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We have measured the thermal properties of suspended membranes from 10 K to300 K for two amplitudes of internal stress (about 0.1 GPa and 1 GPa) and fortwo 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 thethermal conductivity of each SiN membrane over a wide temperature range. Themechanical properties of the same substrates have been measured at heliumtemperatures using nanomechanical techniques. Our measurements show that thethermal transport in freestanding SiN membranes is not affected by the presenceof internal stress. Consistently, mechanical dissipation is also unaffectedeven though Qs increase with increasing tensile stress. We thus demonstratethat the theory developed by Wu and Yu [Phys. Rev. B 84, 174109 (2011)] doesnot apply to this amorphous material in this stress range. On the other hand,our results can be viewed as a natural consequence of the "dissipationdilution" argument [Y. L. Huang and P. R. Saulson, Rev. Sci. Instrum. 69, 544(1998)] which has been introduced in the context of mechanical damping.

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