Record electron self-cooling in cold-electron bolometers with a hybrid superconductor-ferromagnetic nanoabsorber and traps

The Cosmic Microwave Background (CMB) radiation is the only observable that allows studying the earliest stage of the Universe. Radioastronomy instruments for CMB investigation require low working temperatures around 100 mK to get the necessary sensitivity. On-chip electron cooling of receivers is a pathway for future space missions due to problems of dilution fridges at low gravity. Here, we demonstrate experimentally that in a Cold-Electron Bolometer (CEB) a theoretical limit of electron cooling down to 65 mK from phonon temperature of 300 mK can be reached. It is possible due to effective withdrawing of hot electrons from the tunnel barrier by double stock, special traps and suppression of Andreev Joule heating in hybrid Al/Fe normal nanoabsorber.


Samples and experiment description
The maximum responsivity of CEB depends on the absorber volume V N and its electron temperature T e as S ∼ 1/(V N T 4 e ) 21 , which makes it very important to decrease both V N and T e . An entirely normal metal absorber such as Cu 33 is fabricated on top of superconducting Al electrodes because the reliable tunnel barrier is much easier to make on top of Al by its oxidation. As a result, the Cu layer of a SINIS junction is always thicker than the Al electrodes due to technological requirements.
If the absorber is made of Al with suppressed superconductivity, it can be deposited as the first layer and can be made as thin as possible (Fig. 1a). It decreases the absorber volume, the electronic heat capacity, and the electron-phonon coupling, therefore improving sensitivity 23,26,27 . In Fig. 1b, the energy diagram illustrates the hot electron tunneling with its later relaxation in N traps, thus preventing the heat return into the absorber.
The two-particle Andreev current 34,35 is one of the most serious factors limiting the electron cooling efficiency since it dissipates heat in the normal metal. In Fig. 1c, the key advantage of S/F nanoabsorber is illustrated by Energy diagram of CEB. One photon is absorbed by one electron (top red ball), which redistributes its energy between other electrons in absorber N, changing the temperature of Fermi distribution. When voltage V is applied across the NIS junction, the hottest electrons tunnel into S (current I). After that, the electrons move away from the tunnel barrier and lose their energy in N trap. (c) Schematic representation of Andreev current suppression in AlFe due to the presence of Fe grains. Symbols " * " indicate defects and impurities in Al. Paths 1 (reflection) and 2 (Andreev reflection) are present in a typical normal metal. Paths 3 and 4 show that an electron spin is not constant, if the scattering on the magnetic grains happens, decreasing the probability of Andreev reflection. showing the typical trajectories of electrons/ holes in the normal metal. An electron reaches the NIS interface (paths 1-2) after being scattered and finally penetrates the superconductor as a Cooper pair due to Andreev reflection, and a hole is retro-reflected. The Fe sublayer creates the magnetic scattering to destroy time-reversal symmetry in loop 3-4 ( Fig. 1c) with proper dephasing of electron and reflected hole, thus suppressing Andreev reflections and increasing the electron cooling efficiency. Therefore, instead of using external magnetic fields 36,37 , resulting in Abrikosov vortex formation 38 and superconducting gap suppression, we utilize the internal mechanism of Andreev heating current suppression with a thin 0.7 nm Fe layer. Three types of the samples, A, B and C, are shown in Fig. 2a-c with corresponding plots of differential conductivity d, e and f versus the voltage across the bolometer. In sample A, there is a Cr granular layer, and in the samples B and C, there is a Fe granular layer used to suppress the absorber's superconductivity.
Sample A is an early version of the CEB. Even in this sample, the normal metal traps are implemented to prevent the heat return to the absorber. However, both SIN junctions are connected to the traps and the antenna from one side only (one stock for hot electrons). As a result, we have observed rather poor electron cooling due to overheating superconducting electrodes 26 . One can see also a zero bias peak on the conductivity plot (Fig. 2d), appearing at the temperature 150 mK and below, which is a clear signature of the Andreev current.
In sample B, we have significantly improved the absorber cooling by adding a second stock for hot quasiparticles to external superconducting electrodes at both SINIS ends 27,39 (S electrodes contact the antenna from both sides of the absorber, compare with Fig. 2a). The normal metal traps are absent, but the thickness of the superconductive electrodes is increased, and the cooling efficiency of the samples with these modifications is already high enough, so only 6% of the removed heat returns back to the absorber 27 .
Sample C differs from B only by the added normal metal traps for quasiparticles under the superconducting electrodes. The experiments with these samples demonstrated that the return heat is just 0.5%. In other words, the electron cooling reaches its maximal efficiency.
For both samples B and C with a Fe underlayer in the absorber, the differential conductivity does not have a zero bias peak down to 20 mK (Fig. 2e,f). Thus, one can see that the Fe magnetic granular layer, with a thickness of just 0.7 nm, underneath the Al film, has changed the absorber properties significantly.
The parameters of the samples, which will be used for fitting in the next section, are listed in Table 1. All of them are measured experimentally, except for the returning power, which is determined from the solution of heat balance equations (HBE) (2), described below. Here R N is the normal resistance of the NIS junction, and σ N is the absorber electrical conductivity. It can be seen that the parameters of the tunnel junctions are quite similar for the three samples, while the differential conductivities are rather different. That means that the SINIS junctions themselves do not directly determine the cooling efficiency. SEM images of the sample designs with one stock and normal metal traps for quasiparticles (a), with two stocks and without traps (b) and with two stocks and normal metal traps (c). Here the gold antennas are shown in orange, the superconductors in blue, the N traps in magenta, and the absorber in yellow, with a typical volume of its narrow part of 15 nm 3 × 80 nm 3 × 1000 nm 3 . Red arrows in (a,b) show the possible directions for quasiparticles to move. In (a), there is only one direction, which results in the S electrode overheating. Plots on (d,e,f) are differential conductivities of the samples A, B, and C, at various temperatures, respectively. In (d), the presence of Andreev current I A is evident below 150 mK as a slight peak at zero voltage. In (e,f), there is no visible sign of I A down to 20 mK. Much better electron cooling is seen in (e,f) in comparison with (d).

Electron temperature
The easiest way to find the electron temperature of the absorber is from the quasiparticle tunneling current: where V is the voltage across the NIS junction, T e and T s are electron temperatures in the normal metal and the superconductor, respectively, is a density of states in the superconductor, is a superconducting gap, k B is the Boltzmann constant. The current, the voltage, R N and are measurable values, whereas T s can be set to the phonon temperature. Thus, the only unknown quantity T e in Eq. (1) can easily be extracted.
The electron temperatures of the three samples at the phonon temperature T ph = 300mK are shown in Fig. 3a versus the voltage across the bolometer. The sample C reaches the minimum electron temperature T e = 65mK , which is close to a theoretical limit, predicted in 29 . One more curve for T ph = 256mK (green diamonds) is also given for sample C with minimum T e = 48mK . Below 256 mK the minimum T e saturates at 42 mK for this  Fig. 3b,c we plot the experimentally obtained minimum T e versus the phonon temperature for three of our samples, extracted with the help of Eq. (1). The described method is fast, but not always precise, and gives very limited knowledge about the system. Therefore, we also use the heat balance equations (HBE) (2), see "Methods". This allows estimating the contribution of each power flow channel separately. Namely this model helps us to find the best geometrical configuration of the CEB. Along with the cooling efficiency, HBE can be used to calculate the minimal electron temperature in an idealized system and to trace the influence of adverse factors. The HBE use is justified by very fast electron-electron interaction, which at low temperatures below 0.5K is much faster than the tunneling and the electron-phonon interaction, leading to quasi-equilibrium Fermi distribution of electrons in the absorber 13 .
In Fig. 3b,c, the theoretical minimum of T e (thick black curve), calculated for parameters of sample C, is plotted versus phonon temperature. In the calculation of the theoretical minimum, we disregard both the Andreev current I A and the return heat, i.e. I A = 0 and β = 0 . The return heat is characterized by a coefficient 0 < β < 1 , which shows how much power, removed from the absorber, returns back (2). It is also shown here what happens if we add the nonzero return power from superconductor (Fig. 3b) or Andreev current (Fig. 3c) to the HBE. One can see that the two heating sources have different influence on minimum T e . The return power β increases minimum T e for all phonon temperatures, but does not lead to T e saturation at the lowest phonon temperatures. The Andreev current does not change the minimum T e at high phonon temperatures much, but gives a T e limit at low temperatures. I A does not transfer heat through the N/S interface, while generating the Joule heating I A V deposited in the N electrode 40 . That's why the excess heating dominates single-particle cooling 6 at low enough temperatures. In other words, at nonzero β and I A = 0 , the minimal electron temperature will be higher than the theoretical minimum in the whole range of phonon temperatures. But at β = 0 and I A > 0 , it is possible to reach the minimum theoretical electron temperature above a certain T ph value, determined by the value of Andreev current.
The minimum T e = 65mK of sample C coincides with the theoretical curve at the temperature of 300 mK. Below this temperature, T e saturates at 42 mK and does not change anymore with the decrease of T ph due to the tiny Andreev current still persisting in our structure.
For sample B, one can see that only Andreev current cannot describe the dependence of the T e minimum on T ph , therefore we also need to add a small β . We obtain that β = 0.06 for this sample.
Sample A has rather poor cooling properties both due to high Andreev current and due to high β = 0.3 . From this, we conclude that the underlayer of Fe below Al suppresses the Andreev current more efficiently in comparison with Al/Cr system. Below, we obtain the electron temperatures by two different methods: by Eq. (1) and HBE (2) with an account of Andreev current (3) (see "Methods"). Let us show that Eq. (1) works well if a leakage current or I A are negligible compared to a quasiparticle current. In Fig. 4a, we show the electron temperature, obtained from Eq. (1) and the HBE (2), at two temperatures, 300 mK and 20 mK. One can see that both methods give the same results at 300 mK. But at 20 mK, the results are rather different. Eq. (1) overestimates the electron temperature at low voltages because it does not consider the two-particle current I A . At the same time, the minimum electron temperature near the gap has very similar values for both methods though at slightly different voltages.
The results of IV-curves fitting for the samples A, B, C using the HBE model are shown in Figs. 4 and 5 for 20 mK and 300 mK. The heat balance equation (2), supplemented by the Andreev current (3) and heating from it, rather accurately describes the experimental data and does not need additional fitting effects, such as leakage current or gap smearing due to environment-assisted tunneling 41 . The IV-curves agree with the experiment at the proper value of the magnetic scattering parameter τ m (5) (see "Methods"). The quasiparticle current, shown by the blue curve, fits the experimental curve well near the gap, but gives too small current at low voltages. The In sample A, we have an underlayer of Cr with a thickness 0.7 nm, which is also ferromagnetic and could suppress the Andreev current similar to Fe. Indeed, in fitting, we obtain some suppression of Andreev current for this sample, but the effect is weaker than for the samples with Fe.
By comparing the fit of samples A and B, shown in Fig. 5a,b, respectively, one can see that the Andreev current is approximately one order of magnitude larger for the sample A than for B. We assume that this difference is due to both higher barrier transparency for sample A (a factor of two), but mostly because of the Fe underlayer in sample B.

Discussion
Let us discuss several limitations of cooling performance and how to overcome them to get high efficiency of electron cooling. The first limitation arises due to the accumulation of nonequilibrium quasiparticles injected into the S layer near the NIS interface 42,43 . The consequences are the heat back current from hot quasiparticles via phonons in superconductor and substrate to the absorber, and the overheating of the superconducting electrode leading to the gap suppression. Despite the difficulty of theoretical analysis with an account of nonequilibrium effects, there is a practical solution to remove hot quasiparticles from the superconducting electrode by the traps 44 made of an additional normal metal layer covering the S layer. The second limitation arises from the intrinsic multiparticle nature of current transport in NIS junctions consisting not only of single-particle tunneling but also of two-particle Andreev tunneling 45,46 . The single-particle current and the associated heat current, formed by quasiparticles with energies larger than the superconducting gap, are exponentially suppressed in the subgap voltage region at low temperatures. The charge is mainly transferred by means of Andreev reflections of quasiparticles with sub-gap energies 34 , dissipating the heat in the normal metal electrode. Thus, the interplay between the single-particle tunneling and Andreev reflections sets a limiting temperature for the refrigeration, depending on the interface transparency 47 .
A strong reduction of the Andreev current is anticipated in materials, in which the proximity effect is suppressed. Indeed, for this reason the electron cooling efficiency improving was theoretically predicted in the case of ferromagnetic interlayers [48][49][50] , or a spin-filter barriers 29 in SINIS structures. However, there were no experimental observations of this effect so far. On the contrary, very significant excess conductivity, by a factor of three exceeding the minimal dI/dV value, was demonstrated for Cu suspended absorber in 33 .
The suppression of the excess conductance due to Andreev reflections can be done by an external magnetic field 36,37 . However, it leads, for example, to Abrikosov vortex formation 38 and to superconducting gap suppression. Instead, we utilize the internal mechanism of Andreev current suppression, provided by a thin 0.7 nm Fe layer. It does not affect the superconducting gap of S lead, since the S electrodes are protected by the tunnel barrier, but improves the electron cooling 29 .
In this work, we have overcome both limitations and demonstrate the theoretical minimum of the electron temperature experimentally down to 65 mK in SINIS structures at 300 mK phonon temperature. This is an important threshold temperature because it can be reached in 3 He cryostats. We also show electron cooling from 256 mK (which can be reached in two-stage 3 He cryostats) to 48 mK. The suppression of excessive heating was achieved due to the following: the implementation of the hybrid S/F nanoabsorber instead of a normal metal nanoabsorber, the modification of the tunnel junctions electrodes geometry and the addition of specially designed normal metal traps for non-equilibrium quasiparticles. In contrast to the external magnetic field, the internal mechanism by ferromagnetic sublayer is performing two-particle Andreev current suppression in a delicate manner without the S electrodes superconducting gap suppression. Simultaneously, the suppression of two-particle tunneling decreases the shot noise 51 . The deep electron cooling demonstrated in this paper gives www.nature.com/scientificreports/ these CEBs record sensitivity that makes them promising for receivers on prospective future space missions. In addition, the possibility to suppress the heat transfer due to a two-particle current is the next step for reliable quantum caloritronics 14,52,53 .

Online content
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Methods
Sample fabrication. All the samples studied in this work were fabricated at Chalmers University of Technology. For samples A and C, the manufacturing technology consisted of three stages, for sample B is was of two stages, due to the absence of normal metal traps. All layers, except for the bolometers themselves, were formed by the method of lift-off lithography, performed using a laser-writer, and the subsequent deposition of thin films by an electron beam. For the fabrication of bolometers, an electronic lithograph and a shadow evaporation technique were used, making it possible to deposit tunnel junctions without breaking the vacuum. Normal metal traps, such as in sample C, were made of three metals: 1 nm of titanium, 15 nm of gold and 2 nm of palladium. Antennas were made of the same metals, but of increased thickness: 10 nm of titanium, 120 nm of gold and 20 nm of palladium. The bolometers represent SINIS structures, made by the self-aligned shadow evaporation technique. The layer of normal metal is deposited first and is made of two thin films: 0.7 nm of Cr/CrOx and 14 nm of Al for the sample A, or 0.7 nm of Fe and 14 nm of Al for the samples B and C. The thin layer of Cr or Fe below Al is needed to suppress the superconductivity in the absorber. After that, the aluminum with suppressed superconductivity is oxidized, and the electrodes from superconducting aluminum are deposited at two different angles.
Heat balance equation. The electron temperature can be obtained from the IV-curve, using the integral for the tunneling current through a NIS junction (1). It gives a reliable result if the total current is composed only of one-particle component. Otherwise, we have to use more a complicated approach, based on the heat balance equation (HBE) 26,27 : In Eq. (2), P N is the Joule heat in the N absorber, P ph−e = �V N (T 5 ph − T 5 e ) is a heat flow between electron and phonon subsystems, is an electron-phonon coupling constant and V N is the volume of the N absorber. P cool is a cooling power of NIS junction, P S is the net power dissipated in the S electrode, and coefficient β shows how much of P S returns back to the N absorber, and P A = I A V is the heating due to the Andreev current, V is the voltage drop across the NIS junction.
For the planar geometry of the junction at 0 < ε < � , we get that Andreev current is expressed as 47 The parametrized Green function was calculated using Uzadel equation with Kupriyanov-Lukichev boundary conditions 54 taking into account the decay of the state with the wave vector k due to spin scattering Here, the parameter of magnetic scattering τ m is to be found from fitting, W = W 0 ξ 0 /d is the effective tunneling parameter for planar tunnel junctions, used in our CEB, with W 0 = R(ξ 0 )/R N , the standard tunnelling parameter 47 . For aluminium ξ 0 = 100nm and in our samples d = 14nm . R N is the normal resistance of the junction, R(ξ 0 ) is the resistance of Al/Fe absorber of the length ξ 0 . Then we get W 0 ∼ 10 −5 and W ∼ 10 −4 . The fitting parameters related to Andreev current for the sample A are W = 1.5 × 10 −4 and τ m = 1 , for the sample B, they are W = 0.7 × 10 −4 and τ m = 0.5 , for the sample C, we have W = 0.9 × 10 −4 and τ m = 0.5. In Fig. 4, the results of T e calculation from Eq. (1) and from the HBE (2) at 300 mK and 20 mK are shown. Both methods give the same results at 300 mK, but differ at 20 mK, while the minimum electron temperature has very similar values for both methods, though at slightly different voltages.

Data availability
The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.
(2) P N + P ph−e − 2P cool + 2βP S + P A = 0. (3) Scientific Reports | (2020) 10:21961 | https://doi.org/10.1038/s41598-020-78869-z www.nature.com/scientificreports/ Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creat iveco mmons .org/licen ses/by/4.0/.