Heat transport by long mean free path vibrations in amorphous silicon nitride near room temperature

We present measurements of thermal transport in 500-nm-thick, 35-μm-wide, and 806-μm-long micromachined suspended silicon nitride (Si-N) bridges over the temperature range of 77 to 325 K. The measured thermal conductivity of Si-N (for material grown by low-pressure chemical vapor deposition in two different furnaces) deviates somewhat from previously reported measurements and also shows surprising dependence on surface variation at these relatively high temperatures. Addition of discontinuous gold films causes the thermal conductance of Si-N bridges to drop through the entire measured temperature range, before rising again when thicker, continuous films are added. Similar effects occur when continuous but very low-thermal-conductivity alumina films are deposited. The reduction in thermal conductance upon modification of the Si-N surface is strong evidence that vibrational excitations with long mean free paths carry significant heat even at these high temperatures. By measuring a series of film thicknesses the surface-scattering effects can be mitigated, and the resulting experimental values of the thermal conductivity of alumina and Au thin films compare very well to known values or to predictions of the Wiedemann-Franz law. We also present a modified model for the phonon mean free path in thin-film geometries, and use it along with atomic force microsope scans to show that a very small population of phonons with mean free path on the order of 1 μm and wavelength much longer than the expected thermal wavelengths carry up to $50%$ of the heat in Si-N at room temperature.