原子非简谐振动对石墨烯吸附系统电荷分布的影响
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摘要
建立了石墨烯吸附原子系统的物理模型,考虑到原子的非简谐振动和电子-声子相互作用,计算了吸附原子与石墨烯原子的相互作用能,用统计物理理论和方法,得到在石墨烯上吸附原子的概率和金属原子电荷填充数随温度变化的解析表示式.以碱金属为例,探讨了电子-声子相互作用和原子非简谐振动对电荷填充数的影响.结果表明:石墨烯吸附系统的电荷填充数随吸附原子距离的增大而线性地减小,随温度的升高和电子-声子相互作用能的增大而非线性地增大;若不考虑非简谐振动,则电荷填充数与位置、温度等无关.温度愈高、电子-声子相互作用能愈小,非简谐效应愈显著.
In this paper, a physical model of graphene adsorption system is established. The interaction energy between graphene atoms and adatoms is calculated in the case of considering the anharmonic vibration of the atom and the electron-phonon interaction. By means of the statistical physics theory and method, we obtain the probability of adsorption adatoms and the temperature-dependence analytic equation of the number of mental atoms charge filling. Taking alkali metals as an example, we discuss the effect of the electron-phonon interaction and the atomic anharmonic vibration on the number of charge filling. The results show that the charge filling numbers of graphene adsorption system decrease linearly with the enlargement of distances of adatoms and increase nonlinearly with the increase of temperature and electron-phonon interaction energy. If the anharmonic vibration is neglected, the number of charge filling is independent of distance and temperature etc. The anharmonic vibration is more obvious when the temperature becomes higher or the electron-phonon interaction energy becomes smaller.
In this paper, a physical model of graphene adsorption system is established. The interaction energy between graphene atoms and adatoms is calculated in the case of considering the anharmonic vibration of the atom and the electron-phonon interaction. By means of the statistical physics theory and method, we obtain the probability of adsorption adatoms and the temperature-dependence analytic equation of the number of mental atoms charge filling. Taking alkali metals as an example, we discuss the effect of the electron-phonon interaction and the atomic anharmonic vibration on the number of charge filling. The results show that the charge filling numbers of graphene adsorption system decrease linearly with the enlargement of distances of adatoms and increase nonlinearly with the increase of temperature and electron-phonon interaction energy. If the anharmonic vibration is neglected, the number of charge filling is independent of distance and temperature etc. The anharmonic vibration is more obvious when the temperature becomes higher or the electron-phonon interaction energy becomes smaller.
引文
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[18] 陈洪. 量子力学 [M]. 北京: 中国科学文化出版社, 2003.
[19] 郑瑞伦,胡先权,杨国祥. 固体理论及其应用 [M]. 重庆: 西南师范大学出版社, 1996.
[20] 基泰尔C. 固体物理导论 [M]. 杨顺华, 等, 译. 北京: 科学出版社, 1979.
[2] 田文, 袁鹏飞, 禹卓良, 等. 掺杂六角形石墨烯电子输运特性的研究 [J]. 物理学报, 2015, 64: 237.
[3] Fang X Y, Yu X X, Zheng H M, et al. Temperature- and thickness-dependent electrical conductivity of few-layer graphene and graphene nanosheets [J]. Phys Lett A, 2015, 379: 2245.
[4] 蔚翠, 李佳, 刘庆彬, 等. Si面4H-SiC衬底上外延石墨烯近平衡制备 [J]. 物理学报, 2014, 63: 407.
[5] Davydov S Y. On the fermi velocity and static conductivity of epitaxial graphene [J]. Phys Solid State, 2014, 56: 849.
[6] Davydov S Y, Lebedev A A. Evaluation of the effect of adsorption on the conductivity of single-layer graphene formed on a semiconductor substrate [J]. Phys Solid State, 2014, 56: 2580.
[7] Davydov S Y. Relaxation of the monolayer of epitaxial graphene caused by the electron-phonon interaction with a substrate [J]. Phys Solid State, 2013, 55: 229.
[8] 杜一帅, 康维, 郑瑞伦. 外延石墨烯电导率和费米速度随温度变化规律研究 [J]. 物理学报, 2017, 66: 203.
[9] Davydov S Y. Model of adsorption on grapheme [J]. Phys Solid State, 2011, 53: 654.
[10] Davydov S Y. Vibration of an atom absorbed on single-layer graphene: account of electron-phonon interaction [J]. Tech Phys Lett, 2012, 38: 959.
[11] Davydov S Y. Transition metal and rare-earth metal atoms on single-layer graphene: estimations of the charge transfer and adsorption energy [J]. Phys Solid State, 2013, 55: 1536.
[12] Davydov S Y, Lebedev A A. On the electronic state of an atom adsorbed on epitaxial graphene formed on metallic and semiconductor substrates [J]. Phys Solid State, 2015, 57: 213.
[13] 高君华, 刘炜. 空穴浓度和基底对金属基外延石墨烯态密度的影响 [J]. 四川大学学报:自然科学版, 2017, 54: 1067.
[14] Davydov S Y. Concentration dependence of the charge of atoms adsorbed on single-sheet graphene [J]. Techn Phys Lett, 2012, 38: 175.
[15] Davydov S Y. Energy of bonding an adsorbed atom with a single-layer grapheme [J]. Phys Solid State, 2011, 53: 2545.
[16] 万纾民. 固体中原子间相互作用势能函数与碱金属、碱土金属金属弹性的电子理论 [J]. 中国科学: 数学, 物理学, 天文学, 技术科学, 1987, 2: 60.
[17] 郑瑞伦, 吴强. 热力学与统计物理学学习指导与习题解答 [M]. 北京: 中国科学文化出版社, 2006.
[18] 陈洪. 量子力学 [M]. 北京: 中国科学文化出版社, 2003.
[19] 郑瑞伦,胡先权,杨国祥. 固体理论及其应用 [M]. 重庆: 西南师范大学出版社, 1996.
[20] 基泰尔C. 固体物理导论 [M]. 杨顺华, 等, 译. 北京: 科学出版社, 1979.