Effects of uniaxial stress on Mo and Mo/Cu bilayer superconducting transitions

Transition-edge sensors (TES) are widely used as sensing elements in X-ray microcalorimeters. Further improvement of their energy resolution hinges on a thorough understanding of the transition surface (as function of temperature, current, and magnetic field) to achieve high sensitivity (α) and low noise (small β), as well as the capability to repeatably fabricate the proximity superconducting/normal metal bilayers with a predictable transition surface. One aspect that is poorly understood is the impact of film stress on the transition. Data from Mo films deposited using e-beam evaporation onto heated substrates, as well as sputtered films, show a strong correlation between film stress and superconducting transition temperature (≈-0.2K/GPa, corresponding to shift of about -0.1 K for a 0.1% change in biaxial strain). However, this correlation is of opposite sign and much larger than one would expect from the pressure dependence of bulk Mo. Furthermore, modifications in fabrication details of the devices, such as membrane perforations and absorber attachment, have been observed to result in large qualitative differences in the transition surface for otherwise identical TES geometry. It seems reasonable to ask whether associated changes in film stress distribution can cause these differences. To shed some light on this issue, we have subjected a bare Mo film as well as Mo/Cu bilayers to in-situ tunable uniaxial stress produced by a piezo-electric stack. Our results indicate that the direct strain induced changes to the transition temperature are rather small (about +0.3 mK for a 0.1% strain change on a Mo film) and consistent in sign and order of magnitude with that derived from the bulk.