A New Approach for Semi-Analytical Solution of Cross-plane Phonon Transport in Silicon Diamond Thin Films

Transient analysis of phonon cross-plane transport across two consecutively placed thin films is considered, and a new approach is introduced to obtain the semi-analytical solution for the equation of phonon radiative transport. The orthogonality properties of trigonometric functions are used in the mathematical analysis. Silicon and diamond thin films are used to resemble the consecutively placed thin films. The films are thermally disturbed from its edges to initiate the phonon transport, and thermal boundary resistance is introduced at the films interface. Equivalent equilibrium temperature is incorporated to quantify the phonon intensity distribution in the films. It is found that the results of the analytical solution agree well with their counterparts obtained from the numerical simulations. Phonon intensity at the film edges and interface reduces significantly due to boundary scattering. The analytical solution captures phonon scattering at boundaries and interface correctly, and provides considerable simplification of the numerical treatment of the equation for phonon radiative transport. It also reduces significantly the numerical efforts required for solving the transient phonon radiative transport equation pertinent to the cross-plan transport across the thin films in terms of program size and run-time.