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Acta Phys. -Chim. Sin.  2018, Vol. 34 Issue (9): 961-976    DOI: 10.3866/PKU.WHXB201802051
Special Issue: Graphdiyne
REVIEW     
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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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 wordsGraphyne      Stanene      Electronic structure      Deformation potential      Electron-phonon coupling      Mobility     
Received: 03 January 2018      Published: 09 April 2018
MSC2000:  O641  
Fund:  the National Natural Science Foundation of China(21703136);the National Key Research and Development Program of China(2017YFA0204501);the Shanghai Sailing Program, China(17YF1427900)
Corresponding Authors: Zhigang SHUAI     E-mail: zgshuai@tsinghua.edu.cn
Cite this article:

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.

URL:

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

Fig 1 Geometric structures of GYs and GDY 31. (a) α-GY, (b) β-GY, (c) γ-GY, (d) GDY, (e) 6, 6, 12-GY.
Fig 2 Band structures of GYs and GDY at PBE level. (a) γ-GY 42, (b) GDY 42, (c) α-GY 21, (d) β-GY 21, (e) 6, 6, 12-GY 21.
Fig 3 Geometric structures of ANR and ZNR for GDY with different widths (number of C6 hexagons), the red frames represent unit-cells 17.
Fig 4 Band structures of five nanoribbons of GDY 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
Table 1 Band gap Egap, effective mass me*(mh*), deformation potential constant De(Dh), 1D elastic constant C1D and mobility μe(μh) at room temperature (300 K) for five GDY NRs at PBE level 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
Table 2 2D elastic constant C2D, deformation potential constant D, carriers scattering time τe (τh), and mobility μe (μh) at room temperature (300 K) for α-, β-, and 6, 6, 12-GYs, as well as graphene at PBE level 21.
Fig 5 The strength of EPC from LA phonon scatterings in graphene and GYs 30. Contour plots showing the square of EPC matrix elements |gmnλ(k, q)|2 (in eV2) calculated by DFPT and EPW for (a) graphene, (b) α-GY and (c) γ-GY, as a function of LA phonon wave vector q (near the center of the Brillouin zone). k is at the conduction band (CB) minimum (K-point for graphene andα-GY, M-point for γ-GY) and the initial n and final m electronic states are both limited to the CB; (d) The matrix element of LA phonon scattering as a function of phonon wave vector |q| in the long-wavelength limit. The slope is the LA deformation potential constant.
Fig 6 The electron scattering time and mobility as functions of temperature for graphene and GYs 30. (a), (b) and (c) are the scattering times of an electron at the conduction band minimum by different phonon modes as a function of temperature for graphene, α-GY, and γ-GY; (d) Electron mobility limited by LA phonon scattering as a function of temperature for these systems.
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
Table 3 The carriers scattering times and mobilities with different phonon scattering mechanisms for graphene, α-, and γ-GYs at room temperature (300 K) 30.
Fig 7 Geometric structure, band structure and phonon dispersion of stanene 34. (a) Top and side view of stanene; (b) Schematic illustration of the first Brillouin zone and high symmetry points; (c) Band structures of graphene (black-dashed), stanene without spin-orbit coupling (SOC) (red-solid) and with SOC (blue-solid, inset); (d) Phonon dispersions of graphene (black-dashed) and stanene (red-solid).
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
Table 4 Intervalley scattering and intravalley scattering for electrons in stanene and graphene at Dirac point K and 300 K 34.
Fig 8 Strength of electron-phonon coupling as a function of phonon wavevector q at Dirac point K in the conduction band 34. (a) stanene, (b) graphene.
Fig 9 Temperature dependence of scattering time for the conduction band for all phonon modes 34. (a) stanene, (b) graphene.
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
Table 5 The buckling, deformation potential constant DLA, mobility calculated with DPA μDPA compared to that by the full evaluation of ECP μEPC for 2D materials 34.
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