2D Electrical Contacts in the Monolayer WSe2 Transistors: A First

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2D/2D Electrical Contacts in the Monolayer WSe2 Transistors: A First-Principles Study Qiaoxuan Zhang, Jing Wei, Junchen Liu, Zhongchang Wang, Ming Lei, and Ruge Quhe ACS Appl. Nano Mater., Just Accepted Manuscript • DOI: 10.1021/acsanm.9b00290 • Publication Date (Web): 10 Apr 2019 Downloaded from http://pubs.acs.org on April 11, 2019

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ACS Applied Nano Materials

2D/2D Electrical Contacts in the Monolayer WSe2 Transistors: A First-Principles Study Qiaoxuan Zhang,1,§ Jing Wei,1,§ Junchen Liu, 1 Zhongchang Wang,2 Ming Lei,1,* and Ruge Quhe1,*

1State

Key Laboratory of Information Photonics and Optical Communications and School of

Science, Beijing University of Posts and Telecommunications, Beijing 100876, P. R. China 2Department

of Quantum and Energy Materials, International Iberian Nanotechnology

Laboratory (INL), Avenida Mestre Jose Veiga, Braga, 4715-330 Portugal § Q.

Z. and J. W. contributed equally to this article.

*Corresponding

author: [email protected]; [email protected]

ABSTRACT: Seeking a proper electrode contact for two-dimensional materials such as monolayer (ML) WSe2 is of vital importance for ultrathin electronic devices. Here, we investigate a series of novel 2D/2D electrical contacts in sub-10 nm ML WSe2 transistors by first-principles calculations. We find that the NbSe2, borophene, Mo2CF2 and Mo2CO2 electrodes form p-type Ohmic contact with ML WSe2, while the Ti2C(OH)2 forms n-type Ohmic contact and Ti2C forms n-type Schottky contact. Particularly, the on-current, delay time and power dissipation for the NbSe2 and Ti2C(OH)2 electrodes in the transistors approach the international technology roadmap for semiconductors (ITRS) 2013 requirements for high-performance (low power) applications at the gate length of 5 nm (7 nm). A formalism is proposed to analyze the 2D/2D electrical contacts from device application viewpoint, thereby providing guideline for the design of future 2D semiconductor-based devices. KEYWORDS: 2D material, transistor, interface, first-principles calculation, quantum transport

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INTRODUCTION Owing to their excellent scalability and high degree of mechanical flexibility, two-dimensional (2D) transition metal dichalcogenides (TMDCs) receive increasing attentions for the next-generation electronics.1-4 Among the TMDCs, WSe2 captures much interest because it is easy to realize both nand p-type doping due to its balanced valence and conduction band position with respect to metals of different work functions.5 In this regard, 2D WSe2 is particularly promising for complementary metal oxide semiconductor (CMOS) technology.

5-10

However, to realize high-performance CMOS

logic based on WSe2, one of the most urgent issues is the high contact resistance at the interface between metal electrodes and WSe2.7, 8, 10-12 This is of especial importance for the miniaturization of electronic devices because the role of electrode contacts becomes ever increasingly important as the channel scales down. 13, 14 An ideal electrical contact in high-performance devices should possess low contact resistance and be trap-free. Nevertheless, partial Fermi level pinning often occurs between WSe2 and metal electrodes, give rise to high contact resistance.11, 12 To date, a number of attempts have been devoted to improving electrical contacts in the WSe2 transistors, involving the phase engineering,15 surface adsorption,6,

7

substitutional doping,9,

11, 16, 17

and innovative edge contacts.15,

18

In particular, low

dimensional electrodes such as graphene and NbSe2 have been routinely applied to improve device performance based on 2D materials.9, 16-18 The interfacial chemistry between low-dimensional metal and semiconductor in transistors often differs drastically from its bulk metal counterpart. Compared with traditional bulk electrodes, low dimensional ones usually show better gate electrostatics for their weaker electric field screening.13,19 In addition, the Fermi level pining in the devices with 2D electrodes is weak because in most cases the interaction between 2D electrodes and semiconductors is of van der Waals type.18,

20, 21

For

instance, low contact resistance (0.3 KΩ), high drive current (320 μA/μm), and high on/off ratio (> 109) are achieved in monolayer (ML) WSe2 field effect transistors (FETs) with NbSe2 as electrodes.16 However, a systematic study on how different types of 2D electrodes impact WSe2 transistors from theoretical viewpoint remains scarce. Here, a wide variety of 2D metals have been studied as electrodes in the ML WSe2 transistors by first-principles calculations. We find that NbSe2, borophene, Mo2CF2 and Mo2CO2 electrodes form p-type Ohmic contacts to the ML WSe2, while Ti2C(OH)2 and Ti2C form n-type Ohmic and Schottky 2


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contacts, respectively. Among all these electrodes, NbSe2 shows best p-type device performance and TiC2(OH)2 best n-type. We further investigate the effect of some key factors on device performance such as electrode geometry, electronic and transport property.

METHODOLODY The framework for the theoretical investigation of the 2D/2D contact in the monolayer WSe2 field effect transistors is shown in Scheme 1. The structural and electronic calculations were performed within the framework of density functional theory (DFT) using the Vienna ab-initio Simulation Package (VASP).22 The wave functions were described in a plane wave basis set with an energy cutoff of 330–600 eV. The potentials at the core region were treated with projector augmented wave (PAW) pseudopotentials.23 The van der Waals interaction was considered by vdW-DF level of optB86b exchange functional.24 With this functional, the calculated in-layer and out-layer lattice constants of bulk WSe2 (atheo = 3.30 Å and ctheo = 13.10 Å)25 were very close to the experimental data (aexp = 3.28 Å and cexp = 12.96 Å).26 The geometry optimization was performed until the residual force fell below 0.001 eV/Å. The Brillouin zone was sampled by the Monkhorst-Pack method with a sampled k-point mesh 27 with a separation of about 0.01 Å-1. The transport properties were calculated by the Atomistix ToolKit (ATK) package27 using DFT coupled with nonequilibrium Green’s function (NEGF) method.28 A density mesh cutoff of 75 Hartree was applied. The transmission current Id was expressed as: 2e

+∞

𝐼d(Vds,Vg) = h ∫ -∞ {T(E,Vds,Vg)[ fS(E  μS)  fD(E  μD)]}dE

(1)

where T(E, Vds, Vg) was transmission coefficient; fS and fD are Fermi-Dirac distribution function for the source and drain, respectively; and μS and μD are the electrochemical potential for the source and drain. The single zeta polarized basis set (SZP) was adopted. The generalized gradient approximation (GGA) in the form of Perdew-Burke-Ernzerhof (PBE) functional29 was employed to describe the exchange correlation interaction. Detailed description on the methodology is provided in the supporting information (Figure S1, S2).

RESULTS Current experimentally available 2D metals include graphene, TMDCs, borophene and MXenes. 3



Since the contact between graphene and WSe2 has been thoroughly studied,9,30 we focus on the rest three classes in our work. The 1T phase NbSe2 is chosen to represent metallic TMDCs because this phase is the most stable one for NbSe2 and ML NbSe2 has been experimentally explored as electrode for WSe2 transistors.25 Additionally, structural similarity between NbSe2 and WSe2 is expected to be beneficial for carrier injection. On the other hand, borophene is a monolayer metalene synthesized recently and its role as electrodes in WSe2 transistor has not been experimentally explored yet. For the MXenes, they are a family of 2D transition metal carbides and carbonitrides and their surface termination can strongly influence their electronic properties. Experimentally, Ti2C(OH)xFy flakes have been used as electrodes in the complementary metal-oxide-semiconductor inverter with MoS2 (n-channel) and WSe2 (p-channel), which clearly shows signal inversion.31 In addition, previous theoretical works have proposed the promising application of NbSe2 and MXene as electrodes in the TMDCs based electronics.32, 33 Ti2C and Mo2C are therefore chosen as representatives of MXenes and four types of surface terminations (i.e. bare layer, OH, F and O terminated layers) are considered. A total of six types of 2D metals are taken as electrodes in ML WSe2 transistors: NbSe2, borophene, Ti2C, Ti2C(OH)2, Mo2CF2, and Mo2CO2 electrodes. Figure 1 shows the optimized atomic models of the heterostructures between WSe2 and different 2D metals. The interfacial mismatch in these six heterostructures are all within 3%. For simplicity, borophene is abbreviated as Boro. The supercell match patterns of the six heterostructures are (1×1) NbSe2/(1×1) WSe2, (1×2) Boro/(1×1) WSe2, (1×1) Ti2C/(1×1) WSe2, (1×1) Ti2C(OH)2/(1×1) WSe2, (2×2) Mo2CF2/(√3×√3) WSe2, and (2×2) Mo2CO2/(√3×√3) WSe2. The corresponding lattice parameters of the supercells are shown in Table 1. The geometry of ML WSe2 changes slightly when it contacts the six 2D metals. The W–Se bond lengths in the heterostructures are very close to those in the free-standing form (2.544 Å), as seen in Table 1. The distance between the two layers closest to the interface in the Ti2C/WSe2 case is only 2.00 Å, indicating the formation of covalent bonds in this interface. On the other hand, the interlayer distance in other interfaces varies from 2.18 Å to 3.30 Å, indicating that it is van der Waals (vdW) force in the other heterostructures. Such difference in bonding form is verified by the total electron function (Figure S3). To probe charge transfer at the heterostructures, we performed Bader charge analysis (Table 1). The WSe2 gains 0.13 e/Å2 in the Ti2C case and 0.03 e/Å2 in the Ti2C(OH)2 case. Conversely, it loses 4


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0.007, 0.001, 0.022 and 0.058 e/Å2 when it is contacted to the NbSe2, Boro, Mo2CF2 and Mo2CO2, respectively. Figure 2 shows band structures of the six heterostructures. The freestanding ML WSe2 has a direct band gap of 1.48 eV at K point. However, band gap of WSe2 diminishes after contacting to Ti2C, indicative of Ohmic contacts, as also confirmed in the partial density of state (Figure S4). Conversely, the WSe2 layers in the rest systems show semiconducting feature with indirect band gap for NbSe2/WSe2, Ti2C(OH)2/WSe2, and Mo2CO2/WSe2 heterostructures and direct band gap for Boro/WSe2 and Mo2CF2/WSe2. By comparing the relative position of the valence band maximum/conduction band minimum (VBM/CBM) of contacted WSe2 and Fermi level, p-type contacts form for NbSe2, Boro, Mo2CF, and Mo2CO2 electrodes, while n-type for Ti2C(OH)2. The ⊥ and Ф ⊥ ), which is defined as the energy difference vertical Schottky barrier height (SBH) (Фe,T h,T

between VBM/CBM and Fermi level, is zero or small hole SBH in the NbSe2/WSe2, Boro/WSe2, Mo2CF2/WSe2, and Mo2CO2/WSe2 systems and zero electron SBH in the Ti2C(OH)2/WSe2, implying efficient carrier injection along the vertical direction. The change of band gap from direct in freestanding ML WSe2 to indirect in some contact cases is mainly attributed to interlayer coupling between WSe2 and 2D metals. Compared with free-standing ML WSe2, the indirect band gap of WSe2 in the heterostructures originates from either downward shift of the conduction band at the midpoint between Γ and K points (Λ valley) (WSe2/Ti2C(OH)2 and WSe2/Mo2CO2) or the upward shift of the valence band at Γ point (WSe2/NbSe2). The Λ state of the conduction band is characterized by the s orbital of W atom and the pz orbital of Se atom, and the Γ state of the valence band is characterized by the dz2 orbital of W atom and the pz orbital of Se atom.34 Electrons in these states are delocalized in the out-of-plane direction, and the energy of these states are sensitive to the interlayer coupling. We also calculate electronic potential distribution along off-plane direction to probe tunnel barriers, as shown in Figure S5. The tunneling barrier is defined as the electrostatic potential barrier which a carrier at Fermi level of the heterostructure needs to transport from metal to WSe2 layer. Since the electrostatic potential in the interlayer vacuum is below the Fermi level of the heterostructure in all cases, the tunneling barrier turns zero, resulting in high electron injection efficiency and low contact resistance. To gain insights into the electrical contact properties, we built up ML WSe2 transistors using the six 2D metals as electrodes. Figure 3(a) shows model of a representative NbSe2 contacted p-type 5



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FET. The carriers are injected from metal to WSe2 layer along the vertical direction (A→C) and then from the electrode to channel region along the lateral direction (C→E). Figure 3(b-g) shows the spatially resolved local density of states (LDOS) of the transistors projected on the position of ML WSe2. Akin to the DFT results, the transport simulations show no vertical SBH along the vertical ⊥ ⊥ direction (Фe,T or Фh,T ). The SBH difference between the band calculation and device simulation ∥ ∥ can be ascribed to the electrode-channel coupling. The lateral Schottky barrier (Фe,T / Фh,T ) is

calculated by the energy difference between the CBM/VBM of WSe2 and Fermi level. There is no ∥ lateral Schottky barrier except for the Ti2C case with Фe,T

of 0.43 eV. In the NbSe2 and

Ti2C(OH)2 transistors, the WSe2 band gap is smaller in the electrode region than in the channel region, which is caused by the interlayer interaction between NbSe2 (Ti2C(OH)2) and WSe2 in the electrode region, as also shown in the band structure (Figure 2 (a), (d)). It is worthy of noting that the metal induced gap states (MIGS) extend to channel region in the Boro and Ti2C cases. The band diagrams of the 2D metal-WSe2 heterostructures are summarized in Figure 4. One can note a depletion region in the Ti2C case due to the electrode contact, as also reflected by the band bending in the region between the electrode and channel, which would impact gate controllability. Such depletion becomes more apparent as the gate length becomes shorter. Figure 5 shows transport properties of ML WSe2 FET with different electrodes and gate lengths, and Figure 6 shows subthreshold swing (SS) of ML WSe2 FETs as a function of gate length. The SS, which is defined as the gate variation required for one order of magnitude current change, is used to evaluate gate control quantitatively. The SS increases with the decrease of gate length, implying that the gate control is worsened. The swings are poor in the short gate cases because of the large leakage current due to the direct source-to-drain tunneling which is hard to be controlled by gate. At Lg = 7 – 9 nm, the SS is close (63–82 mV/dec) for the FETs with different electrodes. However, there appears clear variation for the SS at Lg = 1 – 5 nm, which originates from the difference of the MIGS and doping in the channel. The appearance of MIGS in the channel region leads to the decrease of the equivalent channel length. Since different electronic levels of the WSe2 layer are raised due to the different metal contacts, the electric field from the gate is screened distinctly, resulting in different gate controllability and thus the swing. We therefore classify the types of electrodes into three groups according to the SS value: Group I with a low SS including NbSe2, Mo2CF2, and Ti2C(OH)2 electrodes, Group II with a moderate SS 6


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including Ti2C and Boro electrodes, and Group III with a high SS including Mo2CO2 electrodes. In the case of Group I, the MIGS is negligible, and the doping of WSe2 channel, which is reflected by the difference of the channel band edge and Fermi level, is weak, as also confirmed by the relatively small Bader charges in Table 1. Note that the states in the blue circle in Figure 3(b) are not MIGS and they stem from the decrease of WSe2 band gap due to NbSe2-WSe2 interaction. Similar situation occurs in the Ti2C(OH)2 case (Figure 3(e)). For the group II electrodes, Ti2C and Boro electrodes have relatively weak gate electrostatics due to the large MIGS (yellow arrows in Figure 3(c) and (d)). The corresponding severe source-to-drain tunneling leakage causes poor off-state behavior. For group III electrode (Mo2CO2), the heavily doped WSe2 channel screens electric field, leading to poor gate electrostatics. Such screening effect becomes stronger as the Lg turns shorter, as evidenced by the upward shift of the channel VBM (Figure S6). Figure 7 shows the on-current, delay time, and power dissipation for the sub-10 nm ML WSe2 transistors with various 2D electrodes. The ITRS 2013 edition requirements for high power (HP) and low power (LP) devices are also given for comparison. The bias voltage Vds (= supply voltage Vdd) is fixed to 0.64 V for Lg = 1–5 nm transistors, 0.69 V for Lg = 7 nm, and 0.72 V for Lg = 9 nm. According to the ITRS 2013 requirements, we set Ioff = 0.1 µA/µm for Lg = 1–9 nm in the HP application. For the LP application, Ioff is set to 5×10-5, 4×10-5, and 2×10-5 µA/µm for the FETs with Lg = 1–5, 7 and 9 nm, respectively. The detailed parameters are summarized in Table S1 and S2. Among the p-type ML WSe2 FETs, the FET with NbSe2 electrode shows the best performance, followed by those with Mo2CF2, Mo2CO2, and Boro electrodes. The on-current of the sub-10 nm NbSe2 contacted ML WSe2 FETs reaches up to 1406 µA/µm for HP application and 526 µA/µm for LP application. Referring to the ITRS standards, the WSe2 FETs with NbSe2 electrodes fulfill 104%, 97% and 79% of HP ITRS requirements, and 115%, 129% and 33% of LP ITRS requirements at Lg = 9, 7 and 5 nm, respectively. The FETs with the Mo2CF2 and Mo2CO2 electrodes possess lower on-state current in comparison to their NbSe2 counterparts. The difference in on-state current between the Mo2CF2 and Mo2CO2 transistors is small for HP application, yet is quite large for LP application. The highest on-state current of the Mo2CF2 and Mo2CO2 contacted sub-10 nm transistors fulfill 43% and 40% ITRS target for HP application, respectively. For LP application, the on-current of Mo2CF2 transistors is 117–400 µA/µm, close to the value in the ITRS requirements (295–458 µA/µm). In contrast, the 7



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on-current of the Mo2CO2 transistors for LP application is only 4.73×10-4–214 µA/µm, much lower than the corresponding data in the ITRS LP requirements. The sub-10 nm ML WSe2 transistors with Boro electrode show quite low on-state current (29–14 µA/µm for HP application and 0.12–70 µA/µm for LP application), far below the corresponding data in the ITRS requirements, which is ascribed to the poor gate electrostatics arising from the MIGS (Figure 3(c)). Although the SS values of the FETs with Mo2CO2 electrodes are even higher than those with Boro electrodes, the on-current for the Mo2CO2 transistors is higher because their high doping density contributes to high source-to-drain current (I = nqv, where n is carrier density) in addition to the screening of the electric field from the gate. Among the n-type ML WSe2 FETs, the Ti2C(OH)2 FET shows a much larger on-current than the Ti2C FET. The sub-10 nm ML WSe2 transistors with Ti2C(OH)2 electrodes possess on-current up to 1220 µA/µm for HP application, which is very close or even surpasses the HP ITRS requirements at Lg = 5–9 nm. As for LP application, the on-state current for the Ti2C(OH)2 FETs fulfills 64–94% of the ITRS 2013 requirements. In addition, the output characteristic of Ti2C(OH)2 FETs show linear behavior (Figure S7). The on-state current for Ti2C transistor fulfills 72–91% of the ITRS standard at Lg = 5–9 nm for HP application and 75–85% at Lg = 7–9 nm for LP application. Moreover, the direct source-to-drain tunneling for the LP Ti2C transistor is severe at Lg = 5 nm and its on-current drops to 4 µA/µm. We also calculated delay time and powder delay profile (PDP) to measure the logic speed and power dissipation of the transistors. Delay time is calculated by τ =

Ct Vdd Ion

,35, 36 where Ct and Ion are

total capacitance and on-current, respectively, and Ct is the sum of fringing capacitance Cf and gate capacitance Cg. The sub-10 nm WSe2 transistors with the Boro, Mo2CO2, and Ti2C electrodes show relatively large delay time (HP: 0.48–9.94 ps, LP: 0.57–1552 ps) due to either the small on-current or the large Ct. PDP is calculated to be 0.03–0.36 fJ/µm for HP application and 0.03–0.45 fJ/µm for LP application using the equation, PDP = CtVdd2. Of the devices, the NbSe2, Mo2CF2 and Ti2C(OH)2 FETs show a relatively low PDP and no apparent degradation until a short gate length (until Lg = 3 nm for HP and Lg = 5 nm for LP).

DISCUSSIONS 8


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It is noted that the device is simulated at the DFT-GGA level and the many body effects are not considered. At the electrode region of an FET device, the electron-electron interaction is greatly screened by the doping carriers. At the channel region, the band gap of ML WSe2 is well-known to be underestimated by the DFT-GGA, which may affect overall transport properties. However, since the electron-electron interaction is partly screened in the FET, previous theoretical calculation results at the DFT-GGA level agree well with experimental data for the MoS2 transistor with bulk metal electrodes.37 For the 2D NbSe2 and NbxW1-xSe2 electrodes, a low-barrier, highly transparent contact or an ohmic contact to the WSe2 channel is formed for the hole injection in the WSe2 transistors.16, 25 These observations are consistent with our simulation results. More studies of the many body effects on the transport properties of FET with 2D/2D electrical contacts are important future task. The calculated maximum current is about 2000–4000 μA/μm, which is relatively high compared with experimental counterpart on FETs based on 2D materials, showing generally an order of 102 μA/μm.38 However, the current could reach the order of 103 μA/μm for e.g. the gate-all-around nanowire transistors (1500 μA/μm)

39

and the epitaxial graphene transistor (Over 2000 μA/μm) 40.

One reason for such high calculated current in the sub-10 nm WSe2 transistor rests with ignorance of the electron-phonon coupling effects, i.e. our calculated current is the ballistic upper limit. About 10% current degradation is predicted in the sub-10 nm phosphorene transistor if the electron-phonon coupling is taken into account.41 Similarly, we also expect a current degradation when the coupling effect is considered. In addition, the perfect channel without defect and the ideal electrical contact also contribute to the high current. The effect of defects in the WSe2 layer is discussed in the supporting information (Figure S8 and S9). To examine the effect of different contact stacking types on device performance, we consider the AB′ and AA stacking for the NbSe2 and Ti2C(OH)2 electrodes (Figure S10) since they show the best performance in the studied p- and n-type WSe2 transistors. Compared with the AB stacking shown above, the AB′ stacked NbSe2/WSe2 and AA stacked Ti2C(OH)2/WSe2 heterostructures show energy difference of only 2.0×10-3 and 6.8×10-3 eV per supercell, respectively. The band structures of the NbSe2/WSe2 and Ti2C(OH)2/WSe2 heterostructures with different stacking types are shown in Figure S11. The overall shapes of the bands for the different stacking types are similar, despite that the band gap of WSe2 differs slightly and the VBM/CBM of WSe2 shifts by 0.01–0.20 eV. Figure 8 9



compares the transport properties of the WSe2 transistors with different electrode stacking type. Given a gate voltage, the difference in current for the WSe2 transistors with different electrode stacking type is less than one order of magnitude. In terms of on-current, there’s no distinct advantage for a specific electrode stacking type. The on-current variation due to different electrode stacking type is 24–47% (22–54%) for NbSe2 electrode and 1–7% (29 –63%) for Ti2C(OH)2 electrode in the HP (LP) devices at Lg = 5–9 nm (Table S3, S4). Figure 9 summarizes the key factors which affect the figure-of-merits (FoM). Transistors with low-dimensional electrodes are expected to show better gate electrostatics than those with bulk ones due to the weaker screening of the electric field

19.

The difference between low-dimensional and

bulk electrodes has been studied in our previous paper,13 and in this work we focus only on the 2D electrodes. The impact of interfacial distance on current are not straightforward through the orbital overlap and tunnel barrier. The negligible MIGS benefits the gate electrostatics due to weak Fermi level pining, and it is also beneficial for suppressing the tunneling leakage from source to drain. The MIGS in our cases is large, implying that these effects are insignificant. The heavy channel doping impedes gate controllability but enhances on- and off-state current. The effect of channel doping is expected to be less apparent for the transistors with longer gate length. Moreover, the gate controllability and current are crucial to affecting other figure-of-merits including on/off current ratio, delay time and PDP. CONCLUSIONS We have performed systematic first-principles calculations of interfacial properties and device performance of sub-10 nm WSe2 transistors with various 2D electrodes including NbSe2, borophene, Ti2C, Ti2C(OH)2, Mo2CF2, and Mo2CO2 electrodes. Of all these electrodes, the NbSe2 and Ti2C(OH)2 in the sub-10 nm ML WSe2 transistors are found to show the best p- and n-type device performance, respectively, where their on-current, delay time and power dissipation can fulfill ITRS requirements for HP (LP) application even when the gate length is scaled down to 5 nm (7 nm). We reveal four key interrelated factors that contribute to high device performance for the 2D/2D contacts, i.e. van der Waals interfacial interaction, small tunneling and Schottky barriers, negligible MIGS, and low doping to the channel. Moreover, a high doping density from the electrode to the channel material is found to degrade the gate electrostatics, especially for the transistors with a gate length less than 5 nm. Our findings provides insights for the 2D/2D electrical contacts in the 2D 10


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semiconductor

based

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devices.


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■ ACKNOWLEDGEMENTS This work was supported by the National Natural Science Foundation of China (NSFC) (Nos. 11604019 and 61574020) and the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications). Z.C.W. acknowledges the support by the NSFC under grant No. 51728202 and from the European Regional Development Fund Project No. NORTE-01-50145-FEDER-000019.

■ SUPPORTING INFORMATION The Supporting Information is available free of charge on the ACS Publications website. Transport properties of the ML WSe2 DG FETs, discussions on the method, electronic properties of the 2D metal/WSe2 heterostructures, doping effects on the channel, output characteristic of ML WSe2 FETs with Ti2C(OH)2 electrode, effects of defects in the WSe2 layer, and stacking orientation of the NbSe2/WSe2 heterostructure (PDF).

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Gaskill, D. K.; Dimitrakopoulos, C.; Avouris, P. Enhanced Performance in Epitaxial Graphene FETs With Optimized Channel Morphology. IEEE Electron Device Letters 2011, 32, 1343−1345. (41) Szabo, A.; Rhyner, R.; Carrillo-Nunez, H.; Luisier, M. Phonon-Limited Performance of Single-Layer, Single-Gate Black Phosphorus n- and p-Type Field-Effect Transistors. IEEE Int. Electron Devices Meeting 2015, 12. 1. 1−12. 1. 4.

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Table 1. Structural and electronic properties of different 2D materials contacted with ML WSe2. Electrode

NbSe2

Boro

Ti2C

Ti2C(OH)2

Mo2CF2

Mo2CO2

a (Å)

3.32

3.10

3.15

3.17

5.70

5.70

b (Å)

3.32

6.12

3.15

3.17

5.70

5.70

dW-Se (Å)

2.55

2.51

2.56

2.53

2.54

2.55

di (Å)

3.04

3.30

2.00

2.18

3.03

2.78

ΔV (eV)

0

0

0

0

0

0

⊥ Фe,B (eV)

––

––

0

0

––

––

⊥ Фh,B (eV)

0

0.20

0

––

0

0

⊥ Фe,T (eV)

––

––

0

0

––

––

⊥ Фh,T (eV)

0

0

0

––

0

0

∥ Фe,T (eV)

––

––

0.43

0

––

––

∥ Фh,T (eV)

0

0

––

––

0

0

Q (Å210-2e)

-0.67

-0.14

13.44

3.01

-2.17

-5.79

dW-Se: average W-Se bond length; di: interlayer distance of the nearest atoms of two adjacent layers; a ⊥ ⊥ ): electron (hole) SBHs in the and b: lattice parameters; ΔV: tunneling barrier height; Фe,B ( Фh,T

vertical direction obtained from band structure calculations;

⊥ ⊥ ( Фh,T ) and Фe,T

∥ ∥ Фe,T (Фh,T ) : the

SBHs of electron (hole) in the vertical and lateral directions calculated by quantum transport approach; Q: the Bader charge per xy plane area transferred from WSe2 layer to metallic 2D materials. Positive number means charge gain for WSe2 and negative one charge loss for WSe2.

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Step 1. 2D Metal Selection

Step 2. DFT Calculation

NbSe2

Borophene Geometry Band Structure MXenes

Electron Distribution Effective Potential

Step 3. Device Simulation Transfer Characteristics Output Characteristics Gate Length Scaling

Scheme 1. Flow chart of the framework for the theoretical investigation of the 2D/2D contact in the monolayer WSe2 field effect transistors.

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Figure 1. Top and side views of optimized ML WSe2 stacked with six different 2D electrodes: (a) NbSe2/WSe2, (b) borophene/WSe2, (c) Ti2C/WSe2, (d) Ti2C(OH)2/WSe2, (e) Mo2CF2/WSe2, and (f) Mo2CO2/WSe2. The quadrilateral dotted lines in the top view mark the unit cell. The interlayer distances di are indicated by black arrows.

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Figure 2. Band structure of (a) NbSe2/WSe2, (b) borophene/WSe2, (c) Ti2C/WSe2, (d) Ti2C(OH)2/WSe2, (e) Mo2CF2/WSe2, and (f) Mo2CO2/WSe2 heterostructures. The red dots represent the projected band structures of ML WSe2 and the grey curves stand for band structure of the whole heterostructure. The Fermi level is set to zero. The Brillouin zones are shown in the bottom right of each graph. The inset in (a) and (d) shows band dispersion near valence band maximum (VBM) and conduction band minimum (CBM) of WSe2, respectively.

19



Figure 3. (a) Schematic model of ML WSe2 FET with NbSe2 electrode. A, C and E denote NbSe2 layer, WSe2 in the electrode contact region, and WSe2 in the channel region, respectively, which are separated by B and D. Electrons or holes are injected from A to C and then to E. Spatially resolved local density of states (LDOS) projected on the position of ML WSe2 in the 5 nm FETs with (b) NbSe2, (c) borophene, (d) Ti2C, (e) Ti2C(OH)2, (f) Mo2CF2, and (g) Mo2CO2 electrodes. To compare directly the different systems, the LDOS is normalized along transverse direction. The vertical lines separate the electrode from channel region. MIGS (metal induced gap state) is marked by the bright yellow arrows. The blue circles in (b) and (e) highlight the hybrid states contributed by WSe2. Both the bias and gate voltages are set to zero.

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Figure 4. Band diagrams for the carrier transfer from 2D metal layer A to the channel region E in the devices with various electrodes: (a) NbSe2, (b) borophene, (c) Ti2C, (d) Ti2C(OH)2, (e) Mo2CF2, and (f) Mo2CO2. Ef is Fermi level. Ec and Ev denote conduction band and valence band edges of ML WSe2, respectively. Dark green arrows point out the flow direction of electrons or holes. Purple and blue lines indicate the existence of hybrid states of WSe2 in n- and p-type devices, respectively.

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Figure 5. Transport properties of the ML WSe2 FETs with various electrodes: (a) NbSe2, (b) borophene, (c) Mo2CF2, (d) Mo2CO2. (e) Ti2C, and (f) Ti2C(OH)2. The black dashed lines represent off-state of HP ITRS standard. The LP ITRS standards are marked by the colored dashed lines with the corresponding gate length. The bias voltage is set equal to the supply voltage (Vds = Vdd), ranging from 0.64 to 0.72 V as the gate length varies. Since the doping levels of the WSe2 layer differ due to different types of electrical contacts, the gate voltages for the on- or off-state are quite different. To show the on- and off-states in each case, the x-scale is given in different length scale.

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Figure 6. SS of ML WSe2 FETs with various electrodes as a function of gate length. The data at Lg = 1 nm are not shown because they are far from those at Lg = 3 – 9 nm.

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Figure 7. On-state current, delay time and PDP for the ML WSe2 FETs with various electrodes as a function of gate length. The ITRS requirements are also given for comparison. (a,b) On-state current for HP (a) and LP (b) devices. (c,d) Delay time for HP (c) and LP (d) devices. (e,f) PDP for HP (e) and LP (f) devices. The dashed lines indicate the ITRS requirements.

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Figure 8. Comparison of (a,b) transfer characteristics and (c,d) on-current for the ML WSe2 transistors with different stacking types at Lg = 1 – 9 nm. (a,c) AB (a) and AB′ (c) stacked NbSe2 electrodes. (b,d) AA (b) and AB (d) stacked Ti2C(OH)2 electrodes.

25



Figure 9. Schematic diagram showing the key factors that affect the figure-of-merits (FoM).

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TOC

27


2D Electrical Contacts in the Monolayer WSe2 Transistors: A First

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