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

TL;DR

This study measures the specific heat of ultra-thin SiN membranes at very low temperatures, revealing unexpectedly high values due to surface effects and internal stress, with implications for low-temperature energy storage.

Contribution

It provides the first detailed measurement of specific heat in thin phonon cavities at millikelvin temperatures, highlighting the roles of surface TLS and internal stress in thermodynamic properties.

Findings

Specific heat exceeds typical amorphous solid values by orders of magnitude.

Thinner membranes exhibit larger specific heat, indicating surface contributions.

Internal stress significantly enhances specific heat, enabling efficient low-temperature energy storage.

Abstract

Specific heat of phonon cavities is investigated in order to analyse the effect of phonon confinement on thermodynamic properties. The specific heat of free standing 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 of specific heat orders of magnitude bigger than the 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 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 2D phonon modes (Lamb waves). The excess specific heat, being thickness dependent, could come from tunneling two level systems (TLS) 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 unprecedentedly high values, making low stress SiN very efficient for energy storage at very low temperature.