The effect of structural defects on the electron transport of MoS2 nanoribbons based on density functional theory
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Using non-equilibrium Green’s function method and density functional theory, we study the effect of line structural defects on the electron transport of zigzag molybdenum disulfide (MoS2) nanoribbons. Here, the various types of non-stoichiometric line defects greatly affect the electron conductance of MoS2 nanoribbons. Although such defects would be lead to the electron scattering, they can increase the transmission of charge carriers by creating new channels. In addition, the presence of S bridge defect in the zigzag MoS2 nanoribbon leads to more the transmission of charge carriers in comparison with the Mo–Mo bond defect. Also, we find that the different atomic orbitals and their bonding structure at the edge affect the electron conductance of MoS2 nanoribbons. Moreover, we calculate the spin-dependent transport of MoS2 nanoribbons and showed that the spin polarization increases at the non-zigzag edges and remains even in the presence of the defect. This study presents a deep understanding of created properties in MoS2 nanoribbons due to the presence of structural defects.
KeywordsMolybdenum disulfide Zigzag nanoribbon Defect Electron transport Density functional theory Non-equilibrium Green’s function
The synthesis of graphene  has created a new field in two-dimensional electronics which has been led to the fabrication of electronic devices based on single or few atom-thick layers. Graphene has the significant features such as quantum anomalous Hall effect [1, 2], high electron mobility [3, 4, 5] and long electron phase coherence length  which are technologically important. However, similar to three-dimensional electronics, in order to fabricate the various types of electronic devices require a group of conductive, semiconductor and insulating materials with tunable properties. A group of the two-dimensional semiconductors and semimetals is called transition metal dichalcogenides, and MoS2 is the most important member of this family with a direct band gap of Δ = 1.8 eV in its monolayer [7, 8]. The electron mobility of MoS2 on HfO2 substrate is about 200 cm2 V s−1 at room temperature which reduces to 0.1–10 cm2 V s−1 range on SiO2 substrate . The various electronic devices such as transistors , logic circuits  and photodetectors  have been fabricated based on MoS2 monolayer whose properties can be easily tuned by adding external atoms, strain or structural and intrinsic defects. In one project, it has been showed that the presence of point defects in this structure can lead to a new photoemission peak and it increases the luminescence intensity of MoS2 monolayer .
The structural defects such as vacancies, grain boundaries and topological imperfections can be found in MoS2 structures which have been studied both theoretically and experimentally [14, 15, 16, 17]. The recent experiments have shown that divacancies can be rarely found in this structure, whereas monovacancies have been often observed . The intrinsic defects in this structure can be created without removing the atoms of the lattice. For instance, the Stone–Wales defect is formed by the rotation of atoms and the reconstruction of interlayer bonds . Moreover, the line defects in MoS2 have attracted lots of attention. The line defects proposed by Enyashin et al. presented mirror plates around the defect in MoS2 monolayer. Hence, the inversion domains were formed which are important in electronics. They have reported the new states within the band gap of this semiconductor . Although the electron transport in pristine MoS2 is isotropic, the strong anisotropy has been reported in the presence of line defects in this structure . Also, it was showed that in the presence of a finite atomic line of sulfur vacancies, the structure can act as a pseudo-ballistic wire for the electron transport .
Among MoS2 nanoribbons, zigzag-edged types have attracted great attention due to their electronic and magnetic properties which are technologically significant [22, 23]. As we know, a MoS2 nanoribbon contains different atoms at its two edges, i.e., sulfur atoms are located at one edge of MoS2 nanoribbon while molybdenum atoms are observed at the opposite edge. Generally, the number of atoms in the width of zigzag nanoribbon can be even or odd so that the structures are symmetric or asymmetric. Note that the transport properties of graphene nanoribbons are strongly dependent on edge symmetry so that there is the spin-dependent transport only in the asymmetric zigzag graphene nanoribbons [24, 25]. Unlike graphene, the transport properties of zigzag MoS2 nanoribbons are independent of the number of atoms in the width of nanoribbon [26, 27].
In this research, we investigate the effect of line structural defects on the electron conductance of zigzag MoS2 nanoribbon and showed that these defects as scattering centers cannot create the effective transport channels, whereas the presence of them changes the electronic conductance of the zigzag MoS2 nanoribbon. From an empirical point of view, we studied the most stable non-stoichiometric defects such as the Mo–Mo bridge (metallic bond) and S bridge . Recently, a group of researchers investigated the effect of these two defects on the spin-dependent transport of MoS2 nanoribbons. In order to increase the spin-dependent transport, they showed that the best position for defects is the middle part of nanoribbon . However, the importance of edge effects in the presence of these types of defects has not been clearly investigated yet, so we calculated the density of energy states and found that the edge effects can play an important role in the electron transport of nanoribbon. Furthermore, we showed that the structure of edge bonds except zigzag-edged state is able to change the electron and spin-dependent properties. Also, using DFT calculations for the first time, we investigate the effect of Stone–Wales defect on the electron and spin conductance of zigzag MoS2 nanoribbon. Our results show that the electron and spin-dependent transport for zigzag MoS2 nanoribbon reduces in the presence of Stone–Wales defect.
Model and method
All computations which have been presented in this research are composed of two main parts: (a) the optimization of electron structure and (b) the computations concerned with electron transport properties. All of these computations have been performed using SIESTA and TranSIESTA softwares [29, 30].
The electron structure of monolayers, atomic positions and lattice vectors were completely optimized applying periodic boundary conditions with a vacuum separation of about 15 Å perpendiculars to monolayers and a vacuum region about 10 Å outside edge atomic sites of nanoribbon until the exerted forces on each atom become less than 0.003 eV/Å. The energy convergence limit 0.001 meV is considered.
The investigation of electron transport properties based on non-equilibrium Green’s function using DFT calculations has been vastly used in such studies. Here, the SZP basis sets were applied for all atoms. For describing exchange–correlation potential, LDA.PZ has been utilized [31, 32]. The kinetic energy cutoff was set to 100 Ry. Also, the Brillouin zone was sampled by using (1 \( \times \) 1 \( \times \) 100) k-points. Thus, the different electron properties such as conductance, density of states and local current have been calculated.
Results and discussion
The electron conductance as a function of energy for 5-MoS2 nanoribbon is shown in Fig. 3a. Number ‘5’ refers to the number of atoms along the width of nanoribbon. The 3p orbitals of sulfur valence shell and 4d orbitals of molybdenum valence shell concerned with the edge of the structure are responsible for effective electron conductance of this nanoribbon.
Here, the electron transport of nanoribbon depends on the presence and type of line defect. The conductance properties are determined by coupling between the electron transport states of optimized wave functions around Fermi energy when the structural defects act as the scattering centers for electrons. In this research, the Mo–Mo and S bridges are located in the middle of nanoribbon so that the mirror symmetry between upper and lower parts of nanoribbon can be preserved. For the S bridging atoms, the electron conductance exhibits a significant enhancement for negative values of energy (Fig. 3b), while in the presence of Mo–Mo metallic bonds, it is observed that the transmission spectrum covers both negative and positive values of energy (Fig. 3c). As a result, this property depends on the type of the defect, the distance of defect from the edges of MoS2 nanoribbon, the width of nanoribbon  and the edge type of structure. The structure (IV) in Fig. 2 has been shown as the elimination of Mo and S atoms at the upper and lower edges of the structure (I), respectively. It shows an effective increase in electron transport around Fermi energy (Fig. 3d), whereas in the structure in Fig. 3e which contains Stone–Wales point defect, the electron conductance decreases greatly. In fact, such defect in the narrow structure (V) breaks lattice symmetry and acts as a scattering center for electrons. Thus, the effect of electron scattering on the defect sites has created a wide transport for the positive values of energy in this structure. Indeed, the Stone–Wales defect which is created due to the rotation of Mo–S bond and the reconstruction of bonds in the hexagonal lattice is the simplest model of the structural defect in honeycomb lattices.
In Fig. 5, the electron difference density (EDD) has been displayed for the various structures. The EDD is the difference between the self-consistent valence electron density and the superposition of atomic valence electron densities. It shows clearly the charge carriers transfer between atoms forming the structure. The blue and red colors show the excess and shortage of electrons, respectively. As shown in this figure, the electron charge density decreases (increases) at the site of Mo (S) atoms. In the structures (III) and (V), the Mo–Mo metallic bond on the defect has stronger bond strength and the local concentration of electrons on them (red-colored regions) is obvious.
To summarize, in this project using non-equilibrium Green’s Function method based on DFT calculations, the effect of structural defects on the zigzag MoS2 nanoribbon was studied. The results show that electron transport in these structures depends on the type and position of the defect. Although these line defects are not channels for the transmission of charge carriers and act as the scattering regions, the presence of them can change the electron transport of the system and even make their around region participate in the electron transport more extensively. According to this, the configuration of S bridges and edge defects in the form of linear is more favorable for the electron transport. These properties are due to different couplings between the electron states of transport which leads to change in the local current in the vicinity of defect positions. Furthermore, in this paper, the contributions of 3p orbitals of S atoms and the 4d orbitals of Mo atoms have been considered which shows that edge atoms have the great effects on the electron properties of MoS2 nanoribbon. Moreover, the investigation of spin conductance in these structures shows that they have the magnetic characteristics and there is more the spin polarization for non-zigzag edges which is not destroyed even in the presence of the defect. Thus, applying the various structural defects in appropriate positions of MoS2 nanoribbon can be a favorable method for creating significant changes in the electron transport.
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