Panpan Wang, Songxuan Han, and Ruge Quhe

State Key Laboratory of Information Photonics and Optical Communications and School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China

Abstract: Owing to the high carrier mobility, two-dimensional (2D) gallium antimonite (GaSb) is a promising channel material for field-effect transistors (FETs) in the post-silicon era. We investigated the ballistic performance of the 2D GaSb metal-oxide-semiconductor FETs with a 10 nm-gate-length by the ab initio quantum transport simulation. Because of the wider bandgap and better gate-control ability, the performance of the 10-nm monolayer (ML) GaSb FETs is generally superior to the bilayer counterparts, including the three-to-four orders of magnitude larger on-current. Via hydrogenation, the delaytime and power consumption can be further enhanced with magnitude up to 35% and 57%, respectively, thanks to the expanded bandgap. The 10-nm ML GaSb FETs can almost meet the International Technology Roadmap for Semiconductors (ITRS) for high-performance demands in terms of the on-state current, intrinsic delay time, and power-delay product.

Key words: 2D GaSb; 10 nm MOSFET; hydrogenation; density functional theory; quantum transport simulation

1. Introduction

In the past few decades, the development of Si-based microelectronics obeys the performance scaling trend predicted by Moore’s law. As the building block of the microelectronics, silicon metal-oxide-semiconductor field-effect transistors (MOSFETs) behave as switches and are integrated into logic circuits to realize logic operations. Nowadays, the continuous and aggressive scaling of MOSFETs has highly increased the capability of calculation. However, traditional Si MOSFET scaling could no longer satisfy the original trend as the power density dissipated by logic chips got about 100 W/cm2[1]. Such a phenomenon originates from the so-called“short channel effects”. In the ultra-short Si MOSFET, it becomes very hard to suppress the source to drain leakage by gating.

Most III−V semiconductors have smaller effective masses than Si, and thus higher drift velocity[13−16], which endows them great potential in high-speed MOSFET. Gallium-based materials possess high carrier mobility, which is advantageous for MOSFETs. Moreover, in the 2D region, research shows that the effective mass of monolayer (ML) GaSb is smaller than ML GaN, GaP, and GaAs, implying high carrier mobility of ML GaSb[17]. Thus, the ultrathin GaSb is of high interest for the post-silicon electronic.

In this paper, we investigate 10 nm double-gated (DG) nand p-type metal-oxide-semiconductor FETs with ML and bilayer (BL) GaSb by using ab initio quantum transport simulations. The DG ML GaSb MOSFETs show on-currents (Ion) ranging from 1.0 × 101to 1.3 × 103μA/μm. Good gate electrostatics with the subthreshold swing ranging from 87 and 120 mV/dec and transconductance from 7.9 × 103to 2.8 ×104μS/μm are observed. The power-delay products (PDP)and delay time (τ) of almost all the studied ML GaSb MOSFETs are lower than the requirements of ITRS and IRDS, which indicates their competitiveness in low-power applications.

2. Model and method

The two-probe 10 nm-gate-length DG MOSFET is constructed with intrinsic ML and BL GaSb and their hydrogenated counterparts as the channel, respectively. The source and drain are highly doped 2D GaSb. The doping concentration is 5 × 1013cm-2[18]. We adopt SiO2dielectric with 3.9 dielectric constant and 0.56 nm equivalent oxide thickness (EOT). The supply voltage (Vdd) is set to 0.45 V (=Vb) in terms of the ITRS standard.

Fig. 1. (Color online) Top and side views and band structures of (a) ML GaSb, (b) ML h-GaSb, (c) BL GaSb, and (d) BL h-GaSb.

We apply the density functional theory (DFT) combined with the nonequilibrium Green’s function (NEGF) formalism in the Atomistix ToolKit package to calculate the electronic and transport properties[19,20]. The following Landauer-Büttiker formula gives the drain currentIds:

whereeis the elementary charge,his the Planck constant,T(E,Vb,Vg) is the probability of transmission at a given gate voltageVgand voltageVb,fSandfDare the Fermi-Dirac distribution function for the source and drain, respectively, andμSandμDare the electrochemical potentials of the source and drain, respectively. OpenMX basis set with a mesh cut-off energy of 200 hatree was used. The temperature was set to 300 K. The Brillouin zone was sampled with separations of 0.01 Å-1[21]. We applied the Neumann boundary condition along the direction out of the GaSb plane, the Dirichlet boundary condition along the transport direction, and the periodic boundary condition along the transverse direction of the transistors. The generalized gradient approximation(GGA) in the form of Perdew-Burke-Ernzerhof (PBE) potential was used to describe the exchange-correlation interaction in the transistor[22].

Table 1. Structural and electronic parameters of monolayer (ML) and bilayer (BL) GaSb. h-GaSb stands for the hydrogenated layer.

3. Results and discussion

We investigate four types of GaSb-based materials: ML GaSb, BL GaSb, and their hydrogenated counterparts. The hydrogenated GaSb is noted as h-GaSb for short. These structures are shown in Fig. 1, and the optimized parameters are listed in Table 1. ML GaSb is a buckled honeycomb structure with an optimized lattice parameter of 4.36 Å and thickness of 0.80 Å. After hydrogenation, the lattice parameter of ML GaSb is slightly increased to 4.37 Å and thickness is increased to 2.19 Å. The increment of the thickness comes not only from the introduction of the H atoms, but also from the deformation of the Ga-Sb bonds.d′ is defined by the distance between two Ga and Sb atomic planes. The full hydrogenation makes Sb atom rise and Ga atom lower, increasingd′ of ML GaSb from 0.81 to 0.87 Å. It is consistent with previous theoretical studies on the ML III-V compounds[15]. BL GaSb is truncated from the zinc-blende bulk structure. The lattice parameters of BL GaSb and h-GaSb are close to their ML counterparts, and the thicknesses are 4.46 and 7.69 Å, respectively. A similar increase ofd′ from 0.81 to 0.90 Å is observed in the BL after hydrogenation.

Freestanding ML GaSb may has dangling bonds on its surface, this feature might affect the stability of the material.While there is no dangling bond on ML h-GaSb, since the surface is passivated. Comparing the phonon spectra of ML GaSb[23]and ML MoS2[24], ML GaSb may not be as dynamically stable as the latter one. However, the previous studies have shown that the formation energy of ML GaSb[23]is lower than that of ML SiC[25], which had been successfully manufactured, so it is possible to synthesis ML GaSb. In addition, selecting lattice-matched high atomic density surfaces of substrates enhances the stability of ML GaSb. A suitable substrate like Pd can energetically stabilize materials during the growth process[26].

Fig. 2. (Color online) (a) Schematic model of DG ML GaSb MOSFET with 10 nm gate length. (b, c) Transfer characteristic of ML GaSb and h-GaSb and BL GaSb and h-GaSb.

The electronic band structures of 2D GaSb and h-GaSb along the high symmetric k-path M-Γ-K-M are shown in Fig. 1. ML GaSb is a semiconductor with a direct bandgap of 1.00 eV. The valence band maximum (VBM) and conduction band minimum (CBM) are located at Γ point. After hydrogenating, the crystal remains a direct bandgap at Γ point with an expended size of 1.38 eV. Compared with the ML ones, the bandgaps of the BL counterparts are much smaller. BL GaSb shows an indirect bandgap of 0.23 eV with VBM located at Γ point and CBM at K point. BL h-GaSb shows a direct bandgap of 0.5 eV at Γ point. A bandgap of at least 0.4 eV is required for the semiconductor as the channel in the transistor[27]so as to achieve an on/off current ratio large enough for practical use. ML GaSb, ML h-GaSb and BL h-GaSb are promising in this regard.

The transfer characteristics of the 2D GaSb MOSFET are shown in Figs. 2(b) and 2(c). The current of p-type devices decreases as the gate voltage increases, and the n-type ones are in contrast, which corresponds with the general trend that devices switch between the off-state and on-state. Additionally, comparing the transfer curves of the n- and p-type devices based on the same material, the ML GaSb MOSFETs have the most symmetrical current trend. The off-current (Ioff)is set to 0.1 and 0.01μA/μm in terms of the high-performance (HP) requirement of 2015 ITRS and 2020 IRDS, respectively. From the pictures, all the devices with ML materials can meet the two requirements forIoff, except for the BL GaSb nand p-MOSFETs. The lowest current of BL GaSb MOSFET in the considered voltage range (-4.5 to 3.5 V) is about one or two orders of magnitude larger than 0.1μA/μmIoff. i.e., the BL GaSb MOSFETs are hard to turn “off”. This phenomenon is related to the small bandgap of 0.23 eV in BL GaSb. Thus, hydrogenation of the BL GaSb is suggested in order to increase the bandgap and thus suppress the source to drain leakage so that to meet the off-current requirement.

WithIoff= 0.1μA/μm selected from the HP requirement of ITRS 2015 edition for 2027 horizons,Ioncan be determined by the supply voltageVdd(0.45 V): |Vg,on-Vg,off| =Vdd. Besides, from the HP standard of IRDS 2020 edition for 2028 horizons, we also calculated theIonwith 0.01μA/μmIoffand 0.65 VVdd. A higherIonindicates a faster logic transition speed of the switch. AllIonof ML GaSb and h-GaSb MOSFETs ranges from 1.0 × 101to 1.3 × 103μA/μm. In comparison,Ionof BL ones is lower than 1μA/μm, which are apparently lower than most ML ones. In Fig. 3(a), we plot the on-current as a function of the effective mass in the 2D semiconductor that we considered except BL GaSb (because the simulated lowest current of the 10 nm BL GaSb MOSFET is larger than theIoffrequirement of 0.1μA/μm). The n-MOSFETs behave better than the p-type counterparts in terms of the on-current mainly because of the much lighter effective mass. Considering materials of electron-effective masses (< 0.087m0),Ionshows an increasing trend with decreasingm*for GaSb.When heavy-hole effective masses of GaSb are relatively higher (> 0.48m0), there is no obvious dependence betweenIonand effective mass. This phenomenon originates from the competition between the factors of mobility and gate controllability. While a small effective mass is beneficial for higher mobility, a larger effective mass implies a larger density of state near the Fermi level and thus better gate controllability. The latter factor becomes especially important in the ultrashort MOSFETs. As a result, no simple linear relation between the effective mass and the on-current is found. It is noted that for ML GaSb MOSFETs (no matter n- or p-type), the hydrogenation enhances theIonof IRDS set, but ITRS ones are opposite.This may result from different slopes of transfer curves at different gate voltage range.

Fig. 3. (Color online) (a) On-current versus the effective mass m*, (b) subthreshold swing versus transconductance, and (c) power-delay products versus delay time. Labels with and without cross-shaped subscripts represent the values calculated according to IRDS and ITRS standards, respectively. The data of other transistors with a similar gate length are also included for comparison: GaSb p-nanowire[29], BP (transfer along zigzag direction)[30], WSe2[31], MoS2 MOSFETs[9], and Si FinFET[32].

It is intriguing to benchmark the performance of ML GaSb MOSFETs against transistors with other channel materials. Almost both the ML GaSb and h-GaSb MOSFETs show higherIonthan Si FinFET with a similar size of 10 nm. Compared with the 10 nm MOSFETs based on other commonly studied 2D materials like WSe2and MoS2[31,33], the ML GaSb and h-GaSb MOSFETs are not inferior inIon. With the 2015 ITRS HP settings,Ionof ML GaSb MOSFETs can fulfill 33%-83%requirement. The latest IRDS requires a lower off-current(0.01μA/μm) and a higher on-current (2.0 × 103μA/μm) for the HP application in 2028. With this off-current, the gap ofIonbetween n- and p-type MOSFETs further extends.Ionof devices with ML materials can meet 52%-69%, and p-type counterparts only satisfy 1%-11% of the IRDS standard. To further increaseIonof GaSb-based MOSFETs, we can manipulate the electronic structure by introducing a compressive biaxial strain. Research indicates that with a 2.0% biaxial compressive strain, the maximum hole mobility of GaSb p-MOSFETs has increased 2.86 times, compared with the freestanding one[4,34−36].

To understand the mechanism of gate control of MOSFETs, we calculate the local density of state for n-type DG MOSFETs with ML GaSb, ML h-GaSb, and BL h-GaSb. We define a maximum hole barrier heightΦBas the energy barrier between the highest energy level of the channel VBM and the source Fermi energy level. In Figs. 4(a)-4(c),ΦBof DG ML freestanding GaSb MOSFET is 0.78 eV whenVg= -0.9 eV at the off-state. It hinders the carrier transport from source to drain, and the current is mainly contributed by the tunneling currentItunnel. With the increase of gate voltage (-0.3 eV), the device turns to the intermediate state, andΦBdecreases to 0.32 eV. Both the tunneling currentItunneland the thermionic currentIthermcontribute significantly to the total current of 16μA/μm. They are separated by the top of barrier height.When enhancing gate voltage to 0.3 eV, the barrier disappears, andIonreaches 3.4 × 103μA/μm withItherm’s main contribution.

Fig. 4. (Color online) Position resolved local density of state and spectral current in the channel region of (a-c) ML GaSb, (d-f) ML h-GaSb and(g-i) BL h-GaSb at different states. μs and μd are the electrochemical potential of the source and drain, respectively. ΦB is the effective barrier height.

Compared with the ML GaSb MOSFET, the ML h-GaSb MOSFET’s gate modulation (Figs. 4(d)-4(f)) is similar on the overall trend, butΦBbecomes larger in every state. From the off-state (Vg= -1.3 eV) to the intermediate-state (Vg=-0.9 eV) to the off-state (Vg= 0.3 eV),ΦBdecreases from 1.69 to 0.9 and to 0 eV, and the current increases from 0.01 to 106 and to 9528μA/μm. However, during the on-off state transition, the BL h-GaSb MOSFET (Figs. 4(g)-4(i)) performs slightly differently. ItsΦBdecreases much smaller than the ML material MOSFET one. In the meantime, the current increases much smaller from 0.07 (off-state) to 0.6 (intermediate-state) and to 4.9μA/μm (on-state). It depicts the worst control ability and the lowest switch speed among three MOSFETs.

In our simulation, SiO2of 0.56 nm thick is used as the dielectrics. Such a thin dielectric will result in a high gate tunneling leakage current in practice. The high gate leakage will lower the circuit performance severely, and it is a critical issue especially in the sub-nanometer scale. Changing SiO2into other high-kdielectrics such as TiO2and HfO2can overcome this disadvantage[43]. High-kmaterials have larger capacitance equivalent thickness than SiO2, and thus a better ability to suppress the leakage.

4. Conclusion

Inspired by the high mobility of III-V binary materials, we simulated the 2D GaSb n- and p-MOSFETs with a gate length of 10 nm based on ab initio quantum transport simulations.BL GaSb MOSFETs perform significantly worse than the ML ones, owing to their relatively smaller bandgap and heavier masses. Additionally, it is found that power-delay products and delay time can be best improved by about 35% and 57%, respectively, with full hydrogenation. The on-currents of ML GaSb MOSFETs range from 1 × 101to 1.3 × 103μA/μm,and the SS cover from 87 to 120 mV/dec. ML GaSb transistors show a fast delay time of 0.24 to 1.10 ps and low powerdelay products of 0.08 to 0.45 fJ/μm. In general, the ML GaSb and h-GaSb MOSFETs perform similarly to the commonly studied ML MoS2and WSe2counterparts with the same gate length of 10 nm, in terms of a few figures of metrics including the on-current, PDP, and delay time. Therefore, making GaSb thinner, ideally fabricating the thinnest ML GaSb, is worthy of being tested for the ultrashort transistors in the experiment.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 91964101), the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications) and the Research Innovation Fund for College Students of Beijing University of Posts and Telecommunications.