## 3 Results and Discussion
### The Mechanism of the Photocatalytic Reaction  
The electronic band structure of the photocatalyst is inevitably linked with the photocatalytic performance. The electronic band structure of S850 was investigated by the Mott-Schottky relationship, which can be applied to approximately estimate the potential of the CB edge of semiconductors. Figure 5 shows the Mott-Schottky plots measured under various AC frequencies for S850. The Ag/AgCl electrode was used as a reference and the measured potentials are thus relative to the Ag/AgCl electrode. Apparently, the positive  
Figure 4: (**a**) Photocatalytic H2 evolution and (**b**) H2 evolution rates of Rh2-yCryO3-loaded GaN:ZnO solid solution, (**c**) cycle stability of Rh2-yCryO3-loaded S850, (**d**) photoluminescence spectra, (**e**) transient photocurrent, and (**f**) EIS Nyquist plots of S750, S850, and S950 samples.  
slopes of the tangent lines of the Mott-Schottky plots reveal the n-type semiconductor characteristic of GaN:ZnO solid solution [42]. The flat band potential obtained from the Mott-Schottky plots shows a frequency dependency. Theoretically, different frequencies have no effect on the flat band potential of the samples. However, it may be inconsistent because of differences in the properties of the samples, such as the degree of dispersion or the thickness of the drop cast films [43]. Using the popular method [43], it can be determined that the flat band potential of S\({}_{850}\) is \(-1.16\) V vs. an Ag/AgCl electrode. For most n-type semiconductors, the bottom of CB is about 0.10-0.30 eV higher than the Fermi level and 0.20 eV was selected for S\({}_{850}\). Moreover, an Ag/AgCl electrode vs. an NHE electrode is 0.22 V. In short, the calculated CB edge potential is \(-1.14\) V vs. an NHE electrode. Combined with the band gap value obtained from the UV-visible absorption spectra, the VB position of S\({}_{850}\) can be calculated as 1.62 V vs. an NHE electrode. The electronic band structure of S\({}_{850}\) is illustrated in Figure 6.  
Figure 5: Mott-Schottky plots of S\({}_{850}\). Electrolyte: 0.2 M Na\({}_{2}\)SO\({}_{4}\). The different AC frequencies were used for the measurements: 1500, 2000, and 2500 Hz. Tangent lines of the Mott-Schottky plots were drawn to obtain the flat band potential.  
Figure 6: A schematic illustration of the electronic band structure and the photocatalytic H\({}_{2}\) generation mechanism of GaN:ZnO solid solution.  
In the process of water splitting for H\({}_{2}\) production, in order to ensure the progress of the reaction, three conditions must be satisfied: (1) the band gap of the photocatalyst should be greater than the theoretical decomposition voltage of water (1.23 V); and (2) the potentials of photogenerated electrons and holes must satisfy the requirements for reducing water to H\({}_{2}\) and oxidizing to O\({}_{2}\), respectively. Specifically, the bottom of CB of the photocatalyst is more negative than the redox potential of H\({}^{+}\)/H\({}_{2}\) (0 V vs. NHE) and the top of VB of the photocatalyst is more positive than the redox potential of O\({}_{2}\)/H\({}_{2}\)O (1.23 V vs. NHE). (3) The energy provided by light needs to be greater than the band gap of the photocatalyst. As shown in Figure 6, the top of VB of S\({}_{850}\) is positive compared to the redox potential of O\({}_{2}\)/H\({}_{2}\)O, and the bottom of CB is negative compared to that of H\({}^{+}\)/H\({}_{2}\). Therefore, the GaN:ZnO solid solution shows efficient performance on photocatalyst water-splitting for H\({}_{2}\) production.