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Photo-Induced Vacancy Ordering and Phase Transition in MoTe2 Chen Si, Duk-Hyun Choe, Weiyu Xie, Han Wang, Zhimei Sun, Junhyeok Bang, and ShengBai Zhang Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.9b00613 • Publication Date (Web): 17 May 2019 Downloaded from http://pubs.acs.org on May 17, 2019

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1

Photo-Induced Vacancy Ordering and Phase Transition in MoTe2

Chen Si1,2, Dukhyun Choe2, Weiyu Xie2, Han Wang2, Zhimei Sun1, Junhyeok Bang3* and Shengbai Zhang2* 1 School

of Materials Science and Engineering, Beihang University, Beijing 100191, People’s Republic of China

2Department

of Physics, Applied Physics, & Astronomy, Rensselaer Polytechnic Institute, Troy, NY 12180, United States

3Spin

Engineering Physics Team, Korea Basic Science Institute (KBSI), Daejeon 305-806, Republic of Korea

Contacts: [email protected] / +82-42-865-3668 (J.B.) [email protected] / +1-518- 276-6127 (S.Z.) Abstract We show that nonequilibrium dynamics plays a central role in the photo-induced 2H-to-1T’ phase transition of MoTe2. The phase transition is initiated by a local ordering of Te vacancies, followed by a 1T’ structural change in the original 2H lattice. The local 1T’ region serves as a seed to gather more vacancies into ordering and subsequently induces a further growth of the 1T’ phase. Remarkably, this process is controlled by photo-generated excited carriers as they enhance vacancy diffusion, increase the speed of vacancy ordering, and are hence vital to the 1T’ phase transition. This mechanism can be contrasted to the current model requiring a collective sliding of a whole Te atomic layer, which is thermodynamically highly unlikely. By uncovering the key roles of photo excitations, our results may have important implications to fine control phase transitions in transition-metal dichalcogenides. KEYWORDS: nonequilibrium, excited state, vacancy ordering, phase transition, nucleation and growth

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2 Transition metal dichalcogenides (TMDs) exhibit noticeable differences in their electronic properties due to their delicate structural differences1: for example, group VI TMDs (MX2 where M is a transition metal Mo or W, and X is a chalcogenide S, Se, or Te) are semiconductors in the trigonal prismatic (2H) phase and metals in the distorted octahedral (1T’) phase.2 These differences have triggered a large number of studies on the TMDs for various applications ranging from logic transistors using 2H TMDs3 to catalysis using 1T’ TMDs.4 Importantly, each phase exhibits additional exotic properties ranging from valley-optoelectronics in the 2H phase by strong spin-orbit coupling and the absence of inversion symmetry5 and novel topological states in the 1T’ phase such as quantum spin Hall insulators,6,7 Weyl semimetals,8 and superconductors.9 Recent works also realized a heterophase homojuction TMD transistor, where the carrier mobility was improved due to the Ohmic contact between the semiconducting 2H phase and metallic 1T’ phase of MoTe2.10 To utilize these robust properties, however, a delicate control of the phases could be essential. So far, several experiments have reported the 2H-to-1T’ phase transition in TMDs through thermal annealing,11, 12 strain,13 and carrier doping.14, 15 Very recently, it was shown that using laser irradiation, controllable phase patterning can be achieved in MoTe2.10 Laser-induced phase transition in MoS2 has also been reported.16 While first-principles total-energy calculations have contributed to the understanding of the thermodynamic aspect of the phase transition in various conditions such as doping, strain, and electronic excitation,17-25 a complete microscopic picture remains elusive, particularly, due to the lack of an understanding on the dynamic aspect of the transition. The latter could be especially important in the presence of an intense laser: not only the transition can quickly occur within the timeframe of the laser irradiation, but also the ultrafast excited-state dynamics triggered by the


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3 laser26 could directly cause a transition. While the laser-induced 2H-to-1T’ transition in MoTe2 has been interpreted based on the relative energies of the electronic excited state,25 such an argument cannot explain why the reverse 1T’-to-2H transition does not spontaneously take place after the laser illumination has ceased. Clearly, thermodynamics is only part of the story. The other part must involve the unique properties of the ultrafast 2H-to-1T’ transition in the electronic excited state, which has so far not been seriously considered. In this work, we present the dynamics of laser-induced ultrafast 2H-to-1T’ phase transition in MoTe2 to show that electronic excitation plays a pivotal role. We find that the transition occurs through two individual processes: first, a Te vacancy ordering is achieved by the diffusion of the vacancies; second, accompanied by the vacancy ordering, a local 2H-to-1T’ structural transition occurs, as the ordering releases the strong repulsion at the interface between the two phases. The local 1T’ region grows as more single vacancies are gathered to the region and ordered. Electronic excitation enhances both the vacancy ordering and the 1T’ phase conversion. Our findings should be contrasted to the conventional collective sliding mechanism for the 2H-to-1T’ phase transition in Figure 1, which is highly unlikely due to the extremely high transition barrier (as will be detailed below). Stabilities of the 2H and 1T’ phases. Figures 1a and b show the atomic structures of monolayer MoTe2. It consists of triple layers where a Mo atomic layer is sandwiched between two Te layers. The 2H structure has an ABA stacking of the Te-Mo-Te layers, as shown in Figure 1a. The 1T structure has an ABC stacking, which is stabilized by a Peierls-type distortion to result in a dimerized 1T’ structure,6 as shown in Figure 1b. Using first-principles calculations [See detail methods in the Supporting Information], we find that the 2H phase is more stable by 0.042 eV/[MoTe2 formula unit (FU)] than the 1T’ phase in the electronic ground state. The phase


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4 transition from the 2H to 1T’ phase requires the collective transversal sliding of a whole Te atomic layer to the hollow sites, and the energy required for the transition is 0.90 eV/FU, as shown in Figure 1c. The relative stability can be changed in the presence of photo-excited carriers. When electrons are excited to the conduction band, leaving holes in the valence band (= placing electrons and holes in their respective excited states), the electrons and holes are quickly relaxed to their respective band edges within several hundred fs.26-28 After that, the carriers will stay until recombination, which for typical semiconductors is on the order of nano to micro seconds.26-28 Due to the large difference in the time scales (fs versus ns or ms), relaxed carriers will contribute to the structural transition.28 Hence, the size of the band gap can be crucial in determining the relative stability of the excited system. Figure 1d shows that 2H-MoTe2 is a semiconductor with a band gap of 1.1 eV. In contrast, Figure 1e shows that 1T’-MoTe2 is a metal with a lowering of the conduction bands and an uplifting of the valence bands. Consequently, it costs much less energy to occupy the band-edge states in 1T’-MoTe2 than those in 2H-MoTe2. In other words, upon optical excitation and carrier relaxation, 2H-MoTe2 can be energetically less stable than 1T’MoTe2. Our calculation shows that the stability transition from the 2H to the 1T’ phase occurs at the 0.2% electron excitation, which is readily achievable in experiments [See the Supporting Information]. Taking the 0.93% electron excitation (= 0.17 electrons per unit cell) in Figure 1c as an example, 1T’-MoTe2 becomes more stable than 2H-MoTe2 by 0.068 eV/FU. Although the energetics above is indicative of a change in the thermodynamic stability upon an electronic excitation, statistically a collective motion of the Te atoms is a rare event which cannot happen within a short radiation time.10 One can estimate the time for the phase transition using the Boltzmann factor, R  f exp[ E B / kT ] , where f is the vibrational frequency of MoTe2,


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5 i.e., 6.5×1012 s-1,29 EB is the energy barrier for the transition, k is the Boltzmann constant, and T is the temperature at about 400 oC according to the experiment.10 When N Te atoms are moved together, EB = N × 0.7 eV. In a typical sample size of ~ 1 μm2 (N ~ 9 × 106), the rate R is extremely small, and the transition cannot occur without a strong perturbation from the surroundings as in the case of martensic phase transition.30 One may, of course, consider the transition in a smaller area. However, this is also forbidden due to the repulsive force at the interface between 2H and 1T’ phases. As an example, Figure 2a shows the translation of one Te atom to a hollow site to form a local (one-unit cell) 1T’-MoTe2. Due to the strong repulsion by two nearby Te atoms, the original 2H-MoTe2 phase is spontaneously recovered (as revealed by our calculation). Dynamics of the laser-induced 2H-to-1T’ phase transition. The 2H-to-1T’ transition of MoTe2 has been observed in Te-deficient samples.10 Transitions near Te vacancies have also been observed, implying that these vacancies may play a key role in the transition. Indeed, Te vacancies can be generated at the top Te layer at an elevated temperature, given the low Te sublimation temperature of about 400 ºC.12, 31 As shown in Figures 2b-d, the presence of linearly ordered vacancies can eliminate the repulsive force to the displaced Te atoms at the 2H/1T’ interface, so under illumination a local transformation into the 1T’ phase becomes possible. This local 1T’ phase will be enlarged, as more vacancies are gathered to the region and ordered. Such a vacancy-mediated transition involves two individual processes: (a) the ordering of vacancies and (b) a structural transition into the local 1T’ phase near the vacancies, as will be elaborated below. (a) Ordering of vacancies. Under thermal equilibrium, vacancy ordering is unlikely. Under non-equilibrium condition, however, it is possible if the following two conditions are met32: (i)


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6 attractive interaction between vacancies and (ii) a relatively high vacancy diffusivity. Often, such an ordering is a diffusion-limited process.32 For condition (i), our calculations show that the binding energy between two vacancies is 0.17 eV, forming a di-vacancy as shown in Figure 2b. For tri- and tetra vacancies, ordering along a line, as shown in Figure 2c and d, is energetically the most favorable, and the binding energies are 0.30 and 0.38 eV for tri- and tetra-vacancies, respectively. For condition (ii), the energy barrier for a single vacancy diffusion in the ground state is 1.62 eV, which is quite large. However, this value, upon optical excitation, is reduced to only 0.61 eV, so the rate of vacancy agglomeration can be significantly increased. Using rate equations, one can quantitatively understand the dynamics of vacancy ordering. Three processes will be considered: 1) the diffusion of a single Te vacancy (1VTe), 2) the ordering of the vacancies [1VTe + nVTe → (n+1)VTe], and 3) the dissociation of ordered vacancies [nVTe → 1VTe + (n-1)VTe]. Here, nVTe denotes the n ordered Te vacancies. The time variation of the concentration of nVTe, denoted as [nVTe], is calculated using the following coupled equations: d [1VTe ]  k o [1VTe ][1VTe ]  dt

 k [1V

Te ][ nVTe ] 

o

k d (2VTe )[2VTe ] 

n 1

k

d ( nVTe )[ nVTe ]

;

n2

d [nVTe ]  k o [1VTe ][(n  1)VTe ]  k o [1VTe ][nVTe ]  k d ((n  1)VTe )[(n  1)VTe ]  k d (nVTe )[nVTe ] , for n ≥ 2, dt

where ko and kd (nVTe) are the ordering and dissociation rate, respectively. Because the ordering is determined by the diffusion of 1VTe (i.e., diffusion limited), ko can be written as k o  2a 2 f exp[ E diff / k B T ] / ln[

1 a  [1VTe ]

] , where Ediff is the diffusion energy barrier for 1VTe and

a is the MoTe2 lattice constant.33 The dissociation rate is, on the other hand, k d (nVTe )  f exp[ E dis (nVTe ) / k BT ] , where Edis(nVTe) is the dissociation energy barrier, given by


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7 the summation of Ediff and the binding energy between 1VTe and (n-1)VTe.32,

34

We use the

calculated binding energies for the di-, tri-, and tetra-vacancy, i.e., 0.17, 0.3, and 0.38 eV, respectively, but set to 0.38 eV for the binding energies of larger ordered vacancies. Note that during vacancy ordering a local 1T’ phase transition is also possible (as detailed below), but for simplicity we ignore such a process here. As an initial conditioning, we set [1VTe] = 2.0×1013 cm-2, which corresponds to 1% isolated vacancies, and [nVTe] = 0 for n  2. In the ground state, Figure 3a shows that, because of the low diffusivity of 1VTe, no vacancy agglomeration can be found until 500 ns. In the electronic excited state, on the other hand, Figure 3b shows that the higher diffusivity of 1VTe leads to 5 vacancy ordering within 10 ns. (b) Transition to a local 1T’-MoTe2 phase near ordered vacancies. Due to the presence of a di-vacancy, the Te atom [labeled by A in Figure 4a] can be stabilized at a hollow site, corresponding to a local 1T’ phase. Figure 4a shows that, in the ground state, the energy of the hollow site is higher by 0.09 eV than the original un-displaced site and the transition barrier is 0.15 eV, while in the electronic excited state, the hollow site is more stable by 0.73 eV than the original site and the barrier disappears. Figure 4b shows that the di-vacancy has three gap levels, originated from Mo-derived states in MoTe2 in the conduction band. As the Te atom moves towards the hollow site, Figures 4b-d show that these levels move down gradually while two Tederived levels rise from the valence band. Due to such a gap level variation, the hollow site is stabilized in the presence of excited carriers, as it places electrons in the lowering Mo states and holes in the rising Te states. The local 1T’ phase will grow in a similar fashion in Figure 4, as more vacancies are gathered to the region and ordered. Among various sites for additional vacancies, a corner at the


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8 1T’ triangle, denoted by the black square in Figure 5, is most stable with a binding energy of 0.30 eV. When the vacancy is trapped to the site, the Te atom denoted by B in Figure 5 can move to a corresponding hollow site with an energy barrier of 0.21 (0.12) eV in the ground (excited) state. Subsequent movement of the Te atom denoted by C is also possible with an energy barrier of 0.67 (0.32) eV in the ground (excited) state. When this happens, the total energy is lowered by 0.01 (0.17) eV in the ground (excited) state. If we add another vacancy, it will be trapped at the other (intact) corner of the triangle, i.e., ordering along a line at the domain boundary, with a binding energy of 0.25 eV. The corresponding transition barriers are in the range of 0.04-0.47 eV. We expect the growth of the 1T’ phase to continue on arrival of additional vacancies, although it is impractical to examine all possible processes using DFT. The reason is because the changes in the local structures will simply be a repeat of those given above. As such, neither the binding energy nor the transition barrier is expected to change significantly. Discussion. DFT calculations show that the vacancies order along a line, i.e., one edge of the triangle(s), see e.g., Figure 2d. This is supported by experiments, e.g., for S vacancies in MoS2.35,

36

Given the high mobility of vacancies at experimental temperature,37,

38

additional

vacancies can easily hover around the 2H/1T’ interfaces. The 1T’ phase growth proceeds when the vacancy approaches an adequate corner of the triangle and gets incorporated. Note that all edges of the triangle are equivalent, so the growth can happen on any of the three edges, as explicitly illustrated in Figure S1 in the Supporting Information. The density of the vacancies is another important point to be considered. For an n vacancy cluster, the corresponding 1T’ region contains n(n-1)/2 Te atoms. In other words, n vacancies displace n(n-1)/2 Te atoms. The ratio between the vacancies and displaced Te is thus ~

n 1  , n2 n

which decreases with n. For example, Figure S2 in the Supporting Information shows that to


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9 create a 1T’-phase area of 100 nm2 one needs 2.3% vacancies, but to create a phase area of 1 μm2 only 0.023% vacancies are needed. Moreover, edges of the 2H flakes can be viewed as linearly ordered vacancies. Figure S3 in the Supporting Information shows that the 1T’ phase transition in the electronic excited state can also take place from these edges. From a physical point of view, the 2H-to-1T’ phase transition is a non-radiative recombination process for the excited carriers, which competes with radiative recombination. As shown in Figure 4b-d, when the structure evolves due to the phase transition, the excited electron- and hole-occupied gap levels approach each other to facilitate a phonon-mediated carrier recombination,39, 40 rather than emitting lights. In addition, note that in our calculation a single layer MoTe2 is considered. As the thickness of MoTe2 increases, the electronic structure is changed from the direct to the indirect band gap. As such, the band-edge optical transition will be dramatically reduced, and this may influence on the phase transition. However, in the previous experiment,10 a pump laser frequency of 532 nm (= 2.33 eV) is much larger than the band gap of MoTe2 (about 1.0 eV41). Such a high energy excitation can excite sufficient electronhole pairs, and the direct to indirect gap change will have a minor effect on the phase transition. In summary, we have investigated the dynamics of laser-induced 2H-to-1T’ structural transition in MoTe2. While the 2H-to-1T’ phase transition has been viewed as a collective sliding of an entire Te atomic layer, the actual transition cannot be so simple (for its exceptionally large energy barrier) but involves a set of successive non-trivial excited-state dynamics: photo-induced Te vacancy diffusion and ordering to generate the nucleus and facilitate its growth of the 1T’ phase. Our findings suggest that the control of the vacancies and simultaneously the excited carriers hold the key to the robust phase engineering of TMDs for promising electronic and energy applications and should be experimentally tested.


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10 ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Calculation methods, estimation of the amount of excitation by laser, additional analyses on the 1T’ phase growth process, and the required vacancy concentration for the 2H-to-1T’ phase transition (PDF)

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] (J.B.) Phone: +82-42-865-3668 *E-mail: [email protected] (S.Z.) Phone: +1-518- 276-6127 Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS CS and ZS acknowledge the National Research and Development Program of China (Grant No. 2017YFB0701700) and the National Natural Science Foundation of China (11874079, 11504015). JB acknowledges the National Research Foundation of Korea (NRF2018R1D1A1B07044564), the National Research Council of Science & Technology (No. CAP18-05-KAERI), and KBSI grant D38614. DC, WX, HW, and SBZ acknowledge the U.S. Department of Energy (DOE) under Grant No. DE-SC0002623.


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Grant, A. J.; Griffiths, T. M.; Pitt, G. D.; Yoffe, A. D. J. Phys. C Solid State Phys. 1975, 8, L17.


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Figure 1. (Color online) Top and side views of atomic structures of (a) 2H and (b) 1T’ MoTe2. Arrow indicates the horizontal displacement of a top-layer Te atom to the hollow site. Purple, pink, and olive balls are Mo, top-layer and bottom-layer Te, respectively. (c) Total energy in the 2H-to-1T’ transition by a collective transversal sliding of top-layer Te atoms. Black and red lines are for the ground state and excited state (with a 0.93% excitation), respectively. Band structures of (d) 2H and (e) 1T’ MoTe2.


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Figure 2. (Color online) (a) In a 2H lattice, a horizontal displacement of a Te atom to an adjacent hollow site (denoted by the pink hollow circle) would lead to a local (one-unit cell) 1T’-MoTe2 phase, which is, however, prohibited by the strong repulsion from the two nearby Te atoms. (b-d) The presence of ordered vacancies removes the repulsion, so the local 1T’ phase transition can happen. Black squares denote vacancies, while blue arrows indicate structural changes in the local 1T’ phase transition. Azury lines denote the interface between the 2H and newly-formed 1T’ phases. A, B, C denote top-layer Te atoms that are displaced. Otherwise, legends are the same as in Figure 1(a).


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Figure 3. (Color online) Time evolution of ordered vacancy concentrations in (left) ground state and (right) electronic excited state with the initial condition: [1VTe] = 2.0×1013 cm-2.


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Figure 4. (Color online) (a) Total energy profile in a local 1T’ phase transition (black line for ground state while red line for electronic excited state). Insets are atomic structures at initial position (b) and final position (d). The local 1T’ regions are denoted by blue triangles. Here for clarity, only atoms surrounding the divacancy are displayed. Legends are otherwise the same as in Figure 1(a). (b)-(d) Band structures during local phase transition at the three positions indicated in (a).


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Figure 5. Energy profile as a result of consecutive shifts of B and C atoms to the corresponding hollow sites when an additional vacancy is introduced (see inset). Blue triangles in the inset indicate the growing of the local 1T’ region.


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