四族元素纳米管带隙的标度律：第一性原理研究

发布时间：2018-02-05 02:22

本文关键词： 第一性原理研究四族元素纳米管带隙标度律　出处：《郑州大学》2017年硕士论文　论文类型：学位论文

【摘要】：最近,通过气相生长方法,成功地在实验上合成了由锡元素组成的二维单层材料。这也就意味着,在得到石墨烯之后,通过各种各样的方法,除铅元素之外的所有四族元素构成的单层材料都在实验上成功被合成,这些单层材料分别命名为硅烯、锗烯、锡烯。和石墨烯类似,这些二维单层材料的电子性质均表现为无质量的狄拉克费米子。因此,这些材料都拥有非常高的载流子迁移率,同样可以实现二维的量子自旋霍尔效应,量子反常霍尔效应,以及拓扑绝缘体等特性。与之类似地,在成功的合成这些二维单层之后,这些元素构成的纳米管的性质同样引发了人们的关注。实际上,早在石墨烯出现之前,碳纳米管就因为其新奇的电子特性以及广泛的应用引发了人们的关注。众所周知,碳纳米管的一个有趣的特性是它可以表现出金属性或半导体性,这取决于碳纳米管的手性。对于硅纳米管来说,它拥有齿轮状的结构,或者说褶皱的结构。先前的研究表明,硅纳米管的带隙对纳米管的手性与尺寸都非常敏感,armchair型的硅纳米管呈现出半导体特性,且带隙随着纳米管半径的增加而减小,zigzag型的硅纳米管的带隙同样出现以3为周期的震荡。利用基于密度泛函理论的第一性原理计算,系统地研究了四族元素纳米管的能带特征,发现纳米管第一布里渊区中的两个特殊点处的带隙决定了纳米管的带隙,分别对应二维结构中的K点与Γ点。K点与Γ点带隙随着纳米管半径的变化遵循两条不同的标度律:K点带隙遵循1/R的标度律,该标度律出现在拥有褶皱结构的硅、锗、锡纳米管中,非常重要的是,K点带隙的标度律与纳米管的组成元素无关而且不受纳米管手性的影响;Γ点处带隙遵循-1/R2+C的标度律,C为常数,与纳米管的组成元素相关。两条标度律共同决定了四族元素纳米管的带隙,对于硅纳米管与大半径的锗、锡纳米管,纳米管的带隙由K点带隙的标度律决定,对于小半径的锗、锡纳米管,带隙由Γ点带隙决定。由此,基于两条标度律,可以通过纳米管的半径确定纳米管的带隙。此外,还预言了锗、锡armchair型纳米管中间接带隙纳米管的存在。
[Abstract]:Recently, two dimensional monolayer materials consisting of tin elements were successfully synthesized experimentally by gas phase growth method, which means that graphene can be obtained by a variety of methods. All four groups of monolayers with the exception of lead were successfully synthesized experimentally. These monolayers were named silicene, germane, stannene, and graphene, respectively. The electronic properties of these two-dimensional monolayers are characterized by massless Dirac fermions. Therefore, these materials have very high carrier mobility and can also realize the two-dimensional quantum spin Hall effect. The properties of quantum anomalous Hall effect and topological insulators. Similarly, after the successful synthesis of these two-dimensional monolayers, the properties of nanotubes formed by these elements have also attracted attention. Long before graphene appeared, carbon nanotubes (CNTs) attracted much attention because of their novel electronic properties and wide applications. One of the interesting properties of carbon nanotubes is that they can exhibit gold or semiconductor properties, depending on the chirality of carbon nanotubes, which have a gear-like structure for silicon nanotubes. Previous studies have shown that the band gap of silicon nanotubes is very sensitive to the chirality and size of nanotubes. And the band gap decreases with the increase of the radius of the nanotubes. The band-gap of the zigzag type silicon nanotubes also oscillates with the period of 3. The first principle calculation based on density functional theory is used. The band-gap at two special points in the first Brillouin region is found to determine the band-gap of the nanotubes. The band gap of K point and 螕 point. K point and 螕 point in two-dimensional structure follow two different scaling laws: K point gap and 螕 point band gap follow the scale law of 1 / R respectively with the change of nanotube radius. The scaling law appears in silicon, germanium and tin nanotubes with fold structure. It is very important that the scaling law of K point gap is independent of the constituent elements of nanotubes and is not affected by the chirality of nanotubes. The band gap at 螕 point follows the scaling law C of -1 / R 2C, which is related to the constituent elements of nanotubes. The two scaling laws together determine the band gap of four groups of elemental nanotubes, and for silicon nanotubes and germanium with large radius. For tin nanotubes, the band gap is determined by the scaling law of K point band gap, and for small radius germanium, tin nanotube, the band gap is determined by 螕 point band gap. Therefore, two scaling laws are used. In addition, the existence of indirect band-gap nanotubes in germanium and tin armchair nanotubes is predicted.
【学位授予单位】：郑州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O469

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