First-principles study of strain-tunable charge carrier transport properties and optical properties of CrI<sub>3</sub> monolayer

Wang Na; Xu Hui-Fang; Yang Qiu-Yun; Zhang Mao-Lian; Lin Zi-Jing

doi:10.7498/aps.71.20221019

Abstract

Because the single-layer CrI₃ is a half semiconductor with indirect band gap and magnetic anisotropy, it has received much attention in the spintronic, magneto-electronic and magnetic storage applications. However, the knowledge of the dependence of carrier mobility and optical property on strain is still rather limited. The uniaxial and biaxial strain dependence of electronic, transport, optical and magnetic properties of single-layer CrI₃ are systematically investigated by using first-principles calculations, and the results are compared with experimental results. The electronic structures under different strains are first calculated by using the accurate HSE06 functional, then the carrier mobility is estimated by the deformation potential theory and the dielectric function is obtained to estimate the optical absorption especially in the visible light range. Finally, the magnetic anisotropy energy used to estimate the magneto-electronic properties is studied by the Perdew-Bueke-Ernzerhof functional including the spin-orbit coupling. It is found that the ferromagnetic CrI₃ is an indirect and half semiconductor with band gap 2.024 eV,$ \Delta {\text{CBM}} $= 1.592 eV, $ \Delta {\text{VBM}} $= 0.238 eV and can be driven into AF-Néel antiferromagnetic phase by applying –6% to –8% (compressive) biaxial stain, exhibiting excellent agreement with the results from the literature. It is found that of single-layer CrI₃ has very low carrier mobility with a value within 10 cm²·V^–1·s^–1 due to the large effective mass and small in-plane stiffness can be remarkably increased by increasing biaxial compression strain attributed to the reduced effective mass. A high electron mobility 174 cm²·V^–1·s^–1 is obtained in the zigzag direction by applying a –8% biaxial strain reaching the level of monolayer MoS₂. The calculated imaginary component of dielectric function along the x (y) direction having two peaks (I, II) in the visible light range is obviously different from that along the z direction, indicating that the single-layer CrI₃ has optical anisotropy, demonstrating the good agreement with results from the literature. It is found that the imaginary part of dielectric function shows that an obvious redshift and peak (I, II) values strongly increase with the increase of compressive strain (biaxial), showing good agreement with the calculated electronic structures and indicating that monolayer CrI₃ possesses high optical adsorption of visible light under a compressive biaxial strain. Furthermore, it is found that the magnetic anisotropy energy of monolayer CrI₃ mainly stemming from the orbital magnetic moment of Cr ions remarkably increases from 0.7365 to 1.08 meV/Cr with g compressive strain increasing. These results indicate that the optoelectronic property of single-layer CrI₃ can be greatly improved by applying biaxial compressive strain and the single-layer CrI₃ is a promising material for applications in microelectronic, optoelectronic and magnetic storage.

Keywords:

Authors and contacts

1.
School of Electrical and Electronic Engineering, Anhui Science and Technology University, Bengbu 233000, China
2.
Department of Physics, University of Science and Technology of China, Hefei 230000, China

Corresponding author: Wang Na, wangn@ahstu.edu.cn

Funds: Project supported by the Natural Science Foundation of Anhui Province, China (Grant No. 2008085QF328), the Natural Science Foundation of the Higher Education Institutions of Anhui Province, China (Grant No. KJ2020A0075), the National Natural Science Foundation of China (Grant No. 12074362), and the Young Core Talents Domestic Visitor Foundation of the Higher Education Institutions of Anhui Province, China (Grant No. gxgnfx2021142).

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References

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[2]	Gong C, Li L, Li Z L, Ji H W, Stern A, Xia Y, Cao T, Bao W, Wang C Z, Wang Y, Qiu Z Q, Cava R J, Louie S G, Xia J, Zhang X 2017 Nature 546 265 Google Scholar
[3]	Mermin N D, Wagner H 1966 Phys. Rev. Lett. 17 1133 Google Scholar
[4]	Sivadas N, Okamoto S, Xu X D, Fennie C J, Xiao D 2018 Nano Lett. 18 7658 Google Scholar
[5]	Guo G X, Bi G, Cai C F, Wu H Z 2018 J. Phys.: Condens. Matter 30 285303 Google Scholar
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图 1 单层CrI₃的结构图及原胞(a), AF-Néel晶胞(b), AF-stripy晶胞(c)和AF-zigzag晶胞(d)

Figure 1. Atomic structure of CrI₃ monolayer together with unit cell (a), AF-Néel crystal cell (b), AF-stripy crystal cell (c) and AF-zigzag crystal cell (d).

DownLoad: Full-Size Img PowerPoint

图 2 单层CrI₃铁磁结构与反铁磁结构的能量差$ \Delta {E_{{\text{FM - AFM}}}} $随应变的变化规律

Figure 2. Variation of energy difference $ \Delta {E_{{\text{FM - AFM}}}} $ between single-layer CrI₃ ferromagnetic and antiferromagnetic structures with strain.

DownLoad: Full-Size Img PowerPoint

图 3 不同应变下的${{\Delta {\rm{CBM}}, \Delta {\rm{VBM}}}}$

Figure 3. The strain dependence of ${{\Delta {\rm{CBM}}, \Delta {\rm{VBM}}}}$.

DownLoad: Full-Size Img PowerPoint

图 4 CBM, VBM和禁带宽度随应变的变化规律

Figure 4. Effect of strain on the CBM, VBM and band gap of CrI₃ monolayer.

DownLoad: Full-Size Img PowerPoint

图 5 双轴应变下单层CrI₃的电子DOS分布　(a1)—(a5) 拉伸应变量ε取0到0.08; (b1)—(b5) 压缩应变量ε取0到–0.08

Figure 5. Biaxial strain dependence of DOS of CrI₃ monolayer: (a1)–(a5) withεranging from 0 to 0.08 for tensile (compressive) strain; (b1)–(b5) with ε ranging from 0 to –0.08 for compressive strain.

DownLoad: Full-Size Img PowerPoint

图 6 双轴应变下单层CrI₃本征载流子沿x (y)方向的迁移率 (e代表电子, p代表空穴)

Figure 6. Biaxial strain dependence of the intrinsic carrier mobility of CrI₃ monolayer in x (y) direction (e represents for electron, p represents for hole).

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图 7 单层CrI₃在可见光区间内的介电函数虚部

Figure 7. The imaginary component of dielectric function of CrI₃ monolayer in the visible light range.

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图 8 双轴应变下的介电函数虚部　(a), (c) 拉伸应变; (b), (d) 压缩应变

Figure 8. Biaxial strain dependence of imaginary component of dielectric function: (a), (c) Tensile strain; (b), (d) compressive strain.

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图 9 单层CrI₃的MAE在y-z面内的拟合曲线图

Figure 9. The curve fitting of MAE in the y-z plane of CrI₃ monolayer.

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图 10 单层CrI₃在不同应变下的MAE (a)和Cr-3d的轨道磁矩(b)

Figure 10. The effect of different strains on the MAE (a) and orbital moments of Cr-3d (b) in CrI₃ monolayer.

DownLoad: Full-Size Img PowerPoint

表 1 单层CrI₃电子和空穴沿x (y)方向的物理参数

Table 1. Physical parameters of electron and hole of CrI₃ monolayer in x (y) direction, respectively.

Carrier	Direction	m*/m₀	m_d/m₀	E_d/eV	C_2D/(N·m^–1)	μ/(cm²·V^–1·s^–1)
Electron	x	5.45	5.79	2.29	25.5	3.26
Electron	y	6.15	5.79	2.25	24.5	2.84
Hole	x	–2.57	2.32	3.87	25.5	6.05
Hole	y	–2.10	2.32	4.01	24.5	6.63

DownLoad: CSV

表 2 双轴应变下单层CrI₃电子和空穴沿x (y)方向的有效质量m*和迁移率μ

Table 2. The biaxial strain dependence of the effective mass m* and carrier mobility μ of electron and hole of CrI₃ monolayer in x (y) direction, respectively.

Strain	m*/(m₀μ)/(cm²·V^–1·s^–1)
	Electron		Hole		Electron		Hole
	$ m_x^* $	$ m_y^* $	$ m_x^* $	$ m_y^* $	μ_x	μ_y	μ_x	μ_y
0.08	8.82	10.122	–1.682	–1.652	1.21	1.11	12.80	11.68
0.06	6.42	8.540	–1.79	–1.740	2.18	1.66	11.37	10.46
0.04	6.15	7.640	–2.15	–1.900	2.42	1.89	8.28	8.37
0.02	6.78	6.780	–2.098	–1.858	2.24	2.21	8.74	8.84
0	5.45	6.150	–2.57	–2.100	3.26	2.84	6.05	6.63
–0.02	1.90	1.940	–1.45	–1.410	28.17	27.54	17.37	16.00
–0.04	0.98	1.180	–1.48	–1.510	98.16	80.48	16.25	14.24
–0.06	1.02	1.050	–0.84	–1.040	97.56	94.28	45.84	33.31
–0.08	0.71	0.970	–0.78	–0.920	173.53	126.24	54.29	41.06

DownLoad: CSV

[1]	Huang B, Clark G, Navarro-Moratalla E, Klein D R, Cheng R, Seyler K L, Zhong D, Schmidgall E, McGuire M A, Cobden D H 2017 Nature 546 270 Google Scholar
[2]	Gong C, Li L, Li Z L, Ji H W, Stern A, Xia Y, Cao T, Bao W, Wang C Z, Wang Y, Qiu Z Q, Cava R J, Louie S G, Xia J, Zhang X 2017 Nature 546 265 Google Scholar
[3]	Mermin N D, Wagner H 1966 Phys. Rev. Lett. 17 1133 Google Scholar
[4]	Sivadas N, Okamoto S, Xu X D, Fennie C J, Xiao D 2018 Nano Lett. 18 7658 Google Scholar
[5]	Guo G X, Bi G, Cai C F, Wu H Z 2018 J. Phys.: Condens. Matter 30 285303 Google Scholar
[6]	Webster L, Yan J A 2018 Phys. Rev. B 98 144411 Google Scholar
[7]	Bacaksiz C, Šabani D, Menezes R M, Milošević M V 2021 Phys. Rev. B 103 125418 Google Scholar
[8]	Kresse G, Furthmüller J 1996 Phys. Rev. B 54 11169 Google Scholar
[9]	Baerends E J 1999 Theor. Chem. Acc. 103 265 Google Scholar
[10]	Wu Z W, Yu J, Yuan S J 2019 Phys. Chem. Chem. Phys. 21 7750 Google Scholar
[11]	Mukherjee T, Chowdhury S, Jana D, Lew Yan Voon L C 2019 J. Phys.: Condens. Matter 31 335802 Google Scholar
[12]	Pizzochero M, Yazyev O V 2020 J. Phys. Chem. C 124 7585
[13]	Heyd J, Scuseria G E, Ernzerhof M 2003 J. Chem. Phys. 118 8207 Google Scholar
[14]	Lou B B, Wen J, Cai J J, Yeung Y Y, Yin M, Duan C K 2021 Phys. Rev. B 103 075109 Google Scholar
[15]	Liu X F, Gao P F, Hu W, Yang J L 2020 J. Phys. Chem. Lett 11 4070 Google Scholar
[16]	Zhang W B, Qu Q, Zhu P, Lam C H 2015 J. Mater. Chem. C 3 12457 Google Scholar
[17]	Dillon J F, Olson C E 1965 J. Appl. Phys. 36 1259 Google Scholar
[18]	Kanazawa K K, Street G B 1970 Phys. Status Solidi B 38 445 Google Scholar
[19]	Guizzetti G, Nosenzo L, Pollini I, Reguzzoni E, Samoggia G, Spinolo G 1976 Phys. Rev. B 14 4622 Google Scholar
[20]	Bučko T, Lebègue S, Hafner J, et al. 2013 Phys. Rev. B 87 064110 Google Scholar
[21]	Larsen A H, Vanin M, Mortensen J J R 2013 Phys. Rev. B 80 2665 Google Scholar
[22]	Bardeen J, Shockley W 1950 Phys. Rev. 80 72 Google Scholar
[23]	Vu T V, Nguyen C V, Phuc H V, Lavrentyev A A, Khyzhun O Y, Hieu N V, Obeid M M, Rai D P, Tong H D, Hieu N N 2021 Phys. Rev. B 103 085422 Google Scholar
[24]	Abboud M, Ozbey D H, Kilic M E, Durgun E 2022 J. Phys. D: Appl. Phys. 55 185302 Google Scholar
[25]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 Google Scholar
[26]	Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188
[27]	Sivadas N, Daniels M W, Swendsen R H, Okamoto S, Xiao D 2015 Phys. Rev. B 91 235425 Google Scholar
[28]	Li P G, Wang C, Zhang J H, Chen S W, Guo D H, Ji W, Zhong D Y 2020 Sci. Bull 65 1064 Google Scholar
[29]	Vishkayi S I, Torbatian Z, Qaiumzadeh A, Asgari R 2020 Phys. Rev. Mater 4 094004 Google Scholar
[30]	Hou B W, Zhang Y M, Zhang H, Shao H Z, Ma C C, Zhang X T, Chen Y, Xu K, Ni G, Zhu H Y 2020 J. Phys. Chem. Lett. 11 3116 Google Scholar
[31]	Zhang D, Hu S, Liu X, Chen Y, Xia Y, Wang H, Wang H, Ni Y 2020 ACS Appl. Energy Mater 4 357
[32]	Cadelano E, Palla P L, Giordano S, Colombo L 2010 Phys. Rev. B 82 235414 Google Scholar
[33]	Liu J Y, Sun Q, Kawazoe Y, Jena P 2016 Phys. Chem. Chem. Phys 18 8777 Google Scholar
[34]	Mak K F, Lee C, Hone J, Shan J, Heinz T F 2010 Phys. Rev. Lett. 105 136805 Google Scholar
[35]	Cai YQ, Zhang G, Zhang Y W 2014 J. Am. Chem. Soc. 136 6269 Google Scholar
[36]	Xu L, Yang M, Wang S J, Feng Y P 2017 Phys. Rev. B 95 235434 Google Scholar
[37]	Komsa H P, Krasheninnikov A V 2013 Phys. Rev. B 88 085318 Google Scholar
[38]	Lu R F, Li F, Salafranca J, Kan E J, Xiao C Y, Deng K M 2014 Phys. Chem. Chem. Phys. 16 4299 Google Scholar
[39]	Prokop J, Kukunin A, Elmers H J 2005 Phys. Rev. Lett. 95 187202 Google Scholar
[40]	Nguyen T P T, Yamauchi K, Nakamura K, Oguchi T 2020 J. Phys. Soc. Japan 89 114710 Google Scholar
[41]	Zhuang H L L, Kent P R C, Hennig R G 2016 Phys. Rev. B 93 134407 Google Scholar
[42]	Zhang J M, Yang B S, Zheng H L, Han X F, Yan Y 2017 Phys. Chem. Chem. Phys. 19 24341 Google Scholar
[43]	Ma X F, Yin L, Zou J J, Mi W B, Wang X C 2019 J. Phys. Chem. C 123 17440 Google Scholar

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First-principles study of strain-tunable charge carrier transport properties and optical properties of CrI₃ monolayer

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Corresponding author: Wang Na, wangn@ahstu.edu.cn

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First-principles study of strain-tunable charge carrier transport properties and optical properties of CrI3 monolayer

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Corresponding author: Wang Na, wangn@ahstu.edu.cn

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First-principles study of strain-tunable charge carrier transport properties and optical properties of CrI₃ monolayer