An Anomalous Formation Pathway for Dislocation-Sulfur Vacancy

Sep 30, 2015 - Our calculated formation energies of SI and VS in GI are in good agreement with their formation energies in monolayer MoS2, which are â...
0 downloads 7 Views 3MB Size
Download PDF
Letter pubs.acs.org/NanoLett

An Anomalous Formation Pathway for Dislocation-Sulfur Vacancy Complexes in Polycrystalline Monolayer MoS2 Zhi Gen Yu,† Yong-Wei Zhang,*,† and Boris I. Yakobson*,§ †

Institute of High Performance Computing, Singapore 138632, Singapore Department of Mechanical Engineering and Materials Science, Rice University, Houston, Texas 77005, United States

§

S Supporting Information *

ABSTRACT: Two-dimensional (2D) molybdenum disulfide (MoS2) has attracted significant attention recently due to its direct bandgap semiconducting characteristics. Experimental studies on monolayer MoS2 show that S vacancy concentration varies greatly; while recent theoretical studies show that the formation energy of S vacancy is high and thus its concentration should be low. We perform density functional theory calculations to study the structures and energetics of vacancy and interstitial in both grain boundary (GB) and grain interior (GI) in monolayer MoS2 and uncover an anomalous formation pathway for dislocation-double S vacancy (V2S) complexes in MoS2. In this pathway, a (5|7) defect in an S-polar GB energetically favorably converts to a (4|6) defect, which possesses a duality: dislocation and double S vacancy. Its dislocation character allows it to glide into GI through thermal activation at high temperatures, bringing the double vacancy with it. Our findings here not only explain why VS is predominant in exfoliated 2D MoS2 and V2S is predominant in chemical vapor deposition (CVD)-grown 2D MoS2 but also reproduce GB patterns in CVD-grown MoS2. The new pathway for sulfur vacancy formation revealed here provides important insights and guidelines for controlling the quality of monolayer MoS2. KEYWORDS: MoS2, grain boundary, S vacancy, first-principles calculations

R

underestimated due to the interface contact problems in FET devices.25 The origin for this low mobility in monolayer MoS2 is, however, not entirely clear. Because intrinsic defects, such as S vacancies and grain boundaries (GBs), were observed in MoS2 samples, it is believed that these defects may be responsible for the dramatic changes in carrier mobility and may thus be the primary sources for the low mobility.13 There were several experimental and theoretical studies on S vacancies in MoS2.16−29 The mechanism for the formation of S vacancy in MoS2, however, still remains elusive. On one hand, Tongay et al. reported experimentally the eminent presence of S vacancies, which led to a new photoemission peak and an enhancement in photoluminescence intensity in monolayer MoS2.16 Qiu et al. presented experimental evidence that S vacancies were present in MoS2 in high concentration and led to localized donor states inside the bandgap.19 On the other hand, comprehensive DFT study on native defects in monolayer MoS2 showed that S vacancy was a deep acceptor with a formation energy of 1.3−1.5 eV under S-poor growth condition and Mo interstitial was a deep acceptor with a formation energy of 4.3 eV under Mo-rich growth condition.17 These reported formation energies suggest that the concentrations of S vacancy and Mo interstitial should be low, and the donor-like defects are unlikely to result in n-type conduction in

ecently, two-dimensional (2D) transition-metal dichalcogenides (TMDs), a new class of 2D materials with a chemical formula of MX2 (M = Mo, W, and so forth, and X = S, Se, and so forth) are considered as promising electronic and optoelectronic materials owing to their chemical and environmental stability and low operating voltages for electronic devices.1−14 Among all the TMD members, MoS2, a direct bandgap semiconductor with low toxicity and high thermal and chemical endurance, has attracted great attention. Recently, several MoS2-based electronic devices have been demonstrated, such as, field-effect transistors,6−8 integrated circuits,9 and phototransistors.10 Currently, two common methods have been widely used to produce monolayer MoS2, that is, mechanical exfoliation and chemical vapor deposition (CVD) growth. It was reported that monolayer MoS2 with grain size ranging from several to 20 nanometers was fabricated by depositing S and Mo atoms on metal surfaces.14 Large-area CVD growth of monolayer MoS2 with a grain size more than 100 μm on Si/ SiO2 substrate using MoO3 and S as precursors was also reported.15 Interestingly, the type and concentration of S vacancy seem to be dependent on the nature of sample origins. For example, single S vacancies were often observed in exfoliated samples,16−21 while double S vacancies were often observed in CVD samples.22,23 Compared to bulk MoS2, however, the reported mobility of monolayer MoS2 is much lower with 0.3−5 cm2 V−1 s−1 for MoS2 monolayer24 versus 200−500 cm2 V−1 s−1 for the bulk.12 It should be noted that the ultralow mobility of 0.3 cm2 V−1 s−1 in layered MoS2 may be © XXXX American Chemical Society

Received: July 13, 2015 Revised: September 22, 2015

A

DOI: 10.1021/acs.nanolett.5b02769 Nano Lett. XXXX, XXX, XXX−XXX

Letter

Nano Letters

agreement with previously reported results.31 On the basis of our optimized monolayer MoS2 model, we build MoS2 GB models for our further investigation. Here, we focus on typical GBs with the (5|7) dislocation atomic structures, which have been widely observed in MoS2.22,23,29 The plane view of the optimized GB model is shown in Figure 1, in which two grains with a misorientation

MoS2. Clearly, the current defect models are unable to explain the high S vacancy concentration in CVD-grown monolayer MoS2. Therefore, it is imperative to resolve this inconsistency between experimental observation and theoretic prediction. Then, a prime question is the following: Where do these S vacancies in monolayer MoS2 come from? We notice that CVD-grown MoS2 samples used in experimental studies are typically polycrystalline and have high GB density.22,23,29 On one hand, it was shown that in monolayer MoS2, GBs typically consist of (5|7) defects.22 Strangely enough, Mo-polar GBs, which contain the Mo−Mo homobonds in the pentagon rings, were robustly observed, while S-polar GBs, which contain the S−S homobonds in the pentagon rings, were sometimes absent.29 On the other hand, images of grain boundaries obtained using scanning transmission electron microscopy (STEM) showed a high concentration of (4|6) defects in GBs and also in GIs.23,29 These observations promote us to raise following questions: Why are the S-polar GBs sometimes absent? What is the nature of the (4|6) defects? Why are the (4| 6) defects present in both GBs and GIs? Can the (4|6) defects form in GBs and then migrate into GIs? Clearly, answers to these questions are not only of great scientific interest but also of technological impact on the improvement of monolayer MoS2 quality and its applications in electronic and optoelectronic devices. Therefore, to answer these questions by piecing together these experimental observations and also resolving the inconsistency for S vacancy formation constitutes the main objective of the present work. With the above objective in mind, we undertake a systematical study on point defects in both GBs and GIs in monolayer MoS2 with aim to understanding their atomic structures and defect formation energetics, and revealing their formation mechanisms. By using state-of-the-art density functional calculations, we reveal an anomalous formation pathway for S vacancies in MoS2. Specifically, in this pathway one Mo atom is embedded interstitially in a (5|7) defect in an S-polar GB due to the low formation energy. Then, the embedded Mo interstitial forms bonds with neighboring S atoms. Subsequently, one MoS2 unit consisting of the Mo interstitial and its bonded two S atoms is removed from the Spolar GB spontaneously, leaving one double S vacancy at the GB. This process converts the (5|7) defect to the (4|6) defect, a dislocation-double S vacancy complex. We further show that the (4|6) defect complex is able to glide and carry the double S vacancy with it into GI at elevated temperature. Through this pathway, the energetic barrier for the formation of the (4|6) dislocation-double S vacancy complex is much lower than the formation energy of S vacancies by directly removing S atoms from GIs. Our proposed pathway not only explains the presence of the (5|7) Mo-polar GBs and sometimes the absence of the (5|7) S-polar GBs but also the dense double S vacancies in monolayer MoS2 GIs from CVD growth and their influence on the native n-type conductivity in pristine MoS2. To explore the energy landscape of point defects in GBs and GIs, we perform first-principles calculations based on density functional theory (DFT). In order to remove the layer−layer interactions, we increase the layer-to-layer spacing c to 18 Å by using periodic boundary conditions (PBCs). The optimized lattice constants of monolayer MoS2 are a = b = 3.184 Å, which are slightly higher than the experimental bulk value of 3.16 Å.30 The optimized S−Mo bond length and S−S distance in optimized monolayer MoS2 are 2.414 and 3.129 Å, respectively, which are nearly equal to those of bulk MoS2, and are in good

Figure 1. Schematic of MoS2 GB atomic structures with Mo-polar (red) and S-polar ⊥ (blue) characters. Blue dashed line shows the zigzag direction in one grain and the red dashed line shows the zigzag direction in the other grain. α is the misorientation angle, which is about 20.6°. Purple balls are Mo atoms and yellow balls are S atoms.

angle of ∼20.6° form two GBs with opposite directions because of the trigonal symmetry: one is Mo-polar, labeled as “ ” and the other is S-polar, labeled as “⊥”. In order to check whether the distance between and ⊥ is large enough to obtain converged results, we calculate the defect formation energy of a double S vacancy V2S in different calculation models. The calculated formation energies are 1.67, 1.0, and 1.0 eV under S rich growth condition, corresponding to the distance between and ⊥ of about 17, 26, and 34 Å, or the model with 96, 150, and 198 atoms, respectively. Hence, we use the simulation model with 150 atoms or the distance of ∼26 Å between and ⊥ for defect calculations. The two types of GBs with hard-shell gourd-like units were also observed in other 2D materials, such as h-BN.32 Using this GB model, we perform an optimization DFT calculation to obtain the GB formation energy, EGB f , which is defined as 1 GB EfGB = E MoS − μMo − 2μS 2 (1) n where EGB MoS2 is the total energy of the GB system and n is the number of MoS2 units in the GB model, μMO, (S) is the chemical potentials of Mo (S) calculated from metallic Mo (solid S) unit cells, respectively. The calculated MoS2 GB formation energy in the GB model is 2.50 eV/unit, which is nearly the same as its crystalline counterpart, which is 2.53 eV/unit. The small difference in these two energies may explain the high density of GBs in MoS2 often observed experimentally.22 We further calculated the GB energy, which is defined as the GB formation energy of per unit GB length, that is, (EML − EGB)/2L, where EML is the total energy of monolayer MoS2 containing the same numbers of S and Mo atoms as the GB model and 2L is the total GB length in the model. The calculated GB energy is B

DOI: 10.1021/acs.nanolett.5b02769 Nano Lett. XXXX, XXX, XXX−XXX

Letter

Nano Letters ∼0.05 eV/Å. This low GB energy again signifies the easy formation of GBs. Using the optimized GB model, we further investigate intrinsic defect formations in GBs. For comparison, the intrinsic defect formations in GI are also investigated. Here, we consider in total seven intrinsic defects: Mo interstitial (MoI), single S interstitial (SI), Mo vacancy (VMo), single S vacancy (VS), double S vacancy (V2S), antisite of substitutional 2S at Mo site (2SMo), and antisite of substitutional Mo at 2S sites (Mo2S). The defect formation energy Ef is also a function of the Fermi level Ee and the chemical potential of host elements μ and can be obtained by def pef Ef = EGB − (EGB ±

∑ Hiμi ) + q(E V + Ee)

(2)

pef where Edef GB and EGB are the total energies of defect-embedded and defect-free GB systems, respectively. ΣHiμi is the sum of the number intrinsic defects Hi multiplied by their individual chemical potential μi. q is the defect charge state and ± denotes interstitial defect (+) or vacancy defect (−). EV is the eigenvalue of the valence band maximum of pristine monolayer MoS2. The calculated formation energies of charged defects are shown in Supporting Information Figure S3, in which, we find that MoI is energetically the most favorable defect under the S poor-condition at the GB. Note that even when the Fermi level moves toward to the bottom of the conduction band due to the presence of extrinsic defects, such as Re in MoS2, the defect MoI would still be the dominant defect.27 In monolayer MoS2, in order to suppress the formation of host element phases, such as solid S and metallic Mo, the chemical potential of S (Mo) should be in the range of −(1/2) EGB ≤ μS ≤ 0 (−EGB ≤ μMO ≤ 0), corresponding to the S f f (Mo)-poor and -rich growth conditions, respectively. Hence the chemical potential of S (Mo) should be in the range of −1.25 eV ≤ μS ≤ 0 (− 2.50 eV ≤ μMO ≤ 0). It should be noted that in our model as shown in Figure 1, there are two types of GBs. We have calculated the formation energies for all the seven intrinsic defects in these two types of GBs. However, we only chose to plot those with relatively lower formation energies. In the Mo-polar GB, we discuss three major defects: S interstitial, Mo vacancy, and antisite of 2S substitutional defect at Mo site as shown in Figure S1 in Supporting Information. In the S-polar GB, we discuss four major defects: Mo interstitial, single S vacancy, double S vacancy, and antisite of substitutional Mo at 2S site (Mo2S) as shown in Figure S2 in Supporting Information. Because the formation energies for Mo interstitial and S vacancy in the S-polar GB are much lower than those in the Mo-polar GB, it is energetically more favorable for these two defects to form in the S-polar GB than that in the Mo-polar GB. Hence, here, we focus on the S-polar GB. The formation energies of these intrinsic defects in GBs and GIs as a function of μS are shown in Figure 2. Importantly, the S−S homobond in the S-polar GB is unstable arising from the embedded native defect (MoI) and would like to convert to the (4|6) defect (more detailed discussion on this will be given later), while the Mo−Mo homobond in the Mo-polar GB is stable because the native defects are energetically unfavorable to embed in this type of GBs. Remarkably, our predictions are in a good agreement with experimental observations that the Mo-polar GBs were robustly present, while the S-polar GBs were sometimes absent.22,23 Hence, in the following we solely focus on the S-polar GB, and thereafter, the notation “GB” refers to the S-polar GB.

Figure 2. Calculated formation energies of selective intrinsic defects in MoS2 as a function of S chemical potential, (a) in GB and (b) in GI. The S chemical potential varies in the range of −(1/2)EGB f ≤ μS ≤ 0 ≤ μMO ≤ 0), corresponding to S-poor and -rich growth (−EGB f conditions, respectively. (Some major defect configurations in the two types of GB are given in Figures S1 and S2 in Supporting Information.).

For the formation energies for selective intrinsic defects in GB and GI shown in Figure 2, it is seen that GB has an exotic formation physics with respect to GI. In GB, as shown in Figure 2a, MoI has the lowest formation energy under the S-poor growth condition and SI is energetically stable under S-rich growth condition. The formation energy of MoI is −1.78 and 0.74 eV when μS = −1.25 eV and μS = 0, respectively. It is worth noting that MoI should be the predominant defect in the wide range of μS (from −1.25 to −0.41 eV), SI should be the predominant defect with a negative formation energy only in the narrow range of μS (from −0.24 eV to 0), and VS would be formed in Mo-polar GB only in the very narrow range of μS (−0.41 to −0.24 eV) as shown in Figure 2a. For other intrinsic defects, they are in minor states and their concentrations should be extremely low due to their high formation energies. In GI, as shown in Figure 2b, SI has the lowest formation energy under the S-rich condition, whereas VS has the lowest formation energy under the S-poor condition. The formation energy of SI is 1.20 eV when μS = 0 and that of VS is 1.49 eV when μS = −1.25 eV, respectively. Our calculated formation energies of SI and VS in GI are in good agreement with their formation energies in monolayer MoS2, which are ∼1.0 and ∼1.5 eV, respectively.17 The most energetically stable configuration of SI in GI is found to be the S adatom on the top of a lattice S atom by forming S−S homobond, which is almost identical to that reported previously for monolayer MoS2.17 Only a small difference exists in the S−S homobond length, that is, 1.93 Å in GI from our work versus 1.91 Å in MoS2 monolayer,17 which may be caused by the different calculation methods: The GGAPBE approximation used here normally results in larger lattice constants and longer bonding lengths than local density approximation (LDA) used in ref 17. The excellent agreements in these formation energies in GI and in monolayer MoS2 indicate that our GB model is accurate and our calculated results are reliable. Next, we analyze the optimized configurations of GB upon embedding MoI and forming V 2S . Their local atomic configurations are shown in Figure 3b,d, respectively. Interestingly, these two configurations are identical. Upon embedding MoI or forming V2S, the initial hard-shell gourd-like C

DOI: 10.1021/acs.nanolett.5b02769 Nano Lett. XXXX, XXX, XXX−XXX

Letter

Nano Letters

Figure 3. Schematic of double S-vacancy formation at S-polar GB. (a) Atomic configuration of the (5|7) dislocation in the S-polar GB with one MoI. (b) The optimized configuration of Mo at GB exhibiting a (4|6) configuration. (c) A MoS2 unit is removed spontaneously from the GB. (d) The optimized configuration after removing one MoS2 unit exhibits a (4|6) configuration. Purple balls denote Mo and yellow balls denote S atoms.

Figure 4. Atomic structure of the (4|6) defect and illustration of its sliding directions and energy barriers. (a) The initial atomic configuration of the (4|6) defect. The green arrow denotes the Burgers vector of the (4|6) dislocation-V2S complex. (b,c) The final atomic configurations of the (4|6) dislocation-V2S complex moving a magnitude of the Burgers vector along the Green arrow and its opposite direction, respectively. The inserted blue hexagon serves as a common reference to illustrate the moving direction and path of the (4|6) dislocation-V2S complex. (d) Sliding energy barriers of the (4|6) dislocation-V2S complex obtained by NEB method. The red and black curves are the spline fitting to the nine date points for two moving directions, respectively. Zero energy points correspond to the initial and the final states.

spontaneous removal of one MoS2 unit in the MoI embedded GB, while the negative formation energy in GI implies that it is energetically unfavorable to remove one MoS2 unit from GI even with MoI. It should be noted that the calculated formation energy ΔE is independent of the chemical potentials of S and Mo since the chemical potential of MoS2 in GB-contained MoS2 is a constant. On the basis of our calculated formation energies, it is seen that under S-rich growth condition μS = 0, the formation energy of V2S (MoI) in the GB is 1.0 eV (0.74 eV) and under S-poor growth condition μS = −1.25 eV, the formation energy of V2S (MoI) in the GB is −1.53 eV (−1.78 eV). Therefore, the formation of V2S would be suppressed by that of MoI because it has a lower formation energy as shown in Figure 2. Additionally, spontaneous removal of the MoS2 unit consisting of the MoI atom and its bonded two S atoms from MoS2 GB creates one V2S. Undergoing this spontaneous process, the (4|6) dislocation-V2S complex becomes the dominant defect in GB. If we substitute the value of ΔE = 0.44 eV in the MoI formation energy, the line that represents the formation energy of MoI will shift down to the dashed line labeled with MoI-V2S in Figure 2a. Hence, the dashed line can be considered as the effective V2S formation energy as a function of μS. Clearly, this pathway requires a lower formation energy than that by directly removing S atoms.

(5|7) configuration is converted to a diamond-like (4|6) configuration. From the chemical stoichiometry point of view, the difference between the MoI embedded GB and the V2S formed GB is just one MoS2 unit. Note that in Figure 3c, the removed MoS2 unit consists of the MoI atom and its bonded two S atoms, resulting in the formation of a double S vacancy V2S and converting the MoI embedded (5|7) dislocation into the (4|6) configuration. Because the (4|6) configuration can be considered as a combination of a double S vacancy V2S and the (5|7) dislocation, therefore, the (4|6) defect is actually a dislocation-V2S complex. This thermodynamic process can be expressed by ΔE

V2S@GB ⇔ MoI@GB − MoS2

(3)

and the energy equilibrium of the derived structures relative to the chemical potential of MoS2 can be written as E V2S@GB = E MoI@GB − μ MoS − ΔE 2

(4)

Here, E V 2S@GB and E MoI @GBare the system energies containing V2S at the GB and MoI at the GB, respectively. μMoS2 is the chemical potential of MoS2 in GB-contained MoS2. ΔE is the formation energy. On the basis of our DFT calculations, we find that ΔE is 0.44 eV in GB and −1.25 eV in GI. The positive formation energy in GB indicates a D

DOI: 10.1021/acs.nanolett.5b02769 Nano Lett. XXXX, XXX, XXX−XXX

Letter

Nano Letters

polycrystalline MoS2 monolayer. Pathway I is mainly controlled by the formation energy of VS while pathway II is mainly controlled by the S-polar GB density and also the gliding energy barrier of the (4|6) dislocation-V2S complex. In order to explicitly explore S vacancy formation, we discuss the effect of temperature on the defect concentration. For Pathway I, in equilibrium, the concentration of VS, N, is mainly controlled by its formation energy, that is, N = N0e(−EVf S/kT), where N0 is the concentration of potential lattice sites for S vacancy formation, k is Boltzmann’s constant, EVf S is the formation energy of VS, and T is the temperature. For single-crystalline MoS2, N0 ≈ 3.49 × 1015 cm−2 and the formation energy of VS is EVf S = 1.49 eV when μS = −1.25 eV The defect concentration versus temperature relation is shown in Figure 5a. It is seen that the

In the above discussion, we have demonstrated an energetically favorable process of forming the (4|6) dislocation-V2S complex in GB mediated by Mo interstitial. According to the calculated formation energies as shown in Figure 2a, the formation of MoI is energetically the most favorable process in the S-polar GB as shown in Figure 3a. To further reduce the system energy, one MoS2 unit is removed from the MoI embedded (5|7) dislocation, and it is converted to the (4|6) configuration, forming a dislocation-V2S complex, as shown in Figure 3b. More specifically, upon removing one MoS2 unit consisting of Mo and 2S (see the atom labels in Figure 3) highlighted by the oval shadow as shown in Figure 3b to reduce dangling bonds, the Mo1 atom moves along the red arrow to the position of the purple ball, and 2S1 atoms move along the blue arrow to the position of the yellow ball. As a result, 2Sl rebond with Mo1 to form a hexagonal ring consisting of 2S1, 2S2, 2S4, Mo1, Mo3, and Mo5 atoms and a diamond ring consisting of Mo4, 2S3, Mo2, and 2S1 atoms as shown in Figure 3d. By comparing the atomic configurations before (Figure 3a) and after (Figure 3d) the removal, we see that the (4|6) dislocation-V2S complex has pseudomigrated both leftwards and downward. It should be noted that the atomic configuration after removing the MoS2 unit is exactly the same as that by directly removing two S atoms (labeling 2S) from the S-polar (5|7) dislocation. However, the former needs a lower energy than the latter. Hence, the concentration of V2S can be considered as that of the (4|6) dislocation-V2S complex, which will be explicitly discussed below. Our above analyses have shown that the (4|6) dislocation-V2S complexes can be formed at S-polar GBs. However, experimental observation showed that they can be present in high density in GI in CVD-grown samples.22,23,29 Then, an important question arises: Why is there a high concentration of the (4|6) dislocation-V2S complexes in GI observed in experiments? Can (4|6) dislocation-V2S complexes glide from GB into GI by thermal activation? To answer these questions, we further calculated the sliding energy barrier for the (4|6) dislocation-V2S complex. Figure 4a shows the initial atomic structure of the (4|6) dislocation-V2S complex. The (4|6) dislocation-V2S complex may glide along the direction indicated by the green arrow (or its opposite direction depending on the stress state) as shown in Figure 4a. Here, we focus on both gliding directions and calculate the gliding energy barriers for the (4|6) dislocation-V2S complex. Using the blue hexagon as a reference, we can see clearly the relative motion of the (4|6) dislocation-V2S complex in Figure 4a−d. Employing the nudged elastic band (NEB) method implemented in the VASP (details are given in Supporting Information), we obtain the saddle points and the minimum energy paths between the initial state (Figure 4a) and the final states (Figure 4b,c) and the calculated results are shown in Figure 4d. In the calculations, we set the energies of the initial and the final states to be zero. The calculated energy barrier is found to be about 0.61 eV along both directions. On the basis of our calculation results as shown in Figure 4d, we see that the (4|6) dislocation-V2S complex is able to glide under the thermal activation at CVD growth temperatures. Hence, it is the glide of (4|6) dislocation-V2S complexes that causes their prominent presence in GI. According to our calculations, there may be two dominant pathways for S vacancies formation in MoS2, that is, Pathway I, forming single S vacancies (VS) through directly removing S atoms from lattices sites in single-crystalline MoS2 monolayer, and Pathway II, forming the (4|6) dislocation-V2S complexes in

Figure 5. Calculated S vacancy concentration. (a) The calculated concentration of VS as a function of the growth temperature. (b) The calculated grain size-dependent D0. Inset shows a typical MoS2 grain with a grain size L, and the blue segment highlights D0 in the grain size range of 5−50 μm.

concentration is generally low. For example, the calculated VS concentration is only ∼3.48 × 109 cm−2 even at the temperature of 1300 K. This result is in reasonably good agreement with the reported value of 3.5 × 1010 cm−2 for mechanically exfoliated MoS2 samples.21 For pathway II, at low temperatures it is expected that (4|6) dislocation-V2S complexes are primarily located at GBs. At elevated temperature, for example, at CVD growth temperature, however, the thermal fluctuations can drive the dislocations into GI. When the (4|6) defects are fully dispersed in MoS2 monolayer, the density of the (4|6) dislocation-V2S complexes (or V2S), D0, can be estimated by S-polar GB density and the linear density of (5|7) dislocations along the GBs. In our GB model, the separation distance between two adjacent (5|7) dislocations along the S-polar GB is b = 8.43 Å. Hence, the linear density of the (4|6) dislocation-V2S complex (V2S) is 1/b. Because experimental results of monolayer MoS2 often showed a triangle pattern,15,23,33 we simplify MoS2 polycrystal as an assembly of identical triangular grains with a grain length of L and an area of (√3/2)L2 as shown in the inset of Figure 5b. Therefore, the upper-bound concentration of the (4|6) dislocation-V2S complex (V2S) can be calculated by using D0 = (√3/2 × L × b)−1. Clearly, the concentration of the (4|6) dislocation-V2S complex is proportional to L‑1. Figure 5b shows the variation of D0 with the grain size L in which the blue segment highlights the V2S concentration in the grain size range of 5−50 μm. Not surprisingly, D0 increases with decreasing the grain size L. For example, D0 = 6.90 × 1013 cm−2 when L = 20 E

DOI: 10.1021/acs.nanolett.5b02769 Nano Lett. XXXX, XXX, XXX−XXX

Letter

Nano Letters μm and D0 = 2.76 × 1014 cm−2 when L = 5 μm. The calculated D0 is in reasonably good agreement with the experimental value of 3.5 × 1013 cm−2 measured in CVD samples.34 It should be noted that the two paths discussed here have different initial and final states. In single crystalline MoS2 (Path 1), we have the direct formation of S vacancies from perfect lattice sites, while in polycrystalline MoS2 (Path 2), the (5|7) defects at S-polar GBs formed during growth turn into a defect complex containing a double S vacancy and a dislocation, which then slides into grain interior. Because these two different paths have different initial and final states, the transition state theory,35 which states that the defect concentration should depend on the defect formation energy only, not on the pathway for the defect production, is not applicable here. It is known that defect concentration can have significant effect on carrier mobility. Below we briefly discuss this effect. In polycrystalline MoS2, the carrier mobility due to defect scattering can be estimated by μI = AI/NI, where AI is a material- and temperature-dependent parameter and NI is the defect concentration.36 Clearly, a higher concentration of defects leads to more scatterings, which result in a lower carrier mobility. Here, we focus on the change in carrier mobility due to the change in the average grain size L. According to our upper-bound calculation results shown in Figure 5b, the S vacancy concentration is 6.90 × 1013 cm−2 at L = 20 μm and decreases to 6.90 × 1011 cm−2 at L = 2 mm. Hence, the mobility in sample with the average grain size of 2 mm is 100 times higher than that in sample with the average grain size of 20 μm. Therefore, the carrier mobility can be significantly enhanced by increasing the grain size in polycrystalline MoS2 samples. The S vacancy formation mechanism proposed here may well explain the experimental observations of high (4|6) defects present in CVD-grown samples while V S present in mechanically exfoliated samples.15,19,22,23,29,34,37 In accordance to Bader-charge analysis, each MoI or V2S provides 0.94e to the conduction band, which results in a carrier concentration of ∼3.24 × 1013 cm−2. This result is in good agreement with the experimental results of carrier concentration of ∼1013−1014 cm−2.19,33 Thus, the above results not only explain the presence of (4|6) dislocation-V2S complexes in GI and but also the carrier concentration measured experimentally.38 Our results also well explain the experimental observation that the (5|7) Mo-polar GBs are stable and easy to be found in samples.19,22,23,29 Our DFT calculation results clearly show that intrinsic defects have relatively higher formation energies in the Mo-polar GBs, thus they are unlikely to embed in. Only 2SMo may embed in the (5|7) Mo-polar GB under an extreme high S chemical potential, which was indeed found in experimental samples.23 It should be noted that this possible GBs stable by antisite doping still keeps Mo-polar maintaining the (5|7) atomic configuration. Our above analysis suggests that the S vacancy concentration and type (VS vs V2S) should depend on the grain size of MoS2 samples. When the grain size is small, the GB-mediated mechanism predominately controls the V2S formation through pathway II and double S vacancies (V2S) are the favorable intrinsic defects. In particular, for samples with a high GB density, the V2S defect concentration can be as high as ∼1013 cm−2. While for low GB density or mechanically exfoliated samples, the V2S formation from GBs would be small. In such cases, the VS vacancies formed through Pathway I become predominant (the formation energy is about 1.49−2.75 eV

when −1.25 eV ≤ μS ≤ 0). Observations on mechanically exfoliated MoS2 using STEM indeed demonstrated that most of the vacancies are single S vacancies, and the measured concentration is in the order of 109 cm−2.20,21 Therefore, our results may explain the large variation in S vacancies (between 108 and 1013 cm−2) measured exeprimentally16,18−21,34 Meanwhile, our work also suggests that increasing the grain size is an effective route to reduce the (4|6) complex concentration, which may significantly improve the electrical properties. It should be noted that in plotting Figure 5b, we have assumed that all the (4|6) defects in the S-polar GBs have dispersed into the grain interiors. Hence, the grain sizedependent S vacancy concentration shown in Figure 5b is actually the upper limit. We have shown that there is a sliding energy barrier of ∼0.61 eV for the (4|6) defects at the grain boundaries to glide into grain interiors. On the basis of this, it is possible to reduce the CVD growth temperature and/or growth time so as to retain a large portion of S-polar GBs and reduce the dispersion of the (4|6) defects into grain interiors during CVD growth. In addition, the GB considered here is a highangle GB, which possesses a high linear density of the (4|6) defects. Through controlling substrate surfaces, it is also possible to control grain orientations so as to form as many low-angle GBs as possible. Hence, we propose to grow MoS2 monolayer on a selective substrate, which facilitates the formation of low-angle GBs, and a low-growth temperature and/or a short growth time, which is able to reduce the dispersion of S-polar GBs. In fact, growing millimeter-sized single-crystalline graphene on selective substrates with a high growth rate using a commercially available cold-wall CVD reactor has been successfully demonstrated.39 Therefore, the S vacancy formation mechanism proposed here for polycrystalline monolayer MoS2 may be useful for experimentalists to reduce S vacancy concentration in CVD growth. In summary, we have studied the intrinsic defect formation in monolayer polycrystalline MoS2. We find that intrinsic defects have lower formation energies in GB than in GI. On the basis of our calculation results, the (5|7) Mo-polar GBs are stable while the (5|7) S-polar GBs are unstable upon the embedding of Mo interstitials. Upon the spontaneous removal of one MoS2 unit, the MoI embedded (5|7) defect in the S-polar GB is converted into the (4|6) dislocation-V2S complex. We further show that the (4|6) dislocation-V2S complexes are able to glide into GI through thermal activation at high temperatures. Our results also indicate that VS should be predominant in mechanically exfoliated monolayer MoS2 while V2S should be predominant in CVD-grown monolayer MoS2. Our present work provides insights into the formation physics of intrinsic defects in monolayer MoS2. In addition, our study here also provides insights into how S vacancies contribute to the native n-type conductivity of monolayer MoS2. Because of the similar structures and properties of the TMD family members, the intrinsic defect formation mechanism proposed here may also exist in other TMDs. The new understandings and insights revealed here may help optimize the growth condition to achieve high-quality TMDs.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.5b02769. F

DOI: 10.1021/acs.nanolett.5b02769 Nano Lett. XXXX, XXX, XXX−XXX

Letter

Nano Letters

■

(21) Lu, C.-P.; Li, G.; Mao, J.; Wang, L.-M.; Andrei, E. Y. Nano Lett. 2014, 14, 4628−4633. (22) Najmaei, S.; Liu, Z.; Zhou, W.; Zou, X.; Shi, G.; Lei, S.; Yakobson, B. I.; Idrobo, J.- C.; Ajayan, P. M.; Lou, J. Nat. Mater. 2013, 12, 754−759. (23) Zhou, W.; Zou, X.; Najmaei, S.; Liu, Z.; Shi, Y.; Kong, J.; Lou, J.; Ajayan, P. M.; Yakobson, B. I.; Idrobo, J.-C. Nano Lett. 2013, 13, 2615−2622. (24) Ayari, A.; Cobas, E.; Ogundadegbe, O.; Fuhrer, M. S. J. Appl. Phys. 2007, 101, 014507. (25) Wang, Q. H.; Kalantar-Zadeh, K.; Kis, A.; Coleman, J. N.; Strano, M. S. Nat. Nanotechnol. 2012, 7, 699−712. (26) Fuhr, J. D.; Saúl, A.; Sofo, J. O. Phys. Rev. Lett. 2004, 92, 026802. (27) Komsa, H.-P.; Krasheninnikov, A. V. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 91, 125304. (28) Liu, D.; Guo, Y.; Fang, L.; Robertson, J. Appl. Phys. Lett. 2013, 103, 183113. (29) Zou, X.; Liu, Y.; Yakobson, B. I. Nano Lett. 2013, 13, 253−258. (30) Böker, T.; Severin, R.; Müller, A.; Janowitz, C.; Manzke, R.; Voß, D.; Krüger, P.; Mazur, A.; Pollmann, J. Phys. Rev. B: Condens. Matter Mater. Phys. 2001, 64, 235305. (31) Li, Y.; Zhou, Z.; Zhang, S.; Chen, Z. J. Am. Chem. Soc. 2008, 130, 16739−16744. (32) Liu, Y.; Zou, X.; Yakobson, B. I. ACS Nano 2012, 6, 7053−7058. (33) Schmidt, H.; Wang, S.; Chu, L.; Toh, M.; Kumar, R.; Zhao, W.; Neto, A. H. C.; Martin, J.; Adam, S.; Ö zyilmaz, B.; Eda, G. Nano Lett. 2014, 14, 1909−1913. (34) Hong, J.; Hu, Z.; Probert, M.; Li, K.; Lv, D.; Yang, X.; Gu, L.; Mao, N.; Feng, Q.; Xie, L.; Zhang, J.; Wu, D.; Zhang, Z.; Jin, C.; Ji, W.; Zhang, X.; Yuan, J.; Zhang, Z. Nat. Commun. 2015, 6, 6293. (35) Glensk, A.; Grabowski, B.; Hickel, T.; Neugebauer, J. Phys. Rev. X 2014, 4, 011018. (36) Sah, C.-T. Fundamentals of Solid State Electronics; World Scientific Publishing Co. Pte Ltd: Singapore, 1991. (37) Komsa, H.-P.; Kurasch, S.; Lehtinen, O.; Kaiser, U.; Krasheninnikov, A. V. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 88, 035301. (38) Bertolazzi, S.; Brivio, J.; Kis, A. ACS Nano 2011, 5, 9703−9709. (39) Miseikis, V.; Convertino, D.; Mishra, N.; Gemmi, M.; Mashoff, T.; Heun, S.; Haghighian, N.; Bisio, F.; Canepa, M.; Piazza, V.; Coletti, C. 2D Mater. 2015, 2, 014006.

Description of the intrinsic defects embedded GB structural models and first-principle calculation method. (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: (Y.-W.Z.) [email protected]. *E-mail: (B.I.Y.) [email protected]. Author Contributions

Z.G.Y. carried out the DFT calculations. All authors performed data analysis and manuscript writing. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This research was sponsored by the Agency for Science, Technology, and Research (A*STAR) and computational resource was provided by A*STAR Computational Resource Centre, Singapore (ACRC).

■

REFERENCES

(1) Lopez-Sanchez, O.; Lembke, D.; Kayci, M.; Radenovic, A.; Kis, A. Nat. Nanotechnol. 2013, 8, 497−501. (2) Baugher, B. W. H.; Churchill, H. O. H.; Yang, Y.; Jarillo-Herrero, P. Nat. Nanotechnol. 2014, 9, 262−267. (3) Pospischil, A.; Furchi, M. M.; Mueller, T. Nat. Nanotechnol. 2014, 9, 257−261. (4) Ross, J. S.; Klement, P.; Jones, A. M.; Ghimire, N. J.; Yan, J.; Mandrus, D. G.; Taniguchi, T.; Watanabe, K.; Kitamura, K.; Yao, W.; Cobden, D. H.; Xu, X. Nat. Nanotechnol. 2014, 9, 268−272. (5) Yun, W. S.; Han, S. W.; Hong, S. C.; Kim, I. G.; Lee, J. D. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 85, 033305. (6) Radisavljevic, B.; Radenovic, A.; Brivio, J.; Giacometti, V.; Kis, A. Nat. Nanotechnol. 2011, 6, 147−150. (7) Zhang, Y.; Ye, J.; Matsuhashi, Y.; Iwasa, Y. Nano Lett. 2012, 12, 1136−1140. (8) Qiu, H.; Pan, L.; Yao, Z.; Li, J.; Shi, Y.; Wang, X. Appl. Phys. Lett. 2012, 100, 123104. (9) Wang, H.; Yu, L.; Lee, Y.-H.; Shi, Y.; Hsu, A.; Chin, M. L.; Li, L.J.; Dubey, M.; Kong, J.; Palacios, T. Nano Lett. 2012, 12, 4674−4680. (10) Yin, Z.; Li, H.; Li, H.; Jiang, L.; Shi, Y.; Sun, Y.; Lu, G.; Zhang, Q.; Chen, X.; Zhang, H. ACS Nano 2012, 6, 74−80. (11) Novoselov, K. S.; Jiang, D.; Schedin, F.; Booth, T. J.; Khotkevich, V. V.; Morozov, S. V.; Geim, A. K. Proc. Natl. Acad. Sci. U. S. A. 2005, 102, 10451−10453. (12) Fivaz, R.; Mooser, E. Phys. Rev. 1967, 163, 743−755. (13) Enyashin, A. N.; Bar-Sadan, M.; Houben, L.; Seifert, G. J. Phys. Chem. C 2013, 117, 10842−10848. (14) Kim, D.; Sun, D.; Lu, W.; Cheng, Z.; Zhu, Y.; Le, D.; Rahman, T. S.; Bartels, L. Langmuir 2011, 27, 11650−11653. (15) van der Zande, A. M.; Huang, P. Y.; Chenet, D. A.; Berkelbach, T. C.; You, Y.; Lee, G.-H.; Heinz, T. F.; Reichman, D. R.; Muller, D. A.; Hone, J. C. Nat. Mater. 2013, 12, 554−561. (16) Tongay, S.; Suh, J.; Ataca, C.; Fan, W.; Luce, A.; Kang, J. S.; Liu, J.; Ko, C.; Raghunathanan, R.; Zhou, J.; Ogletree, F.; Li, J.; Grossman, J. C.; Wu, J. Sci. Rep. 2013, 3, 2657. (17) Noh, J.-Y.; Kim, H.; Kim, Y.-S. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 89, 205417. (18) Bahl, O. P.; Evans, E. L.; Thomas, J. M. Proc. R. Soc. London, Ser. A 1968, 306, 53−65. (19) Qiu, H.; Xu, T.; Wang, Z.; Ren, W.; Nan, H.; Ni, Z.; Chen, Q.; Yuan, S.; Miao, F.; Song, F.; Long, G.; Shi, Y.; Sun, L.; Wang, J.; Wang, X. Nat. Commun. 2013, 4, 2642. (20) Komsa, H.-P.; Kotakoski, J.; Kurasch, S.; Lehtinen, O.; Kaiser, U.; Krasheninnikov, A. V. Phys. Rev. Lett. 2012, 109, 035503. G

DOI: 10.1021/acs.nanolett.5b02769 Nano Lett. XXXX, XXX, XXX−XXX