## 3 Results and Discussion  
Three substrates (B33, D263, and D270) from Schott were used to evaluate the compatibility of the thin-film growth for multilayer thin films. They have very similar optical properties such as transmittance and refractive index. However, the coefficients of thermal expansion in the 25\(\sim\)300 \({}^{\circ}\)C range are 3.3, 7.2, and 9.4 (\(\times\)10\({}^{-6}\)/K), respectively. The SiO\({}_{2}\)/Nb\({}_{2}\)O\({}_{5}\) multilayer thin films were deposited onto these three substrates (B33, D263, and D270) using the sputtering deposition conditions listed in Table 1. Typical XRD patterns of the SiO\({}_{2}\)/Nb\({}_{2}\)O\({}_{5}\) multilayer thin films on the three substrates are shown in Figure 1. The SiO\({}_{2}\)/Nb\({}_{2}\)O\({}_{5}\) multilayer thin films were amorphous regardless of the substrate types. The amorphous peak was located at 20\(\sim\)25\({}^{\circ}\) in the XRD pattern. The XRD patterns representing SiO\({}_{2}\) and Nb\({}_{2}\)O\({}_{5}\) crystal phases did not appear, indicating that the multilayer thin films \begin{table}
\begin{tabular}{c c c} \hline
**Parameters** & **SiO\({}_{2}\) Film** & **NB\({}_{2}\)O\({}_{5}\) Film** \\ \hline \hline \multicolumn{1}{c}{Sputtering Target} & Si & Nb \\ \hline \multicolumn{1}{c}{Base Pressure (Pa)} & 2.0 \(\times\) 10\({}^{-5}\) & 2.0 \(\times\) 10\({}^{-5}\) \\ \hline \multicolumn{1}{c}{Working Pressure (Pa)} & 8.0–9.0 \(\times\) 10\({}^{-1}\) & 8.0–9.0 \(\times\) 10\({}^{-1}\) \\ \hline \multicolumn{1}{c}{O\({}_{2}\) Partial P reassure (O\({}_{2}\)/Ar + O\({}_{2}\))} & 0.3–0.9 & 0.3–0.9 \\ \hline \multicolumn{1}{c}{MF Power (kW)} & 8 & 8 \\ \hline \multicolumn{1}{c}{RF Power (kW)} & 3 & 3 \\ \hline \multicolumn{1}{c}{Target to Substrate Spacing (mm)} & 150 & 150 \\ \hline \multicolumn{1}{c}{Rotating Speed of Substrate (rpm)} & 80 & 80 \\ \hline \multicolumn{1}{c}{Temp. of the substrate (\({}^{\circ}\)C)} & 150 & 150 \\ \hline \multicolumn{1}{c}{Clean Room Temp. (\({}^{\circ}\)C)} & 20 & 20 \\ \hline \multicolumn{1}{c}{Clean Room Relative Humidity (\%)} & 45 & 45 \\ \hline \multicolumn{1}{c}{Deposition Rate (Å/s)} & 6.2–9.29 & 1.67–4.76 \\ \hline \end{tabular}
\end{table} 
Table 1: Experimental deposition conditions of the sputtering methods for SiO\({}_{2}\)/Nb\({}_{2}\)O\({}_{5}\) multilayer thin films. were homogeneous and isotropic. Other studies on SiO\({}_{2}\)/Nb\({}_{2}\)O\({}_{5}\) multilayer thin films deposited by an e-beam or sputtering methods show similar results [4; 11; 12]. The coefficients of thermal expansion of the film materials SiO\({}_{2}\) and Nb\({}_{2}\)O\({}_{5}\) were 0.55 and 5.8 (\(\times 10^{-6}\)/K), respectively [13]. Based on the results, D263 was used in this current work in order to minimize the strain and stress between the substrate and thin films since the coefficient of thermal expansion 7.2 (\(\times 10^{-6}\)/K) of D263 is close to 5.8 (\(\times 10^{-6}\)/K) of Nb\({}_{2}\)O\({}_{5}\)[14]. The SiO\({}_{2}\)/Nb\({}_{2}\)O\({}_{5}\) multilayer thin films were analyzed using X-ray photoelectron spectroscopy (XPS, NEXSA, Thermo Fisher Scientific, Waltham, MA, USA) to analyze the binding energy and chemical composition of the SiO\({}_{2}\) and Nb\({}_{2}\)O\({}_{5}\). During XPS analysis, the pressure was maintained at 1.5 \(\times\) 10\({}^{-9}\) Torr, and Al \(K\alpha\) (hv = 1486.6 eV) was used as the X-ray light source. As shown in Figure 2a, the full spectrum of XPS confirms the presence of Si, O, and Nb on the surface of the SiO\({}_{2}\)/Nb\({}_{2}\)O\({}_{5}\) multilayer thin films. It was confirmed that within the SiO\({}_{2}\) and Nb\({}_{2}\)O\({}_{5}\) optical thin-film layers, major peaks assigned to O1s, Si2p, Si2s, Nb3d\({}_{5/2}\), and Nb3d\({}_{3/2}\) are distinctive indicating the respective components. It is not easy to determine the exact valence state in silicon oxide and niobium oxide thin film. In this study, we aim to compare SiO\({}_{2}\)/Nb\({}_{2}\)O\({}_{5}\) multilayer thin films with previous research reports.