  A nanoscale phononic crystal filter (reflector) is designed for a kinetic
inductance detector where the reflection band is matched to the quasiparticle
recombination phonons with the aim to increase quasiparticle lifetime in the
superconducting resonator. The inductor is enclosed by a 1 um wide phononic
crystal membrane section with two simple hole patterns that each contain a
partial spectral gap for various high frequency phonon modes. The phononic
crystal is narrow enough for low frequency thermal phonons to propagate
unimpeded. With 3D phonon scattering simulations over a 40 dB attenuation in
transmitted power is found for the crystal, which was previously estimated to
give a lifetime enhancement of nearly two orders of magnitude.
