## 3 Results  
### Theoretical Calculations of the Electronic Properties of TiO\({}_{2}\):ZnO/CuO  
Based on the first-principles calculations, we investigated the electronic properties of the TiO\({}_{2}\)/ZnO film doped with Cu and CuO atoms. The results were obtained using a software code [22] that implemented the Car-Porinello quantum mechanical dynamics using a local approximation of the electron density function [23] and a pseudopotential preserving norm from the first principles of [PERSON], [PERSON], and [PERSON] [24].  
In this work, we created a cubic structure of the Fm\(\overline{3}\)m space group for the aforementioned film system. The lattice constants were: TiO\({}_{2}\) (4.84 A), ZnO (4.63 A), Cu (3.62 A), CuO (4.23 A). For further calculations, we took the value of the total lattice constant of 4.33 A as the arithmetic mean among the values of the lattice constants presented.  
To reproduce the infinite TiO\({}_{2}\)/ZnO film doped with Cu/CuO, atomic bases of primitive superlattices cells were created that consisted of successive atomic layers of TiO\({}_{2}\), ZnO, Cu, and CuO relative to the direction of the coordinate axis OZ, as shown in Figure 3f. At the same time, the parameters of the cell were such that in the X and Y directions it was possible to simulate an infinite surface of the film, and free surfaces (100) with a passivating coating in the Z direction.  
To study the mechanism of dissociation of Cu/CuO molecules on the surface of (100) TiO\({}_{2}\)/ZnO, we created four calculation models: (1) TiO\({}_{2}\) film; (2) TiO\({}_{2}\) film doped with ZnO; (3) TiO\({}_{2}\)/ZnO film system with absorbed Cu; and (4) TiO\({}_{2}\)/ZnO/Cu film system with an absorbed O\({}_{2}\) molecule (above Cu (100) atoms; in the interatomic void of Cu (100) atoms).  
We obtained the distributions of valence electrons from the energy bands for the Cu/CuO-doped TiO\({}_{2}\)/ZnO film system. Figure 4 shows the distribution of electrons in energy zones for the G state. At the same time, the horizontal axis shows the deposited energy in atomic units, and the vertical axis shows the number of states per elementary energy interval.  
Figure 3: Mechanism of doping the TiO\({}_{2}\)/ZnO (100) film system with Cu/CuO atoms: (**a**) TiO\({}_{2}\) film; (**b**) TiO\({}_{2}\) film doped with ZnO; (**c**) TiO\({}_{2}\)/ZnO film system with absorbed Cu; TiO\({}_{2}\)/ZnO/Cu film system with an absorbed O\({}_{2}\) molecule ((**d**) above Cu atoms (100); (**e**) in the interatomic void of Cu atoms (100)); and (**f**) TiO\({}_{2}\)/ZnO (100) film system doped with Cu/CuO atoms.  
According to Figure 4, the minimum range of the TiO\({}_{2}\)/ZnO film system doped with Cu/CuO corresponds to the value from E = \(-\)37.24 at.un. to E\(=-\)0.16 at.un. with the maximum population of states of the valence band 10 (Figure 4f). The maximum energy value corresponds to a pure TiO\({}_{2}\) film with an energy range from E = \(-\)111.61 at.un. to E = \(-\)62.06 at.un. The maximum occupancy of the valence band states is equal to 6 (Figure 4a). The number of allowed states was determined by half the number of electrons (electron spin was not taken into account). Comparing Figure 4b,f, we also observe a decrease in the energy of the film system and an increase in the maximum occupancy of the valence band states. As we can see, doping the film with Cu/CuO atoms of the TiO\({}_{2}\)/ZnO film system leads to an improvement in the internal properties of the binary oxides.  
At the same time, analyzing Figure 4d,e, it can be concluded that the absorption of an oxygen molecule on the surface of TiO\({}_{2}\)/ZnO/Cu is more likely in the interatomic void of Cu (100) atoms (Figure 4e). In this case, the energy range takes the value from E = \(-\)44.54 at.un. to E = \(-\)2.30 at.un. The maximum occupancy of the valence band states is equal to 8.