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Complete Separation of Carriers in the GeS/SnS Lateral Heterostructure by Uniaxial Tensile Strain Lei Peng, Chan Wang, Qi Qian, Cheng Bi, Sufan Wang, and Yucheng Huang ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b11613 • Publication Date (Web): 30 Oct 2017 Downloaded from http://pubs.acs.org on November 2, 2017

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ACS Applied Materials & Interfaces

Complete Separation of Carriers in the GeS/SnS Lateral Heterostructure by Uniaxial Tensile Strain Lei Peng, Chan Wang, Qi Qian, Cheng Bi, Sufan Wang, Yucheng Huang* Center for Nano Science and Technology, College of Chemistry and Material Science, The Key Laboratory of Functional Molecular Solids, Ministry of Education, Anhui Laboratory of Molecule-Based Materials, Anhui Normal University, Wuhu, 241000, Peoples’ Republic of China KEYWORDS: GeS/SnS; lateral heterostructure; density functional theory; tensile strain; type II alignment; direct-to-indirect bandgap crossover

ABSTRACT The strategy of forming lateral heterostructures by stitching various twodimensional materials overcomes the limitations due to the restricted properties of singlecomponent materials. In this work, by using first-principles calculations, the electronic properties of GeS/SnS lateral heterostructures, together with the effect of strain, were systematically investigated. The results showed that with increasing tensile strain along the zigzag direction, the bandgap displays an extremely interesting variation: it linearly increases in the beginning until 2.4% strain (region I), then remains nearly constant until 5.7% (region II), and finally linearly decreases within the tensile limit (region III). Meanwhile, the electronic properties successively

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change from quasi-type II alignment to direct bandgap to type II alignment with complete carrier separation. Analysis of the densities of states and partial charge densities indicate that the bandgap increase in region I is due to the change in the orbital contributions to the states of the conduction band minimum (CBM) from Sn-pz to Sn-px, while the bandgap decrease in region III is caused by an increasingly loose distribution of anti-bonding electrons at the CBM. Moreover, it was found that the changes in the orbital constituents from Sn-pz to Sn-px in the CBM and from S-px to S-py in the valence band maximum (VBM) are responsible for the indirect-direct and direct-indirect bandgap crossovers at the junctions of regions I and II and regions II and III, respectively. Finally, through calculations of the carrier concentrations on the basis of deformation potential theory, electrons and holes are demonstrated to be largely separated with the enhancement of strain, and the predicted electron mobilities in the armchair direction at 7% strain are as high as 5860-11220 cm2 V-1 s-1. We believe our work may lead to potential applications for GeS-SnS heterostructures in electronics, optoelectronics and straintronics.


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1. Introduction Since the advent of graphene,1 the interest of scientific communities in two-dimensional (2D) materials has never faded.2-3 Some renowned 2D materials, such as hexagonal boron nitride (hBN),4 transition metal dichalcogenides (TMDs),5 and black phosphorus (BP)6, as well as BPisoelectronic group-VA 2D sheets, including arsenene, antimonene, bismuthene and antimonene oxide7-11, which have been experimentally fabricated or theoretically predicted, are found to present distinctive electronic and photoelectric properties for nanoscale applications.12 However, single-material systems with restricted properties limit their further development and applications. A typical representative is the graphene with a Dirac cone in its band structure.1 In recent years, researchers have begun to shift their focus from monocomponent systems to hybrid systems that are composed of at least two types of different chemical constituents. Burgeoning experimental and theoretical studies regarding 2D heterostructures have been reported.13-15 Due to the formation of heterojunctions and the reduction in dimension, 2D heterostructures often show better physical and chemical properties than their separate counterparts, which greatly extends their potential applications in many fields.16 Generally, 2D heterostructures based on different components can be divided into three types: vertical, lateral or in-plane and hierarchical heterostructures.17-18 Note that other types of heterostructures, which are based on partially engineering the crystal phase in a 2D nanosheet or the generation of multiple phase patterns in 2D noble metal nanostructures, have also received considerable attention recently.19 The vertical heterostructure, which is also known as the van der Waals (vdW) heterostructure, is formed by stacking monolayers of multiple 2D materials vertically layer by layer, with weak layered vdW interactions. However, the interface of the inplane heterostructures is actually one-dimensional (1D), which is a result of the epitaxial growth


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of one kind of 2D material at the boundary of another. In hierarchical heterostructures, it is formed by a vertical growth of aligned ultrathin 2D nanosheet arrays on another ultrathin 2D nanomaterial substrate. The

vdW

heterojunctions,

such

as

graphene/h-BN,20

graphene/MoS2,21

and

C3N4/MoS2 heterojunctions22, have the advantage of integrating the excellent properties of the stacked 2D materials by vdW interactions. However, these heterojunctions also have the inherent disadvantage that the electronic and optical properties are very sensitive to the interlayer distance and twist angle.23 In addition, the possible presence of contaminants between the two monolayers also affects their performance in practical applications.24 By contrast, the lateral heterostructures have the advantages of simpler band alignment and more stable structure due to their unique inplane geometry, together with the covalent bonding interface.7,

25

In particular, the

heterojunctions formed by stitching different single-layered TMDs have demonstrated distinctive electronic and optical properties.26 In experiments, various in-plane 2D TMDs heterostructures, such as MoS2/WS2,27-28 MoS2/MoSe2,29 MoS2/WSe225 and MoSe2/WSe230, have been synthesized by a one-step or modified two-step chemical vapor deposition (CVD) method. Theoretically, a large number of studies based on density functional theory (DFT) calculations have been carried out13,

24, 31-33

, which are devoted to predicting their properties and providing theoretical

support/guidance for the relevant experimental work. It is suggested that a desirable type II semiconductor, which facilitates efficient electron–hole separation for light detection and harvesting, can be achieved by various modulation means for many stitched TMD heterostructures with an original type I alignment. In particular, strain is widely used to effectively tune the electronic properties. For example, Kang et al. and Dai et al. have explored in depth the effects of strain on the electronic properties of lateral heterostructures formed by


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TMDs.24, 33 Transition of the band alignment from type II to I for the MoS2/WS2 heterostructure and direct–indirect bandgap crossover for the MoS2/WSe2 heterostructure are observed when the applied strain changes from lattice contraction to dilation. Recently, group IVA monochalcogenides (MXs), including GeS, SnS, GeSe and SnSe, which are isostructural to the black phase of phosphorene, have attracted intense attention because of their high stability, earth abundance and low toxicity.34-36 Based on the successful fabrication of their ultrathin nanosheets and the advanced synthetic technology of heterostructures,34, 37-38 the synthesis of lateral heterostructures constructed by the MXs should be feasible. Until now, little was known about the electronic properties of the in-plane heterostructures coupled by these phosphorene-like materials. Very recently, our group predicted that GeS and SnS, with the same layers, can form a type II alignment if a van der Walls heterostucture is formed.39 Nevertheless, it can also be anticipated that a lateral heterostructure will be preferentially formed because GeS and SnS have comparable lattice parameters, especially along the armchair direction. The covalent bonding interface on the lateral heterostructure may endow it with novel physical properties. In this work, by building GeS-SnS lateral heterostructures, the effects of strain on the electronic properties are systematically studied. A very interesting transition from type II-like alignment to direct bandgap to type II alignment is observed with the increase in tensile strain along the zigzag direction. We believe that our paper may lead to a potential application for GeSSnS heterostructures in straintronics.

2. COMPUTATIONAL METHODS


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First-principles calculations were performed through the projector augmented wave (PAW)40 method by using the Vienna ab initio simulation package (VASP).41 The generalized gradient approximation (GGA) was used for the exchange-correlation functional with the Perdew–Burke– Ernzerhof (PBE) parameterization.42-43 The cutoff energy for the plane-wave basis was set to 450 eV. The convergence thresholds were set to 10–5 eV and 0.02 eV/Å for energy and force, respectively. A vacuum height of 15 Å in the y direction was adopted to avoid the interaction between two periodically repeated units. The Brillouin zone was represented by a Monkhorst– Pack special k-point mesh of size 5 × 1 × 3 for geometry optimizations, while a larger grid of size 7 × 1 × 5 was used for band structure computations.

3. Results and Discussion 3.1. Width-dependent Stabilities and Electronic Properties The model of the GeS/SnS heterostructure was constructed by stitching two semi-infinite monolayers along the armchair direction. The choice of heterointerface was based on the results of our previous study39 that the mismatch between two monolayers in the armchair direction (4.40 Å for GeS vs. 4.24 Å for SnS) is smaller than that in the zigzag direction (3.68 Å for GeS vs. 3.99 Å for SnS). A smaller lattice mismatch will benefit the formation of heterojunctions thermodynamically with minimum structural defects. Figure 1a schematically illustrates the typical lattice structure of the GeS/SnS heterostructure. To examine the stability of the heterojunction and avoid size-dependent electronic properties,44 the electronic properties of heterojunctions with different widths were first studied. For ease of description, the GeS/SnS heterostructures are denoted as (GeS)n/(SnS)n, where the index n indicates the number of


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different building blocks along the zigzag direction (see the label in Figure 1a). As shown in Figure 1b, the heats of formation (HF) and bandgap values of heterojunctions with various widths were calculated. Here, HF is used to characterize the thermodynamic stability. It is defined as the energy cost per area of the supercell: HF = (EH − EGeS − ESnS)/(Z × LH), where EH is the total energy of the heterostructure; EGeS and ESnS are the total energies of the GeS and SnS monolayers, respectively; and Z and LH are width of the supercell along the zigzag direction and the periodic length along the armchair direction, respectively. It is clearly shown in the figure that HF and the bandgap decrease monotonically as the width increases, which is in qualitative agreement with a very recent theoretical study of MX lateral heterostructures.45 All the values of HF are quite small, which indicates that it is likely possible to synthesize (GeS)n/(SnS)n in the laboratory. Moreover, the decreasing tendency of HF gradually slows when the width exceeds 23.25 Å (for (GeS)3/(SnS)3). The corresponding band structures show that (GeS)n/(SnS)n maintains the semiconducting characteristics with an indirect bandgap, as indicated in Supporting Information, Figure S1. Similar to the variation trend of HF, the bandgap converges when the width increases past a certain value (38.75 Å for (GeS)5/(SnS)5). Taking into consideration of two factors of HF and bandgap, the (GeS)5/(SnS)5 was chosen as a prototype for the following electronic property calculations. Note that the chosen width of (GeS)5/(SnS)5 may be much smaller than its characteristic junction width (W), for example, ~30 nm for the MoS2/WS2 interface predicted by Zhang et al,46 where the large W heavily decays the dipole induced by the accumulated charge near the interline. However, from our calculations, the heterostructure bandgap of (GeS)5/(SnS)5 was found to be 1.41 eV, which is close to the intrinsic bandgap of 1.26 eV derived from individual component, i.e., Anderson limit, at the PBE level of


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theory.45 Such a little difference means both the finite quantum confinement of each semiconductor domain and electrostatic potential due to interfacial dipole are largely minimized. The heterointerface is still covalently bonded after geometry relaxation. This covalent connection will favor the stability and epitaxial quality of (GeS)n/(SnS)n. To verify this, the plane-averaged electron density difference ∆ρ(z) along the zigzag direction and the isosurface of the electron density difference are illustrated in Figure 1c. Here, the plane-averaged electron density difference is used to illustrate the transfer of electrons at the interface. It was evaluated according to the formula ∆ρ(z) = ρGeS/SnS - ρGeS - ρSnS, where ρGeS/SnS is the plane-averaged density of (GeS)n/(SnS)n, and ρGeS and ρSnS are the individual plane-averaged densities of GeS and SnS, respectively. Charge redistribution occurs near the heterointerface and few electrons flow from the SnS monolayer to the GeS monolayer. The electron transfer direction is consistent with the order of the work functions, which are calculated to be 4.43 and 4.32 eV for GeS and SnS, respectively, at the PBE level. However, the small work function difference implies that there is very limited electron transfer across the interface (Fig. S2). As described in the following, electrons and holes are not separated at the strain-free state. Thus, the lack of significant charge transfer indicates that carrier separation may not be driven because there is no effectively formed built-in electric field at the interface. 3.2. Strain-dependent Electronic Properties of (GeS)5/(SnS)5 It is known that bandgap engineering is a common practice for designing materials with desired physical properties. In particular, modulation through the application of different levels of strain is of pivotal importance since strain has been provably realized in the laboratory.47 Obviously, materials with strain-controlled bandgap are favorable for their wider applications.


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First, the tensile limit of the (GeS)5/(SnS)5 heterostructure, as well as those of its individual GeS and SnS monolayer components, have been simulated, which are displayed in Supporting Information, Figure S3. The tensile limit of (GeS)5/(SnS)5 is estimated to be approximately ε=15%. It is less than those of GeS and SnS, which are 24% and 21%, respectively. Here, ε is the strain magnitude (percent), which is defined as ε = ∆a/a0, where a0 is the unstrained cell parameter and ∆a + a0 is the strained cell parameter. Tensile stress is applied along the zigzag direction within the stretch limit. The evolution of bandgap value as a function of strain is shown in Figure 2. According to the change rule of the bandgap, Figure 2 can be divided into three regions: regions I, II and III. In region I, the energy bandgap increases linearly as the strain increases and reaches its highest value of 1.60 eV at ε = 2.4%. However, in region II, the bandgap no longer increases; it remains at a nearly constant value of ~1.59 eV until ε = 5.7%, and then it linearly decreases in region III. This interesting change in energy bandgap under uniaxial strain is very rarely seen. To obtain comprehensive information regarding this phenomenon, the band structures of the (GeS)5/(SnS)5 heterostructure with different levels of strain are shown in Figure 3. Here, three representative band structures were selected in each region. Moreover, partial charge densities of the conduction band minimum (CBM) and valence band maximum (VBM) states with the selected strains are illustrated in Figure 4. It is clearly observed from the band structures that the semiconducting behavior is well preserved when heterojunction is subjected to uniaxial tensile strain. In region I, the CBM and the VBM are located at the Γ point and Γ-M direction, respectively, which is indicative of an indirect band gap. The increase in the bandgap is primarily because the CBM energy monotonously increases, while the VBM energy fluctuates and does not change much (Figure S4, Supporting Information). The CBM states are almost completely


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contributed by SnS (blue lines in Fig. 3), whereas the VBM states are formed through hybridization between SnS and GeS, and the portion of GeS contribution is approximately 5356%. Therefore, a quasi-type II alignment is displayed, which is qualitatively consistent with the aforementioned analysis based on charge transfer. This conclusion is also supported by the partial charge density distributions, as illustrated in Figure 4: the VBM states are delocalized over the whole heterostructure, while the CBM states are localized around the SnS monolayer. With the enhancement of tensile strain (>2.4%), the bandgap remains nearly unchanged in region II (Fig. 2). Interestingly, in this region, the heterostructure displays a direct bandgap characteristic, with both the CBM and VBM located along the Γ-M direction (Table S1, Supporting Information). This conclusion is further verified by the recalculation of the band structures using the HSE06 functional48 (Figure S5, Supporting Information). Note that materials with a direct bandgap can lead to significantly enhanced efficiency for photoluminescence.49 Compositions of the VBM and CBM states in this region are essentially the same as those in region I. However, the states contributed by GeS gradually approach the VBM (red lines in Fig. 3). This phenomenon implies that if the tensile strain increases, the heterostructure may change into a type II alignment. Indeed, the type II alignment is observed when the tensile strain exceeds 5.7%. In region III, the CBM states are still dominated by SnS, but the VBM states are completely contributed by GeS (Fig. 3). Here, energy decline of the CBM is the primary factor for the reduction in bandgap (Figure S6, Supporting Information). The partial charge density distributions also show that the VBM and the CBM states are localized at the GeS and SnS monolayers, respectively (Fig. 4), which suggests that the GeS layer can be used as the electron donor and the SnS layer can be used as the electron acceptor. Thus, complete electron-hole separation is realized by stretching the GeS/SnS heterostucture along the zigzag direction. We


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have observed an extremely interesting phenomenon: transition from type II-like alignment (region I) to direct bandgap (region II) to type II alignment (region III) with increasing strain (Fig. 2). To gain deeper insight into this interesting transition as well as the bandgap variation, we have plotted the total density of states (DOS) and partial density of states in Figure S7. According to the figures, the electronic states of the CBM and VBM are primarily contributed by the p-orbitals of Sn and the p-orbitals of S atoms, respectively. Thus, for clarity, we only illustrate these projected p-orbital DOS (PDOS) in Figure 5. As described above, the bandgap increase in region I mainly stems from the energy increase in the CBM. This situation can be vividly understood from the PDOS, as shown in Figs. 5a and 5b. With the increase in the tensile strain, the orbital compositions of the VBM are almost unchanged, but the contribution to the CBM significantly changes from the Sn-pz to the Sn-px orbital. The position of the Sn-pz orbital in the conduction band (indicated by the blue solid line) shifts away with respect to the Fermi level (Ef), while Snpx (pink solid line) remains unchanged, so the contribution to the CBM is gradually transformed into the px states of Sn. Analysis of the CBM charge density also supports this conclusion: when the strain increases from 1.5% to 2%, the charge distribution in the SnS monolayer changes remarkably (see the insets of Figs. 5a and b). The change in the CBM composition from pz to px may originate from the variation of the Sn-Sn distance and the anti-bonding characteristic of the Sn-Sn bond. At the strain-free state, the pz orbitals of Sn can overlap with each other. However, with the tensile strain imposed along the z-axis, the Sn-Sn distance increases, while becoming shorter along the x-axis. This situation may lead to px-px overlap, which would cause the px orbital to become the dominant contribution to the CBM. The dependence between orbital compositions near the Ef and strain direction has also been found in SnSe2 nanostructures.50


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Accompanying the change in orbital contribution, the position of the CBM moves from the Γ point to the midpoint of Γ-M. In contrast, both GeS and SnS always contribute to the VBM, so its K-point position is still located at the midpoint of Γ-M. Thus, a direct bandgap feature is achieved in the range of 2.4% to 5.7% strain in region II (Figs. 5c, 5d and S7 in Supporting Information). Moreover, the same orbital compositions and charge distributions of the VBM and CBM lead to the invariability of the bandgap. When the strain exceeds 5.7%, i.e., when entering region III, the compositions of the VBM states begin to change, whereas those of CBM remain the same. As shown in Figs. 5d and 5e, the composition of the VBM changes from the S-px orbital under 5% strain to the S-py orbital under 7% strain, which is also evidenced by the charge redistribution (see the inserts of Figs. 5d and 5e). This scenario causes a direct-to-indirect bandgap crossover because the orbital constituents of the states are strongly connected with the K-point position, as noted above. As shown in Fig. 3, the states contributed by GeS gradually take over the VBM, which is accompanied by the shifting of the VBM position from the midpoint of Γ-M to the Γ point. Meanwhile, the compositions of CBM are unchanged (Figs. 5 and S7), so it is still located at the midpoint of Γ-M, thereby resulting in the direct-to-indirect bandgap transition. With the further increase in tensile strain, although the orbital compositions of the VBM and CBM are almost unchanged (Figs. 3, 4 and 5e, 5f), the bandgap displays a decreasing tendency, which is a result of the larger variation of the CBM energy (Fig. S6). A delicate analysis of the CBM state found that an increasingly loose distribution of anti-bonding electrons is present as the strain increases (Fig. 5), which may be caused by a large internal stress along the z-axis overwhelming the interaction of the Sn px-px orbital. 3.3. Carrier Concentrations


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To further identify the effective electron–hole separation by applying the strain, the carrier effective masses as well as the carrier concentrations were calculated along specific directions. The carrier effective mass (m*) is defined as

 d 2 Ek m = ± h  2  dk *

2

−1

   ,

where Ek is the corresponding energy of the wave vector (k). As shown in Table 1, the effective masses of electrons (

me*

) and holes (

mh*

) along the armchair and zigzag directions with the

selected strains in each region are given. The subscripts x and y in the table represent the armchair and zigzag directions, respectively. The calculated effective masses of unstrained (GeS)5/(SnS)5 are closer to the corresponding values of the GeS monolayer,51 but deviate slightly from those of SnS.52 In this case, the anisotropy is not particularly evident. The m* values along the armchair direction (0.209 m0 for electrons and 0.498 m0 for holes) are slightly lower than those along the zigzag direction (0.211 m0 for electrons and 0.581 m0 for holes). However, with increasing strain, the anisotropy becomes significant. According to Table 1, the effective masses along the zigzag direction increase to 5 and 19 times those along the armchair direction for electrons and holes, respectively. Apparently, the enhancement of anisotropy facilitates the electron-hole separation. We further calculate the carrier mobilities based on deformation potential theory.53 The mobility of single-layer material µ2D is defined as

µ 2D =

eh3C 2 D kBTm*md (E1 ) 2

,


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where h is the reduced Planck constant, kB is the Boltzmann constant and T is the temperature (300K).

m*

is the obtained effective mass in the transport direction and

md =

m *x m *y

is the average

effective mass. The elastic modulus C2D is fitted from the quadratic relationship between (E-E0) and (∆l/l0) according to the formula

( E − E0 ) / A0 = ( C 2 D / 2 )( ∆l / lo )2 , where E and E are the 0

total energy before and after applying uniaxial strain (

ε = ∆l / lo ) and A is the area at the 0

equilibrium state. The deformation potential constant E1 is defined as E1 = ∆V / ε , where ∆V represents the shift in band edge due to the application of uniaxial strain. Typical fitting results for E1 under 3.7% tensile strain are shown in Figure S8 in Supporting Information. All of these quantities were computed using the PBE functional, and the corresponding values are summarized in Table 1. Except the strain-free state, the carrier mobilities in the armchair direction are always greater than those along the zigzag direction, which reflects the anisotropy. The anisotropy becomes notable as the strain increases, especially for electrons. Moreover, similar to the cases of GeS and SnS monolayers,52 the electron mobilities are much higher than the hole mobilities. Particularly, it is noticed that with the enhancement of strain, the ratio between electron mobilities and hole mobilities gradually increases, which is an indication of electron-hole separation; meanwhile, electrons are the majority of carriers and the conductivity is greatly strengthened. Note that the predicted electron mobility in the armchair direction at 7% strain reaches 5860-11220 cm2 V-1 s-1, which is comparable to hole mobility of phosphorene along zigzag direction (10000-26000) and superior to electron mobility of phosphorene along armchair direction (1110-1140)6 as well as carrier mobility of monolayer MoS2 sheet and nanoribbons (~200 cm2 V-1 s-1) 54, which indicates that strain is a promising means with which to


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improve the conductivity. This gives the GeS/SnS heterostructure great potential for utilization in electronics, optoelectronics and straintronics.

4. CONCLUSION In summary, systematic first-principles calculations have been carried out to investigate the effect of strain on electronic properties of the GeS/SnS lateral heterostructure. Our results indicate that this kind of heterostructure could be favorably synthesized in the laboratory due to its covalent bonds at the interface and low heat of formation. With tensile strain applied on the zigzag edge of the heterojunction, it exhibits a very interesting change in bandgap: the bandgap linearly increases in region I, remains unchanged in region II, and then decreases in region III. Incredibly, these three regions successively display a quasi-type II alignment, direct bandgap and type II alignment, which can be interpreted based on the analysis of band structures and charge density distributions. It is demonstrated that the increase in the bandgap in region I stems from the change in the contribution to the CBM state from Sn-pz to Sn-px, while the decrease in the bandgap in region III is a result of a looser distribution of anti-bonding electrons at the CBM. Additionally, we have also shown that direct-indirect band gap crossover occurs because the Kpoint position depends strongly on the orbital composition of the electronic states. Carrier concentration calculations further support the conclusion that electron-hole separation occurs with the enhancement of strain. In particular, the predicted electron mobility in the armchair direction at 7% strain reaches 5860-11220 cm2 V-1 s-1. The versatile electronic properties and high carrier concentrations under definite strain may endow GeS-SnS lateral heterostructures with great potential applications in electronics, optoelectronics and straintronics. We believe that


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our work has a guiding significance for the relevant experimental work of exploring materials with new electronic properties.


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FIGURES

Figure 1. (a) Top and side views of the GeS/SnS heterostructure with armchair interline. Yellow/green/gray balls are S/Ge/Sn atoms. (b) Heats of formation (HF) and bandgap values as functions of width (Z). (c) Plane-averaged electron density difference of (GeS)5/(SnS)5. Inset is a 3D isosurface of the electron density difference, and yellow and cyan areas represent electron accumulation and depletion, respectively. The isosurface value is set to 0.0005 e Å–3.


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Figure 2. Evolution of the energy gap as a function of uniaxial tensile strain along the zigzag direction for (GeS)5/(SnS)5.


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Figure 3. Band structures of (GeS)5/(SnS)5 heterostructures under various levels of uniaxial strain along the zigzag direction. The horizontal gray dashed lines represent the Fermi level. The blue and red lines denote the contributions from the SnS monolayer and GeS monolayer, respectively.


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Figure 4. Charge densities at the VBM and CBM states of (GeS)5/(SnS)5 with different levels of uniaxial strain along the zigzag direction. The isosurface value is set to 0.0003 e/Å3. The right graphs illustrate the band edges of GeS and SnS.


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Figure 5. Projected densities of states (PDOSs) of (GeS)5/(SnS)5 at different levels of uniaxial strain along the zigzag direction. The insets illustrate the corresponding charge densities of the CBM and VBM. Vertical gray dashed lines represent the Fermi level. For clarity, only p-orbital DOSs are shown.


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TABLES.

Table 1. Predicted Effective Mass and Carrier Mobility of the GeS-SnS in-plane heterostructure. Effective mass

Deformation potential

Carrier Strain

(eV)

(m0)

Elastic modulus

Mobility

(J m-2)

(103 cm2 V-1 s-1)

type mx

my

E1x

E1y

Cx_2D

Cy_2D

µx_2D

µy_2D

0% (I)

0.209

0.498

3.33±0.19

1.52±0.24

18.36

44.38

0.46-0.58

1.89-3.57

3.7% (II)

0.230

0.46

0.99±0.03

12.4

77.14

3.37-3.81

0.085-0.11

10.66±0.6 Electron

5

7% (III)

0.271

1.38

0.44±0.08

5.46±0.67

12.4

27.44

5.86-11.22

0.018-0.03

0% (I)

0.211

0.581

6.73±0.12

7.51±0.47

18.36

44.38

0.11-0.12

0.073-0.093

3.7% (II)

0.252

0.760

3.41±0.06

12.4

77.14

0.20-0.212

0.041-0.056

12.4

27.44

0.070-0.14

0.001-0.002

10.13±0.7 Hole

8

7% (III)

0.878

16.67

0.90±0.16

2.47±0.49


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ASSOCIATED CONTENT

Supporting Information. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsami.XXX. Band structures of (GeS)n/(SnS)n with different widths, Averaged number of electrons per GeS or SnS in heterostructure, Evolution of stress, VBM and CBM energies as functions of uniaxial tensile strain, K-point position differences of CBM/VBM under various levels of uniaxial strain in region II, Band structure under 3% tensile strain calculated at the HSE06 level, Total density of states and partial density of states at different levels of uniaxial strain, Typical fitting of the deformation potential constant under 3.7% tensile strain. AUTHOR INFORMATION

Corresponding Author *E-mail: [email protected]

ORCID Yucheng Huang: 0000-0002-7818-8811

Notes The authors declare no competing financial interest. ACKNOWLEDGMENTS This work was supported by National Natural Science Foundation of China grants nos. 21573002 (H. Y.) and 21373012 (W. S.). The numerical calculations in this paper were performed on the super-computing system in the Supercomputing Center of the University of Science and


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Technology of China.


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REFERENCES 1.

Novoselov, K. S.; Geim, A. K.; Morozov, S.; Jiang, D.; Katsnelson, M.; Grigorieva, I.;

Dubonos, S.; Firsov; AA, Two-Dimensional Gas of Massless Dirac Fermions in Graphene. arXiv preprint cond-mat/0509330 2005.

2.

Wang, H.; Yu, L.; Lee, Y.-H.; Shi, Y.; Hsu, A.; Chin, M. L.; Li, L.-J.; Dubey, M.; Kong,

J.; Palacios, T., Integrated Circuits Based on Bilayer MoS2 Transistors. Nano Lett. 2012, 12, 4674-4680. 3.

Fiori, G.; Bonaccorso, F.; Iannaccone, G.; Palacios, T.; Neumaier, D.; Seabaugh, A.;

Banerjee, S. K.; Colombo, L., Electronics Based on Two-Dimensional Materials. Nat. Nanotechnol. 2014, 9, 768-779.

4.

Shi, Y.; Hamsen, C.; Jia, X.; Kim, K. K.; Reina, A.; Hofmann, M.; Hsu, A. L.; Zhang, K.;

Li, H.; Juang, Z.-Y., Synthesis of Few-Layer Hexagonal Boron Nitride Thin Film by Chemical Vapor Deposition. Nano Lett. 2010, 10, 4134-4139. 5.

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. 6.

Qiao, J.; Kong, X.; Hu, Z.-X.; Yang, F.; Ji, W., High-Mobility Transport Anisotropy and

Linear Dichroism in Few-Layer Black Phosphorus. Nat. Commun. 2014, 5, 4475. 7.

Zhang, S.; Yan, Z.; Li, Y.; Chen, Z.; Zeng, H., Atomically Thin Arsenene and

Antimonene: Semimetal-Semiconductor and Indirect-Direct Band-Gap Transitions. Angew. Chem. Int. Ed. 2015, 54, 3112-3115.


25


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

8.

Page 26 of 32

Ji, J.; Song, X.; Liu, J.; Yan, Z.; Huo, C.; Zhang, S.; Su, M.; Liao, L.; Wang, W.; Ni, Z.;

Hao, Y.; Zeng, H., Two-Dimensional Antimonene Single Crystals Grown by van der Waals Epitaxy. Nat. Commu. 2016, 7, 13352. 9.

Zhang, S.; Zhou, W.; Ma, Y.; Ji, J.; Cai, B.; Yang, S. A.; Zhu, Z.; Chen, Z.; Zeng, H.,

Antimonene Oxides: Emerging Tunable Direct Bandgap Semiconductor and Novel Topological Insulator. Nano Lett. 2017, 17, 3434-3440. 10.

Zhang, S.; Xie, M.; Cai, B.; Zhang, H.; Ma, Y.; Chen, Z.; Zhu, Z.; Hu, Z.; Zeng, H.,

Semiconductor-Topological Insulator Transition of Two-Dimensional SbAs Induced by Biaxial Tensile Strain. Phys. Rev. B 2016, 93, 245303. 11.

Zhang, S.; Xie, M.; Li, F.; Yan, Z.; Li, Y.; Kan, E.; Liu, W.; Chen, Z.; Zeng, H.,

Semiconducting Group 15 Monolayers: A Broad Range of Band Gaps and High Carrier Mobilities. Angew. Chem. Int. Ed. 2016, 55, 1666-1669. 12.

Bhimanapati, G. R.; Lin, Z.; Meunier, V.; Jung, Y.; Cha, J.; Das, S.; Xiao, D.; Son, Y.;

Strano, M. S.; Cooper, V. R., Recent Advances in Two-Dimensional Materials Beyond Graphene. ACS Nano 2015, 9, 11509–11539. 13.

Komsa, H.-P.; Krasheninnikov, A. V., Electronic Structures and Optical Properties of

Realistic Transition Metal Dichalcogenide Heterostructures from First Principles. Phys. Rev. B

2013, 88, 085318. 14.

Novoselov, K.; Mishchenko, A.; Carvalho, A.; Neto, A. C., 2d Materials and van der

Waals Heterostructures. Science 2016, 353, aac9439. 15.

Fang, H.; Battaglia, C.; Carraro, C.; Nemsak, S.; Ozdol, B.; Kang, J. S.; Bechtel, H. A.;

Desai, S. B.; Kronast, F.; Unal, A. A., Strong Interlayer Coupling in van der Waals


26

Page 27 of 32

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Heterostructures Built from Single-Layer Chalcogenides. Proc. Natl. Acad. Sci. 2014, 111, 61986202. 16.

Zhang, H., Ultrathin Two-Dimensional Nanomaterials. ACS Nano 2015, 9, 9451-9469.

17.

Zhang, M.; Shao, C.; Mu, J.; Huang, X.; Zhang, Z.; Guo, Z.; Zhang, P.; Liu, Y.,

Hierarchical Heterostructures of Bi2MoO6 on Carbon Nanofibers: Controllable Solvothermal Fabrication and Enhanced Visible Photocatalytic Properties. J. Mater. Chem. 2012, 22, 577-584. 18.

Shang, M.; Wang, W.; Zhang, L.; Sun, S.; Wang, L.; Zhou, L., 3D Bi2WO6/TiO2

Hierarchical Heterostructure: Controllable Synthesis and Enhanced Visible Photocatalytic Degradation Performances. J. Phys. Chem. C 2009, 113, 14727-14731. 19.

Huang, X.; Li, S.; Huang, Y.; Wu, S.; Zhou, X.; Li, S.; Gan, C. L.; Boey, F.; Mirkin, C.

A.; Zhang, H., Synthesis of Hexagonal Close-Packed Gold Nanostructures. Nat. Commun. 2011, 2, 292.

20.

Sławińska, J.; Zasada, I.; Klusek, Z., Energy Gap Tuning in Graphene on Hexagonal

Boron Nitride Bilayer System. Phys. Rev. B 2010, 81, 155433. 21.

Yu, L.; Lee, Y.-H.; Ling, X.; Santos, E. J.; Shin, Y. C.; Lin, Y.; Dubey, M.; Kaxiras, E.;

Kong, J.; Wang, H., Graphene/MoS2 Hybrid Technology for Large-Scale Two-Dimensional Electronics. Nano Lett. 2014, 14, 3055-3063. 22.

Ye, L.; Wang, D.; Chen, S., Fabrication and Enhanced Photoelectrochemical

Performance of MoS2/S-doped g-C3N4 Heterojunction Film. ACS Appl. Mater. Interfaces 2016, 8, 5280-5289.

23.

Zhu, X.; Monahan, N. R.; Gong, Z.; Zhu, H.; Williams, K. W.; Nelson, C. A., Charge

Transfer Excitons at van der Waals Interfaces. J. Am. Chem. Soc. 2015, 137, 8313-8320.


27


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

24.

Wei,

W.;

Dai,

Y.;

Huang,

B.,

Straintronics

in

Page 28 of 32

Two-Dimensional

in-Plane

Heterostructures of Transition-Metal Dichalcogenides. Phys. Chem. Chem. Phys. 2017, 19, 663672. 25.

Li, M.-Y.; Shi, Y.; Cheng, C.-C.; Lu, L.-S.; Lin, Y.-C.; Tang, H.-L.; Tsai, M.-L.; Chu,

C.-W.; Wei, K.-H.; He, J.-H., Epitaxial Growth of a Monolayer WSe2-MoS2 Lateral p-n Junction with an Atomically Sharp Interface. Science 2015, 349, 524-528. 26.

Qian, X.; Liu, J.; Fu, L.; Li, J., Quantum Spin Hall Effect in Two-Dimensional Transition

Metal Dichalcogenides. Science 2014, 346, 1344-1347. 27.

Yoo, Y.; Degregorio, Z. P.; Johns, J. E., Seed Crystal Homogeneity Controls Lateral and

Vertical Heteroepitaxy of Monolayer MoS2 and WS2. J. Am. Chem. Soc. 2015, 137, 1428114287. 28.

Gong, Y.; Lin, J.; Wang, X.; Shi, G.; Lei, S.; Lin, Z.; Zou, X.; Ye, G.; Vajtai, R.;

Yakobson, B. I., Vertical and in-Plane Heterostructures from WS2/MoS2 Monolayers. Nat. Mater. 2014, 13, 1135-1142.

29.

Mahjouri-Samani, M.; Lin, M.-W.; Wang, K.; Lupini, A. R.; Lee, J.; Basile, L.;

Boulesbaa, A.; Rouleau, C. M.; Puretzky, A. A.; Ivanov, I. N., Patterned Arrays of Lateral Heterojunctions within Monolayer Two-Dimensional Semiconductors. Nat. Commun. 2015, 6, 7749. 30.

Gong, Y.; Lei, S.; Ye, G.; Li, B.; He, Y.; Keyshar, K.; Zhang, X.; Wang, Q.; Lou, J.; Liu,

Z., Two-Step Growth of Two-Dimensional WSe2/MoSe2 Heterostructures. Nano Lett. 2015, 15, 6135-6141. 31.

Kośmider, K.; Fernández-Rossier, J., Electronic Properties of the MoS2-WS2

Heterojunction. Phys. Rev. B 2013, 87, 075451.


28

Page 29 of 32

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


32.

Gong, C.; Zhang, H.; Wang, W.; Colombo, L.; Wallace, R. M.; Cho, K., Band Alignment

of Two-Dimensional Transition Metal Dichalcogenides: Application in Tunnel Field Effect Transistors. Appl. Phys. Lett. 2013, 103, 053513. 33.

Kang, J.; Sahin, H.; Peeters, F. o. M., Tuning Carrier Confinement in the MoS2/WS2

Lateral Heterostructure. J. Phys. Chem. C 2015, 119, 9580-9586. 34.

Vaughn II, D. D.; Patel, R. J.; Hickner, M. A.; Schaak, R. E., Single-Crystal Colloidal

Nanosheets of GeS and GeSe. J. Am. Chem. Soc. 2010, 132, 15170-15172. 35.

Singh, A. K.; Hennig, R. G., Computational Prediction of Two-Dimensional Group- IV

Mono-Chalcogenides. Appl. Phys. Lett. 2014, 105, 042103. 36.

Tritsaris, G. A.; Malone, B. D.; Kaxiras, E., Optoelectronic Properties of Single-Layer,

Double-Layer, and Bulk Tin Sulfide: A Theoretical Study. J. Appl. Phys. 2013, 113, 233507. 37.

Yoon, S. M.; Song, H. J.; Choi, H. C., p-Type Semiconducting GeSe Combs by a

Vaporization–Condensation–Recrystallization (VCR) Process. Adv. Mater. 2010, 22, 2164-2167. 38.

Li, L.; Chen, Z.; Hu, Y.; Wang, X.; Zhang, T.; Chen, W.; Wang, Q., Single-Layer Single-

Crystalline SnSe Nanosheets. J. Am. Chem. Soc. 2013, 135, 1213-1216. 39.

Huang, Y.; Chen, X.; Wang, C.; Peng, L.; Qian, Q.; Wang, S., Layer-Dependent

Electronic Properties of Phosphorene-Like Materials and Phosphorene-Based van der Walls Heterostructures. Nanoscale 2017, 9, 8616-8622. 40.

Blöchl, P. E., Projector Augmented-Wave Method. Phys. Rev. B 1994, 50, 17953.

41.

Kresse, G.; Furthmüller, J., Efficient Iterative Schemes for Ab Initio Total-Energy

Calculations Using a Plane-Wave Basis Set. Phys. Rev. B 1996, 54, 11169.


29


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

42.

Page 30 of 32

Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Singh, D.

J.; Fiolhais, C., Atoms, Molecules, Solids, and Surfaces: Applications of the Generalized Gradient Approximation for Exchange and Correlation. Phys. Rev. B 1992, 46, 6671. 43.

Perdew, J. P.; Wang, Y., Accurate and Simple Analytic Representation of the Electron-

Gas Correlation Energy. Phys. Rev. B 1992, 45, 13244. 44.

Leenaerts, O.; Vercauteren, S.; Schoeters, B.; Partoens, B., System-Size Dependent Band

Alignment in Lateral Two-Dimensional Heterostructures. 2D Materials 2016, 3, 025012. 45.

Cheng, K.; Guo, Y.; Han, N.; Su, Y.; Zhang, J.; Zhao, J., Lateral Heterostructures of

Monolayer Group- IV Monochalcogenides: Band Alignment and Electronic Properties. J. Mater. Chem. C 2017, 5, 3788-3795.

46.

Junfeng, Z.; Weiyu, X.; Jijun, Z.; Shengbai, Z., Band Alignment of Two-Dimensional

Lateral Heterostructures. 2D Materials 2017, 4, 015038. 47.

He, K.; Poole, C.; Mak, K. F.; Shan, J., Experimental Demonstration of Continuous

Electronic Structure Tuning Via Strain in Atomically Thin MoS2. Nano Lett. 2013, 13, 29312936. 48.

Heyd, J.; Scuseria, G. E.; Ernzerhof, M., Hybrid Functionals Based on a Screened

Coulomb Potential. J. Chem. Phys. 2003, 118, 8207-8215. 49.

Lv, R.; Robinson, J. A.; Schaak, R. E.; Sun, D.; Sun, Y.; Mallouk, T. E.; Terrones, M.,

Transition Metal Dichalcogenides and Beyond: Synthesis, Properties, and Applications of Single-and Few-Layer Nanosheets. Acc. Chem. Res. 2014, 48, 56-64. 50.

Huang, Y.; Ling, C.; Liu, H.; Wang, S.; Geng, B., Versatile Electronic and Magnetic

Properties of SnSe2 Nanostructures Induced by the Strain. J. Phys. Chem. C 2014, 118, 92519260.


30

Page 31 of 32

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


51.

Li, F.; Liu, X.; Wang, Y.; Li, Y., Germanium Monosulfide Monolayer: A Novel Two-

Dimensional Semiconductor with a High Carrier Mobility. J. Mater. Chem. C 2016, 4, 21552159. 52.

Xin, C.; Zheng, J.; Su, Y.; Li, S.; Zhang, B.; Feng, Y.; Pan, F., Few-Layer Tin Sulfide: A

New Black-Phosphorus-Analogue 2D Material with a Sizeable Band Gap, Odd–Even Quantum Confinement Effect, and High Carrier Mobility. J. Phys. Chem. C 2016, 120, 22663-22669. 53.

Bardeen, J.; Shockley, W., Deformation Potentials and Mobilities in Non-Polar Crystals.

Phys. Rev. 1950, 80, 72.

54.

Cai, Y.; Zhang, G.; Zhang, Y.-W., Polarity-Reversed Robust Carrier Mobility in

Monolayer MoS2 Nanoribbons. J. Am. Chem. Soc. 2014, 136, 6269-6275.


31


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Table of Contents Graphic


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SnS ... - ACS Publications

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