  Amorphous Si (a-Si) nanostructures are ubiquitous in numerous electronic and
optoelectronic devices. Amorphous materials are considered to possess the lower
limit to the thermal conductivity (k), which is ~1 W/m-K for a-Si. However,
recent work suggested that k of micro-thick a-Si films can be greater than 3
W/m-K, which is contributed by propagating vibrational modes, referred to as
"propagons". However, precise determination of k in a-Si has been elusive.
Here, we used novel structures of a-Si nanotubes and suspended a-Si films that
enabled precise in-plane k measurement within a wide thickness range of 5 nm to
1.7 um. We showed unexpectedly high in plane k in a-Si nanostructures, reaching
~3.0 and 5.3 W/m-K at 100 nm and 1.7 um, respectively. Furthermore, the
measured in plane k is significantly higher than the cross-plane k on the same
films. This usually high and anisotropic k in the amorphous Si nanostructures
manifests the surprising broad propaganda mean free path distribution, which is
found to range from 10 nm to 10 um, in the disordered and atomically isotropic
structure. This result provides an unambiguous answer to the century-old
problem regarding the mean free path distribution of propagons and also shed
light on the design and performance of numerous a-Si based electronic and
optoelectronics devices.
