Lateral Versus Vertical Growth of Two-Dimensional Layered Transition

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Lateral Versus Vertical Growth of Two-Dimensional Layered Transition-Metal Dichalcogenides: Thermodynamic Insight into MoS2 Shun-Li Shang, Greta Lindwall, Yi Wang, Joan M. Redwing, Tim Anderson, and Zi-Kui Liu Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.6b02443 • Publication Date (Web): 19 Aug 2016 Downloaded from http://pubs.acs.org on August 21, 2016

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Lateral Versus Vertical Growth of Two-Dimensional Layered Transition-Metal Dichalcogenides: Thermodynamic Insight into MoS2

Shun-Li Shang,*,† Greta Lindwall,†, ‡ Yi Wang,† Joan M. Redwing,† Tim Anderson,§ and Zi-Kui Liu†

†

Department of Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States

§

Department of Chemical Engineering, University of Florida, Gainesville, Florida 32611, United States

ABSTRACT Unprecedented interest has been spurred recently in two-dimensional (2D) layered transition metal dichalcogenides (TMDs) which possess tunable electronic and optical properties. However, synthesis of a wafer-scale TMD thin film with controlled layers and homogeneity remains highly challenging due mainly to the lack of thermodynamic and diffusion knowledge, which can be used to understand and design process conditions, but falls far behind the rapidly growing TMD field. Here, an integrated density functional theory (DFT) and calculation of phase diagram (CALPHAD) modeling approach is employed to provide thermodynamic insight into lateral versus vertical growth of the prototypical 2D material MoS2. Various DFT energies are predicted from the layer-dependent MoS2, 2D flake-size related mono- and bilayer MoS2, to Mo and S migrations with and without graphene and sapphire substrates, thus shedding light on the factors that control lateral versus vertical growth of 2D islands. For example, the monolayer MoS2 flake in a small 2D lateral size is thermodynamically favorable with respect to the bilayer counterpart, indicating the monolayer preference during the initial stage of nucleation; while the bilayer MoS2 flake becomes stable with increasing 2D lateral size. The critical 2D flake-size of phase stability between mono- and bilayer MoS2 is adjustable via the choice of substrate. In terms of DFT energies and 1 ACS Paragon Plus Environment

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CALPHAD modeling, the size dependent pressure-temperature-composition (P-T-x) growth windows are predicted for MoS2, indicating that the formation of MoS2 flake with reduced size appears in the middle but close to the lower T and higher P “Gas + MoS2” phase region. It further suggests that Mo diffusion is a controlling factor for MoS2 growth owing to its extremely low diffusivity compared to that of sulfur. Calculated MoS2 energies, Mo and S diffusivities, and size-dependent P-T-x growth windows are in good accord with available experiments, and the present data provide quantitative insight into the controlled growth of 2D layered MoS2.

KEYWORDS: Molybdenum disulfide, controlled synthesis, first-principles calculations, thermodynamic modeling, Mo-S phase diagram

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Recently the two-dimensional (2D) layered transition-metal dichalcogenides (TMDs) (MX2: such as M = Mo and W; and X = S, Se, and Te) have attracted unprecedented scientific and technological interests owing to their rich physical, chemical and electronic properties.1 Many TMDs crystallize in a graphitelike layered structure consisting of stacked, three-atom-thick X-M-X monolayers bound largely by the interlayer van der Waals forces.1 Notably, TMDs exhibit a wide variety of polymorphs with the major one being 2H with space group P63/mmc, i.e., the bilayer hexagonal structure.1-2 Similar to graphene, the atomically thin 2D layered TMDs have potential applications for transparent flexible electronics.1 Unlike graphene which does not have a natural bandgap, the most fascinating behavior of these 2D layered TMDs is the tunable electronic structure as a function of composition, atomic layer, defect, and strain.1-2 For instance, the bulk MoS2 has an indirect bandgap of 1.2 eV while the monolayer MoS2 has a direct bandgap of 1.8 eV;3 and in the case of monolayer MoS2, a bandgap decrease by ~ 45 meV per percent strain and a direct-to-indirect bandgap transition at an applied strain of ~ 1% were observed.4 These 2D layered TMDs are promising candidates for building atomically thin devices such as field-effect transistors with excellent on-off ratios,5 spintronics and valleytronics associated with the spin and valley degrees of freedom,6 and electrocatalysis for hydrogen evolution reaction and photocatalysis for water splitting due to the highly catalytic edge sites.7

To fabricate devices and measure their properties reliably, the prerequisite as well as the unsolved challenge is the synthesis of wafer-scale thin films with controlled layers (monolayer is more preferable for most cases and also the present focus), spatial homogeneity, and high carrier mobility.8-10 Compared to the top-down syntheses via mechanical and chemical exfoliations, which result in very low yields,10 poor uniformity in film thickness,11-12 and extrinsic defects,9 the pathway to realize a large-area thin film may lie in bottom-up syntheses via chemical vapor deposition (CVD) and especially metal-organic CVD (MOCVD) with a better control of chemical potential (i.e., precursors ratio).8-9, 13-16 More examples of the bottom-up syntheses are given in Table S1 in the Supporting Information. Initial CVD/MOCVD experiments point out that a key aspect of monolayer synthesis is the control of vertical versus lateral 3 ACS Paragon Plus Environment

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growth of 2D islands. For example, one of the best MoS2 monolayers with wafer-scale homogeneity was synthesized using the MOCVD method by Kang et al.,8 and the successful synthesis of monolayer was proposed due to Mo diffusion-limited growth (see more in experimental no. 1 in Table S1). Another MOCVD example was demonstrated by Eichfeld et al.:17 the first time growth of a large-area (up to 8 µm), mono- and few-layer WSe2 via the reaction of W(CO)6 + (CH3)2Se. This work indicates that the temperature, pressure, Se:W ratio, and substrate choice have a strong impact on the ensuing atomic layer structure. In terms of the CVD method, Li et al.15 reported a monolayer WSe2-MoS2 lateral p-n junction with an atomically sharp interface through a two-step epitaxial growth on a sapphire substrate. Li et al.15 proposed that the successful synthesis is due to the control of the relative vapor amount of MoO3 and S during the second step MoS2 growth, and they interpreted that the excess in Mo precursors enhances the MoS2 vertical growth, whereas the excess in S vapor promotes the formation of undesired WS2 at the interface. In addition, Kong et al.,18 Gong et al.,19 and Gaur et al.20 proposed that the vertical or lateral growth of 2D islands relates to the competition between growth and nucleation under a given set of conditions, suggesting thermodynamics and diffusion play a vital role in the synthesis of desired thin films.

Despite myriad experiments performed in the rapidly developing TMD field,1-2 very little thermodynamic and diffusion knowledge is currently available to guide the CVD/MOCVD processes, resulting in trialand-error syntheses8-9, 13-16 and the desired thin films (e.g. the aforementioned monolayer MoS2 and WSe2MoS2)8, 15 grown serendipitously. In addition, the mechanism controlling the vertical versus lateral growth of 2D TMD islands (see the above paragraph) is to some extent still a hypothesis due to a lack of understanding about the processing thermodynamics and kinetics, albeit a kinetic model has been developed recently by Rajan et al.21 to predict the variation in shape and size of the grown MoS2. The dearth of this knowledge motivates the present work to provide mainly a thermodynamic insight into the prototypical 2D material MoS2 by addressing the mechanism that controls vertical versus lateral growth of the 2D MoS2 islands and identifying the thermodynamic growth window that guides the deposition of 4 ACS Paragon Plus Environment

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MoS2 thin films. In addition, the present work also provides implications for the vertical versus lateral growth of TMD alloys22-23 and van der Waals heterostructures.24-25

To achieve the present goal, an integrated density functional theory (DFT) and calculation of phase diagram (CALPHAD) modeling approach is hence employed (i) to predict various energies related to the layer-thickness-dependent and the 2D flake-size dependent MoS2 without and with the effect of substrate (mainly graphene) and (ii) to model the nano-size dependent pressure-temperature-composition (P-T-x) phase diagram of the Mo-S system. Note that (a) the mentioned “layer” indicates the mono- or multilayer MoS2 with an infinite-large lateral size, and the terminology “layer-thickness-dependent” will be abbreviated to “layer-dependent” hereinafter; (b) a 2D flake indicates the mono- or multilayer MoS2 with a finite lateral size; and (c) the to be used terminology “free MoS2” indicates the free-standing MoS2 which is not adhered to a substrate.

Energetics of layer-dependent MoS2 from DFT. Figure 1 illustrates the layer-dependent relative energy ∆E of MoS2 in per mole of atom and the associated surface energy σS from DFT calculations. It is found that both the layer-dependent and the 2D flake-size dependent quantities can be measured well using the inverse thickness/size (i.e., the reciprocal thickness/size) in the present work. As shown in Figure 1, bulk MoS2, with the inverse number of layers (1/nL) being 0, possesses the lowest energy (set as reference state and similarly hereinafter unless otherwise stated), and ∆E increases with 1/nL owing to the increased effect of surface. Hence, the farther the 2D layered MoS2 is from bulk case, the lower the phase stability of MoS2. That is, MoS2 prefers forming bulk with respect to being 2D layered structure based on thermodynamics. The variation of ∆E can be fitted perfectly using 1/nL as shown in Figure 1,

∆E (nL ) = 9.006 (1 / nL ) − 0.955 (1 / nL )

2

(1)


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where the energy unit is kJ/mole-atom and the goodness of fit R2 = 1.0000. Specially, ∆E(1) = 8.051 and ∆E(2) = 4.264 according to Eq. (1), agreeing well with the direct DFT values ∆E2 and ∆E3 shown in Table 1. It is more conveniently to represent ∆E in Eq. (1) by using the layer-dependent surface energy σS,

σ S (nL ) = 256.63 − 22.0633 (1 / nL ) − 4.5216 (1 / nL )

2

(2)

where the unit of σS is mJ/m2 and the goodness of fit R2 = 0.9950. Unlike a smooth fitting of ∆E versus 1/nL, Figure 1 shows that the calculated σS values are scattered for large nL values (e.g., nL = 10 ~ 15) due partially to fluctuation of the predicted lattice parameters associated with these MoS2 layers (not shown). Figure 1 and Eq. (2) indicate that the surface energy is layer-thickness-dependent, ranging from 230.0 mJ/m2 for monolayer to 256.6 mJ/m2 for bulk case. The present surface energies are in good agreement with the previous predictions for bulk MoS2: > 250,26 260±20,27 250,28 and 28028 (the units are all mJ/m2); with the exception being the estimated surface energy 46.5 mJ/m2 from the wettability of MoS2,20 which is questionable. Note that the opposite trends of ∆E and σS with increasing 1/nL are caused by the facts that ∆E is an energy difference per atom, while σS relates to the energy difference of all atoms in the supercell.

In addition to the ∆E values for the free MoS2 layers shown in Figure 1 and Eq. (1), Table 1 summarizes more relative energies for mono- and bilayer MoS2 with and without considering substrates (graphene and sapphire), where the reference states are bulk MoS2 and the corresponding substrate when applicable. The ∆E values in Table 1 indicate that the substrate promotes the formation of 2D layered MoS2 by lowering the ∆E energies. For example, the free mono- and bilayer MoS2 have the ∆E values of 8.05 and 4.27 kJ/mole-atom, respectively, and these two values drop to 4.48 and 3.54 kJ/mole-atom for MoS2 on graphene substrate and even negative values -0.79 and -0.91 kJ/mole-atom for MoS2 on sapphire substrate (see Table 1). The present ∆E values due to different substrates are verified indirectly by the larger WSe2 flakes grown on sapphire than those on graphene.17 It is worth mentioning that sapphire (α-Al2O3) is one


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of the best substrates to grow MoS2 due to the negligible lattice mismatch between MoS2 and α-Al2O3 (< 0.34%).29

Energetics of flake-size dependent mono- and bilayer MoS2 from DFT. Besides energies for layerdependent MoS2, understanding the lateral versus vertical growth of MoS2 requires energies of MoS2 molecules and flakes, especially in mono- and bilayer cases. Figure 2 illustrates the DFT relative energies of free-standing mono- and bilayer MoS2 flakes with the reference state being bulk MoS2. Here, two flake shapes are considered: (i) the equilateral triangle based on experimental observations30-31 and (ii) the rhombus consisting of two equilateral triangles due to hexagonal symmetry of MoS2 (see also the Table of Contents Graphics). Similar to the 1D layer case shown in Figure 1, the relative energies for 2D lateral size dependent mono- and bilayer flakes can be fitted well using ඥ1/݊௠ (here, nm is the total number of MoS2 molecules),

∆Emonolayer-tri ( nm ) = 8.050 + 313.745 (1 / nm )

0.5

∆Emonolayer-rhom (nm ) = 8.050 + 286.619 (1 / nm ) ∆Ebilayer-rhom (nm ) = 4.266 + 398.547 (1 / nm )

− 99.701 (1 / nm )

0.5

0.5

(3)

− 71.171 (1 / nm )

(4)

− 128.191 (1 / nm )

(5)

where the goodness of fit R2 = 0.9966, 0.9993, and 0.9999, respectively. Figure 2 and Eqs. (3) and (4) show that the energy of monolayer MoS2 with rhombus shape (∆Emonolayer-rhom) is slightly lower than that with triangle shape (∆Emonolayer-tri), suggesting that the triangle shape from experimental observations (see e.g. Table S1) consists mainly of the primitive 2D cell of rhombuses. Figure 2 shows that the monolayer flake in a small 2D size is thermodynamically favorable compared to the bilayer case, and the critical 2D lateral size is about 9.2×9.2 nm2 in terms of the lattice parameter a0 = 3.161 Å for MoS2 (see Table S3 and similarly hereinafter) and the energetics by Eqs. (4) and (5). The associated critical energy is 17.83 kJ/mole-atom.


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In addition to the above equations, more energies relevant to MoS2 molecules/flakes are listed in Table 1. The cohesive energy of MoS2 with respect to the free Mo and S atoms is 513.27 kJ/mole-atom, and the energy drops greatly to form a free MoS2 molecule (223.97 kJ/mole-atom) and a free monolayer (8.05 kJ/mole-atom, see also Eq. (4)). Furthermore, the values in Table 1 indicate that the edge site of MoS2 flake is energetically favorable to adsorb the small MoS2 molecules/flakes. For example, the energy differences to move the one-MoS2 (i.e., the 1×1 flake with respect to the primitive 2D rhombus cell), (3×3) MoS2, and (4×4) MoS2 flakes from the edge site to the surface top site of the (5×5) MoS2 flake are 177.66, 21.97, and 18.49 kJ/mole-atom, respectively. This feature is also shown by the filled symbols in Figure 2, where the small (3×3) and (4×4) flakes prefer the edge site to the surface top site. When the monolayer MoS2 flake is large enough (e.g., greater than the critical 2D size 9.2×9.2 nm2 as aforementioned), it prefers the surface top site and thus promotes the vertical growth from a thermodynamic viewpoint.

In an effort to examine the effect of substrate on the lateral versus vertical growth of 2D layered MoS2, the semi-infinite MoS2 slab is employed for DFT calculations for the sake of simplicity. Figure 3 shows the DFT relative energies of the semi-infinite MoS2 slabs without and with the graphene substrate. These energies are fitted well using the inverse number of MoS2 molecules along the width direction of the semi-infinite slab (1/nw),

∆Emonolayer-free ( nw ) = 8.050 + 171.953 (1 / nw ) − 57.879 (1 / nw ) ∆Ebilayer-free (nw ) = 4.266 + 341.811 (1 / nw ) − 222.346 (1 / nw )

2

(6)

2

(7)

∆Emonolayer-gra. (nw ) = 4.484 + 618.120 (1 / nw ) − 499.767 (1 / nw )

2

∆Ebilayer-gra. ( nw ) = 3.544 + 1302.327 (1 / nw ) − 3380.057 (1 / nw )

2

(8) (9)

where the abbreviation “gra.” represents the bilayer graphene substrate, the energy unit is kJ/mole-atom, and the goodness of fit R2 = 0.9999, 0.9998, 0.9996, and 0.9993 for Eqs. (6) to (9), respectively. With increasing the width of the semi-infinite slab, the bilayer MoS2 slab become stable with the critical width


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around 14 nm (i.e., nw = 44 and the critical ∆E = 11.94 kJ/mole-atom based on Eqs. (6) and (7) for the free-standing MoS2 case) or 229 nm (i.e., nw = 723 and the critical ∆E = 5.34 kJ/mole-atom via Eqs. (8) and (9) for MoS2 on graphene substrate), indicating that the substrate increases greatly the critical size of the stable monolayer MoS2 flake.

Migration energy and diffusivity of Mo and S atoms from DFT. Besides the relative energies of layerand 2D lateral size dependent mono- and bilayer MoS2, Table 1 summaries also the diffusion-related properties of Mo and S atoms on the semi-infinite MoS2 monolayer. Similar to the adsorption capacity of MoS2 molecule/flake as mentioned above, Table 1 shows that the edge site of the 2D layered MoS2 is the most favorable place to adsorb S and, especially, Mo atoms, since it is extremely difficult to move one Mo or S atom from the edge site to the surface top site of the semi-infinite MoS2 monolayer, see the Ediff1, Ediff2, Ediff3, and Ediff4 values (> 140 kJ/mole-atom) with and without considering the substrate as shown in Table 1. Migration energies (Emig) of Mo and S atoms are calculated on the edge and/or surface top site of the semi-infinite MoS2 monolayer. It should be mentioning that the DFT based CINEB calculations were failed to calculate the Emig values of Mo on the surface top site due to the extreme instability of Mo (Ediff6 ≈ 364 kJ/mole-atom in Table 1).

Calculated Emig values shown in Table 1 indicate that the diffusivity of S atom on the edge site of MoS2 is extremely faster than that of Mo atom. For example, the estimated ratio of diffusion coefficients D(S)/D(Mo) is as large as 108 at 1000 K in terms of (i) the Emig values, e.g. Emig1(free-edge, Mo) = 195 kJ and Emig2(free-edge, S) = 41 kJ as shown in Table 1; (ii) the Arrhenius diffusion equation,32 and (iii) the equal frequency factors of diffusion for both cases. It is further found that the substrate (graphene tested here) has small effect on the Emig values, such as Emig4(edge, S, graphene) = 45 kJ as shown in Table 1, and in turn, the diffusivities of Mo and S atoms. It is expected that the diffusion behaviors of Mo and S on the surface top sites are similar to those on the edge sites, albeit the CINEB calculations failed for Mo on


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the surface top site. The diffusivity of S atom on the edge site (Emig2 = 41 and Emig4 = 45 kJ, see Table 1) is much faster than it on the surface top site (Emig5 = 101 and Emig6 = 119 kJ, see Table 1), and both much larger than the diffusivity of Mo on the edge site. The ultrafast diffusion of S with respect to Mo suggests that the growth of 2D layered MoS2 is controlled by Mo atoms in terms of atomic diffusivities, and the present conclusion agrees well with the finding via the MOCVD experiments by Kang et al.8: the supply of Mo is a controlling factor for lateral growth of MoS2 thin film (see experimental no. 1 in Table S1).

Mo-S phase diagram and growth windows for size-dependent MoS2. Lateral versus vertical growth of 2D layered MoS2 can be understood based on the Mo-S pressure-temperature-composition (P-T-x) phase diagram as well as the DFT energies for the layer- and 2D lateral size dependent MoS2, see Eqs. (1), (3), (4), and (5). Figure 4 shows the Mo-S temperature-composition (T-x) phase diagram under pressure P = 1 atm modelled by CALPHAD method, where the modeling parameters are given in Supporting Information [see Table S4 and the supplementary thermodynamic database (TDB) file in Table S5]. Key temperatures and phase regions are labelled in Figure 4, while a detailed comparison is given in Table S6, showing a good agreement between the modelled and measured temperatures and compositions for invariant reactions and melting points. For example, the modelled temperature is 2004 K under P = 1 atm for the reaction of “liquid (L) = MoS2 + gas (G)”, agreeing well with the measured 2023 ± 50 K.33 The species in gas phase include S, S2, S3, S4, S5, S6, S7, S8, Mo, Mo2, MoS, and MoS2.34 For the sulfur gas species in particular, S2 is dominant, making the total pressure of the gas phase almost identical to the sulfur partial pressure, see Figure S1. The “MoS2 + gas (G)” phase region is the growth window of MoS2 thin film,35 located in the S-rich region (sulfur mole fraction xS > 0.667) and between 734 to 2004 K under P = 1 atm. The S-lean condition (xS < 0.667) results in the secondary phase Mo2S3 (0.5 < xS < 0.667) and even bcc Mo (xS < 0.5), see Figure 4. Note that all the phase regions will be altered by changing the gas pressure, for example, the modelled T-x phase diagram under P = 1 Torr in Figure S2.


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Taking into account the S-rich condition for the growth of MoS2 thin films, Figure 5 illustrates the P-T phase diagram of the Mo-S system with xS = 0.75, showing a large “MoS2 + G” phase region for MoS2 growth. Note that the conclusions from this P-T phase diagram apply to all the S-rich cases. From bulk to the layer-thickness-dependent and 2D flake-size dependent MoS2, the energy for nanoscale MoS2 increases as shown in Figure 1 and Figure 2, due mainly to the effect of surface. Figure 5 shows that the “MoS2 + G” phase region shrinks to the lower T and especially higher P region by adding an extra energy to MoS2 (for example, 1.7, 5.0, 8.3, 11.7, and 15.0 kJ/mole-atom, and these energies can be calculated by e.g. Eqs. (1), (3), (4), and (5) due to size effect), indicating that the smaller the MoS2 size, the smaller the P-T phase region to grow MoS2 will be. The present DFT calculations indicate that the increased energies are 8.05 and 4.27 kJ/mole-atom for the free mono- and bilayer MoS2, respectively (see Table 1 or Eq. (1)). Another example is for the 2D flake-size dependent free MoS2 monolayer, the 10×10 nm2 and the 1×1 µm2 MoS2 flakes correspond to the increased energies of 17.04 and 8.14 kJ/mole-atom, respectively (estimated using Eq. (4) and lattice parameter a0 = 3.161 Å).

It is worth mentioning that the growth direction dependent P-T growth windows can be identified in Figure 5 for simple cases. By assuming that the initial flake size is large enough for a vertical growth of MoS2, the vertical P-T growth windows are the ones given by the phase boundaries obtained when an extra energy from 0 kJ/mole-atom (bulk case) to 8.05 kJ/mole-atom (monolayer case, see Table 1) is added to MoS2, see Figure 5. By assuming only a lateral growth of the monolayer MoS2, the lateral P-T growth windows are given by the phase boundaries obtained when an extra energy of 8.05 kJ/mole-atom or larger is added to MoS2 [see Eqs. (3) and (4)], see the plots in Figure 5. While for a MoS2 flake with a finite 2D lateral size, the lateral or vertical P-T growth windows are 2D lateral size dependent and can be plotted in Figure 5 by adding an extra energy to MoS2 based on Eqs. (3)-(5).

Key bottom-up syntheses of MoS2 thin films via CVD/MOCVD and physical vapor deposition (PVD) are summarized in Table S1. Correspondingly, experimental pressures and temperatures are labelled as the 11 ACS Paragon Plus Environment

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open diamond symbols in Figure 5. Attention should be paid for the pressure difference: the reported pressures from experiments are usually the chamber pressure, which is higher than the total pressure (≈ sulfur partial pressure) of the Mo-S system as shown in Figure 5, since the carrier gases such as Ar/N2/H2 are usually employed to grow MoS2 thin films (see Table S1). Figure 5 shows that these trial-and-error syntheses (experimental no. 1 to no. 20 in Table S1) are located in the large P-T growth window of MoS2. Specially, the layer-controlled growth windows, e.g., the lateral growth, are usually in the middle of the “MoS2 + G” phase region to ensure the formation of small size MoS2 flakes, such as, the experimental nos. 1, 4, 6, 7, and 19 in Table S1 and Figure 5. While the monolayer and/or multilayer MoS2 thin films are ambiguous for other experiments in Table S1 and Figure 5, including the experimental nos. 2, 3, and 17.

It is worth examining the suggestions from experiments regarding the lateral growth of MoS2 monolayer in comparison with the present thermodynamic and diffusion data. For instance, (a) The MOCVD growth of MoS2 monolayer by Kang et al.8 (experimental no. 1 in Table S1 and Figure 5, and similarly thereafter) using the precursors Mo(CO)6, C4H10S, H2, and Ar gas indicated that the growth of MoS2 monolayer is controlled by Mo diffusion. Higher Mo partial pressures no longer enable a layer-by-layer growth mode.8 (b) A two-step CVD growth of MoS2 by Park et al.36 by deposition of Mo and then sulfurization (experimental no. 3) indicated that the layer thickness is controlled by the Mo deposition times. (c) The CVD growth of monolayer WSe2-MoS2 lateral p-n junction by Li et al.15 (experimental no. 4) indicated that the excess in Mo precursors enhances the MoS2 vertical growth. (d) The CVD growth of MoS2 on the SiO2 substrate by Jeon et al.37 (experimental no. 5) indicated that the MoS2 films grow from mono-, to biand trilayer by increasing O2 plasma treatment time of SiO2. (e) The CVD growth of MoS2 by Baek et al.38 (experimental no. 6) indicated that the combination of low pressure, distance between precursors and substrates, and temperature results in the uniform nucleation and growth of monolayer and continuous MoS2 up to 4 cm without triangular shape. (f) A one-step CVD growth of MoS2 by van der Zande et al. 39 (experimental no. 10) indicated that closest to the source (by change chemical potential), the film becomes a mixture of multilayer stacks and other crystal allotropes, whereas furthest from the source, 12 ACS Paragon Plus Environment

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nothing grows. (g) A two-step CVD growth of MoS2 by Gaue et al.20 by deposition of Mo and then sulfurization (experimental no. 11) indicated that chemical conversion due to H2S at high temperatures is much faster than S diffusion into Mo film, and the degree of MoS2 crystallinity increases at high temperatures. And (h) A two-step CVD growth of MoS2 by Wang et al.40 (experimental no. 15) indicated that the number of layers depends on the annealing duration for the reaction of MoO2 plus S vapor.

All these CVD/MOCVD experiments as well as the present work point out the key factors that control the lateral growth of MoS2 monolayer including temperature, pressure, substrate, and chemical potentials. The lateral growth of MoS2 monolayer requires (i) an extremely low Mo partial pressure because of the extremely low diffusivity of Mo atom (see the migration energies in Table 1); (ii) the selection and/or the treatment of substrate since the energy of the size-dependent MoS2 could be altered greatly by substrate (see Table 1); and (iii) MoS2 growth in the middle but close to the lower T and higher P “Gas + MoS2” phase region (see Figure 5) to ensure the growth of the small MoS2 monolayer flakes, where the partial pressure can be adjusted by such as the precursor flow rate and the distance between the MoS2 sample and sources.

It should be mentioned that a single MoS2 solid phase cannot be formed in the S-lean condition, see the PT phase diagrams in Figure S3 with xS = 0.64 and Figure S4 with xS = 0.55, where the “Gas + MoS2” phase region is absent.

Case study of thermodynamics in the Mo-S-O-H system. The above thermodynamic analysis is only for the Mo-S system. It is interesting to probe thermodynamics including all precursors. For the widely used MoO3 and S powders with H2, H2S, Ar, and/or N2 as carrier gases (see experimental nos. 4, 5, 6, 7, 8, 10, 12, 14, 15, and 20 in Table S1), Figure 6 shows the possible reaction Gibbs energies in the Mo-O-H-S system and the equilibrium phases under two cases: the S-rich and the S-lean conditions with the mole fraction ratios Mo:O:S:H = 1:3:4:2 and 1:3:2:4, respectively. Here, the employed thermodynamic 13 ACS Paragon Plus Environment

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database is SGTE-SSUB,34 and the possible reactions are listed in Table 2. Figure 6(a) shows that the lowest reaction Gibbs energy is for the reaction “Mo (s) + 2 S (g) → MoS2 (s)” and the most possible reaction from MoO3/MoO2 to MoS2 is “MoO2 (s) + 2 S (g) → MoS2 (s) + O2 (g)”, where the letters “s” and “g” indicate solid and gas phase, respectively. Note that MoS2 is moisture stable due to the positive reaction Gibbs energy for “MoS2 (s) + 2 H2O (g) → MoO2 (s) + 2 H2S (g)”, unlike the moisture unstable compounds ZrS2 and Si(S,Se)2.34, 41 According to thermodynamics, the final reaction products can be predicted via equilibrium calculations by minimizing the Gibbs energy. Figure 6(b) shows that MoS2 and gas are the products under the S-rich condition at high temperatures (Case 1), while the final products are MoO2, MoS2, and gas under the S-lean condition (Case 2). These results indicate that MoO3 (or MoO2) is an effective precursor to form MoS2 under the S-rich condition.

In summary, an integrated DFT calculations and CALPHAD modeling approach has been employed in the present work to understand the lateral versus vertical growth of the prototypical 2D material MoS2 and provide pressure-temperature-composition (P-T-x) growth windows for the layer-thickness-dependent MoS2 layers and the 2D lateral size dependent MoS2 flakes. Based on DFT energies for layer-dependent MoS2 and 2D lateral size related mono- and bilayer MoS2 flakes with and without substrates (graphene and sapphire), it is found that (i) the energy of layered MoS2 increases with decreasing the number of layers due to the increased contribution from surface; (ii) the monolayer MoS2 flake in a small 2D lateral size is thermodynamically favorable with respect to the bilayer counterpart, while the bi- and multilayer MoS2 flakes are stable in a large 2D lateral size, indicating that the initially small nuclei of MoS2 are going to be monolayer but as they grow larger it will be more favorable for them to become bi- and multilayer; and (iii) the critical 2D lateral size about phase stability between the mono-, bi-, and multilayer MoS2 is adjustable via such as the choice of substrate as shown in the present work. These DFT energies together with the modelled P-T-x phase diagrams enable the prediction of growth windows for the layer-thickness and 2D lateral size dependent MoS2, i.e., the formation of MoS2 flake with reduced size appears in the middle but close to the lower temperature and higher pressure “Gas + MoS2” phase 14 ACS Paragon Plus Environment

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region. In addition to thermodynamics, the present DFT calculations suggest that Mo diffusion is a controlling factor for MoS2 growth owing to its extremely low diffusivity compared to that of sulfur. Beyond the Mo-S system, reaction Gibbs energies for the possible reactions and the reaction products are also analyzed in the Mo-S-H-O system. Calculated MoS2 energies, Mo and S diffusivities, and sizedependent P-T-x growth windows are in good accord with experiments in the literature, and hence providing quantitative insight into the controlled growth of 2D layered MoS2.

Methods DFT calculations. All DFT based first-principles calculations were performed using the Vienna Ab initio Simulation Package (VASP 5.3.5)42 with the ion-electron interaction described by the projector augmented wave (PAW) method.43 The generalized gradient approximation developed by Perdew-BurkeErnzerhof (GGA-PBE)44 together with the van der Waals correction of the D3 method45 were selected to describe the exchange-correlation (X-C) energy functional in the van der Waals solids (MoS2 and graphite/graphene) according to our previous work46 and the present tests shown in the Supporting Information. For example, the PBE+D3 method predicts well the energies of MoS2 such as the enthalpy of formation ∆Hf as shown in Table 1 (calculated -83.77 vs. experimental -91.9±0.8 kJ/mole-atom34, 47), albeit the time-consuming hybrid potential (e.g., HSE0648-49) can improve further the predicted ∆Hf (88.57 kJ/mole-atom). The migration energies of Mo and S were predicted using the climbing image nudged elastic band (CINEB) method50 with five images. The details of CINEB calculations were reported previously32, 51-52 and given in the Supporting Information. Other DFT details and partial DFT results are shown in the Supporting Information including the k-points meshes, cut-off energies, selected supercells, and predicted structural properties in comparison with experiments.

CALPHAD modeling of the Mo-S system. Thermodynamic modeling the Mo-S system was based on the CALPHAD approach53-54 with inputs from experimental data and the SGTE-SSUB database.34,

55


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Specially, the liquid phase was described by the associate model and the modeling work was performed using the Thermo-Calc software.56 More details are given in the Supporting Information including the review of Mo-S thermodynamic data, model for each phase, and modeling results in comparison with experimental data. A complete thermodynamic database of the Mo-S system, i.e., the TDB file, is also given in Table S5 for the readers of interest.

ASSOCIATED CONTENT Supporting information Supporting Information Available: Detailed descriptions and partial results of the bottom-up syntheses of MoS2 thin films, DFT calculations, and CALPHAD modeling. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]

Present Address ‡

Materials Science and Engineering Division, National Institute of Standards and Technology,

Gaithersburg, Maryland 20899, United States

Author Contributions S.L.S. and Y.W. performed the DFT calculations and G.L. performed the CALPHAD modeling with J.M.R., T.A. and Z.K.L. providing supervision. S.L.S wrote the manuscript with inputs from all authors.

Notes 16 ACS Paragon Plus Environment

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The authors declare no competing financial interest.

ACKNOWLEDGMENTS This work was financially supported by National Science Foundation (NSF) with the Grant Nos. CHE1230924 and CHE-1230929, and the Penn State Two-Dimensional Crystal Consortium – Materials Innovation Platform (2DCC-MIP) which is supported by NSF cooperative agreement DMR-1539916. First-principles calculations were carried out partially on the LION clusters at the Pennsylvania State University, partially on the resources of NERSC supported by the Office of Science of the U.S. Department of Energy under contract No. DE-AC02-05CH11231, and partially on the resources of XSEDE supported by NSF with Grant No. ACI-1053575.


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Tables and Table Captions Table 1. Summary of the DFT energies (kJ/mole-atom) of MoS2 in terms of the PBE+D3 method (see Method section and in particular the Supporting Information for details). The reference states for relative energies (marked by symbol ∆) are bulk MoS2 and substrate when applicable except for ∆Hf. The predicted values without decimals are less accurate, especially for the marked ones. Energy ∆Hf

Definition and description Enthalpy of formation of bulk MoS2 with respect to bcc Mo and α-S

∆Ecoh ∆E1 (free molecule) ∆E2 (free monolayer) ∆E3 (free bilayer) ∆E4 (molecule, graphene) ∆E5 (monolayer, graphene) ∆E6 (bilayer, graphene) ∆E7 (monolayer, Al2O3) ∆E8 (bilayer, Al2O3) Ediff1 (free Mo)

Cohesive energy of bulk MoS2 Relative energy of one free MoS2 molecule Relative energy of the free MoS2 monolayer Relative energy of the free MoS2 bilayer Relative energy of one MoS2 molecule on graphene substrate Relative energy of the MoS2 monolayer on graphene substrate Relative energy of the MoS2 bilayer on graphene substrate Relative energy of the MoS2 monolayer on α-Al2O3 substrate Relative energy of the MoS2 bilayer on α-Al2O3 substrate Energy difference to move one Mo atom from the edge site to the surface top site of the free MoS2 semi-infinite monolayer Energy difference to move one S atom from the edge site to the surface top site of the free MoS2 semi-infinite monolayer Energy difference to move one MoS2 molecule from the edge site to the surface top site of the free 7×7 MoS2 free flake/monolayer Energy difference to move 9 MoS2 molecules (3×3 flake) from the edge site to the surface top site of the free 5×5 MoS2 flake/monolayer Energy difference to move 16 MoS2 molecules (4×4 flake) from the edge site to the surface top site of the free 5×5 MoS2 flake/monolayer Energy difference to move one Mo atom from the edge site to the surface top site of the MoS2 semi-infinite monolayer on graphene substrate Energy difference to move one S atom from the edge site to the surface top site of the MoS2 semi-infinite monolayer on graphene substrate Migration energy of Mo atom on the edge site of the free MoS2 semi-infinite monolayer Migration energy of S atom on the edge site of the free MoS2 semi-infinite monolayer Migration energy of Mo atom on the edge site of the MoS2 semi-infinite monolayer on graphene substrate Migration energy of S atom on the edge site of the MoS2 semi-infinite monolayer on graphene substrate Migration energy of S atom on the top site of the free MoS2 semi-infinite monolayer Migration energy of S atom on the top site of the MoS2 semi-infinite monolayer on graphene substrate

Ediff2 (free S) Ediff3 (free 1-MoS2) Ediff4 (free 9-MoS2) Ediff5 (free 16-MoS2) Ediff6 (Mo, graphene) Ediff7 (S, graphene) Emig1 (free-edge, Mo) Emig2 (free-edge, S) Emig3 (edge, Mo, graphene) Emig4 (edge, S, graphene) Emig5 (free-top, S) Emig6 (top, S, graphene)

Valuea -83.77b -88.57c -91.9±0.8d 513.27 223.97 8.05 4.27 218.69 4.48 3.54 -0.79 -0.91 286e 142 177.66 21.97 18.49 364e 144 195 41 189 45 101e 119e

a

Unit is kJ for migration energy. The present prediction by PBE+D3. c The present prediction by PBE+D3+HSE06. d Experimental data at room temperature.34, 47 e Roughly estimated value due to the unstable S and Mo atoms on the surface top site. b


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Table 2. Possible thermodynamic reactions for the MoO3/MoO2 and S powders with H2S and H2 gases, where the letters s, l (L), and g (G) indicates the solid, liquid, and gas species, respectively. The reaction Gibbs energies as a function of temperature are shown in Figure 6. No. Reactions 1 MoO2 (s) + 2 S (l) → MoS2 (s) + O2 (g) 2 MoO2 (s) + S2 (g) → MoS2 (s) + O2 (g) 3 3 MoO2 (s) +2 S3 (g) → 3 MoS2 (s) + 3 O2 (g) 4 MoS2 (s) + 2 H2O (g) → MoO2 (s) + 2 H2S (g) 5 MoO3 (s/l) + 3 H2S (g) → MoS2 (s) + 3 H2O (g) + S (g) 6 MoO3 (s/l) + 3 H2 (g) → Mo (s) + 3 H2O (g) 7 MoS2 (s) + 2 H2S (g) → MoS2 (s) + 2 H2O (g) 8 MoO3 (s/l) + H2 (g) → MoO2 (s) + H2O (g) 9 2 H2 (g) + S2 (g) → 2 H2S (g) 10 4 MoO3 (s/l) + 7 S2 (g) → 4 MoS2 (s) + 6 SO2 (g) 11 Mo (s) + 2 H2S (g) → MoS2 (s) + 2 H2 (g) 12 MoO2 (s) + 2 S (g) → MoS2 (s) + O2 (g) 13 Mo (s) + S2 (g) → MoS2 (s) 14 Mo (s) + 2 S (g) → MoS2 (s)


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Figures and Figure Captions

Figure 1. DFT calculated surface energy and relative energy of 2D layered MoS2 as a function of the inverse number of layers. The fitted lines are shown in Eqs. (1) and (2).

Figure 2. DFT calculated relative energies of the free-standing mono- and bilayer MoS2 flake as a function of the inverse number of MoS2 molecules. The not shown numbers n in the figure equal to 3 and 4, and the fitted lines are shown in Eqs. (3), (4), and (5).


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Figure 3. DFT calculated relative energies of the semi-infinite MoS2 slabs with and without graphene substrate. The fitted lines are shown in Eqs. (6) to (9).

Figure 4. CALPHAD modelled temperature-composition (T-x) Mo-S phase diagram under pressure P = 1 atm, see Table S6 for a detailed comparison with experimental data.


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Figure 5. CALPHAD modelled P-T phase diagram of the Mo-S system under the S-rich condition (S:Mo > 2, here xS = 0.75). The green dashed lines indicate that an extra energy is added to MoS2, labelled by black values with one decimal (unit is kJ/mole-atom). Experimental P and T to grow MoS2 thin films as detailed in Table S1 are marked by blue triangle symbols () together with blue numbers: the explicit monolayer MoS2 claimed by experiments, as well as by red diamond symbols () together with red numbers: the ambiguous monolayer and/or multilayer MoS2 from experiments. Note that experimental P is usually the chamber pressure including more gas species such as Ar, N2, and H2 instead of the pressure for the Mo-S system.


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Figure 6. Gibbs energies for the possible reactions in the Mo-O-H-S system (a) and the equilibrium phases in two cases (b). The numbers in figure (a) indicates the reactions in Table 2, and the SGTE-SSUB database34, 55 was used for thermodynamic calculations.


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Saunders, N.; Miodownik, A. P., CALPHAD (Calculation of Phase Diagrams): A Comprehensive

Guide. Elsevier Science: New York, 1998. (55)

Dinsdale, A. T. CALPHAD 1991, 15, 317.

(56)

Andersson, J. O.; Helander, T.; Hoglund, L. H.; Shi, P. F.; Sundman, B. CALPHAD 2002, 26, 273.


Page 27 of 34

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

Nano Letters

TOC Graphics


Nano Letters

Temperature (°C)

10 10 10 10 10

500 400

Page 28 of 34

200

300

Mo liquid (L) + MoS2

S

1 atm

2

0

-2

gas (G) 3

6

-4

-6

Gas + MoS

2

Vertical

10

4

G + bcc-Mo

Pressure (Torr)

1 2 3 4 5 6 7 8 9 10 11 12 13 14

6

G+L

10

2500 1500 1000 700

ACS Paragon Plus Environment 9 12 15 10,000/T (1 / K)

18

21

Lateral growth

Substrate

Page 29 30 of 10346 5 4

Layer (n )

L 3Nano Letters 2

1

Surface energy (mJ/m )

2

1 2 250 3 4 245 5 6 240 7 235 8 9 230 10 11 0.0 12

6

4

2

Free layered MoS2 ACS Paragon Plus Environment 0.2

0.4

1/nL

0.6

0.8

0 1.0

Relative energy (kJ/mole-atom)

8

255

Nano Letters Page 30 of 34 Number of MoS 2 molecules (nm )

300 50 20 Relative energy (kJ/mole-atom)

1 200 2 3 4 150 5 6 7 100 8 9 10 50 11 12 13 00.0 14 15

10

6

4

3

2

1

Free MoS2 flake

bilayer, rhombus bilayer, rhombus: (5x5):(nxn) monolayer, rhombus monolayer, rhombus: (5x5 + nxn) monolayer, triangle

ACS Paragon Plus Environment 0.2

0.4 0.6 1/2 (1/nm )

0.8

1.0

Page 31 of 34 Nano Letters Number of MoS2 molecules in the width direction (nw) 40 15

6 5

4

3

2

Semi-infinite slab

Relative energy (kJ/mole-atom)

1 120 2 3 100 4 5 80 6 7 60 8 9 40 10 20 11 12 0 13 0.0 14 15

8

On graphene, bilayer On graphene, monolayer Free MoS2, bilayer Free MoS2, monolayer


0.2

1/nw

0.3

0.4

0.5

Nano Letters

P = 1 atm

3000

liquid (L) + gas (G) 2500

bcc-Mo + L 2000

L

2026 K 2004 K

1882 K

1500

bcc-Mo + Mo2S3 1000

Mo2S3 + MoS2

Temperature (K)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Page 32 of 34

902 K

bcc-Mo + MoS2 500 0.0 Mo

MoS2 + G 734 K

MoS2 + L

388 K


0.4 0.6 Mole fraction of S

0.8

1.0 S

Page 33 of 34

10 10 10 10 10

G+L

10

4

14 5,12 8,10 16 15 11,13 7 1 19 4 3 6

2

0

-2

-4

-6

500 400

gas (G)

1.7

200

300

liquid (L) + MoS2

G + bcc-Mo

Pressure (Torr)

1 2 3 4 5 6 7 8 9 10 11 12 13 14

6

G + Mo2S3

10

Nano Letters(°C) Temperature

2500 1500 1000 700 L

xS = 0.75 1 atm

2 17

5.0 8.3

1 11.7

18 20

G + MoS

15.0

2

9

ACS Paragon Plus Environment 3

6

9 12 15 10,000/T (1 / K)

18

21

Equilibrium phases (mole fraction) Reaction Gibbs energy (kJ/mole-atom)

Nano Letters

Page 34 of 34

1 1 50 2 2 3 4 3 5 0 4 5 6 -50 12 7 13 8 9 -100 10 6 9 7 10 11 (a) 14 8 11 12 -150 13 14 gas 15 gas 0.6 16 (Case 1) Mo:O:S:H = 1:3:4:2 (b) 17 (Case 2) Mo:O:S:H = 1:3:2:4 18 0.4 19 MoS2 20 21 MoS2 0.2 22 S (liquid) MoO2 23 24 0.0 ACS Paragon Plus Environment 25 400 600 800 1000 1200 1400 Temperature (K) 26

Lateral Versus Vertical Growth of Two-Dimensional Layered Transition

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