Gap Engineered Superconducting Multilayer Nanobridge Josephson Junctions

Abstract

We report the realization of multilayer three-dimensional nanobridge Josephson junctions based on Nb/NbN and Nb/TiN superconducting stacks fabricated using electron-beam lithography and chlorine-based dry etching. In this architecture, a high-resistivity nitride layer defines the geometrical weak link, while the top Nb layer sets the overall critical temperature and film quality of the stack. This multilayer design enables engineering of the superconducting gap and proximity effects without relying on focused ion beam milling or oxide tunnel barriers. The devices are successfully integrated into dc SQUIDs, demonstrating reliable circuit-level operation. By combining material selectivity with three-dimensional geometry, this platform provides a scalable route toward oxide-free Josephson junctions suitable for superconducting electronics.

Figures (7)

• Figure 1: Schematic overview of the two step fabrication process used to define multilayer 3D nanobridges. The process begins with etching the large features and the planar nanobridge structure. In the second patterning step, only the top portion of the film above the nanobridge is etched, leaving the bottom nitride layer intact to form a high resistance 3D weak link geometry.
• Figure 2: (a) Representative current–voltage (IV) characteristics of NbN based nanobridge Josephson junctions measured at 40 mK. (b) Critical current as a function of normal-state resistance for all measured NbN junctions. Two distinct device populations are observed. Junctions in the gray region exhibit relatively low resistance and are attributed to under etching, where the top Nb layer is not fully removed (schematically shown in the inset). In this regime, the $I_cR_N$ product is independent of the underlying nitride layer due to the residual metallic Nb contribution. For longer etching times, the devices follow the theoretically predicted trend, indicating proper removal of the top layer and correct definition of the nanobridge. The lines correspond to numerical simulations performed using the KO-1 model and our three-dimensional Usadel based model, assuming a bridge length $L=30$ nm and $\xi = 10$ nm for both TiN and NbN as explained in the main text, and adjusting the effective cross section to reproduce the measured normal-state resistance. The level of agreement between simulations and experimental data was quantified through a $\chi_{norm}^2$ analysis. For the NbN junctions $\chi_{norm}^2 = 0.96$ within our model and $3.5$ within the KO-1 framework. (c) Simulated spatial profile of the superconducting energy gap for NbN and TiN based multilayer nanobridge junctions at $T = 0.1T_c$, with $L = 30$ nm and $W = 60$ nm. The structure is shown from the bottom of the junction. Due to proximity effects within the multilayer stack, the superconducting gap in NbN is reduced by approximately $5\%$, whereas in TiN it is enhanced by approximately $60\%$. The smaller variation observed in NbN is attributed to its larger thickness and to a critical temperature closer to that of Nb, which reduces the strength of proximity suppression compared to the TiN case.
• Figure 3: (a) SEM image of a fabricated dc SQUID. Color plots of IV characteristics versus applied flux for (b) NbN based and (c) TiN based devices. The NbN SQUID shows approximately $5\%$ modulation depth, while the TiN device exhibits approximately $20\%$ modulation. The relatively modest visibility is attributed to the large $4 \times 4~\mu m^2$ loop area, resulting in loop inductance comparable to the Josephson inductance, and possible asymmetry between the two junctions.
• Figure 4: Measured SQUID critical current vs flux and corresponding fits. (a) NbN based sample. The inset shows a zoomed view of the data highlighting a small bump, a typical signature of higher harmonic contributions to the CPR. (b) TiN based sample. Solid lines show the best fits to the data, accounting for junction asymmetry and finite loop inductance. The fits were performed using the asymmetric dc SQUID formalism described in the main text, comparing a sinusoidal current phase relation and the nanobridge current phase relation reported in Ref.mypaper
• Figure S.1: Critical temperature $T_C$ and resistivity characterization of the materials used for nanobridge fabrication: (a) Nb, (b) NbN, and (c) TiN. The absence of data points around $3\,\mathrm{K}$ for TiN is due to measurements performed in a different cryostat, which did not allow fine temperature control in this range.