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Sci Rep
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Scientific Reports
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67150
10.1038/s41598-024-67150-2
Article
Tuning the Schottky barrier height in single- and bi-layer graphene-inserted MoS2/metal contacts
Zhao Xumei 1
Xia Caijuan caijuanxia@xpu.edu.cn

1
Li Lianbi 1
Wang Anxiang 1
Cao Dezhong 1
Zhang Baiyu 2
Fang Qinglong qinglong_fang@xpu.edu.cn

1
1 https://ror.org/03442p831 grid.464495.e 0000 0000 9192 5439 School of Science, Xi’an Polytechnic University, Xi’an, 710048 Shaanxi China
2 grid.133342.4 0000 0004 1936 9676 Materials Department, University of California, Santa Barbara, CA 93106-5050 USA
8 9 2024
8 9 2024
2024
14 209054 5 2024
8 7 2024
© The Author(s) 2024
2024
https://creativecommons.org/licenses/by/4.0/ Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
First-principle calculations based on density functional theory are employed to investigate the impact of graphene insertion on the electronic properties and Schottky barrier of MoS2/metals (Mg, Al, In, Cu, Ag, Au, Pd, Ti, and Sc) without deteriorating the intrinsic properties of the MoS2 layer. The results reveal that the charge transfer mainly occurs at the interface between the graphene and metal layers, with smaller transfer at the interface between bi-layer garphene or between graphene and MoS2. And the tunneling barrier exists at the interface between graphene and MoS2, which hinders electron injection from graphene to MoS2. Importantly, the Schottky barrier height (ΦSB,N) decreases upon graphene insertion into MoS2/metal contacts. Specifically, for single-layer graphene, the ΦSB,N of MoS2 contacted with Mg, In, Sc, and Ti are − 0.116 eV, − 0.116 eV, − 0.014 eV, and − 0.116 eV, respectively. Furthermore, with bilayer graphene, when by inserting bi-layer graphene, the negative n-type Schottky barrier of − 0.086 eV, − 0.114 eV, − 0.059 eV, − 0.008 eV, and − 0.0636 eV are observed for MoS2 contacted with the respective metals, respectively. These findings provide a practical guidance for developing and designing high-performance transition metal dichalcogenide nanoelectronic devices.

Keywords

MoS2
Electronic properties
Schottky barrier
First-principle calculations
Subject terms

Materials science
Nanoscience and technology
Physics
Doctoral Program of Xi'an Polytechnic University107020519 107020534 Scientific Research Program Funded by Shaanxi Provincial Education Department22JK0401 23JC037 22JC033 National Key Laboratory of Plasma Physics6142A04230302 6142A04230302 Key Research and Development Program of Shaanxi Province2023-YBGY-196 2023-YBGY-196 Shaanxi Fundamental Science Research Project for Mathematics and Physics22JSY030 22JSY012 22JSQ009 Fundamental Research Funds of Shaanxi Key Laboratory of Artificially-Structured Functional Materials and DevicesAFMD-KFJJ-21207 AFMD-KFJJ-21207 Science and Technology Plan Project of Xi'an2021XJZZ0009 2021XJZZ0009 Natural Science Foundation of Shaanxi Province2023-JC-YB-590 2024JC-YBMS-348 China Postdoctoral Science Foundation2023M742730 Cao Dezhong issue-copyright-statement© Springer Nature Limited 2024
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pmcIntroduction

Two-dimensional (2D) transition metal dichalcogenides (TMDs) have attracted considerable attention as potential channel materials for next-generation nanoelectronic devices due to their atomic thickness, high carrier mobility, low concentration of surface dangling bonds, and suitable band gap1–3. Previous studies on 2D MoS2 transistors have demonstrated excellent field-effect mobility with high on–off ratio at room temperature4–6. However, due to the Fermi level pinning, the contact resistance of MoS2/metal contact is up to 5 kΩ·μm–1 MΩ·μm, which is more than 30 times larger than that of the Si/metal7,8. This high contact resistance poses a significant barrier to realizing the low power application potential of MoS2-based devices.

The origin of high contact resistance for MoS2/metal remains unclear, even though several factors have been proposed, including the wide contact tunnel barrier, the high Schottky barrier (ΦSB), and high intrinsic resistance of semiconductor channel9–11. In principle, the transport properties of 2D materials devices are often limited by the contact tunnel barrier and Schottky barrier rather than the intrinsic resistance. Efforts have been made to mitigate Schottky barrier by employing low work function metals. For instance, Das et al.4 achieved enhanced effective mobilities by using scandium contacts on exfoliated MoS2 flakes covered by a 15 nm Al2O3 film. However, to date, the reported lowest contact resistance using scandium electrode is still far from satisfactory. Novel doping strategies for TMDs have also been explored to reduce the Schottky barrier12–15. However, the reliable doping technology with precise control over doping concentration and doping profile for 2D transistors16. Recent experiments have demonstrated significant Schottky barrier reduction when ultrathin tunnel layer is inserted between MoS2 and metal electrode17–22. For example, through a dry transfer technique and a metal-catalyzed graphene treatment process, Leong et al.23 fabricated nickel-etched-graphene electrodes on MoS2 that yield contact resistance as low as 200 Ω·μm. Du et al.24 claimed that MoS2/graphene/Ti Schottky barrier provides electron injection efficiency up to 130 times higher in the subthreshold regime when compared with MoS2/Ti, which resulted in VDS polarity dependence of device parameters such as threshold voltage (VTH) and subthreshold swing (SS). Chanana et al.25 proposed that unlike MoS2/metal contacts, the projected dispersion of MoS2 remains preserved in MoS2/graphene/metal contacts with shift in the bands on the energy axis. A proper choice of metal may exhibit ohmic nature in a graphene-inserted MoS2/metal contact. Moreover, Qiu et al.26 demonstrated that the contacts of the multi-layered MoS2/graphene have tunable negative barriers in the range of 300 to − 46 meV as a function of gate voltage. Thus, 2D materials insertion shows great potential to effectively adjust the contact properties of MoS2/metal contacts.

Graphene has been identified as an effective approach to adjust the work function of the metal27. it interacts strongly with the metals, such as Co, Ni, Pd and Ti, which involves hybridization between graphene pz states and metal d states and reduces considerably the work function of the metal28. Moreover, the substantial potential drop (8.881 eV) between MoS2 and graphene could promote the charge transfer from graphene to MoS2 layer. In this work, we investigate the electronic properties and Schottky barrier of MoS2/metals (Mg, Al, In, Cu, Ag, Au, Pd, Sc, and Ti) by inserting single- and bi-layer graphene based on density functional theory (DFT). Our study reveals that the tunneling barrier existed at the interface between graphene and MoS2, which hinders electron injection from graphene to MoS2. We achieved the decrease of ΦSB,N upon graphene insertion in MoS2/metal contacts. The results are systematically discussed, and provide valuable insights for design of high-performance device.

Computational details

First-principle calculations based on DFT were carried out by using the Vienna ab initio simulation package (VASP)29,30. The projector augmented wave (PAW) method31 was used to describe the electron–ion core interaction, which is more accurate than the ultra-soft pseudo-potentials. The Perdew-Burke-Ernzerhof (PBE)32 formulation of the generalized gradient approximation (GGA) was chosen to describe the exchange–correlation interaction. Since the semi-local functional, such as, GGA fail to describe weakly interacting systems, the van der Waals interaction in the Grimme approach was adopted to describe the weak interlayer interaction33. The cutoff energy for the plane-waves was chosen to be 450 eV. The Brillouin-zone integration was performed by using an 11 × 11 × 1 k-mesh according to the Monkhorst–Pack scheme and Gaussian smearing broadening of 0.05 eV was adopted. To avoid artificial interactions between the periodic images of the structures, a vacuum region of at least 15 Å was used. A conjugate-gradient algorithm was employed 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 on each ion, respectively. Visualizations of supercell and structure were done with the software VESTA34.

Results and discussions

The optimized structures of single-layer graphene and MoS2 are shown in Fig. 1a,b, with the lattice constants of 2.460 Å and 3.160 Å, respectively, which is consistent with previous experimental and theoretical results.35,36 In the optimized configurations, the bond lengths of C–C and Mo–S are 1.406 and 2.413 Å, respectively. Figure 1c illustrates the slab of the stacking MoS2/graphene/metal contact configuration, containing six layers of metal, single-layer graphene and MoS2. A vacuum of 15 Å in thickness is included to avoid spurious interactions. Due to the the different lattice constants of the components, the supercells of the coincidence site lattice (CSL) in the commensurable structures are commonly different. The in-plane supercells are constructed to minimize the lattice misfit strain between MoS2, graphene, and metal, in which a basis vector on a given metal surface is denoted by h1c1→+h2c2→, with (c1→, c2→) being the basis vector of the primitive cell, and (h1, h2) the integers. Similarly, m1a1→+m2a2→ and n1b1→+n2b2→ are the basis vectors of MoS2 and graphene supercells, respectively, with (a1→, a2→) and (b1→, b2→) being the basis vectors of the the primitive cells, and as (m1, m2) and (n1, n2) are integers. As set of values of m1, m2, n1, and n2 (h1, and h2) are determined so that the lattice mismatch δ1 (δ2) between the supercells of MoS2 and graphene (metal) meets the following condition:1 -δ1≤n1b1→+n2b2→-m1a1→+m2a2→m1a1→+m2a2→≤δ1

2 -δ2≤h1c1→+h2c2→-m1a1→+m2a2→m1a1→+m2a2→≤δ2

Figure 1 Optimized geometries for top view of monolayers (a) graphene and (b) MoS2. Side view of MoS2/metals by inserting graphene: (c) single-layer and (d) bi-layer.

The N×N, and H×H unit cells of graphene and metal are adjusted to the M×M unit cell of MoS2, in which N=n12+n22+n1n2, H=h12+h22+h1h2, and M=m12+m22+m1m2. For the in-plane lattice mismatch within δ1 and δ2 (≤5%), the supercells of the contacts are usually larger with a broken symmetry. Based on this approach, the CSL of MoS2, graphene, and metal are modeled, and the parameters are listed in Table 1. We adopt 3×3 MoS2 and 4×4 graphene supercells to 3×3 Mg(0001) and Cu(111) supercells, 4×4 MoS2 and 5×5 graphene supercells to 4×4 In(101) supercell, 23×23 MoS2 and 19×19 graphene supercells to Al(0001) and Pd(111) supercells, and 23×23 Sc(0001) and Ti(0001) supercells, and 13×13 MoS2 and 19×19 graphene supercells to 4×4 Ag(111) and Au(111) supercells, respectively. As listed in Table 1, the lattice constant mismatches are all less than 5%. Similarly, the MoS2/metal contacts by inserting bi-layer graphene are also constructed and as shown in Fig. 1d.Table 1 In-plane supercell defined by the MoS2 basis vector m1a1→+m2a2→, graphene basis vector n1b1→+n2b2→, and the metal basis vector h1c1→+h2c2→ for MoS2/metal with inserting single-layer graphene.

Metal	m1, m2	n1, n2	h1, h2	δ1 (%)	δ2 (%)	
Mg	3, 0	4, 0	3, 0	3.8	1	
Al	2, 2	3, 2	4, 0	0.8	1.09	
In	4, 0	5, 0	4, 0	2.7	4.15	
Cu	3, 0	4, 0	3, 0	3.8	0.73	
Ag	4, − 1	5, − 2	4, 0	1.9	0.93	
Au	4, − 1	5, − 2	4, 0	1.9	0.81	
Pd	2, 2	3, 2	4, 0	0.8	0.34	
Sc	2, 2	3, 2	2, 2	0.8	3	
Ti	2, 2	3, 2	2, 2	0.8	4.74	
δ1 (δ2) represents the mismatch between the MoS2 and graphene (metal) lattices.

The optimized parameters of MoS2/metal contact by inserting single- and bi-layer graphene are listed in Table 2. For Mg, Al, In, Cu, Ag, Au, and Pd, the the average vertical separations between the metal and graphene (dM-G) are 3.412 Å, 3.167 Å, 3.257 Å, 2.999 Å, 2.828 Å, 3.090 Å, and 2.789 Å, respectively, and they are longer than the covalent bond lengths of Mg–C (2.172 Å), Al–C (1.972 Å), In–C (2.182 Å), Cu–C (2.082 Å), Ag–C (2.212 Å), Au–C (2.122 Å), Pd–C (2.152 Å) pairs, respectively, indicating weak interaction between them.39 For Sc and Ti, the values of dM-G are 2.171 Å and 2.112 Å, respectively, and they are shorter than the covalent bond lengths of Sc-C (2.462 Å) and Ti–C (2.362 Å), respectively, indicating strong interaction between them. The values of dG-G are 3.197 Å, 3.042 Å, 3.141 Å, 3.161 Å, 3.272 Å, 3.298 Å, 3.210 Å, and 3.050 Å for Mg, Al, In, Cu, Ag, Au, Pd, Sc, and Ti, respectively, and they are slightly longer than that of the bi-layer graphene (3.355 Å)40. Furthermore, the dG-MS of single- or bi-layer graphene insertion are comparable with that of MoS2/graphene (3.320 Å), due to the weak van der Waal interaction between them41.Table 2 Calculated interfacial properties of MoS2/metals by inserting single-layer and bi-layer graphene.

Metal	WM (eV)	Single-layer graphene inserted	Bi-layer graphene inserted	
dM-G (Å)	dG-MS (Å)	WM/G (eV)	dM-G (Å)	dG-G (Å)	dG-MS (Å)	WM-2G (Å)	
Mg	4.321

3.66b

	3.412	3.341	3.579	3.393	3.197	3.339	3.933	
Al	3.878	3.167	3.439	3.662

4.04a

	3.354	3.042	3.349	4.213	
In	3.707	3.257	3.298	3.376	3.236	3.141	3.304	3.812	
Cu	4.796

4.65b

	2.999	3.346	4.324

4.40a

	3.075	3.161	3.357	4.345	
Ag	4.321

4.26b

	2.828	3.486	4.013

4.24a

	2.858	3.272	3.349	3.781	
Au	4.925

5.10b

	3.090	3.378	4.566

4.74a

	2.962	3.298	3.345	4.818	
Pd	5.075

5.12b

	2.789	3.425	4.669

4.03a

	2.787	3.298	3.338	4.160	
Sc	3.276

3.50b

	2.171	3.246	3.604	2.188	3.210	3.369	3.929	
Ti	4.266

4.33b

4.58c

	2.112	3.243	3.593

4.17a

	1.952	3.050	3.419	4.053	
dM-G, dG-G, and dG-MS, as marked in Fig. 1c,d, are the average vertical separation between the metal and graphene, between bi-layer graphene, and between graphene and MoS2, respectively. WM and WM/G (WM/2G) are the work functions of the free-standing metal surfaces and adsorbed single-layer (bi-layer) graphene, respectively.

aReference28.

bReference37.

cReference38.

Figures 2 and 3 display the charge density difference of MoS2/metal by inserting single- and bi-layer graphene, respectively. The charge density difference is calculated as:3 Δρ(z)=∫ρcontactdxdy-∫ρMSdxdy-∫ρidxdy-∫ρMdxdy,

in which ρcontact, ρMS, ρi, and ρM are the charge densities of the contact system, the isolated MoS2, inserting layer (single- or bi-layer graphene), and metal, respectively. As shown in Figs. 2 and 3, the charge transfer mainly occurs at the interface between the graphene and metal layers, with smaller transfer at the interface between bi-layer garphene or between graphene and MoS2. Specifically, the charge transfer oscillation occurs near the interface between graphene and Sc/Ti, indicating strong interaction and the formation of interfacial dipole layers. Furthermore, the Bader charge analysis has also been conducted for those interfaces. The Bader charge distribution of MoS2/metal contact by inserting single-layer graphene exhibits the average charge values of 0.035 e, 0.052 e and 0.049 e at the interface of the graphene/Mg, Al, and In, respectively, showing weak interactions. Medium interaction are observed at the interface of graphene/Cu, Ag, and Au with the average charge values of 0.069 e, 0.070 e and 0.073 e, respectively. The average charge values of 0.101 e, 0.125 e and 0.208 e at the interface between the graphene and Pd, Sc, and Ti, respectively, indicating strong interactions between them. However, the average charge values of 0.032 e, 0.042 e, 0.034 e, 0.038 e, 0.042 e, 0.042 e, 0.046 e, 0.039 e, and 0.042 e at the interface between the graphene and MoS2, respectively, indicating weak interactions between them. For MoS2/metal contact by inserting bi-layer graphene, the interactions between metal and graphene, as well as between graphene and MoS2 are similar to that of the MoS2/metal contact by inserting singly-layer graphene.Figure 2 Plane-average charge density difference along the z-direction of MoS2/metals by inserting single-layer graphene.

Figure 3 Plane-average charge density difference along the z-direction of MoS2/metals by inserting bi-layer graphene.

To investigate the effects of the inserting singly-layer and bi-layer graphene on the electron tunnel of MoS2/metal contact, the average effective potential in the x–y plane normal to the interface and the tunneling barrier ΔV are calculated, as shown in Figs. 4 and 5, respectively. The height ΔV defined as the potential energy above EF between graphene and metal, bi-layer graphene, as well as garphene and MoS2, and its width ωB is defined as the full width at half maximum of ΔV. The barrier height reflects the lowest barrier that electrons at EF need to overcome upon injection between neighboring layers. With singly-layer graphene, no tunneling barrier exists at the graphene/metal interface. However, there is noticeable tunneling barrier at exists at the graphene/MoS2 interface with the values of ΔV are 0.568 eV, 1.889 eV, 1.456 eV, 0.309 eV, 1.061 eV, 0.111 eV and 0.313. The corresponding values of ωB are 0.422 Å, 0.826 Å, 0.654 Å, 0.292 Å, 0.562 Å, 0.153 Å, and 0.252 Å for Mg, Al, In, Ag, Au, Pd, and Sc, respectively (excluding Cu and Ti). For inserting bi-layer graphene, the tunneling barrier only exists at the interface between graphene and Al, and the values of ΔV and ωB are 0.420 eV and 0.164 Å, respectively; At the interface between bi-layer graphene for Al, In, Au, and Sc, the values of ΔV are 1.320 eV, 0.620 eV, 0.181 eV, and 0.296 eV, as well as the values of ωB are 0.281 Å, 0.233 Å, 0.246 Å, and 0.192 Å, respectively; At the interface between graphene and MoS2 for Al, Mg, In, Cu, Ag, Au, Pd, Sc, and Ti, the values of ΔV are 1.070 eV, 2.604 eV, 1.990 eV, 0.566 eV, 0.586 eV, 1.270 eV, 0.466 eV, 1.590 eV and 0.360 eV, as well as the values of ωB are 0.389 Å, 0.398 Å, 0.240 Å, 0.179 Å, 0.308 Å, 0.330 Å, 0.299 Å, 0.380 Å and 0.184 Å, respectively. The tunneling probability TB can be evaluated as follows:4 TB=exp-2×2mΔVħ×ωB,

where m is the effective mass of a free electron and ħ is the Planck’s constant. The TB values at the interface between graphene and MoS2 in the MoS2/metal contact by inserting singly-layer graphene are estimated to be 88%, 62.2%, 69.7%, 93.1%, 77.4%, 97.8%, and 94% for MoS2 contacted with Mg, Al, In, Ag, Au, Pd, and Sc, respectively. For MoS2/metal contact with bi-layer graphene insertion, the TB values at the interface between graphene and Al are estimated to be 96.5%; The TB values at the interface between bi-layer graphene are estimated to be 89.7%, 94.0%, 96.5% and 96.5% for Al, In, Au, and Sc, respectively; The TB values at the interface between graphene and MoS2 are estimated to be 87.4%, 80.5%, 89.2%, 95.6%, 92.4%, 88.2%, 93.4%, 85.1%, and 96.4% for Mg, Al, In, Cu, Ag, Au, Pd, Sc, and Ti, respectively. Therefore, inserting graphene is not determinant to the tunneling transmission in MoS2/metal contacts.Figure 4 Plane-average electronic potential along the z-direction of MoS2/metals by inserting single-layer graphene.

Figure 5 Plane-average electronic potential along the z-direction of MoS2/metals by inserting bi-layer graphene.

As shown in Figs. 6 and 7, the partial density of states (PDOS) of graphene and MoS2 sublayers in MoS2/metal contacts by inserting single- and bi-layer graphene has been studied, respectively. While graphene does not introduce an additional contact barrier, it induces significant change of electronic structure on itself. For the MoS2/metal contact by inserting singly-layer graphene, the Dirac cone gets shifted and below Fermi level for Mg, Al, In, Cu, and Ag, but exhibits opposite trend for Au. Moreover, the Dirac nature is completely lost when MoS2 contacted with Pd, Sc, and Ti. The same phenomenon occurs for graphene which is adjacent to metal layer in the MoS2/metal contact by inserting bi-layer graphene, but the Dirac cone is not perturbed for graphene which is adjacent to MoS2 layer. Compared to the free monolayer MoS2, although the semiconductor future is maintained, the energy band alignment and band gap of the MoS2 in MoS2/metal by inserting single- and bi-layer graphene have changed. For inserting singly-layer graphene, the conduction band of MoS2 across Fermi level when contacted with Mg, In, Sc, and Ti, while the Fermi level lies in the band gap and closes to the conduction band minimum of MoS2 when contacted with Al, Cu, Ag, Au, and Pd, indicating an n-type semiconductor. The values of band gap are 1.567 eV, 1.526 eV, 1.540 eV, 1.562 eV, 1.562 eV, 1.553 eV, 1.536 eV, 1.482 eV, and 1.540 eV for MoS2 when contacted with Mg, Al, In, Cu, Ag, Au, Pd, Sc, and Ti, respectively. The same phenomenon occurs for inserting bi-layer graphene except for MoS2 contacted with Pd. And the values of band gap are 1.572 eV, 1.589 eV, 1.544 eV, 1.300 eV, 1.571 eV, 1.544 eV, 1.544 eV, 1.466 eV and 1.593 eV for MoS2 when contacted with Mg, Al, In, Cu, Ag, Au, Pd, Sc, and Ti, respectively. This again implies that graphene is successful in isolating the MoS2 layer from metal with equivalent zero midgap states and only shifts of valence band maximum and conduction band minimum with respect to free MoS2, and the interaction between graphene and metal dictates the amount and nature of shift.Figure 6 Partial density of states (PDOS) of graphene and MoS2 layers in MoS2/metals by inserting single-layer graphene.

Figure 7 Partial density of states (PDOS) of graphene and MoS2 layers in MoS2/metals by inserting bi-layer graphene.

Finally, the Schottky barrier height ΦSB has been calculated and summarized in Fig. 8. The barrier height ΦSB,N are 0.111 eV, 0.146 eV, 0.199 eV, 0.462 eV, and 0.332 eV for MoS2 contacted with Al, Cu, Ag, Au, and Pd by inserting single-layer graphene, respectively. Conversely, when MoS2 is contacting with Mg, In, Sc, and Ti with single-layer graphene insertion, the negative n-type Schottky barrier is formed with the ΦSB,N of − 0.116 eV, − 0.116 eV, − 0.014 eV, and − 0.116 eV, respectively, indicating an ohmic contact. For bi-layer graphene insertion, the barrier height ΦSB,N of MoS2 contacted with Al, Cu, Ag, and Au are 0.492 eV, 0.492 eV, 0.230 eV, and 0.359 eV, respectively. When MoS2 contacted with Mg, In, Pd, Sc, and Ti with bi-layer graphene insertion, the negative n-type Schottky barrier is formed with the ΦSB,N of − 0.086 eV, − 0.114 eV, − 0.059 eV, − 0.008 eV, and − 0.0636 eV, respectively.Figure 8 Schottky barrier height (ΦSB) of MoS2/metals by inserting single-layer and bi-layer graphene.

Conclusions

In this study, the effects of inserting single- and bi-layer graphene on the electronic properties and Schottky barrier of MoS2/metals (Mg, Al, In, Cu, Ag, Au, Pd, Ti, and Sc) are studies by using first-principle calculations based on density functional theory. Our findings indicate significant charge value at the interface between graphene and metals, leading to the absence of tunneling barrier appears in the MoS2/metal contact by inserting singly-layer graphene. By contrast, the tunneling barrier exists at the interface between graphene and MoS2, suggests hindering in electron injection. Additionally, the ΦSB,N is reduced when graphene is inserted in MoS2/metal contacts. When MoS2 contacted with Mg, In, Sc, and Ti by inserting single-layer graphene, the ΦSB,N of − 0.116 eV, − 0.116 eV, − 0.014 eV, and − 0.116 eV, respectively. On the other hand, bi-layer graphene insertion leads to the negative n-type Schottky barriers of − 0.086 eV, − 0.114 eV, − 0.059 eV, − 0.008 eV, and − 0.0636 eV for MoS2 contacted with Mg, In, Pd, Sc, and Ti, respectively, indicating transition to the Ohmic contact. Our findings offer valuable insights for the design and optimization of nanoelectronic devices, utilizing MoS2/graphene/metal interfaces, highlighting the potential for enhanced device performance through graphene insertion.

Acknowledgements

This work was jointly supported by the Doctoral Program of Xi'an Polytechnic University (Grant Nos. 107020519 and 107020534), Scientific Research Program Funded by Shaanxi Provincial Education Department (Grant Nos. 22JK0401, 23JC037 and 22JC033), Natural Science Foundation of Shaanxi Province (Grant Nos. 2023-JC-YB-590 and 2024JC-YBMS-348), China Postdoctoral Science Foundation (Grant No. 2023M742730), National Key Laboratory of Plasma Physics (Grant No. 6142A04230302), Key Research and Development Program of Shaanxi Province (Grant No. 2023-YBGY-196), Shaanxi Fundamental Science Research Project for Mathematics and Physics (Grant Nos. 22JSY030, 22JSY012, and 22JSQ009), Fundamental Research Funds of Shaanxi Key Laboratory of Artificially-Structured Functional Materials and Devices (Grant No. AFMD-KFJJ-21207), and Science and Technology Plan Project of Xi'an (Grant No. 2021XJZZ0009).

Author contributions

Xumei Zhao wrote the manuscript. Qinglong Fang and Caijuan Xia improved the quality of manuscript. All authors participated in the discussion and interpretation of the results and commented on the manuscript.

Data availability

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

Competing interests

The authors declare no competing interests.

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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References

1. Popov I Seifert G Tomanek D Designing electrical contacts to MoS2 monolayers: A computational study Phys. Rev. Lett. 2012 108 156802 10.1103/PhysRevLett.108.156802 22587274
Popov, I., Seifert, G. & Tomanek, D. Designing electrical contacts to MoS2 monolayers: A computational study. Phys. Rev. Lett. 108, 156802 (2012).22587274 10.1103/PhysRevLett.108.156802
2. Liu W Kang J Sarkar D Khatami Y Jena D Banerjee K Role of metal contacts in designing high-performance monolayer n-type WSe2 field effect transistors Nano Lett. 2013 13 1983 1990 10.1021/nl304777e 23527483
Liu, W. et al. Role of metal contacts in designing high-performance monolayer n-type WSe2 field effect transistors. Nano Lett. 13, 1983–1990 (2013).23527483 10.1021/nl304777e
3. Chhowalla M Shin HS Eda G Li LJ Loh KP Zhang H The chemistry of two-dimensional layered transition metal dichalcogenide nanosheets Nat. Chem. 2013 5 263 275 10.1038/nchem.1589 23511414
Chhowalla, M. et al. The chemistry of two-dimensional layered transition metal dichalcogenide nanosheets. Nat. Chem. 5, 263–275 (2013).23511414 10.1038/nchem.1589
4. Das S Chen HY Penumatcha AV Appenzeller J High performance multilayer MoS2 transistors with scandium contacts Nano Lett. 2013 13 100 105 10.1021/nl303583v 23240655
Das, S., Chen, H. Y., Penumatcha, A. V. & Appenzeller, J. High performance multilayer MoS2 transistors with scandium contacts. Nano Lett. 13, 100–105 (2013).23240655 10.1021/nl303583v
5. Lee HS Baik SS Lee K Min SW Jeon PJ Kim JS Choi K Choi HJ Kim JH Im S Metal semiconductor field-effect transistor with MoS2/conducting NiOx van der Waals Schottky interface for intrinsic high mobility and photoswithing speed ACS Nano 2015 9 8312 8320 10.1021/acsnano.5b02785 26169189
Lee, H. S. et al. Metal semiconductor field-effect transistor with MoS2/conducting NiOx van der Waals Schottky interface for intrinsic high mobility and photoswithing speed. ACS Nano 9, 8312–8320 (2015).26169189 10.1021/acsnano.5b02785
6. Radisavljevic B Radenovic A Brivio J Giacometti V Kis A Single-layer MoS2 transistors Nat. Nanotechnol. 2011 6 147 150 10.1038/nnano.2010.279 21278752
Radisavljevic, B., Radenovic, A., Brivio, J., Giacometti, V. & Kis, A. Single-layer MoS2 transistors. Nat. Nanotechnol. 6, 147–150 (2011).21278752 10.1038/nnano.2010.279
7. Baugher BWH Churchill HOH Yang Y Jarilloherrero P Intrinsic electronic transport properties of high-quality monolayer and bilayer MoS2 Nano Lett. 2013 13 4212 4216 10.1021/nl401916s 23930826
Baugher, B. W. H., Churchill, H. O. H., Yang, Y. & Jarilloherrero, P. Intrinsic electronic transport properties of high-quality monolayer and bilayer MoS2. Nano Lett. 13, 4212–4216 (2013).23930826 10.1021/nl401916s
8. Das S Appenzeller J Where dose the current flow in two-dimensional layered systems? Nano Lett. 2013 13 3396 3402 10.1021/nl401831u 23802773
Das, S. & Appenzeller, J. Where dose the current flow in two-dimensional layered systems?. Nano Lett. 13, 3396–3402 (2013).23802773 10.1021/nl401831u
9. Mönch W Valence-band offsets and Schottky barrier heights of layered semiconductors explained by interface-induced gap states Appl. Phys. Lett. 1998 72 1899 1901 10.1063/1.121220
Mönch, W. Valence-band offsets and Schottky barrier heights of layered semiconductors explained by interface-induced gap states. Appl. Phys. Lett. 72, 1899–1901 (1998).10.1063/1.121220
10. Liu H Si M Deng Y Neal AT Du Y Najmaei S Ajayan PM Lou J Ye PD Switching mechanism in single-layer molybdenum disulfide transistors: An insight into current flow across Schottky barriers ACS Nano 2014 8 1031 1038 10.1021/nn405916t 24351134
Liu, H. et al. Switching mechanism in single-layer molybdenum disulfide transistors: An insight into current flow across Schottky barriers. ACS Nano 8, 1031–1038 (2014).24351134 10.1021/nn405916t
11. Gong C Colombo L Wallace RM Cho K The unusual mechanism of partial fermi level pinning at metal-MoS2 interfaces Nano Lett. 2014 14 1714 1720 10.1021/nl403465v 24660782
Gong, C., Colombo, L., Wallace, R. M. & Cho, K. The unusual mechanism of partial fermi level pinning at metal-MoS2 interfaces. Nano Lett. 14, 1714–1720 (2014).24660782 10.1021/nl403465v
12. Yang L Majumder K Liu H Du Y Wu H Hatzistergos M Huang PY Tieckelmann R Tsai W Hobbs C Ye PD Chloride molecular doping technique on 2D materials: WS2 and MoS2 Nano Lett. 2014 14 6275 6280 10.1021/nl502603d 25310177
Yang, L. et al. Chloride molecular doping technique on 2D materials: WS2 and MoS2. Nano Lett. 14, 6275–6280 (2014).25310177 10.1021/nl502603d
13. Suh J Park TE Lin DY Fu D Park J Jung HJ Chen Y Ko C Jang C Sun Y Sinclair R Chang J Yongay S Wu J Doping against the native propensity of MoS2: Degenerate hole doping by cation substitution Nano Lett. 2014 14 6976 6982 10.1021/nl503251h 25420217
Suh, J. et al. Doping against the native propensity of MoS2: Degenerate hole doping by cation substitution. Nano Lett. 14, 6976–6982 (2014).25420217 10.1021/nl503251h
14. Laskar MR Nath DN Ma L Lee EW Lee CH Kent T Yang Z Mishra R Roldan MA Idrobo JC Pantelides ST Pennycook SJ Myers RC Wu Y Rajan S p-type doping of MoS2 thin films using Nb Appl. Phys. Lett. 2014 104 092104 10.1063/1.4867197
Laskar, M. R. et al. p-type doping of MoS2 thin films using Nb. Appl. Phys. Lett. 104, 092104 (2014).10.1063/1.4867197
15. Fang H Chuang S Chang TC Takei K Takahashi T Javey A High-performance single layered WSe2 p-FETs with chemically doped contacts Nano Lett. 2012 12 3788 3792 10.1021/nl301702r 22697053
Fang, H. et al. High-performance single layered WSe2 p-FETs with chemically doped contacts. Nano Lett. 12, 3788–3792 (2012).22697053 10.1021/nl301702r
16. Du Y Liu H Neal AT Si M Ye PD Molecular doping of multilayer MoS2 filed-effect transistors: Reduction in sheet and contact resistances IEEE Electron Device Lett. 2013 34 1328 1330 10.1109/LED.2013.2277311
Du, Y., Liu, H., Neal, A. T., Si, M. & Ye, P. D. Molecular doping of multilayer MoS2 filed-effect transistors: Reduction in sheet and contact resistances. IEEE Electron Device Lett. 34, 1328–1330 (2013).10.1109/LED.2013.2277311
17. Su J Feng L Zeng W Liu Z Controlling the electronic and geometric structures of 2D insertions to realize high performance metal/insertion-MoS2 sandwich interfaces Nanoscale 2017 9 7429 7441 10.1039/C7NR00720E 28530290
Su, J., Feng, L., Zeng, W. & Liu, Z. Controlling the electronic and geometric structures of 2D insertions to realize high performance metal/insertion-MoS2 sandwich interfaces. Nanoscale 9, 7429–7441 (2017).28530290 10.1039/C7NR00720E
18. Wang J Yao Q Huang C Zou X Liao L Chen S Fan Z Zhang K Wu W Xiao X Jiang C Wu W High mobility MoS2 transistor with low Schottky barrier contact by using atomic thick h-BN as a tunneling layer Adv. Mater. 2016 28 8302 8308 10.1002/adma.201602757 27387603
Wang, J. et al. High mobility MoS2 transistor with low Schottky barrier contact by using atomic thick h-BN as a tunneling layer. Adv. Mater. 28, 8302–8308 (2016).27387603 10.1002/adma.201602757
19. Kaushik N Karmakar D Nipane A Karande S Lodha S Interfacial n-doping using an ultrathin TiO2 layer for contact resistance reduction in MoS2 ACS Appl. Mater. Interface 2016 8 256 263 10.1021/acsami.5b08559
Kaushik, N., Karmakar, D., Nipane, A., Karande, S. & Lodha, S. Interfacial n-doping using an ultrathin TiO2 layer for contact resistance reduction in MoS2. ACS Appl. Mater. Interface 8, 256–263 (2016).10.1021/acsami.5b08559
20. Lee S Tang A Aloni S Philip Wong HS Statistical study on the Schottky barrier reduction of tunneling contacts to CVD synthesized MoS2 Nano Lett. 2016 16 276 281 10.1021/acs.nanolett.5b03727 26698919
Lee, S., Tang, A., Aloni, S. & Philip Wong, H. S. Statistical study on the Schottky barrier reduction of tunneling contacts to CVD synthesized MoS2. Nano Lett. 16, 276–281 (2016).26698919 10.1021/acs.nanolett.5b03727
21. Chuang S Battaglia C Azcatl A McDonnell S Kang JS Yin X Tosun M Kapadia R Fang H Wallace RM Javey A MoS2 p-type transistors and diodes enabled by high work function MoOx contacts Nano Lett. 2014 14 1337 1342 10.1021/nl4043505 24568656
Chuang, S. et al. MoS2 p-type transistors and diodes enabled by high work function MoOx contacts. Nano Lett. 14, 1337–1342 (2014).24568656 10.1021/nl4043505
22. Cui X Shih EM Jauregui LA Chae SH Kim YD Li B Seo Pistunova DK Yin J Park JH Choi HJ Lee YL Watanabe K Taniguchi T Kim P Dean CR Hone JC Low-temperature Ohmic contact to monolayer MoS2 by van der Waals bonded Co/h-BN electrodes Nano Lett. 2017 17 4781 4786 10.1021/acs.nanolett.7b01536 28691487
Cui, X. et al. Low-temperature Ohmic contact to monolayer MoS2 by van der Waals bonded Co/h-BN electrodes. Nano Lett. 17, 4781–4786 (2017).28691487 10.1021/acs.nanolett.7b01536
23. Leong WS Luo X Li Y Khoo KH Quek SY Thong JTL Low resistance metal contacts to MoS2 devices with nickel-etched-graphene electrodes ACS Nano 2015 9 869 877 10.1021/nn506567r 25517793
Leong, W. S. et al. Low resistance metal contacts to MoS2 devices with nickel-etched-graphene electrodes. ACS Nano 9, 869–877 (2015).25517793 10.1021/nn506567r
24. Du H Kim T Shin S Kim D Kim H Sung JH Lee MJ Seo DH Lee SW Jo M Seo S Schottky barrier conttrasts in single and bilayer graphene contacts for MoS2 field-effect transistors Appl. Phys. Lett. 2015 107 233106 10.1063/1.4937266
Du, H. et al. Schottky barrier conttrasts in single and bilayer graphene contacts for MoS2 field-effect transistors. Appl. Phys. Lett. 107, 233106 (2015).10.1063/1.4937266
25. Chanana A Mahapatra S Prospects of zero Schottky barrier height in a graphene-inserted MoS2-metal interface J. Appl. Phys. 2016 119 014303 10.1063/1.4938742
Chanana, A. & Mahapatra, S. Prospects of zero Schottky barrier height in a graphene-inserted MoS2-metal interface. J. Appl. Phys. 119, 014303 (2016).10.1063/1.4938742
26. Qiu D Kim EK Electronically tunable and negative Schottky barriers in multi-layered graphene/MoS2 heterostructured transistors Sci. Rep. 2015 5 13743 10.1038/srep13743 26333680
Qiu, D. & Kim, E. K. Electronically tunable and negative Schottky barriers in multi-layered graphene/MoS2 heterostructured transistors. Sci. Rep. 5, 13743 (2015).26333680 10.1038/srep13743
27. Oshima C Nagashima A Ultra-thin epitaxial films of graphite and hexagonal boron nitride on solid surfaces J Phys Condens Matter 1997 9 1 20 10.1088/0953-8984/9/1/004
Oshima, C. & Nagashima, A. Ultra-thin epitaxial films of graphite and hexagonal boron nitride on solid surfaces. J Phys Condens Matter 9, 1–20 (1997).10.1088/0953-8984/9/1/004
28. Khomyakov PA Giovannetti G Rusu PC van den Brocks G Brink J Kelly PJ First-principle study of the interaction and charge transfer between graphene and metals Phys. Rev. B 2009 79 195425 10.1103/PhysRevB.79.195425
Khomyakov, P. A. et al. First-principle study of the interaction and charge transfer between graphene and metals. Phys. Rev. B 79, 195425 (2009).10.1103/PhysRevB.79.195425
29. Kresse G Hafner J Ab initio molecular dynamic of liquid metals Phys. Rev. B 1993 47 558 561 10.1103/PhysRevB.47.558
Kresse, G. & Hafner, J. Ab initio molecular dynamic of liquid metals. Phys. Rev. B 47, 558–561 (1993).10.1103/PhysRevB.47.558
30. Kresse G Hafner J Ab initio molecular-dynamics simulation of the liquid-metal-amorphous-semiconductor transition in germanium Phys. Rev. B 1994 49 14251 14269 10.1103/PhysRevB.49.14251
Kresse, G. & Hafner, J. Ab initio molecular-dynamics simulation of the liquid-metal-amorphous-semiconductor transition in germanium. Phys. Rev. B 49, 14251–14269 (1994).10.1103/PhysRevB.49.14251
31. Blöchl PE Projector augmented-wave method Phys. Rev. B 1994 50 17953 17979 10.1103/PhysRevB.50.17953
Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994).10.1103/PhysRevB.50.17953
32. Perdew JP Burke K Ernzerhof M Generalized gradient approximation made simple Phys. Rev. Lett. 1996 77 3865 3868 10.1103/PhysRevLett.77.3865 10062328
Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).10062328 10.1103/PhysRevLett.77.3865
33. Grimme S Semiempirical GGA-type density functional constructed with a long-range dispersion correction J. Comput. Chem. 2006 27 1787 1799 10.1002/jcc.20495 16955487
Grimme, S. Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J. Comput. Chem. 27, 1787–1799 (2006).16955487 10.1002/jcc.20495
34. Momma K Izumi F Vesta: A three-dimensional visualization system for electronic and structural analysis J. Appl. Crystallogr. 2008 41 653 658 10.1107/S0021889808012016
Momma, K. & Izumi, F. Vesta: A three-dimensional visualization system for electronic and structural analysis. J. Appl. Crystallogr. 41, 653–658 (2008).10.1107/S0021889808012016
35. Jonker BT Morar JF Park RL Surface states and oxygen chemisorption on Ti(0001) Phys. Rev. B 1981 24 2952 2957 10.1103/PhysRevB.24.2951
Jonker, B. T., Morar, J. F. & Park, R. L. Surface states and oxygen chemisorption on Ti(0001). Phys. Rev. B 24, 2952–2957 (1981).10.1103/PhysRevB.24.2951
36. Chen JR Odenthal PM Swartz AG Floyd GC Wen H Luo KY Kawakami RK Control of Schottky barriers in single layer MoS2 transistors with ferromagnetic contacts Nano Lett. 2013 13 3106 3110 10.1021/nl4010157 23746085
Chen, J. R. et al. Control of Schottky barriers in single layer MoS2 transistors with ferromagnetic contacts. Nano Lett. 13, 3106–3110 (2013).23746085 10.1021/nl4010157
37. Michaelson HB The work function of the elements and its periodicity J. Appl. Phys. 1977 48 4729 4733 10.1063/1.323539
Michaelson, H. B. The work function of the elements and its periodicity. J. Appl. Phys. 48, 4729–4733 (1977).10.1063/1.323539
38. Karu AE Beer M Pyrolytic formation of highly crystalline graphite films J. Appl. Phys. 1966 37 2179 2181 10.1063/1.1708759
Karu, A. E. & Beer, M. Pyrolytic formation of highly crystalline graphite films. J. Appl. Phys. 37, 2179–2181 (1966).10.1063/1.1708759
39. Cordero B Gómez V Platero-Prats AE Revés M Echeverría J Cremades E Barragán F Alvarez S Covalent radii revisited Dalton Trans. 2008 21 2832 2838 10.1039/b801115j
Cordero, B. et al. Covalent radii revisited. Dalton Trans. 21, 2832–2838 (2008).10.1039/b801115j
40. Zhou JJ Zhou WW Guan CM Shen JQ Ouyang CY Lei MS Shi SQ Tang WH First-principles study of lithium intercalated bilayer graphene Sci. China Phys. Mech. 2012 55 1376 1382 10.1007/s11433-012-4796-4
Zhou, J. J. et al. First-principles study of lithium intercalated bilayer graphene. Sci. China Phys. Mech. 55, 1376–1382 (2012).10.1007/s11433-012-4796-4
41. Hu W Wang T Zhang R Yang J Effects of interlayer coupling and electric fields on the electronic structures of graphene and MoS2 heterobilayers J. Mater. Chem. C 2016 4 1776 1781 10.1039/C6TC00207B
Hu, W., Wang, T., Zhang, R. & Yang, J. Effects of interlayer coupling and electric fields on the electronic structures of graphene and MoS2 heterobilayers. J. Mater. Chem. C 4, 1776–1781 (2016).10.1039/C6TC00207B
