Two-Dimensional Gold Sulfide Monolayers with Direct Band Gap and

Jun 19, 2019 - It remains a pressing task to search for new two-dimensional (2D) ... and AIMD snapshots of antioxidation test for the α-Au2S monolaye...
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Letter Cite This: J. Phys. Chem. Lett. 2019, 10, 3773−3778

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Two-Dimensional Gold Sulfide Monolayers with Direct Band Gap and Ultrahigh Electron Mobility Qisheng Wu,†,‡,#,¶ Wen Wu Xu,§,‡,# Dongdong Lin,§ Jinlan Wang,*,† and Xiao Cheng Zeng*,‡ †

School of Physics, Southeast University, Nanjing 211189, P. R. China School of Physical Science and Technology, Ningbo University, Ningbo 315211, P. R. China ‡ Department of Chemistry, University of Nebraska-Lincoln, Lincoln, Nebraska 68588, United States §

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S Supporting Information *

ABSTRACT: It remains a pressing task to search for new two-dimensional (2D) semiconducting materials for future-generation electronic applications. By using density functional theory computations and global structure prediction methods, we demonstrate two new gold sulfide monolayers (2D Au2S and AuS), both exhibiting excellent electronic properties and high stabilities. All the gold sulfide monolayers are semiconductors with band gaps in the range 1.0−3.6 eV. In particular, the α-Au2S monolayer is predicted to possess a direct band gap of 1.0 eV and extremely high electron and hole mobilities of 8.45 × 104 and 0.40 × 104 cm2 V−1 S−1, respectively. The phonon dispersion calculations and ab initio molecular dynamics simulations indicate that the gold sulfide monolayers exhibit robust dynamical and thermal stabilities. Moreover, the α-Au2S monolayer appears to show strong oxidation resistibility. The novel electronic properties, coupled with structural and chemical stabilities, endow the new gold sulfide monolayers to be highly promising for future applications in nanoelectronics.

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cence.18 Extensive research efforts have been devoted to investigating various 3D Au−S compounds over recent years.19 As demonstrated previously,20,21 2D materials can possess new and novel properties not seen in their 3D counterparts. In our previous work,22 MoS2-like Au6S2 monolayer was predicted to be a semiconductor with a band gap of 1.48 eV and an electron mobility about ∼3000 cm2 V−1 s−1. These novel features of Au6S2 monolayer prompt us to seek other new 2D Au−S compounds with different stoichiometry and yet having moderate band gap and even higher carrier mobility. In this work, we report our prediction of two new semiconducting 2D materials, Au2S and AuS monolayers, through a global structural search and density functional theory (DFT) computations. The α phase of Au2S monolayer (the αAu2S monolayer) appears to have a highly desired direct band gap of 1.0 eV (based on hybrid functional HSE06 computation). Its electron mobility can reach as high as 8.45 × 104 cm2 V−2 s−1, highly desirable for electronic applications. The β-Au2S monolayer and three phases of the AuS monolayers (namely, α-, β-, and γ-AuS monolayers) are semiconductors with indirect band gaps, ranging from 1.6 to 3.6 eV. All these gold sulfide monolayers have been examined to have dynamical and thermal stabilities. Furthermore, strong oxidation resistibility of the α-Au2S monolayer has been predicted via transition state computation and ab initio molecular dynamics simulations (AIMD). Hence, the like-

ince the debut of graphene,1 two-dimensional (2D) materials have become a hot topic of frontier research2−4 particularly in view of the fact that 2D semiconducting materials can be fabricated for ultrathin channel field-effect transistors (FETs) and miniaturized devices.5 In FETs made of 2D materials, all electronic carriers are confined in two dimension and uniformly influenced by the gate voltage. As such, the leakage of charge carriers can be effectively reduced by a large extent.4 For making high-performance 2D FET devices, however, suitable band gap and high carrier mobility are essential for the 2D materials.6 Graphene exhibits very high carrier mobility due to the presence of Dirac cone, and thus is a promising candidate for FET devices.7 The low on/off ratio of graphene, however, remains an obstacle for practical applications.8 Beyond graphene, 2D transition-metal dichalcogenides (TMDs) and black phosphorus have received considerable research attention owing to their excellent electronic properties. 2D TMDs typically possess moderate band gaps, but relatively low carrier mobilities on the order of a few hundreds of cm2 V−1 S−1.9 2D black phosphorus offers highly desired electronic properties, including a moderate band gap and high carrier mobility.10 But in an oxidizing environment, 2D black phosphorus tends to degrade and results in poor performance.11 So it is still a pressing task to search for new 2D highperformance semiconductors with not only desired direct band gap and high carrier mobility but also high oxidation resistibility.12−15 Gold−sulfur (Au−S) materials have shown a wide range of applications in catalysis,16 medicine,17 and photolumines© 2019 American Chemical Society

Received: May 8, 2019 Accepted: June 19, 2019 Published: June 19, 2019 3773

DOI: 10.1021/acs.jpclett.9b01312 J. Phys. Chem. Lett. 2019, 10, 3773−3778

Letter

The Journal of Physical Chemistry Letters

Table 1. Relative Energies, Lattice Parameters, Au−S Bond Lengths, Nearest Au−Au Distances, Bader Charge Transfers from Au to S Atoms, and Electronic Band Gaps for Au2S and AuS Monolayersa phases

cohesive energy (eV/atom)

lattice parameters

α-Au2S

3.388

β-Au2S

3.387

α-AuS

3.481

β-AuS

3.391

γ-AuS

3.310

a = b = 5.74 Å c = 20.0 Å, θ = 90° a = b = 7.92 Å c = 20.0 Å, θ = 90° a = 3.54 Å, b = 6.18 Å c = 20.0 Å, θ = 90° a = 6.08 Å, b = 6.68 Å c = 20.0 Å, θ = 90° a = 8.18 Å, b = 7.16 Å c = 20.0 Å, θ = 90°

dAu−S (Å)

dAu−Au (Å)

Bader charge transfer (e)

band gaps (eV)c

2.41

2.87

0.15

1.00 (D)

2.31

2.87

0.14

3.54 (I)

2.39 (2.30)b

3.54

0.12 (0.36)b

2.06 (I)

2.33

3.04

0.13

1.61 (I)

2.31

3.58

0.13

3.02 (QD)

a Detailed geometric information can be found in Table S2. bThere are two nonequivalent Au atoms with different coordination numbers in α-AuS monolayer, resulting in two different Au−S distances and Bader charges. c“D”, “I”, and “QD” denote direct, indirect, and quasi-direct band gaps, respectively.

lihood of synthesizing stable Au2S and AuS monolayers in the laboratory is high. The CALYPSO code, based on the particle swarm optimization algorithm, has been extensively applied to perform the global structural search of various materials.23−29 Here, in our structural search, the unit cells involving no more than 16 atoms were adopted for both Au2S and AuS monolayers. Generated 2D structures were fully relaxed by using DFT method as implemented in VASP 5.4 package30 until the energy and force were converged to 10−5 eV and 0.01 eV/Å. A plane-wave cutoff energy of 500 eV and vacuum length of 15 Å were used. The products of lattice constants and k points were set to be around 40 for sampling the first Brillouin zone. Scalar relativistic projector augmented wave (PAW)31 pseudopotentials and the Perdew−Burke−Ernzerhof (PBE) functional32 were adopted. For computing the electronic and optical properties, a more accurate hybrid functional HSE06 was used.33 The van der Waals interactions were described by using the DFT-D3 scheme, which strongly influences the lattice structures of gold sulfide monolayers (see Table S1).34 Spin-polarized calculations prove that all the predicted gold sulfide monolayers have nonmagnetic ground states. QUANTUM ESPRESSO package35 was used to perform the phonon dispersion calculations for examining dynamical stabilities. AIMD simulations were carried out to evaluate thermal stabilities. Spin−orbit coupling (SOC) effects were included in our DFT calculations except for phonon dispersion calculations and AIMD simulations. More computational details can be found in our recent work.22 The global structure searches for the atomic composition of Au:S = 2:1 give rise to two lowest-lying 2D structures, namely, the α- and β-Au2S monolayers. The cohesive energy is first calculated, which is defined as Ecoh = (xEAu + ES − EAuxS)/(1 + x), where the EAu, ES, and EAuxS denote the energy of Au atom, S atom and AuxS monolayer, respectively. The calculated cohesive energies are listed in Table 1. Those cohesive energies are comparable to those of silicene (3.98 eV) and germanene (3.26 eV),36 indicating their possibility of synthesis in experiment. The α-Au2S monolayer exhibits a space group symmetry of P4/nmm (Figure 1a). In this structure, all gold atoms are in the same plane with sulfur atoms bonding with gold atoms on both sides. Each S atom is tetracoordinated with Au atoms, which form a square. The Au−Au and Au−S bond lengths are 2.87 and 2.41 Å, respectively. The β-Au2S monolayer has the same symmetry as α phase, but its

Figure 1. Top and side views of atomic structures for α-Au2S (a) and β-Au2S (b). The dashed black lines indicate primitive cells, while the dashed blue circle marks an Au4 tetrahedron with ST atom centered. Gold and red spheres represent Au and S atoms, respectively. h1 = 2.61 Å and h2 = 5.10 Å imply the heights.

geometric structure is more complex. As shown in Figure 1b, the β-Au2S monolayer has five atomic layers with a thickness of 5.10 Å. Although all S atoms are tetracoordinated with Au atoms, they can be divided into two types, denoted as SP and ST, respectively. The SP atoms lie on both sides of the β-Au2S monolayer and each forms a pyramid with four internal Au atoms. However, the ST atoms are centered in the Au4 tetrahedrons, as indicated by blue dashed circle in Figure 1b. Although different structural arrangements appear in the αAu2S and β-Au2S monolayers, they have very similar chemical bonding. As such, the two different structures are almost degenerate in energy, with a small energy difference of 1 meV/ atom (see Table 1). With the atomic composition of Au:S being 1:1, three lowest-lying 2D structures are obtained in our global structural searches, and these structures are named as α-, β-, and γ-AuS monolayer, respectively. In the α-AuS monolayer (Figure 2a), there are two types of nonequivalent Au atoms with different coordination numbers. For one type of Au atoms, each is bonded with two S atoms. For the other type of Au atoms, each is tetracoordinated with S atoms. According to the Bader charge analyses,37 the two different Au atoms transfer 0.12 and 0.36 electrons to S atoms, respectively. The ratio is exactly 1:3, and thus the two different Au atoms are denoted as AuI and AuIII, respectively. Both appear to be disproportionation from 3774

DOI: 10.1021/acs.jpclett.9b01312 J. Phys. Chem. Lett. 2019, 10, 3773−3778

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The Journal of Physical Chemistry Letters

Figure 2. Top and side views of atomic structures for α-AuS (a), β-AuS (b), and γ-AuS (c) monolayers. Dashed lines indicate primitive cells. Gold and red spheres denote Au and S atoms, respectively. h3 = 2.34 Å, h4 = 3.12 Å, and h5 = 1.48 Å indicate the heights.

two AuII states, a common feature in Au complexes.38 The βand γ-AuS monolayers (Figure 2b,c) are energetically less favorable by hundreds of meV than the α-AuS monolayer, and both have very similar structural features with each other. Each Au atom is bonded with two S atoms, forming AuI state. The S atoms are also bonded with each other in the form of strong covalent bond, as indicated by the computed electron localization function (ELF)39 (Figure S1). The computed band structures and projected density of states (PDOS) of Au2S and AuS monolayers, based on the hybrid functional (HSE06),33 are shown in Figure 3 (band

structures without SOC are given in Figure S2 for comparison). It can be seen that the α-Au2S monolayer is a semiconductor with a direct band gap of 1.0 eV, located at the Gamma point. Since the band curves near valence band maximum (VBM) and conduction band minimum (CBM) are very steep, high carrier mobilities are expected. The mobility is calculated according to the deformation potential theory,40,41 μ2D =

eℏ3C2D kBTm*md (E1)2

where e and ℏ are the electron charge and reduced Planck constant, respectively. The temperature T is chosen to be 300 K, and kB is the Boltzmann constant. m* is the effective mass in the transport direction, and md is the average effective mass. As listed in Table 2, the effective masses for both electrons and Table 2. Computed Effective Mass (m*), 2D Elastic Modulus (C2D), Absolute Value of Deformation Potential Constant (E1), and Hole and Electron Mobility (μ) for the α-Au2S Monolayer carrier

m* (me)

C2D (J m−2)

E1 (eV)

μ (×104 cm2 V−1 S−1)

electron hole

0.06 −0.10

35.59 35.59

1.62 4.32

8.45 0.40

holes are quite small. The 2D elastic modulus C2D is calculated to be 35.59 J/m2 for the α-Au2S monolayer. The absolute values of deformation potentials E1 are computed to be 1.62 and 4.32 eV for electrons and holes, respectively. The electron and hole mobilities are finally computed to be 8.45 × 104 and 0.40 × 104 cm2 V−1 s−1, respectively. The electron mobility for α-Au2S monolayer is very high due to the relatively small deformation potential, which appears to be a quadratic in the denominator of the above equation. The electron mobility is even higher than that of recently reported Bi2O2Se monolayer,6 rendering the 2D Au2S highly desirable for electronic applications. In contrast, the β-Au2S monolayer appears as an indirect semiconductor with a band gap as large as 3.54 eV (Figure 3b). As shown in Figure 4, all the α, β and γ phases of AuS monolayers show semiconducting properties, with indirect band gaps ranging from 1.60 to 3.10 eV. It is worthy of mentioning that the direct and indirect gaps (3.03 and 3.02 eV) of the γ-AuS monolayer are nearly the same, indicating that it is a quasi-direct semiconductor. For all Au2S and AuS monolayers, both Au and S contribute to the states around the VBM and CBM, suggesting the strong hybridizations between

Figure 3. Electronic band structures and projected density of states for α-Au2S (a) and β-Au2S (b) monolayers. 3775

DOI: 10.1021/acs.jpclett.9b01312 J. Phys. Chem. Lett. 2019, 10, 3773−3778

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The Journal of Physical Chemistry Letters

Figure 4. Computed electronic band structures and projected density of states for α-AuS (a), β-AuS (b), and γ-AuS (c) monolayers.

Au and S. We have also considered bilayer systems and corresponding electronic properties for the 2D Au2S and AuS structures by constructing the AA stacking form. After geometry optimizations, α-Au2S, β-Au2S, and β-AuS bilayers stay exactly in their AA stacking form. However, in α-AuS and γ-AuS bilayer systems, two layers shift slightly relative to each other. The bilayer structures are given in Figure S3. Since band calculations with HSE06 functional and SOC effects for bilayer systems are extremely expensive, we only show results of the economic density of states (DOS) calculations. As shown in Figure S4, the band gaps are reduced compared to the monolayer structures, but the semiconducting nature of all the materials is kept. The dynamical stabilities of Au2S and AuS monolayers are examined by computing the phonon dispersion. As displayed in Figure S5, no imaginary frequencies are observed in their phonon dispersion curves, suggesting excellent dynamical stabilities. The highest frequencies of the gold sulfide monolayers amount to ∼400 cm−1, very close to those of black phosphorene (400 cm−1)42 and Cu2Si (420 cm−1),36 indicating strong interactions among Au and S atoms. Next, AIMD simulations are conducted to further verify thermal stabilities of the gold sulfide monolayers at 300 and 400 K, respectively (see Figures S6 and S7). In the AIMD simulations, the time step and time duration are 1.0 fs and 5.0 ps, respectively. Our simulation results show that both Au2S and AuS monolayers can keep their structures intact at 400 K, indicating good thermal stabilities. As pointed out above, chemical stabilities can be an important issue for practical applications of 2D materials. Here, the α-Au2S monolayer is selected for the antioxidation test. As shown in Figure S8, various O2 adsorption geometries are compared by calculating their adsorption energies defined as

Figure 5. (a) Transition state searches by using the CI-NEB calculations. IS, TS, and FS denote initial state, transition state and final state, respectively. (b) Snapshot of the simulated antioxidation test taken at 5 ps for AIMD simulations of the α-Au2S monolayer. Gold, red, and green spheres denote Au, S, and O atoms, respectively.

reactant, indicating that this reaction process is endothermic. The activation energy barrier is ∼2.89 eV, much higher than the energy barrier (∼0.7 eV), which can be overcome at the room temperature (300 K) according to the transition-state theory.44,45 Furthermore, we simulated dynamical oxidation processes at 300 K, by using AIMD simulations, with two O2 molecules preadsorbed on the α-Au2S monolayer. As shown in Figure 5b, no chemical reaction is observed and the geometric structure of the α-Au2S monolayer stays intact. For some other 2D materials (e.g., phosphorene),11 the degradation is caused by coexistence of O2 and H2O. To address this concern, we perform another AIMD simulation with one H2O molecule and one O2 molecule adsorbed on the α-Au2S monolayer at room temperature (300 K). As shown in Figure S9, after a simulation up to 5 ps with the time step of 1 fs, the α-Au2S monolayer structure is kept rather well. Particularly, no chemical reaction ever happens in this condition as well. In the real application, once a suitable substrate is used to support the α-Au2S monolayer, its structure will be less affected by the molecules in the ambient condition. Our antioxidation test show that chemical stability of the α-Au2S monolayer is comparable to previously reported group-III and group-IV monochalcogenides.46,47 In summary, we have found two new Au2S and AuS monolayers with novel electronic properties and very good stabilities. The α- and β-Au2S monolayers as well as α-, β-, and γ-AuS monolayers are likely the global minimum structures based on DFT calculations and a global search run. Our electronic structure calculations, on the basis of the HSE06 hybrid functional, show that all the gold sulfide monolayers are

Eads = Etotal − EO2 − Eα‐ Au 2S

where Etotal, EO2, and Eα−Au2S refer to energies of the adsorbed system, O2 molecule and the α-Au2S monolayer, respectively. It is found that the O2 molecule tends to be adsorbed on the Au−Au bridge site. The small absolute adsorption energy of −3 meV indicates a feature of physical adsorption, suggesting that the α-Au2S monolayer can be oxidation resistant. To further support this conclusion, we examine the possible oxidation pathways by searching for the transition state with the CI-NEB method.43 As presented in Figure 5a, the product of reaction has an energy of 1.88 eV higher than that of 3776

DOI: 10.1021/acs.jpclett.9b01312 J. Phys. Chem. Lett. 2019, 10, 3773−3778

Letter

The Journal of Physical Chemistry Letters semiconductors with different band gaps. Importantly, the αAu2S monolayer not only has a suitable direct band gap of 1.0 eV but also possesses electron and hole mobilities up to 8.45 × 104 and 0.40 × 104 cm2 V−1 S−1, respectively. The predicted Au2S and AuS monolayers demonstrate robust dynamical and thermal stabilities, consistent with our phonon dispersion calculations. As another benchmark test, we have verified that the α-Au2S monolayer entails strong oxidation resistivity. Since the Au2S and AuS monolayers do not have their bulk form, it is suggested that they be synthesized with chemical vapor deposition (CVD) method, which has been extensively utilized for exploration of new 2D materials.48,49 In view of their novel properties, we wish both Au2S and AuS monolayers could be applied to the electronic devices in near future.

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Guangdong joint fund (the second phase) under Grant No. U1501501, and the Holland Supercomputing Center in University of NebraskaLincoln.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.9b01312. Lattice constants for Au2S and AuS monolayers with and without DFT-D3 scheme, atomic fractional coordinates, electron density function images, band structures by HSE06 functional without including SOC effects atomic geometries and DOS of bilayer systems, phonon spectra and AIMD snapshots for Au2S and AuS monolayers and AIMD snapshots of antioxidation test for the α-Au2S monolayer (PDF)

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REFERENCES

AUTHOR INFORMATION

Corresponding Authors

*Email: [email protected]. *Email: [email protected]. ORCID

Wen Wu Xu: 0000-0002-0651-9562 Jinlan Wang: 0000-0002-4529-874X Xiao Cheng Zeng: 0000-0003-4672-8585 Present Address ¶

Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, NM 87131, United States.

Author Contributions #

These authors contributed equally to this work.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS J.W. is supported by Natural Science Funds of China (21525311, 21773027), the National Key Research and Development Program of China (No. 2017YFA0204800), and the Fundamental Research Funds for the Central Universities of China. Q.W. is supported by China Scholarship Council (CSC, 201606090079) and the Scientific Research Foundation of Graduate School of Southeast University (YBJJ1720). W.W.X. is supported by NSFC (11504396) and CSC (201604910285). D.L. is supported by NSCF (11804174) and the Ningbo Natural Science Foundation (2018A610319). The computational resources utilized in this research were provided by Shanghai Supercomputer Center, National Supercomputing Center in Tianjin and Shenzhen, the Big Data Center of Southeast University, the special program for applied research on super computation of the NSFC3777

DOI: 10.1021/acs.jpclett.9b01312 J. Phys. Chem. Lett. 2019, 10, 3773−3778

Letter

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DOI: 10.1021/acs.jpclett.9b01312 J. Phys. Chem. Lett. 2019, 10, 3773−3778