## 3 Results and Discussion
In the Si-rich band, that is, the Nb-deficient region, the EDS intensity of Si \(K\alpha 1\)  
Figure 3: (**a**) Optical transmittance from UV–Vis spectrometer and (**b**) refractive index of a SiO\({}_{2}\) thin film, a Nb\({}_{2}\)O\({}_{5}\) thin film and a D263 bare substrate from spectroscopic ellipsometer. was relatively high, in contrast to Nb \(L\alpha\)1, and conversely the EDS intensity for Nb \(L\alpha\)1 was relatively high in the Nb-rich region. It was shown that there was a clear distinction between the Si and the Nb thin-film layer, indicating that the multilayer thin film was successfully manufactured without observable interfacial diffusion. AFM measurements were performed in order to confirm the information regarding the surface topography of the as-prepared thin films. The 2D and 3D topography of the SiO\({}_{2}\)/Nb\({}_{2}\)O\({}_{5}\) multilayer thin films shows smooth surfaces, as presented in Figure 6. The calculated root mean square (RMS) surface roughness was found to be equal to 2.32 nm \(\pm\) 0.19 nm. A crack-free, densely packed surface was obtained and this was also confirmed by the SEM topography results presented in Figure 4. It is well known that the sputtering method has advantages for obtaining dense and uniform structures because the surface diffusion of sputtered substrates promotes the growth of a homogenous film [25; 26]. Using the sputtering method, many studies have been conducted to improve surface roughness according to sputtering power, process pressure, etc. AFM images of the TiO\({}_{2}\) thin film and SiO\({}_{2}\) thin film presented surface roughness in the range of RMS 0.84-1.04 nm using a sputtering power of 8.1 kW and 6.0 kW, respectively [27]. A similar study reported antireflection films with an Air/SiO\({}_{2}\)/Nb\({}_{2}\)O\({}_{5}\)/SiO\({}_{2}\)/Nb\({}_{2}\)O\({}_{5}\)/SiO\({}_{2}\)/Nb\({}_{2}\)O\({}_{5}\)/glass structure designed by the Macleod program manufactured by a DC sputtering system. As the process pressure decreased, the surface roughness tended to decrease from 1.242 nm to 0.127 nm [28]. [PERSON]  
Figure 4: (**a**) Cross-sectional SEM images and (**b**) top surface image for the SiO\({}_{2}\)/Nb\({}_{2}\)O\({}_{5}\) multilayer thin films deposited by sputtering on D263 substrates. Figure 5: (**a**) Cross-sectional images of 12 layers of the SiO\({}_{2}\)/Nb\({}_{2}\)O\({}_{5}\) thin films for EDS line scanning and (**b**) complementary elemental line profiles for SiO\({}_{2}\) and Nb\({}_{2}\)O\({}_{5}\) along with a white solid line. et al. reported Nb\({}_{2}\)O\({}_{5}\)/SiO\({}_{2}\)/ITO multilayer films prepared using a magnetron sputtering system. The surface roughness of Nb\({}_{2}\)O\({}_{5}\)/SiO\({}_{2}\)/ITO multilayer films was in the range of 0.1-0.4 nm [29]. The current results indicate that the surface condition of SiO\({}_{2}\)/Nb\({}_{2}\)O\({}_{5}\) multilayer thin films with a 2.32 nm \(\pm\) 0.19 nm of surface roughness will not deteriorate the optical properties such as transmittance. SiO\({}_{2}\)/Nb\({}_{2}\)O\({}_{5}\) multilayer thin films were designed and manufactured based on information such as the refractive index (\(n\)) and an extinction coefficient (\(k\)) of SiO\({}_{2}\) and Nb\({}_{2}\)O\({}_{5}\) with the Essential Macleod program. For the application of multilayer thin films to narrow band pass filters, a square bandwidth of the transmittance is essential at a specific wavelength of 500-550 nm. The application of multilayers, with the thickness of each layer being one-fourth of the wavelength, can improve the performance of an AR (anti reflecting) coating. The high transmittance or high reflection at a specific wavelength using multilayer thin films can be explained by the difference in the refractive index between SiO\({}_{2}\) and Nb\({}_{2}\)O\({}_{5}\)[30; 31; 32]. The optical transmittance and reflectance of the SiO\({}_{2}\)/Nb\({}_{2}\)O\({}_{5}\) multilayer thin films deposited were characterized using a UV-Visible spectrometer, as shown in Figure 7a.