# Electronic Properties of Carbon Nanotubes Calculated from Density Functional Theory and the Empirical pi-Bond Model

## TL;DR

This paper compares density functional theory (DFT) and empirical pi-bond models in calculating the electronic properties of semiconducting zigzag carbon nanotubes, highlighting the models' accuracy and limitations across different diameters.

## Contribution

It provides a detailed assessment of the validity of DFT and pi-bond models for CNT electronic properties, especially for small diameters and near band edges.

## Key findings

- DFT effective masses differ from pi-bond by about 9%.
- DFT bandgaps are 20-180 meV smaller than empirical values for certain n.
- Pi-bond model becomes inaccurate for CNT diameters below 1 nm.

## Abstract

The validity of the DFT models implemented by FIREBALL for CNT electronic device modeling is assessed. The effective masses, band gaps, and transmission coefficients of semi-conducting, zigzag, (n,0) carbon nanotubes (CNTs) resulting from the ab initio tight-binding density functional theory (DFT) code FIREBALL and the empirical, nearest-neighbor pi-bond model are compared for all semiconducting n values 5 <(=) n <(=) 35. The DFT values for the effective masses differ from the pi-bond values by +(-) 9% over the range of n values, 17 <(=) n <(=) 29, most important for electronic device applications. Over the range 13 <(=) n <(=) 35, the DFT bandgaps are less than the empirical bandgaps by 20-180 meV depending on the functional and the n value. The pi-bond model gives results that differ signifcantly from the DFT results when the CNT diameter goes below 1 nm due to the large curvature of the CNT. The pi-bond model quickly becomes inaccurate away from the bandedges for a (10, 0) CNT, and it is completely inaccurate for n <(=) 8.