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 a function of temperature, current, and magnetic field) to achieve high sensitivity ($\alpha$ ) and low noise (small $\beta$ ), 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 ( $\approx$$-$ 0.2 K/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.

中文翻译：

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单轴应力对 Mo 和 Mo/Cu 双层超导跃迁的影响

过渡边缘传感器 (TES) 被广泛用作 X 射线微量热仪中的传感元件。其能量分辨率的进一步提高取决于对过渡表面（作为温度、电流和磁场的函数）的透彻理解，以实现高灵敏度（$\alpha$ ）和低噪音（小 $\beta$ )，以及可重复制造具有可预测过渡表面的邻近超导/正常金属双层的能力。一个鲜为人知的方面是薄膜应力对过渡的影响。使用电子束蒸发在加热基板上沉积的 Mo 薄膜以及溅射薄膜的数据显示，薄膜应力与超导转变温度之间存在很强的相关性。 $\大约$$-$ 0.2 K/GPa，对应的位移约为 $-$0.1 K，双轴应变变化 0.1%）。然而，这种相关性是相反的符号，并且比块体 Mo 的压力依赖性所预期的要大得多。 此外，已经观察到设备制造细节的修改，例如膜穿孔和吸收器附件，导致了很大的质量差异在其他相同的 TES 几何形状的过渡表面中 询问薄膜应力分布的相关变化是否会导致这些差异似乎是合理的。为了阐明这个问题，我们对裸钼膜以及钼/铜双层进行了处理就地由压电堆栈产生的可调单轴应力。我们的结果表明，直接应变引起的转变温度变化相当小（对于 Mo 膜上 0.1% 的应变变化，大约为 +0.3 mK），并且在符号和数量级上与体相一致。