Article pubs.acs.org/JPCC
Structural Transitions in Monolayer MoS2 by Lithium Adsorption D. Nasr Esfahani, O. Leenaerts,* H. Sahin, B. Partoens, and F. M. Peeters Universiteit Antwerpen, Departement Fysica, Groenenborgerlaan 171, B-2020 Antwerpen, Belgium ABSTRACT: Based on first-principles calculations, we study the structural stability of the H and T phases of monolayer MoS2 upon Li doping. Our calculations demonstrate that it is possible to stabilize a distorted T phase of MoS2 over the H phase through adsorption of Li atoms on the MoS2 surface. Through molecular dynamics and phonon calculations, we show that the T phase of MoS2 is dynamically unstable and undergoes considerable distortions. The type of distortion depends on the concentration of adsorbed Li atoms and changes from zigzag-like to diamond-like when increasing the Li doping. There exists a substantial energy barrier to transform the stable H phase to the distorted T phases, which is considerably reduced by increasing the concentration of Li atoms. We show that it is necessary that the Li atoms adsorb on both sides of the MoS2 monolayer to reduce the barrier sufficiently. Two processes are examined that allow for such two-sided adsorption, namely, penetration through the MoS2 layer and diffusion over the MoS2 surface. We show that while there is only a small barrier of 0.24 eV for surface diffusion, the amount of energy needed to pass through a pure MoS2 layer is of the order of ≃2 eV. However, when the MoS2 layer is covered with Li atoms the amount of energy that Li atoms should gain to penetrate the layer is drastically reduced and penetration becomes feasible.
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interest from the scientific community.4−8 Other applications for MoS2 are in lithium-ion batteries, since it was recently shown that MoS2 mono- and multilayers exhibit a large lithium storage capacity9−12 or as ultrasensitive photodetectors2 and in valleytronics.13,14 A large amount of theoretical work on MoS2 has emerged in the last couple of years. A tight-binding model has been developed for monolayer and multilayered structures,15 and numerous ab initio calculations have been published. Examples of the latter are the theoretical investigation of the magnetic properties of H-MoS2 in the presence of nonmetallic adatoms16 and the incorporation of Li atoms at MoS2/graphene interfaces.17 For pure MoS2 the semiconducting H structure was found to be more stable than the metallic T structure, both in bulk and monolayer form.18,19 However, experimental and theoretical research on the structural stability of different MoS2 bulk allotropes shows that intercalation of Li atoms can stabilize the metallic 1T structure.1,20−24 Stable 1T structures can also be realized by substitutional doping of MoS2 with Re atoms.25 The main reason for this appears to be the charge doping caused by the Re donor atoms. Our recent studies revealed that the crystal structure of ReS2 single layers is stabilized through the formation of a distorted T phase.26−28 Recently, it was shown that a T → H transition in MoS2 could be induced even without additional new atoms by in situ scanning transmission electron microscopy experiments.29
INTRODUCTION In recent years, transition metal dichalcogenides (TMDs) such as MoS2 have gained renewed interest due to their layered structure. The weak van der Waals interaction between these layers makes it possible to exfoliate monolayers1−3 from the bulk. These monolayers consist of an hexagonally packed sheet of metal ions sandwiched between two hexagonal layers of chalcogen atoms. Consequently, the monolayers come in two varieties, called T and H, in which the metals have octahedral or trigonal prismatic coordination, respectively (see Figure 1).
Figure 1. Top and side views of the H (a) and T (b) structures of MoS2. The Li adsorption sites are marked with black dots.
Due to their two-dimensional (2D) nature, TMDs exhibit a broad range of properties that make them attractive for potential applications in nanoelectronics. A notable example is the potential use of MoS2 monolayers to overcome the scaling problem of the current semiconductor electric field effect transistors (FET), which is attracting an increasing amount of © 2015 American Chemical Society
Received: October 6, 2014 Revised: April 7, 2015 Published: April 7, 2015 10602
DOI: 10.1021/jp510083w J. Phys. Chem. C 2015, 119, 10602−10609
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Figure 2. (a) Zigzag distortion of the T structure (Tz); (b) Diamond-like clustering of Mo atoms (purple) for one-sided Li-covered T structure (Td; Li atoms are not shown).
In another recent study, Kan et al.30 investigated different phases of single-layer MoS2 and how the concentration of adsorbed Li atoms can stabilize T-like phases. They found that Li insertion with concentrations over 20% or electron charging with concentrations over 8.33 × 1014 cm−2 can induce structural transitions. In this paper, we also investigate the possibility of obtaining a H → T transition in monolayer MoS2 through Li adsorption using ab initio calculations. In contrast to the work of Kan et al.,30 we focus on the difference between single and double-sided adsorption and how double-sided adsorption can occur for MoS2 monolayers on a substrate. We systematically investigate the effect of the concentration of Li atoms on the structural properties of monolayer MoS2 and examine the possibility of a two-sided adsorption process in which Li atoms penetrate through the MoS2 layer or diffuse from the edge of the sample. The paper is organized as follows. First we give the computational details of our first-principles calculations. Then we examine the most stable configurations of isolated Li atoms on MoS2 for the two different phases, H and T. Next we investigate how the concentration of Li atoms on one side of the MoS2 layer changes the relative stability of the H and T crystal structure. These calculations are followed by an examination of two-sided adsorption. The stability of the resulting structures is examined with ab initio molecular dynamics (MD) and phonon calculations. In the next part we investigate two processes that can lead to adsorption on both sides of the MoS2 layer: (i) by the diffusion of Li atoms through the MoS2 layer and (ii) by diffusion along the other side of the sample. Furthermore, we examine the actual transition from the H structure to the T structure and calculate the energy barrier for this process.
The basis cutoff energy is lowered to 300 eV in that case in order to increase the speed of the simulations and the supercell size is taken constant. The Verlet algorithm is used to integrate Newton’s equations of motion and we make use of a microcanonical (NVE) ensemble with velocities assigned according to the Maxwell−Boltzmann distribution at different temperatures between 50 and 1000 K. In our MD simulations velocities were normalized every 50 steps and the total simulation time was 2 ps with time steps of 1 fs.
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RESULTS Single-Sided Li Adsorption. As mentioned above, TMDs have two main type of structures in which the metal has octahedral (T) or trigonal prismatic (H) coordination. For most TMDs, the T structure is both energetically and dynamically unstable. The dynamical instability results in an in-plane distortion (dimerization) along one direction and gives rise to the formation of a charge density-wave state (CDW).36−38 For the specific case of MoS2, where the Mo atom contains 2 d-orbital electrons, the CDW state corresponds to a dimerization of Mo atoms along one direction.37 Hereafter, we refer to this structure as Tz (see Figure 2a). This state can be realized by the structural optimization of a 2 × 1 superlattice of a perfect T structure. The dimerization along one direction reduces the total energy by 0.3 eV/Mo in comparison to the nondistorted T structure. Nevertheless, it is still energetically less favorable than the H structure by EH − ETz = −0.55 eV/ Mo. As a first step to investigate the influence of Li adsorption on the stability of the different structural phases, we look for the most stable position of an isolated Li atom on top of a MoS2 monolayer for the two phases, H and Tz. We investigated different adsorption sites (see Figure 1) of which two were found to be local minima, namely, one on top of the Mo atom (Mo) and one above the vacancy in the H phase or the S atom at the other side of the T structure (V). Li atoms adsorbed at other positions were found to relax into one of the two previous adsorption sites. We define the binding energies E(x) a = z − E − E , with x = H, T . The binding energies were E(x) tot x−MoS2 Li calculated in a 4 × 4 supercell (actually a 2 × 4 supercell for the Tz) and are given in Table 1. In this table, we also provide the distance from the Li atom to the Mo layer, dMo, and the magnetization of the system. The most stable adsorption site for both H and Tz phases is found to be above the Mo atom. To investigate the behavior of multiple adsorbed Li atoms, we perform unrestricted MD simulations in a large rectangular supercell (16 × 16.5 Å2) with initially randomly placed Li atoms (see Figure 3, left). After a while, the Li atoms relax into
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COMPUTATIONAL DETAILS Our first-principles calculations are based on density functional theory (DFT) as implemented in the Vienna ab initio simulation package (VASP).31 The exchange-correlation energy is described by the Perdew−Burke−Ernzerhof (PBE)32 functional and the single-particle Kohn−Sham equations are solved by using the projector-augmented wave (PAW) method.33,34 An energy cutoff of 500 eV is used for the plane-wave basis and a 12 × 12 Monkhorst−Pack k-point grid35 is used for Brillouin zone integrations. For density of states (DOS) calculations, we used 140 × 140 number of k-points for 1 × 1 unicell of H structure, and 70 × 140 number of k-points for Tz structure. All the structures are relaxed with residue forces of less than 0.01 eV/ Å. Due to periodic boundary conditions, artificial interactions between neighboring layers are present in the calculations. These are reduced by a vacuum layer of 20 Å and dipole corrections. We also perform ab initio MD simulations. 10603
DOI: 10.1021/jp510083w J. Phys. Chem. C 2015, 119, 10602−10609
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it as Td in the following. In order to refer to distorted T-type structures in general, we use the notation Tx (x = z, d). In Figure 4b we also plot the amount of charge transfer from the Li atoms to the MoS2 layer as calculated with a Bader charge analysis.39,40 Although the charge transfers per Li atom are similar for H and Tx, the Tx structure gains more energy in comparison to the H structure at the same concentration of Li atoms. The larger energy gain for Tx structures upon Li adsorption, can be understood by looking at density of states (DOS) of the H and Tz structures. In Figure 5, we plot the
Table 1. Adsorption Energy Ea (in eV), the Adsorption Distance from the Mo Layer, dMo (in Å), and the Magnetization M of the System (in Units of Bohr Magnetons μB), for Li Adsorption in a 4 × 4 MoS2 Supercell for H and Tz Structures H
Tz
Ea dMo M Ea dMo M
Mo
V
−1.65 3.01 0.00 −3.42 3.09 0.00
−1.50 3.07 0.00 −3.20 3.04 0.00
Figure 3. MD simulation of Li atoms on MoS2: the initial (left) and final (right) structure. Note that one Li atoms appears to be caught at a V adsorption site.
Figure 5. DOS of the H structure and Tz. Occupied states are marked with bold lines and unoccupied states are marked by dashed lines.
a triangular lattice, corresponding to 1 Li atom per Mo atom (see Figure 3, right). This indicates that adsorbed Li atoms will tend to cluster into triangular monolayers of the same size as the underlying MoS2 substrate. We can now use these most stable configurations to investigate the relative stability of the H and Tz phases as a function of Li concentration. In order to model different concentrations, we place Li atoms at one side of a 2 × 2 MoS2 supercell. In order to find the most stable configuration for a specific amount of Li atoms, one Li atom is added to the most stable configuration with one Li atom less. In Figure 4a, the variation of the energy difference (per Mo atom) between the H and T-type structure, ΔE = EH − ET, as a function of the number of adsorbed Li is plotted. As is clear from the plot, upon Li adsorption, the T-type structure gains relatively more energy and at larger Li concentrations a H → T transition occurs, that is, the structure with octahedral symmetry becomes energetically more stable. It is also noteworthy that at large Li concentrations the Tz structure undergoes a transformation from zigzag dimerization to diamond-like clustering of the Mo atoms.30 We picture this state in Figure 2b and we will refer to
density of states of both structures without Li. The unoccupied states are marked with dashed lines, while the occupied states are shown as bold lines. In order to have comparable energy scales, the vacuum potential (i.e., the potential of the vacuum above the layers) is subtracted from the energy scale (vacuum alignment). As is clear from the plot, the energy of extra electrons in the conduction bands is lower for the Tz structure, due to the presence of a large gap in the spectrum of the H structure.38 Therefore, the Tz structure gains more energy in comparison to the H structure upon electron doping. This explains the stabilization of the Tx structure upon Li adsorption. Double-Sided Li Adsorption. Although the Tx structure can become energetically more stable than the H structure for single-sided Li adsorption, we show below that there exists a substantial energy barrier that prohibits the actual transition. Increasing the concentration of Li atoms further can stabilize the Tx even more. If more Li atoms are adsorbed on the MoS2 layer, they will form a second adsorption layer. This layer can be placed at the same side as the previous layer or at the other side. In Table 2, we show the formation energies and charge
Figure 4. Li adsorption for different concentrations. (a) The energy difference between the H and Tx (x = z, d) per Mo atom as a function of the number of adsorbed Li atoms in a 2 × 2 supercell. (b) Corresponding total charge transfer from the Li atoms to MoS2. 10604
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struct.
Li pos.
OS/TS
Ef/Mo (eV)
charge (|e|/Mo)
1 2 3 4 5 6 7
H H Td Td Td Td T
(Mo) (Mo,Mo) (Mo) (V) (Mo,Mo) (Mo,V) (Mo,Mo)
OS TS OS OS TS TS TS
−1.56 −3.14 −1.86 −1.83 −3.90 −3.82 −3.57
0.8 1.6 0.8 0.8 1.6 1.6 1.6
a
Results for both one-sided (OS) and two-sided (TS) adsorption are shown, and also, results for single Li atom adsorption are shown for comparison.
transfer of adsorbed Li layers on one (OS) or two sides (TS). The positions of Li adsorption sites (Mo and V) are shown in Figure 1. This formation energy is defined as Ef = Etot − (EH‑MoS2 + n·ELi), divided by the number of Mo atoms, and n is the number of adsorbed Li atoms. For comparison, we also include results for the nondistorted T structure. This perfect T structure becomes energetically more stable than the H structure in the TS case but, as expected, the Td structure with TS adsorption is the most stable structure. From the charge transfers in Table 2, we can conclude that only Li atoms that are close to the MoS2 layer lead to substantial charge transfers (≈0.8 e/Li atom). The charge transfer for two-sided adsorption is twice as large as for onesided adsorption because both Li layers can donate electrons to the MoS2 layer in that case. This leads to further stabilization of the Td structure. Dynamical Stability of Td-Li2MoS2. To be certain that the previous calculations of the Td-Li2MoS2 were not too restrictive we perform some additional calculations on this system. It is known that other materials in the T phase, such as ReS2, can undergo different structural distortions from the ideal T structure.26−28 Therefore, it is worthwhile to further examine the possible distortions of T-Li2MoS2. MD calculations not only give information about the stability of a given structure at high temperatures but also allow us to monitor the possible structural transitions at a given temperature. Ab initio MD simulations were performed at temperatures of 50, 200, 500, and 1000 K to investigate this. For the MD calculations the plane-wave cutoff was set to 500 eV which is required for finding possible reconstructions and the Brillouin zone is sampled with the Γ-point. For the investigation of temperaturedependent structural changes in Li-covered MoS2, computational cells are constructed with 48 atoms. Integration of the equations of motion proceeds with a time step of 1.0 fs for different temperatures. In each of the simulations, the time scale lies between 2 and 3 ps. As expected, the calculations (see Figure 6) show that the perfect T phase of Li2MoS2 undergoes a significant structural rearrangement even at low temperatures and therefore the T phase is unstable. It can be observed that both the Mo atoms and the Li atoms form diamond clusters, albeit with different centers. Here, one should note that such a reconstructed structure can be obtained only for (2n × 2n × 1) supercells. At elevated temperatures (up to 500 K), the presence of the clusters persists, although some distortions of the Td phase can be seen and a Tz-like structure starts to appear (Figure 6c). Nonetheless, Td can be regarded as a stable phase of Li2MoS2. For temperatures higher than 500 K, Li atoms on both surfaces
Figure 6. Top views of the atomic structures of T-Li2MoS2 at (a) T = 0 K (starting point), (b) T = 50 K, (c) T = 500 K, and (d) T = 1000 K. Mo, S, and Li atoms are shown with purple, yellow and green colors, respectively. For the sake of clarity Mo−S and S−Li bonds are hidden. For the largest Li−Li bond, 3.3 Å is chosen.
become randomly distributed and local S vacancies are formed in the underlying MoS2 layer. The final structure at 1000 K is shown at the bottom right panel of Figure 6. As a final examination of the stability of the Td-Li2MoS2 structure, we investigate its dynamical stability by calculating its vibrational spectrum. To this end, we calculate the phonon dispersions based on the small-displacement method as implemented in the PHON code.41 This analysis relies on properties of phonon dispersions which are calculated based on the force constant matrix. This force constant matrix has to be calculated for a larger supercell than the primitive unit cell. The size of the supercell should be large enough such that the elements of the force constant matrix have fallen off at the boundary of the supercell. For the stability analysis of the TdLi2MoS2, we therefore choose a (4 × 4 × 1) supercell. For the determination of the vibrational characteristics and the dynamical stability of the optimized structures, static firstprinciples calculations were conducted with a precision as high as 10−6eV for the total energy difference between two selfconsistency steps. In the small-displacement method, atoms were displaced with 0.04 Å in independent directions. A reciprocal space mesh of 5 × 5 × 1 is found to be enough for convergence of the elements of the dynamical matrix. We show the phonon dispersion of the Td-Li2MoS2 structure in Figure 7. Here we note that the lowermost acoustic phonon mode of such a layered material has quadratical dispersion and can go below zero at the Γ symmetry point due to an insufficient FFT grid. Here it was corrected by fitting. From the phonon dispersion shown in Figure 7 we see that the first three modes, ZA, TA, and LA, are acoustic modes and the remaining optical modes are well coupled to each other. However, due to the broken symmetry in the Td phase we also see many dispersionless phonon bands which correspond to local vibrations. In conclusion, the presence of strong Li−Li and Li−S bonds, even at high temperatures, and the absence of imaginary eigenmodes in the vibrational spectrum is strong evidence for the dynamical stability of Td-Li2MoS2. 10605
DOI: 10.1021/jp510083w J. Phys. Chem. C 2015, 119, 10602−10609
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doping, the Td-MoS2 becomes energetically more favorable, but there is still a substantial barrier of about ≃0.55 eV to reach this state. The barrier decreases further by increasing the concentration of Li atoms through adsorption on both sides of the MoS2 layer. At full Li coverage, the barrier for the Tz → H transition is reduced to about 0.09 eV. The barrier to reach the most favorable Li2MoS2 structure by shifting the Li atoms to the Mo adsorption sites is of the same order (0.12 eV). As mentioned above, an interesting process is observed during the transition from the H to Td structure. When the S layer of one side is shifted to the V position, the Li atoms at that side tend to follow the S layer. Moreover, for the LiMoS2 case, shearing the S layer which is located on the same side of the Li atoms results in a lower energy barrier than shearing the S layer on the other side. These observations suggest that the Li atoms mediate the transition and reduce the barrier considerably. In other words, the Li atoms are not only important to make the T phase energetically favorable through their charge doping, but also play an important role in the actual phase transition. Possibilities for Double-Sided Adsorption. In the final part of this work, we will investigate the possibility to get Li atoms on both sides of the MoS2 layer. Although two-sided Li adsorption is possible for a free-standing MoS2 monolayer, it might be difficult to achieve if the MoS2 is placed on a substrate, as is usually the case in an experimental setup. In the latter case, the Li atoms should be able to penetrate the MoS2 layer or migrate from the edges of the sample between the substrate and the MoS2 monolayer. In the present analysis we limit ourselves to perfect MoS2 layers without defects. We first look at the possibility that Li atoms pass through the MoS2 layer. To this end, we examine whether the Li atoms can penetrate through the H structure by passing through the center of a Mo−S hexagon (position V in Figure 1). In practice, we calculate the binding energy of a single Li atom at a fixed distance from the MoS2 layer in a 3 × 3 supercell. The distance is kept constant during relaxation by taking the out-of-plane coordinates of the Li and the 3 closest Mo atoms fixed. This choice does not restrict the system in any way and merely defines the distance between the Li atom and the MoS2 layer. The pressures on the supercell were kept around 1 kB by tuning the cell parameters after each relaxation step. The (nonspin-polarized) binding energy is defined in a similar way as the adsorption energy (see above) and vanishes for infinite separation. The binding energy of the Li atom at various distances from H-MoS2 is presented in Figure 9 (squares). The energy is reduced when the Li atom moves from infinity toward the
Figure 7. Phonon dispersion of the 1Td-Li2MoS2 structure.
H to Tx Transition Barrier. Now that we demonstrated the energetical and dynamical stability of the Tx structures, we investigate the actual structural H → Tx transition for systems with different Li concentrations. The calculations are performed with 2 × 2 MoS2 supercells which are suited to match both the H and Tx unit cells. The transition can be regarded as a shift of one S layer in the H structure to the position V (see Figure 1a). Therefore, the barrier energy of the H → Tx transition can be calculated by fixing the Mo atoms and shearing one S layer from the H structure toward the Tx structure, while the other atoms are allowed to relax. We also allow the cell parameters to relax such that the in-plane pressures are kept to a minimum (
