## 2 Materials and Methods
A temperature controller was used to control the heating rate at a step of 1.5 \({}^{\circ}\)C/min, while a thermocouple, on contact with the film surface, was monitoring the temperature during heating and cooling procedures. The variation of IR transmittance at \(\lambda=2000\) nm, known as IR-switching, is defined as (Equation (3))  
\[\Delta\text{Tr}_{\text{IR}}=\text{Tr}(25\ ^{\circ}\text{C})-\text{Tr}(90\ ^{\circ}\text{C}) \tag{3}\]  
where Tr(25 \({}^{\circ}\)C) and Tr(90 \({}^{\circ}\)C) are the transmittance (\(\lambda=2000\) nm) at 25 \({}^{\circ}\)C and 90 \({}^{\circ}\)C, respectively. The integrated solar transmittance (Tr\({}_{\text{sol}}\)) and luminous transmittance (Tr\({}_{\text{lum}}\)) are defined by the following equation (Equation (4)):  
\[\text{Tr}_{\text{i}}(\text{T})=\frac{\int\varphi_{\text{i}}(\lambda)\cdot \text{Tr}(\lambda,\text{T})\cdot\text{d}\lambda}{\int\varphi_{\text{i}}( \lambda)\text{d}\lambda} \tag{4}\]  
where Tr(\(\lambda\),T) denotes the measured transmittance spectrum at a specific temperature, i denotes solar (sol) or luminous (lum), \(\varphi_{\text{sol}}\) is the solar irradiance spectrum for an air mass of 1.5 (corresponding to the sun standing 37\({}^{\circ}\) above the horizon) [47] and \(\varphi_{\text{lum}}\) is the standard luminous efficiency function for photopic vision [48]. Thus, the solar modulation is defined as (Equation (5))  
\[\Delta\text{Tr}_{\text{sol}}\left(\%\right)=\text{Tr}_{\text{sol}}(25\ ^{\circ}\text{C})\left(\% \right)-\text{Tr}_{\text{sol}}(90\ ^{\circ}\text{C})\left(\%\right) \tag{5}\] \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Sample** & **Substrate** & **\%O\({}_{2}\)** & **Thickness** & **Direction of** & **D** & **RMS Roughness** & **E\({}_{\text{g}}\)** \\
**No.** & **in Plasma** & **(nm)** & **VO\({}_{2}\) Planes** & **(nm)** & **(nm)** & **(nm)** & **(eV)** \\ \hline
**1** & Silicon & 3 & 40 & \(\left(10\overline{2}\right)\) & 4.4 & 2.7 & - \\
**2** & K-Glass & 3 & 100 & \(\left(10\overline{2}\right)\) & 11.3 & 15.9 & 1.69 \\
**3** & Fused silica & 1 & 100 & (011) & 6.9 & 5.0 & 1.48 \\
**4** & Flexible glass & 1 & 100 & (011) & 10.4 & 3.7 & 1.74 \\ \hline \end{tabular}
\end{table} 
Table 1: Deposition parameters of the rf sputtered VO\({}_{2}\) films. Finally, the critical transition temperature (T\({}_{\rm C}\)), as well as the width of the transmittance hysteresis loop (\(\Delta\)T\({}_{\rm C}\)), are defined by the following Equations (6) and (7), respectively  
\[\rm T_{C}=(T_{1}=T_{2})/2 \tag{6}\]  
\[\rm\Delta T_{C}=T_{1}-T_{2} \tag{7}\]  
where T\({}_{1}\) and T\({}_{2}\) are the transition temperatures during heating and cooling, respectively; the latter was calculated by recording the transmittance of the films during the heating and cooling procedure at a constant IR wavelength of \(\lambda=2000\) nm and subsequently plotting the derivative of transmittance (dTr/dT) as a function of temperature for each procedure and fitting a Gaussian curve. The temperature that corresponds to the minimum of the Gaussian curve, at which dTr/dT = 0, is defined as the critical transition temperature T\({}_{1}\), T\({}_{2}\) for each procedure [49]. In addition, the Full Width at Half Maximum, as calculated by the Gaussian curve, indicates the sharpness of the transition during the heating (FWHM)\({}_{\rm h}\) and cooling (FWHM)\({}_{\rm c}\) procedures. The lower the value of FWHM, the higher the sharpness of the transition.