ABSTRACT Transition-Edge Sensors (TESs) are sensitive devices us ed in astronomical detectors. Recent projects in ground-based and space astronomy demand the Noise Equivalent Power (NEP) of the TES to be reduced to the limitsneeded for accurate measurements, for example, of the B -mode polarisation of the CMB. Thus, we have measuredthermal conductance of Si x N y bridges of various geometries, and present the results that give insight intothe phonon transport mechanism inside these low-dime nsional structures. We also present a new method formeasuring the NEP of TESs using an on-chip black body radiator.Keywords: Transition-Edge-Sensors, Thermal properties of Si x N y , Johnson noise thermometry, On-chip black-body source 1. INTRODUCTION Silicon rich Silicon-Nitride ( Si x N y ) is the material of choice in many cryogenic devices. It has mechanicaland thermal properties that make it an ideal candidate in the fabrication of TESs operating either as micro-calorimeters or bolometers. Si x