Excellent Thermoelectric Performance Predicted in Two-Dimensional

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Excellent Thermoelectric Performance Predicted in TwoDimensional Buckled Antimonene: a First-Principles Study Kai-Xuan Chen, Shu-Shen Lyu, Xiao-Ming Wang, Yuan-Xiang Fu, Yi Heng, and Dong-Chuan Mo J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 22 May 2017 Downloaded from http://pubs.acs.org on May 30, 2017

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The Journal of Physical Chemistry

Excellent Thermoelectric Performance Predicted in Two-dimensional Buckled Antimonene: a Firstprinciples Study Kai-Xuan Chena, Shu-Shen Lyua, Xiao-Ming Wangb, Yuan-Xiang Fua, Yi Henga and Dong-Chuan Moa, * a

School of Chemical Engineering and Technology, Sun Yat-sen University, Guangzhou 510275,

China. b

Department of Physics and Astronomy, University of Toledo, 2801 W Bancroft ST, Toledo, OH

43606, USA.

ABSTRACT Nowadays, new emerging two-dimensional (2D) materials have become a hot topic in the field of theoretical physics, material science and nanotechnology engineering due to their high surface area, planar structure and quantum confinement effect. Within two-dimensional framework, we systematically concentrate on the buckled and puckered systems consisting of the VA group elements (denoted as arsenene, antimonene and bismuthene). Among these studied systems, the buckled antimonene harbors a thermoelectric figure of merit (ZT) of 2.15 at room temperature.

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This is probably the highest value that has ever been reported in pristine 2D materials. By simple biaxial strain engineering, the ZT can even get enhanced to 2.9 under 3% tensile strain. The enhancement mainly results from both tuning the electronic structures and reducing the thermal conductance. This work predicts a new promising candidate in thermoelectric devices, based on the fact that buckled antimonene has been lately fabricated and proved to be stable at ambient conditions.

INTRODUCTION Thermoelectric materials, which can be used in the energy conversion between heat and electricity, have attracted a lot of attention due to the global energy crisis. To evaluate the performance of a thermoelectric material, a dimensionless parameter ZT1 is adopted with the definition of

σ S 2T κ

(1)

κ = κ el + κ ph

(2)

ZT =

where σ and S are the electronic conductance and Seebeck coefficient, respectively. κ denotes the thermal conductance which can be contributed both by phonons and electrons, respectively.2 In the commercial field, frequently-used thermoelectric materials have a ZT of around unit, which indicates the low energy conversion efficiency. For many years, the development in high performance thermoelectric materials meets its bottleneck since it is difficult to alter any one parameter without greatly affecting the other transport coefficients.3 Then the research on


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thermoelectric materials witnessed great progress in 1993, when Hicks and Dresselhaus3-4 pointed out an effective way to significantly enhance the ZT, by nanostructural engineering. Because in nanoscale size, the interrelation among σ, S and κ may be weakened, due to the quantum confinement. In the frontier experimental research of thermoelectric materials, progress has been made. Many works devoted efforts to reducing the thermal conductivity by nanostructural engineering. Some other studies focused on the band engineering or mobility enhancement, from the point view of tuning the electronic properties. For instances, Venkatasubramanian et al.5 reported a ZT of ~2.4 observed in thin-film p-type Bi2Te3/Sb2Te3 superlattice devices by controlling the transport of phonons and electrons. Yan et al.6 fabricated n-type Bi2Te2.7Se0.3 sample (ZT = 1.04 at 380 K) by the hot pressing of ball-milled powder mainly due to the large increase of electrical conductivity. In the work of Guo et al.7, Tl9BiTe6, was postulated to exceed ZT = 1 above 450 K when prepared by zone-melting and reach ZT = 0.86 at 560 K after hot-pressing via the optimization of the carrier concentration. Zhao et al.2 reported a record of ZT ranging from 0.7 to 2.0 at 300 to 773 K, realized in hole-doped tin SnSe crystals enabled by the contribution of multiple electronic valence bands present in SnSe. Nevertheless, it should be noticed that these reported ZT numbers are still far away from the level which promises sufficient energy conversion efficiency in practical thermoelectric devices. In experiments, 2D materials are more likely to fabricate in large length scale and easier to get used in electronic devices.8 Moreover, they offer great flexibility in terms of tuning their electronic properties.9 In recent years, some research based on two-dimensional thermoelectric materials have been carried on, as listed in Table. 1. However, the challenge still remains in seeking high-performance thermoelectric materials in nanoscale, especially 2D materials.


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Therefore, the objective of this work is to design and predict the thermoelectric properties of new proposed 2D materials, which consist of the VA group elements (As, Sb and Bi). Two distinguishable structural forms in this 2D family, denoted as the buckled and puckered systems, are investigated. Table. 1 The room-temperature ZTmax for typical two-dimensional materials. 2D Monolayer

ZTmax at RT

Graphene

0.009410

Graphyne

0.15710

Silicene

0.3611

Germanene

0.4111

Black Phosphorene

>0.612, 1.4411

Puckered Arsenene

0.8513

MoS2

0.7514, 0.5815, 1.3516

MoSe2

0.8814, 1.3916

WS2

0.7214, 1.5216

WSe2

0.9114, 1.8816

Buckled Antimonene

2.15 (This work)

COMPUTATIONAL METHODS Density functional theory (DFT), as implemented in the package Quantum Espresso17, is adopted in our work. Standard solid state pseudopotentials18 (SSSP) within Perdew–Burke– Ernzerhof (PBE) framework are used. A 15×15×1 Monkhorst–Pack k-mesh is employed with


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energy (charge density) cutoff up to 40 Ry (320 Ry) and a vacuum region of more than 14 Angstroms is used to avoid the periodic image interaction. Convergence thresholds are set to 10-6 Ry/Bohr on force and 10-5 Ry on total energy. Optimized structural parameters are obtained after ion minimization has been fully performed.

For the calculation of electronic structures, ultrasoft pseudopotentials with the Rappe−Rabe− Kaxiras − Joannopoulos (RRKJ) method are adopted with same energy cutoff in ion minimization. The d-orbital electrons are fully taken into consideration. In the process of selfconsistency, a 7×7×1 Monkhorst–Pack k-mesh is employed. The ballistic electron and phonon transports are studied in typical non-equilibrium Green’s function (NEGF) model “LeadConductor-Lead”.19 The interaction of electron–electron, electron–phonon and phonon–phonon are not taken into consideration. Maximally localized Wannier functions (MLWFs) method, as implemented in WanT20, is used to calculated the Bloch states at each k-point in Brillouin zone. To obtain the electron Hamiltonian, 46 Wannier functions are used in buckled systems and 126 functions for the puckered case. The calculation of thermoelectric factors are described as below.14, 21 For ballistic electronic transport, one should firstly calculate the retarded Green’s function of the central conductor as

G r =  ESC − H C − Σ rL − Σ rR 

−1

(3)

where E, HC and SC are the electron energy, Hamiltonian and overlap matrix, respectively. Σr is the self-energy term from the semi-infinite lead, which can be obtained as † † Σ rL = H LC g Lr H LC , Σ rR = H CR g Rr H CR


(4)

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where gr denotes the retarded surface Green’s function from semi-infinite lead. HLC (HCR) represent the Hamiltonian matrix between the left (right) leads and the central conductor. After then, the electronic transmittance matrix T ( E ) can be calculated as Γ β = i ( Σ rβ − Σ aβ ) , β = L, R T ( E ) = Tr ( G r Γ LG a Γ R ) , G a = ( G r )

(5)

†

(6)

Once the electronic transmittance matrix has been obtained, several thermoelectric factors can be worked out. For convenience, Lorenz functions Ln are introduced as

Ln ( µ , T ) =

 ∂f ( E , µ , T )  2 n µ dE T E × E − × ( ) ( ) −  h∫ ∂E   1

f ( E, µ,T ) = e

E −µ k BT

(7)

(8)

+1

where f(E, µ, T) is the Fermi-Dirac distribution function and µ, T, h are the chemical potential, absolute temperature and Planck constant, respectively. Here, The electronic conductance σ, Seebeck coefficient S and electronic thermal conductance κel can be worked out by Equations (9) -(11), respectively.

σ = q 2 L0

S=

1 L1 × qT L0


(9)

(10)

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κ el =

1  L2  ×  L2 − 1  T  L0 

(11)

From the definition of ZT in Equations (1)-(2), now there is only one physical parameter left to be mentioned, the phononic thermal conductance term, which is determined from phononic transport. For ballistic phononic transport, the calculation of phonon transmittance is similar with that of the electron transmittance described above. The interatomic force constant (FC) matrix can be obtained firstly from density functional perturbation theory (DFPT). And then the phonon transmittance T (ω ) can be calculated as

2 G r = (ω + iη ) − FC − Σ rL − Σ rR   

−1

T (ω ) = Tr ( G r Γ LG a Γ R )

(12)

(13)

where ω is the phonon frequency. Then the phononic thermal conductance κph can be obtained as

κ ph (T ) =

h ∞ ∂g (ω,T ) T (ω)ω dω ∫ 2π 0 ∂T

1

g (ω , T ) = e

hω k BT

(14)

(15)

−1

where g(ω, T) is the Bose-Einstein distribution function, in which h and kB denote the reduced Planck constant and Boltzmann constant, respectively.

RESULTS AND DISCUSSION


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A. Structural Information and Phonon Transport. To begin with, we shall introduce the atomistic structures of the 2D family consisting of VA group elements (As, Sb and Bi). As demonstrated in Fig. 1 and Fig. 2, there are two distinguishable structural forms for this 2D family. The first one has a silicene-like crystal structure, denoted as the buckled system, whereas the second one is similar with the black phosphorene22-23, denoted as the puckered system. The buckled systems belong to the D3d group with two non-coplanar atoms included in a hexagonal unit cell. The puckered systems, however, belong to the C2v group with a cubic unit cell, in which four atoms are included in the unit cell. Besides, structural anisotropy in the puckered systems can be observed along armchair and zigzag directions. The detailed crystal parameters of these two forms of 2D materials are tabulated in Table. 2 and Table. 3, respectively, which agree well with the previous research.24-29

Fig. 1 The atomic structures of buckled systems, in which the unit cell is denoted with red solid box. Table. 2 The crystal parameters of the buckled systems.

Structures

a/Å

R/Å


θ/°

8

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Buckled Arsenene

3.61

2.51

92.1

Buckled Antimonene

4.12

2.89

91.1

Buckled Bismuthene

4.29

3.03

90.0

Fig. 2 The atomic structures of puckered systems, in which the unit cell is denoted with red solid box. Table. 3 The crystal parameters of the puckered systems.

Structures

a/Å

b/Å

R1 / Å

R2 / Å

θ1 / °

θ2 / °

Puckered Arsenene

4.76

3.68

2.51

2.49

94.6

100.6

Puckered Antimonene

4.75

4.35

2.94

2.86

95.4

102.5

Puckered Bismuthene

4.73

4.51

3.12

3.04

92.5

104.7

It is worth mentioning that for puckered antimonene and bismuthene, there also exist two different kinds of structures, w-Sb/Bi and aw-Sb/Bi.

30

The difference between w-Sb/Bi and aw-


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Sb/Bi can be found in zigzag views from Fig. 3. It can be distinguished by whether the atoms are coplanar along the up and down surfaces, as shown in Fig. 3(a)-(b). We then simply perform the phonon calculation and plot out the phonon dispersion spectra. Imaginary frequency mode appears in the w-Sb/Bi, indicating the thermodynamic instability. On the contrary, no obvious negative phonon branches can be observed in the aw-Sb/Bi. Consequently, the aw-Sb/Bi is adopted in our study and in the following part, for convenience, aw-Sb/Bi is described as the puckered system.

Fig. 3 The two different atomic structures of puckered systems for (a, b) antimonene and (c, d) bismuthene


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Fig. 4 The atomistic structures, phonon dispersion and transmittance spectrum of 2 × 2 supercell of buckled (a) arsenene, (b) antimonene, (c) bismuthene and puckered (d) arsenene, (e) antimonene, (f) bismuthene. Fig. 4 shows the atomic structures and the corresponding phonon dispersion spectra of all investigated systems. Reciprocal path along the high symmetry point “G(0, 0, 0)-M(1/2, 0, 0)K(1/3, 1/3, 0)-G(0, 0, 0)” is used for buckled systems and “G(0, 0, 0)-X(1/2, 0, 0)-S(1/2, -1/2, 0)-


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Y(0, -1/2, 0)-G(0, 0, 0)” for puckered systems. Here, a 2×2 supercell is employed instead of the unit cell in order to meet the criteria of nearest-neighbor interaction in the following NEGF part. As can be observed from Fig. 4, the cut-off frequency in dispersion spectra decreases with increasing atomic mass, both in buckled and puckered systems. To be specific, from arsenene to bismuthene, the values decrease from ~300 cm-1 to ~150 cm-1. Also, phononic bandgap can be observed in all these systems. It should be mentioned that only negligible imaginary frequencies can be observed in all these systems, indicating the thermodynamic stability of the proposed structures. This provides a theoretical guarantee for the further study of the electronic and thermoelectric properties. As is known, the low-frequency modes mainly dominate the room-temperature thermal transport properties of 2D materials since high-frequency modes cannot be activated at such temperature.19 As for the puckered systems, due to the anisotropy along the armchair and zigzag directions, the phonon transmittance also exhibits anisotropic phenomenon, as shown in Fig.

4(d)-(f). There is no doubt that the phonon transmittance along the zigzag direction is higher than that along the armchair direction12, 31. Such anisotropy in phonon transmittance would definitely lead to the same trend in phononic thermal conductance.

B. Electronic Structures. In the part of electronic structures, MLWFs are adopted to describe the Bloch states at each k-point in the Brillouin zone. A frozen window of [-2.0 eV, 2.0 eV] is chosen in which the subbands are correctly reproduced compared with the bands plotted from DFT data, as demonstrated in Fig. 5. The band structures of buckled antimonene plotted by MLWFs and DFT fit well within the frozen window. It provides strong evidence for the accurate description of MLWFs method in studying electronic structures of these system. Based on this,


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Fig. 6 shows the electronic band structures, transmittance and density of states. All investigated systems exhibit semiconductive properties. Wider electronic bandgaps can be observed in the buckled systems than that in the puckered counterparts. From Fig. 6(a)-(c), the bandgaps seem to decrease with increasing atomic mass, with the value of 1.58 eV, 1.25 eV and 0.56 for buckled arsenene, antimonene and bismuthene, respectively. The bandgaps of 0.76 eV, 0.1 eV, 0.1 eV can be found for puckered arsenene, antimonene and bismuthene, respectively, from Fig. 6(d)(f). The electronic transmittance demonstrates weak anisotropy along the armchair and zigzag directions.13 That is to say the structural anisotropy has more impact on the phononic transport than the electronic transport.

Fig. 5 The electronic band structures of buckled antimonene plotted by MLWFs and DFT, respectively.


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Fig. 6 The electronic band structure and transmittance spectrum of 2×2 supercell of buckled (a) arsenene, (b) antimonene, (c) bismuthene and puckered (d) arsenene, (e) antimonene, (f) bismuthene. Normal DFT calculation generally underestimates the bandgap, compared to that by GW or hybrid functional calculations. However, since the GW or hybrid functional correction won’t change the effective mass greatly, it may not affect the maximal ZT32, but will definitely change the chemical potential at which the ZT is maximized. Since the thermoelectric performance is our main concern in this work and due to the limited resources, the employment of DFT method is reasonable and effective. Moreover, the calculated results agree well with the previous research. For instances, the electronic structures of arsenene are consistent with the research carried out by Kecik et al.33 and Cao et al34 separately. In the work of Aktürk et al.28, the stability and electronic properties of 2D antimonene were studied and the bandgaps for buckled and puckered antimonene were found to be 1.04 eV and 0.16 eV, respectively. Afterwards, buckled


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(puckered) bismuthene were figured out to harbor a direct (indirect) bandgap of 0.547 eV (0.28 eV) 30. It is worth mentioning that for puckered antimonene and bismuthene, the lowest bandgap doesn’t locate along the high-symmetry path “G-X-S-Y-G”, but at the k-point (denoted as A) of ~(0.04, 0.25, 0) and ~(0.055, 0.255, 0), respectively. These certain k-points are figured out by using a dense mesh in the band structures process.

C. Thermoelectric performance. In the final section, we turn to the study of thermoelectric performance. Fig. 7 shows the thermoelectric factors of buckled and puckered systems at room temperature. The nature of electronic bandgap leads to a low electronic conductance at low chemical potential, at which the Fermi surface locates between the valence and conduction subbands. Even though the Wiedemann–Franz law doesn’t work precisely for semiconductor, it can still be found that the electronic thermal conductance shows similar trend with the electronic conductance. This phenomenon mainly results from their similar dependence on the electronic transmittance. At the same chemical potential, the puckered systems harbor higher electronic conductance than the buckled counterparts due to the narrower bandgaps. According to the work of Johnson et al35 and Fan et al36, the relation between Seebeck coefficient S and bandgap Eg can be described as S ≈ − ( k B / e ) ( Eg / 2k BT + 2 ) , where kB is the Boltzmann constant. Higher Seebeck coefficient can generally be discovered in systems with higher bandgap, as shown in Fig. 7(b). It may qualitatively account for the higher Seebeck values appear in buckled systems rather than the puckered counterparts. As for phononic thermal conductance in Fig. 7(c), obviously the buckled systems harbor higher values than the puckered counterparts, which may be attributed to the suppression in the phonon dispersion spectra in Fig. 4. In particular, the value for puckered systems along armchair direction are smaller than that along zigzag direction, resulting from the strong anisotropy that has been mentioned above.


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Fig. 7 The (a) electronic conductance σ, (b) Seebeck coefficient S, (c) phonon thermal conductance κph and (d) ZT of the investigated buckled arsenene, antimonene and bismuthene, respectively. The inset in (a) shows the electronic thermal conductance κel. AC and ZZ denote the armchair and zigzag directions, respectively.


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Fig. 8 (a) The thermoelectric figure of merit of buckled antimonene with biaxial strain deformation. (b) The bandgap and phononic thermal conductance of buckled antimonene with biaxial strain deformation. From buckled to puckered systems, a degeneration of ZT can be observed from Fig. 7(d). This degeneration may mainly due to the decrease of Seebeck coefficient (resulting from the narrower bandgaps). In particular, the buckled antimonene harbors a ZT of 2.15 at room temperature, which is probably the highest value ever reported in pristine 2D materials, as presented in Table.

1. Moreover, in order to further improve the thermoelectric performance, strain engineering is used.37 The biaxial strain is applied to the buckled antimonene at the tensile range of [0%, 8%]. The effect of biaxial strain on the ZT value is significant. As shown in Fig. 8(a), the maximal room-temperature ZT of buckled antimonene get enhanced at low strain but suppressed when strain is larger than 3%. The ZT of 2.9 can be reached at the strain level of 3%, resulting in a 35% enhancement compared to that of the unstrained buckled antimonene. The enhancement mechanism may result from tuning the electronic structures and reducing the phononic thermal conductance by tensile biaxial strain. As shown in Fig. 8(b), the bandgap of buckled antimonene


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increases at low strain deformation and then decreases when tensile strain is larger than 2%. On the contrary, the phononic thermal conductance get reduced at low strain deformation [0%, 3%] and enhanced at high strain [3%, 8%]. According to the definition of ZT in equation (1), high Seebeck coefficient (generally influenced by electronic bandgaps) and low thermal conductance are both required to achieve a high ZT. In our work, the highest ZT of 2.9 would appears when appropriate strain (3%) is applied to buckled antimonene. Generally in the experimental procedure, some factors may limit the intrinsic thermoelectric properties, such as sample size, atmoistic layer nuber, substrate effect, doping level and so on. So the obtained ZT may be lower than the theorectical value to some extent. But with the advancement of tecnology in nanostructural engineering, the reducement may be weakened. Very recently, the few-layers buckled antimonene has been successfully fabricated and proved to be stable at ambient conditions,38-39 which provide strong experimental support. Samples with desired systems are likely to be prepared in the near future. This would definitely make buckled antimonene a star material in the field of thermoelectric application. Our theoretical prediction highlights an excellent candidate in thermoelectric devices for experimental researchers. It may greatly promote the development of high efficiency thermoelectric devices based on these new proposed 2D materials.

CONCLUSIONS In conclusion, by using first-principles calculations, we study the thermoelectric transport properties of two-dimensional family which consists of VA elements (As, Sb and Bi). Both buckled and puckered forms are investigated. All the systems show semiconductive properties


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while the buckled systems possess wider bandgap than the puckered counterparts. Our results find out that the buckled systems beat the puckered counterparts in thermoelectric performance and in particular, buckled antimonene exhibits amazingly high thermoelectric performance, with maximal room-temperature ZT reaching 2.15. Imposing biaxial strain deformation, the ZT value can even get enhanced to 2.9, which make buckled antimonene probably the most excellent 2D thermoelectric material ever reported. We believe that by ways of hole/substitution doping or cutting into nanoribbons, the ZT may get improved to a much higher level, which is totally practical in industrial application.

AUTHOR INFORMATION

Corresponding Author *Tel: +86-020-84112151. E-mail: [email protected].

Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

Notes The authors declare no competing financial interest. ACKNOWLEDGMENT Financial support from the National Natural Science Foundation of China (Grant No. 51676212) and the Fundamental Research Funds for the Central Universities are gratefully acknowledged.


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The simulation work is supported by the National Supercomputer Center in Guangzhou and the high-performance grid computing platform of Sun Yat-sen University. ABBREVIATIONS 2D, two-dimensional; ZT, thermoelectric figure of merit; DFT, density functional theory; SSSP, standard solid state pseudopotentials; PBE, Perdew–Burke–Ernzerhof; RRKJ, Rappe−Rabe− Kaxiras−Joannopoulos; NEGF, Non-equilibrium Green’s function; MLWF, maximally localized Wannier function; DFPT, density functional perturbation theory. REFERENCES 1.

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Excellent Thermoelectric Performance Predicted in Two-Dimensional

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