# Photoconductive TiO\({}_{2}\) Dielectrics Prepared by Plasma Spraying
## 2 Experimental Section
### Characterization Techniques
#### 2.2.2 Dielectric Parameters  
If a difference in electric potential is applied across the plates of a capacitor, an amount of charge will be stored between the parallel plates. This increase is proportional to the relative permittivity of the material used, which is dependent on the degree of polarization or charge displacement in the material. Capacitance describes the ability of a material to concentrate electrostatic flux within the spatial volume that the material occupies. Capacitance recalculated according to the dimensions of the dielectric layer gives the relative permittivity (called also \"dielectric constant\").  
The dielectric parameters of plasma-sprayed TiO\({}_{2}\) were measured on a square sample with a circular measurement electrode, forming a ceramic disc capacitor (CDC). Before the metallization, the sample was ground with the SiC paper to eliminate surface unevenness. Using a mask, a three-electrode system was applied to diminish the stray-current effect during measurement. The bottom face was fully covered with sputtered aluminum. The top face was sputtered to form an internal circle electrode, 16 mm in diameter, and an external ring electrode (earth-connected during the measurements) separated from the internal ring with a 1 mm wide gap.  
Electric field was applied along the spraying direction (i.e., through the thickness). Capacitance of the samples was measured using a programmable impedance analyzer model 4284A (Agilent, Santa Clara, CA, USA), while the sample was clamped using a high-precision sample fixture 16451B (Agilent, Santa Clara, CA, USA).  
The dielectric constant (i.e., relative permittivity) was calculated according to Equation (1),  
\[\epsilon_{\mathrm{r}}=\mathrm{C}\times\mathrm{d}/\epsilon_{0}\times\mathrm{A} \tag{1}\]  
where \(\epsilon_{\mathrm{r}}\) is relative permittivity, C (F) is equivalent parallel capacitance obtained from the measurement, d (m) is sample thickness, A is surface electrode area of the internal circle, and \(\epsilon_{0}\) is permittivity of vacuum (8.85 \(\times\) 10\({}^{-12}\) F/m).  
Thermal coefficient of capacitance (TCC) describes thermal stability of capacitance (and permittivity) when the dielectric measurement is carried out at two temperatures with a difference at least 100 \({}^{\circ}\)C. A low value of TCC is desirable to make the circuit component, based on the studied material, work well during the unavoidable thermal fluctuations. TCC is expressed in ppm/\({}^{\circ}\)C, and in our case, it was calculated using the capacitance measured at 30 \({}^{\circ}\)C and 140 \({}^{\circ}\)C.  
When a sinusoidal alternating voltage is applied to an ideal capacitor, the current advances by \(\pi/2\) in phase. In the case of a practical capacitor, however, the advance in phase is (\(\pi/2-\delta\)), which is smaller than \(\pi/2\). The angle \(\delta\) is referred to as loss angle and its tangent function as loss tangent. The loss tangent (or \"dissipation factor\") is numerically equal to the ratio of the active dissipative current to the reactive (charging) current. The dielectric loss of TiO\({}_{2}\), obtained in the form of the loss tangent Tan \(\delta\), was measured simultaneously with the relative permittivity. Measurements at elevated temperatures were carried out using a programmable furnace Novothem (Novocontrol, Montabaur, Germany) equipped with a special Broadband Dielectric Spectroscopy (BDS) sample fixture 1200 (Novocontrol, Montabaur, Germany).  
The DC volume resistance was measured on the same sample as capacitance using a Keithley 6517-B (Keithley Instruments, Solon, OH, USA) programmable resistoreter. The applied voltage was 50 \(\pm\) 0.2 V. Customized Keithley 6104 shielded test enclosure was usedto avoid errors from any external noise. Resistivity \(\rho\) was calculated from the measured resistance and specimen dimensions using Equation (2),  
\[\rho=(R\cdot A)/d \tag{2}\]  
where R (\(\Omega\)) is sample electrical resistance, A (m\({}^{2}\)) is area of the internal circle electrode, and d (m) is sample thickness.