The 2ϕ-Josephson junctions (JJs), characterized by a dominant second harmonic in the current-phase relationship (CPR), are promising devices for low-power, high-density superconducting digital logic. These junctions eliminate the need for on-chip inductors to store magnetic flux and they reduce bias current requirements. In practical implementations, both first and second harmonic components are typically present in the CPR, affecting the junction dynamics and circuit operation. Understanding this behavior is essential for the reliable design of superconducting logic circuits utilizing these junctions, such as half flux quantum (HFQ) circuits. In this article, a compact Verilog-A model for 2ϕ-JJs is presented that captures the nonlinear behavior of the junctions, accounting for both harmonic contributions and their impact on damping. Two parameter sets are derived from experimental data corresponding to junctions with weak ferromagnetic barriers and ferromagnetic insulator barriers. Based on the inferred parameters, models of each junction type are developed. The model is validated against published experimental results and simulated within a D flip flop cell, demonstrating its use for superconducting circuit design and analysis, including evaluation of circuit behavior under nonideal junction conditions. Stability issues and failure mechanisms introduced by a nonzero first harmonic are analyzed, and underlying junction dynamics are examined to explain the reduction in circuit parameter margins.
The 2ϕ-Josephson junctions (JJs), characterized by a dominant second harmonic in the current-phase relationship (CPR), are promising devices for low-power, high-density superconducting digital logic. These junctions eliminate the need for on-chip inductors to store magnetic flux and they reduce bias current requirements. In practical implementations, both first and second harmonic components are typically present in the CPR, affecting the junction dynamics and circuit operation. Understanding this behavior is essential for the reliable design of superconducting logic circuits utilizing these junctions, such as half flux quantum (HFQ) circuits. In this article, a compact Verilog-A model for 2ϕ-JJs is presented that captures the nonlinear behavior of the junctions, accounting for both harmonic contributions and their impact on damping. Two parameter sets are derived from experimental data corresponding to junctions with weak ferromagnetic barriers and ferromagnetic insulator barriers. Based on the inferred parameters, models of each junction type are developed. The model is validated against published experimental results and simulated within a D flip flop cell, demonstrating its use for superconducting circuit design and analysis, including evaluation of circuit behavior under nonideal junction conditions. Stability issues and failure mechanisms introduced by a nonzero first harmonic are analyzed, and underlying junction dynamics are examined to explain the reduction in circuit parameter margins.
We adopt superconductor/ferromagnet/insulator/superconductor (SFIS) Josephson junctions (JJs) as both switching JJs and intrinsic π phase shifters in superconductor digital circuits. The critical current density (Jc) and characteristic voltage (Vc) of the SFIS junctions are about 22 A/cm2 and 22 μV, respectively. The intrinsic π phase shift is confirmed by measuring the suppressed nominal critical current Icn and half-period-shifted modulation pattern of a π–π–π superconducting quantum interference device (SQUID) that contains three π-JJs in a superconducting loop. A single-flux-quantum (SFQ) circuit composed of a DC/SFQ, Josephson transmission line (JTL), and SFQ/DC converter based on SFIS JJs alone is demonstrated at 4.2 K. The energy dissipation of the SFQ/DC converter decreases by 80% because some JJs are self-biased by the π phase shifter. The intrinsic circulating currents induced by the π phase shifters lead to a narrow bias margin (±5%) and even error function, which can be solved by parameters optimization or circuit initialization in the future. The half-modulation period (Φ0/2) of a half-flux-quantum (HFQ) SQUID (a partial HFQ JTL) exhibits propagation of HFQ between π–π–π SQUIDs, indicating that more complex HFQ circuits can be developed with π-JJs alone in the future.
Josephson junction, as the core nonlinear element underpinning superconducting electronics, is characterized by its current-phase relation (CPR), which fundamentally determines the dynamical properties and functional capabilities of superconducting quantum devices. Traditional Josephson junctions typically exhibit a traditional sinusoidal CPR; however, the junctions characterized by non-sinusoidal CPR have recently attracted considerable attention due to their distinctive physical properties and promising quantum device applications. In this work, a numerical model tailored specifically for junctions exhibiting non-sinusoidal CPR is developed by integrating experimentally measured current-voltage (I-V ) characteristics from Nb/Al-AlOx/Nb junctions into a resistively and capacitively shunted junction (RCSJ) framework. By leveraging this refined model, the influence of CPR skewness on Josephson junction dynamics is systematically investigated. Our results indicate that in underdamped junctions, the critical current significantly diminishes with the increase of CPR skewness, a behavior reminiscent of the adjustable critical currents typically observed in DC superconducting quantum interference devices (SQUIDs). Conversely, in overdamped junctions, the influence of CPR skewness on the I-V characteristics is found to be negligible. However, our numerical simulations under microwave irradiation indicate that nonsinusoidal CPRs readily promote the emergence of half-integer Shapiro steps in overdamped junctions, thereby establishing CPR skewness as a plausible microscopic origin for this phenomenon. In addition, the advanced design system (ADS) simulations is employed to model nonlinear resonators and DC SQUID circuits, offering a detailed investigation into how nonsinusoidal CPRs modulate the Josephson inductance and magnetic flux response. Our findings reveal that engineering the CPR of Josephson junctions provides substantial flexibility in the design of superconducting qubits, parametric amplifiers, and non-magnetic nonreciprocal devices. This tunability underscores significant opportunities for developing next-generation superconducting electronic components. The Josephson junctions with engineered CPR offer expanded functionality for superconducting quantum technologies. This study suggests that customized CPR can enhance control over the dynamical behavior of junctions, and promote the optimized designs of superconducting qubits, parametric amplifiers, and nonmagnetic nonreciprocal devices.
A bistable superconducting quantum interference device (SQUID) exclusively comprising Josephson junctions (JJs) is proposed. The design integrates two 2Φ-JJs within the loop structure, while the state of the SQUID is monitored through a conventional 2π-periodic JJ (0-JJ). This configuration eliminates the need for geometric inductors, leveraging the nonlinear phase dynamics for bistability. Extensive simulations confirm robust bistable operation under controlled external flux bias, positioning the proposed SQUID as an area-efficient building block for superconducting memory cells, sensors for various applications, and SFQ-compatible logic elements.
The all-JJ logic family is a promising area and power efficient, scalable single flux quantum (SFQ) technology for application to exascale supercomputers. All-JJ superconductive logic is based on a superconductor-ferromagnet-superconductor (SFS) bistable JJ, enabling nanometer feature sizes in VLSI complexity superconductive systems. In this paper, a mechanical analogy is proposed to describe the dynamic behavior of these bistable JJs. Novel all-JJ logic gates, such as TFF, DFF, OR, AND, and NOT gates, are presented here. All-JJ circuits are composed of bistable JJs, standard JJs, and bias currents, not requiring large inductors within the storage loops. All-JJ logic cells exhibit less delay and power than standard SFQ cells with the same critical current density. All-JJ systems can operate at high frequencies due to the small capacitance of the SFS JJ. A complex all-JJ circuit from the suite of ISCAS'85 benchmark circuits is also characterized. This complex all-JJ circuit exhibits less delay and power as compared to standard SFQ logic. The bias current in a conventional benchmark circuit and all-JJ benchmark circuit is, respectively, 22 mA and 13 mA. The delay of each cell within the conventional benchmark circuit and all-JJ benchmark circuit is, respectively, approximately 20 and 8 ps. A parasitic inductance in series with the JJs disturbs the current distribution within the all-JJ circuits while degrading the margins. To suppress the effects of this parasitic inductance on SFS JJs, small linear inductors are added to manage the current distribution and improve the parameter margins.
Superconductive logic based on Josephson junctions (JJ) is a promising technology for energy efficient supercomputers and cloud computing. This technology can deliver significant improvements in performance and energy efficiency as compared to CMOS. Superconductive circuits, however, suffer from low density integration as compared to CMOS, primarily due to the limited scalability of the inductors. To improve the scalability of superconductive logic, a logic family based on a novel JJ technology,$2\phi $-JJ, has been proposed that eliminates the inductors. In this brief, three circuits are presented which exploit this scalable inductor-less technology. This novel$2\phi $-JJ technology represents the data as half flux quantum (HFQ) pulses, which improves the energy efficiency and speed as compared to standard superconductive logic such as rapid single flux quantum (RSFQ). Unlike RSFQ, the proposed circuits dynamically switch upon receiving an HFQ pulse, saving energy. These$2\phi $-JJ logic circuits operate 2.25X faster and require 2.6X less energy as compared to RSFQ.
We report optimization of half-flux-quantum (HFQ) circuits composed of SQUIDs containing conventional Josephson junctions and π-shift magnetic Josephson junctions. The SQUID can act as a Josephson junction with an extremely small critical current and be easily switched by a weak driving force with the assistance of the circulating current that is induced due to the π-shift and quantization conditions. It leads to a drastic reduction of both static and dynamic power consumption. However, the parameter margins of the HFQ circuits obtained so far is narrow compared with conventional single-flux-quantum circuits. Since HFQ circuits use many circuit elements and require the two junctions in the SQUID to switch alternately and symmetrically, circuit parameter optimization is much more difficult. In this study, we developed an optimization tool for HFQ circuits, including operation judgment and margin calculation. We improved the critical margin of the HFQ Josephson transmission line to 39%. We also optimized the HFQ splitter, confluence buffer, and D flip-flop. We discuss design guidelines for HFQ circuits based on our systematic exploration of the optimized circuit parameter sets. We suggest that the optimized loop inductances are around 0.5 and 1.5 of Φ0/2 for data transmission and storage, respectively.