【作者】 何焕典；

【导师】 王新强；

【作者基本信息】 重庆大学 ， 凝聚态物理， 2005， 硕士

【摘要】 碳纳米管被认为是新型纳米电子器件的基本结构单元,它的能带结构是其电学性能的基础,而能隙值是电子器件的一个重要参数。因此,碳纳米管的能带结构和能隙已经成为当今碳质材料和凝聚态物理研究的前沿和热点之一。到目前为止,人们已经对一些单壁碳纳米管的能带结构和能隙进行理论计算,并预言它们的导电性能。但是,一方面,那些结论大多数是对孤立的单壁碳纳米管而言的,而且跟实验没有很好的吻合;另一方面,采用的方法大多数是紧束缚计算和基于局域密度近似(LDA)的第一性原理计算。本文采用基于密度泛函理论(DFT)和广义梯度近似(GGA)的第一性原理方法,对锯齿型单壁碳纳米管(7,0)、(8,0)、(9,0)、(12,0)及其相应管束的能带结构和能隙进行理论计算。我们将计算的结果跟别人的研究结果进行对比分析,得出如下主要结论: (1) 管束(7,0)、(8,0)、(9,0)和(12,0)的晶格常数分别为0.96nm,1.02nm,1.12nm,1.34nm。跟Gao GH 的理论计算结果及实验观测值很接近,说明我们计算方案是有效可行的。(2) (7,0)、(8,0)、(9,0)和(12,0)各孤立管的能隙分别为0.237eV,0.626eV,0.070eV,0.045eV。对于(9,0)和(12,0)管,简单的π轨道紧束缚模型认为它们属于金属,而我们的计算结果跟M.Ouyang 的实验观测结果都表明,它们是小能隙的半导体。(3) 我们对各孤立管能隙的计算结果跟简单的布里渊区折叠法和简单的π轨道紧束缚模型所推出的结论有很大的出入,但跟实验观测结果比较接近。经过分析,我们认为这是由于本文计算的都是小直径的碳管,卷曲效应比较明显的缘故。(4) (7,0)、(8,0)、(9,0)和(12,0)各管束的能隙分别为0.194eV,0.559eV,0.059eV,0.034eV。与相应的各孤立管相比,能隙都发生了不同程度的减小。目前尚未见有类似的报道,我们分析认为这是由于管束存在管间相互作用,电子的束缚度减小,改变了原来的能带结构,导致能隙减小。本文的计算结果,有的已经很好的跟实验数据吻合,说明我们的方法是可行的;有的虽然还有待实验验证,但它们对我们进一步探讨卷曲效应更多还原

【Abstract】 Carbon nanotubes are belieVed to be basic structural unit of new nanometer-scale electronic deVices. Their unique electronic properties are derived from their band structures, and the value of energy gap is one of the important parameters of electronic deVices. Therefore, to research the band structures and the band gaps of carbon nanotubes become one hot topic among condensed matter physicists. The band structures and the band gaps of some single-walled carbon nanotubes(SWNTs) were calculated and their conductivities were predicted. HoweVer, most of them are for isolated SWNTs, and they don’t agree with experimental data very well. On the other hand, the most existing studies were carried out by using tight-binding model and first-principles calculations within the local density approximation (LDA). In this paper, first-principles calculations within the generalized gradient approximation (GGA) are carried out on the band gaps of zigzag SWNTs (7,0) (8,0) (9,0) and (12,0). Our calculation includes isolated tubes as well as the corresponding ropes. Comparing our results with those of others, we come to the following conclusions: (1) The lattice constants of the ropes of (7,0) (8,0) (9,0) and (12,0) are 0.955nm 1.015nm 1.124nm 1.335nm respectively, they agree well with the experimental data and the theoretical values of Gao GH. This shows that our calculational scheme is reasonable. (2) The band gaps of isolated tubes of (7,0) (8,0) (9,0) and (12,0) are 0.237eV 0.626eV 0.070eV and 0.045eV, respectively. As for (9,0) and (12,0) , they were predicted to be metallic by the simple π-orbital tight binding model, while our results and experimental data of M. Ouyang show that they are narrow-gap semiconductors. (3) For the band gap of isolated tubes, there is small discrepancy between our results and experimental data, but big discrepancy occurs between our results and the expected values of the simple π-orbital tight binding model. Our analysis indicates that the radius of selected tubes is small, curvature effect is too important to be neglected, as a result, the conclusions derived from the simple πorbital tight binding model are wrong for small radius tubes. (4) The band gaps of selected ropes of (7,0) (8,0) (9,0) and (12,0) are 0.237eV 0.626eV 0.070eV and 0.045eV, respectively. Comparing with those of the corresponding isolated tubes,they decrease, which is still no seen reported in domestic journals. Our analysis indicates that the intertube coupling causes the band gaps decrease due to the electrons in the rope are less confined than those in the isolated tube. Although some of our results still need to be modified by experiments, they have some certain directive purport and reference worth on further investigating curvature effect and intertube coupling effect on electronic structure of carbon nanotubes.更多还原