is given by the relationship;15

$$ \tan \delta = \frac{{\varepsilon_{2} }}{{\varepsilon_{1} }},\quad {\text{and}}\;{\text{the}}\;{\text{loss}}\;{\text{angle}}\;{\text{is}}\quad \delta = \tan^{ - 1} \left( {\frac{{\varepsilon_{2} }}{{\varepsilon_{1} }}} \right) $$
(9)

Figure 14 depicts the relationship between the dielectric loss and photon’s energy hν for the whole set of films before and after heat treatment. From the figure, it can be observed that the dielectric loss for some films have more than one maximum before and/or after annealing, and sharply decrease with the photon’s energy after the fundamental absorption edge.

Fig. 14
figure 14

The plot of the energy loss against the photon’s energy hν for CdS:In films of different thickness before and after annealing. (a) t = 336 nm. (b) t = 401 nm. (c) t = 732 nm. (d) t = 741 nm. (e) t = 801 nm

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The optical conductivity σ of the CdS:In thin films can be determined using the formula;18

$$ \sigma = \frac{\alpha nc}{4\pi } $$
(11)

where cis the speed of light. Figure 15 shows variations in the optical conductivity as a function of the photon’s energy hν. The enhanced optical conductivity at the high energy side is due to the high absorbance of the films in that region. As the figure shows, the influence of annealing is not the same for all samples; σ of samples in (b and e) increased with annealing, that of samples in (a and c) decreased, and σ of the sample in (d) remained approximately unchanged. The oscillations in the high energy side are related to glass which absorbs ultraviolet light. These results can be explained in terms of the Cd:S and In: Cd ratios in the films. The film in (b) has Cd:S equal to 1.01 and its indium content is 2.10 at.%, as mentioned before. The optical conductivity of this film had considerably increased after annealing, as shown in Fig. 15b. It is expected that the same situation applies for the film in €, while the other films may have Cd:S ratio less than 1.0 and they may contain less indium. This is expected for films prepared by the SP technique because it has a dynamic nature.

Fig. 15
figure 15

The plot of the optical conductivity σ against the photon’s energy hν for CdS:In films of different thickness before and after annealing. (a) t = 336 nm. (b) t = 401 nm. (c) t = 732 nm. (d) t = 741 nm. (e) t = 801 nm

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Conclusion

Polycrystalline indium-doped cadmium sulfide thin films were prepared by the SP technique on glass substrates, and the influence of heat treatment in a nitrogen atmosphere on the optical parameters of the films was studied. In general, it has been found that the transmittance and optical bandgap energy decrease with annealing, which is related to the improvement of the crystallinity of the films after annealing. On the other hand, the absorption coefficient, Urbach tail width, extinction coefficient, refractive index, and real part of the dielectric constant, increased with annealing, while the imaginary part of the dielectric constant showed small changes. The dielectric loss and optical conductivity increased for some films and decreased for others, which was explained in terms of Cd:S ratios in the films and their indium contents. These results are important for the use of CdS:In films in optoelectronic devices and thin film solar cells.