物理化学学报 >> 2019, Vol. 35 >> Issue (10): 1142-1149.doi: 10.3866/PKU.WHXB201810040
所属专题: 二维材料及器件
收稿日期:
2018-10-18
录用日期:
2019-02-03
发布日期:
2018-12-07
通讯作者:
周思
E-mail:sizhou@dlut.edu.cn
基金资助:
Nanshu LIU,Si ZHOU*(),Jijun ZHAO
Received:
2018-10-18
Accepted:
2019-02-03
Published:
2018-12-07
Contact:
Si ZHOU
E-mail:sizhou@dlut.edu.cn
Supported by:
摘要:
作为纳米材料中最有前途的的材料之一,石墨烯由于其超高的电导率、优异的热稳定性和机械强度受到了研究者的广泛关注。本文通过非平衡格林函数法结合密度泛函理论计算了石墨烯点缺陷(包括Stone-Waals,反Stone-Waals,单空位和双空位)及其浓度对石墨烯电输运性质的影响。石墨烯的电导在很大程度上依赖于点缺陷的类型及浓度。低浓度的Stone-Waals和反Stone-Waals缺陷不会显著地降低石墨烯的电输运,而双空位可使电导降低约50%左右。石墨烯中明显的电输运行为变化是由带缺陷石墨烯的能带结构决定的——由于点缺陷破坏了石墨烯蜂窝状晶格的对称性,会在费米能级附近引入局域态,进而导致狄拉克点处有能带劈裂。高缺陷浓度的双空位会在费米能级附近引入更多的平带以及在缺陷处更多的局域态,因此可能对载流子进行一定的散射,降低石墨烯的电导。此外,局部电荷密度表现出增强的局域性,阻碍了载流子的运动。石墨烯电导随着缺陷浓度和能带劈裂的增加呈指数下降。这些理论结果为研究真实单层石墨烯的电输运特性提供了重要的理解,并将有助于实验上控制石墨烯基器件的性能。
MSC2000:
刘南舒,周思,赵纪军. 点缺陷石墨烯的电导[J]. 物理化学学报, 2019, 35(10): 1142-1149.
Nanshu LIU,Si ZHOU,Jijun ZHAO. Electrical Conductance of Graphene with Point Defects[J]. Acta Physico-Chimica Sinica, 2019, 35(10): 1142-1149.
Fig 2
Atomic structures of graphene monolayer with various point defects: (a) SW, (b) inverse-SW, (c) SV5-9, (d) SV, (e) DV585 and (f) DV555777 Point defects are indicated by the shadow areas. The solid boxes show the lateral dimensions of supercells (corresponding to defect concentration of 0.39 nm−1). The inset in panel (a) shows the first Brillouin zone of the supercell. Γ and X are the high-symmetry points in the Brillouin zone, and K is the Dirac point. The arrow in (a) indicates the transport direction. "
Table 1
Formation energy (ΔH), energy splitting at the Dirac point (Δ) and ratio between average electrical conductance of graphene monolayer with point defect (Ge) and that of pristine graphene (Ge0) (between ±0.5 eV) at various concentrations (c)"
Point defect | c/nm‒1) | ΔH/eV | Δ/eV | Ge·Ge0−1 |
SW | 0.29 | 4.33 (4.5–5.3) | 0.03 | 0.91 |
0.33 | 4.30 | 0.04 | 0.91 | |
0.39 | 4.34 | 0.05 | 0.79 | |
0.58 | 4.17 | 0.06 | 0.43 | |
0.78 | 4.02 | 0.06 | 0.41 | |
inverse-SW | 0.29 | 4.35 (5.8) | 0.06 | 0.89 |
0.33 | 4.38 | 0.07 | 0.82 | |
0.39 | 4.41 | 0.08 | 0.80 | |
0.58 | 4.51 | 0.12 | 0.38 | |
0.78 | 4.63 | 0.18 | 0.26 | |
SV5-9 | 0.29 | 7.42 (7.3–7.5) | 0.07 | 0.87 |
0.33 | 7.46 | 0.07 | 0.86 | |
0.39 | 7.50 | 0.08 | 0.83 | |
0.58 | 7.54 | 0.11 | 0.40 | |
0.78 | 7.54 | 0.14 | 0.37 | |
SV | 0.29 | 7.64 | 0.09 | 0.75 |
0.33 | 7.70 | 0.10 | 0.66 | |
0.39 | 7.80 | 0.11 | 0.61 | |
0.58 | 7.81 | 0.14 | 0.32 | |
0.78 | 7.88 | 0.19 | 0.29 | |
DV585 | 0.29 | 6.84 (7.2–7.9) | 0.18 | 0.74 |
0.33 | 6.90 | 0.22 | 0.70 | |
0.39 | 6.91 | 0.28 | 0.67 | |
0.58 | 6.82 | 0.29 | 0.28 | |
0.78 | 6.75 | 0.27 | 0.21 | |
DV555777 | 0.29 | 6.13 (6.4–7.5) | 0.33 | 0.38 |
0.33 | 6.21 | 0.37 | 0.38 | |
0.39 | 6.24 | 0.42 | 0.39 | |
0.58 | 6.29 | 0.41 | 0.16 | |
0.78 | 6.34 | 0.43 | 0.12 | |
DV5555-6-7777 | 0.29 | 6.10 (7.0) | 0.27 | 0.50 |
0.33 | 6.16 | 0.31 | 0.45 | |
0.39 | 6.16 | 0.34 | 0.41 | |
0.58 | 5.94 | 0.33 | 0.16 |
Fig 3
Transmission spectra per unit width (T∙w−1) for graphene monolayer with (a) SW, (b) inverse-SW, (c) SV5-9, (d) SV, (e) DV585 and (f) DV555777 defects at various defect concentrations (colored solid lines) The transmission spectrum of perfect graphene is shown by black dashed line. The Fermi energy is shifted to zero. "
Fig 4
Ratio between average electrical conductance of graphene monolayer with point defect (Ge) and that of pristine graphene (Ge0) (between ±0.5 eV) as a function of (a) defect concentration (c) and (b) energy splitting at the Dirac point (Δ) for graphene monolayer with various point defects. The dashed lines are the fit of Ge·Ge0−1 vs c and Ge·Ge0−1 vs Δ with exponential functions "
Fig 5
Band structures (left panels) and density of states (DOS) (right panels) of graphene monolayer with various point defects: (a) SW, (b) inverse-SW, (c) SV5-9, (d) SV, (e) DV585 and (f) DV555777, at defect concentration of 0.39 nm−1 In the left panels, the red circles show the bands from C atoms in the defect region, and the radius of the circles is proportional to the weight. In the right panels, the black solid line shows the total DOS of defective graphene monolayers, the red solid lines show the DOS from C atoms in the defect region, and the light blue dashed line shows the DOS of perfect graphene. The insets display the partial charge densities of the localized states indicated by the cyan dashed arrows, with an isosurface value of 1.5 e·nm‒1. The Fermi energy is shifted to zero. "
Fig 6
Band structure (left panels) and density of states (DOS) (right panels) of graphene monolayer with SW defect at various concentrations: (a) 0.29 nm−1, (b) 0.39 nm−1, (c) 0.58 nm−1 >and (d) 0.78 nm−1 In the left panels, the red circles show the bands from atomic orbitals of C atoms in the defect region, and the radius of the circles is proportional to the weight. In the right panels, the black solid line shows the total DOS of defective graphene monolayers, the red solid lines show the DOS from C atoms in the defect region, and the light blue dashed line shows the DOS of perfect graphene. The insets display the partial charge densities of the localized states indicated by the cyan dashed arrows, with an isosurface value of 1.5 e·nm‒1. The Fermi energy is shifted to zero. "
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