The influence of hot phonons on the electron-phonon scattering rate and Joule heating is studied via an ensemble Monte Carlo (EMC) simulation with a step by step update of the phonon occupation number to account for the generation of hot phonons. The hot phonon contribution to Joule heating appears to be a function of the applied electric force field at room temperature, while it becomes independent of the applied electric force field for higher temperatures. The influence of hot phonons on Joule heating is more pronounced around room temperature and diminishes for higher temperatures. The results of the ensemble Monte Carlo simulation at very high temperatures (around 1800 K and above) suggest that the presence of non-equilibrium phonons may reduce the Joule heating of single-walled carbon nanotubes (SWCNTs).
In contrast with carbon nanotubes, the absence of translational symmetry (or periodical boundary condition) in the restricted direction of zigzag graphene nanoribbon removes the selection rule of subband number conservation. However, zigzag graphene nanoribbons with even dimers do have the inversion symmetry. We, therefore, propose a selection rule of parity conservation for electronphonon interactions. The electron-phonon scattering matrix in zigzag graphene nanoribbons is developed using the tight-binging model within the deformation potential approximation.
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