## 3 Results and Discussion
### Electronic Properties
Likewise, the \(p\)-type Schottky barrier \(\Phi_{\mathrm{p}}\) is the difference in energy  
Figure 2: **(a)** Three-dimensional charge density difference plot and **(b)**\(x\)-\(y\) plane averaged charge density difference for pristine 2D ZnO/graphene heterostructure. **(c)** Atom- and orbital-projected band structures and PDOS of the spin-up and -down channels for the 2D ZnO/graphene system. The size of each circle corresponds proportionally to the orbital contribution of each band. The Fermi level was set to 0 eV. CDD was estimated as follows: \(\Delta\rho=\rho_{\mathrm{2 DZnO/graphene}}-\rho_{\mathrm{2 DZnO}}-\rho_{\mathrm{graphene}}\). In the case of the 3D-CDD, the isosurface level was set to 0.003, while yellow and cyan colors correspond to positive and negative \(\Delta\rho\), respectively. between the Fermi level \(E_{\rm F}\) and valence band maximum (VBM) at the high-symmetry point \(\Gamma\)-point (\(\Phi_{\rm p}=E_{\rm F}-E_{\rm VBM}\)). In our case, the values for \(\Phi_{\rm n}\) and \(\Phi_{\rm p}\) for spin-up/down electrons were determined to be 1.578/1.571 eV and 0.520/0.516 eV, respectively. This result indicates that the 2 DZnO/graphene heterostructure has a \(p\)-type Schottky contact. It was further revealed that the oxygen vacancies and Fe dopants had a significant effect on the charge transfer between 2D ZnO and graphene, and hence the electronic properties of the combined heterostructure (Figures 3-5). As can be seen from Figure 3a,b, the presence of oxygen vacancies leads to the extension of the charge accumulation region in the middle of the heterostructure. Despite the shape of the CDD curve of the 1V\({}_{\rm O}\)-2D ZnO/graphene structure still resembling that of pristine 2D ZnO/graphene, one can note the emergence of slight asymmetry in the interfacial charge distribution (Figure 3c), with a shift of the central positive peak towards graphene and an increase in the charge depletion near the zinc oxide. Such asymmetry becomes more apparent in the case of the 2V\({}_{\rm O}\)-2 DZnO/graphene heterostructure (Figure 3d). Moving to Fe-doped 2D ZnO/graphene heterostructures (Figure 3e-h), it can be concluded that the Fe dopants promote a pronounced charge accumulation from both sides of the graphene, suggesting stronger charge transfer from the 2D ZnO to graphene. This is in good agreement with adhesion analysis results, according to which the adhesion between the Fe-doped 2D ZnO layers and graphene surface is the strongest among all considered structures. Expectedly, the observed peculiarities of the charge distribution at the interfaces containing defects in the zinc oxide layer are reflected in the band structure and PDOS of the investigated heterostructures (Figures 4 and 5). The main observation was the shift of the Dirac point below the Fermi level and the appearance of defect-related energy states near the Fermi level. However, the vdW interaction was confirmed by the well-preserved Dirac cone in graphene, as it was visibly apparent. Table 1 provides a quantitative comparison of the key parameters describing the electronic properties of the heterostructures with a defective 2 DZnO layer. Figure 3: (**a,b**) Three-dimensional charge density difference plot and (**c,d**) \(x\)-\(y\) plane averaged charge density difference for 1V\({}_{\rm O}\)-2 DZnO/graphene and 2V\({}_{\rm O}\)-2 DZnO/graphene heterostructures, respectively. (**e,f**) Three-dimensional charge density difference plot and (**g,h**) \(x\)-\(y\) plane averaged charge density difference for 1 Fe-2 DZnO/graphene and 2 Fe-2 DZnO/graphene heterostructures. Figure 4: Atom- and orbital-projected band structures and PDOS of the spin-up and -down channels for the (**a**) 1V\({}_{\text{O}}\)-2 DZnO/graphene and (**b**) 2V\({}_{\text{O}}\)-2 DZnO/graphene heterostructures. The size of each circle corresponds proportionally to the orbital contribution of each band.