Phonon wave propagation in ballistic-diffusive regime

Abstract

Wide applications of ultra-short pulse laser technique in micromachining and thermophysical properties' measurements make the study on ultrafast transient thermal transport necessarily essential. When the characteristic time is comparable to the phonon relaxation time, phonons propagate in ballistic-diffusive regime and thermal wave occurs. Here, ultrafast transient phonon transport is systematically investigated based on the Monte Carlo (MC) simulations, the Cattaneo-Vernotte (C-V) model, and the phonon Boltzmann transport equation (BTE). It is found that remarkable differences exist between the C-V model and the MC simulations when describing the evolution of the thermal wave excited by the ultra-short heat pulse. The C-V model predicts a non-dispersive dissipative thermal wave, while the MC simulation with Lambert emission predicts a dispersive dissipative thermal wave. Besides, different phonon emissions can significantly influence the evolution of the thermal wave in the MC simulations. A modified C-V model with a time- and position-dependent effective thermal conductivity is derived based on the phonon BTE to characterize the evolution of the transport regime from ballistic to diffusive. The integrations on moments of the distribution function cause the loss of the information of the phonon distribution in wave vector space, making the macroscopic quantities incomplete when describing the ballistic transport processes and corresponding boundary conditions. Possible boundary conditions for the phonon BTE in practice are also discussed on different heating methods.