Heat pulse propagation and nonlocal phonon heat transport in one-dimensional harmonic chains

Abstract

Phonons are the main heat carriers in semiconductor devices. In small devices, heat is not driven by a local temperature gradient, but by local points of heat input and removal. This complicates theoretical modeling. Study of the propagation of vibrational energy from an initial localized pulse provides insight into nonlocal phonon heat transport. We report simulations of pulse propagation in one dimension. The 1d case has tricky anomalies, but provides the simplest pictures of the evolution from initially ballistic toward longer time diffusive propagation. Our results show surprising details, such as diverse results from different definitions of atomistic local energy, and failure to exhibit pure diffusion at long times. Boltzmann phonon gas theory, including external energy insertion, is applied to this inherently time-dependent and nonlocal problem. The solution, using relaxation time approximation for impurity scattering, does not closely agree with the simulated results.