Empirical Ratio of Higher Optical Transitions in Semiconducting SWCNTs
Abstract
In this work, the ‘ratio problem’ among higher
optical transition energies (4th, 5th and 6th transitions) of
semiconducting single-wall carbon nanotube is discussed. A
number of semiconducting single-wall carbon nanotubes having
(n – m) familyrange 2 to 32 with mod (n-m, 3) ≠0 and having
diameter range 1.48nm to 3.44nm are considered. Higher optical
transition energies of all those tubes are recorded from various
experimental reports based on fluorescence and Raman
spectroscopy. Based on that observation, ratio between
consecutive higher transition energies for all semiconducting tube
is expressed empirically through some empirical expressions in
terms of diameter, (n- m) family and mod value. The empirical
ratio matched very well with experiment ratio over the full
diameter range. The proposed empirical way to expressing this
ratio may greatly help in finding the proper ratio of higher
optical transitions without depending on experimental values of
these transitions.The generated pattern from the plot of this
empirical ratio can also help in Photoluminescence based
chirality assignment.
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