## 3 Results and Discussion
### Optoelectronic Properties of the ZnO and Pd/ZnO Thin Films  
To investigate the effects of Pd photodeposition functionalization on the ZnO thin films, diffuse reflectance spectra (DRS) were obtained for both the pristine and Pd-functionalized films, prepared at photofixation doses of 2.5, 5, and 10 J/cm\({}^{2}\). The resulting DRS spectra are presented in Figure 4. The results indicate that Pd functionalization led to reduced reflectance within the 400-600 nm spectral range.  
Figure 3: EDS spectra of Pd/ZnO films photodeposition-functionalized at UV doses of (**a**) 2.5, (**b**) 5, and (**c**) 10 J/cm\({}^{2}\).  
To elucidate the influence of Pd photodeposition on the optical bandgap of ZnO, the reflectance data shown in Figure 4 were converted into an effective absorption coefficient, F(R), using the Kubelka-Munk equation:  
\[\mathrm{F(R)}=\frac{\left(1-\mathrm{R}\right)^{2}}{2\mathrm{R}}, \tag{2}\]  
where R is the wavelength-dependent reflectance. The optical bandgap (\(\mathrm{E_{g}}\)) of the pristine and Pd-modified ZnO thin films was then determined using the Tauc equation:  
\[\mathrm{F(R)}=\frac{\left(\mathrm{hv}-\mathrm{E_{g}}\right)^{2}}{\mathrm{hv}}, \tag{3}\]  
where the cross-section of \(\left(\mathrm{F(R)hv}\right)^{2}\) versus photon energy (hv) yields the \(\mathrm{E_{g}}\) value. The corresponding Tauc plots for pristine ZnO and the Pd-functionalized ZnO films (at doses 2.5, 5, and 10 J/cm\({}^{2}\)) are shown in Figure 5a-d.  
Figure 4: Diffuse reflectance spectra (DRS) for pristine ZnO (black line), 2.5 J/cm\({}^{2}\) Pd/ZnO (red line), 5 J/cm\({}^{2}\) Pd/ZnO (green line), and 10 J/cm\({}^{2}\) Pd/ZnO (blue line).  
Figure 5: Tauc plots for **(a)** pristine ZnO and Pd/ZnO films functionalized at UV doses of **(b)** 2.5 J/cm\({}^{2}\) (2.5 Pd/ZnO), **(c)** 5 J/cm\({}^{2}\) (5 Pd/ZnO), and **(d)** 10 J/cm\({}^{2}\) (10 Pd/ZnO). The red dashed lines indicate the extrapolation points corresponding to the optical band gap values. The band gap values, obtained from the crossing points, along with their respective errors, are shown in the bottom-right corner of each graph. The measured band gap values are effectively identical within the stated errors, and the second decimal point serves only to illustrate the overall trend.  
As illustrated by the Tauc plots in Figure 5, Pd functionalization caused a slight tendency toward a red shift in the ZnO optical bandgap. However, the bandgap values remain statistically identical within the error bars. The measured bandgap values range from 3.26 \(\pm\) 0.10 eV for pristine ZnO to 3.24 \(\pm\) 0.10 eV for Pd/ZnO functionalized at 2.5 J/cm\({}^{2}\), and further to 3.22 \(\pm\) 0.10 eV for both the 5 J/cm\({}^{2}\) and 10 J/cm\({}^{2}\) cases. The identical bandgap values observed when a small quantity of Pd is deposited on ZnO can be attributed to the fact that the localized Pd particles primarily influence the surface properties, such as charge transfer, rather than altering the bulk electronic structure of ZnO or introducing significant lattice defects. This behavior aligns with the role of Pd as a occatalyst, enhancing photocatalytic properties by promoting light absorption and facilitating electron transfer without directly impacting the intrinsic bandgap. Additionally, the similar band gap values may also result from the use of the Tauc plot method, which is based on UV-vis diffuse reflectance spectra. This technique predominantly reflects the bulk absorption characteristics of ZnO, which remain largely unaffected at minimal Pd loading.