Piezoelectricity and dipolar polarization of group V-IV-III-VI sheets: A first-principles study

Applied Surface Science 463 (2019) 918–922

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Piezoelectricity and dipolar polarization of group V-IV-III-VI sheets: A firstprinciples study ⁎

T

⁎

Jin-Peng Lia,b, Hao-Jun Jiaa,c, Dong-Ran Zhua,b, Xiao-Chun Wanga,b, , Fu-Chun Liua,b, , Yu-Jun Yanga,b a

Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012, China Jilin Provincial Key Laboratory of Applied Atomic and Molecular Spectroscopy, Jilin University, Changchun 130012, China c Institute of Physics and Technology, National Research Tomsk Polytechnic University, Tomsk 634050, Russia b

A R T I C LE I N FO

A B S T R A C T

Keywords: Piezoelectricity Two-dimensional materials Out-of-plane dipolar polarization First-principles calculation

Piezoelectricity can realize the mutual conversion between mechanical energy and electrical energy. With the development of science and technology, the biggest challenge now is to look for the materials with higher efficiency piezoelectric effect. Using first-principles calculations, we study the elastic and piezoelectric properties of the V-IV-III-VI sheets: SiN-AlO, GeN-GaO, and SnN-InO. The Young moduli of these three V-IV-III-VI sheets are much smaller than graphene. Among these three V-IV-III-VI sheets, the in-plane piezoelectric coefficient d11 (12.69 pm/V) of SnN-InO is the largest, which is larger than that (3.73 pm/V) of molybdenum disulfide (MoS2) by 3 times. SnN-InO also exhibits the largest out-of-plane piezoelectric coefficient d31 (8.66 pm/V), which is larger than that (0.46 pm/V) of the Janus group-III chalcogenide sheets by 18 times. The broken inversion symmetry and the large electronegativity difference between the atomic top layer and bottom layer of the XN-MO sheet induces the out-of-plane dipolar polarization, leading the out-of-plane piezoelectric effect. The flexible SnN-InO with remarkable out-of-plane piezoelectric properties can be applied in nanoscale energy harvesting devices and nano-sensor in medical devices.

1. Introduction Piezoelectricity, originated in the 1880s, is the coupling between mechanical and electrical behavior of crystals without the inversion center. When the crystals are stretched or distorted under external forces, the charge will appear on its surface. When the crystals are placed in macroscopic electric field, it will be deformed [1]. Because piezoelectricity can realize the mutual conversion between mechanical energy and electrical energy, the materials with piezoelectric effect have a lot of practical applications, such as transistors [2], actuators [3,4], motors [5], locomotive [6] and energy harvesting [7–9] devices. Since the successful exfoliation of graphene sheet from graphite, the two-dimensional (2D) materials attracted a variety of interest owing to their remarkable physical and chemical properties [10–12], Such as the high flexibility of graphene [13], the on-site proton transfer phenomenon [14], H2O molecule dissociation of metal-embedded nitrogendoped graphene [15], and high transmittance of pentagonal ZnO2 in the visible range of light [16]. In addition, 2D materials could be applied in the nanoscale systems. Therefore, the 2D materials opened a new field of nanopiezoelectric research. The nanopiezoelectric materials could be ⁎

widely applied in many nanoelectromechanical systems, such as nanosized robots [17], sensors [18,19], and artificial muscles [20,21]. Unfortunately, graphene sheet does not have the piezoelectric effect because it has the inversion symmetry center. However, its inversion symmetry center can be broken by applying the uniaxial strain [22], introducing the specific structural defects [23], and absorbing the foreign atoms [24]. In the past few years, the piezoelectric effect of 2D doped graphene [25–28], hexagonal boron nitride sheets [29,30], and transition metal dioxides [31] has been studied by first-principles. Currently, the biggest challenge is to look for the materials with higherefficiency piezoelectric effect. Very recently, Jia-He Lin et al proved that the group V-IV-III-VI semiconductor sheets are stable with indirect bandgap [32]. The structures consist of four sublayers stacked in the sequence V-IV-III-VI from the bottom layer to the top layer of the sheets. The structures belong to the 3 m point group, which does not have the inversion center and mirror symmetry. It indicates that they have nonzero in-plane piezoelectric coefficients (e11, d11) and out-of-plane piezoelectric coefficients (e31, d31) [33]. Due to the small thickness of 2D materials, it will be easier in experiment to apply electric fields along the z-direction

Corresponding authors at: Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012, China. E-mail addresses: [email protected] (X.-C. Wang), [email protected] (F.-C. Liu).

https://doi.org/10.1016/j.apsusc.2018.09.004 Received 7 May 2018; Received in revised form 22 August 2018; Accepted 1 September 2018 Available online 05 September 2018 0169-4332/ © 2018 Elsevier B.V. All rights reserved.

Applied Surface Science 463 (2019) 918–922

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(perpendicular to the 2D materials plane) than x- or y-directions [34]. So the out-of-plane piezoelectric effect is useful in devices based on the inverse piezoelectric effect. Furthermore, the electronegativity difference between the nitrogen (N) and oxygen (O) atom layers is large. We expect that the group V-IV-III-VI (V = N; VI = O) sheets could exhibit large piezoelectric effect. In this paper, we use first-principles calculations to study the elastic and piezoelectric properties of the XN-MO sheets (X = Si, Ge and Sn; M = Al, Ga and In): SiN-AlO, GeN-GaO, and SnN-InO.

Table 1 The structural parameters and bandgap width for the XN-MO sheets in reference and this work. a* is the lattice constant. h is the thickness of sheet. l is the distance between the M and X atomic layers. Eg is the bandgap width. The other theoretical calculation data are from Ref. [32]. Material

Other theoretical calculation *

SiN-AlO GeN-GaO SnN-InO

2. Computational details Based on the projector-augmented wave (PAW) method [35], firstprinciples calculations were implemented by the Vienna ab initio Simulation Package (VASP) [36,37]. The generalized gradient approximation (GGA) [38] with the Perdew-Burke-Ernzerhof (PBE) functional [39] was used for the exchange-correlation interactions. The electron wave functions were expanded by plane waves with a 500 eV energy cutoff. A 20 Å vacuum layer along the z-direction was employed to avoid the interactions between neighboring sheets. The reciprocal space was sampled by the Γ–centered grid with an 11 × 18 × 1 k-point mesh [40]. The 10−6 eV and 10−4 eV/Å convergence criteria were set for the total energy change and force. Based on these settings, the calculated lattice constant for SiN-AlO is 2.93 Å, which is well consistent with the previous theoretical result (2.88 Å) [32]. In order to obtain the accurate bandgap width, the band structures were calculated by the Heyd-Scuseria-Ernzerhof (HSE06) functional [41].

This work

a (Å)

h (Å)

Eg (eV)

a* (Å)

h (Å)

l (Å)

Eg (eV)

2.88 3.10 3.21

3.69 3.94 4.14

3.22 2.52 2.06

2.93 3.11 3.44

3.76 3.97 4.49

2.54 2.56 2.94

3.02 2.42 1.19

respectively. For the top view, the M atoms and O atoms form a hexagonal structure, the X atoms and N atoms also form a hexagonal structure. For the side view, the hexagonal MO and XN are connected by the bonds between the M and X atoms. Table 1 lists the lattice constant a* (Å), thickness h (Å) of sheet, distance l (Å) between the M and X atomic layers, and band gap width Eg (eV). For comparison, the a*, h, and Eg in reference [32] also are listed. The a*, h, and Eg in this work show well consistent with those in reference. For example, the difference of a*, h, and Eg for SiN-AlO between this work and reference are 1.74%, 1.90%, and 6.21%, respectively. In order to understand the effect of the charge distribution and the characteristics of bonding, we first study the charge density difference of these three XN-MO sheets. The charge density difference is defined as the difference between the XN-MO sheet and the superposition of atomic charge densities, i.e., Δρ(r) = ρ[XN-MO] − Σμρatom(r-Rμ) [42], which is shown in Fig. 2. For all side views, there is a charge accumulation between the M and X atoms, which indicates that the hexagonal MO and XN are connected by the covalent bonds between the M and X atoms. For all top views, there is a charged accumulation around the O atoms, and a charged depletion around the M atoms, which indicates the ionic bond interaction between the O and M atoms. There is also the ionic bond interaction between the N and X atoms. Moreover, we also perform the Bader charge analysis for these three XN-MO sheets, which can quantitatively study the polarization charge distribution. It is obvious that the O and N atoms in SiN-AlO sheet possess more negatively charged than that in other two sheets. Because the electronegativity difference (1.83) between the O and Al atoms is larger than that (1.63) between the O and Ga atoms, and that (1.66) between

3. Results and discussion The structures consist of four sublayers stacked in the sequence VIV-III-VI from the bottom layer to the top layer of the sheets. The top and side views of XN-MO sheets are showed in Fig. 1(a) and (b),

Fig. 2. The 3D side (upper pattern) and top (lower pattern) views of charge density difference and Bader charge analysis for: (a) SiN-AlO, (b) GeN-GaO, and (c) SnN-InO, respectively. The pink, green, pale blue, brown, blue, black, purple, and pink brown balls represent the O, N, Al, Si, Ga, Ge, In, and Sn atoms, respectively. The yellow and light blue isosurfaces represent the electron accumulation and electron depletion in the isosurface of 0.008 e/Å3, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 1. The structures of the XN-MO sheets. (a) and (b) is the top and side view, respectively. The pink, pale blue, brown, and green balls represent the O, M, X, and N atoms, respectively. a* is the lattice constant of 2D unit cell with rhombus shape. h is the thickness of sheet, which is defined by the distance between the O and N atomic layers. l is the distance between the M and X atomic layers. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) 919

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between dipolar polarization (Pi) and strain (εjk). dij is the coupling between strain (εjk) and macroscopic electric field (Ei) [48]. Utilizing Maxwell relationship, they can be written as:

the O and In atoms. The electronegativity difference (1.14) between the N and Si atoms is larger than that (1.03) between the N and Ge atoms, and that (1.08) between the N and Sn atoms. The polarization charge distribution between the AlO and SiN layer is 0.94 electron/tetragonalcell, which is larger than that 0.10 electron/tetragonal-cell between the GaO and GeN layer, and that 0.06 electron/tetragonal-cell between the InO and SnN layer. Then the elastic properties of these three XN-MO sheets are calculated. Following the theory as previous reports [43], the in-plane elastic stiffness coefficients (C11, C22 and C12) for 2D structures can be calculated by:

C11 =

1 ∂ 2U , 2 A0 ∂ε11

C22 =

1 ∂ 2U , 2 A0 ∂ε22

C12 =

1 ∂ 2U A0 ∂ε11 ∂ε22

(2)

SiN-AlO GeN-GaO SnN-InO

Relaxed-ion

C11

C12

C11

C12

v⊥

Y

287.22 232.29 181.07

72.71 70.45 61.23

237.21 181.30 127.14

73.05 56.89 46.95

0.37 0.44 0.50

214.71 163.45 109.80

⎟

d11 =

e11 C11−C12

(5)

d31 =

e31 C11 + C12

(6)

The in-plane piezoelectric stress coefficients e11 is the change of dipolar polarization (P1) along the x-direction of tetragonal cell in Fig. 1(a) with the uniaxial strain ε11. The out-of-plane piezoelectric stress coefficients e31 is the change of dipolar polarization (P3) along the z-direction with the uniaxial strain ε11. By Berry phase method in VASP, we calculate the dipolar polarizations (P1 and P3) under uniaxial strain ε11 ranging from −0.01 to 0.01 in steps of 0.005, and fit the linear relationship. The slope gives the piezoelectric stress coefficients. Fig. 3 presents the relationship between the dipolar polarizations (P1 and P3) and uniaxial strain ε11 for the XN-MO sheets under the clamped- and relaxed-ion condition. For both clamped- and relaxed-ion conditions, according to the relationship as shown in Fig. 3 and equations (5)–(6), we derive the piezoelectric stress coefficients (e11 and e31) and piezoelectric strain coefficients (d11 and d31) of these three XN-MO sheets, as shown in Table 3. The e11, d11 and d31 of them under the relaxed-ion condition are larger than that under the clamped-ion condition, while the e31 of them under the relaxed-ion condition is smaller than that under the clamped-ion condition. This fact is caused by the relative displacements of atoms during uniaxial strain. Among these three XN-MO sheets, the SiN-AlO exhibits the largest e11 (11.04 × 10−10 C/m). The large polarization charge distribution between the Al and O atoms, Si and N atoms, contribute the P1 to have a large change under uniaxial strain. All these three XN-MO sheets exhibit large e11. Among them, the e11 (10.18 × 10−10 C/m) of SnN-InO is the smallest, but is still remarkably larger than BN (1.38 × 10−10 C/m) [46], and AlN (2.23 × 10−10 C/m) [49], while it has the same order of magnitude as fluorinated AlN sheet (11.04 × 10−10 C/m) [50]. The d11 gradually increases with the row number of atoms in sheets, and that (12.69 pm/V) of SnN-InO is the largest, which is larger than that (3.73 pm/V) of MoS2 by 3 times, that (1.38 pm/V) of BN by 9 times [46], and that (2.75 pm/V) of AlN by 4 times [49]. For out-of-plane piezoelectric effect, among these three XNMO sheets, the d31 (8.66 pm/V) of SnN-InO is the largest, which is larger than that (0.07–0.46 pm/V) of the Janus group-III chalcogenide sheets by more than 18 times [51], because its large Poisson ratio means that the thickness have a large change under uniaxial strain, which contribute the P3 to have a large change under uniaxial strain. The remarkable out-of-plane piezoelectric effect of SnN-InO would endow the sheet multiple functions for piezoelectric applications.

Table 2 The calculated clamped- and relaxed-ion elastic stiffness coefficients (C11 and C12), relaxed-ion Poisson ratio (v⊥), and relaxed-ion Young modulus (Y) for the XN-MO sheets. The elastic stiffness coefficients and Young modulus are in units of N/m. Clamped-ion

(4)

⎟

where i, j, k = 1, 2, 3, which represents the x-, y-, z-direction, respectively. Since the structure of XN-MO sheets does not have the inversion center and mirror symmetry, they have the nonzero in-plane piezoelectric coefficients (e111, d111) and out-of-plane piezoelectric coefficients (e311, d311). Based on the Voigt notation for strain and stress, these piezoelectric coefficients can be simplified as e11, d11, e31, and d31, respectively. Employing the elastic stiffness coefficients and 3 m point group symmetry, the relationship between e11, e31 and d11, d31 can be shown by the following equation [34]:

A 7 × 7 grid with the uniaxial strain ε11 and ε22 in steps of 0.002 from −0.006 to 0.006 is used to calculate the unit-cell energy. If all atoms are fully relaxed under every uniaxial strain, the calculated elastic stiffness coefficients are relaxed-ion elastic stiffness coefficients, which can be measured in experiment. If all atoms are not relaxed under every uniaxial strain, the calculated elastic stiffness coefficients are clamped-ion elastic stiffness coefficients. Table 2 lists the clampedand relaxed-ion elastic stiffness coefficients (C11 and C12) of these three XN-MO sheets. It is obvious that the relaxed-ion elastic stiffness coefficients and the clamped-ion elastic stiffness coefficients of these three XN-MO sheets are different owing to the relative displacements of atoms during uniaxial strain. In addition, we also calculate the relaxedion Poisson ratio (v⊥) and Young modulus (Y). The Poisson ratio describes the change of sheet thickness with the in-plane strain and can be calculated by Δh/h = −v⊥(ε11 + ε22) [45]. The Young modulus de2 2 −C12 scribes the stiffness of crystals and can be calculated by Y = (C11 )/ C11 [34]. The results reveal that the Poisson ratio gradually increases with the row number of atoms in sheets, and that of SnN-InO (0.50) is the largest, which is larger than WTe2 (0.39) [46], and InSe (0.40) [45]. This means that its thickness will have a large change under uniaxial strain. The Young moduli are found to follow the sequence of SiN-AlO (214.71 N/m) > GeN-GaO (163.45 N/m) > SnN-InO (109.80 N/m). Among them, the Young modulus of SnN-InO is the smallest, while that of SiN-AlO is the largest but is much smaller than two-thirds of 341 N/ m for graphene [47]. This means that they are flexible compared to graphene and can have a large uniaxial strain under small stress. The piezoelectric effect is the mutual interaction between mechanical and electrical. The coefficients describing this interaction are the piezoelectric coefficients, which include the piezoelectric stress coefficients (eijk) and piezoelectric strain coefficients (dijk). eij is the coupling

Material

∂εjk ⎞ ∂P dijk = ⎜⎛ i ⎟⎞ = ⎛ ⎝ ∂σjk ⎠E ⎝ ∂Ei ⎠σ ⎜

(1)

1 2 2 C11 (ε11 + ε22 ) + C12 ε11 ε22 2

(3)

⎜

where A0 is the unit-cell area at equilibrium structure; ε11 and ε22 is the uniaxial strain along the x- and y-direction, respectively; U is the unitcell energy corresponding to the uniaxial strain. Due to the hexagonal structure of the XN-MO sheets, the elastic stiffness coefficient C11 = C22 [44]. Thus the change of energy under small uniaxial strain can be expressed as:

ΔU (ε11, ε22) =

∂σjk ⎞ ∂P eijk = ⎜⎛ i ⎞⎟ = −⎛ ∂ ε ∂Ei ⎠ε jk ⎝ ⎝ ⎠E

920

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Fig. 3. The dipolar polarization along the (a) x-direction and (b) z-direction changes with the uniaxial strain ε11 for the XN-MO sheets under the clamped-ion condition, respectively. (c) and (d) are the same ones under the relaxed-ion condition, respectively. The slope gives the clamp- and relaxed-ion piezoelectric stress coefficients e11 and e31.

materials with high-efficiency piezoelectric effect. The flexible 2D material SnN-InO with appreciable out-of-plane piezoelectric properties can be used in many nanoelectromechanical systems, such as nanosized robots, sensors, and artificial muscles.

Table 3 The calculated clamped- and relaxed-ion piezoelectric stress coefficients (e11 and e31) in units of 10−10 C/m, and piezoelectric strain coefficients (d11 and d31) in units of pm/V for the XN-MO sheets. Material

Clamped-ion

Relaxed-ion

Acknowledgements SiN-AlO GeN-GaO SnN-InO

e11

e31

d11

d31

e11

e31

d11

d31

5.80 6.56 6.33

14.36 9.06 15.69

2.70 4.05 5.28

3.99 2.99 6.48

11.04 10.77 10.18

13.93 8.48 15.08

6.73 8.66 12.69

4.49 3.56 8.66

This work was supported by the National Natural Science Foundation of China (Grant No. 11474123), and the Natural Science Foundation of Jilin Province of China (Grant No. 20170101154JC). References

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Based on first-principles calculations, the elastic and piezoelectric properties of the XN-MO sheets are studied. The elastic stiffness coefficients and piezoelectric coefficients of these three XN-MO sheets under the relaxed-ion condition are different from that under the clamped-ion condition owing to the relative displacements of atoms during uniaxial strain. The Young moduli of these three XN-MO sheets mean they are more flexible than graphene. All these three XN-MO sheets exhibit large in-plane piezoelectric coefficients (6.73, 8.66, 12.69 pm/V) and out-of-plane piezoelectric coefficients (4.49, 3.56, 8.66 pm/V). This study illustrates that the broken inversion symmetry and the large dipolar polarization of sheet can remarkably enhance the piezoelectric effect of 2D structure. It gives us a way to find the 921

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