When the size of semiconductors is smaller than the phonon mean free path, phonons can carry heat with no internal scattering. Ballistic phonon transport has received attention for both theoretical and practical aspects because Fourier's law of heat conduction breaks down and the heat dissipation in nanoscale transistors becomes unpredictable in the ballistic regime. While recent experiments demonstrate room-temperature evidence of ballistic phonon transport in various nanomaterials, the thermal conductivity data for silicon in the length scale of 10-100 nm is still not available due to experimental challenges. Here we show ballistic phonon transport prevails in the cross-plane direction of holey silicon from 35 to 200 nm. The thermal conductivity scales linearly with the length (thickness) even though the lateral dimension (neck) is as narrow as 20 nm. We assess the impact of long-wavelength phonons and predict a transition from ballistic to diffusive regime using scaling models. Our results support strong persistence of long-wavelength phonons in nanostructures and are useful for controlling phonon transport for thermoelectrics and potential phononic applications.
Keywords: Thermal conductivity; cross-plane; heat transfer; nanoporous; phononic crystals; thermoelectric.