The chips designed to enable 4-wire resistance measurements (Fig. 5 Left), with absorbers attached using 2 spheres, were wire bonded and assembled on a PCB (Fig. 5 Right) which was then installed inside a Bluefors Dilution Refrigerator on the Quasi-4K flange. Out of the three chips assembled on the PCB, only the one attached with 100g force, 3.0 pickup tool heat and 100\(℃\) stage temperature could be tested so far. Resistance measurements were performed using an SRS SIM921 AC Resistance Bridge at room temperature and as the cryostat was cooling down.
The measurement of the chip (Fig. 6) gives us the total resistance of 1× the Sn absorber resistance + 2× the BiSn sphere resistance + any contact resistance with the gold and the tin + 2× some gold film resistance due to the layout of the gold layer on the chip.
At room temperature, the total resistance was about 94mΩ. Figure 6 shows a sharp transition at 4.1K due to the BiSn spheres and part of them alloying with the Sn absorbers. Normal to superconducting transition temperature (\({T}_{C}\)) of Sn is 3.7K but we do not expect to see the transition due to the low resistance with respect to the large cross-sections of the absorbers. The resistance of a single BiSn sphere joint, just above the transition, is about (16.5–12) mΩ/2 = 2.25 mΩ and the contact resistance of the gold film with the BiSn sphere + some gold film resistance is around 12 mΩ/2 = 6 mΩ (Fig. 6).
For a normal metal, resistance is proportional to thermal conductance through Wiedemann-Franz (W-F) Law given by,
$$\text{G}=\text{T}\times \frac{\text{L}}{{\text{R}}_{\text{e}\text{l}}}$$
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where G is the thermal conductance, T is the temperature, L = \(2.44\times {10}^{-8}\) \({\text{V}}^{2}{\text{K}}^{-2}\) is the Lorenz number and \({R}_{el}\) is the electrical resistance [4]. W-F law is not applicable for superconductor joints; however, we can use it to have an estimate of thermal conductance right before the transition.
At T = 4K and contact resistance \({\text{R}}_{\text{e}\text{l}}\)=6mΩ,
\({\text{G}}_{\text{c}\text{o}\text{n}\text{t}\text{a}\text{c}\text{t}}\) = 160 \(\times {10}^{-7}\) W/K (2)
At T = 100mK,
\({\text{G}}_{\text{c}\text{o}\text{n}\text{t}\text{a}\text{c}\text{t}}\) = 4.1 \(\times {10}^{-7}\) W/K (3)
With glue attachment, thermal conductance between the TES and the bath, G = \(20\times {10}^{-9} \text{W}/\text{K}\). To achieve better conduction with BiSn metal spheres, we want
$${\text{G}}_{\text{c}\text{o}\text{n}\text{t}\text{a}\text{c}\text{t}}>10\text{G} = 2\times {10}^{-7} \text{W}/\text{K}$$
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Since our absorber chip survived the cool down and our estimated thermal conductances turned out to be > 10G, this gives us an idea that it’s clearly not a bad connection.
More tests will be carried out to check the connection strengths of the absorbers and thermal conductivity measurements.
Right Assembled absorbers on the PCB for resistance measurements (Color figure online)
Right Expanded view of the left plot. The sharp transition around 4.1K is most likely due to the BiSn spheres and any part of it that alloyed with the Sn. (Color figure online)