Chapter 5 - Analytical Treatment of Phonon Transport in Thin Films

Abstract

The radiative phonon transport equation is critically important to assess the energy transport characteristics in a thin film. In this chapter, analytical treatment of the radiative transport equation is presented, and the formulation of heat transport due to thermal excitation of the thin film is introduced. The closed form solution for the radiative transport equation is presented with the appropriate boundary conditions for the one-dimensional heating situation. In addition, the closed form solution of the hyperbolic heat equation derived from the electron kinetic theory approach is presented, incorporating the thermal disturbance due to laser short-pulse irradiation of the metallic substrates. Since the metallic materials thermally separate under the nonequilibrium heating situations, thermal coupling in terms of the electron–phonon coupling parameter is introduced for the energy transport across the electron and lattice subsystems. The radiative transport equation is modified for thin metallic films, and thermal coupling across the electron and lattice subsystem is incorporated. The limitations of the two-equation model in micro/nanoscale heating are also discussed.