  Controlling thermal transport at the nanoscale is vital for many
applications. Previously, it has been shown that this control can be achieved
with periodically nanostructured two-dimensional phononic crystals, for the
case of suspended devices. Here we show that thermal conductance can also be
controlled with three-dimensional phononic crystals, allowing the engineering
of the thermal contact of more varied devices without the need of suspension in
the future. We show experimental results measured at sub-Kelvin temperatures
for two different period three-dimensional crystals, as well as for a bulk
control structure. The results show that the conductance can be enhanced with
the phononic crystal structures in our geometry. This result cannot be fully
explained by the simplest theory taking into account the coherent modification
of the phonon band structure, calculated with finite element method
simulations.
