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通过离子辐照产生缺陷, 可以非常有效地调控磷烯诸多物理性质. 本文应用分子动力学方法模拟离子辐照磷烯的过程, 给出了缺陷的形成概率与入射离子能量、离子种类以及离子入射角度之间的关系, 并且应用非平衡态分子动力学计算辐照后磷烯热导率的变化. 以缺陷形成概率为切入点, 系统地研究了辐照离子的能量、辐照剂量、离子的种类以及离子的入射角度对磷烯热导率的影响. 应用晶格动力学方法研究了空位缺陷对磷烯声子参与率的影响, 并计算了声子局域模式的空间分布. 基于量子微扰和键弛豫理论, 指出空位缺陷明显降低磷烯热导率的最重要物理机制是空位缺陷附近的低配位原子对声子强烈散射. 本文研究可为缺陷工程调控磷烯的热输运性质提供理论参考.Defects produced by ion irradiation can effectively modulate many physical properties of phosphorene. In this paper, the molecular dynamics method is used to simulate the ion irradiation process of phosphorene. The relations between the formation probability of defects and the energy of incident ions, ion species and incident angle of ions are revealed. The non-equilibrium molecular dynamics simulation is used to calculate the thermal conductivity of irradiated phosphorene. The effects of the energy of ions, the irradiation dose, the type of ions and the incident angle of ions on the thermal conductivity of phosphorene are systematically investigated. The influence of the vacancies on the phonon participation rate of phosphorene is studied by lattice dynamics method, and the spatial distribution of localized modes is demonstrated. According to the quantum-mechanical perturbation theory and bond relaxation theory, we point out that the dominant physical mechanism of vacancy defects which significantly reduce the thermal conductivity of phosphorene is the strong scattering of phonons by the low-coordinated atoms near the vacancies. This study provides a theoretical basis for tuning the heat transport properties of phosphorene by defect engineering.
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Keywords:
- phosphorene /
- ion irradiation /
- vacancy defect /
- thermal conductivity
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图 1 (a) 离子辐照黑磷模拟示意图, 黑色的原子层为黑磷模型, 黄色小球代表辐照的离子; (b) 计算磷烯热导率的MP模拟方法示意图
Fig. 1. (a) Schematic diagram of ions irradiation black phosphorus simulation, the black atomic layer is the black phosphorus model, the yellow balls represent the irradiated ions; (b) schematic diagram of MP simulation method for calculating the thermal conductivity of phosphene.
图 2 反射、穿透以及损伤的发生概率与入射质子能量之间的关系
Fig. 2. Probability of occurrence versus kinetic energy of protons for reflection, transmission, and damage events.
图 3 不同离子对磷烯造成损伤的概率与入射离子能量之间的关系
Fig. 3. Relationship between the probability of damage and the incident energy of different ions.
图 4 不同入射能量下, 磷烯损伤概率与入射角度之间的关系
Fig. 4. Relationship between the probability of damage and the incident angle in case of different kinetic energy of protons.
图 5 不同辐照剂量下, 磷烯热导率与入射质子能量之间的关系
Fig. 5. Thermal conductivity of phosphorene versus kinetic energy of incident protons at different irradiation dose.
图 6 不同离子的辐照下, 磷烯的热导率与入射离子能量之间的关系
Fig. 6. Thermal conductivity of phosphorene versus kinetic energy of different ions.
图 7 不同能量下, 磷烯的热导率与质子入射角度之间的关系
Fig. 7. Thermal conductivity of phosphorene versus incident angle in case of different kinetic energy of protons.
图 8 没有缺陷的磷烯、以及空位缺陷浓度分别为1.2%和3.2%的磷烯振动模式参与率
Fig. 8. The participation ratios of each vibrational eigen-mode for pristine phosphorene and phosphorene with 1.2% and 3.2% vacancies.
图 9 空位缺陷磷烯局域化振动模式的空间分布图, X, Y位置的颜色代表该位置的局域化程度
Fig. 9. The spatial distribution of localized modes for vacancy-defected phosphorene; the color of X, Y corresponds to the magnitude of localization at that position (X, Y ).
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[1] Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva S V, Firsov A A 2004 Science 306 5695
[2] Qiao J, Kong X, Hu Z X, Yang F, Ji W 2014 Nat. commun. 5 4475
Google Scholar
[3] Xia F, Wang H, Jia Y 2014 Nat. Commun. 5 1
[4] Li L, Yu Y, Ye G J, Ge Q, Ou X, Wu H, Feng D, Chen X H, Zhang Y 2014 Nat. Nanotech. 9 372
[5] Zeng Y J, Feng Y X, Tang L M, Chen K Q 2021 Appl. Phys. Lett. 118 183103
Google Scholar
[6] Cui C, Ouyang T, Tang C, He C, Li J, Zhang C, Zhong J 2021 Carbon 176 52
Google Scholar
[7] Chen X K, Hu X Y, Jia P, Xie Z X, Liu J 2021 Int. J. Mech. Sci. 206 106576
Google Scholar
[8] Zhou W X, Cheng Y, Chen K Q, Xie G F, Wang T, Zhang G 2020 Adv. Funct. Mater. 30 1903829
Google Scholar
[9] Haskins J, Kınacı A, Sevik C, Sevinçli H, Cuniberti G, Cağın T 2011 Acs. Nano. 5 3779
Google Scholar
[10] Chen J H, Cullen W G, Jang C, Fuhrer M S, Williams E D 2009 Phys. Rev. Lett. 102 236805
Google Scholar
[11] Guo Y, Robertson J 2015 Sci. Rep. 5 14165
Google Scholar
[12] Ziletti A, Carvalho A, Campbell D K, Coker D F, Castro Neto A H 2015 Phys. Rev. Lett. 114 046801
Google Scholar
[13] Yuan S, Rudenko A N, Katsnelson M I 2015 Phy. Rev. B 91 115436
Google Scholar
[14] Qin G, Yan Q B, Qin Z, Yue S Y, Cui H J, Zheng Q R, Su G 2014 Sci. Rep. 4 6946
Google Scholar
[15] Ong Z Y, Cai Y, Zhang G, Zhang Y W 2014 J. Phys. Chem. C 118 43
[16] Xu W, Zhu L, Cai Y, Zhang G, Li B 2015 J. Appl. Phys. 1172 14308
[17] Jiang J W 2015 Nanotechnology 26 315706
Google Scholar
[18] Ziegler J F, Biersack J P, Littmark U 1985 The Stopping and Range of Ions in Matter (New York: Pergamon Press) pp93–129
[19] Plimpton S 1995 J. Comput. Phys. 117 1
Google Scholar
[20] Zhang H, Zhou T, Xie G F, Cao J X, Yang Z 2014 Appl. Phys. Lett. 104 241908
Google Scholar
[21] Müllerplathe F 1997 J. Chem. Phys. 106 6082
Google Scholar
[22] Bellido E P, Seminario J M 2012 J. Phys. Chem. C 116 4044
Google Scholar
[23] Lehtinen O, Dumur E, Kotakoski J, Krasheninnikov A V, Nordlund K, Keinonen J 2011 Nucl. Instrum. Meth. Phys. Res. B 269 1327
Google Scholar
[24] Schelling P K, PhillpotS R 2001 J. Am. Ceram. Soc. 84 2997
Google Scholar
[25] Wang Y, Qiu B, Ruan X 2012 Appl. Phys. Lett. 101 013101
Google Scholar
[26] Klemens P G 1955 Proc. Phys. Soc. A 68 1113
Google Scholar
[27] Pauling L 1947 J. Am. Chem. Soc. 69 542
Google Scholar
[28] Sun C Q 2007 Prog. Solid State Chem. 35 1
Google Scholar
[29] Liu Y H, Yang X X, Bo M L, Zhang X, Liu X J, Sun C Q, Huang Y L 2016 J. Raman Spectrosc. 47 1304
Google Scholar
[30] Klemens P G 1958 Solid State Phys. 7 1
[31] Huang W J, Sun R, Tao J, Menard L D, Nuzzo R G, Zuo J M 2008 Nat. Mater. 7 308
Google Scholar
[32] Crespi V H, Chopra N G, Cohen M L, Zettl A, Louie S G 1996 Phys. Rev. B 54 5927
Google Scholar
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