The thermal conductivity of silicon nitride membranes is not sensitive to stress

TL;DR

This study measures the thermal conductivity and specific heat of silicon nitride membranes under different internal stresses and finds that thermal transport is unaffected by stress, challenging existing theories.

Contribution

It provides the first comprehensive experimental analysis showing thermal conductivity in amorphous SiN membranes is insensitive to internal stress levels.

Findings

Thermal conductivity remains unchanged with stress variations.

Mechanical dissipation is unaffected despite increased tensile stress.

The results contradict the Wu and Yu theory for amorphous materials.

Abstract

We have measured the thermal properties of suspended membranes from 10 K to 300 K for two amplitudes of internal stress (about 0.1 GPa and 1 GPa) and for two different thicknesses (50 nm and 100 nm). The use of the original 3 \omega -Volklein method has allowed the extraction of both the specific heat and the thermal conductivity of each SiN membrane over a wide temperature range. The mechanical properties of the same substrates have been measured at helium temperatures using nanomechanical techniques. Our measurements show that the thermal transport in freestanding SiN membranes is not affected by the presence of internal stress. Consistently, mechanical dissipation is also unaffected even though Qs increase with increasing tensile stress. We thus demonstrate that the theory developed by Wu and Yu [Phys. Rev. B 84, 174109 (2011)] does not apply to this amorphous material in this stress range. On the other hand, our results can be viewed as a natural consequence of the "dissipation dilution" argument [Y. L. Huang and P. R. Saulson, Rev. Sci. Instrum. 69, 544 (1998)] which has been introduced in the context of mechanical damping.