Supporting Materials for
Design of high-efficiency visible-light photocatalysts for water splitting: MoS2/AlN(GaN) heterostructures Jiamin Liao#, Baisheng Sa#, Jian Zhou, Rajeev Ahuja, Zhimei Sun*
[*] Mr. J. M. Liao, Mr. B. S. Sa College of Materials, Xiamen University, 361005 Xiamen, P. R. China Dr. J. Zhou, Prof. Dr. Z. M. Sun School of Materials Science and Engineering, and Center for Integrated Computational Materials Science and Engineering, International Research Institute for Multidisciplinary Science, Beihang University, 100191 Beijing, P. R. China Email:
[email protected] Prof. Dr. R. Ahuja Condensed Matter Theory Group, Department of Physics and Astronomy, Uppsala University, 75120 Uppsala, Sweden [#] Authors contributed equally to this work.
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The crystal and electronic structures of 2D MoS2 The crystal structure and electronic properties of the free-standing monolayer MoS2 are firstly studied. Monolayer MoS2 has a hexagonal lattice with honeycomb structure (space group P63/mmc). Considering the weak van der Waals like interaction in the MoS2-based
heterostructures,1
all
calculations
in
this
work
used
the
Perdew-Burke-Ernzerhof (PBE)2 exchange-correction functionals with the approach of Grimme (DFT-D2).3,4 The accuracy for the structural properties of transition metal dichalcogenides such as MoS2 using DFT-D2 method has been verified.4 The optimized lattice parameter for monolayer MoS2 is 3.187Å with the relaxed Mo-S bond length being 2.41 Å, which are consistent with previous work.5 Monolayer MoS2 exhibits a direct band gap with the valence band maximum (VBM) and conduction band minimum (CBM) located at the K point as shown in Figure S1a, which agree well with the previous study.6 The calculated direct band gap of MoS2 is 1.64 eV, which is in excellent agreement with the previous vdW-corrected DFT results (1.63 eV).7 However, a band gap of ~1.9 eV has been experimentally measured for monolayer MoS2.8,9 Obviously, the DFT-D2 method underestimated the band gap of monolayer MoS2 by roughly around 14%. It is well-known that DFT-D2 usually provides accurate crystal structures, but underestimates the band gap for vdW systems. To solve the band gap problem, we used the hybrid functional with the mixing of the Hartree-Fock and DFT exchange terms.10,11 In this case, the total energy is given by the following equation:12 short − ranged exchange short − ranged exchange long − ranged exchange correlation ETotal = xEHartree + (1 − x) EPBE + EPBE + EPBE + Edisp , − Fock
(1) where x is the percentage of the exact Hartree-Fock exchange energy being used. For x = 0.25, it is the Heyd-Scuseria-Ernzerhof (HSE06) hybrid function.13,14 The direct band gap calculated by HSE06 method for monolayer MoS2 is 2.34 eV, agree well with other hybrid functional study.15 However, the value is larger than that of the experimental result, suggesting that x = 0.25 is not a proper value for monolayer 2
MoS2. As the localized nature of the MoS2 band edges contain a very strong self-interaction, in order to reproduce the experimental band gap for monolayer MoS2, a 10% Hartree-Fock short-range exchange in Equation (1) is required. With this value, a direct band gap of 1.92 eV has been obtained, which is in excellent agreement with the experimental result. Thus, the Hybrid-DFT with a 10% Hartree-Fock exchange energy can correctly describe the electronic strucutre of monolayer MoS2. The crystal and electronic structures of 2D AlN and GaN Monolayer hexagonal AlN and GaN share the same 2D honeycomb lattice with monolayer MoS2. Owing to the combination of the trend to form sp2-bonded planar trigonal structure and the large electrostatic energy, monolayer hexagonal AlN and GaN prefer a plannar framework in 2D structures.16 It means that Al (Ga) and N atoms locate at the same layer with zero buckling displacement. The fractional coordinates for Al (Ga) and N are (1/3 1/3) and (2/3 2/3) in the 2D lattice respectively. Hence, the lattice parameter is the only structural variable in monolayer AlN and GaN. The relaxed lattice parameters by DFT-D2 approach for monolayer AlN and GaN are 3.126 Å and 3.258 Å, respectively, in good agreement with previous PBE work.16Base on these results, the lattice mismatch of monolayers AlN (GaN) with MoS2 is -1.9% (+2.3%), which is good for constructing MoS2/AlN and MoS2/GaN vdW heterostructures. The band structures calculated by DFT-D2 method for monolayer AlN and GaN are shown in Figure S1b and c respectively. It is seen that monolayers AlN and GaN exihibit indirect bandgap with the VBM and CBM located at the K and Γ points respectively. The band gaps of monolayer AlN and GaN were calculated to be 2.91 eV and 1.94 eV by the DFT-D2 method. In order to get comparable results with the MoS2 calculations, we have also calculated the electronic structures for monolayers AlN and GaN using the Hybrid-DFT with 10% Hartree-Fock exchange energy. In this case, the calculated band gaps for AlN and GaN are 3.39 eV and 2.48 eV, respectively, which are smaller than the results by standard HSE06 hybrid functionals.16 However, there is no avaliable experiemental data for monolayers AlN and GaN for comparison. Nevertheless, we believe that the Hybrid-DFT with 10% 3
Hartree-Fock exchange energy can correctly describle the electronic strucutre of the MoS2/AlN(GaN) vdW heterostructures.
Figure S1. The band structures for (a) monolayer MoS2, (b) monolayer AlN and (c) monolayer GaN calculated by the DFT-D2 method. The Fermi energy is set to 0 eV.
The electronic structures of MoS2/AlN(GaN) vdW heterostructures The band gaps for MoS2/AlN and MoS2/GaN vdW heterostructures by DFT-D2 calculations are 1.15 eV and 1.14 eV respectively. These values are much smaller than that of the MoS2 (1.64 eV), AlN (2.91 eV) and GaN (1.94 eV) monolayers calculated by the same method, indicating that the formation of the vdW heterostructures reduces the band gaps. Similar behavior has been found in the MoS2/WS2 heterostructure by theoretically calculations, which was attributed to the band offset.17 As shown above, the Hybrid-DFT with 10% Hartree-Fock exchange energy can correctly describe the electronic structure of monolayer MoS2, we have thus calculated the electronic structures for the MoS2-based vdW heterostructures using this method. Now the calculated band gaps are 1.62 eV and 1.52 eV for MoS2/AlN and MoS2/GaN vdW heterostructure respectively. Such band-gap values correspond to the wave length of red light and infrared light, showing the potential application of MoS2-based vdW heterostructures in the photocatalytic water splitting. 4
The effect of rotational component on the electronic structures of the vdW heterostructures There could be some rotational component to the stacking. However, the rotational component should have little influence on the band structure of the heterostructures due to the weak vdW interaction between the layers. For example, in the manuscript we have considered some special rotation angles between adjacent sheets, i.e., 0o, 60o, 120o, 180o, 240o, 300o for the configurations a, b, c, d, e and f as shown in the Fig. 1, respectively. Taking MoS2/AlN heterostructure as an example, Fig. S2 (a), (b) and (c) show the electronic structures for the configurations with 0o, 60o, and 120o rotational stackings, respectively. It is seen that there is no obvious difference among them: firstly, the electronic states of CBM and VBM are not changed by the different rotational stacking; secondly, the size of band gap is only very weakly influenced by the different rotational stacking. Therefore, a rotational component to the stacking to accommodate the strain energy induced by the small lattice mismatch will have negligible effect on the band structure. This also means different stacking order would not change our conclusion qualitatively.
Figure S2. (color online).The band structures of MoS2/AlN vdW heterostructure with different rotational stacking: 0◦(a), 60◦(b), 120◦(c). The Fermi energy is set at 0 eV.
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AUTHOR INFORMATION
Corresponding Author *E-mail:
[email protected] Notes The authors declare no competing financial interests.
Author Contributions Z.M.S. initiated and coordinated the project, and wrote the manuscript. B.S.S. and J.M.L. carried out the project and analyzed the results, and contributed equally to the work. All authors contributed to the data analysis, interpretation and conclusions, and writing of the manuscript.
ACKNOWLEDGMENTS This work is supported by National Natural Science Foundation for Distinguished Young Scientists of China (51225205) and the National Natural Science Foundation of China (61274005).
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