Specific heat of thin phonon cavities at low temperature: Very high values revealed by zeptojoule calorimetry

The specific heat of phonon cavities is investigated in order to analyze the effect of phonon confinement on thermodynamic properties. The specific heat of freestanding very thin SiN membranes in the low-dimensional limit is measured down to very low temperatures (from 6 K to 50 mK). In the whole temperature range, we measured an excess specific heat orders of magnitude bigger than the typical value observed in amorphous solids. Below 1 K, a crossover in cp to a lower power law is seen, and the value of the specific heat of thinner membranes becomes larger than that of thicker ones demonstrating a significant contribution coming from the surface. We show that this high value of the specific…