Synthesis, Crystallography, Microstructure, Crystal Defects, Optical and Optoelectronic Properties of ZnO:CeO₂ Mixed Oxide Thin Films

Abstract

We report the synthesis and characterization of pure ZnO, pure CeO₂, and ZnO:CeO₂ mixed oxide thin films dip-coated on glass substrates using a sol-gel technique. The structural properties of as-prepared thin film are investigated using the XRD technique. In particular, pure ZnO thin film is found to exhibit a hexagonal structure, while pure CeO₂ thin film is found to exhibit a fluorite cubic structure. The diffraction patterns also show the formation of mixed oxide materials containing well-dispersed phases of semi-crystalline nature from both constituent oxides. Furthermore, optical properties of thin films are investigated by performing UV–Vis spectrophotometer measurements. In the visible region, transmittance of all investigated thin films attains values as high as 85%. Moreover, refractive index of pure ZnO film was found to exhibit values ranging between 1.57 and 1.85 while for CeO₂ thin film, it exhibits values ranging between 1.73 and 2.25 as the wavelength of incident light decreases from 700 nm to 400 nm. Remarkably, refractive index of ZnO:CeO₂ mixed oxide-thin films are tuned by controlling the concentration of CeO₂ properly. Mixed oxide-thin films of controllable refractive indices constitute an important class of smart functional materials. We have also investigated the optoelectronic and dispersion properties of ZnO:CeO₂ mixed oxide-thin films by employing well-established classical models. The melodramatic boost of optical and optoelectronic properties of ZnO:CeO₂ mixed oxide thin films establish a strong ground to modify these properties in a skillful manner enabling their use as key potential candidates for the fabrication of scaled optoelectronic devices and thin film transistors.

1. Introduction

Zinc oxide (ZnO) is an essential and promising material for several modern technological applications owing to its high transmittance of visible light, wide direct band gap of 3.37 eV, extremely large exciting binding energy, high electrochemical stability, high semiconductor resistivity and non-toxicity [1,2,3,4]. In recent years, the interest in ZnO thin films has been significantly increased with the realization of devices such as optoelectronics [5,6], LED [7], UV-laser [8], solar cells [9,10], sensors [11] and other optical coating applications [12]. Moreover, ceria (CeO₂) thin film has attracted much attention and widely explored due to its extraordinary characteristics. Mainly, its high transmittance of visible light, wide direct band gap of 3.2 eV, high stability, high dielectric constant and high refractive index [13,14,15], consequently, ceria thin films have been used for technological applications such as optoelectronics [16,17], solid oxide fuel cells [18,19], energy storage [20,21] and catalysts [22,23,24,25]. Moreover, CeO₂ has been used as a corrosion protective coating [26,27].

Non vacuum depositing techniques such as pin coating, dip coating and spray pyrolysis coating are commonly used for the deposition and synthesis of thin films. Owing to their appealing features such as low cost, easiness and simplicity, such methods are considered as important research tools for the preparation of as-grown metal mixed thin films. In particular, spin coating is one of the most important research techniques due to its high reproducibility over a widespread viscosity range. However, this method suffers from a serious drawback as it is not appropriate for large scale industrial production. On the other hand, dip coating is a widely-used method for easy and fast deposition of thin films on substrates of large areas. It is appropriate for depositing materials on both side of large-area substrate. If the deposition rate and power conversion efficiency are high, spray coating can be easily performed for relatively uniform and high-quality coatings.

Previous works have reported that co-deposition of mixed metal oxides such as ZnO:CeO₂ could yield mixtures of exceptional properties such as high UV absorption, controllable optical band gap, good photoluminescence, high extinction coefficient, anticorrosive properties and high refractive index [28]. In recent years, ZnO:CeO₂ mixed oxides thin films have been used for essential applications, such as sensors [29,30], catalysts [31,32], fuel cells applications [33], antibacterial applications [34], corrosion protective coating [35], and UV filters [36].

The motivation to explore, measure and interpret the optical and optoelectronic properties of ZnO:CeO₂ mixed oxide thin films stems from their anticipated optical applications. They have been widely used as key potential components for UV filters and high refractive index optical devices. Sun-proofs and sun-protectors products are used largely especially in regions that are exposed to sunshine for most of the year. They serve as efficient filters for energetic UV-light. As a result, they have been implemented increasingly nowadays to produce materials for human skin protection from the hazardous UV radiations. Owing to their serious drawbacks such as fractional degradation and, consequently high UV absorption, when exposed to UV light, organic UV blockers are not appropriate especially for people with medical records that indicate potential photo allergy [36]. Furthermore, mixed metal oxide thin films are reported as good candidates for the fabrication of single-mode polymer waveguides. The superiority of such guides over other types of waveguides is that a slight adjustment of the refractive index may accomplish the total reflectance and therefore effective wave guiding. However, single-mode polymer waveguides suffer from serious drawback caused by Fresnel losses result from the mismatch in the refractive index values between the metal oxides and the semiconductor-based device. This can be tackled and resolved by choosing metal oxides with high refractive indices [37]. For that reason, thin films exhibit high refractive indices have enticed substantial consideration for advanced optoelectronic devices such as light emitting diode devices [38], photoresists for 193-nm immersion lithography [39], high performance substrates for advanced display devices [40] and micro lens components for charge coupled devices or complementary metal oxide semiconductor [41]. As mentioned before, it is important to investigate the optoelectronic properties of ZnO: CeO₂ mixed oxides thin films. In this study, we report the crystallography, microstructure, crystal defects and optoelectronic properties of ZnO:CeO₂ mixed oxides thin films fabricated by sol–gel method.

2. Experimental Details

2.1. Preparation Pure ZnO and Pure CeO₂ Solution

The pure ZnO/pure CeO₂ solution was prepared by dissolving 4.38 g of zinc acetate dehydrated (Zn (CH₃CO₂)₂ 2H₂O) and 2.21 g of Ce (III) nitrate hexahydrate (Ce(NO₃)₃·6H₂O) separately in 50 mL 2-methoxyethanol. ZnO solution was then mixed thoroughly on a magnetic stirrer for 50 min at room temperature, while CeO₂ solution was then mixed thoroughly on a magnetic stirrer for 60 min at 65 °C. Then, the ethanolamine of 1.7 mL and acetylacetone of 1.5 mL as a stabilizer was added to the ZnO and CeO₂ solutions, respectively, in terms of drop by drop while stirring the solutions until they become transparent. The resulting mixtures was stirred for 40 min to get homogeneous solutions. The solutions were filtered by paper-filter with 0.45 μm in dimension [1,2,42].

2.2. Preparation of ZnO:CeO₂ Mixed Oxides Solution

ZnO:CeO₂ mixed oxides solution was prepared by mixing pure ZnO solution with pure CeO₂ solution with three different concentration ratios (ZnO:CeO₂, 0.75:0.25, 0.50:0.50, 0.25:0.75) using magnetic stirrer for 1 h at room temperature.

2.3. Deposition of ZnO:CeO₂ Mixed Oxides Thin Films

To prepare the desired mixed-oxides thin films, pure ZnO, pure CeO₂ and mixed ZnO:CeO₂ are deposited for 2 h on pre-cleaned glass substrates by dip coating technique. The deposited thin films are then air dried at 110 °C in an oven at atmospheric pressure for 15 min in order to evaporate the solvents and organic residues. In the final step of the synthesis, we anneal the deposited dried pure ZnO, pure CeO₂ and ZnO:CeO₂ mixed oxides thin films in air at 500 °C for 2 h. The procedure followed ensures that the obtained thin films are structurally optimized [1,2].

2.4. Characterizations of ZnO:CeO₂ Mixed Oxides Thin Films

Crystallinity of ZnO:CeO₂ mixed oxides thin films is investigated by Powder XRD (Malvern Panalytical Ltd., Malvern, UK) (220–230 VAC 50/60 Hz 40 A) using Cu Kα₁ ray with a wavelength of 0.1540598 nm at room temperature from angles of incident photon on the surface ranges from 10° to 70° with a step of 0.02° with an energy resolution of 20%. Angular resolution: 0.026° FWHM on LaB_6, and Angular reproducibility < 0.0002°. Maximum angular speed of 15 deg./s. The optical transmittance and reflectance spectra are measured using UV–Vis spectrophotometer (U-3900H) with the total internal integrating sphere at room temperature.

3. Result and Discussion

3.1. X-Ray Diffraction (XRD) Analysis

Figure 1 shows the XRD patterns of pure ZnO, pure CeO₂ and ZnO:CeO₂ mixed oxide thin films annealed at 500 °C for 2 h. Pure ZnO thin films exhibit peaks at Bragg’s angles of 32.13°, 34.75° and 36.58° corresponding to (100), (002) and (101) crystallographic planes, respectively. In addition, XRD patterns confirm that ZnO thin film is polycrystalline and exhibits wurtzite hexagonal structure [3,43]. In addition, the main peaks of pure CeO₂ thin film are observed at Bragg’s angles of 28.89°, 33.54° and 47.88° corresponding to CeO₂ crystallographic planes indexed by Miller indices of (111), (200) and (220), respectively. Comparison of observed and standard ‘$d$’ ($hkl$) planes as matched with JCPDS cards no. 034–394 indicates that CeO₂ thin film is polycrystalline and exhibit cubic phase with fluorite structure [44]. Furthermore, XRD patterns indicate that pure CeO₂ and ZnO thin films have a higher degree of crystallinity than that of ZnO:CeO₂ mixed thin films. Careful examination of XRD patterns reveal that ZnO:CeO₂ mixed thin films encompass distinct crystalline phases of ZnO and CeO₂ components [45]. XRD patterns of ZnO:CeO₂ mixed thin films containing 25%–75% of CeO₂ NPs reveal that the intensity of ZnO reflections at (100), (002) and (101) decrease quite rapidly while that of the CeO₂ (111) peak increases. This could be understood in terms of the amount of scattered X-ray from Ce⁴⁺ and Zn²⁺ ions. The diffraction factor f of Ce⁴⁺ ions is higher than that of Zn²⁺ ions. Since f of an atom depends mainly on $\sin \theta /\lambda$ where $\theta$ is the scattering angle and $\lambda$ is the wavelength of X-ray and atomic number Z, it is challenging to identify lighter atoms in presence of heavier atoms. The diffraction pattern of ZnO is much weaker than that of CeO₂ [44]. Obviously, the individual peak positions of CeO₂ and ZnO remain unchanged in the XRD pattern of ZnO:CeO₂ composite oxides. This provides substantial evidence that XRD pattern of ZnO:CeO₂ consists mainly of distinct phases of ceria and ZnO. The existence of weaker peaks indicates that dissolving of small amount of ZnO in ceria and vice versa is possible for a certain extent. Mixing ZnO hexagonal lattice with CeO₂ fluorite leads to a drastic change of diffraction pattern. Thus, lattice constant of the composite changes significantly. The lattice constant ‘$a$’ for the cubic phase structure and ‘$a \& c$’ for the hexagonal phase structure are evaluated as:

$$\frac{1}{d^2}=\frac{h^2+k^2+l^2}{a^2}$$

(1)

$$\frac{1}{d^2}=\frac{4}{3}\left(\frac{h^2+hk+k^2}{a^2}\right)+\frac{l^2}{c^2}$$

(2)

where $d$ is the inter-planar spacing and can be determined using Bragg’s law ($\lambda =2d_{hkl}\sin {\theta }_{hkl}$). The lattice constants of pure ZnO and CeO₂ thin films are presented in

Table 1. The structure and Lattice constants (a and c) for pure ZnO and pure CeO₂ thin films.

Thin Film Sample	Structure	$\mathit{a} \left(\mathbf{\AA }\right)$	$\mathit{c} \left(\mathbf{\AA }\right)$
ZnO	Hexagonal	3.216	5.161
CeO2	Cubic	5.350	-

. The lattice constants ($a$ and $c$) of pure wurtzite ZnO thin film are calculated to be 3.216 Å and 5.161 Å, respectively, in a good agreement with those reported in [46]. The lattice constant $a$ of pure CeO₂ thin film is found to be 5.350 Å is in a good agreement with that reported in [44].

To elucidate the elastic properties of synthesized mixed oxide thin films, crystallite size $\left(D\right)$ and microstrain $\left(\epsilon \right)$ originated from the lattice misfitting and mismatching are deduced from the peak width and the shift of the 2θ peak position [47]. Fundamentally, average $D$ can be computed from the Debye Scherrer’s formula, $D=k\lambda /\beta \cos \theta$ [48,49] where $\lambda$ is the wavelength of the X-ray ($\lambda =0.154184 \mathrm{nm}$), $\beta$ (in radians) is the full width at half maximum (FWHM), $\theta$ is Bragg’s angle and $k$ = 0.94 is the Scherrer constant [50,51]. The average microstrain $\epsilon =\beta \cot \theta /4$ [48,52]. The estimated values of $D$ and $\langle \epsilon \rangle$ of ZnO:CeO₂ mixed oxide thin films are plotted as functions of CeO₂ concentrations as shown in Figure 2. The value of D of pure ZnO and CeO₂ thin films was found to be 18.93 nm and 9.26 nm, respectively. However, D of ZnO:CeO₂ mixed oxide thin films containing 25%, 50% and 75% of CeO₂ were found to be 12.09 nm, 11.58 nm and 11.50 nm, respectively. Obviously, Figure 2 shows an inverse relationship between $\epsilon$ and D which could be attributed to the decrease in the volume occupied by constituents inside the combined crystalline structure. In addition, as the volume of the unit cells increases, the total surface area is increased causing a shift in planes positions [53].

Scherrer formula considers only the effect of crystallite size on the XRD peak broadening. However, it does not provide details of the intrinsic strain generated in the nanocomposites. It is induced by the point defect, grain boundary, triple junction and stacking faults [54,55]. There are many methods such as Williamsons Hall method (WH), Warren-Averbach method etc., which considers the effect of the strain induced by XRD peak broadening and can be used for the calculation of the intrinsic strain along with the particle size. Among these methods, Williamson–Hall (W–H) method which is considered to be easy, elegant and simple [56]. According to WH method, the line broadening of X-ray diffraction peak occurs due to the size and microstrain of the nanocrystals and the total broadening can be written as:

$${\beta }_{total}={\beta }_{size}+{\beta }_{strain}$$

(3)

In the present work, average particle size and microstrain have been calculated using modified WH equation implementing Uniform deformation model (UDM). The method deliberately uses uniform strain all the way through the crystallographic direction that is induced in the nanocrystals due to crystal imperfections. In other words, UDM considers strain, which is isotropic in nature [57]. This intrinsic strain essentially affects the physical broadening of the XRD profile inducing peak broadening:

$${\beta }_{strain}=4\epsilon \tan \theta$$

(4)

So, the total broadening due to strain and size in a particular peak indexed by hkl Miller indices, can be expressed as:

$${\beta }_{hkl}={\beta }_{size}+{\beta }_{strain}$$

(5)

where, ${\beta }_{hkl}$ is the full width at half of the maximum intensity for different crystallographic diffraction planes. Consequently, WH equation is modified by UDM can be given by:

$${\beta }_{hkl}\cos \theta =\frac{k\lambda }{D}+4\epsilon \sin \theta$$

(6)

By plotting ${\beta }_{hkl}\cos \theta$ along Y-axis as a function of $4\sin \theta$ on the X-axis corresponding to each diffraction peak, we can calculate the values of crystallite size (D) and microstrain (ε). The estimated values of $D$ and $\langle \epsilon \rangle$ of ZnO:CeO₂ mixed oxide thin films are plotted as functions of CeO₂ concentrations as shown in Figure 3. The peaks of ZnO; (100), (002), (101) and the peaks of CeO₂; (111), (200), (220) and (311) are used in equation 6 to calculate D and ε. The value of D of pure ZnO and CeO₂ thin films is estimated to be 28.05 nm and 8.10 nm, respectively. However, D of ZnO:CeO₂ mixed oxide thin films containing 25%, 50% and 75% of CeO₂ were found to be 25.89 nm, 19.85 nm and 12.12 nm, respectively. It can be seen that the calculated crystallite size of the ZnO:CeO₂ mixed oxide thin films does not vary analytically with the Ce concentration. This could be attributed to the lattice disorder, produced in the powder samples at higher Ce concentrations due to the difference in the ionic radii of Zn²⁺ and Ce⁴⁺ species. Obviously, Figure 2 shows an inverse relationship between $\epsilon$ and D which could be attributed to the decrease in the volume occupied by the constituents inside the combined crystalline structure. In addition, as the volume of the unit cells increases, the total surface area is increased causing a shift in planes positions [53].

Our results indicate that the values of the crystallite size using Scherrer method exhibit lower values than those obtained using WH method. However, the average microstrain, an inverse trend is obtained. The two methods differ from each other in the sense that WH method considers the effects of the broadening arise from the crystallite size and the microstrain. Whereas Scherrer method takes into account the broadening of the X-ray diffraction lines originates from the crystallite size only. Thus, Scherrer method considers the films as if they are a perfect system. Another major difference between the two methods lies in the fact that, WH method can be applied to analyze XRD patterns composed of of several diffraction lines, while in case of applying Scherrer method; it does not require more than one diffraction line. We conclude that, WH method is a general method and yields more accurate results than Scherrer method does.

To obtain a deeper insight into crystal defects, we investigate the dislocations that may be caused by internal stresses in the sub-lattices. Dislocations are formed at the boundaries between the glided and the un-slipped regions of the strained structure. The number per unit volume and the strength of dislocations determine the strength and ductility of materials. [58]. We calculate the density of dislocations (δ) by using the line profile analysis of XRD (LPA-XRD) patterns and using simple Williamson-Smallman formula given by $\delta =1/D^2$, where $D$ is the crystallite size calculated using Williamsons Hall equation [48,58,59,60,61]. Figure 4a shows the dislocation density of the ZnO:CeO₂ mixed oxides thin films as a function of CeO₂ concentration. The value of $\delta$ of pure ZnO thin film is found to be $0.12\times {10}^{12}$ lines/cm² and that of pure CeO₂ thin film is $1.17\times {10}^{12}$ lines/cm². The values of $\delta$ of ZnO:CeO₂ mixed oxide thin films containing 25%, 50% and 75% of CeO₂ are calculated to be $0.15\times {10}^{12}, 0.25\times {10}^{12}$ and $0.68\times {10}^{12}$ lines/cm², respectively. The value of (δ) measures the agglomerations of crystalline clusters. The increasing (δ) with increasing the concentration of CeO₂ in the mixed-oxide composite implies a decreasing of the crystallization and significant increasing of vacancies [58,60]. The increasing in dislocation density can be attributed to the internal strain during film formation in addition to the partial interstitial substitution of the Ce⁴⁺ ion instead of Zn²⁺.

The crystallites density (N) of thin films can be calculated from the estimated values of D and given by $N=t/D^3$ [62,63] where $t$ is the film thickness found to be 500 nm estimated using SEM micrograph. Figure 4b shows $N$ of ZnO:CeO₂ mixed oxides thin films as a function of CeO₂ concentration. The value of $N$ of pure ZnO thin film is found to be $0.02\times {10}^{12}$ cryst./cm² while for pure CeO₂ thin film it exhibits a value of $0.63\times {10}^{12}$ cryst./cm². We found that $N$ exhibits values of $0.03\times {10}^{12}, 0.06\times {10}^{12}$ and $0.28\times {10}^{12}$ cryst./cm² for ZnO:CeO₂ mixed oxide thin films containing 25%, 50% and 75% of CeO₂, respectively.

Temperature-induced lattice dynamical vibrations and mechanical-induced phase transitions and deformations are measured by the internal lattice stress. The value of the total internal stress ($\sigma$) can be obtained from the linear region of stress-strain graph, $\sigma =E\ast \langle \epsilon \rangle$ where E is the Young’s Modulus (E). The value of $\sigma$ of pure ZnO thin film is found to be $0.72\times {10}^{12}$ N/m² and that of pure CeO₂ thin film is $1.73\times {10}^{12}$ N/m². For ZnO:CeO₂ mixed oxide thin films containing 25%, 50% and 75% of CeO₂, $\sigma$ takes on values of 0.82 $\times {10}^{12}, 2.41\times {10}^{12}$ and $2.61\times {10}^{12}$ cryst./cm², respectively as displayed in Figure 4c. The strain energy density within thin films $\left(E_d\right)$ [$J/m^3$] is closely related to Young’s modulus of the film, the volume of the unit cell $\left(V\right)$ and the internal micro strain $\langle \epsilon \rangle$. It can be expressed as $E_d=\frac{1}{2}E{\langle \epsilon \rangle }^2$ [59,64]. The calculated value of $E_d$ of pure ZnO thin film is $2.35\times {10}^{12}$ J/m³ and that of pure CeO₂ thin film is $13.54\times {10}^{12}$ J/m³. For ZnO:CeO₂ mixed oxide thin films containing 25%, 50% and 75% of CeO₂, $\sigma$ is computed to be $3.05\times {10}^{12}, 26.38\times {10}^{12}$ and $30.84\times {10}^{12}$ N/m³, respectively, as shown in Figure 4d.

3.2. UV-Vis Spectroscopy Measurements of Optical Properties

Transmittance $T\%\left(\lambda \right)$ spectra of pure ZnO, pure CeO₂ and ZnO:CeO₂ mixed oxides thin films are displayed in Figure 5. Transmittance spectra of pure ZnO thin film show steep rising from about 0% up to 88% as wavelength increases from 300–350 nm. It maintains almost constant value for the 350–700 nm spectral range. Moreover, the transmittance spectra of pure CeO₂ thin film demonstrate fast increasing trend about 0% up to 86% for the 300–420 nm spectral range. Similarly, it attains a constant value for 420–700 nm range. As can be clearly seen from Figure 5, transmittance of ZnO:CeO₂ mixed oxides thin films have the same behavior of pure CeO₂ thin film. However, it exhibits different transmittance values in 420–700 nm range. Interestingly, absorption edge is shifted towards the red region (lower energy) as CeO₂ concentration in ZnO:CeO₂ mixed oxides thin films is increased. Consequently, a considerable decrease in band gap energy is observed. To elucidate the significant reduction in the optical and gap energy, several factors are identified to contribute to this reduction. Among these is the fact that CeO₂ thin films have lower band gap energy than ZnO thin films. In addition, enhanced fs-p interactions between the band electrons of ZnO:CeO₂ mixed oxides and the localized fs electrons of cerium and the strong mismatch between the electronegativities of Ce and Zn in the ZnO: CeO₂ mixed oxide system contribute significantly [65,66,67,68]. Small shoulders in transmittance spectra CeO₂ and ZnO:CeO₂ mixed oxides thin films appear at a wavelength of ~350 confirming the excitonic absorption characteristics of those thin films [69].

Reflectance spectra are shown in Figure 6. The reflectance values of pure ZnO and pure CeO₂ thin film are found to be ranging from 5%–10% and 7%–15% as the wavelength decreases from 700 nm to 400 nm, respectively. Reflectance spectra of ZnO:CeO₂ mixed oxides thin films demonstrate a tuning of $R\%\left(\lambda \right)$ as the concentration of CeO₂ in ZnO:CeO₂ mixed oxides is increased. This can be attributed to the changes in crystalline size and microstrain of ZnO:CeO₂ mixed oxides crystals. In addition, ZnO:CeO₂ mixed oxides thin films exhibit absorb photons of wavelength ranging between 280 nm to 330 nm efficiently. Consequently, incorporation of ZnO with CeO₂ enhance UV–filter efficiency of thin films especially for UVB and UVC irradiation. Overall, ZnO:CeO₂ mixed oxides thin films could be potential candidates for high transparency and UV-filter applications.

3.3. Analysis of Transmittance Spectra

Absorption coefficient ($\alpha )$ describes the intensity attenuation of the electromagnetic waves passing through a thin film [70]. The $\alpha$ parameter can be expressed using the corrected transmission ($T$), as $\alpha =\left(1/d\right)\ln \left(1/T\right)$ [2,71,72], where $d$ is the thickness of thin films measured using SEM micrograph and estimated to be 500 nm. Figure 7 shows the variation of $\alpha$ of pure ZnO, pure CeO₂ and ZnO:CeO₂ mixed oxides thin films with the incident photon wavelength. Obviously, $\alpha$ exhibits higher values just before the absorption edge compared with those after the absorption edge. This can be attributed to the resonance of the frequency of incident photons with that of electronic polarizability. The dramatic reduction of $\alpha$ at the absorption edge could be explained in terms of the coupling occur between electrons of the constituents [73,74,75,76]. Furthermore, the red shift of absorption edge upon the introduction of CeO₂ into ZnO:CeO₂ mixed oxides thin films is due to the change in the width of localized states and consequent changes in the energy gap.

To elucidate the attenuation of electromagnetic waves by the proposed thin films in this work, we calculate the extinction coefficient $k$. It is related to the absorption coefficient, $k=\alpha \lambda /4\pi$ [2]. Figure 8 shows $k$ of pure ZnO, pure CeO₂ and ZnO:CeO₂ mixed oxides thin films as a function of incident photon wavelength. A drastic decrease of k is noticed prior to the absorption edge indicating that thin films allow electromagnetic waves to pass through without any decay or damping for $\lambda \ge 350 nm$. Moreover, k exhibits an increasing trend as the concentration of CeO₂ introduced in ZnO:CeO₂ mixed oxides thin films is increased. Therefore, ZnO:CeO₂ mixed oxides thin films have a larger ability to attenuate incident light by scattering and absorption.

The specific landscapes of the band structure and optical absorption edge of thin films can be simply interpreted by Tauc model [2]. The functional dependence of ${\left(\alpha hv\right)}^2$ of pure ZnO, pure CeO₂ and ZnO:CeO₂ mixed oxides thin films versus photon energy is shown in Figure 9a. The optical band gaps obtained from Tauc plots are 3.296 eV for ZnO thin films and 3.092 eV for CeO₂ thin films. The band gap energy decreases as 25% of CeO₂ is introduced in ZnO:CeO₂ mixed oxides thin films. A slight increase of the band gap is noticed as the concentration of CeO₂ is further increased as shown in Figure 9b. We analyze the decrease in band gap and find that three factors contribute unequally to this decrease. Namely, CeO₂ thin films exhibit lower band gap energy than ZnO thin films. Consequently, the increase of CeO₂ content in the mixed oxide composites decreases the optical band gap. Furthermore, the strong ds-p interactions in ZnO:CeO₂ mixed oxides and the large difference between the electronegativities of Ce and Zn in the ZnO:CeO₂ mixed oxide system contribute to the optical band gap reduction [65,66,67,68]. Urbach energy, $E_U$ parameter can be used effectively to measure the degree of disorder in the thin films [75,77]. Near the optical band edge, absorption coefficient, $\alpha ={\alpha }_0\exp \left(hv/E_U\right)$, where ${\alpha }_0$ is a constant, $hv$ is the incident photon energy and $E_U$ is the Urbach energy. Urbach energy of ZnO thin film is found to be $221 \mathrm{meV}$ and that of CeO₂ thin film is $531 \mathrm{meV}$. For ZnO:CeO₂ mixed oxides thin films, $E_U$ exhibits values intermediate between those of ZnO and CeO₂ thin films. Figure 9c shows the variation of $E_U$ as a function of CeO₂ concentration in ZnO:CeO₂ mixed oxides thin films. We find that $E_U$ increases as concentration CeO₂ is increased. For high CeO₂ concentrations, $E_U$ attains nearly constant value. Furthermore, $E_U$ exhibits the lowest value for pure ZnO thin film indicating minimum disorder before introducing CeO₂ consistent with the value of the microstrain calculated previously in XRD section. Interestingly, a direct relationship between $E_U$ and ε is observed as the concentration of CeO₂ is increased. Linear fitting of the plots shows a direct relation between $E_U$ and ε as illustrated in Figure 9d. $E_U$ and ε follows the empirical relationship:

$$E_U=31982\ast \mathsf{\epsilon }+1.6888$$

(7)

3.4. Refractive Index Analysis

Refractive index, $n$, of a thin film is closely related to electronic polarization of ions and the local electric and lattice fields [78,79]. The $n$ parameter can be expressed as $n=\left(1+R/1-R\right)+\sqrt{\left(4R/{\left(1-R\right)}^2\right)-k^2}$ [2]. Figure 10 shows $n$ of pure ZnO, pure CeO₂ and ZnO:CeO₂ mixed oxides thin films as a function of the wavelength of incident light. Obviously, spectral behavior of n can be divided into two regions. For ($\lambda <400 nm$) called anomalous dispersion region, the frequency of incident photon resonates with plasma frequency leading to strong electron coupling to the oscillating electric field [80]. For $\lambda >400 nm$ (normal dispersion region), n decreases continuously with increasing wavelength and shows significant normal dispersion. We found that n of ZnO and CeO₂ thin films exhibits values ranging between 1.57 and 1.85 and 1.73 and 2.25 as the wavelength decreases from 700 nm to 400 nm, respectively. We found that increasing the concentration of CeO₂ in ZnO:CeO₂ mixed oxides thin films leads to considerable change of n values. This can be attributed to the changes induced in crystalline size and microstrain of ZnO:CeO₂ mixed oxides crystals that leads to change in surface morphology and vacancies inside the crystal structure. High refractive index materials can be used in many optoelectronic applications such as enhancing the visual properties of electronic displays, which includes LCDs, OLEDs, and quantum dot (QDLED) televisions [81,82].

The dispersion of refractive index has been investigated intensively [83,84]. Wemple–DiDomenico (WDD) model is used to relate n with other key optical parameters such as effective single oscillator energy ($E_0$) and dispersion energy ($E_d$). The model has been successful in estimating zero-frequency refractive index and zero-frequency dielectric constant (${\epsilon }_0$) [12,85,86]. WDD model provides physical interpretation of the related optical parameters:

$${\left(n^2-1\right)}^{-1}=\frac{E_0}{E_d}-\frac{{\left(hv\right)}^2}{E_0{E}_d}$$

(8)

Therefore, plotting ${\left(hv\right)}^2$ versus ${\left(n^2-1\right)}^{-1}$ yields the values of the dispersion parameters via fitting the linear relation. Figure 11a shows ${\left(hv\right)}^2$ versus ${\left(n^2-1\right)}^{-1}$ for pure ZnO, pure CeO₂ and ZnO:CeO₂ mixed oxides thin films. The estimated values of $E_d$ and $E_0$ are presented in

Table 2. Estimation of some essential optical parameters of the pure ZnO, pure CeO₂, and ZnO:CeO₂ thin films for various CeO₂ concentrations.

Parameter	ZnO	ZnO:CeO2 (0.75:0.25)	ZnO:CeO2 (0.50:0.50)	ZnO:CeO2 (0.25:0.75)	CeO2
Effective single oscillator energy,${\mathit{E}}_0$(eV)	3.959	3.673	3.723	3.841	3.603
Dispersion energy,${\mathit{E}}_{\mathit{d}}$(eV)	4.625	4.977	4.325	9.716	5.443
zero-frequency refractive index,${\mathit{n}}_0$	1.472	1.535	1.470	1.879	1.585
Zero-frequency dielectric constant,${\mathit{\epsilon }}_0$	2.168	2.355	2.162	3.529	2.511
Average oscillator wavelength,${\mathit{\lambda }}_0$	313.16	337.63	332.94	322.75	344.21
Oscillator length strength,${\mathit{S}}_0\times {10}^{-5}$	1.191	1.189	1.048	2.428	1.275
Density of states,${\mathit{N}}_{\mathit{c}}/{\mathit{m}}^{\ast }\times {10}^{+57}$(${\mathrm{m}}^{-3}.{\mathrm{Kg}}^{-1}$)	1.018	1.645	1.236	2.880	2.041
Charge carrier density,${\mathit{N}}_{\mathit{c}}\times {10}^{+26}$(${\mathrm{m}}^{-3}$)	4.081	6.594	4.955	11.512	8.182
High-frequency dielectric constant,${\mathit{\epsilon }}_{\infty }$	2.868	3.419	2.997	5.349	3.801
Relaxation time,$\mathit{\tau }\times {10}^{-14}$(s)	2.282	2.410	3.929	3.428	4.143

. The value of $E_0$ of pure ZnO and pure CeO₂ thin films are found to be 3.959 eV and 3.603, respectively. The values of $E_0$ for ZnO:CeO₂ mixed oxides thin films are found to be intermediate between those of pure ZnO and pure CeO₂ thin films. Introducing CeO₂ in ZnO:CeO₂ mixed oxides thin films leads to a decrease in the energy of bonding and a change in the iconicity of these bonds in the nanocomposite. Consequently a decrease in the value of $E_0$ [76]. Moreover, the dispersion energy $E_d$ increases upon introducing CeO₂ in ZnO:CeO₂ mixed oxides. This increase could be attributed to the fact that cubic structure has higher dispersion energy than hexagonal structure. The values of $E_0$ and $E_d$ are used to estimate the zero-frequency dielectric constant ${\epsilon }_0$ and the zero-frequency refractive index $n_0$ by rewriting Equation (8) and setting $hv=0$ leading to

$${\epsilon }_0=n_0^2=1+\frac{E_d}{E_0}$$

(9)

The calculated values of ${\epsilon }_0$ are presented in Table 2. It is worth mentioning that the obtained values of $n_0$ are in good agreement with theoretical and the experimental values of the normal refractive index.

Sellmeier model is used to calculate the average oscillator wavelength $\left({\lambda }_0\right)$ and the oscillator length strength $\left(S_0\right)$ parameters [87]. According to this model,

$$n^2-1=\frac{S_0{\lambda }_0^2}{1-\left({\lambda }_0^2/{\lambda }^2\right)}$$

(10)

Plotting ${\left(n^2-1\right)}^{-1}$ against ${\lambda }^{-2}$ gives the oscillator parameters by fitting the linear relationship as demonstrated in Figure 11b. The values $\mathrm{of} S_0$ and ${\lambda }_0$ are presented in Table 2. Our calculations indicate that ${\lambda }_0$ increases as CeO₂ introduces in ZnO:CeO₂ mixed oxides. However, $S_0$-value decreases as 25% and 50% of CeO₂ are introduced in ZnO:CeO₂ mixed oxides. Moreover, inserting 75% of CeO₂ increases $S_0$-value. This is due to the fact that ${\lambda }_0$ is inversely proportional to $E_0$ whereas $S_0$ is directly proportional to $E_d$. Obviously, introducing CeO₂ into ZnO:CeO₂ mixed oxides leads to an increase of ${\lambda }_0$ and a decrease of $S_0$, as a result of the decline of the surface morphology.

To elucidate the dielectric properties of mixed oxides thin film, the square of $n$ is correlated with the density of states ($N/m^{\ast })$ and the high-frequency dielectric constant ${\epsilon }_{\infty }$ as formulated by Spitzer-Fan [88,89]:

$$n^2={\epsilon }^{\prime }={\epsilon }_{\infty }-\frac{1}{4{\pi }^2{\epsilon }_0}\left(\frac{e^2}{c^2}\right)\left(\frac{N_c}{m^{\ast }}\right){\lambda }^2$$

(11)

where $e$ is the electronic charge, $c$ is the speed of light in vacuum, $N_c$ is the charge carrier density and $m^{\ast }$ is the effective mass of the carrier. Plotting $n^2$ versus ${\lambda }^2$ is used to determine $N/m^{\ast }$ and ${\epsilon }_{\infty }$. Figure 11c shows the dispersion nature of the index of refraction of our thin films. The estimated values of both ${\epsilon }_{\infty }$ and $N_c/m^{\ast }$ are listed in Table 2. The values of ${\epsilon }_{\infty }$ of pure ZnO and pure CeO₂ thin films were found to be 2.868 and 3.801, respectively. The values of ${\epsilon }_{\infty }$ of ZnO:CeO₂ mixed oxides thin films are found to increase upon increasing the concentration of CeO₂ in ZnO:CeO₂ mixed oxides thin films consistent with that of n [90,91]. We found that charge carrier density boosts upon increasing CeO₂ content in ZnO:CeO₂ mixed oxides thin films.

The imaginary part of the dielectric function (${\epsilon }^{″}$) in relation to the wavelength of the incident photon could be analyzed to determine the relaxation time ($\tau$) defined by Drude free electron model [88]:

$${\epsilon }^{″}=2nk=\frac{1}{4{\pi }^3{ϵ}_0}\left(\frac{e^2}{c^3}\right)\left(\frac{N_c}{m^{\ast }}\right)\left(\frac{1}{\tau }\right){\lambda }^3$$

(12)

Figure 11d shows the variation of ${\epsilon }^{″}$ with ${\lambda }^3$ for pure ZnO, pure CeO₂ and ZnO:CeO₂ mixed oxides thin films. The relaxation time $\tau$ could be determined from the slope of the plot between ${\epsilon }^{″}$ and ${\lambda }^3$, and from the value of $N_c/m^{\ast }$ calculated from Equation (7) taking $m^{\ast }=0.44m_e$ [43].

4. Summary and Conclusions

In summary, synthesis, crystallography, microstructure, crystal defects, optical and optoelectronic characterization of ZnO:CeO₂ mixed oxide-thin films dip-coated on glass substrates using a sol-gel technique are investigated and interpreted. Pure ZnO thin film is found to exhibit a hexagonal structure whereas that of pure CeO₂ thin film is a fluorite cubic. XRD patterns demonstrate the formation of mixed oxide materials containing semi-crystalline nature from the constituent oxides. ZnO-CeO₂ films were obtained with a hexagonal structure and extremely favored orientation with the c-axis perpendicular to glass substrates. The as-prepared mixed-oxide thin films exhibit several crystallographic orientations determined by the lattice mismatch between ZnO and CeO₂ thin films and the concentration of added CeO₂ thin films.

To elucidate deeper insight into crystal defects, we estimate the average microstrain and the crystallite size of pure ZnO and CeO₂ thin films found to be 18.93 nm and 9.26 nm, respectively. In addition, we found that ZnO:CeO₂ mixed oxide thin films containing 25%, 50% and 75% of CeO₂ exhibit compositional-averaged crystallite sizes of 12.09 nm, 11.58 nm and 11.50 nm, respectively. Transmittance of all investigated thin films is found to attain high values of 85% in the visible region. Moreover, the refractive index of pure ZnO film was found to exhibit values ranging between 1.57 and 1.85, while that of CeO₂ thin film take on values ranging between 1.73 and 2.25 as the wavelength decreases from 700 nm to 400 nm. Interestingly, ZnO:CeO₂ mixed oxides thin films exhibit refractive indices that are strongly dependent on the content level of CeO₂. We found a significant decrease of optical band gap as the concentration of CeO₂ is increased in the mixed oxide thin films. Therefore, band gap engineering is achieved efficiently in this mixed oxide system.

The strong correlation among crystallinity, surface morphology and optical properties of the as-synthesized mixed oxide thin films is investigated and interpreted using XRD and UV-Vis spectroscopy. Different classical models such as WDD model, Sellmeier model, Spitzer-Fan model and Drude free electron model are employed to calculate and interpret the optoelectronic and dispersion properties of ZnO:CeO₂ mixed oxides thin films. Obtaining mixed oxide thin films with controllable refractive index and tunable optical and optoelectronic properties provides a pathway to design smart multi-functional materials. Such materials may act as potential candidates for the fabrication of modern optoelectronic devices and thin film transistors.