Understanding the thermal behaviour of low-dimensional dielectric support structures patterned in <500 nm
dielectric membranes is an essential part of developing ultra-low-noise Transition Edge Sensors for space science.
To advance the technology further, we wish to produce phononic components that minimize low-temperature
(< 500 mK) thermal conductance, heat capacity, and thermal fluctuation noise, and thereby maximize sensitivity,
saturation power, and optical packing. We describe a technique for simulating the low-temperature thermal
behaviour of mesoscopic structures. Ballistic, elastic diffusive, localized and inelastic diffusive transport are
included, and the respective scattering lengths can be comparable with the scale sizes of the patterned features.
The technique computes the average fluxes of components having statistically characterized microstructure, the
spread in behaviour of notionally identical devices, and the RMS thermal fluctuation noise.