Nb-doped Ti2O3 Films Deposited Through Grid-Assisted Magnetron Sputtering on Glass Substrate: Electrical and Optical Analysis

This study was supported by the Government of the State of Santa Catarina through the FUMDES and FAPESC programs.


Introduction
Titanium oxides are semiconductor materials that have two main stoichiometries: TiO 2 and Ti 2 O 3 . Titanium dioxide TiO 2 has been extensively investigated in the last three decades due to its various technological applications in different areas such as catalysis, optical and electronic devices, biology 1,2,3 .
Much research is focused on improving the harvesting of solar light and its conversion into other forms of energy or chemical reactivity. The strategy for this purpose can be done by doping TiO 2 in order to reduce the band-gap energy and to achieve absorption in the visible light region.
In 2005, Furubayashi et al. 4 reported that Nb-doping into TiO 2 (anatase) produced transparent conducting oxide (TCO) films. The resistivity of such films was as low as 10 -4 Ω.cm at room temperature. Since then, many papers have been published on this topic due to the interest in the application of this material in different devices, including flat panel displays (FPD), light-emitting devices (LED), solar cells and photo-induced activity 5,6,7 . Given that, TiO 2 :Nb has been investigated as an alternative material to substitute ITO films due to the toxic nature of the indium. Titanium niobium oxide has been obtained through different processes because niobium is substitutionally incorporated in the TiO 2 host at cationic lattice sites 8 . The changes in the electronic structure of TiO 2 due to Nb doping have already been discussed in the reported literature 9 . Because of the presence of the extra "d" electron, Nb should populate the metal "d" band, thus yielding an oxide metallic system 10 . The Nb donor gives a shallow state, forming Ti 4+ and Nb 5+ ions 11 . The ionic radius of Nb 5+ is slightly larger than that of Ti 4+ (r (Ti4+) =0.605 Å versus r (Nb5+) =0.64 Å) and has dimensions similar to Ti 3+ . Therefore, Nb 5+ can be easily doped into the lattices of TiO 2 and Ti 2 O 3 at high concentration 12 .
In order to facilitate the doping of Nb 5+ ions into the TiO 2 crystalline structure, in place of Ti 4+ , two mechanisms have been proposed: 1) one Ti 4+ cation vacancy is created for every four Nb 5+ ; and 2) reducing Ti 4+ to Ti 3+ for every Nb 5+ incorporated is also possible 13 . The metastable anatase phase of TiO 2 (band gap of 3.2 eV) is of great interest for Nb-doping, which, in optimized conditions, can achieve a resistivity on the order of 10 -4 Ωcm. Nb-doped rutile TiO 2 is resistive, and from photoemission experiments, it has been found that Nb introduces a deep state lying about 0.8 eV below the conduction band 9 .
On the other hand, it was found that TiO 2 should be slightly oxygen-deficient or annealed in a reducing atmosphere, otherwise the donor (Nb) action may not be effective 8 . The problem is that the donors may be compensated by interstitial oxygen anions if the TiO 2 anatase polymorph has high oxygen content. Therefore, to avoid interstitial oxygen in the TiO 2 structure, the films should be deposited with low oxygen partial pressures. When performing deposition through magnetron sputtering, the film should be deposited before the poisoning point threshold on the hysteresis curve of the cathode voltage versus pressure plot. In other words, the deposition of oxygen-deficient film should be carried out in metallic mode. Films deposited in oxygen-deficient conditions correspond to those at Ti 2 O 3 :TiO 2 equilibrium, and it can be expected a mixture of different titanium oxides (TiO 2 and Ti 2 O 3 ), as reported by other authors 14,15 From the literature, the Ti 2 O 3 oxygen-deficient phase has gained less attention in comparison to stoichiometric TiO 2 . However Ti 2 O 3 features thermochromic and photocatalytic properties, allows absorption of visible light, has relatively high electrical conductivity and is able to serve as a transparent conductor (TCO) 16,17 . This paper will study the optical and electrical properties of niobium-doped dititanium trioxide (Ti 2 O 3 :Nb) films. The Ti 2 O 3 :Nb system may improve the film's electrical properties by considering two effects, namely: 1) Ti 2 O 3 may be considered as a sub-oxide of TiO 2 and leads to the donation of electrons in Ti 3d bands; and 2) the donor Nb should also populate the metal "d" band.
Moreover, crystalline Ti 2 O 3 films are easier to obtain than TiO 2 , without recovering by annealing. It is a very important point when films are deposited on a temperature-sensitive substrate, in which thermal annealing is not possible.
It is well known that film crystallinity may be improved through biasing the substrate during film deposition 6 . It increases the energy of the incoming ions, allowing the adatoms to migrate to more suitable sites. Pulsed bias is suitable for deposition of insulator films by reactive sputtering, thus avoiding the accumulation of static charge on the surface of the dielectric film during the deposition process 18,19 . Previous studies have demonstrated improvement of the crystallinity of Ti x O y and Ti x N y films through the negative pulsed biasing substrate 20 . Thus, in an attempt to produce films with good transmittance and low electrical resistivity, the effect of the Nb-doping and the pulsed bias on the electrical and optical properties of oxygen deficient Ti 2 O 3 thin films, deposited by grid assisted magnetron sputtering (GAMS), was investigated.

Experimental Procedure
Ti 2 O 3 :Nb films were deposited onto borosilicate glass substrates (0.16×16×16 mm 3 ) using GAMS. This system differs from conventional magnetron sputtering due to a grounded grid that is strategically placed in front of the target (at approximately 2 cm from the cathode surface). Such an arrangement improves the plasma stability and allows for operating the system at slightly lower pressure. It shifts the first critical point in the hysteresis curve and allows for better control of the sputter process and film properties 21,20,22,23,24 .
In the first step, the process parameters for optimized films with stoichiometry and crystalline structure closest to Ti 2 O 3 , without recovering by annealing, were established. These parameters are shown in Table 1. The process parameter chosen to be studied was the substrate bias, which could be selected on either "DC mode" or "pulsed mode", within a voltage range of 0 V to -200V. The plasma was powered by a DC power supply, controlled in current and voltage up to 2.0 kV. In the current study, the film depositions were carried out with a target power density of 6.0 W/cm 2 .
A set of hysteresis experiments was carried out to determine the conditions for deposition of the sub oxide Ti 2 O 3 . Indeed, from these experiments, the value of reactive gas flow closest to the metallic mode threshold on the hysteresis curve (known as the first critical point) was determined. Figure 1 shows the critical point on the hysteresis curve for the working pressure as a function of the oxygen flow rate. All depositions were made at this threshold of the metallic mode. Results show semi-transparent films with bluish color (shown in detail in Fig. 1), indicating the formation of oxygen-deficient Ti x O y .  Preliminary tests showed that the most effective bias voltage range impacting on the microstructure and crystallinity of films was between -100V and -200V, in both DC and pulsed modes. DC bias voltage below |-100V| is not effective because the ion current drawn at the substrate is not sufficiently energetic; on the higher limit, a bias voltage above |-200V| produced excessive re-sputtering on the film surface. Other authors have found a significant increase in the ion current drawn at the substrate holder due to the pulsing substrate bias voltage in the mid-frequency range 100-350 kHz 14 . However, within this frequency range, the voltage "time off" is too short for cancelling the static positive charge accumulated at the insulator substrate (this neutralization should be done mainly by electrons flowing from the glow discharge).
Pulsed bias voltage were applied at the substrate holder, relative to the ground. During the negative pulse of voltage bias, the positive ions are attracted to the holder; subsequently, when the bias falls to zero volts, electrons and energetic negative ions (e. g. negative oxygen), coming from the plasma, can also impinge on the holder due the lower potential barrier. In this way, by pulsing the bias voltage, it is possible to neutralize the static charges on the surface of the insulator film. The surface of the insulator substrate is thereby bombarded by ions and electrons at every period. In the present case, the required period for efficient pulsed biasing (e. g. the time needed for the current to drop to zero Ampere) was approximately 1 ms. Learning from this, in pulsed mode, the film deposition was carried out with a bias frequency and duty cycle of 1.0 kHz and 20%, respectively. As it will be shown, this bias condition produces relevant changes in film crystallinity.
The deposited films were characterized by X-ray diffraction (Shimadzu XRD-6000), UV-Vis-NIR spectrophotometry (Shimadzu model UV-3101) and four-point probe electrical measurements using the van der Pauw method. The chemical composition of the films was obtained from energy dispersive X-ray fluorescence spectrometer (EDX) analysis using a Shimadzu EDX-720/800HS device. Results showed that Nb/Ti ratio was 0.11±0.02 for all films deposited.
Transmittance T and reflectance R measurements (between 250 nm and 1200 nm) allowed for the determination of the band-gap energy of the Ti 2 O 3 :Nb films through the Tauc Plot method 25 . The absorption coefficient α and film thickness d were fitted using the SCOUT software package 26 through equation 1 27 . (1) The refractive index (η) and extinction coefficient (κ) as a function of the wavelength, as also the thickness of individual layers, can be obtained from the reflectance and transmittance measurements. This can be done because Reflectance (R), Transmittance (T) and Absorptance (calculated from T and R) depend of the optical constants and thickness of those layers. Thus, fitting the data simultaneously with a specific model, the calculation of spectral optical constants, can be performed 28,29,30 . The experimental transmittance and reflectance curves were modelled using a commercial optical simulation program (SCOUT).
The model used in this software assumes that there are several types of oscillators, each one with their own characteristic resonant frequency, allowing calculation on the frequency dependence of the complex dielectric constants r Drude TL where I is the electric current, B is the magnetic field (in Gauss), d is the film thickness, q is the elementary charge, V s is the Hall voltage and R s is the sheet resistance. These measurements were carried out under dark conditions at room temperature, using a four-point probe in the van der Pauw configuration 33 , with a magnetic field of 1.0 T, and using a Keithley 2410 current meter. Table 2 shows the bias current and film thickness for different values of bias voltage. Results indicate that the bias current was higher for pulsed voltage (at peak) than for DC bias. This is attributed to the exchange of static charge on the surface of the dielectric substrate; the surface of the insulator substrate is thereby bombarded by ions and electrons at every period increasing the current on the substrate. The effect of DC bias on the film thickness is negligible. On the other hand, in pulsed mode, a higher bias voltage (-200 V) produces thinner films when compared to a lower voltage (-100 V). It is well known that energetic ions accelerated in high voltage may produce re-sputtering of adatoms, thus decreasing the film thickness 19 . Taking into account the information in Table 2, it is possible to correlate the intensity of XRD peaks with the bias current; that is, the film crystallinity increases as the bias current increases. The ion bombardment promotes the formation of oxygen vacancies and the bluish color can be due to some charge transfer forming Ti 3+ . TiO 2 reduction was seen after neutron and electron 11 bombardment. The oxygen vacancies associated with Ti 3+ valence state originates an in-gap state in the form of an intermediate band just below the conduction band of the host material. No diffraction peaks associated with niobium oxide were detected, despite the high concentration of Nb in the film (Nb/Ti ratio of 0.11 ± 0.02). Thermodynamic data suggest that the synthesis of Ti x O y is more likely than Nb x O y because the heat of formation of the former is greater 34 . In addition, as discussed in the introduction, Ti 4+ and Nb 5+ have a very similar ionic radius, and Ti 3+ has higher radius, allowing for a large solid solution of Nb in the titanium oxide structure. These diffraction peaks appear to be slightly shifted to lower angles (~0.2º), which can be due to the compressive biaxial residual stress usually induced by high substrate polarization. Additionally, this shift to lower angles can also be due to a lattice distortion caused by substitutional Nb atoms, taking into account the aforementioned difference in ionic radius of the metal ions. This data cannot exclude the formation of niobium oxide, which could be located in the grain boundaries. Figure 3 shows the optical transmittance results of ensemble film/substrate. The highest average transmittance (~50%, between 400 nm and 600 nm) was achieved for Ti 2 O 3 :Nb films grown providing bias of -200 V in pulsed mode. However, in this condition, the films are thinner than the rest (see Table 2), and this is the main reason that it has the highest transmittance, as discussed below. Figure 4 shows a standard optical property normalized regarding the film thickness, that is, the intrinsic absorption coefficient α(λ). It was calculated from values of the transmittance (T), reflectance spectra (R, not shown) and thickness (d) of the films obtained through the SCOUT software 26 , as described in ref. 32 . The complex refractive index ñ is usually defined as equation 4.

Results and Discussions
The real part of ñ, namely n, is refrative index, and the imaginary part k is extinction coefficient. The extinction    Fig. 3 shows a wavy curve between 400 and 500 nm that suggests the presence of interference effects because the thickness of films and reflection of air-film and film-glass substrate. In most cases it is possible to ignore multiple reflections between the front and back surfaces 32 and, thus, equation 1 can be used. It is useful when semiconductor laser diodes or optical bistabilities are studied. In many cases, the effects are small enough to be neglected as the results found in the literature 32,27,35 . This is why tables of transparent optical materials properties generally list only the real parts 32,36 .
The simulations obtained with Scout and with equation 1 are very similar in the spectrum range between 400 nm and 1200 nm , and α is about 35x10 5 m -1 , without changing significantly for films obtained with different bias voltages. Therefore, different values of transmittance (as seen in Figure 3) can be attributed mainly to the change in thickness of the coatings. However, from 500 nm to about 1000 nm, an increase in the absorption coefficient is registered, as seen in Figure 4, which can be correlated with the presence of oxygen vacancies. This absorption band is attributed to Ti 3+ -Ti 4+ charge-transfer 37,38 and is also an additional confirmation of the presence of titanium ions in the Ti 3+ oxidation state. Figure 5 shows the refractive index results as a function of wavelength for the produced Ti 2 O 3 :Nb films. The average refractive index values shown are close to those reported in the literature (between 1.9 and 2.3 for Ti 2 O 3 39 , between 2.49 and 2.54 for anatase, and between 2.79 and 2.90 for rutile, for visible range) 40 . According to studies conducted elsewhere 40 , the refractive index depends on properties such as film density and homogeinity, lattice distortion (for example, due to dopants and impurities), degree of crystallinity and residual stress of the film. In this paper, films grown providing -100V pulsed as substrate bias feature a slightly higher refractive index than the rest.
The higher refractive index may be due to the increase in film density and improvement of crystallinity and overall homogeinity caused by moderate ion bombardment during film deposition, as well as due to the presence of a mixture of different titanium oxides. However, these hypotheses need further investigation. Figure 6 shows the Ti 2 O 3 :Nb band-gap energy evolution with applied substrate biasing, calculated through the Tauc method for indirect transitions 25,41 . Results show a small increase of band gap energy from 3.26 ± 0.06 eV to 3.33 ± 0.06 eV for films deposited with voltage bias -100 V and -200 V in DC mode, respectively. An increase from 3.19 ± 0.06 eV to 3.35 ± 0.06 eV was also observed for films grown providing -100 V and -200V in pulsed mode respectively. The band gap energy values are lower than those presented in the literature for TiO 2 :Nb (3.68 eV) 42 , but are close to the values for pristine TiO 2 . Table 3 shows a comparison between band gap values for: TiO 2 8,40 , TiO 2 :Nb 9,42 , Ti 2 O 3 43 , and Ti 2 O 3 :Nb (obtained in this work). In addition, the bluish aspect is an evidence that a fraction of titanium ions exists in Ti 3+ valence state. Nakamura et al 44 proposed a band structure model with oxygen vacancy state lying 0.75 eV below the conduction band. The ionization energy, i.e. band-gap energy between the oxygen vacancy states and conduction band, was calculated using the Tauc plot for direct transitions and is in the range of 0.57 to 0.69 eV in the present films, as shown in Figure 7; this is correlated with the number of oxygen vacancies created during film growth 44 .
These results are in agreement with reported values in the literature, corresponding to localized states that lay between 0.6 and 1 eV below the conduction band 45 . These states are considered important for photocatalytic oxidation processes, and could be responsible for the enhancement in the electrical properties, as shown later in this manuscript. Figure 8 shows the results for electrical resistivity, charge carrier concentration (mainly electrons, as indicated by the Van der Pauw measurements) and electron mobility. An electrical resistivity of ~10 -2 Ωcm for as-deposited Ti 2 O 3 :Nb films was observed. This value is at least five orders of  magnitude lower than electrical resistivity of bulk Ti 2 O 3 , as reported 46 . The decrease in resistivity is attributed to the presence of an extra "d" electron, from Nb, that should populate the conduction "d" band of Ti 2 O 3 :Nb, as discussed above. Fig. 8a shows the resistivity slightly decreasing when the film is deposited with pulsed bias instead of DC bias. It may be related to the improvement in the film crystallinity and decreasing of defects, when the films are deposited with pulsed bias, since this leads to less charge scattering centers. For depositions with the same bias voltage, the observed results are quite interesting because while the charge carrier concentration (Fig. 8b) decreases, the mobility (Fig. 8c) increases. This happens when there is a change in substrate bias mode from DC to pulsed. Although the cause for the decrease in charge carrier is not clear, charge carrier mobility may increase by reducing lattice defects that act as scattering centers. Therefore, increasing mobility (caused by higher crystallinity in pulsed mode) leads to a reduction of film resistivity, despite the results showing a decrease in charge carrier concentration.

Conclusions
When doped with Nb, the sub-oxide Ti 2 O 3 films reveal properties of a transparent conductor oxide (TCO), As-deposited Ti 2 O 3 :Nb films on glass substrate through grid-assisted magnetron sputtering showed electrical resistivity values on the order of 10 -2 Ωcm. However, Ti 2 O 3 :Nb resistivity values are two orders of magnitude greater than those known for TiO 2 :Nb with post annealing.
Regarding the optical properties, Ti 2 O 3 :Nb films show optical transmittance between 30% and 50% for incident radiation between 400 nm and 700 nm, that is, in the visible optical range, this value is close to that achieved for ITO 47 . The estimated band gap energy is similar to that of pristine anatase TiO 2 , of approximately 3.25 eV. The presence of titanium ions in the Ti 3+ oxidation state is in accordance with the results obtained by XRD, with the identification of the Ti 2 O 3 phase, with an absorption band in the region 500-1200 nm, and by the gap state 0.6 eV below the conduction band Electrical property results revealed that DC pulsed substrate biasing decreases the resistivity for Ti 2 O 3 :Nb films. Pulsed bias increases substrate current and improves film    crystallinity and homogeneity, which tends to reduce charge scattering centers and, thus, the electrical resistivity. This GAMS deposition technique was shown to be promising for obtaining low resistivity and high transparency thin films, dispensing with a subsequent heat treatment; hence, more interesting for large-scale production.

Acknowledgments
This study was supported by the Government of the State of Santa Catarina through the FUMDES and FAPESC programs.