## 3 Results  
Well-developed crystalline films of ZnO (intrinsic and doped) were confirmed by the XRD pattern (JCPDS# 79-2 205). XRD patterns of doped ZnO thin films deposited onto soda-time glass substrate are shown in Figure 1.  
The crystallite sizes were quantitatively evaluated from XRD data using the Debye-Scherrer equation (Equation (1)) [19]:  
\[\mathrm{D=k\lambda/\beta cos\theta} \tag{1}\]  
where k is Scherrer constant (0.9 for spherical particles), \(\lambda\) the X-ray wavelength (1.5405 A), \(\beta\) the peak width of half-maximum, and \(\theta\) is the Bragg diffraction angle [20]. The resultant particle size for ZnO films is between 12 nm and 35.5 nm and becomes shorter for doped films as can be seen in Table 1.  
The surface morphology of the doped ZnO thin films is an important parameter for a good performance in PV devices. Figure 2 shows the surface SEM images of doped ZnO layers deposited onto soda-lime glass, from which we could see apparent particles with different particle sizes and shapes of the four samples.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline  & **Voltage** & **Intensity** & **Sheet Resistance** & **Band Gap** & **Transmittance(\%)** & **Crystallite** & **Thickness** \\  & **(V)** & **(mA)** & **(I/sq)** & **(eV)** & **(eV)** & **Size (nm)** & **(nm)** \\ \hline i-ZnO & 3 & 0.017 & 794,117.65 & 3.29 & 87.1 & 12–35.5 & 210 \\ ZnO\({}_{1}\)-x & 0.186 & 0.99 & 829.70 & 3.27 & 92.3 & & \\ Al\({}^{3+}\) & 0.049 & 0.96 & 229.69 & 3.36 & 91.6 & 14–20 & 180 \\ Ga\({}^{3+}\) & 0.084 & 0.98 & 385.71 & 3.33 & 86.6 & 14–22 & 200 \\ In\({}^{3+}\) & 0.032 & 0.98 & 146.94 & 3.35 & 70.3 & 10–25 & 420 \\ \hline \end{tabular}
\end{table}
Table 1: Optical and electrical properties of doped ZnO grown at soda-lime glass.  
Figure 1: XRD spectra of i-ZnO, Al, Ga, and In samples compared with a ZnO pattern.  
The samples presented a thickness between 180 nm and 450 nm, as can be observed in Figure 3 where films' cross-section micrographs are shown.  
Figure 3: Cross section films images (**a**) i-ZnO, (**b**) ZnO:Al, (**c**) ZnO:Ga, and (**d**) ZnO:In.  
Figure 2: Thin films surface morphology (**a**) i-ZnO, (**b**) ZnO:Al, (**c**) ZnO:Ga, and (**d**) ZnO:In.  
Figure 4 shows a comparison of the optical transmittance spectra between doped ZnO films and the intrinsic ZnO film deposited on a soda-lime substrate.  
Taking these results, bandgap values for each film was also obtained. For this first, the absorption coefficient (\(\alpha\)) values were calculated using Lambert's Law as the following equation (Equation (2)) [21]:  
\[\text{A}=1/t\ln(1/\text{T}) \tag{2}\]  
where T is the transmittance, and t is the film thickness. An optical bandgap of thin films was estimated using the equation x by the extrapolation of (\(\alpha\)hv)2 vs. hv (Equation (3)):  
\[\text{Ahv}=\text{A}(\text{hv}-\text{E}\_\text{g})^{(1/2)} \tag{3}\]  
where A is a constant, hv is the photon energy, and Eg is the optical bandgap. The optical bandgap of ZnO and ZnO doped thin films was determined by extrapolating the region of the plot to the energy axis where \(\alpha\)2 = 0, and was 2.  
The optical band gap of doped ZnO is shown in Figure 5. The values obtained are 3.29, 3.35, 3.32, and 3.36 eV for i-ZnO, ZnO:Al, ZnO:Ga, and ZnO:In, respectively. The electrical behaviour of samples is shown in Table 1.