2D Analysis of the Effects of Geometry on the Response of High- $T_{\rm c}$ Superconductive Bolometric Detectors

We present a new approach for analytical modeling and calculating the response of high-T _c superconductive transition edge sensors in a wide range of modulation frequencies for different configurations of the film patterns. The method used here is based on solving the heat transfer differential equation for two different time varying heat sources, which are related to the absorbed radiated power. The used method employs two-dimensional boundary conditions for describing meander-line patterned devices. The results from the applied method are in better agreement with those obtained from the frequency response measurements of the characterized samples, than the previously developed models. In addition, the method is capable of being used for analysing the effect of the device configurative parameters on its ultimate sensitivity. Therefore, it has also been applied to investigate the effects of changing track and spacing width, substrate thickness, and absorption coefficient of the absorber layer on the magnitude of bolometric response. In this calculation, the effect of surface absorption caused by the superconducting thin film and absorber layer, as well as bulk absorption in the depth of the substrate are considered simultaneously. Analytical results are presented and compared with previous analytical works and measured data from YBCO samples. Through extensive numerical calculations, we demonstrate that the responsivity of superconductor bolometers is a strong function of geometry, and there exists an optimal track width to spacing ratio of about 0.2.