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Tuning Carrier Confinement in MoS/WS Lateral Heterostructure Jun Kang, Hasan Sahin, and Francois M. Peeters J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b00814 • Publication Date (Web): 07 Apr 2015 Downloaded from http://pubs.acs.org on April 11, 2015

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The Journal of Physical Chemistry

Tuning Carrier Confinement in MoS2/WS2 Lateral Heterostructure Jun Kang,∗ Hasan Sahin, and François M. Peeters Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerpen, Belgium E-mail: [email protected]

Phone: +32 (0)3 2653661. Fax: +32 (0)3 2653542

∗ To

whom correspondence should be addressed

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Abstract To determine and control the spatial confinement of charge carriers is of importance for nanoscale optoelectronic device applications. Using first-principles calculations, we investigate the tunability of band alignment and charge localization in lateral and combined lateralvertical heterostructures of MoS2 and WS2 . First, we show that a type-II to type-I band alignment transition takes place when tensile strain is applied on the WS2 region. This band alignment transition is a result of the different response of the band edge states with strain, and is caused by their different wavefunction characters. Then we show that the presence of the grain boundary introduces localized in-gap states. The boundary at the armchair interface significantly modifies the charge distribution of the VBM state, whereas in a heterostructure with tilt grain domains, both CBM and VBM are found to be localized around the grain boundary. We also found that the thickness of the constituents in a lateral heterostructure also determines how the electrons and holes are confined. Creating combined lateral-vertical heterostructures of MoS2 /WS2 provides another way of tuning the charge confinement. These results provide possible ways to tune the carrier confinement in MoS2 /WS2 heterostructures, which are interesting for its practical applications in the future.

Keywords: 2D heterostructure, strain, grain boundary, carrier localization

I. Introduction Recent advances of atomic-scale-thick crystal synthesis and characterization techniques have revealed the possibility of designing various nanoscale heterostructures with novel functionalities. 1,2 In an early study Haigh et al. showed the possibility of utilizing graphene-BN vertical heterostructure as an electronic device. 3 In addition, successful synthesis of flexible and transparent memory devices consisting entirely of stacked two-dimensional materials as graphene, BN and MoS2 were reported by Choi et al. 4 More recent works have also demonstrated that vertical and in-plane heterostructures of MoS2 and WS2 can be efficiently used for light detection and harvesting. 5–7


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Performance and functionality of these optoelectronic devices are critically dependent on the alignment of their energy bands. The most common band alignment between two different semiconductors are type-I or type-II. In type-I alignment, one of the materials has a higher valence band maximum (VBM) and a lower conduction band minimum (CBM) with respect to the other material. In type-II alignment, both the CBM and VBM of one material have lower energy than the corresponding band edge states of the other material. Different types of alignment result in different carrier confinement effects and hence they are useful for different applications. 8 Many studies have revealed that the natural band alignment between MoS2 and WS2 is type-II. 9,10 MoS2 and WS2 have very similar lattice constants, allowing to create lateral heterostructures without inducing structural defects. 5 Considering that the band structure of MoS2 and WS2 can be effectively tuned by strain, 11–14 one may raise the question whether it is possible to modify the band alignment between MoS2 and WS2 (e.g., from type-II to type-I) by strain. In addition, seeking for other methods to modify the carrier localization is also a topic of interest. Numerous studies have demonstrated that grain boundaries, 15,16 the size of the different constituents 17,18 and the interaction with other monolayers 19 can greatly affect the electronic properties of two-dimensional materials. In this paper we investigate the electronic properties of lateral heterostructures of MoS2 and WS2 . We show that a transition from type-II to type-I band alignment occurs when tensile strain is applied on the WS2 region. The effect of a grain boundary is also discussed. Moreover, by controlling the material thickness and constructing combined vertical-lateral heterojunctions, we are able to tune the carrier confinement in the heterostructure. The paper is organized as follows. Our computational method is described in Sec. II. Effect of applied strain on the electronic confinement is investigated in Sec. IIIA. The effect of grain boundary at the armchair interface is discussed in Sec. IIIB. Dependence of the electronic properties of lateral heterostructures with varying size are investigated in Sec. IIIC. Modification of the electron confinement characteristics via the creation of combined vertical-lateral heterostructures is investigated in Sec. IIID. Our conclusions are given in Sec. IV, with a discussion of different



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issues of the experimental realization of the proposed device.

II. Methodology We have used the Vienna ab initio simulation package (VASP) 20,21 to perform the calculations. The core-valence interaction is described by the frozen-core projector augmented wave (PAW) method. 22 For the exchange-correlation functional we used the generalized gradient approximation of Perdew-Burke-Ernzerhof (GGA-PBE). 23 The energy cutoff for the plane-wave expansion is set to 400 eV. Brillouin zone sampling is performed with Monkhorst-Pack special k-point meshes 24 including the Γ-point. For the hexagonal unit cell a grid of 12×12×1 is used, and the k-point grid scales with the supercell size. To avoid interaction between adjacent mono and bilayers a vacuum spacing of at least 10 Å is added to the lattice parameter c. Structure relaxation is stopped when the calculated Hellmann-Feynman force on each atom is smaller than 0.01 eV/Å. For the band alignment calculations of MoS2 /WS2 lateral heterostructures the vacuum level is set to zero. For an accurate estimation of the electronic band dispersions we included the spin-orbit interaction that leads to the hole band splitting at the vicinity of the K symmetry point. For the calculations of bilayers, the effect of van der Waals interaction is included by using the empirical correction scheme of Grimme. 25

III. Results Previous studies revealed that monolayer disulphide of molybdenum and tungsten have almost the same structural characteristics, as presented in Figure 1(a). Both structures belong to the point group D3h and the GGA-PBE optimized lattice parameter is 3.18 Å, which is used in the present work. As shown in Figure 1(b), both single layers of MoS2 and WS2 have a direct band gap at the K (K0 ) point. Although the overall electronic dispersion of both materials are similar, larger spin-orbit interaction in WS2 leads to a larger splitting in the vicinity of the K (K0 ) symmetry point. Although MoS2 and WS2 monolayers display similar characteristics in their electronic 4 ACS Paragon Plus Environment

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structure, designing various MoS2 /WS2 heterostructures may result in interesting consequences. In the following subsections we investigate how the electronic properties of such heterostructures can be modified by: i) applied strain, ii) presence of grain boundary, iii) varying size of the constituent and iv) forming combined lateral-vertical heterostructures.

IIIA. Application of Strain

Figure 1: (a) The lattice structure and the Brillouin zone of MoS2 and WS2 , with the most important symmetry points. (b) The band structure of monolayer MoS2 and WS2 with zero strain. (c) The energy of the highest valence band (VBM) at the Γ and K points, and the energy of the lowest conduction band (CBM) at the K point as a function of uniaxial tensile strain along the zigzag direction for monolayer MoS2 and WS2 . The results for the armchair direction are identical. The vacuum level is taken as the zero reference. First, we investigate the effect of applied strain on the electronic properties of single layers of MoS2 and WS2 . In Figure 1(c) we show the evolution of the valence and conduction band edges of MoS2 and WS2 with increasing uniaxial strain. We found that applied strain along the armchair and zigzag directions result in the same kind of modification in their electronic structure. As the strain increases, the VBM and CBM at K (K0 ) shift downwards (i.e., the energy decreases), whereas the VBM at Γ shifts upwards (the energy increases). Therefore, the direct band gap at the K point is turned into an indirect one at Γ-K. This behavior is consistent with the behavior obtained 5 ACS Paragon Plus Environment


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for bi-axially strained MoSe2 . 26 It is also seen that the strain-induced bandgap cross-over in WS2 occurs for higher strain values than MoS2 . These findings reveal how the applied strain affects the electronic properties of such transition-metal dichalcogenides. Next we focus on the band alignment of a MoS2 /WS2 heterostructure. The position of the band edge states determine how the bands are aligned in a heterostructure and therefore it is essential to explore how band alignment is modified by strain. In a strain-free MoS2 /WS2 lateral heterostructure the band alignment between MoS2 and WS2 is type-II. 9,10,27 As a result of the VBM and CBM energies of MoS2 , which are both lower than those of WS2 , the electrons (holes) will localize in the MoS2 (WS2 ) region. To simulate a lateral heterostructure we constructed a MoS2 /WS2 superlattice containing 10 rectangle unit cells of MoS2 and WS2 [(MoS2 )20 /(WS2 )20 ] with armchair interface, as depicted in Figure 2.

MoS2

WS2

MoS2

Figure 2: Perspective side view for the periodic lateral (in-plane) heterostructure of MoS2 /WS2 . Black, purple and yellow balls are used for W, Mo and S atoms, respectively. When tensile strain is applied to single layer WS2 , the lowest VBM energy of -5.76 eV is reached at the cross point, as shown in Figure 1(c). On the other hand, the VBM energy of unstrained MoS2 is -5.87 eV. So compared with unstrained MoS2 , the VBM of WS2 is always higher when strain is applied. However, the case of the CBM is different. When strain on WS2 is less than 4 %, its CBM is still higher than that of unstrained MoS2 . But when the strain exceeds 4%, the CBM of the strained WS2 becomes lower than that of unstrained MoS2 . In this case, the band alignment between unstrained MoS2 and strained WS2 becomes type-I. Thus a type-II to type-I band alignment transition can be achieved by applying tensile strain on the WS2 region. Although single layers of MoS2 and WS2 have qualitatively similar response to applied strain, the electronic properties of their heterostructures may exhibit interesting characteristics upon the 6 ACS Paragon Plus Environment

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application of inhomogeneous strain. In the following we apply such strain to the superlattice of (MoS2 )20 /(WS2 )20 shown in Figure 3. The inhomogeneous strain is induced by stretching the WS2 side along the zigzag direction while the MoS2 region is kept unstrained. It is worth to note that the above mentioned strain analysis reveals that one can obtain similar characteristics either by applying strain on MoS2 or by applying strain along the armchair direction. Therefore, the effect of the inhomogeneous strain on the electronic properties of the lateral heterostructure is independent of the constituent and direction. Another noteworthy issue is that the band alignment in Figure 1 is obtained by taking the vacuum level as reference. In a realistic heterostructure, the results can be affected by the interface dipole introduced by charge transfer between the constituents. The dipole will raise the electrostatic potential of one constituent with respect to the other. Using the core-level alignment method, 28 which takes account of the effect of such an interface dipole, we have compared the results for the band alignment in lateral and vertical heterostructures of MoS2 /WS2 , for the cases with and without interface dipole. We found that in a vertical MoS2 /WS2 heterostructure, the dipole effect is weak and raises the potential of MoS2 by only 36 meV. For lateral MoS2 /WS2 , the dipole effect varies with different strain on WS2 . For strain of 0, 2% and 4%, the MoS2 side is raised by 106 meV, 61 meV and 2 meV, respectively. For strain of 6% and 8%, the WS2 side is raised by 29 meV and 62 meV, respectively. Overall the influence of the interface dipole is not significant, and is of the order of several tens of meV. Evolution of the charge densities of CBM and VBM states of the whole superlattice with increasing strain is presented in Figure 3. The band alignment calculated by the core-level alignment method is also given. At zero strain the superlattice has a type-II alignment as indicated by the separation of CBM and VBM states. For 2% strain on WS2 , the type-II band alignment is preserved, as indicated by the electron-hole separation, because in this case the CBM of WS2 is still higher than that of MoS2 . When strain is increased to 4%, the CBM of WS2 becomes slightly lower (0.02 eV) than that of MoS2 . Since the difference is very small, the confinement effect is weak, and the CBM state is distributed over the whole heterostructure, with a slightly larger charge density on



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Figure 3: The charge density of CBM and VBM states in MoS2 /WS2 heterostructures with different uniaxial strain applied on WS2 along the zigzag direction. A fixed isovalue of 0.0002 e/Å3 for all the charge densities is used. The right panels illustrate the band alignment for different strain values, and the band alignment calculated by the core-level alignment method is also given. VBO stands for valence band offset and CBO for conduction band offset. WS2 . When strain is further increased to 6% or 8%, the confinement effect becomes strong, and the CBM state is completely localized within the WS2 region. In addition, the VBM state is also confined in the WS2 region, confirming the predicted type-I band alignment. In addition, it can be observed that the character of the VBM state changes when strain increases from 4% to 6%, resulting from the change of VBM from K to Γ as discussed above. Thus, Figure 3 confirms that the application of tensile strain on the WS2 region leads to a transition from type-II to type-I band alignment in MoS2 /WS2 lateral heterostructure. Understanding the calculated crossover between band alignment types that stems from the different responses of the band edge states at the Γ and the K(K0 ) requires a deeper investigation. To explore this point, we calculated the wavefunction distribution of the VBM@K, VBM@Γ and CBM@K using the SIESTA code. 29 We take MoS2 as an example, because WS2 has the same band edge characteristics. As shown in Figure 4 the wavefunction of the VBM and CBM at the K point has alternating positive (red) and negative (green) values parallel to the monolayer, and the nodal surfaces between the positive and negative values are perpendicular to the monolayer. The energy shift in the states can be attributed to changes in the distances between these nodal 8 ACS Paragon Plus Environment

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surfaces. 30 When tensile strain is applied, the lattice of the monolayer expands, and the distances between the nodal surfaces increases, resulting in a decrease in kinetic energy. Thus the energy of the VBM and CBM at the K point decreases with increasing tensile strain. On the other hand, the wavefunction of VBM at Γ does not change its sign parallel to the monolayer plane, whereas it has alternating sign perpendicular to the plane. So the nodal surfaces of the wavefunction are parallel to the sheet plane. When tensile strain is applied, due to Poisson’s effect the monolayer is compressed along the perpendicular direction. For instance, under a tensile strain of 6% along the zigzag direction, the perpendicular distance between two S atoms in MoS2 decreases by 0.06 Å compared to the equilibrium state. The compression along the perpendicular direction decreases the distances between the nodal surfaces, leading to a larger kinetic energy. As a result, the energy of the VBM at the Γ point increases with increasing tensile strain. Therefore, the different response of the band edge states at Γ and K, thus the band alignment transition, originates from the different character of the wavefunctions of these band edge states.

Figure 4: Wavefunctions of the VBM at the Γ and K points, and the CBM at the K point, for MoS2 . Red and green isosurfaces correspond to positive and negative values, respectively. The solid lines denote the nodal surfaces. The effect of tensile strain on the surfaces is indicated by arrows.

IIIB. Presence of Grain Boundary Recent experiments have revealed that during the synthesis of MoS2 monolayer grain boundaries are formed. 31,32 These findings suggest that grain boundaries may also exist in MoS2 /WS2 lateral heterostructures, and that they may localize at the contact region. Therefore, the investigation of the effects of their presence at the contact region of the lateral heterostructure is of importance. As 9 ACS Paragon Plus Environment


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an example, here we first study the grain boundary at the armchair interface, which consists of 4and 8-membered rings, as shown in Figure 5a. In this structure, the coordination of Mo and S atoms are not changed as compared with the defectless structure. Hence, there are no dangling bonds at the interface, resulting in a semiconducting band structure, as plotted in Figure 5a. Compared with the defectless system, the general feature of the band structure of the 4-8 boundary does not change much. The main difference is the introduction of in-gap states by the boundary. Very flat bands are observed inside the band gap for the 4-8 structure, indicating that these states are strongly localized. We have further calculated the charge density of the CBM, VBM and in-gap states for the 4-8 structure, and the results are shown in the right panel of Figure 5. As predicted, the in-gap states are strongly localized around the boundary, and similar behaviors are observed in MoS2 monolayer. 31 The CBM state is still confined in the MoS2 region, as in the defectless system, and the contribution from the grain boundary is small. However, the situation of VBM is very different. The grain boundary contributes a lot to the charge density of VBM, and the VBM is not confined in the WS2 region but distributed over the whole system. The different response of CBM and VBM may be associated with their different orbital characters. For MoS2 and WS2 , the CBM state has dz2 character and the VBM state has dx2 −y2 +dxy character. 9 The 4-8 boundary mainly changes the bond angle within the x-y plane between cations and anions, but is less affected along the z direction. As a result, the grain boundary influences the VBM much more than the CBM. For boundaries other than the 4-8 structures here, such as the 5-7 structure, 16 their effect to carrier confinement may also be different. In Figure 5b grain boundaries consisting of 5-7 structure are presented. In this case the domains of MoS2 and WS2 have a relative tilt of 22◦ . The band structure reveals that several in-gap states are introduced. These states, as well as the VBM state, are strongly localized around the boundary. In addition, the grain boundary also contributes a lot to the CBM state, which is different from the case of the 4-8 boundary. Overall, our findings suggest that the confinement effect in MoS2 /WS2 lateral structures can be significantly modified by grain boundaries.


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Figure 5: (a) The structure and energy bands for a MoS2 /WS2 lateral heterostructure with grain boundary at the armchair interface, and the charge density of the CBM, VBM and in-gap states. (b) The same as (a) but now for the 5-7 boundary. A fixed isovalue of 0.0002 e/Å3 is used for the charge density plots.

IIIC. Size Dependence Next we investigate the size-dependent variation of the quantum confinement of the electronic charge carriers in a MoS2 /WS2 lateral heterostructures. We have shown that in a strain-free heterostructure of (MoS2 )20 /(WS2 )20 electrons and holes are spatially localized in different domains, as whoen in Figure 6(a). resulting in lone electron-hole lifetimes. When the width of WS2 decreases to 5 [(MoS2 )20 /(WS2 )10 ], the width refers to the number of rectangle unit cells, a clear separation of electron and hole can still be seen from Figure 6(b), which is similar to the (MoS2 )20 /(WS2 )20 superlattice case. However, notice that the charge carriers become co-localized when further decreasing the WS2 width. When the width of WS2 decreases to 1 [(MoS2 )20 /(WS2 )2 ], which corresponds to the δ -doping case, the CBM and VBM states are extended over the whole superlattice, as presented in Figure 6(c). In this case, the thin WS2 stripe cannot prevent the interaction between neighboring MoS2 stripes and therefore the band edge states become extended over both materials. Therefore, the probability of radiative recombination in the heterostructure increases. It appears that while the (MoS2 )20 /(WS2 )20 superlattice provides clear electron-hole separation, the extent of carrier localization can be tuned by varying the width of the constituents



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of the superlattice.

Figure 6: The charge density of CBM and VBM states in MoS2 /WS2 heterostructures with different WS2 strip width. (a) for (MoS2 )20 /(WS2 )20 , (b) for (MoS2 )20 /(WS2 )10 and (c) for (MoS2 )20 /(WS2 )2 . A fixed isovalue of 0.0002 e/Å3 is used in all plots.

IIID. Combined Vertical-Lateral Heterostructures Except for strain and stripe width, constructing vertical van der Waals heterostructures using monolayers may also affect the confinement effects. 19 In Figure 7 we present the charge density of CBM and VBM for bilayers consisting of pure MoS2 (or WS2 ) and the MoS2 /WS2 lateral heterostructure with AB stacking (i.e., MoS2 /WS2 heterostructure on top of a MoS2 or WS2 monolayer), labeled as Mo-bilayer (for MoS2 ) and W-bilayer (for WS2 ) respectively. In a single monolayer MoS2 or WS2 , the CBM and VBM states are extended. In the Mo- and W-bilayers, The interlayer coupling of the monolayer with the MoS2 and WS2 region of the heterostructure is different, which may lead to confinement effects in the monolayer. From Figure 7 it can be seen that the VBM states are distributed in both the heterostructure layer and the MoS2 (or WS2 ) layer. Moreover, it is confined on the WS2 side of the heterostructure layer. The Mo-bilayer can be viewed as a lateral structure of the MoS2 bilayer and the MoS2 /WS2 bilayer, and the overall VBM distribution is determined by the alignment of the VBMs of the two constituents. For both MoS2 bilayer and MoS2 /WS2 12 ACS Paragon Plus Environment

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bilayer, the VBM states originates from the Γ point of the hexagonal Brillouin zone. 33 The interlayer coupling is strong for these states, and the VBM of the MoS2 /WS2 bilayer is higher than that of the MoS2 bilayer. Therefore, the VBM in the Mo-bilayer has both contributions from the heterostructure layer and the MoS2 layer, and is confined on the MoS2 /WS2 bilayer side. Similarly, the W-bilayer can be viewed as a heterostructure consisting of the WS2 bilayer and the MoS2 /WS2 bilayer. In this case, because the WS2 bilayer has a higher VBM than that of the MoS2 /WS2 bilayer, the VBM is confined on the WS2 bilayer side. Compared with the VBMs, the situation for the CBM states is different. The CBMs are not affected by the interlayer coupling. For the Mo-bilayer, the CBM is extended and distributed in the MoS2 layer. For the W-bilayer, the CBM is localized in the MoS2 region of the heterostructure layer. The reason for this is that the CBM states of the MoS2 bilayer, the WS2 bilayer and the MoS2 /WS2 bilayer are from the K point of the hexagonal Brillouin zone. 33 The interlayer coupling is negligible for these states. Compared with WS2 , MoS2 has a lower CBM. Therefore, in the bilayers, the CBM is localized in the MoS2 regions.

Figure 7: The charge density of CBM and VBM for bilayers consisting of (MoS2 )12 /(WS2 )12 lateral heterostructure and pure MoS2 (or WS2 ) with AB stacking. A fixed isovalue of 0.0002 e/Å3 is used.



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IV. Discussions and Conclusions Before ending we discuss about the experimental realization of the proposed strain engineering in Sec. IIIA. The possible realization scenarios for such strains can be as follows: (i) MoS2 on substrate A and WS2 on substrate B. Thus MoS2 and WS2 are strained by different substrates. Then they can be kept in contact. Therefore we have 2 different strained materials in contact. (ii) One of the structures is put on a substrate and the other one is free standing. This will provide an atomically sharp boundary for regions with different strains. From our calculations we found that a 4% strain was needed to achieve the type-II to type-I transition. Experiment has shown that MoS2 monolayer can sustain strain up to 11%. 34 Therefore, a 4% strain in the MoS2 /WS2 structure is realistic. Another issue is that whether or not it is possible to make the boundary between regions with different strains exactly at the MoS2 /WS2 interface. Therefore, we investigated the effect of a misalignment by localizing the strain boundary within the MoS2 domain or the WS2 domain. We did test calculations for both cases. We found that if the boundary of the different strain is not far from the MoS2 /WS2 interface, the type-I alignment is still maintained. This thus reduces the technical requirement to realize the proposed inhomogeneous strain exactly at the MoS2 /WS2 interface. Such a displacement between the strain and heterostructure interface will also be beneficial for the following issue. At the MoS2 /WS2 interface a grain boundary can be accumulated which would act as a weak spot where the heterostructure can be torn. In summary, we have studied the tunability of band alignment and charge localization in lateral and combined lateral-vertical heterostructures of MoS2 and WS2 . We found a type-II to type-I band alignment transition when tensile strain is applied on the WS2 region. For MoS2 and WS2 monolayers, with increasing tensile strain, the energy of VBM and CBM at the K (K0 ) point decreases, whereas the energy of the VBM at the Γ point increases. Therefore, when strain on WS2 exceeds a critical value, its CBM will become lower than that of MoS2 , leading to a band alignment transition. The different responses of the band edge states with strain originates from their different wavefunction characters. In addition, the presence of a grain boundary introduces localized 14 ACS Paragon Plus Environment

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in-gap states. The boundary at the armchair interface significantly modifies the charge distribution of the VBM state, whereas in a heterostructure with tilt grain domains, both CBM and VBM are found to be localized around the grain boundary. Moreover, the extent of the carrier localization can be tuned by varying the width of the constituents of the superlattice. In the case of a small stripe width, the confinement effect disappears. Finally, the distribution of the VBM states in combined vertical-lateral heterostructures is strongly modified. It distributes over both the MoS2 /WS2 layer and the MoS2 (or WS2 ) layer, and is confined on the WS2 side of the MoS2 /WS2 layer. Our results reveal that a broad variety of lateral heterostructures with different band alignments exhibit tunable carrier localization patterns that can be used to improve the performance of nanoscale optoelectronic devices.

Acknowledgement This work was supported by the Methusalem program of the Flemish government. H.S. is supported by a FWO Pegasus Marie Curie-long Fellowship and J.K. by a FWO Pegasus Marie Curieshort Fellowship.

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