Nb₂O₅-doped TiO₂ film synthesised via sol-gel method – technology and optical characterisation

1. Introduction

Thin layers of titanium dioxide (TiO₂) have enormous application potential because of their chemical and biological neutrality and excellent physical and chemical stability. In addition, TiO₂ exhibits a high refractive index and excellent transparency in the VIS-NIR spectral range. The optical and electrical properties of TiO₂ films are closely related to their structural characteristics, which can be intentionally tailored during the fabrication processes [1–6]. For these reasons, TiO₂ has long been the focus of many research groups [7–10].

TiO₂ thin films may be either amorphous or polycrystalline in the form of anatase or rutile, which are both tetragonal. Polycrystalline films fabricated at low temperatures (below 600 °C) contain only the anatase phase, which is explained by anatase lower surface energy compared to rutile [10–11]. Anatase is a wide-bandgap, n ­type semiconductor. It has a relatively large indirect bandgap (3.2 eV in bulk) and a high refractive index (n ~ 2.5). As a result of the quantum size effect, TiO₂ nanocrystals exhibit a wider optical bandgap than bulk crystals [12–14].

However, due to porosity, the refractive indices of TiO₂ thin films (amorphous and polycrystalline) are often lower than those of anatase single crystals [14, 15].

Doping with niobium (Nb) in the form of Nb₂O₅ improves the stability of TiO₂ at the nanoscale [10]. Nb₂O₃-doped TiO₂ (Nb:TiO₂) is considered a prospective material from the point of view of transparent conductive oxide (TCO) fabrication technology and its applications. This is because it has an excellent optical transparency, a high refractive index and high electrical conductivity. Nb₂O₅ has a wide bandgap of 3.4–3.6 eV and a high refractive index of 2.2–2.6. Nb:TiO₂ thin films have been synthesised using various methods, including magnetron sputtering [16, 17], atomic layer deposition (ALD) [18, 19], chemical vapour deposition (CVD) [20], and the sol-gel method [21–23].

The subject of the reported work is niobium-doped TiO₂ films fabricated by the sol-gel method and dip-coating technique. The sol-gel method offers several advantages, including precise control of material structure over a wide range, low-temperature processing, ability to produce multicomponent materials with molecular-level homogeneity, and flexibility to modify physicochemical properties through doping. The aim of this work is to present the results of investigations on the effect of niobium doping on the optical properties of TiO₂ films. In this paper, we present the impact of a substrate withdrawal speed from the sol on the final thicknesses and refractive indices of Nb:TiO₂ films, the effect of film thickness on the optical bandgap, the dispersion characteristics of the refractive index and the extinction coefficient, and the effect of film thickness on the optical bandgap. In each case, results obtained for the reference TiO₂ films are also presented for comparison.

2. Synthesis and characterisation

2.1. Materials

Titanium (IV) ethoxide (TET, technical grade, SigmaAldrich, Steinheim, Germany) was selected as a precursor for titania dioxide. Niobium(V) ethoxide (99.95%, SigmaAldrich, Steinheim, Germany) served as the niobium oxide source. Polyethylene glycol (PEG-300, M_n = 300, SigmaAldrich, Steinheim, Germany) was employed as a surfactant. Absolute ethanol (EtOH; 99.8%, AR grade) and hydrochloric acid (HCl; 36%, AR grade) were obtained from Avantor Performance Materials (Gliwice, Poland). Soda-lime microscope slides (Menzel Gläser, Thermo Scientific, n = 1.513 at λ = 632.8 nm) of a dimension of 76 × 26 ×1 mm³ and silicon wafers were used as substrates. The sol solutions were filtered using Whatman Puradisc PTFE syringe filters (25 mm diameter, 0.2 µm pore size, Sigma-Aldrich).

2.2. Preparation of sol and film fabrication

The sol for reference TiO₂ films was synthesised using our procedure reported earlier in [15]. The niobium oxidedoped titania sol was prepared using a modified version of the method described in [15]. A total of 0.14 moles of the titanium (IV) ethoxide and 0.016 moles of niobium (V) ethoxide were added to 0.99 moles of absolute ethanol and 0.22 moles of deionised water. Subsequently, 0.02 moles of PEG-300 and 0.06 moles of HCl were added to the reaction mixture under ambient conditions to initiate hydrolysis and condensation. The synthesis was carried out under ultrasound for 2.5 h at 50 °C. The sol was filtered through a syringe membrane and subsequently aged for 24 h. Nb:doped-TiO₂ and undoped TiO₂ films were fabricated on soda-lime glass and silicon wafers using the dip-coating technique. The range of withdrawal speeds used was 3 ÷ 7 cm/min. The films were then annealed for 60 minutes at 500 ° C .

2.3. Methods

The film thickness d and refractive index n were determined using a SENTECH SE400 monochromatic ellipsometer operating at a wavelength of λ = 632.8 nm (SENTECH Instruments GmbH, Germany). All other ellipsometric measurements were performed using a spectroscopic ellipsometer M-2000D from J. A. Wollam, which acquires data at 709 wavelengths in the spectral range from 1690 nm to 193 nm (0.73 eV to 6.52 eV). The probing light, with a beam diameter of approximately 3 mm, was incident on the sample surface at angles near the Brewster angle, specifically 60°, 65°, and 70°. The measurements were conducted at the sample centre and at a 5 mm-spaced square grid consisting of 9 points.

The transmittance and reflectance of the fabricated films were investigated using a UV-VIS AvaSpec-ULS2048LTEC spectrophotometer (Avantes, Apeldoorn, The Netherlands). At room temperature, the transmittance and reflectance were measured using an AvaLight-DH-S-BAL (Avantes) light source over the spectral range of 300–1000 nm.

3. Results and discussion

In the dip-coating technique, the film thickness is primarily controlled by the substrate withdrawal speed v [24]. The effect of substrate withdrawal speed v on the film thickness (d) and refractive index (n) of the TiO₂ and Nb:TiO₂ films is shown in Fig. 1. Blue diamond markers represent experimental data for the reference TiO₂ films, whereas red diamond markers correspond to Nb:TiO₂ films. Solid diamond markers indicate the experimental characteristics d = d(v), while hollow diamond markers indicate n = n(v). The films thicknesses increase with the withdrawal speed of the substrates from the sols while the refractive indices remain constant, equal to n = 2.074 ± 0.001 for undoped TiO₂ films and n = 2.110 ± 0.002 for Nb:TiO₂ films. As shown in Fig. 1, for all v, the Nb:TiO₂ films are thicker than the undoped TiO₂ films. This is due to the increased viscosity of the sol from which the films were deposited. By changing the withdrawal speed of the substrates from sols from 3.2 cm/min to 6.6 cm/min, films with thicknesses from ca. 120 nm to ca. 180 nm were produced, with the thickness of the Nb:TiO₂ film being ca. 5 nm greater for each withdrawal speed.

Fig. 1. Dependence of thickness d and refractive index n on the substrate withdrawal speed for the Nb:TiO₂ and TiO₂ films. All films were annealed at 500 °C for 1 h, λ = 632.8 nm.

The refractive indices of the produced films are lower than that of anatase (n_d = 2.52), indicating that the films are porous. The porosity P of the films was determined using the Lorentz-Lorenz equations:

assuming the pores are filled with air. It was calculated that undoped TiO₂ films have a porosity of 18%, while Nb:TiO₂ films have a slightly lower porosity of 15%, indicating that the Nb:TiO₂ films are more compact than undoped TiO₂ films.

An image of exemplary Nb:TiO₂ and TiO₂ films on a soda-lime glass slide is shown in Fig. 2. The photograph was taken in sunlight. Uniform interference colours can be observed across the entire surface, indicating uniformity in both the refractive index and the film thickness. All prepared films were free of cracks and showed uniformity and continuity.

Fig. 2. Images of selected Nb:TiO₂ and TiO₂ films deposited on soda-lime glass slides. In both cases, the withdrawal speed of the substrates from the sols was the same: v = 6 cm/min.

The optical homogeneity of the films was verified by comparing their reflectance spectra with those of the sodalime glass substrates, as shown in Fig. 3. The reflectance spectra of the tested structures exhibit distinct interference minima and maxima. As shown, for wavelengths greater than 350 nm, both interference minima of the doped film coincide with the reflectance spectrum of the glass substrates used. This is clear evidence of the film optical homogeneity [25]. For the reference film at a wavelength of ∼ 380 nm, the interference minimum is slightly above the substrate reflectance due to the absorption edge.

The transmittance spectra for the same structures are shown in Fig. 4. In both cases, a strong decay of transmittance is visible for wavelength λ = 382 nm (hν = 3.25 eV), which results from the presence of an absorption edge. For wavelength λ < 310 nm (hν > 4.0 eV), the transmittance disappears completely. The Tauc method was applied to the transmittance spectra to determine the optical bandgaps in this spectral range [14, 26].

Figure 5 shows the exemplary plot of (α · hν)^1/2 and (α · hν)² on the energy photon for Nb:TiO₂ (d = 169 nm) film deposited on a glass substrate of the same kind. To determine the optical bandgap, a straight-line segment of the normalised absorption vs. photon-energy graph is used. This segment is approximated by a linear relationship, extrapolated to its intersection with the horizontal axis (hν). The photon energy at the intersection point equals the optical bandgap E_g. The determined values of the indirect and direct energy bandgaps were 3.45 eV and 3.75 eV, respectively.

The influence of the film thickness (d) on values of optical bandgaps (E_g) for direct and indirect transitions is presented in Fig. 6. Full circles and diamonds mark the energy bandgaps for indirect optical transitions, while empty circles and diamonds correspond to direct optical transitions. In each case, the experimental dependences were approximated by linear functions. The relationships for niobium-doped films (Nb:TiO₂) are plotted in red and for undoped films (TiO₂) in blue. All graphs show slight decreases in the energy bandgap with increasing film thickness, a typical effect in thin films.

As can be clearly seen, the energy bandgap of niobiumdoped films is larger than that of undoped films over the

Fig. 3. Reflectance spectra of selected Nb:TiO₂ and TiO₂ films on soda-lime glass slides.

Fig. 4. Transmittance spectra of selected Nb:TiO₂ and TiO₂ films on soda-lime glass slides.

Fig. 5. Normalised absorption coefficients vs. photon energy for Nb:TiO₂ films, d = 169 nm.

Fig. 6. The influence of film thickness on the energy bandgaps.

entire thickness range. However, for indirect optical transitions, there are no significant differences between the optical bandgaps for doped and undoped films. The indirect optical bandgap for Nb:TiO₂ is in the range of 3.42 eV to 3.45 eV. These energies are higher than the optical bandgap of anatase, which is equal to 3.2 eV (bulk crystal). This blue-shifted energy bandgap is a quantum-size effect. Based on the magnitude of this shift, the diameters of anatase nanocrystals were estimated to be ca. 4 nm, as described in our earlier works [14, 15]. In [15, 24], we showed that the diameters of anatase nanocrystals determined in this way are comparable to the diameters determined from TEM images.

The spectral dispersion characteristics of the ellipsometric angles Ψ and Δ were recorded over wavelengths from 200 to 1700 nm, for selected sample illumination angles of 60 °, 70 °, and 75 °. The characteristics Ψ(λ) and Δ(λ) recorded for the Nb:TiO₂ on silicon substrate are presented in Figs. 7 and 8, respectively. A two-stage approach was used to develop the results. In the first stage, the upper wavelength limit for fits was set at 400 nm, corresponding to an energy of 3.1 eV. The choice can be easily justified based on Figs. 7 and 8. For energies higher than ca. 3.1 eV, the observed beats change their form, an effect occurring due to light absorption. The second limit was set at 270 nm (4.6 eV). For shorter wavelengths,

Fig. 7. Example of the dependence of the ellipsometric angle Ψ on the wavelength of the incident light, for the angle of incidence equal to 60°, 65°, and 70°. Data were collected for the sample manufactured from Nb:TiO₂. Black dots correspond to the fitted B-spline model.

Fig. 8. Example of the dependence of the ellipsometric angle Δ on the wavelength of the incident light and the incidence angle (60°,65°,70°). Data were collected for the sample, which consisted of undoped Nb:TiO₂. Black dots correspond to the fitted B-spline model.

beats disappear entirely, indicating that the incident light is completely absorbed in the material and reflected only at the upper surface of the film. The latter renders the analysis flawed due to the assumptions underlying the models used to fit the ellipsometric data. At first, the sample thickness was calculated using the Sellmeier approximation, which is valid in the transparent spectral region and is often used to model the optical constants of transparent dielectric materials. The Sellmeier approximation allowed us to determine the film thickness at each test point, while other parameters were kept constant across all points. The results were averaged across the tested samples. Next, using the above results, the entire spectrum (up to 270 nm) was fitted with B-spline polynomials, imposing Kramers–Kronig order, and a positive imaginary part of the dielectric constant. The fit quality was assessed by minimising the mean-squared error between the measured and modelgenerated parameters across all measurement wavelengths. Finally, the results were averaged. Spectral dispersion characteristics of the real n (λ) and imaginary κ (λ) part of the refractive index, determined in this way for the Nb:TiO₂ films and the pure TiO₂ films on silicon substrates, respectively, are shown in Figs. 9 and 10. As shown, over the entire spectral range, the refractive index of the Nb:TiO₂ film is higher than that of the undoped film. This means that niobium-doped titania films are more compact than undoped films. However, the extinction coefficients of both films are zero for wavelengths > 400 nm and attain significant values only below 400 nm. For this reason,

Fig. 9. Dispersion of refractive index found for the samples studied.

Fig. 10. Dispersion of extinction coefficient found for the samples studied.

the minima of the reflectance spectra shown in Fig. 3 in the spectral range below 400 nm are not associated with the substrate reflectance characteristics.

The refractive indices of Nb:TiO₂ and TiO₂ films on silicon substrates are approximately 0.15 higher than the refractive indices of the same films on soda-lime glass substrates (Fig. 1). The lower refractive indices of the films on soda-lime glass substrates are the result of sodium ion diffusion from the substrate into the film, which promotes TiO₂ crystallisation, i.e., the formation of a more differentiated, more porous film structure [27].

4. Conclusions

Optically uniform niobium oxide-doped and undoped TiO₂ films have been deposited on soda-lime glass substrates and silicon wafers using the sol-gel method and dip-coating technique. The results of the study presented here on the effect of niobium doping on the optical properties of these films demonstrated the impact of doping on sol viscosity. As a result, doped and undoped films produced at the same withdrawal speeds differ in thickness. Spectrophotometric measurements confirmed the optical homogeneity of both niobium-doped and undoped TiO₂ films.

Authors’ statement

Conceptualisation, investigation, formal analysis, writing – original draft, writing – review and editing, visualisation, M.Z.; investigation, software, formal analysis, writing – original draft, writing – review and editing, visualisation; supervision, funding acquisition, C.T.; investigation, formal analysis, validation, Z.O.; investigation, formal analysis, K.B.; investigation, formal analysis, validation; writing – original draft, J.N.; investigation, formal analysis, validation, E.G.; conceptualisation, formal analysis, writing – original draft, writing – review and editing, visualisation, supervision, P.K.

Acknowledgements

This publication has been co-financed from the state budget under the Ministry of Education and Science’s ”Polish Metrology II” programme (project no. PM‑II/SP/0042/ 2024/02); the amount of co-financing is PLN 1 000 000 and the total value of the project is PLN 1 000 000.

Additional support was provided by the Faculty of Electrical Engineering at the Silesian University of Technology via grant BKM‑533/RE4/2025.

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