High-performance sub-10 nm monolayer Bi₂O₂Se transistors

Abstract

A successful two-dimensional (2D) semiconductor successor of silicon for high-performance logic in the post-silicon era should have both excellent performance and air stability. However, air-stable 2D semiconductors with high performance were quite elusive until the air-stable Bi₂O₂Se with high electron mobility was fabricated very recently (J. Wu, H. Yuan, M. Meng, C. Chen, Y. Sun, Z. Chen, W. Dang, C. Tan, Y. Liu, J. Yin, Y. Zhou, S. Huang, H. Q. Xu, Y. Cui, H. Y. Hwang, Z. Liu, Y. Chen, B. Yan and H. Peng, Nat. Nanotechnol., 2017, 12, 530). Herein, we predict the performance limit of the monolayer (ML) Bi₂O₂Se metal oxide semiconductor field-effect transistors (MOSFETs) by using ab initio quantum transport simulation at the sub-10 nm gate length. The on-current, delay time, and power-delay product of the optimized n- and p-type ML Bi₂O₂Se MOSFETs can reach or nearly reach the high performance requirements of the International Technology Roadmap for Semiconductors (ITRS) until the gate lengths are scaled down to 2 and 3 nm, respectively. The large on-currents of the n- and p-type ML Bi₂O₂Se MOSFETs are attributed to either the large effective carrier velocity (n-type) or the large density of states near the valence band maximum and special shape of the band structure (p-type). A new avenue is thus opened for the continuation of Moore's law down to 2–3 nm by utilizing ML Bi₂O₂Se as the channel.

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Introduction

As silicon technology approaches its physical limit, the identification of a new channel material could provide a pathway toward the continued scaling of complementary metal–oxide–semiconductor (CMOS) technology in the next few decades.^1,2 Two-dimensional (2D) semiconducting materials emerge as promising channel material candidates, mainly because of their ideal gate electrostatics, dangling-bond-free surfaces, and uniform thicknesses.^3,4 In addition to a proper band gap (preferably greater than 0.4 eV (ref. 5)), a successful 2D semiconductor successor of silicon for high performance (HP) electronics should probably meet two criteria: (1) a high drive current, which often requires a high carrier mobility; and (2) a high ambient stability. Unfortunately, 2D semiconductors that meet the two criteria have been quite elusive. With the moderate band gaps, 2D MoS₂ and phosphorene are among the most intensively studied materials for electronics.^6–8 2D MoS₂ is the first 2D semiconductor that has been fabricated into field effect transistors (FETs) in the sub-10 nm regime.^9–11 However, the experimental low on-currents (less than 250 μA μm⁻¹),^9–11 probably due to the relatively low carrier mobility, render 2D MoS₂ more suitable for low power (LP) applications than HP applications. Theoretically, in terms of ab initio quantum transport simulation, the on-currents of the sub-10 nm MoS₂ transistors even in extremely optimistic conditions (absence of defects, ideal geometry, and ballistic transport) also fail to meet the International Technology Roadmap for Semiconductors (ITRS) requirements¹² for HP application in the next decades.¹³ Phosphorene and emerging 2D InSe have high carrier mobility, but their poor stability leads to rapid device performance degradation when exposed to air.^14,15 Therefore, the identification of a 2D semiconductor with a proper band gap, high carrier mobility, and ambient stability is critical for post-silicon HP electronics.

Recently, atomically thin 2D Bi₂O₂Se has been successfully synthesized by chemical vapor deposition (CVD) on a mica substrate.^16,17 The Bi₂O₂Se crystal is a semiconductor with a layer dependent band gap of 0.31–1.14 eV at the generalized gradient approximation (GGA) level. The electron mobility of the 2D Bi₂O₂Se is as high as 450 cm² V⁻¹ s⁻¹ at room temperature and 29 000 cm² V⁻¹ s⁻¹ at 1.9 K.¹⁶ Moreover, 2D Bi₂O₂Se shows excellent stability against oxidation and moisture in air. These features make 2D Bi₂O₂Se very attractive for the next generation electronics. The fabricated top-gated FETs with 21 μm-long Bi₂O₂Se channels exhibit large on/off current ratios of up to 10⁶ and near-ideal subthreshold swing values down to 65 mV dec⁻¹ at room temperature.¹⁶ Three fundamental questions arise naturally: (1) What is the device performance limit of 2D Bi₂O₂Se based FETs? (2) How does this device performance compare with that of other 2D semiconductor FETs? (3) Can 2D Bi₂O₂Se FETs meet the HP device requirement of ITRS?

In this paper, we investigate for the first time the performance limit of the n- and p-type sub-10 nm double-gated (DG) monolayer (ML) Bi₂O₂Se metal–oxide semiconductor FETs (MOSFETs) using accurate ab initio quantum transport simulations. The on-currents of the sub-10 nm ML Bi₂O₂Se MOSFETs are much larger than those of their ML MoS₂ counterparts across most of the size range tested. The optimized n- and p-type DG ML Bi₂O₂Se transistors can reach or nearly reach the ITRS goals for the on-state current, delay time and power-delay product (PDP) of the HP devices until the gate lengths are scaled down to 2 nm and 3 nm, respectively. On the basis of the available data, we reveal that either a very small or a very large effective electron (hole) mass favors a large on-state current for the 2D semiconductor FETs.

Results

ML Bi₂O₂Se is modeled by buckled [Bi₂O₂] layers in the middle with planar Se layers terminating both the top and bottom surfaces, to keep the bulk inversion symmetry (Fig. 1(a)).¹⁶ The outermost Se layers are passivated by H atoms in accordance with the previous study.¹⁶ The optimized lattice parameter of the Bi₂O₂Se monolayer is 4.03 Å, in agreement with other theoretical calculations.¹⁸ The band structure of the ML Bi₂O₂Se with H atom termination is shown in Fig. 1(b), and an indirect band gap of 1.14 eV is observed with a conduction band minimum (CBM) and valence band maximum (VBM) located at the Γ and X points, respectively. The band near the CBM is quite steep, leading to a very small effective mass of 0.20m₀ for the electrons. On the contrary, the band near the VBM is relatively flat, leading to a large effective mass of 1.40m₀ for holes. From the projected density of states, the states near the CBM mainly originate from the Bi atoms, while the states near the VBM are from the Se atoms.

Fig. 1 Crystal and electronic structures of ML Bi₂O₂Se. (a) Side and top views of ML Bi₂O₂Se. The dashed rectangle indicates the primitive unit cell. (b) Band structure and projected density of states. The inset shows the first Brillouin Zone.

A gated two-probe model of the DG ML Bi₂O₂Se MOSFET is constructed with intrinsic ML Bi₂O₂Se as the channel and degenerately doped ML Bi₂O₂Se as the electrodes, as shown in Fig. 2(a). The underlap (UL) configuration, i.e. the spacer region between the gate and electrode, has also been considered to improve the device performance.^19–22 We apply silicon dioxide as the dielectric material. The equivalent oxide thicknesses (t_ox) in the MOSFETs are set to 0.41–0.54 nm according to the ITRS 2.0 2013 edition requirement.

Fig. 2 (a–c) Schematic model (a) and transfer characteristics (b,c) of the DG ML Bi₂O₂Se MOSFETs with gate lengths of 1 to 9 nm. (d, e) Subthreshold swing (d) and gate conductance (e) of the sub-10 nm ML Bi₂O₂Se MOSFETs as a function of the gate length. The supply voltage is 0.64 V and UL = 0 nm in (b–e). The arrows in (b,c) indicate the change of gate length from 1 to 9 nm with a step size of 2 nm. The vertical dashed lines in (b,c) separate the subthreshold and superthreshold regions.

We first investigate the device performance without the UL configuration and with the electron/hole concentration of ρ = 5 × 10¹³ cm⁻² in both the source and the drain. This level of doping concentration has commonly been applied in the previous 2D materials-based device simulations.^23–27 Experimentally, the doping strategy for 2D layered materials includes substitutional doping,^28,29 ion implantation,^30,31 plasma treatment,³² surface charge transfer,³³ and photoinduced doping.³⁴ With the introduction of AuCl₃ dopants, a p-type doped MX₂ transistor with a hole concentration of 5 × 10¹³ cm⁻² is achieved.³⁵ By Nb atom substitution²⁸ or UV photoinduced doping,³⁴ a hole or electron concentration (about 10¹⁴ cm⁻²) that is even higher than our modeled value is achieved in MoS₂. Theoretically, we model the effect of doping by changing the number of electrons of the system with respect to the neutral case. Correspondingly, the electrostatic potential acting on the Kohn–Sham one-electron states is modified.

The transfer characteristics of the Bi₂O₂Se n- and p-MOSFETs at a supply voltage V_dd = 0.64–0.72 V are shown in Fig. 2(b) and (c). At a given gate voltage Vg, the currents of the n-MOSFETs are generally higher than those of the p-MOSFETs due to the smaller effective mass (m_e = 0.20m₀vs. m_h = 1.40m₀) and thus higher carrier mobility of electrons than holes. As the gate length L_g decreases, the current increases apparently in the subthreshold region, a result associated with the more severe source to drain direct tunneling.

From the transfer characteristics, we extract the subthreshold swing (SS) and transconductance (g_m) values to evaluate the gate control ability in the ML Bi₂O₂Se MOSFETs in the subthreshold and superthreshold regions, respectively. A small SS value implies weak short-channel effects, and the smallest SS achievable in thermionic devices at room temperature is 60 mV dec⁻¹. As shown in Fig. 2(d), the SS values of n- and p-MOSFETs show similar degradation behavior at shorter L_g, and the former degrade faster. At L_g = 9 nm, the nearly ideal SS value of 60 mV dec⁻¹ is achieved in both the n- and p-MOSFETs. As L_g decreases to 1 nm, the SS values increase to 600 and 500 mV dec⁻¹ in the n- and p-MOSFETs, respectively. The trend to larger SS values at shorter L_g is consistent with the stronger gate controllability at the band edge location (Fig. S1†). The gate control ability in the superthreshold region also decreases with the shorter L_g, as evidenced by the smaller g_m values (Fig. 2(e)). Notably, the ML Bi₂O₂Se n-MOSFETs show generally larger g_m values (7–12 mS μm⁻¹) than the p-MOSFETs (2–5 mS μm⁻¹), implying a better superthreshold gate control for the former over the latter.

In a digital device, a higher on–state current is beneficial for achieving a faster logic transition speed. The off–current is fixed to 0.1 μA μm⁻¹ according to the ITRS 2.0 2013 edition standards for HP applications, and the on-current is evaluated under a supply voltage (V_dd = V_b) of 0.64–0.72 V (Table S1†). As shown in Fig. 4(a), the on-currents of the n- and p-MOSFETs without a UL fulfill the ITRS HP requirements of 900–1350 μA μm⁻¹ until L_g = 7 nm and 5 nm, respectively. Remarkably, the on-current in the Bi₂O₂Se n-MOSFET at L_g = 9 nm reaches 3500 μA μm⁻¹. This on-current is the highest among the simulated sub-10 nm transistors based on the stable 2D semiconductors at the ab initio quantum transport level, to the best of our knowledge.^13,19,26

To further improve the device performance, utilization of the UL structure is a viable solution. The UL could improve the subthreshold electrostatics because it increases the effective channel length and thereby suppresses the source to drain leakage. We consider the symmetric UL structure in the ML Bi₂O₂Se MOSFETs with L_g ≤ 5 nm; the length of the UL is chosen under the precondition of keeping the whole channel length (L_ch = L_g + 2 × UL) at less than 10 nm. As shown in Fig. S2,† the transfer characteristics of the 1 nm-gate-length n- and p-MOSFETs become steeper in the subthreshold region with the increasing UL. As the UL increases from 0 to 4 nm, the SS values decrease from 660 to 168 mV dec⁻¹ and from 474 to 111 mV dec⁻¹ for the 1 nm-gate-length n- and p-MOSFETs, respectively. This enhanced electrostatic effect by the UL also occurs in all the other studied cases. As shown in Fig. S3(a and b),† the longer UL always renders a smaller SS. The SS decreases by 28–75% with the aid of the UL, and the magnitude of the SS reduction is larger for devices with shorter L_g.

The improved gate control in the subthreshold region by using the UL is also reflected in the enhanced modulation of the band edge location by V_g. Take the ML Bi₂O₂Se p-MOSFET at L_g = 1 nm as an example. In Fig. 3, we define a maximum hole barrier height ϕ_max as the energy barrier for the holes at the VBM of the source (E = −0.32 eV) to transport to the drain. To keep the same off-current of 0.1 μA μm⁻¹ in the off-state, ϕmax is largest at UL = 0 nm followed by UL = 2 nm and UL = 4 nm (Fig. 3(a)–(c), respectively), and the peaks of the three spectral current curves are of the same order of magnitude (Fig. 3(d)). Under the gate modulation of 0.64 eV, the VBMs of the ML Bi₂O₂Se MOSFETs in the channel move upward, and the devices are turned to the on-state. ϕ_max decreases slightly by 0.10 eV at UL = 0 nm, while it decreases significantly by 0.31 eV at UL = 2 nm and by 0.25 eV at UL = 4 nm (Fig. 3(e)–(g)). The enhanced subthreshold electrostatics induced by the UL are advantageous for boosting the on-current. As shown in Fig. 3(h), the peak of the spectral current increases apparently with the longer UL. Remarkably, the current chiefly comes from those transmissions with the energy below the chemical potential of the source μ_s (namely out of the bias window) in terms of the spectral current. The maximum enhancement of the on-current by the UL is 21 times in the ML Bi₂O₂Se MOSFET with L_g ≤ 5 nm (Fig. S3(c and d)†). After applying the UL, the on-currents of the ML Bi₂O₂Se p-MOSFET at L_g = 3 nm and n-MOSFET at L_g = 2 nm reach 1127 and 871 μA μm⁻¹, respectively, fulfilling or almost fulfilling the ITRS requirement of 900 μA μm⁻¹ (Fig. 4(a)).

Fig. 3 Comparison of the local density of states (a–c, e–g) and spectral currents (d,h) of the ML Bi₂O₂Se p-MOSFETs at the off- and on-states with different ULs. L_g = 1 nm; μ_s and μ_d are the electrochemical potential of the source and the drain, respectively. The off-state has a current of 0.1 μA μm⁻¹, and the on-state is the state with a gate difference of V_dd = 0.64 V to the off-state. The maximum hole barrier height ϕ_max is labeled. The spectral current is defined as .

Fig. 4 Benchmark of the on-state current, intrinsic delay time, and power-delay product of the sub-10 nm ML Bi₂O₂Se MOSFETs against the ITRS 2013 edition requirements for HP applications. The supply voltage is 0.64–0.72 V. Only the devices whose performances fulfill or almost fulfill the requirements are shown. The red and blue colors indicate the n-MOSFET and p-MOSFET, respectively, and the solid and empty circles indicate the MOSFETs without a UL and with the optimal UL, respectively.

Next, we check the intrinsic gate delay time (τ) and PDP, which are two key figures of merit reflecting the switching speed and power efficiency for the transistor operation, respectively. The fringing capacitance C_f is included by assuming it is twice the intrinsic gate capacitance C_g according to the ITRS requirements. The total capacitance C_total is the sum of C_g and C_f. The delay time is calculated by τ = C_totalC_dd/I_on. Without the UL, the calculated delay times (0.10–42.00 ps) of the ML Bi₂O₂Se n- and p-MOSFETs meet the ITRS HP requirements of 0.423–0.446 ps until L_g = 7 nm and 5 nm, respectively (Fig. 4(b)). The introduction of the UL brings τ of the ML Bi₂O₂Se n- and p-MOSFETs below 0.26 ps at L_g ≤ 5 nm, thus meeting the ITRS HP goal even at L_g = 1 nm. PDP is calculated according to the equation PDP = V_ddI_onτ = C_totalV_dd.² Even without the UL, PDPs of the sub-10 nm ML Bi₂O₂Se n- and p-MOSFETs range from 0.03 to 0.37 fJ μm⁻¹ and decrease with shorter L_g values (Fig. 4(c)). The use of the optimal UL makes PDP decrease by 20%–110% in the ML Bi₂O₂Se MOSFETs at L_g < 5 nm. Therefore, the sub-10 nm ML Bi₂O₂Se n- and p-MOSFETs require low energy during on–off state switching, in terms of the smaller PDP compared with the ITRS requirements for HP application (0.24–0.45 fJ μm⁻¹).

We have also explored the potential of the sub-10 nm ML Bi₂O₂Se n- and p-MOSFETs for LP application. The details are provided in Table S2 and Fig. S4.† For the n-MOSFETs, the leakage current is too large to be lower than the ITRS off-current requirement of 10⁻⁵ μA μm⁻¹, due to the small effective mass and short channel barrier. For the p-MOSFETs, only those with 7- and 9 nm gate lengths could fulfill the ITRS LP requirements for the on-current and the application of a UL does not help. Apparently, ML Bi₂O₂Se is less satisfactory for LP applications in the sub-10 nm region.

Discussions

It is intriguing to compare the on-currents of the sub-10 nm ML Bi₂O₂Se MOSFETs with those of other typical 2D semiconductor MOSFETs, such as ML phosphorene,^21,36 arsenene,^19,26 antimonene,^19,26 InSe,²⁰ and MoS₂ MOSFETs. Fig. 5 shows the highest reported on-currents of the MOSFETs so far calculated at the ab initio quantum transport level. The UL configuration has been considered in this comparison. The p-type ML phosphorene MOSFETs and n-type ML arsenene/antimonene MOSFETs generally show higher or similar overall on-currents compared with those based on ML Bi₂O₂Se. However, the stability issues of phosphorene³⁷ and arsenene remain a major obstacle. The possible formation of highly toxic arsenic trioxide in the fabrication of 2D arsenene is another concern.³⁸ ML antimonene is air stable,³⁸ but ML antimonene transistors with high performance have not been fabricated yet. Compared with the ML InSe MOSFETs, the n-type ML Bi₂O₂Se MOSFETs have superior on-current at L_g ≥ 5 nm and the p-type ML Bi₂O₂Se MOSFETs are superior at L_g ≥ 3 nm but they give worse or similar performance at small gate lengths (L_g < 5 nm for the n-type MOSFETs and L_g < 3 nm for the p-type MOSFETs). However, spontaneous surface oxidation of InSe in ambient conditions is harmful for mobility and degrades the device performance greatly.¹⁵

Fig. 5 Comparison of the on-currents of the optimal ML Bi₂O₂Se, black phosphorus (BP),^21,36 arsenene (As),^19,26 antimonene (Sb),^19,26 InSe,²⁰ and MoS₂ MOSFETs at different gate lengths obtained from the ab initio quantum transport simulations. The presented on-current has been optimized by using a UL. The detailed computational parameters are provided in Table S4.†

Remarkably, the on-currents of the ML Bi₂O₂Se MOSFETs exceed those of the ML MoS₂ ones, and the difference increases with increasing L_g. At L_g = 9 nm, the on-currents of the ML Bi₂O₂Se n- and p-MOSFETs are 15.6 and 3.6 times, respectively, those of their ML MoS₂ counterparts. Besides the on-state current, the sub-10 nm ML Bi₂O₂Se MOSFETs also show generally superior performance to ML MoS₂ in terms of the delay time and PDP (Table S3†). We are aware that the recently fabricated semiconductor tellurene (2D tellurium) also possesses both high carrier mobility and air stability,³⁹ but its performance limit is unclear.

To interpret the difference in the on-current of the above 2D material-based transistors, it is helpful to check the dependence of the on-current on the effective mass of the channel materials along the transport direction (). A small effective mass of the channel material produces two effects: (1) it implies a large carrier effective velocity along the transport direction, which is beneficial for achieving a large on-current. (2) It implies a small density of states (DOS) near the VBM or CBM (, where the symbols ‖ and ⊥ indicate the transport and transverse directions, respectively). This is a disadvantage for achieving a large on-current, because a small DOS near the VBM or CBM indicates that a large variation of the gate voltage ΔV_g is needed to drive a certain variation of the channel charge ΔQ_ch, leading to a small transconductance g_m. Another disadvantage, namely large tunneling leakage induced by a small , is not discussed here as this has been depressed by the aid of the UL.

In Fig. 6(a) and (b), we provide the on-current as a function of the effective mass in the 2D semiconductor n- and p-MOSFETs, respectively, with L_g fixed at 5 nm. In the range of small effective masses , the on-current shows an increasing trend with decreasing m* for both the n- and p-MOSFETs. In the range of large effective masses , the on-current shows an increasing trend with increasing for the p-MOSFETs. The relation between and on-current (I_on) in the n- and p-MOSFETs can be well fitted by the linear functions and , respectively (except for the armchair-directed ML phosphorene p-MOSFET).

Fig. 6 (a–c) On-currents of the n-MOSFET, p-MOSFET, and both n- and p-MOSFETs versus the effective masses of the ML channel material along the transport direction at L_g = 5 nm.^{19–21,26,36} All the data here are obtained from ab initio quantum transport simulations. The solid lines in (a,b) are linear fitted to the data (excluding BP in (b)). The solid line in (c) is for guidance to the eyes. (d–f) Total transmission spectra, k-point resolved transmission spectra, and transmission eigenstates of the ML Bi₂O₂Se p-MOSFET at the on-state. L_g = 9 nm and UL = 0 nm. The inset in (e) shows the 2D Brillouin zone of ML Bi₂O₂Se and the 1D Brillouin zone of the transistor. In (f), E = −0.5 eV.

To establish an overall picture, we replot the data in Fig. 6(a) and (b) as a whole in Fig. 6(c). Among all the 2D semiconductors in Fig. 6(c), ML phosphorene is anisotropic while the other channel materials are isotropic . For the armchair-directed ML phosphorene p-MOSFETs, the noticeably large on-current (4500 μA μm⁻¹) comes from the fact that it possesses both a small and large at the same time. Thereby, it can achieve both a large carrier effective velocity and a large DOS near the VBM. For the other cases, the two effects introduced by the effective masses are always in opposition, and the effective mass needs to be optimized so that a balance between the two effects is established. Compared with the case of MoS₂, ML Bi₂O₂Se, InSe, arsenene, and antimonene n-MOSFETs give full play to the advantage of the large carrier effective velocity while ML Bi₂O₂Se, InSe and phosphorene p-MOSFETs maximize the advantage of the large DOS in the on-current. Therefore, not only those 2D semiconductors with very small but those with large are worthy of exploration for ultra-scaled electronics. The ML MoS₂ MOSFET with shows the lowest I_on in Fig. 6(c). However, more studies are needed to precisely locate the I_on minimum point since no data is available in the range of 0.45m₀–1.40m₀. Another question that needs more exploration is to what extent the increasing trend of the on-current at continues.

It is noteworthy that the special shape of the valence band of ML Bi₂O₂Se contributes to the large on-current in the ML Bi₂O₂Se p-MOSFETs. In the valence band, there is a local maximum at point A with an energy of about 0.1 eV lower than that of the VBM at the point X (Fig. 1(a)). The hole effective mass of ML Bi₂O₂Se at the point A is 0.21m₀, only 15% of the hole effective mass at the VBM (1.40m₀). The key role of the point A in the transport properties of ML Bi₂O₂Se can be found by checking its contribution to the on-state transmission of the device.

Fig. 6(d) and (e) shows the on-state transmission spectrum and the k-point resolved transmission spectrum of the 9 nm ML Bi₂O₂Se p-MOSFET. The left inset in Fig. 6(e) shows the 2D Brillouin zone of ML Bi₂O₂Se, and the right inset shows the 1D Brillouin zone of the device, with K_‖ indicating the transverse direction. Point A_‖ is the projection of the point A to the 1D Brillouin zone. The transmission peak closest to the Fermi level is located at E = −0.5 eV, and the corresponding largest transmission contribution is from the point A_‖, as shown in the k-point resolved transmission spectrum. The significant contribution of A_‖ to the transmission can also be found in the transmission eigenstates (Fig. 6(f)). At E = −0.5 eV, the incoming wave function of both the points A_‖ and X_‖ spread over the whole transistor. The wave function of the point A_‖ covers both the Bi and Se atoms, while the wave function of the point X_‖ is mainly localized near the Se atoms. This is related to the fact that both the orbitals of the Bi and Se atoms contribute to the point A while only the orbitals of the Se atoms contribute to the point X in the band structure (Fig. S5†).

The excellent performance of the ML Bi₂O₂Se MOSFETs is predicted in the Ohmic contact limit, which is ensured by the degenerately doped source and drain. Experimentally, it is rather challenging to heavily dope the 2D semiconductors,³ and the metal is often applied as the source and drain electrodes in the devices. This metal-contacted FET is termed a Schottky barrier FET (SBFET). A Schottky barrier might exist at the metal-ML Bi₂O₂Se interfaces and hinder the carrier injections. To achieve the predicted excellent performance in practice, it is essential to find a proper metal electrode that forms a barrier-free Ohmic contact with ML Bi₂O₂Se. The ab initio simulations reveal that Pt, Sc and Ti electrodes would form a desirable n-type Ohmic contact with ML Bi₂O₂Se.⁴⁰ With these metals as electrodes, the ML Bi₂O₂Se SBFETs are highly likely to approach the predicted performance limit of the corresponding MOSFETs.

Conclusion

Stimulated by the recent experimental fabrication of air-stable 2D Bi₂O₂Se FETs with high electron mobility, we predict the performance limit of the sub-10 nm ML Bi₂O₂Se n- and p-MOSFETs based on rigid ab initio quantum transport simulations. The sub-10 nm ML Bi₂O₂Se MOSFETs show on-currents lower than those of the air-unstable ML phosphorene MOSFETs, and similar to those of the air-unstable ML InSe MOSFETs, but significantly higher than those of the air-stable ML MoS₂ MOSFETs. The on-currents, delay times, and power-delay products of the optimized n- and p-type ML Bi₂O₂Se MOSFETs can fulfill or nearly fulfill the ITRS requirements for HP devices until the gate lengths are scaled down to 2 and 3 nm, respectively. The simultaneous possession of excellent device performance and high ambient stability renders the sub-10 nm ML Bi₂O₂Se MOSFETs superior to other existing 2D semiconductor counterparts as a post-silicon-era candidate channel material. Based on the analysis of a variety of ML 2D semiconductor FETs, we find that either a very small or a very large effective electron (hole) mass is beneficial for a large on-current.

Computational method

The transport properties are studied based on density functional theory (DFT) combined with the nonequilibrium Green's function (NEGF) formalism, as implemented in the Atomistix ToolKit package.⁴¹ Following the Landauer–Bűttiker formula, the drain current at a given bias voltage V_b and gate voltage V_g is calculated by the equation below:⁴²where T(E, V_b, V_g) is the transmission coefficient, f_L and f_R are the Fermi–Dirac distribution functions for the left and right electrodes, respectively, and μ_L and μ_R are the electrochemical potentials of the left and right electrodes (μ_R − μ_L = eV_b), respectively.

The transmission coefficient T(E) is the average of k-dependent transmission coefficients T^k_‖(E) over the Brillouin zone. The k-dependent transmission coefficient at energy E is

where G^k_‖(E) and ((G^k_‖(E))^† are the retarded and advanced Green functions, respectively, and is the level broadening originating from the left (right) electrode expressed by the electrode self-energy .^43,44

The electrostatics are treated by solving the Poisson equation self-consistently via a real space solver. The periodic and Neumann conditions are used on the boundaries along the transverse direction and the direction normal to the Bi₂O₂Se surface, respectively. To make sure of the charge neutrality in the electrode region, the Dirichlet boundary condition is applied on the electrode-channel boundaries along the transport direction. The k-point grids⁴⁵ are sampled with a separation of 0.01 Å⁻¹ in the Brillouin zone. The double-ζ plus polarization (DZP) basis set is adopted. The temperature is set to 300 K.

We utilize the generalized gradient approximation (GGA) in the form of the Perdew–Burke–Ernzerhof (PBE) exchange–correlation functional.⁴⁶ Because the electron–electron interaction is significantly screened by doping carriers, the single electron approximation (DFT-PBE) is a good approximation to describe the electronic structure of the device.^{26,41,47–50} The reliability of the quantum transport simulation at the DFT-PBE level in predicting the sub-10 nm FET performance is validated by the comparison of the performance of the simulated 2D MoS₂ transistors and the experimental ones. A general agreement in the overall transfer characteristics in the 1 nm-gate-length 2D MoS₂ transistors with extremely thin effective oxide thicknesses is found.^1,21 Especially in the subthreshold region, a SS of 66 mV dec⁻¹ in the simulated device agrees well with the observed 65 mV dec⁻¹.^1,21 We further calculate the 5–9 nm-channel-length ML MoS₂ n-type MOSFETs, and the drive currents in the ballistic transport limit are predicted to be 270–290 μA μm⁻¹ at a bias of V_b = 0.64 V (Fig. S6†). These values are close to the drive current of approximately 180 μA μm⁻¹ at V_b = 1 V in the fabricated 10 nm-channel-length ML MoS₂ FET with the nearly Ohmic graphene-MoS₂ contact and are still working in the diffusive regime.⁹

Author contributions

J.L. conceived the idea. J.L. and M.L. supervised the work. R.Q. carried out the simulations. J.L., M.L., and R.Q. co-wrote the paper. All authors discussed the results and commented on the manuscript.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 11604019, 11674005, and 61574020), the National Materials Genome Project (No. 2016YFB0700601), the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), the Special Fund of the Education Department of Shaanxi Province, China (No. 17JK0138), and the key research and development program of Ningxia (No. 2018BEE03023).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c8nr08852g

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