圆盘形石墨烯量子点双光子吸收性质的理论研究

发布时间：2018-05-08 01:03

本文选题：圆盘形 + 石墨烯量子点　；参考：《云南师范大学》2017年硕士论文

【摘要】：现在人们已经能够在单层石墨烯材料的基础上,通过多种手段获得石墨烯量子点。石墨烯量子点材料具有优良的物理和化学性能,在光激发、细胞生物成像和生物分子探测等方面应用前景广阔,其中双光子吸收由于其激发波长长、穿透深度深以及空间分辨率高的优势,在这些应用中被广泛采用。本文首先在第一章介绍了石墨烯的结构和性质,石墨烯量子点的性质、制备方法和应用范围。接着在第二章中通过采用紧束缚方法研究了单层石墨烯的能带结构,获得了石墨烯能带结构计算公式,并在此基础上推导出了石墨烯中电子所满足的狄拉克方程。研究表明:在石墨烯中狄拉克点的附近,电子是狄拉克费密子具有许多令人惊奇的性质。本文的主要工作是:先从狄拉克方程出发,分别采用无限质量边界条件和有限差分法,解析并数值求解了圆盘形石墨烯量子点的电子能态,分析了尺寸和边界对圆盘形石墨烯量子点电子能态的影响。研究表明:石墨烯量子点的能带中出现了一个带隙,相邻能级间的间隔较小。无论是导带还是价带,能带都呈现出了不同程度的对称性。因为石墨烯量子点具有量子尺寸效应,当量子点的尺寸增大时,其禁带宽度将变窄,能级间隔将变小。此外,具有锯齿型边界的圆盘形石墨烯量子点表现出半金属的属性;具有扶手型边界的圆盘形石墨烯量子点则表现出典型的半导体属性。接下来从二阶含时微扰理论,得到单位体积内电子吸收两个能量为ηω的光子发生跃迁的速率。然后依据之前已经获得的圆盘形石墨烯量子点电子能态,推导出双光子吸收系数或者吸收截面的公式,同时得到了双光子跃迁的选择定则。描绘了圆盘形石墨烯量子点的双光子吸收谱,讨论了在不同的尺寸和边界等参量下,量子点双光子吸收系数的变化情况。研究表明:尺寸和边界对调节圆盘形石墨烯量子点的双光子吸收系数起了很大的作用。这些研究成果对非线性光学理论和光电器件的设计优化等实际应用都有着极为重大的意义。
[Abstract]:It is now possible to obtain graphene quantum dots by various means on the basis of monolayer graphene materials. Graphene quantum dots have excellent physical and chemical properties, and have a wide application prospect in the fields of photoexcitation, cell biological imaging and biomolecular detection, among which two-photon absorption is due to its long excitation wavelength. The advantages of deep penetration and high spatial resolution are widely used in these applications. In the first chapter, the structure and properties of graphene, the properties of graphene quantum dots, the preparation methods and applications are introduced. In chapter 2, the band structure of graphene monolayer is studied by using the tight-binding method, and the formula for calculating the band structure of graphene is obtained. On this basis, the Dirac equation satisfied by the electrons in graphene is derived. It is shown that near the Dirac point in graphene, the electron is a Dirac fermion with many surprising properties. The main work of this paper is as follows: firstly, starting from Dirac equation, the electronic energy states of disk graphene quantum dots are solved by using infinite mass boundary condition and finite difference method, respectively. The effects of size and boundary on the electronic energy states of disk graphene quantum dots are analyzed. The results show that there is a band gap in the band of graphene quantum dots and the gap between the adjacent energy levels is small. Both the conduction band and the valence band show different degrees of symmetry. Because graphene quantum dots have quantum size effect, when the size of quantum dots increases, the band gap will become narrow and the energy level interval will become smaller. In addition, disk graphene quantum dots with zigzag boundaries exhibit semi-metallic properties, while disk graphene quantum dots with armrest boundaries exhibit typical semiconductor properties. Then, from the second order time-dependent perturbation theory, the rate of transition of two photons with energy 畏蠅 absorbed by electrons per unit volume is obtained. Then, based on the previously obtained electronic energy states of disk graphene quantum dots, the formulas of two-photon absorption coefficient or absorption cross section are derived, and the selection criterion of two-photon transition is obtained. The two-photon absorption spectra of disk graphene quantum dots are described. The variation of two-photon absorption coefficient of quantum dots under different parameters such as size and boundary is discussed. The results show that the size and boundary play an important role in regulating the two-photon absorption coefficient of the disk graphene quantum dots. These results are of great significance to the practical applications of nonlinear optics theory and optoelectronic device design optimization.
【学位授予单位】：云南师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O613.71;TB383.1

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