Abstract
Monolayer transition metal dichalcogenides/metal (MX_{2}/metal) based transistors have been widely studied. However, further development is hindered by the large contact resistance between MX_{2} and metal contact. In this paper, we demonstrated that interfacial charge transfer between MX_{2} and metal is the key for tuning contact resistance. With the lattice misfit criterion applied to screen combination of MX_{2}s and metals, it has been found out that both phase stability of MX_{2} and contact nature between MX_{2} and metal will be sensitively affected by interfacial charge transfer. Additionally, we have identified seven MX_{2}/metal systems that can potentially form zero Schottky barrier contacts utilizing phase engineering. On base of interfacial charge calculations and contact resistance analysis, we have presented three types of MX_{2}/metal contacts that can be formed with distinguished contact resistance. Our theoretical results not only demonstrate various choice of MX_{2}/metal designs in order to achieve different amounts of interfacial charge transfer as well as manipulate contact resistance, but also shed light on designing ohmic contacts in MX_{2}/metal systems.
Introduction
The difficulty of extending Moore’s law on classic silicon devices largely limits the further development of logic transistors. Successful fabrication of 2D materials opens the gate of extending the scaling limit of nanoelectronic devices. Compared with the conventional metal oxide semiconductor based on Si, GaAs et al., the lack of trapping states at interface and surface, atomic thin thickness and controllable electronic structure of 2D materials, making them as promising candidates for devices with high performance. However, for some of the 2D materials, such as graphene, hBN, the band gaps are inappropriate for channel materials. Even though the value of band gap can be tuned with defects,^{1,2,3,4,5} doping^{4,6} or strain engineering,^{1,6} the precise control is always challenging both experimentally and theoretically. Among all the 2D materials identified to date, monolayer transition metal dichalcogenides (MX_{2}s) offer wide space of tunable band gaps,^{7,8,9} therefore have been widely investigated in field effect transistors (FET) based nanodevices.^{10,11,12}
However, the large contact resistance between MX_{2}s and metal substrate hinders the direct application of MX_{2}s as highperformance FET devices.^{11,13} As a result, reducing the contact resistance between MX_{2}s and the metal substrate has become one of the critical problems to be solved.^{14,15,16,17,18,19} As can be inferred from several previous studies, interfacial orbital overlapping will facilitate electron tunneling through the interface.^{11,13,20,21} However, systematic investigation on the influence of interfacial charge transfer on MX_{2}/metal design is still absent. More specifically, the amount of charge transfer will be affected by interfacial lattice coherency, work function of metals as well as how MX_{2} is stacked on top of metals. Meanwhile, with the electron polarization from metal into MX_{2} layer, the phase stability of MX_{2} membrane may also be altered,^{22,23} which lead to drastic change of contact nature. There have already been several experimental reports^{6,24} on applying phase engineering techniques to improve the performance of MX_{2} based transistors. Nevertheless, studies about how metal substrate can affect the phase stability is still missing. With adequate investigation of those topics above, a design strategy can be proposed for manipulating contact resistance of MX_{2}/metal system.
In this work, a computational framework based on the density functional theory (DFT), bader charge analysis^{25,26,27} and contact nature evaluation have been presented to screen potential metal candidates with 3d or 4d orbitals and their contacts with five types of MX_{2}, i.e., MoS_{2}, MoSe_{2}, WS_{2}, WSe_{2}, and MoTe_{2}. The potential stacking sequence and 2H→T (1T, 1T’ and 1T”) phase transformation are considered in the structure screening process. It has been found that several MX_{2}/metal systems would be energetically more stable with T phases in MX_{2.} This phase transition will consequently lead to ohmic contact behavior at the interface. Meanwhile, large variations of band alignment are observed as a result of interfacial charge transfer, which are supported by the simulated ARPES images. This study not only offers a systematic consideration of the contact nature at MX2/metal systems, but also predicts new types of MX_{2}/metal interfaces with low interfacial electrical resistance.
Results and discussion
Phase stability and energetics
The potential of phase stability transition from 2H phase to T phases on different metal substrate (1T, 1T’ or 1T”) has been investigated by DFT calculated energetics. Our calculations indicate that the 1T phase will always have much higher energy compared with other phases. Therefore, the interfacial charge will not likely to induce the 2H→1T phase transition, which is also consistent with previous studies.^{7,22,23,44} As a result, we construct the phase stability profile as presented in Fig. 1(a) with the description of competition between 2H with either 1T’ or 1T” phases. To compare the energetics of MX_{2} on top of different substrates, the reference energy \({\mathrm{E}}_{2{\mathrm{H}}(1{\mathrm{T}},1{\mathrm{T}}^\prime ,1{\mathrm{T}}^\prime\prime )}\) is defined as \({\mathrm{E}}_{2{\mathrm{H}}(1{\mathrm{T}},1{\mathrm{T}}^\prime ,1{\mathrm{T}}^\prime\prime )} = {\mathrm{E}}_{{\mathrm{MX}}_2{\mathrm{/metal}}}  {\mathrm{E}}_{{\mathrm{metal}}}\). While both \({\mathrm{E}}_{{\mathrm{MX}}_2{\mathrm{/metal}}}\) and E_{metal} are the total energies calculated from DFT.
Several features can be identified from the energetic diagrams as shown in Fig. 1a. In all the examined MX_{2}/metal contacts, the most energetically favorable T phase can be either 1T’ or 1T”. Meanwhile, for each type of MX_{2} monolayer, the energetics differ quite a bit depending on the type of metal with which to form the interfaces. Moreover, for several MX_{2}/metal contacts, i.e., MoSe_{2}Sc, WS_{2}Zr, WS_{2}V, WSe_{2}Ti, WSe_{2}Sc, NbMoTe_{2}, and CrMoTe_{2} systems, 1T’(1T”) phases turned out to be more energetically favorable compared with the original 2H phase.
All those phenomena can be explained with the significant charge transfer at MX_{2}/metal contacts. For all the interfaces examined, they all have relatively small lattice mismatch compared with those not selected. Small lattice mismatch allows for more orbital overlapping between the bottom layers of X (S or Se) atoms and the topmost metal atoms, which is in accordance with the phenomenon that the energetics of 2H phase is significantly depending on the interface type as shown in Fig. 1a. For those MX/metal systems with phase stability transition, more charge is transferred from metal into MX_{2} monolayer compared to those without phase transition. As being pointed out by our previous study and various experimental reports, enough amount of charge injection into MX_{2} will trigger the structural transition into T phases.^{44,45,46,47} To support this explanation, we visualize the charge transfer at the interface and the corresponding lattice distortion within two selected systems as demonstrated in Fig. 1b. Meanwhile, the quantitative analysis of charge transfer is illustrated by the bader charge calculations as presented in Fig. 2.
The charge transfer can be directly visualized by the isosurface of deformation charge density. Figure 1b illustrates the deformation charge density isosurface in MoS_{2} (MoS_{2}Cu) and WS_{2} (WS_{2}V), which correspond to the smallest and largest charger transfer amount that can happen between metal and adjacent S layer, respectively. By comparing the two extreme cases, one can get that T phases generally obtain more electrons from the metal surface, which makes the interlayer distance in 1T”/metal contact smaller. By analyzing the bader charge in all systems as shown in Figs. 2a, we found that for MoS_{2}, MoSe_{2}, WS_{2} and WSe_{2} contact with metals, the charge will always polarized from the metal side to the MS_{2} or MSe_{2} layer, which lead to the bader charges in MS_{2} or MSe_{2} layer higher than the one of free standing case (black line). However, two exceptions for MoTe_{2}/Ru and MoTe_{2}/Rh systems can be observed for MoTe_{2}/metal systems. In both cases, electrons would transfer from the Te atom to Ru and Rh surface.
The variation of charge transfer conditions at MX_{2}/metal interfaces is dependent on the different work functions of metal surfaces as well as the interface coherency of MX_{2}/metal. By comparing the work functions of the substrate metals (Fig. 2f), we can obtain that generally the higher the work function is, the more difficult to make it lose electrons. Consistently, for those systems with more charge transferred to MX_{2}s, the work functions of the corresponding metal surface are generally lower. Meanwhile, it is worthy to mention that among those metal surfaces with similar calculated surface work function, lower work function does not always mean more interfacial charge transfer. For instance, although the work function of Ti (001) surface (4.37 eV) is slightly larger than that of W (001) surface (4.26 eV), larger amount of charge transfer from metal to MX_{2} is observed in MSe_{2}/Ti systems rather than in the MSe_{2}/W system. This phenomenon mainly originates from the discrepancies in interface coherency. To minimize the misfit strain, for MSe_{2}/Ti system, we designed a \(2\sqrt 3 \times 2\sqrt 3\) supercell of MSe_{2} aligning with a 4 × 4 supercell of Ti (001) surface (Table 1), in this case, in each periodic unit of the interface model, 12 Se atoms will interact with 16 Ti atoms at interfaces. When comes to MSe_{2}/W system, a 4 × 4 supercell of MSe_{2} is put on top of a 33 supercell of W (001) surface to minimize the misfit strain, in which 16 atoms interact with 9 W atoms at interfaces in each periodic unit of the interface model. As a result, less charge transfer would happen in MSe_{2}/W systems as presented in Figs. 2, c. One other thing worth mentioning is that for those cases with large charge transfer so that phase transition could occur, the fluctuation of charge transfer is generally more significant as demonstrated by the error bar, which also illustrate that the interfacial atomic orientation plays a significant role. To sum up, with all the MX_{2}/metal system identified, there would be a wide tunable space for interfacial charge transfer as well as structural phase transition of MX_{2} with the selection of various metal and design of interface orientation.
Electronic structure of MX_{2}/metal contacts
Due to the metallization at the MX_{2}/metal interface, the electronic structure of MX_{2} will be largely modified due to (transition from orbital overlap) the chemical bond formation. Moreover, for those MX_{2}/metal interface with phase transition, the modification of electronic structure would be more significant due to the strong charge transfer. DFT calculations on superlattice models are always applied to analyze such systems with interfaces, however, unfolded band structure would be more useful and convenient to illustrate the interfacial charge transfer behavior.^{48,49} Therefore, the unfolded band structures, which can be measured using the angleresolved photoemission spectroscopy (ARPES) in experiment, have been calculated and demonstrated in Fig. 3. Meanwhile, a more zoomed in version can be found in Fig. S1 in supplementary information.
As illustrated in Fig. 3, when compared to 2HMoS_{2} phase with the same metal substrate, more impurity states appear in the band structure of 1T” phase, which is also reflected by the density of states. Those are consistent with the bader analysis results shown in Fig. 2. Besides, for 2HMoS_{2} on top of Cu, the impurity states appear mostly from −4 to −2 eV below the fermi level. However, when 2HWS_{2} is placed on top of V, the impurity states appear on both valence and conduction bands. This phenomenon illustrates more significant charge transfer from metal into monolayer WS_{2} so that both bonding and antibonding states are rearranged as a result. This observation is supported by the corresponding PDOS in Figs. 3a, b. The enhanced electronic structure evolution in 2HWS_{2}/V is also in consistent with the larger geometry distortion and more transferred charge demonstrated in Figs. 1b and 2.
Contact properties of MX_{2}/metal
Because of controllable charge transfer in MX_{2}/metal interface, the electron injection efficiency would be tuned with the selection of MX_{2} and metal candidate. As a consequence of metallization, the electron tunnel barrier from metal into MX_{2} membrane will vanish^{13,20,21} (see Fig. S2 in Supplementary information). The efficiency of electron injection will thus be determined by Schottky barriers at MX_{2}/metal interface, which can be calculated as the energy difference between the fermi level of the MX_{2}/metal contact (E_{F}) and the band edges of free standing MX_{2}s. To be more specific, the energy difference between the fermi energy of the hybrid system and conduction band minimum (E_{C}–E_{F}) of free standing MX_{2}s yields the Schottky barrier of electrons while the energy difference between the corresponding fermi energy and valence band maximum (E_{F}–E_{V}) indicates the Schottky barrier of holes. To give a direct schematic view of this method, the \({\mathrm{\Phi }}_{SB}^{electron}\) and \({\mathrm{\Phi }}_{SB}^{hole}\) of 2HMoS_{2}/Cu are indicated in the band structure plot in Fig. 4a as one example. The fermi level of this contact is set as 0 eV, while the band structure of free standing MoS_{2} is plot on top of the contact band structure to show the band alignment. Based on this strategy, the Schottky barrier of all the MX_{2}/metal contact has been calculated. Due to the variation of phase stability, we only show the Schottky barriers for the contacts with the structure of the lowest energy as a representative of the equilibrium contact status. That is to say, 1T’MX_{2}/metal contact or 1T”MX_{2}/metal contact will be demonstrated for those systems with potential structural phase transition in MX_{2} monolayer as shown in Fig. 1.
As being demonstrated in Figs. 4a, b all the contacts can be divided into two categories. For those metal contact with 2H MoS_{2} and MoSe_{2}, low resistance interfaces are formed when MoS_{2} or MoSe_{2} possess ntype doping. For example, V/MoS_{2} and Mo/MoSe_{2} are expected to have the lowest Schottky barrier under N doping. For WS_{2} and WSe_{2} contacts with the studied metals, the hole barrier is always lower than the electron barrier (Figs. 4c, e). For MoTe_{2}/metal contacts, the Schottky hole barriers of MoTe_{2}/Ru and MoTe_{2}/Rh turn out to be 0 eV, meanwhile the Schottky electron barrier is the same as the bandgap of monolayer MoTe_{2}. This can be understood by the fact that electrons in MoTe_{2} will be polarized into Ru or Rh once the contacts are formed (shown by Fig. 2e), which shift the fermi level of the contact system below the original valance band maximum.
Moreover, for those MX_{2}/metal contacts with structural phase transition, 1T’(1T”)MX_{2}/metal contact will be formed at equilibrium state. In those contacts, i.e., 1T”MoSe_{2}/Sc, 1T”WS_{2}/Zr, 1T”WS_{2}/V, 1T”WSe_{2}/Sc, 1T”WSe_{2}/Ti 1T”MoTe_{2}/Cr and 1T’MoTe_{2}/Nb, both \({\mathrm{\Phi }}_{SB}^{electron}\) and \({\mathrm{\Phi }}_{SB}^{hole}\) will vanish. The reason is mainly due to the fact that significant charge transfer will finally shift the fermi energy of the MX_{2}/metal system above the conduction band minimum of 2HMX_{2}, in this case no energy barrier is needed to overcome for electron transport from MX_{2}/metal to the channel.
With the information obtained from contact analysis, we suggest that three types of MX_{2}/metal contacts can be formed depending on the amount of interfacial orbital overlapping and charge transfer. As illustrated by Fig. 5a, the first type would induce the largest interfacial resistance for MX_{2}/metal contact, this mostly applies to all the MX_{2}/metal contacts that possess very large lattice misfit, some of them are reported in literature^{13,20,21} but were screened out using the lattice misfit criterion we described above. Typically, there would be significant interfacial lattice incoherency in such MX_{2}/metal system, which inhibit effective orbital overlapping as being shown in Fig. 3. As a consequence, a sizable tunnel barrier as well as Schottky barrier should be overcome when electrons travel from metal to MX_{2} channel. This is also the main problem that occurs in previous investigated MX_{2}/metal contacts^{13,20,21}. As suggested by our study, if we can increase the orbital overlapping to some degree, the metallization of MX_{2} would occur at interface, which can vanish the tunnel barrier between MX_{2} and metal (Fig. 5b). Because of lattice coherency and orbital overlapping, the metal systems studied in this study generally have very small or zero tunneling barrier. Therefore, the Schottky barrier would be the main factor to limit the contact resistance. Among all the identified candidates, those with smallest \({\mathrm{\Phi }}_{SB}^{electron}\) or \({\mathrm{\Phi }}_{SB}^{hole}\) would be optimal contacts since small size of Schottky can be easily reduced with adequate gating. Additionally, for those 7 systems, we would expect the formation of third types of contact as shown in Fig. 5c if 1T’(1T”)MX_{2} is the energetically stable structure. In this case, structural phase transition would happen in MX_{2} domain that is contacted with metal. Meanwhile, since the fermi level of 1T’(1T”)MX_{2}/metal is higher than the conduction band minimum of 2HMX_{2}, the Schottky barrier would vanish as a consequence. Meanwhile, utilizing the states of art phase engineering techniques, the contact nature of such systems can be flexibly engineered. To give one example, MX_{2} monolayer can be first deposited on top of metal to form 2HMX_{2} contact. Due to the finite activation barrier required for 2H→1T’(1T”), contact type as shown in Fig. 5b would be formed. Furthermore, as already been reported in experiments, thermal fluctuation,^{45,50} plasmonic hot electrons^{51} or electron beam^{47} can be effective options to trigger the 2H→1T’(1T”) structure transformation. Accompanied by the phase transition, direct injection of electrons without Schottky barriers would be achieved while the contact type transforms from type 2 (Fig. 5b) to type 3 (Fig. 4c).
To conclude, we have systematically investigated the influences of interface interaction on phase stability of MX_{2}s. With the lattice misfit criterion, 28 MX_{2}/metal systems with strong interface interaction have been identified. Based on interfacial charge calculations and contact resistance analysis, all MX_{2}/metal contacts can be categorized into three groups. The first type of contact would possess zero tunnel barrier between MX_{2} and metal, while the Schottky barrier can be tuned with injection of electron or holes. In the second contact type, there is a significant charge transfer between the MX_{2} layer and metal substrate, which induces the structure transformation of MX2 layer from 2H to 1T’(1T”). In this case, both the tunnel barrier and the Schottky barrier vanish. Finally, we presented several schematic designs for applying our theoretical findings, among which the techniques are already reported in experiments. Our research not only provide realistic theoretical reference for the contact behavior for all MX_{2}/metal systems, but also shed lights on potential solutions for conquering the bottleneck of concurrent 2D transistors.
Methods
Atomistic modeling of MX_{2}/metal interface
All the 3d and 4d transition metal are visited for evaluating the performance in metalMX_{2} contact. Meanwhile, as being reported in experiments, nontransition metals such as Al,^{28,29} Ga,^{30,31} In^{24,32} are also considered. The smallest lattice misfit strain that can exist between MX_{2} and metal is used to screen metal contacts with MX_{2} since large lattice misfit could not provide enough orbital overlapping^{11,13,20,21} so that charge transfer between MX_{2} and transition metals are relatively weak. A threshold value of 2% lattice misfit is used to screen MX_{2}/metal systems as a result. Meanwhile, it is worth noting that with such a small lattice misfit strain, very small artificial strain will be enforced for DFT simulation so that the results will be more reasonable.
During the screening process, we first construct low index surfaces of metals, i.e., (001) (110) and (111), due to relatively low surface free energies and better thermodynamic stability.^{33,34} After then we considered three types of orientations which correspond to –30, 0, and 30 degrees of rotation between the [100] orientation of MX2 and metal substrate. Other interfacial rotations, which might exist in experiments and lead to certain moiré patterns, cannot guarantee enough orbital overlapping due to the small lattice coherency. Besides, other rotations require supercells with more than thousands of atoms, thus it is very challenge or impossible for DFT calculations. Therefore, we do not consider other rotation angles in this investigation. For each orientation considered, the charge transfer amount for all the possible stacking sequences are calculated.
Employing this criterion, we have identified 11 metal and 28 MX_{2}/metal contacts from the periodic table (Fig. 6e). Examples of the selected MX_{2}/metal contact atomic model are demonstrated in Figs. 6a–c. Those models can be applied to study the properties of contact nature in MX_{2}/metal based transistor as shown in Fig. 6d. All the selected metals are summarized in Fig. 6e, in each box, the name of the metal is put on top followed by the lattice type and facet selected to form the MX_{2}/metal interface. Meanwhile, the lattice misfit at interface has also been indicated in Fig. 6e. For visual convenience, different colors are filled in the box to illustrate the amount of interfacial strain. The green color indicates the metal can form MX_{2}/metal interface with misfit less than 1%, while orange means the misfit strain is about 1–2%. For some of the metals, they can form small misfit interface with two types of MX_{2}s but with different level of misfit strain, mixing of corresponding colors has been adopted for those situations. Meanwhile, the supercell of both MX_{2} and metal used to construct the smallest periodic unit for MX_{2}/metal interface have been given in Table 1.
DFT calculations
Firstprinciples DFT calculations employing the PerdewBurkeErnzerhof functional^{35} and projector augmentedwave^{36} method were performed using the Vienna ab initio simulation package for structure optimization and energetic calculations. The dispersive van der Waals interactions between the MoS_{2} and metals were included using the DFTD2 method of Grimme.^{37,38,39} In each calculation, kpoint grids are benchmarked to be sufficient for accurate calculation. The energy cutoff has been set as 400 eV for all the MX_{2}/metal interface models and it has been tested to be large enough for energy convergence. A vacuum space of 20 Å perpendicular to each slab model is used to eliminate image interactions. When performing the structure optimizations, the system is regarded as converged when the force per atom is less than 0.01 eV/Å. Being ware of the fact that traditional GGA method failed to provide accurate estimation of band edges,^{40} we have implemented the consideration of spin orbital coupling (soc) in our calculations. As being demonstrated in previous studies, both the band gaps and the soc induced energy splitting can be well captured with such calculation setup.^{7,41,42,43}
Meanwhile, it should be noted that small lattice misfit still exists in the MX_{2}/metal systems (see Fig. 6e). Since we are mainly interested in how electron transfer from metal to MX_{2} can influence the phase stability, it would be better not to deform the MX_{2} lattice as in this case the phase stability will be affected by both strain and charge transfer, making it difficult to decouple the two effects. As a result, for all systems, we deform slightly the metal lattice to fit into the MX_{2} monolayer.
Data availability
The data related to the findings of this work are available from the corresponding author subject to reasonable request.
References
Ouyang, B. & Song, J. Strain engineering of magnetic states of vacancydecorated hexagonal boron nitride. Appl. Phys. Lett. 103, 102401 (2013).
Ouyang, B. & Song, J. Covalent pathways in engineering hBN supported graphene. Carbon 98, 449–456 (2016).
Song, J., Ouyang, B. & Medhekar, N. V. Energetics and kinetics of Li intercalation in irradiated graphene scaffolds. ACS Appl. Mater. Interfaces 5, 12968–12974 (2013).
Ouyang, B., Meng, F. & Song, J. Energetics and kinetics of vacancies in monolayer graphene boron nitride heterostructures. 2D Mater. 1, 035007 (2014).
Ouyang, B., Chen, C. & Song, J. Conjugated π electron engineering of generalized stacking fault in graphene and h BN. Nanotechnology 29, 09LT01 (2018).
Ouyang, B. & Song, J. Tuning magnetic states of planar graphene/hBN monolayer heterostructures via interface transition metalvacancy complexes. J. Phys. Chem. C. 120, 23529–23535 (2016).
Ouyang, B., Mi, Z. & Song, J. Bandgap transition of 2H transition metal dichalcogenides: predictive tuning via inherent interface coupling and strain. J. Phys. Chem. C. 120, 8927–8935 (2016).
Lu, N. et al. MoS2/MX2 heterobilayers: bandgap engineering via tensile strain or external electrical field. Nanoscale 6, 2879–2886 (2014).
Mak, K. F., Lee, C., Hone, J., Shan, J. & Heinz, T. F. Atomically thin MoS2: a new directgap semiconductor. Phys. Rev. Lett. 105, 136805 (2010).
Desai, S. B. et al. MoS2 transistors with 1nanometer gate lengths. Science 354, 99–102 (2016).
Allain, A., Kang, J., Banerjee, K. & Kis, A. Electrical contacts to twodimensional semiconductors. Nat. Mater. 14, 1195–1205 (2015).
Radisavljevic, B., Radenovic, A., Brivio, J., Giacometti, V. & Kis, A. Singlelayer MoS2 transistors. Nat. Nano. 6, 147–150 (2011).
Kang, J.., Liu, W.., Sarkar, D.., Jena, D.., & Banerjee, K.. Computational study of metal contacts to monolayer transitionmetal dichalcogenidesemiconductors. Phys. Rev. X4, 031005 (2014).
Gong, C. et al. Metal contacts on physical vapor deposited monolayer MoS2. ACS Nano 7, 11350–11357 (2013).
Smyth, C. M., Addou, R., McDonnell, S., Hinkle, C. L. & Wallace, R. M. Contact metal–MoS2 interfacial reactions and potential implications on MoS2based device performance. J. Phys. Chem. C. 120, 14719–14729 (2016).
Leong, W. S. et al. Low resistance metal contacts to MoS2 devices with nickeletchedgraphene electrodes. ACS Nano 9, 869–877 (2015).
Bruix, A. et al. Singlelayer MoS2 on Au(111): band gap renormalization and substrate interaction. Phys. Rev. B 93, 165422 (2016).
Cook, M. et al. Influence of interface coupling on the electronic properties of the Au/MoS2 junction. Phys. Rev. B 92, 201302 (2015).
Zhou, Y. et al. Compliant substrate epitaxy: Au on MoS2. Phys. Rev. B 93, 054106 (2016).
Popov, I., Seifert, G. & Tománek, D. Designing electrical contacts to MoS2 monolayers: a computational study. Phys. Rev. Lett. 108, 156802 (2012).
Wang, Y. et al. Does ptype ohmic contact exist in WSe2metal interfaces? Nanoscale 8, 1179–1191 (2016).
Ouyang, B., Ou, P., Wang, Y., Mi, Z. & Song, J. Phase engineering of MoS2 through GaN/AlN substrate coupling and electron doping. Phys. Chem. Chem. Phys. 18, 33351–33356 (2016).
Ouyang, B., Xiong, S., Yang, Z., Jing, Y. & Wang, Y. MoS2 heterostructure with tunable phase stability: strain induced interlayer covalent bond formation. Nanoscale 9, 8126–8132 (2017).
Srivastava, S. K. & Avasthi, B. N. Synthesis and characterization of indium intercalation compounds of molybdenum diselenide, In x MoSe2 (0 ≤ x ≤ 1). J. Mater. Sci. 24, 1919–1924 (1989).
Tang, W., Sanville, E. & Henkelman, G. A gridbased Bader analysis algorithm without lattice bias. J. Phys. Condens. Matter 21, 084204 (2009).
Yu, M. & Trinkle, D. R. Accurate and efficient algorithm for Bader charge integration. J. Chem. Phys. 134, 064111 (2011).
Henkelman, G., Arnaldsson, A. & Jónsson, H. A fast and robust algorithm for Bader decomposition of charge density. Comp. Mater. Sci. 36, 354–360 (2006).
Kanthavel, K., Sumesh, K. R. & Saravanakumar, P. Study of tribological properties on Al/Al2O3/MoS2 hybrid composite processed by powder metallurgy. Alex. Eng. J. 55, 13–17 (2016).
Li, N., Feng, L.p., Su, J., Zeng, W., & Liu, Z.t. Optical and electrical properties of Al:WS2 films prepared by atomic layer deposition and vulcanization. RSC Adv. 6, 64879–64884 (2016).
Ye, Y. et al. Electrical generation and control of the valley carriers in a monolayer transition metal dichalcogenide. Nat. Nano. 11, 598 (2016).
Gardos, M. N. An Analysis of the Ga/In/WSe2 Lubricant Compact. ASLE Trans. 28, 231–238 (1985).
Deshpande, M. P., Patel, P. D., Vashi, M. N. & Agarwal, M. K. Effect of intercalating indium in WSe2 single crystals. J. Cryst. Growth 197, 833–840 (1999).
Xiong, S. et al. Size and shape dependent surface free energy of metallic nanoparticles. J. Comput. Theor. Nanosci. 8, 2477–2481 (2011).
Xiong, S. et al. Modeling size effects on the surface free energy of metallic nanoparticles and nanocavities. Phys. Chem. Chem. Phys. 13, 10648–10651 (2011).
Perdew, J., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).
Blöchl, P. E. Projector augmentedwave method. Phys. Rev. B 50, 17953–17979 (1994).
Grimme, S., Ehrlich, S. & Goerigk, L. Effect of the damping function in dispersion corrected density functional theory. J. Comput. Chem. 32, 1456–1465 (2011).
Grimme, S. Semiempirical GGAtype density functional constructed with a longrange dispersion correction. J. Comput. Chem. 27, 1787–1799 (2006).
Grimme, S., Antony, J., Ehrlich, S. & Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFTD) for the 94 elements HPu. J. Chem. Phys. 132, 154104 (2010).
Zhong, H. et al. Interfacial properties of monolayer and bilayer MoS2 contacts with metals: beyond the energy band calculations. Sci. Rep. 6, 21786 (2016).
Kormányos, A., Zólyomi, V., Drummond, N. D. & Burkard, G. Spinorbit coupling, quantum dots, and qubits in monolayer transition metal dichalcogenides. Phys. Rev. X 4, 011034 (2014).
Kuc, A. & Heine, T. The electronic structure calculations of twodimensional transitionmetal dichalcogenides in the presence of external electric and magnetic fields. Chem. Soc. Rev. 44, 2603–2614 (2015).
Kormányos, A. et al. Monolayer MoS2: trigonal warping, the valley, and spinorbit coupling effects. Phys. Rev. B 88, 045416 (2013).
Ouyang, B., Lan, G., Guo, Y., Mi, Z. & Song, J. Phase engineering of monolayer transitionmetal dichalcogenide through coupled electron doping and lattice deformation. Appl. Phys. Lett. 107, 191903 (2015).
Guo, Y. et al. Probing the dynamics of the metallictosemiconducting structural phase transformation in MoS2 crystals. Nano Lett. 15, 5081–5088 (2015).
Kappera, R. et al. Phaseengineered lowresistance contacts for ultrathin MoS2 transistors. Nat. Mater. 13, 1128–1134 (2014).
Lin, Y.C., Dumcenco, D. O., Huang, Y.S. & Suenaga, K. Atomic mechanism of the semiconductingtometallic phase transition in singlelayered MoS2. Nat. Nano. 9, 391–396 (2014).
Medeiros, P. V. C., Tsirkin, S. S., Stafström, S. & Björk, J. Unfolding spinor wave functions and expectation values of general operators: Introducing the unfoldingdensity operator. Phys. Rev. B 91, 041116 (2015).
Medeiros, P. V. C., Stafström, S. & Björk, J. Effects of extrinsic and intrinsic perturbations on the electronic structure of graphene: Retaining an effective primitive cell band structure by band unfolding. Phys. Rev. B 89, 041407 (2014).
Voiry, D., Mohite, A. & Chhowalla, M. Phase engineering of transition metal dichalcogenides. Chem. Soc. Rev. 44, 2702–2712 (2015).
Kang, Y. et al. Plasmonic hot electron induced structural phase transition in a MoS2 monolayer. Adv. Mater. 26, 6467–6471 (2014).
Acknowledgements
This work is supported by the Jiangsu provincial natural science funding Project No. BK20160308, NSF of China under Grants No. 11304059, the NSF of Heilongjiang Province of China under Grants No. QC2015001 and the International Postdoctoral Exchange Fellowship Program No. 20140016.
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B.O. designed this research; B.O. and Y.J. performed calculations and data analysis; B.O., S.X., and Y.J. wrote this paper.
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Ouyang, B., Xiong, S. & Jing, Y. Tunable phase stability and contact resistance of monolayer transition metal dichalcogenides contacts with metal. npj 2D Mater Appl 2, 13 (2018). https://doi.org/10.1038/s4169901800591
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DOI: https://doi.org/10.1038/s4169901800591
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