# Temperature-dependence of the optical transitions of spray pyrolysis derived Sn doped Co3O4 thin films

T. Zribi, M.-B. Bouzourâa, H. Essaidi, Saad Touihri, Abdelwahab Boukhachem, Aotmane En Naciri

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T. Zribi, M.-B. Bouzourâa, H. Essaidi, Saad Touihri, Abdelwahab Boukhachem, et al., Temperature-dependence of the optical transitions of spray pyrolysis derived Sn doped Co3O4 thin films. Optik, 2025, 331, pp.172372. 10.1016/j.ijleo.2025.172372. hal-05054417

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# Temperature-dependence of the optical transitions of spray pyrolysis derived Sn doped Co₃O₄ thin films

T. Zribi<sup>a,b,*</sup>, M.-B. Bouzourâa<sup>a</sup>, H. Essaidi<sup>b</sup>, S. Touihri<sup>b</sup>, A. Boukhachem<sup>c</sup>, A. En Naciri<sup>a,**</sup>

## ARTICLE INFO

**Keywords:**

Co₃O₄ thin films

Sn doping

Temperature dependence

Spectroscopic ellipsometry

Varshni model

## ABSTRACT

Understanding the temperature dependence of physical properties is essential for optimizing the performance of Co₃O₄ films, particularly with respect to their optical behavior. Previous studies have shown that Sn doping can influence the physical characteristics of Co₃O₄ films. In this work, the temperature-dependent optical properties of undoped and 2 mol% Sn doped Co₃O₄ (SCO) thin films, deposited on glass substrates via the spray pyrolysis technique, are investigated. The temperature effects were investigated using Raman, UV-Vis-IR spectroscopy and *in-situ* ellipsometry measurements. Raman analysis demonstrated that room temperature to 623 K domain is notably interesting as a stable single-phase range for both samples. Through an exhaustive ellipsometric analysis, including experimental and modeling studies, the evolution with temperature of key optical parameters such as film thickness, dielectric function, absorption coefficient, transition energies and Urbach energies have been successfully determined. The results highlight the influence of the applied heating on the optical responses. Particularly, the electronic transitions were found to decrease as the temperature increases. This dependence was analysed using the well-known Varshni model and the corresponding physical parameters were extracted.

## 1. Introduction

Spinel Cobalt oxide Co₃O₄ has recently attracted significant interest due to its remarkable physico-chemical properties, combined with its abundance low manufacturing costs and low toxicity. These features make it as a promising candidate for a wide range of optoelectronic applications, including photocatalysis [1], selective gas sensing [2], solar cells [3] and lithium-ion batteries [4].

Among the various cobalt oxide crystalline forms, spinel cobalt (II, III) oxide structure is the most stable. It exhibits a normal spinel configuration consisting of Co³⁺ cations in octahedral site and Co²⁺ cations in tetrahedral sites [5], resulting in the overall formula [Co²⁺ Co³⁺ O₂⁻]. The multivalent nature of Co₃O₄ leads to multiple electronic transitions, mainly due to the crystal field splitting of Co 3d states at both octahedral and tetrahedral cobalt sites, as well as cation-anion orbital hybridization [6]. Consequently, substitution of Co cations can significantly influence the band edge characteristics, affecting the electronic transitions. In this context, Sn doping was found to modify the physical characteristics of Co₃O₄ and enhance its performance [7–9]. Controlling the features of this material is

<footnote><sup>a</sup> Université de Lorraine, LCP-A2MC, Metz F57000, France</footnote>

<footnote><sup>b</sup> L2NE, Université de Tunis El Manar, Tunisia</footnote>

<footnote><sup>c</sup> LANSER, Centre de Recherches et des Technologies de L'Energie Technopole Borj Cedria, Hammam Lif 2050, Tunisia</footnote>

<footnote>* Corresponding author at: Université de Lorraine, LCP-A2MC, Metz F57000, France</footnote>

<footnote>** Corresponding author.</footnote>

<footnote>E-mail addresses: zribi.tesnime17@gmail.com (T. Zribi), ennaciri5@univ-lorraine.fr (A. En Naciri).</footnote>
essential for optimizing its functionality. Additionally, the temperature stability of the optical properties beyond room temperature requires further investigation to achieve more tunable response.

In the present paper, a detailed study of the temperature-dependent behavior of optical properties, such as dielectric function, absorption coefficient, transition energies and Urbach energies, is performed beyond room temperature for undoped and 2 mol% doped Co₃O₄ (CSO) thin films. The samples were prepared using a cost-effective spray pyrolysis technique, which is particularly suitable for producing uniform thin films over large areas.

Raman analysis performed between room temperature and 623 K confirmed the stability of the Co₃O₄ phase. In-situ temperature-dependent transmittance spectroscopy revealed how the optical properties change with increasing temperature. To further probe these changes, in-situ spectroscopic ellipsometry (SE) was employed, as it provides detailed insights into the evolution of optical properties with temperature, although it requires rigorous modeling since it is an indirect technique. An appropriate physical model coupled with a dispersion law is critical for accurate SE analysis. Among various laws, such as Cauchy, Adachi and Forouhi-Bloomer, the Tauc-Lorentz dispersion law, which combines Tauc's empirical expression for the band edge with the Lorentzian broadening, was proven to be effective for modeling SE spectra [7]. The novelty of this study lies in extracting in-situ temperature-dependent optical responses. The shift in electronic transition values was accurately fitted by the commonly used Varshni equation [10], and suggested an almost linear character beyond room temperature.

## 2. Experimental

### 2.1. Sample preparation

The undoped and 2 mol% Sn doped Co₃O₄ (CSO) thin films were deposited via a simple spray pyrolysis technique. Cobalt chloride hexahydrate (CoCl₂·6H₂O) and tin (II) chloride dihydrate (SnCl₂·2H₂O), were the precursors for cobalt and tin, respectively. Precise quantities of these two chemical salts were dissolved in distilled water with a few drops of acetic acid, acting as a stabilizing agent, to prepare a 0.01 M aqueous solution. To guarantee homogeneity, the obtained solution was vigorously stirred for thirty minutes with a magnetic stirrer.

Glass substrates were preheated gradually to 773 K, and the temperature was controlled by an electronic temperature controller connected to the heater. The substrates were sprayed with 100 mL of the precursor solution with flow rate of 10 mL/min. The spray nozzle was mounted on an XX' scanning system at a fixed distance of Z = 24 cm from the heating plate allowing it to cover the entire active surface through regular and successive passes of the jet. As a result, uniformly thick layers were grown across a large surface area. The possible chemical reaction that occurs on the substrate surface is as follows:

$$3\text{CoCl}_2 + 2\text{H}_2\text{O} + \text{O}_2 \xrightarrow{\Delta} \text{Co}_3\text{O}_4 \downarrow + 3\text{Cl}_2 \uparrow + 2\text{H}_2 \uparrow$$

After the deposition process, the films were cooled gradually on the heating plate to ambient temperature to avoid thermal shock.

### 2.2. Characterization

The in-situ variable-temperature characterizations, conducted between 293 K and 623 K, were performed by introducing a LINKAM heating stage to precisely control the sample's temperature. Raman spectra were recorded using a LabRAM HR800 spectrometer with 633 nm HeNe laser excitation at a fixed power of 4 mW. The temperature dependence of the optical response was investigated using a phase modulated ellipsometer (Horiba Jobin Yvon, UVISEL) in the photon energy range from 0.65 to 4 eV, with the incident angle kept constant during the experiment. Transmission spectra were recorded at normal incidence, and the absorption coefficient (α) was derived from the transmittance data using the relation $α = -\frac{\ln(T)}{d}$, where T and d represent the transmittance and the film thickness, respectively. To validate the results retrieved from transmittance analysis, temperature dependent spectroscopic ellipsometry (SE) spectra were collected at a fixed incident angle of 70°. For accurate SE measurements, the back surfaces of the samples were roughened to minimize secondary reflections from the glass substrate. The SE data were analyzed using Horiba numerical software. The temperature stability is controlled by the real-time dynamic monitoring of the ellipsometer and UV-Vis-NIR spectroscopy combined with the temperature control system of the LINKAM cell. Before recording the spectra, the temperature is stabilized for at least 5 minutes, and variations of measured parameters at a fixed wavelength are carried out. Once stability is reached, spectroscopy measurements proceed. The maximum temperature is set to 350°C to avoid significantly altering the sample's structure. The heating rate is carefully controlled and is typically set to 10 °C/min. We note that the ambient during heating is air. Temperature-dependent measurements were carried out as follows: Initial measurements were performed at room temperature. The temperature was then increased at a rate of 10 °C/min. Upon reaching 50 °C, the system was stabilized for at least 5 minutes, as monitored in real time. The same procedure was repeated at 100 °C, maintaining the same heating rate of 10 °C/min. This stepwise heating and stabilization process was continued up to a final temperature of 350 °C. All measurements were conducted under ambient air conditions.

## 3. Results and discussions

### 3.1. Raman spectroscopy analysis

Raman spectroscopy is an effective analytical technique that allows the determination of phase characteristics when investigating the effect of temperature variations. In this study, Raman spectra of the prepared thin films were recorded in a temperature range from
<figure><img src="image_3.png" /><figcaption>Fig. 1. Raman spectra of a) Co₃O₄ and b) CSO thin films at different temperatures.</figcaption></figure>

<caption>**Table 1**</caption>

Raman parameters of the A₁g peak (peak position, FWHM and integrated intensity) of the Co₃O₄ and CSO thin films as function of the temperature.

<table><thead><tr><th rowspan="2">Temperature (K)</th><th colspan="2">Peak Position of A<sub>1g</sub> (cm<sup>-1</sup>)</th><th colspan="2">FWHM of A<sub>1g</sub> (cm<sup>-1</sup>)</th><th colspan="2">Integrated intensity of A<sub>1g</sub> (arb.u.)</th></tr><tr><th>Co<sub>3</sub>O<sub>4</sub></th><th>CSO</th><th>Co<sub>3</sub>O<sub>4</sub></th><th>CSO</th><th>Co<sub>3</sub>O<sub>4</sub></th><th>CSO</th></tr></thead><tbody><tr><td>298</td><td>671.86</td><td>667.72</td><td>22.64</td><td>24.94</td><td>5584.37</td><td>4561.18</td></tr><tr><td>323</td><td>673.55</td><td>669.48</td><td>21</td><td>24</td><td>5338.45</td><td>4617.62</td></tr><tr><td>373</td><td>673.41</td><td>669.55</td><td>18.52</td><td>21.08</td><td>6292.63</td><td>4608.22</td></tr><tr><td>423</td><td>675.46</td><td>672.96</td><td>18.55</td><td>18.47</td><td>5722</td><td>5180.67</td></tr><tr><td>473</td><td>672.52</td><td>673.3</td><td>19.07</td><td>17.81</td><td>6475.09</td><td>5126.34</td></tr><tr><td>523</td><td>673.19</td><td>674.01</td><td>17.08</td><td>16.3</td><td>3656.52</td><td>3846.92</td></tr><tr><td>573</td><td>672.05</td><td>672.47</td><td>18.48</td><td>16.29</td><td>2955.6</td><td>2749.83</td></tr><tr><td>623</td><td>670.49</td><td>670.78</td><td>19.3</td><td>17.46</td><td>2136.84</td><td>2326.43</td></tr></tbody></table>

298 K to 623 K at intervals of 50 K. The Raman spectra of the undoped and 2 mol% Sn doped Co₃O₄ (CSO) thin films in the region of 100–800 cm⁻¹ are shown in Fig. 1. From Co₃O₄ Raman spectra, three distinguishable peaks are observed at around 191.24 cm⁻¹, 472.27 cm⁻¹ and 671.86 cm⁻¹. As labeled in Fig. 1, they belong respectively to the F₂g Eg, and A₁g Raman active modes of the normal spinel cobalt oxide [Co²⁺ Co²⁺ O²⁻] [11]. These peaks originate from the lattice vibrations of the spinel structure, where Co²⁺ and Co³⁺ cations are located at tetrahedral and octahedral sites, respectively, within the face-centred cubic structure. The assignment of
## 3.2. UV-Vis-NIR Spectroscopy

<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Temperature-dependent absorption coefficient of a) Co₃O₄ and b) CSO thin films.</figcaption></figure>

precise atomic motions in the spinel lattice remains unclear in literature due to the multivalent nature of the Co₃O₄ cations. However, many researchers assume that the highest frequency A₁g mode involves the Raman vibration of Co³⁺–O²⁻ within the octahedral sites (CoO₆) while the F₂g mode is attributed to the Co²⁺–O²⁻ motion within the tetrahedral sites (CoO₄) [12–15]. No phase transition was detected with the increase in temperature up to 623 K for both undoped and Sn doped samples, as indicated by the absence of peaks related to other phases. Moreover, the Raman peaks are influenced by temperature variations, with the A₁g peak being the most sensitive. To further discern the effect of temperature on both samples, the evolution of the position, full width at half maximum (FWHM) and integrated intensity of the A₁g peak were explored. For this, Lorentzian fit was performed and the obtained Raman parameters are detailed in Table 1.

At room temperature, the A₁g peak broadened, shifted to lower wavenumbers and decreased in intensity after doping. These changes suggest the incorporation of the Sn ions in the Co₃O₄ lattice affecting the octahedral coordination environment (CoO₆) [13].

It is known that the vibrational frequency variations scale inversely with the atomic weight of metallic cations and is proportional to M⁻¹/² [16]. Thus, the presence of Sn with higher atomic weight (M~Sn ~ 118.71 u) compared to the atomic weight of Co (M~Co ~ 58.93 u), leads to an increase in the effective atomic weight in octahedral sites. Consequently, the A₁g peak associated with the vibrational motion of Co³⁺–O²⁻ tends to shift towards lower frequencies after doping. On the other hand, the presence of Sn, which has larger ionic radius (r~Sn4+ ~ 0.69 Å) than Co cations (Co³⁺ ~ 0.545 Å), results in an increase in the bond length of (Co³⁺–O²⁻) and weakens their bond energy [17].

For both samples, increasing the temperature up to 473 K results in an increase in peak intensity. Furthermore, the A₁g peak shifts towards higher wavenumbers, with a more pronounced shift of approximately Δν ~ 6 cm⁻¹ in the doped sample. This can be attributed
<figure><img src="image_5.png" /><figcaption>Fig. 3. Tauc plots of a) Co₃O₄ and b) CSO thin films at different temperatures.</figcaption></figure>

to the increased susceptibility of the weaker bonds in the octahedral sites, which are altered by the presence of Sn ions, to temperature changes.

However, beyond 523 K, the intensities decreased significantly, and the peaks shifted towards lower wavenumbers. This is consistent with findings of Sparks *et al.* [18], where that Raman modes were observed vanished at temperatures between 600 K and 1000 K. This behavior can be explained by thermal expansion of the lattice [18]. Another possible explanation could be related to temperature effects due to the absorption of the 633 nm incident laser radiation used in this study. Co₃O₄ exhibits high absorption at this excitation wavelength, corresponding to the ligand-to-metal charge transfer (O²⁻ → Co²⁺). Furthermore, this laser wavelength involves all lower-energy transitions (due to d-d charge-transfer) occurring between the different 3d orbitals of Co ions. This results in local heating that modifies the phonon modes [7,19,20].

## 3.2. UV-Vis-NIR spectroscopy

To investigate the heating effect on the optical behavior of Co₃O₄ thin films, with and without doping, in *situ* UV-Vis-NIR spectroscopy was performed. The resulting variations in the absorption coefficients as a function of photon energy for both samples in the range of 0.65–4 eV are displayed in Fig. 2.

At room temperature, all spectra show low absorption below 1.38 eV. For higher photon energies, the absorption increases significantly and reaches values in order of magnitude of 10⁵ cm⁻¹, with higher values for the doped sample. Two distinct absorption bands are detected at approximately 1.4–1.8 eV (I) and 2–3 eV (II), which implies the existence of charge-transfer transitions between the existing ionic sites within this range.
<table><caption>**Table 2**
Optical transition values of Co₃O₄ and CSO thin films determined by UV-Vis-NIR spectroscopy.</caption><thead><tr><th rowspan="2">Temperature (K)</th><th colspan="3">E₁ (eV)</th><th colspan="2">E₂ (eV)</th></tr><tr><th>Co₃O₄</th><th>CSO</th><th>Co₃O₄</th><th>CSO</th><th>Co₃O₄</th></tr></thead><tbody><tr><td>298</td><td>1.45 ± 0.01</td><td>1.41 ± 0.02</td><td>2.07 ± 0.01</td><td>2.00 ± 0.03</td><td>1.99 ± 0.03</td></tr><tr><td>323</td><td>1.43 ± 0.01</td><td>1.40 ± 0.02</td><td>2.05 ± 0.01</td><td>1.99 ± 0.03</td><td>1.98 ± 0.03</td></tr><tr><td>373</td><td>1.40 ± 0.01</td><td>1.38 ± 0.02</td><td>2.03 ± 0.01</td><td>1.98 ± 0.03</td><td>1.98 ± 0.03</td></tr><tr><td>423</td><td>1.36 ± 0.01</td><td>1.36 ± 0.02</td><td>2.02 ± 0.01</td><td>1.98 ± 0.03</td><td>1.97 ± 0.03</td></tr><tr><td>473</td><td>1.34 ± 0.01</td><td>1.32 ± 0.02</td><td>1.10 ± 0.01</td><td>1.97 ± 0.03</td><td>1.96 ± 0.03</td></tr><tr><td>523</td><td>1.32 ± 0.01</td><td>1.30 ± 0.02</td><td>1.98 ± 0.01</td><td>1.96 ± 0.03</td><td>1.95 ± 0.03</td></tr><tr><td>573</td><td>1.30 ± 0.01</td><td>1.28 ± 0.02</td><td>1.96 ± 0.01</td><td>1.95 ± 0.03</td><td>1.93 ± 0.03</td></tr><tr><td>623</td><td>1.28 ± 0.01</td><td>1.25 ± 0.02</td><td>1.95 ± 0.01</td><td></td><td></td></tr></tbody></table>

<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /><figcaption>**Fig. 4.** Temperature dependent transition energies and Varshni model fits for **a-b)** Co₃O₄ and **c-d)** CSO films.</figcaption></figure>

This result is in agreement with several previous works reporting that Co₃O₄ thin films exhibit multiple direct optical transitions. Efforts have been made to assign electronic transitions to these absorption bands [6,7,21,22]. The lowest band (I) has been ascribed to metal to metal (d-d) charge transfer (MMCT) resulting from the coupling of crystal field splitting between tetrahedral Co²⁺ and octahedral Co³⁺ cations. This process is also considered an internal oxidation-reduction process involving transition between d states of heterovalent Co ions E₁: Co³⁺ (t₂g) → Co²⁺ (t₂g). Some researchers identified this transition as the effective band gap of Co₃O₄ [22–24]. The broad absorption band (II) has been associated to ligand to metal (p-d) charge transfer transition (LMCT) from p states of O⁻ anions to the d states of divalent Co²⁺ cations, (E₂): O⁻ (2p) → Co²⁺ (t₂g). Because p-d type excitation has a higher oscillator strength, it is stronger than d-d type transitions [6]. This inter-band transition is considered by several authors as the “true” band gap of the Co₃O₄ material, involving O(2p) orbitals in the valence band, while the conduction band has a strong Co²⁺(3d) character [25, 26]. The presence of trivalent Co³⁺ cations creates a sub-band within the band gap and generates inter-valence excitations.
<table><caption>**Table 3**

Varshni parameters of Co₃O₄ and CSO thin films.</caption><thead><tr><th>Transition energy</th><th>Varshni parameters</th><th>Co<sub>3</sub>O<sub>4</sub></th><th>CSO</th></tr></thead><tbody><tr><td rowspan="3">E<sub>1</sub> (eV)</td><td>E(0) (eV)</td><td>1.52 ± 0.01</td><td>1.49 ± 0.03</td></tr><tr><td>α (eV/K)</td><td>7.37 × 10<sup>-4</sup> ± 6 × 10<sup>-5</sup></td><td>7.00 × 10<sup>-4</sup> ± 10<sup>-5</sup></td></tr><tr><td>β (K)</td><td>523 ± 26</td><td>525 ± 6</td></tr><tr><td rowspan="3">E<sub>2</sub> (eV)</td><td>E(0) (eV)</td><td>2.12 ± 0.01</td><td>2.03 ± 0.02</td></tr><tr><td>α (eV/K)</td><td>5.14 × 10<sup>-4</sup> ± 2 × 10<sup>-5</sup></td><td>2.78 × 10<sup>-4</sup> ± 10<sup>-5</sup></td></tr><tr><td>β (K)</td><td>525 ± 12</td><td>525 ± 12</td></tr></tbody></table>

As seen in Fig. 2(b), the CSO samples exhibit absorbing characteristics comparable to those of undoped samples, with a slight redshift and higher absorption coefficient values, which is consistent with prior findings [7].

Quantifying the electronic transition values of the materials allows to better understand the temperature effect on the films. In this regard, the Tauc method was employed considering the direct nature of the cobalt oxide bandgap. This method is based on the relationship between the absorption coefficient α and the photon energy (hν) for semiconductors expressed by the following equation:

$$ (\alpha h \nu)^n = A(h \nu - E_{\text{gap}}) \qquad (1) $$

where h is the Planck constant, ν is the frequency of the incident photon, A is a proportionality constant, E<sub>g</sub> is the optical band gap. The exponent n is equal to 2 due to the direct nature of Co₃O₄ electron transitions. Fig. 3 presents graphs of (αhν)² as a function of photon energy (hν) at different temperatures. The electron transitions values E₁ and E₂ were derived by extrapolating the linear parts of the plot to the photon energy abscissa. The obtained transitions E₁ and E₂ for both samples are listed in Table 2.

At room temperature, the values are lower than the bulk values of cobalt oxide, which are 2.85 eV and 1.70 eV [26]. Moreover, after doping the E₁ and E₂ values decrease from 2.07 and 1.46 eV to 2 and 1.41 eV, respectively. This shrinkage is due to structural changes and imperfections in the material, such as distortions, dislocations and defects induced by Sn atoms in the cubic spinel structure of Co₃O₄. These imperfections generate impurity energy levels inside the bandgap, leading to reduced electronic transitions. Furthermore, as the temperature increases, the transition values gradually decrease, indicating a linear relationship. This behavior is commonly observed in many semiconductors [27]. The temperature-dependence of the bandgap energy is mainly attributed to the shift in the relative positions of the conduction and valence bands.

The primary factors contributing to this shift include volume deformation due to changes in bond length and lattice parameter expansion, as well as electron-lattice interactions. This observation is consistent with the Raman results, which highlighted the effect of thermal volume expansion [10,27].

As illustrated by the solid lines in Fig. 4, the temperature dependence of E₁ and E₂ are analyzed by applying Varshni's empirical equation [10] to fit the data:

$$ E(T) = E(0) - \frac{\alpha T^2}{T + \beta'} \qquad (2) $$

where E(0) is the transition energy at 0 K, α and β are the Varshni coefficients. At low temperatures, the transitions follow a quadratic dependence governed by the term -αT<sup>2</sup>/β<sup>2</sup> indicating a slow decrease in their values. In contrast, at high temperatures, E(T) is proportional to T with the coefficient (-α) representing the linear slope. This causes the bandgap to decrease more rapidly with temperature. In this study, the measurements start from room temperature which corresponds to a range near the Debye temperature of cobalt oxide (θ<sub>D</sub> ~525 K) [28]. This proximity justifies the observed linear trend in the evolution of the transition energies [10].

The E(0), α and β parameters used to fit the temperature dependent optical transitions are listed in Table 3. Notably, the β values obtained are close to the Debye temperature of Co₃O₄, indicating that Varshni's model is highly reliable for describing the temperature dependence of the bandgap, particularly in the range above room temperature.

### 3.3. Spectroscopic ellipsometry study

While the UV-Vis-NIR technique is useful for determining the evolution of absorption with temperature, it does not allow the determination of the material's complex refractive index. In this context, temperature-dependent *in situ* spectroscopic ellipsometry (SE) measurements, combined by the application of a suitable model, can provide valuable information about the thickness of each layer, as well as the absorption coefficient α and dielectric functions (ε<sub>r</sub> and ε<sub>i</sub>). This non-destructive technique measures the changes in the polarization state of light after it reflects off the surface of materials. The SE parameters are Ψ and Δ. While Ψ describes the amplitude ratio between the parallel (p) and perpendicular (s) reflection coefficients, Δ represents their phase difference. This relation is expressed as:

$$ r_p/r_s = \tan\psi e^{i\Delta}, \qquad (3) $$

where r<sub>p</sub> and r<sub>s</sub> represent the Fresnel reflection coefficients for (p) and (s) polarized light states, respectively.

Herein, the I<sub>S</sub> and I<sub>C</sub> ellipsometric parameters were collected. They are related to the Ψ and Δ angles via the following relations [29]:
<figure><img src="image_10.png" /><figcaption>Fig. 5. Spectral dependence of ellipsometric parameters $I_S$ and $I_C$ for (a-b) $Co_3O_4$ and (c-d) CSO films at various temperatures.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Fig. 6. Physical model used for SE data fitting.</figcaption></figure>

$$I_S = \sin2\psi\sin\Delta \text{ and } I_C = \sin2\psi\cos\Delta. \qquad (4)$$

These parameters are closely related to the material’s complex optical properties.

Fig. 5 illustrates the temperature-dependent in situ ellipsometric spectra measured for both $Co_3O_4$ and CSO thin films across the spectral range of 0.65 eV to 4 eV. The data reveal noticeable variations in $I_C$ and $I_S$ as the temperature increases, indicating significant changes in the optical properties of the films.

To minimize unwanted secondary reflections, the back surfaces of the samples were roughened. This process scatters the probing
<figure><img src="image_12.png" /><figcaption>Fig. 7. Experimental and simulated ellipsometric parameters (Is, Ic) of a) Co₃O₄ and b) CSO thin films at room temperature.</figcaption></figure>

light in random directions, effectively reducing incoherent light from the glass surface. As a result, the oscillations in the Ic and Is spectra at room temperature are relatively broad, particularly in the visible region. This indicates the high absorption characteristics of Co₃O₄ over an extended energy range. This behavior is consistent with the multiple optical transitions observed in the UV-Vis-NIR analysis. As the temperature increases from 293 K to 623 K, the broadening of the oscillations becomes more pronounced, suggesting enhanced absorption properties of the material. The Is and Ic spectra also exhibit a noticeable redshift and a decrease in intensity with increasing temperature, as highlighted in the insets of Fig. 5. This redshift corresponds to a decrease in the optical transition energies, consistent with the temperature-induced narrowing of the bandgap discussed in the previous section.

To accurately determine the optical function spectra, a suitable physical model of the Co₃O₄ film, along with an appropriate dispersion law, must be selected, given the indirect nature of SE. Previous structural studies have shown that Co₃O₄, prepared via the spray pyrolysis technique, consists of two porous sublayers deposited on glass substrates [7]. Consequently, the physical model employed in SE data analysis represents each layer as a mixture of Co₃O₄ and void, as illustrated in Fig. 5. This model is defined by an effective dielectric function based on the Bruggeman effective medium theory [30].

Additionally, the Tauc-Lorentz dispersion equations were identified as the most suitable for fitting the parameters (Is, Ic), given the indirect approach of SE. It describes the dielectric function ε(E), which is expressed as:

$$ \epsilon_{TL}(E) = \epsilon_r(E) + i \epsilon_i(E) \qquad (5) $$

The imaginary part is given by [31]:

$$ \epsilon_{i, TL} = \begin{cases} \frac{1}{E} \frac{AE_0 C(E - E_g)^2}{(E^2 - E_0^2)^2 + C^2 E^2} \text{for } E > E_{\text{gap}} \\ 0 \text{ for } E \le E_{\text{gap}} \end{cases} \qquad (6) $$

where A, E₀ and C are the amplitude, the energy position of the optical transition and the broadening of the oscillator, respectively.
<table><caption>**Table 4**
Thickness and void fraction of Co₃O₄ and CSO layers at room temperature.</caption><thead><tr><th rowspan="2"></th><th colspan="2">L<sub>1</sub></th><th colspan="2">L<sub>2</sub></th></tr><tr><th>Thickness (nm)</th><th>Void fraction (%)</th><th>Thickness (nm)</th><th>Void fraction (%)</th></tr></thead><tbody><tr><td>Co<sub>3</sub>O<sub>4</sub></td><td>48 ± 0.2</td><td>0</td><td>15 ± 0.1</td><td>20 ± 0.2</td></tr><tr><td>CSO</td><td>132 ± 0.3</td><td>16 ± 0.3</td><td>52 ± 0.3</td><td>30 ± 0.1</td></tr></tbody></table>

<figure><img src="image_13.png" /><figcaption>**Fig. 8.** Temperature-dependence of a-d) α, b-e) ε<sub>r</sub> and c-f) of Co<sub>3</sub>O<sub>4</sub> and CSO thin films determined by SE.</figcaption></figure>

The real part ε<sub>r</sub> is deduced using the Kramers-Kronig relation:

$$ \epsilon_r = \epsilon_{\infty} + \frac{2}{\pi} P \int_{E_s}^{\infty} \frac{\xi. \epsilon_{i,TL}(\xi)}{\xi^2 - E^2} d\xi, \qquad (7) $$

where ε<sub>∞</sub> is the high-frequency dielectric constant and P denotes the Cauchy principal value of the integral.

To achieve an effective analytical representation of the material, an optical model consisting of four Tauc-Lorentz oscillators was developed using the Delta Psi2 software. This software employs a regression-based Levenberg-Marquardt algorithm to minimize the difference between the experimental data and the model fit.

The quality of the fit is evaluated by the root mean square error (RMSE), defined as [32]:

$$ \chi^2 = \frac{1}{2N} \sum_{i=1}^{N} \left( \frac{I_{C_i(\text{model})} - I_{C_i(\text{exp})}}{\delta I_c} \right)^2 + \left( \frac{I_{S_i(\text{model})} - I_{S_i(\text{exp})}}{\delta I_s} \right)^2. \qquad (8) $$

The terms (I<sub>C<sub>i</sub>(model)</sub>, I<sub>S<sub>i</sub>(model)</sub>), (I<sub>C<sub>i</sub>(exp)</sub>, I<sub>S<sub>i</sub>(exp)</sub>) and (δI<sub>c</sub> and δI<sub>s</sub>) represent the simulated, experimental, and estimated data errors for the (I<sub>s</sub>, I<sub>c</sub>) parameters, respectively. N stands for the total number of collected data points.

As seen in Fig. 7, the good agreement between experimental data and the proposed physical model. The obtained thickness values
<table><caption>**Table 5**
Urbach energy values of Co₃O₄ and CSO films at different temperatures.</caption><thead><tr><th rowspan="2">T (K)</th><th colspan="2">Co<sub>3</sub>O<sub>4</sub></th><th colspan="2">CSO</th></tr><tr><th>E<sub>U1</sub> (meV)</th><th>E<sub>U2</sub> (meV)</th><th>E<sub>U1</sub> (meV)</th><th>E<sub>U2</sub> (meV)</th></tr></thead><tbody><tr><td>298</td><td>54</td><td>218</td><td>167</td><td>253</td></tr><tr><td>323</td><td>55</td><td>220</td><td>173</td><td>256</td></tr><tr><td>373</td><td>58</td><td>228</td><td>186</td><td>268</td></tr><tr><td>423</td><td>65</td><td>230</td><td>194</td><td>281</td></tr><tr><td>473</td><td>67</td><td>240</td><td>260</td><td>295</td></tr><tr><td>523</td><td>75</td><td>244</td><td>319</td><td>316</td></tr><tr><td>573</td><td>67</td><td>248</td><td>323</td><td>323</td></tr><tr><td>623</td><td>90</td><td>251</td><td>336</td><td>345</td></tr></tbody></table>

and void fraction for each layer are listed in Table 4.

The change in film thickness between 298 K and 623 K can be determined using the equation:

$$ \Delta L = \alpha \cdot L_0 (T-T_0) \qquad (9) $$

Where $\alpha$ is the thermal expansion coefficient, equal to $6 \times 10^{-6} \text{ K}^{-1}$ [28]. For the undoped and Sn doped films, with initial thicknesses of 63 nm and 184 nm at 298 K, the maximum thickness variations $\Delta L$ are calculated to be 0.12 nm and 0.36 nm, respectively. Consequently, the Co₃O₄ thickness remains almost constant with temperature ($L=L_0+\Delta L \approx L_0$). This results in a nearly unchanged optical path length, which explains the similar oscillations observed in the SE spectra as temperature increases. Therefore, during the fitting process, the physical model and film thickness were maintained the same at all temperatures ranging from 298 K to 623 K.

Fig. 8 presents the obtained absorption coefficient, the real and imaginary parts of the dielectric function for both samples at different temperatures. The spectra obtained at 293 K are generally similar to the room temperature data reported in our previous study [7]. Both samples exhibit a high absorption coefficient, reaching a magnitude of $10^5 \text{ cm}^{-1}$, with the doped sample having higher values. The $\alpha$ and $\epsilon_i$ spectra clearly display three absorption peaks, suggesting the presence of an additional electronic transition $E_{0,SE}$ below 1 eV, which was not detected in UV-Vis-NIR spectroscopy. This transition is attributed to 3d-d ligand field transitions inside the homovalent Co²⁺ tetrahedra [6,7].

As the temperature increases, noticeable changes occur in the optical spectra. The variations in the $\epsilon_r$ values may be assigned to the increased electric polarization and the expansion of distances between charge pairs in the Co₃O₄ films under heating [33]. The uncertainty in terms of the determined values of the dielectric function is less than 0.02 across the entire spectral range. To ensure the reliability of our fitted parameters, we systematically calculated the correlation matrix to monitor any significant parameter interdependencies. Specifically, we verified that, in the case of a single-layer model, the volume fraction is not correlated with the Tauc-Lorentz amplitude (A) or the oscillator broadening parameter (C). Across all temperature conditions, the uncertainty associated with parameter A remains approximately 0.05, while that of C is around 0.04. For the sake of clarity and to maintain focus, the current manuscript emphasizes the influence of temperature on the optical bandgap energies. The corresponding uncertainties are explicitly included in Table 6. A detailed analysis of the Tauc-Lorentz parameters was already provided in our previous publication on Sn-doped Co₃O₄ thin films [7]. As an illustrative example, we present here the result obtained from the fitting process on Is and Ic for undoped Co₃O₄ at room temperature using four Tauc-Lorenz (TL) oscillators. The iterations number is 19 and the RMSE is 0.081, the obtained parameters are $E_g = 0.795 \pm 0.014$, $\epsilon_\infty = 1.616 \pm 0.044$, $A_1 = 4.367 \pm 0.050$, $E_1 = 1.572 \pm 0.038$, $C_1 = 0.202 \pm 0.048$, $A_2 = 2.988 \pm 0.048$, $E_2 = 2.287 \pm 0.017$, $C_2 = 0.329 \pm 0.063$, $A_3 = 10.702 \pm 0.029$, $E_3 = 2.637 \pm 0.046$, $C_3 = 1.477 \pm 0.023$, $A_4 = 18.784 \pm 0.076$, $E_4 = 4.513 \pm 0.049$. For this fitting, the correlation matrix shows low correlations (near zero, -0.083), such as between $E_g$, $\epsilon_\infty$ and TL parameters (-0.083), suggest these parameters are independently determined. However, $\epsilon_\infty$ is not independent from TL4. Indeed, the value of correlation matrix is 0.79, which may cause issues during optimization if all parameters are not fixed.

As can be seen on Fig. 7, the model accurately reproduces the overall experimental spectrum, with an MSER value around 0.081, which demonstrates the validity of the physical model. This fitting procedure was performed for all measurement temperatures. Here, we present the example corresponding to room temperature.

The absorption edges in $\alpha$ and $\epsilon_i$ spectra illustrate decreased amplitudes and red shift features with temperature increasing, a result of both thermal and Urbach effects. Urbach tails manifest as nonzero absorbance below the absorption edge. As illustrated in Fig. 8, both $\alpha$ and $\epsilon_i$ exhibit an exponential increase below the electronic transition at each temperature. An example of these tails is indicated by an arrow in the inset (g) of Fig. 8. These absorption tails are generally associated with localized energy states within the bandgap, which are often caused by impurities and structural defects [34]. The Urbach energy ($E_U$) is associated with $\alpha$ near the absorption edge following this relation [34,35]:

$$ \alpha = \alpha_0 \times \exp\left(\frac{h\nu}{E_U}\right) \qquad (10) $$

where $\alpha_0$ is a pre-exponential factor. The value of $E_U$ was determined from the inverse slope of the straight line in the $\ln(\alpha)$ versus photon energy plot. Two distinct linear regions were identified in the energy ranges 0.65-0.8 eV and 1.2-1.7 eV, corresponding to two Urbach energies, $E_{U1}$ and $E_{U2}$. As shown in Table 5, the CSO films exhibit a higher Urbach energy compared to the undoped films,
<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /></figure>

<figure><img src="image_16.png" /></figure>

<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /></figure>

<figure><img src="image_19.png" /><figcaption>Fig. 9. Temperature dependent transition energies and Varshni model fits for a-b-c) $Co_3O_4$ and d-e-f) CSO films.</figcaption></figure>

which can be attributed to the increase of lattice defects introduced by Sn doping. Furthermore, the Urbach energy displays a clear temperature dependence in the range of 293 K to 623 K. The thermal effect leads to increased phonon excitation. Consequently, this dependence is probably due to enhanced electron-phonon interactions and elevated structural disorder as the temperature rises.

Moreover, the temperature dependence of $E_U$, observed from 293 K to 623 K, is linked to phonon-induced broadening and enhanced electron-phonon interactions at elevated temperatures. These effects result in the exponential absorption tails (Urbach tails) becoming more pronounced, as clearly depicted in Fig. 8. The presence of two distinct Urbach regimes ($E_{U1}$ and $E_{U2}$), each corresponding to different energy ranges, further suggests the coexistence of multiple types of disorder—possibly static (defect-related) and dynamic (phonon-related). These results highlight the significant influence of both thermal effects and doping-induced structural disorder on the optical absorption characteristics,

The optical transition values of $E_{0,SE}$, $E_{1,SE}$ and $E_{2,SE}$ were numerically extracted from the Tauc plot method using the absorption coefficient values obtained through spectroscopic ellipsometry. These energies were subsequently modeled using the Varshni equation, as seen in UV-Vis-NIR spectroscopy analysis. The temperature dependence of the three optical transitions is well described by
<table><caption>**Table 6**

Varshni parameters of Co₃O₄ and CSO thin films obtained by spectroscopic ellipsometry.</caption><thead><tr><th>Transition energy</th><th>Varshni parameters</th><th>Co<sub>3</sub>O<sub>4</sub></th><th>CSO</th></tr></thead><tbody><tr><td rowspan="3">E<sub>0,SE</sub> (eV)</td><td>E(0) (eV)</td><td>0.79 ± 0.03</td><td>0.75 ± 0.04</td></tr><tr><td>α (eV/K)</td><td>1.70 x 10<sup>-4</sup> ± 6 x 10<sup>-6</sup></td><td>3.56 x 10<sup>-4</sup> ± 2 x 10<sup>-5</sup></td></tr><tr><td>β (K)</td><td>525 ± 10</td><td>525 ± 17</td></tr><tr><td rowspan="3">E<sub>1,SE</sub> (eV)</td><td>E(0) (eV)</td><td>1.57 ± 0.03</td><td>1.53 ± 0.03</td></tr><tr><td>α (eV/K)</td><td>4 x 10<sup>-4</sup> ± 2 x 10<sup>-5</sup></td><td>3.86 x 10<sup>-4</sup> ± 10<sup>-5</sup></td></tr><tr><td>β (K)</td><td>524 ± 17</td><td>525 ± 7</td></tr><tr><td rowspan="3">E<sub>2,SE</sub> (eV)</td><td>E(0) (eV)</td><td>2.28 ± 0.04</td><td>2.11 ± 0.04</td></tr><tr><td>α (eV/K)</td><td>5.68 x 10<sup>-4</sup> ± 4 x 10<sup>-5</sup></td><td>2.1 x 10<sup>-4</sup> ± 2 x 10<sup>-5</sup></td></tr><tr><td>β (K)</td><td>525 ± 20</td><td>524 ± 24</td></tr></tbody></table>

Varshni's model and the best fits are illustrated in Fig. 9. The fitting curves exhibit a linear dependence above room temperature. The parameters E (0), α and β obtained from this modeling are summarized in Table 6. Notably, the transition energies at 0 K show a slight decrease with doping, and the β parameter is found to be in the vicinity of the Debye temperature θ<sub>D</sub>. These results are in agreement with UV-Vis-NIR spectroscopy findings. Overall, the Varshni equation provides a good fit to the data, even though no literature values for the fitting parameters of cobalt oxide were available for comparison.

## 4. Conclusion

In conclusion, high-quality undoped and 2 mol% Sn doped Co₃O₄ thin films were successfully prepared using the spray pyrolysis technique. *In situ* Raman measurements performed between room temperature and 623 K, confirmed the phase stability of both films. The Raman spectra exhibited temperature-dependent, with more pronounced changes in the doped sample, attributed to combined effects of thermal expansion and doping-induced lattice alterations

The optical properties of the films were thoroughly investigated across the UV to near-infrared range using *in situ* UV-Vis-IR spectroscopy and spectroscopic ellipsometry (SE), yielding consistent results. A physical model comprising two porous sublayers on the glass substrate, combined with the Tauc-Lorentz dispersion law using four oscillators, proved to be an effective approach for accurately resolving the SE spectra and extracting the optical functions of the material. The as-deposited film displayed multiple optical transitions, assigned to the interaction between crystal field splitting of cations in tetrahedral and octahedral sites, and cation-anion orbital hybridization. As the temperature increases, the absorption spectra revealed increasing Urbach tails in the sub-bandgap region. The doped sample exhibited significantly higher E<sub>U</sub> values, resulting from the cumulative effects of lattice defects induced by doping and structural and thermal disorders. Moreover, the electronic transition energies indicate temperature-induced narrowing. The Varshni model effectively reproduced the temperature dependence of these optical transitions. The extracted β parameter was found to be close to the Debye temperature (θ<sub>D</sub> = 525 K) reported in the literature.

This study highlights the impact of temperature and doping on the optical properties of Co₃O₄ films, offering valuable insights for potential applications where temperature stability and optical performance are crucial.

## CRediT authorship contribution statement

**Touihri Said:** Writing – original draft, Conceptualization. **Boukhachem Abdelwaheb:** Writing – original draft, Methodology, Data curation, Conceptualization. **Bouzoura M.-B.:** Writing – original draft, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Essaidi Hatem:** Writing – review & editing, Writing – original draft, Validation, Methodology, Investigation, Formal analysis, Conceptualization. **EN NACIRI Aotmane:** Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Software, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. **Zribi Tasnim:** Writing – review & editing, Writing – original draft, Visualization, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization.

## Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgements

We gratefully acknowledge P. FRANCETTI for his technical assistance with the Raman measurements used in this research.

## Data Availability

Data will be made available on request.
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