Microscale Thermal Energy Transfer Over a Combined System of Thin Films: Analytical Approach

An analytical approach for the solution of the equation for phonon transport is presented for the combination thin films system. The transient phonon radiative transport model is considered and the combination of the silicon–diamond–silicon films is accommodated in the analysis. The multi-film system is thermally disturbed from the edges through introducing temperature difference across the combined films. Equivalent equilibrium temperature is considered quantifying the distribution of the phonon intensity in the films. Equivalent equilibrium temperature obtained from the analytical approach is compared with that predicted from the numerical solution. It is found that numerical predictions of equivalent equilibrium temperature agree well with those obtained from the analytical approach. The boundary scattering of phonons at the film edges causes equivalent equilibrium temperature jump at film edges, which becomes apparent in the early heating periods. Phonon scattering in the combined films causes sharp decay of temperature in the films, which is more pronounced in the silicon film than that of the diamond.