Calculating the Band Gaps of Perfect Carbon Nanotube through Tight Binding Method

Eighty three types perfect carbon nanotubes (PCNTs) are chosen between the diameter range of 0.3 nm - 3.9355 nm. These PCNTs include armchair, chiral and zigzag tubes leaving out those zigzag tubes which are metallic in nature.16 of these 83 PCNTs are metallic (armchair) and 67 are semiconductor (chiral and zigzag). The band gaps of chiral and zigzag tubes are calculated with increasing chiral angle from 0.3 nm to 3.9355 nm diameters (67 in numbers) in order of increase in indices (n, m). The tube diameter and the calculated value of band gap in also given. It is observed that irrespective of the chiral angle, with the increase in diameter the band gap decreases. Further it may be seen that for the tube of about the same diameter with different chirality shall have about the same band gap. Therefore it is seen that the band gap of the semiconducting tubes depend inversely upon the diameter. Also calculated that the armchair (n, n) tubes band gap of the order of 0.011eV remain independent of diameter.