We report specific heat and thermal conductivity of gadolinium- and yttrium-doped amorphous silicon thin films measured using silicon-nitride membrane-based microcalorimeters. Addition of gadolinium or yttrium to the amorphous silicon network reduces the thermal conductivity over a wide temperature range while significantly increasing the specific heat. This result indicates that a large number of non-propagating states are added to the vibrational spectrum that are most likely caused either by localized vibration of the dopant atom in a Si cage, or softening of the material forming the cage structures. High-resolution cross-sectional electron micrographs reveal columnar features in Gd-doped material which do not appear in pure amorphous silicon. Scattering from both the nanoscaled columns and the filled-cage structures play a role in the reduced thermal conductivity in the rare-earth doped amorphous semiconductor. The overall result is an amorphous solid with a large bump in $C/T^{3}$ and no plateau in thermal conductivity.
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