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Joule heating in single-walled carbon nanotubes ͑CNTs͒ using a quantum mechanical approach is presented in this paper. The modeling is based on the energy transfer between the electrons and both acoustic and optical phonons. In this formulation, only the knowledge of the full energy dispersion relation, phonon dispersion relation, and the electron-phonon coupling potential is required for the calculations. For verification of the proposed model, the current-voltage relation for extremely long nanotubes is calculated and the results are compared with the experimental data. The electric field dependence of the amount of energy generated by Joule heating is plotted. Moreover the effect of the thermal environment on the behavior of Joule heating is studied. The formulation proposed in this paper can also be used for structures other than CNTs. Computations indicate that, contrary to popular opinion, metallic CNT does not follow Joule's law of P = IV. Joule heating in CNT is significantly less than what is predicted with Joule law ͑P = IV͒, which would make it a perfect candidate to replace copper as interconnect material in electronics.

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