  The effect of substrate thickness and its Debye temperature on the bolometric
response of the freestanding-membrane type of superconductor transition-edge
detectors is investigated. The investigation is based on the calculation of the
variation of the specific heat per unit volume and the heat conductivity using
the finite-size scaling method for different Debye temperatures and micron size
thickness of substrate. We also calculated the heat capacity and time constant
for various materials with Debye temperatures in the range of 600-1400K. The
calculated results are compared to previously reported response values obtained
theoretically and experimentally for the thermal-based infrared detectors. The
IR response versus substrate thickness of these types of devices for different
modulation frequencies is also presented. This inspected response at low
thicknesses of substrate shows anomalistic behavior with respect to the
previously reported results of response analyses. Here, we also obtained the
optimized substrate thickness and Debye temperatures for maximum responsivity
of these types of devices.
