Nano-sized blue spectral shift in sol–gel derived mesoporous titania films

The principal processes of sol–gel technology are described in detail by Brinker and Scherer [21]. The major problems in texturing titania is the high reactivity of Ti alkoxide precursors towards to rapid hydrolysis and condensation reactions. Rapid condensation processes lead to the formation of oxo-oligomers, clusters or small polymers prior to the formation of the textured template. However, the control of hydrolysis and condensation, through the addition of condensation inhibitors such as chelating agents or mineral acids, can overcome the problem [21‐23]. As a consequence in the presented here research, the titania films were fabricated using the tetraethoxyorthotitanate Ti(OEt)₄ (TET) as a precursor for titania, water H₂O, ethyl alcohol C₂H₅OH (EtOH) as homogenizing agent and hydrochloric acid HCl as a condensation inhibitor. Two types of gel were synthesized, which were used for synthesis of the TiO₂ films possessing different porosity and refractive indices.

The first sol, which will be indicated as sol-A, was prepared with the following molar ratios of the components: TET:EtOH:H₂O:HCl = 1:15:2.8:0.7. The second one, which will be indicated as sol-B, has been prepared similarly to the sol-A. To the sol-B it was additionally added acetylaceton (Acac) as a chelate and non-ionic surfactant Triton X-100 as a template. Tetraethoxytitanate was mixed with acetylaceton in the molar ratio TET:Acac = 1:1. A non-ionic surfactant Triton X-100 was added in the volume ratio TET:Triton X-100 = 1:0.5. to the starting solutions. After mixing of the components, the sols formation was performed during 3 h in a sealed glass crucible at temperature about 50 °C, using ultrasonic mixing. Ultra clean soda-lime glass substrates (microscope slides, Menzel-Glaser), was cleaned by a method described in the Ref. 15. The films were deposited on the cleaned substrates by dip coating method. The such prepared film were annealed at temperature of 500 °C during 1 h. For the substrate withdrawal speed from the sol-A of 1.7÷3.0 cm/min we have obtained films with thickness varying within 71–89 nm. For sol-B and the same withdrawal speed we have synthesized films with thickness varying within 113–130 nm. Sol-B containing Triton X-100 had higher viscosity with respect to sol-A. As a consequence, the thickness of the film fabricated from sol B is higher than those one fabricated from sol A at the same withdrawal rate of substrate.

At the beginning precursor was solvated in water-less ethanol and afterwards HCl acid was added successively. The chemical reactions in the Ti(OR)₄/EtOH/H₂O/HCl were studied in details by Soler-Illia and co-workers [22‐24]. Upon dissolution, Ti(OR)₄ precursors undergo fast exchange reactions with EtOH and HCl molecules, leading to formation of Ti(OR)_n−x(OEt)_x, TiCl_n−x(OEt)_x nanoclusters, or a mixture of both. Subsequently, polycondensation reactions between metal alkoxides can occur, yielding metal-oxo condensates with general formula Ti(OR)_x(OH)_yO_2−(x+y)/2 or TiCl_x(OH)_yO_2−(x+y)/2. Typically, x ≈ 0.3−0.7 and y ≈ 0−0.2; while the value of y increases with the water content, x decreases [22‐24].

The role of Triton X-100 as a surfactant has been described by Avnir and co-workers in Ref. [25]. Dag and co-workers have fabricated mesoporous TiO₂ using Ti(OEt)₄ as precursor and non-ionic surfactant CH₃(CH₂)_n(OCH₂CH₂)_mOH [26], which is similar to Triton X-100. Their studies have shown that appeared nanoclusteres during process of controlled Ti(OEt)₄ effectively interact with surfactant CH₃(CH₂)_n(OCH₂CH₂)_mOH which favors formation of nanoclaster/non-ionic surfactant “titanotropic” mesophase that undergoes hydrolytic polycondensation to give mesostructured titania with a wormhole structure, an amorphous titania framework, and uniform pore size distribution. The surfactant pre-organizes the clusters, which are attached to its head group [26]. We assume that for the case of use the Triton X-100 the similar reaction should be observed.

The such prepared surface of the TiO₂ films have been monitored by atomic force microscope (AFM), using Ntegra Prima (NT-MDT), monochromatic ellipsometer Sentech SE400 (Sentech, model 2003, Germany). Additionally spectrophotometer UV–VIS HR4000CG (OceanOptics) with spectral resolution 0.75 nm within 200–1,100 nm spectral wavelength range was used. The AFM experiments for TiO₂ thin films were performed using semi-contact mode AFM. In AFM measurements the HA_NC (NT-MDT) silicon cantilever with nominal curvature radius of a tip equal to 10 nm and resonance frequency of 250 kHz was used. The AFM image analysis was carried out using commercial NOVA 1.0.26.1644 (NT-MTD) software procedures to evaluate Root-Mean-Square (RMS) surface roughness. The ellipsometric measurements were done for wavelength of He–Ne cw laser λ = 633 nm and spectroscopic measurements were carried out in the spectra range within 200–1,100 nm.

Figure 1 shows typical semi-contact AFM images of surface of the studied titania film fabricated from sol-A. Such titania films exhibit typical grain-type surface morphology. Following the Fig. 1a one can see clear aggregates possessing diameters equal of about 240 nm. More detailed analysis is presented in the Figs. 1b and 2a, which clarify that such aggregates are built from the less grains. The root mean square surface roughness is 0.88 nm over a 0.5 × 0.5 μm² area. Figure 2b shows a line profile taken along the surface presented in Fig. 2a. It is the same surface as presented in Fig. 1. The maximum grain height is equal to about 7 nm, while the maximum grain width for this film is equal to about 35 nm.

Figure 3 shows typical semi-contact AFM images of surface for the titania film fabricated from sol B. It is clear seen that in this case the surface of the film is more rough with respect to the film originated from gel A (Fig. 1). It is visible, that the film has a grain structure. The root mean square surface roughness is 2.70 nm over a 0.5 × 0.5 μm² area.

Figure 4b shows a line profile taken along the surface presented in Fig. 4a. It is the same surface as presented in Fig. 3. The maximum grain height is estimated to be about 12 nm, while the maximum grain width for this film is equal to about 38 nm. One can clearly see that for the two types of layers the grain diameters are comparable, however the maximal heights of the grains for the film produced from sol-B are substantially higher with respect to those obtained from sol-A.

The presented here results concerning the AFM demonstrate substantial influence of non-ionic surfactant Triton X-100 on the morphology if the such synthesized films. In the layers formed in sol B containing surfactant the grains do not form the aggregates, on the contrary to the layer formed from sol A (see Fig. 1). The surfactant decreases the capillary stresses and avoids a destroying of the layered structure during drying process [25]. As a consequence the layer structure is more modified and its surface is more rough. For both types of the layers the maximal grain sizes are comparable, however, the maximal heights of grains are substantially different. The lower maximal values of grain heights (about 7 nm) for the layers formed from sol A without surfactant are caused by effect of collapse of structure for the layers formed from A during the drying and annealing processes.

Refractive index of films fabricated from sol-A was equal to about 2.15 (at wavelength 632.8 nm) and ones fabricated from sol-B was equal about 1.61 (at wavelength 632.8 nm). Using the measured values n of the refractive index of the fabricated titania films, their volume percentage porosity P was determined. For this purpose, the Lorentz-Lorenz equation was applied:where n _d is the refractive index of anatase ≈ 2.52 (at wavelength 632.8 nm). So one can assume that in the presented here layers, which are annealed at temperature 500 °C there is present only anatase [3]. Rutyl appears in the layers of TiO₂which are thermoannelaed at temperatures higher 600 °C [17, 27, 28]. Assuming that the pores of these layers are filled up solely with air, their porosity calculated on the basis of (1) is P _A  ≈ 16% for films fabricated from sol-A and P _B  ≈ 46% for films fabricated from sol-B. Using the simplified effective medium approximation (EMA) n = n _air P + n _d (1 − P) with n _air  = 1 the porosity are equal to P _A  = 24% and P _A  = 60%, respectively. So the determined porosity is dependent on the used model of EMA. The difference between porosities obtained from various EMA models can be significant and increase as the index of refraction of the continuous phase material increases [29]. The review of EMA models is presented in Ref. [30].

Figure 5 shows the transmittance spectra of titania films fabricated from the sol-A. Every spectral curve clearly shows the occurred interference patterns. It can be observed that with the increase of the thickness d of the titania film, its refractive index n is increasing because increased coating rates (increased film thickness) results in particle ordering [21].

In order to determine the optical band energy gap of the TiO₂ films the absorption coefficient α of the film was evaluated from the transmittance T of the film and its thickness d:The transmittance was experimentally evaluated from the UV–Vis spectra. If to assume parabolic energy distribution of density of states for valance and conducting band, the E _g of the titania films was determined by analysing the relationship between absorption coefficient α and photon energy hν using Tauc equation [31]:where E _g is a bend gap of the material, C is a constant, and a = 1 for direct transition between the edges of valence and the conduction bend and a = 4 for indirect transition. The energy gaps value are determined by extrapolation of the linear part of the plots of the absorption coefficient \( \left( {\alpha h\nu } \right)^{{{2 \mathord{\left/ {\vphantom {2 a}} \right. \kern-\nulldelimiterspace} a}}} \) versus photon energy hν.

The Fig. 6 presents the dependence of the \( \left( {\alpha h\nu } \right)^{2} \) versus photon energy. One can see that the TiO₂ possess the direct energy gap (a = 1). Because the dip coating method gives a possibility to obtain the films from two sides of the substrate the energy gap was determined from summary film thickness 2d = 162 nm and the energy gap was equal to E _g  = 3.749 eV. In turn for the films with total 2d = 178 nm the energy gap was equal to E _g  = 3.720 eV. So one can clearly see that with the decreasing of film thickness occurs energy gap is increasing. It is a consequence of the varying materials structure with the varying thickness. The thicker sol layers are dried more quickly, so the TiO₂ particle after crystallization may form higher nanocrystallites, with the lower energy gaps E _g . The evaporation of the solvents from the layer favours the changes of their features, which may cause a restraining of nanocrystallite growth.

The transmittance spectra of the mesoporous films TiO₂, formed by gel B are presented in the Fig. 7. For this case thicknesses of the layers are substantially higher with respect to the synthesized from sol A (Fig. 5). However, the maximums and minimums of the interference are weakly visible. It is a consequence of light depolarization in the studied materials. In Ref [32]. it was shown that the porous layers demonstrate strong depolarized features. It can be observed that with the increase of the thickness d of the porous titania film, its refractive index n is decreasing. Such dependence are typical for a polymeric sol, where the polymers are weakly charged and the condensation rate is high [21].

Figure 8 presents the spectral dependences of the normalized absorption coefficient. It is a principal difference because there occurs the indirect inter-band transition (a = 4) edge E _g  = 3.40 eV.

For the two studied types of films the energy gaps are higher with respect to the energy gap of the bulk anatase specimens E _bulk  = 3.20 eV. This is a consequences of quantum size effects [33‐37]. It is crucial that following the values of spectral shift (blue energy shift) of the energy gap one can evaluate the diameters of the crystallites.

For parabolic energy band near the band-gap, the average value of the crystallite diameter 2R may be estimated from the formula [34‐36, 40]:where \( \hbar = 1.0 5 4 5 \times 10^{ - 3 4} {\text{Js}} \) is the reduced Planck’s constant, m _e is the effective mass of the electron, m _h is the effective mass of the hole, ε ₀ is the permittivity of free space, ε is the dielectric constant of anatase TiO₂, \( E_{Ry}^{*} = {{e^{4} } \mathord{\left/ {\vphantom {{e^{4} } {\left( {2\varepsilon^{2} \hbar^{2} \left( {m_{e}^{ - 1} + m_{h}^{ - 1} } \right)} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {2\varepsilon^{2} \hbar^{2} \left( {m_{e}^{ - 1} + m_{h}^{ - 1} } \right)} \right)}} \) is the effective Rydberg energy. ΔE is a blue shift of the band-gap energy results of two competing mechanisms: a widening due to the Burstein-Moss effect, and a narrowing due electron–electron and electron–ion scattering [38, 41].

Figure 9 shows calculated dependence blue shift band gap energy on the crystalline size (2R) calculated on the base Eq. 4. In the calculations we have been taken into account the parameters as follow; effective masses of the electron m _e  = m ₀ = 9.11 × 10⁻³¹ kg and the hole m _h  = 0.65 m ₀ [39], dielectric constant of anatase ε = 31.

For the titania films fabricated from sol-A the blue energy shift is in the range 0.52–0.55 eV, but for the titania films fabricated from sol-B the blue energy shift is about 0.2 eV. Following the dependences presented in the Fig. 9 we have determined diameters of the anatase nanocrystallites, which were equal to 2R ≈ 2.5 nm for the layers produced from sol A and 2R ≈ 4 nm for the layers synthesized fir sol-B. As a consequence the grains presented in the figures (Sect. 3.1) have the polycrystalline structure. So one can see that presence of Triton X-100 leads not only to higher roughness of the synthesized layers, however, also to higher diameters of anatase nanocrystallites.

The effective Bohr radius of the exciton calculated from the formula [36, 37]:is a _B  = 0.823 nm.