van der Waals graphene/MoS₂ heterostructures: tuning the electronic properties and Schottky barrier by applying a biaxial strain

Abstract

First principles calculations are performed to study the effects of the interlayer distance and biaxial strain on the electronic properties and contact properties of graphene/MoS₂ heterostructures. The interlayer interaction is weakened and the charge transfer from the graphene layer to the MoS₂ layer is reduced with increasing interlayer distance in graphene/MoS₂ heterostructures, resulting in a shift of the Fermi level to a high energy state. The n-type Schottky barrier is formed with Φ_SB,N values of 0.647 eV, 0.568 eV, 0.509 eV, and 0.418 eV when the interlayer distances are 3.209 Å, 3.346 Å, 3.482 Å, and 3.755 Å, respectively. The interlayer distance and charge density difference change slightly, but the electronic structure of the graphene/MoS₂ heterostructure changes obviously by applying the biaxial strain. For the biaxial strain from −4% to +6%, the Φ_SB,P gradually increases for the graphene/MoS₂ heterostructure, while the Φ_SB,N increases initially and then decreases. Moreover, the Φ_SB,N is only 0.080 eV under a biaxial strain of +6%, indicating that the Ohmic contact is nearly formed. The results demonstrate the significant effects of a biaxial strain on the physical properties of 2D heterostructures.

---

1. Introduction

Since the discovery of graphene in 2004, its unique physics and novel applications have triggered extensive research.^1–3 Although the extremely high electrical conductivity makes graphene a potential candidate material to replace silicon-based electronic devices, Klein tunneling causes the electrical transport of Dirac fermions insensitive to the electrostatic potentials, which leads to a low current on/off ratio of graphene-based field effect transistors.^4–6 In order to realize graphene electronics, it is very important to manipulate the electronic properties without impairing its high mobility.

An important milestone is the creation of heterostructures based on graphene and other two dimensional (2D) materials, which can be assembled into three dimensional stacks with atomic layer precision.^7–9 Such layered structures have already demonstrated a range of fascinating physical phenomena. Wang et al. found that for the MoS₂/ZnO heterostructure the strong optical absorption in the visible region indicates that it has potential for application in photovoltaic and photocatalytic devices.¹⁰ The type-II band alignment occurs at MX₂/graphene-like zinc oxide interfaces, together with the large built-in electric field across the interface.^11,12 Due to the inherent weak absorption characteristics and small built-in potential of 2D material photodetectors, their external quantum efficiency is severely limited to the range of ∼0.1–1%.^13,14 Duan et al.¹⁵ modulated the amplitude and polarity of photocurrent in the gated vertical garphene/MoS₂ heterostructures via the electric field of an external gate. The maximum external quantum efficiency and internal quantum efficiency are estimated to be 55% and 85%, respectively. Moreover, graphene/MoS₂ heterostructures display highly sensitive photodetection and gate tunable persistent photoconductivity.¹⁶ The responsivity of the heterostructures is nearly 1 × 10¹⁰ A W⁻¹ at 130 K and 5 × 10⁸ A W⁻¹ at room temperature. The heterostructures could also function as a rewritable optoelectronic switch or a memory device when irradiated by the time-dependent photoillumination, where the persistent state shows almost no relaxation or decay within experimental timescales, indicating near-perfect charge retention.

Compared with metal/2D material heterostructures, the use of 2D materials to construct van der Waals vertically stacked heterostructures is one of the effective and feasible ways to reduce the effect of Fermi level pinning. Graphene has potential applications in 2D transistors due to its excellent electrical conductivity, for example, in high-performance devices and circuits based on graphene/MoS₂ heterostructures, where MoS₂ is used as the transistor channel and graphene as contact electrodes.¹⁷ As we all know, there are two mechanisms by which charge can be injected into a semiconductor: thermionic emission over the semiconductor and field emission across the semiconductor. The thermionic emission–diffusion theory describes the current–voltage characteristics of a metal/semiconductor heterostructure as a function of the Schottky barrier height. Carrier recombination can also be a current-limiting process if an inversion layer is present near the contact. Contrary to the bulk case, where the diffusion region extends both laterally and vertically into the semiconductor, in a metal/2D semiconductor heterostructure with no hybridization, the position of the bands vary only laterally, so that charge carriers injected far from the contact edge first encounter the flat-band region before the diffusion region. In this case, the relative contributions from thermionic emission and tunnelling become difficult to predict. On the basis of a thermionic field emission model, the barrier height at the graphene/MoS₂ heterostructure was determined to be 0.23 eV and the tunability of graphene work function with electrostatic doping significantly improves the Ohmic contact.¹⁸ Wei-Qing Huang et al.¹⁹ found that the transformation from an n-type Schottky barrier to a p-type Schottky barrier can be realized in MoS_xSe_(2−x)/graphene heterostructures when the Se concentration is greater than 25%. Interestingly, the Schottky type, Schottky barrier height, and contact types at the interface can be tuned by an external electric field.^19,20 On the other hand, because of their excellent Young's modulus, graphene and MoS₂ hold promise for applications in flexible electronic devices. A highly flexible transistor was developed based on an exfoliated MoS₂ channel and CVD-grown graphene source/drain electrodes, and a low Schottky barrier (∼22 meV) forms.^21–24 The graphene/MoS₂ heterostructures exhibit a Young's modulus that is about three times that of monolayer MoS₂, while correspondingly exhibiting a yield strain that is about 30–40% smaller than that of monolayer MoS₂ due to lateral buckling of the outer graphene layers.²⁵ Zhou et al.^26–28 found that the tensile strain can enhance the optical absorption in the visible range and increase the solar energy conversion efficiency for 2D heterostructures.^26–28 Moreover, with an appropriate compressive strain of 2% and 3%, the WTe₂-As heterostructures show transition from the type-I to type-II band alignment, which could slow down electron–hole pair recombination.²⁹ However, to date the effects of the strain on the structural and electronic properties of the graphene/MoS₂ heterostructures have not yet been studied systematically.

Herein, first principles calculations are done to systematically study the effects of the interlayer distance and biaxial strain on the electronic structure and contract properties of the graphene/MoS₂ heterostructures. Although the charge transfers from the graphene layer to MoS₂ layer, the electronic band structure seems to be a simple sum of those of each constituent when graphene stacks on top of the MoS₂ layer. And the contact properties are insensitive to the interlayer distance. While the biaxial strain engineering is a valuable method to modulate the electronic structure and contact properties of the graphene/MoS₂ heterostructures.

2. Computational method

All calculations are performed using VASP based on density functional theory.^30,31 The electron–ion core interaction and the exchange–correlation interaction are described by the projector augmented wave potentials³² and the Perdew–Burke–Ernzerhof formulation of the generalized gradient approximation,³³ respectively. The DFT–D2 approach in the Grimme scheme is adopted to include the contribution from the vdW interaction between layers.³⁴ The cutoff energy for the plane-waves is chosen to be 400 eV. According to the Monkhorst–Pack scheme, Brillouin zone integration is performed by using an 11 × 11 × 1 k-mesh and Gaussian smearing broadening of 0.2 eV is adopted. In order to relax the ions to the ground states with an energy convergence of 1.0 × 10⁻⁵ eV and a force convergence of 0.02 eV Å⁻¹ on each ion, a conjugate-gradient algorithm is employed. Visualizations of supercells and structures are done with the software VESTA.³⁵

The thermodynamic stability of graphene/MoS₂ heterostructures is evaluated by calculating the binding energy (E_b) as shown in the following equation:

E_b = [E_{graphene/MoS2} − (E_graphene + E_MoS2)]/N_C, (1)

where E_b, and E_{graphene/MoS2}, E_graphene, and E_MoS2 are the binding energy, and the total energy of the graphene/MoS₂ heterostructure, graphene and MoS₂ monolayers, respectively. N_C is the number of carbon atoms in the supercell. When E_b is negative, the system is stable. And the larger the absolute value of the E_b value, the stronger the heterostructure binding. To gain further insight into the bonding nature and interlayer interaction, the plane-averaged charge density difference (Δρ) was calculated as shown in the following equation:

Δρ = ρ_{graphene/MoS2}−ρ_graphene−ρ_MoS2, (2)

in which ρ_{graphene/MoS2}, ρ_graphene, and ρ_MoS2 are the plane-averaged charge densities of the graphene/MoS₂ heterostructure, graphene and MoS₂ monolayers, respectively.

3. Results and discussion

3.1 Graphene/MoS₂ heterostructure

The optimized lattice constants of monolayer graphene and MoS₂ are 2.460 Å and 3.160 Å [as shown in Fig. 1(a and b)]. To limit the lattice mismatch between graphene and MoS₂ in our calculations, the simulation cell is built from a 5 × 5 graphene supercell and a 4 × 4 MoS₂ supercell [Fig. 1(c)]. The lattice constant of the graphene/MoS₂ heterostructure is fixed as that of MoS₂ and changes the lattice constant of graphene to adjust to those of MoS₂, where graphene is under a biaxial tensile strain of 2.69% and no significant changes in the electronic properties in the heterostructure. Additionally, previous work has indicated that the structural and electronic properties of the graphene/MoS₂ heterostructure are independent of the atomic configuration.³⁶ Thus, the other atomic configuration of graphene adsorbed on MoS₂ is not taken into account.

Fig. 1 Optimized geometries for the top view of (a) graphene and (b) MoS₂ monolayers, and (c) graphene/MoS₂ heterostructure. (d) Binding energy of graphene per C as a function of the interlayer distance between graphene and the topmost S atom of MoS₂ for the graphene/MoS₂ heterostructure.

The equilibrium structure is yielded by applying the two-step optimization on the designed lattice. For step one, the interlayer distance is changed and the binding energy was calculated, and also the results were fitted into the well-known Buckingham potential equation:

in which A, B, and C are fitting parameters of −7.492 eV, 1.158 Å, and −136.063 eV Å, respectively.⁶d and E_b are the interlayer distance and the binding energy, respectively. The binding energy as a function of the interlayer distance and fitting curve is shown in Fig. 1(d). The predicted equilibrium interlayer distance read from the fitting curve is about 3.410 Å. For step two, a structure with an interlayer distance of 3.410 Å is constructed and placed into a full relaxation to yield the final equilibrium structure. After optimization, the interlayer distance between the monolayer MoS₂ and graphene is 3.414 Å, with a binding energy of −39 meV per C atom, which is of the same order of magnitude as that of other heterostructures such as MoS₂/graphene,³⁷ black phosphorene/graphene,^38–41 and arsenene/graphene.^42,43

Next, the calculated electronic band structure of the graphene/MoS₂ heterostructure is displayed in Fig. 2(c). For comparison, the electronic band structures of pristine graphene and isolated MoS₂ monolayers are also shown in Fig. 2(a and b). For the graphene/MoS₂ heterostructure, the electronic band structure seems to be a simple sum of those of each constituent. The linear dispersion bands of graphene appear in the large energy gap of MoS₂, and the character of the electronic band structure of pristine graphene seems to be preserved, indicating the weak interaction between graphene and MoS₂. In Fig. 3(a), the band alignment is schematically demonstrated to show the formation of interlayer excitons. In particular, excited electrons from graphene migrate to MoS₂, while holes go oppositely owing to the difference between their Fermi levels, and the electrons and holes can be held together by strong Coulomb interactions. The charge difference of graphene/MoS₂ heterostructure is calculated. As expected, the charge redistribution mainly occurs at the interface between the layers, with an accumulation of electrons on the MoS₂ layer and a depletion of charges on the graphene layer [Fig. 3(b and c)]. Furthermore, it can be found that the potential of graphene (8.881 eV) in the graphene/MoS₂ heterostructure is deepened as shown in Fig. 3(d). The large potential drop of the grapene/MoS₂ heterostructure indicates a strong electronic field across the interface, which may affect the kinetics of photo-generated carriers.⁴⁴

Fig. 2 Band structures of (a) graphene and (b) MoS₂ monolayers, as well as (c) graphene/MoS₂ heterostructure. The Fermi level is indicated by the green line.

Fig. 3 (a) Schematic representation of the band alignment for graphene and MoS₂ monolayers, as well as the graphene/MoS₂ heterostructure. (b) Plane averaged charge density differences, (c) three dimensional isosurface of the charge density difference, and (d) plane averaged effective potential of the graphene/MoS₂ heterostructure. The red and green areas represent electron accumulation and depletion, respectively, and the isosurface value is 2 × 10⁻⁴ e Å⁻³.

3.2 Effects of interlayer distance on the graphene/MoS₂ heterostructure

Charging the interlayer distance is an effective approach to tune the electronic properties of the van der Waals heterostructure. Moreover, the interlayer distance in the van der Waals heterostructure can be easily controlled in experiments by vacuum thermal annealing, nanomechanical pressure, or a diamond anvil cell.^45–47 Thus, it is necessary to consider the influence of the interlayer distance on the electronic properties of the graphene/MoS₂ heterostructure.

Fig. 4 displays the charge density difference of the graphene/MoS₂ heterostructure as the interlayer distance changes. From Fig. 4(a), one can observe that the fluctuation of the differential charge density curve increases when the interlayer distance is reduced from 3.755 Å to 3.209 Å, indicating the more charge transfers from the graphene layer to the MoS₂ layer. Moreover, according to Mulliken charge analysis, 0.120 e, 0.107 e, 0.088 e, and 0.062 e transfer from the graphene layer to MoS₂ layer when the interlayer distances are 3.209 Å, 3.346 Å, 3.482 Å, and 3.755 Å, respectively. The Fermi level of the graphene shifts downwards due to its charge transfers to the MoS₂ layer, while the electronic band structures of pristine graphene and MoS₂ monolayers are preserved. The band gaps of the MoS₂ layer in heterostructures are 1.747 eV, 1.737 eV, 1.747 eV, and 1.757 eV when the interlayer distances are 3.209 Å, 3.346 Å, 3.482 Å, and 3.755 Å, respectively (Fig. 5). All these results indicate that the interlayer distance is effective to control the charge transfer, while limited to regulate the electronic structure (Table 1).

Fig. 4 (a) Plane averaged charge density difference and (b) three dimensional isosurface of the charge density difference of the graphene/MoS₂ heterostructure at various interlayer distances.

Fig. 5 Band structures of the graphene/MoS₂ heterostructure at various interlayer distances: (a) 3.209 Å, (b) 3.346 Å, (c) 3.482 Å, and (d) 3.755.

Table 1 Interlayer distance d (Å), bond lengths of C–C L_C–C (Å) and Mo–S L_Mo–S (Å), and binding energy E_b (Å) of the graphene/MoS₂ heterostructure under a biaxial strain

Strain (%)	d (Å)	L C–C (Å)	L Mo–S (Å)	E b (meV C^−1)
−4	3.246	1.402	2.381	−10
−2	3.386	1.430	2.393	−55
0	3.414	1.460	2.406	−39
+2	3.423	1.489	2.421	47
+4	3.437	1.518	2.436	195
+6	3.453	1.547	2.453	397

---

3.3 Effects of biaxial strain on the graphene/MoS₂ heterostructure

It is worth noting that the electronic properties of the MoS₂ monolayer are very sensitive to the strain.^48,49 The electronic properties of the strained transition metal dichalcogenides have been invested both experimentally and theoretically in which the monolayer MoS₂ can deform up to 11%. The flexible property gives an engineering so-called “straintronics”. The direct to indirect gap transition in MoS₂ occurs at 2.7% biaxial strain.⁵⁰ Wang et al.⁵¹ found that the band gap monotonically decreases with increasing strain. Moreover, the conduction band minimum shifts toward the Fermi level, leading to a semiconductor to metal transformation at 10% biaxial strain.⁵² To investigate the effect of strain on the properties of the heterostructure, the graphene/MoS₂ heterostructure under xy-plane biaxial compressive and tensile strain is studied. The biaxial strain is applied along the xy-plane by varying the lattice constant of the heterostructure and can be defined as follows:

ε = (a−a₀)/a, (4)

where a and a₀ are the equilibrium and strained lattice constant, respectively. One can observe that under the varying biaxial strain from −4% to +6%, the interlayer distance and bond lengths of C–C in the graphene layer and Mo–S in the MoS₂ layer increase. Particularly, the interlayer distances of the graphene/MoS₂ heterostructure are 3.246 Å, 3.386 Å, 3.423 Å, and 3.453 Å under a biaxial strain of −4%, −2%, +2%, and +6%, respectively. Moreover, when biaxial compressive strain is applied the binding energy maintains a negative value. In contrast, when the biaxial tensile strain is applied the binding energy changes to a positive value, indicating the weakened interaction between graphene and MoS₂.

Fig. 6 shows the charge density difference of the graphene/MoS₂ heterostructure under the biaxial strain. It is found that the fluctuation of the differential charge density curve decreases when the biaxial strain changes from −4% to +6%, indicating the less charge transfers from the graphene layer to MoS₂ layer [Fig. 6(a)]. The same phenomenon can observe through the three dimensional isosurface of the charge density difference of the graphene/MoS₂ heterostructure as shown in Fig. 6(b). According to Mulliken charge analysis, 0.062 e, 0.059 e, 0.055 e, and 0.051 e are transferred from the graphene layer to the MoS₂ layer under a biaxial strain of −4%, −2%, +2%, and +6%, respectively. Thus, by applying biaxial strain, the interlayer distance and charge density difference change slightly. However, there is an obvious change in the electronic structure of the graphene/MoS₂ heterostructure by applying the biaxial strain. Although the electronic band structures of pristine graphene is still preserved, the band structure of MoS₂ substantial changes under the biaxial strain. In particular, the band gaps of the MoS₂ layer in the heterostructure are 1.669 eV, 1.806 eV, 1.352 eV, and 0.618 eV under a biaxial strain of −4%, −2%, +2%, and +6%, respectively (Fig. 7).

Fig. 6 (a) Plane averaged charge density differences and (b) three dimensional isosurface of the charge density difference of the graphene/MoS₂ heterostructure under a biaxial strain.

Fig. 7 Band structures of the graphene/MoS₂ heterostructure under a biaxial strain: (a) −4%, (b) −2%, (c) +2%, and (d) +6%.

It is obvious that the graphene/MoS₂ heterostructure is characterized by the metal/semiconductor heterostructure. In the graphene/MoS₂ heterostructure, the n-type Schottky barrier height (Φ_SB,N) is Φ_SB,N = E_CBM − E_F, whereas the p-type Schottky barrier height (Φ_SB,P) is Φ_SB,P = E_F − E_VBM. E_CBM, E_VBM, and E_F represent the conduction band minimum, valence band maximum, and Fermi level, respectively. Fig. 8 displays the evolution of the n- and p-type Schottky barrier height (Φ_SB,N and Φ_SB,P) of the graphene/MoS₂ heterostructure at the various interlayer distance and under the biaxial strain. When the interlayer distance is reduced, the Φ_SB,N gradually increases, but Φ_SB,P gradually decreases. Moreover, the value of Φ_SB,P is always larger than that of Φ_SB,N, indicating a n-type Schottky contact. The Φ_SB,N values are 0.647 eV, 0.568 eV, 0.509 eV, and 0.418 eV when the interlayer distances are 3.209 Å, 3.346 Å, 3.482 Å, and 3.755 Å, respectively [Fig. 8(a)]. For applying the biaxial strain from −4% to +6%, the Φ_SB,P gradually increases for the graphene/MoS₂ heterostructure, while the Φ_SB,N increases initially and then decreases [Fig. 8(b)]. Furthermore, the Φ_SB,N is only 0.080 eV under a biaxial strain of +6%, indicating that the Ohmic contact is nearly formed.

Fig. 8 The evolution of the n- and p-type Schottky barrier height (Φ_SB,N and Φ_SB,P) of the graphene/MoS₂ heterostructure: (a) at various interlayer distances and (b) under a biaxial strain.

4. Conclusions

First principles calculations are performed to study the effects of the biaxial strain on the electronic properties and Schottky barrier of graphene/MoS₂ heterostructures. It is found that the interlayer interaction is weakened and the charge transfer from the graphene layer to MoS₂ layer is reduced with increasing interlayer distance, resulting in a shift of the Fermi level to a high energy state. The n-type Schottky barrier is formed with Φ_SB,N values are 0.647 eV, 0.568 eV, 0.509 eV, and 0.418 eV when the interlayer distances are 3.209 Å, 3.346 Å, 3.482 Å, and 3.755 Å, respectively. The interlayer distance and charge density difference change slightly, while there is an obvious change in the electronic structure of the graphene/MoS₂ heterostructure by applying the biaxial strain. For a biaxial strain of −4% to +6%, the Φ_SB,P gradually increases for the graphene/MoS₂ heterostructure, while the Φ_SB,N increases initially and then decreases. Furthermore, the Φ_SB,N is only 0.080 eV under a biaxial strain of +6%, indicating that the Ohmic contact is nearly formed. Our results provide a detailed understanding of the interfacial properties of graphene/MoS₂ heterostructures and help to predict the performance of 2D material-based devices.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was jointly supported by the Doctoral Program of Xi'an Polytechnic University (Grant No. 107020519 and 107020534), the National Natural Science Foundation of China (Grant No. 11674264 and 51771144), and the Natural Science Foundation of Shaanxi Province (Grant No. 2019TD-020, 2017JZ015, 2019JM-083, 2020JQ-823 and 2019JLM-30). This work was carried out using the HPCC platform at Xian Jiaotong University.

References

1. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva and A. A. Firsov, Science, 2004, 306, 666–669.
2. A. K. Geim and K. S. Novoselov, Nat. Mater., 2007, 6, 183–191.
3. Y. D. Ma, Y. Dai, M. Guo, C. N. Niu, L. Yu and B. B. Huang, Nanoscale, 2011, 3, 2301–2306.
4. Y. Wu, Y. Lin, A. A. Bol, K. A. Jenkins, F. Xia, D. B. Farmer, Y. Zhu and P. Avouris, Nature, 2011, 472, 74–78.
5. L. Liao, Y. C. Lin, M. Bao, C. Rui, J. Bai, Y. Liu, Y. Qu, K. L. Wang, Y. Huang and X. Duan, Nature, 2010, 467, 305–308.
6. Y. Xie, S. Cao, X. Wu, B. Y. Yu, L. Y. Chen and J. M. Zhang, Physica E, 2020, 124, 114252.
7. S. J. Haigh, A. Gholinia, R. Jalil, S. Romani, L. Britnell, D. C. Elias, K. S. Novoselov, L. A. Ponomarenko, A. K. Geim and R. Gorbachev, Nat. Mater., 2012, 11, 1–4.
8. C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard and J. Hone, Nat. Nanotechnol., 2010, 5, 722–726.
9. K. S. Novoselov, Rev. Mod. Phys., 2011, 83, 837–849.
10. S. Wang, C. Ren, H. Tian, J. Yu and M. Sun, Phys. Chem. Chem. Phys., 2018, 20, 13394–13399.
11. S. Wang, H. Tian, C. Ren, J. Yu and M. Sun, Sci. Rep., 2018, 8, 12009.
12. S. Wang, N. T. Hung, H. Tian, M. S. Isiam and R. Saito, Phys. Rev. Appl., 2021, 16, 024030.
13. Y. Liu, R. Cheng, L. Liao, H. L. Zhou, J. W. Bai, G. Liu, L. X. Liu, Y. Huang and X. F. Duan, Nat. Commun., 2011, 2, 579.
14. T. J. Echtermeyer, L. Britnell, P. K. Jasnos, A. Lombardo, R. V. Gorbachev, A. N. Grigorenko, A. K. Geim, A. C. Ferrari and K. S. Novoselov, Nat. Commun., 2011, 2, 458.
15. W. J. Yu, Y. Liu, H. L. Zhou, A. X. Yin, Z. Li, Y. Huang and X. F. Duan, Nat. Nanotechnol., 2013, 8, 952.
16. K. Roy, M. Padmanabhan, S. Goswami, T. P. Sai, G. Ramalingam, S. Raghavan and A. Ghosh, Nat. Nanotechnol., 2013, 8, 826.
17. J. Y. Kwak, J. Hwang, B. Calderon, H. Alsalman, N. Munoz, B. Schutter and M. G. Spencer, Nano Lett., 2014, 14, 4511–4516.
18. L. L. Yu, Y. H. Lee, X. Ling, E. J. G. Santos, Y. C. Shin, Y. X. Lin, M. Dubey, E. Kaxiras, J. Kong, H. Wang and T. Palaxios, Nano Lett., 2014, 14, 3055–3063.
19. C. Lee, X. Wei, J. W. Kysar and J. Hone, Science, 2008, 321, 385.
20. K. Yin, T. Huang, H. Y. Wu, Y. Si, J. C. Lian, Y. W. Xiao, Z. Zhang, W. Q. Huang, W. Hu and G. F. Huang, J. Phys. D: Appl. Phys., 2021, 54, 265302.
21. T. Huang, Q. Chen, M. Q. Cheng, W. Q. Huang, W. Hu and G. F. Huang, J. Phys. D: Appl. Phys., 2019, 52, 305104.
22. S. Bertolazzi, J. Brivio and A. Kis, ACS Nano, 2011, 5, 9703–9709.
23. A. Castellanos−Gomez, M. Poot, G. A. Steele, H. S. J. van der Zant, N. Agraït and G. Rubio−Bollinger, Adv. Mater., 2012, 24, 772.
24. J. Pu, Y. Yomogida, K. K. Liu, L. J. Li, Y. Iwasa and T. Takenobu, Nano Lett., 2012, 12, 4013–4017.
25. J. W. Jiang and H. S. Park, Appl. Phys. Lett., 2014, 105, 033108.
26. H. Zhang, D. Wu, Q. Tang, L. Liu and Z. Zhou, J. Mater. Chem. A, 2013, 1, 2231–2237.
27. H. Zhang, Y. Li, Q. Tang, L. Liu and Z. Zhou, Nanoscale, 2012, 4, 1078–1084.
28. I. Shahid, S. Ahmad, N. Shehzad, S. Yao, C. V. Nguyen, L. Zhang and Z. Zhou, Appl. Surf. Sci., 2020, 523, 146483.
29. N. Shehzad, I. Shahid, S. Yao, S. Ahmad, A. Ali, L. Zhang and Z. Zhou, Int. J. Hydrogen Energy, 2020, 45, 27089–27097.
30. G. Kresse and J. Hafner, Phys. Rev. B: Condens. Matter Mater. Phys., 1993, 47, 558–561.
31. G. Kresse and J. Hafner, Phys. Rev. B: Condens. Matter Mater. Phys., 1994, 49, 14251–14269.
32. P. E. Blöchl, Phys. Rev. B: Condens. Matter Mater. Phys., 1994, 50, 17953–17979.
33. J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996, 77, 3865–3868.
34. S. Grimme, J. Comput. Chem., 2006, 27, 1787–1799.
35. K. Momma and F. Izumi, J. Appl. Crystallogr., 2008, 41, 653–658.
36. Y. D. Ma, Y. Dai, M. Guo, C. W. Niu and B. B. Huang, Nanoscale, 2011, 3, 3883–3887.
37. W. Hu, T. Wang, R. Zhang and J. Yang, J. Mater. Chem. C, 2016, 4, 1776–1781.
38. J. E. Padilha, A. Fazzio and A. J. R. da Silva, Phys. Rev. Lett., 2015, 114, 066803.
39. W. Hu, T. Wang and J. Yang, J. Mater. Chem. C, 2015, 3, 4756–4761.
40. B. Liu, L. J. Wu, Y. Q. Zhao, L. Z. Wang and M. Q. Cai, Phys. Chem. Chem. Phys., 2016, 18, 19918–19925.
41. Y. Cai, G. Zhang and Y. W. Zhang, J. Phys. Chem. C, 2015, 119, 13929–13936.
42. C. Xia, B. Xue, T. Wang, Y. Peng and Y. Jia, Appl. Phys. Lett., 2015, 107, 193107.
43. Y. Wang and Y. Ding, Phys. Chem. Chem. Phys., 2015, 17, 27769–27776.
44. W. J. Zhang, C. P. Chu, J. K. Huang, C. H. Chen, M. L. Tsai, Y. H. Chang, C. T. Liang, Y. Z. Chen, Y. L. Chueh, J. H. He, M. Y. Chou and L. J. Li, Sci. Rep., 2014, 4, 3826.
45. S. Tongay, W. Fan, J. Kang, J. Park, U. Koldemir, J. Suh, D. S. Narang, K. Liu, J. Ji, J. Li, R. Sinclair and J. Wu, Nano Lett., 2014, 14, 3185–3190.
46. M. Dienwiebel, G. S. Verhoeven, N. Pradeep, J. W. M. Frenken, J. A. Heimberg and H. W. Zandbergen, Phys. Rev. Lett., 2004, 92, 126101.
47. S. Clark, K. J. Jeon, J. Y. Chen and C. S. Yoo, Solid State Commun., 2013, 154, 15–18.
48. H. J. Conley, B. Wang, J. I. Ziegler, R. F. J. Haglund, S. T. Pantelides and K. I. Bolotin, Nano Lett., 2013, 13, 3626–3630.
49. P. Johari and V. B. Shenoy, ACS Nano, 2012, 6, 5449–5456.
50. L. Wang, A. Kutana and B. I. Yakobson, Ann. Phys., 2014, 526, L7–L12.
51. S. Wang, M. S. Ukhtary and R. Saito, Phys. Rev. Res., 2020, 2, 033340.
52. P. Johari and V. B. Shenoy, ACS Nano, 2012, 6, 5449–5456.

---