从能带理论出发,采用电子紧束缚能量色散关系,推导锯齿,扶手椅和手性单壁碳纳米管(SWCNT)的电子能带结构表达式,指出单壁碳纳米管或为金属或为半导体的判据。结果表示:单壁碳纳米管的电子结构与其几何结构密切相关,如扶手椅型单壁碳纳米管是金属性的,而对其它类型的单壁碳纳米管是与碳纳米管的手性指数有关,只有手性指数n和m的差别等于3的倍数时,单壁碳纳米管是金属性的,否则会显出有带隙的半导体特性。这意味着单壁碳纳米管是由特殊的电子传输和光学性质,在纳米电子学领域具有巨大的潜在应用价值。 Based on the theory of energy banding, the electron band structure of sawtooth, armchair and single-walled carbon nanotubes (SWCNTs) was deduced by using the energy-dispersion relationship of electron-tight binding. It was pointed out that single- walled carbon nanotubes are metal or semiconducting Criteria. The results show that the electronic structure of single-walled carbon nanotubes is closely related to their geometric structure, such as the armchair type single-walled carbon nanotubes is metallic, while the other types of single-walled carbon nanotubes and carbon nanotubes chiral index Only when the difference between the chiral indices n and m is equal to a multiple of 3, the single-walled carbon nanotubes are metallic or show a semiconducting characteristic with a band gap. This means that single-walled carbon nanotubes have great potential applications in the field of nanoelectronics because of their special electron transport and optical properties.