A new analytical model for predicting SWCNT band-gap from geometrical properties

In the following paper we present a complete analytical model that predicts the band-gap (Eg) of Single-Walled Carbon nanotubes (SWCNTs) directly from their diameter (d) and chiral angle (θ). The proposed analytical model is based on two mathematical expressions that have been derived by curve-fitting the outcome generated from the third-nearest-neighbor Tight-Binding (TB) method in conjunction with the zone-folding technique. Tests performed on the model demonstrated that 82% of a set of both metallic and semiconducting CNTs were accurately distinguished. In addition, the maximum band-gap error recorded for the semiconducting tubes was 10%. The model was also verified against previously published experimental data where 17 out of 21 tubes were correctly predicted. Finally, it is shown that the proposed model computes Eg with a speed that is 10⁵ times faster compared to the third-nearest-neighbor TB method with zone-folding. The outcome of this work offers a fast and accurate technique for engineers who are seeking to simulate CNT based devices and want to ascertain the CNT’s electronic properties with respect to the geometrical variation manifested in their synthesis process.