Demonstration of high-impedance superconducting NbRe Dayem bridges Open Access

Rhenium is a superconductive material with a bulk critical temperature $T c bulk ∼ 2.4$ K.¹ When grown in thin films, its superconductive properties slightly change, and the critical temperature becomes $T c film ∼ 1.85$ K,² with a coherence length of $ξ ∼ 150$ nm.³ Rhenium compounds, in general, have attracted growing interest due to their unconventional superconductive properties.⁴ NbRe is a relatively high critical temperature (⁠ $T c bulk ∼ 9$ K⁵) non-centrosymmetric superconductor,⁶ which was proposed as a suitable material for superconducting single-photon detectors (SSPD).^7–10 Thanks to a coherence length as short as $ξ ∼ 5$ nm, this material might provide a platform for the realization of ultra-thin superconducting films (thickness $t NbRe ≃ 3.5$ nm¹¹) with large critical temperatures (⁠ $T c ≃ 5.3$ K), easily accessible in ⁴He closed-cycle refrigerators. Such a short coherence length is the consequence of a sizable normal-state resistivity (⁠ $ρ N ∼ 3.0 × 10 − 5 Ω$ m deduced by the normal state resistance and the dimensions of our structures), resulting in a high $I S R N$ product, where $I S$ is the switching current and $R N$ is the normal-state resistance of the device, which is quite uncommon for full metallic systems due to their usually low resistances. This peculiar characteristic can be achieved with the use of dirty superconductors, such as NbN. In contrast, in our NbRe films, this feature stems from their highly disordered nature.¹¹ Another crucial figure of merit of NbRe is its high kinetic inductance, which makes the devices based on this material appealing for all those applications requiring a high inductance, such as superinductors,^12–14 fluxonium qubits,¹⁵ high Q-factor resonators,¹⁶ radiation sensors,^17,18 superconductive oscillating circuits,^19,20 and high inductance memory elements.²¹ Here, we report on devices based on a Dayem-bridge (DB) geometry made of NbRe films with different stoichiometry. The DB structure can serve as a tool to realize several monolithic devices, such as superconducting quantum interference devices (SQUIDs), magnetometers,²² and logic gates.²³ Furthermore, the opportunity to suppress the supercurrent of the DB via an external gate voltage²⁴ makes this kind of structure appealing for the realization of variable kinetic inductors with high dynamic range or nanosized superconducting switches with high output voltage due to the high $I S R N$ product (⁠ $≳ 100$ mV).^23,25,26

In this work, we have investigated two different types of composition of NbRe thin films, i.e., composition A and B, which have a stoichiometric ratio of Nb_0.1Re_0.9 and Nb_0.18Re_0.82, respectively.

We start by describing the fabrication process for the samples with composition A. The Re–Nb films were prepared via magnetron sputtering using an ATC series UHV Hybrid deposition system (AJA International, Inc.) with a base pressure of $1 × 10 − 8$ Torr. The Re target (ACI Alloys, Inc., 99.99% purity) and the Nb target (Testbourne, Ltd., 99.95% purity) were both accommodated inside 1.5 in. diameter DC guns. The sapphire substrate (AdValue Technology, thickness $650 μ$m, C-cut) was cleaned thoroughly with isopropyl alcohol before it was mounted on the holder. In the chamber's configuration, the substrate holder is at the center of the chamber facing upward, while the sputtering guns are located at the top. The substrate is rotated in plane throughout the whole deposition process to ensure a homogeneous deposition layer over the whole surface. A pre-deposition in situ cleaning of the substrate involved heating it up to $700 °$C for 10 min followed by a gentle bombardment of Ar⁺ ions at $600 °$C for 5 min using a Kauffman source at 0.75 mTorr. Plasma striking for guns was performed at 30 mTorr with shutters closed and with the initial power 30 W for each target. Then the gun powers were ramped up to 150 W for Nb and 500 W for Re, with a decrease in the chamber pressure to 5 mTorr in Ar flow. Afterward, the deposition of Nb and Re took place. For better adhesion, the Re shutter was opened for 10 s later than the Nb shutter. Simultaneous Nb and Re sputtering lasted 150 s, after that the Re shutter was closed, and, in 10 s, the Nb shutter was also closed. After this, the temperature was again raised to $900 °$C for in situ annealing during 30 min and then cooled down to ambient temperature. All the heating/cooling protocols consistently used a $30 °$C/min ramp rate. To pattern the DB structures via reactive ion etching (RIE), a positive electron beam lithography (EBL) was performed with a PMMA mask on the sputtered films. Then 60 nm of aluminum (Al) was deposited with an e-beam evaporator in order to have an Al hard mask, which is resistant to fluorine etching, on top of our NbRe film. The films were etched using a CF₄, Ar, and O₂ gas mixture of 40/6/4 sccm at a power of 150 W. Finally, the removal of the Al hard mask in an alkaline solution provides the finished device, as shown in Fig. 1(a).

The composition B films were sputtered via a stoichiometry NbRe (Nb_0.18Re_0.82) target (Testbourne Ltd., 99.95% purity) with a power of 250 W and an Ar pressure of 3 mTorr at a base pressure of $1 × 10 − 8$ mTorr, which resulted in a deposition rate of 0.33 nm/s. The 20-nm-thick NbRe films were sputtered on Al₂O₃ substrates (Crystec GmbH, thickness 430  $μ$m, A-cut). To pattern the DBs via RIE, a negative lithography was performed with an etching-resistant negative resist. The etching was performed with an inductively coupled plasma–reactive ion etcher (ICP-RIE), where the samples were etched for 30 s (at first, 15 s, and then three steps with 5 s after each checking the resistance in the wafer prober) in 26 sccm Ar + 26 sccm Cl₂ at 10 mTorr with an RIE power of 20 W and an ICP power of 750 W (the sample plate was cooled to 10 °C). A representative device with composition B, produced with this process, is shown in Fig. 1(b).

Both deposition methods have advantages and drawbacks. In fact, the stoichiometry of the samples with composition A can be changed in order to change the film properties, which is clearly an advantage. However, the deposition method is more complicated and less reproducible with respect to the technique used for composition B samples. Moreover, the different etching processes used also present advantages and drawbacks: although the Al hard mask process with CF₄ RIE etching used for composition A samples requires more fabrication steps, it relies on a positive resist lithography, which can be more precise, and the etching mask is removed very simply; the negative resist and the Ar/Cl ICP RIE process used for composition B samples is faster but often presents issues regarding the negative resist mask removal after the etching process.

The devices were then wired, as displayed in Fig. 1(a), with a four-wire standard setup in order to take the full characterization of their properties. The samples were cooled down in ⁴He cryogen-free cryostats with a base temperature of $3$ K. In Fig. 1(c) the characteristic R vs T shows that the critical temperature of the devices with composition A is $T c 1 A exp ∼ 7.4$ K, while, for composition B, it is $T c 1 B exp ∼ 6.1$ K [see Fig. 1(d)]. The $T c exp$ value for both samples is taken when $d R / d T$ is maximum [dashed lines in Figs. 1(c) and 1(d)]. We note that both devices have only one visible transition in the curve shown in Figs. 1(c) and 1(d): this is because the coherence length (⁠ $ξ ∼ 5$ nm) of this material is much lower than the lateral dimensions of the DB (see Table I), resulting in a negligible change of $Δ ( T )$ in the constriction.

Figure 4(a) shows several I-V curves measured at 2 K for increasing values of the external perpendicular-to-plane magnetic field for a device with composition B. The full trend of the switching and retrapping currents as a function of the magnetic field is highlighted in Fig. 4(b). Up to 2 T (i.e., the maximum magnetic field that our magnet could support), the NbRe DB still shows a sizable switching current of the order of $∼ 6 μ$A. This suggests that NbRe has a perpendicular-to-plane critical magnetic field at least comparable to other high-kinetic inductance superconductors.^35,36 We emphasize that the robustness of this material to magnetic fields makes it an optimal candidate for experimental situations and applications where high magnetic fluxes cannot be avoided or are even required such as, e.g., quantum Hall experiments in hybrid platforms.³⁷ 

In general, we can conclude that by varying the Re percentage of these films, one can explore the parameter space and find better performances in terms of $L K □$ and $I S R N$ for a given geometry.

In summary, we have reported the fabrication and characterization of NbRe superconducting Dayem nanobridges. The better performance, in terms of $T c$⁠, $L K$⁠, and $I S R N$⁠, of the devices with composition A suggests that a higher percentage of Re is beneficial for applications requiring these characteristics. The achievable values of the kinetic inductance, which are higher than the ones reported in the literature for NbN,⁴⁰ suggest that the NbRe can be used in several applications requiring high $L K$ such as superinductors,^12–14 radiation sensors,^7–9 and high-quality factor resonators.¹⁶ Moreover, the sizable critical magnetic field highlights its possible exploitation in qubit systems.¹⁵ Given all these features, we believe that this superconducting metal might be considered as a promising alternative to more conventional Nb compounds (e.g., NbN and NbTiN) for quantum technology applications.²⁶ 

We acknowledge the EU's Horizon 2020 Research and Innovation Framework Programme under Grant Nos. 964398 (SUPERGATE) and 101057977 (SPECTRUM), and the PNRR MUR Project No. PE0000023-NQSTI for partial financial support. We also acknowledge partial support of this research by U.S. ONR, under Grant Nos. N00014-21-1-2879, N00014-20-1-2442, and N00014-23-1-2866.

The authors have no conflicts to disclose.

S. Battisti: Conceptualization (equal); Data curation (equal); Investigation (equal); Methodology (equal); Resources (equal); Software (equal); Writing – original draft (equal). J. Koch: Conceptualization (equal); Data curation (equal); Investigation (equal). A. Paghi: Methodology (equal); Writing – review & editing (equal). L. Ruf: Methodology (equal). A. Gulian: Investigation (equal); Supervision (equal); Writing – review & editing (equal). S. Teknowijoyo: Investigation (equal); Methodology (equal). C. Cirillo: Investigation (equal); Methodology (equal). Z. Mahdoumi Kakhaki: Investigation (equal); Methodology (equal). C. Attanasio: Investigation (equal); Methodology (equal). E. Scheer: Investigation (equal); Supervision (equal); Writing – review & editing (equal). A. Di Bernardo: Conceptualization (equal); Investigation (equal); Methodology (equal); Supervision (equal); Writing – review & editing (equal). G. De Simoni: Data curation (equal); Investigation (equal); Supervision (equal); Writing – review & editing (equal). F. Giazotto: Conceptualization (equal); Investigation (equal); Methodology (equal); Resources (equal); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding authors upon reasonable request.