Radiative ballistic phonon transport in silicon-nitride membranes at low temperatures

We studied the phonon transport in free-standing 1 µm thick silicon-nitride membranes at temperatures around 100 mK. By varying the geometry of the membranes and the dimensions of the heater element, we are able to distinguish between radiative and diffuse phonon transport. The data indicate that the transport is radiative ballistic with a lower limit to a phonon mean-free path of about 1 mm and that the probability for specular reflection from the surface is at least 0.99. The tested silicon-nitride membranes were grown on Si(100), Si(110), and polycrystalline-Si and the transport properties show no dependency on the substrat