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 heat cannot be explained by the sole contribution of two-dimensional phonon modes (Lamb waves). The excess specific heat, being thickness dependent, could come from tunneling two-level systems that form in low-density regions of amorphous solids located on the surfaces. We also show that the specific heat is strongly tuned by the internal stress of the membrane by orders of magnitude, giving high values, making low-stress SiN very efficient for energy storage at very low temperature.