## 3 Results and Discussion
This can also be confirmed in Figure 4b, where the value of the lattice parameter c for CIGS thin films is larger than the well-known range. The Tauc plot method may be less appropriate than the first derivative of absorbance method if the absorption coefficient does not vary linearly with photon energy in the band gap region, as shown in Figure 5b, due to defect states or other non-idealities present in the thin films. The band gap of the CIGS:Te thin films is estimated by taking the energy at which the maximum of the first derivative (\(dA/dE\)) of the absorbance spectrum with respect to photon energy occurs in Figure 5c [46; 47; 48]. The band gap of the CIGS:Te thin films from the first derivative of absorbance decreased from 1.554 to 1.548 eV under condition (3) and increased rapidly to 1.556 eV under condition (6), which shows a similar trend to the extrapolated values from the Tauc plot, as shown in Figure 5d. Hall-effect measurements were performed to analyze the electrical properties, including carrier concentration (\(n\)), carrier mobility (\(\mu\)), and resistivity (\(\rho\)), of the CIGS:Te thin films, as shown in Figure 6. The electrical conductivity type of CIGS thin films can be influenced by various factors, including the ratio of In and Ga, Cu-deficiency, and the presence or absence of Se-excess during film fabrication. Neumann reported that the electrical conductivity type was determined by the deviations \(\Delta m\) and \(\Delta s\)[49], and Karthikeyan verified and further developed this relationship [28, 45, 50]. Hall-effect measurements showed n-type conductivity in the CIGS thin film without Te, with \(\Delta m<0\) and \(\Delta s<0\), as shown in Figures 6a and 2d, which reported that CIS thin films with \(\Delta m<0\) always had n-type conductivity regardless of \(\Delta s\) in terms of the point defect model, and CIGS and CIAS thin films showed similar trends [29, 51]. The electrical conductivity type dramatically changed the p-type conductivity in all CIGS:Te thin films, even though the thin films still showed deviations of \(\Delta m<0\) and \(\Delta s<0\), as shown in Figure 2d. The p-type conductivity of CIGS  
Figure 5: Optical properties of the CIGS:Te thin films with different Te co-sputtering times of (1) 0, (2) 270, (3) 510, (4) 750, (5) 945, and (6) 1140 s. (**a**) Optical transmittance. The inset shows the mean optical transmittance in the visible and near-infrared (NIR) spectral regions. Magnitude of the optical transmittance in the visible spectral region is also shown in the inset. (**b**) Absorption coefficient. Mean absorbance in the visible and NIR spectral regions is shown in the inset. (**c**) The first derivative of absorbance as a function of incident photon energy for determination of the band gap. (**d**) Magnitude of the first derivative of absorbance spectrum. The inset shows the estimated band gap. thin films is typically attributed to the formation of Cu vacancies and their interaction with Ga, which leads to the formation of a p-type defect complex [52]. The influence of the ratio of In and Ga is well known that CIGS thin films with a higher Ga content tend to have a higher hole concentration and therefore p-type conductivity. The CIGS thin films prepared under Se-excess exhibit p-type conductivity, whereas the thin films prepared under Se-deficiency exhibit n-type conductivity [53]. However, the same Cu-deficient target was used in all conditions of this study; so, the relative atomic percentage of In, Ga, and Se, and the composition ratio of Ga/(In + Ga) were nearly constant across all conditions (Figure 2b,c). Therefore, this is because of the surplus In + Ga atoms (Figure 2e), indicating the presence of positive ions in the crystal. The electrical conductivity types exhibited different behaviors because of the thin films with larger \(\Delta m\) and \(\Delta\)s in this study, and the electrical conductivity types with larger \(\Delta m\) and \(\Delta\)s could not be determined in terms of the point defect model [49].