The effects of oxidation on the electronic, thermal and mechanical properties of antimonene: First-principles study

Accepted Manuscript Research paper The effects of oxidation on the electronic, thermal and mechanical properties of antimonene: First-principles study Shuai-Kang Zhang, Tian Zhang, Cui-E Hu, Yan Cheng, Qi-Feng Chen PII: DOI: Reference:

S0009-2614(18)30934-5 https://doi.org/10.1016/j.cplett.2018.11.013 CPLETT 36084

To appear in:

Chemical Physics Letters

Received Date: Revised Date: Accepted Date:

7 September 2018 3 November 2018 7 November 2018

Please cite this article as: S-K. Zhang, T. Zhang, C-E. Hu, Y. Cheng, Q-F. Chen, The effects of oxidation on the electronic, thermal and mechanical properties of antimonene: First-principles study, Chemical Physics Letters (2018), doi: https://doi.org/10.1016/j.cplett.2018.11.013

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The effects of oxidation on the electronic, thermal and mechanical properties of antimonene: First-principles study Shuai-Kang Zhang 1, Tian Zhang2, Cui-E Hu 3,*, Yan Cheng 1, *, Qi-Feng Chen 4 1

Institute of Atomic and Molecular Physics, College of Physical Science and Technology, Sichuan University, Chengdu 610065, China; 2

School of Physics and Electronic Engineering, Sichuan Normal University, Chengdu 610066, China;

3

College of Physics and Electronic Engineering, Chongqing Normal University, Chongqing 400047, China;

4

National Key Laboratory for Shock Wave and Detonation Physics Research, Institute of Fluid Physics, Chinese Academy of Engineering Physics, Mianyang 621900, China

Abstract: We calculate the electronic, thermal and mechanical properties of antimonene with different oxygen compositions (Sb, 2Sb-O and 2Sb-2O). Results show that the band gaps gradually decrease with the increase of the oxidation degree. We also study the lattice thermal conductivities of the three materials and find that the oxidation would greatly reduce the lattice thermal conductivity k of antimonene which is due to the decline of corresponding phonon lifetime. In addition, oxidation reduces the stiffness of antimonene. Our work provides a new perspective for the adjustment of thermal transport which will facilitate the design of thermal materials. Key words: Antimonene, oxidation, lattice dynamics, thermal conductivity, *

Corresponding authors. E-mail: [email protected]; [email protected]

1

first-principles

1.

Introduction Two-dimensional (2D) materials has attracted wide attention since the discovery

of one-atom thick graphene with a high electron mobility[1] and excellent thermal conductivity.[2] However, the gapless characteristic of graphene impedes its applications on electronics and optoelectronics.[3] Many 2D materials, such as silicene, phosphorene, and transition metal dichalcogenides, are now considered for various practical usages due to their distinguished properties. [4,5] Campi et al. predicted the existence of monolayer antimonene through theoretical calculation in 2012.[6] Subsequently, Sb monolayer (antimonene) is successfully synthesized on various substrates via van der Waals epitaxy growth and liquid-phase exfoliation.[7,8] The atomic structure of exfoliated one-atom thick antimonene shows clearly a hexagonal periodicity, which is also known as β-phase antimonene. Thermal transport plays a critical role in nanoelectronic applications, especially in reduced dimensional materials.[9] The thermal conductivity of graphene is as high as 2000–5000 Wm-1K-1. Thus, it has great potential applications in the field of electronic cooling.[10] The thermal transport of antimonene has been widely investigated in theory, including electron and phonon parts. [11-13] In general, the total thermal conductivity of non-magnetic crystals includes the contributions of electrons and phonons, and the phonon is dominant in semiconductors and insulators. Electronic transport can be optimized by adjusting the geometry size, and phonon

2

transport usually adjusted by external pressure. Strain can effectively tune the intrinsic physical properties of 2D materials, such as the electronic and thermoelectric properties. [14-17] Zhang et al. studied the effects of stress on the lattice thermal conductivity k of antimonene film. With strain increasing from -1% to 6%, the lattice thermal conductivity increases from 1.6 to 7.5 Wm-1 K-1.[17] Filler is a good method to adjust the phonon transport of three-dimensional materials,[18-20] and some relative theories have also been proposed. Slack and Tsoukala put forward a theory to explain the reduction of k in filled skutterudites, implying that the fillers move independently from the host matrix (Einstein motion) and effectively scatter phonons.[21] In addition, chemical functionalization is also a universal method to tune the mechanical, electronic and other properties of 2D materials.[22,23] Zhang et al. studied the effects of different functional groups (H, F, Cl, Br) on the lattice thermal conductivities k of antimonene film.[24] By means of first-principles calculations, Zhang et al. demonstrated the feasibility to realize a new class of 2D materials, antimonene oxides with different content of oxygen in 2017. [25] Especially, the antimonene oxide (18Sb-18O) is a 2D topological insulator with a sizable global band gap of 177 meV, which has a high application prospect. However, the influence of oxidation and the corresponding mechanism on thermal transport properties is still uninvestigated. In this work, we calculate the electronic band structures of antimonene films and two oxides of antimonene (2Sb-O and 2Sb-2O) using the first-principles. In addition, we also calculate the lattice thermal conductivities k using the first-principles with the

3

Boltzmann transport equation (BTE) for phonons. Our calculation results show that oxidation can greatly reduce the band gap and thermal conductivity of antimonene. In addition, oxidation can significantly reduce the deformable range of antimonene and significantly reduce the stiffness in antimonene.

2.

Methods The first-principles calculations are performed by using the Vienna ab initio

simulation package (VASP) based on density functional theory (DFT). [26,27] We choose

the

generalized

gradient

approximation

(GGA)

[28]

in

the

Perdew-Burke-Ernzerhof (PBE) parametrization for the exchange-correlation functional and the projector augmented wave (PAW) method.[29] For the three materials studied in this work, the energy cutoffs are taken as 300 eV (Sb), 450 eV (2Sb-O) and 550 eV (2Sb-2O) for the expansion of the wave function by plane-wave basis sets and the length of unit cell along the z direction are taken as 2.00 nm (Sb), 2.00 nm (2Sb-O) and 2.40 nm (2Sb-2O). These structures are fully relaxed until the energy differences are converged within 10 -8 eV and the maximal Hellmann–Feynman force is smaller than 10-4 eVÅ-1, with a 15×15×1 gamma-centered Monkhorst–Pack grid. The lattice thermal conductivity of antimonene is calculated by using the Boltzmann transport equation (BTE) within the single-mode relaxation time approximation as implemented in AlmaBTE, [30] in which the thermal conductivity is given by

4

k 

1 N qV

C



2 q ,n q ,n , q ,n

v

(1)

n ,q

where Nq is the number of uniformly spaced q points in the Brillouin zone, V is the volume of the unit cell, Cq,n, vq,n,α and τq,n are specific heat, group velocity along transport direction α, and relaxation time of the phonon mode with wave vector q and polarization n, respectively. The AlmaBTE package is used to solves the BTE which needs harmonic second-order and anharmonic third-order interatomic force constants (IFCs) as inputs.[31] The phonon dispersion relation is obtained using the harmonic IFCs, and subsequently the group velocity vq,n,α and specific heat Cv can be obtained. The anharmonic third-order IFCs play a significant role in determining the phonon scattering rate, which is the inverse of τq,n. All IFCs are determined from a 3×3×1 supercell with a 7×7×1 q-mesh. Andrew et al. presented an equation of states (EOS) applicable to 2D structures which provides a simple way to calculate the 2D bulk modulus. [32] In the theory, the two-dimensional equivalent of bulk pressure is force per unit length (denoted F) where an in-plane hydrostatic force causes a uniform change in area of the two-dimensional lattice. Force per unit length could be expressed as the first derivative of the energy with respect to surface area F=-

E , and has units Nm−1. S

Positive F represents a hydrostatic 2D compression while negative F represents a uniform stretching. The two-dimensional equivalent of the bulk modulus, which we refer to as the layer modulus, is then defined as  =-S

F .The layer modulus S

represents the resistance of a 2D material to stretching, just as the bulk modulus represents the resistance of a bulk material to compression. 5

One can derive a similar two-dimensional EOS relating the applied F to the surface area for any 2D material:

2   F  2 0     0   2    0     0    0 0    3   where the equibiaxial Eulerian strain is given by  

(2)

S0 S , S0, γ0, γ0', and γ0'' are the 2

1

equilibrium values for the unit-cell area, layer modulus, the force per unit length derivative, and the second derivative of the layer modulus at F = 0. Thus, we can obtain the energy EOS:

1 1 1  E( S )  E0  4S0 0   2      0   3    0    0    0 0    4  3 6 2 

3.

(3)

Results and discussion

3.1 Geometry and electron structure Antimonene (β-phase) possesses a buckled honeycomb structure. A similar structure configuration can be found in silicene, arsenene, and stanene with a small buckling. The optimal lattice structures of the antimonene monolayer and the two kinds of antimonene oxide monolayer (denoted as Sb, 2Sb-O and 2Sb-2O) are shown in Fig. 1. The relaxed lattice parameter of antimonene is 4.12 Å with a Sb-Sb bond length of 2.89 Å, which is in good agreement with the previous theoretical and experimental studies.[33,34] The relaxed lattice parameter of antimonene is 4.372 Å with a Sb-Sb bond length of 2.93 Å and a Sb-O bond length of 1.83 Å for 2Sb-O. The obtained lattice constants 5.18 Å for 2Sb-2O with a Sb-Sb bond length of 3.14 Å and a Sb-O bond length of 1.84 Å. We calculated their electronic band structures using the 6

PBE functional, and the results show that the band gaps of Sb/2Sb-O/2Sb-2O are 1.26/0.42/0 eV. The band gap of Sb is in good agreement with previous theoretical and experimental. [7,33-35] PBE will underestimates the band gaps, and the spin orbital coupling (SOC) has important effects on electronic structures of antimonene. So, we calculated the electronic structure using the HSE06 hybrid functional with SOC. The band gaps of Sb/2Sb-O/2Sb-2O are 1.55/0.48/0.15 eV, as shown in Fig. 2. With the increase of oxidation degree, the band gap gradually decreases and changes from indirect band gap to direct band gap. For 2Sb-O, the energy band is significantly split. This is because the symmetry of 2Sb-O is destroyed. We further calculate partial densities of states (PDOS) of Sb, 2Sb-O and 2Sb-2O, as shown in Fig. 3. The PDOS spectra of pristine antimonene suggest that the 5p states of Sb dominate the electronic states near Fermi level coupled with small amount of 5s states. For antimonene oxides, Sb and O atoms can form dative bond. As the oxygen concentration increases, the contribution of O 2p state gradually increases. In addition, we calculate the electronic band structures of 2Sb-2O using the PBE and HSE06 hybrid functional without and with spin-orbit coupling (SOC), as shown in Fig. 4. Using the HSE06 hybrid functional, the band gap is changed from 0 to 0.15eV when considering the influence of SOC. This shows that 2Sb-2O is a 2D topological insulator. 3.2 Thermal properties The unit of thermal conductivity k of a three-dimensional material is Wm-1 K-1. But, the unit should be WK-1 for 2D materials. So, the k obtained by the software should be normalized by multiplying the length of unit cell along the z direction.

7

Some literature call it thermal sheet conductance.[36] In general, both electrons and phonons contribute to the total thermal conductivity k of non-magnetic crystals. The k in Sb, 2Sb-O and 2Sb-2O are mainly from phonons because of the insulator characteristics, and thus the AlmaBTE package is suitable to obtain their reasonable thermal conductivities. Fig. 5 shows the change of thermal conductivities of Sb, 2Sb-O and 2Sb-2O with temperature. The lattice thermal conductivities of Sb, 2Sb-O and 2Sb-2O are 14.06 nWK-1, 0.86 nWK-1, and 0.05 nWK-1, respectively. The lattice thermal conductivity of antimonene is predicted to be 15.1 Wm-1 K-1[17], 13.8 Wm-1 K-1[11] and 2.3 Wm-1K-1[24] based on first-principles calculations and the phonon Boltzmann equation. The reason for the significant difference between these results may be that the thicknesses of antimonene is different. [17] As the oxidation degree increases, the thermal conductivity becomes lower and lower. The thermal conductivity of Sb is approximately 16 times of 2Sb-O (340 times of 2Sb-2O). Compared with pressure, adsorption is more effective in reducing the k of antimonene. The k of these antimonene films is universally low, which is very favorable to realize high thermal efficiency, especially as a topological insulator. Compared with other 2D materials, the lattice thermal conductivity of antimonene is relatively small (MoS2≈ 4-8 Wm-1K-1,[37] blue phosphorene ≈ 78 Wm-1 K-1,[38,39] silicene ≈ 7-11 Wm-1 K-1,[40] stanene≈11.6 Wm-1 K-1

[41]

and arsenene≈7.8 Wm-1 K-1

[42]

). But by oxidation, we get a

lower lattice thermal conductivity. Furthermore, we also used ShengBTE package to calculate the thermal conductivity of three materials.[43] The results are 13.729 Wm-1 K-1, 0.870 Wm-1 K-1 and 0.044 Wm-1 K-1 for Sb, 2Sb-O and 2Sb-2O in 300 K,

8

respectively. The relative contributions of acoustic and optical phonon modes to the total lattice thermal conductivity are shown in Table 1. Like the case of graphene, the total contribution of acoustic branches is more than 99% for Sb, implying that the contribution of optic phonons to k is negligible.[44] With the increase of oxidation degree, the contribution of optical branch increases gradually. But even for 2Sb-2O, the contribution of optical support to the thermal conductivity of the entire lattice is less than 30%. Therefore, in order to study the reason why the oxidation can significantly reduce the thermal conductivity of antimonene, we will analyze its effect on acoustic branch.

Table 1 Phonon modes contribution to total lattice thermal conductivity in Sb, 2Sb-O and 2Sb-2O at 300 K. ZA (nWK-1)

TA (nWK-1)

LA (nWK-1)

Optical (nWK-1)

k (nWK-1)

Sb

0.718(5.23%)

7.368(53.66%)

5.52(40.21%)

0.124(0.90%)

13.729

2Sb-O

0.148(16.98%)

0.352(40.39%)

0.193(22.13%)

0.178(20.50%)

0.870

2Sb-2O

0.00062 (1.40%)

0.01524(34.66%)

0.01536(34.94%)

0.01274(29.00%)

0.04397

Phonon spectra and phonon density of states (PDOS) of the antimonene films obtained are presented in Fig. 6, where the phonon spectrum of the Sb is well consistent with that by Wang et al.[33] There is no imaginary frequency appears in the phonon spectrum of the three materials. In addition, we also calculate the formation energies of 2Sb-O and 2Sb-2O, respectively -0.54eV and -1.69 eV, to demonstrates 9

the chemical stability of these two oxides. It is clearly seeing that there is a phonon band gap between acoustic and optical branches, which is due to the violation of the reflection symmetry selection rule in the harmonic approximation, being different from the common gap formation mechanism by significant mass differences between the constituent atoms.[45] Based on the elastic theory, the ZA phonon branch near Γ point should have quadratic dispersion when the sheet is free of stress.

[46]

However,

the Sb, 2Sb-O and 2Sb-2O monolayers have linear components in the dispersions of ZA branches. There are two possible reasons for additional linear components. When calculating the phonon spectrum, the effects of the anharmonic effect are not considered. The IFCs in Phonopy codes are only corrected by enforcement of translational invariance, without enforcement of crystal symmetry and rotational invariance.

[47]

It is noted that the range of acoustic branch has a less partial PDOS of

O atoms, and the high frequency range is dominated by the vibrations of O atoms for 2Sb-O and 2Sb-2O. Oxidation results in a significant reduction in the acoustic frequency of antimonene. The acoustic branches of all three materials have frequencies below 2THz. It is known from Eq. (1) that V, Cv, vλ and τλ can influence the value of k. The volume V of the three unit cells did not differ much, so the difference in V was not the main reason for the significant decrease in thermal conductivity. For most of the heat conductive modes Cv approaches to the classic value kB at room temperature, and thus Cv cannot influence the k value although the greater number of phonon modes may lead to a slight increase in the total heat capacity. We make a particular comparison

10

for vλ of three acoustic branches of Sb, 2Sb-O and 2Sb-2O, as shown in Fig. 7 (a-c). It can be seeing that the group velocities of three acoustic branches for the three materials is different, but it does not reach the change of order of magnitude. For TA and ZA, which contribute more than 60% to thermal conductivity, the value of vTA are 1.8 kms-1, 1.9 kms-1, and 1.6 kms-1 and vzA are 3.0 kms-1, 2.7 kms-1 and 2.2 kms-1 for Sb, 2Sb-O and 2Sb-2O, respectively. The difference of vλ is too small to explain the reduction of k. Hence, we believe that τλ should be the main factor for the decrease of k in 2Sb-O and 2Sb-2O. To identify the underlying mechanism of oxidation-dependent lattice thermal conductivity, the phonon lifetime for LA, TA and ZA branches is shown in Fig. 7 (d-f). As can be see, the relaxation time of LA is larger than those of TA and ZA below the frequency. The phonon lifetime of three acoustic branches decreases with the increase of oxidation degree. The phonon lifetime of Sb, 2Sb-O and 2Sb-2O is different by an order of magnitude. This result is consistent with the change of thermal conductivity that we obtained. This confirms that the reduction of τλ is the main reason for the decrease of k. We plot the cumulative lattice thermal conductivity as a function of phonon MFPs at 300 K in Fig. 8. With the increase of oxidation degree, the average phonon MFPs which contributes to thermal conductivity decreases. The cumulative thermal conductivity increases as the MFPs increases, and phonons with MFPs between 4 nm and 52 μm, 0.44 nm and 5 μm, 0.03 nm and 270 nm contribute to the thermal conductivity in Sb, 2Sb-O and 2Sb-2O, respectively. The phonons with MFPs below

11

40 mm contribute more than 70% to the total thermal conductivity, indicating that minimizing the sample size will be able to reduce the thermal conductivity effectively in antimonene. 3.3 Mechanical properties Bulk equations of state are only valid for expansions and compressions in a range of ±10% about the equilibrium volume. Therefore, we only calculated the energy value of relative area S/S0 at 95%-110%, and performed EOS fitting according to Eq. (3). The layer modulus γ0 can be obtained by fitting.

Table 2 The EOS fit parameters for Sb, 2Sb-O and 2Sb-2O. S0 (Å2)

γ0 (Nm-1)

γ0 '

γ0'' (mN-1)

Sb

14.69

19.21

3.86

-0.18

2Sb-O

16.58

13.74

2.59

-1.34

2Sb-2O

23.21

6.06

2.19

-1.74

For 2D materials, the elastic matrix containing four non-zero elastic constants C11, C12, C22 and C66. For the hexagonal lattice, C11 is equal to C22. The elastic constant has the same unit as F, which is Nm-1. We calculated the elastic constants of three materials at equilibrium by VASP. In addition, the layer modulus can be obtained from the elastic constant,  0 = expressed as Y 2 D 

C11  C12 , Young's modulus of 2D materials is 2

C112  C122 . We compare the layer modulus obtained by EOS C11

fitting and the layer modulus calculated by elastic matrix. The results obtained by the 12

two methods are basically the same. This also illustrates the correctness of EOS. The results for Sb, 2Sb-O and 2Sb-2O are shown in Table 3. The greater the value of γ0 (represents the ability to resist strain), the greater the pressure F required to make the material undergo unit strain, i.e. the greater the strain resistance. As the oxidation degree increases, γ0 decreases obviously. It can be seen that oxidation could significantly reduces the stiffness of Sb.

Table 3 The parameters γ01 (by EOS fitting), γ02 (by elastic matrix), elastic constants (C11, C12, C66), and Young's modulus for Sb, 2Sb-O and 2Sb-2O. γ01(Nm-1)

γ02(Nm-1)

C11(Nm-1)

C12(Nm-1)

C66(Nm-1)

Y(Nm-1)

Sb

19.82

19.21

33.09

6.54

13.27

31.79

2Sb-O

14.24

13.74

23.03

5.45

8.79

21.74

6.06

7.94

4.03

1.96

5.89

2Sb-2O 5.98

In addition, we predict the stretch range by calculating the phonon spectrum of Sb, 2Sb-O and 2Sb-2O under different relative area S/S0. Here, only phonon dispersion curves with relative area from 90% to 100% are plotted in Fig. 9. For Sb, the change of ZA is the most obvious among all acoustic branches. When the relative area decreases gradually, the frequency of ZA near Γ point decreases gradually. Virtual frequency occurs when relative area is between 93% and 94%. The situation of 2Sb-O is similar to that of Sb, and imaginary frequency occurs between 95% and 96% of the relative area. For 2Sb-2O, the strain has a great influence on ZA and TA. 13

As the relative area decreases, the frequency of ZA and TA near M point decreases obviously. When the relative area is between 98% and 99%, TA will appear imaginary frequency near M point. We also calculate the phonon spectrums when the relative area increased. For Sb, the frequency of optical branch decreases with the increase of relative area. When the relative area increased to 126%-127%, the virtual frequency of TA appeared near K point. For 2Sb-O, the increase of relative area causes the acoustic branch to generate imaginary frequency near Γ point when the relative area increased to 125%-126%. For 2Sb-2O, the strain causes the optical branch to generate imaginary frequency near Γ point when the relative area increased to 145%-146%. By observing Fig. 9, we can get the conclusion: as the oxidation degree increases, antimonene becomes more and more unstable, and the deformation range decreases significantly.

4.

Conclusions The electronic, thermal and mechanical properties of antimonene and its two

oxides are calculated. We find that the band gap decreases to 0.15 eV with the increase of oxidation degree. We predicate that antimonene has a low lattice thermal conductivity, as low as 14.06 nWK-1 at 300 K based on first-principles calculations combined with Boltzmann transport equation (BTE) formalism. Moreover, with the increase of oxidation degree, the thermal conductivity of antimonene decreased significantly. The lattice thermal conductivity of 2Sb-O and 2Sb-2O is 0.86 nWK-1 and 0.05 nWK-1 respectively at 300 K. The contribution of the thermal conductivity of

14

the three materials mainly comes from the acoustic branch. The results show that oxidation can significantly reduce the acoustic phonon life, which is the main reason for the decrease of thermal conductivity. We fit the equation of state of three materials and verified its correctness. In addition, we also find that compare with antimonene, the γ0 of its oxide has significantly decreased (19.2 Nm-1 for Sb, 13.74 Nm-1 for 2Sb-2O and 6.06 Nm-1 for 2Sb-2O), which indicates that the oxidation has significantly reduced the stiffness of antimonene. By analyzing the phonon spectrum of antimonene and its oxides under different relative area, it was found that the deformation range is 94%-145%, 96%-126% and 99%-125% for Sb, 2Sb-O and 2Sb-2O. It shows that the oxidation made the deformation range significantly decreased.

5.

Acknowledgments The authors would like to thank the support by the NSAF Joint Fund Jointly

setup by the National Natural Science Foundation of China and the Chinese Academy of Engineering Physics under Grant No. U1830101 and the Science Challenge Project under Grant No. TZ2016001

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Fig. 1 (Color online) Top and side views of (a) Sb, (b) 2Sb-O and (c) 2Sb-2O. The gray atoms are the Sb atoms, and the orange atoms are the O atoms.

19

(a) 2

(b) 2

(c) 2

1.55eV 0.79eV 0

0

0

-2

-2

-2

-4









-4









-4

0.15eV







Fig. 2 The electronic band structure of Sb (a), 2Sb-O (b) and 2Sb-2O (c) using the HSE06 hybrid functional with spin-orbit coupling, respectively.

20



(a)

(b)

(c)

6

12 Sb

O

4

8

2

4

Total Sb-s Sb-p

0.5

0.0

0

0 -4

-2 0 Energy (eV)

2

-4

-2 0 Energy (eV)

-4

2

6

-2 0 Energy (eV)

2

12 Sb

Density of States

Density of States

1.0

4

8

2

4

O Total O-s O-p

0

0 -4

-2 0 Energy (eV)

2

-4

-2 0 Energy (eV)

Fig. 3 (Color online) Total and partial density of states calculated using HSE06 functional with spin-orbit coupling for Sb (a), 2Sb-O (b) and 2Sb-2O (c) in the energy range from -4 to 2 eV.

21

2

Energy (eV)

PBE

PBE+SOC

2

2

0

0

-2

-2

-4







-4

HSE06

0.146eV







HSE06+SOC

2

2

0

0

-2

-2

-4







-4

0.152eV







Fig. 4 Electronic band structures of 2Sb-2O using the PBE and HSE06 hybrid functional functional without and with spin-orbit coupling, respectively.

22

Sb 2Sb-O 2Sb-2O

k (nW/K)

10

1

0.1

0.01 200

300

400

500

600

700

800

900

1000

Temperature (K)

Fig. 5 (Color online) The thermal conductivities of Sb, 2Sb-O, and 2Sb-2O at different temperatures.

23

(a)

(b)

Frequency (THz)

8

8

(c)

27

27

25

25

24

24

24

24

23

23

6

6

4

4

4

4

4

4

2

2

2

2

2

2

0

0

0

0

0 

M K



0 1 2 3

PDOS



M K



0.0 0.6 1.2

PDOS

0 

M K



0.0 0.6 1.2

PDOS

Fig. 6 (Color online) Phonon spectra and phonon density of states (PDOS) for (a) Sb, (b) 2Sb-O and (c) 2Sb-2O. The red, blue and black line represent oxygen atoms, antimony atoms that are adjacent to oxygen atoms and antimony atoms that are not adjacent to oxygen atoms in (b). The red and black lines represent oxygen and antimony atoms in (c).

24

group velocity (km/s)

(a)

(b)

1.5

2.0

Sb 2Sb-O 2Sb-2O

ZA

3.0

TA

LA

2.5 1.5

1.0

2.0 1.0

1.5

0.5

1.0 0.5 0.5

0.0 0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0.0

Frequency (THz)

Frequency (THz)

(d) 10

10

Life time (ps)

(c)

2

10

1

10

0

10

10

Sb 2Sb-O 2Sb-2O

ZA

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Frequency (THz)

1.5

2.0

(f)

10

5

10

4

10

3

10

2

10

1

10

0

TA

-1

-2

1.0

Frequency (THz)

(e)

3

0.5

10

-1

10

-2

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Frequency (THz)

10

3

10

2

10

1

10

0

10

-1

10

-2

0.0

LA

0.5

1.0

1.5

2.0

Frequency (THz)

Fig. 7 (Color online) Group velocities and Phonon lifetimes for (a, d) ZA, (b, e) TA, and (c, f) LA, respectively.

25

1.0

Sb 2Sb-O 2Sb-2O

Normalized Accumulation

0.8

0.6

0.4

0.2

0.0 -2 10

-1

10

0

1

2

3

10 10 10 10 Phonon Mean Free Path (nm)

4

10

5

10

Fig. 8 (Color online) Cumulative lattice thermal conductivity by total lattice thermal conductivity with respect to the phonon mean free path at 300 K for Sb, 2Sb-O, and 2Sb-2O, respectively.

26

(b) 26

(a)

Sb

(c) 25

2Sb-O

25

6

95% 96% 100%

Frequency (THz)

5

3

2 2 1

1 0

0 

M

K

Sb

100% 25 145% 24 146%

6

0

 

(e) 26

(d)

M

K

 

(f) 25

2Sb-O

M



K

2Sb-2O 100% 125% 126%

100% 24 126% 127%

5 Frequency (THz)

98% 99% 100%

24

4

93% 94% 4 100% 3

3

2Sb-2O

4

4

3

3 3

2 2 1 1 0 0

0 

M

K

 

M

K

 

M



K

Fig. 9 (Color online) Phonon band structures of (a, d) Sb, (b, e) 2Sb-O and (c, f) 2Sb-2O with different relative area (S/S0).

27

Graphical abstract

28

Highlights Oxidation reduces the energy band gap of antimonene to 0eV.

Compared with strain, oxidation reduces the lattice thermal conductivity k of antimonene. And the main reason for the decrease of k is the decrease of phonon lifetime.

Oxidation greatly reduces the deformable range of antimony.

29