Electronic structures of defects and magnetic impurities in MoS2 monolayers
© Lu and Leburton; licensee Springer. 2014
Received: 7 October 2014
Accepted: 1 December 2014
Published: 13 December 2014
We provide a systematic and theoretical study of the electronic properties of a large number of impurities, vacancies, and adatoms in monolayer MoS2, including groups III and IV dopants, as well as magnetic transition metal atoms such as Mn, Fe, Co, V, Nb, and Ta. By using density functional theory over a 5 × 5 atomic cell, we identify the most promising element candidates for p-doping of MoS2. Specifically, we found VB group impurity elements, such as Ta, substituting Mo to achieve negative formation energy values with impurity states all sitting at less than 0.1 eV from the valence band maximum (VBM), making them the optimal p-type dopant candidates. Moreover, our 5 × 5 cell model shows that B, a group III element, can induce impurity states very close to the VBM with a low formation energy around 0.2 eV, which has not been reported previously. Among the magnetic impurities such as Mn, Fe, and Co with 1, 2, and 3 magnetic moments/atom, respectively, Mn has the lowest formation energy, the most localized spin distribution, and the nearest impurity level to the conduction band among those elements. Additionally, impurity levels and Fermi level for the above three elements are closer to the conduction band than the previous work (PCCP 16:8990-8996, 2014) which shows the possibility of n-type doping by Mn, thanks to our 5 × 5 cell model.
Recently, two-dimensional (2D) materials have attracted intensive attentions due not only to the rich and fundamental physics brought by them but also to their potential for nanoscale device applications . Graphene [2–5] is the most well-known member in the family of 2D materials, but its gapless band structure has been deemed as a considerable drawback for realizing switching operation, which is essential for digital logic devices. Even though the bandgap of graphene can be engineered by depositing on particular substrates  or fabricating nanoribbons [7, 8], it deteriorates the mobility. For this reason, researchers have turned to other kinds of 2D materials called transition metal dichalcogenides (TMDCs) . These materials can also be exfoliated into 2D layers from their stacked crystal structure by using the same method as for graphene production . Most intriguingly, their band structures are layer-thickness-dependent despite the weak interlayer van de Waals forces, which indicates they are electronically tunable via thickness control. As the number of layer reduces from bulk value to monolayer, the bandgap of several TMDC materials changes from indirect to direct . Among those and the most widely studied materials, monolayer MoS2 has emerged as a semiconducting alternative to graphene because of its large intrinsic direct bandgap of approximately 1.8 eV , which makes it suitable for optoelectronic and nanoelectronic applications. In addition, easy fabrication using exfoliation method, absence of interface dangling bonds, and superb electrostatic behavior are the main reasons why MoS2 is the subject of nanotechnology research and is a competitive candidate for logic devices of the next generation . Recent experimental works have shown transistors made of single-layer or few-layer unintentionally doped MoS2 exhibiting very high on/off ratios, exceeding 1 × 108, close-to-ideal SS (approximately 70 mV/dec), ultralow standby power, and mobility of at least 100 cm2/Vs  or even up to 700 cm2/Vs when high-k dielectrics are applied , which is competitively comparable to those of current Si-based CMOS technology. On the other hand, good performances were also observed in unintentionally doped multi-layer MoS2 transistors .
Many unintentionally doped MoS2 transistors reported in the literature show either n-type  or p-type  behaviors, with their related defects or impurities altering the transport properties. Although simulations of the electronic and transport properties of MoS2 containing various dopants [16, 17] have been reported, to the best of our knowledge, there is still lack of comprehensive and coherent understanding of the groups III and IV dopants on MoS2, even in the most recent reports . For magnetic impurities, although there are a number of theoretical reports on Mn, Fe, and Co [17, 18], our model on a 5 × 5 computational cell shows impurity levels and the Fermi levels located closer to the conduction band by about 0.1 ~ 0.2 eV and ~0.2 eV, respectively. In this paper, we provide a systematic study on the properties of various p-type dopants, vacancies, and magnetic impurities in monolayer MoS2 including group III dopants, i.e., B, Al, and Ga and group IV dopants, i.e., C, Si, and Ge, as well as magnetic transition metal elements such as V, Nb, and Ta. For the first time, the electronic properties of groups III and IV elements are studied comprehensively in a 5 × 5 simulation supercell of single-layer MoS2 in addition to the investigation of a large number of magnetic transition metal elements on their electronic states, formation energies, and spin properties. Moreover, Mo as an adsorbate in MoS2 is considered. Our objective is to identify the most promising candidates of p-type dopants and magnetic impurities for MoS2. The information will come in handy when fabricating doped devices such as field-effect transistors (FETs), optoelectronic devices, and all those requiring p-n junctions. In addition, the study of spin distribution around magnetic elements provides the basic knowledge for future applications of MoS2 spintronics, which is one of the possible scenarios in the beyond-CMOS technology.
In this work, density functional theory (DFT) is employed to perform ab initio calculations on the electronic and magnetic properties of monolayer MoS2 doped with impurities using the Quantum ESPRESSO software package .
where is the total energy of the defective MoS2 with Mo (S) vacancy.
Results and discussion
Calculated formation energy ( E form ) for Mo-rich condition and the magnetic moment (m) of various impurities and defects in MoS 2 monolayers
Mo adatom on Mo
For group III elements, such as B, Al, and Ga atoms, all of them have three valence electrons less than S atoms. Our calculations show that each of these doped systems has only one remaining unpaired electron, resulting in a magnetic moment of 1 μB (Table 1). Figure 5c,d,e show the DOSs of B, Al, and Ga doped MoS2, with all these systems forming two gap states with opposite spins. The two states formed by the boron substitution in MoS2 are relatively close to the VBM with the partially unoccupied down-spin state separated from the VBM by less than 0.1 eV and exhibiting a spin splitting as small as 0.07 eV. Thus our result shows that the separation between these impurity states and the VBM is less than 50% of the data reported by Qu Yue et al.  (approximately 0.3 eV), which is due to the fact that we use a larger computational cell, thereby resulting in a more accurate binding energy. With an increasing atomic number, group III dopants are characterized by a different trend than group V dopants. The B doping induces impurity states located closest to the VBM than any other groups III and IV dopants. Although these states are slightly higher than that of As, the much lower formation energy of B doping still makes it a highly promising choice for achieving p-type doping in MoS2. When considering Al and Ga dopants, the defect states shift further away from the VBM with large energy differences, i.e., 0.25 eV for Al and 0.9 eV for Ga, and the formation energy also increases from 0.22 eV to around 2 eV (Table 1). To summarize our calculations on the doping at the S site, we find the two smallest atoms (B, C) in our study require the lowest two formation energies. This is because if the size difference between the dopant atoms and Mo are larger, the dopants will be bonded closer and stronger to Mo and the more negative binding energies subsequently cause the lower formation energies. On the other hand, the hybridization between p-orbital of dopant atoms and d-orbital of Mo leads to the impurity states, like the mechanism of Mo-S bonding. Therefore, to introduce gap states near the edge of valence band, the dopants must bring about a valence band structure very similar to what S does. In our work, P, As, and B do the best jobs and prove our theory by showing the closest gap states to VBM.
We used density functional theory over a 5 × 5 atomic cell to investigate systematically the electronic properties of various impurities, vacancies, adatoms, and magnetic impurities in monolayer MoS2, including groups III and IV dopants, as well as magnetic TM atoms such as Mn, Fe, Co, V, Nb, and Ta. Without being computationally prohibitive, the use of 5 × 5 atomic cells provide a more accurate description of the band structure than the single MoS2 cells by relaxing the boundary conditions on the electronic wave functions. Specifically, by investigating the density of states and formation energy of single atom vacancies as well as adatoms in MoS2, we found that the Mo adatom can be a possible source of tail states as reported in experiment. In addition, the use of a 5 × 5 cell indicates that the B dopants in MoS2 induce impurity states that is very close to the VBM, with a low formation energy around 0.2 eV, which is the second lowest among the column III ~ V dopants, and is therefore a highly promising candidate for achieving p-type doping in monolayer MoS2. Our results also indicate that VB group impurity elements such as V, Nb, and Ta have very low formation energies for their substitution of a Mo atom in MoS2, achieving the most negative value for Ta, which has not been reported before. All these impurity states sit at less than 0.1 eV from the VBM, making them optimal candidates for p-type dopants in MoS2. Lastly, when considering Mn, Fe, and Co, with 1, 2 to 3 magnetic moment per atom, respectively, our 5 × 5 atomic cell model provides spin distribution of the three elements that becomes less localized as atomic number increases. Among them, Mn has the lowest formation energy, which makes it a potential candidate for spintronics applications of MoS2.
SCL and JPL thank the Department of Electrical and Computer Engineering and Beckman Institute at University of Illinois at Urbana-Champaign for their continued support, and also gratefully acknowledge supercomputer time provided by the Extreme Science and Engineering Discovery Environment (XSEDE) ECS130001.
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