Intense electron-phonon scattering near the peak electric field in a semiconductor device results in nanometer-scale phonon hotspots with power densities on the order of 1 W/μm3. To study the impact of the hotspot on phonon transport, we solve the phonon Boltzmann transport equation under the relaxation time approximation to yield the departure from equilibrium amongst phonon modes. The departure function is split into two contributions: one arising from the far-from-equilibrium emitted phonons and the other from the near-equilibrium thermal phonons. The model predictions are compared with existing data on ballistic phonon transport in silicon. Computations of transient and steady state phonon occupation numbers for a device geometry show the predominance of longitudinal optical phonons for electric fields on the order of 1 MV/m. Due to the low group velocity of these modes, there is an energy stagnation at the hotspot which results in an excess temperature rise of about 13% for a 90 nm bulk silicon device. During device switching, emitted phonons have sufficient time to relax completely when the duty cycle is 30% on a period of 100 ps.

Sinha, S., Pop, E., & Goodson, K. E. (2004). A Split-Flux Model for Phonon Transport Near Hotspots. Electronic and Photonic Packaging, Electrical Systems Design and Photonics, and Nanotechnology, 75–85.