# Characterization of Monovacancy Defects in Vanadium Diselenide Monolayer: A DFT Study
## 1 Introduction
Another theoretical study has demonstrated the thermodynamic stability of the H phase and T phase VSe\({}_{2}\) monolayers and evaluated the phase transition temperature of 200 K, at which the phase transition between the H phase and T phase in the VSe\({}_{2}\) monolayers occurs [30]. A thin film of VSe\({}_{2}\) has been successfully synthesized by various approaches; for instance, an ultrathin VSe\({}_{2}\) composed of four to eight layers has been synthesized via liquid exfoliation of a bulk VSe\({}_{2}\) crystal in a formamide solvent [33]. A one-pot colloidal method has been applied to fabricate a 0.4 nm thick ultrathin VSe\({}_{2}\) nanosheet consisting of five layers [34]. Similar to other 2D materials, 2D TMDs have a high surface-to-bulk ratio, and, as a consequence, there is a strong possibility of defects forming on their surface [35; 36; 37; 38; 39; 40; 41]. Native point defects may inevitably form in 2D TMDs under various production and usage conditions, for example, during the growth of 2D TMDs at relatively high temperatures. The concentration of defects in 2D materials also depends on the various growth and usage conditions, such as pressure, temperature, and environmental conditions [42; 43; 44]. Obviously, due to the reduced dimensionality of 2D TMDs, defects have a much stronger impact on their properties than the bulk TMDs [45]. It is well known that defects influence the optoelectronic and magnetic properties of 2D TMDs [46; 47; 48; 49]. For instance, defects in 2D MoS\({}_{2}\), such as vacancies, dislocations, and grain boundaries, reduce its charge carrier mobility [47]. On the other hand, the presence of a small concentration of defects in high-quality crystalline TMD samples can be desirable for their application. However, it is necessary to identify the type and concentration of defects in TMDs before their properties can be controlled via defect engineering. This is a non-trivial task; for example, scanning tunneling microscope techniques allow the spatial imaging, measurement, and manipulation of surfaces at the atomic level [50], while the use of a transmission electron microscope may damage ultrathin 2D samples [39; 47]. Consequently, understanding the structure of defects is an important step in the understanding of their impact on various properties of 2D TMDs. Recently, a comprehensive analysis of defects in bilayer MoS\({}_{2}\) at the atomic level using aberration-corrected transmission electron microscopy has shown that an increase in the concentration of the S vacancies leads to their aggregation into larger defect complexes, which, in turn, impacts the interlayer stacking in MoS\({}_{2}\)[51]. The electron beam irradiation is an effective tool to control the spatial location and density of defects in layered materials [38; 52]. For example, [PERSON] et al. have proposed electron energy loss spectroscopy and scanning transmission electron microscopy techniques to assign types of impurities/defects in low-dimensional WS\({}_{2}\) structures with different optical properties [53]. Computational studies play an important role in the study of defects in 2D TMDs. A systematic density functional theory (DFT)-based study has shown how to control the magnetic and electronic properties of the MoSe\({}_{2}\) monolayer via the incorporation of point defects on its surface [54]. Another systematic investigation on vacancies in the MoSe\({}_{2}\) monolayer by the scanning transmission electron microscope imaging and DFT-basedsimulations demonstrated that minimizing the concentration of antisite defects in the MoSe\({}_{2}\) monolayer is needed for its application in electric transport devices, as the introduced antisite defects produce local magnetic moments in the MoSe\({}_{2}\) monolayer [55]. A number of DFT-based simulations have also been used to identify the local defect states within the band gap of 2D TMDs obtained by scanning transmission electron microscopy [37; 56; 57; 58].