Nanoscale Multilayer Transition-Metal Dichalcogenide

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Letter pubs.acs.org/JPCL

Nanoscale Multilayer Transition-Metal Dichalcogenide Heterostructures: Band Gap Modulation by Interfacial Strain and Spontaneous Polarization Liangzhi Kou,*,† Thomas Frauenheim,† and Changfeng Chen‡ †

Bremen Center for Computational Materials Science, University of Bremen, Am Falturm 1, 28359 Bremen, Germany Department of Physics and Astronomy and High Pressure Science and Engineering Center, University of Nevada, Las Vegas, Nevada 89154, United States

‡

S Supporting Information *

ABSTRACT: Using density functional theory calculations, we unveil intriguing electronic properties of nanoscale multilayer transition-metal dichalcogenide (TMDC) heterostructures, (MoX2)n(MoY2)m (X, Y = S, Se or Te). Our results show that the structural stability and electronic band structure of the TMDC heterostructures depend sensitively on the choice of constituent components and their relative thickness. In particular, the electronic band gap can be tuned over a wide range by the intrinsic mismatch strain and spontaneous electrical polarization at the interface of the heterostructures, which suggests desirable design strategies for TMDC-based devices with an easily adjustable band gap. These interfacial effects also make the electronic properties more susceptible to the influence of a bias electric field, which can induce sensitive and considerable changes in the band gap and even produce a semiconductor−metal transition at relatively low electric fields. Such effective electronic band gap engineering via a combination of internal (i.e., the composition and layer thickness) and external (i.e., a bias field) control makes the TMDC-based heterostructures promising candidates for applications in a variety of nanodevices. SECTION: Physical Processes in Nanomaterials and Nanostructures

S

some basic nanodevices, for example, MoS2 transistor and integrated circuits, have been fabricated based on them.10,11,15 Other applications, such as those in optoelectronics and photovoltaics, have been also proposed and investigated.16,17 For applications in nanodevices, modulating the electronic phase in a well-controlled manner is crucial. Alternative approaches of electronic modulation through an external force, field, or doping have been proposed in many nanostructures.18,19 Recent theoretical investigations reveal that applied strain can turn the direct band gap of singlelayer TMDCs to an indirect gap, even leading to a semiconductor−metal transition with a critical strain depending on the chalcogen atoms.20,21 In addition, an external electric field is found to be capable of modulating the band gap of bilayer TMDCs.22,23 These findings suggest that strain and an external electric field are effective and promising tools to control physical properties of low-dimensional nanomaterials. There exist, however, problems in practical implementation of these approaches; for instance, a large external strain up to 10% and a very high electric field of 10 V/nm are required to achieve the predicted semiconductor−metal transition, but these physical conditions are difficult to realize in practical

uccessful experimental isolation of two-dimensional graphene and their outstanding properties have spurred tremendous interests in the class of two-dimensional layered nanostructures; however, the absence of a band gap in pristine graphene considerably hinders its application in semiconducting nanodevices, such as FET.1,2 Besides various strategies to open the band gap of graphene,3−5 more and more attention is devoted to search for alternative layered materials. Among the most promising materials to replace graphene are layered transition-metal dichalcogenides (TMDCs) of TX2 type (T = Mo, W, Nb, Re, Ti, Ta, etc.; X = S, Se, Te, etc.),6−9 not only because monolayer TMDCs have similar layered structural characteristics but also because they show a wide range of electronic, optical, mechanical, chemical, and thermal properties that are comparable to or better than those of pristine graphene (high mobility, large on/off ratios: 1 × 108, and sizable band gaps).10,11 Unlike graphene, which is one atomic layer in thickness, a monolayer of TX2 is composed of three atomic layers, a transition-metal layer sandwiched between two chalcogen layers. The sandwich layer is tightly bound internally and interacts with neighboring sandwich layers only through weak van der Waals (vdWs) interaction.12 Thus, the fabrication of ultrathin layered TX2 is possible by micromechanical cleavage and exfoliation methods, such as the scotch tape method or lithium-based iteration.13,14 Recently, single- and multilayer TMDCs have been synthesized experimentally, while © XXXX American Chemical Society

Received: March 27, 2013 Accepted: May 6, 2013

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rechecked all of the findings here using the GGA methods as implemented in Vienna ab initio simulation package (VASP) code, where the vdWs interaction is included (see below for details). We first examined the lattice vectors and physical characteristics of monolayer MoX2 (X = S, Se, and Te). The optimized values of lattice constants after full relaxation are 3.12 (MoS2), 3.26 (MoSe2), and 3.49 Å (MoTe2), which increase from S to Se to Te because of the increasing radius of the chalcogen atoms. In calculations of the band structure of the unstrained monolayer MoX2, all of the investigated systems exhibit a direct band gap with the valence band maximum (VBM) and conduction band minimum (CBM) located at the same highsymmetry points (not shown here). The band gaps of monolayers MoS2, MoSe2, and MoTe2 were calculated to be 1.91, 1.66, and 0.97 eV, respectively. It is well-known that the semilocal functionals in DFT underestimate the band gap, but the data obtained here for monolayer TMDCs are very consistent with previously reported results.35 These results lend confidence to the reliability of our calculations in predicting general trends of the electroinc properties of the TMDCs studied in the present work. As the lattice mismatch between the two constituents in TMDC heterostructures may lead to stacking disorder or Moiré superstructures (see, e.g., the hybrid structure composed of graphene and boron nitride sheets reported by Sachs et al.),36 we first estimate and compare the strain and adhesive energies for the possible heterogeneous TMDC structures (MoS2@ MoSe2, MoSe2@MoTe2, and MoS2@MoTe2). For simplicity, the energies of the heterobilayers are studied as shown in Figure S1 (Supporting Information), which are obtained by stacking one monolayer TMDC above another. We notice that the strain energies (energy difference between the freestanding state and the strained state as in heterogeneous TMDC) of MoS2 (0.134 eV/unit-cell) and MoSe2 (0.196 eV/unit-cell) in MoS2@MoSe2 are relatively small because of the small lattice mismatch (∼2.2%), and the raised strain energies can be easily compensated for by the adhesive energy at the interface (−0.843 eV/unit-cell; energy difference between heterogeneous TMDC and two corresponding strained monolayer TMDCs). Thus, the surperlattice heterostructure composed of MoS2 and MoSe2 is stable. For the MoSe2@MoTe2, the strain energies are much larger than the values in MoS2@MoSe2 as a result of the increased mismatch strain between the two constituents, but the sum is still lower than that of the adhesive energy. However, the strain energies of MoS2@MoTe2 are greater than the adhesion energy by 0.326 eV/unit-cell. As a result, the lattice mismatch between MoS2 and MoTe2 will persist, and strain will be released by realizing different stacking configurations as in the Moiré structure. Below, we will systematically study the first two heterostructures (MoS2−MoSe2 and MoSe2−MoTe2) with superlattice structures, while one Moiré structure of heterobilayer MoS2−MoTe2 is constructed to investigate the stacking disorder on electronic properties. Note that the results of the heterobilayer MoS2−MoTe2 with Moiré structure will be discussed at the end of the Letter; they are referred to as MoS2−MoSe2 and MoSe2−MoTe2 cases. We show in Figure 1a and b the structural models used in the present work. The heterostructures are obtained by stacking one type of TMDC on top of another. The adjacent layers of a multilayer TMDC can be arranged in either AA or AB pattern. To determine the most stable stacking pattern, we have calculated and compared the total energies of AA and AB

situations.20−23 Placing the studied objects on a substrate to induce strain deformation due to lattice misfit is an alternative and commonly used strategy to achieve this goal. Previous investigations indicate that the band gap of Ge grown on a Si substrate was reduced by tensile strain.24 Ghosh et al. demonstrated that the structural, electrical, and optical properties of polycrystalline ZnO thin films on substrates were affected by substrate-induced strain.25 Meanwhile, heterostructures also possess electronic properties beyond those offered by individual constituent parts due to the interactions at the interfaces, and this strategy is often used to engineer the electronic properties of semiconductors. For example, the bilayer heterostructure composed of MoS2 and WS2 has a smaller band gap than the value of either constituent component, owing to the band offset.26 The band gap of graphene can be slightly opened when MoS2 and MoSe2 are absorbed on graphene, which could be synthesized experimentally by blending the MoSe2 monolayer with suspensions of graphene.27−29 A recent study of hybrid structures of MoS2/ Au and MoS2/Ti contacts indicates that the nature of the contacts plays an important role in determining the properties of the hybrids.30 All of these results suggest that the electronic properties of heterogeneous TMDCs may offer new functionalities that may play a pivotal role in their applications in nanodevices In this work, we explore the structural stability and electronic band structure of heterogeneous multilayer TMDC structures composed of (MoX2) and (MoY2) (X,Y = S, Se, or Te) by firstprinciple calculations. We find that the binding energies of TMDC heterostructures sensitively depend on the relative thickness of the constituent components, and they are smaller than the corresponding homogeneous TMDCs because of the elastic deformation induced by the lattice mismatch at their interface. The mismatch strain and spontaneous electrical polarization at the interface lead to a large variation of the electronic properties of the TMDC heterostructures that possess much reduced band gaps. Moreover, a bias electric field can effectively modulate the band gap of heterogeneous TMDCs, resulting in band gap reduction or enhancement depending on the magnitude and direction of the bias field and, eventually, leading to a semiconductor−metal transition. It is noted that a bubble between the layers will appear in the heterojunction when placing MoS2 on the MoTe2 surface due to the coexistence of different stacking patterns. We performed our calculations using the SIESTA package31 with the local density approximation (LDA) for the exchange− correlation XC) function.32 The double-ζ polarized numerical atomic orbital basis sets for all atoms are used in all of the reported calculations. All atoms are allowed to relax until the force on each atom is less than 0.02 eV/Å. The Brillouin integration is sampled with 10 × 10 × 1 Monkhorst meshes. An equivalent plane wave cutoff of 300 Ry is employed. Vacuum layers of at least 10 Å are chosen along the thickness direction. We note that while standard DFT calculations underestimate electronic band gaps, they are expected to capture the rearrangement of the electron density at interfaces that is important for predicting trends in electronic level alignment and band offsets.33 In general, the LDA-type functional does not describe accurately vdWs forces. However, it has been shown that the LDA/GGA is able to reproduce the interlayer spacing and the binding energy of layered chalcogenides.34 To correct for the vdWs interaction and confirm our results from the LDA calculations, we preformed additional calculations and 1731

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the lattice constant, it is easy to conclude that the MoX2 part will be under a tensile state with ε1 = x(aY/aX − 1), whereas the MoY2 part will be under a compressive state with ε2 = (1 − x)(aX/aY − 1). For instance, (MoS2)3(MoSe2)3 undergoes a 2.24% tensile strain for the MoS2 part and a −2.24% compressive strain for the MoSe2 part, while the corresponding values are 2.99 and −1.5% for (MoS2)2(MoSe2)4, respectively. Such stressed states have a significant impact on the structural properties, leading to the rise of the binding energy. To quantitatively characterize the interface mechanical properties, the binding energy per layer of the heterogeneous TMDCs is calculated as Eb =

(Etot − nE X − mE Y ) (m + n)

where Etot, EX, and EY are the energies of the composite, isolated MoX2 monoayer, and MoY2 monolayer, respectively. Figure 1d shows the evolution of the binding energy per layer as a function of the relative thickness and the compositional constituents. It is clear that the binding of the heterostructures is weaker than that of either of the corresponding constituent TMDCs because of the presence of the inner strain. The values reach the maximum when the layer numbers of the two constituents are equal to each other (n = m). Because of their larger differences in the lattice constants, the binding energies of (MoSe2)n(MoTe2)m are considerably lower than those of (MoS2)n(MoSe2)m. It is noted that the inner strain will not lead to structure breakage or plastic deformation because it is within the elastic limit.21 The strain induced by the lattice mismatch in heterogeneous TMDCs also leads to significant changes of their physical properties. Similar to the 2D TMDC alloys studied by Komsa et al.,37 the band gap varies almost continuously with changing composition (see Figure 2a). However, in stark contrast to the monotonously increasing/decreasing band gap from MoX2 to MoY2 in alloys, the values of all of the heterostructures are significantly reduced compared with those of the corresponding

Figure 1. Side view (a) and top view (b) of the structural models of (MoX2)m(MoY2)n, where X,Y = S, Se, or Te and m and n are layer numbers of each TMDC. The green shaded region indicates the unit cell used in our calculations. The cyan and yellow balls represent Mo and S atoms, respectively, and the red balls stand for Se or Te atoms. (c) The lattice constant as a function of relative thickness of heterogeneous TMDCs. (d) The binding energy of heterogeneous TMDCs, which is defined as Eb = [Etot − nEX − mEY]/(m + n).

stacking TMDCs. It is found that AA stacking of MoS2−MoSe2 (MoSe2−MoTe2) is higher in energy by 0.187 eV/unit (0.334 eV/unit) than the AB stacking pattern. Meanwhile, the AB stacking is preferred in both homogeneous bulk and multilayer TMDCs21 and recent investigations also showed that the main features of the electronic structure are quite insensitive to the stacking pattern;26 we thus will focus on the binding energies and electronic properties of AB-stacked TMDCs in the current work. The stacking pattern is held between adjacent layers in each TMDC (MoX2 or MoY2) and between the layers at the interface of the heterostructures (i.e., between MoX2 and MoY2; see Figure 1b). A heterostructure with m layers of MoX2 stacked on n layers of MoY2 is denoted as (MoX2)m(MoY2)n, where X,Y = S, Se, or Te. It has been shown8 that the band gap (indirect) of the multilayer TMDC is nearly converged to the corresponding bulk value when the layer number reaches six; we thus concentrate on the cases with n + m = 6 in this work. We first examine the structural characteristics and binding energies of the heterogeneous TMDCs. Results shown in Figure 1c reveal that the lattice constant of the TMDCs strongly depends on the relative thickness of the two constituents because the lattice mismatch at their interface increases monotonically as the portion of the heavier chalcogen TMDCs increases. From a phenomenological observation of the optimized values, the lattice constant of (MoX2)n(MoY2)m can be fitted with a linear interpolation and expressed according to the relative thickness and lattice constants of the corresponding constituents as a = (1 − x)aX + xaY, where x = m/(n + m). Because this lattice constant is between those of the two constituents (aX < a < aY; see Figure 1c), the heterostructures undergo an inner homogeneous biaxial deformation in both directions. From the relative change of

Figure 2. (a) Band gap of heterogeneous TMDCs and (b) band gap variation of monolayer TMDCs under strain. The vertical dashed lines indicate the optimize lattice constant and band gap at the strain free state. 1732

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Figure 3. RDOS of (a) (MoS2)3(MoSe2)3 and (b) (MoSe2)3(MoTe2)3. In the DOS figures, black lines are the total DOS, while red, blue, and green lines are the RDOS of MoS2, MoSe2, and MoTe2 constituents, respectively. (c,d) Layer-by-layer RDOS. The shaded areas are the projected density of states (PDOS) from TM atoms (blue) and chalcogen atoms (pink) of the interface layers. (e) Electron transfer when stacking three-layer MoS2 on three-layer MoSe2, where the isosurface value is 5 × 10−4 e/A3. (f) Electrostatic potential distribution of (MoS2)3(MoSe2)3.

A recent report on the MoS 2 −WS 2 heterojunction demonstrated that the significant band gap reduction in such a structure is attributed to the band offset (band edge states forming a type-II arrangement) with VBM and CBM states localized on opposite layers;26 this is, however, not the case for the TMDC heterostructures studied in the present work. To illustrate this point, we present in Figure 3a and b the resolved density of state (RDOS) for (MoS2)3(MoSe2)3 and (MoSe2)3(MoTe2)3. It is clear that the VBM state of the heterostructures is dominated by the state from the TX2 constitute, with X being lighter chalcogen atoms [e.g., MoS2 of (MoS2)3(MoSe2)3 or MoSe2 of (MoSe2)3(MoTe2)3], giving rise to the different spatial distributions of the energy levels near the Fermi level. This is caused by increased delocalization of the atomic orbits as one goes down the column of chalcogen atoms in the periodic table (from S to Te), which leads to reduced interaction between the transition-metal and chalcogen atoms. Meanwhile, the shifting of the energy levels in the stretched TX2 constitute (X being the lighter chalcogen atom) is more significant than the compressed TY2 constitute (Y being the heavier chalcogen atom); see Figure 2b. As a result, the gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of MoS2 in (MoS2)3(MoSe2)3 is 0.3 eV, but the corresponding value for MoSe2 is 0.48 eV; see Figure 3a. The same phenomena are also observed in other TMDC heterostructures (see Figure 3b and the Supporting Information). The different electronic properties of the constituents in heterogeneous TMDCs provide strong evidence for nonuniform strain distribution, thus suggesting a new type of band engineering. To facilitate a closer inspection, we have examined the layerby-layer RDOS of (MoS2)3(MoSe2)3, as shown in Figure 3c and d. For MoSe2, the energy levels of the VBM states of each layer increase from the top outmost surface to the center, but the CBM states remain nearly unchanged; see Figure 3c. In

homogeneous TMDCs. The band gaps of (MoS2)6−n(MoSe2)n and (MoSe2)6−n(MoTe2)n rely on the compositional portion of the TMDCs, and they generally decrease with increasing proportion of MoSe2 and MoTe2, respectively. The intriguing electronic modulation of the heterogeneous TMDCs is attributed to the inner strain deformation, which is similar to the situation in recently reported monolayer TMDCs.20,21 To confirm this scenario, we calculated the band gap evolution of monolayer MoS2, MoSe2, and MoTe2 under homogeneous biaxial strain deformation, as shown in Figure 2b. The lattice constant of each monolayer is changed from 3.12 to 3.49 Å, which is the range of deformation of the heterostructures, as indicated in Figure 1c. It is found that both the biaxial tensile and compressive strain can effectively tune the band gap, even leading to gap closure (semiconductor−metal transition) at a critical strain. For example, monolayer MoS2 becomes metallic when the lattice constant approaches that of MoTe2 and vice versa. The band gap of MoSe2 is also found to remarkably decease when the lattice constant approaches the value of MoS2 or MoTe2. A transition from direct to indirect gap is also observed when biaxial strain is applied, which is consistent with previous reports.20 The band gap modulations are not symmetrical relative to the strain-free state, indicating different response of the electronic band structure under tensile and compressive strain conditions. The obtained results from monolayer TMDCs explain the significant reductions of the band gap of heterostructure TMDCs. Taking (MoS2)3(MoSe2)3 as an example, the optimized lattice constant is ∼3.2 Å, and the constituents undergo ±2.24% biaxial strain for MoS2 and MoSe2, respectively. The band gap of monolayer MoS2 is decreased to ∼1.2 from 1.91 eV, whereas the value of monolayer MoSe2 at the strained state is slightly reduced to 1.6 eV (Figure 2b). Therefore, the band gap reduction of heterostructure (MoS2)3(MoSe2)3 can be regarded as the result of combined effects of band gap reduction of both constituents. 1733

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sharp contrast, the CBM states of each MoS2 layer decrease from the bottom outmost surface to the center, whereas the VBM states are pinned; see Figure 3d. As a result, the CBM state of (MoS2)3(MoSe2)3 is determined by the states from the center MoS2 layer (L4) at the interface. The VBM state of the heterostructure also originates from the surface MoS2 rather than MoSe2, owing to the larger electronegativity of S compared to that of Se, although the VBM state of the MoSe2 layer (L3) at the interface is significantly lifted upward. Distinct from the MoS2−WS2 heterobilayer,26 both the VBM and CBM states of the TMDC heterojunctions studied here are distributed in the same TMDC constituent. Although the electronic properties of heterogeneous TMDCs can be effectively tuned in a well-controlled manner, the hybridization between the two constituents is rather weak, as evidenced by the small amount of electron transfer (Δρ = ρtot − ρMoS2 − ρMoSe2); Figure 3e. The electron transfer only happens at the adjacent two layers of the interface, whereas other layers are almost completely unaffected. From a Mulliken population analysis, we find that the S atom of L4 MoS2 gains only 0.01 e, while the Se atom of L3 MoSe2 losses only 0.03 e, which also replicates closely the trend of electron affinity of the chalcogen atoms. The above analysis qualitatively explains our findings, but a more quantitative description is still desired. The band gaps of the heterogeneous TMDCs are generally smaller than the corresponding values of homogeneous TMDCs even taking into consideration the strain effects. This is due to an important factor that was not taken into account in earlier studies, namely, the spontaneous electrical polarization at the interface. Because of different electronegativity of the chalcogen atoms, the stacking of MoS2 on MoSe2 (or MoSe2 on MoTe2) gives rise to an electrostatic potential difference between the two constituents, leading to an spontaneous polarization at the interface, which generates a vertical electric field pointing from the TMDC layer with the heavier chalcogen atoms to that with the lighter ones (e.g., from MoSe2 to MoS2); see the electrostatic potential profile of (MoS2)3(MoSe2)3 in Figure 3f. Therefore, another reason for the band gap reduction in the heterogeneous TMDCs is a giant Stark effect induced by the vertical intrinsic electric field. This conclusion is also corroborated by the asymmetrical band modulations under a vertical electric field (see below) and the results of recent studies reported that the band gap of bilayer and multilayer TMDCs can be effectively modulated, even achieving a semiconductor−metal transition at a high critical electric field of about 3 V/nm.22 To further explore the intrinsic electric field induced by spontaneous polarization and examine its effect on the electronic properties of the TMDC heterostructures, we applied a vertical external (bias) electric field across the TMDCs. As shown in Figure 4, the band gap of the heterostructures is almost continuously tuned under the external vertical electric field because of the giant Stark effect, eventually achieving a semiconductor−metal transition at critical fields. However, the response of the electronic properties to positive and negative fields (see the direction defined in the inset) is distinct because of the asymmetrical structures along the thickness direction and the intrinsic polarization. Under a positive electric field, the band gap of (MoS2)3(MoSe2)3 [(MoSe2)3(MoTe2)3] continuously decreases with increasing applied electric field, eventually achieving a semiconductor−metal transition at ∼0.1 V/Å

Figure 4. Band gap of TMDC heterostructures as a function of external vertical electric field. The inset indicates the positive direction of the electric field, pointing from MoSe2 to MoS2 (MoTe2 to MoSe2).

(0.05 V/Å), which shares the same qualitative trend with the cases of corresponding bilayer structures.22,23 However, the critical field here is much smaller than that of bilayer MoS2 (0.3 V/ Å)22 or armchair MoS2 ribbons (1 V/Å)23 due to the presence of the intrinsic spontaneous polarization, which has a superimposing effect with the external field. This suggests that the heterogeneous TMDCs are more susceptible to the influence of an external electric field and thus more responsive to tuning by a bias field. In contrast, a different response is observed when a negative electric field is applied. Opposite to the linear decrease seen under a positive field, the band gap first increases until −0.05 V/Å, reaching up to 0.45 eV (0.28 eV) for (MoS2)3(MoSe2)3 [(MoSe2)3(MoTe2)3], but then, it decreases linearly and finally turns metallic at ∼0.15 V/Å (−0.1 V/Å). The initial increase of the band gap results from the gradual neutralization of the intrinsic polarization of heterogeneous TMDCs under a negative electric field. One noticeable feature here is that the critical electric field for the semiconductor− metal transition in (MoSe2)3(MoTe2)3 is obviously lower than that of (MoS2)3(MoSe2)3. Besides the smaller band gap, this is due to the increasingly diffuse nature of the valence pz orbitals from S to Te, which facilitates more charge transfer from the chalcogen to Mo atoms at the same electric field. Because the lattice mismatch between MoS2 and MoTe2 is relatively large, which makes it hard to form a structure such as MoS2−MoSe2 or MoSe2−MoTe2, we thus construct a very large heterogeneous supercell constituting a 10 × 10 MoS2 single layer on a 9 × 9 MoTe2 single layer; both of them keep the lattice constant to their experimental values (3.166 and 3.52 Å) without any lattice deformation. After a full structural relaxation, we found that there is still strain existing in the supercell although the lattice constants of the two constituents remain at their bulk values. The two TMDC layers form a Moiré structure with stacking disorder (see Figure 5), just like the case of the graphene/BN heterogeneous sheet.36 From the relaxed structure, one notices that the AA and AB stacking patterns coexist. Because the interlayer distance of the AA stacking is larger than that of the AB stacking cases,21 a bubble around the AA stacking region appears with a height of about 0.5 Å. The bubble will stretch the surrounding atoms and create a local strain deformation, which not only increases the binding energies to −0.188 eV/unit but also reduces the band gap to 0.78 eV (the gaps are 1.76 and 1.25 eV for monolayer MoS2 and MoTe2, respectively). These results suggest that similar phenomena can be expected when constructing such a supercell model with MoS2 and MoSe2 (MoSe2 and MoTe2), although they are not calculated here because of computational constraints. The present results indicate that strain has a non1734

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge useful discussions with Tim Wehling. L.K. acknowledges the financial support by the Alexander von Humboldt Foundation of Germany. C.F.C. was supported by the Department of Energy through Cooperative Agreement DE-FC52-06NA26274.

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Figure 5. Top view (left top) and side view (left bottom) of a supercell placing a 10 × 10 MoS2 on a 9 × 9 MoTe2 layer. The band structure of the heterojunction is also presented (right panel).

negligible effect in determining the structural and electronic properties. In concluding this section, a final remark about the predicted band gaps and critical fields for the semiconductor−metal transition is in order. With respect to the band gaps, it is wellknown that semilocal XC functionals typically underestimate experimental band gaps. To confirm the obtained trends from our LDA (using SIESTA) calculations, we additionally performed calculations for all of the studied heterogeneous TMDCs using the GGA-PBE method as implemented in VASP, where the vdWs interaction is introduced by adding a semiempirical dispersion potential to the conventional KS DFT energy (through a pairwise force field following Grimme’s DFT-D2 method). All of the GGA results, including the binding energies, band gaps, and their variations under vertical applied electric fields, are presented in the Supporting Information. Compared with the LDA findings here, we find that the trends from using different codes and different methods are almost the same, although the predicted magnitudes are different quantitatively. Thus, it can be concluded that the calculations above have captured the main underlying physics of the heterogeneous TMDCs. In summary, we have investigated the structural stability and electronic properties of heterogeneous TMDCs composed of MoX2 and MoY2 (X,Y = S, Se, or Te). Our results show that the intrinsic strain induced by the lattice mismatch and a spontaneous electric polarization at the interface of the heterostructures have a significant impact on the structural and electronic properties. The band gaps of the heterogeneous TMDCs are tunable over a wide range below those of the homogeneous TMDC structures, and a semiconductor−metal transition is achieved at much reduced critical fields compared to the values needed for the corresponding homogeneous TMDC structures. The intriguing electronic modulation in heterogeneous TMDCs suggests promising new directions for design and fabrication of novel electronic and photonic devices.

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REFERENCES

(1) Castro Neto, A. H.; Guinea, F.; Peres, N. M. R.; Novoselov, K. S.; Geim, A. K. The Electronic Properties of Graphene. Rev. Mod. Phys. 2009, 81, 109−162. (2) Rao, C. N. R.; Sood, A. K.; Subrahmanyam, K. S.; Govindaraj, A. Graphene: The New Two-Dimensional Nanomaterial. Angew. Chem., Int. Ed. 2009, 48, 7752−7777. (3) Cocco, G.; Cadelano, E.; Colombo, L. Gap Opening in Graphene by Shear Strain. Phys. Rev. B 2010, 81, 241412(R). (4) Castro, E. V.; Novoselov, K. S.; Morozov, S. V.; Peres, N. M. R.; Lopes dos Santos, J. M. B.; Nilsson, J.; Guinea, F.; Geim, A. K.; Castro Neto, A. H. Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect. Phys. Rev. Lett. 2007, 99, 216802. (5) Denis, P. A. Band Gap Opening of Monolayer and Bilayer Graphene Doped with Aluminium, Silicon, Phosphorus, And Sulfur. Chem. Phys. Lett. 2010, 492, 251−257. (6) 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. (7) Splendiani, A.; Sun, L.; Zhang, Y. B.; Li, T. S.; Kim, J.; Chim, C. Y.; Galli, G.; Wang, F. Emerging Photoluminescence in Monolayer MoS2. Nano Lett. 2010, 10, 1271−1275. (8) Gutierrez, H. R.; Perea-Lopez, N.; Elias, A. L.; Berkdemir, A.; Wang, B.; Lv, R.; Lopez-Urias, F.; Crespi, V. H.; Terrones, H.; Terrones, M. Extraordinary Room-Temperature Photoluminescence in WS2 Triangular Monolayers. Nano Lett. 2012, DOI: 10.1021/ nl3026357. (9) Kumar, A.; Ahluwalia, P. K. Electronic Structure of Transition Metal Dichalcogenides Monolayers 1H−MX2 (M = Mo, W; X = S, Se, Te) from Ab-Initio Theory: New Direct Band Gap Semiconductors. Eur. Phys. J. B 2012, 85, 186. (10) Radisavljevic, B.; Radenovic, A.; Brivio, J.; Giacometti, V.; Kis, A. Single-Layer MoS2 Transistors. Nat. Nanotechnol. 2011, 6, 147−150. (11) Yoon, Y.; Ganapathi, K.; Salahuddin, S. How Good Can Monolayer MoS2 Transistors Be? Nano Lett 2011, 11, 3768−3773. (12) Verble, J. L.; Wietling, T. J.; Reed, P. R. Rigid-Layer Lattice Vibrations and Van der Waals Bonding in Hexagonal MoS2. Solid State Commun. 1972, 11, 941−944. (13) Novoselov, K. S.; Jiang, D.; Schedin, F.; Booth, T. J.; Khotkevich, V. V.; Morozov, S. V.; Geim, A. K. Two-Dimensional Atomic Crystals. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 10451−10453. (14) Coleman, J. N.; Lotya, M.; O’Neill, A.; Bergin, S. D.; King, P. J.; Khan, U.; Young, K.; Gaucher, A.; De, S.; Smith, R. J. TwoDimensional Nanosheets Produced by Liquid Exfoliation of Layered Materials. Science 2011, 331, 568−571. (15) Radisavljevic, B.; Whitwick, M. B.; Kis, A. Integrated Circuits and Logic Operations Based on Single-Layer MoS2. ACS Nano 2011, 5, 9934−9938. (16) Eda, G.; et al. Photoluminescence from Chemically Exfoliated MoS2. Nano Lett. 2011, 11, 5111−5116. (17) Shanmugam, M.; Bansal, T.; Durcan, C. A.; Yu, B. Molybdenum Disulphide/Titanium Dioxide Nanocomposite-Poly-3-hexylthiophene Bulk Heterojunction Solar Cell. Appl. Phys. Lett. 2012, 100, 153901− 153904.

ASSOCIATED CONTENT

S Supporting Information *

Adhesive/strain energies of heterogeneous TMDCs, resolved DOS of all (MoX2)n(MoY2)m (X,Y = S, Se, or Te), and results from VASP calculations. This material is available free of charge via the Internet at http://pubs.acs.org. 1735

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(18) Son, Y.; Cohen, M. L.; Louie, S. G. Electric Field Effects on Spin Transport in Defective Metallic Carbon Nanotubes. Nano Lett. 2007, 7, 3518−3522. (19) Kou, L.; Tang, C.; Guo, W.; Chen, C. Tunable Magnetism in Strained Graphene with Topological Line Defect. ACS Nano 2011, 5, 1012−1017. (20) Scalise, E.; Houssa, M.; Pourtois, G.; Afanas’ev, V.; Stesmans, A. Strain-Induced Semiconductor to Metal Transition in the TwoDimensional Honeycomb Structure of MoS2. Nano Res. 2012, 5, 43− 48. (21) Bhattacharyya, S.; Singh, A. K. Semiconductor−Metal Transition in Semiconducting Bilayer Sheets of Transition-Metal Dichalcogenides. Phys. Rev. B 2012, 86, 075454. (22) Ramasubramaniam, A.; Naveh, D.; Towe, E. Tunable Band Gaps in Bilayer Transition-Metal Dichalcogenides. Phys. Rev. B 2011, 84, 205325. (23) Dolui, K.; Pemmaraju, C. D.; Sanvito, S. Electric Field Effects on Armchair MoS2 Nanoribbons. ACS Nano 2012, 6, 4823−4834. (24) Ishikawa, Y.; Wada, K.; Cannon, D. D.; Liu, J.; Luan, H.-C.; Kimerling, L. C. Strain-Induced Band Gap Shrinkage in Ge Grown on Si Substrate. Appl. Phys. Lett. 2003, 82, 2044. (25) Ghosh, R.; Basak, D.; Fujihara, S. Effect of Substrate-Induced Strain on the Structural, Electrical, And Optical Properties of Polycrystalline ZnO Thin Films. J. Appl. Phys. 2004, 96, 2689. (26) Kośmider, K.; Fernández-Rossier, J. Electronic Properties of the MoS2−WS2 Heterojunction. Phys. Rev. B 2013, 87, 075451. (27) Shi, Y.; Zhou, W.; Lu, A.-Y.; Fang, W.; Lee, Y.-H.; Hsu, A. L.; Kim, S. M.; Kim, K. K.; Yang, H. Y.; Li, L.-J.; Idrobo, J.-C.; Kong, J. van der Waals Epitaxy of MoS2 Layers Using Graphene As Growth Templates. Nano Lett. 2012, 12, 2784−2791. (28) Ma, Y.; Dai, Y.; Wei, W.; Niu, C.; Huang, B. First-Principles Study of the Graphene@MoSe2 Heterobilayers. J. Phys. Chem. C 2011, 115, 20237−20241. (29) Ma, Y.; Dai, Y.; Guo, M.; Niu, C.; Huang, B. Graphene Adhesion on MoS2 Monolayer: An Ab Initio Study. Nanoscale 2011, 3, 3883. (30) Popov, I.; Seifert, G.; Tománek, D. Designing Electrical Contacts to MoS2 Monolayers: A Computational Study. Phys. Rev. Lett. 2012, 108, 156802. (31) Soler, J. M.; Artacho, E.; Gale, J. D.; García, A.; Junquera, J.; Ordejón, P.; Sánchez-Portal, D. The SIESTA Method for Ab Initio Order-N Materials Simulation. J. Phys.: Condens. Matter 2002, 14, 2745−2779. (32) Ceperley, D. M.; Alder, B. J. Ground State of the Electron Gas by a Stochastic Method. Phys. Rev. Lett. 1980, 45, 566. (33) Wu, Z.; Neaton, J. B.; Grossman, J. C. Charge Separation via Strain in Silicon Nanowires. Nano Lett 2009, 9, 2418−2422. (34) Björkman, T.; Gulans, A.; Krasheninnikov, A. V.; Nieminen, R. M. Van der Waals Bonding in Layered Compounds from Advanced Density-Functional First-Principles Calculations. Phys. Rev. Lett. 2012, 108, 235502. (35) Johari, P.; Shenoy, V. B. Tuning the Electronic Properties of Semiconducting Transition Metal Dichalcogenides by Applying Mechanical Strains. ACS Nano 2012, 6, 5449−5456. (36) Sachs, B.; Wehling, T. O.; Katsnelson, M. I.; Lichtenstein, A. I. Adhesion and Electronic Structure of Graphene on Hexagonal Boron Nitride Substrates. Phys. Rev. B 2011, 84, 195414. (37) Komsa, H.; Krasheninnikov, A. V. Two-Dimensional Transition Metal Dichalcogenide Alloys: Stability and Electronic Properties. J. Phys. Chem. Lett. 2012, 3, 3652−3656.

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