Computational discovery of metallic MBenes for two-dimensional semiconductor contacts approaching the quantum limit

Abstract

The realization of ultralow-resistance contacts in two-dimensional semiconductors such as transition metal dichalcogenides (TMDs) is pivotal for advancing transistor scaling toward the end of technology roadmap. In this work, by means of high-throughput first-principles calculations, we identify that highly stable two-dimensional metallic MBenes with large abundance of density of states are potential for achieving low-resistance MBene-TMD contacts at the quantum limit. We reveal that local built-in electric field at MBene-MoS₂ interfaces driven by interfacial polarization enables tunable band shift of MoS₂ channel, which allows for obtaining p-type Ohmic contact. The strong van der Waals interactions between MBenes and MoS₂ induces a delicate balance between the Fermi-level pinning and carrier tunneling efficiency, resulting in ultralow contact resistance down to 41.6 Ω μm. The contact performance of screened Nb₂BO₂-MoS₂ and Nb₂B(OH)₂-MoS₂ junctions can be competed with previous records using semimetals Sb and Bi as the contacts of MoS₂ devices.

Introduction

As Si-based field-effect transistors (FETs) approach physics limits in scaling, thus the exploration of new-generation electronics requires dimensional scaling of the channel materials down to the two-dimensional (2D) limit without the impact of short-channel effects^1,2. 2D semiconductors such as black phosphorus (BP), indium selenide (InSe), and transition metal dichalcogenides (TMDs) are ideally suitable for post-Moore era transistors due to their ultrathin body thickness, dangling-bond-free surface, and high carrier mobility^3,4,5,6. Especially, atomically thin TMDs with high structural stability and dangling-bond-free surface facilitates electrostatic gate modulation and channel length scaling, which is of particular importance for achieving high-performance FETs^7,8. For example, recent studies demonstrated that the room-temperature hole mobility of 2D FETs with p-type monolayer WSe₂ channel could arrive at 1000 cm²V⁻¹s⁻¹ and the contact resistance of n-type monolayer MoS₂ transistors could approach the quantum limit^9,10. Therefore, 2D FETs with excellent device performance can satisfy the ITRS or IRDS standards and extend Moore’s Law until the channel length is scaled down to 1 nm^11,12. Moreover, the integration of 2D semiconductors into advanced technologies have been also scheduled into the technology roadmaps of worldwide semiconductor chip companies, including TSMC, Intel, and Samsung¹³.

Although significant achievements have been made in 2D semiconductor devices, achieving low-resistance metal-semiconductor (M-S) contacts at nanoscale dimension poses an increasing challenge, especially for extreme scaling of device channel length. An ideal metal-semiconductor junction (MSJ) presents a trap-state-free interface with tunable carrier polarity and ultralow contact resistance^14,15. However, the conventional MSJs based on 2D semiconductors usually suffer from large contact resistance (R_C) in the range of 10³ ~ 10⁵ ohm micrometers¹⁴, which mainly originates from large Schottky barrier heights (SBHs) and Fermi-level pinning (FLP) effect^16,17. The large SBHs arise from the energy mismatch between the work function (W_m) of metal electrodes and electron affinity of 2D semiconductors, which can be potentially solved by two strategies: (i) the selection of metal electrodes with appropriate W_m and (ii) heavily doping in 2D semiconductors¹⁸. Owing to ultrathin thickness of 2D semiconductors, heavily doping easily leads to the lattice disorders and structural defects¹⁹. Hence, the deposition of metal films on 2D semiconductor channel surfaces incurs discontinuous M-S interfaces by the chemical bonding, resulting in the interface and surface states (Bardeen pinning effect) localized in the bandgap of semiconductors²⁰. The so-called metal-induced gap states (MIGS) is responsible for severe FLP effect¹⁷, which is a main reason why previously reported 2D devices often suffer from uncontrollable Schottky barriers and low carrier mobilities²¹. Therefore, considerable efforts have been devoted to developing efficient strategies for the suppression of FLP effect in the metal-2D semiconductor interfaces, including the replacement of bulk metal films by 2D metals such as metallic TMDs and mechanical transfer of metal films^22,23,24. The use of 2D metals has been verified as an efficient strategy to suppress the FLP effect, allowing for the fabricated FET devices with tunable carrier polarity²⁵. However, the existence of interlayer vdW gap brings an additional tunneling barrier and reduces the carrier injection efficiency, making that typical R_C values are several orders of magnitude higher than the quantum limit¹⁵. The enhancement of M-S orbital hybridization was proposed to improve metal-2D semiconductor contacts, including semi-metallic contacts and edge contacts^26,27,28. For instance, high-performance TMD transistors with ultralow R_C down to 42 Ω μm have been demonstrated by the use of semi-metallic Sb electrodes⁹. However, the semimetal and edge contact schemes are significantly limited by a narrow range of metal work functions and they are only suitable for specific 2D semiconductor channel materials. Typically, there is a lack of appropriate metals with high W_m to form p-type Ohmic contact with monolayer MoS₂. Hence, the exploration of new metal systems with a wide range of W_m is essential for achieving low-resistance metal-2D semiconductor contacts with weak FLP.

Transition metal borides (i.e., MBenes) emerged as a new family of 2D materials have drawn substantial interest in electronics, optoelectronics, and energy-storage and conversion devices owing to their high stability, superior electrical conductivity, and outstanding physicochemical properties^29,30,31. The first experimental report on MBenes could be traced back to 2015³², which regarded them as an analogue of MXenes. The subsequent development of synthetic techniques makes that various types of MBenes have been demonstrated, including M₂B, M₂B₂, M₂B₃ and M₃B₄ (M = transition metal element)³⁰. The use of chemical etchants easily induce the exposed transition-metal faces in MBenes terminated with different functional groups such as O, OH, F, Cl and others³³. The structural diversity and abundant surface terminations of MBenes offer a large degree of freedom to tailor their electronic properties, including work function and electrical conductivity. Hence, the utilization of MBenes as contact electrodes of 2D semiconductors will possess several remarkable advantages: (i) Highly structural and chemical stabilities. Unlike the conventional 2D metals and semimetals, MBenes can greatly resist external stress and air oxidation due to their ceramic nature³⁴. (ii) Excellent electrical conductivity. The strong s-d and p-d orbital hybridization between the transition metal and boron atoms induce large band dispersion at the proximity of Fermi level, which facilitates carrier transport for high electrical conductivity. (iii) Tunable work functions. The structural diversity and abundant surface terminations of MBenes makes that their work functions can be modulated in a wide range³⁵, which is crucial for constructing high-performance MSJs with desired contact types. Typically, MoS₂ is one of the most studied 2D semiconductors, but it is difficult to be used as a p-type channel due to the lack of appropriate metals with high W_m ( > 6.6 eV) to match with the electron affinity of MoS₂³⁶. The O/F-terminated MBenes were reported as high work-function metals that could potentially induce p-type Ohmic contact with MoS₂³⁷. Furthermore, versatile surface terminations of MBenes create a possibility to improve the M-S contacts by engineering the interfacial interactions between MBenes and 2D semiconductors, which is essential for the development of high-performance devices with low-resistance contacts at the quantum limit. Despite large potential of MBenes for 2D semiconductor contacts, the electrical transport and contact properties of MBenes/semiconductor junctions have been rarely explored to date.

In this work, we perform high-throughput computational screening of metallic MBenes for low-resistance 2D semiconductor contacts approaching the quantum limit by using density-functional theory (DFT) calculations combined with non-equilibrium Green’s function (NEGF) method. The initial database of 870 functionalized MBenes with a general chemical formula of M₂BT₂ (T = O, F, Cl, OH) are established by the variation of chemical elements and crystal phase, and 40 MBenes are selected by a set of screening criteria including the structural stability, abundance of density of states, and electrical conductivity. We further identify that Nb-based and Tc-based MBenes exhibit high structural stability, large range of W_m from 2.58 to 6.51 eV, and excellent electronic properties and they are verified to induce both n-type and p-type Ohmic contacts with typical 2D semiconductors, such as MoS₂, MoSe₂, WS₂, WSe₂, and MoTe₂. Especially for MBene-MoS₂ MSJs, local build-in electric field driven by the interfacial polarization can tune the band alignment of MoS₂ channel, which allows for forming p-type Ohmic contact. The strong vdW interactions between MBenes and 2D semiconductors (e.g., MoS₂) balance a delicate competition between the FLP and carrier tunneling barrier via the interfacial orbital hybridization, resulting in ultralow contact resistances down to 41.6 Ω μm at the carrier concentration of 2.93 × 10¹³ cm⁻². Furthermore, using the FLP factor and contact resistance as the descriptors, Nb₂BO₂ and Tc₂BF₂ are identified as optimal contacts for p-type TMD devices and Nb₂B(OH)₂ and Tc₂B(OH)₂ are promising contacts for n-type TMD devices.

Results

High-throughput screening of metallic MBenes

The workflow and framework of high-throughput screening of metallic MBenes are illustrated in Fig. 1. To find highly stable metallic MBenes, a fundamental database including 870 initial structures have been firstly established. The MBene structures with a general chemical formula of M₂BT₂ are created by varying transition-metal elements M and surface functional groups T into six potential crystal phases (i.e., H1-H3 and T1-T3), as shown in Fig. 1a, b (see Methods for more details on the crystal phase of MBenes). For a given M₂BT₂, only the lowest-energy phase structure is chosen by the energy comparison among six potential phases. Hence, 145 MBenes are screened from 870 initial structures (Supplementary Fig. S1), and then they are evaluated by their structural stability, including both the thermodynamic and dynamic stabilities (Fig. 1c). Furthermore, highly stable MBenes are further screened by the electronic and electrical parameters, including the abundance of density of states (D_F) and electrical resistance (ρ). Based on above screening procedure, potential candidates of metallic MBenes are obtained and used as the electrodes for 2D semiconductors.

Fig. 1: High-throughput computational screening protocol for the discovery of promising 2D MBenes.

a Element composition of 2D functionalized MBenes with a general chemical formula of M₂BT₂ (M = transition metal elements; T = O, F, Cl, OH). b Six potential phase structures of MBenes including H1-H3 and T1-T3. The red and blue shadow regions correspond to the atomic arrangement in trigonal prismatic geometry and octahedral geometry, respectively. The purple, green, and yellow balls represent the transition metal atoms, boron atoms, and surface function groups, respectively. c Computational screening workflow and framework of metallic MBenes.

We firstly focus on the trend in the structural stability and work function of 145 MBenes in the lowest-energy phase. Figure 2a presents the formation energies (E_f) of MBenes with and without (w/o) surface functional groups (T = O, F, Cl, and OH). The details on the structural and energetic data of 2D MBenes are listed in supplementary Table S1–S4. We find that the majority of MBenes present negative E_f, indicating that they are thermodynamically stable. Moreover, the surface passivation induces a significant reduction in E_f, suggesting that the functional-group passivation on MBene surfaces contributes to the enhancement of structural stability. Figure 2b shows the adsorption energy (E_a) of functionalized MBenes. We find that the E_a values of all functionalized MBenes are negative, implying that the surface passivation is energetically favorable. Furthermore, the structural stability of some energetically favorable MBene structures has been also examined by their phonon band dispersions (Supplementary Fig. S2). The calculated phonon spectra do not include any imaginary frequency modes, implying that they are dynamically stable. Based on the energetic data and stability analysis, 40 promising MBene structures including M₂BT₂ (M= Sc, Y, Hf, Ti, Nb, Zr, V, Ta, Cd, and Tc) have been selected as candidates for further evaluation of electrical properties since they exhibit relatively larger negative E_f and E_a values.

Fig. 2: Formation energies, adsorption energies, and work functions of 2D MBenes terminated with different surface functional groups.

a Formation energies (E_f) of MBenes with and without (w/o) surface functional groups. b Adsorption energies (E_a) of functionalized MBenes. c Work functions (W_m) of bare and functionalized MBenes.

Prior to electrical evaluation, the electronic structures of 145 MBenes have been firstly calculated, including their band structures and work functions. The calculated band structures indicate that all these MBenes are metals, as shown in Supplementary Figs. S3–S10. The W_m values of bare and functionalized MBenes are plotted in Fig. 2c, indicating a strong dependence on the surface functional groups. The OH-passivated MBenes tend to induce the reduction of W_m and the F/O-terminated MBenes induces the increase of W_m as compared to bare MBenes. The surface-termination-dependent W_m have been also demonstrated in the functionalized MXenes^37,38. Among these functionalized MBenes, Ir₂BF₂ has the largest W_m (9.20 eV) and Zr₂B(OH)₂ indicates the smallest W_m (1.17 eV). The ultrawide range of W_m originates from the orbital hybridization between the transition metals and surface function groups, which offers a large degree of freedom to design 2D MBene-semiconductor junctions with desired contact type.

An ideal electrode material is expected to have low electrical resistance and good transport properties, which essentially depends on the distribution of density of states (DOS) at the proximity of Fermi level (Fig. 3a). Thus, we introduce the abundance of DOS (D_F) to identify the potential of metallic MBenes as contact electrodes for 2D semiconductors, and D_F is defined as follows,

$${{\rm{D}}}_{{\rm{F}}}={\int }_{{E}_{F}-2}^{{E}_{F}+2}D(E)dE$$

(1)

where D(E) is density of states with the energy range from E_F – 2 to E_F + 2 eV. The selection of the integration window arises from the following reasons: (i) the electrons at the lower-energy bands (< E_F–2 eV) are difficult to move or transit onto the Fermi surface, thus they almost do not contribute to the formation of electric current under bias voltage. (ii) Few electrons can be distributed at the higher-energy bands (>E_F + 2 eV) under room-temperature condition according to the Fermi-Dirac distribution, so high-energy electronic states do not also participant in the electrical transport. Figure 3b shows the D_F values of 40 highly stable functionalized MBenes mentioned above. The D_F values of MBenes are sensitive to the changes in both the transition metals and surface functional groups, suggesting that the abundance of DOS around the Fermi level originates from a synergetic effect of the p-d hybridization between the M and B atoms and orbital hybridization between the M-d and T-p states (Supplementary Fig. S11). Overall, Nb-, Ta-, and Tc-based MBenes present relatively larger D_F ( >14 e) and Sc-, Y-, Cd-based MBenes show relatively smaller D_F ( <13 e). Considering that potential candidates should have high D_F, 15 MBene materials have been chosen for further electrical evaluation. To evaluate electrical transport properties of the functionalized MBenes, their simulated output (I_d-V_d) curves are plotted in Fig. 3c. The slop of I_d-V_d curves in these MBene materials are different, and the output current (I_d) covers a large range from 55 to 422 mA/μm at the bias voltage (V_d) of 2V, indicating that they exhibit different electric resistances. In order to quantify the magnitude of electric resistance of these MBene candidates, the electrical resistivity (ρ) of Nb-based and Tc-based MBenes has been calculated and presented in Fig. 3d. Since MXenes are regarded as one of the most promising electrode materials for 2D semiconducting contacts from previous studies^37,38,39, the ρ of Nb- and Tc-based MXenes has been also calculated for the comparison. The ρ of Nb-based and Tc-based MBenes locates in the range of 2 ~ 5 × 10⁻⁸ Ω m, which is superior to that of Nb- and Tc-based MXenes. Especially for Tc-based MBenes, their ρ values are about three times smaller than those of Tc-based MXenes. Based on above results, Nb- and Tc-based MBenes are selected as the electrodes for 2D semiconductor devices owing to their high structural stability, tunable work functions, and low ρ values.

Fig. 3: Abundance of density of states (DOS) and electric transport of 2D metallic MBenes.

a Schematic illustration of abundance of DOS (D_F) that essentially determines the carrier transport of metallic MBenes, b D_F values of 40 selected highly stable MBenes M₂BT₂ (T = O, F, Cl, OH). c Output (I_d-V_d) curves of 15 selected high-D_F MBenes M₂BT₂ (T = O, F, Cl, OH). d Electrical resistivity (ρ) of Nb₂BT₂ and Tc₂BT₂ (T = O, F, Cl, OH). The ρ of Nb- and Tc-based MXenes for the comparison.

Schottky barrier and contact type of 2D MBene-TMD junctions

Based on the screened functionalized MBenes (Nb₂BT₂ and Tc₂BT₂), 2D MBene-semiconductor junctions were constructed by vdW integration of MBenes and atomically thin TMD semiconductors such as MoS₂, MoSe₂, MoTe₂, WS₂, and WSe₂ along the out-of-plane direction (Fig. 4a). The selection of semiconducting TMDs as the channel materials stems from their huge potential for electronic and optoelectronic applications^5,6,7,8. The allowed lattice mismatch between MBenes and semiconducting TMDs in the MSJs is smaller than 5%. Although strain effect induced by the lattice mismatch could lead to small changes in the electronic structures of MBenes and TMDs (see Supplementary Fig. S12 and Table S5 for the details), the overall results of MBene-MoS₂ junctions, including the contact type and SBHs, cannot be significantly affected by the in-plane mismatched strain. In order to determine the contact type of MBene-TMD junctions, their SBHs have been calculated. The SBH (Φ_SBH) is defined as the energy difference between the Fermi level of a given MSJ and band-edge energies of TMD channel in the MSJ^20,40.

$${\Phi }_{e}={E}_{C}-{E}_{F},\,{\Phi }_{{\rm{h}}}={E}_{F}-{E}_{V}$$

(2)

where Φ_e and Φ_h are the SBHs for electrons and holes, respectively. E_C, E_V, and E_F are the energy of conduction band minimum (CBM) and valence band maximum (VBM) of TMD semiconductors and Fermi level in the MSJs, respectively. According to the definition of SBHs, there are three contact types (Supplementary Fig. S13): Schottky contact (Φ_e > 0 and Φ_h > 0), n-type Ohmic contact (Φ_e ≤ 0), and p-type Ohmic contact (Φ_h ≤ 0). The contact type of an ideal MSJ can be predicted by the Schottky-Mott rule and its SBH can be directly obtained by comparing the W_m of metals with band-edge energies of semiconductor channels. Figure 4b presents the CBM and VBM energies of five TMD semiconductors and W_m of eight metallic MBenes relative to the vacuum level. Based on the Schottky-Mott rule, the contact type of 2D MBene-TMD junctions is predicted in Supplementary Fig. S14. Except for MoS₂-based MSJs, all three contact types can be achieved in MBene-TMD junctions. If MBene-TMD junctions obey the Schottky-Mott rule, the p-type Ohmic contact should not be realized in MoS₂-based MSJs. However, the SBH of a practical MSJ is not only dependent on the band alignment of constitutive metal and semiconductor but also affected by the interfacial coupling between the metal and semiconductor.

Fig. 4: Interfacial polarization effect on Schottky barrier and contact type in 2D MBene-TMD junctions.

a Schematic of atomic model of 2D MBene-TMD junctions. b Band-edge (CBM and VBM) energies of 5 semiconducting TMD monolayers and work functions of 8 metallic MBenes relative to the vacuum level. c The Φ_e and Φ_h of 2D MBene-MoS₂ junctions. The MSJs with the n-type ohmic contact, p-type Ohmic contact, and Schottky contact are labelled by blue, red, and green balls, respectively. d Electrostatic potential distribution (V_E) of Tc₂B(OH)₂-MoS₂ junctions along the out-of-plane direction. The arrow indicates the interfacial polarization direction. e The μ of MBene-MoS₂ junctions as a function of ΔV_E. f The ΔΦ_SBH of MBene-MoS₂ junctions as a function of ΔV_E. ΔΦ_e (ΔΦ_h) is defined as the difference between the real and ideal Φ_e (Φ_h) values. The insets indicate the band shift of MoS₂ in the MSJs relative to independent MoS₂ at ΔV_E > 0 and ΔV_E < 0.

In order to reveal the interfacial coupling effect on the SBHs of 2D MBene-TMD junctions, the projected band structures of MBene-MoS₂ junctions are calculated by the HSE06 functional, as shown in Supplementary Fig. S15. The corresponding Φ_e and Φ_h values are plotted in Fig. 4c. Different from the prediction based on the Schottky-Mott rule, p-type Ohmic contact can be also achieved in MBene-MoS₂ junctions (Nb₂BO₂-MoS₂ and Tc₂BF₂-MoS₂). Moreover, we find that the SBHs of MBene-MoS₂ junctions more or less deviate from ideal Φ_e and Φ_h values. For example, the Φ_e of Nb₂BCl₂-MoS₂ junction should be 0.60 eV based on the Schottky-Mott rule, but its real Φ_e value is 0.57 eV according to the calculated band structure. These results reflect that the SBHs of MBene-TMD junctions are significantly affected by the interfacial coupling effect. To insight into the deviation of SBHs from the prediction of Schottky-Mott rule, the electrostatic potential distribution (EPD) of MBene-MoS₂ junctions is investigated (Supplementary Fig. S16). Taking Tc₂B(OH)₂-MoS₂ junction as an example, its EPD (V_E) displays an asymmetric distribution along the out-of-plane direction (Fig. 4d). More specifically, the vacuum level of MoS₂ side is notably smaller than that of Tc₂B(OH)₂ side, resulting in the electrostatic potential difference (ΔV_E) of 1.85 eV and dipole moment (μ) of 0.08 Deby. This implies that there exists an interfacial polarization (P) pointing from the semiconducting (MoS₂) layer towards the metallic (Tc₂B(OH)₂) layer (Fig. 4d). The ΔV_E and μ of eight MBene-MoS₂ junctions are plotted in Fig. 4e. It can be seen that there is a linear relationship between the ΔV_E and μ values. For the MSJs (e.g., M₂B(OH)₂-MoS₂ junctions) with positive ΔV_E and μ values, the P points from the semiconductor (S) layer to the metal (M) layer. For the MSJs (e.g., F/O-terminated MBenes-MoS₂ junctions) with negative ΔV_E and μ values, the P points from the M layer to the S layer.

In order to quantify the role of interfacial polarization in the SBHs, the ΔΦ_e and ΔΦ_h of MBene-MoS₂ junctions as a function of ΔV_E are plotted in Fig. 4f. The ΔΦ_e (ΔΦ_h) is defined as the difference between ideal and real Φ_e (Φ_h) values. The positive (negative) ΔΦ_e and ΔΦ_h values represent the increase (reduction) of SBHs relative to the ideal values derived from the Schottky-Mott rule. The calculated results indicate two interesting trends: (i) the magnitude of ΔΦ_e and ΔΦ_h shows a linear variation with ΔV_E, suggesting that strong polarization is responsible for large SBH deviation³⁷. (ii) The positive ΔV_E leads to the increase of Φ_h and reduction of Φ_e, while the negative ΔV_E makes a reverse trend. The results originate from the formation of local build-in electric field (E_in) induced by the interfacial polarization (Fig. 4d). For P pointing from MoS₂ to MBenes (ΔV_E > 0), the build-in electric field drives the band upshift of both the MBene and MoS₂ layers (insets of Fig. 4f), which is responsible for the increase of Φ_h and reduction of Φ_e. In contrast, for P pointing from MBenes toward MoS₂ (ΔV_E < 0), the build-in electric field induces the band downshift of the MBene and MoS₂ layers. This is the reason why Nb₂BO₂-MoS₂ and Tc₂BF₂-MoS₂ junctions exhibit p-type Ohmic contact.

Fermi-level pinning and contact resistance of MBene-MoS₂ junctions

As mentioned above, the Schottky-Mott rule cannot accurately predict the SBHs in MBene-MoS₂ junctions owing to the existence of FLP effect induced by the interfacial interactions. To quantify the FLP strength in MBene-MoS₂ junctions, the FLP factor S for a given semiconducting channel (MoS₂) is calculated as follows,

$$S=\frac{d{\Phi }_{SBH}}{d{W}_{{\rm{m}}}}$$

(3)

where S_e = 1 (Φ_SBH = Φ_e) or S_h = −1 (Φ_SBH = Φ_h) represents that the Schottky-Mott limit is achieved, and S_e or S_h = 0 denotes strong FLP in the MSJs or Bardeen limit²⁰. The Φ_e and Φ_h of eight MBene-MoS₂ junctions as a function of W_M are plotted in Fig. 5a, b, respectively. The plot of Φ_e exhibits a positive slope with increasing W_M, while the plot of Φ_h indicates a negative slope with increasing W_M. Based on a linear fit with the Eq. (3), the FLP factor S_e and S_h for the MBene-MoS₂ junctions are 0.58 and −0.55, respectively. Although the S_e and S_h of MBene-MoS₂ junctions are smaller than those (0.65–0.97) of 2D metal-TMD junctions (Fig. 5c)^41,42, they are far larger than those of 3D metal-TMD junctions (0.06–0.2)^43,44. This means that the use of MBenes as contact electrodes of MoS₂ leads to weak FLP that can be verified by the projected band structures of MBene-MoS₂ junctions. As shown in Supplementary Fig. S15, there is almost no metal-induced gap states (MIGS) formed in the bandgap of MoS₂. Moreover, the band structure of MoS₂ in the MSJs is largely consistent with that of the freestanding MoS₂ monolayer. In contrast, for 3D metal-MoS₂ junctions such as Au-MoS₂, Ag-MoS₂ and Pt-MoS₂, the MIGS can be clearly identified in the projected band structures (Supplementary Fig. S17). Therefore, the FLP in MSJs inherently correlate with the interfacial coupling between the metal and semiconductor via the orbital hybridization. To understand the interfacial coupling effect on the FLP in TMD-based MSJs, their interfacial binding energies (γ_int) are calculated. We find that 2D metal-TMD junctions indicate relatively smaller γ_int in the range of 0.25 ~ 0.63 J/m², while 3D metal-TMD junctions present relatively larger γ_int in the range of 0.97 ~ 3.40 J/m². MBene-MoS₂ junctions exhibit medium interfacial coupling with the γ_int of 0.26 ~ 1.14 J/m², which originates from the orbital hybridization between the electronic states of MBenes and MoS₂ (Supplementary Fig. S18). For the aspect of suppression of FLP effect, the formation of weak interfacial coupling in the MSJs is more expected.

Fig. 5: FLP, Carrier tunneling probability, and contact resistance of MBene-MoS₂ junctions.

a Φ_e and (b) Φ_h of MBene-MoS₂ junctions as a function of W_m of MBenes. The slope of linear fitting curves corresponds to the FLP factor S (S_e for electrons and S_h for holes). c FLP factor S versus interfacial binding energy (γ_int) in various TMD-based MSJs, including MBene-MoS₂, 2D metal-TMD, 3D metal-TMD junctions. The experimental and theoretical S values of TMD-based MSJs are from previous literatures^{20,41,42,43,44}. d Electrostatic potential (V) of Nb₂BF₂-MoS₂ junction along the out-of-plane direction. Φ_TB and ω_TB are the tunneling barrier height and width of the MSJ, respectively. e Φ_TB, ω_TB, and corresponding color mapped tunneling probability (P_TB) of MBene -MoS₂ junctions. f Contact resistance (R_CW) of MoS₂ devices with different types of contact electrodes, including MBenes (stars), MXenes (diamonds), 2D metals (squares), semimetals (hexagons), and bulk metals (triangles). The experimental and simulated R_CW of state-of-the-art devices based on bulk semiconductor and MoS₂ channels are presented for the comparison^9,28,29,45. The blue dash line denotes the quantum limit. are marked by gray symbols. g Schematic of MoS₂ FET device using MBenes as the contacts. h output (I_d-V_d) curve of low-resistance MoS₂ device with Tc₂BF₂ and Nb₂B(OH)₂ contact electrodes. i I_d-V_d curve of high-resistance MoS₂ device with Nb₂BCl₂ contacts.

In addition to achieving Ohmic contacts with weak FLP, the promotion of carrier tunneling probability (P_TB) is essential for the improvement of contact performance of MSJs. The carrier tunneling probability (P_TB) of a MSJ can be calculated as follows⁴⁰,

$${P}_{TB}=\exp \left(\frac{2{w}_{TB}}{\hslash }\sqrt{2m{\varPhi }_{TB}}\right)$$

(4)

where $\hslash$ is the reduced Planck constant, m is the mass of free electron, Φ_TB and ω_TB denote the tunneling barrier height and width, respectively. The Φ_TB and ω_TB can be subtracted from the EPD of a given MSJ. Taking Nb₂BF₂-MoS₂ junction shown in Fig. 5d as an example, the EPD displays that Φ_TB and ω_TB are 2.97 eV and 0.98 Å, respectively. According to the Eq. (4), the P_TB of the MSJ can be estimated to be 17.9%. Similarly, the Φ_TB, ω_TB, and P_TB of other MBene-MoS₂ junctions are plotted in Fig. 5e. More detailed data for the determination of P_TB of the MSJs are listed in Supplementary Table S6. The estimated P_TB of the MSJs is 15% ~ 50%, which is superior to that of 2D metal-MoS₂ vdW junctions (<15%) from previous reports²⁰. Such a result reflects that both the Φ_TB and ω_TB of MSJs depends on the interfacial coupling. More specifically, strong orbital hybridization at M-S interfaces contributes to the reduction of Φ_TB and ω_TB, which is responsible for obtaining high P_TB. Hence, the interfacial coupling leads to a delicate competition between the carrier tunneling efficiency and FLP effect in the MSJs. An optimal contact may be achieved in the MSJs with medium interfacial coupling that can balance the FLP and carrier tunneling efficiency.

Based on the estimated SBHs and carrier tunneling probabilities P_TB, the contact resistance (R_C) of 2D MBene-MoS₂ junctions at the quantum limit is predicted (The details for the determination of R_C are presented in the section of Methods). The R_CW of MBene-MoS₂ junctions as a function of carrier concentration is plotted in Fig. 5f. The carrier concentration (n_2D) of MBene-MoS₂ junctions is shown in Supplementary Fig. S19. The contact resistance of other state-of-the-art MSJs from previous studies are also presented for the comparison. For MBene-MoS₂ junctions with Schottky contact (e.g., Nb₂BCl₂-MoS₂ and Tc₂BCl₂-MoS₂), they show the larger R_CW at 610 ~ 2200 Ω μm because of their large SBHs that induce low n_2D (1.62 × 10¹¹ ~ 7.41 × 10¹¹ cm⁻²). For MBene-MoS₂ junctions with Ohmic contact such as Tc₂B(OH)₂- MoS₂ and Nb₂BO₂-MoS₂) indicate ultralow R_CW down to 41.6 Ω μm due to their high n_2D (2.89 × 10¹³ ~ 9.92 × 10¹³ cm⁻²). Moreover, the contact resistance of MBene-MoS₂ junctions is lower than that of state-of-the-art devices based on bulk semiconductors and MoS₂ and can be competed with the previous record using Sb-MoS₂ and Bi-MoS₂ junctions (Fig. 5f and Supplementary Table S7)^9,28,29,45. Based on the results of SBHs, FLP factor, and R_C, Nb₂B(OH)₂ and Tc₂B(OH)₂ are identified as optimal contacts for the devices with the n-type MoS₂ channel, Nb₂BO₂ and Tc₂BF₂ is the best contact for the devices with the p-type MoS₂ channel.

In order to verify the contact performance of MBene-MoS₂ junctions, the electric transport properties of MoS₂ FETs with MBene electrodes are simulated by the NEGF method. The schematic of MoS₂-based FET devices is displayed in Fig. 5g. For the comparison, the devices with Ohmic contact and Schottky contact are investigated, respectively. When Tc₂BF₂ and Nb₂B(OH)₂ are used as contact electrodes (Fig. 5h), the output (I_d-V_d) curves indicate a nearly linear change trend, confirming the formed Tc₂BF₂-MoS₂ and Nb₂B(OH)₂-MoS₂ junctions with Ohmic contact. In contrast, for the device with Nb₂BCl₂ electrodes (Fig. 5i), the I_d shows a nonlinear increase with increasing V_d, supporting that the formed Nb₂BCl₂-MoS₂ junction exhibits Schottky contact. Moreover, the output current of MoS₂ device with Ohmic contact (i.e. using Tc₂BF₂ and Nb₂B(OH)₂ as the contact electrodes) is about two orders of magnitude higher than that of the MoS₂ device with Schottky contact (e.g., using Nb₂BCl₂ as the electrodes). In addition, the contact resistance of the MoS₂ devices can be also predicted by the I_d-V_d curves. For example, by fitting the I-V curves, the total resistance (R_T) of MoS₂ devices is 2.4 × 10⁵ Ω and 4.7 × 10⁵ Ω for the use of Nb₂B(OH)₂ and Tc₂BF₂ as the contract electrodes, respectively. According to the Eq. (8) (see Methods for the details), the R_CW of Nb₂B(OH)₂-MoS₂ and Tc₂BF₂-MoS₂ junctions is 51.84 and 92.34 Ω μm, respectively. The calculated results largely agree with the contact resistances obtained by analytical model (i.e., Eq. (11)), as shown in Fig. 5f. The above results suggest that MBene-MoS₂ junctions with Ohmic contact are promising for developing the low-resistance MoS₂ FETs with weak FLP.

Discussion

In summary, we reported an efficient strategy to achieve ultralow-resistance contacts in TMD-based MSJs at the quantum limit by utilizing functionalized MBenes as the contact electrodes. Based on high-throughput DFT calculations combined with NEGF method, 8 highly stable 2D metallic MBenes were screened from 870 initial MBene structures. The selected Nb-based and Tc-based MBenes exhibit large D_F, low electric resistance, and a broad range of W_m from 2.58 to 6.51 eV, which offers a large degree of freedom for constructing 2D MBene-TMD junctions with desired contact type.

By vdW integration of 2D metallic MBenes with semiconducting TMD channels, we demonstrated that the formed MBene-TMD junctions could exhibit both Schottky contacts and Ohmic contacts. Especially, the interfacial polarization of MBene-TMD junctions produces local built-in electric field that enables the band shift of TMD channels, which is responsible for achieving p-type Ohmic contact in MBene-MoS₂ junctions. Furthermore, we revealed that the strong vdW interactions between MBenes and TMDs (e.g., MoS₂) could lead to a delicate balance between FLP and P_TB, resulting in MBene-MoS₂ junctions with ultralow contact resistance down to 41.6 Ω μm at the carrier concentration of 2.93 × 10¹³ cm⁻². Moreover, the contact performance of screened Nb₂BO₂-MoS₂ and Nb₂B(OH)₂-MoS₂ junctions is superior to that of most state-of-the-art MoS₂-based MSJs and can be competed with previous record using semimetals Sb and Bi as the contact electrodes of MoS₂ devices. These findings suggest huge potential of metallic MBenes for the development of high-performance low-resistance contacts in TMD-based devices.

Methods

Structural Models

The initial database of 2D MBenes was constructed by varying transition-metal element M and surface functional group T (T = O, F, Cl, and OH) into six different M₂BT₂ phases, as shown in Fig. 1. For a given M₂BT₂, only the lowest -energy phase was considered for subsequent calculations and obtained by the energy comparison among six potential phase structures (i.e., H1, H2, H3, T1, T2, and T3). For H1 phase (Fig. 1b), M and B atoms are coordinated with a trigonal prismatic (H) geometry, leading to a H-H-H atomic arrangement. For T1 phase, M and B atoms are coordinated with an octahedral (1 T) geometry, indicating a T-T-T atomic arrangement. Other four phase structures are actually mixed with the atomic arrangement sequence of 2H and 1 T geometries, including H-T-H (H2), H-H-T (H3), T-H-T (T2), and H-T-T (T3). Then the structural stability of the lowest-energy MBene phase structures were further screened by their formation energies (E_f) that were calculated as follows,

$${E}_{f}=({E}_{tot}-{n}_{TM}{E}_{TM}-{n}_{{\rm{B}}}{E}_{B}-{n}_{T}{E}_{T})/({n}_{TM}+{n}_{B}+{n}_{T})$$

(5)

where E_tot is the total energy of a given MBene structure, E_TM is the total energy per transition metal atom in bulk, E_B is the total energy per B atom of borophene, and E_T is the total energy of surface functional groups. The adsorption stability of various surface functional groups on MBenes was evaluated by their adsorption energies (E_a) as follows,

$${E}_{a}=({E}_{tot}-{E}_{bare}-{n}_{T}{E}_{T})/{n}_{T}$$

(6)

where E_tot and E_bare are the total energy of a given MBene structure with and without surface functional groups, respectively. Based on the selected MBenes, MBene-TMD junctions were created by vdW integration of metallic MBenes and semiconducting TMDs. The allowed lattice mismatch of MBene-TMD junctions is smaller than 5%, and their optimal interfacial structures were determined by the energy comparison among various possible configurations.

DFT calculations

All calculations were performed within the density-functional theory (DFT) as implemented in the Vienna ab initio Simulation Package (VASP)^46,47. The projector augmented wave (PAW) method was used to describe the interaction between valence electrons and ionic cores⁴⁸. The generalized-gradient approximation (GGA) functional in the form of Perdew-Burke-Ernzerh (PBE) was employed to treat the electronic exchange-correlation energy⁴⁹. A kinetic energy cutoff was set to 500 eV for the plane-wave expansion set. A vacuum layer of > 16 Å along the out-of-plane direction was intercalated between adjacent slabs to avoid spurious interactions. The interfacial coupling between MBenes and TMDs was treated by DFT-D3 correction in Grimme’s scheme⁵⁰. The dipole corrections along the out-of-plane direction were also included in the calculations. The Monkhorst-Pack scheme was applied for the k-point sampling in the Brillouin zone with the grid of 16 × 16 × 1 and 6 × 6 × 1 for MBenes and MBene-TMD junctions, respectively. All structural models were fully optimized until the energy and force acted on each atom were less than 10⁻⁴ eV/atom and 10⁻² eV/Å, respectively. Considering that the PBE functional usually underestimates the bandgap of 2D semiconductors, the electronic structures of MoS₂ and MBene-MoS₂ junctions were calculated by using the hybrid functional of Heyd-Scuseria-Ernzerhof (HSE06)⁵¹. To verify dynamic stability of selected MBenes, their Phonon band dispersions were calculated by using the Phonopy package within the harmonic approximation⁵². The calculations were performed using a supercell approach within the framework of the density functional perturbation theory (DFPT) and frozen cell method⁵³.

Calculation of contact resistance

The contact resistance (R_C) of MBene-MoS₂ junctions was predicted as^9,54

$${R}_{C}W=\frac{\pi h}{4{q}^{2}{k}_{F}}\times \frac{1}{{P}_{TB}}$$

(7)

where h and q are Planck’s constant and elementary charge, respectively. W is the channel length, P_TB is the carrier tunneling probability and can be estimated by Eq. (4), and k_F is the Fermi wavelength that is equal to$\sqrt{2\pi {n}_{2D}}$, where n_2D is the carrier concentration of 2D semiconductors. The carrier concentration of electrons (n_n) and holes (n_p) was determined as follows⁵⁵,

$${n}_{n}=\frac{4\pi {m}_{e}^{\ast }kT}{{h}^{2}}\,{\mathrm{ln}}\left(1+\exp \left(\frac{{E}_{F}-{E}_{C}}{kT}\right)\right)$$

(8)

$${n}_{p}=\frac{4\pi {m}_{h}^{\ast }kT}{{h}^{2}}\,{\mathrm{ln}}\left(1+\exp \left(\frac{{E}_{V}-{E}_{F}}{kT}\right)\right)$$

(9)

where m_e^* (m_h^*) is electron (hole) effective mass, T is the temperature, k is Boltzmann constant. E_F-E_C (E_V-E_F) is the energy difference between the Fermi level and CBM (VBM), and it can be directly extracted from the calculated band structures. The m_e^* and m_h^* were calculated from the band curvature at the CBM and VBM, respectively, by using the following formula,

$$\frac{1}{{m}^{\ast }}=\frac{1}{{\hslash }^{2}}\frac{{d}^{2}E(k)}{d{k}^{2}}$$

(10)

where E(k) is the energy of band-edge states (VBM and CBM) at wave-vector k, and $\hslash$ is the reduced Plank constant.

Electric transport calculations

The transport properties of MoS₂-based FETs with MBene electrodes were simulated by DFT method combined with nonequilibrium Green’s function (NEGF) formalism as implemented by the Nanodcal package⁵⁶. Two-probe model was used to investigate the role of MBene electrodes in the electric transport properties of MoS₂ devices. The two-probe model is composed of the left and right MBene electrodes and the central MoS₂ channel region (see Supplementary Fig. S20). The left and right leads are semi-infinite and contact with the central region via van der Waals interactions. The central MoS₂ channel length was set to ~3.5 nm. The physical quantities were expanded with linear combination of atomic orbital (LCAO) basis at the double zeta basis plus polarization (DZP) level⁵⁷ and the exchange correlation potential was treated by the PBE functional. The plane-wave cutoff energy was set to 80 Hartree. The energy convergence criterion of Hamiltonian matrix was set to be 10⁻⁶ eV. The k-point grid mesh of the central scattering region and the electrode was set to 15 × 1 × 1 and 15 × 100 × 1, respectively. The current was calculated using the Landauer- Bütttiker equation as follows⁵⁸,

$$I({V}_{b})=\frac{2e}{h}{\int }_{{\mu }_{L}}^{{\mu }_{R}}T(E,{V}_{b})[{f}_{L}(E)-{f}_{R}(E)]{dE}$$

(11)

where f_L(R) is the distribution function of electron on left (right) lead, V_b is the loading bias voltage, μ_L(R) is the potential of left (right) lead, and T(E, V_b) is the transmission coefficient. Based on the calculated I-V curves, the R_C of MoS₂ devices with MBene electrodes can be also predicted as follows,

$${R}_{T}=2{R}_{C}+{R}_{semi}=2{R}_{C}+\frac{{R}_{SH}l}{w}$$

(12)

where R_T and R_semi are the total resistance between two contacts and resistance of the semiconductor channel, respectively, R_SH is the sheet resistance (2.0 × 10⁵ Ω) that can be determined by fitting the I-V curves of MoS₂ device with two different channel lengths, l and w are the distance between two contacts and width of the contact electrodes, respectively.