[01] G. R. Ahmed Jamal, Department of Electrical and Electronic Engineering, University of Asia Pacific, Dhaka, Bangladesh. [02] S. M. Mominuzzaman, Department of Electrical and Electronic Engineering, Bangaldesh University of Engineering and Technology, Dhaka, Bangladesh.

In this work, the ‘ratio problem’ between first and second optical transition energies of semiconducting single-wall carbon nanotube is discussed. Possible reasons behind the deviation of experimentally observed ratio between first two optical transitions from theoretically predicted ratio is mentioned. A number of semiconducting single-wall carbon nanotubes having chiral index (n, m) with mod (n-m, 3) ≠ 0, and having diameter in between diameter range of 0.4 nm and 3 nm are considered. First and second optical transition energies of all those tubes are recorded from various reports of optical spectroscopic experiments and recoded data was closely scrutinized. Based on that observation, ratio of first and second optical transition energies for all semiconducting tubes is expressed empirically through an empirical expression in terms of diameter, chiral index (n, m) and mod value. The empirical ratio matched very well with experimental ratio over the full diameter range. The proposed empirical way of expressing this ratio may greatly help in finding the proper ratio of first two optical transitions without depending on experimental values of two transitions. The generated pattern from the plot of this empirical ratio can also help in Photoluminescence based chirality assignment.

Single Wall Carbon Nanotube, Optical Transition, Tight Binding Model, Ratio Problem, Chiral Index

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