## 3 Results and Discussion
### Optical Characterization  
Transmission spectra of the CdTe films as deposited by VTE and RF-MS onto glass substrates were first plotted to compute their corresponding thicknesses by constructing the two envelopes, superior and inferior, around the maxima and minima of the interference fringes within the transparency region (see Figure 7a,b, respectively). By exploiting the relation between the maxima and minima positions as well as the refractive index, the linear dependence of \(\frac{1}{2}\) as a function of \(\frac{\mathbf{n}}{\lambda}\) could then be represented (see the insets of Figure 7a,b, respectively), and the slope of the linear regression is twice the film thickness, according to Equation (5):  
\[\frac{1}{2}=2\,\mathrm{h}\Big{(}\frac{\mathbf{n}}{\lambda}\Big{)}-\mathrm{m}_{0} \tag{5}\]  
where \(\mathrm{I}=0.1\),\(2\),\(\ldots\),\(n\) is the refractive index, \(\mathrm{h}\) is the CdTe film thickness, \(\lambda\) is the wavelength associated with a minimum or a maximum, and \(\mathrm{m}_{0}\) is the unknown order of the first interference fringe [43]. The evaluated thickness values of the deposited CdTe films were (1032 \(\pm\) 24.5) nm for the VTE sample and (1366 \(\pm\) 21.6) nm for the RF-MS sample (see Tables 1 and 3), where the errors were estimated from the standard errors (SEs) of the linear regression fits (see the insets of Figure 7a,b, respectively). These values were similar to those evaluated by cross-sectional SEM analysis, proving the computation accuracy of the optical spectroscopy method. The thickness of the ECD-prepared CdTe film was only estimated by direct SEM inspections (with the SE calculated over multiple SEM measurements), due to the extremely low transparency of the Au-coated Si substrate used here, in the spectral range of 500-1500 nm. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Deposition Method** & \(\mathbf{h\pm SE\left(nm\right)}\) & \(\mathbf{D_{ef}^{(111)}\left(nm\right)}\) & \(\mathbf{E_{g}\left(eV\right)}\) \\
**Control Sample** & \(\mathbf{h\pm SE\left(nm\right)}\) & \(\mathbf{D_{ef}^{(111)}\left(nm\right)}\) & \(\mathbf{E_{g}\left(eV\right)}\) \\ \hline VTE & & & \\ CdTe/glass & 1032 \(\pm\) 24.5 & 81 & 1.43 \\ \hline RF-MS & & & \\ CdTe/glass & 1366 \(\pm\) 21.6 & 64 & 1.44 \\ \hline ECD & & & \\ CdTe/Au/Tl/Si & 553 \(\pm\) 13.4 & 21 & 1.48 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Collection of morpho-structural data, showing the variation of the band gap energy (\(\mathrm{E_{g}}\)) with the crystallite size (\(\mathrm{D_{ef}^{(111)}}\)) and film thickness (\(\mathrm{h}\)) for the CdTe layers deposited by VTE, RF-MS, and ECD, respectively. \(\mathrm{E_{g}}\) values are shown with an estimated accuracy of \(\pm\)0.01–0.03 eV. The thickness values collected in Tables 1 and 3 were subsequently used to compute the optical band gap energies (E\({}_{\text{g}}\)) of the fabricated CdTe thin films by employing the absorption spectra (see Figure 7c-e) and [PERSON]'s plot method. CdTe is a direct band gap semiconductor, and as such the E\({}_{\text{g}}\) value corresponding to \(\Gamma\) point in the first Brillouin zone can be easily computed from the dependence of the absorption coefficient on the energies of the incident photons near the fundamental absorption edge:  
\[\alpha=\text{C}\cdot\frac{\left(\hbar\omega-\text{Eg}\right)^{1/2}}{\hbar\omega} \tag{6}\]  
Figure 7: **(a,b)** The transmission spectra of the CdTe films deposited by VTE (**a**) and RF-MS (**b**). The insets represent linear fitting plots used for thickness evaluation. The obtained slope values and associated standard errors (SEs) are indicated. R\({}^{2}\) represents the coefficient of determination. (**c–e**) The absorption spectra obtained for CdTe films fabricated by VTE (**c**), RF-MS (**d**), and ECD (**e**). The CdTe films were deposited onto pristine optical glass substrate, except for the ECD samples, which were synthesized on a common Au-coated Si substrate.