Thermal conductivity of amorphous germanium at low temperatures

The thermal conductivity of free-standing films of $a-\mathrm{G}\mathrm{e}$ has been measured in the temperature range 0.03-5 K. The films were prepared by evaporation under a variety of conditions to obtain various densities, thicknesses, and impurity levels. The data can be accounted for by scattering of the thermal phonons from two-level tunneling systems, cylindrical inhomogeneities, and the boundaries of the sample. The strengths of the first two scattering mechanisms are found to be correlated inversely with the mass density of the film. The two-level tunneling systems are therefore associated predominantly with the defect regions of the material.