## 3 Results  
The XRD patterns of the rf sputtered VO\({}_{2}\) films deposited on different substrates are presented in Figure 1. It can be seen that apart from K-Glass and Si substrates, the characteristic peak of (011) plane at 20 = 27.8 \({}^{\circ}\) (JCPDS Card No. 44-0252) appeared in all films, confirming the monoclinic low-temperature phase of VO\({}_{2}\). For the K-Glass substrate, the peak could not be detected because it is close to the (110) plane of the SnO\({}_{2}\) buffer layer located at 26.6\({}^{\circ}\) (JCPDS Card No. 41-1445). However, for both K-Glass and Si substrates, a characteristic peak at 20 = 33.4\({}^{\circ}\) corresponding to the \(\left(10\overline{2}\right)\) plane of monoclinic VO\({}_{2}\) (JCPDS Card No. 44-0252). The crystallite size of the films was calculated using Equation (1) for the above-mentioned characteristic peaks of VO\({}_{2}\) and found to be between 4.4 nm for the Si substrate and 11.3 nm for the K-Glass substrate, as these are shown in Table 1. These values are in agreement with those of [PERSON] et al. [50], which prepare VO\({}_{2}\) films by PLD at an oxygen pressure of 0.1 Pa at a substrate temperature of 500 \({}^{\circ}\)C on glass substrates; however, they are lower compared to those of [PERSON] et al. [51], which deposited VO\({}_{2}\) films using the sputtering technique on glass substrates at temperatures higher than 350 \({}^{\circ}\)C.  
Figure 1: XRD diagrams of VO\({}_{2}\) films deposited on different substrates. The morphology of the films was examined by scanning electron microscopy, and the images are presented in Figure 2. It becomes clear that the films on Si, fused silica and flexible glass substrates (Figure 2a,c,d, respectively) were of high homogeneity, having small grains. However, the films have different morphology, depending on the substrate. In particular, the surface of the film deposited on the Si substrate (Figure 2a) shows some cracks, the one that was deposited on the fused silica substrate (Figure 2c) is porous and the film's surface on the flexible glass substrate (Figure 2d) is very smooth. These variations can be attributed to the different characteristics of each substrate, such as thickness or surface morphology. This is also confirmed by the corresponding RMS roughness values that were extracted by AFM measurements, and they are listed below in Table 1. Contrastingly, the VO\({}_{2}\) films that were grown on the K-Glass substrate (Figure 2b) appeared to have larger grains and aggregated particles, in accordance with the greater RMS roughness value (Table 1), possibly due to the SnO\({}_{2}\) buffer layer of the K-Glass substrate as well as to the higher thickness of K-glass substrate (4 mm). It is known that SnO\({}_{2}\) has a tetragonal structure with lattice parameters similar to those of the high-temperature tetragonal rutile phase of VO\({}_{2}\)[31]. Thus, it promotes the formation of VO\({}_{2}\) with greater grains compared to the bare substrates. Figure 2: SEM images of VO\({}_{2}\) films deposited on (**a**) Silicon; (**b**) K-Glass; (**c**) fused silica; and (**d**) flexible glass substrates. The surface changes upon heating from room temperature (-25 \({}^{\circ}\)C) that is well below T\({}_{\rm C}\) to 100 \({}^{\circ}\)C, which is far above the T\({}_{\rm C}\), where investigated by Temperature-dependent AFM. The AFM images of VO\({}_{2}\) films at four different temperatures, 25, 60, 80 and 100 \({}^{\circ}\)C, for each substrate are shown in Table 2. It can be seen that the surface morphology is different for each substrate at RT; however, the RMS roughness (Table 1) is much higher in the K-Glass substrate, probably due to the SnO\({}_{2}\) buffer layer, the RMS roughness of which was equal to 11.1 nm.