# Fully Superconducting Josephson Bolometers for Gigahertz Astronomy
## 4 Experimental Realization of JES and Nano-TES
### Bias Current Control of Resistance versus Temperature Characteristics
**(b)** Selected normalized resistance (\(R/R_{N}\)) versus temperature (\(T\)) characteristics recorded for different values of bias current (\(I\)). **(c)** Dependence of the escape temperature (\(T_{e}\)) on the ratio between the zero-temperature critical current and the bias current (\(I_{C,0}/I\)) for two different 1D-JJs. critical magnetic field of \(A\) that was measured to be about 21 mT [34]. Therefore, the self generated magnetic field does not affect the properties of the device. Furthermore, the superconducting properties of the Al/Cu bilayer dominate the behavior of \(A\). In fact, the energy gap expected for a non-superconducting Al/Cu bilayer as originated by lateral proximity effect is \(E_{g}\simeq 3\hbar D_{A}/l^{2}\simeq 5\)\(\mu\)eV [55]. This value is about 1/4 of the measured \(\Delta_{A}\) (see Section 4.2). The device in Figure 5a fulfills all the requirements of a 1D-JJ (see Section 2). Therefore, it can be used to investigate the impact of \(I\) on the \(R(T)\) characteristics. To this end, excitation currents with amplitude ranging from 15 nA to 370 nA were imposed through the device. Figure 5b shows that the \(R(T)\) characteristics monotonically move towards low temperatures by rising the current from \(\sim\)3% and \(\sim\)65% of \(I_{C,0}\). Furthermore, the resistance versus temperature characteristics preserve the same shape up to the largest bias currents. We stress that the use of an AC bias allowed to resolve the \(R\) vs. \(T\) characteristics near the critical temperature. In fact, values of DC bias higher than the retrapping current (\(I_{DC}>I_{R}\)) would cause the sudden transition of the device resistance to \(R_{N}\). Instead, the AC bias has always a part of the period lower than \(I_{R}\) thus enabling the precise measurement of the entire \(R(T)\) traces. In order to maximize the part of the period with \(I\sim I_{C}\), the AC signal should be a square wave with the upper level close to \(I_{C}\) and the lower value obeying to \(I_{L}<I_{R}\). If the duty cycle of the signal is 95 % in the upper level, the sensor operates most of the time near \(I_{C}\) thus providing high sensitivity. Despite the \(R(T)\) curves shift towards low temperatures by increasing the bias current, the active region electronic temperature (\(T_{A}\)) at the middle of the superconducting-to-dissipative-state transition under current injection does not coincide with \(T_{\text{bath}}\). In fact, Joule dissipation (for \(R\
eq 0\)) causes the quasiparticles overheating in \(A\) yielding \(T_{A}>T_{\text{bath}}\). Therefore, the operation of the sensor as a nano-TES is not possible without the additional shunting resistor (see Figure 3b). By contrast, the operation as a JES (at \(R=0\)) guarantees that the electronic temperature of \(A\) coincides with the bath temperature. From the \(R\) vs. \(T\) curves, we can specify the current-dependent escape temperature (\(T_{e}(I)\)). The values of \(T_{e}\) are shown in Figure 5c as a function of \(I_{C,0}/I\) for two different devices. The escape temperature is monotonically reduced by rising the bias current with a minimum value \(\sim\)20 mK for \(I=370\) nA, that is \(\sim\)15% of the intrinsic critical temperature of the active region, \(T_{C}^{i}\sim 130\) mK. As a consequence, the bias current is the ideal tool to in situ tune the properties of the 1D-JJ when operated as a JES.