(Invited) Phonon Dispersion Engineering and Thermal Transport in Si Membranes

Present silicon technology provides single crystal films and membranes with thicknesses on the order of 10 nm and below. Along the years, the thermal studies on such structures have shown a reduction of the thermal conductivity consistent with the decrease of the characteristic size. Although the lowering of thermal conductivity is detrimental for heat dissipation processes in nanoelectronic devices, it becomes advantageous to increase the figure of merit (ZT) of Si and turning it as a promising material for thermoelectric applications. It is widely accepted that, for submicrometer thicknesses and down to 20 nm, the reduction of the in-plane thermal conductivity is mainly determined by the shortening of the phonon mean free path due to the diffusive scattering of phonons at the boundaries. In this case an analytical model that adopts the phonon bulk properties and includes the boundary scattering by a conductivity reduction factor is shown to match the experimental trend of systematical reduction of the thermal conductivity as the thickness of the film or membrane decreases.

In this talk we will report on the modification of the phonon properties in Si membranes, such as the dispersion relation, and its dependence on the thickness. The thermal conductivity in Si results from the cumulative contribution of the transport of phonons with a broad range of wavevectors and mainly from long-wavevector phonons. Thus, heat transport at room temperature can be influenced by the reduction of the membrane thickness as the dispersion relation of the short-wave-phonons starts to be affected by emerging new vibrational modes arising from the boundary conditions at the membrane surface. Our measurements of the thermal conductivity in ultra-thin sub-20 nm Si membranes have demonstrated this extreme and, in fact, we have been able to disentangle the effects of phonon confinement from those related to surface morphology and chemical composition. Finally, we will discuss the prospects of employing the increased modification of phonon dispersion relation achieved in phononic crystals in controlling heat transport. While some applications require the existence of absolute band gaps, the approach to reduce the thermal conductivity is more linked to the decrease of phonon’s group velocity and phonon-phonon interactions in an extended range of frequencies.