Alloying as a Route to Monolayer Transition Metal Dichalcogenides

Article Cite This: ACS Appl. Energy Mater. XXXX, XXX, XXX−XXX

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Alloying as a Route to Monolayer Transition Metal Dichalcogenides with Improved Optoelectronic Performance: Mo(S1−xSex)2 and Mo1−yWyS2 Zhiming Shi, Qingyun Zhang, and Udo Schwingenschlögl* Physical Science and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia S Supporting Information *

ABSTRACT: On the basis of first-principles and cluster expansion calculations, we propose an effective approach to realize monolayer transition metal dichalcogenides with sizable band gaps and improved optoelectronic performance. We show that monolayer Mo(S1−xSex)2 and Mo1−yWyS2 with x = 1/3, 2/3 and y = 1/3, 1/2, 2/3 are stable according to phonon calculations and realize 1T′ or 1T″ phases. The transition barriers from the 2H phase are lower than for monolayer MoS2, implying that the 1T′ or 1T″ phases can be achieved experimentally. Furthermore, it turns out that the 1T″ monolayer alloys with x = 1/3, 2/3 and y = 1/3, 2/3 are semiconductors with band gaps larger than 1 eV, due to trimerization. The visible light absorption and carrier mobility are strongly improved as compared to 2H monolayer MoS2, MoSe2, and WS2. Thus, the 1T″ monolayer alloys have the potential to expand the applications of transition metal dichalcogenides, for example, in solar cells. KEYWORDS: transition metal dichalcogenide, monolayer, trimerization, band gap, light absorption

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intercalated.19,20 Restacked 1T phases of LiMoS2 and KMoS2 have been confirmed by electron diffraction, 21,22 and stabilization by substitutional doping of Re, Tc, Mn, and Sn atoms, which serve as electron donors, has been observed.23,24 Phase engineering of ultrathin VIB TMD nanosheets from the 2H to the 1T phase turns out to be an effective method to improve the conductivity25 and therefore to enhance the material performance in electrocatalytic hydrogen evolution,26 low-resistance contact transistors,27 and electrochemical supercapacitors.28 Stability of the 1T′ and 1T″ phases under ambient conditions has been demonstrated by many techniques, including scanning transmission electron microscopy, electron diffraction, Raman, and X-ray photoelectron spectroscopy,29,30 in agreement with theoretical results.31,32 The 1T′ phase synthesized by intercalating hydrogenated Li turns out to be stable in air for more than three months.33 For nanoelectronics and photovoltaics, it is of basic importance to realize semiconductor nanostructures with continuously tunable band gaps. Alloying is an efficient approach to achieve this goal. For example, the band gap and light emission of low-dimensional ternary semiconductors can be modified gradually by changing the constituent stoichiometries.34,35 On the other hand, calculations have shown that monolayer alloys of the type Mo(S,Se,Te)2 are thermodynami-

INTRODUCTION In recent years, access to more and more two-dimensional materials, such as graphene,1 hexagonal boron nitride,2,3 transition metal dichalcogenides (TMDs),4 and black phosphorene,5,6 has led to the discovery of fundamentally new physics and to technological interest for a variety of applications. Belonging to the most studied two-dimensional materials, most TMDs undergo a transition from indirect to direct band gap semiconductors by exfoliation from bulk to monolayer, which results in great potential in electronic and optoelectronic devices.7,8 One special feature of MoS2 is polymorphism, with phases of distinct electronic characteristics. Given by the arrangement of the S atoms, monolayer MoS2 appears in 2H (trigonal prismatic D3h) and 1T (octahedral Oh) symmetries, the 2H phase being semiconducting and the 1T phase being metallic.9,10 The phases can be easily transformed into each other by intralayer atomic plane gliding, i.e., a transversal displacement of one of the S planes. For pristine monolayer MoS2, MoSe2, and WS2 the 2H phase is energetically favorable and semiconducting, while the 1T phase is metastable and metallic.11−13 Pristine monolayer PtSe2 shows the opposite properties.14 Distorted 1T phases with dimerization (1T′) and trimerization (1T″) of the metal atoms recently have been reported for the group VIB TMDs, giving rise to interesting phenomena (quantum spin Hall effect,15 ferroelectricity,16 Weyl semimetallicity17,18). The 2H phase of MoS2 has been reported to convert into a 1T phase when alkali atoms, such as Li and K, are © XXXX American Chemical Society

Received: February 24, 2018 Accepted: April 19, 2018

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DOI: 10.1021/acsaem.8b00288 ACS Appl. Energy Mater. XXXX, XXX, XXX−XXX

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ACS Applied Energy Materials

Figure 1. Mixing energy of 2H bulk (a) Mo(S1−xSex)2 and (d) Mo1−yWyS2. (b, e) 2H monolayer structures obtained from the bulk ground state structures. (c, f) Distorted (1T′ or 1T″) monolayer structures obtained from the 2H monolayer structures. Yellow, cyan, orange, and blue spheres represent S, Mo, Se, and W atoms, respectively.

cally stable at room temperature for all compositions.36 Twodimensional ternary TMDs, including Mo(S1−xSex)2 and Mo1−yWyS2,37−44 are receiving much attention due to tunable band gaps38−42 and high catalytic activity for hydrogen generation.43,44 In addition, excellent contact and defect properties give rise to great potential in photovoltaic applications.45−50 The most widely used approaches to prepare 2H mono- and few-layer TMDs are mechanical exfoliation,51 chemical vapor deposition,52,53 and chemical liquid exfoliation,2,54,55 the latter providing high productivity. Regrettably, the consequences of the transition from the 2H into the 1T′ or 1T″ phase are not known. For this reason, we employ systematic first-principles calculations to investigate the structural and electronic properties of monolayer Mo(S1−xSex)2 and Mo1−yWyS2. We show that a semiconducting behavior can been realized in 1T″ monolayer alloys and that the optoelectronic properties are improved with respect to 2H monolayer MoS2, MoSe2, and WS2.

thicker than 15 Å are applied to avoid interlayer interaction. We use 0.3 Å−1 Monkhorst−Pack k-grids in the structural relaxations and 21 k-points between high symmetry points of the Brillouin zone in the band structure calculations. The force and total energy convergence thresholds are set to 0.01 eV/Å and 10−6 eV, respectively. Phase transition barriers are obtained by the climbing image nudged elastic band method60 with 10 images along the pathway from the 2H structure to the 1T′ or 1T″ structure. The forces are converged to 0.02 eV/Å. G0W0 calculations are performed on 9 × 9 × 1 Monkhorst−Pack kgrids using 450 empty bands. These k-grids have the same point density as a 15 × 15 × 1 k-grid in the case of the primitive unit cell of MoS2, for which the band gap is found to deviate only by 0.01 eV from the value obtained for a 19 × 19 × 1 k-grid. This indicates that the k-grids of the G0W0 calculations are wellconverged.

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RESULTS AND DISCUSSION Cluster Expansion Calculations. Experimentally, 1T′ and 1T″ monolayer TMDs can be obtained by Li-assisted chemical exfoliation from 2H bulk TMDs. The primitive unit cell of the 2H bulk phase contains two monolayers. We built 2H bulk Mo(S1−xSex)2 and Mo1−yWyS2 alloys by cluster expansion and determine the thermodynamic ground state structures, which are displayed in Figure S1. The mixing energy is given in Figure 1. Two ground states are obtained for 2H bulk Mo(S1−xSex)2, for x = 1/3 and 2/3, see the convex hull (red lines) in Figure 1a. We note that these structures are composed of two identical monolayers with 33% and 67% Se atoms, respectively, which previously has been predicted by cluster expansion for 2H monolayer Mo(S1−xSex)2.61 Eight ground states are obtained for 2H bulk Mo1−yWyS2, for y = 1/8, 1/4, 1/3, 5/12, 7/12, 2/3, 3/4, and 7/8, see the convex hull (red lines) in Figure 1d. For y = 1/8, 5 /12, 7/12, and 7/8, the structures are composed of two different monolayers, as shown in Figure S1. Separation and subsequent relaxation result in a total of seven monolayer alloys: Mo(S1−xSex)2 with x = 1/3 and 2/3, Mo1−yWyS2 with y = 1/4, 1 /3, 1/2, 2/3, and 3/4. The 1T′ or 1T″ monolayers are obtained by transversal displacement of one of the S/Se planes. Imaginary frequencies in the phonon spectra, see the path M (1/2, 0, 0) to Γ (0, 0, 0) to K (1/3, 1/3, 0) in Figure S2, demonstrate that Mo0.25W0.75S2 and Mo0.75W0.25S2 are unstable, while the other five monolayer alloys show no imaginary frequencies (except for tiny regions around the Γ point due to artifacts of the numerical procedure used) and therefore are

METHODOLOGY Supercells of the alloys under investigation are constructed and sampled by the alloy-theoretic automated toolkit.56 To measure the quality of the cluster expansion, we use the cross-validation score57 1 M

M

∑ (EiDFT − EiCE)2 i

where EiCE is the energy predicted by cluster expansion based on M − 1 structures, and EiDFT is the corresponding energy from first-principles calculations. We use M = 55 for Mo(S1−xSex)2 and M = 61 for Mo1−yWyS2. The supercells include at most 24 atoms for Mo(S1−xSex)2 and 36 atoms for Mo1−yWyS2, with cross-validation scores of 3.4 and 0.4 meV/ atom, respectively, which means that the cluster expansions are well-converged. We find for both Mo(S1−xSex)2 and Mo1−yWyS2 that the effective cluster interaction is converged when the cluster diameter exceeds 5.5 Å. Total energies are calculated by first-principles calculations using the generalized gradient approximation in the Perdew− Burke−Ernzerhof (PBE) flavor and projector-augmented wave potentials, as implemented in the Vienna Ab-initio Simulation Package.58 The cutoff energy determining the number of plane wave basis functions is set to high a value of 500 eV. Band structures are calculated using the Heyd−Scuseria−Ernzerhof (HSE06) hybrid functional.59 In all calculations, vacuum slabs B


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the 1T than for the 2H phases and obtain the following transition barriers (per formula unit): 1.57 eV for MoS2, 1.35 eV for MoSe2, 1.69 eV for WS2, 1.29 eV for Mo(S0.67Se0.33)2, 1.37 eV for Mo(S0.33Se0.67)2, 1.43 eV for Mo0.67W0.33S2, 1.56 eV for Mo0.5W0.5S2, and 1.41 eV for Mo0.33W0.67S2. Thus, the transition barriers of the monolayer alloys are lower than that of monolayer MoS2; i.e., phase transition is easier than for MoS2 (for which it has been achieved experimentally). We also find that the recovery barrier back to the 2H phase is at least 0.793 eV for the considered alloys, i.e., higher than for pristine MoSe2 (0.638 eV) and WS2 (0.792 eV), indicating that spontaneous recovery is very difficult under ambient conditions. Because the phase transitions in MoS2 happen during the process of alkali atom intercalation (charge injection from the alkali atoms into the sample), we address in Figure 2b the transition barrier for negatively charged Mo(S0.67Se0.33)2 as an example (1, 2, or 3 electrons per formula unit). Results for the other monolayer alloys are qualitative similar, see Figure S3. The transition barrier decreases significantly when the negative charge increases. The fact that the 1T″ phase of Mo(S0.67Se0.33)2 is more stable than the 2H phase in the −3 charge state implies that charge injection supports the phase transition, similar to the case of monolayer MoS2.63,64 Semiconducting Monolayer Alloys. The band structures in Figure 3 display semiconducting states for 1T″ Mo(S 0 . 6 7 Se 0 . 3 3 ) 2 , Mo(S 0 . 3 3 Se 0 . 6 7 ) 2 , Mo 0 . 6 7 W 0 . 3 3 S 2 , and Mo0.33W0.67S2 with direct band gaps at the Γ point. According to Table 1, see also the band structures in Figure S4, the band

stable. In the case of Mo0.5W0.5S2, chains of MoS2 and WS2 alternate along the zigzag direction as in the 1T′ phase.15 The structures for x = 1/3 and 2/3 (y = 1/3 and 2/3) contain one Se and S (W and Mo) atom, respectively, per √3 × √3 supercell of MoS2 and MoSe2 (MoS2 and WS2). We observe that these atoms realize √3 × √3 patterns, implying that alloying provides an approach to realize 1T″ phases. The 1T″ MoS2 has been predicted to have 22 meV per formula unit lower energy than the 1T′ structure.62 We also find that relaxation of 1T′ structures results in 1T″ structures, which therefore are more stable. In addition, relaxation of the 2H and 1T″ structures of Mo(S0.67Se0.33)2 and Mo(S0.33Se0.67)2 (Figure 1b,c) shows that clustering of the S and Se atoms is energetically unfavorable. In all 2H monolayer alloys (Figure 1b,e) the bond lengths resemble those of the pristine monolayers (2.41, 2.53, and 2.41 Å for the Mo−S, Mo−Se, and W−S bonds, respectively), reflecting negligible distortions, while the 1T′ and 1T″ monolayer alloys show significant distortions (Figure 1c,f). Ab-initio molecular dynamics simulations (10 ps) have been performed at 300 K for each 1T″ monolayer alloy, employing a 4√3 × 4√3 supercell with 144 atoms, to confirm thermodynamic stability. 2H−1T Phase Transition. To evaluate whether the 1T′ and 1T″ monolayer alloys can be achieved experimentally, we calculate the phase transition barriers and compare with the pristine monolayers, see Figure 2a. We find higher energy for

Table 1. PBE and HSE06 Band Gaps (in eV) 1T′ or 1T″ phase Mo(S0.67Se0.333)2 Mo(S0.33Se0.67)2 Mo0.67W0.333S2 Mo0.5W0.5S2 Mo0.33W0.67S2 MoS2 MoSe2 WS2

Figure 2. Energy along the minimum barrier pathways from the 2H phase into the 1T′ or 1T″ phase for (a) the uncharged monolayers and (b) charged monolayer Mo(S0.67Se0.33)2.

2H phase

PBE

HSE06+SOC

PBE

0.73 0.67 0.80 0 0.82 0 0 0

1.28 1.16 1.25 0 1.25 0 0 0

1.64 1.57 1.66 1.74 1.71 1.74 1.50 1.89

Figure 3. Band structures of the monolayer alloys. Solid lines refer to the PBE level and dashed lines to the HSE06+SOC level. C


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ACS Applied Energy Materials gaps at the PBE level are less than half as compared to the 2H phase. Since the generalized gradient approximation typically underestimates the band gaps of semiconductors, and the spin− orbit coupling (SOC) cannot be neglected, we have repeated the band structure calculations with the HSE06 hybrid functional. It turns out that the conduction bands shift to higher energy, and the band gaps grow significantly, see Table 1, being comparable to widely used silicon (1.1 eV). The effect of the SOC is weak at the valence band edges but leads to band splitting at the conduction band edges. Our results are similar to previous reports on Rashba splitting in pristine 1T″ TMDs.16,62 For 1T′ Mo0.5W0.5S2 we observe band crossing at the Fermi level between the Y and Γ points, similar to 1T′ MoS2, for which a quantum spin Hall state with large gap has been predicted.15 The mechanism of band gap opening in the 1T″ monolayer alloys turns out to be intriguing and gives rise to a new strategy for materials design. We use 1T″ Mo(S0.67Se0.33)2 as an example to reveal the mechanism. According to Figure 4, in unrelaxed

Figure 5. Densities of states projected on the Mo 4d orbitals in (a, c, e) unrelaxed 1T Mo(S0.67Se0.33)2 and (b, d, f) 1T″ Mo(S0.67Se0.33)2 with the Se atoms at the positions indicated by orange in the insets.

relative shifts of the Mo atoms along the x, y, or z axis. What is the consequence of such a shift? For instance, for a shift along the x axis the overlap between the Mo dxy, dxz orbitals and the S/Se 3p orbitals increases; i.e., the dxy and dxz states shift to higher energy with respect to the dyz states, and a band gap is opened. Indeed, the partial densities of states in Figure 5b,d,e show that the conduction band minimum is composed of dyz, dxz states, dxy, dyz states, or dxy, dxz states depending on the direction in which the respective Mo atom is shifted. We have calculated 200 random structures (2√3 × 2√3 supercells) for each Mo(S0.67Se0.33)2, Mo(S0.33Se0.67)2, Mo0.67W0.33S2, and Mo0.33W0.67S2 to confirm that they undergo trimerization and exhibit band gaps similar to our results for the √3 × √3 supercells, see Figure S5. Carrier Mobility and Absorption Properties. The sizable band gaps of the semiconducting 1T″ monolayer alloys call for evaluation of the potential in solar cells, the absorption coefficient and carrier mobility being the most important parameters. To this aim, we employ the G0W0 method combined with the Bethe−Salpeter equation to consider exciton effects and to obtain accurate frequency-dependent dielectric tensors. The absorption coefficients are shown in Figure 6a (solid lines) and are compared to monolayer MoS2, MoSe2, and WS2 (dotted lines). The visible light range (1.62− 3.11 eV) is highlighted. The first absorption peaks of monolayer MoS2, MoSe2, and WS2 are found at energies of 1.97, 1.75, and 2.20 eV, respectively, while they appear at energies of 1.03, 0.92, 1.03, and 1.05 eV for 1T″ Mo(S 0 . 6 7 Se 0 . 3 3 ) 2 , Mo(S 0 . 3 3 Se 0 . 6 7 ) 2 , Mo 0 . 6 7 W 0 . 3 3 S 2 , and Mo0.33W0.67S2. We obtain for the monolayer alloys stronger absorption than for the pristine monolayers in the low energy range from 1.62 to 2.42 eV and in the infrared range. However, in the high energy range (2.42−3.11 eV) monolayer MoS2 and WS2 show the strongest absorption. The HSE06+SOC band gaps are used to construct the band alignment diagram of Figure 6b. It turns out that a type-II band alignment (for the separation of electrons and holes) can be formed by any two monolayer alloys. The electrical transport is key for solar cell devices. Table 2 shows that the hole effective masses of the monolayer alloys are comparable to that of monolayer MoS2, whereas the electron

Figure 4. Densities of states of unrelaxed 1T MoS2 and Mo(S0.67Se0.33)2 as well as the semiconducting 1T″ monolayer alloys.

1T MoS2 the electronic states near the Fermi level originate from hybridized Mo 4d and S 3p orbitals. Both unrelaxed 1T MoS2 and Mo(S0.67Se0.33)2 show metallicity, i.e.; alloying with Se without structural relaxation does not open a band gap. However, it enhances the Mo 4d contributions with respect to the S/Se 3p contributions at the Fermi level. In unrelaxed 1T MoS2 the Mo atoms are octahedrally coordinated by S atoms so that the five 4d orbitals split into dxy, dyz, and dxz states (occupied by a total of two electrons, which leads to metallicity) and d3z2−r2, dx2−y2 states (unoccupied). Structural relaxation opens a substantial and unexpected band gap, see Figure 4. To investigate its origin, we plot orbitally decomposed densities of states in Figure 5. In the case of unrelaxed 1T Mo(S0.67Se0.33)2 the states near the Fermi level are still due to almost degenerate dxy, dyz, and dxz states, see Figure 5a,c,e. Interestingly, it turns out that the structural distortions developing around the three nonequivalent Mo atoms per supercell are distinctively different, see the insets in Figure 5b,d,f. We find that the distortions are well-approximated by D


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Figure 6. (a) Absorption coefficients and (b) band alignment diagram (HSE06+SOC level) with band gaps.

Table 2. Carrier Effective Masses, Deformation Potentials, Elastic Moduli, and Carrier Mobilities along the Armchair (x) and Zigzag (y) Directions at T = 300 K (PBE Level) structure

electron/hole

mx*/m0

my*/m0

Elx (eV)

Ely (eV)

Cx (J/m2)

Cy (J/m2)

μx (cm2/(V s))

μy (cm2/(V s))

Mo(S0.67Se0.33)2

electron hole electron hole electron hole electron hole

5.3 0.6 3.7 0.7 3.0 0.7 1.6 0.6

6.4 0.6 14.5 0.6 2.4 0.8 1.6 0.7

−2.5 −4.1 −2.3 −0.9 −1.6 −3.6 −0.5 −3.8

−2.2 −3.2 −2.5 −7.2 −1.9 −2.8 −2.9 −2.7

101 101 107 107 115 115 117 117

102 102 107 107 117 117 119 119

11 396 17 5311 120 344 4421 474

12 649 3 101 108 569 118 799

Mo(S0.33Se0.67)2 Mo0.67W0.33S2 Mo0.33W0.67S2

effective masses are much higher.65 The carrier mobilities can be estimated from the expression66

CONCLUSION

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ASSOCIATED CONTENT

We have shown that alloying provides a feasible route to realizing semiconducting monolayer TMDs with sizable band gaps and improved optoelectronic performance. Combination of first-principles and cluster expansion calculations has enabled us to identify stable 1T′ and 1T″ monolayer alloys: Mo(S0.67Se0.33)2, Mo(S0.33Se0.67)2, Mo0.67W0.33S2, Mo0.5W0.5S2, and Mo0.33W0.67S2. The fact that the transition barriers from the 2H phase are lower than in the case of monolayer MoS2 implies that these alloys can be achieved experimentally. Most interestingly, we observe that 1T″ Mo(S0.67Se0.33)2, Mo(S0.33Se0.67)2, Mo0.67W0.33S2, and Mo0.33W0.67S2 exhibit sizable band gaps, induced by trimerization of the metal atoms, amounting to 1.23, 1.16, 1.24, and 1.16 eV at the HSE06+SOC level, respectively. Their behavior thus is fundamentally different from metallic 1T′ monolayer MoS2, MoSe2, and WS2. In addition, as compared to 2H monolayer MoS2, MoSe2, and WS2, the absorption of light is enhanced in the low energy visible region, and 1T″ Mo(S0.33Se0.67)2 and Mo0.33W0.67S2 provide very high carrier mobilities along the armchair direction. Thus, the predicted 1T″ monolayer alloys are of great interest for the fields of two-dimensional electronics and optoelectronics.

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μ=

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eℏ C kBTme*md (Eli)2

where m*e denotes the carrier effective mass in the transport direction, and md = mx*m*y , with x and y being the armchair and zigzag directions, respectively. Furthermore, Eil = ΔVi/(Δl/ l0) is the deformation potential of the valence band maximum (holes) or conduction band minimum (electrons), where ΔVi is the corresponding energy shift when the system is compressed or dilated by a distance Δl in the transport direction (equilibrium distance l0). Finally, C is the elastic modulus related to the longitudinal acoustic wave in the transport direction, derived from 2(E − E0)/S0 = C(Δl/l0)2, where E is the total energy, and S0 is the equilibrium area of the monolayer. We use for Δl/l0 five points in the range from −0.5% to 0.5% to obtain C and Eil by fitting. The calculated carrier mobilities in Table 2 reflect for 1T″ Mo(S0.33Se0.67)2 and Mo0.33W0.67S2 strong directional anisotropy. In addition, along the armchair direction, both alloys are found to outperform the carrier mobilities of monolayer MoS2 (340 cm2/(V s)), MoSe2 (240 cm2/(V s)), and WS2 (1103 cm2/(V s)),65 as well as that of phosphorene (2300 cm2/(V s)),67 which can be attributed to small deformation potentials (weak response of the states at the band edge to phonons), i.e., to reduced scattering of the carriers by phonons.

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsaem.8b00288. E


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Top and side views of ground state structures, phonon spectra of the ground state structures, minimum energy pathways, PBE band structures, and band gaps (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Udo Schwingenschlögl: 0000-0003-4179-7231 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The research reported in this publication was supported by funding from King Abdullah University of Science and Technology (KAUST).

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