Impact of the Absorber-Coupling Design for Transition-Edge-Sensor X-Ray Calorimeters

Transition-edge sensors (TESs) are the selected technology for future spaceborne x-ray observatories, such as Athena, Lynx, and HUBS. These missions demand thousands of pixels to be operated simultaneously with high energy-resolving power. To reach these demanding requirements, every aspect of the TES design has to be optimized. Here we present the experimental results of tests on different devices where the coupling between the x-ray absorber and the TES is varied. In particular, we look at the effects of the diameter of the coupling stems and the distance between the stems and the TES bilayer. Based on measurements of the ac complex impedance and noise, we observe a reduction in the excess noise as the spacing between the absorber stem and the bilayer is decreased. We identify the origin of this excess noise to be internal thermal fluctuation noise between the absorber stem and the bilayer. In addition, we see an impact of the coupling on the superconducting transition in the appearance of kinks. Our observations show that these unwanted structures in the transition shape can be avoided with careful design of the coupling geometry. The stem diameter appears to have a significant effect on the smoothness of the TES transition. This observation is still poorly understood, but is of great importance for both ac and dc biased TESs.

Figure 1

(a) Schematic of the layout of the TESs. We vary only two aspects of the design: the diameter of the absorber stem $D$ and the spacing between the bilayer and the stem $X$. (b) Overhead view of the four different designs studied: a single design with $D=10\mu \mathrm{m}$ and $X=0\mu \mathrm{m}$ and three designs with $D=5\mu \mathrm{m}$ and varying spacing, $X=0,5$, and $10\mu \mathrm{m}$. The green structures are the niobium leads. (c) Close-up view of the connection between the absorber stems and the bilayer for the $D=10\mu \mathrm{m}$ (top) and $D=5\mu \mathrm{m}$ (bottom) designs.

Figure 2

Schematic of the FDM readout and the two-body thermal model. The TES is coupled to an LC resonator and is readout using a two-stage SQUID. The bias voltage $V_{\mathrm{ac}}$ is applied via a shunt resistor $R_{\mathrm{sh}}$ and bias capacitor $C_{\mathrm{bias}}$. In the two-body thermal model as used in Sec. 3 the detector is separated into two bodies, where one body is connected with a thermal conductance $G_{\mathrm{itfn}}$ to a second body that is connected to the thermal bath via $G_b$.

Figure 3

Results of complex impedance and noise measurements for low-bias-frequency pixels with different stem-bilayer separations: (a) $\alpha$ and (b) $\beta$ extracted from complex impedance measurements for the relevant part of the normal to superconducting transition; (c) ratio of $\alpha /\beta$ computed for the same bias points as those shown in (a) and (b).

Figure 4

Example noise spectra measured for the different $D=0\mu \mathrm{m}$ pixels, measured at $R\sim 0.15R_n$. Dashed lines represent the calculated noise models: SQUID noise (purple), phonon and additional low-frequency noise (orange), voltage noise from the RSJ model (green), and ITFN (red). The total of all noise sources is given by the solid black line.

Figure 5

(a) Excess noise factor defined with respect to expected noise in the RSJ model $S_{V,\mathrm{RSJ}}$ for the same bias points shown in Fig. 3 and (b) $G_{\mathrm{itfn}}$ required to minimize the excess noise factor for each bias point.

Figure 6

Estimated value of $G_{\mathrm{arm}}$, assuming a constant bilayer thermal conductance given by the Wiedemann-Franz law (green dashed line). The blue dashed line shows the arm thermal conductance when it remains superconducting (ignoring the temperature dependence of the gap). The red dashed line shows the arm thermal conductance when it is in the normal state (and, thus, follows the Wiedemann-Franz law). We take the effective length of the arm equal to $X+D/2$.

Figure 7

Measured $\alpha$ versus $R/R_n$ for pixels with different stem diameters. We show three sets of pixels at different bias frequencies: (a) 1.1–1.5 MHz, (b) 2.4–2.6 MHz, and (c) 4.1–4.3 MHz.

Figure 8

(a) Excess noise $M^2$ and (b) $M^2$ / $\alpha$ for low-frequency pixels with different stem diameters. In (a), data are shown for the $X=0$, $D=10\mu \mathrm{m}$ (red) and $X=0$, $D=5\mu \mathrm{m}$ (green) devices. In (b), also the data for the $X=5\mu \mathrm{m}$ (blue) and $X=10\mu \mathrm{m}$ (yellow) devices are shown as a reference.

Figure 9

(a) Measured NEP and (b) small-signal limit energy resolution calculated using Eq. (7). The NEP is measured at the optimal bias frequency for each value of $R/R_n$.