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碳纳米管独特的电子性质使其在纳米电子器件中有很好的应用前景,而其电子性质强烈依赖于其手征性和长度,这使得研究它的有限尺寸效应有重要意义。该文采用一维线性链模型模拟有限长度扶手椅型碳纳米管的轴向边界条件,通过求解紧束缚近似下的一维线性链的本征值和本征矢,得到了碳纳米管能隙随着长度的振荡特性,并且给出了它最低未占据分子轨道和最高占据分子轨道的波函数模的平方。此方法计算得到的波函数模的平方与利用四轨道紧束缚方法计算碳纳米管体系所得的结果,在形状以及量值方面吻合得很好。证明了一维线性链模型可以描述纳米管的轴向边界条件进而给出纳米管的电子结构性质。
The unique electronic properties of carbon nanotubes make them promising applications in nanoelectronic devices. Their electronic properties strongly depend on their chirality and length, which makes it very important to study the limited size effect of carbon nanotubes. In this paper, a one-dimensional linear chain model is used to simulate the axial boundary conditions of a finite length armchair carbon nanotubes. By solving the eigenvalues and eigenvectors of a one-dimensional linear chain with a tight binding approximation, the energy gap The length of the oscillation characteristics, and gives its lowest unoccupied molecular orbital and the highest occupied molecular orbital wave function of the square. The square of the wave function modulus calculated by this method is in good agreement with that of the carbon nanotube system using the four-rail tight-binding method. It is proved that the one-dimensional linear chain model can describe the axial boundary conditions of nanotubes and then give the electronic structure properties of nanotubes.