## 2 Materials and Methods  
Thin films were prepared by gas impulse magnetron sputtering [25; 26; 27]. The metallic Ti target with a diameter of 30 mm and thickness of 3 mm was sputtered in an Ar:O\({}_{2}\) gas mixture with 20% and 30% oxygen content. The flow rates of the working gases were equal to 8 sccm and 32 sccm, and 12 sccm and 28 sccm, for O\({}_{2}\) and Ar, respectively. The gas impulses, injected directly into the target, were synchronised with the magnetron supply unit (MSS2 type, Dora Power System). The locally ignited plasma was obtained at \(<\)6 \(\times\) 10\({}^{-3}\) mbar, with a supply power of 500 W (500 V, 1 A) and 250 W (500 V, 0.5 A). In both cases, the plasma ignition time was 30 ms and the interval between pulses was 70 ms. The coatings were deposited on substrates of n-type (100) silicon (ITE), fused silica (Neyco), and ceramic (BVT Company) substrates mounted on a special holder. The distance between the substrates and the target was 80 mm. The deposition processes were carried out under so-called oxygen-deficient (TiO\(\mathrm{x}^{\mathrm{ODC}}\)) and oxygen-rich conditions (TiO\(\mathrm{x}^{\mathrm{ORC}}\)), consisting of 20% and 30% O\({}_{2}\), respectively. The sputtering time in both processes was equal to 30 min. The deposition rate was around 6.6 nm/min. and 20 nm/min. for ORC and ODC, respectively. The coatings were also annealed in an ambient air atmosphere (at 100 \({}^{\circ}\)C, 200 \({}^{\circ}\)C, 300 \({}^{\circ}\)C, 400 \({}^{\circ}\)C, 600 \({}^{\circ}\)C, and 800 \({}^{\circ}\)C for 2 h) in a tubular furnace equipped with a quartz tube.  
The coatings deposited on silicon were used for the surface and cross-sectional morphology measurements, while the coatings deposited on fused silica were used for the optical and structural measurements. The gas-sensing measurements were performed using the coatings deposited on BVT-ceramic substrates with integrated electrodes.  
The thickness was determined using a Talysurf CCI optical profiler (Taylor Hobson). The thicknesses of the coatings deposited under oxygen-rich (ORC) and oxygen-deficient (ORD) conditions were equal to 200 and 600 nm, respectively. There was no significant change in thickness after additional annealing. The optical properties of the coatings were analysed based on transmittance (T\({}_{\lambda}\)) and reflectance (R\({}_{\lambda}\)) measurements in the range of 250 nm to 2250 nm. Measurements were obtained using UV-Vis and NIR spectrophotometers (NIR 256 and QE 65000, Ocean Optics), and a coupled deuterium-halogen light source (DH-BAL 2000, Micropac). The optical band gap energy (E\({}_{\mathrm{g}}^{\mathrm{opt}}\)) for the permitted indirect transitions was determined on the basis of Tauc plots. The Hitachi SU6600 scanning electron microscope (SEM) was used for surface and cross-sectional observations. The Empyrean PIXel3D (Panalytical) diffractometer was used for structural studies. XRD patterns were recorded in the grazing incidence mode (GXRD) at a 3\({}^{\circ}\) angle with Cu K\(\alpha\) radiation (0.15406 nm). Patterns were analysed using MDI JADE 5.0 software. Gas-sensing properties were measured using 3.5% of H\({}_{2}\) in Ar. The gas response was determined at 200 \({}^{\circ}\)C based on resistance changes and measured with a Keithley 4200-SCS Semiconductor Characterisation System, which was used as an ohmmeter. Before the introduction of a gas, the samples were stabilised in an air environment for 1 h. The continuous flow of air and hydrogen gas was equal to 500 cm\({}^{3}\)/min.