3-Fold-Periodic Size-Dependence in Electronic Properties of

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Surfaces, Interfaces, and Catalysis; Physical Properties of Nanomaterials and Materials

3-Fold-Perioidic Size-Dependence in Electronic Properties of Monolayer-TMDC Nano-Triangles Xiaoli Fan, Yurong An, Zhifen Luo, Yan Hu, Baihai Li, and Woon-Ming Lau J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b00449 • Publication Date (Web): 05 Mar 2018 Downloaded from http://pubs.acs.org on March 5, 2018

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The Journal of Physical Chemistry Letters

3-Fold-Perioidic Size-Dependence in Electronic Properties of Monolayer-TMDC Nano-Triangles Xiao-Li Fan1*, Yu-Rong An1, Zhi-Fen Luo1, Yan Hu1, Bai-Hai Li3, Woon-Ming Lau2,3* 1

State Key Laboratory of Solidification Processing, Center for advanced lubrication and seal

Materials, School of Material Science and Engineering, Northwestern Polytechnical University, 127 YouYi Western Road, Xi’an, Shaanxi 710072, China 2

Center for Green Innovation, School of Mathematics and Physics, University of Science & Technology Beijing, Beijing 100083, China

3

School of Energy Science & Engineering, University of Electronic Science & Technology, China, Chengdu, Sichuan, China

ABSTRACT Stable nano-triangles of monolayer transitional metal dichalcogenides (referred therein as MS2 mNTs) grown via ordinary deposition conditions, when M=Mo or W, exhibit a peculiar 3-fold periodic size-dependence in electronic and chemical properties. For “k” being the number of M atoms per edge, mNTs are: (a) intrinsic-semiconducting when k=3i+1, such as k=7,10,13,16; (b) metallic-like with no bandgap when k=3i; (c) n+ semiconducting when k=3i-1. Besides changes in electronic properties, the catalytic properties for hydrogen evolution reaction also switch from active for k=3i and 3i-1 to inactive for k=3i+1. The peculiar periodic size-dependence roots from the chemistry of edge-reconstruction and the consequential evolution of band structure. Further, such chemistry and thereby the size-dependence can be manipulated by adding or depleting the atomic concentration of sulfur atoms along the mNT edges.

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Research on the monolayer form of transition metal dichalcogenides (m-TMDCs) has already emerged as a high-impact branch in nanoscience and nanotechnology, with known results not only showing unusual chemical and physical properties1-4 of m-TMDCs but also demonstrating relevant applications in catalysis,5-8 electronics and optoelectronics.9-12 Evidently, the growth of m-TMDCs starts with the island-formation of nanopolygons including nanotriangles3-6,8,13,14 (therein referred as mNTs) and nanorectangles,15-17 and the assemblages of mNTs and nanorectangles in subsequent growth leads to the formation of nanopolygons with versatile morphologies and finally large 2D domains of m-TMDCs. These nanopolygons are particularly important because they possess a high density of edge-sites and apex-sites, sites which both have chemical reactivity higher than those sites on the basal plane and have electronic/optical site-specific-properties different from those on the basal plane. Overall, research on mNTs and other nanopolygons of m-TMDCs, particularly research on the atomic engineering of their edges and apexes, promise further enhancement of the scope of industrial applications and the impact of m-TMDCs. In reference to atomic edge-engineering, MS2 mNTs are more versatile than the best known 2D monolayer materials of graphene because cutting graphene obviously only yields carbon-edges but cutting m-MS2 can give either metal-edges or sulfur-edges.18-26 Among all known research results on MS2 mNTs, those on MoS2 mNTs are dominating, with those on WS2 and then VS2 mNTs following their popularity. As such, we focus our present study on MoS2 mNTs, and expand our scope of comprehensiveness with brief discussions about WS2 and VS2 mNTs. In MoS2 mNTs, Mo-edge termination is more stable than S-edge termination when Mo-edges are further sulfur-passivated to various degrees of saturation.18,27,28 The relative stability of the different modes of S-passivation have already been thoroughly clarified and articulated by Bollinger, et al.,29 who showed that MoS2 mNTs with 50%-passivation are the most stable and are formed preferentially in the conditions of common chemical vapor deposition. Here, 50%-passivation means one passivating sulfur atom (referred therein as S-passivator atom) being added to each edge-Mo atom. In comparison, mNTs of the 100%-passivation mode (two S-passivator atoms per edge-Mo) are slightly less stable than those of the 50%-passivation mode.22,27,29,30,31 For the sake of clarity, we focus our present work on the mNTs of the 50%-passivation mode; even under this strategic plan of research, our present work still covers a comprehensive study of 36 different MS2 mNTs, for MoS2[k], WS2[k] and VS2[k], with k being the number of M atoms per edge, and with k=5,6,7,…,15,16. The atomic structures of MoS2


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mNT[k] are summarized in Figure S1, together with some additional structural data included in SI. A size range of k=5,6,7…16 is chosen in this work from a practical perspective because small mNTs such as those with k=2 and 3 are embryonic nuclei with relatively low stability and are thus difficult to prepare and manipulate experimentally. On the other hand, both quantum confinement and edge-specific influence become relatively unimportant for large mNTs with k>16. However, even with the twelve MoS2 mNTs (as shown in Figure S1) having a size range of k=5,6,7…16, a vastly expanded scope of these molecular configurations can be readily perceived when one or more of S-passivator atoms are added or subtracted to form meta-stable counterparts of the bench-marking MoS2 mNTs having one S-passivator atom per edge-Mo atom. Experimentally, this atomic defect-engineering by precisely controlling the degree of Mo-edge passivation has already been realized by tuning the relative supply of S and Mo in the growth of MoS2 mNTs.18, 22, 28-30

It is also known that brief exposure to atomic hydrogen can also deplete sulfur atoms from

MoS2 mNTs for the manipulation of the properties of such nanoclusters.32,33 In short, atomic defect-engineering of MS2 mNTs is a rich and practical subject deserving intensive research. Although atomic defect-engineering of MS2 mNTs is still in an infancy stage of development, interesting results have already been found. For example, while a large domain of monolayer-MS2, for M being Mo or W, is known to be semiconducting with a bandgap of about 1.8-2.0 eV,1-3,9,34 MS2 mNTs (M=Mo or W) with each edge-M atom being 100% sulfur passivated are known to be metallic with no energy gap.3,35-37 In comparison, whether the most stable mNTs which have Mo-edge termination under the 50%-passivation mode are metallic or semiconducting remains controversial. While the early works in this topic29,36 have proposed that all such MoS2 mNTs are semiconducting, our recent study38 calls for a correction. Briefly, we surveyed k=4,5,6,7 for the case of MS2 mNTs (M=Mo, W or V) with each edge-M atom passivated by one sulfur atom, and found that VS2 mNTs for all k, and MS2 mNTs (M=Mo or W) for k=5,6 are metallic. Peculiarly, only MS2 mNTs (M=Mo or W) with k=4,7 are intrinsic-semiconducting among those with k=4,5,6 and 7. In the present work, we employ first-principles calculations in a computational materials-genome approach with which MS2 mNTs with each edge-M atom passivated by one sulfur atom, and with k=5,6,7…16 for M=Mo, W and V, are surveyed and analyzed, to find the correlations among size, edge-condition, stability, bonding configuration, band structure, and metallic/semiconducting property. The first objective is erecting a model for describing the ACS Paragon Plus Environment


electronic property (semiconducting/metallic) of each mNT in reference to its size and edge-conditions, and for explaining the science governing the changes. The second objective is extending such a model of the nature of MS2 mNTs to a set of design rules for guiding the practical manipulative-change of a specific MS2 mNT from semiconducting to metallic and vice versa. Again, the computational genome approach is adopted for accomplishing this second objective; in this case, atomic defect-engineering of a specific MS2 mNT is conducted by adding or eliminating the most obvious defect-engineering-attribute: sulfur atoms passivating the M-edge of MS2 mNTs. For each defect configuration, the correlations among composition, size, edge-condition, stability, bonding configuration, band structure, and metallic/semiconducting property are tracked and analyzed. Surprisingly, our calculations show a remarkable 3-fold k-periodic evolution of band-structure (separate vs. overlapping valence and conduction bands) and electronic properties (semiconducting vs. metallic) as a function of nano-cluster size for the stable MS2 mNTs with M=Mo or W. The essence of this peculiar nature, for M=Mo as an example, is outlined in the following size-dependence model: Each mNT[k] in the“k=3i+1”case, with the respective atomic structures and band structures for k=7,10,13 and 16 shown in Figures S1a and 1a, is intrinsic-semiconducting with its Fermi level amid its separate valence and conduction band. The intrinsic-semiconducting property resembles that of the nominally infinitely-large m-MoS2, except that the bandgap of mNTs are smaller (from 0.7 to 0.9 eV) than that of m-MoS2 (1.8 eV). These mNTs are chemically inactive for hydrogen evolution reaction (HER) because38 the atomic 1s state of hydrogen falls in the bandgap of these mNTs and cannot form any bonding molecular state to facilitate hydrogen adsorption on mNT. Each mNT[k] in the“k=3i”case, with the respective atomic structures and band structures for k=6,9,12 and 15 shown in Figures S1b and 1b, is metallic-like with its Fermi level amid its overlapping valence and conduction bands. The development of such a band-overlap is traced to the shift of some Mo-edge DOS downwards from the conduction band minimum and the shift of some edge-related DOS upwards from the valence band maximum, in reference to the situation of the k=3i+1 case in which a bandgap is present. We refer mNT with k=3i as metallic-like because although such an mNT has no bandgap, the density of electronic states near its Fermi level is low and the conductivity is expected to be much lower than an ordinary metal. Each mNT[k] in the“k=3i-1”case, with the respective atomic structures and band structures for ACS Paragon Plus Environment

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k=5,8,11 and 14 shown in Figures S1c and 1c, is n+ semiconducting with its Fermi level slightly above the conduction band edge which is separated from the valence band maximum by a bandgap. Each of these n+ semiconducting mNTs has its Fermi level amid a relatively high density of states and well into the conduction band. This has been mistaken as metallic-like in our recent report36 on MS2 mNTs; but the DOS results in this previous report are no different from those of mNT[5] in the present work. In accord to this recent report38, each of these mNTs and those for k=3i possesses a low density of DOS to form molecular bonding states with the atomic 1s state of hydrogen, and is thus qualified to facilitate HER. To assure the validity of the aforementioned model, we repeat our computation by the Perdew-Burke-Ernzerh

generalized

gradient

approximation39

with

the

more

accurate

Heyd-Scuseria-Ernzerh method40,41 for mNTs having k=5-10. This repetition addresses the fact that the calculated band structures, particularly bandgap results, are known to be sensitive to the computational methods. The detailed results of the validity-check is included in SI (particularly Figure S4). In brief, the aforementioned model is valid because the relative differences between the PBE and HSE methods, in computational bandgaps, are less than 15% in the present work. While the above 3-fold periodic size-dependence model is derived from the results in Figures S1a-c and Figures 1a-c which are extracted from our computational results on MoS2 mNTs, our computational results on WS2 mNTs also support the above model and scenario. However, our computational analysis reveals, in consistence with other recent reports on MS2 mNTs,42-45 that for M=V, all MS2 mNTs of all sizes are metallic with overlapping valence and conduction bands due to the presence of unpaired-spins. This spin-polarized nature leading to the overlap of valence and conduction bands has already been thoroughly detailed elsewhere42-45 and needs no clarification here. A thorough analysis of the DOS data (Figure 1) and charge-carrier distribution results (Figure 2) offer further insights to the physics and chemistry forging the 3-fold periodic size-dependence of MoS2 mNTs. Particularly, from the data for MoS2 mNTs with k=3i+1 (Figures 1a and 1d), one clearly sees that the partial DOS near the valence band edge of an mNT are the sum of those partial DOS belonging to both constituent-atoms at the edge and those near the edge. Here, “near-edge” labels the constituent-atoms with bonding configurations like those in an infinitely-large m-MoS2. In this context, Figures 1a and 1d clearly show that the valence band edge is influenced but not dictated by the edge-configuration of mNTs with k=3i+1. On the contrary, Figures 1a and 1d clearly show that the conduction band edge of an mNTs with k=3i+1 ACS Paragon Plus Environment


is always dictated by the partial DOS of edge-atoms. Noticeably, the electronic states of the edge-Mo atoms form a new conduction band edge well below the conduction band edge of the constituent-atoms off the edge. Clearly these electronic states of the edge-Mo atoms are the dominating root-causes of the shrinkage of the bandgap when m-MoS2 is trimmed to an mNT. The charge-carrier distribution maps in Figure 2a, which show the spatial distributions of holes or electrons near the Fermi level, further pictorially articulate the physics and chemistry of the above DOS analysis. Particularly, all mNTs with k=3i+1 show the peculiar reconstruction of the bonding configuration of the edge-Mo atoms in that all edge-Mo atoms group themselves into a number of linear trimers. This trimer-formation is also highlighted in the ball-and-stick plots of mNTs of all sizes (Figures S1a-c), a highlight which gives evidence of the presence of trimers in all other mNTs. In this context, mNTs with k=3i+1 are different from other mNTs in that they only have trimers at their edges without any other edge-reconstruction features. Since trimers are common edge-reconstruction features in all mNTs for MoS2 and WS2, additional information on them are further elaborated. First, the average Mo-Mo distance within a trimer is 2.9 Å but the Mo-Mo distances between the adjacent trimers are either 3.1 or 3.5 Å. Second, Figure 2a clearly shows that trimers have slightly different bonding configurations and charge-carrier distributions. Third, all mNTs with k=3i+1 have edge-Mo atoms all reconstructing themselves into trimers with no exception. With these clues, we further examine the band structures of all mNTs with k=3i+1 and thereby infer that mNTs fitting the edge-reconstruction configuration with edge-Mo atoms forming only trimers possess a band-structure basis of intrinsic-semiconducting with Fermi level amid the gap between the separate valence and conduction bands of mNTs. Deviating from this trimer edge-reconstruction condition, mNTs can be “infected” by defect states in the bandgap or at the band-edge, and, therefore, become either metallic or n+ semiconducting. The nature of such deviation is further articulated by examining the change from mNT[3i+1] to mNT[3i]. For example, mNT[7] having its 18 edge-Mo atoms in a configuration of 6 linear trimers around its perimeter, but mNT[6] has 15 edge-Mo atoms and the edge reconstruction changes to a combination of 2 trimer, plus 1 linear tetramer and 1 bent pentamer, as shown in Figures S1a and S1b. In fact, each of all mNTs for k=3i commonly comprises one linear tetramer and one bent pentamer on its edge-perimeter, with the remaining edge-Mo atoms forming trimers. The DOS analysis (Figures 1b and 1e) and charge-carrier density analysis (Figure 2b) both explicitly show that the formation of the linear tetramer leads to the extension of some conduction ACS Paragon Plus Environment

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band states into the bandgap to reach the Fermi level (the green domain in Figure 2b), and the formation of the bent pentamer leads to the extension of some valence band states into the bandgap to reach the Fermi level (the red domain in Figure 2b). With the distributions of these defect states reaching the Fermi level from both the conduction band and valence band, mNTs[3i] are thus metallic-like. An extension of this analysis can also adequately explain the n+ semiconducting nature of mNTs[3i-1]. Taking mNT[5] as an example, we note that the atomic structure of mNT[5] clearly shows the Mo-edge reconstruction comprising, on each edge, a trimer with two apex Mo-monomers. Similarly, all mNTs[3i-1] commonly have, on each edge, two apex Mo-monomers each passivated by three S-passivator atoms, with all remaining edge-Mo atoms in the trimer configuration. In this edge-configuration, the semiconducting nature of the Mo-trimer is expressed in mNTs[3i-1] and the well passivated apex Mo-monomers apparently do not introduce any gap states. However, each mNTs[3i-1] is electron rich and has its Fermi level above the bottom of the conduction band. By comparing the nature of mNT[3i+1] with that of mNT[3i-1], we speculate that the apex-Mo monomer is an electron donor. In closing the discussion about mNT[3i-1], we emphasize an outstanding feature of these mNTs in that their charge-carrier distribution maps, as shown in Figure 2c, clearly show the domination of edge-constituents in the interesting n+ semiconducting behavior of these mNTs. We only plot the distributions of electrons in the conduction band in Figure 2c, with no distribution of any hole states because mNTs[3i-1] are n+ semiconducting and have virtually no holes. To further validate and articulate our identification of the presence of the bent pentamer and linear tetramer as the root causes of bandgap states in mNT[3i], we plot the partial DOS of all the edge-reconstruction features which we have identified so far from mNTs with k=5, 6, and 7 in reference to the Fermi level of these mNTs, including the apex-monomer, linear trimer, linear tetramer and bent pentamer, in the upper panel of Figure S5. Clearly this comprehensive plot of the partial DOS “genomes” of these basic elements of the edge-reconstruction features, for all mNTs having each of their edge-Mo atom passivated by one S-passivator atom, gives a powerful database for tracking and innovating changes in electronic properties of mNTs via atomic edge-engineering. Particularly, the plot shows explicitly that the presence of a linear tetramer leads to defect-states well below the conduction band minimum, and that of a bent pentamer leads to defect-states above the valence band maximum; obviously, such presences should be prevented or promoted to cater for applications demanding semiconducting or metallic mNTs. We also note



from the plot that whenever trimers are accompanied by an apex-monomer, they change from intrinsic-semiconducting to n+ semiconducting; as such, an apex-monomer is not only n+ semiconducting itself but also effectively fills electrons to the conduction band edge of its associated trimers. Although the presence of a 3-fold periodic size-dependence of mNTs in their electronic properties is fascinating, this nature is a nuisance in practice because it is virtually impossible to grow mNTs with a single size or with a specific size-grouping (k=3i-1, k=3i or k=3i+1). In fact, the exemplary experimental work by Besenbacher, et al.,25 has demonstrated that a broad size-distribution is typical in producing mNTs. By projecting this experimental limitation to the size-dependence nature, one can infer straightforwardly that a mixture of semiconducting and metallic mNTs is inevitably produced in growing mNTs. To circumvent this practical problem against the production of either only semiconducting or only metallic mNTs for the development and optimization of mNT applications, we explore if the size-dependent change-sequence of intrinsic-semiconducting/metallic/n+ semiconducting in mNTs can be altered and manipulated. The strategic objective in this exploration is to find a simple and practical means to produce mNTs all being semiconducting regardless of their sizes. Once the semiconducting basis is found, various defect-engineering processes can then be adopted to put back defect-states into the bandgap for the design and production of metallic mNTs. In fact, adding S-passivator atoms to reach the 100% sulfur-passivation condition is readily known to produce metallic mNTs, regardless of the mNT size. 35-37 Hence, the remaining task is to find a practical way to produce semiconducting mNTs regardless of the mNT size; an obvious approach is depleting S-passivator atoms. In fact, there is good experimental evidence27,32-33 that an exposure of sulfide to atomic hydrogen can cause sulfur depletion. Our thorough analysis of energy changes relevant to the depletion of S-passivator atoms also reveals that depleting one S-passivator atom per mNT correlates to a relative low energy cost in the presence of atomic hydrogen. For example, for mNT[5] of MoS2, the energy cost is 4.30 eV for eliminating the S-passivator atom from the apex of the mNT, lower than that for eliminating the S-passivator atom from the edge-Mo atom next to the apex (4.64 eV), and much lower than that associated with the edge-Mo atom further away from the apex (5.12 eV). In addition, our computation study also finds that the enthalpy for eliminating a second sulfur atom from an mNT is typically about 1 eV more than that of the elimination of the first sulfur atom. The detailed site-dependence and other relevant thermodynamic data are summarized in SI,


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particularly in Table S1. These thermodynamic data assure that experimental control of depleting only one sulfur atom from an mNT is feasible, with a good possibility of depleting only the apex S-passivator atom. The appropriateness of using atomic hydrogen to drive S-depletion is also supported by thermodynamics because the bond-strength of H-S is known to be around 3.6 eV, and thus the enthalpy cost of around 4.5 eV can be compensated with the enthalpy gain by forming H2S. Such a prediction is well supported by known experiments.32-33 To summarize a rather large set of original data supporting our proposed manipulability of the size-dependent change-sequence of intrinsic-semiconducting/metallic/n+ semiconducting in mNTs, we first plot in the bottom panels of Figure S5 the DOS of MoS2 mNTs for k=5, 6 and 7 with the depletion of one S-passivator atom from one of the apex-Mo atom in each mNT, to highlight the evidence of accomplishing our strategic goal of assuring all modified mNTs being semiconducting. Consistently, similar plots for all mNTs with k=5-16 depict the band structure of a semiconductor, in dependent to the size of these mNTs, with bandgaps ranging 0.5 to 0.7 eV. The relevant DOS data for these modified mNTs are included in Figure 3a-3c. Second, we highlight the new reconstruction-configurations of the edge-Mo atoms in all modified mNTs for k=5-16, in the simple format of balls as atoms and sticks as bonds, as shown in Figures S7a-4c. By summing up all the edge-reconstruction features of mNT[3i+1] in Figures S7a, with those of mNT[7] forming the inner-most triangle and those of mNT[16] forming the outer-most triangle, we demonstrate that all modified mNT[3i+1] commonly comprise a bent trimer with the remaining edge-Mo atoms reconstructing themselves only in the linear trimer format. From the partial DOS “genome” plot in Figure S5, one finds that both bent trimer and linear trimer are semiconducting, and one thus can infer the semiconducting behavior of all modified mNT[3i+1]. The same insight can be drawn from the plots in Figures 3b and S7b for those modified mNT[3i] and Figures 3c and S7c for those modified mNT[3i-1]. From Figure 3 and Figure S7, one sees clearly that our proposed depletion of one sulfur-passivator atom from each mNT leads to the elimination of the edge-reconstruction features of linear tetramer and bent pentamer, and to the creation of linear dimer, bent trimer, or ben tetramer. Since the eliminated features are those causing mid-gap states and the created features are all semiconducting, our proposed edge-engineering yields mNTs all being semiconducting. In principle, the “genome” database in Figure S5 can be expanded by adding the correction linking each of any new reconstruction features induced by any atomic edge-engineering means to the characteristic partial DOS of the specific reconstruction feature. Such a “genome” approach is



perhaps the most systematic way to guide edge-engineering of nanopolygons of m-TMDCs for specific functional applications. In summary, we discover a fascinating nature of the technologically important mNTs of MoS2 and WS2, in that their electronic properties follow a 3-fold periodic size-dependent change-sequence of intrinsic-semiconducting/metallic/n+ semiconducting. In essence, this fascinating nature is best articulated with the physics and chemistry of the evolution in edge-reconstruction and band-structure with a 3-fold periodically repetitive pattern as the mNT size increases. Beyond formulating this scientific principle, we also find a practical way to manipulate this nature. The methodology in this work is also expected to be relevant to the studies of other nanopolygons of m-TMDCs.

ACKNOWLEDGEMTNS This work was supported by the National Natural Science Foundation of China (NNSFC) (21273172), the program for New Century Excellent Talents in University (NCET-13-0471). This work was also supported by the 111 Project (B08040). The supports from the University of Science and Technology Beijing and the University of Electronic Science and Technology China are appreciated. ASSOCIATED CONTENT Supporting Information The supporting information available: Calculation methods, Figures S1-S7 and Table S1. AUTHOR INFORMATIONS Corresponding Author *E-mail: [email protected]; [email protected] Notes The authors declare no competing financial interest.

REFERENCES


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(b)

(a)

(d)

(e)

(c)

(f)

Figure 1. (a)-(c) showing the density of states and(d)-(f) showing the projected density of states

for MoS2 monolayer-nanotriangles (mNT[k], k being the number of Mo atoms per edge of the triangle).



(a)

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MoS2-mNT[16]

MoS2-mNT[13]

MoS2-mNT[7] MoS2-mNT[10]

(b)

MoS2-mNT[15]

MoS2-mNT[12]

MoS2-mNT[6]

MoS2-mNT[9]

(c)

MoS2-mNT[14]

MoS2-mNT[11]

MoS2-mNT[5] MoS2-mNT[8]

Figure 2. Partial charge-carrier density of MoS2 monolayer-nanotriangles (mNT[k]): (a)carriers

accumulated around the Fermi level within the respective energy range of ±0.47, ±0.42, ±0.40 and ±0.38 eV for these mNTs; (b)carriers accumulated around the Fermi level within the respective energy range of ±0.1, ±0.08, ±0.07 and ±0.07 eV for these mNTs; and (c)carriers accumulated above the Fermi level within the respective energy range of 0.01, 0.03, 0.04 and 0.05 eV for these mNTs. Isosurface value is 0.001e/Å3. k is the number of Mo atoms per edge of the triangle. Green


Page 17 of 18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


depicting electrons in conduction band and red depicting holes in valence band.



(a)

(b)

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(c)

Figure 3. Density of states of MoS2 monolayer-nanotriangles (mNT[k]) with one S-passivator

atom depleted from an apex-Mo atoms.


3-Fold-Periodic Size-Dependence in Electronic Properties of

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