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Character of defect states in vacancy-doped MoTe2 monolayer: Spatial localization, flat bands and hybridization gap
Superlattices and Microstructures 130 (2019) 528–538
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Superlattices and Microstructures journal homepage: www.elsevier.com/locate/superlattices
Character of defect states in vacancy-doped MoTe2 monolayer: Spatial localization, flat bands and hybridization gap Xiongying Dai a, b, Zhixiong Yang c, Aolin Li a, Jianyu Yang b, Fangping Ouyang a, c, * a
School of Physics and Electronics, Hunan Key Laboratory for Super-Microstructure and Ultrafast Process, Central South University, Changsha, 410083, People’s Republic of China College of Science, Hunan Institute of Engineering, Xiangtan, 411104, People’s Republic of China c Powder Metallurgy Research Institute, State Key Laboratory of Powder Metallurgy, Central South University, Changsha, 410083, People’s Republic of China b
A R T I C L E I N F O
A B S T R A C T
Keywords: MoTe2 monolayer First-principle calculations Vacancy defects Electronic structures
The structural and electronic properties of vacancy-doped 1H and 1T0 MoTe2 monolayers are systematically investigated based on first-principles calculations. Te vacancy is found energeti cally favored over Mo vacancy for both phases, and Te double vacancy is more favored as it is formed by missing two Te atoms from opposite sides. Vacancy induced defect states are strongly spatially localized on the atoms within two or three shell surrounding the point defect. This strongly localized nature leads to weak dependence of the defect formation energy on defect concentrations, sharply peaked density of states, and flat bands. Moreover, the calculation sug gests that Te vacancy opens a band gap in the 1T0 MoTe2 monolayer, which can be tuned by lattice strain or external force. These results might give a guidance for the research on the application of MoTe2 in electronics and optoelectronics.
1. Introduction Two-dimensional (2D) materials have inspired high hopes to miniaturization the current electronic devices since the exotic properties of graphene were published in 2004 [1]. Though graphene exhibits high mobilities and stabilities, its application in many active components (like diode, transistor and optoelectronic devices) is limited because of its zero gap. Lots of relative researching interest has then been put on other 2D materials, such as transition metal dichalcogenides (TMDs) [2–4], arsenic sulfide [5,6]. TMDs are a group of layered compounds with a general formula MX2, where M is a transition metal, and X represents a chalcogen. Among these TMDs, the group-VI TMDs (M ¼ Mo or W) possess an intrinsic gap and have potential application in electronic devices [7]. The performance of MoS2-based field-effect transistors (FETs) has been studied in many works [8–14]. A MoS2 FET can exhibit large transconductance (4.4 mS/μm), high on-off ration (>1010) and excellent short channel behavior [11], but at the same time it is limited by low mobility, high contact resistance and large background n-doping [15]. Therefore, MoS2 is desired by low energy dissipation applications but still challenged for high performance applications. Some recent studies suggested the challenges on MoS2 devices might be overcome by MoTe2 devices. In theoretical research within the deformation potential approximation, long wave acoustic phonon limited mobilities for 2D MoTe2 can be up to 2526 cm2 V 1 s 1 at * Corresponding author. School of Physics and Electronics, and Institute of Super-microstructure and Ultrafast Process in Advanced Materials, Central SouthUniversity, Changsha, 410083, People’s Republic of China. E-mail address: [email protected] (F. Ouyang). https://doi.org/10.1016/j.spmi.2019.04.044 Received 31 January 2019; Received in revised form 21 April 2019; Accepted 29 April 2019 Available online 10 May 2019 0749-6036/© 2019 Elsevier Ltd. All rights reserved.
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room temperature, which is much higher than the value of 340 cm2 V 1 s 1 for MoS2 [16]. MoTe2 has the smallest energy difference between the semiconducting phase (1H) and the metallic phase (1Tor 1T0 ) among the group-VI TMDs and can form stable homo junction contacts by phase transition [17]. Ohmic contact has been realized in MoTe2 devices by setting a heterophase structure as a buffer contact layer [18,19]. Moreover, intrinsic MoTe2 FETs exhibit ambipolar transfer characteristics [20] and their carrier type can be modulated through rapid thermal annealing under a controlled O2 environment and benzyl viologen doping [21]. Recently, many efforts have been put on the preparation of high quality 2D MoTe2 [22–24]. Few layers or monolayers of MoTe2 have been fabricated through chemical vapor deposition [22–24]. The electronic properties inevitably influenced by defects whether they are artificial or natural. The roles of defects in 2D materials, such as inducing magnetism [25], creating new topological states [26], generating localized and single photon emission [27] et al., have been revealed in various compound by many researches. TEM and STEM images show that there are many vacancies in the prepared MoTe2 [28]. These vacancies have been found to play an important role on the stability for MoTe2 materials [29,30]. A 3% or more concentration of Te vacancies can cause 1H-1T0 transition in the 2D MoTe2 [19]. On the other hand, vacancies may also produce significant effects on the electronic and optical properties [31,32]. However, there is still lack of systemically study on the electronic structure of vacancy doped MoTe2 monolayer, especially on 1T0 MoTe2 monolayer. With regard of this, a systemically study has been done on the structural properties and electronic properties of twelve kinds of vacancy-doped 1H and 1T0 MoTe2 monolayers in this work. The primary contents are organized as follow. Firstly, the structures and electronic structures of pristine MoTe2 monolayers have been calculated with atomic localized orbitals basis sets. Then, the local nature of vacancy-induced defect states is introduced followed by a discussion on the relationship between formation energy and defect concentration. After that, the electronic structures for various vacancies are presented with a focus on the mid-gap states in 1H phase and gap opening in 1T0 phase. Finally, the vacancy effects in different defect concentration and the evolution of vacancy-induced gap in 1T0 phase are discussed. 2. Computational methods First principles calculations are performed using software package Atomistix Tool Kit (ATK). Hartwigsen, Goedecker, Hutter (HGH) pseudopotential together with Tier 4 basis sets is used [33]. This combination of pseudopotential and basis sets has been carefully checked by comparing the calculated results for pristine monolayer with other methods. Generalized gradient approximation (GGA) of Perdew–Burke–Ernzerhof form is adopted for electronic interaction [34]. The integration of potential and charge density are per formed in a grid mesh with cut-off energy of 75 Hartree. The density of k-point mesh used for integrations over the first Brillouin zone is
Fig. 1. (a) Top view of atomic structure of 1H MoTe2 monolayer; (b) top view of atomic structure of 1T0 MoTe2 monolayer; (c) side view of atomic structure of 1H MoTe2 monolayer; (d) side view of atomic structure of 1T0 MoTe2 monolayer; (e) band structure, total density of states (TDOS) and partial density of states (PDOS) of 1H MoTe2 monolayer; (f) band structure, TDOS and PDOS of 1T0 MoTe2 monolayer. 529
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set 15 Å in relaxation self-consistent calculations and 21 Å in density of state (DOS) calculations [35]. Atomic structures are fully optimized until the force on each atom is less than 0.01 eV/Å. The vacancy formation energy in MoTe2 monolayer is calculated as Ef ¼ Etotal Emonolayer þ Eatom, where Etotal and Emonolayer are the total energies of the monolayer with and without vacancies, respectively, and Eatom is the chemical potential for host atoms, which depends on the material growth conditions and satisfies the boundary conditions. 3. Results and discussions 3.1. Atomic structures and electronic structures of MoTe2 monolayer in various phase The relaxed atomic structures of 1H and 1T0 MoTe2 monolayers are presented in Fig. 1(a–d). The top view of 1H MoTe2 monolayer presents as a hexagonal sheet, where Mo atoms occupy one sublattice and Te atoms occupy the other. The side view shows the Mo atoms form a layer and are sandwiched between two Te layers. A Mo atom is surrounded by six Te atoms with trigonal prismatic coordination. The 1T0 structure is a distortion version of 1T structure, of which one Te layer glides to the hexagon center as compared to 1H phase. The distortion causes the unit cell of 1T0 being rectangle and existing two inequivalent Te sites. As shown in Fig. 1(d), one Te site denoted as Tel is close to the Mo layer than the other denoted as Teh. The equilibrium lattice constant, bond length, bond angle and height between two Te atom planes are given in Table 1. The calculated lattice constants are 3.59 Å for 1H phase, and 3.52 Å (a), 6.36 Å (b) for 1T0 phase. The corresponding values calculated with the projected-augmented wave (PAW) method plus a plane-wave basis set are 3.55–3.56 Å, 3.44–3.455 Å and 6.368–6.39 Å, which have only about 1%, 2% and 1% relative difference with our calculation, respectively [17,36–38]. Whereas the local density approximation (LDA) gives a much lower prediction of 3.46 Å for 1H phase [38,39]. The lattice constants of 1T0 monolayer agree well with the experimental measurement of 3.52 Å and 6.33 Å [40]. Fig. 1(e and f) shows the band structures, total DOS (TDOS) and partial DOS (PDOS) of perfect MoTe2 monolayers. The calculated band gap of 1H MoTe2 monolayer is a direct gap of 1.01 eV along Γ-X direction, which is close to the experimental value of 1.1 eV [41] and the PAW predicted value of 1.07 eV [42]. 1T0 MoTe2 monolayer exhibits metallic character with d-p hybridized bands across the Fermi level. The difference between electronic structures of 1H and 1T0 MoS2 has been known as a result of their different coordination environments of Mo atom based on crystal field theory [38]. Because the crystal field is contributed by neighboring atoms, the un derstanding for other kinds of TMDs or bulk TMDs is also applicable for MoTe2 monolayer except magnitude difference of crystal field. Mo d orbitals in 1H structure are split into three groups by the trigonal prismatic crystal field, which are a1 ðdz2 Þ, eðdx2 y2 ; dxy Þ and 0 e ðdxz ; dyz Þ in order of ascending energy. The orbitals of e overlap with the chalcogen p orbitals forming bonding states and antibonding states. Theoretical calculations also proved there exists strong interband hybridization between a1 and e [43], which re sults in the bandgap larger than the splitting energy between a1 and e. As a result, valence bands and conduction bands of 1H phase are composed of dz2 ; dx2 y2 ; dxy and p components [38,43]. This is consistent with our calculated DOS which shows d-p hybridization character around the Fermi level, particularly in the deep valence region and upper conduction region. The PDOS of 1T0 MoTe2 monolayer also exhibits heavily mixing of the Mo d and Te p orbitals around the Fermi level, but this region is overlapped with the Mo d dominated region. Hence, there is no band gap existing in 1T0 phase. The differences between 1T0 phase and 1H phase are that the distorted octahedral splitting is smaller than the trigonal prism splitting and the shorter Mo–Mo bond in distortion structure makes a larger overlap of d orbitals [44]. This leads to 1T0 MoTe2 monolayer have smaller d orbital splitting energy and wider d band width, and thus the band gap closes. Moreover, it should be notice Mo d orbitals in a regular octahedral crystal field are split into two groups, namely, one lower t2g (that contains dxy ; dxz ; dyz orbitals) and one higher eg (that contains dz2 ; dx2 y2 orbitals), which is different from the trigonal prism splitting [38]. Compared to the bulk counterpart, MoTe2 monolayer loses the interlayer interaction. Out-of-plane oriented orbitals, such as metal dz2 orbitals and chalcogen p orbitals, are predicted to have larger interlayer interaction than other orbitals [43]. It is well known as a semiconducting TMD is reduced from bulk to monolayer its band gap transit from indirect to direct. This is because the conduction band minima on the K point (due to a rectangle supercell is used, the K point is folded to the ΓX line in our case) is composed of a higher weight of out-of-plane oriented orbitals than the original conduction band edge [38], and it shifts down below the latter as the interlayer interaction missing. This change has been revealed by photo luminescence spectra experiment for MoTe41 2 and captured by our calculation. A lack of interlayer interaction also changes the electronic structure of 1T0 MoTe2 monolayer as compared to its bulk counterpart, but keeps the metallic character, indicating a heterophase homojunction of 1H and 1T0 MoTe2 monolayer is a metal-semiconductor junction. Our results for band gap, band composition and DOS are consistent with previous studies [23]. It is shown the calculation with Tier 4 basis sets can capture all the important characters of the structure and electronic structures for both 1H MoTe2 and 1T0 MoTe2. Table 1 Calculated lattice constant, bond length, bond angle, height between two Te atom planes, and band gap values for optimized 1H and 1T0 MoTe2 monolayers. 1H 1T0
Lattice Constant(Å)
Bond length (Å)
Bond angle (�)
Height (Å)
Band Gap(eV)
a ¼ 3.59 a ¼ 3.52 b ¼ 6.36
l ¼ 2.77 l1 ¼ 2.74 l2 ¼ 2.86
θ ¼ 82.90 θ1 ¼ 77.76 θ2 ¼ 116.41
d ¼ 3.66 d1 ¼ 4.20 d2 ¼ 3.00
1.01 0.00
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3.2. Structures and stabilities of vacancy-doped MoTe2 monolayer Vacancy is generated due to the missing lattice atom. Generally, both Mo and Te atom in the MoTe2 monolayer are possible missing to form Mo vacancy and Te vacancy. The effects of atomic vacancies on the properties of MoTe2 monolayer are studied by constructing one or two atomic vacancy in a rectangular supercell of various sizes. Fig. 2 (a) shows the structures of four vacancy defects within 1H MoTe2 monolayer and eight vacancy defects within 1T0 MoTe2 monolayer. The defect VMo represents a single Mo atom vacancy, VTe is a single Te atom vacancy, and DVTe, DV0 Te are double Te atom vacancies. The superscript (0 ) appears or not represents the two missing Te atoms are on different Te sides or the same side. For 1T0 MoTe2 monolayer, the inequivalent Te sites are distinguished from the postfix in subscript, where “-h” corresponds to the higher site, “-l” corresponds to the lower site, “-hl” corresponds to one absence from higher site and one from lower site. The vacancy point defects are placed in rectangular supercells, as shown in Fig. 2 (b). Supercells of varying cell sizes are adopted to investigate the effect of defect concentration, including 2 � 2, 3 � 2, 4 � 2, 4 � 3 and 4 � 4. In the case of only one defect within the supercell, the defect concen tration is calculated to be 1/Ncells, where Ncells is the number of primitive unit cells per supercell. Cell sizes and the corresponding defect concentrations, defect separations, area densities are listed in Table 2. Fig. 2 (c) presents the calculate formation energy for all considered systems, separated in single vacancy defects and double vacancy defects. It is noted that the formation energy of a single Mo vacancy is much larger than that of a single Te vacancy. This can be intuitively understood because the number of broken Mo–Te bonds in creating a Mo vacancy is twice of that in creating a Te vacancy. The similar conclusion has also been made for many members of the TMD family [42]. Nevertheless, it should be noticed Mo vacancy can also be found in the monolayer with a relatively low concentration [45]. In 1T0 monolayer, the formation energies of a lower site Te vacancy are almost 1 eV smaller than that of a higher site vacancy. This result indicates that Te vacancies in 1T0 monolayer prefer to appear on the lower sites, which have longer bond with Mo atoms as given in Table 1. For double vacancies, the energetically favorable vacancy type in 1H monolayer is DVTe. The formation energy of DVTe is about 0.8 eV lower than that of DV0 Te. In comparison with the formation energy of a VTe, the formation energy per missing atom is lower for a DVTe. Hence, double vacancies formed by missing two neighboring Te atoms on the same side are more thermodynamically favored over single Te vacancies in the 1H MoTe2. In 1T0 case, the smallest formation energy of double vacancies varies with concentration. The energetically most favorable double Te vacancy is DV0 Te-l for concentration of 12.5% and is DVTe-l for concentration larger than 6%.
Fig. 2. (a) Twelve vacancy structures considered in this study, four (left column) for 1H MoTe2 monolayer and eight (right two columns) for 1T0 MoTe2 monolayer; (b) The rectangular supercells of monolayer MoTe2, used to simulate a defect concentration of 3.1%. The red circles indicate positions of missing atoms; (c) The relationship between formation energies and concentration for single vacancies; （d）The relationship between formation energies and concentration for double vacancies. 531
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Table 2 Concentrations, defect separation and area density of vacancy point defects in MoTe2 monolayers, corresponding to one defect in varying cell size. Cell size
2�2
3�2
4�2
4�3
4�4
defect concentration (%) defect separation 1H (Å) defect separation 1T (Å) area density 1H (1013 cm 2) area density 1T (1013 cm 2)
12.5 7.1 7.0 11.54 11.16
8.3 10.7 10.4 7.70 7.44
6.3 12.4 12.7 5.77 5.58
4.2 14.3 14.1 3.85 3.72
3.1 14.3 14.1 2.88 2.80
3.3. Localized nature of defect states The vacancies alter the periodic potential of perfect 2D crystal and thus change the motion of electrons. Especially, the non-bonding electrons of atoms around the vacancies are usually localized. The two most stable single vacancies VTe and VTe-l are chosen as ex amples to discuss the localization of defect states in vacancy-doped 1H and 1T0 MoTe2. The localized nature of defect states is analyzed with the local DOS (LDOS) of Mo atoms along a line in armchair direction starting on the defect (atoms a) and moving away from it (atoms b, c, d), as shown in Fig. 3. The LDOS of atom d is already close to the LDOS of a Mo atom in the perfect monolayers for both 1H and 1T0 phase. The LDOS of atom a, however, has some peaks that are not presented in corresponding perfect monolayer. Those peaks significantly fall in the atoms b and c, indicating the defect states is strongly localized on the atoms directly surrounding the vacancy. The observation of strong localization of vacancy defect states in MoTe2 is similar with the situation in MoS2 monolayer of which the defect states also distribute on atoms within two or three shell surrounding the vacancy [46]. The strong localization of defect states can be seen from the relationship between the defect formation energy and defect con centrations as shown in Fig. 2 (c). The defect states distribute primarily on the atoms directly surrounding the vacancy, indicating the electronic interactions between neighboring vacancies are very small when they are separated by a few shells of atoms. In our case, the tensest arrangement of defects corresponds to a high concentration of 12.5%. Single vacancies arranged in this way are separated by only one shell of Mo atoms. The formation energies for single vacancies show little change as the concentration reduces. This result provides another evidence for the strong localization of the defect states in MoTe2. On the other hand, some double vacancies, such as DV0 Te-l and DV0 Te-h, directly connect with each other in the tensest arrangement scheme, which are line defects in fact. Thus, the formation energies change seriously at high defect concentration region. As the concentration reduces to 6.3%, the defect formation energies of double vacancies become independent on the concentration. This result also agrees well with the LDOS, in which the defect induced peaks are visible only on the two or three shells of atoms near the vacancy.
Fig. 3. （a）The structure and LDOS of VTe doped 1H MoTe2 monolayer; (b)The structure and LDOS of VTe-l doped 1T0 MoTe2 monolayer. The defect concentration is 3.1%. 532
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3.4. Defect effects on the electronic structures: in-gap state in 1H and band gap opening in 1T0 The TDOS and band structures for various defective MoTe2 monolayers are presented in Fig. 4 and Fig. 5 to investigate the effects of vacancies on the electronic structure. The calculated TDOS and band structures of vacancy doped 1H MoTe2 is similar with that of 1H MoS2. A common characterization is the in-gap states. As shown in Fig. 5, a VMo defect induces five nearly flat bands in the band gap, and a VTe or a DVTe induces two flat bands. Correspondingly, several density peaks appear in the total DOS. For VMo doped monolayer, the two flat bands of lower energy and the two bands of higher energy are nearly double degenerated, making the two higher peaks in the total DOS. The middle singly band forms another lower peak. Those in-gap states originate from the dangling bonds around the removed Mo atom or Te atom [47]. The dangling bonds of the Mo atoms should be responsible for the in-gap states for VTe and DVTe doped monolayer. The difference of the electronic structures between VTe and DVTe is the relative energy shift of gap states. Gap states induced by DVTe are closer to the conduction band bottom than that induced by VTe. This is also the case in MoS2 [46]. The band structure shows a DV0 Te induces four unoccupied flat bands in the gap, which is twice of the in-gap states induced by single vacancy VTe or divacancy DVTe. This increase in the number of in-gap states can be regarded as the result of that removing two Te atoms in the same side leads to five Mo dangling bonds while a VTe or a DVTe leads to three dangling bonds only. For all vacancies, those occupied levels are far from the conduction band bottom and those unoccupied levels are far from the valence band top. This character may lead seldom electrons transitions between defect-induced levels and the conduction (valence) band and thus result in a low concentration of doping carriers. However, it still needs more advanced methods to precisely determine the position of the in-gap states, like quasi particle based electronic structure methods. They are computationally very demanding and go beyond the scope of the present work. Vacancy effects on the electronic structures of metallic 1T0 MoTe2 monolayer lead to a change in the state densities around its Femi level. As shown in Fig. 4, several density peaks appear in the DOS of defective 1T0 MoTe2. The number of peaks varies with the vacancy type. VMo gives rise to three density peaks in the TDOS of 1T0 MoTe2, one occupied and the other two unoccupied, which is similar with that of VMo on 1H MoTe2 and can also be attributed to dangling bonds. Here, we highlight the small band gaps in band structures of VTe0 l and DVTe-hl doped structures, which suggests a transition from metal to semiconductor and a dramatical change in conductivity of 1T MoTe2. Other Te vacancies such as VTe-h, DV0 Te-h and DVTe-h also have serious effects on the band structure of 1T0 MoTe2 for their conduction band bottoms are crossed by Fermi level and separated from the valence top by a gap. This indicates that VTe-h, DV0 Te-h and DVTe-h doped 1T0 MoTe2 exhibit a semi-metallic characterization. Vacancy can expose the Mo atom of MoTe2 monolayer to air and create unpaired electrons on the neighboring atom, which may influence the chemical reactivities surrounding the vacancy. This has been reflected by the position of DOS peaks corresponding to defect states. Some vacancies, such as VMo, have a DOS peak below the Fermi level, from which electrons can be transferred to ad sorbates of acceptor-type or with oxidability. Because the energy of VMo states is higher than the valence band top in the 1H MoTe2, electron losing from the vacancy vicinity will be easier than from other position. For the same reason, vacancies that induce DOS peaks above the Fermi level make the vacancy vicinity being easier to accept electrons from absorbates of donor-type or with reducibility, such as a VTe on 1H MoTe2. The change of chemical reactivity in the defective MoTe2 monolayer can also been from the Fukui function in Fig. 6, which is defined as the difference of electron density between the neutral system and the system added one electron ðf þ ðrÞÞ or removed one electron ðf ðrÞÞ. Both phases exhibit reactivity change on the vacancy vicinity but the semiconducting phase changes more serious as their Fukui functions have greater weights around vacancy. Moreover, the Fukui function reflects a detail for the VMo doped 1H MoTe2, in which atoms surrounding the vacancy have different chemical reactivities even though they are equivalent in the pristine monolayer, like atoms marked with number in Fig. 6 (a). This is a result of structure distortion near the VMo, which can be further attributed to Jahn-Teller effects. 3.5. Dependence of electronic structure on defect concentration The defects are periodically arranged on the lattice in this work, which is not the situation in the practical materials. Even so, as the
Fig. 4. The change in TDOS of MoTe2 monolayer induced by the considered point defects with a concentration of 6.3%. 533
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Fig. 5. The change in band structure of MoTe2 monolayer induced by the considered point defects with a concentration of 6.3%. The red dot lines present the band structures for perfect monolayers. The in-gap states of vacancy-doped 1H MoTe2 are highlighted in color and the inserts zoom in the bands close to the Fermi level which indicates a transition from metal to semiconductor or semimetal occurring.
concentration of defect drops to a certain level, the calculated electronic structure may provide a suitable scope to the effects of an individual defect due to the strongly localization of defect states. On the other hand, vacancies in prepared MoTe2 can be occasionally close to each other, thus the interaction between the closely embedded defects can be investigated from the periodic model of high concentration. A discussion on the evolution of DOS with the decrease of defect concentration is then necessary. For simply, the most stable single vacancy and divacancy for each phase are taken as examples. That is, VTe and DVTe for 1H MoTe2, VTe-l and DVTe-l for 1T0 MoTe2. The total DOS per unit cell for VTe and DVTe doped 1H MoTe2 with concentration ranging from 12.5% to 3.1% is presented in Fig. 7. The TDOS for a perfect monolayer is also given to compare the defect induced DOS difference. Because the Fermi level shifts in the defective structure with respect to that in the perfect structure, the total DOS for the perfect monolayer are moved in energy to fit well with the DOS for corresponding defective monolayer. The DOS appearing only in the defective monolayer are marked in pink, as shown in Fig. 7. As it is expected, the relative DOS difference between defective monolayer and perfect monolayer reduces with lowering concentration. At the highest defective level (12.5%), the in-gap states are in forms of extend state and overlap in energy with the bulk states, suggesting the interaction between defects in such compact arrangement is strong. When the concentration drops from 12.5% to 3.1%, the in-gap state corresponded peaks get narrower due to the increase in defect separation weakening the defect interaction. Until the concentration is lowered to 6.3%, the bulk electronic structure is almost left intact and the energy positions of defect states become independent on the concentration. This result again indicates the defect interaction is dominated by the defect separation. The defect induced changes in the DOS of 1T0 MoTe2 monolayer also decrease with lowering the concentration due to their strongly localized nature. The most important effect of defect concentration on the electronic structures of 1T0 MoTe2 is the tuning of the gap or pseudo-gap. As shown in Fig. 8, the DOS for 6.3% VTe-l forms a gap at the position of Fermi level and the DOS for 6.3% DVTe-l forms a pseudo-gap above the Fermi level (indicated by the arrow). When the concentration decreases to 4.2%, the Fermi level for VTe-l moves in the lowest conduction band and the pseudo-gap for DVTe-l are closed. The Bloch states and the band structures in strained VTe-l doped structure are shown in Fig. 9 to further analyze the reason for the gap in 1T0 MoTe2. The state A corresponding to the X point of the lowest conduction band has considerable distribution over all the supercell, indicating it is composed mainly by bulk states. The state B corresponding to the X point of the highest valence band has more contribution around the Te vacancy compared to other positions, suggesting the composition of the highest valence band are primarily defect states mixing with some bulk states. This composition indicates the conduction band and the valence band are the 534
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Fig. 6. (a) The Fukuifunctions f þ ðrÞ for 6.3% vacancy-doped MoTe2 monolayers; (b) the Fukuifunctions f ðrÞ for vacancy-doped MoTe2 mono layers. The isosurface is set to be �0.001 e/Å3, with red color indicating positive value and blue color indicating negative value.
Fig. 7. The TDOS for the most energy favorable single and double vacancy defect models (VTe and DVTe) with defect concentrations varying from 3.1% to 12.5%. The black dotted lines represent the DOS shape in perfect structure after shifting energy to fit well with the DOS of corresponding defective monolayers. The blue dot-dash lines at zero represent the Fermi-energy.
hybridization between bulk states and defect states. Hence, the band gap and the pseudo gap in defective 1T0 MoTe2 monolayer should be a result of the interaction between defect band and bulk band. The hybridization magnitude is certainly relative to the defect concentration as well as the defect separation. This interprets why the band gap depends on the defect concentration. Moreover, the calculated band structure for 4.2% VTe doped monolayer is sensitive to the lattice strain as shown in Fig. 9(b and c). As 1% strain is applied, 4.2% VTe doped monolayer possesses a gap agian. This is because applying strain to the lattice can also change the magnitude of the hybridization. It is suggested the conductivity of defective 1T0 MoTe2 monolayer may be sensitive to the external force.
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Fig. 8. The TDOS for the most energy favorable single and double vacancy defect models for 1T0 MoTe2 monolayer (VTe-l and DV0 Te-l) with defect concentrations varying from 3.1% to 12.5%. The black dotted lines represent the DOS shape of perfect structure. The blue dot-dash lines at zero represent the Fermi-energy.
Fig. 9. (a) Electronic Bloch states in 6.3% VTe-l doped 1T0 MoTe2 monolayer corresponding to the X point of the lowest conduction band (A) and the highest valence band (B). The isosurface is set to be 0.1; (b) The band structures of strained 6.3% VTe-l doped 1T’MoTe2 monolayer; (c) The band structures of strained 4.2% VTe-l doped 1T’MoTe2 monolayer. The Fermi level is set to be zero. The strains are from 2% to 2%.
4. Conclusion In summary, the stability and electronic structure of vacancy doped MoTe2 monolayer have been systemically studied with first principles method. The energetically most favorable vacancy types are found to be VTe, DVTe in 1H phase and VTe-l, DV0 Te-l of high concentration or DVTe-l of low concentration in 1T0 phase. The LDOS show that vacancy induced defect states are strongly localized on 536
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the two or three atomic shells around vacancy sites. This strong localized nature results in the formation energy being independent on the defect concentration as the neighboring defect are separated by about 1 nm. Similarly, the electronic structure also shows little dependence on vacancy concentration as concentration is less than 6.3%. In the low concentration case, doping1H phase with va cancies introduces flat bands in the band gap, which give rise to effects of deep level doping. For 1T0 MoTe2, various vacancies lead to sharply peaked DOS and small band gaps in the DOS and band structures. The small band gaps can be attributed to the hybridization between the defect states and bulk states, and the position of gap varies with the energy of defect states. According to the position of gap with respect to Fermi level, the defective 1T0 MoTe2 can be semiconductor, semimetal and metal. Moreover, it is found the location of Fermi level relative to the defect-induced gap is sensitive to concentration and strain. Therefore, the electronic conductivity can be sensitive to the environment, such as temperature, substrate or charge doping and so on. This paper provides the first principle results of the electronic structures for defective 1H and 1T0 MoTe2 monolayers, which will be useful to the further study on electronic and optic properties of MoTe2 monolayer. Acknowledgment This work is supported by the National Natural Science Foundation of China (Nos. 51701071 and 51272291), the Distinguished Young Scholar Foundation of Hunan Province (No. 2015JJ1020), the Central South University Research Fund for Innovation-driven program (No. 2015CXS1035), the Central South University Research Fund for Sheng-hua scholars, and State Key Laboratory of Powder Metallurgy, Central South University. References [1] K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. 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Superlattices and Microstructures journal homepage: www.elsevier.com/locate/superlattices
Character of defect states in vacancy-doped MoTe2 monolayer: Spatial localization, flat bands and hybridization gap Xiongying Dai a, b, Zhixiong Yang c, Aolin Li a, Jianyu Yang b, Fangping Ouyang a, c, * a
School of Physics and Electronics, Hunan Key Laboratory for Super-Microstructure and Ultrafast Process, Central South University, Changsha, 410083, People’s Republic of China College of Science, Hunan Institute of Engineering, Xiangtan, 411104, People’s Republic of China c Powder Metallurgy Research Institute, State Key Laboratory of Powder Metallurgy, Central South University, Changsha, 410083, People’s Republic of China b
A R T I C L E I N F O
A B S T R A C T
Keywords: MoTe2 monolayer First-principle calculations Vacancy defects Electronic structures
The structural and electronic properties of vacancy-doped 1H and 1T0 MoTe2 monolayers are systematically investigated based on first-principles calculations. Te vacancy is found energeti cally favored over Mo vacancy for both phases, and Te double vacancy is more favored as it is formed by missing two Te atoms from opposite sides. Vacancy induced defect states are strongly spatially localized on the atoms within two or three shell surrounding the point defect. This strongly localized nature leads to weak dependence of the defect formation energy on defect concentrations, sharply peaked density of states, and flat bands. Moreover, the calculation sug gests that Te vacancy opens a band gap in the 1T0 MoTe2 monolayer, which can be tuned by lattice strain or external force. These results might give a guidance for the research on the application of MoTe2 in electronics and optoelectronics.
1. Introduction Two-dimensional (2D) materials have inspired high hopes to miniaturization the current electronic devices since the exotic properties of graphene were published in 2004 [1]. Though graphene exhibits high mobilities and stabilities, its application in many active components (like diode, transistor and optoelectronic devices) is limited because of its zero gap. Lots of relative researching interest has then been put on other 2D materials, such as transition metal dichalcogenides (TMDs) [2–4], arsenic sulfide [5,6]. TMDs are a group of layered compounds with a general formula MX2, where M is a transition metal, and X represents a chalcogen. Among these TMDs, the group-VI TMDs (M ¼ Mo or W) possess an intrinsic gap and have potential application in electronic devices [7]. The performance of MoS2-based field-effect transistors (FETs) has been studied in many works [8–14]. A MoS2 FET can exhibit large transconductance (4.4 mS/μm), high on-off ration (>1010) and excellent short channel behavior [11], but at the same time it is limited by low mobility, high contact resistance and large background n-doping [15]. Therefore, MoS2 is desired by low energy dissipation applications but still challenged for high performance applications. Some recent studies suggested the challenges on MoS2 devices might be overcome by MoTe2 devices. In theoretical research within the deformation potential approximation, long wave acoustic phonon limited mobilities for 2D MoTe2 can be up to 2526 cm2 V 1 s 1 at * Corresponding author. School of Physics and Electronics, and Institute of Super-microstructure and Ultrafast Process in Advanced Materials, Central SouthUniversity, Changsha, 410083, People’s Republic of China. E-mail address: [email protected] (F. Ouyang). https://doi.org/10.1016/j.spmi.2019.04.044 Received 31 January 2019; Received in revised form 21 April 2019; Accepted 29 April 2019 Available online 10 May 2019 0749-6036/© 2019 Elsevier Ltd. All rights reserved.
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room temperature, which is much higher than the value of 340 cm2 V 1 s 1 for MoS2 [16]. MoTe2 has the smallest energy difference between the semiconducting phase (1H) and the metallic phase (1Tor 1T0 ) among the group-VI TMDs and can form stable homo junction contacts by phase transition [17]. Ohmic contact has been realized in MoTe2 devices by setting a heterophase structure as a buffer contact layer [18,19]. Moreover, intrinsic MoTe2 FETs exhibit ambipolar transfer characteristics [20] and their carrier type can be modulated through rapid thermal annealing under a controlled O2 environment and benzyl viologen doping [21]. Recently, many efforts have been put on the preparation of high quality 2D MoTe2 [22–24]. Few layers or monolayers of MoTe2 have been fabricated through chemical vapor deposition [22–24]. The electronic properties inevitably influenced by defects whether they are artificial or natural. The roles of defects in 2D materials, such as inducing magnetism [25], creating new topological states [26], generating localized and single photon emission [27] et al., have been revealed in various compound by many researches. TEM and STEM images show that there are many vacancies in the prepared MoTe2 [28]. These vacancies have been found to play an important role on the stability for MoTe2 materials [29,30]. A 3% or more concentration of Te vacancies can cause 1H-1T0 transition in the 2D MoTe2 [19]. On the other hand, vacancies may also produce significant effects on the electronic and optical properties [31,32]. However, there is still lack of systemically study on the electronic structure of vacancy doped MoTe2 monolayer, especially on 1T0 MoTe2 monolayer. With regard of this, a systemically study has been done on the structural properties and electronic properties of twelve kinds of vacancy-doped 1H and 1T0 MoTe2 monolayers in this work. The primary contents are organized as follow. Firstly, the structures and electronic structures of pristine MoTe2 monolayers have been calculated with atomic localized orbitals basis sets. Then, the local nature of vacancy-induced defect states is introduced followed by a discussion on the relationship between formation energy and defect concentration. After that, the electronic structures for various vacancies are presented with a focus on the mid-gap states in 1H phase and gap opening in 1T0 phase. Finally, the vacancy effects in different defect concentration and the evolution of vacancy-induced gap in 1T0 phase are discussed. 2. Computational methods First principles calculations are performed using software package Atomistix Tool Kit (ATK). Hartwigsen, Goedecker, Hutter (HGH) pseudopotential together with Tier 4 basis sets is used [33]. This combination of pseudopotential and basis sets has been carefully checked by comparing the calculated results for pristine monolayer with other methods. Generalized gradient approximation (GGA) of Perdew–Burke–Ernzerhof form is adopted for electronic interaction [34]. The integration of potential and charge density are per formed in a grid mesh with cut-off energy of 75 Hartree. The density of k-point mesh used for integrations over the first Brillouin zone is
Fig. 1. (a) Top view of atomic structure of 1H MoTe2 monolayer; (b) top view of atomic structure of 1T0 MoTe2 monolayer; (c) side view of atomic structure of 1H MoTe2 monolayer; (d) side view of atomic structure of 1T0 MoTe2 monolayer; (e) band structure, total density of states (TDOS) and partial density of states (PDOS) of 1H MoTe2 monolayer; (f) band structure, TDOS and PDOS of 1T0 MoTe2 monolayer. 529
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set 15 Å in relaxation self-consistent calculations and 21 Å in density of state (DOS) calculations [35]. Atomic structures are fully optimized until the force on each atom is less than 0.01 eV/Å. The vacancy formation energy in MoTe2 monolayer is calculated as Ef ¼ Etotal Emonolayer þ Eatom, where Etotal and Emonolayer are the total energies of the monolayer with and without vacancies, respectively, and Eatom is the chemical potential for host atoms, which depends on the material growth conditions and satisfies the boundary conditions. 3. Results and discussions 3.1. Atomic structures and electronic structures of MoTe2 monolayer in various phase The relaxed atomic structures of 1H and 1T0 MoTe2 monolayers are presented in Fig. 1(a–d). The top view of 1H MoTe2 monolayer presents as a hexagonal sheet, where Mo atoms occupy one sublattice and Te atoms occupy the other. The side view shows the Mo atoms form a layer and are sandwiched between two Te layers. A Mo atom is surrounded by six Te atoms with trigonal prismatic coordination. The 1T0 structure is a distortion version of 1T structure, of which one Te layer glides to the hexagon center as compared to 1H phase. The distortion causes the unit cell of 1T0 being rectangle and existing two inequivalent Te sites. As shown in Fig. 1(d), one Te site denoted as Tel is close to the Mo layer than the other denoted as Teh. The equilibrium lattice constant, bond length, bond angle and height between two Te atom planes are given in Table 1. The calculated lattice constants are 3.59 Å for 1H phase, and 3.52 Å (a), 6.36 Å (b) for 1T0 phase. The corresponding values calculated with the projected-augmented wave (PAW) method plus a plane-wave basis set are 3.55–3.56 Å, 3.44–3.455 Å and 6.368–6.39 Å, which have only about 1%, 2% and 1% relative difference with our calculation, respectively [17,36–38]. Whereas the local density approximation (LDA) gives a much lower prediction of 3.46 Å for 1H phase [38,39]. The lattice constants of 1T0 monolayer agree well with the experimental measurement of 3.52 Å and 6.33 Å [40]. Fig. 1(e and f) shows the band structures, total DOS (TDOS) and partial DOS (PDOS) of perfect MoTe2 monolayers. The calculated band gap of 1H MoTe2 monolayer is a direct gap of 1.01 eV along Γ-X direction, which is close to the experimental value of 1.1 eV [41] and the PAW predicted value of 1.07 eV [42]. 1T0 MoTe2 monolayer exhibits metallic character with d-p hybridized bands across the Fermi level. The difference between electronic structures of 1H and 1T0 MoS2 has been known as a result of their different coordination environments of Mo atom based on crystal field theory [38]. Because the crystal field is contributed by neighboring atoms, the un derstanding for other kinds of TMDs or bulk TMDs is also applicable for MoTe2 monolayer except magnitude difference of crystal field. Mo d orbitals in 1H structure are split into three groups by the trigonal prismatic crystal field, which are a1 ðdz2 Þ, eðdx2 y2 ; dxy Þ and 0 e ðdxz ; dyz Þ in order of ascending energy. The orbitals of e overlap with the chalcogen p orbitals forming bonding states and antibonding states. Theoretical calculations also proved there exists strong interband hybridization between a1 and e [43], which re sults in the bandgap larger than the splitting energy between a1 and e. As a result, valence bands and conduction bands of 1H phase are composed of dz2 ; dx2 y2 ; dxy and p components [38,43]. This is consistent with our calculated DOS which shows d-p hybridization character around the Fermi level, particularly in the deep valence region and upper conduction region. The PDOS of 1T0 MoTe2 monolayer also exhibits heavily mixing of the Mo d and Te p orbitals around the Fermi level, but this region is overlapped with the Mo d dominated region. Hence, there is no band gap existing in 1T0 phase. The differences between 1T0 phase and 1H phase are that the distorted octahedral splitting is smaller than the trigonal prism splitting and the shorter Mo–Mo bond in distortion structure makes a larger overlap of d orbitals [44]. This leads to 1T0 MoTe2 monolayer have smaller d orbital splitting energy and wider d band width, and thus the band gap closes. Moreover, it should be notice Mo d orbitals in a regular octahedral crystal field are split into two groups, namely, one lower t2g (that contains dxy ; dxz ; dyz orbitals) and one higher eg (that contains dz2 ; dx2 y2 orbitals), which is different from the trigonal prism splitting [38]. Compared to the bulk counterpart, MoTe2 monolayer loses the interlayer interaction. Out-of-plane oriented orbitals, such as metal dz2 orbitals and chalcogen p orbitals, are predicted to have larger interlayer interaction than other orbitals [43]. It is well known as a semiconducting TMD is reduced from bulk to monolayer its band gap transit from indirect to direct. This is because the conduction band minima on the K point (due to a rectangle supercell is used, the K point is folded to the ΓX line in our case) is composed of a higher weight of out-of-plane oriented orbitals than the original conduction band edge [38], and it shifts down below the latter as the interlayer interaction missing. This change has been revealed by photo luminescence spectra experiment for MoTe41 2 and captured by our calculation. A lack of interlayer interaction also changes the electronic structure of 1T0 MoTe2 monolayer as compared to its bulk counterpart, but keeps the metallic character, indicating a heterophase homojunction of 1H and 1T0 MoTe2 monolayer is a metal-semiconductor junction. Our results for band gap, band composition and DOS are consistent with previous studies [23]. It is shown the calculation with Tier 4 basis sets can capture all the important characters of the structure and electronic structures for both 1H MoTe2 and 1T0 MoTe2. Table 1 Calculated lattice constant, bond length, bond angle, height between two Te atom planes, and band gap values for optimized 1H and 1T0 MoTe2 monolayers. 1H 1T0
Lattice Constant(Å)
Bond length (Å)
Bond angle (�)
Height (Å)
Band Gap(eV)
a ¼ 3.59 a ¼ 3.52 b ¼ 6.36
l ¼ 2.77 l1 ¼ 2.74 l2 ¼ 2.86
θ ¼ 82.90 θ1 ¼ 77.76 θ2 ¼ 116.41
d ¼ 3.66 d1 ¼ 4.20 d2 ¼ 3.00
1.01 0.00
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3.2. Structures and stabilities of vacancy-doped MoTe2 monolayer Vacancy is generated due to the missing lattice atom. Generally, both Mo and Te atom in the MoTe2 monolayer are possible missing to form Mo vacancy and Te vacancy. The effects of atomic vacancies on the properties of MoTe2 monolayer are studied by constructing one or two atomic vacancy in a rectangular supercell of various sizes. Fig. 2 (a) shows the structures of four vacancy defects within 1H MoTe2 monolayer and eight vacancy defects within 1T0 MoTe2 monolayer. The defect VMo represents a single Mo atom vacancy, VTe is a single Te atom vacancy, and DVTe, DV0 Te are double Te atom vacancies. The superscript (0 ) appears or not represents the two missing Te atoms are on different Te sides or the same side. For 1T0 MoTe2 monolayer, the inequivalent Te sites are distinguished from the postfix in subscript, where “-h” corresponds to the higher site, “-l” corresponds to the lower site, “-hl” corresponds to one absence from higher site and one from lower site. The vacancy point defects are placed in rectangular supercells, as shown in Fig. 2 (b). Supercells of varying cell sizes are adopted to investigate the effect of defect concentration, including 2 � 2, 3 � 2, 4 � 2, 4 � 3 and 4 � 4. In the case of only one defect within the supercell, the defect concen tration is calculated to be 1/Ncells, where Ncells is the number of primitive unit cells per supercell. Cell sizes and the corresponding defect concentrations, defect separations, area densities are listed in Table 2. Fig. 2 (c) presents the calculate formation energy for all considered systems, separated in single vacancy defects and double vacancy defects. It is noted that the formation energy of a single Mo vacancy is much larger than that of a single Te vacancy. This can be intuitively understood because the number of broken Mo–Te bonds in creating a Mo vacancy is twice of that in creating a Te vacancy. The similar conclusion has also been made for many members of the TMD family [42]. Nevertheless, it should be noticed Mo vacancy can also be found in the monolayer with a relatively low concentration [45]. In 1T0 monolayer, the formation energies of a lower site Te vacancy are almost 1 eV smaller than that of a higher site vacancy. This result indicates that Te vacancies in 1T0 monolayer prefer to appear on the lower sites, which have longer bond with Mo atoms as given in Table 1. For double vacancies, the energetically favorable vacancy type in 1H monolayer is DVTe. The formation energy of DVTe is about 0.8 eV lower than that of DV0 Te. In comparison with the formation energy of a VTe, the formation energy per missing atom is lower for a DVTe. Hence, double vacancies formed by missing two neighboring Te atoms on the same side are more thermodynamically favored over single Te vacancies in the 1H MoTe2. In 1T0 case, the smallest formation energy of double vacancies varies with concentration. The energetically most favorable double Te vacancy is DV0 Te-l for concentration of 12.5% and is DVTe-l for concentration larger than 6%.
Fig. 2. (a) Twelve vacancy structures considered in this study, four (left column) for 1H MoTe2 monolayer and eight (right two columns) for 1T0 MoTe2 monolayer; (b) The rectangular supercells of monolayer MoTe2, used to simulate a defect concentration of 3.1%. The red circles indicate positions of missing atoms; (c) The relationship between formation energies and concentration for single vacancies; （d）The relationship between formation energies and concentration for double vacancies. 531
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Table 2 Concentrations, defect separation and area density of vacancy point defects in MoTe2 monolayers, corresponding to one defect in varying cell size. Cell size
2�2
3�2
4�2
4�3
4�4
defect concentration (%) defect separation 1H (Å) defect separation 1T (Å) area density 1H (1013 cm 2) area density 1T (1013 cm 2)
12.5 7.1 7.0 11.54 11.16
8.3 10.7 10.4 7.70 7.44
6.3 12.4 12.7 5.77 5.58
4.2 14.3 14.1 3.85 3.72
3.1 14.3 14.1 2.88 2.80
3.3. Localized nature of defect states The vacancies alter the periodic potential of perfect 2D crystal and thus change the motion of electrons. Especially, the non-bonding electrons of atoms around the vacancies are usually localized. The two most stable single vacancies VTe and VTe-l are chosen as ex amples to discuss the localization of defect states in vacancy-doped 1H and 1T0 MoTe2. The localized nature of defect states is analyzed with the local DOS (LDOS) of Mo atoms along a line in armchair direction starting on the defect (atoms a) and moving away from it (atoms b, c, d), as shown in Fig. 3. The LDOS of atom d is already close to the LDOS of a Mo atom in the perfect monolayers for both 1H and 1T0 phase. The LDOS of atom a, however, has some peaks that are not presented in corresponding perfect monolayer. Those peaks significantly fall in the atoms b and c, indicating the defect states is strongly localized on the atoms directly surrounding the vacancy. The observation of strong localization of vacancy defect states in MoTe2 is similar with the situation in MoS2 monolayer of which the defect states also distribute on atoms within two or three shell surrounding the vacancy [46]. The strong localization of defect states can be seen from the relationship between the defect formation energy and defect con centrations as shown in Fig. 2 (c). The defect states distribute primarily on the atoms directly surrounding the vacancy, indicating the electronic interactions between neighboring vacancies are very small when they are separated by a few shells of atoms. In our case, the tensest arrangement of defects corresponds to a high concentration of 12.5%. Single vacancies arranged in this way are separated by only one shell of Mo atoms. The formation energies for single vacancies show little change as the concentration reduces. This result provides another evidence for the strong localization of the defect states in MoTe2. On the other hand, some double vacancies, such as DV0 Te-l and DV0 Te-h, directly connect with each other in the tensest arrangement scheme, which are line defects in fact. Thus, the formation energies change seriously at high defect concentration region. As the concentration reduces to 6.3%, the defect formation energies of double vacancies become independent on the concentration. This result also agrees well with the LDOS, in which the defect induced peaks are visible only on the two or three shells of atoms near the vacancy.
Fig. 3. （a）The structure and LDOS of VTe doped 1H MoTe2 monolayer; (b)The structure and LDOS of VTe-l doped 1T0 MoTe2 monolayer. The defect concentration is 3.1%. 532
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3.4. Defect effects on the electronic structures: in-gap state in 1H and band gap opening in 1T0 The TDOS and band structures for various defective MoTe2 monolayers are presented in Fig. 4 and Fig. 5 to investigate the effects of vacancies on the electronic structure. The calculated TDOS and band structures of vacancy doped 1H MoTe2 is similar with that of 1H MoS2. A common characterization is the in-gap states. As shown in Fig. 5, a VMo defect induces five nearly flat bands in the band gap, and a VTe or a DVTe induces two flat bands. Correspondingly, several density peaks appear in the total DOS. For VMo doped monolayer, the two flat bands of lower energy and the two bands of higher energy are nearly double degenerated, making the two higher peaks in the total DOS. The middle singly band forms another lower peak. Those in-gap states originate from the dangling bonds around the removed Mo atom or Te atom [47]. The dangling bonds of the Mo atoms should be responsible for the in-gap states for VTe and DVTe doped monolayer. The difference of the electronic structures between VTe and DVTe is the relative energy shift of gap states. Gap states induced by DVTe are closer to the conduction band bottom than that induced by VTe. This is also the case in MoS2 [46]. The band structure shows a DV0 Te induces four unoccupied flat bands in the gap, which is twice of the in-gap states induced by single vacancy VTe or divacancy DVTe. This increase in the number of in-gap states can be regarded as the result of that removing two Te atoms in the same side leads to five Mo dangling bonds while a VTe or a DVTe leads to three dangling bonds only. For all vacancies, those occupied levels are far from the conduction band bottom and those unoccupied levels are far from the valence band top. This character may lead seldom electrons transitions between defect-induced levels and the conduction (valence) band and thus result in a low concentration of doping carriers. However, it still needs more advanced methods to precisely determine the position of the in-gap states, like quasi particle based electronic structure methods. They are computationally very demanding and go beyond the scope of the present work. Vacancy effects on the electronic structures of metallic 1T0 MoTe2 monolayer lead to a change in the state densities around its Femi level. As shown in Fig. 4, several density peaks appear in the DOS of defective 1T0 MoTe2. The number of peaks varies with the vacancy type. VMo gives rise to three density peaks in the TDOS of 1T0 MoTe2, one occupied and the other two unoccupied, which is similar with that of VMo on 1H MoTe2 and can also be attributed to dangling bonds. Here, we highlight the small band gaps in band structures of VTe0 l and DVTe-hl doped structures, which suggests a transition from metal to semiconductor and a dramatical change in conductivity of 1T MoTe2. Other Te vacancies such as VTe-h, DV0 Te-h and DVTe-h also have serious effects on the band structure of 1T0 MoTe2 for their conduction band bottoms are crossed by Fermi level and separated from the valence top by a gap. This indicates that VTe-h, DV0 Te-h and DVTe-h doped 1T0 MoTe2 exhibit a semi-metallic characterization. Vacancy can expose the Mo atom of MoTe2 monolayer to air and create unpaired electrons on the neighboring atom, which may influence the chemical reactivities surrounding the vacancy. This has been reflected by the position of DOS peaks corresponding to defect states. Some vacancies, such as VMo, have a DOS peak below the Fermi level, from which electrons can be transferred to ad sorbates of acceptor-type or with oxidability. Because the energy of VMo states is higher than the valence band top in the 1H MoTe2, electron losing from the vacancy vicinity will be easier than from other position. For the same reason, vacancies that induce DOS peaks above the Fermi level make the vacancy vicinity being easier to accept electrons from absorbates of donor-type or with reducibility, such as a VTe on 1H MoTe2. The change of chemical reactivity in the defective MoTe2 monolayer can also been from the Fukui function in Fig. 6, which is defined as the difference of electron density between the neutral system and the system added one electron ðf þ ðrÞÞ or removed one electron ðf ðrÞÞ. Both phases exhibit reactivity change on the vacancy vicinity but the semiconducting phase changes more serious as their Fukui functions have greater weights around vacancy. Moreover, the Fukui function reflects a detail for the VMo doped 1H MoTe2, in which atoms surrounding the vacancy have different chemical reactivities even though they are equivalent in the pristine monolayer, like atoms marked with number in Fig. 6 (a). This is a result of structure distortion near the VMo, which can be further attributed to Jahn-Teller effects. 3.5. Dependence of electronic structure on defect concentration The defects are periodically arranged on the lattice in this work, which is not the situation in the practical materials. Even so, as the
Fig. 4. The change in TDOS of MoTe2 monolayer induced by the considered point defects with a concentration of 6.3%. 533
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Fig. 5. The change in band structure of MoTe2 monolayer induced by the considered point defects with a concentration of 6.3%. The red dot lines present the band structures for perfect monolayers. The in-gap states of vacancy-doped 1H MoTe2 are highlighted in color and the inserts zoom in the bands close to the Fermi level which indicates a transition from metal to semiconductor or semimetal occurring.
concentration of defect drops to a certain level, the calculated electronic structure may provide a suitable scope to the effects of an individual defect due to the strongly localization of defect states. On the other hand, vacancies in prepared MoTe2 can be occasionally close to each other, thus the interaction between the closely embedded defects can be investigated from the periodic model of high concentration. A discussion on the evolution of DOS with the decrease of defect concentration is then necessary. For simply, the most stable single vacancy and divacancy for each phase are taken as examples. That is, VTe and DVTe for 1H MoTe2, VTe-l and DVTe-l for 1T0 MoTe2. The total DOS per unit cell for VTe and DVTe doped 1H MoTe2 with concentration ranging from 12.5% to 3.1% is presented in Fig. 7. The TDOS for a perfect monolayer is also given to compare the defect induced DOS difference. Because the Fermi level shifts in the defective structure with respect to that in the perfect structure, the total DOS for the perfect monolayer are moved in energy to fit well with the DOS for corresponding defective monolayer. The DOS appearing only in the defective monolayer are marked in pink, as shown in Fig. 7. As it is expected, the relative DOS difference between defective monolayer and perfect monolayer reduces with lowering concentration. At the highest defective level (12.5%), the in-gap states are in forms of extend state and overlap in energy with the bulk states, suggesting the interaction between defects in such compact arrangement is strong. When the concentration drops from 12.5% to 3.1%, the in-gap state corresponded peaks get narrower due to the increase in defect separation weakening the defect interaction. Until the concentration is lowered to 6.3%, the bulk electronic structure is almost left intact and the energy positions of defect states become independent on the concentration. This result again indicates the defect interaction is dominated by the defect separation. The defect induced changes in the DOS of 1T0 MoTe2 monolayer also decrease with lowering the concentration due to their strongly localized nature. The most important effect of defect concentration on the electronic structures of 1T0 MoTe2 is the tuning of the gap or pseudo-gap. As shown in Fig. 8, the DOS for 6.3% VTe-l forms a gap at the position of Fermi level and the DOS for 6.3% DVTe-l forms a pseudo-gap above the Fermi level (indicated by the arrow). When the concentration decreases to 4.2%, the Fermi level for VTe-l moves in the lowest conduction band and the pseudo-gap for DVTe-l are closed. The Bloch states and the band structures in strained VTe-l doped structure are shown in Fig. 9 to further analyze the reason for the gap in 1T0 MoTe2. The state A corresponding to the X point of the lowest conduction band has considerable distribution over all the supercell, indicating it is composed mainly by bulk states. The state B corresponding to the X point of the highest valence band has more contribution around the Te vacancy compared to other positions, suggesting the composition of the highest valence band are primarily defect states mixing with some bulk states. This composition indicates the conduction band and the valence band are the 534
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Fig. 6. (a) The Fukuifunctions f þ ðrÞ for 6.3% vacancy-doped MoTe2 monolayers; (b) the Fukuifunctions f ðrÞ for vacancy-doped MoTe2 mono layers. The isosurface is set to be �0.001 e/Å3, with red color indicating positive value and blue color indicating negative value.
Fig. 7. The TDOS for the most energy favorable single and double vacancy defect models (VTe and DVTe) with defect concentrations varying from 3.1% to 12.5%. The black dotted lines represent the DOS shape in perfect structure after shifting energy to fit well with the DOS of corresponding defective monolayers. The blue dot-dash lines at zero represent the Fermi-energy.
hybridization between bulk states and defect states. Hence, the band gap and the pseudo gap in defective 1T0 MoTe2 monolayer should be a result of the interaction between defect band and bulk band. The hybridization magnitude is certainly relative to the defect concentration as well as the defect separation. This interprets why the band gap depends on the defect concentration. Moreover, the calculated band structure for 4.2% VTe doped monolayer is sensitive to the lattice strain as shown in Fig. 9(b and c). As 1% strain is applied, 4.2% VTe doped monolayer possesses a gap agian. This is because applying strain to the lattice can also change the magnitude of the hybridization. It is suggested the conductivity of defective 1T0 MoTe2 monolayer may be sensitive to the external force.
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Fig. 8. The TDOS for the most energy favorable single and double vacancy defect models for 1T0 MoTe2 monolayer (VTe-l and DV0 Te-l) with defect concentrations varying from 3.1% to 12.5%. The black dotted lines represent the DOS shape of perfect structure. The blue dot-dash lines at zero represent the Fermi-energy.
Fig. 9. (a) Electronic Bloch states in 6.3% VTe-l doped 1T0 MoTe2 monolayer corresponding to the X point of the lowest conduction band (A) and the highest valence band (B). The isosurface is set to be 0.1; (b) The band structures of strained 6.3% VTe-l doped 1T’MoTe2 monolayer; (c) The band structures of strained 4.2% VTe-l doped 1T’MoTe2 monolayer. The Fermi level is set to be zero. The strains are from 2% to 2%.
4. Conclusion In summary, the stability and electronic structure of vacancy doped MoTe2 monolayer have been systemically studied with first principles method. The energetically most favorable vacancy types are found to be VTe, DVTe in 1H phase and VTe-l, DV0 Te-l of high concentration or DVTe-l of low concentration in 1T0 phase. The LDOS show that vacancy induced defect states are strongly localized on 536
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the two or three atomic shells around vacancy sites. This strong localized nature results in the formation energy being independent on the defect concentration as the neighboring defect are separated by about 1 nm. Similarly, the electronic structure also shows little dependence on vacancy concentration as concentration is less than 6.3%. In the low concentration case, doping1H phase with va cancies introduces flat bands in the band gap, which give rise to effects of deep level doping. For 1T0 MoTe2, various vacancies lead to sharply peaked DOS and small band gaps in the DOS and band structures. The small band gaps can be attributed to the hybridization between the defect states and bulk states, and the position of gap varies with the energy of defect states. According to the position of gap with respect to Fermi level, the defective 1T0 MoTe2 can be semiconductor, semimetal and metal. Moreover, it is found the location of Fermi level relative to the defect-induced gap is sensitive to concentration and strain. Therefore, the electronic conductivity can be sensitive to the environment, such as temperature, substrate or charge doping and so on. This paper provides the first principle results of the electronic structures for defective 1H and 1T0 MoTe2 monolayers, which will be useful to the further study on electronic and optic properties of MoTe2 monolayer. Acknowledgment This work is supported by the National Natural Science Foundation of China (Nos. 51701071 and 51272291), the Distinguished Young Scholar Foundation of Hunan Province (No. 2015JJ1020), the Central South University Research Fund for Innovation-driven program (No. 2015CXS1035), the Central South University Research Fund for Sheng-hua scholars, and State Key Laboratory of Powder Metallurgy, Central South University. References [1] K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. 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