Strain control of two-dimensional ferroelectric In<sub>2</sub>Se<sub>3</sub>/InSe vertical heterojunction energy band

Li Yong-Ning; Xie Yi-Qun; Wang Yin

doi:10.7498/aps.70.20211158

Abstract

In recent years, two-dimensional ferroelectric heterojunctions have shown potential applications in the fields of high-density storage and optoelectronic devices. The development of novel two-dimensional ferroelectric heterojunctions is an important current research direction. In this work, first-principles calculations are used to study the band structure and stress control of In₂Se₃/InSe vertical heterojunction composed of two-dimensional ferroelectric material α-In₂Se₃ and monolayer InSe. The calculations show that the In₂Se₃/InSe heterojunction is an indirect band gap semiconductor with type-II band matching. When the polarization direction of In₂Se₃ is perpendicular to the surface facing outward, the band gap is 0.50 eV, and the top and bottom of the valence band originate from InSe and In₂Se₃ respectively; when the polarization direction of In₂Se₃ points inward the plane, the band gap decreases by 0.04 eV, and the sources of the top of the valence band and the bottom of the conduction band are interchanged. Under in-plane stretching, the greater the degree of stretching, the smaller the band gap is. After a certain threshold is exceeded, the heterojunction changes from a semiconductor into a conductor, which can also change the heterojunction with an indirect band gap into that with a direct band gap. The research results of this work show that changing the polarization direction and applying stress is an effective way to control the two-dimensional In₂Se₃/InSe ferroelectric heterojunction, which can provide a theoretical reference for designing the relevant ferroelectric devices.

Keywords:

two-dimensional ferroelectric heterojunction /
band modulation /
mechanical strain /
first principles

Authors and contacts

1.
Department of Physics, Shanghai University, Shanghai 200444, China
2.
Department of Physics, Shanghai Normal University, Shanghai 200030, China

Corresponding author: Wang Yin, yinwang@shu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11774217, 11804216, 51871156)

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References

[1]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A 2004 Science 306 666 Google Scholar
[2]	Lu W, Nan H, Hong J, Chen Y, Zhu C, Liang Z, Ma X, Ni Z, Jin C, Zhang Z 2014 Nano Res. 7 853 Google Scholar
[3]	Lalmi B, Oughaddou H, Enriquez H, Kara A, Vizzini S, Ealet B, Aufray B 2010 Appl. Phys. Lett. 97 183
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[6]	Bertolazzi S, Krasnozhon D, Kis A 2013 ACS Nano 7 3246 Google Scholar
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Cited By

图 1 (a) InSe/In₂Se₃异质结的3种堆叠方式, 黑色虚线箭头标注了异质结不同层的In原子的位置关系; (b) 3种结构在不同层间距下的能量; (c)图1(b)中黑色虚框部分的局部放大图

Figure 1. (a) Three stacking methods of InSe/In₂Se₃heterojunctions, where black dashed arrows mark the positional relationship of In atoms in different layers of the heterojunction; (b) formation energy of the three structures at different layer spacings; (c) a partial enlarged view of the black dashed part in Fig.1 b).

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图 2 (a) In₂Se₃/InSe (I)和In₂Se₃/InSe (II)的晶格结构, 黑色虚框表示晶格, 红色箭头表示异质结中In₂Se₃的自发极化方向; (b) In₂Se₃/InSe (I)和In₂Se₃/InSe (II)的结合能对比

Figure 2. (a) Lattice structure of In₂Se₃/InSe (I) and In₂Se₃/InSe (II), where the black dashed frame represents the crystal lattice, and the red arrow represents the spontaneous polarization direction of In₂Se₃; (b) binding energy comparison of In₂Se₃/InSe (I) and In₂Se₃/InSe (II).

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图 3 (a) In₂Se₃/InSe (I)的能带结构及(b)态密度; (c) In₂Se₃/InSe (II)的能带结构及(d)态密度. 能带图中红色和蓝色表示InSe及In₂Se₃对能带的贡献, 黑色箭头表示带隙, 由CBM指向VBM;(e)In₂Se₃/InSe (I)和In₂Se₃/InSe (II) CBM和VBM所在能带的电荷空间分布

Figure 3. (a) Band structure of In₂Se₃/InSe (I) and (b) density of states; (c) band structure of In₂Se₃/InSe (II) and (d) density of states, where the red and blue in the energy band diagram indicate the contribution of InSe and In₂Se₃ to the energy band, and the black arrow indicates the band gap, pointing from CBM to VBM; (e) decomposed charge densities of CBM and VBM for In₂Se₃/InSe (I) and In₂Se₃/InSe (II).

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图 4 (a) In₂Se₃/InSe (I) 和 (b) In₂Se₃/InSe (II)沿Z方向的平面平均差分电荷密度. 图中黄色和青色包络面分别表示电子的聚集和耗尽区

Figure 4. (a) Plane-averaged charge density difference forIn₂Se₃/InSe (I) and (b) In₂Se₃/InSe (II) at equilibrium distance along the Z direction, where the yellow and cyan envelope areas representelectron accumulation and depletion, respectively.

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图 5 双轴应变(左)和单轴应变(右)的晶胞选取以及应变施加方向.

Figure 5. Unit cell selection and strain application direction of biaxial strain (left) and uniaxial strain (right).

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图 6 (a) 不同双轴应变下In₂Se₃/InSe (I)的带隙; (b)不同双轴应变下In₂Se₃/InSe (II)的带隙

Figure 6. (a) Band gap of In₂Se₃/InSe (I) under biaxial strain; (b) band gap of In₂Se₃/InSe (II) under biaxial strain.

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图 7 (a)−(d)4%、8%、–4%和–8%双轴应变下In₂Se₃/InSe (I)的投影能带结构; (e)−(h) 2%、8%、–2%和–8%双轴应变下In₂Se₃/InSe (II)的投影能带结构. 能带图中红色部分表示InSe对能带的贡献, 蓝色部分表示In₂Se₃对能带的贡献

Figure 7. (a)−(d) The projected band structure of In₂Se₃/InSe (I) under 4%, 8%, –4% and –8% biaxial strain; (e)−(h) Projected band structure of In₂Se₃/InSe (II) under 2%, 8%, –2% and –8% biaxial strain. The red part of the energy band indicates the contribution of InSe, the blue part indicates the contribution of In₂Se₃.

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图 8 –4%和–8%双轴应变下In₂Se₃/InSe(I)CBM和VBM所在能带的电荷空间分布以及–2%及–8%双轴应变下In₂Se₃/InSe (II)CBM和VBM所在能带的电荷空间分布

Figure 8. Decomposed charge densities of CBM and VBM for In₂Se₃/InSe (I) under –4% and –8% biaxial strain and thedecomposed charge densities of CBM and VBM for In₂Se₃/InSe (II) under –2% and –8% biaxial strain.

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图 9 (a) x方向与y方向单轴应变和双轴应变下In₂Se₃/InSe (I)的带隙; (b) x方向与y方向单轴应变和双轴应变下In₂Se₃/InSe (II)的带隙

Figure 9. (a) Band gap of In₂Se₃/InSe (I) under x-axis strain, y-axis strain and biaxial strain; (b) band gap of In₂Se₃/InSe (II) under x-axis strain, y-axis strain and biaxial strain.

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图 10 (a)−(d)x和y方向10%、–10%应变下In₂Se₃/InSe (I)的投影能带结构; (e)−(h)x和y方向10%、–4%应变下In₂Se₃/InSe (II)的投影能带结构. 能带图中红色部分表示InSe对能带的贡献, 蓝色部分表示In₂Se₃对能带的贡献

Figure 10. (a)−(d) Projected band structure of In₂Se₃/InSe (I) under 10%, –10% x-axis strain and 10%, –10% y-axis strain; (e)−(h) projected band structure of In₂Se₃/InSe (II) under 10%, –4% x-axis strain and 10%, –4% y-axis strain. The red part of the energy band indicates the contribution of InSe, the blue part indicates the contribution of In₂Se₃.

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表 1 双轴应变下In₂Se₃/InSe (II)及In₂Se₃/InSe (I)的带隙.

Table 1. Band gap of In₂Se₃/InSe (I) and In₂Se₃/ InSe(II) under biaxial strain.

μ/%	In₂Se₃/InSe (I)		In₂Se₃/InSe (II)
μ/%	Gap/eV	Character	Gap/eV	Character
–10	0.28	direct	0.08	direct
–8	0.60	direct	0.34	direct
–6	0.84	direct	0.50	indirect
–4	0.70	indirect	0.55	indirect
–2	0.56	indirect	0.53	indirect
0	0.50	indirect	0.46	indirect
2	0.21	indirect	0.37	indirect
4	0.07	indirect	0.20	indirect
6	—	metallic	0.02	indirect
8	—	metallic	—	metallic
10	—	metallic	—	metallic

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[1]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A 2004 Science 306 666 Google Scholar
[2]	Lu W, Nan H, Hong J, Chen Y, Zhu C, Liang Z, Ma X, Ni Z, Jin C, Zhang Z 2014 Nano Res. 7 853 Google Scholar
[3]	Lalmi B, Oughaddou H, Enriquez H, Kara A, Vizzini S, Ealet B, Aufray B 2010 Appl. Phys. Lett. 97 183
[4]	Guo J, Chen X, Jin S, Zhang M, Liang C 2015 Catal. Today 246 165 Google Scholar
[5]	Haigh S J, Gholinia A, Jalil R, Romani S, Britnell L, Elias D C, Novoselov K S, Ponomarenko L A, Geim A K, Gorbachev R 2012 Nat. Mater. 11 764 Google Scholar
[6]	Bertolazzi S, Krasnozhon D, Kis A 2013 ACS Nano 7 3246 Google Scholar
[7]	Tongay S, Fan W, Kang J, Park J, Koldemir U, Suh J, Narang D S, Liu K, Ji J, Li J, Sinclair R, Wu J 2014 Nano Lett. 14 3185 Google Scholar
[8]	Shim G W, Yoo K, Seo S B, Shin J, Jung D Y, Kang I S, Ahn C W, Cho B J, Choi S Y 2014 Acs Nano 8 6655 Google Scholar
[9]	Zhao Z, Xu K, Ryu H, Zhu W 2020 ACS Appl. Mater. Interf. 12 51820 Google Scholar
[10]	Ayadi T, Debbichi L, Badawi M, Said M, Kim H, Rocca D, Lebègue S 2019 Physica E: Low-dimens. Syst. Nanostruct. 114 113582 Google Scholar
[11]	Li Y, Chen C, Li W, Mao X, Liu H, Xiang J, Nie A, Liu Z, Zhu W, Zeng H 2020 Adv. Electron. Mater. 6 2000061 Google Scholar
[12]	Zheng Z, Yao J, Yang G 2017 ACS Appl. Mater. Interf. 9 7288 Google Scholar
[13]	Ayadi T, Debbichi L, Badawi M, Said M, Rocca D, Lebègue S 2021 Appl. Surf. Sci. 538 148066 Google Scholar
[14]	Zhou B, Jiang K, Shang L, Zhang J, Li Y, Zhu L, Gong S J, Hu Z, Chu J 2020 J. Mater. Chem. C 8 11160 Google Scholar
[15]	Dhakal K P, Roy S, Jang H, Chen X, Yun W S, Kim H, Lee J, Kim J, Ahn J H 2017 Chem. Mater. 29 5124 Google Scholar
[16]	Desai S B, Seol G, Kang J S, Fang H, Battaglia C, Kapadia R, Ager J W, Guo J, Javey A 2014 Nano Lett. 14 4592 Google Scholar
[17]	Guo Y, Li B, Huang Y, Du S, Sun C, Luo H, Liu B, Zhou X, Yang J, Li J, Gu C 2020 Nano Res. 13 2072 Google Scholar
[18]	Liu X, Song C, Wu Z, Wang J, Pan J, Li C 2020 J. Phys. D: Appl. Phys. 53 385002 Google Scholar
[19]	Rahimi K 2021 Mater. Lett. 282 128680 Google Scholar
[20]	Grimme S, Antony J, Ehrlich S, Krieg H 2010 J. Chem. Phys. 132 154104 Google Scholar
[21]	Ding Y M, Shi J J, Xia C, Zhang M, Du J, Huang P, Wu M, Wang H, Cen Y L, Pan S H 2017 Nanoscale 9 14682 Google Scholar
[22]	Hu T, Zhou J, Dong J 2017 Phys. Chem. Chem. Phys. 19 21722 Google Scholar
[23]	Ding W, Zhu J, Wang Z, Gao Y, Xiao D, Gu Y, Zhang Z, Zhu W 2017 Nat. Commun. 8 14956 Google Scholar
[24]	Zhou B, Gong SJ, Jiang K, Xu L, Zhu L, Shang L, Li Y, Hu Z, Chu J 2019 J. Phys.: Condens. Matter. 32 055703
[25]	Bultinck P 2007 Faraday Discuss. 135 347 Google Scholar
[26]	Catalan G, Lubk A, Vlooswijk A H G, et al. 2011 Nat. Mater. 10 963 Google Scholar
[27]	Cao Y, Chen L Q, Kalinin S V 2017 Appl. Phys. Lett. 110 202903 Google Scholar

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Strain control of two-dimensional ferroelectric In₂Se₃/InSe vertical heterojunction energy band

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Corresponding author: Wang Yin, yinwang@shu.edu.cn

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Strain control of two-dimensional ferroelectric In2Se3/InSe vertical heterojunction energy band

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Strain control of two-dimensional ferroelectric In₂Se₃/InSe vertical heterojunction energy band