Modeling Joule heating in carbon nanotubes with Monte Carlo simulations

The ensemble Monte Carlo simulation is used to calculate the Joule heating per unit length of single-walled carbon nanotubes under an electric field applied through the nanotube axis. The electronic system and the ionic system are decoupled from each other. The rate of energy transferred from the electronic system to the ionic system in the form of the emission or absorption of longitudinal acoustic and longitudinal optical phonons is calculated stochastically to determine the Joule heating. Complete unabridged energy and phonon dispersion relations are included in order to obtain more accurate results. The effect of the temperature and the electric field magnitude on the heat generated is also taken into account. Results are compared with a prediction based on quantum mechanical integral form that calculates the electron occupation probability based on a modified Fermi-Dirac distribution. Results show a quantitative agreement between the two methods, however, the method proposed in here we believe is more accurate, because it does not make simplifications for the electron occupation probability as in the modified Fermi-Dirac distribution.