Article pubs.acs.org/JPCC
Cite This: J. Phys. Chem. C 2018, 122, 24535−24541
Lithium Intercalation in Graphene−MoS2 Heterostructures Daniel T. Larson,†,∥ Ioanna Fampiou,‡,∥ Gunn Kim,¶ and Efthimios Kaxiras*,†,§ †
Department of Physics, Harvard University, Cambridge, Massachusetts 02138, United States Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, United States ¶ Graphene Research Institute and Department of Physics and Astronomy, Sejong University, Seoul 05006, Korea § John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States
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‡
ABSTRACT: Two-dimensional (2D) heterostructures are interesting candidates for efficient energy storage devices due to their high carrier capacity by reversible intercalation. We employ here density functional theory calculations to investigate the structural and electronic properties of lithiumintercalated graphene/molybdenum disulfide (Gr/MoS2) heterostructures. We explore the extent to which Li intercalates at the interface formed between graphene (Gr) and molybdenum disulfide (MoS2) layers by considering the adsorption and diffusion of Li atoms, the energetic stability, and the changes in the structural morphology of MoS2. We investigate the corresponding electronic structure and charge distribution within the heterostructure at varying concentrations of Li. Our results indicate that the maximum energetically allowed ratio of Li to Mo (Li to C) is 1:1 (1:3) for both the 2H and 1T′ phases of MoS2. This is double the Li concentration allowed in graphene bilayers. We find that there is 60% more charge transfer to MoS2 than to Gr in the bilayer heterostructure, which results in a maximum doping of Gr and MoS2 of nC = 3.6 × 1014 cm−2 and nMoS2 = 6.0 × 1014 cm−2, respectively.
1. INTRODUCTION In the search for energy storage technologies that can deliver high energy power density and longer cycle life than current Liion batteries, 2D van der Waals heterostructures consisting of stacked layers of graphene (Gr) and transition metal dichalcogenides such as molybdenum disulfide (MoS2) layers have attracted considerable attention.1 Such materials have the potential to improve Li-ion battery technology, taking advantage of the excellent mechanical strength and electrical conductivity of graphene and the greater Li intercalation capacity of MoS2.2−4 First-principles electronic structure calculations can provide insights into the electronic properties and the intercalation mechanisms between such layered structures and are useful in complementing advances in their fabrication and experimental characterization.5 Previous theoretical studies have explored the energetic stability, charge transfer, and electronic structure of Li-Gr/MoS2 bilayers.6−8 Miwa et al.6 showed that intercalation between the layers is energetically favored over adsorption on either side. Ahmed et al.7 highlighted the features in the electronic structure arising from the two separate components, namely, the gap between MoS2 conduction and valence bands crossed by the Dirac cone arising from graphene. Using an alternative supercell structure, Shao et al.8 explored the charge transfer as a function of the intercalated amount of Li. In all of these works, MoS2 is assumed to have trigonal prismatic coordination, as in the most stable, naturally occurring bulk 2H structure (also referred to as 1H for the monolayer MoS2). However, experimental studies9−11 show clear evidence that bulk MoS2 undergoes a © 2018 American Chemical Society
structural transformation from the semiconducting 2H to the octahedral metallic or semimetallic 1T structure in response to Li intercalation. In addition, theoretical studies12,13 of phase transitions in bilayer MoS2 indicate that a sequence of transformations occur due to increasing Li concentration, from the trigonal 2H to the octahedral 1T and then to one or more distorted structures (variously called DT, ZT, or 1T′), with MoS2 remaining in a metastable octahedral structure even during deintercalation. Since we consider here single-layers of MoS2 we will refer to the coordination as simply H or T′, and we focus on the octahedral structure with distortion as it is the most relevant for comparison with experiment. In the present work, we have carried out detailed density functional theory calculations on bilayer heterostructures comprising Gr and Hor T′-MoS2 with varying concentrations of Li to determine the maximum amount of ions allowed to intercalate. We find that the energetic stability of the heterostructure, Li diffusion barriers, and charge transfer are relatively insensitive to the MoS2 morphology. The MoS2 polymorph, however, greatly affects the electronic properties of the heterostructure, switching between a semimetal in the H structure with a Dirac cone crossing the MoS2 bandgap to a metallic T′ structure without a gap. As the Li concentration increases, the Dirac cone of graphene shifts to lower energies relative to the MoS2 bands and further distorts the pattern of electronic states Received: August 3, 2018 Revised: September 28, 2018 Published: October 9, 2018 24535
DOI: 10.1021/acs.jpcc.8b07548 J. Phys. Chem. C 2018, 122, 24535−24541
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The Journal of Physical Chemistry C in the pristine bilayers. For the bilayer structure consisting of Gr and H-MoS2, flat bands peel off the bottom of the conduction band, indicating filled states with high effective mass. In the Gr/T′-MoS2 bilayer, reduced dispersion and band inversion near the Γ point arise due to increased Li concentration. From the reaction potential and intercalation energy, we estimate a maximum concentration of intercalated ions equal to one Li per Mo atom with corresponding electron carrier doping of Gr (MoS2) nC = 3.6 × 1014 cm−2 (nMoS2 = 6.0 × 1014 cm−2). The remainder of this article is organized as follows. In section 2, we present computational details of our calculations. Results and discussion for Li intercalation, diffusion, and electronic structure are presented in section 3. Concluding remarks are provided in section 4.
Figure 1. Top and side view of the 5 × 5-Gr/4 × 4-MoS2 bilayer supercell, with (a) H-MoS2 and (b) T′-MoS2. Mo, S, and C atoms are represented by cyan, yellow, and gray spheres, respectively.
2. COMPUTATIONAL DETAILS All calculations were performed using the Projector Augmented Wave (PAW) method14 to describe the core and valence electrons, as implemented in the Vienna ab initio simulation package (VASP).15−18 The Perdew−Burke−Ernzerhof19 form of the Generalized-Gradient Approximation was employed to describe electron exchange and correlation. Van der Waals interactions were included using the zero damping DFT-D3 method of Grimme.20 The optimized lattice constants of Gr and MoS2 at this level of theory are 2.47 and 3.16 Å, respectively. All calculations were performed on a Gr-5 × 5/MoS2-4 × 4 (98 atoms) periodic supercell structure. Due to the lattice mismatch between the two materials, some amount of strain in the layers is unavoidable. Since the Young’s modulus for graphene (Y ≈ 2400 ± 400 GPa)21 is nearly ten times as large as that of MoS2 (Y ≈ 270 ± 100 GPa),22 a reasonable choice is to use a simulation cell with an unstrained graphene layer, which introduces 2.5% uniform compression of MoS2. For completeness, we have also considered the opposite situation, that is, an unstrained MoS2 layer and a graphene layer expanded by 2.6%, and show that our main conclusions are insensitive to the choice of which layer is strained. We point out in the discussion the places where the strain has noticeable effects. Over 17 Å of vacuum space was used along the direction perpendicular to the layers (z-axis) to prevent spurious image interactions. A Γ-centered k-point sampling of 5 × 5 × 1 was used for structural relaxations until all forces were below 0.01 eV/Å in magnitude. A k-point mesh of 11 × 11 × 1 was used for electronic density of states (DOS) and band structure calculations. All calculations were spin polarized and performed with a kinetic energy cutoff of 400 eV. When relaxing the ions within the supercell, one Mo atom was held fixed as a reference point, and the C atom directly above it was held fixed in the plane of the graphene layer to preserve the registration of the two layers but was allowed to relax freely along the z-axis. All other atoms were unconstrained. The top and side views of the pristine bilayer supercells with the H and T′ MoS2 structures are shown in Figure 1. For comparison, we also carried out calculations using the same computational setup but replacing the graphene layer with either MoS2 or boron nitride (BN), with appropriately modified supercell lattice constants. To estimate the energetic stability of the different configurations, we determined the intercalation energy per Li atom, EI, which indicates the energy change when n Li atoms move from bulk Li into the system, and the reaction potential,
ER, which is the average potential for extracting one Li atom from the system. EI and ER are defined as 1 E I = [E(Li nM ) − E(M ) − nE(Li)] (1) n E R = E(Li n − 1M ) + E(Li) − E(Li nM )
(2)
where E(LinM), E(M) and E(Li) are the total energies of the Li-intercalated Gr-MoS2 system, the pristine Gr-MoS2 system, and a Li atom in bulk Li, and n is the number of Li atoms. The system is stable if EI < 0 and ER > 0.
3. RESULTS AND DISCUSSION 3.1. Li Intercalation and Diffusion. We first consider intercalation of a single Li atom between Gr and MoS2 layers. Due to the difference in crystal lattice structures, there are many inequivalent Li adsorption sites. For the bilayer Gr/HMoS2, we have considered 18 different initial locations and sampling combinations of bridge, hollow, and on-top sites with respect to the position of C, Mo, and S atoms. After relaxation, ten distinct local minima were identified, and their relative energies are displayed in red in Figure 2. The different markers label the local environment of the Li atom, and the energy is measured with respect to the energy of the most stable
Figure 2. Energy of a single Li atom in a bilayer Gr/MoS2 structure, measured relative to the most stable location. Red (blue) points correspond to Gr/H-MoS2 (Gr/T′-MoS2). Filled (empty) markers indicate Mo on-top (MoS2 hollow) sites. 24536
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Figure 3. (a) Interpolated energy contours and (b) diffusion barriers, for a single Li ion in bilayer Gr/H-MoS2. (c) Comparison of diffusion barriers for a single Li ion in Gr/H-MoS2 and Gr/T′-MoS2 structures. The numbers correspond to the five paths indicated in (a), with energies measured relative to E0, the energy at the initial point on each path.
intercalation site. Our results indicate that the site on top of a Mo is the energetically most favorable Li intercalation site, as was previously shown for MoS2 monolayers23 and that the relative location of Li with respect to MoS2 affects the energetic stability of the intercalant more than the C environment of graphene, in agreement with ref 6. The T′-MoS2 structure has a relative shift between the upper and lower S planes and also distortions in the Mo−Mo bond distances (Figure 1). This leads to lower symmetry and a more complicated alignment between the Gr and MoS2 layers. However, the local environments available for an intercalating Li atom are quite similar to Gr/H-MoS2. We identified seven distinct local minima for a single Li intercalant in the Gr/T′MoS2 bilayer, and the relative energies are represented with blue-colored markers in Figure 2, measured relative to the energy of the lowest minimum for the Gr/T′-MoS2 structure. We observe again in this case that Li preferably intercalates at Mo on-top sites, irrespective of its location relative to C atoms in graphene. In order to estimate the feasibility of Li intercalation between the layers, we investigate Li ion diffusion by obtaining the energy difference between intermediate locations of Li along the lines connecting the local minima identified previously (Figure 3a). We considered three intermediate states for each path, at which the Li ion was constrained in plane but allowed to relax in the z direction. This simple constrained-path approach is an upper bound for the diffusion barriers and represents a reasonable approximation at minimal computational cost. In Figure 3a, we combine the results from the energy minimization calculations and interpolate the ground state energy surface for a single Li atom located inside
the Gr/H-MoS2 bilayer. Among the different pathways considered here, there are possible diffusion paths with energy difference less than 350 meV, which indicates that Li can easily diffuse laterally between Gr and H-MoS2 layers. Figure 3b shows the calculated diffusion barriers for five different paths between Mo on-top sites in the H structure, all of which fall in the range of 300 to 450 meV. This compares favorably with the computed barrier of 320 meV for bilayer MoS2,23 especially considering our values are upper bounds. A comparison between the energy differences for diffusion in Gr/H-MoS2 and Gr/T′-MoS2 heterostructures is provided in Figure 3c. Our results indicate the barriers are qualitatively similar. In some cases (such as segment 1), the T′ barriers are slightly lower, and in other cases (like segment 3), they are slightly higher. Finally, we determine the maximum amount of Li that is energetically allowed to intercalate in the two Gr/MoS2 heterostructures. The total energy of the system with increasing number of Li atoms was calculated by successively adding Li atoms, placing each one at a Mo on-top site and relaxing the system completely before the addition of the next one. These results allow us to compute the intercalation energy EI and reaction energy ER as described in section 2. The energetic stability turns out to be controlled by the reaction potential, which is shown in Figure 4. The red data points show the values of ER for Gr/MoS2, with circles (squares) representing the H- (T′-) MoS2 structure. The energetic stability of the system is maintained with up to 16 Li atoms in the supercell, which corresponds to one Li atom per Mo atom. After this, ER turns negative abruptly, indicating that it would require more than 1 eV for an additional Li intercalant to be 24537
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corresponds to a concentration of 1.2 × 1015 Li atoms per cm2. The corresponding charge depletion from Li toward graphene scales linearly with the number of Li atoms and is estimated to be ne = 3.6 × 1014 e/cm2. Valence charge density difference isosurfaces for the bilayer system with 16 Li atoms in Figure 5
Figure 4. (a) Reaction energy (ER) as a function of the number of intercalated Li ions for heterobilayers Gr/H-MoS2, Gr/T′-MoS2, BN/ H-MoS2, and BN/T′-MoS2. The two empty symbols show ER for the case where the MoS2 layer is unstrained, but the graphene layer is expanded. (b) ER for unstrained bilayers of H-MoS2, T′-MoS2, and graphene (Gr). The maximum number of intercalated Li ions in a supercell containing MoS2 is 16 (1 Li/Mo), after which ER becomes negative. Data points for Gr/Gr are adapted from ref 24.
added into the system. Figure 4 also shows the reaction energy ER for intercalation of Li between bilayers of MoS2 and BN/ MoS2, extracted from reference calculations that we performed on these systems for direct comparison with Gr/MoS2 heterostructures, and for bilayers of graphene, adapted from ref 24. The role of a MoS2 layer in effectively increasing the Li capacity of Gr/MoS2 heterostructures is further emphasized by the fact that the heterobilayer can accommodate double the concentration of Li atoms compared to bilayer graphene. It also indicates that the addition of graphene does not reduce the Li intercalation capacity of bilayer MoS2. This is significant, since graphene has the benefit of added structural integrity, allowing for cycling of Li without formation of lithium sulfides, which is a known challenge for intercalation in bulk MoS2. Such stability has recently been demonstrated in actual devices.5 The above results are based on the supercell in which MoS2 is slightly compressed. In the opposite extreme, where MoS2 is unstrained and the graphene lattice is expanded by 2.6%, the qualitative results are the same, though the magnitude of ER increases slightly, as shown by the open symbols in Figure 4a for the case of a single Li intercalant. 3.2. Electronic Structure Analysis. The amount of charge made available for conduction in either the graphene or MoS2 layer is of significant experimental interest since it can be used as a direct measurement of device capability and performance. Bader charge analysis25 allows us to quantify the amount of charge that was exchanged among the Gr/MoS2 system constituents after Li intercalation. Considering the case of a single Li atom at the most stable on-top Mo site in the Gr/ H-MoS2 heterostructure, we find that each Li atom donates approximately 0.8 electrons to the bilayer, with 0.5 electrons accumulated on the nearest layer of S atoms and 0.3 electrons donated to the C atoms in graphene. A similar result was found in ref 8 for up to nine Li atoms. We extend the analysis to the maximum allowed number of 16 Li atoms per supercell, which
Figure 5. Valence charge density difference isosurfaces for (a) 16Li− Gr/H-MoS2 and (b) 16Li−Gr/T′-MoS2. On the right, we show the corresponding valence charge density projected onto the z-axis perpendicular to the layers, showing the total charge in the intercalated system and bilayer without Li (left panel) and their difference along with the charge of isolated Li atoms (right panel).
indicate the charge depletion near the Li atoms and charge accumulation at the nearest S atoms and C layer. The results are identical, to within the accuracy of the calculations, for a supercell in which MoS2 is unstrained and graphene is expanded. As a cross-check of the Bader analysis, we project the electron charge density onto the z-axis perpendicular to the material layers. The valence charge is then summed in a window (in z) about each atomic plane. Subtracting the projected charge of the bilayer from that of the total structure gives an indication of charge redistribution. Using this method we find that, for both the Gr/H-MoS2 and Gr/T′-MoS2 structures, 0.43e per Li atom are transferred to S and 0.38e per Li atom to graphene, and 0.81e are depleted per Li atom. This method confirms that more of the charge donated by Li winds up on the S of MoS2, though the disparity is smaller than that computed with the full Bader analysis. These theoretical results can be compared with recent experimental measurements reported in ref 5. The measured carrier concentration in the Gr (MoS2) layer is approximately 2 × 1013 (8 × 1013) cm−2, which gives a ratio nC:nMoS2 = 1:4, 24538
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Figure 6. Band structure and density of states (DOS) for the pure and fully Li intercalated Gr/H-MoS2 (left panels) and Gr/T′-MoS2 (right panels). In each case, the strained layer is shown in angle brackets ⟨···⟩, indicating MoS2 compressed by 2.5% or graphene expanded by 2.6%. The zero of energy is chosen to be the Dirac point with a dashed red line at the Fermi energy. States originating from C p-orbitals and Li s-orbitals are indicated with orange and cyan circles, respectively; those arising predominantly from Mo d-orbitals or S p-orbitals can be inferred from the peaks in the adjacent DOS plots.
As a last step in the electronic structure analysis, we investigate in detail the effect of Li intercalation and type of MoS2 structure on the electronic band structure of bilayer Gr/ MoS2, given that the H-MoS2 layer is a large gap semiconductor, whereas the T′ is a small gap or metallic crystal. As described in ref 13, increasing Li concentration first causes a transition from the trigonal coordination (H phase) to an octahedral coordination (T phase) and then to a distorted T′ phase. Both experiments5 and theory13 indicate that the transition to T′-MoS2 occurs well before achieving maximum intercalation at the ratio of 1 Li per Mo atom. The exact concentration of Li for the various transitions to occur is also sensitive to the strain induced in the MoS2 layer. Increasing the supercell lattice constant decreases the energy difference between structures with trigonal prismatic and octahedral coordination, demonstrating that compressive strain increases the amount of Li required to make the transition energetically favorable. The T′ phase is metastable and will persist until annealing returns it to the H phase.5 Figure 6 shows the change in the band structure and density of states of Gr/H-MoS2 (left panel) and Gr/T′-MoS2 (right
significantly lower than the 3:5 ratio predicted by the Bader analysis above. However, the experimental Gr/MoS2 bilayer is encapsulated in boron nitride (BN), which presents further interfaces where Li could intercalate. Intercalation between the graphene layer and surrounding BN is expected to be small.24 However, calculations with the graphene layer replaced by boron nitride indicate that intercalation between MoS2 and BN could be comparable to that at the Gr/MoS2 interface (see Figure 4), but with all the charge donated to MoS2. So as a simple estimate, if we assume Li intercalates the BN/MoS2 and Gr/MoS2 interfaces equally, with no intercalation at the Gr/ BN interface, we would predict the ratio of charge carriers to be nC:nMoS2 = 1:4.3, much closer to the measured ratio. The total measured carrier concentration of 1 × 1014 cm−2 is a factor of 10 lower than the prediction from the theoretical estimate for maximum Li intercalation. This might mean that in actual devices Li intercalation stops well below the Li/Mo ratio of 1:1. However, it might also indicate that a significant amount of donated charge is taken up by defects or other localized states and not contributing to the measurements of the Hall current. 24539
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diffusion properties of the bilayer system are relatively insensitive to the MoS2 polymorph, the electronic structure changes dramatically when MoS2 transitions from the H to the T′ structure. Since this is observed to happen with increasing Li concentration, both in DFT calculations and experimentally, it suggests that the interplay between intercalant concentration and layer polymorphs will be an important parameter to take into consideration when designing such heterolayer structures for device applications.
panel) between the pure and the fully intercalated with Li heterobilayer structures. Note that the pure H-type bilayer is lower in energy than the pure T′-type bilayer by 0.65 eV per MoS2 formula unit, reflecting the energetic preference toward the H-MoS2 structure in the absence of Li. The Dirac point of graphene is a useful reference, so it has been chosen as the zero of energy in both cases. First, comparing empty bilayers, we see that for Gr/T′-MoS2 the Dirac point falls in the valence band of MoS2, which means that the graphene sheet donates electrons to the metallic T′-MoS2. This metastable state would be relevant for a deintercalated heterostructure prior to annealing. As electrons and Li ions enter the bilayer during intercalation, the Fermi level rises above the Dirac point. In both systems the lowest Li states above the Fermi level are nearly 1 eV above the Dirac point. For the H-type bilayer this is the same energy as the lowest MoS2 states. In contrast, for the T′-type bilayer there are plenty of MoS2 states surrounding the Dirac point. Thus, intercalating electrons pay a lower energy cost to fill these MoS2 states, explaining the larger reaction energy for the T′ system. For both the H and T′ cases, as the Li concentration increases, the Dirac point of graphene moves lower relative to the bands in MoS2. As the number of Li atoms increases from zero to the maximum value (16 in the model we study), states at the lower edge of the conduction band peel off to lower energy and create separated, flat bands that manifest as a peak in the Mo DOS just below the Fermi level, providing conduction channels, but the flatness of the bands indicates localized states with large effective masses. Upon reaching maximal Li doping (16 Li atoms), the Fermi level lies at the van Hove singularity of graphene, indicating increased electrical conductivity. We also find Li states near the Fermi level. This means that the Li atoms are forming a two-dimensional metallic network between the graphene and MoS2 layers, as shown by the Li projected DOS, which crosses the Fermi level at maximum Li intercalation. This is reasonable since for fewer Li intercalants the distance between Li ions in the supercell can be longer than the third nearest neighbor distance in bulk BCC Li metal, a = 3.38 Å, as obtained with our computational parameters. This ceases to be the case for five or more Li atoms, when the distance between at least some of them decreases to approximately 3 Å, comparable to the nearest neighbor distance in the bulk metal. For the Gr/T′-MoS2, low Li concentration causes some band splitting and reduced dispersion, particularly visible at the Γ point. At the highest Li concentrations, we again see evidence for the 2D metallic network of Li as the distances between Li atoms decrease to become comparable to distances in the bulk metallic state. The MoS2 band structure demonstrates some sensitivity to the amount of strain in the MoS2 layer. Therefore, in Figure 6, we show the band structure for both the case with MoS2 compressed (a−d) and with graphene expanded (e−h).
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Daniel T. Larson: 0000-0001-8528-0280 Ioanna Fampiou: 0000-0002-9598-2478 Author Contributions ∥
Both authors contributed equally to this work.
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The computations in this article were carried out on the Odyssey cluster supported by the FAS Division of Science, Research Computing Group at Harvard University and the Texas Advanced Computing Center (TACC) at The University of Texas at Austin, which is part of the Extreme Science and Engineering Discovery Environment (XSEDE), supported by National Science Foundation grant number ACI1548562. We thank K. Bediako and P. Kim for discussions about experimental observations of this system. We thank S. Shirodkar for helpful discussions. We acknowledge support from the ARO MURI Award No. W911NF-14-0247. G.K. acknowledges support from the Priority Research Center Program (Grant No. 2010-0020207) and the Midcareer Researcher Program (Grant No. 2016R1A2B2016120) through the National Research Foundation funded by the Korea government.
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REFERENCES
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4. CONCLUSIONS In summary, we have determined the maximum amount of Li intercalated within Gr/MoS2 bilayer structures and conclude that electron carrier doping of up to nC = 3.6 × 1014 cm−2 (n MoS 2 = 6.0 × 1014 cm−2 ) is theoretically possible. Investigating the charge exchange within the system constituents, we find that MoS2 accepts 60% more electrons from Li than graphene. Furthermore, while the intercalation and 24540
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