Electrically-active defects in reduced and hydrogenated rutile TiO2

We report on electrically-active defects located between 0.054 and 0.69 eV below the conduction band edge in rutile TiO2 single crystals subjected to reducing and hydrogenating heat treatments. Deep-level transient spectroscopy measurements recorded on TiO2 samples subjected to different heat treatments are compared. In samples annealed in H2 gas, three defect levels are commonly observed. One of these levels, E192 , located 0.43 eV below the conduction band edge is tentatively assigned to a hydrogen-impurity complex. Two levels at 0.054 and 0.087 eV below the conduction band edge, which were present after all different heat treatments, are tentatively assigned as being related to O vacancies or Ti self-interstitials. Deep-level transient spectroscopy spectra of samples heat-treated in N2 display a larger number of defect levels and larger concentrations compared to samples heat-treated in H2 gas. N2 treatments are performed at considerably higher temperatures. Four energy levels located between 0.28 and 0.69 eV, induced by annealing in N2 , are tentatively attributed to O vacancy- or Ti interstitial-related complexes with impurities.


Introduction
Rutile titanium dioxide (TiO 2 ) is a wide bandgap semiconductor (E g = 3.2 eV [1][2][3][4]) that is well-known for its photocatalytic properties [5,6], enabling applications such as photocatalytic water-splitting and water purification [6][7][8][9][10]. Reduced and/or hydrogenated TiO 2 (TiO 2−x :H) has gained interest because it displays enhanced photocatalytic activity [11][12][13]. The photocatalytic performance of TiO 2 can be Original Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. improved further by the presence of defects that promote the transfer of charges to reactive species [1,14]. Additionally, defects can extend the optical absorption of TiO 2 into the visible part of the electromagnetic spectrum [15][16][17]. Recently, Nitta et al identified a correlation between the photocatalytic performance of certain TiO 2 powders and the energy distribution of shallow electron traps [9,18]. For TiO 2−x :H, hydrogen (H) and intrinsic defects whose formation is favourable under reducing conditions, such as oxygen vacancies and and Ti self-interstitials [16,19], can be expected to play a key role.
In applications, TiO 2 is usually used in the form of powders or nano-crystals [9,18], making fundamental studies concerning the electronic properties of defects in the materials challenging. In contrast, single-crystalline TiO 2 can function as a model system for defect studies. Particularly, single crystals which have been subjected to hydrogenating and/or reducing heat treatments might display a defect chemistry comparable to the one found in TiO 2 used for photocatalysis, and are therefore important to study.
Deep-level transient spectroscopy (DLTS) is a powerful method for investigation of electrically-active defects [20]. However, reports regarding DLTS on defects in TiO 2 are scarce [21][22][23]. One reason for this is the challenge of fabricating high quality Schottky barrier diodes (SBDs) on TiO 2 . In our recent paper, we have shown that Schottky barrier diodes between Pd and TiO 2−x :H suitable for space-charge spectroscopy can be fabricated [24]. Using DLTS, we identified several defect-related charge state transition levels in TiO 2−x :H [23], but no clear assignments to certain defects have so far been made. The heat treatments consisted of anneals in either closed ampoules filled with H 2 gas or in flowing gas, such as forming gas (FG) or N 2 . Three defect energy levels with positions of about 0.070, 0.095, and 0.12 eV below the conduction band edge, E c , occurred in all the studied samples, irrespective of the sample production batch and the heat treatment used. In samples annealed in FG flow, seven distinct levels in the range 0.057-0.63 eV were detected. In samples annealed in H 2 gas, four distinct levels in the range 0.049-0.47 eV were detected. In samples annealed in N 2 flow, six distinct levels in the range 0.063-0.40 eV were detected. No defect with a charge state transition level in the 0.20-0.70 eV range below E c was present after all of the different heat treatments, indicating a strong influence on deep-level defects by the post-growth heat treatments employed [23].
The present paper aims to further investigate electricallyactive defects in TiO 2 single crystals subjected to reducing and/or hydrogenating heat treatments. Here, we extend the previous study to different annealing temperatures and durations, and follow the evolution of different defects. This data are crucial for identification of the defects. Additionally, the paper examines the role of H in electrically-active defects in TiO 2 . The interstitial hydrogen concentration, [H i ], of crystals annealed in H 2 gas, is deduced from Fourier-Transform infrared spectroscopy measurements, prior to electrical measurements. The correlation between [H i ] and transition level concentrations is investigated.

Samples
The study described here was performed on float-zone (FZ) grown rutile TiO 2 single crystals with a surface orientation of (001), purchased from MTI Corporation [25]. Asreceived crystals were 0.5 mm thick, nominally undoped, transparent, and semi-insulating with a conductivity of σ < 10 −7 Ω −1 cm −1 . Doping by heat treatments was necessary to perform electrical measurements on the TiO 2 single crystals. Conductive n-type TiO 2 single crystals are known to display a bluish color [26][27][28][29][30][31][32]. Conductive n-type TiO 2 samples of bluish colour was obtained by heat treatments in hydrogenating and/or reducing atmospheres [23,24]. Hydrogen was introduced either by annealing in FG flow (N 2 + H 2 with [H 2 ] / [N 2 ] ≈ 1/9) at 600-740 • C for 25-90 min or by annealing in closed ampoules filled with approximately 0.5 bar of H 2 gas at 400-600 • C for 10-60 min. Additionally, samples were annealed in N 2 flow for 1-25 h. Samples heat treated in N 2 flow were annealed at the same time in the furnace, but were exposed to different temperatures in the range 900-1200 • C due to their different locations inside the furnace. For the N 2 -annealed samples the temperatures were determined to 900 • C, 1050 • C and 1200 • C within ±30 • C by measuring the temperature-profile of the furnace with a thermocouple element. In the following, the crystals are labelled according to their heat treatment; TiO 2 -N 2 (annealed in N 2 flow), TiO 2 -FG (annealed in FG flow) and TiO 2 -H 2 (annealed in closed ampoules with H 2 gas). The samples are labelled according to their annealing temperature (T anneal ) and annealing duration (t anneal ), for example, 450 C-60 min.
In order to have a reference sample that had not been heattreated, rutile TiO 2 single crystals doped with 0.01 wt% of Nb were purchased from Shinkosha [33]. These crystals were 0.5 mm thick with a surface orientation of (001), and were grown by the Verneuil (V) method. The as-received TiO 2 -Nb crystals exhibited n-type conductivity and a bluish color, with a conductivity of 0.048 Ω −1 cm −1 . The Nb-doped sample is denoted as TiO 2 -Nb.
Schottky barrier diodes (SBDs) were obtained by e-beam evaporation of 150 nm Pd on the (001) surface of the TiO 2 crystals [24]. The Pd contacts were deposited using Si or Al shadow masks with typical diameters between 300 and 500 µm. InGa or Ti/Al was used as Ohmic back contact. Characterization of the crystals and the SBDs are described in detail elsewhere [24].

Experimental set-up
The electrical conductivity, σ, of TiO 2 single crystals was determined by using a four-point probe measurement according to the van-der-Pauw method [34,35]. The measurement utilized a Keithley 7001 switching system, a Keithley 2182A nano-volt-meter and a Keithley 6221 current source. Eutectic InGa pads were used as Ohmic contacts in the corners of the samples.
Fourier-Transform infrared (FT-IR) spectroscopy was used to determine [H i ] in TiO 2 single crystals prior to metal contact deposition. Infrared (IR) transmittance spectra were measured using an evacuated Bruker IFS 125HR spectrometer equipped with a globar light source, a KBr beamsplitter, and a liquidnitrogen-cooled InSb detector. The IR beam was kept at normal incidence (±3 • ) with respect to the (001) surface of the  [36] using a calibration factor determined by Johnson et al [37]. Secondary ion mass spectrometry (SIMS) measurements were performed using a Cameca IMS 7f instrument with a primary beam of 10 keV O 2 + ions. Rutile TiO 2 samples implanted with Cr, Al, Si or Fe were used as references to obtain absolute concentration values. For other residual elements, relative concentrations were determined. A constant erosion rate was assumed for depth-calibration, where the crater depths were measured using a surface Stylus Profilometer.
Capacitance-voltage (CV) measurements were carried out at room temperature using an Agilent 4284A LCR meter or a Boonton 7200 capacitance meter, respectively. The donor concentration, N d , was deduced from CV measurements, using the depletion approximation [38], a probing frequency of f meas = 1 MHz, and assuming a value of ϵ TiO2 = 160 at room temperature for the static relative dielectric constant of TiO 2 [39,40].
DLTS was conducted using a refined version of the setup described elsewhere [41], which utilizes a Boonton 7200 capacitance meter and a closed-cycle He cryostat. During measurements, reverse bias voltages between −6 V and −2 V were applied. Filling pulses with an amplitude of 2-6 V and a duration of 50 ms were employed. The DLTS signal was extracted from the acquired capacitance versus time transients using a lock-in weighting function with six different rate windows in the range from (20 ms) −1 to (640 ms) −1 or a GS-4 weighting function with five different rate windows in the range of (40 ms) −1 to (640 ms) −1 [20,42,43]. A delay time of 5 ms and a temperature (T) resolution of 0.5-1 K were used. Measurements were performed during heat-up in the temperature range 20-300 K. The apparent capture cross-section, σ ap , and the thermal activation energy, E A , for the deep-level defects were deduced from simulating the DLTS spectra as described in detail in [44]. The peaks in the DLTS spectra are labelled after the peak temperature position of the longest time window measured (rate window [640 ms] −1 ). The defect concentration, N, can be deduced from the DLTS signal, assuming a uniform and sufficiently low ≤ 0.1N d defect distribution, where [20].
Here, ∆C is the amplitude of the measured capacitance transients [20,42], while C rb is the steady-state reverse bias capacitance.

Impurities and interstitial hydrogen concentration
The impurity content of TiO 2 crystals was investigated with SIMS. A typical mass spectrum of a conductive TiO 2 crystal is shown in figure 1(a). The measurements reveal that Al, Si, Cr and Fe are present in the crystals. It should be noted that the mass spectrum shown in figure 1(a) is not a direct measurement of impurity concentrations because the count rates depend on both the concentration and the ionization probability of an impurity. In order to deduce the concentrations, one has to measure a calibration sample with known impurity concentrations. For the sample for which data are shown in figure 1(a) Heat treatments in H 2 gas, FG flow or N 2 flow led to TiO 2 single crystals with a bluish color and n-type conductivity in the range from (0.5 − 8) × 10 −2 Ω −1 cm −1 . Figure 1(b) shows IR absorption coefficient spectra of the 3278 cm −1 H i LVM for as-received and heat-treated samples. Data are shown for the wavenumber region where optical absorption associated with a local vibrational mode of H i can be seen [36]. In the as-received, nominally undoped crystals,  figure 1(b). The difference between the spectra is smaller than the measurement uncertainty.
[H i ] was measured to be 1.8 × 10 16 cm −3 in the as-received TiO 2 -Nb crystal, which is an order of magnitude lower than [H i ] in the as-received, nominally undoped crystals.  figure 1(b). For the most conductive sample, which was annealed at 600 • C for 10 min, the strong absorption due to charge carriers masks the OH spectral region, and prevents quantitative evaluation of [H i ]. For this sample, [H i ] was estimated to be 8.9 × 10 18 cm −3 from its value for σ, assuming that the linear relationship between [H i ] and σ holds [47]. All DLTS spectra of TiO 2 -H 2 samples display three defect levels; two shallow levels located around 0.087 and 0.11 eV below E c (E 40 and E 55 ), and a level located at 0.43 eV below E c (E 192 ). Measurements using different reverse biases do not reveal Poole-Frenkel effect for E 40 , E 55 and E 192 , which suggests acceptor nature. These levels correspond to E 3,H2 , E 4,H2 and E 5,H2 reported in our previous paper [23]. E 192 is the dominating peak in the TiO 2 -H 2 samples. [E 192 ] is in the range of 2 × 10 15 cm −3 to 2 × 10 16 cm −3 , one order of magnitude larger than the concentrations of the shallow levels present in the same spectra. A comparison of the three  samples that were annealed at 450 • C for different durations, shows that [H i ] and N d both increase with annealing time. However, the corresponding DLTS spectra do not display a similar dependence. The DLTS spectrum recorded for the sample annealed at 600 • C, with significantly larger [H i ], display DLTS peaks with similar amplitudes compared to those in spectra recorded for samples annealed at 450 • C.

TiO 2 -FG crystals.
Similar to the hydrogenating treatment in closed ampoules filled with H 2 gas, the forming gas heat treatment also increases the [H i ] compared to that of the as-grown crystal ( figure 1(b)). Annealing in FG, however, requires higher temperatures and/or longer annealing times for achieving sufficiently conductive crystals for junction spectroscopy. For instance, annealing of a crystal in H 2 gas at 600 • C for 10 min was sufficient in order to fabricate suitable SBDs. In comparison, TiO 2 -FG crystals required an annealing duration in the order of 1 h to achieve conductive crystals and to fabricate suitable SBDs [24]. This is corroborated by comparing FT-IR spectra shown in figure 1. [H i ] is similar for the TiO 2 -H 2 sample annealed at 450 • C for 60 min and the TiO 2 -FG sample annealed at 600 • C for 25 min. Therefore, TiO 2 -FG samples are expected to be more heavily reduced, compared to TiO 2 -H 2 samples, and other defects may appear, that were not present in TiO 2 -H 2 samples. Another major difference between the annealing procedures in FG flow and H 2 gas is the cooling process afterwards. While the TiO 2 -H 2 samples were allowed to cool down inside the ampoule until they reached room temperature, FG annealed samples were quenched in air, or cooled down in flowing gas, placed at the cooler part of the annealing tube. The exposure to air at elevated temperatures might lead   E 132 and E 157 correspond to E 5,N and E 6,N previously detected in FZ-grown TiO 2 -N 2 [23]. The three TiO 2 -N 2 samples in figure 4 (1200 C-25 hr, 1050 C-25 hr and 900 C-25 hr) originate from a single wafer.
The annealing data reveal an intricate formation kinetics for E 132 and E 157 . E 132 appears in the sample annealed at 900 • C, and has a higher concentration in the sample annealed  at 1050 • C. However, an increased T anneal of 1200 • C results in a lower concentration. In contrast, E 157 hardly appears in the sample annealed at 900 • C, but shows a strong growth with increasing T anneal . E 293 and E 263 demonstrate a similar behaviour as E 132 and E 157 : E 293 is present in the sample annealed at lower T anneal , but [E 293 ] nearly stabilizes for T anneal > 1050 • C. E 263 , on the other hand, shows a strong growth with increasing T anneal , similar to E 157 .

Shallow levels
Four DLTS peaks are visible in the temperature region 25-55 K. E 25 , observed in some DLTS spectra recorded on TiO 2 -FG samples, appears at very low temperatures and was not resolved for all the measurements performed. E 33 is observed Table 1. Defect levels present in rutile TiO 2 samples. Activation energy, E A , and apparent capture cross-section, σap, were deduced from simulations of DLTS spectra [44]. The uncertainties of E A and σap is around 10% and one order of magnitude, respectively.  [22]. We determined a slightly higher activation energy of 0.43 eV for this level. However, variations between different samples are observed when calculating E A [23]. The value for the energy level reported by Duckworth et al falls within the range of E A that we determine, taking into account fitting errors and the scatter between the measured samples [23]. Duckworth et al estimated σ ap to be 3 × 10 −16 cm 2 [22], which is one order of magnitude larger than σ ap,192 deduced here (see table 1). Duckworth et al also reported two small features on the low temperature side of the main peak in the DLTS spectrum. There is no indication of several contributions to the E 192 peak in the DLTS spectra shown in figure 2 or figure 3. Furthermore, analysis of the data using the GS4 weighting function [43], which provides a better energy resolution than the lock-in weighting function, did not reveal any additional contributions to this peak.

Observed in crystal
As mentioned in previous sections, the recorded concentrations of E 132 , E 157 , E 263 , and E 293 indicate that the levels have an intricate formation kinetics. For example, for the data shown in figure 4, E 132 starts to grow prior to E 157 , and stabilizes or even decrease at higher temperatures. In contrast, E 157 starts to grow after E 132 , and [E 157 ] increases monotonically with temperature. The dependence of [E 132 ] and [E 157 ] on annealing temperature is shown in figure 6. Such a behaviour can be explained if E 132 is a precursor for E 157 . Besides, E 132 and E 157 have electronic levels close to each other, which may indicate their similar nature. We observe formation of E 132 and E 157 after N 2 treatment at ∼1000 • C, which is expected to introduce V O and Ti i . Thus, both E 132 and E 157 can be tentatively attributed to V O -or Ti i -related defects. One can put forward the following speculation of the formation kinetics: where X is an impurity. Similar considerations can be put forward for E 263 and E 293 . In table 1, the activation energy determined by DLTS, the apparent capture cross-section and tentative assignments, are summarized. E A is the activation energy for thermally-induced electron emission from a defect, and is the sum of the single thermodynamic charge-state transition level, E t , and the corresponding energetic barrier for electron capture [34,53].

Conclusion
The effect of annealing temperature on electrically-active defects in single-crystalline rutile TiO 2 was investigated by annealing nominally undoped TiO 2 in H 2 gas, FG flow, or N 2 flow. DLTS spectra recorded after different heat treatments were compared to the DLTS spectrum of a Nb-doped reference sample that had not been annealed. The spectra recorded on the reference sample display a single peak, E 192 . This peak responds to treatment in H 2 , but does not directly follow the [H i ] determined from IR measurements. Therefore, we tentatively assign E 192 to an impurity-hydrogen complex, denoted A-H, where A = Si, Al, Cr, or Fe.
In spectra recorded on heat-treated samples, the two levels E 40 and E 55 are commonly observed regardless of the type of heat treatment. A strong correlation between [E 40 ] and [E 55 ] demonstrates that the two levels are related to either different charge states of the same defect or different structural configurations of the same defect. Since E 40 and E 55 respond to reducing heat treatments, they are attributed to V O -and/or Ti irelated defects.
Four additional charge state transition levels, E 132 , E 157 , E 263 and E 293 , located between 0.28 eV and 0.69 eV below E c , are induced by annealing in N 2 . These levels are tentatively attributed to V O -or Ti i -related defects. Their formation kinetics seem to suggest E 132 and E 293 being precursors to E 157 and E 263 , respectively.