1. Introduction

Since photo-induced water splitting was demonstrated using a titanium dioxide (TiO₂) electrode by Fujishima and Honda in 1972 [1], optical properties of titanium dioxide such as photocatalytic activity in ultraviolet (UV) region, photostability, UV filtering and high reflectivity have been heavily investigated due to its potential applications in photocatalyst [2,3], photovoltaic devices such as dye sensitized solar cells [4,5], UV filters [6], pigment [7], etc. Particularly in the development of the solar energy conversion devices using titanium oxide, its relatively large energy band gap (3.0 and 3.2 eV for rutile and anatase TiO₂, respectively) compared to the solar spectrum becomes a critical hurdle. The intrinsic TiO₂ is only sensitive to UV light corresponding to only ~4% of solar energy rather than the visible light corresponding to ~45% of solar energy [8].

To extend photocatalytic activity of TiO₂ to the solar spectrum or visible light, noble or transition metals such as Pt, Au, Ag, Cr, Co, Mn, Fe and Zr are doped into TiO₂ [2,9–14]. However, doping with metals is not favored because of their thermal instability, photo corrosion, expensive dopants and photocatalytic activity degradation due to the recombination of photoinduced charge carriers by the dopant states [9,13]. Thus this leads to make an attempt to extend photo activity of TiO₂ by doping with non-metals such as S, N, F and C [2,3,8,15–19].

Especially, among the non-metal dopants, carbon is a favorable one because high photocatalytic efficiency in water splitting up to 8.4% was demonstrated by carbon doped titanium oxide [17]. The numerous empirical [2,3,17–19] and theoretical studies [2,3,18,20–22] have been performed for synthesis of carbon doped TiO₂ (TiO_xC_y) as well as the origin of the improved photocatalytic activity.

Further the recombination of photoexcited charge carriers (photo-electrons and holes) in titanium oxide limits the photocatalytic activity [23]. To improve the photocatalytic activity of titanium oxide, carbon materials such as quantum dots, carbon nanotubes and graphene are attached on the surface of titanium oxide (C-TiO₂) instead of just doping them (TiO_xC_y) [22–25]. As a result, photogenerated electrons in titanium oxide can be transferred freely to conducting carbon materials. This allows separation, stabilizing and hindering the recombination of photogenerated charge carriers, and largely enhances the photocatalytic activity of titanium oxide [24].

Often optical transmittance and absorbance of titanium oxide are investigated for characterization of its optical properties. However, titanium oxide thin films show diverse optical properties [26,27] which can be originated from their chemical composition, crystalline properties, surface roughness, particle or grain size and shape, etc. These physical parameters are varied with synthetic methods such as sol-gel method, hydrothermal method, thermal evaporation and direct current (DC) or radio frequency (RF) sputtering deposition and the processing conditions [28–32]. To understand, design and improve the optical properties of titanium oxide, the correlation among the parameters is necessary but not fully studied yet due to the complexity even though there are bulk of partial correlation studies [26–32].

In this work, a scalable sputter-deposition method is employed among the various film preparation methods. Non-stoichiometric titanium oxide (TiO_x) thin films are sputter-deposited on fused quartz substrates and thermally annealed at from 100 to 450 °C with flowing of hydrogen (H₂) and argon (Ar) gas mixture. The optical properties are investigated by UV-Vis spectroscopy. Further, their crystalline property, chemical properties, and depth dependent chemical profiles were characterized by x-ray diffraction (XRD) spectroscopy, Raman spectroscopy and time-of-flight secondary ion mass spectroscopy (TOF-SIMS).

The optical properties of titanium oxide films are simulated with two approaches, which are able to account the optical properties of heterogeneous films with diverse structure parameters such as shape and filling factors of nanostructures. They are Bruggeman effective medium theory (BR-EMT) [33] and a full wave three dimensional finite difference time domain (3D-FDTD) method with combination of Lorentz-Drude model and transfer matrix method [34]. The optical simulations indicate that the optical properties of titanium oxide are largely varied with its chemical composition of the host materials as well as the filling, shape and size parameters of the embedded nano-particles in the host materials. Further the FDTD simulation suggests that the annealed titanium oxide films become porous. This study shows that the sputter deposited titanium oxide films are amorphous, become crystalline anatase titanium dioxide, carbon doped (TiO_xC_y) and carbon coated (C-TiO₂) by simply annealing them at relatively low temperatures from 100 °C to 450 °C.

2. Experiments and characterization

Deposition of non-stoichiometric titanium oxide thin films

Eight sputter-deposited non-stoichiometric titanium oxide (TiO_x) thin films on fused quartz (FQ) substrates (700 μm in thickness) were prepared for the annealing temperature dependent studies. The detailed experimental procedures for sputtered-titanium suboxide (TiO_x) thin films on fused quartz substrates were also shown in the previous work [34].

Annealing process of non-stoichiometric titanium oxide thin films

The non-stoichiometric TiO_x thin films deposited on FQ substrates (TiO_x/FQ) were placed into the center of a chemical vapor deposition (CVD) quartz reactor, and then the CVD reactor was evacuated below 1 mTorr. After stabilizing the system at a desired annealing temperature, the prepared samples were annealed in a flowing gas mixture of 5 sccm hydrogen and 50 sccm argon for 30 minutes.

Characterization

The optical properties of FQ, as-deposited TiO_x/FQ, and annealed TiO_x/FQ at a desired annealing temperature were investigated by a UV-Vis photospectrometer (Scinco, S-4100). The depth dependent chemical species were investigated by time-of-flight secondary ion mass spectroscopy (TOF-SIMS) using Cs⁺ and Bi⁺ ion source for sputter (area of 300 × 300 μm) and analysis (area of 100 × 100 μm), respectively. The crystalline properties of TiO_x/FQ were evaluated by a high resolution X-ray diffractometer with a Cu Kα line X-ray source (Rigaku, ATX-G) and Raman spectroscopy (Horiba JY co.) with a 514.5 nm Ar-ion laser as an excitation light source.

3. Results and discussion

Crystalline and chemical properties

Figure 1(a) shows X-ray diffraction (XRD) spectra of the annealed TiO_x/FQ at temperatures from 100 to 450 °C in H₂/Ar atmosphere. The annealed samples below 400 °C show only the broad background features originated from the FQ substrates. However, the annealed ones above 400 °C show a strong (101) peak and relatively weak (200) and (221) peaks corresponding to anatase phase of TiO₂ as shown Fig. 1(a) [35]. This indicates that the as-deposited amorphous titanium oxide films are converted into the crystalline anatase titanium dioxide films by annealing them above 400 °C.

 

Fig. 1 (a) X-ray diffraction spectra and (b) photo images of the annealed TiO_x/FQ at (1) 100, (2) 150, (3) 200, (4) 250, (5) 300, (6) 350, (7) 400 and (8) 450 °C in H₂/Ar atmosphere.

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The anatase crystalline size (L_TiO2) in the annealed films above 400 °C from the XRD pattern shown in Fig. 1(a) is estimated using Scherer relation [35],_{$L_{Ti{O}_2}=k_0\lambda /\Delta \theta \cos \theta$} and ~21 nm where k₀ is a shape factor related constant (~0.9), λ is the x-ray source wavelength, θ is the diffraction angle of an interesting diffraction peak, and Δθ is the full width at half maxima (FWHM) of the peak in radian.

The color of the annealed TiO_x/FQ is varied with the annealing temperature from bluish (below 350 °C) to light yellowish (above 400 °C) as shown in the photo images of Fig. 1(b). This clearly indicates that the crystalline property of the samples (Fig. 1(a)) is directly related to the color appearance (Fig. 1(b)).

The Raman spectra of the annealed TiO_x/FQ samples vary with the annealing temperature and show the distinct features related to anatase TiO₂ (100 to 1000 cm⁻¹) and graphitic carbon (1000 to 2000 cm⁻¹) as shown in Fig. 2(a) and 2(b), respectively. The carbon related features are attributed to adsorption and reaction of residual carbon sources such as carbon dioxide or hydrocarbon during the titanium sputtering deposition and the annealing process.

 

Fig. 2 Raman spectra of annealed titanium oxide films deposited on fused quartz glass. Raman spectra are (a), in the low wave number region, showing features related to titanium dioxide and (b), in high wave number region, showing features (D, G band) related to graphitic carbon materials. (c) The intensity ratio (□) of D band to G band and position (△) of G band of annealed TiO_x/FQ as a function of annealing temperature. (d) The calculated in-plane crystalline length (L_G) of carbon for the annealed TiOx/FQ above 150 °C.

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At lower annealing temperatures than 400 °C, the only broad features related to amorphous titanium oxide are observed in the low wave number region (100 to 1000 cm⁻¹) as shown in Fig. 2(a). At higher annealing temperatures than 350 °C, Raman peaks (E_g, E_g, B_1g, A_1g, and E_g and B_1g mode) related to stoichiometric anatase titanium dioxide phase are observed at 143, 197, 398, 516, 633 and 798 cm⁻¹, respectively [36]. This crystalline phase transition observed in Raman spectra is consistent with that in the XRD spectra shown in Fig. 1(a).

The TiO₂ phase related Raman signal intensities from the annealed at 400 °C are higher than those at 450 °C. This is attributed that the enhancement of the Raman signal is caused by the higher graphitic carbon density at the surface of the annealed film at 400 °C as shown in Fig. 2(b) and the TOF-SIMS profiles of Fig. 3(a) [37].

 

Fig. 3 Normalized ion depth profiles of (a) C⁺, Si⁺, Ti⁺ and (b) O⁺ of annealed TiO_x thin films on fused quartz glass substrates at 100, 150, 200, 250, 300, 350, 400 and 450 °C.

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In region from 1000 to 2000 cm⁻¹, the in-plane bond-breathing mode, D (A_1g) and the stretching mode, G (E_2g) of graphitic carbon are shown in Fig. 2(b). The broad G band features in region of 1440 to 1670 cm⁻¹are observed in the annealed ones below 300 °C while the D band is barely visible. The G band (△) peak position is located around from 1578 to 1573 cm⁻¹up to the annealing temperature of 250 °C as shown in Fig. 2(b) and 2(c).

This indicates that the carbon species shown in the annealed ones below 300 °C correspond to tetrahedral amorphous carbon with high sp³ bonding characteristics [38,39]. When the annealing temperature is above 300 °C, the broad D band features develop gradually in the region of 1200 to 1530 cm⁻¹ and overlap with the G band features as shown in Fig. 2(b) whereas the G band peak position largely shifts to 1595 cm⁻¹ when the annealing temperature is higher than 250 °C as shown in Fig. 2(c).

This clearly indicates that tetrahedral amorphous carbon becomes graphitic nano-crystal with increasing sp² bonding characteristics as the annealing temperature increases [38,39].

However the intensity ratio of D and G band (□) increases and decreases before and after annealing temperature of 400 °C, respectively, as shown in Fig. 2(c). This is attributed to that the higher temperature annealing in H₂/Ar atmosphere causes the higher reaction of the amorphous carbon with hydrogen before forming the graphitic carbon.

Based on the G band shift as well as the intensity ratio of the D band (I_D) to the G band (I_G) shown in Fig. 2(c), the in-plane crystalline length (L_G) of amorphous carbon and nano-crystalline carbon can be estimated. For the annealing temperature lower than 300 °C, the in-plane crystalline length of the tetrahedral amorphous carbon can be obtained by using the relation of_{$L_G=\sqrt{\left(\frac{I_D}{I_G}\right)/C\text{'}(\lambda )}$}, which is proposed by A. C. Ferrari [39]. However, for the annealing temperature higher than 300 °C, the in-plane crystalline length (L_G) can be obtained by the Tuinstra and Koenig (TK) relation of_{$L_G=C(\lambda ){(I_D/I_G)}^{-1}$}. C’(λ) and C(λ) are proportionality parameters and 0.0055 and 44 Å at 514.5 nm wavelength, respectively.

The estimated in-plane carbon lengths of the annealed ones below 300 °C is less than 1 nm as shown in Fig. 2(c) and this indicates that the observed most carbon species are amorphous. The annealed one at 300 °C shows the dramatic increase of the in-plane length (L_G) as much as 7 nm. Above annealing temperature of 300 °C, the in-plane length (L_G) decreases with the annealing temperature as shown in Fig. 2(d). As mentioned above, this is attributed to the higher reaction rate of the amorphous carbon species with the H₂/Ar gas flow at the higher annealing temperature.

The XRD and Raman spectra shown in Fig. 1 and 2 clearly indicate that amorphous TiO_x thin films are converted into crystalline anatase TiO₂ by annealing above 400 °C while the carbon species incorporated into TiO_x during the sputtering and annealing process are also converted into a graphitic carbon. This suggests that the environmental carbon species can act as a dopant (TiO_xC_y) or a coating material (C-TiO_x, C-TiO₂).

Depth dependent chemical species

The depth dependent chemical species of the annealed TiO_x/FQ at 100, 150, 200, 250, 300, 350, 400 and 450 °C are investigated by TOF-SIMS. The SIMS intensity profile of C⁺ (black), Ti⁺ (blue), Si⁺ (red) and O⁺ (black) ions of the annealed titanium oxide thin films on fused quartz glass (SiO₂) substrates are normalized by the Si⁺ ion signals in the glass substrate region and plotted as shown in Fig. 3.

The Ti⁺ ion SIMS depth profiles shown in Fig. 3(a) can be divided into three regions as a few nanometer thick near surface region with high intensity due to the relatively highly oxidized layer as shown in Fig. 3(b), a main film region with relatively flat medium intensity, and a ten nanometer thick interface region between the film and the substrate with highly modulated signal intensities [34]. The flat region indicates that the titanium, carbon and oxygen are uniformly distributed along the depth. The highly modulated features near the interface between the Ti oxide layer and the fused quartz substrates (SiO₂) can be caused by multiple effects [40,41] related to the densification of Ti atoms during sputtering process caused by the energetic ion bombardment as well as the enhancement of the relative sensitivity factor (RSF) of Ti atom due to the highly oxidized substrate of SiO₂. Due to titanium (silicon) diffusion into and reaction with substrate (titanium oxide), the titanium (silicon) signal is shown in the substrate (titanium oxide) region as shown in Fig. 3(a). Based on the interface between TiO_x and SiO₂ (black arrows), the estimated thicknesses of the annealed TiO_x/FQ at 100, 150, 200, 250, 300, 350, 400 and 450 °C are in the range of 58.8 to 68.6 nm.

The C⁺ signals shown along with the Ti⁺ signals indicate that carbon species are almost uniformly coexisted with Ti. The uniform distribution of carbon species suggests that carbon atoms can be appeared as a dopant of TiO_x (TiO_xC_y) while the surface coating of TiO_x particles with graphitic carbon species can't be excluded.

The relatively low C⁺ ion signals near the surface are attributed to the annealing process in H₂/Ar environment. The samples annealed at 150 and 400 °C show the relatively high carbon signals in the film and on the surface, respectively. This is consistently observed in the Raman spectra shown in Fig. 2. This indicates that a competition between carbon adsorption and diffusion on/in TiO_x and reaction with H₂/Ar atmosphere has occurred and depends on the annealing temperature. The more carbon adsorption or doping on titanium oxide is observed at 150 °C but the more reaction of carbon species with H₂/Ar atmosphere is occurred with the higher annealing temperature. Additionally there is another competitive component, which is the less reactive graphitic carbon formation at the higher annealing temperature. The annealing temperature dependent interplay among the adsorption, reaction with annealing gas and crystallization of carbon species modulates C⁺ ion signal intensities as shown in Fig. 3(a). These trends are consistently observed in the Raman spectra as shown in Fig. 2.In addition to the carbon doping of titanium oxide, the less reactive graphitic carbon layer may coat the surface of titanium oxide.

The normalized O⁺ ion signals with respect to the Si⁺ ion signals in the glass substrate region (SiO₂) are shown in Fig. 3(b). Based on the O⁺ ion signal intensity in the substrate region, the O⁺ ion signals in the film region increase with the annealing temperature. This suggests that the titanium oxide films become more oxidized with the annealing temperature. Further in the interface region of TiO_x/FQ, the oxygen signals show a high peak indicating the reaction between titanium and the silicon oxide substrate was high below the 300 °C annealing temperature. However, at the higher annealing temperatures, the reaction of titanium suboxide is more active with the residual oxygen species than with the substrate SiO₂.

As shown in the inset of Fig. 3(a), a periodic modulation (in the flat region at the other low annealed temperatures) of the Ti⁺ signal is observed in the annealed TiO_x/FQ at 450 °C. This Ti⁺ signal intensity modulation with the XRD and Raman studies as shown in Fig. 1 and Fig. 2 clearly indicates that the non-uniform Ti distribution is attributed to the crystallization and stoichiometric TiO₂ nanoparticle formation at 450 °C.

Optical transmittance

Optical transmittance spectra of the as-deposited TiO_x/FQ samples (black line) and the annealed (red line) at (a) 100, (b) 150, (c) 200, (d) 250, (e) 300, (f) 350, (g) 400 and (h) 450 °C for 30 minutes in H₂/Ar atmosphere are shown in Fig. 4. For the as-deposited TiO_x/FQ, the optical transmittance (black line) increases with decreasing wavelength from near infrared to a maxima point of optical transmittance (λ_max~400 nm) and then decreases rapidly as the wavelength decreases after λ_max. This suggests that the as-deposited TiO_x thin films are showing strong resonant absorption in the near UV region and can be suitable for UV filters as well as visible blue and green light transmission windows [34].

 

Fig. 4 Optical transmittance spectra of TiO_x thin films deposited on fused quartz glass substrates before (black line) and after (red line) annealed in H₂/Ar atmosphere at (a) 100, (b) 150, (c) 200, (d) 250, (e) 300, (f) 350, (g) 400 and (h) 450 °C. For comparison, the transmittance spectra of bare quartz substrates are also shown.

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After the annealing process in H₂/Ar atmosphere for 30 minutes, the optical transmittance spectra (red line) of the annealed TiO_x/FQ largely increase with the annealing temperature as shown in Fig. 4. In general, the absorption band edge shifts to lower energy (longer wavelength) in the near UV region. This is attributed to the stoichiometry change of TiO_x and the carbon doping as shown in Figs. 1, 2 and 3. The optical transmittance of the annealed TiO_x/FQ increases but the details depend on the annealing temperature as shown in Fig. 4.

The optical transmittance of the annealed TiO_x/FQ at 100 to 300 °C increases in proportional to the annealing temperature in the longer wavelength region than λ_max as shown in Fig. 4(a)-(e). Above 300 °C, the absorption band edge largely shifts to the longer wavelengths compared to those annealed at lower temperature than 300 °C. Further the optical transmittance of the annealed TiO_x/FQ largely increases and the enhancement of the transmittance for the wavelength longer than 450 nm is proportional to the wavelength. As a result, a broad valley is observed in the region of 400 nm to 500 nm wavelength. The valley becomes narrower with increasing the annealing temperature as shown in Fig. 4(f)-(h). These are related to the stoichiometry change of TiO_x, carbon doping and nano-crystalline TiO₂ formation as indicated by the studies shown in Figs. 1, 2 and 3.

Optical modeling by BR-EMT

The optical transmittance spectra of the as-deposited TiO_x/FQ as well as the annealed TiO_x/FQ were perfectly fitted with the Bruggeman-effective medium theory (BR-EMT) for the films [32] combined with Lorentz-Drude model for the constituent materials, and transfer matrix method for the film/substrate layer structures. The detailed fitting parameters are shown in the appendix Table 1 and Table 2 for the as-deposited and the annealed TiO_x/FQ, respectively. The detailed optical simulation methods using the Lorentz-Drude model and the transfer matrix method are shown in the previous work [34].

Table 1. The BR-EMT optical simulation parameters for the 8 as-deposited TiO_x/FQ samples.

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Table 2. The BR-EMT optical simulation parameters for the 8 annealed TiO_x/FQ samples at various temperatures.

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Based on the observation shown in Figs. 1, 2, and 3, the Bruggeman effective medium theory (BR-EMT) is employed to explain the heterogeneous attribute of the films, which are assumed as a composition of fully oxidized TiO₂ and carbon doped and partially oxidized TiO_xC_y where x + y ≤ 2. The effective dielectric constant based on the Bruggeman model for the inhomogeneous effective medium consisted of TiO₂ and TiO_xC_y can be given by [33]

From the BR-EMT fitting of the transmittance spectra of the annealed TiO_x/FQ (Fig. 4) using Eq. (1), the extracted real and imaginary part of the effective optical dielectric constants are shown in Fig. 5 whereas the employed dielectric constants of titanium dioxide, which are extracted from the reference [42], are also plotted together in Fig. 5(b) and 5(d).

 

Fig. 5 Real part ((a), (b)) and imaginary part ((c), (d)) of annealed TiO_x/FQ dielectric constants in H₂/Ar atmosphere at (a), (c) 100, 150, 200, 250, (b), (d) 300, 350, 400 and 450 °C, respectively. For comparison, the real and imaginary part of dielectric constants of titanium dioxide thin films (gray) are plotted in (b) and (d) [42].

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In the near UV region, the real part effective dielectric constants (ε₁) of the annealed TiO_xC_y/FQ exponentially decay with wavelength at shorter than 450 nm, increase with the annealing temperature and become close to that of titanium dioxide as shown in Fig. 5(a) and 5(b).

The imaginary part dielectric constants (ε₂) decrease with wavelength to a minima point in the UV region. This is related to the optical transmittance maxima shown in Fig. 4. After the minima point, the imaginary part dielectric constants (ε₂) linearly increase with wavelength as shown in Fig. 5(c) and 5(d). Overall, after the minima point of ε₂, the ε₂ values of dielectric constants decrease with the annealing temperature and become closer to that of TiO₂ above the annealing temperature of 400 °C as shown in Fig. 5(c) and 5(d). This implies that the TiO_x thin films are not fully converted to TiO₂. Further, the dielectric constants of the annealed at 400 (green) and 450 °C (blue) are overlapped each other as shown in Fig. 5(b) and 5(d).The annealed ones above 400 °C show a small broad peak in the imaginary part dielectric constants (ε₂) around the wavelength region of 400 ~600 nm. This is attributed to the carbon doping of TiO_x or graphitic carbon coating on TiO_x.

Since the ε₂ value of TiO₂ is assumed to be zero in the longer wavelength than 375 nm as shown in Fig. 5(d), the extracted ε₂ of the effective medium from the BR-EMT simulation is solely determined by that of TiO_xC_y. Thus this allows analyzing the effect of TiO_xC_y caused by the partial oxidation or carbon doping for the optical response of the annealed TiO_x/FQ in region of visible to near IR (375-1000nm).

One can find in the appendix Table 2, the contribution of the Drude terms to ε₂ is two orders of magnitude smaller than those of the Lorentz terms. Thus Fig. 6(a) and Fig. 6(b) only show the bound oscillatory dependent ε₂ with the electron resonant energy of ω₁ (black), ω₂ (red), ω₃ (green) and ω₄ (blue) in TiO_xC_y for annealed at 100, 150, 200 and 250 °C, and 300, 350, 400 and 450 °C, respectively.

 

Fig. 6 Imaginary part of oscillator dependent dielectric constants of TiO_xC_y extracted from the optical modeling of annealed TiO_x/FQ at (a) 100 (solid), 150 (dashed-dotted), 200 (dotted), and 250°C (dashed), at (b) 300 (solid), 350 (dashed-dotted), 400 (dotted) and 450 °C (dashed). ω₁, ω₂, ω₃ and ω₄ oscillators are colored by black, red, green and blue, respectively.

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Generally, the ε₂ (imaginary part) originated from ω₁ (black) oscillators continuously increases with wavelength over the whole wavelength region as shown in Fig. 6. The peak values of ε₂ in the UV region shown in Fig. 5 are largely contributed by ω₃ (green) oscillators, but the influence of ω₃ (4.02 ± 0.27 eV, green) oscillators exponentially decays with wavelength as shown in Fig. 6. As shown in Fig. 6(b), the ε₂ values contributed by ω₂ (2.9 ± 0.37 eV, red) oscillators are broad over the entire visible region but high in the region from 400 to 500 nm. This is related to the valley shown in the optical transmittance spectra of the annealed above 350 °C (Fig. 4(f)-4(h)).

The resonance energy of ω₁ oscillators (1.35 ± 0.15 eV) for the annealed samples below 400 °C is not significantly changed but their ε₂ values are varied with the annealing temperature because their strengths (f₁) are varied with the annealing temperature as shown in Table 2. For the annealed ones above 400 °C, the resonance energies of ω₁ oscillators shift to higher energy (shorter wavelength) in the visible range. As a result, the ε₂ becomes higher in the entire visible region. This is causing the increase of a broad optical absorption in the visible region. The peak shifts of the ω₁ and ω₂ oscillators are largely related to the carbon doping or graphitic carbon coating as well as the stoichiometry change of the titanium oxide indicated by the Raman spectra (Fig. 2), SIMS profile (Fig. 3) and XRD spectra (Fig. 1).

The extracted volume fraction (p₁) and screening factor (k₁) of TiO₂ (Table 1 and 2 in the Appendix) are shown for the as-deposited and the annealed TiO_x/FQ in Fig. 7(a) and 7(b), respectively. With increasing the annealing temperature, the volume faction of TiO₂ almost linearly increases up to ~0.83.

 

Fig. 7 (a) The volume fraction and (b) screening factor of TiO₂ extracted from BR-EMT model before (black) and after (red) annealing process as listed in Table 1 and 2, respectively.

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This indicates that the TiO_x thin films were not fully converted into TiO₂ by the employed low temperature annealing process for 30 minutes.

Before the annealing process, the screening factors (k₁) are almost ~1, indicating that the shape of TiO₂ is close to a rod shape [32]. After the annealing process, the screening factors largely increase with the annealing temperature up to 200 °C, and then decrease with the annealing temperature up to 400 °C as shown in Fig. 7(b). At the annealing temperature of 400 °C, the k₁ values are very close to 2 (red dashed line) corresponding to a spherical shape. The k₁ value of the annealed one at 450 °C slightly increases again.

Optical modeling by 3D-FDTD

Even though the BR-EMT theory accounts the fill factor and shape parameter of the heterogeneous films, the information regarding the specific size of the particles is not accounted. To consider the size effect, the optical properties of the annealed film at 400 °C estimated by BR-EMT are compared with those by full wave Finite Difference Time Domain (FDTD) approach. For the FDTD simulation, it is assumed that crystalline titanium dioxide ellipsoidal particles (r₁, r₂, r₃) having a specific size with a possible void (α) are randomly dispersed in TiO_xC_y which is a host medium formed during the annealing process at 400 °C as shown in Fig. 8.The void formation is considered because crystalline anatase TiO₂ nano-particle formation from the as-deposited amorphous films by annealing can cause the phase separation between the TiO₂ nano-particles and the host matrix as indicated by the XRD (Fig. 1), Raman (Fig. 2) and SIMS (Fig. 3) studies. Additionally, a 2.5 nm thick TiO₂ thin layer is assumed as the outmost layer based on the high oxygen signal in the TOF-SIMS profiles (Fig. 3(b)). The diameters of TiO₂ particles are assumed as ~21 nm based on the analysis of the XRD spectra (Fig. 1). The dielectric constants of the host materials, TiO_xC_y, extracted from the BR-EMT based fitting (Table 2) are employed (See the Appendix). Sellmeier formula for glass [43] are used. To save the simulation burden, the employed thickness of the glass is chosen as 14 nm even though the FQ substrate is 700 μm. Figure 9(a) and 9(b) show 3D-FDTD simulation results with varying the void size (α) and the number of TiO₂ particles as well as the optical transmittance spectra of the annealed TiO_x/FQ at 400 °C, respectively.

 

Fig. 8 The dimension is defined as 500 × 500 × 100 nm³ and thickness of FQ substrates (SiO₂) is limited as 14 nm. For a TiO₂ ellipsoid, length r₁, r₂ and r₃ are radius and the ratio of r₁to r₂ is 0.946 based on the results of BR-EMT model and the radius r₁ is 10.5 nm (based on the XRD). For the size of air shell structure, additional length, α is added to all axes.

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Fig. 9 Replot of the optical transmittance spectra of TiO_x/FQ annealed at 400 °C shown in Fig. 4(g) (black continuous lines). The simulated transmittance spectra (open circle) using three-dimensional FDTD with varying (a) void size and (b) the number of TiO₂ particles, respectively. For comparison, the simulated results of the mediums that only consist of TiO₂ ( × ) or TiO_xC_y (red open circle) are plotted also shown in (a) and (b), respectively.

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For comparison, the FDTD simulated results of TiO₂ ( × ) as well as TiO_xC_y (red circle) for the given thickness of the film are plotted as shown in Fig. 9(a) and 9(b), respectively. The simulation result is shown in Fig. 9(a) by varying the void size (α) from 0 to 2 nm when the number of TiO₂ particles is 3024.

When the void is zero (red circled in Fig. 9(a)), the simulated transmittance is far less than the experimental one. Further when the film is only the homogeneous film of TiO₂ (x marked in Fig. 9(a)), the transmittance is still less than the experimentally observed one. This clearly indicates that the annealed film is neither homogeneous nor a close-packed two component system of TiO₂ nano-particles in TiO_xC_y. As shown in Fig. 9(a), the simulated transmittance increases with void size and becomes close to the experimental one. This strongly suggests that the annealed samples become porous as the annealing temperature increases.

While the void size is fixed to be 1.5 nm, the number of TiO₂ particles varies from 0 to 3024 and the result is shown in Fig. 9(b). The simulated optical transmittance of the host only films (red circled in Fig. 9(b)) is very low as shown in Fig. 9(b). With increasing the number of TiO₂ particles with void, the transmittance increases and becomes similar to the experimental one. The 3024 TiO₂ particles in the given volume is very close to the estimated volume fraction of the annealed TiO_x/FQ at 400 °C based on the BR-EMT. When the void size is 1.5 nm, the simulated results are very close to the optical transmittance of the annealed TiO_x/FQ at 400 °C as shown in Fig. 9. The full wave simulation results clearly indicate that the 400 °C annealed TiO_x/FQ is a mixed heterogeneous structure which consists of TiO₂ nano-particles embedded in TiO_xC_y with some voids.

In the simulation by the full wave FDTD, the employed films are assumed that as a random distribution of nano-particles with uniform size in diameter while the partial overlapping among the nano-particles is allowed. However, the FDTD simulation results show a deviation from the experimental one. This indicates that the employed structures may not be equivalent to the structure of the 400 °C annealed TiO_x/FQ. Another possible origin is related to the effect of the graphitic carbon layer formed on the TiO₂ nano-particles, which are not included in this FDTD simulation because it is out of scope in the present study. Particularly the role of the graphitic carbon layer should be further studied in the crystalline titanium oxide nano-particle formation as well as their optical properties.

4. Conclusions

In conclusion, the sputter deposited non-stoichiometric TiO_x films on fused quartz glass substrates show stoichiometric crystalline phase change, nano-particle formation, chemical composition change, carbon doping or carbon-coating by thermally gentle annealing them in H₂/Ar atmosphere. Carbon bonding state is changed from amorphous carbon to nano-crystalline graphitic carbon, of which the in-plane size is varied from 0.5 nm to 7.4 nm with annealing temperature. The effective medium theory BR-EMT allows getting information of the volume fraction and screening factor related to shape of components while the FDTD method allows considering not only the shape but also the size of TiO₂ particles with a void. The BR-EMT study shows that the ω₁ (1.35 ± 0.15 eV) and ω₂ (2.9 ± 0.37 eV) oscillators are located in the visible region. This is attributed to the carbon doping and oxygen deficiency in titanium oxide, which can play the key roles for photo catalytic ability in the visible region. The volume fraction of TiO₂ obtained from the BR-EMT simulation increases up to ~0.83, indicating that the amorphous TiO_x thin films were mostly converted into TiO₂. The 3D-FDTD simulation indicates that the films become porous by the annealing process. Through this study, their photoresponse behaviors of the annealed TiO_x/FQ are correlated to its chemical composition, crystalline properties, nanostructure shape and size and void. These parameters can be manipulated for various applications such as photocatalyst and solar cell etc.