Acoustic phonon scattering at sapphire surfaces coated with epitaxial silicon

Heat transport by long mean free path vibrations in amorphous silicon nitride near room temperature

“…50,51 This is a modification of the usual Casimir limit of phonon boundary scattering appropriate for a bulk sample with square cross-sectional area. For all structures discussed in this paper n = 70.…”

Thermal Properties of Silicon Nitride Beams Below 1 Kelvin

“…To estimate the phonon mean free path, we use the boundary limited phonon scattering model [13,14]. For a sample with large side ratio, the boundary diffusive reflection limited phonon mean free path [13] is…”

“…The Kronecker delta function ensures that a correct phonon counting procedure is made. Eddison and Wybourne [14] describe in detail how the phonon mean free path changes with the diffusive scattering probability at surface when the two narrow sides of the samples are treated for a complete diffusive scattering due to the edge's roughness. We apply the model to our thermal test structure data because of the similarity of the model and our devices.…”

“…The mean free path ratio of phonons between 30 µm beams and 20 µm beams depends on the fraction of phonon diffusive reflection at the surface, as is shown in the inset of FIGURE 3. [13,14] is used for the calculation.…”

Radial phononic thermal conductance in thin membranes in the Casimir limit: Design guidelines for devices

“…Later, the results was generalized for cases, where the surface scattering was only partially diffusive, 3,8 and for more complex cross-sectional shapes and effects of crystalline symmetries. [9][10][11][12] Note also that the typical Casimir theory does not take into account end effects, in other words effects due to bulk contacts to a rod with a finite length. 13 In experiments in the beam geometry, [14][15][16][17][18][19][20][21] heat flow is indeed uni-directional, and the standard Casimir theory can at least in principle be compared with the experiments.…”