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.

针对组合薄膜系统，提出了一种求解声子传输方程的解析方法。考虑了瞬态声子辐射传输模型，并在分析中考虑了硅-金刚石-硅膜的组合。通过在组合的薄膜之间引入温差，多层薄膜系统会受到边缘的热干扰。等效平衡温度被认为可以量化薄膜中声子强度的分布。将分析方法获得的等效平衡温度与数值解所预测的平衡温度进行比较。发现等效平衡温度的数值预测与从分析方法获得的数值预测非常吻合。声子在膜边缘的边界散射会在膜边缘引起等效的平衡温度跃迁，这在早期加热阶段就变得明显。结合膜中的声子散射会引起膜中温度的急剧下降，这在硅膜中比金刚石更明显。