# Characterization of Monovacancy Defects in Vanadium Diselenide Monolayer: A DFT Study
## 1 Introduction  
Two-dimensional transition metal dichalcogenides (TMDs) are layered materials consisting of one layer of transition metal atoms, such as Mo, V, and W, that are stacked between two layers of chalcogen atoms (S, Se, or Te) [1]. There are some exceptions, such as M\({}_{2\times 3}\) having 2:3 quintuple layers [2] and MX metal chalcogenides [3]. TMDs are used in various electronic, optoelectronic and energy devices, such as transistors [4; 5; 6], flexible and transparent displays [7; 8], and sensors [9]. There are a large number of TMDs, such as molybdenum disulfide and tungsten disulfide [10]. They can be obtained through micromechanical design or through the chemical vapor deposition and chemical vapor transport approaches [11]. Two-dimensional TMDs have several stable polymorphs: the trigonal prismatic H phase, the octahedral T phase and the distorted octahedral atomic configurations (T\({}^{\prime}\) phase or T\({}^{\prime\prime}\) phase) [12; 13]. For example, 2D MoS\({}_{2}\) has several polymorphs differing in the coordination of the Mo atom. The various phases of 2D MoS\({}_{2}\) possess different fundamental properties. Two-dimensional MoS\({}_{2}\) may show semiconducting, metallic or insulating behavior depending on the stacking of the S/Mo/S atomic planes [12]. It has been shown that controllable phase transformations in 2D TMDs are possible via electron beam [14], metal treatment [15] and laser irradiation [16]. Two-dimensional materials in which phase transition is associated with insignificant atomic structure rearrangement, not leading to a change in the material stoichiometry, have enhanced physical behavior. The energetics of the phase transitions in various 2D TMDs have been studied extensively, both experimentally and theoretically [17; 18; 19; 20]. In the case of 2D MoS\({}_{2}\), first-principles calculations have shown that it is unstable in the T phase [18] and spontaneously rearranges into the metastable T\({}^{\prime}\) phase, while the metastable T\({}^{\prime}\) phase transforms to the stable H phase after annealing, as was experimentally observed [21; 22]. On the other hand, it is known that strong electron doping of the system can lead to phase transformations. It has been shown that strong \(n\)-type doping of 2D MoS\({}_{2}\), induced by the alkali metal intercalation or by the electron transfer from the substrate to the MoS\({}_{2}\), makesthe T\({}^{\prime}\) phase more energetically favorable than the H phase in 2D MoS\({}_{2}\)[23; 24; 25; 26; 27; 28]. In addition, the phase transition in 2D TMDs also occurs under in situ electron beam irradiation in the transmission electron microscope [29]. Vanadium diselenide (VSe\({}_{2}\)) is another member of the TMD family, with a trigonal T phase atomic configuration in the bulk form. It consists of layers of V atoms trapped between two layers of Se atoms, and these Se\(-\)V\(-\)Se layers are stacked in the (001) direction. Despite having a similar structure to MoS\({}_{2}\), VSe\({}_{2}\) exists only in the T phase, while MoS\({}_{2}\) also exists in the H phase, with the Mo atoms in octahedral coordination with S atoms [30]. The phase transition from the T phase to the H phase in VSe\({}_{2}\) can be realized via temperature control or applying strain, and the H phase of VSe\({}_{2}\) is usually more stable up to high temperatures [31]. An extensive computation study has shown a comparison of the structural stability and properties of VSe\({}_{2}\) in bulk, thin film, nanoribbon, monolayer and nanotube forms [32]. It has been shown that the VSe\({}_{2}\) in all these forms is ferromagnetic, while exhibiting different electronic properties, such as a bulk and few-layer T phase and H phase. The VSe\({}_{2}\) and a T phase VSe\({}_{2}\) monolayer are metallic, while the H phase VSe\({}_{2}\) monolayer is a semiconductor.