## 3 Results
In specific, the E\({}_{\rm g}\) of VO\({}_{2}\) films deposited on K-Glass (1.69 eV) and flexible glass (1.74 eV) are close to those that have been reported by [PERSON] et al. (1.67 eV) [55] and [PERSON] et al. (1.71 eV) [56], while the E\({}_{\rm g}\) of the film grown on fused silica substrate (1.48 eV) was lower enough, indicating the possible existence of structural defects. However, it is higher enough compared to the works of [PERSON] et al. (0.52 eV) [57] and [PERSON] et al. (0.49-0.51 eV) [58]. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{Substrate} & \multirow{2}{*}{\(\mathbf{T_{1}}\)} & \multirow{2}{*}{\(\mathbf{T_{2}}\)} & \multirow{2}{*}{\(\mathbf{T_{C}}\)} & \multirow{2}{*}{\(\mathbf{\Delta T_{C}}\)} & \(\mathbf{\Delta T_{IR}}\) & \multirow{2}{*}{\(\mathbf{\Delta T_{sol}}\)} & \(\mathbf{T_{1}}\) & \multirow{2}{*}{\(\mathbf{\Delta T_{sol}}\)} & \(\mathbf{(FWHM)_{h}}\) & \(\mathbf{(FWHM)_{h}}\) \\  & (\({}^{\circ}\)C) & (\({}^{\circ}\)C) & (\({}^{\circ}\)C) & (\({}^{\circ}\)C) & (\({}^{\circ}\)C) & (\%) & (\%) & (\%) & (\%) \\ \hline
**Si** & 49 & 44 & 46.5 & 5 & 6 & 1.5 & - & 29 & 19 \\ K-glass & 59 & 50 & 54.5 & 9 & 20 & 6 & 38 & 11 & 9 \\ fused silica & 41 & 34 & 37.5 & 7 & 28 & 4 & 38 & 20 & 17 \\ flexible glass & 56 & 45 & 50.5 & 11 & 36 & 5 & 34 & 39 & 32 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Thermochromic performance of VO\({}_{2}\) films. The thermochromic characteristics of VO\({}_{2}\) films were investigated by optical measurements. Figure 5 presents the transmittance of VO\({}_{2}\) films at temperatures below (RT) and above (90 \({}^{\circ}\)C) the T\({}_{\rm C}\). In addition, all the films had a thermochromic behavior independent from the substrate, however, with different features. From the transmittance spectra and by using Equations (3)-(5), the IR-switching, the luminous transmittance and the solar transmittance modulation were calculated, and they are listed in Table 3. Moreover, the transmittance hysteresis loop at \(\lambda\) = 2000 of VO\({}_{2}\) films is shown in Figure 6. Using these and following the procedure described in the experimental section, the critical transition temperatures, T\({}_{1}\) and T\({}_{2}\), were determined (Figure 7). Applying these values in Equations (6) and (7), the critical transition temperature, as well as the width of the transmittance hysteresis loop, were calculated and listed in Table 3. In the same table, the (FWHM) during the heating and cooling procedures is presented, indicating the sharpness of each transition. Figure 4: Tauc plot-(ahf)\({}^{1/2}\) vs. hf- of VO\({}_{2}\) films deposited on different substrates. The arrows point the value of optical energy band gap where (ahf)\({}^{1/2}\) = 0. Figure 3: RMS roughness of VO\({}_{2}\) films upon heating from RT to 100 \({}^{\circ}\)C.  
Figure 5: Transmittance spectra at 25 \({}^{\circ}\)C (blue line) and 90 \({}^{\circ}\)C (red line) of VO\({}_{2}\) films grown on different substrates. Figure 6: Transmittance hysteresis loop, at \(\lambda\) = 2000 nm, during heating (red square dots) and cooling (blue square dots) procedures, of VO\({}_{2}\) films grown on (**a**) silicon; (**b**) K-glass; (**c**) fused silica glass; and (**d**) flexible glass substrates. From this, it becomes clear that the critical transition temperature is strongly dependent on the substrate, ranging from 37.5 \({}^{\circ}\)C (fused silica) to 54.5 \({}^{\circ}\)C (K-Glass), while the width of the transmittance hysteresis loop varied from 5 \({}^{\circ}\)C (Si) to 11 \({}^{\circ}\)C (flexible glass). The reduced values of critical transition temperature compared to this of pristine material one (68 \({}^{\circ}\)C) can be attributed to the low crystallinity of the films as a result of the low deposition temperature. For the same reason, the transition is of low sharpness for the films grown on Si, fused silica and flexible glass substrates, while it is of high sharpness for those grown on K-Glass (Table 3), probably due to the presence of SnO\({}_{2}\) buffer layer.