Quasi-Ballistic Heat Transfer From Metal Nanostructures on Sapphire

Quasi-ballistic phonon transport, where heat transfer does not obey Fourier’s law, occurs when length scales become comparable to the phonon mean free path (MFP). Understanding this regime of heat transport is of fundamental interest, as the manner in which the heat transport deviates from Fourier’s law reveals important information about the phonon mean free path distribution. While ultrafast techniques can provide the time resolution to observe heat transfer in this regime, the minimum size of the heated region is restricted by diffraction to approximately 1 μm, which is larger than phonon MFPs in many materials. To circumvent this limit, we study heat transfer from metallic dot arrays with sub-micron diameters on sapphire fabricated using electron beam lithography. We describe heat transfer models which allow us to determine how the heat transfer in sapphire deviates from Fourier’s law at these small length scales. Our results indicate that quasi-ballistic transport occurs in sapphire when length scales are on the order of hundreds of nanometers.