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Optically transparent and electrically conductive semiconducting titanium suboxide nanometer thick films, which are technologically important in a wide variety of applications, show a nonlinear dependency of optical and electrical properties on film thickness and oxidation time. The optical, electrical, chemical, and structural properties of the sputter-deposited titanium suboxide nanofilms on fused quartz glass at room temperature are investigated by varying the film thickness, and the additional oxidation is controlled by the duration of air exposure. The optical properties of the nanofilms are simulated by considering them as both a homogeneous film as well as an inhomogeneous film with the combination of the Lorentz Drude model and the Maxwell Garnett effective medium theory (MG-EMT). Their electrical properties are simulated with the MG-EMT. The optical transmittance, electrical conductivity, secondary ion mass spectroscopy, x-ray photoemission spectroscopy analysis, and simulation of titanium suboxide nanofilms indicate that inhomogeneous film growth and oxidation are responsible for the nonlinear dependency. The oxygen atomic ratios to titanium for the as-deposited films depend on the deposition time and vary in 1.60–1.73, while those exposed to air for seven days increase to 1.79–1.99.
© 2016 Optical Society of America
1. Introduction
Metallic titanium (Ti) and its oxide form, wide-band-gap semiconducting TiO2, have been heavily investigated and utilized for various applications [1–9] because of their unique physical properties. These properties include their extremely high tensile strength per mass density [1] and strong corrosion resistance of the metallic Ti protected by an oxide layer, which naturally forms on Ti in the atmosphere [1,2], and their photocatalytic properties and high dielectric constant of wide-band-gap semiconducting TiO2 [3–10].
Additionally, titanium suboxide (TiOx) films have been widely studied because of their broad potential for applications, including use as a photocatalyst in the UV and visible regions [10–13] as well as in electronic memory devices [14,15], transparent electrodes [16], heat mirrors [16], field-effect transistors [17], and sensors [18] due to their relatively high visible-light activity caused by an oxygen vacancy helping the photoexcitation process at lower energy [10–13] due to their extraordinary electronic properties [14–18]. The outstanding properties of TiOx films vary by their chemical compositions and structures, which depend on their deposition methods [7–9,17,19,20]. The various deposition processes for titanium suboxide films have been studied [7–9,17,19,20]. Among them, the dc (direct current) reactive sputtering process in the presence of ambient gas in the deposition vacuum system is often used for preparation of titanium suboxide film with adjustable chemical composition [20], and it is adapted in this study. In previous works, the various optical modeling investigations for Ti [21] and TiO2 [22] are reported. However, the research on the optical and electrical modeling for TiOx films is not readily available yet.
In this study, optically transparent titanium suboxide thin films were directly sputter-deposited on fused quartz glass substrates at room temperature. Further, the titanium suboxide thin films were intentionally oxidized by atmospheric exposure for various durations. Their physical properties were nonlinearly varied with the deposition and air exposure times. To understand these behaviors, the surface morphology, chemical composition, sheet resistance, and optical transmittance of the titanium suboxide thin films were systematically investigated. The optical properties of the deposited nanofilms were simulated by considering the films as homogenous films as well as inhomogeneous films with the Lorentz-Drude (LD) model and the Maxwell Garnett effective medium theory (MG-EMT). The extracted dielectric properties of the optically transparent titanium suboxide nanometer thick films based on these two approaches were compared [21,23]. The parameters extracted from the optical modeling based on MG-EMT allowed us to estimate the reasonable electrical conductivities, which agree with the experimental ones. The inhomogeneous film growth is related to the sputtering process, which generates titanium and titanium suboxide clusters where titanium clusters are oxidized with ambient oxygen species. The inhomogeneous film growth and the oxidation are responsible for the nonlinear dependencies. From the comparative studies and the simulations, the atomic composition of TiOx is assigned.
2. Experimental details
A. Deposition and native oxidation of titanium suboxide nano-thin films on glass
Titanium suboxide nanofilms were deposited on fused quartz (FQ) glass substrates of 25 × 25 × 0.7 mm3, which were supplied by Crystal Bank in South Korea. The deposition processes of titanium suboxide thin films were as follows. The substrates were cleaned by an ultra-sonicator with acetone and IPA (isopropyl alcohol) for 15 minutes, respectively. The cleaned substrates were loaded into a vacuum chamber and then the chamber was evacuated at a relatively medium vacuum (~ 10-4 Torr). Then high purity (99.99%) argon gases of 20 sccm as a sputtering gas were injected by controlling the flow with an MFC (mass flow controller). Titanium was deposited on glass substrates by sputtering (with power of ~ 80 W) a 2-inch round titanium target (purity 99.99%) using a dc magnetron sputter for a desired time at room temperature. Titanium suboxide thin films are deposited on the substrates due to the reaction of highly reactive Ti with ambient oxygen species such as oxygen and water, which are present in the chamber during the deposition at the pressure of ~ 1 mTorr. The target and the substrates are apart by about 9 cm. Before deposition of Ti on glass substrates, the Ti target was sputtered for 3 minutes to eliminate the possible surface oxide layer of the titanium target. The sputter-deposited Ti suboxide thin films were exposed to air for 10 minutes, 2 days, and 7 days before characterization of them was done, and they are referred as Ti-10m, Ti-2D and Ti-7D, respectively.
B. Characterization
The optical and electrical properties of titanium suboxide films deposited on FQ glass substrates were investigated by taking their optical transmittance spectra using a UV-vis photospectrometer (Scinco S-4100) and measuring their sheet resistance using a 4-point prober with a 2400 sourcemeter (Keithely). For surface chemical composition analysis, x-ray photoemission spectra (XPS) were taken at normal emission using a PHI 5000 VersaProbe (Ulvac-PHI) with a monochromatic Al Kα (1486.6 eV) x-ray source. The surface morphologies of the titanium suboxide thin films were investigated by an atomic force microscope (AFM), which was operated in noncontact mode. The depth profile and the chemical species of the titanium suboxide films were investigated using time-of-flight secondary ion mass spectroscopy (TOF-SIMS) with Cs+ and Bi+ ion guns for sputter (area of 300 μm × 300 μm) and analysis (area of 100 μm × 100 μm), respectively.
3. Surface morphology and chemical composition
Figure 1 shows AFM images of titanium suboxide films deposited for one, two, five, and nine minutes and exposed to the air atmosphere for 2 days. Figure 1 clearly shows that the surface morphologies significantly vary with the deposition time. The surface of the one-minute deposited film is relatively flat with a few islands of ~10 nm in diameter [Fig. 1(a)]. However, the surface of the two-minute deposited film becomes rougher, with some disconnected spherical islands of ~20 nm in diameter [Fig. 1(b)]. The surface of the five-minute deposited film shows a large number of spherical islands, while their diameters are maintained [Fig. 1(c)]. The nine-minute deposited film shows many islands with large connection among the particles, while their diameters are ~20 nm [Fig. 1(d)]. The relatively flat surface at the thinnest film thickness [Fig. 1(a)] and the surface formation with spherical islands having relatively uniform diameters as the film thickness increases suggest that the direct bombardment of sputter-generated clusters to the substrate induces flat surfaces or interface [24].
Fig. 1 AFM images of titanium suboxide films deposited for (a) one, (b) two, (c) five, and (d) nine minutes, respectively. Before taking the images, they are exposed to the air atmosphere for 2 days. The image size is 200 nm by 200 nm. The top right corner shows the expanded scale bar of the vertical scales for better visibility.
Figure 2 shows the Ti 2p and O 1s XPS core-level spectra taken from a ~58-nm-thick titanium suboxide film deposited on glass with air exposure for two days. The core level spectra of Ti 2p2/3 are deconvoluted into four Gaussians with peaks at 455.3, 456.5, 457.5, and 458.7 eV, corresponding to Ti1+, Ti2+, Ti3+, and Ti4+, respectively [25]. The Ti 2p core-level spectra corresponding to metallic Ti (Ti0) species (peaks at 454.4 eV) [25] were not observed. This indicates that the metallic Ti may not exist due to oxidation during the deposition, or the native oxide layer covering Ti due to air exposure for 2 days may be thicker than the escape depth (~1.5 nm) of electrons in TiOx [26].
Fig. 2 (a) Ti 2p and (b) O 1s XPS core-level spectra of TiOx (58.2nm)/FQ exposed to the atmosphere for 2 days.
4. Thickness and bulk chemical species
The thickness and the bulk chemical species of one-, two-, five-, and seven-minute deposited TiOx films on FQ glass substrates with a two-day air exposure are investigated by TOF-SIMS as shown in Fig. 3. There are significant signals from Ti+, TiO+, Si+, and O+, which originated from the films as well as the FQ glass substrates as shown in Figs. 3(a) and 3(b). The depth-dependent profiles from the relatively thick films show three distinct regions: the surface region with relatively high signal intensity, the middle region with almost flat signal intensity, and the interface region with highly modulated signal intensity with two peaks.
Fig. 3 (a) TOF-SIMS Ti+ and Si+ ion profiles, and (b) TiO+ and O+ ion profiles of TiOx thin films deposited on FQ glass for one, two, five, and seven minutes. (c) The deposition duration dependent thickness of TiOx thin films.
In the few-nanometer-thick surface region (depth), the relatively high signal intensities of Ti+ [Fig. 3(a)], TiO+, and O+ [Fig. 3(b)] are observed, and this is often attributed to the enhancement of relative sensitive factors by relatively significant surface oxidation as indicated by the XPS studies shown in Fig. 2.
In the interface region, two modulated peaks are observed in Ti+, TiO+, and O+ signals near by the interface as shown in Figs. 3(a) and 3(b). The modulations can be related to the flattened film at the interface between the film and the substrate as suggested by Fig. 1, even though the origin of the modulation may be complicated with interfacial roughness, charging effects, or matrix effect, to name a few [27]. It is not pursued in this study because it is beyond the scope of the present work.
The flat regions are relatively free from the surface and interface effects. The flat signal intensities suggest that the films are relatively uniformly deposited. However, in the narrow region between the flat region and the interface region, Ti+ signal intensities are relatively low compared to those in the flat region. This suggests that the layer in the narrow region is relatively porous, even though this may not exclude the possible interference with the interface effect.
The titanium suboxide film thickness is determined from the depth profiles of Ti+ and Si+, which originated from the films and the substrates, respectively, as shown in Fig. 3(a). The thicknesses of the TiOx thin films are 7.3, 18.9, 34.3, and 51.5 nm, corresponding to 1-, 2-, 5-, and 7-minute depositions, respectively. The nanofilm thickness almost linearly increases with the deposition duration as shown in Fig. 3(c).
The present SIMS measurements do not allow for quantitative analysis but indicate the chemical species that appeared in the films. The relatively uniform depth profile of TiO+ and O+ shown in Fig. 3(b) shows that the nanofilms are significantly oxidized [28].
5. Optical transmittance and sheet resistance
Figure 4(a) shows optical transmittance spectra of sputter-deposited titanium suboxide thin films on FQ glass substrates for one (black), two (red), five (green), and seven (blue) minutes, with air exposure for 10 minutes (solid), 2 days (dashed), and 7 days (dotted lines). The transmittance of bare glass substrates are shown also. Overall, the transmittance of titanium suboxide films on glass substrates decreases as the deposition time increases, but the transmittance reduction depends on the wavelength and is not linear with the deposition time.
Fig. 4 (a) Optical transmittance spectra of TiOx deposited for one (black), two (red), five (green), and seven (blue) minutes on fused quartz glass substrates: As-deposited (Ti-10m, solid line), and exposed for 2 days (Ti-2D, dotted line) and for 7 days (Ti-7D, dashed line) to atmosphere. The experimental transmission spectra are fitted with optical models based in homogeneous as well as inhomogeneous mediums. The optical spectra of the 7-minute deposited TiOx films are vertically shifted by - 0.2 for the clear presentation. (b) Sheet resistance of titanium suboxide films on quartz glass substrates with variations in thickness and ambient air exposure durations.
In the UV region, optical transmittance rapidly increases with wavelength (λ) up to the maximum transmittance (at λp ~350 nm). This indicates that there is a strong resonant absorption or reflection at the wavelength just below 350 nm (~energy bandgap of TiOx). In the visible region, the transmittance decreases with the wavelength, while in the near-infrared (IR) region the transmittance is fairly flat. This indicates that the nanofilms act as a transmittance window for the visible region, while they act as a filter for the UV region. The transmittance window in the visible region becomes narrower with the thickness of the titanium suboxide film. This nonlinear depenence on the deposition time could be related to the contributions of the oscillators in the IR region, or it could be that the free-charge carriers become stronger with deposition time, even though the origin should be uncovered.
When titanium suboxide films are exposed to the ambient atmosphere, transmittance in the UV region is lowered, but the transmittance of titanium suboxide films becomes higher in the visible and near-infrared region with increasing the exposure time. As a result, the peak wavelength (λP) corresponding to the maximum transmittance shifts to longer wavelengths, as shown in Fig. 4(a). The longer air exposure reduces the absorption edge energies (longer wavelength), and this can enhance the visible light photoresponsivities. However, the air exposure increases the transmittance uniformly over the region of a wavelength longer than λP. This suggests that the oscillatory strength in the UV region becomes stronger with the air exposure, while the oscillator strengths located at the near IR region and the free electron contributions become weaker by the additional oxidation.
The measured sheet resistance of titanium suboxide films with variations in thickness and ambient air exposure time is shown in Fig. 4(b). For the as-deposited titanium suboxide films (Ti-10m), the sheet resistance is not inversely proportional to the film thickness. Additionally the sheet resistance with the air exposure largely increases by 5 ~23 times and depends on the deposition time, as shown in Fig. 4(b). Compared to the thicker films, the thinner (one and two-minute deposited) films show a higher sheet resistance change with the air exposure, even at only a two-day exposure. Unexpectedly, the seven-minute deposited films show higher sheet resistance than that of the five-minute deposited films. These nonlinear behaviors in optical transmittance and electrical resistance suggest that the films grow inhomogeneously.
6. Optical modeling
XPS core level spectra (Fig. 2), SIMS studies (Fig. 3), nonlinear optical transmittance [Fig. 4(a)], and nonlinear sheet resistance [Fig. 4(b)] indicate that the nanofilms consist mostly of titanium suboxides and are inhomogeneous. During the sputter deposition of titanium, titanium clusters together with atomic titanium can be sputter-generated and cause the formation of spherical islands [24]. During the deposition, the surface of the cluster can be oxidized with ambient oxygen species.
However, the core of the cluster can exist as metallic Ti due to protection from oxidation by the covered oxide layers. Thus, in the fitting of the optical transmittance spectra shown in Fig. 4(a), the titanium suboxide nanofilms are considered as two possible forms: homogeneous films and inhomogeneous films. The dielectric properties of the titanium suboxide films are modeled with the LD model having four oscillators. The optical transmittance spectra of the nanofilms are simulated as homogenous films using the LD model and as inhomogeneous films using MG-EMT, with titanium suboxide as a host and metallic titanium as a guest. The details are shown as follows. The dielectric properties of constituent metallic titanium and semiconducting titanium suboxide are modeled with the LD model. In both approaches, the curved fittings are perfectly matched with experimental ones as shown in Fig. 4(a).
A. Optical transmittance of TiOx film on FQ glass
The optical transmittance spectra of titanium suboxide thin films were fitted with the relations obtained by a transfer matrix method [29]. The titanium suboxide film on a fused quartz glass substrate is considered as double layers of a homogeneous (or inhomogeneous) TiOx layer and FQ glass surrounded by atmosphere as shown in Figs. 5(a) and 5(b).
Fig. 5 Schematic diagram of the titanium suboxide thin film (optical constants: n1-jk1) with thickness of t1 on a glass (n2) substrate with thickness of t2 in air (n0 = n3 = 1) for (a) homogenous and (b) inhomogeneous medium based models.
Optical transmittance of the double-layer system at normal incidence of light with a wavelength of λ can be given by Eq. (1) [29]:
where andand andwhere t1, n1 and k1 are the thicknesses and the real and imaginary parts of the optical constants of titanium suboxide films, while t2 and n2 are the thicknesses and optical constants of FQ glass, respectively.Due to thick glass substrates and the monochromatic coherent property of the light source employed in the simulation, multiple reflections in the thick medium cause interference features. Since the experimental transmittances of the samples were taken using an incoherent light source, interference in the simulation is avoided by intentionally adding phase terms (δ) of 0, 2π/3 and 4π/3 to the phase term (γ2) related to the substrates.
The optical constants of FQ glass substrates are calculated by using the Sellmeier formula from the experimental optical transmittance spectra of FQ glasses shown in Fig. 4(a) [30]. The obtained Sellmeier coefficients for the employed glass substrates are listed in Table 1 (see the Appendix).
Table 1. Extracted Sellmeier Coefficients from Transmission Spectra of FQ Glass Substrates Shown in Fig. 4(a)
The optical constants are related to dielectric constants by
B. Lorentz–Drude model
The Lorentz–Drude (LD) model is adapted for the optical dielectric constants of the titanium suboxide thin films [22]. εr (ω) = εr(f) (ω) + εr(b) (ω), where εr(f) (ω) and εr(b) (ω) are related to free electrons and bound electrons, respectively. The complex dielectric function of free electrons based on the Drude model is given by
where ωp, f0, and Γ0 are plasma angular frequency, oscillatory strength, and collision-rate constant of free electrons, respectively. The employed bulk plasma energy (ℏωp) of titanium is 7.29 eV [21]. The complex dielectric function of bound electrons is given bywhere ωi, fi, and Γi are resonant frequency, oscillatory strength, and resonance width of oscillator i, respectively. In this study, four oscillators for bounded electrons are chosen.The real part (ɛ1) and imaginary part (ɛ2) of the effective complex dielectric constants (εr = ε1 – jε2) can be expressed, respectively, as below:
The optical transmittance spectra of titanium suboxide films on FQ glass substrates shown in Fig. 4(a) are fitted based on the homogeneous medium models [Fig. 5(a)] using Eq. (1), and the fitting parameters are shown in Table 2 (see the Appendix).
Table 2. Extracted Oscillatory Strength (fi), Damping Rate (Γi) and Resonance Energy (ωi) of TiOx Thin Films Based on Homogeneous Medium Models for As-deposited (Ti-10m), 2 Day (Ti-2D) and 7 Day (Ti-7D) Exposed Titanium Suboxide Films to Atmosphere
C. Effective medium theory (Maxwell-Garnett) for inhomogeneous films
To simulate the inhomogeneous films as shown in Fig. 5(b), the Maxwell–Garnett effective medium theory (MG-EMT) is employed. The effective dielectric constants based on MG-EMT is given by [23]
where εg, and εh are dielectric constants of Ti, and TiOx, respectively, and p and k are the fill factor and shape related to the screening factor of the guest material, respectively. The optical transmittance spectra of titanium suboxide thin films based on the inhomogeneous medium models are fitted using Eq. (1) and Eq. (17), and they are perfectly matched with the experimental optical transmittance spectra shown in Fig. 4(a). The previously reported LD-model-based dielectric constants for Ti are used in the simulation [21]. The fitting parameters are listed in Table 3 (see the Appendix).Table 3. MG-EMT Fitting Parameters of Fill Factor (p), Screening Factor (k), Oscillatory Strength (fi), Damping Rate (Γi), and Resonance Energy (ωi) for TiOx When As-deposited (Ti-10m), 2 Day (Ti-2D), and 7 Day (Ti-7D) Air Exposed Titanium Suboxide Films Are Considered as Inhomogeneous Mediums That Consist of Ti (Guest) and TiOx (Host)
7. Optical dielectric constants
From the curve fittings based on homogeneous (black lines) and inhomogeneous (red lines) medium models complex dielectric constants are extracted, and their real (ɛ1) and imaginary parts (ɛ2) are plotted as a function of titanium suboxide film thickness and air exposure times, as shown in Figs. 6(a)-6(d) and Figs. 6(e)-3(h), respectively. For comparison, the real and imaginary dielectric constants of TiO2 [22] and Ti [21] extracted from the literature are plotted by gray (TiO2) and brown (Ti) solid lines in Figs. 6(d) and 6(h) and in Figs. 6(a) and 6(e), respectively.
Fig. 6 Based on homogeneous film (black lines) and inhomogeneous film (red lines) models, the extracted real [(a) - (d)] and imaginary part [(e) - (h)] of the effective dielectric constants of titanium suboxide thin films deposited for (a) one, (b) two, (c) five, and (d) seven minutes: As-deposited (Ti-10m, solid line), and exposed for 2 days (Ti-2D, dotted line) and 7 days (Ti-7D, dashed line) to atmosphere. For comparison, the real and imaginary parts of the dielectric constants of metallic Ti (brown) and TiO2 (gray) are plotted in (a) and (d) and (e) and (h), respectively [21,22]. In graphs of (a), (b), (e), and (f), dashed-dotted lines appeared and are caused by the large overlapping of curves for Ti-2D (dotted) and Ti-7D (dashed).
When the as-deposited nanofilms (Ti-10m) are considered as homogeneous mediums, the real part dielectric constants (ɛ1) are positively high at around 300 nm in wavelength, then monotonically decrease as the wavelength increases, and cross the zero value in the visible wavelength range of 450 ~550 nm. The cross point depends on the film thickness as well as the air exposure duration, as shown in Figs. 6(a)-6(d). The films exposed to air show the positively higher ɛ1, particularly at the UV and IR regions. Thus zero cross points shift to longer wavelengths with air exposure.
The imaginary parts (ɛ2) show a dip in the visible wavelength region (400 ~600 nm) corresponding to the transmission window, as mentioned in Fig. 4(a), and they increase with a shorter wavelength in the UV region and with a longer wavelength in the near IR region. This suggests that the resonance energies of oscillators with a relatively strong oscillatory strength are located in UV region (ω3 and ω4) and near IR region (ω1), as shown in Table 2. With longer air exposure, the imaginary parts (ɛ2) become significantly lower as the wavelength increases in the visible and IR region.
When films are considered as inhomogeneous mediums and their transmission spectra are fitted with MG-EMT [Eq. (17)], the wavelength-dependent behaviors of the extracted effective dielectric constants are also shown in Fig. 6 (red curves). The overall trends are similar to those based on the assumed homogeneous films as shown in Fig. 6. Particularly, for the two and five-minute deposited films, the extracted dielectric constants based on the two approaches largely resemble each other as shown in Figs. 6(b), 6(c), 6(f), and 6(g). This suggests that the two- and five-minute deposited films are relatively homogeneous compared to the one- and seven-minute deposited films.
For one-minute as-deposited thin films, the real part (ɛ1) of the extracted dielectric constants based on the effective medium theory is small at short wavelengths, and becomes negative slowly, unlike those based on the homogeneous systems as shown in Fig. 6(a. However, their imaginary parts (ɛ2) are higher than those based on the homogeneous systems shown in Fig. 6(e). Unlike this, the real part (ɛ1) of the extracted dielectric constants for the seven-minute deposited films based on the effective medium theory show higher values compared to those based on the homogeneous medium model, particularly at the short wavelength as shown in Fig. 6(d).
In both approaches, the minima of ɛ2 is located around 400 nm in wavelength due to the weak contributions of bounded and free electrons to the dielectric constants, as expected from the peak in the transmission spectra, shown in Fig. 4(a). As the light wavelength moves away from the resonant wavelengths, the bounded electron oscillatory strength exponentially decays and the free electron contribution to ɛ2 linearly increases. This causes the wavelength-dependent minima points of ɛ2. At these regions with small ɛ1, transmittance is high (transmission window) as shown in Fig. 4(a). After the minima points of ɛ2, the ɛ2 continuously increases, because the contribution of free electrons and the IR oscillators increase proportionally to the wavelength.
8. Oscillatory strength changes
When titanium suboxide films are exposed to air, ɛ1 becomes more positive with the increase of ambient gas exposure time for both models, as shown in Figs. 6(a)-6(d), while ɛ2 increases at the shorter wavelength region but decreases at longer wavelengths than the wavelength of the minima of ɛ2, as shown in Figs. 6(e)-6(h). This is related to the oscillatory strength changes as shown in Fig. 7. The oscillatory strength of the optically transparent titanium suboxide thin films extracted from the both models based on the homogenous films (upper panels, □) and the inhomogeneous films (lower panels, △) varies with the deposition time as well as the air exposure duration, as shown in Fig. 7.
Fig. 7 Upper panels: From simulations for as-deposited (Ti-10m, red) and exposed for 2 days (Ti-2D, green) and 7 days (Ti-7D, blue) to atmosphere of one-, two-, five-, and seven-minute deposited titanium suboxide films as homogenous films (□), the extracted the oscillatory strengths of (a) free electron (ƒ0) and (b) - (e) bound electrons (f1, f2, f3, f4). Lower panels: From the simulations of the titanium suboxide films as inhomogeneous films (MG-EMT) (∆), the extracted oscillatory strengths of (a) free electron (f0´) and (b) - (e) bound electrons (f1´, f2´, f3´, f4´) for the host TiOx.
In the homogenous film-based simulation of titanium suboxide films, the fill factor f0 corresponding to free electrons for the most films is less than 0.2 but is ~0.39 for the one-minute deposited films. The strongest (~0.6) oscillators (ω4) are mostly located at 4.6 ± 0.2 eV except for the seven-minute deposited films, of which the ω4 oscillators are located at 6.5 ± 0.8 eV as shown in Table 2. The strengths of the other oscillators are relatively weak and are less than 0.2. Particularly, the strength of ω2 (~3 eV) oscillators located in the visible range is the weakest and less than 0.1.
The strength of the ω4 oscillators increases with the air exposure time as shown in the upper panel of Fig. 7(e). The strength of ω4 oscillators for the five-minute deposited films is less than the others. In contrast, the oscillatory strength of ω3 (4.2 ± 0.1 eV) for five-minute deposited films is the highest among them as shown in the upper panel of Fig. 7(d). The ω3 oscillatory strength also increases with air exposure.
However, the oscillatory strengths of ω1 (1.4 ± 0.1 eV) and ω2 (3.1 ± 0.1 eV) decrease with the air exposure time as shown in the upper panel of Figs. 7(b) and 7(c), respectively, as expected. This implies that the oscillators of ω1 and ω2 in the IR and visible range are related to partially oxidized titanium species with a low oxygen composition ratio to titanium. Oscillators of ω3 and ω4 in the UV region are related to titanium suboxides with a high oxygen composition ratio to titanium.
In the case of the simulation based on inhomogeneous mediums, the fill factors of Ti are mostly less than 0.1 except for the one minute deposited films as shown in Fig. 8(a). The oscillatory strength f0' of the as-deposited films is barely varied with the deposition time, while further oxidization in the air reduces their strength, as shown in the lower panel of Fig. 7(a). This is attributed to partially oxidized titanium with low oxygen concentration that is vulnerable to additional oxygen exposure.
Fig. 8 (a) Fill factors of Ti (□) and TiOx (∆) and (b) screening factor obtained using MG-EMT as a function of deposition time and exposure time. (c) The effective thickness of the titanium suboxide films obtained by the SIMS studies ( × ) and the optical modelings (based on homogeneous (□) and inhomogeneous (∆) films) as function of deposition time and exposure time. (d) The calculated resistivities of the films (□) (1/σeff) and the host TiOx only ( × ) (1/σh) based on the measured sheet resistance and the effective thickness. The oxygen-to-titanium ratio-dependent resistivity (diamond) is extracted from the literature [18].
The oscillatory strength of ω1' (1.35 ± 0.05 eV) increases with deposition time. The oscillatory strength of ω1' for one- and seven-minute deposited films is insensitive to the air exposure, but the two- and five-minute deposited films show significant reduction of ω1' oscillatory strength with the air exposure, as shown in the lower panel of Fig. 7(b). The behaviors of the oscillators corresponding to ω2' (3.15 ± 0.05 eV) are opposite those of ω1' oscillators, as shown in the lower panel of Fig. 7(c).
The oscillator strength of ω3' (4.1 ± 0.1 eV) increases with air exposure except for the one-minute deposited films, as shown in the lower panel of Fig. 7(d). This again suggests that the ω3' oscillators are related to the titanium suboxide species with higher oxygen concentration. The oscillator strength of ω4' (4.8 ± 0.5 eV) depends less on deposition time and air exposure time except for the one- and seven-minute deposited films, as shown in the lower panel of Fig. 7(e). This also suggests that the ω4' oscillators are largely related to the highly oxidized titanium species.
The simulation based on the mixtures of titanium guest and homogeneously distributed host TiOx indicates that the TiOx with low x are sensitively oxidized with air exposure. Thus the fraction of TiOx with high x increases with the additional air exposure. This suggests that the f0' and f1' are largely related to highly oxygen-deficient TiOx, but the ω3' and ω4' oscillators are related to almost fully oxidized species.
9. Fill factors, screening factors, conductivity and stoichiometry
The fill factors of Ti obtained by MG-EMT are slightly varied with deposition time and air exposure time, as shown in Fig. 8(a). However, the screening factors are largely varied as shown in Fig. 8(b). The screening factors for the nanofilms are less than 1 except for the one-minute deposited as-deposited films (~2), and they become smaller with the air exposure as shown Table 3 and Fig. 8(b). This suggests that the shape of the Ti guest largely varies with the deposition time as well as the air exposure duration. The guest titanium becomes more rod-shaped with air exposure [23], while the one-minute deposited as-deposited film acts like a continuous film, as expected from Fig. 1(a).
The Ti fill factors of seven-minute deposited films are insensitive to air exposure, and this indicates that metallic Ti is largely protected by thick-enough titanium suboxide layers [31]; thus, the screening factor changes are also minimal. On the other hand, for one-minute deposited very thin films, air exposure causes the relatively large variation in the fill factor as well as the large change in the screening factor.
The thickness of the two-day air exposed films was determined from the SIMS studies shown in Fig. 3. Based on these, the effective thickness for the other films is determined with optical simulations shown in Table 2, Table 3, and Fig. 8(c). The effective thickness increases with air exposure due to increasing oxidation as shown in Fig. 8(c). Using the measured sheet resistance shown in Fig. 4(b) and the thickness shown Fig. 8(c), the resistivities with variants in thickness and ambient air exposure time are estimated as shown in Fig. 8(d). For the as-deposited TiOx films (Ti-10m, red square marks), the resistivity nonlinearly depends on the films thickness [Fig. 8(d)] and the trends resemble the inverse of the screening factor [Fig. 8(b)].
The relatively smooth one-minute deposited film shown in Fig. 1(a) shows a relatively high screening factor as expected. This is attributed to the fact that sputter-generated clusters become flattened due to the direct bombardment of titanium clusters on the glass substrates. This is evidenced by the signal intensity modulation at the interfacial region in the SIMS data shown in Fig. 3. But the films deposited for longer times show larger spherical islands as shown in Fig. 1. Particularly, the onset for significant island formation occurred at the two-minute deposition time, as shown in Fig. 1(b). After exposure to the air, the resistivity significantly increased with the air exposure time in a nonlinear manner, as shown in Fig. 8(d) (green and blue squares for 2- and 7-day air exposure, respectively). Especially, the resistivity of TiOx films deposited for two minutes largely increased after exposure to the atmosphere for seven days. This indicates that TiOx films deposited for two minutes are significantly oxidized due to the relatively large effective surface area of the nonconnected islands for oxygen adsorption.
Effective conductivity (σeff) of the titanium suboxide thin films is given by the fill factor [Fig. 8(a)], screening factor [Fig. 8(b)], and effective thickness [Fig. 8(c)] extracted from the fitted optical transmission spectra, based on the MG-EMT and the Ti conductivity (σg) from the literature [32] as below [33].
where σg and σh are conductivities of the guest (Ti) and the host (TiOx), respectively.The conductivity of the host titanium suboxide films is obtained by
The calculated resistivities of the effective titanium suboxide films (1/σeff) and the host (1/σh) are shown in Fig. 8(d) (□ and x, respectively). The lower fill factor [Fig. 8(a)] causes higher resistivity as indicated by Eq. (18). Another factor to influence the conductivity is the screening factor (k) as shown in Eq. (18) and Eq. (19). Screening factors for the seven-minute deposited films [Table 3 and Fig. 8(b)] show the lowest values, which indicate the thinnest rod shape of the guest Ti [23]. Thus the MG-EMT predicts the highest resistivities for two-minute deposited films, and this agrees with the experimental results shown in Fig. 8(d).
In comparison with the stoichiometry-dependent conductivity of TiOx from the literature [18], the atomic composition ratio (x) of oxygen to titanium of the investigated host films is assigned. This shows that, for the as-deposited films of TiOx for one, two, five, and seven minutes, the atomic composition ratios (x) are 1.60, 1.75, 1.72, and 1.73, respectively. With the seven-day air exposure, their ratios largely increase to 1.92, 1.99, 1.79 and 1.90, respectively. These are consistent with the XPS, SIMS, optical ,and electrical studies shown in Figs. 2, 3, and 4, respectively.
10. Conclusions
In conclusion, titanium suboxide nanofilms show nonlinear optical and electrical responses to film thickness and air exposure duration. This is because the optically transparent titanium suboxide thin films deposited by sputtering at room temperature on glass substrates are grown as inhomogeneous films rather than homogeneous films. Particularly, the shape of the Ti guest plays important roles in the nonlinear optical and electrical responses to the film thickness and oxidation. During sputtering in a medium vacuum, the titanium clusters are deposited and oxidized on glass substrates. However, the inner core of the clusters is not fully oxidized, even with further air exposure at room temperature. The MG-EMT-based modelings on the dielectric, electrical, and chemical properties of the titanium suboxide nanofilms are relevant to the experimental observations. The optically transparent, electrically conductive titanium suboxide nanofilms shown in this study can be useful for various electro-optical applications.
Appendix Tables
The tables below show Sellmeier coefficients, medium models, fitting parameters, and other pertinent information outlined in this paper.
Acknowledgment
This research was supported by Basic Science Research Program through the National Research Foundation of South Korea (NRF) funded by the Ministry of Education (NRF-2013R1A1A2063162).
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