Sub-amorphous thermal conductivity in ultrathin crystalline silicon nanotubes

Thermal transport behavior in nanostructures has become increasingly important for understanding and designing next generation electronic and energy devices. This has fueled vibrant research targeting both the causes and ability to induce extraordinary reductions of thermal conductivity in crystalline materials, which has predominantly been achieved by understanding that the phonon mean free path (MFP) is limited by the characteristic size of crystalline nanostructures, known as the boundary scattering or Casimir limit. Herein, by using a highly sensitive measurement system, we show that crystalline Si (c-Si) nanotubes (NTs) with shell thickness as thin as ∼5 nm exhibit a low thermal conductivity of ∼1.1 W m(-1) K(-1). Importantly, this value is lower than the apparent boundary scattering limit and is even about 30% lower than the measured value for amorphous Si (a-Si) NTs with similar geometries. This finding diverges from the prevailing general notion that amorphous materials represent the lower limit of thermal transport but can be explained by the strong elastic softening effect observed in the c-Si NTs, measured as a 6-fold reduction in Young's modulus compared to bulk Si and nearly half that of the a-Si NTs. These results illustrate the potent prospect of employing the elastic softening effect to engineer lower than amorphous, or subamorphous, thermal conductivity in ultrathin crystalline nanostructures.