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Register a new userSuperconducting circuits without inductors based on bistable Josephson junctions
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Magnetic flux quantization in superconductors allows the implementation of fast and energy-efficient digital superconducting circuits. However, the information representation in magnetic flux severely limits their functional density presenting a long-standing problem. Here we introduce a concept of superconducting digital circuits that do not utilize magnetic flux and have no inductors. We argue that neither the use of geometrical nor kinetic inductance is promising for the deep scaling of superconducting circuits. The key idea of our approach is the utilization of bistable Josephson junctions allowing the representation of information in their Josephson energy. Since the proposed circuits are composed of Josephson junctions only, they can be called all-Josephson junction (all-JJ) circuits. We present a methodology for the design of the circuits consisting of conventional and bistable junctions. We analyze the principles of the circuit functioning, ranging from simple logic cells and ending with an 8-bit parallel adder. The utilization of bistable junctions in the all-JJ circuits is promising in the aspects of simplification of schematics and the decrease of the JJ count leading to space-efficiency.
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New technology for superconductor integrated circuits has been developed and is presented. It employs diffusion stoplayers (DSLs) to protect Josephson junctions (JJs) from interlayer migration of impurities, improve JJ critical current (Ic) targeting and reproducibility, eliminate aging, and eliminate pattern-dependent effects in Ic and tunneling characteristics of Nb/Al/AlOx/Nb junctions in integrated circuits. The latter effects were recently found in Nb-based JJs integrated into multilayered digital circuits. E.g., it was found that Josephson critical current density (Jc) may depend on the JJs environment, on the type and size of metal layers making contact to niobium base (BE) and counter electrodes (CE) of the junction, and also change with time. Such Jc variations within a circuit reduce circuit performance and yield, and restrict integration scale. This variability of JJs is explained as caused by hydrogen contamination of Nb layers during wafer processing, which changes the height and structural properties of AlOx tunnel barrier. Redistribution of hydrogen impurities between JJ electrodes and other circuit layers by diffusion along Nb wires and through contacts between layers causes long-term drift of Jc. At least two DSLs are required to completely protect JJs from impurity diffusion effects - right below the junction BE and right above the junction CE. The simplest and the most technologically convenient DSLs we have found are thin (from 3 nm to 10 nm) layers of Al. They were deposited in-situ under the BE layer, thus forming an Al/Nb/Al/AlOx/Nb penta-layer, and under the first wiring layer to junctions CE, thus forming an Al/Nb wiring bi-layer. A significant improvement of Jc uniformity on 150-mm wafer has also been obtained along with large improvements in Jc targeting and run-to-run reproducibility.
We present a fabrication scheme and testing results for epitaxial sub-micrometer Josephson junctions. The junctions are made using a high-temperature (1170 K) via process yielding junctions as small as 0.8 mu m in diameter by use of optical lithography. Sapphire (Al2O3) tunnel-barriers are grown on an epitaxial Re/Ti multilayer base-electrode. We have fabricated devices with both Re and Al top electrodes. While room-temperature (295 K) resistance versus area data are favorable for both types of top electrodes, the low-temperature (50 mK) data show that junctions with the Al top electrode have a much higher subgap resistance. The microwave loss properties of the junctions have been measured by use of superconducting Josephson junction qubits. The results show that high subgap resistance correlates to improved qubit performance.
Recent progress in superconductor electronics fabrication has enabled single-flux-quantum (SFQ) digital circuits with close to one million Josephson junctions (JJs) on 1-cm$^2$ chips. Increasing the integration scale further is challenging because of the large area of SFQ logic cells, mainly determined by the area of resistively shunted Nb/AlO$_x$-Al/Nb JJs and geometrical inductors utilizing multiple layers of Nb. To overcome these challenges, we are developing a fabrication process with self-shunted high-J$_c$ JJs and compact thin-film MoN$_x$ kinetic inductors instead of geometrical inductors. We present fabrication details and properties of MoN$_x$ films with a wide range of T$_c$, including residual stress, electrical resistivity, critical current, and magnetic field penetration depth {lambda}$_0$. As kinetic inductors, we implemented Mo$_2$N films with T$_c$ about 8 K, {lambda}$_0$ about 0.51 {mu}m, and inductance adjustable in the range from 2 to 8 pH/sq. We also present data on fabrication and electrical characterization of Nb-based self-shunted JJs with AlO$_x$ tunnel barriers and J$_c$ = 0.6 mA/{mu}m$^2$, and with 10-nm thick Si$_{1-x}$Nb$_x$ barriers, with x from 0.03 to 0.15, fabricated on 200-mm wafers by co-sputtering. We demonstrate that the electron transport mechanism in Si$_{1-x}$Nb$_x$ barriers at x < 0.08 is inelastic resonant tunneling via chains of multiple localized states. At larger x, their Josephson characteristics are strongly dependent on x and residual stress in Nb electrodes, and in general are inferior to AlO$_x$ tunnel barriers.
We study the spectrum of Andreev bound states and Josephson currents across a junction of $N$ superconducting wires which may have $s$- or $p$-wave pairing symmetries and develop a scattering matrix based formalism which allows us to address transport across such junctions. For $N ge 3$, it is well known that Berry curvature terms contribute to the Josephson currents; we chart out situations where such terms can have relatively large effects. For a system of three $s$- or three $p$-wave superconductors, we provide analytic expressions for the Andreev bound state energies and study the Josephson currents in response to a constant voltage applied across one of the wires; we find that the integrated transconductance at zero temperature is quantized to integer multiples of $4e^2/h$, where $e$ is the electron charge and $h = 2pi hbar$ is Plancks constant. For a sinusoidal current with frequency $omega$ applied across one of the wires in the junction, we find that Shapiro plateaus appear in the time-averaged voltage $langle V_1 rangle$ across that wire for any rational fractional multiple (in contrast to only integer multiples in junctions of two wires) of $2e langle V_1 rangle/(hbar omega)$. We also use our formalism to study junctions of two $p$- and one $s$-wave wires. We find that the corresponding Andreev bound state energies depend on the spin of the Bogoliubov quasiparticles; this produces a net magnetic moment in such junctions. The time variation of these magnetic moments may be controlled by an external applied voltage across the junction. We discuss experiments which may test our theory.
We present theory of dc Josephson effect in contacts between Fe-based and spin-singlet $s$-wave superconductors. The method is based on the calculation of temperature Greens function in the junction within the tight-binding model. We calculate the phase dependencies of the Josephson current for different orientations of the junction relative to the crystallographic axes of Fe-based superconductor. Further, we consider the dependence of the Josephson current on the thickness of an insulating layer and on temperature. Experimental data for PbIn/Ba$_{1-x}$K$_{x}$(FeAs)$_2$ point-contact Josephson junctions are consistent with theoretical predictions for $s_{pm}$ symmetry of an order parameter in this material. The proposed method can be further applied to calculations of the dc Josephson current in contacts with other new unconventional multiorbital superconductors, such as $Sr_2RuO_4$ and superconducting topological insulator $Cu_xBi_2Se_3$.
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