Monolayer Bismuthene-Metal Contacts: A Theoretical Study - ACS

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Monolayer Bismuthene-Metal Contacts: a Theoretical Study Ying Guo, Feng Pan, Meng Ye, Xiaotian Sun, Yangyang Wang, Jingzhen Li, Xiuying Zhang, Han Zhang, Yuanyuan Pan, Zhigang Song, Jinbo Yang, and Jing Lu ACS Appl. Mater. Interfaces, Just Accepted Manuscript • Publication Date (Web): 09 Jun 2017 Downloaded from http://pubs.acs.org on June 11, 2017

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ACS Applied Materials & Interfaces

Monolayer Bismuthene-Metal Contacts：：a Theoretical Study Ying Guo1,2 *, Feng Pan1, Meng Ye2, Xiaotian Sun5, Yangyang Wang4*, Jingzhen Li2, Xiuying Zhang2, Han Zhang2, Yuanyuan Pan2, Zhigang Song2, Jinbo Yang2,3, Jing Lu2,3 * 1

School of Physics and Telecommunication Engineering, Shaanxi Key Laboratory of Catalysis，Shaanxi University of Technology, Hanzhong 723001, P. R. China 2

State Key Laboratory of Mesoscopic Physics and Department of Physics, Peking University, Beijing 100871, P. R. China

3 4

Collaborative Innovation Center of Quantum Matter, Beijing 100871, P. R. China

Nanophotonics and Optoelectronics Research Center, Qian Xuesen Laboratory of Space Technology, China Academy of Space Technology, Beijing 100094, P. R. China

5

College of Chemistry and Chemical Engineering, Luoyang Normal University, Luoyang 471 022, P. R. China *

Corresponding author: [email protected], [email protected], [email protected] ABSTRACT

Bismuthene, a bismuth analogue of graphene, has a moderate band gap, high carrier mobility, topological nontriviality, high stability at room temperature, and easy transferability, and is very attractive for electronics, optronics, and spintronics. The electrical contact plays a critical role in an actual device. The interfacial properties of monolayer (ML) bismuthene in contact with the metal electrodes spanning a wide work function range in a field effect transistor configuration are systematically studied for the first time by using both first-principles electronic structure calculations and quantum transport simulations. ML bismuthene always undergoes a metallization upon contact with the six metal electrodes owing to a strong interaction. According to the quantum transport simulations, apparent metal induced gap states are formed in the semiconductor-metal interface and give rise to a strong Fermi level pinning. As a result, ML bismuthene forms n-type Schottky contact with Ir/Ag/Ti electrodes with electron Schottky barrier heights of 0.17, 0.22, and 0.25 eV, respectively, and p-type Schottky contact with Pt/Al/Au electrodes with hole Schottky barrier heights of 0.09, 0.16, and 0.38 eV, respectively. The effective channel length of the ML bismuthene transistors is also significantly reduced by the metal induced gap states (MIGS). However, the MIGS are eliminated, and the effective channel length is increased when ML graphene is used as electrode, accompanied by a small hole SBH of 0.06 eV (quasi Ohmic contact). Hence, an insight is provided into the interfacial properties of the ML bismuthene-metal composite systems, and a guidance is provided for the choice of metal electrodes in ML bismuthene devices.

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Keywords: Bismuthene, Metal electrode, Interfacial properties, Schottky barrier, Density functional theory, Quantum transport simulation

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1. Introduction Two-dimensional (2D) atomic layer materials have the potential for alternative channel materials of next-generation transistors, because they have a high controllability by the gate, few traps on the interface of the semiconductor-dielectric, and a high degree of vertical scaling

1-3

. Although 2D group-IV-enes (include graphene 4, silicene

stanene

9-10

5-7

, germanene8, and

) have been synthesized, the zero or small band gap limits its application in the

effective field effect transistors (FETs) at room temperature. On the other hand, 2D 11-12

group-V-enes 17-25

(including phosphorene

13-14

, arsenene

15

, antimonene

16

, and bismuthene

), a new family of 2D atomic layer materials, exhibit a wide range band gap (0-2.62 eV)

and thereby is more suitable for FETs. Monolayer (ML) or multilayer phosphorene FETs have been successfully fabricated with a tunable band gap and orthorhombic structure in early 2014 26

. However, the practical applications of phosphorene are limited by the instability in air.

Multilayer arsenene nanoribbons

27

and multilayer and even ML antimonene

28

have been

successfully synthesized. Antimonene is stable in the ambient condition. In addition to the common layer-dependent band gap from 0 (more than two layers) to 0.54 eV (ML)

22-23, 29-30

,

bismuthene has several advantages: (1) A high carrier mobility from 300 (ML) to 5.7 × 106 cm2 /V·s (in bulk) 31. (2) It is a topological insulator and the topology is independent of the layer number

30, 32-34

. (3) Functionalized bismuthene (namely bismuthane) remains a

topological insulator and has the largest bulk band gap among the known topological insulators

35-38

. (4) Stability at room temperature 17. (5) Easy transferability from the original

epitaxial substrate to another substrate and the transferred bismuth films kept structural, electrical, optical and properties comparable to the as grown epitaxial films 31. In an actual 2D device, 2D materials typically have to contact with metal electrodes. Searching for a low-resistance metal contact is the biggest challenge for the FETs, as low-resistance metal contact is an impact factor of the current flow in the FETs channel

2, 39

.

In the interfacial of metals and semiconductors, Schottky barrier is often formed, which would decrease the injection efficiency of electron or hole and thus degrade the performance of the device. Hence, electrical contact plays a role as important as the semiconductor itself in an actual 2D device. Unfortunately, the Schottky barrier height (SBH) is not simply 3



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determined by the difference between the work function of a metal and the conduction band minimum (CBM) or the valence band maximum (VBM) of semiconducting 2D materials due the complex Fermi level pinning. A first principles energy band calculation and often a quantum transport simulation are needed to address the complex Fermi level pinning issue in the metal-semiconductor interface so as to determine the reliable SBH (the difference between the work function of a metal and the CBM or the VBM of semiconducting 2D materials often gives artificial Ohmic contact). The interfacial properties of graphene, silicene, germanene, stanene, phosphorene and metal contacts have been intensively investigated

5, 7-8, 10, 40-44

.

However, to our knowledge, the interfacial properties of ML bismuthene and metal contact have not been reported. In this article, we systematically study for the first time the contact properties of hexagonal ML bismuthene (we use ‘bismuthene’ to represent ‘ML bismuthene’ in the following unless otherwise specified) and the metal electrodes covering a wide work function range (Al, Ti, Ag, Au, Ir, Pt) in a FETs configuration by using first principles energy band calculation and quantum transport simulation. The Au, Al, Ag, and Ir electrodes preserve the hexagonal buckled structure of bismuthene, while the Pt and Ti electrodes distort it. Bismuthene undergoes a metallization on the six metal electrodes due to a formation of covalent bond between them. The quantum transport simulations based on a two-probe model reveal that owing to the strong Fermi level pinning induced by the metal induced gap states (MIGs), no lateral Ohmic contact is present in our device simulation although the difference between the work functions of several metals (or metal electrodes) and the CBM or the VBM of bismuthene points to Ohmic contact. Instead, bismuthene forms n-type lateral Schottky contact with Ag, Ti, and Ir electrodes and p-type lateral Schottky contact with Al, Au, and Pt electrodes. On the other hand, by contact with ML graphene, a p-type lateral Schottky barrier with a small hole SBH of 0.06 eV (quasi Ohmic contact) is formed, the MIGS are eliminated, and there is no Fermi level pinning in the interface. Our study not only presents an insight into the bismuthene-metal interfaces but also helps in bismuthene based device design.

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2. Computational methods Bismuthene with hexagonal structure is used, and the previous calculations demonstrate that this phase and washboard phase have the lowest energy

22, 45

. Six commonly used as

contact metals Al, Ag, Au, Ti, Ir, and Pt are considered, whose work function varies from 4.11 to 5.61 eV. A slab model consisting of six atomic layers is chosen to imitate the metal substrates, and the lattice constant of the metals is adapted that of bismuthene. The mismatches of lattice constant are indicated in Table 1, ranging from 0.21 to 3.43 %. Bismuthene mainly interacts with the several top layers’ metal atoms, and therefore the atomic positions of the top five layers of metal are relaxed but the bottom layer is kept fixed. A vacuum buffer space more than 15 Å along the z-axis is chosen to avoid false interaction between the periodic images. The geometry optimization and electronic structure calculations are performed in the Vienna ab initio simulation package (VASP)

46-47

by using the plane-wave pseudopotential

formulation within the framework of density functional theory (DFT). The interaction term of electron-ion is described by the projector-augmented-wave (PAW) potential, and the kinetic energy cutoff of plane wave is 400 eV

48

. The atomic coordinates are fully relaxed, the

convergence with the force on each atom is underneath 0.001 eV/Å and the energy on each atom within 1 × 10-6 eV. The Brillouin integration is sampled with 9×9×1 and 24×24×1 k-point Monk-horst meshes in the geometry optimization and energy band calculation, respectively 49. We add a semi-empirical dispersion potential term (Grimme's DFT-D3) in the conventional Kohn-Sham DFT energy 50-51. Because the slab is asymmetric in the z direction, we considered a dipole correction to remove the fake interaction in the compounds systems 52. Bi is a heavy element, and thus the spin-orbit coupling (SOC) effect is explicitly considered in the energy band structure calculations. The calculation of total electron density and the Mulliken population analysis (charge transfer)

53

are performed by using CASTEP code by

using ultrasoft pseudopotential plane wave method 54-55, and the kinetic energy cutoff of plane wave is 400 eV. The bismuthene transistor is simulated by a two-probe model, with the most stable 5



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bismuthene-metal interfaces as the electrodes and the pure bismuthene as the channel (about 50 Å along the transport direction). The left electrode and right electrode are semi-infinite. The FET’s transport properties are calculated by the DFT coupled with the nonequilibrium Green's function (NEGF) method, as implemented in the ATK 2016 package. The Single- ζ Polarized (SZP) basis set by the FHI pseudopotentials is used. The temperature is set at 300 K.

The boundaries of the vertical direction to the interface is the Neumann condition, therefore to ensure the charge neutrality in the source and the drain region the interfaces of the electrodes and the central region is Dirichlet boundary condition. The irreducible Brillouin zone both are sampled with 50×1×50 k-point Monk-horst meshes in for central region and electrodes of FET. The generalized gradient approximation (GGA) of the Perdew Burke Ernzerh (PBE) form to the exchange and correlation functional is employed through this paper. The transmission parameter Tk(E) (k is a reciprocal lattice vector point along a parallel direction (orthogonal to the transmission direction) in the irreducible Brillouin zone (IBZ)) is obtained from the retarded Green’s functions: Tk(E)=Tr [Gk(E)ΓLk(E)Gk†(E)ΓRk(E) ] where

Gk(E) (Gk†(E))

is

the

retarded

(advanced)

(1) Green

Function,

ΓkL(R)(E) = i(ΣkL(R)(E) - Σk†L(R)(E)) describes the level broadening due to left electrode/right electrodes expressed in terms of the electrode self-energies ΣkL(R)(E), which describe the influence of the electrodes on the scattering region. The transmission parameter at a given energy T(E) is averaged over 100 kx-points perpendicular to the transport direction in the IBZ.

3. Results and discussion Geometry and stability of the bismuthene-metal interfacial systems Bismuthene is a kind of buckled 2D hexagonal structure with lattice constant of a = 4.36 Å and Bi-Bi bond length of 3.05 Å. The top (upper panel) and side views (lower panel) of the free-standing bismuthene are shown in Figure 1(a). The rhomboid stands for the primitive cell and the buckling height is marked in the lower panel as ∆ = 1.73 Å. This buckled honeycomb structure of bismuthene helps stabilize the layered structure, similar to silicene, germanene, stanene, and blue phosphorene. However, the electronic properties of bismuthene are 6


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significantly different from them. In semimetallic silicene, germanene, and stanene, the electron densities of the valence-band top and conduction-band bottom consist of π-type bonding states. In contrast, the electronic properties of bismuth atom (6s26p2) in bismuthene are similar to arsenene and antimonene. Three σ-bonding orbitals are formed and there is a lone pair of electrons, which cannot form π-type bonding states. Consequently, bismuthene owns a buckled rather than planar structure. The energy band structure of bismuthene without inclusion of the spin-orbit coupling (SOC) is shown in Figure 1(b). It is a semiconductor with a direct band gap of Eg = 0.54 eV and a conical-like structure at the Γ point. When the SOC is considered, the degenerate bands on the top of the valence band at the Γ point have a splitting of Rashba-type and generate an indirect band gap (Figure 1(c)) of Eg = 0.47 eV, which is in close agreement with the previous result 56. In light of the small difference in the band gap (0.07 eV) and the limitation of the computational resource, the SOC is not taken into consideration in the subsequent quantum transport simulations. Three different initial configurations of bismuthene are considered: Bi atoms are on the top surface site, the hollow fcc surface site, and the hollow hcp surface site. After relaxation, the obtained most stable configuration of bismuthene on the six metal substrates are shown in Figure 2. The hexagonal structure of bismuthene on the Ag, Au, Al, and Ir substrates is kept very well even though bismuth atoms in the superlattice commonly have more than two different heights (Figure 2a-2d and Figure 3a-3d). The buckling heights here are defined as the vertical distance between the top and bottom atoms layer of bismuthene and are 1.78, 1.81, 1.83, and 1.94 Å on the Ag, Au, Al, and Ir substrates, respectively, which are all higher than that of free-standing bismuthene (∆= 1.73 Å). In contrast, the hexagonal structure of bismuthene on the Pt substrate is distorted (Figure 2e lower panel and Figure 3e) with a larger buckled height of 2.43 Å. In the bismuthene-Ti contact, bismuth atoms are almost flat except for two Bi atoms in the supercell located exactly on the top site of metal substrates, resulting in a much higher ∆= 2.93 Å (Figure 2f and Figure 3f). As for the metal surfaces, the topmost layer of all the metals is no longer flat, with buckling heights of 0.012 (Ir), 0.013 (Al), 0.013 (Au), 0.094 (Ag), 0.178 (Pt), and 0.837 Å (Ti) (Table 1), respectively. 7



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We set the initial vertical distance (d0) from the bottom bismuthene atom layer to the topmost metal atom layer to be 3 Å. After relaxation, d0 varies from 1.76 to 2.72 Å, as shown in Table 1. The dmin is the minimum atom-to-atom distance between the metal and Bi atoms and is 2.94 (Al), 3.09 (Ag), 2.84 (Au), 2.60 (Ti), 2.69 (Pt), and 2.69 (Ir), respectively. rSn + rM is the sum of the single-bond covalent radii of bismuthene and metal atoms and is 2.77 (Al), 2.79 (Ag), 2.75 (Au), 2.87 (Ti), 2.74 (Pt), and 2.73 (Ir), respectively. Comparing the values of dmin with rSn + rM, we find that a covalent bond is formed between bismuthene and the metals. The dmin values of bismuthene-Ti/Pt/Ir are shorter than that of the rSn + rM, suggestive of a stronger binding, while those of bismuthene-Al/Ag/Au are longer than that of the rSn + rM, suggestive of a weaker binding. The binding energy of the bismuthene-metal compound system is defined as Eb: Eb = (EBi + EM – EBi-M) / NBi

(2)

where NBi is the number of Bi atoms per supercell, and EBi, EM, and EBi-M are the relaxed energies of free-standing bismuthene, pure metal substrate, and compound system per supercell, respectively. The calculations of Eb (eV/Bi atom) for different compound systems in the order of Al (0.76) < Ag (1.09) < Au (1.16) < Ti (1.83) < Ir (1.92) < Pt (1.98). According to the binding energy, bismuthene bonds relatively weakly to the Al, Ag, and Au substrates with larger dmin (2.94, 3.09, 2.84 Å) and d0 (2.72, 2.61, 2.60 Å) than to the Ti, Pt, and Ir substrates with smaller dmin (2.60, 2.69, 2.69 Å) and d0 (1.76, 2.17, 2.28 Å). The different intensities of Eb for the bismuthene-metal composite systems mainly produced by the physical properties of different metals. Al atom (3s2p1) with only one unpaired electron for opening p-shell. Ag atom (4d105s1) and Au atom (5d106s1) also have only one unpaired electron for half-filled s-orbital. Therefore, Eb’s of these three composite systems are weak. Ti atom (3d24s2) and Ir atom (5d76s2) have two and three unpaired electrons for opening d-shell, respectively; Pt atom (5d96s1) has two unpaired electrons for opening d-shell and half-filled s-orbital. Therefore, Eb’s of these three composite systems are strong due to the more numbers of unpaired electrons the metals atoms have. The calculated binding energies for graphene/silicene/germanene/stanene/bismuthene on the Al, Ag, Au, and Pt substrates are 0.027/0.35/0.39/0.72/0.76 (Al substrate), 0.043/0.41/0.34/0.84/1.09 (Ag 8


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substrate), 0.03/0.63/0.47/1.13/1.16 (Au substrate), and 0.038/1.74/1.17/1.56/1.98 (Pt substrate) eV per C/Si/Ge/Sn/Bi atom

7-8, 10, 44, 57-58

, respectively. The intensity of the binding

energy generally increases mostly in the order of Eb (graphene) < Eb (germanene) < Eb (silicene) < Eb (stanene) < Eb (bismuthene). The stronger binding energy between bismuthene and metal compared with group-IV-enes and metal is ascribed to the fact that bismuthene has two electrons (lone pair electron) to bond with metal while group-IV-enes only have one unpaired electron to do so. Electronic structures of the bismuthene-metal interfacial systems The total electron distributions of bismuthene on the six metal substrates in real space are shown in Figure 4. The accumulation of electrons is clear in the region between bismuthene and the metal layers, indicating formation of covalent bond between them. The degrees of electron accumulation between bismuthene and Au, Ti, Pt and Ir are higher than those between bismuthene and Ag and Al, a result consistent with the degree of the binding strength. The Mulliken population analysis (Table 1) shows that every Bi atom gets 0.17, 0.14, 0.13, 0.127, 0.117, and 0.1 electrons on Al, Au, Ti, Ag, Pt, and Ir composite systems, respectively. Hence, the bond type between bismuthene and metal is a mixed covalent bond and charge transfer interaction. Figure 5 shows the band structures of bismuthene-metal systems with inclusion of SOC, the radii of red dots represent the weight of bands contributed by the Bi atoms in the interfacial systems. When bismuthene contacts the six metals, the bands of bismuthene are strongly distorted due to a band hybridization between bismuthene and the metal substrates, another typical feature of covalent bond. The hybridization levels of bismuthene on the Al, Ag, and Au substrates are weaker than the ones on the Ti, Pt, and Ir substrates, a result consistent with the difference in the binding degrees. In particular, the Fermi level crosses all the bismuthene-derived bands, and thus bismuthene on the six metal supports has undergone a metallization. Figure 6 shows the cumulative partial density of states (PDOS) of s-, p-, and d-orbitals of free-standing bismuthene and projected Bi atoms in the bismuthene-metal composite systems. The p-orbital (red line in Figure 6) of Bi atoms dominates the states near the Fermi level of 9



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the bismuthene-metal composite systems. This feature is similar to cases of the phosphorene/germanene/stanene-metals

composite

systems

8,

10,

42

.

In

germanene/stanene-metals composite systems, the pz-orbital has more contribution than pxand py-orbitals. While in phosphorene/bismuthene-metals composite systems, the px-, py-, and pz-orbitals contribute almost equally

8, 10, 41-42

, as shown in Supplementary Figure S1.

Compared with the PDOS of free-standing bismuthene, there is exactly no band gap of bismuthene supported by metals, confirming the metallization of bismuthene on metals. Hence, bismuthene and the six metals forms a good Ohmic contact in the vertical direction The densities at the Fermi level in bismuthene-Au/Ir/Pt/Ti composite systems are larger than those of bismuthene-Ag/Al composite systems, suggestive of smaller contact resistance in the former four contacts. The distortion of honeycomb configuration bismuthene is also a significant factor to affect the energy band of bismuthene on the metal substrates. We show the band structures for bismuthene peeled from the Ag, Al, Au, Ir, Ti, and Pt surfaces in supplementary Figure S2. The hexagonal configurations of unsupported bismuthene layer are different from the Ag, Al, Au, and Ir substrates to the Pt and Ti substrates. The semiconductor property of bismuthene peeled from the Ag, Al, Ir and Au substrates is kept very well, and the band structure is similar to Figure 1 (c), and the indirect band gap is 0.47, 0.49, 0.54, and 0.47 eV, respectively, which are mostly the same as the band gap of free-standing bismuthene (0.47 eV). By contrast, bismuthene peeled from the Ti and Pt substrates loses its features of semiconductor, the band gap has vanished and the Fermi level cross the bismuthene states, the peeled bismuthene has metallic character. Quantum transport simulation of the bismuthene FETs Because all the six bismuthene-metal composite systems are metallization in the vertical direction, Schottky barriers may exist in the lateral direction of the bismuthene FETs with the metal electrodes, as shown in Figure 7. Such an interface model has been used in the MoS2-, graphdiyne-, WSe2- and phosphorene-metal contact study 42, 59-60. Work function approximation (WFA) is often used to estimate the lateral SBH of a FET, under which the electron/hole SBH ΦeW /ΦhW (list in Table 1) is determined by the energy 10


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difference between the Fermi level of the bismuthene-metal composite systems and the CBM/ VBM of the channel bismuthene. As shown in Supplementary Figure S3, under this WFA, bismuthene forms p-type Schottky contact with Ti, Ag, and Al electrodes with SBHs of ΦhW = 0.19, 0.20, and 0.26 eV, respectively, while it forms an p-type Ohmic contact with Au, Pt, and Ir electrodes since the composite system Fermi level is lower than the VBM of channel bismuthene. The difference between the work function of pure metal with the CBM/VBM of channel bismuthene gives more Ohmic contact (Supplementary Figure S3). However, under the WFA, the coupling between metallized bismuthene and channel bismuthene is ignored, and thus potential Fermi level pinning is not considered at all. Therefore, the value of SBH coming from the WFA is unreliable, and a pseudo Ohmic contact is often obtained by the WFA. A more reliable method to evaluate the SBH is to perform a quantum transport simulation based on two-probe model, where the metallized bismuthene and channel bismuthene are treated as a whole and thus the coupling of them is considered. For example, the WFA and the quantum transport simulation give a hole SBH of 0.02 and 0.26 eV

42

,

respectively, for the phosphorene FET with Ni electrode, and the latter one is in much better agreement with while the extracted experimental value of 0.35 ± 0.02 eV

61

. For another

example, the WFA gives an artificial Ohmic contact for the MoS2 FET with Sc electrode 39, while both the quantum transport simulation

39

and the experiment give a Schottky contact

with a small SBH 62. Figure 8 shows the zero-bias transmission spectra of the bismuthene FETs with Al, Au, Pt, Ag, Ti, and Ir electrodes and a channel length of about 5 nm. The hole SBH is determined from the difference between the Fermi level and the valence band top, and the electron SBH is determined from the difference between the Fermi level and the conduction band bottom. Different from the WFA, no Ohmic contact is present in the quantum transport simulation. From Figure 8, the bismuthene FET with Pt and Al electrodes have strong p-type Schottky barrier with hole SBHs of 0.09 and 0.16 eV, respectively, and bismuthene forms weak p-type or neutral contact with Au electrode with the hole SBH of 0.38 eV. While Ir, Ti, and Ag are chosen as electrodes, n-type Schottky barrier FET is formed with electron SBH ΦeT of 0.17, 0.25, and 0.22 eV, respectively. It is interesting to compare the polarity of the Schottky 11



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contact between bismuthene and phosphorene. In terms of the quantum transport simulation, Al and Au form p-type Schottky contact with bismuthene, but in terms of the quantum transport simulation

42, 63-64

and the experiment

65

, Al and Au form n-type Schottky contact

with ML phosphorene. Ti forms n-type Schottky contact with bismuthene, but it forms p-type Schottky contact with ML42 phosphorene theoretically and few layer (thicker than 2 nm) phosphorene experimentally 66. Ag forms n-type Schottky contact with both bismuthene and ML phosphorene 42. Figure 9 shows the local density of states (LDOS) in color coding of the bismuthene FETs with Al, Au, Pt, Ag, Ti, and Ir electrodes. It is found that both the electron/hole Schottky barrier height (SBH) are in accordance with those from the transmission spectra due to the flat feature of the conduction and valence bands. Such a flat feature of the conduction and valence bands of channel bismuthene implies little charge change of channel bismuthene. The band diagrams of the bismuthene FETs are shown in Supplementary Figure S4. The transport gap is a

sum of electron and hole SBH: T = ΦhT + ΦeT , and the values for Al, Ir, Ag, Pt, Ti, and Au as g

electrodes are 0.77, 0.80, 0.81, 0.82, 0.91, and 0.94 eV, respectively. The transport gap is somewhat larger than the gap (0.54 eV) from the energy band energy calculation at the GGA level (VASP). It is noteworthy that the actual transport gap is found to often be larger than the gap from the energy band energy calculation at the GGA level by a factor of about 10% due to the many body effect. For example, the calculated DFT at the GGA level for phosphorene and the measured transport gap is 0.91 and 0.99 eV, respectively 42. The actual transport gap in the bismuthene FETs is estimated to be about 0.6 eV. The present quantum transport simulation has slightly overestimated the transport gap. The lateral direction electron/hole SBHs of the bismuthene FETs obtained by the WFA and quantum transport simulations are compared in Figure 10 (a). It is found that there are big differences in the lateral electron/hole SBHs for Al, Ir, Ti, Ag, Au and Pt electrodes between the two approaches. The contact type (Ohmic or Schottky barrier) is completely different for Ir, Au and Pt electrodes, and the contact polarity is even opposite for Ti and Ag electrodes, indicative of a strong coupling or a complex Fermi level pinning between the metallized bismuthene and the intrinsic channel bismuthene. The reason lies in that under the WFA, the 12


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source/drain region (metal and bismuthene-metal composite system) and the channel semiconductor are calculated separated, and thus the coupling among them is not considered at all. In an actual device, metal electrodes often induce gap states in the channel in the case of strong adhesion, which are responsible for the Fermi level pinning. The electron SBHs of bismuthene vs the metal work function is plotted in Figure 10 (b). To coarsely determine the divergence from the Schottky-Mott model, we apply a linear fit to the data. The slope is referred to as pinning factor S. S = 1 means following the Schottky-Mott model and no Fermi level pinning, and S = 0 indicates a complete Fermi level pinning. The calculated pinning factor is 0.12 for the bismuthene-bulk metal contacts, implying a strong Fermi level pinning effect. The Fermi level pinning effect in bismuthene-bulk metals is illustrated more clearly in Figure 10 (c). Actually, the strong metal induced gap states (MIGs) are apparent in the contact interfaces in the quantum transport simulations, as shown by black double-headed arrow in Figure 9. MIGs will shorten the effective channel length, serve as source for electrons or holes and induce a Fermi level pinning. Because of a heavy covalent interaction between the six metals and bismuthene, the decay length of MIGs are 0.7 (0.7), 1.0 (1.0), 1.0 (1.2), 1.6 (1.6), 1.6 (1.8), and 2.2 (1.2) nm in the Ag, Pt, Al, Au, Ir, and Ti left (right) electrodes, respectively. The MIGs result in a reduction of 1.4, 2.0, 2.2, 3.2, 3.4, and 3.4 nm in the effective channel length with Ag, Pt, Al, Au, Ir, and Ti electrodes, respectively. Due to the strong Fermi level pinning, the smaller SBH of the bismuthene FETs is expected not to decrease much even the transport gap is reduced in a more accurate calculation. Apparently the device performance of the bismuthene FETs will be degraded by the MIGs due to a reduced effective channel length. Insertion of a BN or graphene monolayer between bismuthene and the metal electrode is expected to eliminate the MIGs and reduce the Fermi level pinning in the bismuthene-metal contact because of the weak Van der Waals interaction between BN/graphene and bismuthene 67. Using graphene itself as electrode is also expected to decrease MIGs and the Fermi level pinning because of the same cause68-70. It is interesting to check a weak coupling between bismuthene and contact. To this end, we use ML graphene as an electrode. The band structure of bismuthene is preserved very well in 13



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contact with graphene (Figures 11a and b), typical of weak Van der Waals interaction. We have a direct band of Eg = 0.58 eV and a small hole SBH (0.12 eV) in the vertical direction without the SOC (Figures 11a) and indirect band gap of Eg = 0.41 eV and p type Ohmic contact in the vertical direction with the SOC (Figures 11b). Figure 11c and 11d show the zero-bias and zero-gate voltage without inclusion of the SOC transmission spectrum and LDOS in color coding of the bismuthene FET with graphene. Electrons are transferred from channel bismuthene to electrodes when graphene is used as electrode, causing a band upward bending of channel bismuthene at the interface (illustrated in Supplementary Figure S4 (c). A strong p-type lateral Schottky barrier with a small hole SBH of 0.06 eV (quasi Ohmic contact) is formed, and the MIGS are eliminated. There should be no Fermi level pinning, and the effective channel length is increased. Apparently, 2D graphene electrode is superior to the bulk metal electrodes.

4. Conclusion In summary, we present the first comprehensive study of the interfacial properties between bismuthene and metal (Al, Ag, Au, Ir, Ti, Pt) contacts in a FET configuration by using first-principles energy band calculation and quantum transport simulation. The hexagonal buckled structure of bismuthene is preserved very well on the Au, Al, Ag, and Ir electrodes, with the buckling height is slightly changed. By contrast, on the Pt and Ti electrodes, the hexagonal buckled structure of bismuthene is distorted. Bismuthene on the metal undergoes a metallization, and the vertical direction is Ohmic contact. The quantum transport simulation based on a two-probe model shows that there is apparent metal induced gap states in the channel, which lead to the complex Fermi level pinning and absence of Ohmic contact in the lateral direction. Bismuthene forms n-type Schottky contact with Ag, Ti, and Ir electrodes and p-type Schottky contact with Al, Au, and Pt electrodes. The meal induced gap states also remarkably reduce the effective channel length of the bismuthene FETs. However, the effective channel length is increased with 2D graphene as electrode because the MIGS are eliminated. The obtained interfacial properties of the bismuthene-metal contacts are expected

to help on the selection of the metal electrodes in bismuthene devices.

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Acknowledgement This work is supported by the National Natural Science Foundation of China (Nos. 11674005, 1274016, 11474012, 11547039), the National Basic Research Program of China (Nos. 2012CB619304, 2013CB932604, 2016YFB0700600). Supporting Information The supporting information is available free of charge on the ACS Publication website at DOI: PDOS of Bi p-orbitals for bismuthene on the Ag, Al, Au, Ir, Pt, and Ti surfaces with inclusion of the SOC, respectively, energy band structures of bismuthene peeled from the stable √7× √7 Al, Ag, Au, Pt, Ir, and Ti surfaces with inclusion of the SOC, respectively, line-up of the work functions of the interfacial systems and pure metals with the electronic band of channel bismuthene with inclusion of the SOC, and schematic band diagram of the ML bismuthene FETs.

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Table 1. Calculated interfacial properties of bismuthene-metal contacts. ε is the lattice mismatch between the metals and bismuthene, d0 the vertical distance from the bottom bismuthene atom layer to the topmost metal atom layer, dmin the minimum distance of atom to atom from Bi to the metals. rBi + rM is the sum of the most recent predictions of single-bond covalent radii for Bi and metal atoms. ∆ is the vertical distance from the topmost layer to the bottom atom layer of bismuthene supported by metals, ∆M the height of buckling for the topmost metal layer of the composite systems. Eb is the binding energy (each Bi atom) needed to remove bismuthene layer from the metal substrates. Q is the Mulliken charge per Bi atom transferred from the metal surfaces to bismuthene. WM and W are the work functions for each pure metal substrate and the bismuthene-metal composite systems. ΦeW (ΦW ) is the electron (hole) Schottky barrier height (SBH) obtained from the work function approximation. ΦeT (ΦT ) is the electron (hole) SBH obtained from the transport simulation. ETg is the transport gap, define as ETg = ΦeT + ΦT . The lattice constant, the buckling height, and the work function of free-standing bismuthene are 4.36 Å, 1.73 Å, and 3.93 eV, respectively.

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Figure 1. (a) Top and side view of free-standing bismuthene. The rhomboid stands for the unit cell. (b) Band structure of bismuthene calculated without the SOC. (c) Same as (b) but with the SOC.

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Figure 2. Side and top views of the stable configuration for (√3×√3) bismuthene on the (√7×√7) (a) Ag (111), (b) Au (111), (c) Al (111), (d) Ir (111), (e) Pt (111), and (f) Ti (001) substrates, respectively. The Bi atoms in purple have an apparently longer distance to the metal surfaces than other Bi atoms (green).

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Figure 3. Side view of the geometrical structures and average electrostatic potentials (AEP) of bismuthene on the Ag (a), Au (b), Al (c), Ir (d), Pd (e), and Ti (f) substrates, respectively, and the SOC is considered. The Fermi level is at zero energy.

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Figure 4. Electron density difference of bismuthene on the six metal substrates with inclusion of the SOC.

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Figure 5. Energy band structures of bismuthene on the Ag, Au, Al, Ir, Pt, and Ti surfaces with inclusion of the SOC, respectively. Gray dots correspond to the bismuthene-metal system. Red dots correspond to the states with valid contribution from bismuthene, and the radii of the dots are proportional to the weight. The Fermi level is at zero energy.

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Figure 6. Partial density of states (PDOS) (DOS on Bi atom and orbitals) of free-standing bismuthene and bismuthene on the Ag, Al, Au, Ir, Pt, and Ti surfaces with inclusion of the SOC.

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Figure 7. Schematic cross-sectional view of a typical intrinsic bismuthene in contact with metal. B is the vertical interface between metal and underlying bismuthene, and D is the lateral interface between contacted and uncontacted bismuthene. The arrows denote the pathway (A→B→C→D→E) of electron or hole injection from the contact metal (A) to the channel bismuthene (E). Inset: a bismuthene FET.

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Figure 8. Transmission spectrum of the bismuthene FET with Al, Au, Pt, Ag, Ti, and Ir electrodes under the zero-bias and zero-gate voltage without inclusion of the SOC, and the channel length is about 5 nm. The Fermi level is at zero energy.

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Figure 9. Local density of states (LDOS) in color coding of the bismuthene FET with Pt, Al, Au, Ir, Ag, and Ti electrodes under the zero-bias and zero-gate voltage without inclusion of the SOC, and the channel length is about 5 nm. The Fermi level is at zero energy. The electron (hole) SBHs are indicated by the white double-headed arrow and the interface states are indicated by the black double-headed arrow.

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Figure 10. (a) Lateral electron and hole SBHs of the bismuthene FET with Al, Ag, Ti, Au, Ir, and Pt electrodes. The light (deep) blue and yellow rectangle present the electron and hole SBH obtained from the transport simulations and the work function approximation (WFA), respectively. The SOC is not included. (b) Comparison of the lateral electron SBHs for the bismuthene FETs against the metal work function. (c) Illustration of the Fermi level pinning in bismuthene. S is the pinning factor obtained from the Schottky−Mott rule.

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Figure 11. Band structure of bismuthene with graphene electrode calculated without the SOC (a) and with the SOC (b). Gray dots correspond to the bismuthene-metal system. Red dots correspond to the states with valid contribution from bismuthene, and the radii of the dots are proportional to the weight. (c) Transmission spectrum and (d) Local density of states (LDOS) in color coding of the bismuthene FET with graphene electrode under the zero-bias and zero-gate voltage without inclusion of the SOC. The channel length is about 5 nm, and the Fermi level is at zero energy.

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TOC

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Monolayer Bismuthene-Metal Contacts: A Theoretical Study - ACS

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