Chirality (n, m) dependence of band gap of semiconducting SWCNT

Abstract

Experimental band gap energies of 208 semiconducting single-wall carbon nanotubes (n, m) from 0.4 nm to 3 nm are analyzed by dividing them in mod (n-m, 3) =1 and 2 types. Eects of nanotube curvature and chirality (n, m) on their band gap energies are closely investigated. An exponential empirical relation of band gap of SWCNTs with its diameter and chiral index (n, m) is devised for both mod 1 and mod 2 type semiconducting SWCNTs. The proposed empirical relation enables the simplest tight binding model to predict band gap of all semiconducting SWCNTs with higher accuracy. Calculated empirical values of band gap energies closely match with experimental data with less than 1% average absolute error over the full diameter range. The proposed empirical relation greatly improves simple tight binding model and removes its quantitative and qualitative failure in predicting band gap of semiconducting SWCNTs.