(Invited) Phonon Transport in Holey Silicon Nanostructures
Authors: Lee Jaeho , Yang Peidong 
Published: February 2020

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 great attention for understanding heat conduction in nanomaterials and managing heat dissipation in nanoelectronics. While past experiments on thin films and nanowires focused on the size effect in lateral dimensions such as film thickness and nanowire diameter, few reports demonstrated the size dependence in the same direction as heat flow. Recent experiments are showing the length dependent thermal conductivity and the possible presence of ballistic phonons in SiGe nanowires and silicon membranes in the length scale of 1 µm or greater. However, the thermal conductivity demonstration in the length scale of 10-100 nm range, or below the phonon mean free path in silicon, is not available due to challenges associated with sample preparation and low measurement sensitivity. Here we demonstrate the length dependence through cross-plane thermal conductivity measurements of holey silicon in the length scale of 35-200 nm, which has direct relevance to nanoscale transistors and potential phononic devices. The thermal conductivity scales linearly with the length (i.e. thickness of holey silicon layer) up to 200 nm at room temperature, even though the lateral dimension is as narrow as 20 nm. We attribute this to the strong presence of ballistic phonon transport and the large contribution of long-wavelength phonons that can carry the heat from top to bottom surfaces through the narrow channels. We assess the impact of long-wavelength phonons and predict a transition from ballistic to diffusive regime using scaling models based on the frequency dependent mean free path. The frequency dependent boundary scattering may be responsible for the unique size effect and the non-classical low-temperature dependence because low-frequency phonon is less susceptible to surface disorder.
We also demonstrate the in-plane thermoelectric measurement results using a fully integrated experimental platform that allows simultaneous characterization of electrical conductivity, Seebeck coefficient, and thermal conductivity. The integrated platform improves the thermoelectric measurement accuracy and allows systematic investigation of electron and phonon transport through varying neck size, porosity, and doping concentration. The holey silicon nanostructure devices are fabricated with a pitch size of 60 nm and neck sizes in the range of 16 -34 nm, which opens up the possibility of studying incoherent and coherent phonon transport in periodic structures. The detailed analysis on the thermoelectric figure of merit indicates that the doping concentration, the pitch, and the neck size are critical parameters for fabricating all-silicon based thermoelectric devices.
The holey silicon nanostructures offer unique opportunities to study phonon transport at the nanoscale and beyond the limit of classical approaches, which can provide new pathways of manipulating phonons for thermoelectric energy harvesting and potential phononic information-processing applications.

Figure 1