Many-body Effect, Carrier Mobility, and Device Performance of

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Many-body Effect, Carrier Mobility, and Device Performance of Hexagonal Arsenene and Antimonene Yangyang Wang,†,‡ Pu Huang,‡ Meng Ye,‡ Ruge Quhe,∥ Yuanyuan Pan,‡ Han Zhang,‡ Hongxia Zhong,‡ Junjie Shi,*,‡ and Jing Lu*,‡,§ †

Nanophotonics and Optoelectronics Research Center, Qian Xuesen Laboratory of Space Technology, China Academy of Space Technology, Beijing 100094, P. R. China ‡ State Key Laboratory for Mesoscopic Physics and School of Physics, Peking University, Beijing 100871, P. R. China § Collaborative Innovation Center of Quantum Matter, Beijing 100871, P. R. China ∥ State Key Laboratory of Information Photonics and Optical Communications & School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, P. R. China S Supporting Information *

ABSTRACT: Two-dimensional (2D) semiconductors are very promising channel materials in next-generation field effect transistors (FETs) due to the enhanced gate electrostatics and smooth surface. Two new 2D materials, arsenene and antimonene (As and Sb analogues of graphene), have been fabricated very recently. Here, we provide the first investigation of the many-body effect, carrier mobility, and device performance of monolayer (ML) hexagonal arsenene and antimonene based on accurate ab initio methods. The quasi-particle band gaps of ML arsenene and antimonene by using the GW approximation are 2.47 and 2.38 eV, respectively. The optical band gaps of ML arsenene and antimonene from the GW-Bethe−Salpeter equation are 1.6 and 1.5 eV, with exciton binding energies of 0.9 and 0.8 eV, respectively. The carrier mobility is found to be considerably low in ML arsenene (21/66 cm2/V·s for electron/hole) and moderate in ML antimonene (150/510 cm2/V·s for electron/hole). In terms of the ab initio quantum transport simulations, the optimized sub-10 nm arsenene and antimonene FETs can satisfy both the low power and high performance requirements in the International Technology Roadmap for Semiconductors in the next decade. Together with the observed high stability under ambient condition, ML arsenene and antimonene are very attractive for nanoscale optoelectronic and electronic devices.

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substrate.16,17 Very recently, ML and multilayer antimonene have been obtained by mechanical exfoliation, liquid-phase exfoliation, and epitaxy growth.18−22 More importantly, they are highly stable under ambient conditions.18−21 The conventional density functional theory (DFT) with generalized gradient approximation (GGA) and hybrid functional calculations show that ML arsenene and antimonene are semiconductors with a wide band gap.23−29 Together with their highly stability under ambient conditions, arsenene and antimonene appear quite attractive for optoelectronic and electronic devices. Up to date, several fundamental issues remain open for ML arsenene and antimonene. (1) There are two types of common observable band gaps in a semiconductor: fundamental (or quasi-particle) and optical gaps. The fundamental gap is dominated by the electron−electron

INTRODUCTION Inspired by the graphene boom, searching for its analogue in other elements becomes an area of intense interest recently. The group IV analogues of graphene, silicene,1−4 germanene,3,5−9 and stanene10−12 have been synthesized. However, the zero or small band gap prevents group IV-enes from being an effective transistor operating at room temperature despite their high carrier mobility. By contrast, the group V analogy of graphene, monolayer (ML) or multilayer black phosphorus (BP, α-phase phosphorene with orthorhombic structure), has a tunable band gap and a high carrier mobility (1000 cm2/V·s) and has become a popular star in the two-dimensional (2D) material community since the successful fabrication of phosphorene transistors in early 2014.13,14 However, BP is not stable under ambient conditions, and thus, its application in real devices is controversial.15 The other two heavier group V-enes, ML hexagonal (β-phase) arsenene and antimonene, have attracted great interest. Experimentally, multilayer arsenene/antimonene nanoribbons have been successfully synthesized on an InAs/InSb © 2017 American Chemical Society

Received: November 17, 2016 Revised: January 4, 2017 Published: March 1, 2017 2191

DOI: 10.1021/acs.chemmater.6b04909 Chem. Mater. 2017, 29, 2191−2201

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Chemistry of Materials

2013.45 Hence, ML arsenene and antimonene are suitable candidates for nanoscale optoelectronic and electronic devices.

interaction effect and should be calculated by an ab initio GW approach, while the optical gap is dominated by the electron− hole interaction (excitonic effect) and should be described by a GW approach plus the Bethe−Salpeter equation (BSE).30 In a 2D semiconductor, many-body effect is more prominent due to enhanced Coulomb interaction with the reduced dimension, and the two band gaps can differ by more than 1 eV.31,32 Although hybrid functionals can yield a good bulk fundamental gap, they become unreliable in predicting the fundamental gap for nanostructures and surfaces, and the given band gap typically falls in a region between quasi-particle and optical band gaps.33 For example, the Heyd−Scuseria−Ernzerhof (HSE) band gap of ML MoS2 is 2.2 eV,34 which is equal to neither the fundamental gap (∼2.8 eV from the GW calculation)35−38 nor the optical gap (1.88 eV from both the experiment39 and the GW-BSE calculation35). Hence, determination of the fundamental band gap based on the GW approach and optical band gap based on the GW-BSE approach is highly desirable to characterize ML hexagonal arsenene and antimonene.24 (2) Carrier mobility is a key figure of merit of a semiconductor. Although the higher carrier mobility in bulk gray As over bulk MoS2 has been observed,40 a recent simulation based on the deformation potential approximation (without full consideration of electron−phonon coupling) predicts that the carrier mobilities of β-phase ML arsenene and antimonene (∼101 cm2/V·s)41 are lower than that of ML MoS2. Considering a possible large discrepancy between the carrier mobility values calculated by the deformation potential approximation and the first-principles method,42−44 it is necessary to investigate the carrier mobility of ML β-phase arsenene/antimonene based on the first-principles method. (3) Computing technology requires field effect transistors (FETs) with a channel length smaller than 10 nm in the next decade. However, Moore’s law is approaching its physical limit because scaling Si transistors to 10 nm and below would be exceptionally difficult and is predicted to fail below 5 nm. 2D materials are an alternative channel material in the sub-10 nm region because they have well-controlled electrostatics, fewer traps on the semiconductor-dielectric interface, and a high degree of vertical scaling. In view of the large band gaps in ML arsenene and antimonene, apparently their device performance in the sub-10 nm region and especially the suitability for low power (LP) are greatly desired. In this work, we investigate for the first time the many-body effect and device performance of ML hexagonal arsenene and antimonene using ab initio GW, GW-BSE, and quantum transport approaches, and we simulate the carrier mobility of ML arsenene/antimonene based on the first-principles electron−phonon interaction method. The calculated fundamental band gaps of ML arsenene and antimonene are 2.47 and 2.38 eV, respectively, luckily, both in agreement with the hybrid functional’s results. The calculated optical absorption band gaps of ML arsenene and antimonene are only 1.6 and 1.5 eV, respectively, due to the significant exciton effect. The acoustic phonon-limited intrinsic electron/hole mobilities calculated from the ab initio approach are 21/66 and 150/510 cm2/V·s for ML arsenene and antimonene, respectively. The simulated sub-10 nm ML arsenene and antimonene double-gated (DG) metal oxide semiconductor FETs (MOSFETs) based on the ab initio quantum transport approach show excellent device performances and can fulfill both the LP and high performance (HP) application requirements of the next decade in the International Technology Roadmap for Semiconductors (ITRS)

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METHODOLOGY

Geometry Optimization and Electronic Calculations. The geometry optimizations are based on DFT performed by using the CASTEP code.46 Enough k-point sampling (13 × 13 × 1) is used for the structure relaxation. The GGA with the Perew−Burke−Ernzerhof (PBE) functional is adopted.47 Energy cutoff is set to 550 eV, and structural optimization is carried out until the maximum energy difference and residual forces converge to 10−5 eV and 0.01 eV/Å. The electronic calculation is performed subsequently with the same setting but using a denser k-point mesh (26 × 26 × 1). The quasi-particle and optical absorption spectrum calculations are carried out in the BerkeleyGW package.48 The quasi-particle energies Enk are obtained within the GW approximation by solving the Dyson equation:49

[H0 + Σ(Enk )]Ψnk = Enk Ψnk

(1)

where H0 is the Hamiltonian in the Hartree approximation, ∑ is the electron self-energy, and Ψnk is the quasi-particle wave function. The optical spectrum including excitonic contributions is obtained by solving the BSE of the two-particle Green’s function:50,51 (Eck − Evk )]A vcS k +

∑

< vc k|K eh|v′c′k′ > A vS′ c ′ k ′ = ΩSA vcS k

v′c′k′

(2) ASvck

eh

where is the exciton amplitude, K is the electron−hole interaction kernel, and |ck>/|vk> is the quasi-electron/hole wave function. In practice, quasi-particle wave functions are assumed to be the same as the DFT wave functions. The DFT wave functions and eigenvalues are obtained by solving the Kohn−Sham equations using a local density approximation (LDA) exchange-correlation functional with Troullier− Martins norm-conserving pseudopotentials,52,53 as implemented in the Quantum Espresso code.54 A kinetic energy cutoff of 150 Ry is used for the wave function. During the GW calculations, we chose a 12 × 12 × 1 k-point mesh; moreover, the number of involved unoccupied conduction bands used for calculating the dielectric function and selfenergy is about 10 times the occupied valence band number. To perform the BSE calculations, we interpolate the electron−hole interaction kernel on a finer 24 × 24 × 1 k-point mesh. This choice of parameters yields well-converged exciton eigen energies and sufficient accuracy in our calculations. In order to eliminate the interaction between periodic images of these 2D layer structures in adjacent supercells, the vacuum space is chosen as 30 Å. Carrier Mobility Calculations. The phonon-limited carrier mobility of the monolayer is obtained by solving the Boltzmann transport equation (BTE) in the relaxation time approximation:42,55,56

μ = −e

∑k, n τk, nvk2, n·∂f (εk, n)/∂εk, n ∑k, n f (εk, n)

(3)

where τk,n is the momentum relaxation time for electrons in state |k,n⟩, vnk their group velocity, εk,n the band energy, and f the Fermi−Dirac distribution function. For the case of scattering of electrons due to phonons, τk,n can be obtained by using Fermi’s golden rule:42,44

1 2π = τk, n ℏ

∑ q, λ , n ′

1 − f (εk + q, n ′) 1 − f (εk, n)

(1 − cos θ k, k + q)

|gqλ, k, n , n ′|2 [nq, λδ(εk + q, n ′ − ℏωq, λ − εk, n) + (1 + n‐q, λ)δ(εk + q, n ′ + ℏω‐q, λ − εk . n)]

(4)

gλq,k,n,n′

is the electron−phonon interaction matrix element, θk,k+q where the scattering angle, ωq,λ the phonon frequency, nq,λ the Bose−Einstein distribution function, and δ the Dirac delta function. The carrier mobility is calculated using the Atomistix ToolKit (ATK) 2016 package57 with the PBE-GGA functional for the exchangecorrelation functional and double-zeta-polarized (DZP) basis set. The 2192


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Chemistry of Materials many-body effect is not included since it affects the dispersion relation of bands (and therefore the electron−phonon interaction) slightly. In the electronic structure calculation, a 17 × 17 × 1 k-mesh is used. The phonon dispersion and bulk electron−phonon interaction is obtained from a 7 × 7 × 1 supercell calculation in the case of arsenene and a 17 × 17 × 1 supercell for antimonene.42 In arsenene and antimonene, the states near the conduction band minimum (CBM) or valence band maximum (VBM) provide the dominant contribution to the transport process at room temperature since their band gaps are larger than 1 eV, and only the long-wavelength acoustic branches of phonons need to be considered if the intervalley transition events are not included. We use a 20 × 20 × 1 q-mesh around Γ ([0, 0, 0]) and a 20 × 20 × 1 k-mesh around the CBM/VBM k-point to simulate the electron/hole mobility. The chosen k-mesh corresponds to an energy window of about 0 to ±0.15 eV around CBM/VBM. Only the three acoustic branches of phonons are taken into account. Device Models and Simulations. The performance limits of ML β-phase arsenene/antimonene are examined using a DG two-probe MOSFET model. The source and drain are n-doped with a doping level of Ne = 5 × 1012 ∼ 1014 cm−2. Ballistic transport properties are calculated by using the DFT coupled with the nonequilibrium Green’s function (NEGF) method, as implemented in the ATK 2016 package.57 The DZP basis set and the GGA of the PBE form to the exchange-correlation functional are adopted.47 In our device model, ML arsenene/ antimonene is doped by the dual gates in the channel region and seriously n-doped in the source/drain region. In this case, DFT is a good approximation to the GW approach in describing the transport gap due to the significantly screened electron−electron interaction by doping carriers.58,59 Therefore, the many-body effect is also not included in the transport simulation. The ML arsenene/antimonene is located in the xz plane, and the transport is along the z direction. The k-point meshes for the central region and electrodes are sampled with 50 × 1 × 1 and 50 × 1 × 50 separately. The transmission coefficient at energy E averaged over 50 kxpoints is obtain by

T (E) = Tr[Gr ΓS(E)Ga ΓD(E)]

Figure 1. Band structures of ML (a) arsenene and (b) antimonene calculated with PBE and GW approaches, respectively.

atoms are located in the same layer for the latter. In other words, the thinner 2D structure has a stronger Coulomb interaction. Although the HSE band gap (2.234/1.561 eV) of ML MoS2/ phosphorene is between the GW-BSE (1.78−1.8835,36/1.2− 1.462,63 eV) and GW (2.82−2.8435,36/2.0−2.262,63 eV) values (Table 1), the HSE band gaps of ML arsenene/antimonene (2.0−2.49/2.28 eV)23−25 are fortunately quite close to the GW (2.47/2.38 eV) value. Table 1. Comparison of the Band Gaps Calculated at Different Levels of ML Arsenene, Antimonene, BP, and MoS2 (in Units of eV) material arsenene

(5)

where Gr(a) is the retarded (advanced) Green function, and ΓS(D)(E) = i(∑rS(D) − ∑aS(D)) is the line width function of the source/drain electrode expressed in terms of the electrode self-energy ΣS(D). The drain current is calculated with the Landauer−Bű ttiker formula:60

Id(Vds , Vg ) =

2e h

antimonene

+∞

∫−∞

{T (E , Vds , Vg )[fS (E − μS )

− fD (E − μD )]}dE

(6)

GGA/LDA present work others

1.76

present work others

1.65

1.5,23 1.64,27 1.625

BPa

others

1.04,26 0.76,29 1.4,28 1.7724 0.961

MoS2b

others

1.939

HSE

GW

BSE

2.47

1.6

2.38

1.5

2.263 2.062 2.8435 2.8236

1.463 1.262 1.8835 1.7836

2.2,23 2.49,24 2.025

1.55,26 2.2824 1.561 2.234

where T(E, Vg, Vbias) is the transmission probability at a given gate voltage Vg and bias voltage Vds, f S/D the Fermi−Dirac distribution function for the source/drain electrode, and μS/μD the electrochemical potential of the source/drain electrode. The temperature is set to 300 K.

The observed fundamental and optical band gaps of ML BP are 2.2 and 1.3 eV, respectively.63 bThe observed optical band gap of ML MoS2 is 1.88 eV.39

RESULTS AND DISCUSSION Fundamental and Optical Band Gaps. The optimized lattice constant, height of the buckling layer, and bond lengths are 3.52 Å (4.10 Å), 1.35 Å (1.66 Å), and 2.43 Å (2.89 Å), respectively, for ML hexagonal arsenene (antimonene). The calculated work functions of ML arsenene and antimonene, defined as the energy difference between the vacuum level and band gap center of the semiconductor, are 4.439 and 4.863 eV, respectively. The band structures of ML hexagonal arsenene and antimonene with PBE and GW approaches are shown in Figure 1a and b, respectively, from which the self-energy correction can be found apparently. The indirect band gap is 1.76 (1.65) eV at the PBE level for ML hexagonal arsenene (antimonene) and noticeably increases to 2.47 (2.38) eV at the GW level. The 40− 44% quasi-particle correction for the band gap is much smaller than that of 150% obtained for graphdiyne31 owing to the atomic distribution at different layers for the former, whereas all the

Figure 2a and b shows the calculated imaginary part of the dielectric functions for ML arsenene and antimonene, respectively, which is closely related to the optical absorption. The optical absorption occurs at 1.6 (1.5) eV within red wavelength for arsenene (antimonene). Such optical gaps are comparable with that (1.88 eV) of ML MoS2 and render them as attractive for photoelectronic devises as ML MoS2.64,65 The exciton binding energy, given by the difference between the electronic and optical band gaps, is found to be 0.9 (0.8) eV for ML arsenene (antimonene). These exciton binding energies are comparable with those found in semiconducting monolayer phosphorene (0.8−0.9 eV),62,63 graphdiyne (0.55 to 1.17 eV),31 monolayer MoS2 (∼1.0 eV),35,36,66 zigzag graphene nanoribbons (0.67 eV for 8-ZGNR),67 and SWCNTs (∼1.00 eV for the (8,0) tube).30 Moreover, the exciton wave function is centered on a hole in the valence band with the full width at half-maximum of 1.42 nm (Figure S1), which is commonly observed in organic

a

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Figure 2. Calculated imaginary part of the dielectric function ε2 for ML (a) arsenene and (b) antimonene with and without the electron−hole (e-h) interaction.

Figure 3. Bulk electron−phonon interaction matrix elements |gλk,q,n,n| (in unit of eV) in ML (a,b) arsenene and (c,d) antimonene. The interaction is illustrated as a function of phonon wave vector q for k at the (a,c) CBM and (b,d) VBM k-point. Only the ZA phonons are plotted.

semiconductors and indicates the enhanced electron−hole interaction.68 Our fundamental and optical band gap calculations are performed on suspended pristine ML arsenene and antimonene, while in experimental measurements of the quasi-particle bandgap and exciton binding energy, ML arsenene and antimonene often need to be placed on a substrate. Because of its ultrathin thickness, the quasi-particle and exciton binding energies of a 2D semiconductor can be strongly affected by the environment. In the scanning tunneling microscopy measurements, ML transition metal dichalcogenides (MX2) is placed on a substrate like graphite (HOPG) or bilayer graphene (BLG).69−72 Because of the screening by the metallic substrate, both the electron−electron and electron−hole interaction are reduced; as a result, both the quasi-particle bandgap and the exciton binding energy of a 2D semiconductor are reduced compared to its isolated phase. However, if the metallic substrate is taken into account in the GW and GW-BSE calculations, the reduced quasiparticle band gap and exciton binding energy can be well reproduced. For example, after taking the metallic substrate screening into consideration, the calculated quasi-particle gap (2.13 eV) and exciton binding energy (0.52 eV) of ML MoSe2 on BLG substrate are in good agreement with the experimental measured 2.18 and 0.55 eV, respectively.71 On the other hand, in the typical optical measurement approach, the ML semiconductor is placed on an insulator substrate such as SiO2,63,73−76 and in this case, the observed quasi-particle band gap and exciton binding energy become closer to the calculated values based on the free-standing ML semiconductor model because the screening of the insulating substrate is much smaller than that of the metallic substrate. For example, the quasi-particle gap (2.2 ± 0.1 eV) and exciton binding energy (0.9 ± 0.12 eV) of ML black phosphorene on SiO2 extracted using photoluminescence agree with the calculated values of its isolated phase perfectly (2.2 and 0.8 eV, respectively).63 Intrinsic Mobility Calculations. We investigate the electron−phonon interaction matrix elements of three acoustic branches: the out-of-plane acoustic (ZA) and the transverse acoustic (TA) and the longitude acoustic (LA) phonons. The ZA phonons provide the dominant contribution to the electron− phonon interaction in ML arsenene and antimonene, just like that in silicene.44 Figure 3 shows the electron−phonon interaction matrix elements obtained for the electrons at the

CBM and VBM k-point as a function of ZA phonon wave q. Obviously, the electron−phonon interaction strength in arsenene is significantly larger in comparison with that of antimonene. Since the electronic structures of arsenene and antimonene are quite similar, and the effective masses at the CBM/VBM k-point are both about 0.28/−0.43 me, the carrier mobility of antimonene should be much higher than that of antimonene. On the other hand, the average interaction strength in Figure 3a,c is obviously larger than that in Figure 3b,d, although the maximum value in these two figures are comparable. This difference suggests that there are more phonons which have large interaction strength with electrons at CBM than that with electrons at VBM in arsenene (antimonene) and imply that the hole mobility should be higher than the electron mobility in arsenene and antimonene. The intrinsic acoustic phonon-limited electron/hole mobilities calculated at room temperature (300 K) are approximately 21/66 and 150/510 cm2/V·s for ML arsenene and antimonene, respectively. The hole mobility is about three times higher than electron mobility in both ML arsenene and antimonene. The carrier mobility differences between arsenene and antimonene and between electron and hole are in good agreement with our above analysis based on the phonon−electron interaction strength. The carrier mobility of ML arsenene is less satisfactory despite the higher carrier mobility in bulk gray As over bulk MoS2.24,40 The carrier mobility of ML antimonene is about 1 order of magnitude higher than that of ML arsenene and comparable with that of ML MoS2 (∼200 cm2/V·s)44 and graphane (∼170 cm2/V·s).77 Performance of ML Arsenene and Antimonene DG MOSFETs. We begin with a 10 nm-gate-length ML arsenene DG n-MOSFET without underlap (UL) structure, as shown in Figure 4a. The equivalent oxide thickness (EOT) and supply voltage Vdd are adapted from the ITRS 2013 tables for the LP technology at Lg = 10.1 nm for the 2022 horizon. An optimized source and drain doping concentration (Ne) is required in the MOSFET to ensure efficient carrier injection and meanwhile bridle the tunneling leakage at the off-state. The transfer characteristics for three different Ne ranging between 1013 and 1014 cm−2 are shown in Figure 4b. The SS is 53−55 mV/dec, and such a sub-60 mV/ dec switching indicates that not only the thermionic emission 2194


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Figure 4. ML arsenene DG MOSFET with Lg = 10 nm. (a) Schematic of an arsenene DG MOSFET without UL structures. (b) Transfer characteristics for different source and drain electron doping concentrations (Ne) on log (left-hand axis) and linear scales (right-hand axis). Position resolved LDOS in the channel region at Vg = (c) −0.8, (d) −0.4, and (e) 0 V for Ne = 5 × 1013 cm−2. The responding conduction band profiles along the channel are given in (f). The white solid line represents the Fermi level at the source or drain. Illustrated in c as an example, red dashed arrows represent the thermionic and tunneling electron transports, and ΦB is the effective barrier height. (g) Transmission eigenstates at E = Vds/2 and k = (1/3, 0) for Vg = −0.8, − 0.4, and 0 V, respectively. The isovalue is 0.2 au.

Table 2. Benchmark of the Ballistic Performance Upper Limits of the ML Arsenene DG n-MOSFETs (Ne = 5 × 1013 cm−2 unless Otherwise Specified) against the ITRS 2013 Requirements for HP and LP Devices of the Next Decadesa arsenene ITRS LP 2022 ITRS HP 2021 arsenene ITRS LP 2024 ITRS HP 2022 arsenene ITRS LP 2027 ITRS HP 2025 arsenene arsenene (UL = 2 nm) ITRS LP 2028 ITRS HP 2028

LP HP

LP HP

LPa HP

LPa HPa LP HP

Lg (nm)

EOT (nm)

Vdd (V)

SS (mV/dec)

Ioff (μA/μm)

Ion (μA/μm)

Ion/Ioff

Cg (fF/μm)

τ (ps)

PDP (fJ/μm)

10.0

0.54

0.72

55

0.54 0.56 0.49

0.72 0.74 0.69

8.5 8.8 6.4

0.49 0.54 0.43

0.69 0.72 0.65

6.4 6.7 5.0

0.43 0.47 0.41

0.65 0.68 0.64

5.0

0.41

0.64

5.9 5.1

0.41 0.41

0.64 0.64

1750 2912 461 1450 1325 2941 395 1330 560 2536 334 1100 152 655 341 2030 295 900

8.75 × 107 2.91 × 104 2.31 × 107 1.45 × 104 6.63 × 107 2.94 × 104 1.98 × 107 1.33 × 104 1.40× 107 2.54× 104 8.35 × 106 1.10× 104 3.04 × 106 6.55 × 103 6.82 × 106 2.03 × 104 5.90 × 106 9.00 × 103

0.183

10.1 9.7 8.5

2 × 10−5 0.1 2 × 10−5 0.1 2 × 10−5 0.1 2 × 10−5 0.1 4 × 10−5 0.1 4 × 10−5 0.1 5 × 10−5 0.1 5 × 10−5 0.1 5 × 10−5 0.1

0.075 0.045 1.562 0.475 0.071 0.032 1.555 0.471 0.089 0.027 1.420 0.445 0.253 0.059 0.101 0.017 1.497 0.427

0.137 0.124 0.52 0.51 0.050 0.072 0.42 0.45 0.032 0.063 0.31 0.33 0.052 0.053 0.023 0.032 0.28 0.24

63

74 96

113 113 77

1.00 0.93 0.136 0.89 0.87 0.077 0.105 0.73 0.72 0.060 0.060 0.054 0.69 0.60

a EOT, equivalent oxide thickness; SS, subthreshold swing; Vdd, supply voltage; Cg, intrinsic gate capacitance; τ, delay time; PDP, power dissipation; LPa and HPa, data for the optimal LP and HP devices at Ne = 1013 cm−2, which are given only when Ne = 5 × 1013 cm−2 is not the optimal choice.

other two higher doping cases as shown in Figure 4b. With Ioff fixed at 2 × 10−5 μA/μm according to the ITRS LP requirement, Ion of the LP device is 540, 1750, and 1238 μA/μm, respectively, at Ne = 1013, 5 × 1013, and 1014 cm−2, all fulfilling the LP application target (461 μA/μm) for the 2022 horizon. For the

transport but also the tunneling transport takes place in the 10 nm ML arsenene MOSFET because the latter is responsible for the steep sub-kT/q switching characteristics. The maximum on-current is greatly suppressed when the source and drain concentration is 1013 cm−2 compared with the 2195


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Figure 5. ML arsenene DG MOSFET with Lg = 5 nm. (a) Schematic of an arsenene DG MOSFET with symmetric UL structures. (b) Optimal transfer characteristics without UL (blue lines with stars) and with UL = 2 nm (red lines with circles). Position resolved LDOS in the channel region (c,d) without and (e,f) with the UL structures. c and e are for the LP off-state, and d and f are for the LP on-state. The white solid line represents the Fermi level at the source or drain. Illustrated in c as an example, red dashed arrows represent the thermionic and tunneling electron transports, and ΦB is the effective barrier height.

HP device on-current is almost undegraded (2536 μA/μm). However, the LP device on-current is degraded dramatically to 50 μA/μm and no longer fulfills the ITRS LP requirement (330 μA/μm) for the 6.4 nm transistor. By adopting a lower Ne = 1013 cm−2, the SS can be improved to 74 mV/dec, with significantly improved LP device on-current of 560 μA/μm, fulfilling the ITRS LP requirement (Figure S3a and Table 2). It is interesting to explore the potential limit of the ML arsenene MOSFETs beyond the roadmap by further decreasing the gate length to 5 nm. EOT and Vdd here are the adapted values of the smallest 5.9 nm LP node as requested by the ITRS 2013 for the 2028 horizon. The optimal Ne is 1013 cm−2 for both the 5 nm HP and LP devices without UL (see Figure S2a and Table S1). The calculated transfer characteristic at optimal Ne is shown in Figure 5b, and the SS is increased to 113 mV/dec due to the increased short channel effect. Therefore, a large |Vg(off)−Vth| of 0.48 V is needed in order to achieve the ITRS LP off-current of 5× 10−5 μA/μm, which inevitably limits the overdrive voltage | Vg(on) − Vth|, and hence lowers the on-current or the device performance. The LP on-current is only of 152 μA/μm, unable to satisfy the ITRS requirement (295 μA/μm). The LDOS for the LP off- and on-states also confirm this point, as shown in Figure 5c and d, respectively. A large barrier height of 0.70 V is needed to achieve the specified Ioff for the LP application, and this leads to a high barrier of 0.24 V at the on-state with fixed Vdd and thus a degraded Ion. For the HP application, the on-current is of 655 μA/μm, smaller than the ITRS required 900 μA/μm. Unlike the LP situation limited by the SS, the HP on-current is mainly restricted by the low maximum on-current induced by the insufficient doping in the source and drain (Figure 5b). To suppress the short-channel effect, symmetric UL structures (schematically in Figure 5a) are introduced in the 5 nm node. UL structures increase the effective channel length and reduce the source/drain-channel coupling, thereby significantly lowering tunneling leakage current and the SS. Taking the LP device (at

HP application, Ioff is fixed at 0.1 μA/μm, and Ion of the HP device is 559, 2912, and 2033 μA/μm, respectively, at Ne = 1013, 5 × 1013, and 1014 cm−2. The latter two Ion are significantly larger than the ITRS required 1450 μA/μm for the 2021 horizon. In terms of the LP and HP on-state currents, Ne of 5 × 1013 cm−2 is optimal for the 10 nm node, and it is also generally the optimal electron doping concentration in all our investigated MOSFETs except the 5 nm HP and LP node and 6.4 nm LP node without UL (more details are discussed and provided in Supporting Information, Figures S2 and S3 and Table S1). Therefore, in the following context, the data and analyses are given at Ne = 5 × 1013 cm−2 unless otherwise specified. To reveal the gate modulation mechanism, the position resolved local density of states (LDOS) at Vg = −0.8, −0.4, and 0 V are given in Figure 4c−e, respectively. The effective barrier height ΦB is 0.45 V at Vg = −0.8 V (subthreshold region), significantly suppressing the thermionic current. As Vg increases, ΦB is greatly reduced and becomes 0.14 V at Vg = −0.4 V and zero at Vg = 0 V (superthreshold region), which is more clearly illustrated from their conduction band profiles summarized in Figure 4f. Therefore, the current is logarithmically increased to saturation as Vg increases. The gate modulation effect can also be reflected from the transmission eigenchannels of the device at E = Vds/2 and k = (1/3, 0) as shown in Figure 4g. The transmission eigenvalue increases dramatically from 1.08 × 10−8 at Vg= −0.8 V to 3.64 × 10−3 and 0.38 at Vg= −0.4 and 0 V. Correspondingly, the incoming electron wave function is forbidden to pass through the channel at Vg = −0.8 V, partially passes through at Vg = −0.4 V, and reaches the drain region at Vg = 0 V. As the gate length is decreased to 8.5 nm, the performance of the ML arsenene n-MOSFET keeps almost as good as that at the 10 nm node case with slightly higher SS of 63 mV/dec and almost unchanged Ion of 1325 (2941) μA/μm for the LP (HP) application (Table 2). When Lg shrinks to 6.4 nm, the SS is further increased to 96 mV/dec at Ne = 5 × 1013 cm−2, and the 2196


Article

Chemistry of Materials optimal Ne = 5 × 1013 cm−2) as an example, a significantly lower barrier height of 0.42 V is enough to realize the LP requirement of Ioff (Figure 5e) due to the effectively increased barrier width, and the corresponding barrier height at the on-state vanishes (Figure 5f). The SS is improved to 77 mV/dec, and the oncurrent for the LP and HP applications is significantly improved to 341 and 2030 μA/μm, respectively, exceeding the respective ITRS required 295 and 900 μA/μm. Therefore, with the assistance of UL structures, the ML arsenene MOSFET can be a perfect candidate for both the LP and HP applications even beyond the ITRS. We benchmark the calculated optimal Ion versus Lg for the ML arsenene LP and HP DG MOSFETs against those for ML MoS2 DG Schottky barrier FETs (SBFETs) with Ti electrode78 at the ab initio level and the ITRS requirements in Figure 6. In terms of an obvious advantage of large Ion, both the ML arsenene LP and HP DG MOSFETs outperform the ML MoS2 SBFETs at all the sub-10 nm scales.

μm), our devices are found to cost less switching energy (0.023− 0.137 fJ/μm) during the fast switching. The field effect mobility for the electron conduction can be extracted from the peak transconductance value of n-MOSFETs by gm = μnCOX(W/L)Vds, where gm is the transconductance, μn is the field effect electron mobility, W and L are the channel width and length, respectively, and Cox = εSiO2/EOT (εSiO2 is the dielectric constant for SiO2). The calculated field effect electron mobility is 27.8, 23.2, and 21.2 cm2/V·s for the 5-, 8.5-, and 10 nm ML arsenene MOSFETs, respectively. With 2 nm UL structures, the electron mobility of the 5 nm ML arsenene MOSFET is decreased to 13.7 cm2/V·s. The extracted field effect mobilities are in good agreement with our previously predicted intrinsic acoustic phonon-limited electron mobilities of 21 cm2/V·s. The Id-Vg curves of a 5 nm ML antimonene MOSFET at different Ne with or without UL structures are provided in Figure S4, exhibiting similar characteristics to those of their arsenene counterparts. The performance of the 5 nm ML antimonene MOSFETs are summarized in Table S2, which is comparable to the arsenene ones. Because ML antimonene shares similar electronic properties with ML arsenene, ML antimonene DG nMOSFETs are expected to satisfy both the LP and HP requirements at the sub-10 nm scale as well. In our MOSFET simulations, a degenerate doping of 5 × 1013 cm−2 is adopted to ensure Ohmic barrier free source/drainchannel contacts. However, in practice the existing state-of-theart doping strategy is not applicable in 2D material FETs because their atomically thin nature makes doping challenging and usually suffering from stability issues. Owing to the lack of a proper and sustainable doping strategy in 2D material devices, low or high work function metal electrodes are generally used to inject electrons or holes into the respective bands of 2D materials. Such metal−semiconductor contacts are often associated with a formation of a finite Schottky barrier, which induces a large contact resistance and decreases the carrier injection efficiency. Apparently, the performance of SBFETs is limited by the difficulties in making optimized Ohmic metal contacts. Unfortunately, due to the Fermi level pinning, it is quite challenging to realize a vanishing Schottky barrier in SBFETs. In this circumstance, a “seamless” contact between metallic electrode and 2D semiconducting channel is particularly expected to improve the contact quality. The seamless contacts between metallic 1T-MoS2/semiconducting 2H-MoS280 and metallic 1T′-MoTe2/semiconducting 2H-MoTe281 have been fabricated by using phase engineering. The lowest ever reported contact resistance of 0.2 kΩ·μm is produced in MoS2 FETs, and substantially decreased energy barrier height from 200 to 10 meV is observed in MoTe2 FETs.80,81 However, 1T-MoS2 is thermodynamically unfavorable and usually stabilized by electron donation,80,82−87 which has been observed to gradually transform to 2H phase at room temperature.88 Although 1T′MoTe2 is stable up to 300°, as fabricated by laser-induced phase transition, a thinning effect was observed after laser irradiation, indicating the existence of laser-induced structure destruction.81 In practice, as tri- and higher layer arsenene and bi- and higher layer antimonene are metallic verified by the DFT calculations,24 they can be directly used to “natively” bond with the semiconducting ML arsenene or antimonene and form a naturally seamless contact. Therefore, a relatively low contact resistance can be easily achieved in MOSFETs based on ML arsenene and antimonene.

Figure 6. Optimal on-current versus the gate length for the ML arsenene (red and orange), antimonene (cyan and magenta), and MoS2 (purple and green) DG n-MOSFETs, and ML MoS2 SBFETs with Ti electrodes78 (blue) in the (a) LP and (b) HP applications. Black dashed lines represent the ITRS requirements. MoS2−Cao90(Liu91)-SE and arsenene (antimonene)-SE89 represent the values obtained by the SE-NEGF methods (dashed line with open symbols). Other values: DFT-NEGF method (solid line with solid symbols).

The intrinsic gate capacitance Cg and delay time τ are another two major device figures of merit, and the latter directly reflects the ability to handle rapid operation. The gate capacitance is calculated by Cg =

∂Q ch ∂Vg

, where Qch is the total charge of the

channel. The gate capacitance is 0.054−0.183 fF/μm, generally smaller than the ITRS values by 1 order of magnitude (Table 2), partly because of the presumption of ideal gates. The calculated small Cg is in accordance with the previous calculations for the ML MoS278 and silicene nanomesh FETs,79 where Cg is about 0.07−0.26 fF/μm. The calculated delay time τ =

CgVdd Ion

is 0.071−

0.253/0.017−0.059 (LP/HP) ps, generally smaller than the ITRS requirements of 1.420−1.562/0.427−0.475 (LP/HP) ps due to the small Cg, indicating the ability of fast switching. Power consumption is another major concern for MOSFETs in very large-scale integration applications. We estimate the power dissipation (PDP) per width of the ML arsenene MOSFETs by the equation PDP = (Qon − Qoff)Vds/W as listed in Table 2, where Qon and Qoff are the total charges of the channel in the on- and off-states, respectively, and W is the channel width. Generally, it costs more switching energy as the channel length increases. Compared with the ITRS requirements (0.24−0.52 fJ/ 2197



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During the preparation of this manuscript, we were aware of a work of Pizzi et al.,89 which predicts the transport properties of the ML arsenene and antimonene DG MOSFETs based on the semiempirical (SE) method. Compared with our full treatment of electron−phonon interaction, they overestimated the electron/hole mobilities for ML arsenene and antimonene to 630/1737 and 635/1700 cm2/V·s, respectively, based on the SE deformation potential method without considering the ZA phonons, which are several to dozens of times higher than our ab initio values (21/66 cm2/V·s and 150/510 cm2/V·s for arsenene and antimonene, respectively). The same overestimation of the carrier mobility by the deformation potential method 43 compared with the full treatment of electron−phonon interaction42,44 is also found in silicene, where the carrier mobilities predicted by the former and latter are 105 and 1200− 2100 cm2/V·s, respectively, at room temperature. Compared with our accurate ab initio method, the SE approach has overestimated the on-state currents of the ML arsenene and antimonene DG MOSFETs by a factor of 1.5−2.5 (Figure 6b) at 5 nm < Lg < 7 nm. The same overestimation of the on-state current by the SE method also persists for the ML MoS2 FETs (Figure 6b)90,91 if the performance of a ML MoS2 DG SBFET with Ti electrode approaches that of a MoS2 DG MOSFET (with degenerately doped version of the channel as electrodes).78 HP and LP devices are equally important in ITRS, but they only reveal the suitability of the ML arsenene and antimonene MOSFETs for the ITRS HP application, whereas according to our calculations, the ML arsenene and antimonene MOSFETs are suitable for both the ITRS HP and LP applications. Finally, they found that the smaller the doping concentration the better are the SS and performance. However, we find that it is not the case and that often a medium doping concentration is favored. The above differences fully show the necessity of the accurate first-principles calculations against the SE ones in the transport property prediction of the ML arsenene and antimonene MOSFETs. We are also aware of a breakthrough that 1 nm-gate-length ML and few layer MoS2 transistors using a single-walled carbon nanotube as the gate electrode have been fabricated and exhibit excellent switching characteristics with a SS of ∼65 mV/dec and a maximum on/off current ratio of 106.92 This work confirms the idea of enabling Moore’s law down to 10 nm by using 2D materials and will stimulate the realization of sub-10 nm ML arsenene and antimonene MOSFETs proposed herein because they even appear to outperform ML MoS2 transistors.

Article

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.6b04909. Exciton wave function for ML arsenene; transfer characteristics of the 5-, 6.4-, and 8.5-nm ML arsenene DG MOSFETs for different Ne; transfer characteristics of 5 nm ML antimonene DG MOSFETs at Ne = 1013 and 5 × 1013 cm−2; summary of the performances of the ML arsenene DG n-MOSFETs with and without UL structures at different Ne and the ITRS 2013 requirements for the HP and LP devices of the next decades; and ballistic performance limits of the 5 nm ML antimonene DG nMOSFETs (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*(J.S.) E-mail: [email protected]. * (J.L.) E-mail: [email protected]. ORCID

Yangyang Wang: 0000-0003-3992-3796 Ruge Quhe: 0000-0001-8991-8640 Han Zhang: 0000-0002-1483-5899 Author Contributions

Y.W., P.H., M.Y., and R.Q. contributed equally to this work. J.L. conceived the idea. Y.W. performed the device transport simulations. M.Y. calculated the carrier mobilities. P.H. and R.Q. performed the quasi-particle and optical band gap calculations. The data analyses were performed by Y.W., M.Y., and P.H. Y.P., H. Zhang, H. Zhong, and J.S. helped with discussions. This manuscript was written by Y.W., M.Y., P.H., and J.L. All authors reviewed this manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (No. 11274016/11474012/11674005/ 11274233) and the National Basic Research Program of China (No. 2013CB932604/2012CB619304/2016YFA0301300/ 2016YFB0700600).

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CONCLUSION On the basis of ab initio many-body Green’s function approach within the GW approximation, we predict the fundamental band gaps of ML arsenene and antimonene to be 2.47 and 2.38 eV, respectively. The calculated optical absorption/photoluminescence band gaps of ML arsenene and antimonene from the GWBSE approach are 2.5/1.6 and 2.3/1.5 eV, respectively, with a large exciton binding energy of 0.9 and 0.8 eV, respectively. Accurate treatment of electron−phonon coupling gives low and moderate carrier mobilities for ML arsenene and antimonene, respectively. Ab initio quantum transport simulations demonstrate that the simulated sub-10 nm arsenene and antimonene DG MOSFETs can satisfy both the LP and HP requirements for all the studied nodes, down to 5 nm. Our work suggests that ML arsenene and antimonene are promising candidates for nanoscale optoelectronic and electronic devices.

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