Letter Cite This: J. Phys. Chem. Lett. 2017, 8, 5959−5965
pubs.acs.org/JPCL
Electronic and Optical Properties of Pristine and Vertical and Lateral Heterostructures of Janus MoSSe and WSSe Fengping Li, Wei Wei,* Pei Zhao, Baibiao Huang, and Ying Dai* School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China S Supporting Information *
ABSTRACT: On the basis of electron−electron self-energy corrections, quasiparticle band structures of Janus MoSSe and WSSe are identified, and the excitonic effects are demonstrated to play a dominate role in the optical response. Combining together MoSSe and WSSe monolayers to form vertical heterostructures (VHTs) and lateral heterostructures (LHTs) rarely leads to a simple arithmetic sum of their properties, giving rise to novel and unexpected behaviors. In particular, Rashba polarization can be enhanced in VHTs due to improved out-of-plane electric polarity. In the case of LHTs, photoresponse and absorption coefficients show optical activity in a wide visible light range. It is of interest that both VHTs and LHTs reveal type-II band alignment, enabling the separation of excitons. Besides, grain boundaries (GBs) of large angle (60°) in Janus MoSSe due to chalcogen effects behave as one-dimensional (1D) metallic quantum wires, suggesting the possible formation of 1D electron or hole gas in such electronic heterostructures.
T
transfer, while LHTs can be acquired though the CVD approach.41−44 It has been found that VHTs and LHTs composed of 2D TMDCs manifest exciting novel properties. Inspired by this, in this work, we propose VHTs and LHTs composed of the polarized Janus MoSSe and hypothetical WSSe to investigate the unprecedented novel properties by means of first-principles calculations (the computational details are described in the Supporting Information). Because the properties of WSSe are intrinsically similar to those of MoSSe, results for MoSSe are presented and discussed. In the case of WSSe, dynamic and thermal stability have been verified by a phonon spectrum and BOMD calculations. As shown in Figure S1, the phonon spectrum shows no imaginary frequency, and the BOMD results indicate small energy fluctuation, confirming the stability and thus the possibility of experimental realization. As indicated in Figure 1a, Janus MoSSe presents in-plane asymmetry with two trigonal prismatic lattices while it shows mirror symmetry with respect to the Mo plane breaks. The hexagonal Mo plane is sandwiched in between the S and Se layers with unequal distance. The lattice parameter is calculated to be 3.25 Å, and Mo−S and Mo−Se bond lengths are 2.42 and 2.53 Å, respectively. In consideration of the discrepancy in electronegativity for S and Se atoms, a vertical dipole moment of 0.25 D appears. The planar average of the electrostatic potential is indicated in Figure 1b, and the energy difference of 0.5 eV is in fact the work function difference between S and Se layers. On the basis of Bader charge analysis,45 S and Se atoms obtain 0.6 and 0.4 e, respectively, while Mo atom loses 1.0 e, which results in the net
wo-dimensional (2D) transition metal dichalcogenides (TMDCs) MX2 (M = Mo, W; X = S, Se) have attracted extensive attention in high-end electronics and optoelectronic devices.1−5 2D TMDCs indicate intrinsic in-plane asymmetry with direct band gaps of 1.1−1.9 eV, giant spin−orbit coupling (SOC), and favorable electronic and mechanical properties, which endow TMDCs great application potential in field-effect transistors (FETs), photonics, and valleytronics.6−13 It has been demonstrated that the electronic and optical properties can be regulated through effective control of the alloy composition of the 2D TMDCs, such as in MoSxSe2−x, MoxW1−xS2, and WS2xSe2−2x.14−18 Recently, the organized Janus MoSSe in the 2H phase has been successfully obtained by fully replacing one of two of the S (Se) layers with Se (S) atoms within MoS2 (MoSe2) at an applicable temperature mainly though the chemical vapor deposition (CVD) method.19,20 Different from 2D MX2 with mirror symmetry, Janus MoSSe reveals an intrinsic out-of-plane electric field due to the mirror asymmetry and thus demonstrates large Rashba band splitting and out-ofplane piezoelectricity.21−24 It has been extensively identified that combining distinct 2D materials to construct heterostructures can engineer the electronic properties and bring new exciting physical phenomena, which now is a central concept in nanoscale electronic and photovoltaic devices.25−31 As a consequence, the range of application of 2D TMDCs could be widely broadened by considering different stacking or combination patterns. In particular, 2D TMDCs can be vertically stacked layer by layer, forming the van der Waals (vdW) heterostructures.32−35 On the other hand, TMDCs can also be stitched seamlessly within the 2D plane to realize the lateral (in-plane) heterostructures (LHTs) with the formation of atomically sharp one-dimensional (1D) interfaces (interlines).36−40 Experimentally, vertical heterostructures (VHTs) can be obtained through mechanical © 2017 American Chemical Society
Received: October 26, 2017 Accepted: November 24, 2017 Published: November 24, 2017 5959
DOI: 10.1021/acs.jpclett.7b02841 J. Phys. Chem. Lett. 2017, 8, 5959−5965
Letter
The Journal of Physical Chemistry Letters
Figure 1. Top and side views of the MoSSe monolayer (a), with bond lengths labeled. Planar average of the electrostatic potential energy (navy line) and planar average of the charge density (red line) perpendicular to the MoSSe surface (b). Imaginary part of the macroscopic dielectric function of the MoSSe monolayer from G0W0+BSE+SOC; A1 and B1 indicate the two low-energy bound excitons (c). Orbit-projected band structures of MoSSe near the Fermi level from PBE+SOC (d,e); the bigger the dot size, the more the orbitals contribute to the wave functions at various k points; the Fermi level is set to zero.
Table 1. Band Gap Eg (eV), Valence Band Splitting λkv (meV) at the VBM, Conduction Band Splitting λkc (meV) at the CBM, Momentum Offset kR (Å−1), Rashba Energy ER (meV), and Rashba Parameter αR (eV Å)a MoSSe WSSe VHTs a
PBE+SOC G0W0+SOC PBE+SOC G0W0+SOC PBE+SOC G0W0+SOC
Eg (eV)
λkv (meV)
λkc (meV)
kR (Å−1)
ER (meV)
αR (eV Å)
1.47 2.69 1.42 2.59 0.61 1.83
170 179 444 478 446 454
13 26 31 33 14 21
0.005 0.004 0.010 0.007 0.005 0.004
1.4 1.3 3.6 2.5 3.1 1.9
0.53 0.65 0.72 0.71 1.22 0.95
The Rashba coefficient can be expressed as αR = 2ER/kR.
electric field pointing from Se to S. In Figure 1b, the charge density also demonstrates less charge aggregation on Se atoms. Furthermore, the cohesive energy is calculated for MoSSe according to the following equation: Ec = Et − μMo − uS − uSe, where Et, uMo, uS, and uSe indicate the total energy of the MoSSe monolayer and the chemical potentials of Mo, S, and Se atoms, respectively. The cohesive energy is −2.34 eV for MoSSe, which is comparable with that of MoS2 (−2.63 eV) and large enough to guarantee stability. In the case of Janus WSSe, a vertical dipole moment of 0.24 D, work function difference of 0.6 eV, and cohesive energy of −2.06 eV can be obtained. Band structures of MoSSe and WSSe obtained from manybody G0W0, screened hybrid HSE06, and PBE are presented in Figure S2 in the Supporting Information. It is clear that the direct band gaps at the K point at the HSE06 level of theory are obviously larger than those from PBE, while they are smaller than those from the G0W0 approximation. In the case of MoSSe, band gaps are 1.56 (PBE), 2.03 (HSE06), and 2.64 eV (G0W0), respectively. It should be pointed out that the scissor rule is absent in the G0W0 corrections, and therefore, the dispersion relationship of the quasiparticle band structures has been obviously changed after considering the nonlocal exchange interactions in comparison with the PBE and HSE06 results. With respect to the optical absorption properties of the monolayers, e−h interactions can be taken into account with the BSE approach based on the quasiparticle corrections. As shown in Figure 1c, the imaginary part of the transverse dielectric constant ε2(ω) shows two obvious excitonic absorption peaks at 1.85 and 2.06 eV due to the strong SOC effects, which correspond to the two bound excitons of A1 and B1 found in MoS2.46−48 In particular, the excitation energy (1.85 eV) of the first exciton with a binding energy of 0.79 eV is in agreement with the experimentally
measured optical gap of 1.68 eV. In Janus MoSSe and WSSe, the strong excitonic effects can be attributed to reduced screening between excited electrons and holes. It is worth noting that the mirror symmetry breaking will certainly cause in-plane Rashba as well as out-of-plane valley spin polarizations.49 In order to better address the band splitting in MoSSe, orbital-projected band structures at the PBE level considering SOC are shown in Figure 1d,e. It can be observed that the conduction band minimum (CBM) at the K point is composed of out-of-plane Mo-dz2 states, while the valence band maximum (VBM) is mainly contributed to by inplane Mo-dx2−y2 and Se-px states. It also can be observed that Mo-dz2 and S-pz states play a dominant role in the in-plane Rashba spin splitting in MoSSe that occurred at the Γ point. The symmetry for MoSSe is trigonal C3v, which is different from the space group of monolayer MX2 (D3h) owing to this out-of-plane asymmetry I (I ≠ Z → −Z). The band splitting Hamiltonian can be written as H(k) = vk(kxσy − kyσx) + λk(3kx2 − ky2)kyσz, k = kx 2 + k y 2 , and vk = (1 + αk2), where α, σi, and λi are the Rashba parameter, Pauli matrices, and warping parameter, respectively. The first and the second terms bring out the in-plane and out-of-plane band splitting at Γ and K points, respectively, as indicated in Figure S3a,b. Furthermore, for the out-of-plane band splitting λc at the CBM and λv at the VBM, the relevant Rashba parameters such as the Rashba energy ER, momentum offset kR, and Rashba coefficient αR have been calculated though PBE+SOC and G0W0+SOC approaches, and the results are summarized in Table 1. kR and ER are the shift of bands in the momentum space and the energy difference of the split state at the Γ point and are indicated in Figure S3b. The trigonal C3v symmetry induces a net electric dipole moment acting on Mo atoms, which plays an important role in the out-of-plane valley band splitting. 5960
DOI: 10.1021/acs.jpclett.7b02841 J. Phys. Chem. Lett. 2017, 8, 5959−5965
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Figure 2. Side view of the VHTs composed of MoSSe and WSSe monolayers; the layer distance and the intralayer (I) and interlayer exciton (II) are denoted (a). Upper panel: planar average of the electrostatic potential energy (navy line) and planar average of the charge density (red line) of the VHTs composed of MoSSe and WSSe. Bottom panel: planar average of the charge density difference of the VHTs composed of MoSSe and WSSe; the inset shows the spatial charge redistribution (b). Orbit-projected band structure of VHTs; contributions from MoSSe and WSSe are distinguished by the peach and azure dotted lines, respectively (c). Schematic diagram of the type-II band alignment; the intralayer and interlayer exciton are denoted (d). Orbit-projected band structure of the CBM (upper) and VBM (bottom) of the VHTs from PBE+SOC (e); the bigger the dot size, the more the orbitals contribute to the wave functions at various K points; the Fermi level is set to zero.
Figure 3. Atomic configuration of the LHTs composed of MoSSe and WSSe for two probe devices (a). Hexagonal and rectangular Brillouin zones (b). Variation of the band gap as the length of LHTs changes (c). Orbit-projected band structure of n = 9 LHTs; contributions from MoSSe and WSSe are distinguished by peach and azure dotted lines, respectively (d); the bigger the dot size, the more the orbitals contribute to the wave functions at various k points; the Fermi level is set to zero. Schematic diagram of the type-II band alignment with the band offsets denoted (e). Photoresponse coefficient for n = 9 LHTs (f). Absorption coefficient (g).
dynamic stability of VHTs has been verified by the phonon spectrum in which all branches over the entire Brillouin zone demonstrate positive frequencies, as show in Figure S6c. Consequently, the most stable AB stacking model is used for the following discussion about the VHTs; see also Figure 2a. The planar average of the electrostatic potential energy and the charge density difference are displayed in Figure 2b. In this case, the work function difference increases to 1.1 eV, and Bader charge analysis suggests an interlayer charge transfer of about 0.02 e from WSSe to MoSSe. The charge density difference shows that charge depletion is mainly located on the Se atoms of WSSe, and charge accumulation mainly occurs within the interface region. As shown in Figure 2c, the band structure manifests an indirect band gap of 1.08 eV and a direct band gap of 1.23 eV at the K point for VHTs. It clearly illustrates a type-II band alignment, which will result in the separation of electrons and holes. The band-decomposed charge density for VHTs is provided in Figure S5a,b, which reveals that the VBM and CBM are mainly constricted on Mo and W atoms, respectively. As
Importantly, the broken mirror symmetry is certain to facilitate the Rashba term due to the existence of the electric polarity. As summarized in Table 1, it is concluded that WSSe shows larger out-of-plane band splitting ((λc/λv)) and in-plane Rashba effects due to the heavy W atoms. It is known that vdW heterostructures play a crucial role in novel optoelectronic and photovoltaic applications, in light of their unique electronic and optical properties. In order to obtain the possible stacking pattern between MoSSe and WSSe, five VHTs of high symmetry are checked, as shown in Figure S4. After relaxation, the interlayer distance is in a range from 3.06 to 3.70 Å. The stability of these configurations can be estimated by the binding energy, which can be calculated according to the following equation: Eb = Et − EMoSSe − EWSSe, where Et, EMoSSe, and EWSSe represent the total energies of VHTs and isolated MoSSe and WSSe, respectively. The one with the lowest binding energy among the five configurations is the AB stacking, in which the chalcogen atoms of MoSSe are directly above the W atoms of WSSe and the Mo atoms are located above the hexagonal hole position. Additionally, the 5961
DOI: 10.1021/acs.jpclett.7b02841 J. Phys. Chem. Lett. 2017, 8, 5959−5965
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Figure 4. Side views of the 60° GBs in MoSSe with n = 2, 5, and 9 (a). Corresponding band structures of the MoSSe with 60° GBs as n = 2 (b), 5 (c), and 9 (d); contributions from edge and boundary Mo atoms are indicated by azure and peach dotted lines, respectively. The bigger the dot size, the more the orbitals contribute to the wave functions at various k points; the Fermi level is set to zero. Macroscopic average of the electrostatic potential energy (solid lines) along the direction perpendicular to the GBs for MoSSe with n = 2 (green), 5 (peach), and 9 (azure) and the planar average of the electrostatic potential energy (dashed line) along the direction perpendicular to the GBs for MoSSe with n = 9 (e).
which indicates the stability of the LHTs. In the case of n = 9, thermal stability by means of BOMD has been addressed, and the result is shown in Figure S6d, which reveals that the free energy oscillates slightly within a small range, further illustrating the stability. In addition, the electronegativity difference determines the strength connecting two constituents in LHTs. In Figure S7, the microscopy average of the electrostatic potential indicates the difference between MoSSe and WSSe, and the Bader charge analysis also indicates the in-plane electric field pointing from MoSSe to WSSe. It is interesting that LHTs display type-II band alignment, with the CBM and VBM localized on MoSSe and WSSe, respectively, as shown in Figure 3d. It is further confirmed by the charge densities of the CBM and VBM, as indicated in Figure S5e,f. As schematically plotted in Figure 3e, a ΔEc of 0.23 eV and a relatively small ΔEv of 0.11 eV due to the hybridization between WSSe and MoSSe can be derived. As a consequence of the type-II band alignment, excitons generated near interlines could be separated into opposite sides. In short, in both cases of VHTs and LHTs, electron−hole separation has important significance for the conversion efficiency of solar energy in application in photovoltaics. In addition, the photoresponses with different polarization angles (θ) are also discussed to address the optical absorption ability for LHTs. In Figure 3a, the schematic diagram for two probe devices is shown, in which the scattering region is illuminated by linearly polarized light. Upon illumination, the excited electron−hole pairs propagate from the left anode to right cathode. The light polarization angle (θ) is defined as the intersection angle with the y direction, in which y(e1) and z(e2) are set as the basis vector for the linearly polarized light. The absorption starts from 1.5 eV, and the photoresponse coefficient reaches 8 a20/photon (α0 stands for the Bohr radius), which is much higher than that for the S-doped black phosphorus and the graphene p−n junction.50,51 Furthermore, Figure 3g shows wide and intensive absorption in the visible light range. It should be pointed out that defects are likely to appear during the growth of TMDCs. Especially, 60° grain boundaries (GBs) derived from chalcogen defects have been extensively discovered in TMDCs such as MoS2 and MoSe2.52,53 In the present work, we discuss the electronic characters of the 60° GBs for the Janus MoSSe. In Figure 4a, the mostly observed 60° GBs in MoS2 and MoSe2 are presented for MoSSe. In our calculations, nanoribbon (NR) models are adopted with the length n = 2, 5, and 9 (n is defined as the number of Mo rows within half of the NRs), and the edges are terminated by Mo atoms. These NRs for 60° GBs display slight bending due to
shown in Figure S5c, the electron localization function (ELF) indicates that nearly no electrons are localized in the interlayer region, illustrating weak vdW interactions in the VHTs. In Figure 2d, the band alignment is schematically demonstrated to show the formation of interlayer excitons. In particular, excited electrons from WSSe migrate to MoSSe, while holes go oppositely owing to the band offset (ΔEc = 0.91 eV, ΔEv = 0.76 eV), and the electrons and holes can be held together by strong Coulomb interactions. It is worth noting that for VTHs of AB stacking it illustrates an obviously larger Rashba coefficient αR compared with isolated MoSSe and WSSe monolayers due to the enhanced vertical electric field, as shown in Table 1. As displayed in Figures 2e, the CBM at the K point is mainly composed of in-plane Mo dx2−y2 orbitals, while the VBM at the Γ point is determined by in-plane W dx2−y2 with the Rashba spin polarization. Interestingly, indirect−direct band gap transition can be found by adjusting the interlay distance. As shown in Figure S6a,b, the position of the VBM at the Γ point gradually decreases, while at the K point it increases, leading to a direct band gap at the K point when the interlayer distance is larger than 3.86 Å. In contrast to the weak vdW interactions within the VHTs, interfacial covalent bonds make LHTs hold robust electronic and optical properties. It is most likely to realize the LHTs with the formation of 1D interlines along the zigzag direction,41−44 and there is no intrinsic strain due to almost the same lattice parameters of the constituent MoSSe and WSSe. In our calculations, rectangular superlattice models are used to construct the LHTs. The length of LHTs n is defined as the number of Mo or W rows, and, for example, LHTs with n = 9 are shown in Figure 3a. In this case, the Brillouin zone for calculating the band structure is a rectangular one; see Figure 3b. It should be noted that the band gap of LHTs decreases as n increases. As shown in Figure 3c, the band gap decreases by 0.06 eV as n increases from 3 to 9, indicating decoupled interactions between two interlines. In Figure 3d, the band structure along the Γ−X direction is presented for n = 9 LHTs because the decisive features are along this direction. It can be found that a direct band gap of 1.53 eV exists at a k point located approximately two-thirds of the way from Γ to X. The formation energy Ef can be calculated according to Ef = (Et− ∑i Niμi)/N, with Et being the total energy of the LHTs, Ni and μi the number and chemical potential of the ith atoms (i = Mo, W, S, Se), respectively, and N the total number of atoms in the heterojunctions. The chemical potential of metal is defined as the energy of a single atom in the bulk phase, while the chemical potential of chalcogen is referred to as the energy of a single atom in the S8 (Se8) cluster. As n = 9, Ef is −6.5 eV, 5962
DOI: 10.1021/acs.jpclett.7b02841 J. Phys. Chem. Lett. 2017, 8, 5959−5965
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the difference in the bond length of Mo−S and Mo−Se. The corresponding band structures are presented in Figure 4b−d, with the electronic contributions from the edge and boundary Mo atoms indicated by different colors. As n = 2, strong interactions between the edge and boundary states can be seen, and the edge and boundary states turn to decouple when n increases to 5 and 9. As n increases from 5 to 9, therefore, the change in band structures is small. It is of importance that, as unraveled in band structures with dispersive bands crossing the Fermi level, 60° GBs are characterized in metallic materials. As shown in Figure S8 for the charge density distribution near the Fermi level for 60° GBs (n = 9), it further confirms the 1D metallic quantum wires. In this case, 1D electron or hole gas can probably be realized. It is of interest that as n increases from 5 to 9 energy bands of edge Mo atoms shift upward, while those of the boundary Mo atoms shift downward. In other words, electrons will migrate from edges to the GBs as the length increases. This phenomenon results from the polar discontinuity, which leads to the potential difference between the edge and GBs. In turn, the built-in in-plane electric field promotes electrons (holes) to migrate to the edge (GBs), giving rise to the 1D metallic wires within the instead semiconducting TMDCs.54 Further evidence for the electric field induced by the polar discontinuity is presented in Figure 4e, which displays the macroscopic average of the electrostatic potential energy ṽ(x). It is found that the slope of ṽ(x) reduces while the potential energy difference ΔV increases as the length increases, which explains the presence of polarization charge.55 The formation of the 1D metallic GBs in electronic heterostructures of Janus TMDCs indicates great potential in electronic applications. In conclusion, many-body effects (e−e and e−h interactions) have been identified in Janus MoSSe and WSSe monolayers, that is, quasiparticle corrections strongly change the band dispersion relationship and the excitonic effects dominate the optical response. VHTs and LHTs composed of Janus MoSSe and WSSe have been proposed in this work, bringing new properties and great potential in applications such as electronics, spintronics, and optoelectronics. In particular, both VHTs and LHTs illustrate type-II band alignment, which is beneficial to exciton dissociation and thus highly desirable for energy conversion. In the case of VTHs, larger Rashba spin polarization can be expected due to the enhanced out-of-plane electric dipole in comparison to isolated single layers. In addition, interlayer charge transfer and tunable electronic properties are addressed in VHTs. In the case of LHTs, a wide range of visible absorption and appreciable photoresponse intensity can be detected. It is interesting to find that 60° GBs in MoSSe show metallic properties, behaving as 1D metallic quantum wires and suggesting the formation of 1D electron or hole gas in such electronic heterostructures. These findings are of interest in exploring novel electronic, spintronic, and optoelectronic nanodevices.
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Letter
AUTHOR INFORMATION
Corresponding Authors
*E-mail:
[email protected] (W.W.). *E-mail:
[email protected] (Y.D.). ORCID
Ying Dai: 0000-0002-8587-6874 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work is supported by the National Natural Science Foundation of China (No. 11404187, 11374190, and 21333006), the Taishan Scholar Program of Shandong Province, and the Young Scholars Program of Shandong University (YSPSDU).
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.7b02841. Computational details and relevant electronic properties for MoSSe/WSSe and the vertical and lateral heterostructure (PDF) 5963
DOI: 10.1021/acs.jpclett.7b02841 J. Phys. Chem. Lett. 2017, 8, 5959−5965
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DOI: 10.1021/acs.jpclett.7b02841 J. Phys. Chem. Lett. 2017, 8, 5959−5965
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The Journal of Physical Chemistry Letters Dimensional Honeycomb Insulators. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 88, 161411.
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DOI: 10.1021/acs.jpclett.7b02841 J. Phys. Chem. Lett. 2017, 8, 5959−5965
