  Diminution of the thermal conductivity is a crucial aspect in thermoelectric
research. We report a systematic and significant reduction of the cross-plane
thermal conductivity in a model system consisting of DC sputtered TiNiSn and
HfNiSn half-Heusler superlattices. The reduction of $\kappa$ is measured by the
3$\omega$ method and originates from phonon scattering at the internal
interfaces. Heat transport in the superlattices is calculated based on
Boltzmann transport theory, including a diffusive mismatch model for the
phonons at the internal interfaces. Down to superlattice periodicity of 3 nm
the phonon spectrum mismatch between the superlattice components quantitatively
explains the reduction of $\kappa$. For very thin individual layers the
interface model breaks down and the artificial crystal shows an enhanced
$\kappa$. We also present an enhanced ZT value for all investigated
superlattices compared to the single TiNiSn and HfNiSn films.
