Phonon scattering and internal friction in dielectric and metallic films at low temperatures

We have measured the heat conduction between 0.05 and 1.0 K of high-purity silicon wafers carrying on their polished faces thin dielectric films of e-beam amorphous Si, molecular beam epitaxial (MBE) Si, e-beam polycrystalline ${\mathrm{CaF}}_2,$ and MBE ${\mathrm{CaF}}_2,$ and polycrystalline thin metallic films of e-beam Al, sputtered alloy Al 5056, e-beam Ti, and e-beam Cu. Using a Monte Carlo simulation to analyze the conduction measurements, we have determined the phonon mean free path within the films, and found all of them to be much shorter even than in typical bulk amorphous solids, with no exceptions. We have also measured the internal friction of these films below 10 K, and found their internal friction at low temperatures to be strikingly close to that of amorphous solids, both in magnitude and temperature independence, with the exception of the MBE Si and alloy Al 5056, whose internal friction is even much smaller than that of amorphous solids. Using the tunneling model the internal friction results indicate the phonon scattering in these thin films ought to be much smaller than is actually observed. Thus we conclude that heat conduction measurements do not support the picture that the lattice vibrations of these films are glasslike, as had been surmised earlier for thin metallic films, on the basis of low-temperature internal friction measurements alone [Phys. Rev. B $59,$ 11 767 (1999)]. At the least, the films must contain additional scattering centers which lead to the very small phonon mean free path. Most remarkably, the MBE Si shows the same strong scattering of thermal phonons as do other films, while having the negligible internal friction expected for a perfect film. The disorder causing the strong scattering of the thermal phonons in this film is completely unknown.