Electronic structure of graphene nanoribbons under external electric field by density functional tight binding

Cui Yang; Li Jing; Zhang Lin

doi:10.7498/aps.70.20201619

Abstract

In recent years, the rapid development of electronic information technology has brought tremendous convenience to people’s lives, and the devices used have become increasingly miniaturized. However, due to the constraints of the process and the material itself, as the size of the devices made of silicon materials is further reduced, obvious short channel effects and dielectric tunneling effects will appear, which will affect the normal operations of these devices. In order to overcome this development bottleneck, it is urgent to find new materials for the devices that can replace silicon. Carbon has the same outer valence electron structure as silicon. Since 2004, Geim [Novoselov K S, Geim A K, Morozov S V, et al. 2005 Nature 438 197] prepared two-dimensional graphene with a honeycomb-like planar structure formed by sp² hybridization, graphene has received extensive attention from researchers and industrial circles for its excellent electronic and mechanical properties. However, graphene is not a true semiconductor, and it has no band gap in its natural state. The energy gap can be opened by preparing graphene nanoribbons. On this basis, the electronic structure of the nanoribbons can be further controlled by using an external electric field to destroy the symmetric structure of the nanoribbons. In this paper, the tight-binding method based on density functional theory is used to calculate and study the influence of external transverse electric field on the electronic structure and electron population of un-hydrogenated/hydrogenated armchair graphene nanoribbons. The calculation results show that whether there is hydrogen on the edge of the graphene nanoribbons or not, the energy gap changed at the Г point shows a three-group periodic oscillation decreasing law, and as N increases, the energy gap will disappear. Under the external electric field, the band structure and the density of states of the nanoribbons will change greatly. For un-hydrogenated nanoribbons with semiconducting properties, as the intensity of the external electric field increases, a semiconductor-metal transition occurs. At the same time, the electric field will also have a significant influence on the energy level distribution, resulting in significant changes in the peak height and peak position of the density of states. The external electric field causes the electron population distribution on the atoms in the nanoribbons to break its symmetry. The greater the electric field strength, the more obvious the population asymmetry is. The edge hydrogenation passivation can significantly change the population distribution of atoms in nanoribbons.

Keywords:

Authors and contacts

1.
Key Laboratory for Anisotropy and Texture of Materials, Northeastern University, Shenyang 110819, China
2.
The State Key Laboratory of Rolling and Automation, Northeastern University, Shenyang 110819, China
3.
School of Materials Science and Engineering, Northeastern University, Shenyang 110819, China

Corresponding author: Zhang Lin, zhanglin@imp.neu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51671051) and the National Key R&D Program of China (Grant No. 2016YFB0701304)

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References

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Cited By

图 1 (a) N = 5的未加氢钝化的纳米带; (b) N = 5的氢钝化的纳米带

Figure 1. (a) Un-hydrogenated nanoribbons with N = 5; (b) hydrogenated nanoribbons with N = 5.

DownLoad: Full-Size Img PowerPoint

图 2 不同宽度的氢化/未氢化的扶手椅型石墨烯纳米带在Г点处的能隙

Figure 2. Energy gap of hydrogenated/un-hydrogenated armchair graphene nanoribbons with different widths.

DownLoad: Full-Size Img PowerPoint

图 3 N = 5的未加氢钝化的纳米带的带隙随电场强度的变化

Figure 3. Band gap of un-hydrogenated nanoribbons with N = 5 under different electric field intensity.

DownLoad: Full-Size Img PowerPoint

图 4 不同电场强度时N = 5的未加氢钝化的纳米带的能带结构及态密度　(a) E = 0 V/nm; (b) E = 3 V/nm; (c) E = 5 V/nm

Figure 4. Band structure and density of states of un-hydrogenated nanoribbons with N = 5 under the external electric field: (a) E = 0 V/nm; (b) E = 3 V/nm; (c) E = 5 V/nm

DownLoad: Full-Size Img PowerPoint

图 5 不同电场强度时N = 5的氢钝化的纳米带的能带结构及态密度　(a) E = 0 V/nm; (b) E = 3 V/nm; (c) E = 5 V/nm

Figure 5. Band structure and density of states of hydrogenated nanoribbons with N = 5 under the external electric field: (a) E = 0 V/nm; (b) E = 3 V/nm; (c) E = 5 V/nm.

DownLoad: Full-Size Img PowerPoint

图 6 不同电场强度下N = 5的未加氢钝化的纳米带的电子布居数　(a) E = 0 V/nm; (b) E = 3 V/nm; (c) E = 5 V/nm

Figure 6. The electron population of un-hydrogenated nanoribbon with N = 5 under the external electric field: (a) E = 0 V/nm; (b) E = 3 V/nm; (c) E = 5 V/nm.

DownLoad: Full-Size Img PowerPoint

图 7 不同电场强度下N = 5的氢钝化的纳米带的电子布居数　(a) E = 0 V/nm; (b) E = 3 V/nm; (c) E = 5 V/nm

Figure 7. The electron population of hydrogenated nanoribbon with N = 5 under the external electric field: (a) E = 0 V/nm; (b) E = 3 V/nm; (c) E = 5 V/nm.

DownLoad: Full-Size Img PowerPoint

图 8 N = 5的未加氢钝化/加氢钝化的纳米带最大最小布居数之差随电场强度的变化

Figure 8. The difference between the maximum and minimum populations of the un-hydrogenated/hydrogenated nanoribbons with N = 5 varies with the electric field intensity.

DownLoad: Full-Size Img PowerPoint

map

[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]	Schwierz F 2010 Nat. Nanotechnol. 5 487 Google Scholar
[3]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Katsnelson M I, Grigorieva I V, Dubonos S V, Firsov A A 2005 Nature 438 197 Google Scholar
[4]	Lee C, Wei X, Kysar J W, Hone J 2008 Science 321 385 Google Scholar
[5]	Balandin A A, Ghosh S, Bao W Z, Calizo I, Teweldebrhan D, Miao F, Lau C N 2008 Nano Lett. 8 902 Google Scholar
[6]	Nair R R, Blake P, Grigorenko A N, Novoselov K S, Booth T J, Stauber T, Peres N M R, Geim A K 2008 Science 320 1308 Google Scholar
[7]	Son Y W, Cohen M L, Louie S G 2006 Phys. Rev. Lett. 97 216803 Google Scholar
[8]	Fujita M, Wakabayashi K, Nakada K, Kusakabe K 1996 J. Phys. Soc. Jpn. 65 1920 Google Scholar
[9]	Huang B, Yan Q M, Li Z Y, Duan W H 2009 Front. Phys. China 4 269 Google Scholar
[10]	Wang G 2012 Chem. Phys. Lett. 533 74 Google Scholar
[11]	Barone, Verónica, Hod O, Scuseria G E 2006 Nano Lett. 6 2748 Google Scholar
[12]	Jaiswal M, Haley Y X L C, Bao Q 2011 ACS Nano 5 888 Google Scholar
[13]	Cai J, Ruffieux P, Jaafar R, Bieri M, Braun T, Blankenburg S, Muoth M, Seitsonen A P, Saleh M, Feng X, Müllen K, Fasel R 2010 Nature 466 470 Google Scholar
[14]	Zhang H, Lin H, Sun K, Chen L, Zagranyarski Y, Aghdassi N, Duhm S, Li Q, Zhong D, Li Y, Müllen K, Fuchs H, Chi L 2015 J. Am. Chem. Soc. 137 4022 Google Scholar
[15]	Kimouche A, Ervasti M M, Drost R, Halonen S, Harju A, Joensuu P M, Sainio J, Liljeroth P 2015 Nat. Commun. 6 10177 Google Scholar
[16]	Basagni A, Sedona F, Pignedoli C A, Cattelan M, Nicolas L, Casarin M, Sambi M 2015 J. Am. Chem. Soc. 137 1802 Google Scholar
[17]	Ruffieux P, Cai J, Plumb N C, Patthey L, Prezzi D, Ferretti A, Molinari E, Feng X, Müllen K, Pignedoli C A, Fasel R 2012 ACS Nano 6 6930 Google Scholar
[18]	Talirz L, Sode H, Dumslaff T, Wang S, Sanchez-Valencia J R, Liu J, Shinde P, Pignedoli C A, Liang L, Meunier V, Plumb N C, Shi M, Feng X, Narita A, Müllen K, Fasel R, Ruffieux P 2017 ACS Nano 11 1380 Google Scholar
[19]	Chen Y C, de Oteyza D G, Pedramrazi Z, Chen C, Fischer F R, Crommie M F 2013 ACS Nano 7 6123 Google Scholar
[20]	Abdurakhmanova N, Amsharov N, Stepanow S, Jansen M, Kern K, Amsharov K 2014 Carbon 77 1187 Google Scholar
[21]	Huang H, Wei D, Sun J, Wong S L, Feng Y P, Neto A H C, Wee A T S 2012 Sci. Rep. 2 983 Google Scholar
[22]	Ellert C, Corkum P B 1999 Phys. Rev. A 59 R3170 Google Scholar
[23]	王藩侯, 黄多辉, 杨俊升 2013 62 07310 Google Scholar Wang F H, Huang D H, Yang J S 2013 Acta Phys. Sin. 62 07310 Google Scholar
[24]	Rai D, Joshi H, Kulkarni A D, Gejji S P, Pathak R K 2007 J. Phys. Chem. A 111 9111 Google Scholar
[25]	李亚莎, 谢云龙, 黄太焕, 徐程, 刘国成 2018 67 183101 Google Scholar Li Y S, Xie Y L, Huang T H, Xu C, Liu G C 2018 Acta Phys. Sin. 67 183101 Google Scholar
[26]	杜建宾, 冯志芳, 韩丽君, 唐延林, 武德起 2018 67 223101 Google Scholar Du J B, Feng Z F, Han L J, Tang Y L, Wu D Q 2018 Acta Phys. Sin. 67 223101 Google Scholar
[27]	李世雄, 吴永刚, 令狐荣锋, 孙光宇, 张正平, 秦水介 2015 64 043101 Google Scholar Li S X, Wu Y G, Linghu R F, Sun G Y, Zhang Z P, Qin S J 2015 Acta Phys. Sin. 64 043101 Google Scholar
[28]	徐国亮, 谢会香, 袁伟, 张现周, 刘玉芳 2012 61 043104 Google Scholar Xu G L, Xie H X, Yuan W, Zhang X Z, Liu Y F 2012 Acta Phys. Sin. 61 043104 Google Scholar
[29]	曹欣伟, 任杨, 刘慧, 李姝丽 2014 63 043101 Google Scholar Cao X W, Ren Y, Liu H, Li S L 2014 Acta Phys. Sin. 63 043101 Google Scholar
[30]	Son Y W, Cohen M L, Louie S G 2006 Nature 444 347 Google Scholar
[31]	Chang C P, Huang Y C, Lu C L, Ho J H, Li T S, Lin M F 2006 Carbon 44 508 Google Scholar
[32]	Chen S C, Chang C P, Lee C H, Lin M F 2010 J. Appl. Phys. 107 4579 Google Scholar
[33]	Wu L J, Zhang L, Qi Y 2017 Sci. Adv. Mater. 9 1775 Google Scholar
[34]	Wu L J, Zhang L, Shen L H 2018 Appl. Surf. Sci. 447 22 Google Scholar
[35]	Wu L J, Dong Y, Springborg M, Zhang L, Yang Qi 2015 Comp. Theo. Chem. 1074 185 Google Scholar
[36]	Wu L J, Xu X M, Zhang L, Qi Y 2019 Superlattice Microst. 135 106261 Google Scholar
[37]	吴丽君, 随强涛, 张多, 张林, 祁阳 2015 64 42102 Google Scholar Wu L J, Sui Q T, Zhang D, Zhang L, Qi Y 2015 Acta. Phys. Sin. 64 42102 Google Scholar
[38]	Hourahine B, Aradi B, Blum V, et al. 2020 J. Chem. Phys. 152 124101 Google Scholar
[39]	Elstner M, Porezag D, Jungnickel G, Elsner J, Haugk M, Frauenheim T, Suhai S, Seifert G 1998 Phys. Rev. B 58 7260 Google Scholar
[40]	Witek H, Irle S, Morokuma K 2004 J. Chem. Phys. 121 5163 Google Scholar
[41]	Mulliken R S 2004 J. Chem. Phys. 23 1841 Google Scholar
[42]	Elstner M 1998 Ph. D. Dissertation (Germany: University of Paderborn)
[43]	Raza H, Kan E C 2008 Phys. Rev. B 77 245434 Google Scholar

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