Electronic Properties of van der Waals Heterostructure of Black

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Electronic Properties of van der Waals Heterostructure of Black Phosphorus and MoS2 Kewei Tang,† Weihong Qi,*,†,§ Yejun Li,‡ and Tianran Wang† †

School of Materials Science and Engineering and ‡Hunan Key Laboratory of Super Microstructure and Ultrafast Process, School of Physics and Electronics, Central South University, Changsha 410083, P. R. China § State Key Laboratory of Solidification Processing, Center of Advanced Lubrication and Seal Materials, Northwestern Polytechnical University, Xi’an 710072, Shanxi, P. R. China ABSTRACT: Combining two different layered structures to form van der Waals (vdW) heterostructure has recently emerged as an intriguing way of designing electronic and optoelectronic devices. Using first-principles calculation, the electronic and optoelectronic properties of the black phosphorus and MoS2 (BP/MoS2) heterostructure were investigated and the results give a theoretical explanation of the reported high photodetection responsivity. Linear dichroism and the carrier mobility of the heterostructure were calculated to be preserved compared to that of free BP. The carrier transport performance is expected to be enhanced in practical applications by the predicted synergistic effect. Our work demonstrates that by combing BP with monolayer MoS2, outstanding electronic and optoelectronic attributes can be achieved, which may shed light on the electronics and optoelectronics applications of the BP/MoS2 heterostructure.

1. INTRODUCTION Since the discovery of graphene (G),1 two-dimensional (2D) materials have emerged as a kind of most attractive nanomaterials for their high flexibility and fascinating electronic and optical properties. Following the research upsurge on twodimensional materials, many novel 2D materials, such as hexagonal boron nitride (h-BN), transitional metal dichalcogenides (TMDs), silicone, and phosphorene, have been discovered and investigated.2−5 More recently, researchers have moved their focus on to two-dimensional vertical heterostructures, such as BMLs/MoS2,6 G/h-BN,7 black phosphorus (BP)/BN,8 BP/TMDs,9 TMDs/TMDs,10,11 and MoS2/SiC,12 as well as lateral heterostructures, such as TMDs/ TMDs13,14 and G/BN,15−17 for the vdW heterojunction formed between participating materials. This strategy could not only overcome the lattice mismatch-induced defects in participating materials synthesized by epitaxial growing18 (for vertical stacking) but can also induce excellent physical properties, thus leading to some very intriguing phenomena such as Hofstadter’s butterfly spectrum,19,20 strongly bound excitons,21,22 and spin valley polarization.23,24 Black phosphorus (BP), a novel two-dimensional isomer of white phosphorus, which is also the most stable phosphorus allotrope at room temperature,25,26 was named and synthesized under high pressure and temperature in 1914 by Bridgman.27 But for a century, there had not been much progress on BP until the superconductivity at high pressures were discovered in 1960s.25,28 The synthesis of BP is too difficult and the characterization technologies are not very advanced at the © XXXX American Chemical Society

moment, as well as the less interest in BP as an electronic device is due to its narrow band gap. The discovery of graphene brought mechanical exfoliation (the most convenient synthesis method) into the two-dimensional material research field, which promotes the investigations of BP. Since 2014, many experimental and theoretical works revealed the intriguing electronic properties (high carrier mobility, direct band gap, etc.) of monolayer BP (phosphorene) and few-layer BP,5,29−31 which makes BP a potential candidate for electronics and optoelectronics applications. Although it possesses outstanding electronic properties, the applications of BP or phosphorene are still greatly limited because its chemical activity is too high and it can’t last long at ambient condition32,33 and the large exciton binding energy of BP also limits its photoemission applications.34 Stacking other two-dimensional materials on BP can not only protect it from being damaged by external adsorbates but also may achieve fascinating physical properties. For instance, Sun et al. reported a BP/G hybrid material serving as a high capacity anode for sodium-ion batteries, which shows a specific capacity of 2440 mA h g−1 (calculated using the mass of BP).35 Liu et al. reported the quantum tunneling effect can be tuned by adding a vertical stacking MoS2 layer onto BP.36 Deng et al. reported a photodetector based on BP/MoS2 that exhibits a maximum photodetection responsivity of 418 mA W−1.37 Chen et al. Received: February 11, 2018 Revised: February 21, 2018

A

DOI: 10.1021/acs.jpcc.8b01476 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

Figure 1. Designed structure and high symmetry lines in the Brillouin zone (for band calculation) of the BP/MoS2 heterostructure.

reported a field-effect transistor based on BP/BN which allows a high field-effect mobility of ∼1350 cm2 V−1 s−1 and on−off ratios exceeding 105 at room temperature.8 Although there is already some experimental work targeting electronics devices based on the BP/MoS2 heterostructure,8,36−41 and considerable progress has been made, few theoretical works have devoted to the basic electronic properties of the BP/MoS2 heterostructure to get a deeper understanding of the experimental phenomena. In this work, the electronic properties of the BP/MoS2 heterostructure were investigated. It is found that by stacking BP onto layered MoS2, BP becomes a p-doping semiconductor with type-II band alignment to MoS2. Moreover, the linear dichroism of BP is preserved, as the high carrier mobility. A synergistic effect on the carrier transport of the whole material is predicted, which may enhance the carrier transport performance in practical use. Considering both the enhanced absorption at visible light range and the reduced electron−hole recombination rate due to strong carrier confinement, it is concluded that the responsivity of BP/MoS2 heterostructure should be much higher than that of pure BP, which explains a recent experiment.37

μ2D =

eℏ3C2D kBTme*ma*E i 2

(1)

where m*e is the effective mass on calculating direction x or y, which is given as me* = ℏ2 /

∂ 2E0(k) ∂k 2

(2)

where E0 is the band energy at conduction band minimum (CBM) or valence band maximum (VBM) and m*a is the averaged effective mass given by ma* = mx*m*y . Ei is the deformation potential constant given by E i = ΔVi /

( Δl l ), where

ΔVi represents the energy change of CBM or VBM (adjusted by internal bands). C2D is the in-plane elastic modulus (in both x and y directions), which can be derived from 2 E − E0 C ⎛ Δl ⎞ = 2D ⎜ ⎟ S0 2 ⎝ l0 ⎠

(3)

where E − E0 represents the total energy change, S0 is the area of xy plane, Δl represents the deformation in x or y direction.

2. COMPUTATIONAL METHODS The first-principle calculation was carried out within density functional theory using the projector-augmented wave method, performed with Vienna Ab initio Simulation Package.42 Exchange-correlation interaction was dealt with the generalized gradient approximation developed by Perdew−Burke−Ernzerhof.43 OptB88 functional44 was selected to take care of the vdW corrections as it yields better results for BP.29 The energy cutoff was set to 400 eV using a 5 × 21 × 1 Monkhorst−Pack grid for Brillouin zone integration. The break criterion for the electronic self-consistent loop was set to 10−5 eV. The optic calculation was carried out within random phase approximation; the total number of bands was set to be twice that of the static calculation. For charge analysis, the Bader charge analysis code was used.45−48 Note that for accuracy and computational convenience considerations, geometry optimization was split into two steps. First, a series of static calculations with different interlayer spacing were performed to get the interlayer binding energies to fit into the well-known Buckingham potential, to achieve the as-equilibrium interlayer distance, hence the as-equilibrium structure. Second, the as-equilibrium structure was further used for full relaxation (with ISIF set to 3) to get the fully optimized structure. Band, density of states (DOS), and other results were all calculated on the basis of the fully optimized structure. The carrier mobility was calculated on the basis of the following expression29

l0

The absorption coefficient is calculated from the dielectric function using the following expression 2πε2

α (λ ) =

λ ( ε12 + ε22 + ε1)/2

(4)

where ε1 and ε2 are the real and imaginary parts of the dielectric function and λ is the wavelength of incident light. The absorption spectra is then calculated on the basis of the absorption coefficient using the expression29 A(λ) = 1 − e−α(λ)·Δz

(5)

where Δz is the cell size in z direction.

3. RESULTS AND DISCUSSION 3.1. Equilibrium Structure of BP/MoS2 Heterostructure. The designed structure of the BP/MoS2 heterostructure is shown in Figure 1; the equilibrium structure is yielded by applying the two-step optimization on the designed lattice (the details can be found in the Computational Methods section). For step one, we change the interlayer distance and calculate the binding energy and fit the results into the well-known Buckingham potential equation, as shown below E b = A e−Bh − B

C h6

(6) DOI: 10.1021/acs.jpcc.8b01476 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C A, B, and C are fitting parameters, h is the interlayer spacing, and Eb represents the interlayer binding energy. The binding energy as a function of the interlayer spacing and fitting curve is shown in Figure 2.

reduce the electron−hole recombination rate within the participating materials, hence increasing the internal gain as well as responsivity.49,50 Note that the prediction of the reduced electron−hole recombination rate is consistent with the results of a time-domain ab initio calculation.51 The band gap is an indirect gap of 0.398 eV, which is also consistent with that in the previous calculation,39 although there is a small gap opening of about 0.1 eV in the formation of the heterostructure. The conduction band near the Fermi level is mostly contributed by MoS2, whereas the valence band near the Fermi level is mostly contributed by BP so that the BP/MoS2 heterostructure may still take the advantages of the high hole mobility of the BP layer5 and the high electron mobility of the MoS2 layer.52 To further confirm the conjecture, the exact carrier mobility was calculated on the basis of the band structure, as shown in Table 1. It clearly shows that the hole mobility in y direction is just slightly declined, whereas the hole mobility in x direction and electron mobility is slightly enhanced comparing to that of free BP.29 By adding MoS2 layer onto monolayer BP, the stiffness and the deformation potential of the structure are both greatly increased so that the general transport performance is neither declined nor enhanced too much. The electron transport anisotropy is tremendously declined for the conduction bands near the Fermi layer is mostly contributed by MoS2, which holds nearly equivalent deformation potential in both directions. In general, the electronic properties of MoS2 will be more accurately predicted with consideration of spin−orbit coupling (SOC). However, the present interlayer coupling is very weak and the SOC effect on the BP layer can be ignored and thus the spin−orbit coupling induced by d orbitals of Mo atoms was not considered. From the PDOS in Figure 3b, it is shown that the DOS of BP is distributed uniformly across the whole spectrum, whereas the DOS of MoS2 is rather concentrated in the energy range from −7 to 2 eV. The hybridization among s, p, and d orbitals of MoS2 remains unbroken; the interlayer coupling is rather weak.

Figure 2. Calculated interlayer binding energies (per P atom) as a function of a series of interlayer spacing and Buckingham potential fitting curve.

The predicted equilibrium interlayer distance read from the fitting curve is about 3.28 Å. For step two, a structure with an interlayer distance of 3.28 Å is constructed and placed into a full relaxation to yield the final equilibrium structure. The averaged interlayer spacing between the monolayer BP and MoS2 (the nearest S atom layer) of the fully optimized structure is 3.30 Å, with an interlayer binding energy of −67.06 meV/P atom. The fully optimized structure differs only slightly from its designed one. 3.2. Electronic Structure of the BP/MoS2 Heterostructure. Figure 3a shows the projected band structure of the BP/MoS2 heterostructure, which shows a type-II band alignment with a large offset on valence bands. Such a large offset can exhibit strong carrier confinement effects, which will

Figure 3. (a) Projected band structure of the BP/MoS2 heterostructure; the band projected onto BP and MoS2 are rendered blue and red, respectively. The dot size reflects the weight of each species in the bands. The inset shows the band alignment, the green dashed line represents the Fermi level. (b) Projected density of states (PDOS) of the BP/MoS2 heterostructure; the DOS projected onto BP and MoS2 are plotted in blue and red, respectively. The short dotted line represents d orbitals of MoS2. The orange dashed line indicates Fermi energy. C

DOI: 10.1021/acs.jpcc.8b01476 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C Table 1. Predicted Carrier Mobility of the BP/MoS2 Heterostructure and Cited Carrier Mobility of BP in Bracketsa carrier type

direction

C2D (J m−2)

me* (m0)

Ei (eV)

electron

x y x y

147.17 228.60 147.17 228.60

0.1587 0.4714 0.1538 6.7727

7.5773 7.3741 4.4973 0.24781

hole

μ2D (103 cm2 V−1 s−1) 1.258 0.6945 0.9871 11.4688

(1.123b) (0.088b) (0.674b) (15.518b)

C2D represents the in-plane elastic modulus. m*e is the effective mass. Ei represents the deformation potential constant. Carrier mobility μ2D is calculated according to eq 2 at 300 K. bCarrier mobility of monolayer BP computed from the results (C2D, me*, Ei) calculated by Qiao, etc.29 a

Figure 4. Absorption coefficient of the BP/MoS2 heterostructure and monolayer BP in (a) x direction and (b) y direction in the visible light range. (c) Optical absorption spectra of BP and the BP/MoS2 heterostructure for light incident in z direction and polarized along x and y direction in the infrared light range.

Figure 5. (a) Plane-averaged differential charge density (DCD) along z direction and side views of the isosurfaces of DCD of the BP/MoS2 heterostructure with an isovalue of 0.00015 e Å−3. The yellow region indicates gain of electrons, whereas the cyan region indicates loss of electrons. (b) Plane-averaged electrostatic potential along z direction of the BP/MoS2 heterostructure.

to 3500 nm. So it is confirmed that the BP/MoS 2 heterostructure also holds the linear dichroism feature just as pure BP. 3.3. Charge Transfer and Redistribution. To understand the heterojunction formed between BP and MoS2, which is very important for electronic device applications, the charge redistribution and transfer between the two layers in these heterostructures was calculated on the basis of the fully optimized structures. Figure 5a shows the calculated differential charge density (DCD) distribution of the BP/MoS2 heterostructure, which clearly depicts that the BP layer donates electrons to the MoS2 layer. Bader charge analysis is performed to get the exact charge transfer, which is 4.85 × 10−3 e/P atom, driven from BP to MoS2. After stacking with monolayer MoS2, BP becomes p-doping semiconductor. Figure 5b shows the plane-averaged electrostatic potential along the stacking direction. It clearly shows that there is a potential drop of

The linear dichroism feature of BP is expected to be preserved because there exists only py state from BP near the valence band maximum (VBM). To further confirm this, an optic calculation is performed. The absorption coefficient of the BP/MoS2 heterostructure and monolayer BP in a wavelength range of 300−900 nm is shown in Figure 4a,b. In the wavelength range of 300−900 nm, the absorption coefficient of the BP/MoS2 heterostructure is always significantly greater than that of monolayer BP, indicating enhanced quantum efficiency (QE) and then enhanced responsivity compared with monolayer BP. On the basis of the calculated absorption coefficient, the absorption spectra are calculated and shown in Figure 4c. In pure BP, the absorbance of the x-polarized incident light dominates the spectra, whereas the y-polarized incident light absorbance is almost zero in the wavelength range from about 1500 to 3500 nm. In the BP/MoS2 heterostructure, this feature is still there but in a smaller wavelength range from about 2000 D

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(5) Liu, H.; Neal, A. T.; Zhu, Z.; Luo, Z.; Xu, X.; Tománek, D.; Ye, P. D. Phosphorene: An Unexplored 2D Semiconductor with a High Hole Mobility. ACS Nano 2014, 8, 4033−4041. (6) Ouyang, B.; Xiong, S.; Yang, Z.; Jing, Y.; Wang, Y. MoS2 Heterostructure with Tunable Phase Stability: Strain Induced Interlayer Covalent Bond Formation. Nanoscale 2017, 9, 8126−8132. (7) Behera, S. K.; Deb, P. Controlling the Bandgap in Graphene/hBN Heterostructures to Realize Electron Mobility for High Performing FETs. RSC Adv. 2017, 7, 31393−31400. (8) Chen, X.; Wu, Y.; Wu, Z.; Han, Y.; Xu, S.; Wang, L.; Ye, W.; Han, T.; He, Y.; Cai, Y.; et al. High-Quality Sandwiched Black Phosphorus Heterostructure and Its Quantum Oscillations. Nat. Commun. 2015, 6, No. 7315. (9) You, B.; Wang, X.; Zheng, Z.; Mi, W. Black Phosphorene/ monolayer Transition-Metal Dichalcogenides as Two Dimensional van Der Waals Heterostructures: A First-Principles Study. Phys. Chem. Chem. Phys. 2016, 18, 7381−7388. (10) Lu, N.; Guo, H.; Li, L.; Dai, J.; Wang, L.; Mei, W. N.; Wu, X.; Zeng, X. C. MoS2/MX2 Heterobilayers: Bandgap Engineering via Tensile Strain or External Electrical Field. Nanoscale 2014, 6, 2879− 2886. (11) Ouyang, B.; Mi, Z.; Song, J. Bandgap Transition of 2H Transition Metal Dichalcogenides: Predictive Tuning via Inherent Interface Coupling and Strain. J. Phys. Chem. C 2016, 120, 8927−8935. (12) Min, L.; Yu, E. X.; Xi, S. Y. Tunable Band Gap of MoS2-SiC van Der Waals Heterostructures under Normal Strain and an External Electric Field. AIP Adv. 2017, 7, No. 015116. (13) Sahoo, P. K.; Memaran, S.; Xin, Y.; Balicas, L.; Gutiérrez, H. R. Sequential Edge-Epitaxy in 2D Lateral Heterostructures. 2017, arXiv preprint arXiv:1706.07014. https://arxiv.org/abs/1706.07014, pp 1 27. (14) Zhang, Z.; Chen, P.; Duan, X.; Zang, K.; Luo, J.; Duan, X. Robust Epitaxial Growth of Two-Dimensional Heterostructures, Multiheterostructures, and Superlattices. Science 2017, 357, 788−792. (15) Bernardi, M.; Palummo, M.; Grossman, J. C. Optoelectronic Properties in Monolayers of Hybridized Graphene and Hexagonal Boron Nitride. Phys. Rev. Lett. 2012, 108, No. 226805. (16) Ouyang, B.; Meng, F.; Song, J. Energetics and Kinetics of Vacancies in Monolayer Graphene Boron Nitride Heterostructures. 2D Mater. 2014, 1, No. 035007. (17) Song, L.; Liu, Z.; Reddy, A. L.; Narayanan, N. T.; Taha-Tijerina, J.; Peng, J.; Gao, G.; Lou, J.; Vajtai, R.; Ajayan, P. M. Binary and Ternary Atomic Layers Built from Carbon, Boron, and Nitrogen. Adv. Mater. 2012, 24, 4878−4895. (18) Alivov, Y. I.; Ö zgür, Ü ; Do, S.; Johnstone, D.; Avrutin, V.; Onojima, N.; Liu, C.; Xie, J. Photoresponse of N - Zn O/P - Si C Heterojunction Diodes Grown by Plasma-Assisted Molecular-Beam Epitaxy Photoresponse of N-ZnO/P-SiC Heterojunction Diodes Grown by Plasma-Assisted Molecular-Beam Epitaxy. Appl. Phys. Lett. 2015, 86, No. 241108. (19) Kuhl, U.; Stöckmann, H. J. Microwave Realization of the Hofstadter Butterfly. Phys. Rev. Lett. 1998, 80, 3232−3235. (20) Dean, C. R.; Wang, L.; Maher, P.; Forsythe, C.; Ghahari, F.; Gao, Y.; Katoch, J.; Ishigami, M.; Moon, P.; Koshino, M.; et al. Hofstadter’s Butterfly and the Fractal Quantum Hall Effect in Moiré Superlattices. Nature 2013, 497, 598−602. (21) Olsen, T.; Latini, S.; Rasmussen, F.; Thygesen, K. S. Simple Screened Hydrogenic Model of Excitons in Two-Dimensional Materials Supplementary Material. Phys. Rev. Lett. 2016, 116, No. 056401. (22) Qiu, D. Y.; da Jornada, F. H.; Louie, S. G. Optical Spectrum of MoS 2: Many-Body Effects and Diversity of Exciton States. Phys. Rev. Lett. 2013, 111, No. 216805. (23) Rivera, P.; Seyler, K. L.; Yu, H.; Schaibley, J. R.; Yan, J.; Mandrus, D. G.; Yao, W.; Xu, X. Valley-Polarized Exciton Dynamics in a 2D Semiconductor Heterostructure. Science 2016, 351, 688−691. (24) Li, Y. M.; Li, J.; Shi, L. K.; Zhang, D.; Yang, W.; Chang, K. LightInduced Exciton Spin Hall Effect in van Der Waals Heterostructures. Phys. Rev. Lett. 2015, 115, No. 166804.

3.43 eV in the BP/MoS2 heterostructure. The potential drop can drive the electrons from BP to MoS2 easily so that the hole concentration in BP and the electron carrier concentration in MoS2 can be magnified. Considering that the BP/MoS2 heterostructure can still take the advantage of the high hole mobility of the BP layer and the high electron mobility of the MoS2 layer, it is suggested that the BP layer and the MoS2 layer may exhibit a positive synergistic effect on the general carrier transport performance of the whole material.

4. CONCLUSIONS In conclusion, the equilibrium structure and electronic properties of the BP/MoS2 heterostructure is investigated using first-principles calculation. By hybridization with MoS2, the stability of BP is expected to be enhanced. Both linear dichroism and high mobility of free BP is preserved in the heterostructure. The transport performance could be enhanced in practical applications considering the synergistic effect on carrier transport, which is induced by the electrostatic potential drop in the p−n junction formed between these two layers. The hole−electron recombination is expected to be reduced for the strong carrier confinement induced by the large offset on valence bands, and the quantum efficiency (QE) is much higher in the BP/MoS2 heterostructure than in pure BP because the light absorption is much stronger. These results suggest that the BP/MoS 2 heterostructure can exhibit a much higher responsivity than that of BP, hence giving a theoretical explanation of the nearly 100 times higher responsivity of a BP/MoS2 photodetector than that of BP diodes reported by Deng,37 which proves the BP/MoS2 heterostructure a good candidate for photodetection application. Beyond that, it is also useful for unipolar electronic device applications for its type-II heterojunction with strong carrier confinement effects and most importantly, its excellent carrier transport performance.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Weihong Qi: 0000-0003-4498-0648 Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (No. 21373273). REFERENCES

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