## 2 Materials and Methods  
The thermochromic VO\({}_{2}\) films were grown using the rf sputtering technique (Nordico RFG2500) using a high purity (99.95%) metal Vanadium target. The deposition was taken place at a low substrate temperature of 300 \({}^{\circ}\)C on 4 different substrates those are Silicon (Si), K-Glass (Pilkington, 4 mm thick, Low-e, SnO\({}_{2}\) pre-coated), fused silica glass (1 mm thick) and flexible glass (Corning, 0.2 mm thick). The Oxygen content percentage (%) in Oxygen-Argon plasma (% O\({}_{2}\) = [f(O\({}_{2}\))/(f(O\({}_{2}\)) + f(Ar))] \(\times\) 100%, where f is the flow of each gas) was 1% for the films deposited on fused silica and flexible glass substrates and 3% for those deposited on Si and K-Glass substrates, since those were the values leading to the optimum thermochromic performance of VO\({}_{2}\) films, depending on the substrate used according to our previous works [7; 43; 44; 45]. The substrates were cleaned using acetone, propanol and deionized water, and they were dried with Nitrogen gas before they were placed in the sputtering chamber. The latter was initially evacuated at a pressure lower than 10\({}^{-6}\) mbar, while the total pressure during deposition was 6.7 \(\times\) 10\({}^{-3}\) mbar. The sputtering power was constant at 400 W. A profilometer (Veeco Dektak 150, Veeco, Plainview, NY, USA) was employed to determine the film thickness. The deposition parameters of the films are presented in Table 1.  
The structural properties of the films were studied by the X-Ray Diffraction (XRD) technique (Rigaku RINT-2000, Rigaku, Tokyo, Japan) using Cu K\({}_{\alpha}\) X-Rays at \(\lambda\) = 0.154 nm. All films were examined using the Grazing Incident XRD (GIXRD) method at \(\theta\) = 1\({}^{\circ}\) and 20 = 10\({}^{\circ}\)-60 \({}^{\circ}\), with a step of 0.02 \({}^{\circ}\)/s. From the XRD pattern, the crystallite size of the films was calculated using [PERSON]'s formula, which is described below in Equation (1):  
\[\text{D (nm)}=0.9^{\circ}0.154/(\text{FWHM})^{\star}\text{cos}\theta_{\text{o}} \tag{1}\]where (FWHM) is the Full Width Half Max of the diffraction peak at an angle of 20 and \(\theta_{0}=20/2\), the corresponding angle. The surface morphology was investigated by Scanning Electron Microscopy (SEM; JEOL/JSM-IT700 HR, JEOL, Tokyo, Japan) as well as by Temperature-dependent Atomic Force Microscopy (T-AFM, Keysight 5500 Microscope, Keysight, Santa Rosa, CA, USA). The latter was combined with Multi75-G silicon cantilevers (Budget Sensors, Sofia, Bulgaria) having 3 nm\({}^{-1}\) spring constant and 75 kHz resonance frequency, while the characterization was performed in the tapping mode. The temperature was increased at a rate of 1 \({}^{\circ}\)C/min, followed by 1 h relaxation time on every terminal value before AFM measurements. Moreover, T-AFM allows the monitoring of the surface changes of the VO\({}_{2}\) films during heating; thus, the RMS roughness of the films can be measured upon the phase change of the material. The optical energy band gap (E\({}_{\text{g}}\)) was calculated by optical measurements using a spectrophotometer (Perkin Elmer Lambda 950 UV/Vis/NIR, Perkin Elmer, Waltham, MA, USA) working at \(\lambda=250\)-2500 nm. By employing the standard Tauc plot [46] resulting from the transmittance measurements and the thickness of the films, the E\({}_{\text{g}}\) was extracted using the equation:  
\[(\alpha\text{hf})^{\text{n}}=\text{A}(\text{hf}-\text{E}_{\text{g}}) \tag{2}\]  
where \(\alpha\) is the absorption coefficient, hf is the photon energy, h is [PERSON]'s constant, A is a constant and n is 1/2 or 2 for allowed indirect or direct transitions, respectively. The thermochromic performance of the VO\({}_{2}\) films was determined by optical measurements as a function of temperature by employing the above-mentioned spectrophotometer. The transmittance spectra of the films at temperatures below (25 \({}^{\circ}\)C) and above (90 \({}^{\circ}\)C) the critical transition temperature were recorded using a homemade heating stage.