Temperature dependence of boundary conditions in phonon hydrodynamics of smooth and rough nanowires

In the analysis of nanosystems, the phonon-wall interaction must be incorporated to the usual description of phonon hydrodynamics, as surface effects become comparable to bulk effects in these systems. In the present paper, we analyze the temperature dependence of two phenomenological coefficients describing the specular and diffusive collisions, on one side, and backscattering collisions, on the other side, in silicon nanowires. Furthermore, we also propose for them a qualitative microscopic interpretation. This dependence is important because it strongly influences the temperature dependence of the effective thermal conductivity of nanosystems.