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Effect of Tensile and Compression Deformation on the Electronic Structure and Optical Properties of Single-layer Black Phosphorus

Wang Jia-Xin, Wang Ying, Liu Gui-Li, Wei Lin, Zhang Guo-Ying

PII: S0921-4526(19)30655-6DOI: https://doi.org/10.1016/j.physb.2019.411755Reference: PHYSB 411755

To appear in: Physica B: Physics of Condensed Matter

Received Date: 09 March 2019Accepted Date: 05 October 2019

Please cite this article as: Wang Jia-Xin, Wang Ying, Liu Gui-Li, Wei Lin, Zhang Guo-Ying, Effect of Tensile and Compression Deformation on the Electronic Structure and Optical Properties of Single-layer Black Phosphorus, (2019), Physica B: Physics of Condensed Matter https://doi.org/10.1016/j.physb.2019.411755

This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

© 2019 Published by Elsevier.

Funding: This work was supported by the National Natural Science Foundation of China [Grant Number

51371049] and the Natural Science Foundation of Liaoning Province [Grant Number 20102173].

†Corresponding author E-mail: wangying30@hotmail.com

Adress:No.111 Shenliao Westroad Economic and Technological Development District Shenyang, Liaoning PR ChinaPhone number:+86-18940216198

Effect of Tensile and Compression Deformation on the

Electronic Structure and Optical Properties of Single-layer

Black Phosphorus

Wang Jia-Xin Wang Ying† Liu Gui-Li Wei Lin Zhang Guo-Ying

(College of architecture and civil engineering，Shenyang University of Technology，

Shenyang ，Liaoning 110870，China)

(College of physics, Shenyang Normal University, Shenyang 110034, China)

Abstract:

Based on the first-principles method of density functional theory, the electronic

structure and optical properties of single-layer black phosphorus under tensile and

compression deformation were calculated. It is found that the overall trend of

single-layer black phosphorus stability decreased with the increase of tensile and

compression deformation; In the interval where the tensile deformation changes from

0% to 2.5%, the band gap of single-layer black phosphorus tends to increase first and

then decrease. Under compression deformation, the band gap of single-layer black

phosphorus decreased as the compression deformation increased; The highest

absorption and reflection peaks of the light were blue-shifted first when the value of

tensile deformation was small. Then, as the tensile deformation increased, both were

red-shifted. Under compression deformation, as the compression deformation

increased, the highest absorption and reflection peaks of the light were red-shifted

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gradually.

Keywords: black phosphorus; tensile deformation; compression deformation; band

structure; density of states; optical properties

1. Introduction

Black phosphorus is a black, metallic luster semiconductor whose lattice is a

six-membered ring that is linked to each other and each atom is connected to three

other atoms. Studies have shown that the excellent properties of black phosphorus

make it an undisputed huge potential application in nanoelectronic devices such as

electronics, optoelectronics, and thermoelectrics[1-5].

In 1914, the researcher Bridgman first converted white phosphorus to black

phosphorus under high temperature and high pressure conditions[6]. Research on the

properties of black phosphorus has been carried out one after another. The study on

the electrical properties of black phosphorus dates back to the 1950s[7]. In recent

years, with the rapid development of science and technology, the importance of black

phosphorus has become increasingly prominent, and its research has become a hot

spot[8-12]. Zhang Yuanbo and Chen Xianhui[13] obtained a black phosphorus crystal

with nanometer thickness by using a method similar to that of exfoliating graphene.

Park and Jiang et al.[14] described in detail the anisotropy of a single-layer black

phosphorus under tensile and compressive stresses. Liu[2] et al. found that in-plane

stretching and compression had a certain influence on the band gap of

two-dimensional black phosphorus when stress was applied to the two-dimensional

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black phosphorus surface. Wang Jingru et al.[15] found that the defects and sulfur

doping could change the band gap of single-layer black phosphorus, and the range of

band gap changes was large. Wang et al.[16] demonstrated the relationship between the

band gap of two-dimensional black phosphorus and the number of layers. The smaller

the number of layers, the larger the band gap. The single-layer black phosphorus had

the largest band gap. Qu Weiwei et al.[17] studied the band gap of single and

multi-layer black phosphorus crystals due to the applied stress and the number of

layers.

Previous studies have focused on intrinsic single-layer black phosphorus, and

little research has been done on the electronic structure and optical properties of

single-layer black phosphorus in deformation[18,19]. However, single-layer black

phosphorus is inevitably subjected to various deformations in applications such as

electrons and optoelectronics. Tensile and compression deformation are two common

types. Therefore, it is especially important to study the changes in electronic structure

and optical properties under tensile and compression deformation. In this paper, the

influence of tensile and compression deformation on the electronic structure and

optical properties of single-layer black phosphorus is investigated by calculation and

analysis, which can provide guidance for the application of single-layer black

phosphorus materials in optoelectronic devices.

2. Calculation method and model

In this paper, the CASTEP module[20] in Acclerys Material Studio 6.1 is used to

optimize the simulation and calculation of the intrinsic single-layer black phosphorus

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and the single-layer black phosphorus under different tensile and compression

deformation variable. Generalized gradient approximate gradient (GGA) and

Perdew-Burke-Ernzerhof (PBE) functional are used in the process of optimization and

calculation. In inverted lattice space, the cutoff energy of planar wave expansion is

500eV. The Brillouin district k grid points based on the Monkhorst-Pack lattice

choose to use 9×9×1 integral to calculate the system's total energy and electronic

structure[21]. The convergence value of iterative accuracy is 5.0x10-6ev/atom. The

internal stress convergence standard is 0.02GPa. The interaction force between atoms

is less than 0.01eV/Å[22]. A vacuum layer with a thickness of 15 Å is set to avoid the

influence of the effect of adjacent layers on its calculation results[23]. The method of

applying deformation effect to single-layer black phosphorus is shown in Fig. 1. For

the sake of simplicity, different atomic rows are represented by different colors. b0

and b respectively represent the lattice constants of the intrinsic 3 × 3 single-layer

black phosphorus and the 3 × 3 single-layer black phosphorus after tensile or

compression deformation. When tensile deformation is applied to single-layer black

phosphorus, first, apply 0.5(b-b0) tensile deformation to the left of the red part and

0.5(b-b0) tensile deformation to the right of the yellow part, and fix the coordinates of

the two rows of edge atoms. The same applies to the method of compressing

single-layer black phosphorus. The red and yellow phosphorus atoms are deformed in

the same magnitude and opposite direction as the tensile deformation. The

intermediate atoms are geometrically optimized to determine their stable positions.

After geometric optimization, the phosphorus atoms in the middle are also subjected

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to a corresponding proportion of tensile and compression deformation. In this paper

the tensile and compression of single-layer black phosphorus is along the armchair

direction. The Poisson’s ratio of single-layer black phosphorus in armchair direction

is 0.17[24]. The influence of Poisson’s ratio on the electronic structure and optical

properties of single-layer black phosphorus under the tensile and compression

deformation is considered in the calculation. The results show that the tensile and

compression deformation with Poisson’s ratio and without Poisson’s ratio have

slightly different effects on the binding energy, energy band structure, density of

states and optical properties of single-layer black phosphorus, but little effect on its

overall trend. Therefore, the influence of Poisson’s ratio on the electronic structure

and optical properties of single-layer black phosphorus under the tensile and

compression deformation is not included in this paper.

(a) (b)

Fig. 1. Single-layer black phosphorus stress diagram: (a) the main view; (b) the top

view.

3. Result and discussion

3.1 Effect of tensile and compression deformation on the stability of

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single-layer black phosphorus

The stability of the single-layer black phosphorus structure can be characterized

by binding energy. In order to study the structural stability of single-layer black

phosphorus, the binding energy of the single-layer black phosphorus system with the

tensile and compression deformation variable changed from 0% to 2.5% is calculated.

The calculation formula for binding energy is[25]:

Ebind=Estru-Eatom (1)

Among them, Estru is the total energy of single-layer black phosphorus; Eatom is

the sum of the energy of each atom of single-layer black phosphorus. When the sum

of energy in the discrete states of single-layer black phosphorus is greater than the

total energy of single-layer black phosphorus, that is, the binding energy of

single-layer black phosphorus is negative, the structure is stable. The greater the

absolute value of the binding energy, the higher the stability of the single-layer black

phosphorus structure.

The calculation results of single-layer black phosphorus binding energy after

tensile and compression deformation are shown in Table 1. Binding energy 1 is the

binding energy of single-layer black phosphorus under tensile deformation; Binding

energy 2 is the binding energy of single-layer black phosphorus under compression

deformation. The data in the table shows that in the 3×3 single-layer black

phosphorus model established in this paper, there is a total of 36 phosphorus atoms in

the crystal cell, and the total binding energy of the intrinsic single-layer black

phosphorus is -196.08eV. Therefore, the binding energy of intrinsic single-layer black

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phosphorus per atom is -5.45ev /atom, which is not much different from that of black

phosphorus per atom in reference [26]. With the increase of tensile and compression

variables from 0% to 2.5%, the binding energy of single-layer black phosphorus is

negative and in a stable structural state. However, with the increase of tensile and

compression deformation, the overall trend of structural stability decreases gradually.

Table 1 Effect of different tensile and compression deformation variable on the

binding energy of single-layer black phosphorus.

Tensile/compression

deformation0% 0.5% 1.0% 1.5% 2.0% 2.5%

Binding energy 1/eV -196.08 -195.24 -194.88 -194.34 -194.22 -193.26

Binding energy 2/eV -196.08 -195.77 -195.73 -195.68 -194.86 -194.20

3.2 Effect of tensile and compression deformation on energy band

structure and density of states of single-layer black phosphorus

The band gap of single-layer black phosphorus is the energy difference from the

bottom of the conduction band to the top of the valence band. In semiconductors,

electrons in the valence band are excited to transition to conduction band. There are

free electrons in the conduction band and holes in the valence band. Both are two

carriers in a semiconductor. Only when carriers are generated can they conduct

electricity. Therefore, the size of the band gap reflects the minimum energy required

for the valence band electrons in the semiconductor to be excited to the conduction

band to generate carriers. Fig. 2 shows the energy band structure and density of states

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of the intrinsic single-layer black phosphorus. As shown in Fig. 2(a), the intrinsic

single-layer black phosphorus band gap is 0.715eV, which is close to 0.735eV in the

paper [27]. As can be seen from Fig. 2(b), the intrinsic single-layer black phosphorus

has a density of states of zero at the Fermi level, and the peak of the maximum density

of states occurs when the energy value is about -2eV.

Table 2 shows the single-layer black phosphorus band gap values subjected to

different tensile and compression deformation variable. In Table 2, Band gap 1 is the

band gap of single-layer black phosphorus under tensile deformation; Band gap 2 is

the band gap of single-layer black phosphorus under compression deformation. The

band structures of single-layer black phosphorus subjected to different tensile

deformation is shown in Fig. 3. As the tensile deformation variable increases, the

band gap of single-layer black phosphorus also increases. When the tensile

deformation variable reaches 0.5%, the band gap value rises to the highest. However,

as the tensile deformation variable continues to increase, the band gap tends to

decrease. That is, in the interval where the tensile deformation variable changes from

0% to 2.5%, the band gap tends to increase first and then decrease. The single-layer

black phosphorus band structures affected by different compression deformation are

shown in Fig. 4. As the compression deformation increases, the band gap of

single-layer black phosphorus decreases gradually.

Fig. 5(a) and Fig. 5(b) are the diagrams of density of states of single-layer black

phosphorus subjected to different tensile and compression deformations and partial

enlarged views of the density of states at the Fermi level. As can be seen from Fig. 5,

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the intrinsic single-layer black phosphorus has the largest value of density of states at

the peak of the density of states. When the tensile and compression deformation

variable becomes 2.5%, the density of states value of single-layer black phosphorus is

the smallest. The energy value at which the density of states reaches the maximum

peak decreases as the degree of tensile and compression increases. Under tensile

deformation, the region of density of states 0 at Fermi energy level increases first and

then decreases with the increase of tensile deformation. Under compression

deformation, the region of density of states 0 at Fermi energy level decreases with the

increase of compression deformation.

Table 2 Band gap of single-layer black phosphorus under different tensile and

compression deformation variable.

Tensile/compressio

n deformation0% 0.5% 1.0% 1.5% 2.0% 2.5%

Band gap 1/eV 0.715 0.876 0.874 0.790 0.729 0.657

Band gap 2/eV 0.715 0.650 0.486 0.310 0.041 0.027

(a) (b)

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Fig. 2. (a) the band structure of intrinsic single-layer black phosphorus; (b) the density

of states of intrinsic single-layer black phosphorus.

(a) (b)

(c) (d)

(e) (f)

Fig. 3. (a) - (e) band structures with tensile deformation of 0.5%, 1.0%, 1.5%, 2.0%

and 2.5%, respectively; (f) the variation trend of single-layer black phosphorus band

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gap.

(a) (b)

(c) (d)

(e) (f)

Fig. 4. (a) - (e) band structures with compression deformation of 0.5%, 1.0%, 1.5%,

2.0% and 2.5%, respectively; (f) the variation trend of single-layer black phosphorus

band gap.

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(a) (b)

Fig. 5. (a) density of states of single-layer black phosphorus subjected to different

tensile deformation variable; (b) density of states of single-layer black phosphorus

subjected to different compression deformation variable.

3.3 Effect of tensile and compression deformation on optical properties of

single-layer black phosphorus

In order to study the optical properties of single-layer black phosphorus under

different tensile and compression deformation variable, the light absorption

coefficient and reflectivity of the system are calculated and plotted. As shown in Fig.

6, Fig. 6(a) and (d) are overall diagrams of the light absorption coefficient of the

intrinsic single-layer black phosphorus and the single-layer black phosphorus under

different tensile and compression deformation. Fig. 6(b), (c), (e) and (f) are partial

enlarged views thereof. It can be seen from the Fig. 6(b) and (e) that single-layer

black phosphorus has no absorption of light when the wavelength is less than about 62

nm. As can be seen from the Fig. 6(c), when the wavelength is about 244 nm, the

intrinsic single-layer black phosphorus reaches a maximum absorption peak of about

109111 cm-1. The highest absorption peak is blue-shifted when the value of tensile

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deformation variable is small. The absorption peak is red-shifted as the tensile

deformation variable increases. The peaks are arranged in order from large to small:

the single-layer black phosphorus when the tensile deformation variable becomes

0.5%, 1.0%, 1.5%, 2.0%, 2.5%, and 0%. As can be seen from Fig. 6(f), the absorption

peak is gradually red-shifted with the increase of compression deformation. The peak

values are arranged in order from large to small: single-layer black phosphorus with

compression deformation of 0%, 0.5%, 1.0%, 1.5%, 2.0%, and 2.5%. As shown in

Fig. 6(a) and Fig. 6(d), when the wavelength of light is about 7800 nm, single-layer

black phosphorus stops absorption of light.

Fig. 7(a) and (d) are overall views of the light reflectivity of single-layer black

phosphorus under different tensile and compression deformation variable. Fig. 7(b),

(c), (e) and (f) are partial enlarged views thereof. As can be seen from the Fig. 7(b)

and (e), when the wavelength is about 62 nm, single-layer black phosphorus starts to

reflect light. As shown in Fig. 7(c), as the tensile deformation variable increases, the

reflectivity first is blue-shifted and then is red-shifted. The highest peak of reflectivity

occurs when the stretched shape variable becomes 0.5%, and its value is about 0.43.

The intrinsic single-layer black phosphorus has the smallest value at the reflectivity

peak and has a value of about 0.4. As shown in Fig. 7(f), the reflectivity is gradually

red-shifted as the compression deformation increases. The overall trend of reflectivity

peak decreases with the increase of compression deformation.

The red shift or blue shift of the absorption coefficient and reflectivity of light is

closely related to the size of the band gap. When the band gap becomes large, the

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peaks of the two are blue-shifted, and when the band gap becomes small, the peaks of

the two are red-shifted. This is consistent with the conclusions in the literature

[28-31].

(a) (b)

(c) (d)

(e) (f)

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Fig. 6. (a) is the absorption coefficient of light of single-layer black phosphorus under

different tensile deformation variable; (b) and (c) are partial enlarged views of (a); (d)

is the absorption coefficient of light of single-layer black phosphorus under different

compression deformation variable; (e) and (f) are partial enlarged views of (d).

(a) (b)

(c) (d)

(e) (f)

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Fig. 7. (a) is the reflectivity of single-layer black phosphorus under different tensile

deformation; (b) and (c) are partial enlarged views of (a); (d) is the light reflectivity of

single-layer black phosphorus under different compression deformation; (e) and (f)

are partial enlarged views of (d).

4 Conclusion

Based on the first principle of density functional theory, the binding energy, band

structure, density of states and optical properties of intrinsic single-layer black

phosphorus and single-layer black phosphorus under different tensile and

compression deformation variable are calculated.

The calculation results of binding energy showed that when the tensile and

compression deformation variable was in the range of 0%-2.5%, with the increase of

the tensile and compression deformation variable, the single-layer black phosphorus

was in a stable state but the overall stability trend was reduced.

The analysis of band structure and density of states showed that at the early stage

of small tensile deformation, the band gap of single-layer black phosphorus increased.

The single-layer black phosphorus band gap decreased with the increase of tensile

deformation. With the increase of compression deformation, the single-layer black

phosphorus band gap decreased. The value of intrinsic single-layer black phosphorus

was the largest at the peak of density of states.

The calculation of the optical properties of single-layer black phosphorus showed

that when the value of tensile deformation variable was small, the absorption

coefficient of light and the peak of the reflectivity were blue-shifted. When the value

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of tensile deformation variable was large, both the absorption coefficient of the light

and the peak of the reflectivity were red-shifted. With the increase of compression

deformation, the absorption coefficient and reflectivity of light were gradually

red-shifted. Under tensile deformation, the absorption coefficient and reflectivity peak

of intrinsic single-layer black phosphorus were the smallest. When the tensile

deformation was small, the peak values of absorption coefficient and reflectivity

increased. Then, with the increase of deformation, the peak value gradually decreased.

Under compression deformation, the absorption coefficient and reflectivity peak of

single-layer black phosphorus decreased with the increase of compression

deformation.

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There are no conflicts of interest

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