ion etching (DRIE) to release the membrane from its supporting Si substrate[@glowacka2012fabrication]. Through this method we have been able to fabricate narrow legs, down to $W=$ 700nm, with a high degree of reliability and reproducibility. This method was also used to fabricate our previous few-mode ballistic devices, and we have successfully produced prototype interferometers using OL. The devices reported in this paper, however, used EBL and RIE to pattern the membranes. This required the development of direct-write EBL processing to pattern the legs and define the sputtered Nb bias leads. These new techniques then had to be combined with conventional OL to fabricate the main body of the TES. Using this hybrid method, we have been able to fabricate interferometers and ring resonators having leg cross sections of only 300 $\times$ 200nm, which ensures that only 4 elastic modes are excited in each bar of a structure for temperatures below 100mK.

![\[fig:TES\_Images\] (a) Optical microscopy of a typical ultra-low-noise TES with four long diffusive SiN$_{\rm x}$ support legs and a far-infrared absorber. Insets (b)-(g) show representative phononic legs of each type tested. These are labelled mI for an interferometer style, or mR for a ring resonator style, where m is 