Structural stability, electronic properties, and physical modulation effects of armchair-edged C<sub>3</sub>B nanoribbons

Cao Sheng-Guo; Han Jia-Ning; Li Zhan-Hai; Zhang Zhen-Hua

doi:10.7498/aps.72.20222434

Abstract

C₃B monolayer is a typical graphene-like two-dimensional material, which has been successfully prepared experimentally. Here, we use the density functional theory to study the structural stability, electronic properties and physical regulation effects of its armchair-edged nanoribbons. The results show that for the bare-edged nanoribbons, if the ribbon edges are composed of C atoms completely (AA-type), their electronic phase is a semiconductor; when both ribbons edges consist of C and B atoms (BB-type) jointly, their electronic phase is a metal; if one edge of the ribbon is composed of C atoms and the other edge is comprised of B and C atoms (AB-type), their electronic phase is also a metal. This suggests that the B atom located at the ribbon edge plays an important role in determining whether nanoribbons is a metal or semiconductor. While for the H-terminated nanoribbons, they are all direct or indirect band-gap semiconductors. The carrier mobility of H-terminated nanoribbons is generally lower than that of bare-edged nanoribbon, which is closely related to their larger effective mass and higher deformation potential values. Meanwhile, it is found that the semiconducting nanoribbons are very sensitive to physical regulation, especially under applied compressive strain and external electric field, the band gap of the nanoribbons becomes very smaller, which is favorable for the absorption of light energy and development of novel optical devices.

Keywords:

Authors and contacts

Hunan Provincial Key Laboratory of Flexible Electronic Materials Genome Engineering, Changsha University of Science and Technology, Changsha 410114, China

Corresponding author: Zhang Zhen-Hua, zhzhang@csust.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61771076), the Hunan Provincial Key Laboratory of Flexible Electronic Materials Genome Engineering, China (Grant No. 202020), and the Hunan Provincial Innovation Foundation For Postgraduate, China (Grant No. CX20210823).

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References

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图 1 (a) C₃B单层原子结构, 其中浅绿色菱形表示它的原胞, 考虑沿X轴方向剪裁形成各种扶手椅型纳米带, 其中蓝色、黄色阴影分别表示A型、B型边缘; (b)—(k)分别表示13-AA(Ⅰ), 15-AA(Ⅱ), 15-BB(Ⅰ), 13-BB(Ⅱ), 14-AB, 13H-AA(Ⅰ), 15H-AA(Ⅱ), 15H-BB(Ⅰ), 13AH-BB(Ⅱ), 14H-AB纳米带, 黑色虚线框表示纳米带单胞

Figure 1. (a) Atomic structure C₃B monolayer, where light green rhombus represents its primitive cell, tailoring C₃B monolayer along the X-axis direction to form various armchair edged nanoribbons, the blue and yellow shadows indicate the A-type and B-type edges, respectively; (b)–(k) several typical ribbons 13-AA(Ⅰ), 15-AA(Ⅱ), 15-BB(Ⅰ), 13-BB(Ⅱ), 14-AB, 13H-AA(Ⅰ), 15H-AA(Ⅱ), 15H-BB(Ⅰ), 13AH-BB(Ⅱ), and 14H-AB respectively, the black dashed box denotes the unit cell of nanoribbons.

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图 2 裸边和H端接C₃B纳米带的热力学稳定性模拟, 即在NVT系综件下使用温度为500 K的Nose Hoover热浴, 按每步1 fs运行8 ps后获得的结果 (a) 13-AA(Ⅰ), (b) 15-AA(Ⅱ), (c) 15-BB(Ⅰ), (d) 13-BB(Ⅱ), (e) 14-AB, (f) 13H-AA(Ⅰ), (g) 15H-AA(Ⅱ), (h) 15H-BB(Ⅰ), (i) 13AH-BB(Ⅱ), (j) 14H-AB; (k)裸边C₃B纳米带边能随宽度变化; (l) H端接C₃B纳米带边能随宽度变化

Figure 2. Examining the thermal stability of bare-edge and H-terminated C₃B ribbons, the obtained results for running the simulation by 8 ps with a time step of 1 fs under the Nosé heat bath scheme, which is used in the NVT ensemble at 500 K: (a)13-AA(Ⅰ), (b)15-AA(Ⅱ), (c)15-BB(Ⅰ), (d)13-BB(Ⅱ), (e)14-AB, (f)13H-AA(Ⅰ), (g)15H-AA(Ⅱ), (h)15H-BB(Ⅰ), (i)13AH-BB(Ⅱ), (j)14H-AB; (k) edge energy versus widths of the bare-edge C₃B nanoribbons; (l)edge energy versus widths of the H-terminated C₃B nanoribbons.

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图 3 几种典型裸边C₃B纳米带的能带结构、态密度(DOS)和原子投影态密度(PDOS)　(a) 13-AA(Ⅰ), (b) 15-AA(Ⅱ), (c) 15-BB(Ⅰ), (d) 13-BB(Ⅱ), (e) 14-AB; 相对应纳米带的能带1和2的部分电荷密度: (f) 13-AA(Ⅰ), (g) 15-AA(Ⅱ), (h) 15-BB(Ⅰ), (i) 13-BB(Ⅱ), (j) 14-AB, 部分电荷密度等值面设置为0.03 |e|·Å^–3

Figure 3. Band structure, density of states (DOS) , and atom-projected density of states (PDOS) of several typical bare-edge C₃B ribbons: (a) 13-AA(Ⅰ), (b) 15-AA(Ⅱ), (c) 15-BB(Ⅰ), (d) 13-BB(Ⅱ), (e) 14-AB. Partial charge density of subbands 1 and 2 for the corresponding ribbons: (f) 13-AA(Ⅰ), (g) 15-AA(Ⅱ), (h) 15-BB(Ⅰ), (i) 13-BB(Ⅱ), (j) 14-AB. The isosurface for partial charge density is set to 0.03 |e|·Å^–3.

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图 4 几种典型的H端接的C₃B纳米带的能带结构, 态密度(DOS)和原子投影态密度(PDOS)　(a) 13H-AA(Ⅰ), (b) 15H-AA(Ⅱ), (c) 15H-BB(Ⅰ), (d) 13AH-BB(Ⅱ), (e) 14H-AB; 相对应纳米带的能带1和2的部分电荷密度: (f) 13H-AA(Ⅰ), (g) 15H-AA(Ⅱ), (h) 15H-BB(Ⅰ), (i) 13AH-BB(Ⅱ), (j) 14H-AB, 部分电荷密度等值设为0.03 |e|·Å^–3

Figure 4. Band structure, density of states (DOS) and atom-projected density of states (PDOS) for several typical H-terminated C₃B ribbons: (a)13H-AA(Ⅰ), (b)15H-AA(Ⅱ), (c)15H-BB(Ⅰ), (d)13AH-BB(Ⅱ), and (e)14H-AB. Partial charge density of subbands 1 and 2 for the corresponding ribbons: (f) 13H-AA(Ⅰ), (g)15H-AA(Ⅱ), (h)15H-BB(Ⅰ), (i)13AH-BB(Ⅱ), and (j)14H-AB. The isosurface for partial charge density is set to 0.03 |e|·Å^–3.

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图 5 不同类型C₃B纳米带的 (a)有效质量, (b)形变势, (c)弹性模量以及(d)载流子迁移率(其中h为空穴, e为电子)

Figure 5. (a) Effective mass, (b) deformation potential, (c) elastic modulus, and (d) carrier mobility for different types of C₃B nanoribbons (h is expressed as holes, e is expressed as electrons).

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图 6 13-AA(Ⅰ)纳米带的应变调控效应　(a)纳米带压应力示意图; (b)能带结构随施加应变值的变化; (c)带隙及应变能随施加应变值的变化; (d) 13-AA(Ⅰ) VBM在Gama点的布洛赫态, 布洛赫态等值面为0.1 |e|·Å^–3

Figure 6. The strain regulation effect of 13-AA(Ⅰ) ribbon: (a) Schematic diagram of compressive stress in nanoribbons; (b) variation of energy band structure with applied strain; (c) band gap and the strain energy with the applied strain; (d) 13-AA(Ⅰ) bloch state of VBM at Gama point. The isosurface value is set as 0.1 |e|·Å^–3.

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图 7 C₃B纳米带带边(CBM及VBM)随应变变化　(a) 13-AA(Ⅰ); (b) 15-AA(Ⅱ); (c) 13H-AA(Ⅰ); (d) 15H-AA(Ⅱ); (e) 15H-BB(Ⅰ); (f)13AH-BB(Ⅱ); (g) 14H-AB

Figure 7. Band edges (CBM and VBM) of C₃B nanoribbons change with strain: (a) 13-AA(Ⅰ); (b) 15-AA(Ⅱ); (c) 13H-AA(Ⅰ); (d) 15H-AA(Ⅱ); (e) 15H-BB(Ⅰ); (f) 13AH-BB(II); (g) 14H-AB.

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图 8 (a) 14H-AB纳米带的电场调控效应; (b)能带结构随电场变化; (c)带隙及电场能随电场变化; (d), (e) CBM和VBM的布洛赫态能随电场变化, 布洛赫态等值面为0.1 |e|·Å^–3

Figure 8. (a) Electric field regulation effect of ribbon14H-AB; (b) band structure changes with the electric field; (c) band gap and electric field energy changes with the electric field; (d), (e) Bloch states of CBM and VBM changes with the electric field, their isosurface is set to 0.1 |e|·Å^–3.

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图 9 C₃B纳米带带边(CBM、VBM)随外部电场的变化　(a) 13-AA(Ⅰ); (b) 15-AA(Ⅱ); (c) 13H-AA(Ⅰ); (d) 15H-AA(Ⅱ); (e) 15H-BB(Ⅰ); (f) 13AH-BB(Ⅱ); (g) 14H-AB

Figure 9. Band edges for the C₃B nanoribbon varies with external electric field: (a) 13-AA(Ⅰ); (b) 15-AA(Ⅱ); (c) 13H-AA(Ⅰ); (d) 15H-AA(Ⅱ); (e) 15H-BB(Ⅰ); (f) 13AH-BB(Ⅱ); (g) 14H-AB.

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表 1 不同宽度裸边C₃B纳米带带隙

Table 1. Band gaps of bare-edge C₃B nanoribbons with different widths.

Structure	Band gap/eV	Structure	Band gap/eV	Structure	Band gap/eV
5-AA(Ⅰ)	0.928	19-AA(Ⅱ)	0.696	13-BB(Ⅱ)	0
9-AA(Ⅰ)	0.730	7-BB(Ⅰ)	0	17-BB(Ⅱ)	0
13-AA(Ⅰ)	0.710	11-BB(Ⅰ)	0	8-AB	0
17-AA(Ⅰ)	0.710	15-BB(Ⅰ)	0	10-AB	0
7-AA(Ⅱ)	0.718	19-BB(Ⅰ)	0	12-AB	0
11-AA(Ⅱ)	0.675	5-BB(Ⅱ)	0	14-AB	0
15-AA(Ⅱ)	0.692	9-BB(Ⅱ)	0	16-AB	0

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表 2 H端接C₃B纳米带的带隙

Table 2. Band gaps for H-terminated C₃B nanoribbons.

Structure	Bandgap/eV	Structure	Bandgap/eV	Structure	Bandgap/eV
5 H-AA(Ⅰ)	1.753	19 H-AA(Ⅱ)	0.774	13 H-BB(Ⅱ)	0.872
9 H-AA(Ⅰ)	1.098	7 H-BB(Ⅰ)	1.040	17 H-BB(Ⅱ)	0.833
13 H-AA(Ⅰ)	0.890	11 H-BB(Ⅰ)	0.907	8 H-AA(Ⅱ)	1.157
17 H-AA(Ⅰ)	0.809	15 H-BB(Ⅰ)	0.850	10 H-AA(Ⅱ)	1.014
7 H-AA(Ⅱ)	1.263	19 H-BB(Ⅰ)	0.820	12 H-AB(Ⅰ)	0.953
11 H-AA(Ⅱ)	0.930	5 H-BB(Ⅱ)	0.976	14 H-AB(Ⅰ)	0.897
15 H-AA(Ⅱ)	0.823	9 H-BB(Ⅱ)	0.948	16 H-AB(Ⅰ)	0.869

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[1]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonosn S V, Grigorieva I V, Firsov A A 2004 Science 306 666 Google Scholar
[2]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Katsnelson M I, Grigorieva1 I V, Dubonos S V, Firsov A A 2005 Nature 438 197 Google Scholar
[3]	Zhang Y, Tan Y W, Stormer H L, Kim P 2005 Nature 438 201 Google Scholar
[4]	Kim Y J, Bae G Y, Chun S, Park W 2016 J. Nanosci. Nanotechnol 16 2769 Google Scholar
[5]	Blase X, Rubio A, Louie S G, Cohen M L 1995 Phys. Rev. B 51 6868 Google Scholar
[6]	Cahangirov S, Topsakal M, Aktürk E, Sahin H, Ciraci S 2009 Phys. Rev. Lett. 102 236804 Google Scholar
[7]	Kuang W, Hu R, Fan Z Q, Zhang Z H 2019 Nanotechnology 30 145201 Google Scholar
[8]	Xiao D, Liu G B, Feng W, Xu X, Yao W 2012 Phys. Rev. Lett. 108 196802 Google Scholar
[9]	Zhang S, Yan Z, Li Y, Chen Z, Zeng H 2015 Angew. Chem. Int. Ed. 54 3112 Google Scholar
[10]	Zhang S, Xie M, Li F, Yan Z, Li Y, Kan E, Liu W, Chen Z, Zeng H 2016 Angew. Chem. 128 1698 Google Scholar
[11]	Yang B, Zhang X, Zhao M 2017 Nanoscale 9 8740 Google Scholar
[12]	Ding C, Gao H, Geng W, Zhao M 2021 Nanoscale Adv 3 1127 Google Scholar
[13]	Palsgaard M, Gunst T, Markussen T, Thygesen K, Brandbyge M 2018 Nano. Lett. 18 7275 Google Scholar
[14]	Wines D, Ersan F, Ataca C 2020 ACS Appl. Mater. Interfaces 12 46416 Google Scholar
[15]	Zhu M, Zhang L, Li X, He Y, Li X, Guo F, Zang X, Wang K, Xie D, Li X, Wei B, Zhu H. 2015 J. Mater. Chem. A 3 8133 Google Scholar
[16]	Midya A, Ghorai A, Mukherjee S, Maiti R, Ray S 2016 J. Mater. Chem. A 4 4534 Google Scholar
[17]	Sun F, Liu R, Suo Y Q, Niu L L, Fu H Y, Ji W F, Li Z L 2019 Acta. Phys. Sin. 68 178502 Google Scholar
[18]	Liu R, Bao D L, Jiao Y, Wan L W, Li Z L, Wang C K 2014 Acta. Phys. Sin. 6 068501 Google Scholar
[19]	Hu Y, Zhang S, Sun S, Xie M, Cai B, Zeng H 2015 Appl. Phys. Lett. 107 122107 Google Scholar
[20]	Pereira V M, Neto A H C 2009 Phys. Rev. Lett. 103 046801 Google Scholar
[21]	Son Y W, Cohen M L, Louie. S. G 2006 Phys. Rev. Lett. 97 216803 Google Scholar
[22]	Son Y W, Cohen M L, Louie S G 2006 Nature 444 347 Google Scholar
[23]	Niu L L, Fu H Y, Suo Y Q, Liu R, Sun F, Wang S S, Zhang G P, Wang C K, Li Z L 2021 Physica E 128 114542 Google Scholar
[24]	Fu H Y, Sun F, Liu R, Suo Y Q, Bi J J, Wang C K, Li Z L 2019 Phys. Lett. A 383 867 Google Scholar
[25]	Aftab S, Samiya M, Liao W, Iqbal M W, Ishfaq M, Ramachandraiah K, Ajmal H M S, Haque H M U, Yousuf S, Ahmed Z, khan M U, Rehman A U, Iqbal M Z 2021 J. Mater. Chem. C 9 3998 Google Scholar
[26]	He T, Lan C, Zhou S, Li Y, Yin Y, Li C, Liu Y 2021 J. Mater. Chem. C 9 3846 Google Scholar
[27]	Liu S Y, Liu S, Li D J, Dang H, Liu Y, Xue S, Xue W, Wang S 2013 Phys. Rev. B 88 115434 Google Scholar
[28]	Tanaka H, Kawamata Y, Simizu H, Fujita T, Yanagisawa H, Otani S, Oshima C 2005 Solid. State. Commun. 136 22 Google Scholar
[29]	Ding Y, Wang Y, Ni J 2009 Appl. Phys. Lett. 94 073111 Google Scholar
[30]	Miyamoto Y, Rubio A, Louie S G, Cohen M L 1994 Phys. Rev. B 50 18360 Google Scholar
[31]	Zhang Y, Wu Z F, Gao P F, Fang D Q, Zhang E H, Zhang S L 2018 RSC. Adv. 8 1686 Google Scholar
[32]	Senturk A E, Oktem A S, Konukman A E S 2020 Mol. Simul. 46 879 Google Scholar
[33]	Su Y, Cao S, Shi L B, Qian P 2020 Appl. Surf. Sci. 531 147341 Google Scholar
[34]	Liu G, Wu M S, Ouyang C Y, Xu B 2013 Mod. Phys. Lett. B 27 1350110 Google Scholar
[35]	Wu Y, Xia W, Zhang Y, Zhu W, Zhang W, Zhang P 2020 Phys. Rev. Appl. 14 014073 Google Scholar
[36]	Ozdemir B, Barone V 2015 Comput. Mater. Sci. 109 248 Google Scholar
[37]	Yang Z, Ni J 2012 Appl. Phys. Lett. 100 183109 Google Scholar
[38]	Yang Z, Ni J 2010 Appl. Phys. Lett. 97 253117 Google Scholar
[39]	Zhang H, Tang Y, Chai H, Chen W, Zhao M, Dai X 2019 Mol. Phys. 117 125 Google Scholar
[40]	Meng C, Zhao K, Yang M, Liang Y, Bu X 2021 Phys. E 132 114762 Google Scholar
[41]	Qie Y, Liu J, Wang S, Gong S, Sun Q 2018 Carbon 129 38 Google Scholar
[42]	Zhao J, Cheng N, He Y 2019 Phys. Chem. Chem. Phys. 21 19567 Google Scholar
[43]	Zhang C, Jiao Y, He T, Bottle S, Frauenheim T, Du A 2018 J. Phys. Chem. Lett. 9 858 Google Scholar
[44]	Zhao P, Wan Y, Zhang S, Gao A, Guo P, Jiang Z, Zheng J 2020 Phys. Status. Solidi. RRL 14 2000012 Google Scholar
[45]	Dutta S, Wakabayashi K 2013 J. Mater. Chem. C. Mater. 1 4854 Google Scholar
[46]	Brandbyge M, Mozos J L, Ordejon P, Taylor J, Stokbro K 2002 Phys. Rev. B 65 165401 Google Scholar
[47]	Taylor J, Guo H, Wang J 2001 Phys. Rev. B 63 245407 Google Scholar
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Structural stability, electronic properties, and physical modulation effects of armchair-edged C₃B nanoribbons

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Structural stability, electronic properties, and physical modulation effects of armchair-edged C3B nanoribbons

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Structural stability, electronic properties, and physical modulation effects of armchair-edged C₃B nanoribbons