## 3 Results
Moreover, upon heating, there is no morphological change of the films' surfaces compared to that at RT, except from the film that was grown on Si substrate, which seems to have a different surface morphology at 80 \({}^{\circ}\)C as well as at 100 \({}^{\circ}\)C. These changes may be attributed to the smaller thickness (40 nm) of the films that were deposited on the Si substrate compared to those that were deposited on other substrates (100 nm). It should be noticed that a thickness of 40 nm was the optimum concerning the thermochromic performance of the Si substrate. Furthermore, the values of RMS roughness of VO\({}_{2}\) films that were deposited on different substrates upon heating from RT to 100 \({}^{\circ}\)C are presented in Figure 3. It can be noticed a slight decrease of RMS roughness after the temperature of 60 \({}^{\circ}\)C, which is higher than the T\({}_{\rm C}\) one, for films grown on Si, fused silica and flexible glass. This observation confirms the structural transition, which is accompanied by the MIT as well as the optical transition [52]. This decrease in RMS roughness can be attributed to the transition of the VO\({}_{2}\) crystal structure from monoclinic (T \(<\) T\({}_{\rm C}\)) to tetragonal (T \(>\) T\({}_{\rm C}\)) upon heating. According to this transition, the V\({}^{4+}\)-V\({}^{4+}\) pair in the form of a zig-zag along the \(a\)-axis, with alternate distances of 0.265 nm and 0.312 nm, tilting in the c-axis, of the low-temperature monoclinic structure turns to simple rutile tetragonal structure with lower size at higher temperature [1]. This structural transition upon heating is accompanied by strain effects [53] as well as variations in grain boundaries of the film [42], leading to surface changes. Thus this explanation might be the reason for the decrease in RMS roughness with heating. In contrast to other substrates, the RMS roughness of VO\({}_{2}\) film on K-Glass was increased upon heating between RT and 60 \({}^{\circ}\)C, and then it was decreased with further heating to 80 and 100 \({}^{\circ}\)C. The reason for this might be the fact that the critical transition temperature VO\({}_{2}\)/K-Glass film, as this was calculated by optical measurements, is equal to 54 \({}^{\circ}\)C (Table 3), that is, close to 60 \({}^{\circ}\)C, which means that the surface changes do not immediately follow the optical ones. This is in accordance with the works of [PERSON] [54] and [PERSON] [15], in which they supported the existence of an intermediate phase between the monoclinic and the rutile one, also known as monoclinic (M2). As a result, the MIT, as well as the IR optical changes, happened at 68 \({}^{\circ}\)C, while the structural phase change happened at a slightly increased temperature. In addition, the results are similar to those of [PERSON] et al. [42], which investigated the thermochromic properties of VO\({}_{2}\) films deposited using the PLD technique on the Si substrate using Temperature-dependent AFM. They observed the existence of the M2 monoclinic phase as an intermediate phase between the low-T monoclinic phase (M1) and the high-T tetragonal rutile (R) phase, resulting in a structural transition at a critical temperature slightly higher than this of electric or optical transition. It should be noticed that when the films were cooled down to room temperature their topography returns to the initial one, confirming the reversibility of the transition. Figure 4 shows the Tauc plot resulting from the transmittance measurements (Figure 5, 25 \({}^{\circ}\)C) and using Equation (2) for VO\({}_{2}\) thermochromic films deposited on K-glass, fused silica and flexible glass substrates, assuming allowed indirect transitions (n = 1/2). Extrapolating the linear region, the E\({}_{\rm g}\) is defined as the interception with the energy axis. The values of E\({}_{\rm g}\) are shown in Table 1, from which it becomes clear that the substrate affected the optical band gap.