Transient ballistic and diffusive phonon heat transport in thin films

Abstract

Ballistic and diffusive phonon transport under small time and spatial scales are important in fast-switching electronic devices and pulsed-laser processing of materials. The Fourier law represents only diffusive transport and yields an infinite speed for heat waves. Although the hyperbolic heat equation involves a finite heat wave speed, it cannot model ballistic phonon transport in short spatial scales, which under steady state follows the Casimir limit of phonon radiation. An equation of phonon radiative transfer (EPRT) is developed which shows the correct limiting behavior for both purely ballistic and diffusive transport. The solution of the EPRT for diamond thin films not only produces wall temperature jumps under ballistic transport but shows markedly different transient response from that of the Fourier law and the hyperbolic heat equation even for predominantly diffusive transport. For sudden temperature rise at one film boundary, the results show that the Fourier law and the hyperbolic heat equation can significantly over- or underpredict the boundary heat flux at time scales smaller than the phonon relaxation times.