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外加横向电场作用下石墨烯纳米带电子结构的密度泛函紧束缚计算

崔洋 李静 张林

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外加横向电场作用下石墨烯纳米带电子结构的密度泛函紧束缚计算

崔洋, 李静, 张林

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

Cui Yang, Li Jing, Zhang Lin
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  • 采用基于密度泛函理论的紧束缚方法计算研究了外加横向电场对边缘未加氢/加氢钝化的扶手椅型石墨烯纳米带的电子结构及电子布居数的影响. 计算结果表明, 石墨烯纳米带的能隙变化受其宽带影响. 当施加沿其宽度方向的横向外加电场时, 纳米带的能带结构及态密度都会产生较大的变化. 对于具有半导体性的边缘未加氢纳米带, 随着所施加电场强度的增加, 会发生半导体-金属的转变. 同时, 电场也会对能级分布产生显著影响. 外加电场导致纳米带内原子上电子布居数分布失去对称性, 电场强度越大, 其布居数不对称性越明显. 边缘加氢钝化可以显著改变纳米带内原子上的布居数分布.
    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.
      通信作者: 张林, zhanglin@imp.neu.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 51671051)和国家重点研发计划(批准号: 2016YFB0701304)资助的课题
      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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    徐国亮, 谢会香, 袁伟, 张现周, 刘玉芳 2012 物理学报 61 043104Google Scholar

    Xu G L, Xie H X, Yuan W, Zhang X Z, Liu Y F 2012 Acta Phys. Sin. 61 043104Google Scholar

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    曹欣伟, 任杨, 刘慧, 李姝丽 2014 物理学报 63 043101Google Scholar

    Cao X W, Ren Y, Liu H, Li S L 2014 Acta Phys. Sin. 63 043101Google Scholar

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    Chang C P, Huang Y C, Lu C L, Ho J H, Li T S, Lin M F 2006 Carbon 44 508Google Scholar

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    Chen S C, Chang C P, Lee C H, Lin M F 2010 J. Appl. Phys. 107 4579Google Scholar

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    Wu L J, Zhang L, Qi Y 2017 Sci. Adv. Mater. 9 1775Google Scholar

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    Wu L J, Zhang L, Shen L H 2018 Appl. Surf. Sci. 447 22Google Scholar

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    Wu L J, Dong Y, Springborg M, Zhang L, Yang Qi 2015 Comp. Theo. Chem. 1074 185Google Scholar

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    Wu L J, Xu X M, Zhang L, Qi Y 2019 Superlattice Microst. 135 106261Google Scholar

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    吴丽君, 随强涛, 张多, 张林, 祁阳 2015 物理学报 64 42102Google Scholar

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    Hourahine B, Aradi B, Blum V, et al. 2020 J. Chem. Phys. 152 124101Google Scholar

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    Elstner M, Porezag D, Jungnickel G, Elsner J, Haugk M, Frauenheim T, Suhai S, Seifert G 1998 Phys. Rev. B 58 7260Google Scholar

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  • 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

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

    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

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

    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

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

    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

    Fig. 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

    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

    Fig. 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.

    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

    Fig. 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.

    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

    Fig. 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.

    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

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

  • [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 666Google Scholar

    [2]

    Schwierz F 2010 Nat. Nanotechnol. 5 487Google 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 197Google Scholar

    [4]

    Lee C, Wei X, Kysar J W, Hone J 2008 Science 321 385Google Scholar

    [5]

    Balandin A A, Ghosh S, Bao W Z, Calizo I, Teweldebrhan D, Miao F, Lau C N 2008 Nano Lett. 8 902Google 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 1308Google Scholar

    [7]

    Son Y W, Cohen M L, Louie S G 2006 Phys. Rev. Lett. 97 216803Google Scholar

    [8]

    Fujita M, Wakabayashi K, Nakada K, Kusakabe K 1996 J. Phys. Soc. Jpn. 65 1920Google Scholar

    [9]

    Huang B, Yan Q M, Li Z Y, Duan W H 2009 Front. Phys. China 4 269Google Scholar

    [10]

    Wang G 2012 Chem. Phys. Lett. 533 74Google Scholar

    [11]

    Barone, Verónica, Hod O, Scuseria G E 2006 Nano Lett. 6 2748Google Scholar

    [12]

    Jaiswal M, Haley Y X L C, Bao Q 2011 ACS Nano 5 888Google 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 470Google 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 4022Google Scholar

    [15]

    Kimouche A, Ervasti M M, Drost R, Halonen S, Harju A, Joensuu P M, Sainio J, Liljeroth P 2015 Nat. Commun. 6 10177Google Scholar

    [16]

    Basagni A, Sedona F, Pignedoli C A, Cattelan M, Nicolas L, Casarin M, Sambi M 2015 J. Am. Chem. Soc. 137 1802Google 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 6930Google 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 1380Google Scholar

    [19]

    Chen Y C, de Oteyza D G, Pedramrazi Z, Chen C, Fischer F R, Crommie M F 2013 ACS Nano 7 6123Google Scholar

    [20]

    Abdurakhmanova N, Amsharov N, Stepanow S, Jansen M, Kern K, Amsharov K 2014 Carbon 77 1187Google 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 983Google Scholar

    [22]

    Ellert C, Corkum P B 1999 Phys. Rev. A 59 R3170Google Scholar

    [23]

    王藩侯, 黄多辉, 杨俊升 2013 物理学报 62 07310Google Scholar

    Wang F H, Huang D H, Yang J S 2013 Acta Phys. Sin. 62 07310Google Scholar

    [24]

    Rai D, Joshi H, Kulkarni A D, Gejji S P, Pathak R K 2007 J. Phys. Chem. A 111 9111Google Scholar

    [25]

    李亚莎, 谢云龙, 黄太焕, 徐程, 刘国成 2018 物理学报 67 183101Google Scholar

    Li Y S, Xie Y L, Huang T H, Xu C, Liu G C 2018 Acta Phys. Sin. 67 183101Google Scholar

    [26]

    杜建宾, 冯志芳, 韩丽君, 唐延林, 武德起 2018 物理学报 67 223101Google Scholar

    Du J B, Feng Z F, Han L J, Tang Y L, Wu D Q 2018 Acta Phys. Sin. 67 223101Google Scholar

    [27]

    李世雄, 吴永刚, 令狐荣锋, 孙光宇, 张正平, 秦水介 2015 物理学报 64 043101Google Scholar

    Li S X, Wu Y G, Linghu R F, Sun G Y, Zhang Z P, Qin S J 2015 Acta Phys. Sin. 64 043101Google Scholar

    [28]

    徐国亮, 谢会香, 袁伟, 张现周, 刘玉芳 2012 物理学报 61 043104Google Scholar

    Xu G L, Xie H X, Yuan W, Zhang X Z, Liu Y F 2012 Acta Phys. Sin. 61 043104Google Scholar

    [29]

    曹欣伟, 任杨, 刘慧, 李姝丽 2014 物理学报 63 043101Google Scholar

    Cao X W, Ren Y, Liu H, Li S L 2014 Acta Phys. Sin. 63 043101Google Scholar

    [30]

    Son Y W, Cohen M L, Louie S G 2006 Nature 444 347Google Scholar

    [31]

    Chang C P, Huang Y C, Lu C L, Ho J H, Li T S, Lin M F 2006 Carbon 44 508Google Scholar

    [32]

    Chen S C, Chang C P, Lee C H, Lin M F 2010 J. Appl. Phys. 107 4579Google Scholar

    [33]

    Wu L J, Zhang L, Qi Y 2017 Sci. Adv. Mater. 9 1775Google Scholar

    [34]

    Wu L J, Zhang L, Shen L H 2018 Appl. Surf. Sci. 447 22Google Scholar

    [35]

    Wu L J, Dong Y, Springborg M, Zhang L, Yang Qi 2015 Comp. Theo. Chem. 1074 185Google Scholar

    [36]

    Wu L J, Xu X M, Zhang L, Qi Y 2019 Superlattice Microst. 135 106261Google Scholar

    [37]

    吴丽君, 随强涛, 张多, 张林, 祁阳 2015 物理学报 64 42102Google Scholar

    Wu L J, Sui Q T, Zhang D, Zhang L, Qi Y 2015 Acta. Phys. Sin. 64 42102Google Scholar

    [38]

    Hourahine B, Aradi B, Blum V, et al. 2020 J. Chem. Phys. 152 124101Google Scholar

    [39]

    Elstner M, Porezag D, Jungnickel G, Elsner J, Haugk M, Frauenheim T, Suhai S, Seifert G 1998 Phys. Rev. B 58 7260Google Scholar

    [40]

    Witek H, Irle S, Morokuma K 2004 J. Chem. Phys. 121 5163Google Scholar

    [41]

    Mulliken R S 2004 J. Chem. Phys. 23 1841Google Scholar

    [42]

    Elstner M 1998 Ph. D. Dissertation (Germany: University of Paderborn)

    [43]

    Raza H, Kan E C 2008 Phys. Rev. B 77 245434Google Scholar

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出版历程
  • 收稿日期:  2020-09-29
  • 修回日期:  2020-10-25
  • 上网日期:  2021-02-22
  • 刊出日期:  2021-03-05

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