The electron-phonon energy dissipation bottleneck is examined in silicon and carbon nanoscale devices. Monte Carlo simulations of Joule heating are used to investigate the spectrum of phonon emission in bulk and strained silicon. The generated phonon distributions are highly non-uniform in energy and momentum, although they can be approximately grouped into one third acoustic (AC) and two thirds optical phonons (OP) at high electric fields. The phonon dissipation is markedly different in strained silicon at low electric fields, where certain relaxation mechanisms are blocked by scattering selection rules. In very short (∼10 nm) silicon devices, electron and phonon transport is quasi-ballistic, and the heat generation domain is much displaced from the active device region, into the contact electrodes. The electron-phonon bottleneck is more severe in carbon nanotubes, where the optical phonon energy is three times higher than in silicon, and the electron-OP interaction is entirely dominant at high fields. Thus, persistent hot optical phonons are easily generated under Joule heating in single-walled carbon nanotubes suspended between two electrodes, in vacuum. This leads to negative differential conductance at high bias, light emission, and eventual breakdown. Conversely, optical and electrical measurements on such nanotubes can be used to gauge their thermal properties. The hot optical phonon effects appear less pronounced in suspended nanotubes immersed in an ambient gas, suggesting that phonons find relaxation pathways with the vibrational modes of the ambient gas molecules. Finally, hot optical phonons are least pronounced for carbon nanotube devices lying on dielectrics, where the OP modes can couple into the vibrational modes of the substrate. Such measurements and modeling suggest very interesting, non-equilibrium coupling between electrons and phonons in solid-state devices at nanometer length and picoseconds time scales.
Vibrational modes and low-temperature thermal properties of graphene and carbon nanotubes: Minimal force-constant model
