# Characterization of Monovacancy Defects in Vanadium Diselenide Monolayer: A DFT Study
## 3 Results
Despite H-VSe\({}_{2}\) being usually more stable up to high temperatures, the phase transition between T-VSe\({}_{2}\) and H-VSe\({}_{2}\) could be realized via temperature control or applying strain [31]. Therefore, in this work, only the migration process of monovacancies in the T-VSe\({}_{2}\) monolayer is considered. The migration process of the VSe and V\({}_{\rm V}\) defects in the T-VSe\({}_{2}\) monolayer, together with the calculated \(E_{\rm migration}\), are shown in Figures 3 and 4. The detailed pathway, including the initial state (IS), an intermediate transition state (TS), and the final state (FS) for the migration process of the VSe in the T-VSe2 monolayer, are presented in Figure 3a. According to Figure 3b and Table 1, the calculated energy barrier \(E_{\text{migration}}\) for the VSe in the T-VSe2 monolayer is 0.88 eV. Similarly, the detailed pathway, including the IS, an intermediate TS and the FS for the migration process of the VV in the T-VSe2 monolayer, are presented in Figure 4a. Based on Figure 4b and Table 1, the calculated \(E_{\text{migration}}\) is found to be 1.24 eV. It is seen that the formation and migration of the VV in the T-VSe2 monolayer are significantly less favorable than the formation and migration of the VSe. It is well known that defects change the local electronic properties of 2D materials due to the breaking of their lattice periodicity [85]. Furthermore, the electronic structure of VSe- and VV-containing T-VSe2 and H-VSe2 monolayers are studied. Figure 5 shows the atomic structure (Figure 5a,d), LDOS (Figure 5b,e) and band structure (Figure 5c,f) plots for the T-VSe2 monolayer containing VSe and VV defects. It is found that the VSe and VV point defects tend to enhance the electron localization and, hence create a defect-induced  
Figure 4: The illustration of the migration process of the VV in the T-VSe2 monolayer (**a**). Energetic profiles of the reaction pathway obtained from NEB calculations (**b**). Figure 3: The illustration of the migration process of the VSe in the T–VSe2 monolayer (**a**). Energetic profiles of the reaction pathway obtained from NEB calculations (**b**). localized state, as seen in the LDOS diagram of the T-VSe\({}_{2}\) monolayer containing V\({}_{\rm Se}\) and V\({}_{\rm V}\) defects in Figure 5b. Furthermore, significant changes in the local electronic properties of the H-VSe\({}_{2}\) monolayer upon the introduction of monovacancies are found. Figure 6 shows the atomic structure (Figure 6a,d), LDOS (Figure 6b,e) and band structure (Figure 6c,f) plots for the H-VSe\({}_{2}\) monolayer containing V\({}_{\rm Se}\) and V\({}_{\rm V}\) defects. Specifically, the presence of the V\({}_{\rm Se}\) defect leads to a significant band redistribution and results in a semiconductor-to-metal transition (Figure 6c), with the defect-induced states appearing in the vicinity of the Fermi level and the conduction bands crossing the Fermi level. Interestingly, the presence of the V\({}_{\rm V}\) defect leads to a significant downward shift of the VBM by \(\sim\)0.15 eV and CBM by \(\sim\)0.05 eV (Figure 6f). In addition, the conduction bands cross the Fermi level, which signifies a semiconductor-to-metal transition in the H-VSe\({}_{2}\) monolayer containing the V\({}_{\rm V}\) defect. These changes can be explained by the presence of dangling bonds in the core of the defect and the significant hybridization of states of the Se atoms in the core of the defect and neighboring V and Se atoms. Therefore, the V\({}_{\rm Se}\) and V\({}_{\rm V}\) defects in the T-VSe\({}_{2}\) and H-VSe\({}_{2}\) monolayers induce remarkable changes in their band diagram and, thus, can be detected via photoemission spectroscopy techniques [86]. Due to their outstanding functionality, 2D materials are widely applied in optoelectronic nanodevices [87; 88; 89]. Yet the functionality of 2D materials may be altered by defective engineering to facilitate their application [90].