Figure 1 presents high-magnification SEM images of the same samples. The TiO₂-350 sample (Figure 1a) yielded a SEM observation depicting a perfectly smooth surface, using magnifications of up to 100,000. As for the TiO₂-500 sample (Figure 1b), it is homogeneous and seems to be constituted of small platelet particles, ranging from 30 to 100 nm in length, and from 10 to 20 nm in thickness, embedded in a continuous phase which may be a rest of amorphous phase. Indeed, from XRD measurements (Figure 2) [22], we concluded that at 350 °C the TiO₂ films are amorphous, but crystallize in anatase form when heated up to 500 °C.

AFM images (Figure 3) show the surface morphologies of the both samples and from these images, the Roughness Mean Square (RMS) values were measured at 1.65 nm and 3.26 nm for TiO₂-350 and TiO₂-500 films, respectively. TiO₂-350 film has an extremely small roughness which is consistent with the smooth surface observed by SEM analysis. On the other hand, TiO₂-500 film shows a slightly greater roughness which is also consistent with its SEM image, showing two morphologies. Thus, the roughness seems to be dependent on the annealing temperature value. Our results and observations agree with the work of Mechiakh et al. [24] who reported that the RMS value was found to increase from 0.617 to 3.713 nm for sol-gel TiO₂ thin films annealed at 350 and 450 °C, respectively; and that the increase in the roughness is due to the increase in the grain size. Similarly, Urlacher et al. [25] found, in the case of sol-gel ZrO₂ waveguides, that the amorphous film exhibits a smoother surface than the crystallized one, and the RMS varies from 0.2 to 2.1 nm, when increasing temperature from 300 up to 600 °C. From their analysis, this result is mainly due to crystallite growth when increasing temperature.

Due to our small roughness values, we may predict low optical losses for the waveguiding properties of the films. These properties are studied hereunder.

The waveguiding features of TiO₂ thin films are investigated by dark m-lines spectroscopy technique [23,26]. This well known method allows us to obtain the optogeometric parameters of waveguiding thin films, such as thickness and refractive index. A right angle rutile prism is mounted onto a precise rotary stage (0.001°), which can be turned by a feedback-controlled DC motor. The mode profiles in both the TE (transverse electric) and TM (transverse magnetic) polarizations are obtained by measuring the reflected intensity of a He-Ne laser beam operating at a 632.8 nm wavelength, as a function of the incidence angle. The corresponding effective mode indices can thus be calculated. Consequently, we can determine the refractive indices n_TE and n_TM for the TE and TM polarization, respectively, and the thickness of films. Figure 4, Figure 5 display typical TE and TM guided mode spectra of the TiO₂ films for two samples TiO₂-350 and TiO₂-500, respectively. We observe the excitation of two guided modes for TE and TM polarization for the TiO₂-350 sample and two guided modes for TE and only one guided mode for TM for the TiO₂-500 sample.

From the angular position of the reflectivity dips we compute the effective mode indices, which then serve to calculate the refractive indices and the thickness of the layer through the following dispersion relationship [23]: (1) where: (2)

For TE mode ρ = 0 and n = n_TE and for the TM mode ρ = 1 and n = n_TM; Φ_{(n, na)} and Φ_{(n, ns)} are the phase shift at air/film and film/substrate interfaces, d is the film thickness, λ is the wavelength of the light in vacuum, n_a and n_s are, respectively, the air and substrate refractive indices, m the mode number and N_m is the effective index of the m^th mode.

From the angular position of TE and TM guided modes (Figure 4, Figure 5) we deduced the corresponding effective indices. These values are then used to compute the thin film parameters: ordinary refractive index (n_TE), extraordinary refractive index (n_TM) and thickness (d). The calculation is based on the least square method widely discussed by Kersten [27]. In the case of Figure 4 (T = 350 °C), we found n_TE = 1.9720, n_TM = 1.9895 and d = 358 nm. While for the case of Figure 5 (T = 500 °C), we found n_TE = 1.9949, n_TM = 2.0092 and d = 336 nm. Finally, from the refractive index and thickness, we computed the theoretical effective indices of the thin films. The results are reported in Table 1. We notice a very good agreement between measured and calculated values of effective indices.

The results show that refractive index increases with annealing temperature while thickness decreases due to shrinkage and densification of the films. These results are in good agreement with the work of Wang et al. [28] who found, in the case of sol-gel TiO₂ waveguides, that the film thickness decreases and the refractive index increases when the heat treatment temperature increases. Urlacher et al. [25] reported, in the case of ZrO₂ film, that the thickness roughly decreases between 300 and 400 °C indicating a high densification of the layer before crystallization. Refractive index simultaneously increases as a consequence of densification, organic compound removal and structural change in the material.

The sharpness of the reflectivity dips, observed on Figure 4, Figure 5, indicates a good optical confinement of the light beam into the thin films. Measurements of the losses will bring more insight about this point. Indeed, the determination of optical attenuation in waveguides is of great interest for designing integrated optical devices. Practical use of such structures directly depends on the measurement of this parameter. Several techniques have been used for loss measurement among which the end-fire coupling [29], the prism coupling method [30], and a new approach that uses a prism-in coupling method to feed the light into the waveguide and the end-fire coupling to measure the transmitted light [31].

For optical losses measurement, we used the prism-in coupling method (Metricon Model 2010) in which the exponential decay of light is measured by a fiber probe scanning down the length of the propagation streak. A least square exponential fit is then made to the intensity as a function of distance patterns and the loss is calculated in decibels per centimeter (dB/cm). The overall loss measured is the combined total of both scattering loss from particles or other scattering centers and surface roughness, and the inherent absorption of the waveguide material.

The results of the optical attenuation of the fundamental TE mode in TiO₂ thin films annealed at 350 and 500 °C are shown in Figure 6a,b. The optical losses have been estimated around α = 0.5 dB/cm and α = 0.80 dB/cm, respectively, using the following equation: (3) where I₀ is the initial light intensity, and I_L is the light intensity at the considered position L, measured in centimeters.

Table 2 summaries the structural and optical characteristics of both samples.

As we reported above, TiO₂-350 sample is amorphous while TiO₂-500 is crystallized and the film thickness decreases with annealing temperature. From our results, we can deduce that increasing annealing temperature leads to increasing RMS, refractive index and optical losses. Similar results on the increase of optical losses with the annealing temperature were already reported on sol-gel ZrO₂ [25,32] and TiO₂ [33] films. For the former, Ehrhart et al. [32] reported that in order to obtain ZrO₂ thin films with a high refractive index (n = 1.96) and low optical losses (0.29 dB/cm), the best heat-treatment corresponds to an annealing at 400 °C, thus preserving an amorphous phase, while optical losses increase at a temperature of 450 °C when the crystallization into a metastable tetragonal phase appears; Urlacher et al. [25] also found that ZrO₂ optical losses increase when the annealing temperature and film crystallinity increase: they obtained 0.8 and 2.5 dB/cm as attenuation coefficients for the amorphous film heat treated at 300 °C and the crystallized film annealed at 600 °C, respectively. For the latter, Bahtat et al. [33] reported that at lower temperatures (450 °C), the films’ structure consists of a mixture of amorphous TiO₂ and anatase nanocrystals and its surface is smooth. On the contrary, when increasing the annealing temperature, crystallization increases yielding a higher roughness and the films’ waveguiding properties disappear.