# Microwave SINIS Detectors
## 2 Electron Cooling  
The effect of electron cooling ostensibly seems very promising; however, its effects are twofold. In actuality, electron cooling leads to a decrease in the current response and an increase in the shot noise. As a result, it does not contribute much to the improvement of the NEP. Since the noise emerging from the electron-phonon heat flow is \(\text{NEP}_{\text{e-ph}}^{2}=10\text{k}\
u\Sigma\) (\(T_{\text{e}}\)\({}^{6}+T_{\text{ph}}\)\({}^{6}\)), in which \(k\) is the Boltzman constant, \(\
u\) is the absorber volume, and \(\Sigma\) is the material constant [29], the total \(\text{NEP}_{\text{e-ph}}\) is mainly determined by the highest temperature, and only cooling the electron component does not improve the performance of the device much compared to cooling both components. If we take \(T_{\text{e}}\) = 0.1 K and \(T_{\text{p}}\) = 0.3 K for electron cooling only, and compare the results to \(T_{\text{e}}\) = \(T_{\text{p}}\) = 0.1 K for the cooling of both, the difference between \(\text{NEP}_{0.3}\) and \(\text{NEP}_{0.1}\) is 20 times. Besides this, a shot noise component derived from electron cooling heat flow \(P_{\text{cool}}\) will add \(\text{NEP}^{2}=4 kT_{0}P_{\text{cool}}\) and additional shot noise due to the higher dc current bias, \(\text{NEP}_{\text{SIN}}\)\({}^{2}=2\text{el}_{\text{dc}}/(dI/dP)^{2}\). This is accompanied by the problem of the heat sink from the superconducting electrodes in the high-dc bias mode required for electron cooling, which can lead to an increase in both the superconductor electron temperature and the phonon temperature of the chip.  
As mentioned in [30], and shown in Figure 3, at voltages below the superconducting gap, the electron temperature \(T_{\text{e}}\) at the substrate temperature \(T\)\(\sim\)0.1 K is \(\sim\)0.23 K due to overheating caused by spurious radiation. At the substrate temperature \(T\)\(\sim\)0.3 K, the electron temperature is close to the substrate temperature \(T_{\text{e}}\approx T\). In both cases, with an increase in bias voltage, \(T_{\text{e}}\) decreases due to electron cooling and reaches 0.19 K at a voltage corresponding to the maximum response. The response at \(T\) = 0.1 K is greater than that at \(T\)\(\sim\)0.3 K by a factor of 5-6. Thus, the cooling of electrons alone does not provide the same responsivity as the cooling of the detector as a whole.  
Thus, our direct experiment does not support our hypothesis that without decreasing the phonon temperature of the SINIS detector, it is possible to achieve optimal responsivity. Such cooling requires dilution cryostats or adiabatic demagnetization refrigerators (ADR); using 3 He sorption cryostats is not enough, and electron cooling does not help.  
On the other hand, if we fabricate a suspended N absorber in the SINIS structure, it is much easier to achieve both electron cooling and phonon cooling in the long N absorber, especially when the material of the absorber is different from that of the superconducting electrodes, such as for a Pd and Al pair. In this case, the acoustic mismatch provides moderate thermal insulation for phonon temperature, and substantial phonon cooling can be achieved.