Electric-Field Tunable Band Offsets in Black Phosphorus and MoS

Jun 13, 2015 - specifically, the band offset is critical to many properties such as quantum .... is in great agreement with experimental results of De...
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Electric-Field Tunable Band Offsets in Black Phosphorus and MoS2 van der Waals p‑n Heterostructure Le Huang, Nengjie Huo, Yan Li, Hui Chen, Juehan Yang, Zhongming Wei,* Jingbo Li,* and Shu-Shen Li State Key Laboratory for Superlattice and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China ABSTRACT: The structural and electronic properties of black phosphorus/MoS2 (BP/ MoS2) van der Waals (vdW) heterostructure are investigated by first-principles calculations. It is demonstrated that the BP/MoS2 bilayer is a type-II p-n vdW heterostructure, and thus the lowest energy electron−hole pairs are spatially separated. The band gap of BP/MoS2 can be significantly modulated by external electric field, and a transition from semiconductor to metal is observed. It gets further support from the band edges of BP and MoS2 in BP/MoS2 bilayer, which show linear variations with E⊥. BP/MoS2 bilayer also exhibits modulation of its band offsets and band alignment by E⊥, resulting in different spatial distribution of the lowest energy electron−hole pairs. Our theoretical results may inspire much interest in experimental research of BP/MoS2 vdW heterostructures and would open a new avenue for application of the heterostructures in future nano- and optoelectronics.

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Meanwhile, inspired by their applications, researchers recently start focusing on vdW heterostructure based on BP and other 2D materials. It is reported that hybrid graphene/BP nanocomposite exhibits stronger optical absorption, especially in the visible light range.20 Deng et al. demonstrated that a gatetunable p-n diode based on a p-type BP/n-type monolayer MoS2 vdW p-n heterojunction shows a maximum photodetection responsivity of 418 mA/W at the wavelength of 633 nm.21 An anomalous photoluminescence quenching is observed in artificial heterostacks of monolayer TMDs and few-layer BP.22 Few theoretical works, however, report the electronic properties of BP/MoS2 vdW heterostructure. So far, band offsets of BP/MoS2 bilayer are completely unknown. Band offsets of semiconducting heterostructures are important and necessary parameters in material and device design. More specifically, the band offset is critical to many properties such as quantum confinement and dopability.23−25 In this work, we study the electronic properties of BP/MoS2 bilayer using firstprinciples calculations, but the main points are the electrically tunable band alignment of BP/MoS2 bilayer and interesting electronic properties enabled by its band offsets. Our results show that BP interacts overall weakly with MoS2 via vdW interactions, and thus their intrinsic electronic properties can be preserved in hybrid BP/MoS2 nanocomposite. Moreover, perpendicular electric field can induce tunable band gaps and a transition from semiconductor to metal in BP/MoS2 bilayer. This would lead to the realization of band engineering and modulated luminescence. It is found that the band offset is also

wo-dimensional (2D) materials such as graphene and transition-metal dichalcogenide (TMD) MoS2 have great potential in next-generation electronic and photonic applications owing to their extraordinary fundamental physical properties and applications in electronic devices.1−5 For example, the field-effect transistors based on monolayer or few-layer MoS2 have been reported to exhibit an excellent on/ off ratio and room-temperature mobility.1 The layered TMDbased photodetectors have been demonstrated to have very high responsivity and fast photoresponse.6,7 The isolation of various 2D materials in recent years8 has raised the possibility of designing van der Waals (vdW) heterostructures, which provide more opportunities for achieving desired electronic or optoelectronic properties. For example, the calculated electric-field tunability of graphene/BN bilayer bandgap suggests a new application of this system in semiconductor devices.9 Electron−hole pair separation and high photovoltaic performance can be realized in MoS2−WS2 p-n heterojunction.10,11 MoOx based on TMDs shows promising potential as an efficient hole injection layer for pFETs.12 Both moderate electronic band gap and low carrier effective mass are indispensable factors for application of semiconductors in high-speed field-effect transistors devices. Recent works have demonstrated that a new 2D semiconducting material with a direct bandgap, namely, the few-layer black phosphorus (BP), has been successfully isolated.13−15 BP shows a finite direct band gap that can be modified from 1.51 eV for a monolayer to 0.59 eV for the five layers.16 It possesses great transport properties such as high hole mobility up to 1000 cm2/ (V s),17 which makes BP a potential candidate for applications in nanoelectronics and optoelectronics.18,19 © XXXX American Chemical Society

Received: May 11, 2015 Accepted: June 13, 2015

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DOI: 10.1021/acs.jpclett.5b00976 J. Phys. Chem. Lett. 2015, 6, 2483−2488

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The Journal of Physical Chemistry Letters sensitive to external electric field, resulting in different spatial separation of the lowest energy electron−hole pairs. The external electric-field-dependent band alignment offers a practical route to tune the Schottky barrier height, which can lead to more efficient carrier injection in BP/MoS2 electronic devices. The structures of monolayer BP and MoS2 as well as BP/ MoS2 vdW heterostructure are presented in Figure 1. A

monolayer MoS2 are aM = 3.19 Å and bM = 5.53 Å, and the calculated lattice constants of monolayer BP are aP = 3.30 Å, bP = 4.62 Å. Because the properties of monolayer BP and MoS2 are very sensitive to any strain condition,26,27 the lattice constants of the supercell employed here are a = 3.24 Å and b = 22.5 Å. The overall induced strain in both BP and MoS2 lattice is E⊥ >0.6 V/Å (saturation range). Then, the band gap comes to a linear decrease range with increasing E⊥ >0.8 V/Å (L-decrease range). In contrast, in the presence of a reverse E⊥, the band gap declines linearly with E⊥ increases numerically (L-decrease range). When E⊥ < −0.5 V/ Å, the BP/MoS2 bilayer experiences a transition from semiconductor to metal (metal range). To gain further insight, the band edges of (or dominated by) BP or MoS2 under various E⊥ are calculated and shown in Figure 4b. EC_P(M) and EV_P(M) are the CBM and VBM of BP (MoS2) in BP/MoS2 bilayer. First of all, the band gap of BP/ MoS2 bilayer gives the same variation trend in every corresponding range of E⊥. Second, both the CBM and VBM of BP show a linear decline with E⊥, while the CBM and VBM of MoS2 increase linearly. The external electric field exerts little influence on the respective band gap of BP and MoS2. Furthermore, the conduction (valence) band offset is defined as ΔEC = EC_P − EC_M (ΔEV = EV_P − EV_M). The ΔEC and ΔEV show similar variation trend and decrease linearly with E⊥, as shown in Figure 4a. Additionally, the BP/MoS2 bilayer experiences a transition from type-II to type-I when E⊥ is ∼0.6 V/Å and a transition from type-I to type-II when E⊥ is ∼0.8 V/Å, resulting in different spatial distribution of the

reported results is obtained, agreeing well with the reported band gap of monolayer MoS2 under equal tensile strain.30,31 The strains resulting from the mismatch between BP and MoS2 exert little influence on the reasonability of our conclusions in this work. The charge accumulation (blue) and depletion (violet) of the BP/MoS2 bilayer is given in Figure 3e. There is a little charge transfer between the BP and MoS2 layer, indicating a weak interlayer coupling between BP layer and MoS2 layer. As a result, the Fermi level shifts to the CBM of MoS2 and VBM of BP after they compose the BP/MoS2 bilayer heterostructure, forming a p-n BP/MoS2 vdW heterostructure. Meanwhile, the work function (W = Evac − EF, where Evac and EF are the vacuum level and Fermi level, respectively) of the BP/MoS2 bilayer is a little smaller than that of monolayer MoS2 and a little larger than that of monolayer BP, as shown in Figure 2b. In comparison with their band structures, band offsets of semiconducting heterostructure are even more important in material and device design. In Figure 2, it is clear that the VBM and the CBM are localized on BP and MoS2, respectively. The p-type BP and n-type monolayer MoS2 form an atomically sharp type-II heterointerface through vdW interactions, which is in great agreement with experimental results of Deng et al.21 In a type-II heterostructure, free electrons and holes will be spontaneously separated, which is suitable for optoelectronics and solar energy conversion. These band edges are the relevant states for interband optical experiments, and thus the lowest energy electron−holes pairs are spatially separated with electrons and holes locating in MoS2 and BP layer, respectively. In addition, the BP/MoS2 bilayer band gap lead by the spatial separation of the lowest energy bands is 0.39 eV, significantly smaller than that of the monolayers. It is reported that the p-n diodes based on BP/MoS2 heterojunction showed a good photodetection responsivity.21 Figure 3 shows the band structure and the isosurfaces of charge accumulation and depletion of bilayer BP/MoS2 in the presence of an applied external perpendicular electric field (E⊥). 2485

DOI: 10.1021/acs.jpclett.5b00976 J. Phys. Chem. Lett. 2015, 6, 2483−2488

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bilayer. VD is the conduction band offset of BP/MoS2 bilayer without an E⊥. V⊥ = E⊥·d is the external electric potential, which leads to the divergence of the quasi-Fermi levels. d is the interlayer distance, which is a constant in this system. Upon application of a forward E⊥, the band gap increases linearly with E⊥. Now Eg = Eg_BP − e(VD − V⊥) = Eg_BP − eVD + eE⊥d

It obtains its maximum when the forward E⊥ ranges from 0.6 to 0.8 V/Å. Eg = Eg_BP ≈ 0.9 eV

In the case of E⊥ > 0.8 V/Å, the band gap comes to its Ldecreases range. Then Eg = Eg_BP − e(E⊥ − 0.8)d

In the contrast, the band gap of BP/MoS2 bilayer under a reverse E⊥ shares the same variation relationship with that of Lincrease range of forward E⊥. It decreases linearly with the strength of E⊥ and reaches zero when |E⊥| > 0.5 V/Å. As a result, the BP/MoS2 bilayer becomes a metal. In this case, the Fermi level is lower than the VBM of BP and higher than the CBM of MoS2, as can be seen in Figure 4b. Electrons tend to transfer efficiently from the BP layer to the MoS2 layer, inducing a p-type doping in the BP layer. All of the results about band alignment are in great agreement with the evolution of band gap and band edges as a function of E⊥. Moreover, it can be forecasted that the variation of band gap would play a major role in the electrical transport properties of the BP/MoS2 heterostructure-based electronics. We assume to construct a field-effect tunneling transistor based on BP/MoS2. The BP/MoS2 heterostructure are sandwiched between graphene layers, and the applied bias on graphene can act as a vertical electric field to modulate the band gap of the heterostructure. The tremendous tunneling current would be formed under reverse bias because of the metal state of heterostructure, while the current is limited under forward bias due to the presence of band gap, which can lead to a super current rectification effect. Similarly, the applied gate voltage (V ⊥ ) can also modulate the band gap of BP/MoS 2 heterostructure in field-effect transistors where the source and drain electrodes are located on two terminals of our heterostructure system and gate electrode is on bottom Si. A negative V⊥ can induce zero band gap of the system, thus

Figure 4. (a) Evolution of the band gap and band offsets of BP/MoS2 bilayer as a function of the external field. (b) Evolution of the band edges of BP and MoS2 in BP/MoS2 bilayer as a function of the field. EC_P(M) and EV_P(M) are the CBM and VBM of BP (MoS2) in BP/ MoS2 bilayer. The Fermi level (red dashed line) is set as zero. The regions labeled I−V are metal range, L-decrease range, L-increase range, saturation range, and L-decrease range, respectively.

lowest energy electrons and holes. These conclusions are further supported by the band-decomposed electron densities of the VBM and CBM under various E⊥, as shown in Figure 5b,c. More charge transfer between BP layer and MoS2 suggests a stronger interlayer interaction, leading to the shift of band edges, which also results in the modulation of band gap and band offsets. Similar evidence also comes from the band alignment of BP/ MoS2 bilayer under external electric field E⊥, as shown in Figure 5a. EF_P(M) is the quasi-Fermi level of BP(MoS2) in BP/MoS2

Figure 5. (a) Band alignment of BP/MoS2 bilayer evolves with the external electric field. EF_P(M) is the quasi-Fermi level of BP(MoS2) in BP/MoS2 bilayer. VD is the conduction band offset without an external electric field. Isosurfaces of band decomposed charge density of (b) CBM and (c) VBM of BP/MoS2 heterostructure under applied external electric field of −0.7, −0.4, 0, 0.4, 0.7, and 0.9 V/Å, respectively. The isosurface is taken as 0.0015 e/Å3. 2486

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J.L. acknowledges financial support from the CAS/SAFEA International Partnership Program for Creative Research Teams.

increasing the source-drain current (Isd) significantly; however, a moderate positive V⊥ opens up a sizable band gap, leading to the large impedance and decreased Isd. This can also lead to an obvious current rectification effect. Although many factors influence the charge transport in this device model, such as the V⊥-induced charge distribution inside the system, the variation of band gap can be the major factor. Overall, the emerging rectification effect reveals the huge potential in logical device application. In summary, we have provided band offset calculations for the p-type BP/n-type MoS2 bilayer and investigated its structural and electronic properties from first-principles calculations. Our calculation results including the intrinsic type-II band alignment and the modulation of the band gap pave the way for experimental research and indicate great application potential of BP/MoS2 vdW heterostructures in future optoelectronics. For example, the type-II band alignment can facilitate the separation of photoexcited electrons and holes, enabling the high efficiency of photovoltaic effect and photodetection performance. More importantly, the band offset and band gap can be significantly modulated by external electric field, ranging from 0.9 to 0 eV (the transition from semiconductor to metal). Further insight can be given by the variations of band edges of BP and MoS2 in BP/MoS2, which turn out to change linearly with E⊥ due to the modulated charge transfer process. A straightforward model based on VD and V⊥ is also proposed to set forth the influence of an external electric field on both the band gap and the carrier distribution of BP/MoS2 bilayer. According to our results, the BP/MoS2 vdW p-n heterojunction will present abundant opportunities for application of the heterostructures in future nano- and optoelectronics such as photovoltaic cell, photodetector, and logical device.

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COMPUTATIONAL METHODS The calculations are performed by using the projectoraugmented plane-wave (PAW) method32,33 within the framework of DFT in the Vienna ab initio Simulation Package (VASP).34 The generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE) functional35 is adopted for electron exchange and correlation. The vdW interlayer interaction is described by the pairwise force field in the DFTD2 method of Grimme.36 A vacuum larger than 12 Å is used to eliminate the interaction between adjacent images. The cutoff energy for the plane-wave basis set is set to 500 eV, and the first Brillouin zone is sampled with a (15 × 15 × 1) Monkhorst− Pack grid for relaxation of BP and MoS2 unit cells.37 A (5 × 20 × 1) Monkhorst−Pack grid is used for relaxation of supercells. All of the structures are fully relaxed with a force tolerance of 0.01 eV/Å.

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REFERENCES

AUTHOR INFORMATION

Corresponding Authors

*Z.W.: E-mail: [email protected]. *J.L.: E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China under grant no. 91233120 and the National Basic Research Program of China (2011CB921901). 2487

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