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物理化学学报  2018, Vol. 34 Issue (9): 961-976    DOI: 10.3866/PKU.WHXB201802051
所属专题： 石墨炔
综述     
石墨炔与锡烯层状体系的形变势和电声耦合及载流子传输理论研究
奚晋扬1,中村悠马2,赵天琦2,王冬2,帅志刚*()
1 上海大学材料基因组工程研究院，上海 200444
2 清华大学化学系，有机光电子与分子工程教育部重点实验室，北京 100084
Theoretical Studies on the Deformation Potential, Electron-Phonon Coupling, and Carrier Transports of Layered Systems
Jinyang XI1,Yuma NAKAMURA2,Tianqi ZHAO2,Dong WANG2,Zhigang SHUAI*()
1 Materials Genome Institute, Shanghai University, Shanghai 200444, P. R. China
2 MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing 100084, P. R. China
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摘要：

我们对sp + sp2杂化的碳同素异形体—石墨炔，以及锡烯等层状体系的电子结构、形变势、电声耦合和电荷输运性质进行了回顾。有些二维石墨炔具有类似石墨烯的狄拉克锥，同时石墨炔电子结构可通过将其沿不同方向裁剪成不同宽度一维纳米带来调节。采用玻尔兹曼输运方程和形变势近似，结合第一性原理计算，我们预测石墨炔电荷载流子室温迁移率可达104–105 cm2·V-1·s-1，尤其6, 6, 12-石墨炔，因有两个狄拉克锥及比石墨烯弱的电声耦合，其室温迁移率甚至能高于石墨烯。因此具有独特电子结构和高迁移率的石墨炔能成为继石墨烯之后未来的纳米电子器件材料。此外我们着重分析了形变势方法的适用性：密度泛函微扰理论和瓦尼尔插值技术能精确计算任意波矢和模式的声子对载流子散射，该方法在石墨烯和石墨炔上的运用表明二维平面碳材料中对载流子输运起主导作用的是长波长纵声学声子散射，因而形变势方法是适用的；但通过对锡烯等二维非平面buckling结构的材料声子散射和迁移率的计算，发现此类不具备σh对称性的材料有较强的面外声子散射和横声学声子谷间散射，使得常用的形变势失效。
关键词： 石墨炔;  锡烯;  电子结构;  形变势;  电声耦合;  迁移率    
Abstract:

The electronic structures, deformation potential, electron-phonon couplings (EPCs), and intrinsic charge transport of layered systems — the sp +sp2 hybridized carbon allotropes, graphynes (GYs) and graphdiynes (GDYs), as well as sp2 + sp3 hybridized structure with buckling, such as stanine — have been investigated theoretically. Computational studies showed that, similar to graphene, some GYs can possess Dirac cones (such as α-, β-, and 6, 6, 12-GYs), and that the electronic properties of GYs and GDYs can be tuned by cutting into nanoribbons with different widths and edge morphologies. Focusing on the features of Dirac cones, band structure engineering can provide a clue for tuning electronic transport in 2D carbon-based materials. Based on the Boltzmann transport equation and the deformation potential approximation (DPA), the charge carrier mobilities in GYs and GDYs were predicted to be as high as 104–105 cm2·V-1·s-1 at room temperature. Interestingly, due to lower EPC strength and longer relaxation time, the charge carrier mobility in 6, 6, 12-GY with double Dirac cones structure was found to be even larger than that of graphene at room temperature. The unique electronic properties and high mobilities of GYs and GDYs make them highly promising candidates for applications in next generation nanoelectronics. Additionally, through the full evaluation of the EPC by density functional perturbation theory (DFPT) and Wannier interpolation, the EPCs with different phonon branches and wave-vectors as well as charge carrier mobilities for graphene, GYs and stanene have been discussed. This showed that the longitudinal acoustic (LA) phonon scattering in the long wavelength limit is the main scattering mechanism for GYs and graphene, and thus the DPA is applicable. Due to stronger LA phonon scattering, the electron mobilities (∼104 cm2·V-1·s-1) of α-GYs and γ-GYs were predicted to be one order of magnitude smaller than that of graphene at room temperature by full evaluation of the EPC. However, the DPA would fail if there was buckling in the honeycomb structure and the planar symmetry was broken (absence of σh), such as in stanene, where the inter-valley scatterings from the out-of-plane acoustic (ZA) and transverse acoustic (TA) phonons dominate the carrier transport process and limit the electron mobilities to be (2–3) × 103 cm2·V-1·s-1 at room temperature. In addition to our calculations, others have also found that the main scattering mechanisms in layered systems with buckling, such as silicene and germanene, are ZA and TA phonons. Thus, these results give us new insights into the role of EPCs and the limitation of the DPA for carrier transport in layered systems. They also indicate that the carrier mobilities of systems without σh-symmetry can be improved by suppressing the out-of-plane vibrations, for example by clamping by a substrate.
Key words: Graphyne    Stanene    Electronic structure    Deformation potential    Electron-phonon coupling    Mobility
收稿日期: 2018-01-03 出版日期: 2018-04-09
中图分类号:  O641  
基金资助: 国家自然科学基金(21703136);国家重点研发计划(2017YFA0204501);上海市青年科技英才扬帆计划(17YF1427900)
通讯作者: 帅志刚     E-mail: zgshuai@tsinghua.edu.cn
作者简介: 帅志刚，1962年出生。1989年博士毕业于复旦大学。现为清华大学化学系长江特聘教授、博士生导师。主要研究领域为理论化学、材料的功能理论计算与模拟
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引用本文:

奚晋扬,中村悠马,赵天琦,王冬,帅志刚. 石墨炔与锡烯层状体系的形变势和电声耦合及载流子传输理论研究[J]. 物理化学学报, 2018, 34(9): 961-976, 10.3866/PKU.WHXB201802051

Jinyang XI,Yuma NAKAMURA,Tianqi ZHAO,Dong WANG,Zhigang SHUAI. Theoretical Studies on the Deformation Potential, Electron-Phonon Coupling, and Carrier Transports of Layered Systems. Acta Phys. -Chim. Sin., 2018, 34(9): 961-976, 10.3866/PKU.WHXB201802051.

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http://www.whxb.pku.edu.cn/CN/10.3866/PKU.WHXB201802051    或    http://www.whxb.pku.edu.cn/CN/Y2018/V34/I9/961

图1  常见二维石墨炔的平面结构31
图2  基于PBE计算的石墨炔能带结构
图3  GDY中两种不同类型、不同宽度的纳米带(以六边形个数代表宽度)，红色线框为重复单胞17
图4  五种GDY纳米带能带结构17
NR Egap/eV mh*/m0 me*/m0 Dh/eV De/eV C1D/(eV·cm-1) μh/(cm2·V-1·s-1) μe/(cm2·V-1·s-1)
2-ANR 0.954 0.086 0.081 7.406 2.006 1.244 × 104 0.711 × 103 10.580 × 103
3-ANR 0.817 0.087 0.086 6.790 1.730 1.864 × 104 1.253 × 103 19.731 × 103
2-ZNR 1.205 0.216 0.281 4.386 1.972 1.035 × 104 0.426 × 103 1.418 × 103
2.5-ZNR 1.015 0.174 0.207 4.776 2.054 1.420 × 104 0.679 × 103 2.829 × 103
3-ZNR 0.895 0.149 0.174 4.786 2.000 1.787 × 104 1.073 × 103 5.015 × 103
表1  PBE泛函计算的不同宽度ANRs和ZNRs的GDY纳米带带隙Egap、电子(空穴)的有效质量me*(mh*)、形变势常数De(Dh)、一维弹性常数C1D和室温(300 K)迁移率μe(μh) 17
acetylenic linkage/(%) axis D/eV C1D/(J·m-2) τh/ps τe/ps μh/(cm2·V-1·s-1) μe/(cm2·V-1·s-1)
α-GY 100 a 2.94 94.30 2.84 2.83 3.316 × 104 3.327 × 104
b 2.97 95.19 2.80 2.79 2.960 × 104 2.716 × 104
β-GY 66.67 a 2.99 131.41 5.82 6.40 1.076 × 104 0.892 × 104
b 3.11 130.65 5.37 5.91 0.856 × 104 0.798 × 104
6, 6, 12-GY 41.67 a 3.07 199.37 12.31 17.75 42.92 × 104 54.10 × 104
b 3.56 150.52 6.93 9.99 12.29 × 104 24.48 × 104
graphene 0 a 5.14 328.02 13.80 13.94 32.17 × 104 33.89 × 104
b 5.00 328.30 13.09 13.22 35.12 × 104 32.02 × 104
表2  PBE泛函计算的α-、β-、6, 6, 12-GYs以及石墨烯的二维弹性常数C2D，形变势常数D，以及室温(300 K)电子(空穴)弛豫时间τe (τh)和迁移率μe (μh) 21
图5  石墨烯和石墨炔中LA声子散射的电声耦合强度30
图6  石墨烯和GYs中的电子弛豫时间和迁移率随温度的关系30
phonon mode graphene α-GY γ-GY
hole electron hole electron hole electron
τ/ps LA 14.28 12.78 2.17 2.33 0.56 1.25
TA 161.32 111.46 711.64 882.80 16.30 20.27
LO 27.78 26.43 68.74 70.06 17.07 22.61
TO 74.98 76.02 33.57 34.29 59.19 79.78
total 7.97 7.24 1.97 2.11 0.52 1.10
μ/(104 cm2·V-1·s-1) LA 41.38 34.12 0.99 1.07 0.39 2.42
TA 591.81 304.75 314.66 380.06 7.30 13.04
LO 82.43 78.22 73.41 75.12 7.61 10.05
TO 218.06 222.53 59.16 59.70 27.82 37.81
total 23.49 20.05 0.96 1.03 0.35 1.62
表3  室温(300 K)石墨烯、α-和γ-GYs被不同声子散射的电子(空穴)弛豫时间τ和迁移率μ 30
图7  锡烯几何结构、能带结构和声子谱34
Scattering rate/s--1 stanene graphene
intravalley intervalley total intravalley intervalley total
ZA 1.27 × 103 1.84 × 1012 1.84 × 1012 1.15 × 10-4 2.33 × 107 2.33 × 107
TA 9.11 × 107 1.16 × 1012 1.16 × 1012 6.43 × 109 1.08 × 107 6.44 × 109
LA 1.74 × 1010 4.68 × 109 2.21 × 1010 2.12 × 1011 5.89 × 107 2.12 × 1011
ZO 2.01 × 108 1.29 × 1010 1.31 × 1010 1.41 × 107 8.83 × 109 8.85 × 109
TO 6.96 × 1010 1.23 × 1010 8.19 × 1010 7.70 × 109 6.62 × 109 1.43 × 1010
LO 6.62 × 1010 1.62 × 1011 2.29 × 1011 5.66 × 109 4.75 × 1010 5.32 × 1010
表4  室温(300 K)下锡烯和石墨烯狄拉克锥点电子被不同模式声子散射的谷内和谷间散射率34
图8  锡烯和石墨烯导带底狄拉克锥点电子与不同声子模式及不同波矢q相互作用的电声耦合强度等高图34
图9  锡烯和石墨烯中不同声子模式散射的电子弛豫时间与温度的关系图34
Buckling/nm DLA/eV μDPA/(cm2·V-1·s-1) μEPC/(cm2·V-1·s-1) symmetry Dominant phonon
stanene 0.085 34 0.48 34 (3 -4) × 106 34 2000 -3000 34 D3d ZA, TA 34
germanene 0.069 78, 79 1.16 80 6.2 × 105 80 2800 76 D3d ZA, TA 76
silicene 0.045 81, 82 2.13 83 2 × 105 83 2100 77, 1200 66, 750 76 D3d ZA 66, 76, 77, TA 66, 76
graphene 0.0 5.14 29, 4.24 30 (2 -3) × 105, 3 × 105 29, (2 -3) × 105, 2 × 105 30, D6h LA 30
1 × 105 84 1.5 × 105 77
α-graphyne 0.0 7.34 30 3 × 10421 1 × 104 30 D2h LA 30
Monolayer MoS2 – 4.5 66, 5.29 -11.36 85 72 -200 85 400 77, 130 66, 410 67, D3h LA 66, 67, LO]67
150 86, 230 87
表5  常见二维材料buckling、形变势常数DLA、室温DPA方法计算的迁移率μDPA及精确电声计算的迁移率μEPC对比34
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