Room temperature quasi-ballistic thermal transport in amorphous silicon nitride and the mean free path distribution

Ballistic thermal transport is difficult to observe in amorphous solids, especially at room temperature, because the disordered atomic structure results in exceedingly short mean free paths (MFPs) for heat carriers. Here, by measuring the cross-plane thermal conductivity of the amorphous SiN (a-SiN) thin films κfilm as a function of film thickness d, we observe a large divergence exponent β of 0.8 for the κfilm∝dβ power law as d reduces below 15 nm, which provides unambiguous experimental evidence on quasi-ballistic thermal transport in a-SiN at room temperature (β = 1 for purely ballistic transport). Remarkably, κfilm drops to 0.34 W m−1 K−1 for the 2.2 nm thick film, which is only 21% of the bulk thermal conductivity κbulk. We further reconstruct the thermal conductivity accumulation function for a-SiN, revealing that approximately half of κbulk is already contributed by heat carriers with MFPs shorter than 2.0 nm. Our results offer new insights into thermal transport in amorphous solids beyond the well-studied case of amorphous Si and also hold direct relevance for thermal management in microelectronics, where a-SiN thin films are among the most technologically important amorphous materials.