Controlling the thermal conductivity of semiconductors is of practical interest in optimizing the performance of thermoelectric and phononic devices. The insertion of inclusions of nanometer size in a semiconductor is an effective means of achieving such control; it has been proposed that the thermal conductivity of silicon could be reduced to 1 W/m/K using this approach and that a minimum in the heat conductivity would be reached for some optimal size of the inclusions. Yet the practical verification of this design rule has been limited. In this work, we address this question by studying the thermal properties of silicon metalattices that consist of a periodic distribution of spherical inclusions with radii from 7 to 30 nm, embedded into silicon. Experimental measurements confirm that the thermal conductivity of silicon metalattices is as low as 1 W/m/K for silica inclusions, and that this value can be further reduced to 0.16 W/m/K for silicon metalattices with empty pores. A detailed model of ballistic phonon transport suggests that this thermal conductivity is close to the lowest achievable by tuning the radius and spacing of the periodic inhomogeneities. This study is a significant step in elucidating the scaling laws that dictate ballistic heat transport at the nanoscale in silicon and other semiconductors.
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