【摘要】 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。更多还原

【Abstract】 The unique electronic properties of carbon nanotubes (CNTs) give CNTs great potential in nanoelectronic devices. The electronic properties of CNTs depend greatly on their chiralities and lengths, which makes the quantum size effect of CNTs a very important research topic. The quantum effects were simulated, using a one-dimensional (1-D) armchair linear chain as the axial boundary condition, with calculations of the eigenvalues and eigenvectors of the 1-D linear chain under the tight-binding approximation. The analysis predicts the oscillations of the energy gap, Eg, with tube length as well as the square of the module of wave function |ψ|2 along the tube axis for the highest occupied molecular orbital state and the lowest unoccupied molecular orbital state. The patterns as well as the scales of |ψ|2 obtained by this method are consistent with predictions on the CNTs using the four-orbital tight-binding method. This work verifies that the 1-D linear chain can effectively simulate the electronic structure of carbon nanotubes.更多还原