Ballistic-phonon heat conduction at the nanoscale as revealed by time-resolved x-ray diffraction and time-domain thermoreflectance

We use time-resolved measurements of the evolution of surface and buried layer temperatures to quantify the contribution of ballistic phonons to heat transport on nanometer length scales. A laser pulse heats a $100\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ thick Al film which cools by conduction into a GaAs substrate. The top $120--250\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ of the GaAs substrate is doped with In to create a buried layer with a distinct lattice constant. The cooling of the Al film is monitored by time-domain thermoreflectance and, in the second set of experiments, the heating and cooling of the GaAs:In buried layer are monitored by time-resolved x-ray diffraction. The combination of these data shows that thermal transport by ballistic phonons accounts for nearly 20% of the heat flow across the buried layer on nanosecond time scales.