## 3 Results and Discussion
### The Optical Characteristics of the Photocatalysts  
H\({}_{2}\)O\({}_{2}\) plays an indispensable role in CMP, as it is essential for the formation of complexes through the reaction of Cu(II) with the complexing agent. Therefore, the optical absorption characteristics of CeO\({}_{2}\) and H-CeO\({}_{2}\) were characterized using UV-Vis absorption spectroscopy. As shown in Figure 2a, CeO\({}_{2}\) exhibits an absorption edge at 547 nm. The charge-transfer transition peak observed at 324 nm is due to the charge transfer between the fully occupied 2p (O) orbital and the empty 4f (Ce) orbital [20; 21]. After the addition of hydrogen peroxide, a blue shift in the absorption peak is observed. This is attributed to the Fenton-like reaction between CeO\({}_{2}\) and H\({}_{2}\)O\({}_{2}\):  
\[Ce^{3+}+H_{2}O_{2}+H^{+}\to Ce^{4+}+OH\cdot+H_{2}O \tag{1}\]  
The oxidation of \(Ce^{3+}\) to \(Ce^{4+}\) results in a reduction in the concentration of \(Ce^{3+}\), which is typically associated with a high number of oxygen vacancies in CeO\({}_{2}\). As the amount of \(Ce^{3+}\) decreases, these oxygen vacancies also diminish, lattice defects are filled, and crystallinity increases [22; 23]. UV spectra show that the absorption ranges of both CeO\({}_{2}\) and H-CeO\({}_{2}\) are primarily between 250 and 500 nm, covering most of the ultraviolet and visible regions including violet, blue, and part of the cyan regions. Additionally, the optical band gap energy was determined based on the Kubelka-Munk function using the Tauc plot equation (as shown in Equation (2)) [24]:  
\[(ahv)^{1/n}=A(hv-E_{g}) \tag{2}\]  
Figure 2: (a) UV-Vis diffuse reflectance spectra of CeO\({}_{2}\) and H-CeO\({}_{2}\), (b) Optical bandgap diagram of CeO\({}_{2}\) and H-CeO\({}_{2}\). where \(\alpha\) is the absorption coefficient, \(h\) is [PERSON]'s constant, \(v\) is the photon frequency, \(A\) is a proportionality constant, \(n=1/2\) for the direct bandgap, and \(n=2\) for the indirect bandgap. The optical bandgaps of the two materials are shown in Figure 2b. The optical bandgap of pure CeO\({}_{2}\) was 2.27 eV, while the optical bandgap increased to 2.30 eV with the addition of hydrogen peroxide. After the Fenton-like reaction, a significant amount of hydroxyl radicals is generated, which, in conjunction with CeO\({}_{2}\), greatly enhances the material's oxidative capability [25]. A 365 nm wavelength light source was chosen for photocatalytic reactions using both CeO\({}_{2}\) and H-CeO\({}_{2}\). PL spectroscopy was employed to investigate the recombination efficiency of electron-hole pairs and the photocatalytic activity of the catalyst. Figure 3a shows the PL spectrum of CeO\({}_{2}\) with an excitation wavelength of 350 nm. A peak is observed around 460 nm, which is attributed to the charge transition from the 4f band to the CeO\({}_{2}\) valence band, causing the blue emission peak [26]. Upon adding H\({}_{2}\)O\({}_{2}\), a significant reduction in the PL emission peak is observed. PL spectroscopy is also a method to measure the lifetime of photogenerated carriers in semiconductors; therefore, we used time-resolved fluorescence spectroscopy to calculate the fluorescence lifetime of CeO\({}_{2}\), as shown in Figure 3b. The average fluorescence lifetime is obtained using Equation (3). \[\tau_{average}\ =\ \sum(A_{i}\times\tau_{i}^{2})/\sum(A_{i}\times\tau_{i}) \tag{3}\]  
The average fluorescence lifetime of CeO\({}_{2}\) is 0.0218 ns, and it increases to 0.043 ns after the addition of hydrogen peroxide. The decrease in PL peak intensity and the increase in fluorescence lifetime after adding H\({}_{2}\)O\({}_{2}\) can be attributed to the filling of the material's oxygen vacancies. The lattice defects are reduced, which reduces surface defects and enhances carrier mobility, thereby reducing the recombination rate of photogenerated carriers [27].