incorporate micromachined phononic filters into the low-dimensional legs of low-noise TESs in order to reduce the NEP below the ballistic quantised limit.

The incorporation of phononic filters would have a number of benefits: First, it should be possible to manufacture low-$G$ devices having legs that are significantly shorter than their long-legged diffusive counterparts. Second, the reduction in $G$ would be brought about by a phase coherent scattering process, which is likely to have a beneficial effect on the thermal fluctuation noise in the legs, as compared with that generated by a dissipative diffusive process. Third, we would like to manufacture devices using crystalline Si membranes [@ThermalSilicon; @SiliconCMB], as this would significantly reduce the heat capacity of the device, but the dispersion curves of Si are very similar to those of SiN$_{\rm x}$, and the elastic attenuation length considerably larger due to the low density of TLSs. Therefore phononic filters are needed if crystalline Si-membrane devices, which would have exceedingly long phonon mean free paths, are to be produced having NEPs of better than 10$^{-18}$WHz$^{-1/2}$.

The objectives of the exploratory work described here were as follows: (i) to determine whether TESs having low-dimensional phononic filters can be manufactured at all; (ii) 