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Article
Realizing Indirect-to-Direct Band Gap Transition in Few-Layer Two-Dimensional MX (M= Mo, W; X= S, Se) 2
Zhi Gen Yu, Boris I. Yakobson, and Yong-Wei Zhang ACS Appl. Energy Mater., Just Accepted Manuscript • DOI: 10.1021/acsaem.8b00774 • Publication Date (Web): 20 Jul 2018 Downloaded from http://pubs.acs.org on July 26, 2018
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Realizing Indirect-to-Direct Band Gap Transition in Few-Layer Two-Dimensional MX2 (M=Mo, W; X= S, Se) Zhi Gen Yu,† Boris I. Yakobson,*,‡ and Yong-Wei Zhang*,† † ‡
Institute of High Performance Computing, Singapore 138632, Singapore
Department of Mechanical Engineering and Materials Science, Rice University, Houston, Texas 77005, United States
ABSTRACT In the applications of two-dimensional (2D) transition metal dichalcogenides (TMDs) for solar cell and optoelectronic devices, two challenging issues remain: 1) the directto-indirect band gap transition from single layer to few-layer and 2) the absence of effective and robust doping procedure. In this study, we explore the feasibility to realize indirect-to-direct band gap transition and control the Fermi level by intercalating few-layer TMDs with embedded metals. Specifically, utilizing density functional theory calculations, we examine the electronic properties of few-layer MX2 (M=Mo, W; X=S, Se) intercalated with metals (Zn, Sn, Mg and Ga). Our calculation results reveal that 1) Ga intercalation can realize an indirect-to-direct band gap transition in few-layer TMDs, and as a result, the absorption efficiency is increased by two orders compared with that of pristine MX2; and 2) intercalated Ga acts as an ntype shallow donor, which markedly increases the charge density and electrical conductivity. Therefore, Ga intercalation may provide a potential practical route for manipulating few-layer TMDs for high performance solar and optoelectronic devices. KEYWORDS: Two-dimensional materials, transition metal dichalcogenides, DFT, chemical doping, band gap, indirect-to-direct transition
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1. INTRODUCTION Transition metal dichalcogenides (TMDs) have attracted great attention recently owing to their fascinating electronic properties and their potential applications in optoelectronic devices.1.2 It is known that TMDs are layered semiconductors with strong layer-dependent electronic properties.3−8 Although they have been used for fabricating field-effect transistors,9−11 integrated circuits 12 and phototransistors,13 the reduced band gap and the direct-to-indirect transition with the number of layers hamper their applications, especially in optoelectronic devices. Taking MoS2 for example, the single-layer MoS2 is a direct semiconductor with a band gap of 1.8 eV. However, bilayer MoS2 is already an indirect semiconductor with a reduced band gap of 1.6 eV and the bulk form is also an indirect semiconductor with a further reduced band gap of 1.29 eV.5 Not surprisingly, a high photoluminescence in single-layer MoS2 decreases drastically with the number of layers, arising from the indirect-to-direct band gap transition in this d-electron system.5,14 Hence, it is highly desirable to tune the indirect to direct band gap to achieve a high photoluminescence efficiency in few-layer TMDs. Intensive studies have been performed to address this critical issue in few-layer TMDs. For example, strain effect on the band structure of few-layer TMDs, such as MoS2, has been explored to achieve the indirect-to-direct transition.15−19 However, it presents a significant challenge to apply a controllable strain to fewlayer TMDs in real devices. Besides, thermal and electric field effects have also been demonstrated as controlling factors to achieve the indirect-to-direct transition in few-layer TMDs.20,21 Traditionally, chemical manipulation has been a proven way to modify the band structure and band gap in bulk semiconductors. For example, it has been widely reported that chemical doping was able to tune the band gap and band structure in oxides.22,23 Moreover, the effect of chemical manipulation on the electronic properties of 2D materials are expected to be much stronger than
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that of their bulk counterparts due to the stronger quantum confinement effect. Then, an interesting question arises: Can chemical manipulation be used to achieve the indirect-to-direct transition in few-layer TMDs? Clearly, answer to this question is crucial for the improvement of the optoelectronic performance of few-layer TMDs and promoting their wide applications in optoelectronic devices. In this study, we screen four metallic elements (Zn, Sn, Mg and Ga) and try to find suitable dopants for inducing the indirect-to-direct band gap transition in few-layer MX2 (M=Mo, W; X=S, Se). Our study, using first-principles calculations, shows that among considered elements, only Ga intercalation in MX2 is able to realize the indirect-to-direct band gap transition in fewlayer TMDs. Moreover, Ga intercalation also provides additional free electrons in the conduction band in TMDs, causing an increase in their n-type conductivity. Our study demonstrates a possible practical route to achieve the indirect-to-direct band gap transition in few-layer TMDs, which may substantially promote the applications of 2D TMDs in optoelectronic devices.
2. RESULTS AND DISCUSSION Since the interaction between layers causes the direct-to-indirect band gap transition occurring from single-layer to few-layer TMD, thus, weakening the interlayer interaction is a promising method to tune the indirect back to direct band gap in few-layer TMDs. Herein, we propose to use metal intercalation in between TMDs layers to weaken their interlayer interaction. Here, we focus on bilayer TMDs. The same approach is also applicable for few-layer TMDs. First, we would like to check our calculation procedure by examining the most stable pristine bilayer configurations of MX2 and comparing with existing results.20,24 Based on the crystal structure of MX2, there are five possible stacking configurations as shown in Figure S1, that is, (I) AA stacking with a mirror symmetry between the top and bottom layers (X over X and M over M); (II) AA′ stacking with an anti-mirror symmetry between the top and bottom layers (X over M and M over X); (III) A′B stacking with X superimposing on X; (IV) AB stacking with X
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superimposing on M, and (V) AB′ stacking with M superimposing on M. Previous studies on the structure stability of pristine TMDs showed that the AA′ stacking is the most stable.20,25 Our calculated relative ground-state total energies for each stacking configuration of TMDs with respect to the AA′ stacking are shown in Table S1. Not surprisingly, our calculations also show that the AA′ is the most stable stacking configuration among all four studied compounds. We have also calculated the interlayer distances (the Mo-to-Mo distance between two neighboring layers) for the most stable bilayer stacking (AA′), which are 6.52, 6.66, 6.59 and 6.62 Å for pristine MoS2, MoSe2, WS2 and WSe2, respectively. These calculated results are in excellent agreement with previously reported.24 The relative ground-state total energies of intercalated Ga in bilayer MX2 for three possible sites in five stacking configurations using supercell (4×4×1) are shown in Table S1. Note that there are 32 M and 64 X atoms in the supercell, and the concentration of intercalated Ga is about 1%. Based on our calculation results, we find that Ga intercalation at C site in AB stacked bilayer MX2 has the lowest relative formation energy as shown in Table S1. The optimized layer distances are slightly larger than those in their corresponding pristine bilayer MX2. The calculated layer distances are 6.75, 7.08, 7.11 and 7.19 Å for Ga-intercalated MoS2, MoSe2, WS2 and WSe2, respectively. Based on the calculated relative energies of the three possible sites, we adopt the embedded Ga at the site of C in AB bilayer for our further study unless otherwise mentioned. Next, we investigate the metal intercalation in bilayer MX2. According to the atomic structure and symmetry of MX2, intercalated elements may occupy three possibly embedded sites as shown in Figure S2. The first and the second embedded sites are the intercalated elements sitting on the top of M and X elements denoted as A and B, respectively. The third possible embedded site is the intercalated elements sitting in the middle of the hexagonal ring (top view) denoted as
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C. Prior to our band structure calculations; we have also investigated the most stable embedded site of the intercalation in bilayer MX2. Herein, Zn, Sn, Mg and Ga are selected in our study. To find promising elements for realizing the indirect-to-direct band gap transition in bilayer MX2, we have performed calculations by using bilayer MoS2 as a representative due to the same structure of all the four family members in MX2. We have found that the intercalated structure with AB stacking is the most stable one. For bilayer MoS2, the calculated band structures of all the four possible metal-intercalated MoS2 AB bilayers are shown in Figure S3. It is seen that Zn, Sn and Mg intercalation generate localized defect states nearly in the middle of the band gap. For Ga intercalation, however, the defect state is very near the bottom of the conduction band and the Ga-intercalated MoS2 shows a direct band gap characteristic. Hence, we only focus on the structure stability and electronic properties of Ga-intercalated bilayer MX2 (M = Mo, W; X=S, Se) and demonstrate the realization of the indirect-to-direct band gap transition in few-layer MX2. The chemical bonding between the intercalated Ga and host elements can be evaluated by calculating the charge accumulation and depletion. The charge density difference for the intercalated Ga and bilayer MX2 using the formula ∆ߩ = ߩ(Ga+MX2 ) − ൫ߩGa + ߩMX2 ൯, where ߩ(Ga+MX2 ) , ߩGa and ߩMX2 represent the charge density of the Ga-intercalated bilayer MX2, isolated Ga and pristine bilayer MX2, respectively. Our calculated results of the charge density difference for the Ga-intercalated MX2 are shown in Figure 1, in which, the magenta shows the electron depletion, and the aqua shows the electron accumulation. Based on our calculated results, it can be seen that the electron transfer occurs between the intercalated Ga and its adjacent X atoms. Clearly, Ga donates electrons to its bonded X atoms, leading to the electron accumulation in S atoms and depletion in Ga atoms. Therefore, strong chemical bonds form between the intercalated Ga and its adjacent X atoms, and these strong chemical bonds ensure the stability of the Ga-intercalated
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bilayer MX2.
Figure 1. The calculated charge difference in Ga-intercalated bilayer MX2: (a) MoS2, (b) MoSe2, (c) WS2 and (d) WSe2. Ga, Mo, W, S, and Se are denoted by blue, light blue, gray, and green balls, respectively. The isosurface is taken at 0.0015 e/Å3. The magenta shows electron depletion while the aqua shows electron accumulation. With the optimized Ga-intercalated bilayer MX2 models in hand, we further investigate the electronic properties of the four bilayer TMDs intercalated with Ga. The calculated band structures of Ga-intercalated MX2 are shown in Figure 2 (bottom panel). It is well- known that only singlelayer TMDs have the direct band structure, and the direct-to-indirect band gap transition occurs when the layer number is more than one. Not surprisingly, our calculations reproduce the band structures of pristine bilayer MX2 with AB stacking (the top panel of Figure 2) and the pristine
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bilayer MX2 indeed has an indirect band structure, which is consistent with previously reported results.20,24,26,27 In order to explore the contribution of intercalated Ga to the electronic band characteristics of AB bilayer MX2, as a benchmark, we also plot the band structures of 4×4×1 MX2 supercell in Figure 2 (middle panel). The calculated band structures of Ga-intercalated MX2 are shown in Figure 2 (bottom panel). It is seen that the VBM is shifted to K from the Γ point denoted by the red lines; while the CBM is shifted to K point as well. Hence, the Ga-intercalated bilayer MX2 possesses a direct band structure characteristic, thus realizing the indirect-to-direct band transition in bilayer MX2. The calculated direct band gaps are 1.52, 1.29, 1.67 and 1.40 eV, corresponding to Ga-intercalated MoS2, MoSe2, WS2 and WSe2 bilayers, respectively. In comparison, the calculated indirect band gaps of the pristine bilayer MX2 are 1.54, 1.28, 1.66 and 1.38 eV, corresponding to AB bilayer MoS2, MoSe2, WS2 and WSe2, respectively. Therefore, Gaintercalation exerts a negligible effect on the magnitude of the band gap in AB bilayer MX2. It is well-known that the calculated PBE band gap is in general underestimated compared with the experimental value. However, the PBE functional can provide reliable results for the band characteristics, e.g., direct or indirect band structure. It should be noted that our calculated values are the fundamental band gaps dominated by electron-electron interaction. More accurate band gap energies can be obtained by using more advanced DFT methods, such as HSE06 and GW.28
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Figure 2. The calculated band structures of the pristine bilayer (top panel), with a 4×4×1 supercell (middle panel), and Ga-intercalated MX2 (bottom panel), respectively. The red and blue lines show the VBM and the CBM, respectively. The Fermi level denoted by horizontal dotted line is set at zero energy.
Figure 3. The isosurface of wavefunctions of the CBM (top panel) and the VBM (bottom panel) of Gaintercalated MX2. (a) and (e) are Ga-intercalated MoS2, (b) and (f ) are Ga-intercalated MoSe2, (c) and (g) are Ga-intercalated WS2, and (d) and (h) are Ga-intercalated WSe2, respectively. Ga, Mo, W, S, and Se are denoted by blue, light blue, gray, and green balls, respectively. The isosurface is taken at 0.001 e/Å3.
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Based on our calculated band structures of Ga-intercalated MX2, we also find that the intercalated Ga drives the Fermi level towards the top of the conduction band as shown in the bottom panel of Figure 2. Obviously, the intercalated Ga donates free electrons to the conduction band, and thus acts as an n-type dopant in bilayer MX2. Relying on the distance between the bottom of the conduction band and the Fermi level, we see that the intercalated Ga acts as the shallow donor to bilayer MX2. We calculate the charge transfer between the intercalated Ga and bilayer MX2 using Bader charge analysis,29 and find that there are 0.783e, 0.663e, 0.734e and 0.614e injected to the conduction band by the intercalated Ga. Based on the calculated amount of Bader charges, we can estimate the carrier concentration based on the amount of charges per unit surface area (cm−2), and the calculated carrier concentrations are 5.63×1013, 4.45×1013, 5.29×1013 and 4.07×1013 cm−2 for Ga-intercalated bilayer MoS2, MoSe2, WS2 and WSe2, respectively. Our predicted carrier concentrations are slightly higher than the experimental values of ~1.0×1013 cm−2 and 2.5×1012 cm−2 for few-layer MoS2 and WSe2 realized by surface charge transfer by potassium.30 Due to the high level of Ga doping concentration (1%), the Ga-interaction has given rise to heavily doped semiconducting MX2. A similar degenerate doping of n-type TMDs by K surface adsorption and that of p-type TMDs by Nb substitution have also been reported.31,32 Since many semiconductor devices, for example, injection laser and bipolar transistors,33 are often heavily doped, it is expected that the heavily Ga-doped MX2 may find many interesting applications. It should be noted that a concentration threshold for realizing indirect-to-direct band gap transition should exist. It should be noted that there may be a concentration threshold in realizing the indirect-to-direct band gap transition. To examine the doping concentration threshold, we extend the supercell size to 5×5×1 with 100 S and 50 Mo atoms, and take Gadoped MoS2 as an example. In this case, the doping concentration is reduced to 0.67%. The calculated band structure is shown in Figure S4. It is seen that the indirect-to-direct transition still can be achieved. However, we found that the values of the VBM at Γ and K are nearly the same. Therefore, the estimated doping concentration threshold to achieve the indirect-to-direct transition should be about 0.67%. In order to achieve in-depth understanding on the electronic properties of the Ga-intercalated MX2, we plot the isosurfaces of band-decomposed charge density of the valence band maximum
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(VBM) and the conduction band minimum (CBM), and the results are shown in Figure 3. Based on the calculated results, it can be seen that M-d and Ga-2p orbitals mainly contribute to the CBM; while the hybridization of X-p and M-d orbitals primarily contribute to the VBM. The isosurfaces of band-decomposed charge density of the CBM in pristine bilayer MX2 are shown in the top panel, and these of the VBM are shown in the bottom panel. It can be seen clearly that the CBM and the VBM are mainly composed of strongly hybridized M-d and X-p orbitals, resulting in a highly dispersive character of the CBM and VBM. Apparently, it is the substantial contribution of intercalated Ga to the CBM and VBM that results in the indirect-to-direct band gap transition in the Ga-intercalated bilayer MX2. We also calculate the total density of states (TDOS) and the projected density of states (PDOS) with and without Ga-intercalation to gain an in-depth understanding of the electronic properties of Ga-intercalated bilayer MX2, and the results are shown in Figure 4. For pristine MX2, as shown in the top panel, the VBM and the CBM are mainly composed of the hybridization of M-d orbital and X-s orbital. In contrast, the CBM is partially contributed by Ga-2p orbitals, and the VBM is primary composed of the hybridization of Ga-2s and M-d orbitals in Ga-intercalated MX2. Based on the results of DOS, it can be seen that Ga-2s orbital and -2p orbitals contribute to the VBM and the CBM of Ga-intercalated MX2, respectively. Therefore, the hybridization of Ga-2p, M-d and X-s orbitals causes the conduction band valley in between Κ and Γ points to shift downwards. These results are consistent with the calculated band structures shown in Figure 2. We have shown that Ga intercalation is able to realize the indirect-to-direct band gap transition in bilayer MX2. As a result, the optical transitions between band edges are allowed. Figure 5 shows the results from our optical property calculations. It is seen that all Ga-intercalated MX2 bilayers show improved optical absorptions due to their direct band gap characteristic. Compared with the pristine bilayer MX2, the absorption coefficient is found to increase by two
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orders. What is more, we also found that Ga-intercalated MX2 bilayers show strong optical anisotropies. The out-of-plane optical absorption is much weaker than in the in-plane optical absorption. Owing to this property, Ga-intercalated MX2 bilayers could be good candidates for polarized optical sensors.
Figure 4. The calculated total density of states (TDOS) and projected density of states (PDOS) of pristine bilayer (top panel) and Ga-intercalated (bottom panel) MX2. (a)−(d) are pristine bilayer MoS2, MoSe2, WS2 and WSe2. (e)−(h) are Ga-intercalated bilayer MoS2, MoSe2, WS2 and WSe2, respectively. The Fermi level is set at zero energy. Inserts show the zoomed in results around the Fermi level. It is important, as explained in the introduction, to consider the effects of Ga-intercalation more than one layer MX2. As an example of few-layer of MX2, we calculate the band structure of three-layer Ga-intercalated MoS2 as shown in Figure S5 and find that Ga-intercalation can also induce an indirect-to-direct transition in three-layer MoS2 and produce an n-type conductivity. 11 ACS Paragon Plus Environment
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Hence, the route for engineering the band structure demonstrated here through Ga intercalation could also be extended to few-layer TMDs.
Figure 5. The calculated optical absorption coefficients of pristine and Ga-intercalated bilayer MX2 in the x-y plane. (a)−(d) are pristine and Ga-intercalated bilayer MoS2, MoSe2, WS2 and WSe2, respectively.
For the band structure of Ga-intercalated bulk MoS2, the calculated results are shown in Figure S6 (b). It is seen that a direct band gap can still be achieved although the VBM becomes very fiat and two valleys at the CBM appear near K point. In comparison with the band structure of Ga-intercalated bilayer and trilayer MoS2, the direct band gap characteristic of the Gaintercalated bulk MoS2 is weakened. The reduced quantum confinement effect with increasing the number of layers may weaken the influence of Ga-intercalation on the indirect-to-direct band gap transition. Therefore, few-layer TMDs are ideal for realizing the strong direct band gap characteristic via Ga intercalation, which are promising for applications in high-performance optoelectronic devices.
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3. CONCLUSIONS In conclusion, using the first-principles calculations, we have demonstrated a feasible route to realize the indirect-to-direct band gap transition via Ga intercalation in few-layer MX2 (M=Mo, W; X=S, Se). The intercalated Ga also acts as a donor to few-layer MX2, leading to an enhancement in charge density and electrical conductivity. We have also shown that the Ga-intercalated few-layer MX2 possesses a high light absorption coefficient due to its direct band gap characteristic. Our results reported here may provide a practical route to realize the indirect-to-direct band gap transition in few-layer TMDs, and the Ga-intercalated few-layer TMDs with remarkably high optical efficiency are promising for applications in high-performance optoelectronic devices.
AUTHOR INFORMATION Corresponding Authors *E-mail:
[email protected] (B.I.Y) *E-mail:
[email protected] (Y.W.Z) ORCID Zhi Gen Yu: 0000-0002-3718-6027 Yong-Wei Zhang: 0000-0001-7255-1678 Author Contributions ZGY carried out the DFT calculations. All authors performed data analysis and manuscript writing. Notes The authors declare no competing financial interest. Acknowledgement This research was sponsored by the Science and Engineering Research Council of Singapore with Grant No. 152-70-00017 and computational resource was provided by A*STAR Computational Resource Centre, Singapore (A*CRC) and the National Supercomputing Centre Singapore (NSCC).
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Supporting Information Available This material is available free of charge via the Internet at http://pubs.acs.org/. Computation method, stacking configurations (Figures S1- S2 and Table S1), band structures (Figures S3-S6), and references. REFERECNCES (1) Geim, A. K.; Novoselov, K. S. The Rise of Graphene. Nat. Mater. 2007, 6, 183–191. (2) Wang, Q. H.; Kalantar-Zadeh, K.; Kis, A.; Coleman, J. N.; Strano, M. S. Electronics and Optoelectronics of Two-Dimensional Transition Metal Dichalcogenides. Nat. Nanotechnol. 2012, 7, 699–712. (3) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Katsnelson, M. I.; Grigorieva, I. V.; Dubonos, S. V.; Firsov, A. A. Two-Dimensional Gas of Massless Dirac Fermions in Graphene. Nature (London) 2005, 438, 197–200. (4) Zhang, Y.; Tan, Y.-W.; Stormer, H. L.; Kim, P. Experimental Observation of the Quantum Hall Effect and Berry’s Phase in Graphene. Nature (London) 2005, 438, 201–204. (5) Mak, K. F.; Lee, C.; Hone, J.; Shan, J.; Heinz, T. F. Atomically Thin MoS2: A New Direct-Gap Semiconductor. Phys. Rev. Lett. 2010, 105, 136805. (6) Schwierz, F. Graphene Transistors. Nat. Nanotechnol. 2010, 5, 487–496. (7) Liao, L.; Lin, Y.-C.; Bao, M.; Cheng, R.; Bai, J.; Liu, Y.; Qu, Y.; Wang, K. L.; Huang, Y.; Duan, X. High-Speed Graphene Transistors with A Self-Aligned Nanowire Gate. Nature (London) 2010, 467, 305–308. (8) Najmaei, S.; Liu, Z.; Zhou, W.; Zou, X.; Shi, G.; Lei, S.; Yakobson, B. I.; Idrobo, J.-C.; Ajayan, P. M.; Lou, J. Vapour Phase Growth and Grain Boundary Structure of Molybdenum Disulphide Atomic Layers. Nat. Mater. 2013, 12, 754–759. (9) Radisavljevic, B.; Radenovic, A.; Brivio, J.; Giacometti, V.; Kis, A. Single-Layer MoS2 Transistors. Nat. Nanotechnol. 2014, 6, 147–150. (10) Zhang, Y.; Ye, J.; Matsuhashi, Y.; Iwasa, Y. Ambipolar MoS2 Thin Flake Transistors. Nano Lett. 2012, 12, 1136–1140. (11) Qiu, H.; Pan, L.; Yao, Z.; Li, J.; Shi, Y.; Wang, X. Electrical Characterization of Back-Gated Bi-Layer MoS2 Field-Effect Transistors and the Effect of Ambient on Their Performances. Appl.
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