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Thermal Properties of Silicon Nitride Beams Below One Kelvin

We have investigated thermal properties of 1 μm thick silicon nitride beams of different lateral dimensions. We measured the thermal conductance by simultaneously employing a TES both as a heater and as a sensor. Based upon these measurements, we calculate the thermal conductivity of the beams. We utilize a boundary limited phonon transport model and assume a temperature independent phonon mean free path. We find that the thermal conductivity is determined by the fraction of diffusive reflection at surface. The following results are obtained from 0.30 K to 0.55 K: the volume heat capacity is 0.082T+0.502T3 J/m3-K . The width dependent phonon mean free path is 6.58 μm, 9.80 μm and 11.55 μm for 10 μm, 20 μm and 30 μm beams respectively at a 29% surface diffusive reflection.