Validity of approximations applied in calculations of single-wall metallic carbon nanotube current-voltage characteristics

The calculation results of dependencies of electric current in the infinitely long single-wall metallic carbon nanotubes of armchair type with different diameter values on the strength of constant and uniform longitudinal electric field applied to them are presented in this study. On the one hand the results have been obtained by an accurate numerical self-consistent tight-binding full-band solution of the Boltzmann transport equations for electrons and phonons in the electric quantum limit. On the other hand the results have been obtained by solution of these equations after application of a number of commonly used simplifications and approximations. It is ascertained that the approximately calculated dependencies considerably diverge from the rigorously calculated ones. In addition the relaxation time of non-equilibrium phonons in the single-wall metallic carbon nanotubes has been estimated by means of comparison of the calculation results with the well-known experimental data. Its value is equal to 2.2+/-0.1 ps.