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Specific heat of phonon cavities is investigated in order to analyse theeffect of phonon confinement on thermodynamic properties. The specific heat offree standing very thin SiN membranes in the low dimensional limit is measureddown to very low temperatures (from 6~K to 50~mK). In the whole temperaturerange, we measured an excess of specific heat orders of magnitude bigger thanthe typical value observed in amorphous solids. Below 1~K, a cross-over in$c_p$ to a lower power law is seen, and the value of specific heat of thinnermembranes becomes larger than that of thicker ones demonstrating a significantcontribution coming from the surface. We show that this high value of thespecific heat cannot be explained by the sole contribution of 2D phonon modes(Lamb waves). The excess specific heat, being thickness dependent, could comefrom tunneling two level systems (TLS) that form in low density regions ofamorphous solids located on the surfaces. We also show that the specific heatis strongly tuned by the internal stress of the membrane by orders ofmagnitude, giving unprecedentedly high values, making low stress SiN veryefficient for energy storage at very low temperature.

Specific Heat of Thin Phonon Cavities at Low Temperature: Very High Values Revealed by ZeptoJoule Calorimetry