#
Electron Transport Properties of Graphene/WS_{2} Van Der Waals Heterojunctions

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{2}heterojunctions. It is observed that the formation of heterojunctions does not lead to the opening of the Dirac point of graphene. Instead, the respective band structures of both graphene and WS

_{2}are preserved. Therefore, the heterojunction follows a unique Ohm’s law at low bias voltages, despite the presence of a certain rotation angle between the two surfaces within the heterojunction. The transmission spectra, the density of states, and the transmission eigenstate are used to investigate the origin and mechanism of unique linear I–V characteristics. This study provides a theoretical framework for designing mixed-dimensional heterojunction nanoelectronic devices.

## 1. Introduction

_{2}Te

_{3}crystals via low-pressure chemical vapor deposition (CVD). The crystallized Bi

_{2}Te

_{3}was synthesized directly using spin-coated coring (SCCA). This procedure avoided any degradation of the nanoplates and significantly improved the quality of the heterojunction sample [15]. Hu et al. utilized a polymethyl methacrylate (PMMA)/polydimethylsiloxane (PDMS) blend to transfer metal-catalyzed CVD-fabricated graphene/SiNWS heterojunctions onto stretchable polytetrafluoroethylene (PTFE) substrates. The high preparation efficiency and outstanding quality were extremely encouraging for daily industrial production and life [16]. Ren et al. developed a novel flexible self-powered photodetector that transfers electrons through a solid electrolyte. The developed flexible WS

_{2}/graphene photodetector displayed a quick photo response time and high photosensitivity [17]. Liu et al. fabricated Bi

_{2}Se

_{3}/graphene heterojunctions using molecular beam epitaxy and observed a spiral growth mechanism during the growth process [18]. By vertically stacking single-layer MoS

_{2}/h-BN/graphene, Lee’s team created random access memory with tunneling. It had excellent stretchability, long retention times, and highly dependable memory performance [19]. Additionally, Liu et al. investigated different conceivable atomic configurations of phosphorene/graphene in-plane heterojunctions and their effects on interfacial heat conductivity by using density functional theory calculations and molecular dynamics simulations [20]. Gao et al. simulated the heat transfer properties of graphene/MoS

_{2}heterojunctions using nonequilibrium molecular dynamics simulations and found that the degree of lattice matching of graphene and MoS

_{2}had an effect on phonon thermal transport [21]. However, the majority of these studies on graphene heterojunctions primarily focused on their electronic structures [22], preparation methods [23], and applications [24]. Little research has been conducted on their electron transport properties and intrinsic mechanisms.

_{2}has a lot of potential uses in nanodevices [25]. In particular, in recent years, there have been significant breakthroughs in its synthesis and applications. For example, Prof. Feng’s group produced monolayer triangular WS

_{2}single crystal wafers with excellent uniformity, large size, and high quality by controlling the nucleation density by changing the time of the introduction of the sulfur precursor and the distance between the tungsten source and the growth substrate [26]. Furthermore, some researchers have used chemical doping to significantly improve the optoelectronic performance of WS

_{2}field-effect transistors [27]. Inspired by these advancements, we selected monolayer WS

_{2}to create a series of graphene/WS

_{2}heterojunction models and design nanoelectronic devices. We systematically investigated their electronic structures and transport properties using first-principles methods based on the density functional theory (DFT) and nonequilibrium Green’s function (NEGF) [28].

## 2. Results and Discussions

_{2}was the same as that of graphene. For graphene and WS

_{2}, the optimized lattice parameters were 2.45 Å and 3.15 Å, respectively. The unit cell parameters we calculated closely matched experimental results [29,30].

_{2}heterojunctions, we used a 3 × 3 × 1 supercell of WS

_{2}and a 4 × 4 × 1 supercell of graphene with 68 total atom numbers, and a 4 × 4 × 1 supercell of WS

_{2}and a 5 × 5 × 1 supercell of graphene with 109 total atom numbers. In this orientation, both components maintained their original hexagonal lattices without surface rotation and exhibited slight lattice mismatches of 3.1% and 2.4%, respectively. The interlayer spacings of the equilibrium geometries of these two heterojunctions were 3.41 Å and 3.46 Å, respectively, which are typical distances in graphene-based vdW heterostructures with weak interactions.

_{2}vdW heterojunctions were calculated to assess the system stability, as follows:

_{2}) represent the total energy of the heterojunctions, graphene layers, and WS

_{2}layers, respectively. The calculated binding energies are presented in Table 2. The negative binding energies in the table indicate the stability of these systems. Upon comparison, we observed that the most stable heterojunction was Gr/WS

_{2}-1. Another regularity we found was that smaller heterojunctions were more stable when the two layers were not rotated. However, when there exist rotation angles between the two layers, the stability of the heterojunctions decreased and the larger heterojunctions were more stable.

_{2}-1 and Gr/WS

_{2}-2 to determine whether they can be transported as electronic devices. As plotted in Figure 2a, graphene exhibits metallic properties with a zero bandgap semiconductor, where the top valence band and bottom conduction band intersect at the K point. In contrast, WS

_{2}is a semiconductor with a direct band gap of 1.95 eV, as shown in Figure 2b. It is worth noting that our calculations closely aligned with other theoretical predictions and were slightly lower than experimental values [31]. This discrepancy can be attributed to the inherent limitations of the GGA-PBE method, which tends to overestimate lattice constants and underestimate band gaps. Hybrid functionals, such as meta-GGA, HSE06, etc., are known to provide more accurate bandgap calculations [32]. However, the WS

_{2}bandgap calculated by meta-GGA was 2.13 eV, which was only slightly higher than the PBE value (1.95 eV). Thus, we believe that the GGA-PBE approach was accurate enough for our calculation and did not significantly impact other aspects of the analysis, such as energy band structure and electron transport.

_{2}-1 and Gr/WS

_{2}-2, which are simple superpositions of graphene and WS

_{2}and preserve their electronic systems. Notably, the valence band’s top and the conduction band’s bottom still intersected at the K point in the Brillouin zone, indicating that the Dirac point still exists in the heterojunction. Gr/WS

_{2}-1 behaved as an N-type semiconductor, with the E

_{c}and E

_{v}of WS

_{2}shifting downwards. Additionally, the Fermi energy level turned from near the top of the valence band to near the bottom of the conduction band. Conversely, Gr/WS

_{2}-2 exhibited P-type semiconductor properties, with the Fermi energy level still close to the top of the valence band, but the conduction band bottom and valence band top shifted from the original G to the K point. This indicates that factors such as layer spacing, the degree of mismatch, and lattice parameters within the heterojunction influence its electronic energy band.

_{2}-1 as an example. According to Figure 2e, near the Fermi level, the 2p orbital of the carbon atom in graphene plays a vital role in the density of states. The 5d orbital of the W atom also makes a contribution. Contributions from other valence electron orbitals can be disregarded. The absence of resonance peaks indicates that there was no bonding between WS

_{2}and C. Instead, weak van der Waals forces maintained the interlayer stability between the heterojunctions, corresponding to optimized interlayer spacing of around 3.4 Å. This weak hybridization between the graphene and WS

_{2}is another indication of why the graphene’s Dirac points are still present in the heterojunctions.

_{2}, its effect on the energy band is little. But when the lattice parameter of heterojunctions is increased to around 8 Å, the Dirac cone of graphene shifts from K to G point due to the inequivalent K and K’ points being folded and coupled into the same G-point (Figure 3e,f). However, the Dirac cone does not open. We predicted that these six heterojunctions had comparable electronic transport properties. Consequently, nanoelectronic devices could be built using heterostructures with rotation angles to reduce device size while maintaining their high transport properties.

_{2}-3 and Gr-1 (composed of graphene, with the same lattice parameter and rotation angle as Gr/WS

_{2}-3), we built two devices, as depicted in Figure 4. As seen in the enlarged area, the rotation angle between graphene and WS

_{2}was still maintained. The poles of the device formed by themselves, the current transport direction was along the Z-axis, and the surface was perpendicular to the X-axis.

_{2}and graphene. A nonlinear relationship only began to emerge at high bias voltages. Compared to other graphene-based heterojunctions, the transport current of graphene/WS

_{2}was nearly one order of magnitude higher than that of graphene/MoS

_{2}in-plane heterojunctions [33,34], graphene/BN heterojunctions [35], and so on. In addition, when compared to other WS

_{2}-based heterojunctions, such heterojunctions could behave up to two orders of magnitude higher than that of WS

_{2}/WSe

_{2}heterojunctions [36], with greater performance than that of MoS

_{2}/WS

_{2}heterojunctions [37]. Thus, we can conclude that such heterojunctions can greatly enhance the transport current and decrease the contact resistance, which will be very important for achieving superior optoelectronic devices such as vertical field-effect transistors (FETs). Our calculations can reveal why graphene/WS

_{2}heterojunctions are widely used to build FETs and have superior behavioral properties [38,39,40,41]. In addition, the heterojunction used in our calculations not only maintained the perfect transport properties but also largely reduced the size of the electronic devices, which is very important in the post-Moore era.

_{2}and graphene. The most understandable depiction of the behavior of electron transport was the transmission spectrum T(E), and the transmission coefficient of each energy point was determined by diagonalizing the transmission matrix from the eigenvalues of electron transmission. Therefore, we calculated the transmission spectra of the above devices to further study their transport properties.

_{2}-3 devices displayed quantum steps between −1 eV and 1 eV, resembling the ideal one-dimensional nanowires. And the electron transmission probability at the Fermi energy level was almost zero, which shows a band gap feature between the conduction and valence bands, corresponding to a Dirac cone in the energy band structure. Although the system had almost no electrons passing through at this energy, at higher energies electrons could easily tunnel through the potential barrier, increasing their mobility and the step transmission coefficient, which indicates that there were several electron transmission channels in these devices. After the formation of the heterojunction, many spikes appeared away from the Fermi energy level, showing that the coupling between the graphene and WS

_{2}was weak. The band gap of graphene was not open, although it tends to be open, which does not have a significant influence on its transport properties.

_{2}-3, more than twice that of the Gr-1. The highest peaks in the valence band region were observed at −1.92 eV, while those in the conduction band region were found at 1.44 eV. These peaks serve to protect fewer delocalized states near the Fermi level.

_{2}in Gr/WS

_{2}-3 was almost negligible.

_{2}-3 devices under 0.4, 0.8, 1.2, 1.6, and 2.0 to further reveal their transport phenomena (Figure 6a,b). The bias window’s perimeter is represented by the colored parts. The effective integral area of the transmission curve within the bias window grew with increased bias, producing a linear I–V characteristic, as we can see from both devices. However, when the bias window increased to 1.2 V, the step transmission spectrum started to change shape and expand in an arc, so the I–V curve began to show non-linear features, and the slope subsequently increased. It is evident from the transmission spectrum that quantum steps are always present within the bias window at different bias voltages and that the steps shift as the bias window expands. The movement tendency of the steps in the conduction and valence band regions was indicated by the arrows, respectively. The number of wave valleys within the bias window in the Gr/WS

_{2}-3 devices progressively increased. Spikes far from the Fermi energy level moved in the opposite direction and were unable to move inside the bias window, so the contribution of these spikes to the transport properties was almost negligible. Interestingly, the lowest transmission probability was always located at the boundary of the bias window, and as the bias increased from 0 V to 2 V, the gap shifted to the boundary of the bias window.

_{2}-3 devices were calculated at different bias voltages. Before 2.0 V, the transmission eigenstates of both devices were mainly contributed by the two transmission channels of graphene. However, when the bias voltage increased to 2.0 V, the transmission channels at the Fermi level of Gr/WS

_{2}-3 changed from two to multiple channels, as shown in Figure 6c,d. WS

_{2}started to participate in the transport, but its electronic state was localized at the left electrode and the transmission eigenvalue was so small that it can still be disregarded.

## 3. Computational Method

_{2}heterostructures. The exchange–correlation function is a generalized gradient approximation (GGA) [42] of Perdew–Burke–Ernzerhof (PBE) [43]. The selected valence electron configurations in our calculation were W 5d

^{4}6s

^{2}, S 3s

^{2}3p

^{4}, C 2s

^{2}2p

^{2}. In order to meet the computational precision, the linear combination of atomic orbitals (LCAO) basis was selected for all atoms. Double-ζplus polarization (DZP) basis sets were adopted for the local atomic numerical orbitals, and norm-conserving pseudo-potentials were employed. The Monkhorst–Pack k-points of 5 × 5 × 1 were used to sample the Brillouin zone [44]. The cut-off energy for the density mesh and the electron temperature were set to 75 Ha and 300 K, accordingly.

^{−4}eV. Before analyses, the devices were fully optimized by the quasi-Newton approach until all residual stresses on each atom were less than 0.05 eV. The devices’ electronic properties were investigated by computing their currents, the density of states, and the transmission spectra, and the current I through the device was calculated using the Landauer–Buttiker equation [45]:

## 4. Conclusions

_{2}heterojunctions using first-principal calculations. Unique linear I–V characteristics were found among the devices. Even though there was an angle between the two surfaces, the heterojunction continued to exhibit this intriguing Ohm’s law behavior. The transmission spectra, the density of states, and the transmission eigenstate were calculated to explain this phenomenon. After forming the heterojunctions, the quantum steps near the Fermi level approximated an ideal one-dimensional nanowire. The DOS shows that the vdW heterojunctions significantly increased the number of peaks and improved the maximum value of peaks, which protected less delocalized states near the Fermi level. The transmission eigenstates showed that the high transport properties came from the π orbitals of the C atoms in the graphene armchair direction. This study provides valuable insights into the transport properties of graphene heterojunctions and the potential fabrication of mixed-dimensional heterojunctions.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Coleman, J.N.; Lotya, M.; O’Neill, A.; Bergin, S.D.; King, P.J.; Khan, U.; Young, K.; Gaucher, A.; De, S.; Smith, R.J. Two-dimensional nanosheets produced by liquid exfoliation of layered materials. Science
**2011**, 331, 568–571. [Google Scholar] [CrossRef] [PubMed] - Britnell, L.; Ribeiro, R.M.; Eckmann, A.; Jalil, R.; Belle, B.D.; Mishchenko, A.; Kim, Y.-J.; Gorbachev, R.V.; Georgiou, T.; Morozov, S.V. Strong light-matter interactions in heterostructures of atomically thin films. Science
**2013**, 340, 1311–1314. [Google Scholar] [CrossRef] - Yu, W.J.; Liu, Y.; Zhou, H.; Yin, A.; Li, Z.; Huang, Y.; Duan, X. Highly efficient gate-tunable photocurrent generation in vertical heterostructures of layered materials. Nat. Nanotechnol.
**2013**, 8, 952–958. [Google Scholar] [CrossRef] [PubMed] - Chhowalla, M.; Jena, D.; Zhang, H. Two-dimensional semiconductors for transistors. Nat. Rev. Mater.
**2016**, 1, 16052. [Google Scholar] [CrossRef] - Novoselov, K.S.; Colombo, L.; Gellert, P.; Schwab, M.; Kim, K. A roadmap for graphene. Nature
**2012**, 490, 192–200. [Google Scholar] [CrossRef] - Sun, Z.; Chang, H. Graphene and graphene-like two-dimensional materials in photodetection: Mechanisms and methodology. ACS Nano
**2014**, 8, 4133–4156. [Google Scholar] [CrossRef] - Kandpal, H.; Anand, S.; Vaishya, J. Experimental observation of the phenomenon of spectral switching for a class of partially coherent light. IEEE J. Quantum Electron.
**2002**, 38, 336–339. [Google Scholar] [CrossRef] - Lee, C.; Wei, X.; Kysar, J.W.; Hone, J. Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science
**2008**, 321, 385–388. [Google Scholar] [CrossRef] - Yang, J.; Tang, L.; Luo, W.; Feng, S.; Leng, C.; Shi, H.; Wei, X. Interface engineering of a silicon/graphene heterojunction photodetector via a diamond-like carbon interlayer. ACS Appl. Mater. Interfaces
**2021**, 13, 4692–4702. [Google Scholar] [CrossRef] - Xia, F.; Wang, H.; Jia, Y. Rediscovering black phosphorus as an anisotropic layered material for optoelectronics and electronics. Nat. Commun.
**2014**, 5, 4458. [Google Scholar] [CrossRef] - Haberer, D.; Vyalikh, D.; Taioli, S.; Dora, B.; Farjam, M.; Fink, J.; Marchenko, D.; Pichler, T.; Ziegler, K.; Simonucci, S. Tunable band gap in hydrogenated quasi-free-standing graphene. Nano Lett.
**2010**, 10, 3360–3366. [Google Scholar] [CrossRef] [PubMed] - Kaplan, D.; Swaminathan, V.; Recine, G.; Balu, R.; Karna, S. Bandgap tuning of mono-and bilayer graphene doped with group IV elements. J. Appl. Phys.
**2013**, 113, 183701. [Google Scholar] [CrossRef] - Geim, A.K.; Grigorieva, I.V. Van der Waals heterostructures. Nature
**2013**, 499, 419–425. [Google Scholar] [CrossRef] [PubMed] - Shin, Y.; Kwon, J.; Jeong, Y.; Watanabe, K.; Taniguchi, T.; Im, S.; Lee, G.H. Graphene Via Contact Architecture for Vertical Integration of vdW Heterostructure Devices. Small
**2022**, 18, 2200882. [Google Scholar] [CrossRef] - Lan, J.-C.; Qiao, J.; Sung, W.-H.; Chen, C.-H.; Jhang, R.-H.; Lin, S.-H.; Ng, L.-R.; Liang, G.; Wu, M.-Y.; Tu, L.-W. Role of carrier-transfer in the optical nonlinearity of graphene/Bi
_{2}Te_{3}heterojunctions. Nanoscale**2020**, 12, 16956–16966. [Google Scholar] [CrossRef] - Hu, J.; Li, L.; Wang, R.; Chen, H.; Xu, Y.; Zang, Y.; Li, Z.; Feng, S.; Lei, Q.; Xia, C. Fabrication and photoelectric properties of a graphene-silicon nanowire heterojunction on a flexible polytetrafluoroethylene substrate. Mater. Lett.
**2020**, 281, 128599. [Google Scholar] [CrossRef] - Ren, X.; Wang, B.; Huang, Z.; Qiao, H.; Duan, C.; Zhou, Y.; Zhong, J.; Wang, Z.; Qi, X. Flexible self-powered photoelectrochemical-type photodetector based on 2D WS
_{2}-graphene heterojunction. FlatChem**2021**, 25, 100215. [Google Scholar] [CrossRef] - Liu, Y.; Weinert, M.; Li, L. Spiral growth without dislocations: Molecular beam epitaxy of the topological insulator Bi
_{2}Se_{3}on epitaxial graphene/SiC (0001). Phys. Rev. Lett.**2012**, 108, 115501. [Google Scholar] [CrossRef] - Vu, Q.A.; Shin, Y.S.; Kim, Y.R.; Nguyen, V.L.; Kang, W.T.; Kim, H.; Luong, D.H.; Lee, I.M.; Lee, K.; Ko, D.-S. Two-terminal floating-gate memory with van der Waals heterostructures for ultrahigh on/off ratio. Nat. Commun.
**2016**, 7, 12725. [Google Scholar] [CrossRef] - Liu, X.; Gao, J.; Zhang, G.; Zhang, Y.-W. Design of phosphorene/graphene heterojunctions for high and tunable interfacial thermal conductance. Nanoscale
**2018**, 10, 19854–19862. [Google Scholar] [CrossRef] - Gao, Y.; Liu, Q.; Xu, B. Lattice mismatch dominant yet mechanically tunable thermal conductivity in bilayer heterostructures. ACS Nano
**2016**, 10, 5431–5439. [Google Scholar] [CrossRef] - Sun, X.; Li, X.; Zeng, Y.; Meng, L. Improving the stability of perovskite by covering graphene on FAPbI3 surface. Int. J. Energy Res.
**2021**, 45, 10808–10820. [Google Scholar] [CrossRef] - Wang, X.; Long, R. Rapid charge separation boosts solar hydrogen generation at the graphene–MoS2 Junction: Time-domain Ab initio analysis. J. Phys. Chem. Lett.
**2021**, 12, 2763–2769. [Google Scholar] [CrossRef] [PubMed] - Wang, H.; Gao, S.; Zhang, F.; Meng, F.; Guo, Z.; Cao, R.; Zeng, Y.; Zhao, J.; Chen, S.; Hu, H. Repression of interlayer recombination by graphene generates a sensitive nanostructured 2D vdW heterostructure based photodetector. Adv. Sci.
**2021**, 8, 2100503. [Google Scholar] [CrossRef] [PubMed] - Cong, C.; Shang, J.; Wang, Y.; Yu, T. Optical properties of 2D semiconductor WS
_{2}. Adv. Opt. Mater.**2018**, 6, 1700767. [Google Scholar] [CrossRef] - Yue, Y.; Chen, J.; Zhang, Y.; Ding, S.; Zhao, F.; Wang, Y.; Zhang, D.; Li, R.; Dong, H.; Hu, W. Two-dimensional high-quality monolayered triangular WS
_{2}flakes for field-effect transistors. ACS Appl. Mater. Interfaces**2018**, 10, 22435–22444. [Google Scholar] [CrossRef] [PubMed] - Iqbal, M.W.; Iqbal, M.Z.; Khan, M.F.; Kamran, M.A.; Majid, A.; Alharbi, T.; Eom, J. Tailoring the electrical and photo-electrical properties of a WS
_{2}field effect transistor by selective n-type chemical doping. RSC Adv.**2016**, 6, 24675–24682. [Google Scholar] [CrossRef] - Brandbyge, M.; Mozos, J.-L.; Ordejón, P.; Taylor, J.; Stokbro, K. Density-functional method for nonequilibrium electron transport. Phys. Rev. B
**2002**, 65, 165401. [Google Scholar] [CrossRef] - Jiang, J.-W. Graphene versus MoS2: A short review. Front. Phys.
**2015**, 10, 287–302. [Google Scholar] [CrossRef] - Georgiou, T.; Yang, H.; Jalil, R.; Chapman, J.; Novoselov, K.S.; Mishchenko, A. Electrical and optical characterization of atomically thin WS
_{2}. Dalton Trans.**2014**, 43, 10388–10391. [Google Scholar] [CrossRef] - Ding, Y.; Wang, Y.; Ni, J.; Shi, L.; Shi, S.; Tang, W. First principles study of structural, vibrational and electronic properties of graphene-like MX2 (M=Mo, Nb, W, Ta; X=S, Se, Te) monolayers. Phys. B Phys. Condens. Matter
**2011**, 406, 2254–2260. [Google Scholar] [CrossRef] - Heyd, J.; Scuseria, G.E.; Ernzerhof, M. Hybrid functionals based on a screened Coulomb potential. J. Chem. Phys.
**2003**, 118, 8207, Erratum in J. Chem. Phys.**2006**, 124, 219906. [Google Scholar] [CrossRef] - Li, W.; Wei, J.; Bian, B.; Liao, B.; Wang, G. The effect of different covalent bond connections and doping on transport properties of planar graphene/MoS2/graphene heterojunctions. Phys. Chem. Chem. Phys.
**2021**, 23, 6871–6879. [Google Scholar] [CrossRef] [PubMed] - Zhou, Y.; Yang, Y.; Guo, Y.; Wang, Q.; Yan, X. Influence of length and interface structure on electron transport properties of graphene-MoS_2 in-plane heterojunction. Appl. Surf. Sci.
**2019**, 497, 143764. [Google Scholar] [CrossRef] - Dong, J.C.; Li, H. Monoatomic Layer Electronics Constructed by Graphene and Boron Nitride Nanoribbons. J. Phys. Chem. C
**2012**, 116, 17259–17267. [Google Scholar] [CrossRef] - Kim, H.; Kim, J.; Uddin, I.; Phan, N.A.N.; Whang, D.; Kim, G.-H. Dual-Channel WS
_{2}/WSe_{2}Heterostructure with Tunable Graphene Electrodes. ACS Appl. Electron. Mater.**2023**, 5, 913–919. [Google Scholar] [CrossRef] - Zhou, Y.; Dong, J.C.; Li, H. Electronic transport properties of in-plane heterostructures constructed by MoS
_{2}and WS_{2}nanoribbons. RSC Adv.**2015**, 5, 66852–66860. [Google Scholar] [CrossRef] - Zheng, J.; Li, E.; Ma, D.; Cui, Z.; Wang, X. Effect on Schottky Barrier of Graphene/WS
_{2}Heterostructure with Vertical Electric Field and Biaxial Strain. Phys. Status Solidi (b)**2019**, 256, 1900161. [Google Scholar] [CrossRef] - Georgiou, T.; Jalil, R.; Belle, B.D.; Britnell, L.; Gorbachev, R.V.; Morozov, S.V.; Kim, Y.J.; Gholinia, A.; Haigh, S.J.; Makarovsky, O. Vertical field-effect transistor based on graphene-WS
_{2}heterostructures for flexible and transparent electronics. Nat. Nanotechnol.**2013**, 8, 100–103. [Google Scholar] [CrossRef] - Bai, Z.; Xiao, Y.; Luo, Q.; Li, M.; Peng, G.; Zhu, Z.; Luo, F.; Zhu, M.; Qin, S.; Novoselov, K. Highly Tunable Carrier Tunneling in Vertical Graphene-WS
_{2}-Graphene van der Waals Heterostructures. ACS Nano**2022**, 16, 7880–7889. [Google Scholar] [CrossRef] - Xia, C.; Xiong, W.; Xiao, W.; Du, J.; Jia, Y. Enhanced Carrier Concentration and Electronic Transport by Inserting Graphene into van der Waals Heterostructures of Transition-Metal Dichalcogenides. Phys. Rev. Appl.
**2018**, 10, 024028. [Google Scholar] [CrossRef] - Perdew, J.P.; Burke, K.; Wang, Y. Generalized gradient approximation for the exchange-correlation hole of a many-electron system. Phys. Rev. B
**1996**, 54, 16533. [Google Scholar] [CrossRef] - Perdew, J.P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett.
**1996**, 77, 3865. [Google Scholar] [CrossRef] [PubMed] - Monkhorst, H.J.; Pack, J.D. Special points for Brillouin-zone integrations. Phys. Rev. B
**1976**, 13, 5188. [Google Scholar] [CrossRef] - Pastawski, H.M. Classical and quantum transport from generalized Landauer-Büttiker equations. Phys. Rev. B
**1991**, 44, 6329. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**Top views of (

**a**) Gr/WS

_{2}-1, (

**b**) Gr/WS

_{2}-2, (

**e**) Gr/WS

_{2}-3, (

**f**) Gr/WS

_{2}-4, (

**g**) Gr/WS

_{2}-5, (

**h**) Gr/WS

_{2}-6, (

**i**) Gr/WS

_{2}-7, and (

**j**) Gr/WS

_{2}-8 ball-and-stick models. Side views of (

**c**) Gr/WS

_{2}-1 and (

**d**) Gr/WS

_{2}-2.

**Figure 2.**Band structures of the stand-alone (

**a**) graphene and (

**b**) WS

_{2}; (

**c**,

**d**) are band structures of Gr/WS

_{2}-1 and Gr/WS

_{2}-2. The red and blue lines represent the top of the valence band and the bottom of the conduction band. (

**e**) The PDOS and DOS of the graphene and WS

_{2}components in the vdW Gr/WS

_{2}-1.

**Figure 3.**Band structures of (

**a**) Gr/WS

_{2}-3, (

**b**) Gr/WS

_{2}-4, (

**c**) Gr/WS

_{2}-5, (

**d**) Gr/WS

_{2}-6, (

**e**) Gr/WS

_{2}-7, and (

**f**) Gr/WS

_{2}-8. The orange and blue lines represent the top of the valence band and the bottom of the conduction band.

**Figure 4.**The device configuration with (

**a**) Gr/WS

_{2}-3 and (

**b**) Gr-1. (

**c**) I–V characteristics of devices.

**Figure 5.**Transmission spectrum and DOS of (

**a**) Gr-1 device and (

**d**) Gr/WS

_{2}-3 device at a free applied bias (0.0 V). Transmission eigenstate of Gr-1 (

**b**,

**c**) and Gr/WS

_{2}-3 (

**e**,

**f**) around Fermi level with an isovalue of 0.21.

**Figure 6.**Transmission spectra of (

**a**) Gr-1 device and (

**b**) Gr/WS

_{2}-3 device at nonzero bias voltage. Transmission eigenstates of Gr-1 (

**c**) and Gr/WS

_{2}-3 (

**d**) at 2.0 V with an isovalue of 0.21. The colored arrows represent the movement of the steps in the conduction and valence band regions.

Heterojunction | Lattice Parameters of Graphene (Å) | Rotation Angle of Graphene (°) | Lattice Parameters of WS_{2} (Å) | Rotation Angle of WS_{2} (°) | Lattice Mismatch (%) |
---|---|---|---|---|---|

Gr/WS_{2}-1 | a = b = 9.8 | 0.0 | a = b = 9.5 | 0.0 | 3.1 |

Gr/WS_{2}-2 | a = b = 12.3 | 0.0 | a = b = 12.6 | 0.0 | 2.4 |

Gr/WS_{2}-3 | a = b = 6.5 | 21.8 | a = b = 6.3 | 60.0 | 3.1 |

Gr/WS_{2}-4 | a = b = 6.5 | 141.8 | a = b = 6.3 | 60.0 | 3.1 |

Gr/WS_{2}-5 | a = b = 6.5 | 21.8 | a = b = 6.3 | 180.0 | 3.1 |

Gr/WS_{2}-6 | a = b = 6.5 | 141.8 | a = b = 6.3 | 180.0 | 3.1 |

Gr/WS_{2}-7 | a = b = 8.5 | 0.0 | a = b = 8.3 | 21.8 | 2.1 |

Gr/WS_{2}-8 | a = b = 8.5 | 120.0 | a = b = 8.3 | 21.8 | 2.1 |

Heterojunction | Energy of Graphene (eV) | Energy of WS_{2} (eV) | Energy of Heterojunction (eV) | Binding Energy (eV) |
---|---|---|---|---|

Gr/WS_{2}-1 | −5038.3 | −10,206.0 | −15,246.9 | −2.6 |

Gr/WS_{2}-2 | −7874.7 | −18,145.4 | −26,022.2 | −2.1 |

Gr/WS_{2}-3 | −2204.4 | −4563.7 | −6741.6 | −0.6 |

Gr/WS_{2}-4 | −2204.4 | −4563.7 | −6741.6 | −0.6 |

Gr/WS_{2}-5 | −2204.4 | −4563.7 | −6741.6 | −0.6 |

Gr/WS_{2}-6 | −2204.4 | −4563.7 | −6741.6 | −0.6 |

Gr/WS_{2}-7 | −3779.3 | −7939.2 | −11,719.4 | −0.9 |

Gr/WS_{2}-8 | −3379.3 | −7939.2 | −11,719.4 | −0.9 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Guo, J.; Dai, X.; Zhang, L.; Li, H.
Electron Transport Properties of Graphene/WS_{2} Van Der Waals Heterojunctions. *Molecules* **2023**, *28*, 6866.
https://doi.org/10.3390/molecules28196866

**AMA Style**

Guo J, Dai X, Zhang L, Li H.
Electron Transport Properties of Graphene/WS_{2} Van Der Waals Heterojunctions. *Molecules*. 2023; 28(19):6866.
https://doi.org/10.3390/molecules28196866

**Chicago/Turabian Style**

Guo, Junnan, Xinyue Dai, Lishu Zhang, and Hui Li.
2023. "Electron Transport Properties of Graphene/WS_{2} Van Der Waals Heterojunctions" *Molecules* 28, no. 19: 6866.
https://doi.org/10.3390/molecules28196866