Van der Waals Epitaxial Growth of Transition Metal Dichalcogenides

Sep 2, 2014 - Molecular Beam Epitaxy of Transition Metal Dichalcogenides. Lee A. Walsh , Rafik Addou , Robert M. Wallace , Christopher L. Hinkle. 2018...
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Van der Waals Epitaxial Growth of Transition Metal Dichalcogenides on Pristine and N‑Doped Graphene Wissam A. Saidi* Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, United States S Supporting Information *

ABSTRACT: The stability and the electronic structure of layered heterostructures MX2 (M = Mo or W and X = S or Se) and graphene (GA) are systematically investigated using firstprinciples methods. The calculations cover pristine and defected GA systems with up to 12% nitrogen substitutional defects. It is found that the van der Waals (vdW) epitaxy of MX2 on undoped GA substrate, whether pristine or defected, follows a Volmer−Weber growth-mode resulting in thick MX2 films. On the other hand, nitrogen doping of pristine GA (NGA) and also of GA with Stone−Wales (SW) defects increases the MX2/GA heterostructure adhesion energy favoring the growth of ultrathin MX2 layers. This growth-mode change in MoS2 due to nitrogen doping is in agreement with recent experiments. Furthermore, our study demonstrates that the yield of ultrathin MX2 films can be increased if the N-GA samples have a larger concentration of SW defects or nitrogen. The underpinnings of the extra stability of these N-GA substrates are due to charge-transfer effects that decrease the Pauli repulsion between the two layered systems.

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memory cells,13 Li-ion batteries,14 and electronics.15 Both MX2 and GA have hexagonal lattice structures with a relatively large lattice mismatch, but nevertheless GA can serve as an epitaxial substrate for MoS2,16−20 as well as other TMD members such as MoSe220 and WS2.21 Additionally, it was demonstrated that the MoS2 layers can be transferred to arbitrary substrates.22 This is an example of vdW epitaxy because the two layered materials are free of dangling bonds.11 Thickness is one of the fundamental parameters that define the optical, thermal, and electronic properties of 2D heterostructures. However, a precise control of the number of MoS2 layers grown on the GA surface has not been achieved. Less is known about the other TMDs. It is found that MoS2 grew into thicker flakes on the GA surface that eventually transform into a continuous film.16 This growth mode is similar to Volmer−Weber type.23 Nitrogen chemical substitution in GA is a very effective doping mechanism that is used in modulating the electronic properties of GA and enhancing its range of applications24 and is currently a topic of great interest.25 Chang et al. recently showed that nitrogen doping of the GA substrate has a dramatic effect on the growth of MoS 2 , where they demonstrated a facile process for the synthesis of ultrathin MoS2 on nitrogen-doped GA (N-GA) substrates. These MoS2/ N-GA composites exhibited exceptionally high initial reversible capacity and outstanding cyclic stability as lithium-ion battery

INTRODUCTION Two-dimensional (2D) materials with only a single-atom or a single-polyhedral thickness are an emerging class of systems with exotic electrical, optical, and mechanical properties.1−4 Graphene (GA) is the prime example of this class that has created much excitement in materials science since its exfoliation in its free-standing form in 2004.5,6 Other 2D materials of interest include BN7 and the transition-metal dichalcogenides (TMDs), MX2 where M = metal and X = S, Se, or Te.2,6,8 The electronic nature of these 2D systems varies where GA has a conical Dirac spectrum of energy states without a bandgap and a linear dispersion, whereas BN is an insulator,7 and the TMDs like MoS2 are semiconductors9 in their ground state structure. In these layered materials, the properties at the single layer are generally distinct from the bulk due to quantum confinement effects. For instance, MoS2 in bulk form is an indirect band insulator (∼1.3 eV), while as a monolayer, it has ∼1.8 eV direct bandgap.9 This indirect-to-direct bandgap change has a dramatic effect on the optical properties where the MoS2 monolayer emits light strongly and exhibits more than 104 increase in luminescence quantum efficiency compared with the bulk material. 9 Recently, a similar indirect-to-direct bandgap transition was also observed in MoSe2.10 Advances in materials synthesis have reached a stage where 2D materials can be used as building blocks that can be restacked layer-by-layer in precisely chosen sequences yielding composites with unusual properties.11 In this regard, MX2/GA nanocomposites find many potential applications such as catalysts for hydrogen evolution reactions,12 nonvolatile © 2014 American Chemical Society

Received: January 22, 2014 Revised: May 27, 2014 Published: September 2, 2014 4920

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anodes.18 By comparing different substrates, XRD characterization showed that the MoS2 morphologies have different thicknesses, in the order of MoS2/N-GA, MoS2/GA, and MoS2 where the growth of MoS2 on N-GA resulted in the thinnest MoS2 films.18 Thus, the growth mode of MoS2 on N-GA is similar to Frank-van der Merwe or Stranski−Krastanov23 type. In this study, the interaction of MX2 with GA and N-GA substrates is investigated to provide more insight into the growth mechanism of the heterostructures. In addition to pristine GA, we also considered defected GA where the defects are of the form of a monovacancy (MV), divacancy 5−8−5 defect (DV), and Stone−Wales (SW). Defects are always present in carbon materials, and in particular the SW type usually emerges during the growth process of GA because of their low formation energies.26 The central goal of this study is to understand the role of nitrogen doping in determining the growth mode of the TMDs on graphene-based substrates that is seen experimentally for MoS218 and further how to optimize the nitrogen distribution or the GA substrate for a better stability of the MX2/GA heterostructure or to control the number of grown MX2 layers. The rest of the paper is organized as follows. The next section gives a description of the computational setup and the various tests employed to validate the accuracy. In the following section, we show the main findings of the paper: (i) The growth of MX2 follows Volmer−Weber growth mode because MX2/MX2 is more stable than MX2/GA. (ii) Nitrogen doping increases the stability of MX2/GA if the GA substrate has no defects or has SW-type defects, whereas carbon vacancies in the GA substrate have the opposite effect. The underpinnings of this behavior are related to charge-transfer effects that increase with N-doping for pristine and SW GA. (iii) The sine-wave rumpling in SW defected GA substrates that increases the stability of isolated undoped GA27 becomes less stable with nitrogen doping and also decreases the stability of the MX2/GA heterostructure compared with the flat GA substrate. It should be noted that all of these results are based on thermodynamic considerations. However, considering that the epitaxy is driven by van der Waals interactions (vide inf ra), it is unlikely that there would be any kinetic hindrances to the growth mechanisms suggested in the study. Finally, the paper discusses possible applications where these N-GA substrates can be utilized for the growth of TMD nanoparticles supported on GA. This can be done by selectively decorating the GA substrate with nitrogen dopants that would direct the growth of MX2 nanoparticles into these regions only.

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tier-1 basis set results in binding energies that differ from those obtained using the larger basis set by less than 0.1 and 0.01 eV for MX2/GA and MX2/MX2, respectively. The MX2/GA heterostructure is built using (5 × 5) and (4 × 4) lateral supercells for GA and MX2, respectively. This choice minimizes the lattice strain to less than ∼3% for MoS2 and WS2, and ∼7% for MoSe2 and WSe2. The MoS2/GA interface was studied before using a similar supercell approach.19,32 TMDs with larger lattice constants are not considered here because these require a larger supercell to minimize the strain. The lattice mismatch is computed from the bulk lattice constant of GA, a = 2.46 Å, and those of MX2 as described (see Table 1). We used a hexagonal lattice with a side constant of a = b =

Table 1. Optimized Structural Parameters for Bulk MX2a MoS2 MoSe2 WS2 WSe2

a=b

c/a

dM−X

dX−X

dM−M

∠X−M−X

3.15 3.27 3.16 3.28

4.12 4.55 4.40 4.46

2.40 2.55 2.43 2.55

3.91 4.47 4.17 4.35

6.85 7.70 7.20 7.57

81.3 84.1 82.6 84.1

a

a and c define the parameters of the hexagonal lattice. dM−X is the distance between M and X belonging to the same trilayer, dX−X is the shortest distance between X (S, Se) atoms belonging to different trilayers, dM−M is the distance between the two transitions metals M in the unitcell, and ∠X−M−X is the angle between the three atoms belonging to the same trilayer. Distances are in Å and angles are in degrees. 12.30 Å determined using the GA lattice constant for all heterostructures including defected and pristine GA, and more than 15 Å along the nonperiodic direction to minimize the fictitious interactions between images. For the MoX2 heterostructures, we also repeated the calculations using a supercell with a = b = 12.52 Å that has a better lattice match with MoS2 but found similar results to the smaller lattice constant. This partially shows that employing a larger supercell to minimize the geometric strain between MoS2 and GA will not affect the results of the study. Finally, because of the large supercell for both GA and MX2 systems, the Brillouin zone (BZ) is sampled using a Γ-centered 2 × 2 surface Monkhorst−Pack k-point grid, which is validated to yield binding energies that are accurate to more than 0.05 eV. The stability of the heterostructure is measured using the interface binding energy, defined as

ΔE bind = E MX2 /GA − E MX2 − EGA

(1)

where EMX2/GA is the heterostructure energy, EMX2 is the energy of an isolated MX2 monolayer, and EGA is the energy of the GA-based system. To gain insight into the nature of the binding energy, we partition ΔEbind into two components: short-range, ΔESR, as described by the PBE exchange-correlation functional, and long-range vdW attraction, ΔEvdW, that is,

COMPUTATIONAL DETAILS AND METHODOLOGY

The first-principles density functional theory (DFT) calculations are carried out using the all-electron FHI-aims program28 employing the PBE exchange-correlation functional29 and DFT+vdW dispersion corrections.30 Relativistic corrections are accounted for using the atomic zero-order regular approximation (ZORA). During geometry optimization, all atoms are relaxed using a convergence threshold of 0.05 eV/Å on the atomic forces. The Kohn−Sham wave functions are expanded using tier-2 numerical atom-centered basis sets31 for all of the atoms but without the highest angular momentum basis functions. This amounts to ∼4000 basis functions for the MX2/GA system. For the MX2 heterostructures without the GA substrate, we used a tier-1 basis set that is shown to be more than adequate. In this case, the number of basis functions for (MX2)3 is ∼5000. We have done extensive systematic tests to ensure that finite-basis set errors are less than 0.05 eV. To this end, it is found that the full optimization using the smaller

ΔE bind = ΔEvdW + ΔESR

(2)

The short-range contribution is obtained by freezing the geometries of the interface, MX2, and GA-based systems to those predicted using PBE+vdW, and calculating ΔEbind via eq 1 using self-consistent energies from the PBE only. The long-range vdW contribution is given by the damped sum of pairwise additive dispersion terms between atoms, whose strength is modulated by a C6 coefficient that depends on the chemical environment and the bonding hybridization state. This approach has been applied to several systems yielding results that are in good agreement with experiment for semiconducting33−36 and metallic systems.37−41

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RESULTS AND DISCUSSION We first computed the bulk properties of MX2 to validate our computational setup. The bulk unit cell has two MX2 trilayers. 4921

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very small as shown in Figure S1, Supporting Information, because of the very shallow potential surface, we have started the optimization of the heterostructures from the same initial configuration. The optimization of the MX2/GA heterostructure results in relatively small changes to the two subsystems compared with the noninteracting case. This indicates that the bonding between MX2 and GA does not significantly perturb the strong planar-bonding in either layered system, which is in line with other vdW bonded systems43 and is consistent with the previous study on MoS2/GA.32 Table 2 summarizes the interfacial interactions and average distance, dSG, for the heterostructures. Also, as a measure of the smoothness of the GA sheet in the heterostructure, we show the rumpling, δG defined as the difference between the smallest and largest displacements from the two-dimensional nuclear framework. As seen from the table, the stabilization energy, ΔEbind, of the heterostructure is due to vdW interactions, ΔEvdW. In fact, the short-range contribution, ΔESR, is even repulsive. In contrast, it was previously shown that ΔEbind of MoS2/GA obtained using LDA is negative, which is indicative of the stability of the heterostructure.19,32 This is not surprising because LDA suffers from overbinding, often giving interaction energies for weakly bound vdW systems that are approximately correct.43−47 To investigate the origin of the short-range repulsive term, ΔESR, we examined the deformation energy of the isolated systems, defined as the energy penalty due to bonding in the heterostructure. This is computed as the difference between the energies of MX2 and GA systems with the same structure as in the MX2/GA composite, and the optimum energy of the two noninteracting systems in isolation. For MX2 and the GA systems, the deformation energy is less than 0.1 eV that is smaller than the repulsive term ΔESR. This shows that ΔESR is mostly due to a Pauli repulsion between MX2 and GA and not due to any structural changes in the monolayers. Overall, these findings are consistent with other vdW bonded layer materials.43,48 The introduction of defects in the undoped GA system has little effect on the binding energies, changing ΔEbind by less than 0.1 eV, as seen in Table 2. Both pristine and SW GA systems are the most stable substrates for MX2 epitaxy. Because the heterostructure is dominated by vdW forces, it would be

Overall the results, summarized in Table 1, compare favorably with previous calculations.32,42 In particular, the in-plane lattice constants, a, of MX2 are in perfect agreement with previous results42 that employed the PBE functional in conjunction with a planewave basis set and a projector-augmented-wave representation of the core electrons and the electron−nuclei interactions. This good agreement with the previous study,42 which did not account for vdW forces, indicates that dispersion interactions have minimal effects on the MX2 layer that is held by the strong in-plane bonding.43 The calculated out-of-plane lattice constant, c, is smaller than the corresponding PBE value,42 which is expected because of the vdW interactions between the two trilayers in the bulk primitive cell. Interaction of MX2 with Undoped Graphene Systems. We probe the binding energy of MX2 on pristine and defected GA systems where the defects are of the MV, DV, or SW types. Figure 1 shows a top-down view of the heterostructure for GA

Figure 1. Top-down view of the MoS2/GA structure where the GA system has a SW defect. Carbon is green, sulfur is yellow, and molybdenum is purple. Other TMDs show relatively similar structures.

with a SW defect. Other heterostructures have fairly similar structures except that the distances between the MX2 and GA layers vary (see Table 2). Because the interaction in the heterostructures is dominated by vdW interactions (vide inf ra), there are several adsorption configurations of relatively similar energies that differ mainly in the stacking registry sequence, as shown in Figure S1, Supporting Information. This is also discussed in the previous study of MoS2/GA that employed the local density approximation (LDA) but without vdW corrections.32 To minimize any bias in the energies, although

Table 2. Interaction Energies, ΔEbind, with Their Breakdown into Short Range, ΔESR, and Dispersion ΔEvdW Components, Bonding Distance between GA and Closest Sulfur Layer, dSG, and Rumplings, δG (only for GA substrates), for MX2/GAa

a

substrate

ΔESR

ΔEvdW

ΔEbind

MoS2 (MoS2)2 P SW SWSD DV MV WS2 (WS2)2 P SW SWSD DV MV

0.51 0.59 0.56 0.55 0.66 0.52 0.51 1.01 1.09 0.51 0.49 0.66 0.48 0.48

−5.42 −5.68 −4.16 −4.16 −4.06 −3.96 −4.05 −5.38 −5.59 −3.97 −3.96 −3.91 −3.79 −3.87

−4.92 −5.09 −3.60 −3.61 −3.40 −3.45 −3.54 −4.37 −4.50 −3.46 −3.51 −3.25 −3.31 −3.40

dSG

δG

3.37 3.37 3.51 3.39 3.39

0.13 0.12 0.97 0.08 0.57

3.40 3.40 3.43 3.41 3.41

0.09 0.36 0.82 0.08 0.58

substrate

ΔESR

ΔEvdW

ΔEbind

MoSe2 (MoSe2)2 P SW SWSD DV MV WSe2 (WSe2)2 P SW SWSD DV MV

0.61 0.55 0.49 0.48 0.65 0.54 0.50 0.96 1.05 0.47 0.44 0.67 0.45 0.46

−5.57 −5.60 −4.13 −4.14 −4.06 −4.03 −4.06 −5.41 −5.58 −3.99 −3.99 −3.96 −3.82 −3.90

−4.96 −5.05 −3.64 −3.66 −3.41 −3.48 −3.56 −4.45 −4.53 −3.52 −3.55 −3.28 −3.38 −3.45

dSG

δG

3.50 3.48 3.53 3.47

0.09 0.28 0.78 0.10

3.51 3.50 3.52 3.52 3.52

0.09 0.30 0.70 0.07 0.57

P refers to pristine GA. Energies are in eV, and distances are in Å. 4922

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Figure 2. Optimum nitrogen doping sites on GA. The doping sites for N = 1, 2, 3, 4, and 6 are located at (a) 1, 12, 123, 1244, and 124466 for pristine; (b) 1, 12, 133, 1233, and 123366 for MV; (c) 1, 12, 123, 1234, 123466 for SW; and (d) 1, 12, 333, 3336, and 123336 for DV. Here the notation “124466” means that the six nitrogen atoms are located at sites 1, 2, 4, 4, 6, and 6 as labeled in each panel.

whereas the extra stability of MX2/MX2 is due to vdW interactions. This is due to two factors. First, the number of atoms involved in the interaction is larger for MX2/MX2 than that for MX2/GA for the same surface cell. This will lead to smaller ΔEvdW due to the additivity of the vdW interactions. Second, the vdW C6 coefficients30 (in hartree bohr6) of Mo (C6 = 514.3), W (C6 = 423.9), S (C6 = 67.0), and Se (C6 = 105.0) are larger than that of C (23.3), which would provide more stable dispersion interactions for MX2/MX2 compared with MX2/GA. This argument is applicable at least outside the region of the damping function that is used in the semiempirical dispersion correction, which is nearly the case here because of the large separations between the two layered systems, d ≥ 3 Å. Influence of Nitrogen Doping on Stability of MX2/GA Heterostructure. We next investigate the role of nitrogen doping of the GA substrate on the stability of the MoS2/GA heterostructure. We used up to N = 6 nitrogen substitutions resulting in 2−12% N-doping concentration. The differences in the electronegativities between carbon and nitrogen (respectively, 2.5 and 3.0 as determined by Pauling) polarizes the Cδ+− Nδ− bond resulting in charge transfer from carbon to nitrogen. However, it is not clear how overall this charge rearrangement would affect the stability of the heterostructure. Additionally, the presence of the defects complicates this simple charge arrangement picture. Recently, the interplay between nitrogen doping and various point defects on GA with up to four nitrogen substitutions was systematically investigated.49 This study showed that nitrogen substitutions are more favorable near the defects especially for sites associated with the largest bond shortenings. Also, defects and nitrogen doping showed cooperative effects where defects increased the stability of N-GA and vice versa. Furthermore, in contrast to defect-free GA where the interaction between nitrogen dopants is repulsive, it was shown in this study that the aggregation of nitrogen in defected GA is favorable near the defect sites.49 In the present study, we used the optimum configurations for the defected N-GA that were previously obtained for N ≤ 4 nitrogen dopants.49 For a partial set, we have verified that these are the lowest energy configurations using our computational

expected that GA vacancies would decrease the stability of the heterostructure due to the additivity of vdW interactions. Additionally, in the absence of hybridization effects between GA and MX2 systems, it is expected that the short-range interactions will become less repulsive due to carbon vacancies, which in turn would lead to a more stable heterostructures. The results shown in the table corroborate these expectations, where the decrease in the repulsive part somewhat counteracts the decrease in the dispersion attractive energy. However, as seen in the table, all of the energy changes are relatively small. For all the TMDs shown in Table 2, the interaction energy between two MX2 layers in their optimum configuration is smaller than that between MX2 and the undoped GA systems. For example, for MoS2, the interaction energy with GA is approximately −3.4 eV, while that with MoS2 substrates is approximately −5 eV. For other TMDs, these interactions energies are relatively similar where the interactions between two TMD layers are the weakest, approximately −4.5 eV, for WX2 and the strongest, approximately −5 eV, for MoX2. As seen in the table, differences between MoX2 and WX2 are mostly due to ΔESR, which for (WX2)2 is nearly a factor of 2 larger than (MoX2)2. The increase in ΔESR for (WX2)2 is because of the shorter distance between the two W layers (6.20 Å) compared with the Mo layers (6.34 Å), that results in the stronger electrostatic repulsion between them. Growing MX2 onto thicker MX2 substrates as in (MX2)2 does not affect the adhesion energy significantly as seen from the table. The small differences are due to the change in the stacking mode from AB in (MX2)2 to ABA in (MX2)3. Therefore, thermodynamically, it is more advantageous for MX2 to grow into thicker slabs rather than thin slabs on pristine GA or even GA with low-energy defects. This is even more favorable for MoX2 than for WX2 because (MoX2)2 is more stable than (WX2)2. Thus, the vdW epitaxy of MX2 on GA follows a Volmer−Weber growth-mode type. In the case of MoS2, these findings agree with recent experiments, which showed that the epitaxial growth of MoS2 on GA substrate favors thicker MoS2 films.16,18 The energy dissection of eq 2 into short-range, ΔESR, and vdW contributions, ΔEvdW, gives an understanding of the energy preferences for the heterostructures. Table 2 shows that ΔESR values for MX2/MX2 and MX2/GA are very similar, 4923

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Figure 3. Changes in the interfacial binding energy, ΔEbind, of MX2/GA with respect to the undoped system, plotted against number of nitrogen dopants.

framework, which employs a smaller 5 × 5 surface supercell for GA instead of 9 × 9 that was employed in the previous study.49 Additionally, we determined the optimum configurations of the defected GA systems with N = 6 and for the pristine GA with N ≤ 6, because these structures were not previously determined. The N = 6 structures in the defected systems are obtained by starting from the optimum structures with N = 4 and finding the lowest-energy configuration for the two additional nitrogen substitutions. For the defect-free GA system, we examined more than 20 possible configurations to obtain the lowest energy structure. All of the optimum structures are shown schematically in Figure 2. The changes in the binding energy of the heterostructure due to the introduction of the substitutional N-dopants are depicted in Figure 3. Detailed energy decomposition is shown in Tables S1, S2, S3, and S4, Supporting Information. Overall all systems show similar behavior that is indicative that the results are applicable to other members of the TMD family. For MV and DV defects, it is seen that N-doping decreases the stability of MX2/GA, where this decrease correlates with the increase of nitrogen dopants. In contrast, N-doping makes the interaction between GA and MX2 more attractive for pristine GA or for GA with SW defects, where the strength of the interaction correlates with the nitrogen concentration. The exceptions to this behavior are the cases with low nitrogen dopants, N ≤ 3, for MoSe2, WS2, and WSe2. This will be discussed further in the next section. It is expected that the increase in the adhesion energy will transform the Volmer−Weber-like growth mode for undoped GA to Frank-van der Merwe or Stranski−Krastanovlike on N-GA . To quantify the changes of the adhesion energy in terms of probabilities for MX2 deposition, we note that for N = 6 nitrogen doping, the probability for growth of MX2 onto the GA substrate at room temperature is enhanced by a factor of exp(δEbind/(KBT)) ≈ 20 compared with the undoped GA. Recently, nitrogen doping was shown to result in ultrathin MoS2 layers on GA,18 which is in line with the current findings. Moreover, our study shows that the GA substrates in these experiments have a smaller concentration, if they have any, of MV or DV defects and that the yield of the ultrathin MoS2 layers can be increased by creating more SW defects in GA or

by increasing the nitrogen-doping concentration. Additionally, our results support the conclusion that other TMDs are likely to exhibit a similar growth behavior on doped or undoped GA substrates. In particular, MoSe2 is expected to show similar behavior, while for WX2, it is expected that this would yield even thinner MX2 layers in comparison to MoS2 because MoS2/MoS2 is more stable than WX2/WX2 (vide supra). What is the mechanism for the extra stability of the MX2/GA with N-GA substrates? As seen in Tables S1 and S2, Supporting Information, for pristine and SW defected GA, nitrogen doping makes the vdW interactions less attractive and the short-range interactions less repulsive. These two competing effects result in a stronger adhesion energy with nitrogen doping. The decrease in the dispersion component can be understood because nitrogen (C6 = 12.1 hartree bohr6) is less polarizable than carbon (C6 = 23.3 hartree bohr6). On the other hand, the origin for the decrease in the short-range interactions is not obvious at first (vide inf ra). From the optimized structures, it can be inferred that nitrogen doping does not introduce new binding sites for MX2. This observation is supported by the fact that both N-GA and MX2 layers have little rumplings in their planar structures, which is relatively similar to the case of the undoped-GA substrate. To gain further insight into the effect of nitrogen doping on the stability, we compute the plane-averaged charge densities that can provide a quantitative picture of the charge distribution due to bonding. In particular, we examine Δρ(z) = ρMX2/GA − ρMX2 − ρGA, where z is perpendicular to the GA plane, ρMX2/GA is the plane-averaged density of MX2/GA heterostructure, and ρMX2 and ρGA are, respectively, the plane-averaged densities of the isolated MX2 and GA subsystems adapting their structures in the optimized MX2/GA system. Positive (negative) values in Δρ(z) indicate accumulation (reduction) of the electron charge density. To quantify the amount of charge transfer, we also examined the cumulative charge-rearrangement Q(z) = ∫ z0Δρz′) dz′, which measures the amount of electron transfer per unit cell from left to the right of a plane located at z.50 Figure 4 shows Δρ(z) and Q(z) for MoS2 with SW and DV GA substrates and different nitrogen dopant concentrations. The 4924

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Figure 4. Plane-averaged charge distribution, Δρ(z), for undoped (N0) and N-doped (N1, N2, N3, N4, and N6) (a) SW and (b) DV GA systems. Only the region of the supercell around the monolayers is shown. The electron charge is −e.

pristine GA and the MV cases are similar to SW and DV, respectively. Also, the other TMDs show similar profiles except that the amount of charge transfer increases in the order of MoS2 > MoSe2 > WS2 > WSe2 (vide supra). As shown in Figure 3, the adhession energies of the interfaces also correlate with the amount of charge transfer. For the SW case shown in Figure 4a, we see from Δρ(z) that there is a depletion of the electron charge density near the GA layer that is closest to MoS2 and, concomitantly, a pronounced charge accumulation above the top of sulfur layer that is bonded to GA. This charge accumulation on the sulfur layers drives oscillatory charge rearrangements in MoS2 that decay in the region of the second sulfur layer. Using the Hirshfeld charge decomposition scheme with neutral atoms described using Hartree-Fock51 as the references states,52 we find that both nitrogen and the carbon atoms contribute to the charge transfer from N-GA systems to MX2. The charge density profile in Figure 4a is not symmetric with respect to the two GA sides, where the electron density on the side closest to MoS2 is more depleted than that on the other side. A similar behavior was also reported before for MoS2 on an undefected GA substrate.32

This charge response is attributed to Pauli pushback because the electron charge density of the tailing electron cloud of MoS2 is still significant close to GA as can be seen from inspecting the charge densities of the isolated subsystems (not shown). The amount of charge transfer correlates with the nitrogen concentration as shown in Figure 4a. The profile of Q(z) shows a minimum that is located in the interlayer region indicating a charge transfer from GA to MoS2, where the amount increases with nitrogen concentration up to 0.39 electron for N = 6. This behavior is indicative that the bonding between GA and MoS2 becomes stronger as the nitrogen content increases, which corroborates the same finding obtained before from the energetics. Other TMDs show similar profiles except that the amount of charge transfer is smaller. For example, for N = 6, the minima of Q(z) are in the interface region and have magnitudes of approximately −0.32, −0.26, and −0.21 electron for MoSe2, WS2, and WSe2, respectively. Overall, the charge analysis explains the findings based on the adhesion energies shown in Table 2 and Figure 3 for MX2 on SW and pristine GA substrates; namely, the stability of the MX2/GA heterostructure 4925

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this decrease is correlated with a similar decrease in the magnitude of the rumplings of the GA surface. Thus, the buckled SD structure becomes less stable than the flat sheet for denser nitrogen substitutions. As argued before, the SD instability is a strain-relief mechanism in a perfect honeycomb lattice that is triggered by the rotation of a carbon−carbon bond to form the SW defect.27 This explains why this instability becomes nonfunctional in N-GA because nitrogen doping creates asymmetries in the perfect sp2 network; thus, offering lower-energy paths than the SD instability to release the strain that is induced by the SW defect. Although the effects of the SD instability are considerably diminished with nitrogen substitutions of GA especially for large concentrations of nitrogen, it is of interest to see their effect on the stability of the MX2/GA heterostructure especially for MoS2. To this end, we studied the interaction of MoS2 with a SW GA substrate that supports a SD instability. Results are shown in Table 3. For N ≤ 3, the total energy of MoS2/GA with SD is smaller than the corresponding one with flat surface, but the difference between them decreases with nitrogen doping and for N > 3, and the flat substrate becomes more favorable. Interestingly, the adhesion energy of MoS2/GA with the SD is less favorable than that with the flat surface as indicated by δEbind in Table 3. The SD feature decreases the total energy of the MX2/GA but the decrease of energy is larger than that of GA alone, and thus, this makes the adhesion strength of MX2/GA smaller than the case with a flat GA surface. Comparing the rumplings of the flat- and sine-like GA for the MoS2/GA with the GA case in Table 3, we see that these have opposite trends. The magnitude of the rumplings increases in MoS2/GA compared with the isolated system for the flat GA substrate but decreases for the substrates that support a SD. This behavior can be understood due to the repulsive interactions between GA and MoS2 that would favor a flat GA surface. It is also expected that the other TMDs will show similar behavior. Finally, we note that the SD instability gives a better understanding of the results of Figure 3, in particular that for MX2 (with the exception of MoS2); the stability of the MoS2/ SW heterostructures increases for N ≤ 3 compared with N = 0 case. The reason for this behavior is that the GA substrates in the optimum heterostructures have a SD although the initial starting configuration was deliberately chosen as flat. MoS2/SW did not suffer from the SD, and the GA substrate was relatively flat after optimization. Overall, the SD instability and the smaller amount of charge transfer (vide supra) from GA to MX2 compared with the MoS2 case explain why the adhesion energies for MoSe2, WS2, and WSe2 with the SW GA substrate are not as strong as that of MoS2.

increases with nitrogen doping due to a decrease in the Pauli repulsion between the two layered materials. Despite the similarities between the charge profiles for the SW and DV cases shown in Figure 4a,b, there are some notable differences. First, for the DV substrates, the amount of charge redistribution is significantly reduced compared with the SW case. This indicates that heterostructures with SW defects are more stable than those with DV defects in all cases. Additionally, for the DV case, the amount of charge transfer does not show any appreciable dependence on the number of nitrogen substitutions. This explains why the short-range interaction is not sensitive to the nitrogen concentration (see Table S3, Supporting Information). Nevertheless, Figure 3 shows that the heterostructure stability decreases with the nitrogen content for DV and MV cases due to the decrease in attractive vdW interactions because nitrogen is less polarizable than carbon (vide supra). Effects of Sine-Wave Instability on MX2/GA Heterostructure. It has recently been shown that GA with SW defects has an instability that induces an out-of-plane wavelike defect structure that extends over several nanometers; this is dubbed the sine-wave defect (SD) due to the similarity with the sine function.27 Compared with the unrumpled or flat GA surface, this instability lowers the formation energy of the SW defect by δE = 200−300 meV as estimated using PBE and δE = (96 ± 20) meV from quantum Monte Carlo for the 5 × 5 supercell.27 Our obtained value for δE is 335 meV, which is close to the previous value of 269 meV27 computed with a similar 5 × 5 supercell but with the PBE functional. This good agreement indicates that dispersion vdW interactions have little effect on this defect, which is also corroborated with the results in Table 3 showing that the short-range, δESR, and total, δE, binding energies are fairly similar. Nitrogen-substitutions are found to decrease the stability of the buckled SD compared with the flat surface as shown in Table 3, where δE decreases from 335 meV for undoped-GA to 7 meV for N = 6 nitrogen doping. Also, as shown in the table, Table 3. Comparison between Flat and SD Substrates with Different Nitrogen Concentrationsa rumpling, δG (Å)

energy (meV) no. N GA SW 0 1 2 3 4 6 MoS2/SW 0 1 2 3 4 6

δESR

δE

−359 −257 −161 −37 −21 −15

−335 −237 −145 −23 −10 −7

−250 −185 −147 −106 −87 −70

−125 −73 −26 9 28 41

δEbind

209 163 119 32 38 48

flat

buckled

0.000 0.010 0.010 0.008 0.006 0.007

0.992 0.987 0.986 0.994 0.874 0.755

0.122 0.113 0.110 0.095 0.096 0.095

0.885 0.853 0.813 0.559 0.523 0.476

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CONCLUSION AND OUTLOOK In this study, we analyzed using first-principles methods the effects of native GA defects and nitrogen doping on the vdW epitaxial growth of MX2 on undoped and N-GA. The GA substrates consider defects of the form of monovacancies, divacancies, and Stone−Wales. We show that epitaxial growth of MX2 on GA results in thicker MX2 slabs because the adhesion energy between two MoS2 layers is larger than that between MX2 and GA. Nitrogen doping of undefected GA and GA with SW defects enhances the stability of the MX2/GA heterostructure and transforms the growth modes of MX2 from Volmer−Weber like on pristine GA to Frank-van der Merwe or

a Second and third columns show difference in short-range, δESR, and total, δE, energy due to SD compared with the flat GA substrates. Fourth column shows the difference in adhesion energy, δEbind, of MoS2 between flat and buckled GA substrates. Fifth and sixth columns show the rumplings, δG, of GA.

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Stranski−Krastanov like on N-doped GA. These results are consistent with recent experiments on MoS2.53 Also, based on our first-principles calculations, we expect that the GA samples in these experiments have negligible concentrations of MV or DV, which we demonstrated will decrease the stability of MX2/ GA compared with the undoped substrates. Additionally, our results show that the stability of MoS2/GA, and hence the yield of ultrathin MoS2 layers will increase if the GA samples have SW defects or support a larger concentration of nitrogen. We find that the stability of the MX2/GA system arises from a synergy between direct bonding and vdW attraction, where the role of vdW interactions is significant. It is also found that nitrogen doping does not introduce new binding sites but nevertheless leads to more stable heterostructures due to a charge-transfer effect. These studies indicate a promising method for identifying appropriate substrates or nitrogen-doping concentrations for the vdW epitaxy of MX2 with tailored thicknesses. Additionally, the enhanced interaction between N-GA and the TMDs can provide a route for the growth of ultrathin nanoparticles of TMDs on a N-GA substrate. This can be done by carefully decorating a GA substrate with nitrogen in selected regions that will drive the TMDs to reside primarily near the nitrogen dopants during their synthesis and will inhibit their transformation into continuous films. Region-specific GA decorations with nitrogen can be potentially accomplished using a plasma-based technique in conjunction with a physical masking technique as developed by Walton and co-workers.54 One attractive application for these systems would be in hydrogen reduction reactions (HER). TMDs, and in particular MoS2 and WS2, have excellent catalytic activities toward HER where the active sites are located at the edges.55 The ultrathin MX2 nanoparticles on a N-GA substrate would be the optimum choice for this catalyst because the number of edge sites compared with the TMD weight is maximized. Additionally, the choice of the nitrogen doped GA substrate will also be beneficial considering that N-GA has better conductivity than GA.56 Indeed the activity of the semiconducting TMDs is primarily limited by their poor conductivity, which hinders charge transfer kinetics, and thus would be enhanced substantially using a conductive substrate.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

Total energies for all the systems studied and top-down views of five conformers of MoS2/N-GA. This material is available free of charge via the Internet at http://pubs.acs.org.

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Article

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Calculations are performed in part at the University of Pittsburgh Center for Simulation and Modeling. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation Grant Number OCI-1053575. 4927

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