## 3 Results and Discussion
The transmittances of the SiO\({}_{2}\)/Nb\({}_{2}\)O\({}_{5}\) multilayer thin films in the range of 500 nm to 550 nm were approximately 96.14% in this work. The transmittances of ED and IS commercial thin films in the 500-550 nm range were 91.44% and 84.99%, respectively, as shown in Figure 7b. As a result of comparing the transmittance of the current work with those of the commercial products in the 500 to 550 nm range, the difference in the transmittance of the commercial thin films from ED and IS company was 4.7 and 11.15%, respectively. The thin film of ED, composed of SiO\({}_{2}\) and Ta\({}_{2}\)O\({}_{5}\) (refractive index 2.1476 @ 530 nm), has a total thickness of 9.15 \(\upmu\)m with approximately 130 layers. The total thickness of the IS thin film, which is composed of SiO\({}_{2}\) and TiO\({}_{2}\) (refractive index 2.541 @ 530 nm), is 2.60 \(\upmu\)m with approximately 36 layers. In particular, it was confirmed that the deviation of transmittance in the 500 to 550 nm range was more than 5%. In this work, high transmittance was attributed to the flat top surface and square bandwidth, as shown in Figure 7. As explained in Figure 4, there was almost no difference in the thickness of each SiO\({}_{2}\), Nb\({}_{2}\)O\({}_{5}\) layer of the designed and fabricated SiO\({}_{2}\)/Nb\({}_{2}\)O\({}_{5}\) multilayer thin films. Additionally, no significant interfacial diffusion was observed between the SiO\({}_{2}\) and Nb\({}_{2}\)O\({}_{5}\) layers. Figure 6: AFM surface (**a**) 2D and (**b**) 3D topography of SiO\({}_{2}\)/Nb\({}_{2}\)O\({}_{5}\) multilayer thin films on D263 substrates. Hardness (\(H\)) is defined as the resistance to local plastic deformation. The Berkovich indenter has a very flat profile and has the same projected area-to-depth ratio as a Vickers indenter. Hardness (\(P_{max}/A_{p}\)\({}^{2}\)) can be explained as the maximum indentation load \(P_{\max}\) divided by the projected contact area \(A_{p}\). The projected contact area \(A_{p}\) can be estimated from this relationship (\(A_{p}\) = C\({}_{\rm o}\)\(\times\)\(h_{c}\)), where C\({}_{\rm o}\) is 24.6 for the Berkovich indenter and \(h_{c}\) is the contact depth [33]. The hardness properties of a thin film can be measured by using a nano indenter equipped with a modified Berkovich indenter. The Oliver-Pharr method using the obtained load vs. displacement curve was used to calculate the hardness of the thin films [34]. Since thin films are very soft compared with substrate materials, an accurate hardness evaluation of thin film is difficult to attain due to the substrate effect. Therefore, it is recommended that the penetration depth of indentation should be within 10% of the thin-film thickness to minimize the influence of the substrate [35]. Figure 8a shows the load-penetration depth curve of a SiO\({}_{2}\) and Nb\({}_{2}\)O\({}_{5}\) single-layer thin film on D263 substrates. The load-penetration depth curve was obtained as the corresponding peak load was held for 15 sec at the maximum penetration depth (\(H_{\max}\)). After being unloaded, the penetration depth was not completely recovered, which indicates irreversible plastic deformation in the SiO\({}_{2}\) and Nb\({}_{2}\)O\({}_{5}\) single-layer thin films. It was observed that the \(P_{\max}\) reached 3 mN and 0.711 mN for the SiO\({}_{2}\) single layer with 600 nm thickness and the Nb\({}_{2}\)O\({}_{5}\) single layer with 1200 nm thickness, respectively. The hardness of the SiO\({}_{2}\) and Nb\({}_{2}\)O\({}_{5}\) single-layer thin films was 10.73 GPa and 6.3 GPa, respectively. Previous works on the hardness of SiO\({}_{2}\) and Nb\({}_{2}\)O\({}_{5}\) thin films reported a hardness in the ranges of 10.4-11.9 GPa and 6.5-6.8 GPa, respectively [33; 36]. The hardness (6.6 GPa) of the SiO\({}_{2}\)/Nb\({}_{2}\)O\({}_{5}\) multilayer thin films on B33 substrates showed a value that was more than 30% greater than the hardness (4.4 GPa) of the SiO\({}_{2}\)/Nb\({}_{2}\)O\({}_{5}\) multilayer thin film on D263 substrates.