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Understanding ballistic phonon transport effects in transientthermoreflectance experiments and explaining the observed deviations fromclassical theory remains a challenge. Diffusion equations are simple andcomputationally efficient but are widely believed to break down when thecharacteristic length scale is similar or less than the phonon mean-free-path.Building on our prior work, we demonstrate how well-known diffusion equations,namely the hyperbolic heat equation and the Cattaneo equation, can be used tomodel ballistic phonon effects in frequency-dependent periodic steady-statethermal transport. Our analytical solutions are found to compare excellently torigorous numerical results of the phonon Boltzmann transport equation. Thecorrect physical boundary conditions can be different from those traditionallyused and are paramount for accurately capturing ballistic effects. Toillustrate the technique, we consider a simple model problem using twodifferent, commonly-used heating conditions. We demonstrate how this frameworkcan easily handle detailed material properties, by considering the case of bulksilicon using a full phonon dispersion and mean-free-path distribution. Thisphysically transparent approach provides clear insights into the nonequilibriumphysics of quasi-ballistic phonon transport and its impact on thermal transportproperties.

Modeling ballistic effects in frequency-dependent transient thermal transport using diffusion equations